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NOAA Technical Report NWS 23 ArMO's ,- Meteorological Criteria for Standard Project us lr Hurricane and Probable Maximum Hurricane Windfields, Gulf and East Coasts of the United States - All U Washington, D.C. 40 September 1979 d w U. S. DEPARTMENT OF COMMERCE NOAA COASTAL SERVICES CENTER 2234 SOUTH HOBSON AVENUE - C)09 CHARLESTON, SC 29405-2413 -.-- U.S. DEPARTMENT OF COMMERCE d< ~ . I, Juanita M. Kreps, Secretary OZ~ >rnf lS National Oceanic and Atmospheric Administration i Pr o 4 Richard A. Frank, Administrator National Weather Service 2 2cdo. Richard E. Hallgren, Director ?~ .) g Property of CSC Library CONTENTS PAGE ABSTRACT ...... ............. 1 1. Introduction . . . . . . . . . . . . . . . . ... . . . 1.1 Authorization and funding . . . . . . . . . ..... 1 1.2 Definitions . . . . . . . . . . . . . . . . 2 1.2.1 SPH . ..... 2 1.2.2 PMH ........................ 2 1 2.3 Steady state . .. . . . . . . . . . . . . . 1.3 Purpose . . . . . . . . . . . ........ . 1.4 Scope . . . . . . . . . . . . . . . . . . 5 1.5 Previous studies . . . . . . . . . . . . . 7 1.5.1 SPH . .. 7 1.5.2 PM ................... 7 1.5.3 Hurricane climatology . . . . . . . . . . .... 7 1.5.4 Comparisons between previous SPH and P1MH studies and this report . . . . . . . . . . . ... . 8 1.6 Organization . . . . . . . . . . . . . . . . ... . 2. Executive summary . . . . . . . . . . . . . ...... 11 2.1 Introduction . .............. . . 11 2.2 Results of the study . . . . . . . . . . . . .... 11 2.2.1 Pressure profile formula (chapter 6) . . . . . . . 11 2.2.2 Peripheral pressure (chapter 7) . . . . . . . . . . 12 2.2.3 Central pressure (chapter 8) . . . . . . . . . . . 12 2.2.4 Radius of maximum winds (chapter 9) . . . . . . . . 12 2.2.5 Forward speed (chapter 10) . . . . . . . . . ... 18 2.2.6 Track direction (chapter 11) . . . . . . . . ... 18 2.2.7 Overwater winds (chapter 12). ... . . . . . . . 23 2.2.7.1 Maximum gradient winds (Vgx). . . 23 2.2.7.2 Ten-meter 10-minute overwater winds . . . . . . . 24 2.2.8 Relative wind profiles (chapter 13) . . . . . . 26 2.2.9 Limits of rotation of wind fields (chapter 13). . 28 2.2.10 Wind inflow angle (chapter 14) . . . . . . . . . . 29 2.2.11 Adjustment of wind speed for frictional effects (chapter 15) . 31 2.2.12 Adjustment of wind speed because of filling overland (chapter 15).............. . 34 2.2.13 The stalled PMH (chapter 16). 35 2.3 Comparison of SPH and P1MH with record hurricanes . 38 3. Application of criteria ................ 52 3.1 Introduction . . . . . . . . . . . . . . . . . . . . 52 3.2 Overwater wind fields (refer to table 3.1) . . . . . 52 3.3 Adjustment of overwater wind field for frictional effects . . . .. . . . . . . . . . . . . . . . . . 55 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . 55 3.3.2 Wind Paths . . . . . . . . . . . . . . . . . . . . 55 iiiz PAGE 3.3.3 Friction coefficients . . . . . . . . . . . . . . 69 3.3.4 Examples of computations of surface frictionally adjusted wind speed near shore . . . . 69 3.3.4.1 Wind path X - X . . . . . . . . . . . . . . . . . . 69 3.3.4.2 Wind path Y - Y . . . . . . . . . . . . . . . . . . 74 3.4 Adjustment of wind field when hurricane center moves overland. . . . . . . . . . . . . . . . . . . . . 75 3.5 Adjustment of wind field for a stalled PMH. . . . . .. 76 4. Data. . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . 77 4.2 Source of data. . . . . . . . . . ....... . . . . 77 4.2.1 Hurricanes. . . . . . . . . . . ...... . . . . . 77 4.2.1.1 Hurricanepressure data . . . . . . . . . . .... 78 4.2.1.2 Hurricane radius of maximum winds (R) data. .... 79 4.2.1.3 Hurricane forward speed (T) and track direction (G) 79 4.2.2 Typhoons ......... ..... 80 4.3 Limitations on use of typhoon data. . . . . . . ... 80 5. Meteorological and other parameters and their interrelations. ........... . . . . . . . . . 99 5.1 Introduction. . . . . . . . . . . . . . . . . . . . 99 5.2 Definition of meteorological parameters . . . . . ... 99 5.3 Interrelations between pairs of parameters. . . . . .. 100 5.3.1 Zero-order linear correlation coefficients. ..... 100 5.3.2 Plots of data . . . . . . . . . . . . . . . . . 101 5.3.2.1 Interrelations with central pressure (p) . . . . 106 5.3.2.2 Interrelations with latitude (.). 108 5.4 Multiple interrelations between sets of parameters. . 109 5.5 Summary ............ . . . . . . . . . . . . 112 6. Pressure profile formula. ........... . . . . . 113 6.1 Introduction. .. . . . . . . . . . . . . . . . 113 6.2 Development and early use of the Hydromet formula . . . 13 6.3 Pressure profile formulas tested and data sample . . . . 115 6.4 Comparison of eye-fitted hurricane pressure profiles with pressure profiles from formulas. ....... . 115 6.4.1 In general. . ......... . . . . . . . . . . . 115 6.4.2 At 40 and 80 nautical miles (74 and 148 kilometers) . 119 6.4.3 For five intense hurricanes . . . . . . . . . . . . 121 6.4.4 Hurricane Camille . . . .. .. . . . . . . 121 6.5 Conclusions ........... . . . . . . . . . . . 122 7. Peripheral pressure . . . . . . . . . . . . . . . . 123 7.1 Introduction. ........ . . . . . . . . . . . . . 123 7.2 Methods of determining peripheral pressure. . . . . .. 123 7.3 Comparison of Pw and Pwi with pnx . . . . . . 124 7.4 Interrelations among pw, Pwi' latitude and p . . . . . 124 7.4.1 Plots containing p . 124 7.4.2 Plots containing Pwi. . . 128 iv ,I PAGE 7.4.3 Plots of latitude vs. pw and p wi for western North Pacific typhoons ................ 129 7.5. Conclusions ..................... 129 8. Central pressure .................... 135 8.1 Introduction ................... 135 8.2 Central pressure for the SPH ............. 135 8.2.1 Introduction ................... 135 8.2.2 Basic data ..................... 135 8.2.3 Historical storms ................. 136 8.2.4 Procedure ..................... 136 8.3 Central pressure for the PMH ............. 148 8.3.1 Introduction .................... 148 8.3.2 Lowest observed p's ............... 148 8.3.3 PMH p south of 2g�N .... 148 8.3.3.1 Hydrostatic approximation . . . . . . 148 8.3.3.2 Construction of tropical PMH sounding ...... 149 8.3.3.3 Calculation of p ................ 156 8.3.3.4 Comparison of computed PMH p with other estimates 156 8.3.4 PMH p0 at Cape Hatteras ............. 157 8.3.5 PMH p near 45�N .................. 157 8.3.5.1 From a sounding . . . 157 8.3.5.2 From historical storms .............. 161 8.3.5.3 From previous estimates ............. 163 8.3.5.4 Recommended value of PMH p near 45�N ...... 163 8.3.6 Sensitivity of adopted PMH p computation for changes in input factors. ? ........... 163 8.3.7 Generalized alongshore variation of p for the PMH ....................... 165 8.3.7.1 East coast .................... 165 8.3.7.2 Gulf coast .................... 167 8.4 Comparison of SPH and PMH pressure drop ...... 178 9. Radius of maximum winds .............. 180 9.1 Introduction ..................... 180 9.2 Data ......................... 180 9.3 Range in R for the SPH ............... 180 9.4 Range in R for the PMH ................ 186 9.4.1 Lower limit of R for the PMH ............ 186 9.4.2 Upper limit of R for the PMH ........... 189 9.4.3 Coastal Analysis of lower and upper limits of R for the PMH ..................... 192 9.4.4 Application of R criteria ............ 194 10. Forward speed .................... 195 10.1 Introduction ..................... 195 10.1.1 Use of forward speed ............... 195 10.1.2 Forward speeds of historical hurricanes ..... 195 10.1.3 Ranges of T ................... 195 10.2 Forward speed for the PMH .............. 195 PAGE 10.2.1 Upper limit of T. . . . . . . . . . . . . ..... 195 10.2.1.1 Rio Grande to Mayport, Fla. (latitude 30.50N) . 195 10.2.1.2 Mayport, Fla. to latitude 45�N. . . . . . . ... 199 10.2.2 Lower limit of T . . . . . . . . . . . . . .... 199 10.2.2.1 Rio Grande to Savannah, Ga. . . . . . . . . ... 199 10.2.2.2 Savannah, Ga. to latitude45�N. . . . . . . ... 200 10.3 Forward speed for the SPH . . . . . . . . . . .... 200 10.3.1 Upper limit of T. . . . . . . . . . . . . ..... 200 10.3.1.1 Gulf coast. . . . . . . . . . . . . . . 200 10.3.1.2 East coast. . . . . . . . . . . ... ..... 202 10.3.2 Lower limit of T. . . . . . . . . . . . . ..... 202 10.3.2.1 Rio Grandeto Cape Hatteras, N.C . . . . . . ... 202 10.3.2.2 Cape Hatteras to Latitude 45�N. . . . . . . .. 202 11. Track direction ............... . . 203 11.1 Introduction. ................... . 203 11.2 Definition of track direction (0) . . . .. ... 203 11.3 Variation in 0 shown by hurricanes of record . . .. 203 11.4 Generalized coastal orientations. . . . . . . . ... 206 11.5 Track direction for the PMH . . . . . . . . ..... 206 11.5.1 Range in 0 over the open ocean . . . . . . . . .. 206 11.5.2 Range in 0 along the coast before smoothing . . 213 11.5.2.1 Depending on forward speed and angle of approach. 213 11.5.2.2 Range in 4 for individual coastal segments. . . . 215 11.5.3 Range in 0 along the coast after smoothing .... 218 11.6 Track direction for the SPH . . . ..... 221 11.6.1 Range in 0 over the open ocean . 221 11.6.2 Range in 0 along the coast before smoothing. . . 221 11.6.2.1 Dependency on forward speed and angle of approach 221 11.6.2.2 Range in 0 for individual coastal segments. . . 222 11.6.3 Range in 9 along the coast after smoothing. ..... 223 11.7 Interpretation of results of sections 11.5 and 11.6 . 223 12. Overwater winds .................... 227 12.1 The maximum gradient wind speed equation . . . . . ... 227 12.1.1 Introduction ................... .. 227 12.1.2 Derivation ................ ..... 227 12.1.3 Determination of the K coefficient. . . . . . . ... 231 12.1.3.1 Background. . . . . . . . . . . . ....... . . . 231 12.1.3.2 Adopted variation in K. 231 12.2 Ten-meter, 10-minute overwater winds. 234 12.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . 234 12.2.1.1 Recommended reduction factors (F) for SPH and PMH . 235 12.2.2 Winds in a stationary hurricane . . . . . . . . . . 235 12.2.3 Winds in a moving hurricane . . . . . . . . . . . . . 236 12.2.3.1 The asymmetry factor. 236 12.2.3.2 Adopted SPH and PMH maximum 10-m, 10-min overwater wind equations . . . . . . . . . . . . . . . . . 237 12.2.3.3 SPH and PMH 10-m, 10-min overwater wind equation at any r .................... 237 12.3 Values of V and V for record hurricanes. . . . . .. 239 gx x vi PAGE 12.4 Vgx and Vx for the SPH and PMH. . . . ... 240 12.5 Comparison with other research ...... 240 13. Relative wind profiles .. ... 243 13.1 Introduction. . . . . . . . . . . . . . . . . . . . 243 13.2 Development of standardized profiles for winds outward from R. . .. . . . . . . . ... 243 13.2.1 Data . . . . . . . . . . . . . .. : . . . .. 243 13.2.2 Analysis .. ... . . . . . . . . . . . . . . 245 13.2.3 Results . .......... .. .. .. 247 13.3 Development of a standardized profile for winds within R 249 13.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . 249 13.3.2 Analysis. . . . . . . . . . . . . . . . . . . . . . . 250 13.3.3 Results ................... . 251 13.4 Concluding remarks on relative wind profiles. ..... 251 13.5 Limits of rotation of wind fields . . . . . . . . . . . 253 13.5.1 Introduction. . ... .... 253 13.5.2 Location of region of maximum winds in severe hurricanes. . . . . . . . . . . . . ....... . 254 13.5.3 Adopted limits of rotation for the SPH and PMH. . . . 256 14. Wind inflow angle ......... 257 14.1 Introduction . . . . . . . . . . . . . . 257 14.2 Results of other studies . . . . . . . . . . . . . . . 257 14.3 Estimation of inflow angles using ship data ... . 260 14.4 Recommended inflow angles for the SPH and the PMH . . . 260 14.4.1 Assumptions or constraints. . . . . . . . . . . . . . 260 14.4.2 Analysis . . . . . . . . . . . . .. 261 14.5 Comparison of results with other research . . . . . . . 263 15. Adjustments of wind speed for frictional effects and for filling overland . . . . . . . . . . . . . . . . . . . 264 15.1 Introduction. . . . . . . . . . . . . . . . . . . . . . 264 15.2 Adjustment of wind speed for frictional effects . . . . 264 15.2.1 Background . . . . . .... . . . . .264 15.2.2 Lake Ontario data from IFYGL . . . ... 265 15.2.3 Definition of friction categories . . ..... 266 15.2.4 Adopted adjustment of wind speed for frictional effects 266 15.2.4.1 Onshore winds ....... 266 15.2.4.2 Offshore winds . . . . . . 267 15.2.4.3 The surface friction coefficient . ..... 268 15.3 Adjustment of wind speed for filling overland . . 271 15.3.1 Introduction. . . . . . . . . . 271 15.3.2 Reasons for and effects of filling of hurricanes overland .. . . . . . . . . . . . . . . . . . . . 271 15.3.3 Data . . . ..... 271 15.3.4 Analysis . ....... . . . . 273 15.3.5 Discussion of analysis .. . . ... 277 15.3.6 Results . . . . . . . . . . . . . . . . . . . . . . . 278 15.3.7 Discussion of results . . . . ... 280 15.3.7.1 Comparison of SPH and PMH adjustment factors. . . . 280 vii PAGE 15.3.7.2 Other research involving overland filling ..... 282- 15.3.7.3 PMH or SPH crossing Florida peninsula from east to west ....................... 283 16. The stalled PMH ...................... 284 16.1 Introduction ...................... 284 16.2 Background ....... ...... 284 16.2.1 Effects of sea-surface temperature on crossovor typhoons ...................... 285 16.2.2 Geographic variation in sea-surface temperature drops. 286 16.3 Data .286 16.4 Stalled PM1 south of 36.5�N .. 290 16.4.1 Variation in intensity ............... 290 16.4.1.1 Ap before and after time of stall. 290 16.4.1.2 Variation of Ap over AP with time after AP . .290 16.4.1.3 Variation of APmax with Ap after maximum intensity 293 16.4.1.4 Variation of PMH wind speed with time after stall. 293 16.4.2 Variation in forward speed ............... 294 16.4.3 Track direction .................... 296 16.4.4 Radius of maximum winds and inflow angle ....... 296 16.4.5 Length of stall ..................... 297 16.4.6 Reintensification when the stall is over ....... 297 16.5 Stalled PMH north of. 36.50N ............... 298 16.5.1 Introduction ....................... 298 16.5.2 Rate of decrease of wind speed ............ 298 16.5.3 Decrease in T for a PMH north of the Virginia-North Carolina border ...... ............. 298 16.5.3.1 Maximum and minimum rates of decreasing forward speed (T) ........................ 299 16.5.3.2 Choosing 0.300 16.5.3.3 Definition of the point where T decreases below the � minimum limit.. .................. 300 16.5.3.4 Determination of LT point knowing point of stall . 300 16.5.4 Decrease of intensity for a nonstalled former PMH moving slower than the lower limits of T (T L). . . 301 16.5.4.1 General considerations involving p. 301 16.5.4.2 Procedure for decreasing wind spee2 at LT point to wind speed at stall point ............. 301 16,5.5 Forward speed ..................... 302 16.5.6 Track direction .................... 303 16.5.7 Radius of maximum winds and inflow angle .... 303 16.5.8 Reintensification when the stall is over ....... 303 16.5.9 Limitations ...................... 304 16.5.10 Additional remarks ................. 304 16.5.11 Example of calculation of decrease in PMH winds north of 36.5�N ......... ............ 305 PAGE 16.6 Effect of land on storm weakening. . . . . . . . . . . . 306 16.7 Other research... .................. 307 Acknowledgments 308 References 309 Conversions 317 -. 4~~~~~~i FIGURES PAGE 1.1. Locator map with coastal distance intervals ........ 1.2. Chart used for presenting various types of alongshore data analyses .9...................... 2.1. Plot showing the adopted SPH Po .p.0......... 13 2.2. Plot showing the adopted PMH po ............. 14 2.3. Comparison of pressure drop (Ap) for the PMH and SPH . . . 15 2.4. Adopted upper and lower limits of radius of maximum winds for the SPH ...................... 16 2.5. Adopted upper and lower limits of radius of maximum winds for the PMH ................. 17 2.6. Adopted SPH upper and lower limits of T .......... 19 2.7. Adopted PMH upper and lower limits of T .......... 20 2.8. Maximum allowable range of SPH 0 after smoothing ..... 21 2.9. Maximum allowable range of PMH 0 after smoothing ..... 22 2.10. Values of latitude-dependent K coefficient for the SPH. . 24 2.11. Values of the latitude-dependent K coefficient for the PMHt 25 2.12. Adopted standardized wind profiles outward from R for the stationary SPH and PMH ............. 27 2.13. Variation of relative wind speed with relative distance within the radius of maximum winds for the stationary SPH and PMH ............... ......... . 28 2.14. Adopted SPH inflow angles vs. distance from the hurricane center ......................... 29 2.15. Same as figure 2.14 except for the PMH .......... 30 2.16. Offshore to overwater winds ratio (ke) .......... 32 2.17. Graphical solution for Q ..... 33 2.18. Schematic of nearshore frictional adjustments ...... .:� 34 2.19. Smoothed adjustment factor curves for reducing hurricane wind speeds when center is overland ........... 36 2.20. Limits of three geographic regions (A, B, and C) .37 X PAGE 2.21. Stalling adjustment factor (sf) curve for the PMH to be used south of the Virginia - North Carolina border (36.5�N) . . . . . . . . . . . . . . . . . . . . . . . . 38 2.22. Maximum gradient wind speed for lower (VGL) and upper (VGU) limits of R for the stationary SPH . . . . . . . . . . . 44 2.23. Maximum 10-m,-10-min overwater wind speed for the SPH for the lower limit of R and upper limit of T (VLU) and lower limit of R and lower limit of T (VLL) . . . . . . . . . . 45 2.24. Same as figure 2.23 except for the upper limit of R and upper limit of T (VUU) and upper limit of R and lower limit of T (VUL) . . . . . . . . . . . . . . . . . . 46 2.25. Same as figure 2.22 except for the stationary PMH . . . 47 2.26. Same as figure 2.23 except for the PMH . . . . . . . . 48 2.27. Same as figure 2.24 except for the PMH . . . . . . . . 49 3.1. Overwater PMH wind field computed for the example in section 3.2 . . . . . . . . . . . . . . . . . . . . . 67 3.2. Example of wind directions and sketched wind paths for the PMH ....................... 68 3.3. Overwater PMH wind field and locations of points A to L for which adjustments are given . . . . . . . . . . . . . 70 5.1. Central pressure (po) vs. radius of maximum winds (R) 106 5.2. Central pressure (p) vs. track direction (0) ..106 ~~~~~~~~~~~06 5.3. Central pressure (po) vs. forward speed (T) . . . . . . 107 5.4. Latitude (i) vs. forward speed (T) . . . . . . . . . . 107 5.5. Latitude (i) vs. central pressure (po0) . . . . . . . . 109 5.6. Latitude (i) vs. track direction (0) . . . . . . . . . 110 5.7. Latitude (i) vs. radius of maximum winds (R) ..... 111 6.1. Smoothed pressure profiles of Florida hurricanes using observed pressure values . . . . . . . . . . . . . . 114 6.2. Eye-fitted and computed pressure profiles, Camille 1969 118 xi PAGE 7.1. Latitude (v) vs. peripheral pressure (p ) for east coast hurricanes. 128 7.2. Latitude (4) vs. peripheral pressure (Pw) for gulf coast hurricanes. 129 7.3. Central pressure (p ) vs. peripheral pressure (pw) for all hurricanes . . . . . 130 7.4. Latitude (4) vs. peripheral pressure (Pwi) for all hurricanes 131 7.5. Central pressure (p ) vs. peripheral pressure (p wi) for all hurricanes. 132 7.6. Latitude (9) vs. peripheral pressure (p w) for intense typhoons,1960-74. 133 8.1. Plot showing averages of the five lowest p 's (black dots) within 500-n.mi. (927-km) lengths overlapping by 50 n.mi. (93 km) for all hurricanes ................ 142 8.2. Plot showing smoothed curves through averages of the seven lowest p 's within 500-n.mi. (927-km) lengths overlapping by 50 n.mi. (93 km) .................. 144 8.3. Plot showing smoothed curves through averages of the seven lowest p 's within 500-n.mi. (927-km) lengths overlapping by 50 n.mi. (93 km) after anchoring the relative variation into the 1938 hurricane and Helene (1958) . . . . . .. 145 8.4. Plot showing the adopted SPH po and p 's from three previous studies. . . . . . . . . . . . . . . . . . . . 147 8.5. Adopted tropicalPMH sounding. . . . . . . . . . . ..... 155 8.6. Adopted PMH soundings for Cape Hatteras, N.C., and Caribou, Maine . . . . . . . . . . . . . . . . .. ...... . 159 8.7. 99th percentile sea-surface temperatures along the gulf and east coasts ..................... 166 8.8. Plot showing the adopted PMH p , a preliminary p for the eastern Gulf of Mexico and the p0 from a study completed in 1968 .168 8.9. Schematic summary of typhoons used for guidance on filling rate of PMH after recurvature over the northeast gulf coast. . . . . . . . . . . . . . . . . . . . 172 xii PAGE 8.10. Variation of central pressure with time (a) typhoon Nancy (1961) ................ 174 (b) typhoon Violet (1961) ................ 175 8.11. Likely paths of the PMH into northeastern gulf coast . . . 177 8.12. Comparison of pressure drop (Ap) for the PMH and SPH . . 179 9.1. Radius of maximum winds for hurricanes with central pressure <28.35 in. (96.0 kPa) listed beside each data point... 181 9.2. Variation of radius of maximum winds with central pressure for western North Pacific typhoons and (a) gulf coast hurricanes ................ 182 (b) east coast hurricanes ................ 183 9.3. Adopted upper and lower limits of radius of maximum winds for the SPH.. . ...................... 185 9.4. Latitude vs. Rlim ..................... 187 9.5. Vm vs. R ......................187 9.6. Variation of radius of maximum winds with central pressure for western North Pacific typhoons and hurricanes .... 189 9.7. Variation of the lower limit and upper limit of PMH radius of maximum winds with latitude ............. 190 9.8. Adopted upper and lower limits of radius of maximum winds for the PMH ....................... 193 10.1. Adopted PMH upper and lower limits of T .......... 196 10-.2. Forward speed (T) vs. central pressure (po) for typhoons listed in table 10.1 .................. 199 10.3. Adopted SPH upper and lower limits of T .......... 201 11.1. Track direction for landfalling or bypassing hurricanes along the gulf and east coasts of the United States. . . 204 11.2. Track direction for landfalling or bypassing hurricanes along the gulf and east coasts of the United States with po < 28.05 in. (95.0 kPa) to milepost 2200 or with Po < 28.41 in. (96.2 kPa) north of milepost 2200 ..205 ~~~~~~~~~~~~~~~~~05 11.3. Generalized straight line segments depicting orientation of gulf and east coasts of the United States ...... 207 xiii PAGE 11.4. Schematic representation of PMH near the coast . . . . . . 214 11.5. Permissible limits of 0 for the PMH . . . . . . . . . . . 219 11.6. Maximum allowable range of PMH 0 after smoothing . . . . . 220 11.7. Permissible limits of 0 for the SPH . . . . . . . . . . . 224 11.8. Maximum allowable range of SPH 0 after smoothing . 225 12.1. Blocks used to calculate sea-surface temperatures in determining latitudinal variation of K coefficient . . . 232 12.2. Sea-surface temperature along the gulf and east coasts during August . . . . . . . . . . . . . . . . . . . . . 233 12.3. Values of latitude-dependent K coefficient for the SPH . . 234 12.4. Values of the latitude-dependent K coefficient for the PMH. 234 12.5. Illustration of the relation between track direction (0), tangential wind direction (0 ), and actual surface wind direction (0) along the radial through point of maximum wind (radialaM) .......... 238 13.1. Relative wind speed profiles outward from R vs. distance from center for Donna (1960) . . . . . . . . ...... 245 13.2. Vs/Vxs for r/R of 2 vs. radius of maximum winds . . . . . . 246 13.3. Vs/Vxs for r/R of 4 vs. radius of maximum winds . . . . . . 246 s xs 13.4. V /V for r/R of 8 vs. radius of maximum winds . . . . . 247 s xs 13.5. V /V for r/R of 12 vs. radius of maximum winds.. 247 � Xs 13.6. Adopted standardized wind profiles outward from R . . . . 248 13.7. Vs/Vxs for r/R = 4 vs. central pressure . . . . . . . . . . 249 13.8. Vs/Vxs for r/R = 8 vs. central pressure . . . . . . . . . . 249 s Xs 13.9. Relative wind speed profiles within the radius of maximum winds for stationary hurricanes in table 13.2 . . . . . . 251 13.10. Relative wind speed profiles within the radius of maximum winds for stationary hurricanes (four groupings). 252 PAGE 13.11. Variation of relative wind speed with relative distance within the radius of maximum winds for the stationary SPH and PMH ...................... 253 13.12. Track of hurricane Celia (Aug. 1970) and wind reports near point of landfall ............... 255 14.1. Inflow angles from earlier SPH and PMH studies applied to smallest and largest R values of the present study . . 257 14.2. Inflow angles from Malkus and Riehl (1960) applied to smallest and largest R values of the present study . . 258 14.3. Nomogram for determining inflow angles at a distance of 87 n.mi.(161 km) from the hurricane center . . . . . . 258 14.4. Inflow angles at 120 n.mi. (222 km) (a) 240 and 360 n.mi. (445 and 667 km) from the typhoon center; (b) from the hurricane center for four storm quadrants; (c) from the typhoon center for four quadrants .................. 259 14.5. Inflow angles based on ship reports from the vicinity of hurricane Celia on August 3, 1970 . . . . . . . . . 261 14.6. Adopted SPH inflow angles vs. distance from the hurricane center at selected R values . . . . . . . . . . . . . 262 14.7. Same as figure 14.6 except for the PH . . . . . . . . 262 14.8. Same as figure 14.5 with SPH/PMH curves superimposed . . 262 15.1. Onshore to overwater winds ratio (kc) . . . . . . . . . 266 15.2. Offshore to overwater winds ratio (k ) . . . . . . . . . 267 15.3. Graphical solution for Q . . . . . . . . . . . . . . . . 269 15.4. Schematic of nearshore frictional adjustments . . . . . 270 15.5. Partial tracks of hurricanes of September 1928, August 1932, September 1938, September 1941, August 1949, Carol (1954), Betsy (1965), Camille (1969), and Celia (1970) . . . . . . ... . . . . . . . . . . . . . . . . 272 15.6. Partial tracks of hurricanes of September 1945, Connie (1955), Audrey (1957), Gracie (1959), Donna (1960), and Carla (1961) . . . . . . . . . . . . . . . . . . 273 Xv PAGE 15.7. Increase of central pressure (po) with time for hurricane (a) Gracie (1959) after she crossed the South Carolina coast (b) Camille (1969) after she crossed the Missis- sippi coast .................... 275 15.8. Variation of peripheral pressure (p w) with time for hurri- cane (a) Gracie (1959) after she crossed the South Carolina coast (b) Camille (1969) after she crossed the Missis- sippi coast ..................... . 276 15.9. Map showing extended boundaries of regions A, B, and C.. 277 15.10. Variation in adjustment factors with time for three geo- graphic regions ..................... 277 15.11. Smoothed adjustment curves for reducing hurricane wind speeds when center is overland ............. 278 15.12. Limits of the three geographic regions (A, B, and C). . . 279 16.1. Partial hurricane tracks and approximate locations of reported sea-surface temperature drops ......... 288 16.2. Partial tracks of (a) selected hurricanes (b) selected typhoons ................ ........ 289 16.3. Variation in pressure drop (Ap) for'(a) selected stalling hurricanes (b) selected stalling typhoons ....... 291 16.4. Variation in pressure drop (Ap) from the maximum pressure drop reached in (a) selected stalling hurricanes (b) selected stalling typhoons ............. 292 16.5. Variation of maximum pressure drop with pressure drop (Ap) (a) 24 hours later; (b) 36 hours later; (c) 48 hours later for selected stalling hurricanes and typhoons ...................... 294 16.6. Ratio of pressure drop (Ap) to the maximum pressure drop. 295 16.7. Stalling adjustment factor (sf) curve for the PMH to be used south of the Virginia-North Carolina border... � 295 16.8. Variation of forward speed (T) with time for (a) selected stalling hurricanes (b) selected stalling typhoons... 296 16.9. Stalling adjustment factor (sf) curves for the PMH to be used north of the Virginia-North Carolina border. . . 299 Xvi2 TABLES PAGE 2.1. Relation between forward speed (T) and track direction (9) (a) for the PMH (b) for the SPH . . . . . . . . . . . . . . . . . . . . 23 2.2. Onshore to overwater winds ratio (k . . . . . . . . . . 31 C Notes for tables 2.3 to 2.6 . . . . . . . . . . . . . . . 39 2.3. Ranges of maximum gradient and 10-m, 10-min overwater winds at 100-n.mi. intervals for the SPH (English units) . . . 40 2.4. Ranges of maximum gradient and 10-m, 10-min overwater winds at selected intervals for the SPH (metric units) . . . . 41 2.5. Ranges of maximum gradient and 10-m, 10-min overwater winds at 100-n.mi. intervals for the PMH (English units) . . . 42 2.6. Ranges of maximum gradient and 10-m, 10-min overwater winds at selected intervals for the PMH (metric units) . . . . 43 3.1. Overwater wind field computation form . . . . . . . . . . 56 3.2. Example of application of table 3.1 . . . . . . . . . . . 61 Notes for tables 4.1 to 4.4 . .. . . . . . . . . . . . . 81 4.1. U.S. gulf coast hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronologically (metric units) . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2. U.S. east coast hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronologically (metric units) ........................ 85 4.3. U.S. gulf coast hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronologically (English units) 87 4.4. U.S. east coast Hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronologically (English units) . . . . . . . . . . . . . . . . . . . . . . . . . 90 Notes for table' 4.5 afid 4.6 . . . . . . . . . . . . . . . 92 4.5. Western North Pacific typhoons (1960-74) with central pressure < 29.10 in. (98.5 kPa) listed chronologically (metric units) .................... 93 zvii PAGE 4.6. Western North Pacific typhoons (1960-74) with central pressure < 29.10 in. (98.5 kPa) listed chronologically (English units). . . . . . . . . . . . .... . 96 Notes for tables 5.1 and 5.2 . . . . 102 5.1. Linear correlation coefficients between pairs of meteoro- logical and other parameters . . .. 103 5.2. Multiple correlation coefficients involving meteorologi- cal and other parameters . . . ... . . ...... 105 6.1. Pressure profile formulas tested in addition to the Hydromet formula . . . . . . . . . . . . . . . . . . 116 6.2. Comparison of storm and three pressure profile formulas. . 117 6.3. Summary of differences in pressure for formulas H, I and II 120 6.4. Summary of pressure differences from table 6.2 for formulas H and I for five intense hurricanes .. .. . 121 7.1. Comparison of three peripheralpressures for gulf and east coast hurricanes, 1900-75 ...... ........ 125 7.2. Comparison of two peripheral pressures for typhoons with p <27.46 in. (93.0 kPa), 1960-74 . . . . . . . . .... 134 0- 8.1. Hurricane central pressure (po) - U.S. gulf coast .. . . . 137 8.2. Hurricane central pressure (po) - U.S. east coast ...139 8.3. Selected extreme hurricanes prior to 1900 . ....... 140 8.4. August 10-kPa (2.95-in.) average heights during the period 1946-55 ..........; ........... 151 8.5. Computation of po for the tropical North Atlantic . . . .. 154 8.6. Computation of p for Cape Hatteras . . . . . . . . .... 158 8.7. Computation of po for Caribou, Maine (applied to 45�N).. . 160 8.8. Lowest observed p 's for New England, Nova Scotia and New- foundland during hurricane passages . . . . . . . .... 162 8.9. Lowest observed po for selected latitude bands (Japan). . . 162 8.10. Sensitivity of computed PMH po to changes in input factors. 164 8.11. Smoothed typhoon data used as guidance to recurvature filling ................... 173 Xozviii .~~~~~~~~~~~~~~ PAGE 10.1. Forward speeds of western North Pacific typhoons (1961-75) with po < 26.81 in. (90.8 kPa) at time of lowest po. . . 198 11.1. Coastal segments, observed severe hurricane direction and permissible track direction limits before smoothing for the PMH and SPH . . . . . . . . . . . . . . . . . . . . 208 11.2. Relation between forward speed (T) and the allowable angles between the coast and track direction (0) for the PMH . . . . . . . . . . . . . . . . . . . . . . . . . . .215 11.3. Relation between forward speed (T) and the allowable angles between the coast and track direction (0) for the SPH. . 222 12.1. Comparison of maximum sustained 1-min, 10-m winds (Atkinson and Holliday 1977) with 10-min, 10-m PMH winds adjusted to 1-min, 10-m winds .................. 242 13.1. Available hurricane wind profile data . . . . . . . . . . 244 13.2. Selected severe hurricane data for development of a wind profile within the radius of maximum winds . . . . . . . 250 15.1. Onshore to overwater winds ratio (kc) . . . . . . . . . . 267 15.2. Classification of hurricanes . . . . . . . . . . . . . . . 274 15.3. Hurricane pressure drop at landfall and computed wind speed adjustments . . . . . . . . . . . . . . . . . . . 281 16.1. Sea-surface temperature (T ) changes associated with the .S passage of various hurricanes . . . . . . . . . . . . . 287 16.2. Most intense stalled hurricanes and typhoons selected for analysis ........................ 288 MX ABBREVIATIONS by : bypassing �C : degrees Celsius CoE : Corps of Engineers ex : exiting ft : feet �F : degrees Fahrenheit GMT : Greenwich Mean Time gpm : geopotential meter(s) HMR : Hydrometeorological Report hr : hour(s) Hydromet : Hydrometeorological in. : inch(es) �K : degrees Kelvin km : kilometer(s) kPa : kilopascal(s) kt : knot(s) Lat. : Latitude Long. : Longitude m : meter(s) mb : millibar(s) mi : mile(s) min : minute(s) n.mi. : nautical mile(s) N/A : Not Applicable NHC : National Hurricane Center NHEML : National Hurricane and Experimental Meteorology Laboratory NtRP : National Hurricane Research Project NOAA : National Oceanic and Atmospheric Administration NRC : Nuclear Regulatory Commission NWS : National Weather Service PMH : Probable Maximum Hurricane sec : second(s) sig : significant xx SPH : Standard Project Hurricane U.S. : United States WMID : Water Management Information Division <�f.1 SYMBOLS A : category of central pressure (6.4.2)* : category of forward speed (PMH - 11.5.2.1; SPH - 11.6.2.1) : asymmetry factor (12.2.3.1) : geographical region along gulf coast (15.3.4) A : discrete value used in obtaining smoothed frequency value l+n F. (8.2.4) 1 B : category of central pressure (6.4.2) : category of forward speed (PMH - 11.5.2.1; SPH - 11.6.2.1) : geographical region along south Florida coast (15.3.4) C : constant of proportionality for pressure profile formulas I and II (6.4.1) : category of forward speed (PMH - 11.5.2.1; SPH - 11.6.2.1) geographical region along east coast (15.3.4) DW : average distance from the pressure center to the points where w~~ Pw is calculated (15.3.7.2) e : base of Naperian logarithms - 2.71828 (6.2) f : coriolis parameter (9.4.1) F : factor for reducing gradient wind speed to 10-m, 10-min wind speed (12.2.1) F. : smoothed frequency value (8.2.4) 1 ff : filling adjustment factor (15.3.4) g : acceleration of gravity (8.3.3.1) H : Hydromet pressure profile formula (6.2) Hg : mercury (table 6.3) i : exponent; i.e., k = k R (6.2) 1 : undefined parameter in HMR 31 (6.3) I : pressure profile formula I (6.3) II : pressure profile formula II (6.3) j : undefined parameter in HMR 31 (6.3) k = r [In = klR (6.2) surface friction coefficient (15.2.4.3) *Section where the symbol is defined or first referenced. xkii K density coefficient = p-) (12.1.1) kc : onshore to overwater wind speed ratio at the coast (15.2.4.1) k. at the coast for onshore winds (15.2.4.3) ke : offshore to overwater wind speed ratio (15.2.4.2) [equilibrium surface friction coefficient (15.2.4.3)] k. : previous surface friction coefficient at the last upwind boundary between surface friction categories (15.2.4.3) : k at the coast for onshore winds (15.2.4.3) c kl :mR (6.2) Ri LR : lower limit of R (tables 2.3 to 2.6) LT : lower limit of T (tables 2.3 to 2.6) : point where T first falls below TL (16.5.3.3) M a radial through Vx (12.2.3..3.1) MSG missing (tables 4.1 to 4.6) n undefined parameter in HMR 31 (table 6.1) a number (8.2.4)' N sample size (tables 5.1 and 5.2) p pressure (6.2) P pressure (8.2.3) PC : mean sea-level pressure for typhoons (12.4) PH4O : pressure computed at 40 n.mi. (74 km) from a hurricane center using H (6.4.2) PHO8 : pressure computed at 80 n.mi. (148 km) from a hurricane center using H (6.4.2) P140 : pressure computed at 40 n.mi. (74 km) from a hurricane center using Formula I (6.4.2) : pressure computed at 80 n.mi. (148 km) from a hurricane center PI80 using Formula I (6.4.2) PII40 : pressure computed at 40 n.mi. (74 km) from a hurricane center using Formula II (6.4.2) PII80 : pressure computed at 80 n.mi. (148 km) from a hurricane center using Formula II (6.4.2) PL : pressure at lower surface of a layer (8.3.3.1) ,n : asymptotic peripheral pressure (7.1) Pnx : hurricane peripheral pressure from table 3-1 of NHRP Report No. 5 (7.1) xxiii pO : central pressure (5.2) p40 :hurricane pressure observed or estimated at 40 n.mi. (74 km) from center (6.4.2) PS80 :hurricane pressure observed or estimated at 80 n.mi. (148 km) from hurricane center(6.4.2) PU pressure at upper surface of a layer (8.3.3.1) pw : peripheral pressure from weather maps (5.2) Pw Pwi :peripheral pressure from last closed isobar (7.2) Q interpolation coefficient used in computing the surface friction coefficient, k (15.2.4.3) r :zero-order correlation coefficient (5.3.1) distance from storm center (6.2) distance to the coast from a circle representing the PMH (11.5.2.1) R : radius of maximum winds (5.2) r' : multiple correlation coefficient (5.4) rI2 : reduction of variance (5.4) r : outer radius from which inflow air originates with negligible momentum relative to the earth (9.4.1) Rim :limiting radius of maximum winds (9.4.1) R.H. mean relative humidity (tables 8.5 to 8.7) s distance from a surface friction category boundary (15.2.4.3) S surge (8.2.3) syx standard error of estimate (5.4) y'x sf : stalling adjustment factor (16.4.1.4) t : landfall time (15.3.4) : some specified time (15.3.6) T forward speed (5.2) t temperature in �Celsius (see conversion table) c tf temperature in �Fahrenheit (see conversion table) ~tk :temperature in �Kelvin (see conversion table) T :mean temperature (8.3.3.2.2) T dew-point temperature (8.3.3.2.3) ~~d .3)~~~~~~~av Xxiv T : minimum forward speed permissible for maintaining PMH intensity (16.5.3.2) T : forward speed unit parameter (12.2.3.1.1) 0 T : sea-surface temperature (8.3.3.2.2) T : mean adjusted virtual temperature (8.3.3.1) v UT : upper limit of R (tables 2.3 to 2.6) UT : upper limit of T (tables 2.3 to 2.6) V : hurricane. (typhoon) wind speed (12.1.3.1) : 10-m, 10-min overwater wind speed at a point (12.2.3.3) V : cyclostrophic wind speed (12.1.2) V : maximum cyclostrophic wind speed (12.1.2) cx Vg : gradient wind speed (12.1.2) Vgx : maximum gradient wind speed (12.1.1) gx Vk : 10-m, 10-min wind speed adjusted for underlying terrain (15.2.4.3) V :. maximum sustained surface wind speed for typhoons (12.4) m Vmax maximum wind at Rlim (9.4.1) max maximum wind corresponding to APmax (16.4.1.4) V: overwater wind speed in a stationary hurricane at radius r (12.2.3.3) V : maximum 10-m, 10-min overwater wind speed (12.2.3.2) x Vxs Vx for a stationary hurricane (12.2.2) VGL V for the lower limit of R (2.3) gx VGU V for the upper limit of R (2.3) gx VLL V for the lower limit of R and the lower limit of T (2.3) x VLU Vx for the lower limit of R and the upper limit of T (2.3) VUL : Vx for the upper limit of R and the lower limit of T (2.3) VUU : V for the upper limit of R and the upper limit of T (2.3) x WC : overwater wind speed at landfall (15.3.6) WI : overland wind speed at some specified time after landfall (15.3.6) Wn : weighting function (8.2.4) XXV x one of the variables in a normal distribution (5.3.1) : empirical constant (12.2.3.1.1) X-X a wind path (3.3.4.1) y one of the variables in a normal distribution (5.3.1) empirical constant (12.2.3.1.1) ordinate (16.5.4.2) Y regression function of a random variable (5.4) Y-Y a wind path (3.3.4.2) z height (8.3.3.1) a coefficient employed in fitting mathematical expression to filling adjustment curves (15.3.6) fraction of tangential component of momentum generated in the inflow layer, between ro and Rlim, that is dissipated by surface stress (9.4.1) angle between track direction and surface wind direction (12.2.3.1.2) coefficient employed in fitting mathematical expression to filling adjustment curves (15.3.6) : angle between track direction and surface wind direction computed along radial M (12.2.3.3.2) E1 : coefficient for expressing stress opposition to coriolis force (9.4.1) CZ: summation (6.4.3) 0 track direction (5.2) 0 : surface wind direction (12.2.3.1) 0e : equivalent potential temperature (8.2.4) Gt : tangential wind direction (12.2.3.3.1) X : longitude (tables 5.1 and 5.2) p : population correlation coefficient (5.3.1) : air density (8.3.3.1) : standard deviation (5.4) : wind inflow angle (5.2) geopotential (8.3.3.1) : wind inflow angle at r (12.2.3.3.1) : wind inflow angle at r = R (12.2.3.3.1) : latitude (tables 5.1 and 5.2) xzvi : angular velocity of rotation of earth (12.1.1) Ap : pressure drop, or peripheral pressure (Pw) minus central pressure (po) (8.4) : pressure at upper surface of a layer minus pressure at lower surface of same layer (tables 8.5 to 8.7) APmax : greatest pressure drop for a given storm (16.4.1) Ap � : change in central pressure with changes in other parameters (table 8.10) Apt : pressure drop at hurricane landfall (15.3.4) Ap/DW : average pressure gradient (15.3.7.2) * : significant correlation between variables (tables 5.1 and 5.2) � : duplicate hurricanes (tables 4.1 to 4.4) 5 hurricane symbol (fig. 12.5) + storms for which analyzed wind fields were not available (13.2.1) i' 'L .;" xxVii METEOROLOGICAL CRITERIA FOR STANDARD PROJECT HURRICANE AND PROBABLE MAXIMUM HURRICANE WIND FIELDS, GULF AND EAST COASTS OF THE UNITED STATES RICHARD W. SCHWERDT, FRANCIS P. Ho, AND ROGER R. WATKINS WATER MANAGEMENT INFORMATION DIVISION OFFICE OF HYDROLOGY, NATIONAL WEATHER SERVICE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION U.S. DEPARTMENT OF COMMERCE ABSTRACT. Criteria for determining wind fields along the Gulf and East coasts of the United States for the most severe hurricane reasonably characteristic of a region, Standard Project Hurricane (SPH), and for the hurricane that will produce the highest sustained wind that can probably occur at a specified coastal location, Probable Maximum Hurricane (PMH), are presented. A single limiting value for the meteorological parameters of peripheral pressure (pw) and central pressure (p), was determined. Upper and lower limits were determined for the radius of maximum winds (R), forward speed (T), track direction (0), and inflow angle (~). Interrelations between the several parameters po R, T, 0, latitude (4) or longitude (X) were investigated. 1. INTRODUCTION 1.1 AUTHORIZATION AND FUNDING Concentrated effort to determine revised values of meteorological parameters for wind fields prescribed by the Standard Project Hurricane (SPH) and Probable Maximum Hurricane (PMH) started in early 1975. Funding for the studies was provided jointly by the U.S. Nuclear Regulatory Commission (NRC) Contract No. AT (49-24)-120, and the Corps of Engineers (CoE), Department of the Army. 2 1.2. DEFINITIONS 1. 2. 1. SPH The SF1- is a steady state* hurricane having a severe combination of values of meteorological parameters that will give high sustained wind speeds reasonably characteristic of a specified coastal location. By reasonably characteristic is meant that only a few hurricanes of record over a large region have had more extreme values of the meteorological parameters. The "SPE wind field" is specified from the parameters. One of several uses of the wind field is to compute critical storm surge at coastal points. The SPH wind field is also a factor in calculating wind load. A frequency can be determined for any combination of values of meteoro- logical parameters that define an SPH wind field. This combined frequency for the total wind field will generally have a recurrence interval of several hundred years. 1.2.2. PMH The PNH is a hypothetical steady state* hurricane having a combination of values of meteorological parameters that will give the highest sustained wind speed that can probably occur at a specified coastal location. From values of the parameters, a wind field is specified which is termed the "PMH wind field." One of several possible uses of the values of meteorological parameters is to compute maximum storm surge at coastal points when the hurricane approaches along the most critical track. The PMH1- wind field is also a factor to be considered for calculating wind load. The PMH~ is a rare event. As with the SPH, frequency could be determined for a combination of meteorological parameters used to develop any specific PMH1 wind field and then combined to determine the recurrence interval for that total event. Other combinations of parameters would give different PMH1 wind fieldsand frequencies could be determined for each. These frequencies would have such a large uncertainty as to make the effort meaningless . *See par. 1.2.3. 1.2 3. -TEADY STATE By steady state in this report we mean there is no change in the values of Pw' Po, R, T, 0, 0, wind speed, and limits of rotation of wind fields during at least the last several hours before an SPH or PMH makes landfall. The SPH is a steady state hurricane. The PMH is a steady state hurricane except for the coast between mileposts 900 and 1300 (fig. 1.1). Here it is not steady state because it is defined as a recurving, weakening hurri- cane, i.e., p- is increasing with time. If the user wishes to consider the PMH steady state in this area, he must use the po at the coast. We consider the SPH and PMH to be steady state because there is not enough tropical cyclone data to define the time variation of the pertinent parameters. 1.3 PURPOSE Abnormally high winds, pounding waves, and storm surge from hurricanes produce severe damage and a threat to life. The CoE is responsible for assessing the potential for damage resulting from hurricanes along coasts, proposing and designing structures to alleviate this damage, and consulting with State and local communites on these matters. Local records of hurricane behavior are inadequate for these purposes, not only because of often incomplete water-level observations but also these and other records may be available for only a few years. In addition, hurricanes may cross a particular section of coast infrequently. Communities that have been spared a severe storm for decades or may never have experienced a severe hurricane in recorded history are not immune to this danger in the future. In order to bring to bear the entire: body of knowledge of hurricane behavior in a consistent manner, the concept of the SPH has been developed for the gulf and east coasts.as a bench.mark against which to judge the hazards for particular communities. : In addition to the SPH, there is a need for defining the wind fields associated with the PMH. Such a storm may be used by the CoE in planning and design of barriers near the coast to protect life. Guidance by 4 95~ 9O~_______ 850 800 750 76' 65 VT *~N0 2900 ~ 600 50N.MI ALA. A. CHT1 19~~~~200 200 ~~~~~~~~~~~~~~~~~~~~~~~~HOEGULFO EiC ~~~~~~~~~~~~~~~~~~~~~~~200 100 ______________~~~~~~~~~~~~~~60 950~~~~~~~~~~~~~~~~20 Figure~~~~~~~~MIS AL. 1.-oao1a90t0osa itac nevl are nnuia miles~~~~~~---- -------------s the NRC for planning and design of nuclear power plants suggests the use of PMH in locations where high winds, waves and storm surge could pose a threat to the public health and safety from a hurricane-induced accident at a nuclear power plant. Consistency is needed in developing values of various parameters for both the SPH and PMH. For example, the interrelations between central pressure and other parameters, while not necessarily the same for both the SPH and PMH, should be consistent and must be evaluated. 1.4 SCOPE The geographical region covered by this report is the U.S. Gulf of Mexico and east coasts from Texas to Maine. Hurricane (through 1979 and typhoon (through 1974) data were used. An understanding of hurricane behavior through 1977 was used for studying and evaluating values of parameters for the SPH and PMH. The meteorological parameters evaluated are: central pressure (po) 0 peripheral pressure (p radius of maximum winds (R) forward speed (T) track direction (05 inflow angle (4) Other necessary considerations for defining wind fields are covered in this report. These include the wind speed distribution and limits of rotation of wind fields. The study develops a meteorologically consistent set of criteria. We describe in chapters 2 and 3 how these parameters can be used to develop SPH and PMH wind fields. The application of these wind fields to surge genera- tion, erosion of beaches, wind load, etc., is a task for oceanographers, engineers, and others, and is left to them. 6 We assumed that p (relative to pw) is the most important meteorological parameter. We developed our procedure by first establishing values of Ap = Pw - Po at all coastal points for the SPH and the PMH. For the PMH, a primary maximization is in the determination of Ap. The other meteorologi- cal parameters are not assigned a single value, but ranges of allowable values are given to be used in conjunction with Ap to produce a variety of possible wind fields. The user must select the combination that'is most critical for a given problem. The criteria developed in this report are for hurricanes making landfall'' (entering hurricanes) along the U.S.. gulf and east coasts. Criteria have not been developed for exiting hurricanes except for small peninsulas or the tips of capes, e.g., Cape God, the Mississippi Delta, etc., where the SPH or PMH is allowed to exit after crossing a small land area.' Generalized criteria for exiting storms is beyond the scope of this report. Analysis of the few extreme coastal data required smoothing. Large variations over short distances were avoided unless supported by data or theoretical considerations. The study is to be used along relatively smooth unbroken sections of coastline. Application to bays and other places where the coastline undergoes sharp changes in orientation would_ require modifications to the criteria in this study. Criteria are given for the SPH and the PMH only. No attempt should be made to simply interpolate between SPH and PMH to establish criteria for a hurricane stronger than SPH but weaker than PMH. Another study would be needed for this purpose. Hurricanes are a threat to life and property not only from high winds, waves, and storm surge but from rain-induced floods.- This latter problem is not considered in the present study. The frequency and areal distribu-- tion of tropical storm rainfalls in a form suitable for use in engineering design along the gulf coast is the subject of a report by Goodyear"(1968). Extreme limits of rainfall (Probable Maximum Precipitation) are the subject of National Weather Service Hydrometeorological-Reports. 7 1.5 PREVIOUS STUDIES 1.5.1 SPH Generalized meteorological specifications for the SPH for the gulf and east coasts were first given in a study, "Meteorological Considerations Pertinent to Standard Project Hurricane, Atlantic and Gulf Coasts of the United States," by Howard E. Graham of the Hydrometeorological Section, Hydrologic Services Division, U.S. Weather Bureau, and Dwight E. Nunn of the Office of Chief of Engineers, CoE. This was published as National Hurricane Research Project (NHRP) Report No. 33 (Graham and Nunn 1959). Hereafter this report will be referred to as NHRP 33. This work brought together and generalized numerous earlier specifications for the SPH developed by the Hydrometeoro- logical Branch for several locations along the gulf and east coasts. These earlier studies were conducted for and funded by the CoE. The specifications in NHRP 33 were partially revised in an unpublished study (National Weather Service 1972). The revision incorporated data from storms since 1956, which indicated the wind fields should be stronger than shown in NHRP 33 for selected coastal regions. 1.5.2 PMH The first PMH studies were requested by the CoE for the Narragansett Bay and New Orleans regions (U.S. Weather Bureau 1959a and b). The central pressures were determined as a ratio to the central pressure for the SPH. The remaining factors for the PMH were essentially the same as for the SPH. An unpublished PMH study (U.S. Weather Bureau 1968) generalized criteria for the PMH along both coasts. The central pressure and peripheral pressure differed from that of the SPH; values of the other parameters remained unchanged even though the list of hurricanes of record was updated. 1.5.3 HURRICANE CLIMATOLOGY NO/A Technical Report NWS 15 (Ho et al. 1975) presented a climatology of hurricane factors important to storm surge for the gulf and east coasts. This climatology was an analysis of all available hurricane data beginning with the storm tracks of 1871. Data for most other factors were available subsequent to 1900. Discussions were presented to provide possible explanations of the alongshore variations of the parameters, but the analyses were not extensively modified on the basis of subjective reasoning. In the SPHT, and particularly the PMTH, considerably more smoothing beyond what has occurred is necessary for an estimate of what can happen. I1.5. 4 COMPARISONS BETWEEN PREVIOUS SPH AND PMH STUDIES AND THIS REPORT Previous SPH and PMH studies defined values of meteorological parameters that could occur within broad coastal zones (seven zones covered the coast from Texas to Maine). Data points representing each zone were joined by smooth curves to permit interpolation along the coast. This technique is a more generous smoothing than used in the present study. Here, alongshore variations were determined by developing estimates within each of more than 60 overlapping zones and smoothing between designated points. 1.6 ORGANIZATION Figure 1.1 shows the coastline and distances from an initial starting point south of the United States - Mexico border. Geographical names are shown to aid identification. Figure 1.2 is a chart showing distance as the abscissa. Along the top, locations are given for easy identification of coastal points. This figure will be used throughout the report for presenting various types of data analyses. Chapter 2 presents a summary of the major results of this report. Chapter 3 gives procedures for constructing SPHT and PMH wind fields and an example. Chapter 4 describes the data used in the report. Limitations of the observed data are given. Chapter 5 defines each of the pertinent meteorological parameters and gives their interrelations. Chapter 6 develops the pressure profile equation. This equation is basic to defining the wind field. EASTPORT, ME.- U.) BOSTON. MASS - 0- cm cc~~~~~~~~~~~~~~~~~~~~~~~' NEW YORK, N.Y. > CHINCOTEAGUE. VA.- - to CAPE HATTERAS. N.C.-- - - -c o� CHARLESTON. S.C. - Co DAYTONA BEACH. FLA. - 0 '> x - z 0$ LJ(. -a kt MIAMI. FLA. - e. ., I- ~ ~ ~ ~ ~ ~ ~ ~ 9 FT. MYERS, FLA.- -, ul o TARPON SPRINGS, FLA. -- APALACHICOLA. FLA.-*, - - 02 PENSRCOLA. FLA.-> - to C-o GALVESTON, TEFL-A - cz PENT SACOLA, FLA.-- co PORT ISABEL. TEX.- '- 4 10 Chapters 7 through 11 consider separately five of the six meteorological parameters (all but ~) and describe the methods used to determine our estimates of values for the SPH and PMH. Magnitudes of the parameters are shown as profiles along the coasts except for Pw which is constant. Chapter 12 is concerned with computation of maximum overwater winds. Gradient winds are calculated first. These are then reduced to 10-m (32.8-ft) 10-min overwater winds (Vx). Tables 2.3 to 2.6 give some values of meteorological factors and parameters for the SPH and PMH at 100-n.mi. (185.3-km) mileposts to provide a general overview of the magni- tude of possible wind speeds. The user should compute wind speeds for many values of parameters at specific coastal locations to determine the one most critical for his use. This chapter also discusses 10-m, 10-min overwater winds other than at V x Chapter 13 develops relative wind profiles from the radius of maximum'- winds (R) to 300 n.mi. (556 km) from the eye of the SPH and the PMH. Relative wind profiles are also determined for inside R to the hurricane center. Limits of rotation [the range of angles within which the maximum winds can be placed relative to track direction (0)] are also given in this chapter. Chapter 14 describes the method of determining inflow angle (~). Chapter 15 discusses 1) the adjustment to wind fields when the hurricane approaches the coast, and 2) the adjustment to wind fields after the center crosses the coast. Chapter 16 looks at problems associated with a stalling PMH. 2. EXECUTIVE SUMMARY 2.1 INTRODUCTION This chapter presents a summary of the results of chapters 6 to 16 (sec. 2.2) and a comparison of computed maximum SPH and PMH winds with computed winds for hurricanes of record using observed or estimated values of meteoro- logical parameters or factors for each hurricane (sec. 2.3). All wind compu- tations are based on equations 2.2, 2.6, and 2.7. Information is often given in figures and tables with brief definitions and explanations. Ranges of permissible values are given for several parameters. The user should determine for his particular application the- most critical values within these ranges. Complete documentation of the logic and data supporting the results can be found in the chapter listed next to each subsection. The basic data on Gulf of' Mexico and North Atlantic hurricanes (within 150 n.mi. of the U.S. coast) and on western north Pacific typhoons used in this study are listed in chapter 4. A more complete definition of the para- meters used in this study and their interrelations are given in chapter 5. Chapter 3 describes how to compute wind fields. It refers only to this summary chapter for needed information. 2.2 RESULTS OF THE STUDY 2.2'.1 PRESSURE PROFILE FORMULA (CHAPTER 6) The pressure profile formula used to develop the maximum gradient wind speed equation for the SPH and the PMH is: P -Po -R/r ~~ e -R/r ~~~~~~(2.1) Pw -Po where p is the sea-level pressure at distance r from the hurricane center and po, Pw' and R are as defined in the following three subsections. 12 2.2.2 PERIPHERAL PRESSURE (CHAPTER 7) Peripheral pressure (p ), the sea-level pressure at the outer limits of w the hurricane circulation, is the average pressure around the hurricane where the isobars change from cyclonic to anticyclonic curvature. In this study, Pw was determined at four equally spaced points around the storm center (north, east, south, and west). We adopted 29.77 in. (100.8 kPa) as the Pw for the SPH and 30.12 in. (102.0 kPa) as the Pw for the PMH. 2.2.3 CENTRAL PRESSURE (CHAPTER 8) Central pressure (p o) is simply the lowest sea-level pressure at the hurricane center. Figures 2.1 and 2.2, respectively, show the adopted coastal variation of p for the SPH and for the PMH. In general, po increases with latitude for both the SPH and the PMH. Coastal orientation relative to possible hurricane tracks results in the sharp rise in po between the southern New England coast and the Boston area. Figure 2.3 shows Ap or p - p for the SPH and the PMH. It compares the relative magnitude of the most important parameter used in computing hurricane wind speeds. 2.2.4 RADIUS OF MAXIMUM WINDS (CHAPTER 9) The iadius of maximum winds (R) is the radial distance from the hurricane center to the. band of strongest winds within the hurricane wall cloud, just outside the hurricane eye. Figures 2.4 and 2.5 show the adopted coastal variation of the permissible range in R for the SPH and the PMH, respec- tively. R generally increases with latitude for both the SPH and thc PMH. R is also somewhat dependent on po. The PMH is envisioned as a fully developed, tightly wound hurricane whose R for any particular coastal point is less than the R of the SPH at that location. 13 (bJ~) o 0 0 0 0 0 0 0 0 0. 0. 0. 0� 0. 0r a EASTPORT. ME.-- I BOSTON, MASS-- a - NEW YORK, N.Y.- CHINCOTEAGUE. VA.-.- CAPE HATTERAS, N.C.- -c o ~ CHARLESTON. S.C. PL co0 DAYTONA BEACH, FLA.-> C'j 44- x i c o- MIAMI , FLA. -- "0 Q- - ~ ~ ~ ~ ~ ~ ~ ~ v z z~~~~~~~~~~~~~~ z< - o FT. MYERS. FLA.-- - TARPON SPRINGS, FLA.-3 - APALACHICOLA, FLA.-, . c0 PENSACOLA. FLA.-- w- BILOXI, MISS.- CD N-~~~~~~~~~~~~~~~~~~~~~~~~' LAKE CHARLES, LA.-- GALVESTON, TEX.- PORT ISABEL. TEX.-j In Cl 0 N In Ck 4 0 An (o Cl Cl Cl Cl 4 Cl Cl C4 ('NI) annSs3ad IVllN3D 14 A n 0 0 0 04 aO EASTPORT , ME NI I I -a N~~~ cu~~~~~' BOSTON, MASS- N o- C D cc NEW YORK, NY-> CHINCOTEAGUE, VA -1- CAPE HATTERAS, NO cm ou - I- 1u C.' CHARLESTON, SC Il. 0 ~ ~~~~~~~~- N -C - X DAYTONA BEACH, FLA -, - z w uj~ cu tm N Z MIAMI, FLA -9 FT MYERS, FLA - IC TARPON SPRINGS, FLA-* - - - P-I N I APALACHICOLA, FLA.-- N0 PENSACOLA, FLA-Lo BILOXI, MISS - c o N-- LAKE CHARLES, LA-- GALVESTON, TEX -al PORT ISABEL, TEX -- 0 tt] O VA 00 in ' 0 ii 0 cm '0 cm cm N '0 cm C.' e' C CND C. C. e (N C" I. (Nil flnSS31d 1V~llN3D 15 (bd)I '6 (N o0 0 0 EASTPORT, ME--I I I ICD I I C., BOSTON, MASS-- I0 [ I - 4 NEW YORK, NY / / CHINCOTEAGUE, VA-3 I-" CAPE HATTERAS, NC-, o. = CHARLESTON. S3C-p - C C I -p -~ DAYTONA BEACH. FLA -- c" I MIAMI, FLA- Ico "\~~~ I FT MYERS, FLA cli TARPON SPRINGS, FLA - - I 1 APALACHICOLA, FLA.---- - PENSACOLA, FLA. s-e- BILOXI. MISS- * - cu- N;~~~~~~~~~~~~~~~~~ '0 LAKE CHARLES. LA-* GALVESTON, TEX- b cm PORT ISABEL, TEX i. I I ,I I I I 0 to) 0 S)O 0 ) to 0 o (NI) dV 14~~ 16 (W)I) 0% co N 0 CM - 0 EASTPORT, IlE.LA4 1 I I I BOSTON, MASS co - cc NEW YORK, NX.-Y . CHINCOTEAGUE, VA.- _ - CM CAPE HATTERAS, N.C.-N- 0- Cl l CHARLESTON. S.C.- 9 - I- DAYTONA BEACH, FLA. -o 2- - 0 CD~~~~~~~ Z MIAMI. FLA. -D u to - a FT. MYERS, FLA.-- N /r Cl 0 TARPON SPRINGS, FLA.-- - - APALACHICOLA, FLA.-, I/o . PENSACOLA, FLA.- co BILOXI, MISS. -* - - c'- -4 0 LAKE CHARLES, LA.-- cc-- GALVESTON, TEX.-- ' "Ji PORT ISABEL, TEX.-* 0 tn 0 W) 0 on 0 Ito 0 '0 0 ~~~~~~~~~o cl ) , o ,~o~, o OW N) SCINIM WfIWIX V (JO ni - - (1W N) SGNIM WnWIXVW ~O sflIUv~ 17 (W )I EASTPORT. ME.-- I 3 I BOSTON, MASS- LO- - NEW YORK, N.Y. *-0 ri co~~~~c CHINCOTEAGUE, VA.-~' CAPE HATTERAS, N.C.-N' 0O-___ _____ CHARLESTON. S.C.-- - 0 DAYTONA BEACH, FLA. -* 0 - MIAMI. FL A.- -- _, I FT. MYERS, FLA. TARPON SPRINGS, FLA.-- APALACHICOLA. FLA.-, - PENSACOLA, FLA. BILOXI, MISS. - - N- -~ t LAKE CHARLES, LA.-- GALVESTON, TEX.-- I - C,' PORT ISABEL, TEX.- O I N I I I I s l 0 0 uSt 0 i'3 0 ae) 0 0 0 (, (,' (%4 �C4 - (1W N) SQNIM WflWIXYW :10 SflQI~ 2.2.5 FORWARD SPEED (CHAPTER 10) Forward speed (T) refers to the-rate of translation of the hurricane center from one geographical point to another. It is one component of the wind field of a moving storm and results in higher winds on the right side of the storm and lower on the left. Figure 2.6 shows the adopted coastal variation of the permissible range in T for the SPH and figure 2.7 shows this variation for the PMH. Available data indicate that the upper limit of T for severe storms should be held constant with latitude to about milepost 1800. Similarly; the lower limit is constant for the PMH except for the northeastern Gulf, where the PMH is defined as a recurving, faster-moving hurricane. The lower limit for the SPH is constant to Cape Hatteras. North of Cape Hatteras, the lower and upper limits of both the PMH and SPH increase with latitude, although the increase is only slight north of Cape Cod. The range of PMH forward speeds is less than that for the SPH. Very slow speeds weaken a hurricane (see chapters 10 and 16). Very fast speeds result in a very asymmetrical wind field which is considered more possible with an SPH than a PMHi. 2.2.6 TRACK DIRECTION (CHAPTER 11) The track direction (0), or the path of forward movement along which the hurricane is coming (measured clockwise from north), is considered to be noninstantaneous in this report, i.e., the SPH and the PMH are not allowed to change course during the last several hours before striking the coast. Figures 2.8 and 2.9 show the permissible range of 0 for the SPH and the PMH, respectively. Limiting O's are based on possible directions over the open ocean, further constrained by sea-surface temperatures and other meteorological features. The permissible range is also a function of forward speed (T). As the angle between the coastal orientation and 0 decreases, the slower hurricane weakens more than the faster-moving hurri- cane. Table 2.1 gives the T, by category, required for using figures 2.8 and 2.9. 19 (I~H/W)I ) G o N 'o V) v co cm EASTPORT, ME. D.' ' ' ' BOSTON, MASS - N L cm U.' CHINCOTEAGUE, VA. -* CAPE HATTERAS. N.C.-- q0 cm CHARLESTON. S.C.- 9. ( DAYTONA BEACH, FLA. - '- MIAMI, FLA. - co FT. MYERS, FLA.- TARPON SPRINGS, FLA.- - wo- APALACHICOLA, FLA. - PENSACOLA, FLA.-* L BILOXI. MISS.-- LAKE CHARLES8, LA. GALVESTON, TEX.--. PORT ISABELI TEX' a eO - 20 PJH/W)I I 0 0 0 00O00 00 0 a. co tn v cop cm EA\STPORT, ME.- _ I BOSTON, MASS-I NEW YORK, N.Y. %-~~~~ CHINCOTEAGUE. VA.-- U -J~~~~r CAPE HATTERAS, N.C--> -1 CHARLESTON, S.C.-. - n DAYTONA BEACH, FLA. -z - x - MIAMI, FLA. -L I-~ ~ ~ ~ ~~~~+ FT. MYERS, FLA. wj I ~~~~~~-p TARPON SPRINGS, FLA.->- o 1 APALACHICOLA FLA. PENSACOLA, FLA.- se ib BILOXI. MISS.-- - LAKE CHARLES, LA. GALVESTON, TEX.-, PORT ISABEL, TEX. 0 0 0IN 03a 0 0 0bo '0 *l C3 C') ( WIJ1 (I33dS CI~VMIOJ 21 -Ist EASTPORT. ME.-- ' - T 1x, 4> r\~I. C., C N~~~~~~~~~~~~~' 7- t BOSTON, MASS -- "' 7q) co U ~~P0 co -Z D 00 NEWYORK. N.Y.- 0 , - I.- CHINCOTEAGUE, VA.- -f- 9 o,~~~9 CAPE HATTERAS, N.Cm 0 t~~~~~o CHARLESTON, S.C.-- -I- DAYTONA BEACH. FLA.- - 0 I tu N~~~~~~~. 0/ N___ t- U., MIAMI. FLA. -' - FT. MYERS, FLA. N TARPON SPRINGS, FLA.--' a, cj~~0 8- \ -. APALACHICOLA, FLA. 3, PENSACOLA. FLA. - BILOXI, MISS.-- - 7- ) I co o LAKE CHARLES, LA.-~ i .'.i., _t GALVESTON, TEX.-- I CNI~ PORT ISABEL. TEX.-- I o8 o 0 0 0 0 C N ~ ~~~ N 0 ue 0. C,' -. -4 - (6eP) NOI1D34IG NDVNI 22 EASTPORT, ME.- T -'.- BOSTON, MASS-- "o . CiCO r o NEWYORK, N.Y. >i mi uiL -SX UIU N L) C-4 CHINCOTEAGUE, VA. al. A I cY~ tox CAPE HATTERAS, N.C.- -r-> I~ _ ~ CHARLESTON, S.C.-- -- >< DAYTONA BEACH. FLA. -~i --- CO- MIAMI, FLA, s. u FT. MYERS, FLA.- TARPON SPRINGS, FLA.-- 2- APALACHICOLA, FLA.- - C PENSACOLA, FLA.-* -Z "--~~~~~' U.,1 BILOXI, MISS.- I _ LAKE CHARLES, LA. GALVESTON, TEX;-- j I PORT ISABEL. TEX.-* I cm cm c m c ,j, (Y (Y N 23 Table 2.1.--ReZation between forward speed (T) and track direction (0) a. For the PMH Speed category Forward speeds (T) A 6 kt < T < 10 kt (11 km/hr < T < 19 km/hr) B 10 kt < T < 36 kt (19 km/hr < T < 67 km/hr) C T > 36 kt (T > 67 km/hr) b. For the'SPH Speed category Forward speeds (T) A 4 kt < T < 10 kt (7 km/hr < T < 19 km/hr) B 10 kt < T < 36 kt (19 km/hr < T < 67 km/hr) C T > 36 kt (T > 67 km/hr) 2.2.7 OVERWATER WINDS (CHAPTER 12) 2.2.7.1 MAXIMUM GRADIENT WINDS (VGX). Gradient wind is defined as a wind blowing under conditions of circular motion, parallel to the isobars, in which the centripetal and coriolis accelerations together exactly balance the horizontal pressure-gradient force per unit mass. The gradient wind, inde- pendent of duration, is computed by solving the equation: V ='K (Pw po)l/2 _Rf Vgx (Pw 0P) 2 (2.2) where Pw, p0, and R are as previously defined and f = coriolis parameter,dependent on latitude K =()/ = density of the air (p) computed from sea-surface temperatures; e = 2.71828 24 Values of K along both coasts are graphed in figures 2.10 and 2.11 for the SPH and PMH, respectively. These are based on the variation of sea-surface temperatures. For the PMH, the 0.99 probability level was used. For the SPH we used the 0.75 level. 80 0 I' I I I I ' I I I 78 - /K IMPH, IN.) 76 - 74 - o 72 - 0 70 - K (KM/HR, kPa) IMETRICI 68- 66- K (KT,IN.I (ENGLISH) 64 I , I , , , , I I ,,' - 25 30 35 40 45 LATITUDE C(N) Figure 2.10.-- Values of Zatitude-dependent K coefficient for three units of measurement for the SPH. 2.2.7.2 TEN-METER 10-MINUTE OVERWATER WINDS 2.2.7.2.1 WINDS IN A STATIONARY HURRICANE. Observed maximum 10-m (32.8-ft), 10-min winds (Vx) over open water in hurricanes of above average intensity have been found to vary from about 75 to slightly over 100% of Vgx. We have adopted two empirical equations for estimating Vx in a stationary hurricane. V = 0.9 Vg , for the SPH (2.3) x gx Vx = 0,95 Vgx, for the PMH (2.4) The 0.95 for the PMH was selected on the grounds of representing a more extreme condition. 25 Vx for a stationary hurricane, we shall call V . Knowing V X,we can use thXfo xs V xs' the information on relative wind profiles (sec. 2.2.8) to determine 10-m, 10-min overwater winds at any distance from the hurricane center. 80 .i i * ! I K (MPH. IN.) 78- 76 - 74- I- ,z 72- 8~~~~72-~~~~~~~~~~~ ~K (KM/HR, kPa) (METRIC) o 70- 68 K (KT, IN.) NGLISH) 66 - 64 I I . . I , , I . . I 25 30 35 40 45 LATITUDE (ON) Figure 2.11.--Values of the latitude-dependent K coefficient for three units of measurement for the PMH. 2.2.7.2.2 WINDS IN A MOVING HURRICANE. Equations 2.3 and 2.4 are simpli- fied forms of a general equation for V that includes an asymmetry factor, x A. This factor is 0 63 0.37 A = 1.5 (T ) (To ) cos (2.5) 0 where T = forward speed s ~~~~~~~~~~~-1 T = 1 when units are in kt, 0.514791 when units are in ms , 1.853248 O -1 -1 when units are in km hr ,and 1.151556 when units are in mi hr, 26 = the angle between track direction (0) and the surface wind direc- tion. 1 varies around the hurricane at any constant radial (r) and along a radial with varying distances from tke hurricane center. A is added to the winds on the right of a storm track and subtracted from those on the left. When we add A to equations 2.3 and 2.4, we arrive at our adopted SPH and PMH V for a moving hurricane. For the SPH x V 0.9 V + 1.5 (T0'63) (T 0 37)cos (2.6) x ~gx For the PMH 0.63 0.37 V = 0.95 V + 1.5 (T (T ) cos 1 (2.7) x gx V occurs at the point along the circumference of maximum winds where the x surface wind direction is parallel to track direction (0). Here r =0 and cos 1 = 1. The inherent relation between 1 and inflow angle (~) requires the point at which V occurs to fall in the right-rear quadrant of ahurri- x cane. Section 2.2.9 will set allowable limits of rotation for this point. The general equation for 10-m, 10-min overwater winds at any point other than where V occurs is: x 1. 5 T '63) 0.37) V = V + 1.5 (TO63) (T 0.37) cos 1 (2.8) 5 0 where V is the wind speed at radius r and V is the wind speed in a station- s ary hurricane at radius r. Relative wind profiles for computing Vs are discussed in sec. 2.2.8. The example in chapter 3 shows how 1 is computed along any radial out from the center of a hurricane. 2.2.8 RELATIVE WIND PROFILES (CHAPTER 13) The adopted variation of wind speed outward from R for a stationary storm is given in figure 2.12. These profiles (based on actual storms of record) are R dependent and are expressed in terms of relative winds (Vs/Vxs) and .s XS - distance outward from R. Figure 2.13 shows the variation of relative wind speed (Vs/Vxs) with relative distance (r/R)inward from R for a stationary hurricane. This profile is not R dependent and is based on wind profiles of (KM) 50 1OO 150 200 250 300 350 400 450 500 550 > .7 .6 ui) .4 R=4 R=6 R10 =1 R=20 R=3 = R5O (N MI) .3 Lii .2 .1 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 DISTANCE, r, (N MI) Figure 2. 12.--Adop ted standardized wind profiles outward from R for the stationary SPH and PRlE. 28 intense hurricanes. The relative wind profiles (figs. 2.12 and 2.13) are identical for the SPH and PMH. The relative wind profiles shown in figures 2.12 and 2.13 enable us to determine values of Vs at various r's given Vxs. Once we have determined Vs. we can compute actual winds (V) in a moving hurricane by using eq. 2,8. The example in chapter 3 shows how we do this. I I I I I I I I , 1.0 - 0.9 - 0.8- ' 0.7 - a 0.6 - 0.5- / 0.4- 0.3 - 0.2 - 0.1- G 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RELATIVE DISTANCE (r/R] Figure 2.13.--Variation of relative wind speed with relative distance within the radius of maximum winds for the stationary SPH and PMH. 2.2.9 LIMITS OF ROTATION OF WIND FIELDS (CHAPTER 13) The SPH and PMH 10-m, 10-min overwater wind equations developed in section 2.2.7.2.2 require the region of maximum winds in these hurricanes to fall in the right rear quadrant. Observational data indicate that this constraint is too restrictive. We will allow,:the isotach maximum of the SPH or PMH to occur at any position between 0� and 1800 clockwise from the track direction as defined in sec. 2.2.6. 29 2.2.10 WIND INFLOW ANGLE (CHAPTER 14) Hurricane winds blow spirally inward and not along a circle concentric with the hurricane center. The angle between the true wind direction and a tangent to one of these circles is known as the inflow angle (4). Figures 2.14 and 2.15 show the adopted inflow angle criteria for the SPH and the PMH, respectively. These criteria are for selected values of R for a continuum of distances from the hurricane center out to 130 n.mi. (241 km) (KM) 35 2 40 60 80 D1 120 140 160 80 200O 22 240 4 130 ,- __-^ 40 (74) X- _-35 (65) E 230 (56) 25my\~~ ~~~~25 (46) Z "a~'o~~~ ' , ~~-20 (37) - L,_ I15 (28) E z M [ A--/- 10 (18) 0 10 0 0 i 5 (9) ,-.I 1 0 1 1- 1 I I �20 40 60 80 100 120 DISTANCE FROM HURRICANE CENTER (N. MI) Figure 2.14.--Adopted SPH inflow angles vs. distance from the hurricane center at selected R values. Open circles denote maximum inflow angle at each R. 30 and are based on a number of assumptions and constraints. The dashed line on each figure delineates a line of maximum 4 which is helpful when inter- polating for intermediate R values. (KM) 20 40 60 80 100 120 140 160 180 200 220 240 ,,..- -8 (70) 30 ,- -.- "35 (65) Q 30 (56) 25 1 25 (46) 120 (37) z 20 z -I .1 a15 (28) zL 0I 55 (9) I0 'I I,* I I ., i I I I 4 (7) 20 40 60 80 I00 120 DISTANCE FROM HURRICANE CENTER '(N- MI) Figure 2.15.--Same as figure 2.14"exc'ept for the PMH. The inflow angle profiles of figures 2.14 and 2.15 indicate no inflow at the center of the SPH or PMH. The range of � for a small value of R is less than the range in � for storms with a larger value of R. For example, for the SPH (fig. 2.14), a storm with an R of 10 n.mi. (19 km) has a range in $ from 0 to 190 and a storm with an R of 20 n.mi. (37 km)has a range in 4 ,from 0 to 26�. 31 2.2.11 ADJUSTMENT OF WIND SPEED FOR FRICTIONAL EFFECTS (CHAPTER 15) At the coast, onshore winds will abruptly decrease as a result of a change in surface friction characteristics. We developed adjustment ratios to account for this effect.! These ratios are given in table 2.2. As the wind path continues around the storm, further reductions in wind speed occur until an equilibrium is reached or the wind path again crosses the coast to an open water area. After crossing the coast this second time, the wind will regain its full strength. We developed ratios between offshore and overwater winds (fig. 2.16) for the other friction categories: awash, land, and rough terrain. We applied these same ratios to the onshore winds after the immediate reduction for the coastal effect. Table 2.2.---Onshore to Overwater Winds Ratio (k ) Water to land : 0.89 Water to awash : 0.95 Water to rough terrain : 0.83 Definitions of the four categories are: Water--open water with no signifi- ,cant obstructions to surface winds, e.g., oceans (including all tidewater to the indicated coastline) and large-inland water bodies. Awash--normally dry ground with tree or shrub growth, hills or dunes, which are noninundated during a storm surge. Land--relatively flat noninundated terrain or build- ings. Rough terrain--major urban areas, dense forests, and mountains with abrupt changes in elevation over short distances. The adopted ratios of offshore to overwater winds vary with wind speed. Use of the surface friction coefficient increases these ratios to unity 10 n.mi. (19 km) offshore. The awash curve lies halfway between the land curve and 1.0. The dashed curve for rough terrain is based on the 0.4 factor from winds at Brookhaven National Laboratory, N.Y., considered a "rough" location. These ratios were developed to permit the construction of a wind field as a hurricane approached and crossed the coast. They should only be applied within a reasonable distance of the open coast. They do not take 32 into consideration the effects of significant mountain ranges such as the Blue Ridge Mountains in Virginia. (KM/HR) 20 40 60 80 100 120 140 160 180 200 220 .90- ' FOR AWASH .80 - FOR LAND u1 .70 -'_--�' .60 - Z z ,x LU .50- 0 .30 - .20 - .10 h _ 0 10 20 30 40 50 60 70 80 90 100 110 120 OVERWATER WINDS (KT) Figure 2.16.--Offshore to overwater winds ratio (ke). In general, the 10-m, 10-min frictionally reduced wind speed near shore can be determined from Vk = k V (2.9) where V = the 10-m, 10-min overwater wind speed for a given location. Vk = the 10-m, 10-min wind speed adjusted for underlying terrain. The onshore and offshore winds are assumed to reach equilibrium after being over any underlying friction surface a distance of 10 n.mi. (19 km). The change in the surface friction coefficient after crossing to a new friction category is determined from: 33 k = ke + Q (ki - k) (2.10) e 1 e where k = the equilibrium surface friction coefficient at a point .(fig. 2.16). e ki = the previous surface friction coefficient at the last upwind boundary between surface friction categories; ki = k at the i c boundary between water and other surfaces for onshore winds. Q = an interpolation coefficient ranging in value from 1.0 to 0. The value of Q is determined from Q = 1 - 0.195s + 0.0095s2, (2.11) (KM) where I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 s = distance from sur- I0- face friction cate- 0.9- gory boundaries. Q is defined as 0 0.8 - when s> 10 n.mi. (19 km). At the initial boundary of any sur- 0.6 - face friction cate- gory, Q = 1.0. e 0.5 - Figure 2.17 shows 0.4 - the graphical form of equation 2.11. 0.3 - Figure 2.18 is a schematic 0.2 - picture of the frictional ad- Q\I-0.I95s+0.0095s2 0.1 \ justments which may be help- ful to the user. The k , I , I, ,I I , e 0 2 3 4 5 6 7 8 9 10 values shown are for over- (N MI) s (DISTANCE ALONG WIND PATH) water wind speeds > 73 kt (135 km/hr). Figure 2.17.--Graphical solution for Q (eq. 2.11). 34 (KM) 0 5 10 15 20 0 5 10 15 20 WIND PATH > > > > BOUNDARY WATER TO BOUNDARY NONWATER L1 / NONWATER SURFACE TO WATER SURFACE LL LL Ke IWATER) - -K - K< K ,-- -Ke (WATERI LIi K =.a'--.-.9 KK(AWASH)I= O. 89 c) 1. 0 K, KC=0.9 ------------ o0 .8 _3Ki= KC.83q i Ke (LAND)= 0.78 / LL la.. 6 _ -- \(G NOTE: Ke VALUES FOR OCs) Ke IROUGH / WIND SPEEDS>73 l TERRAIN)= 0.4S KT (135 KM/HR) C) K=Ke+Q (Ki -Ke) FROM WATER NONWATER TO WATER c . 0 I II I l! l l I o0 5 10 0 5 10 (N MI) DISTANCE ALONG WIND PATH (S) Figure 2.18.--Schematic of near shore frictional adjustments. 2.2.12 ADJUSTMENT OF WIND SPEED BECAUSE OF FILLING OVERLAND (CHAPTER 15) After the center of a hurricane crosses from sea to land, central pressure rises faster than any change in peripheral pressure [the pressure drop (Pw - Po) decreases] and winds begin to decrease. Adjustment factors were determined for the reduction of SPH and PMH wind speeds anywhere in the hurricane after landfall. This reduction can then be coupled with the 35 adjustment of wind speed near shore (sec. 2.2.11) to yield a total wind field adjustment after landfall. It is a percentage adjustment applied to the computed wind fieldadjusted for surface friction effects. Figure 2.19 shows three curves of smoothed adjustment factors vs. time after landfall for three geographic regions for the SPH and PMH. Figure 2.20 shows the three regions A, B, and C and also dashed lines between the lettered curves, where linear interpolation should be used in figure 2.19. 2.2.13 THE STALLED PMH (CHAPTER IO) Scouring and erosion at the beach may result from hurricanes. These conditions are augmented when the storm is slow moving. It is greatest with a stalled hurricane since storm winds and waves will continue to cause scouring and erosion at the same location as long as the storm remains stationary. We define a stalled hurricane as one which maintains a T < 5 kt (9 km/hr) for aperiod of 24 hours or longer. We have not con- sidered stalls of lesser duration. A stalled hurricane may also loop but not all' looping hurricanes stail. The percentage decrease in PMH winds with time after stall is shown by the curve in figure 2.21. This curve may be used along the gulf and east coasts south of the Virginia-North Carolina border (milepost 2260). Stalls are limited to a maximum of 120 hours (5 days). The solid portion of the curve is based on data from two or more hurricanes or typhoons. The dashed portion beyond 60 hours is an extrapolation beyond this data. Forward speed (T) for a stalled former PMH is given by definition, i.e., < 5 kt (9 km/hr). Since looping and other erratic storm motions may accompany a stalled former PMH, no limiting values are assigned to track direction (0) for a stalie-d PMH. For radius of maximum winds(R) and inflow angle (p), the user should continue to refer to figures 2.5 and 2.15, respectively. After stalling, a former PMH south of the Virginia- Nkrth Carolina-'border may reintensify to its maximum intensity before stalling after moving'at T > 5 kt (9 km/hr) for a period approximately 60 percent as long as the- length of the stall. ADJUSTMENT FACTOR (f f) o o o o o 0 o o o C c4 '-I Zi z Figure 2.19.--Smoothed: adjustment factor curves for%:reducing hurricane wind speeds when center is overland for the three geographice regions defined in figure 2.20.. 37 EASIPORT, ME. 0 0~~~0 BOSTON, MASS-- ~ - - A -~~~~~~~~~~~~~~~~~~- I ~x I,)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~% DAYTONA BEACH, FLA. CQ- I z C. MIAMI, FLA. - C- I' z I-~ ~ ~~~~~~~~~~~~~~P FT. MYERS, FLA.- TARPON SPRINGS, FLA.-- - I I~~~~~~~~~~ -pr APALACHICOLA. FLA.-, * - PENSAdOLAi PLA.-3 - BILOXIi MIS &-a - x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~j C-:5t c~i- - , �at LAKE CHARLES, LA. Wu~~~~ - co GALVES SPRft fEX.;- 8- a,~~~~~~~~~~~~~~~~~~~~~~~~~r)v PORT IWE6 TEX.-*'d~ 38 ~,~~ I III I I I I I~~I I 1.0' D 0.8-A BORDER (35 ,_ 0.6- z L: a 0.4 - ok I I I | I | I I I | II I I I I I 12 24 36 48 60 72 84 96 108 120 TIME FROM BEGINNING OF STALL (HR) Figure 2.21.--StaZZing adjustment factor (sf) curve for the PMH to be used south of the Virginia - North Carolina border (36.50 N). I~~~~~~~~~~~~~~~~~~~~~~~~~~~-' Figure 2.21 is to be applied to the former PXH south of milepost 2260. From there northward, the lower limit of T increases rapidly and criteria for a stalled hurricane may not be valid until we first consider'the weakening that would occur when a PMH travels at speeds less than the lower limit of T but greater than the stall speed. We have not studied this problem but have nevertheless developed an empirical procedure based on judgment. It is a reasoned extension of the procedures for more southerly latitudes. This procedure is given in section 16.11. 2.3 COMPARISON OF SPH AND PMH WITH RECORD HURRICANES Tables 2.3 to 2.6 list computed values of V and V for both the SPH gx x and PMH at 100-n.mi. (185-kmn) intervals in both metric and English units for the following six categories: - VGL = V for the lower limit of R. gx VLL = V for the lower limit of R and lower limit of T. x VLU = V for the lower limit of R and upper limit of T. X VGU = Vg for the upper limit of R. VUL = V for the upper limit of R and lower limit of T. VUU = V for the upper limit of R and upper limit of T. <[ .-.~ 39 These values were computed using equations 2.2 and 2.6 for the SPH and equations 2.2 and 2.7 for the PMH. Values of K in the tables were taken from figure 2.10 (SPH) or figure 2.11 (PMH). A peripheral pressure of 29.77 in. (100.8 kPa) was used for the SPH and 30.12 in. (102.0 kPa) for the PMH (see sec. 2.2.2). The central pressure for the SPH comes from figure 2.1 and for the PMH from figure 2.2. The upper and lower limiting values of R come from figure 2.4 for the SPH and figure 2.5 for the PMH. The upper and lower limiting values of T are from figure 2.6 (SPH) and figure 2.7 (PMH). Table notes appear on the page preceding the tables. The computed wind speeds for the six categories are also shown in figures 2.22 to 2.24 for the SPH and 2.25 to 2.27 for the PMH. Two curves are plotted on each graph. The data NOTES FOR TABLES 2.3 TO 2.6 MPOST = milepost (n.mi. or km) LAT = latitude PW = peripheral pressure PO = central pressure 1/2 K =-t ; see section 2.27 LR = lower limit of radius of maximum winds UR = upper limit of radius of maximum winds LT = lower limit of forward speed UT = upper limit of forward speed VGL = maximum gradient wind speed (V ) for LR - hurricane stationary VGU = maximum gradient wind speed (V x) for UR - hurricane stationary VLL = maximum 10-m, 10-min overwater wind speed (Vx) for LR and LT VUL = maximum 10-m, 10-min overwater wind speed (Vx) for UR and LT VLU = maximum 10-m, 10-min overwater wind speed (Vx) for LR and UT VUU= maximum 10-m, 10-min overwater wind speed (Vx) for UR and UT ~~~~KM/H = km/hr~~x KM/H =km/hr 40 TabZe 2.3.--Ranges of maximwn gradient and 10-m, 10-min overwater winds at 100-n.mi. intervals for the SPH (English units). MPOST LAT PW PO K LR UR LT UT VGL VLL VLU VGU VUL VUU N MI DEG IN. IN. KT-INNMI NMI KT KT KT KT KT KT KT KT 100. 25.5 29.77 27.23 67.3 6. 28. 4. 25. 106.6 99.5 107.3 104.1 97.3 105.1 200. 26.9 29.77 27.26 67.2 6. 28. 4. 25. 105.8 98.8 106.6 103.1 96.4 104.2 300. 28.5 29.77 27.29 67.1 6. 28. 4. 25. 104.9 98.0 105.8 102.2 95.5 103.4 400. 29.3 29.77 27.29 67.0 6. 28. 4. 25. 104.8 97.9 105.7 101.9 95.3 103.1 500. 29.6 29.77 27.29 66.9 6. 28. 4. 25. 104.6 97.7 105.5 101.7 95.2 103.0 600. 29.1 29.77 27.29 67.0 7. 28. 4. 25. 104.6 97.8 105.6 101.9 95.3 103.2 700. 29.2 29.77 27.29 67.0 7. 29. 4. 25. 104.6 97.8 105.6 101.8 95.2 103.0 800. 30.2 29.77 27.29 66.8 7. 30. 4. 25. 104.3 97.4 '05.3 101.2 94.7 102.5 900. 30.4 29.77 27.55 66.8 8. 31. 4. 25. 98.3 92.1 ''9.9 95.3 89.4 97.2 1000. 29.8 29.77 27.76 66.9 9. 32. 4. 25. 93.6 87.9 95.7 90.6 85.2 93.0 1100. 29.5 29.77 27.79 67.0 9. 32. 4. 25. 93.1 87.4 95.Z 90.1 84.7 92.5 1200. 28.0 29.77 27.55 67.1 8. 31. 4. 25. 98.9 92.6 100.4 96.0 90.0 97.8 1300. 26.5 29.77 27.29 67.2 6. 30. 4. 25. 105.1 98.2 106.0 102.3 95.7 103.5 1400. 25.2 29.77 27.08 67.3 5. 28. 4. 25. 109.8 102.4 110.2 107.2 100.1 107.9 1500. 26.5 29.77 27.17 67.2 5. 29. 4. 25. 107.7 100.6 108.4 104.9 98.0 105.8 1600. 28.2 29.77 27.32 67.1 6. 31. 4. 25. 104.3 97.5 105.3 101.2 94.7 102.5 1700. 29.6 29.77 27.46 66.9 7. 32. 4. 25. 100.6 94.2 102.0 97.4 91.2 '99.0 1800. 31.1 29.77 27.55 66.8 8. 33. 4. 25. 98.3 92.1 99.9 94.9 89.0 96.8 1900. 32.5 29.77 27.52 66.7 9. 33. 4. 26. 98.7 92.4 100.5 95.3 89.3 97.4 2000. 33.5 29.77 27.46 66.7 9. 33. 4. 30. 99.9 93.5 102.7 96.4 90.4 99.6 2100. 34.5 29.77 27.46 66.7 9. 33. 4. 35. 99.9 93.5 104.0 96.3 90.3 100.8 2200. 35.6 29.77 27.52 66.7 10. 34. 4. 39. 98.4 92.1 103.6 94.7 88.8 100.3 2300. 37.3 29.77 27.64 66.3 11. 35. 4. 43. 94.9 89.0 101.5 91.1 85.6 98.0 2400. 38.8 29.77 27.73 65.9 12. 36. 6. 47. 92.1 87.5 99.8 88.1 84.0 96.3 2500. 40.1 29.77 27.82 65.6 14. 38. 12. 50. 89.2 87.5 97.9 85.2 83.8 94.3 2600. 41.0 29.77 27.88 65.1 15. 39. 16. 53. 86.9 86.8 96.5 82.8 83.1 92.8 2700. 41.7 29.77 27.91 64.9 16. 40. 19. 54. 85.7 86.7 95.7 81.5 83.0 91.9 2800. 42.5 29.77 28.17 64.6 19. 43. 22. 54. 78.2 80.9 88.9 73.9 77.1 85.1 2900. 43.9 29.77 28.23 64.4 20. 44. 23. 54. 76.2 79.4 87.1 71.8 75.4 83.1 3000. 44.5 29.77 28.26 64.3 21. 45. 24. 55. 75.0 78.6 86.3 70.6 74.7 82.3 3100. 45.3 29.77 28.29 64.2 22. 45. 24. 55. 73.9 77.6 85.2 69.6 73.8 81.4 41 Table 2.4.--Ranges of maximum gradient and 10O-m, 10-min overwater winds at selected intervals for the SPH (metric units). MPOST LAT PH PO K LR UR LT UT VGL VLL VLU VGU VUL VUU KM DEG KPA KPA MKPAKM KM KM/H KM/H KM/H KM/H KM/H KM/H KM/H KM/H 185. 25.5 100.8 92.2 68.2 11. 52. 7. 46. 197.5 184.4 198.9 192.9 180.3 194.7 371. 26.9 100.8 92.3 68.1 11. 52. 7. 46. 196.0 183.0 197.5 191.1 178.7 193.2 556. 28.5 100.8 92.4 68.0 11. 52. 7. 46. 194.5 181.7 196.1 189.4 177.1 191.5 741. 29.3 100.8 92.4 67.9 11. 52. 7. 46. 194.1 181.4 195.8 188.9 176.7 191.1 927. 29.6 100.8 92.4 67.8 11. 52. 7. 46. 193.8 181.1 195.6 188.5 176.3 190.8 1112. 29.1'100.8 92.4 67.9 13. 52. 7. 46. 193.9 181.2 195.6 188.9 176.7 191.2 1297. 29.2 100.8 92.4 67.9 13. 54. 7. 46. 193.9 181.2 195.6 188.7 176.5 190.9 1483. 30.2 100.8 92.4 67.7 13. 56. 7. 46. 193.3 180.6 195.1 187.6 175.5 190.0 1668. 30.4 100.8 93.3 67.7 15. 57. 7. 46. 182.3 170.7 185.2 176.6 165.6 180.1 1853. 29.8 100.8 94.0 67.8 17. 59. 7. 46. 173.5 162.8 177.3 168.0 157.8 172.3 2039. 29.5 100.8 94.1 67.9 17. 59. 7. 46. 172.5 161.9 176.4 167.0 156.9 171.4 2224. 28.0 100.8 93.3 68.0 15. 57. 7. 46. 183.2 171.6 186.0 178.0 166.8 181.3 2409. 26.5 100.8 92.4 68.1 11. 56. 7. 46. 194.8 182.0 196.5 189.6 177.3 191.8 2595. 25.2 100.8 91.7 68.2 9. 52. 7. 46. 203.4 189.7 204.2 198.7 185.4 199.9 2780. 26.5 100.8 92.0 68.1 9. 54. 7. 46. 199.7 186.4 200.8 194.5 181.7 196.1 2965. 28.2 100.8 92.5 68.0 11. 57. 7. 46. 193.3 180.6 195.1 187.6 175.5 189.9 3151. 29.6 100.8 93.0 67.8 13. 59. 7. 46. 186.5 174.5 189.0 180.5 169.1 183.5 3336. 31.1 100.8 93.3 67.7 15. 61. 7. 46. 182.2 170.7 185.1 175.9 165.0 179.5 3521. 32.5 100.8 93.2 67.6 17. 61. 7. 48. 182.8 171.2 186.2 176.6 165.6 180.5 3706. 33.5 100.8 93.0 67.6 17. 61. 7. 56. 185.2 173.3 190.4 178.7 167.5 184.6 3892. 34.5 100.8 93.0 67.6 17. 61. 7. 65. 185.1 173.3 192.7 178.5 167.3 186.8 4077. 35.6 100.8 93.2 67.6 19. 63. 7. 72. 182.3 170.8 192.1 175.6 164.7 185.9 4262. 37.3 100.8 93.6 67.2 20. 65. 7. 80. 175.9 165.0 188.1 168.8 158.6 181.7 4448. 38.8 100.8 93.9 66.8 22. 67. 11. 87. 170.7 162.2 185.0 163.4 155.6 178.5 4633. 40.1 100.8 94.2 66.5 26. 70. 22. 93. 165.3 162.1 181.5 157.8 155.3 174.7 4818. 41.0 100.8 94.4 66.0 28. 72. 30. 98. 161.1 160.9 178.9 153.4 154.0 172.0 5004. 41.7 100.8 94.5 65.8 30. 74. 35.100. 158.9 160.8 177.3 151.1 153.8 170.3 5189. 42.5 100.8 95.4 65.5 35. 80. 41.100. 144.9 149.9 164.8 137.0 142.8 157.7 5374. 43.9 100.8 95.6 65.3 37. 82. 43.100. 141.1 147.1 161.3 133.1 139.8 154.1 5560. 44.5 100.8 95.7 65.2 39. 83. 44.102. 139.1 145.8 159.9 130.9 138.4 152.5 ,5745. 45.3 100.8 95.8 65.1 41. 83. 44.102. 137.0 143.9 158.0 129.0 136.7 150.8 42 TabZe 2.5.--Ranges of maximum gradient and 10-m, 10-min overwater winds at 100-n.mi. intervals for the PME (EngZish units). NPOST LAT PH PO K LR UR LT UT VGL VLL VLU VGU VUL VUU N MI DEG IN, IN. KT-IN,.NII NMI KT KT KT KT KT KT KT KT. 100. 25.5 30.12 26.16 69.2 5. 21. 6. 20. 137.1 134.9 140.1 135.3 133.2 138.4 200. 26.9 30.12 26.19 69.2 5. 21. 6. 20. 136.5 134.4 139.6 134.6 132.6 137.8 300. 28.5 30.12 26.19 69.1 5. 21. 6. 20. 136.3 134.1 139.4 134.3 132.2 137.5 400. 29.3 30.12 26.19 69.1 5. 21. 6. 20. 136.3 134.1 139.4 134.2 132.2 137.4 500. 29.6 30.12 26.19 69.1 5. 21. 6. 20. 136.3 134.1 139.4 134.2 132.1 137.4 600. 29.1 30.12 26.22 69.1 6. 21. 6. 20. 135.7 133.5 138.8 133.7 131.7 137.0 700. 29.2 30.12 26.22 69.1 6. 21. 6. 20. 135.7 133.5 138.8 133.7 131.7 137.0 800. 30.2 30.12 26.22 69.0 6. 22. 7. 20. 135.4 133.8 138.6 133.3 131.8 136.6 900. 30.4 30.12 26.25 69.0 6. 22. 9. 20. 134.9 134.2 138.1 132.8 132.1 136.1 1000. 29.8 30.12 26.28 69.1 6. 22. 13. 20. 134.6 135.4 137.8 132.5 133.4 135.8 1100. 29.5 30.12 26.31 69.1 7. 23. 15. 20. 134.0 135.5 137.2 131.9 133.6 135.2 1200. 28.0 30.12 26.25 69.1 6. 22. 12. 20. 135.2 135.6 138.3 133.2 133.7 136.4 1300. 26.5 30.12 26.16 69.2 5. 20. 7. 20. 137.1 135.3 140.1 135.3 133.7 138.4 1400. 25.2 30.12 26.11 69.2 4. 20. 6. 20. 138.2 135.9 141.2 136.4 134.2 139.5 1500. 26.5 30.12 26.13 69.2 4. 20. 6. 20. 137.7 135.5 140.7 135.8 133.7 138.9 1600. 28.2 30.12 26.19 69.1 5. 20. 6. 20. 136.3 134.1 139.4 134.5 132.4 137.6 1700. 29.6 30.12 26.22 69.1 6. 21. 6. 20. 135.6 133.5 138.8 133.7 131.7 136.9 1800. 31.1 30.12 26.25 69.0 6. 21. 6. 20. 134.9 132.8 138.1 132.9 130.9 136.1 1900. 32.5 30.12 26.28 68.9 7. 22. 7. 22. 134.0 132.4 137.8 131.9 130.4 135.8 2000. 33.5 30.12 26.31 68.8 8. 23. 8. 26. 133.1 132.0 138.1 130.9 130.0 136.1 2100. 34.5 30.12 26.37 68.7 8. 24. 9. 29. 131.9 131.2 137.8 129.5 129.0 135.5 2200. 35.6 30.12 26.40 68.7 9. 25. 10. 34. 131.1 131.0 138.4 128.7 128.7 136.1 J 2300. 37.3 30.12 26.49 68.3 10. 26. 17. 38. 128.6 131.1 137.0 126.0 128.7 134.6 2400. 38.8 30.12 26.61 68.0 11. 28. 26. 41. 125.7 131.1 134.9 122.9 128.4 132.3 2500. 40.1 30.12 26.75 67.6 12. 29. 32. 44. 122.0 129.2 132.2 119.1 126.5 129.4 2600. 41.0 30.12 26.81 67.3 13. 31. 36. 47. 120.2 128.5 131.1 117.1 125.5 128.2 2700. 41.7 30.12 26.84 66.9 14. 33. 39. 49. 118.7 127.8 130.2 115.4 124.7 127.0 2800. 42.5 30.12 27.23 66.4 17. 34. 40. 50. 109.9 119.8 122.1 106.9 116.9 119.2 2900. 43.9 30.12 27.40 65.9 18. 36. 40. 50. 105.3 115.4 117.7 102.1 112.3 114.6 3000. 44.5 30.12 27.43 65.8 19. 37. 41. 50. 104.4 114.7 116.8 101.1 111.6 113.6 3100. 45.3 30.12 27.46 65.6 20. 38. 41. 50. 103.2 113.6 115.7 99.9 110.4 112.5 43 Table B. 6.--Ranges of maximumgradient and 10-m, 10-min overwater winds at selected intervals for ~he PMH (metric units~. RPOST LAT PW PO K/vtK LR UR LT UT VGL VLL VLU VGU VUL VUU KM DEG KPA KPA ~-KPAKM KM KM/H KM/H KM/H KM/H KM/H KM/H KM/H KM/H 185. 25.5 102.0 88.6 70.2 9. 39. 11. 37. 254.1 250.0 259.7 250.7 24�.8 256.5 371. 26.9 102.0 88.7 70.2 9. 39. 11, 37. 253.1 249.0 258.8 249.5 245.7 255.4 556. 28.5 102.0 88.7 70.1 9. 39. 11. 37. 252.6 248.6 258.3 248.9 245.1 254.8 741. 29.3 102.0 88.7 70.1 9. 39. 11. 37. 252.6 248.6 258.3 248.8 244.9 254.7 927. 29.6 102.0 88.7 70.1 9. 39. 11. 37, 252 6 248.6 258.3 248.7 244.9 254.7 1112. 29.1 102.0 88.8 70.1 11. 39. 11. 37. 251 4 247.4 257.2 247.9 244.1 253.8 1297. 29.2 102.0 88.8 70.1 11. 39. 11, 37. 251 4 247.4 257.2 247.8 244.0 253.8 1483. 30.2 102.0 88.8 70.0 11, 41. 13. 37. 251 0 247.9 256.8 247.1 244.2 253.1 1668. 30.4 102.0 88.9 70.0 11. 41. 17. 37. 250 0 248.6 255,9 246.1 244.9 252.1 1853. 29.8 102.0 89.0 70.1 11. 41. 24. 37. 249 5 251.0 255.3 245.6 247.3 251.7 d039. 29.5 102.0 89.1 70.1 13. 43. 28. 37. 248 3 251.2 254.2 244.4 247.5 250.6 Z224. 28.0 102.0 88.9 70.1 11. 41. 22. 37. 250.5 251.3 256.3 246.8 247.8 252.9 2409. 26.5 102.0 88.6 70.2 9. 37. 13. 37. 254.0 250.8 259.7 250.8 247.7 256.6 2595. 25.2 102.0 88.4 70.2 7. 37. 11. 37. 256.1 251.9 261.6 252.8 248.7 258.5 2780. 26.5 102.0 88.5 70.2 7. 37. 11. 37. 255.Z 251.0 260.8 251.7 247.7 257.5 2965. 28.2 102.0 88.7 70.1 9. 37. 11. 37. 252.6 248.6 258.4 249.2 245.3 255.1 3151. 29.6 102.0 88.8 70.1 11. 39. 11. 37. 251.4 247.4 257.2 247.8 244.0 253.7 3336. 31.1 102.0 88.9 70.0 11. 39. 11. 37. 250,0 246.1 255.9 246.2 242.5 252.3 3521. 32.5 102.0 89.0 69.9 13. 41. 13. 41. 248.4 245.4 255,4 244.4 241.7 251.7 3706. 33.5 102.0 89.1 69.8 15. 43. 15. 48. 246.7 244.7 256.0 242.7 240.8 252.2 3892. 34.5 102.0 89.3 69.7 15. 44. 17. 54. 244.4 243.2 255 3 239.9 239.0 251,1 4077. 35.6 102.0 89.4 69.7 17. 46. 19. 63. 243.0 242.7 256 5 238,5 238.4 252.2 4262. 37.3 102.0 89.7 69.3 19. 48. 32. 70. 238.3 242.9 253 9 233.6 238.5 249.4 4448. 38.8 102.0 90.1 68.9 20. 52. 48 76. 232.9 242.9 250 1 227.7 238.0 245.2 4633. 40.1 102.0 90.6 68,5 22. 54. 59 82. 226.1 239.5 245 0 220.8 234.4 239,9 4818. 41.0 102.0 90.8 68.2 24. 57.67 87. 222.7 238.1 243 0 216.9 232.7 237.5 5004. 41.7 102.0 90.9 67.8 26. 61. 72 91. 219.9 236.9 241 2 213.8 231.0 235.4 5189. 42.5 10Z.O 92.2 67.332. 63. 74 93. 203.7 2ZZ.O 226.2 198.2 216.7 220.9 5374. 43.9 102.0 92.8 66.8 33. 67. 74 93. 195.Z 213.9 218.2 189.2 208.1 212.4 5560. 44.5 102.0 92.9 66.7 35. 69. 76. 93. 193.4 212.6 216.4 187.3 206.8 210.6 5745. 45.3 102.0 93.0 66.5 37. 70. 76. 93. 191.3 210.6 214.4 185.1 204.6 208.5 44 '0 03 '0 0( ar EASTPORT. ME.-- ' - ~~~~~~~~~~~~~~~~w IL ,' r* BOSTON. MASS m CL o 0 NEW YORK. N.Y.-- > c i -o CHINCOTEAGUE, VA.-* 't CAPE HATTERAS. N.C.--> to CHARLESTON. S.C. u r. ,4, - _ 0) DAYTONA BEACH, FLA. -g 0 x - 9L-3~ 9Lto - I MIAMI, FLA.-- W CIA U, 4 - ~~- ..o~ -+ FT. MYERS, FLA. LU cm j _ __ TARPON SPRINGS, FLA.-t' i- a-~~ ~~~~~~~~~~~~~~~~~~~~ )ij w~~~~ APALACHICOLA. FLA.--- - - PENSACOLA. FLA.-- 5 - / X - BILOXI. MISS.-- - a.- - C~~~IA Nu- iz - LAKE CHARLES, LA.-- N I < GALVESTON, TEX. -10 Q I Cl 19 PORT ISABEL, TEX.-I (1)1) 033dS GNIM 45 ISH/W)I) 0) Si) 0 ii 0 Si) '.1 0u E%. EASTPORT, ME.-- $ I III I o'-" j1 BOSTON, MASS- / - # II o Sr I9 Il NEWYORK, N.Y. z___ CHINCOTEAGUE. VA.- . M)- 04 CAPE HATTERAS, N.C.--- ' O uj oli CHARLESTON, S.C.-- r - INOI r DAYTONA BEACH. FLA. -3 0 x Z'oO r MIAMI, FLA. -1 ) la z co - co FT. MYERS, FLA.-- 1 - TARPON SPRINGS, FLA.-- - C.'~~~~~~~~~~~) 0. APALACHICOLA, FLA, - / - - o PENSACOLA. FLA.-0 .1 - BILOXI, MISS.-- - LUIN X~~~~~~~~~r z LAKE CHARLES, LA.---> GALVESTON, TEX.-- --I V - ~~~~~~~co PORT ISABEL, TEX.- 7 0 0 11)1) (333dS QNIA& 46 (LIH/W~)I 0 '00. 1 0; Nc cm c EASTPORT, ME.-- . I i J _ BOSTON, MASS-- La I N NEW YORK, N.Y.~ l :1 1 -r CHINCOTEAGUE, VA.--. N St ,,~~~~~~~~~c CAPE HATTERAS, N.C.- ' - / 0 -4 CHARLESTON, S.C. -o \) z/I ,i - DAYTONA BEACH, FLA. -> 0 r x~~~~ w co- ~~~~~~~~~~~~0 N V- - z4 MIAMI, FLA. u /wo.p z - z -I ULI�ZV F LUQ -~~~~C;OD---- ~~~~ U rZ FT. MYERS, FLA.-- TARPON SPRINGS, FLA.--* -. -> - 0 APALACHICOLA. FLA.-i N PENSACOLA, FLA. / Lu BILOXI, MISS.- * u~~~~~~~L gm C LAKE CHARLES, LA.-- - GALVESTON, TEX.- PORT ISABEL, TEX.-/c uj.0 (1)1) cm coIM CGU 3?S GNIM 47 (MH/WI) n Sn (4 0 N, ' EASTPORT, ME. 0 /1 _ -J BOSTON, MASS "' NEW YORK, N.Y. Ii 0 CHINCOTEAGUE, VA.-* LI U un -e rh a~~~~~a CAPE HATTERAS, N.C.- 0 - ) A I, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~I LU0 CHARLESTON, S.C. W - zu s 0 III~~~~~~~- COI, - DAYTONA BEACH. FLA. - - 2 - w , clu MIAMI, FLA.-- II Q z.0 -l P 4- *l U)- 9 FT. MYERS, FLA. -:00 TARPON SPRINGS. FLA.-30 -. APALACHICOLA, FLA.---. LD~~~~~' - t PENSACOLA, FLA.- I LU N 0. BILOXI, MISS.-- I -. C',- J u -~ N-~ ~~~ - C' j - a LAKE CHARLES, LA.-- GALVESTON, TEX.- 30 - I ~ ~ ~ ~ ~ *�'0 - I Vo ~.'CZ PORT ISABEL. TEX. - / -.~~ I ] II (IX) C3RdS ONIM 48 (EII/W)II EASTPORT, ME. BOSTON, MASS-~ "? '0 NEW YORK, N.Y. ll - f/ \ -. - - CHINCOTEAGUE, VA.-- F l Isr, -C CAPE HATTERAS, N.C.-- o- ZW N CHARLESTON. S.C.- L L - - I~ C LU~~~~~~~~0 cq J ~~~~~~~~~o W Iii - . Z'- C_9 z 9 FT. YES MIAMI. FLA.-1 ou 0-10 z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3i Ot 25 ~~~~~~1L co I ~ ~~ II I U) - cmJ TARPON SPRINGS, FLA.-- > CQ Lu cli ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~c APALACHICOLA. FLA.-0 _ o PENSACOLA, FLA.-- I w0 BILOXI, MISS.-- - I, - r,~~~~~~L q ~ ~~~ - C.-- I U -Y 5t~ LAKE CHARLES, LA.- GALVESTON, TEX.-, - PORT ISABEL. TEX. I Lf (1)11 U33dS ONIM 49 (QH/W)Ii 0~~V 0 or N, (1 0 NY ('4 ('4 ('4 (' . EASTPORT. ME.-- I I I _ BOSTON, MASS - I! "-~~~~~~~~~~~~~~~~~~~~~~~ \ I0, NEW YORK, N.Y. \ \ I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: CHINCOTEAGUE. VA. C4 7 ~I -' > cm CAPE HATTERAS. N.C.-- 0 I CHARLESTON, S.C. co -JI - N~~~~~~~n cu~~~~~~~~~ - co DAYTONA BEACH, FLPtA. -- _ U. _ _ I.: _ _ - v, ~ ~ at -v sTu aYERSI - . Z-QO u'i Z MIAMI, FLA. -lN - aI Z fit: Lu ~ ~ ~ ~ l APALACHICOLA. FLA.- 0 PENSACOLA, FLA.-* N- co BILOXI, MISS.-------' -f I F ~~LAKE CHARLES, LA.- GALVESTON, TEX ------ Z:P PORT ISABEL, TEX.-~-c I ~I 11)1) C133dS (INUA ~~NIM~, 50 on the figures are computed V and V winds for hurricanes of record using gx x observed or estimated values of meteorological parameters and factors for each hurricane. SPH criteria and equations 2.2 and 2.6 were used for all storms except Camille and the Labor Day hurricane of 1935. For these latter storms, PMH criteria and equations 2.2 and 2.7 were used. Coastal values of VGL and VGU are shown in figure 2.22 for the SPH. Wind speeds generally decrease with increasing latitude. The gulf coast minimum near milepost 1100 is in agreement with the central pressure (po) maximum in that area. Forward speed is a factor present in figures 2.23 (VLU and VLL)and 2.24 (VUU and VUL) for the SPH. Wind speeds decrease with increasing latitude but a noticeable maximum appears along the North Carolina coast. This maxi- mum is a result of somewhat lower po's in this area and in the case of VLU higher forward speeds may also be important. The V winds of the Labor Day hurricane of 1935, Camille, and Helene gx exceed the SPH VGL and SPH VGU winds in figure 2.22. The V winds of the x Labor Day hurricane and Camille exceed the winds represented by the four curves in figures 2.23 and 2.24. Helene and the New England hurricane of 1938 exceed all but the VLU curve. Coastal values of VGL and VGU are shown in figure 2.25 for the PNH. Wind speeds generally decrease with increasing latitude. The gulf coast minimum is near milepost 1100 but is not as pronounced as the SPH minimum (fig. 2.22). -The nonstationary storm is considered in figures 2.26 (VLU and VLL) and 2.27 (VUU and VUL) for the PMH. The two upper limit of T curves record their maxima along the southern Texas coast and the Florida Keys. A tertiary maximum appears near Cape Hatteras, where higher forward speed more than compensates for the latitudinal increase in po. This effect diminishes north of Cape Hatteras where p0 increases much more rapidly. This maximum is not evident in the VLL and VUL curves. These latter curves have their gulf coast minima near milepost 700. Recurving relatively fast moving storms near milepost 1100 contribute to these minima near milepost 700. The VLU and VLL curves and the VUU and VUL curves converge near 51 milepost 1100. This convergence is a result of rapidly increasing lower limit PMH forward speed in this area while the upper forward speed remains constant. The PMH V and V winds exceed all the hurricane V and V winds shown gx x gx x in figures 2.25 to 2.27. The Labor Day hurricane of 1935 and Camille (the two storms with the lowest central pressure near the east and gulf coasts of the United States) are exceeded by a lesser margin. - . , 4 . ~~:~;� ~s. vs 52 3. APPLICATION OF CRITERIA 3.1 INTRODUCTION This chapter illustrates procedures for computing SPH and PMH overwater wind fields resulting from the interaction of these hurricanes with land. Coastal values of V and VX for 100-n.mi. (185-km) intervals along the coast gx x for upper and lower limits of R and T, where appropriate, are given in tables 2.3 to 2.6. Smoothed alongshore graphs of these wind values are shown in figures 2.22 to 2.27. Determination of SPH or PMH overwater wind fields can be done with a compu- tation form, table 3.1. Part I of this table lists the information needed for these computations and where it is given. Part II covers the maximum wind speeds for a stationary hurricane; Part III, the profile of wind speed for a stationary hurricane; and Part IV covers adjustments for asymmetry due to forward speed (T). Necessary notes or instructions for using table 3.1 are given in section 3.2. Table 3.2 is an example of the use of table 3.1 for a selected PMH. The example was selected to illustrate one of many possible combinations of meteorological parameters and some terrain situa- tions that could be encountered. We then cover: Adjustment of overwater wind field for frictional effects (sec. 3.3). Adjustment of wind field when hurricane center moves overland (sec. 3.4). Adjustment of wind field for a stalled PMH (sec. 3.5). 3.2 OVERWATER WIND FIELDS (REFER TO TABLE 3.1) Part I. Designated hurricane location and values of meteorological para- meters. Fill in blank spaces by making reference to the designated figures for the required SPH or PMH. Part 22. Maximum wind speeds (V and V ) for a stationary hurricane. ax Xs a. Substitute appropriate values from Part I into equation 2.2. !' ? ~ " '! '' � ..... 53 b. Multiply value in a. by 0.9 (0.95) for the SPH (PMH) to obtain Vxs: the maximum 10-m (32.8 ft), 10-min overwater wind speed for a station- ary hurricane. Part III. Profile of wind speed for a stationary hurricane. a. Outward from R to 130 n.mi. (241 km) [R < r < 130 n.mi.] 1. Enter figure 2.12 with designated R to obtain Vs/Vxs at numerous distances from R. Tabulate distance and ratios in columns 1 and 2 of table, respectively. 2. Multiply ratios of column 2 by Vs of Part IIb to obtain V values. Tabulate in column 3 of table. b.. Hurricane center to R (r < R) 1. Using designated R, compute r. Tabulate in column 3 of table. 2. Compute V values using V of Part IIb. Tabulate in column 4 of S XS table. c. Plot the wind speeds, V, of the tables against distance, r. S Part IV. Adjustment for asymmetry due to storm forward speed CT). V = V + 1.5 (T0'63) (T 0.37) cos (3.1) s ~~~0603 A, the assymetry factor, = 1.5 (T ) (T 0.37) cos (3.2) Note: T = 1 when T, V and V are in kt. O S T = 0.514791 when T, V, and V are in m s . 0 S T = 1.151556 when T, V, and V are in mi hr1 O~~~~~~~~~~ T = 1.853248 when T, �, an4 V are in km hr1. a. For a radial through the point of maximum wind (radial M): at r R: 3 =3r R (3.) at r?= R: 8 =qR R 0 (3.4) 54 1. For the SPH, enter figure 2.14 (use fig. 2.15 for the PMH) with the designated R to obtain ~ for any distance (r) of Part III. Tabulate r's and corresponding �'s in columns 1 and 2 of table. 2. Using S (eq. 3.3 and 3.4), compute SM's(3's for radial M). List in column 3. List cos M in column 4. 0.63 0.37 3. With cos 8M, T 3, and To 037 compute A's (eq. 3.2). Tabulate in column 5. 4. Add A's to V values of Part III to obtain values of V. Tabulate in 5 column 6. 5. Plot these V values vs. r. This is the asymmetry adjusted radial M. b. For other radials: 1. Copy values of r and M from columns 1 and 3 of Part IVa to columns M 1 and 2. 2. Determine the degree of rotation (counterclockwise) between radial M and another radial. 3. Add number of degrees (item 2) to the M values (col. 2) for corresponding distances r (col. 1). This gives B values for the desired radial. Tabulate in column 3. List cos 3 in column 4. 4. Compute A values using equation 3.2 and tabulate in column 5. 5. Add these A values to V values of Part III to obtain values of V. s Tabulate in column 6. 6. Plot these V values vs. r. This is the asymmetry adjusted radial. 7. Repeat steps 1 through 6 for as many radials as required to adequately define the isotachs over all portions of the hurricane. e. Plot resulting winds on a map and analyze. Part V. Miscellaneous a. Spot C values (from fig. 2.14 for the SPH or 2.15 for the PNH) on map of Part IV for the degree of detail needed. 55 b. If desired, rotate isotachs of Part I-V keeping point of maximum wind O0 to 1800 clockwise from e. Table 3.2 shows application of table 3.1 to a specific PMH. The resulting wind field determined from many radials is shown in figure 3.1. 3.3 ADJUSTMENT OF OVERWATER WIND FIELD FOR FRICTIONAL EFFECTS 3.3.1 INTRODUCTION This section gives a procedure for evaluating the effects of surface fric- tion on overwater wind speed as an SPH or PMH approaches shore. Application would be best accomplished with a high-speed computer. For instance, with computer application we could make computations of the frictionally adjusted wind speed at very close intervals allowing for better resolution of the analysis near shore. We first summarize the procedure and then provide some examples of frictionally reduced winds for different terrain situations. 3.3.2 WIND PATHS Steps to determine wind paths are as follows: a. Go to figure 2.14 (for the SPH) or figure 2.15 (for the PMH) and extract inflow angles at various distances from the hurricane center for an R of interest. b. Plot these on a polar coordinate diagram of the same scale as the determined overwater wind field. c. Sketch lines of wind paths. Such a wind path diagram is shown in figure 3.2. This is for a PMH with an R of 15 n.mi. (28 km) (table 3.2, fig. 3.1). d. Center the wind path diagram over the overwater wind field. e. Outline the coast and pertinent terrain features (as described in sec. 2.2.11) drawn to the same scale and placed in position relative to the overwater wind field. 56 (sheet 1 of 5) Table 3.1.--Overwater wind field computation form Part I. Designated hurricane location and values of meteorological parameters SPH D and PMH M (check one) a. Milepost (fig. 1.1): b. Latitude in degrees (4) (fig. 1.1): c. Coriolis parameter (f) = 2 Q sin i (sec 1) = 14.584 X 10-5 sin J (sec-1) sin P = sin _ = 14.584 X 10-5sin p (sec ) = SPH PMH d. Peripheral pressure (pw)*: e. Central pressure (po), fig. 2.1 fig. 2.2 - f. Radius of max. winds (R), fig. 2.4 fig. 2.5 g. Forward speed (T), fig. 2.6 fig. 2.7 h. Track direction (0), fig. 2.8 fig. 2.9 i. Density coefficient (K), fig. 2.10 fig. 2.11 *SPH: pw = 29.77 in. (Hg); Pw = 100.8 kPa; Pw = 1008 mb *PMH: Pw = 30.12 in. (Hg); Pw = 102.0 kPa; Pw = 1020 mb Part II. Maximum wind speeds (Vgx and V5s) for a stationary hurricane: 1g2 Rf a. Maximum gradient wind speed (Vg ) = K ( pl/2.2) ~gx w d(2.2) b. Vgx adjusted to maximum 10-m, 10-min value (Vxs) for a stationary hurricane. SPH: 0.9 Vgx = 0.9 ( ) = = Vxs PMH: 0.95 V = 0.95 ( )= V ~~~~~gx ~~~xs 57 (sheet 2 of 5) Table 3.1 (continued) Part III. Profile of wind speed for a stationary hurricane a. Outward from R to 130 n.mi. (241 km) [R < r < 130 n.mi.]: (1) (2) (3) Distance V V from center, r (fig. 2.12) (. ) xs ( ) 58 (sheet 3 of 5) Table 3.1 (continued) b. Hurricane center to R Cr < R): (1) ~(2) (3)(4 R v (fi'g. 2.13)( ) ( ) 1.0 1.000 0.9 0.937 0.8 0.771 0.7 0.491 0.6 0.330 0.5 0.206 0.4 0.118 0.3 0.060 0.2 0.020 0.1 0.010 59 (sheet 4 of 5) TabZe 3.1 (continued) Part IV. Adjustment for asymmetry due to storm forward speed (T). a. For a radial through point of maximum wind (radiaZ M): 0.63 0.37 T- T T 0 (1) (2) (3) (4) (5) (6) ~r �*v M cos A V ( ) (deg.) (deg.) ( ) 0.1R= 0.2R= 0.3R= 0.4R= 0.5R= � 0.6R= . 0.7R= 0.8R= I 0.9R= R= 4-J *From figure 2.14 or 2.15. 60 (sheet 5 of 5) Table 3.1 (continued) b. For other radials: Degree of counterclockwise rotation from M T0.63 T 0.37 0 (l)* (2)A (3). (4) (5) (6) = 8+ angle between M and other r radial osA V ( ) (deg.) (deg.) ) I 1R= 0.2R= 0.3R= 0.4R= a) 0.5R= 0.6R= 0.7R= M*8R= 0.9R= R= *Copy from column 3, Part IVa. 61 (sheet 1 of 6) Table 3.2.--ExampZe of application of tabZe 3.1 Part I. Designatedhurricane location and values of meteoroZogica-Z parameters SPH O and PMH [] (check one) a. Milepost (fig. 1.1): 2000 b. Latitude in degrees (P) (fig. 1.1): 33.5 c. Coriolis parameter (f) = 2 Q sin i (sec-1) = 14.584 X 10-5 sin i (sec-1) sin 1 = sin.33.5� = 0.55Z 14.584 X 10-5 sin i (sec -1) =86.49 X /0 5s ec/=a290r SPH PMH d. Peripheral pressure (Pw)*: 30./2 i/7. (//1) e. Central pressure (po), fig. 2.1 fig. 2.2 26.3J in. f. Radius of max. winds (R), fig. 2.4 fig. 2.5 /5 f. r/. g. Forward speed (T), fig. 2.6 fig. 2.7 /O kf h. Track direction (O), fig. 2.8 fig. 2.9 /80$ i. Density coefficient (K), fig. 2.10 fig. 2.11 68. B *SPH: Pw = 29.77 in. (Hg); Pw = 100.8 kPa; Pw = 1008 mb *PMH: Pw = 30.12 in. (Hg); Pw = 102.0 kPa; Pw = 1020 mb Part II. Maximum wind speeds (Vgx and Vxs) for a stationary hurricane: 1/2 Rf a. maximum gradient wind speed (Vgx) = K (Pw P) (2.2) g12.1 0 2 62 (sheet 2 of 6) Table 3.2 (continued) b. V adjusted to maximum 10-mn, 10-min value (V )for a stationary gx Xs hurricane. SPH: 0.9 V =0.9 (___ ___ gx Xs PMH: 0.95 V . 095 (1.32 I-IZ=/5.5 A-9 -,V5 gx X 63 (sheet 3 of 6) Table 3.2 (continued) Part III. Profile of wind speed for a stationary hurricane a. Outward from R to 130 n.mi. (241 km) [R < r < 130 n.mi.]: (1) (2) (3) Distance V from center, r s (fig. 2.12) V (? VXS (. 2 ) / 5 /. ooo /25.5 30 .87o /0 .2 60 .590 74.o /00 .42e 53.7 20o .250 31.4 300 ,/58 / .8 64 (sheet 4 of 6) Table 3.2 (continued) b. Hurricane center to R Cr < R): (1) ~~(2) (3)() 1.0 1.000 /-5.0 125.5 0.9 0.937 /-3.5 /7.6 0.8 0.771 /20 f 0.7 0.491 0.6 0.330 904. 0.5 0.206 7.5 25.8E 0.3 0.060 7.5 0.2 0.020 3.0 2.5 0.1 0.010 A-3 65 (sheet 5 of 6) Table 3.2 (continued) Part IV. Adcustment for asymmetry due to storm forward speed (T). a. For radial through point of maximum wind (radial M) T /O t T063 = 426C 6t Th T_ _37 (1) (2) (3) (4) (5) (6) r c* cos A V (n.Ini. ) (deg.) (deg.) 0.2R= 0.3R= P 0.4R= .0o.5R R H0.6R= O.7R= /0.5 4,0 3556.5 . '/98?14- 0.8R= 0.9R= R= 15 7.2 0.0 /.10c'O 6,4 /31.9 I 30 23.6 /16-4 .95931 4 1z 1/5.4 (10 24.5 /7.3 .954 7K .1 80.1 A0O0 2029 /3.7 .I97/55 .2 .545' 200 /5.96. .74S6495 c3 37.7 .300 /4.2 7.0 5192 55 4.4 276.2 *From figure 2.14 or 2.15. 66 (sheet 6 of 6) Table 3.2 (continued) b. For other radials: Degree of counterclockwise rotation from M 3 a T = /o/0f T0�63 4.2~1Ihk 0.37= M* MA(2)A (3) (4) (5) (6) + angle between M and other r x radial Cos A V (P7.ri.) (deg.) '(deg.) ( ,7 ) ( M- 0.1R= 15 .3.31 3/ f? 997, 72 0.2R= 0.3R= o.4R= 0.5R= 0.6R= 0.7R= 10,.5 35. -a ,9 4L 5.7 d 7.3 0.8R= 0.9R= R= 16/5 .50.0 131, 0 30 /i*.4 4* 4 .9593/ 4. / 6 I /7.3 473 91954 7 4.3 78, 3 /61- 1 /3.7 43.7 $7155 4.- 58.3 20 89.7 36.7 .9~�-9 5.0 34.4 300 70 37o .255 5.24.9 A Copy from column 3, Part IVa. C dopy from column 1, Part 1T1a. 67 0~~~~~~~~ C ~ ~ - I;~~~~~~~~~~~~~~~~~3 20* AC 4 6,0 8 100 + ~~~~~~~~DISTANCE SCALE Figure 3.1.--Overwater M I 5nm. wind J'ield computed for the exofnple (sec. 3.2). If desiredthis'wind field may be rotated keeping the point of maximum wind within 00 to 1.800 clockwise from G. 68 INFLOW ANGLE INDICATOR WIND PATHS 0 20 40 60 8,0 190 DISTANCE SCALE Figure 3.2.--Example of wind directions and sketched wind paths for PM with- R = 15 n.mi. (see sec. 3.3.2). , g 69 f. Trace wind paths over the portion of the wind field that is overland. (The wind path chart can be rotated to obtain additional paths, if required.) 3.3.3 FRICTION COEFFICIENTS Summarizing from chapter 2: Vk = kV (3.5) kk = ke + Q(ki ke) (3.6) i e~~~~~~~~36 k is the friction coefficient at a point along a wind path (definition of k e and k. are given in sec. 2.2.11). The interpolation device Q (sec. 2.2.11), 1 is: Q = 1 - 0.195s + 0.0095s2 (3.7) where s = distance downstream from a change in surface friction category. 3.3.4 EXAMPLES OF COMPUTATION OF SURFACE FRICTIONALLY ADJUSTED WIND SPEED NEAR SHORE The following computations of surface frictionally adjusted winds are fcr the previously determined PMH overwater wind field with an R of 15 n.mi.(28 km) in figure 3.1, Points along two wind paths that intercept the coast at a certain time for which computations are made are shown in figure 3.3. Wind paths X - X and Y - Y were traced onto this figure from figure 3.2. 3.3.4.1 WIND PATH X - X Computational procedure for Vk (eq. 3.5) Remarks Point A V = 51 kt (overwater wind speed at A) Computation of Vk at coast: water-rough terrain boundary s = 0 n.mi. (initial boundary point) point. Q = 1.0 (from fig. 2.17 or eq. 3.7) k. = k 0.83; from table 2.2 1 c 70 ROUG TERRAIN x x~~~~~~~~~~~~4 * ~ 0 +10DITNE3CL Figure 3. 3--Overwate P~tH (R =152~n.)wn il ndlctoso'pit A t~~~~~~~~~oLfowhcadutetaegie(sc3.) 60~~~~~~~~~~~~~j Computational procedure for Vk (eq. 3.5) Remarks Point A - Continued k- + Q (ki - ke) from eq. 3.6 k = ki = 0.83 1 Vk = k V = 0.83 (51) = 42 kt Point B V = 52 kt (overwater wind speed at B) Computation of Vk at a point < 10 n.mi. downstream from s = 6 n.mi. (distance from A to B) coastal boundary point. Q = 0.17 (from fig. 2.17 or eq. 3.7) k. = 0.83 (k of point A) ke= 0.40 (rough terrain curve from fig. 2.16 for V = 52 kt) k = k + Q (ki - ke) from eq. 3.6 k = 0.40 + 0.17 (0.83 - 0.40) = 0.47 Vk = k V = 0.47 (52) = 24 kt Point C V = 53 kt (overwater wind speed at C) Shows that friction coef- s = 10 n.mi. (distance from A to C) ficient k = ke at s = 10 n.mi. (Q - 0) Q - 0 by definition) k. = 0.83 (k of point A) ke = 0.41 (rough terrain curve from fig. 2.16 for V - 53 kt) k k + Q (ki - ke) from eq. 3.6 k= k IV k = k V = 0.41 (53) = 22 kt 72 Computational procedure for Vk (eq. 3.5) Remarks Point D V = 54 kt (overwater wind speed at D) Shows procedure for computing V at s >10 n.mi. downstream s = >10 n.mi. (distance from A to D); Vk at s >10 n.mi. downstream from onshore boundary point. Q = 0 (by definition) Also shows that at D (a ki = 0.83 (k of point A) boundary point itself) we k = 0.41 (rough terrain curve still measure s from A. from fig. 2.16 for V = 54 kt) k = ke Q (ki - ke) from eq. 3.6 k= k vk = k V = 0.41 (54) = 22 kt Point E V = 55 kt (overwater wind speed at E) Computation of Vk after passing from one inland s = 8 n.mi. (distance from D to E) terrain surface to another. Q = 0.05 (from eq. 3.7 or fig. 2'.17) ki = 0.41 (k of point D) k = 0.67 (land curve from fig. 2.16 for V = 55 kt) k = ke + Q (ki - ke) from eq. 3.6 k = 0.67 + 0.05 (0.41 - 0.67) = 0.66 Vk = k V = 0.66 (55) =36 kt Point F V = 60 kt (overwater wind speed at F) Shows that Q = 0 after 10 n.mi. and k - k no matter s = >10 n.mi. (distance from D to F) e what kind of terrain surface Q = 0 (by definition) we are passing over. ki = 0.41 (k of point D) Computation the same as point D though this is not 73 Computational procedure for Vk (eq. 3.5) Remarks Point F - Continued ke = 0.70 (land curve from fig. 2.16 a boundary point. for V = 60 kt) k =ke + Q (ki - ke) from eq. 3.6 k=k e Vk5 k V = 0.70 (60) = 42 kt Point G V = 75 kt (overwater wind speed at G) Procedure follows that given for points D and F except s = > 10 n.mi. (distance from D to G) now we are computing Vk at Q = 0 (by definition) the offshore boundary point k. = 0.41 (k of point D) between land and water. 1 k = 0.78 (land curve from fig. 2.16 for V = 75 kt) k = k + Q (ki - k ) from eq. 3.6 e i e k= k e Vk = k V = 0.78 (75) = 58 kt Point H V = 78 kt (overwater wind speed at H) Shows how to compute over- water V for offshore wind. s = 7 n.mi. (distance from G to H) water Vk for offshore wind. Q = 0.10 (from eq. 3.7 or fig. 2.17) k. = 0.78 (k from point G) k = 1.00 (equilibrium k for water) e k ke + Q (ki - ke) from eq. 3.6 k = 1.00 + 0.10 (0.78 - 1.00) = 0.98 Vk = k V = 0.98 (78) = 76 kt 74 Computational procedure for Vk (eq. 3.5) Remarks 3.3.4.2 WIND PATH Y - Y Point I V = 64 kt (overwater wind speed at I) Procedure follows that given for point A but for land s = 0 n.mi. (initial boundary point) rather than rough terrain. Q = 1.0 (from fig. 2.17 or eq. 3.7) ki = kc = 0.89 (from table 2.2) k = ke + Q (ki - ke) from eq. 3.6) k = ki = 0.89 Vk = k V = 0.89 (64) = 57 kt Point J V = 73 kt (overwater wind speed at J) Procedure follows that given for point D but now we arp s = > 10 n.mi. (distance from I to J) at boundary point between Q = 0 (by definition) land and an awash area. k. = 0.89 (k of point I) k = 0.78 (land curve from fig. 2.16 for V = 73 kt) k - ke + Q (ki - ke) from eq. 3.6 k= k Vk = k V = 0.78 (73) = 57 kt Point K V = 80 kt (overwater wind speed at K) Shows how to use awash curve s = > 10 n.mi. (distance from J to K) in fig. 2.16. Q= 0 (by definition) ki = 0.78 (K of point J) 1 75 Computational procedure for Vk (eq. 3.5) Remarks Point K - Continued k = 0.89 (awash curve from fig. 2.16 e atV = 80 kt) k ke +Q (ki ke) from eq. 3.6 k k e V =k V = 0.89 (80) = 71 kt k PointL V = 83 kt (overwater wind speed at L) Shows that the procedure followed when computing off- s = 8 n.mi. (distance from K to L) shore overwater winds after Q = 0.05 (from eq. 3.7 or fig. 2.17) leaving an awash area is k. =0.89 (k of point K) the same as that followed at point H after leaving k = 1.00 (equilibrium k for water) ~~~~~~~~e ~~land. Of course, the k.'s k k + Q (ki . ke) from eq. 3.6 are different. e I e ~~~~~~~~are different. k = 1.00 + 0.05 (0.89 - 1.00) = 0.99 Vk = k V = 0.99 (83) = 82 kt 3.4 ADJUSTMENT OF WIND FIELD WHEN HURRICANE CENTER MOVES OVERLAND When the center of a hurricane crosses the coast, overwater wind speeds are reduced because of filling by a factor which decreases with time after landfall. (The adjustments for near shore friction given in sec. 3.3 would have to be accomplished first.) Determination of the filling factor and its application to a wind field are as follows: a. Enter figure 2.20 at the specified project location or milepost and determine which filling adjustment factor curve (A, B, C, or an interpolation between these curves) to use. 76 b. Use figure 2.19 to determine the filling adjustment factor for the specific time after landfall of interest. c. Multiply all wind field isotach values by the filling adjustment factor for the indicated time after landfall. d. Interpolate for desired isotach interval. 3.5 ADJUSTMENT OF WIND FIELD FOR A STALLED PMH When a PMH stalls offshore south of the Virginia-North Carolina border, overwater wind speeds are reduced (because of upwelling and mixing) by a factor which decreases with time after landfall. (Unlike sec. 3.4, adjust- ments for frictional effects given in sec. 3.3 should be completed after the wind field has been reduced.) Determination of the stalling factor and its application to a wind field follows: a. South of the Virginia-North Carolina border, immediately use the curve in figure 2.21 to determine the stalling adjustment factor for the specific time of interest after stalling begins. [From Virginia northward, the lower limit of T (TL) is too fast (fig. 2.7) for a PMH to reach a stall speed in a period of a few hours or less. The PMH will weaken before it reaches its stall speed; it will weaken at a lesser rate than during a stalled condition. An empirical procedure was developed to compute this lesser rate of weakening. It is given in sec. 16.11.] b. Multiply all wind field isotach values by the stalling adjustment factor for the indicated time after stalling begins. c. Interpolate for desired isotach interval. 77 4. DATA 4.1 INTRODUCTION Observations from hurricanes occurring near the United States Gulf of Mexico and east coasts and from western North Pacific typhoons are used throughout most of this study to determine SPH and PMH criteria. Definitions of the several meteorological parameters used are given in chapter 5. Data presented in this chapter are used in later chapters of the report. If additional data are required for a specific purpose, it is given in the chapter where required. Such data may be found in chapters 7, 8, 10 and 16. 4.2 SOURCES OF DATA 4.2.1 HURRICANES Original sources of hurricane data are barograph traces from land stations and ships, wind records from National Weather Service and military stations, aircraft reconnaissance flight data, radar data, miscellaneous pressure and wind reports, and textual descriptions in scientific literature. The descrip- tions have appeared in the periodicals Monthly Weather Review (published since June 1872) and Climatological Data National Summary (since 1950), National Hurricane Research Project Report No. 39 (Graham and Hudson 1960), NOAA Technical Memorandum NWS SR-56 (Sugg et al. 1971), the book Tropical Cyclones (Cline 1926), and other sources. Tables 4.1 to 4.4 list gulf coast and east coast hurricanes during the years 1900-78 with central pressure (p ) < 29.00 in. (98.2 kPa). Values of 0 meteorological parameters used in this report are given for these hurricanes. The storms occurred within 150 n.mi. (278 km) of the coast. Hurricanes whose centers passed through the Florida Keys are listed inthe gulf and east coast tables for the convenience of the user. Tables 4.1 and 4.2 provide informa- tion in metric units (kilometers, kilometers/hr, and kilopascals*) and tables 4.3 and 4.4 give the English values (nautical miles, knots, and inches.) Both measurement systems are provided because the report is being issued at the time of transition from one system to another. These tables are an update and extension of tables 1 and 2 in NOAA Technical Report NWS 15 (Ho et al. *A kilopascal is equal to 10 millibars. 78 1975). There are two changes in the previously published data. On the basis of additional data discovered since the 1975 study, we revised the radius of maximum winds for Carla to 30 n.mi. (56 km) from 20 n.mi. (37 km). and the central pressure for Donna (near the Florida Keys) to 27.45 in. (93.0 kPa) from 27.55 in. (93.3 kPa.) 4.2.1.1 HURRICANE PRESSURE DATA. The criterion for tables 4.1 to 4.4 (Po 529.00 in., 98.2 kPa) was based on the consideration that the maximum cyclostrophic wind speed, computed from the Hydrometeorological Branch model (Myers 1954, eq. 6), with a p of 29.00 in. (98.2 kPa) and a Pw of 30.00 in. (101.6 kPa) is 63 kt (117 km/hr), or about the wind speed required for classification as a hurricane. In tables 4.1 to 4.4, if a hurricane crossed the coast on one side of the Florida peninsula with a po <29.00 in. (98.2 kPa) and decreased in intensity to po >29.00 in. when it was >50 n.mi. (93 km) from the opposite coast, it was listed for only the initial coastline it crossed. The specific p values given for hurricanes in tables 4.1 to 4.4 are the lowest po either measured by barometer or a dropsonde from reconnaissance aircraft. If the measurement was not very close to the hurricane center, p was estimated from observations. The Hydrometeorological Branch pressure profile formula (chapter 6) was used to estimate po, particularly for earlier hurricanes. For some hurricanes prior to 1942, po's were adjusted back to the coast where the storm entered land. This was done for those Po's for which the lowest observed pressure was from a station well inland or at a coastal station when the storm was emerging from land to sea. These adjustments were made for 13 hurricanes and were carried over from Ho et al. (1975) and earlier reports including Graham and Nunn (1959). They were based on the average'rate of filling developed in chapter 5 of Myers (1954). We did not recompute these p 's using information contained in our chapter 15 because the 13 hurricanes were all relatively weak (p > 28.17 in., 95.4 kPa) and, thus, would not affect our determination of SPH or PMH po. In addition, recomputed Po's employing knowledge gained since 1954 would still be close to Myers' results. 79 A virtual absence of pressure data made it necessary to omit one storm altogether--the Louisiana hurricane of August 6, 1918, in which the closest recorded pressure was some 90 n.mi. (167 km) from the path of the storm center. An estimate of p from such a distance would be so unreliable as to be useless. Two hurricanes appearing in NHRP 33 are not presented in tables 4.1 to 4.4. They are the storms of September 11, 1903 (gulf coast) and October 20, 1924 (east coast). Both storms crossed the Florida peninsula. Upon reanalysis of the data, it was determined that both had weakened to tropical storm strength before they reached a point 50 n.mi. (93 km) from where they exited the coast. 4.2.1.2 HURRICANE RADIUS OF MAXIMUM WINDS (R) DATA. The values of R for hurricanes were derived from several sources listed in decreasing order of preference: a. wind speed records from land stations b. approximation from hurricane "eye" radii gathered by aircraft or radar c. wind reports from aerial reconnaissance d. computed from the Hydromet Pressure Profile Formula e. narrative or tabular data in the Monthly Weather Review or other publications. A detailed description of these procedures are found in NOAA Technical Report NWS 15 (Ho et al. 1975, pp 41-46). 4.2.1.3 HURRICANE FORWARD SPEED (T) AND TRACK DIRECTION (0). In tables 4.1 to 4.4, T and 0 (measured clockwise from north) of landfalling, alongshore and exiting hurricanes were extracted from storm track charts. Hurricane tracks from Cry (1965) and the Monthly Weather Review (National Oceanic and Atmospheric Administration 1965-73, American Meteorological Society, 1974-78) were used. These charts give 12-or 24-hr positions that sometimes indicate lower or higher T or different 0 than more detailed tracks showing hourly positions. Detailed track charts (e.g., Myers 1954, Graham and Hudson 1960) depicting hqurly or two-hourly positions in the vicinity of the coast exist for many hurricanes, and these were used 80 if available. The listed T and e pertain to the time of landfall, exit or closest approach to the coast. 4.2.2 TYPHOONS Records show there have been numerous western North Pacific typhoons with central pressures considerably lower than hurricanes of the Atlantic Ocean, including the Caribbean Sea and Gulf of Mexico. We made use of meteoro- logical parameters observed or estimated for these typhoons as guidance for certain determinations in this study. Typhoons were selected from lists given in the Annual Typhoon Report (U.S. Department of Defense 1960-74) if their central pressures were < 29.10 in. (98.5 kPa) when near the coasts of Japan, Taiwan and the Philippine Islands. Table 4.5 lists data from these typhoons in metric units and table 4.6 provides the same items in English units. Values of parameters were determined from reconnaissance flight data taken every 6 hours on the average. T is a 6-hr average forward speed closest to the time when p0 was selected. This definition differs from the definition of T for North Atlantic hurricanes where T pertains to the time of landfall or closest approach to the coast. 0 is the track direction from which the typhoon moves(measured clockwise from north)and is also at or near the time of P. For the time of po, R was approximated by adding 25% to the reported radius of the typhoon eye. The 25% is an estimate we made from data given by Shea and Gray (1972). 4.3 LIMITATIONS ON USE OF TYPHOON DATA There are indications that the typhoons from the western North Pacific may not fit into the same family as U.S. coastal hurricanes. In general, storms of the western North Pacific draw moisture from a much larger water surface than those of the North Atlantic. The typhoon data also span a larger range in latitude. Nonetheless, we believe the added storm data are helpful in making judgments and drawing conclusions. Data from tropical cyclone regions other than the North Atlantic and western North Pacific were not used in this study. NOTES FOR TABLES 4.1 TO 4.4 V gx .Gradient wind speed (see chapter 12). � Same hurricane as previous line. V Maximum 10-m, 10-min sustained wind speed. by Bypassing hurricane. x 'To convert to 1-min sustained winds divide 1 ex Exiting hurricane. by 0.863 (see chapter 12). MSG Missing. : Peripheral pressure estimated at or near time of p0 (see chapter7). *: Date applies to the time hurricane was at time of Po (see chapter 7). or closest to the approximate coastal P O Central pressure (see chapter 8). reference point. R Radius of maximum winds observed or com- Refers to the lowest p within 150 n.mi. puted at or near time of Po' Computed (278 km) seaward of the coast or 50 n.mi. values are used where a station or (93 km) landward. Lower p0 beyond these specific location is not given (see l limits were not considered. chapter 9). t Point at which hurricane entered, exited, or T Forward speed pertaining to the time of came closest to the coast (fig. 1.1). These landfall or closest approach to the points are generally different from Ho et al. coast (see chapter 10). (1975), who read the points in terms of rounded : Track directon from which the hurricane latitudinal and longitudinal values and then moves measured clockwise from north and converted these to reference, distances. In this pertaining to the time of landfall or study we read the reference distances directly. closest approach to the coast (see chapter : Latitude or longitude of coastal reference point 11). or point at which hurricane was closest to the Data not used in determining values of most coastal reference point. meteorological parameters for the SPH or PMH. It is included here to update tables through 1978 (no hurricanes qualified in 1978.) Thom, H.C.S., "Distributions of Extreme Winds Over Oceans," Proceedings of the ASCE, Waterways, Harbors and co Coastal Engineering Division, February 1973. A Table 4.1.--U.S. gulf coast hurricanes (1900-78) with centraZ pressure < 29.00 in. (98.2 kPa) Zisted c o chronologicaZZlly (metric units). Approximate Track coastal ref. direction Pot Location at po Pw Station(s) where gx point (km)t Date (GM4T)* Name Lat. Long.e (8) (kPa) Lat. Long. (kPa) (km) R was observed (km/hr) (km/hr) (km/hr) 723 Sept 9,1900 29.2 95.1 130 93.6 29.2 95.1 101.2 26 19 184 178 1269 Aug 15,1901 29.3 89.7 195 97.3 29.3 89.7 101.3 61 26 328 130 2585 June 17,1906 25.1 81.1 185 97.9 25.1 81.1 101.3 48 19 120 120 1445 Sept 27,1906 30.4 88.5 160 96.5 30.4 88.5 101.3 80 Mobile, AL 30 138 141 2585 Oct 18,1906 25.2 80.9 230 97.7 25.0 81.0 101.0 65 11 116 113 704 July 21,1909 29.0 95.2 115 95.9 29.0 95.2 101.5 35 22 156 154 1205 Sept 20,1909 29.2 90.2 150 98.0 29.2 90.2 101.2 MSG 20 MSG MSG 2595 Oct 11,1909 by 24.7 81.1 235 95.7 24.7 81.1 100.9 41 Key West, FL 19 151 147 2465 Oct 18,1910 26.0 81.8 200 94.1 24.5 82.9 100.8 30 20 173 168 704 Aug 17,1915 29.1 95.2 130 94.9 29.1 95.2 101.2 54 Galveston & Houston, TX 20 164 160 1223 Sept 29,1915 29.1 90.2 170 93.2 27.0 89.3 100.9 48 New Orleans, LA & other stations 19 182 176 1427 July 5,1916 30.4 89.0 160 96.1 30.4 89.0 101.1 83 Mobile, AL 46 141 148 343 Aug 18,1916 27.0 97.5 115 94.8 27.0 97.5 101.4 46 20 169 165 1593 Oct 18,1916 30.4 87.2 200 97.4 30.4 87.2 101.2 35 Pensacola, FL 39 128 134 1668 Sept 29,1917 30.4 86.6 230 96.4 30.4 86.6 101.5 61 Pensacola, FL 24 145 145 2502 Sept 10,1919 by 24.7 82.9 110 92.9 24.7 82.9 101.2 28 15 193 184 408 �Sept 14,1919 27.3 97.5 105 94.8 27.3 97.5 101.2 MSG 37 MSG MSG 1130 Sept 21,1920 29.2 90.9 155 98.0 29.2 90.9 101.3 52 52 117 128 593 June 22,1921 28.6 96.4 175 95.4 28.6 96.4 101.4 32 20 163 159 2224 Oct 25,1921 28.1 82.8 235 95.2 28.1 82.8 101.0 33 19 160 156 2505 Oct 21,1924 25.9 81.6 250 97.2 24.7 82.9 101.2 35 15 132 129 1112 Aug 26,1926 2 91.3 180 95.9 29.3 91.3 101.5 50 19 154 151 1566 Sep't 20,1926 30.3 87.5 120 95.-5 30.3 87.5 101.4 32 Pensacola, FL 13 161 154 2650 Oct 21,1926 by 25.1 80.1 220 93.2 23.6 81.8 100.8 39 30 183 181 See notes preceding table 4.1. Table 4.1.--U.S. gulf coast hurricanes (metric units), continued Approximate Track coastal ref. direction Po Loc R Station(s)where gtx x or Loca~~~~~~ti atin s w e e point (km)t Date (GMT)* Name Lat. Long.o (8) (kPa) Lat. Long. (kPa) (km) R was observed (km/hr) (km/hr) (km/hr) 2261 Sept 17,1928 27.7 81.7 120 95.8 27.7 81.7 101.2 MSG 22 MSG MSG 556 June 28,1929 28.5 96.5 130 96.9 28.5 96.5 100.9 24 28 133 135 1798 S Sept 30,1929 29.7 85.4 160 97.5 29.7 85.4 101.3 102 Pensacola, FL 11 119 116 723 Aug 14,1932 29.1 95.0 135 94.2 29.1 95.0 101.3 22 28 178 176 241 Aug 5,1933 25.7 97.1 70 97.5 25.7 97.1 101.3 46 Brownsville, TX 19 127 126 2252 Sept 4,1933 27.8 81.1 120 96.4 27.8 81.6 101.2 54 Tampa,FL 20 142 141 259 Sept 5,1933 26.2 97.1 90 94.9 26.2 97.1 101.2 37 Brownsville, TX 15 166 160 1093 June 16,1934 29.3 91.2 180 96.6 29.3 91.2 100.6 69 30 127 130 2613 Sept 3,1935 24.8 80.9 130 89.2 24.8 80.9 101L4 11 17 242 241 2585 Nov 5,1935 ex 25.2 81.1 65 97.3 25.6 80.4 101.6 19 Miami, FL 28 139 140 1668 July 31,1936 30.4 86.5 150 96.4 30.4 86.5 101.6 35 17 150 146 834 Aug 8,1940 29.9 93.9 140 97.0 29.9 93.9 101.4 20 15 137 133 686 Sept 23,1941 28.9 95.4 180 95.9 28.9 95.4 101.1 39 24 150 149 1881 Oct 7,1941 29.9 84.7 170 98.1 29.9 84.7 101.6 33 20 123 123 612 Aug 30,1942 28.5 96.2 135 95.1 28.5 96.2 101.0 33 26 161 159 788 July 27,1943 29.5 94.5 110 97.5 29.5 94.5 101.4 30 Houston, TX 15 130 128' 2335 Oct 19,1944 27.0 82.5 195 94.9 24.7 82.9 101.2 50 24 165 163 612 Aug 27,1945 28.6 96.2 200 96.7 28.6 96.2 101.0 33 7 135 128 2669 Sept 15,1945 25.5 80.3 130 95.1 25.5 80.3 101.4 44 Miami, FL 19 166 161 2492 Sept 18,1947 ex 26.2 81.8 85 94.9 26.3 81.3 101.6 63 13 169 161 1371 � Sept 19,1947 29.7 89.5 115 96.6 29.8 90.3 101.4 43 New Orleans, LA 30 142 144 2557 Sept 21,1948 24.5 81.5 210 93.5 24.5 81.5 101.0 13 15 185 177 2567 Oct 5,1948 24.7 81.3 230 97.7 24.7 81.3 101.0 57 Miami, FL 24 117 119 2317 Aug 27,1949 27.2 81.2 130 96.1 27.2 81.2 101.5 43 W.Palm Beach, FL 26 153 152 667 Oct 4,1949 28.8 95.6 190 96.3 28.8 95.6 101.2 37 Composite of many 20 146 144 TX stations 1520 Aug 31,1950 Baker 30.2 88.0 190 97.9 30.2 88.0 100.4 39 20 102 112 See notes preceding table 4.1. Co LW Table 4.1.--U.S. gulf coast hurricanes ~metric units), continued. 0 Approximate Track -| coastal ref ~~~~~~direction oI Lcto tg w R Station(s) where T Vgx point (km)-t Date (GMT)* Name Lat. Long.oo (e) (kPa) Lat. Long. (kPa) (km) R was observed [km/hr) (km/hr) (km/hr) 2131 Sept 5,1950 Easy 28.6 82.8 230 95.8 29.1 83.1 100.9 28 [6 150 141 2224 Oct 18,1950 King 28.0 81.6 150 97.8 28.0 81.6 101.4 MSG 32 MSG MSG 1677 Sept 24,1956 Flossy 29.2 89.6 235 97.4 30.3 86.5 101.3 41 Burrwood, LA 19 129 128 852 June 27,1957 Audrey 29.8 93.6 200 94.6 29.8 93.6 100.7 35 26 162 160 2595 Sept 10,1960 Donna 24.7 80.9 140 93.0 24.3 80.5 101.2 37 Near Conch Key, FL 17 191 183 1381 Sept 15,1960 Ethel 30.4 86.1 175 97.2 26.6 89.3 101.5 33 Keesler AFB, MS 19 137 135 547 Sept 11,1961 Carla 28.4 96.4 170 93.1 28.4 96.4 100.8 56 11 182 172 1103 Oct 3,1964 Hilda 29.5 91.4 175 95.9 29.5 91.4 101.5 39 Near 26�N, 92�W 13 156 150 2502 Oct 14,1964 Isbell 25.8 81.3 220 96.4 24.3 82.7 101.3 19 Near 24�N, 83�W 28 149 149 2548 Sept 8,1965 Betsy 25.2 82.1 90 94.8 25.2 82.1 101.3 35 W. of Cape Sable,: 28 169 168 FL 1186 �Sept 10,1965 Betsy 29.2 90.3 135 94.1 28.2 89.2 101.1 59 Port Sulpher, LA 32 173 172 1909 June 9,1966 Alma 30.1 84.3 200 97.1 29.1 84.3 101.5 43 Near 30�N, 84�W 17 139 136 2632 Oct 4,1966by Inez 24.9 80.6 65 97.7 24.1 84.2 101.3 35 Key West, FL 13 125 122 278 Sept 20,1967 Betulah 26.1 97.2 155 92.3 24;8 96.3 100.9 46 Brownsville, TX 16 194 185 2113 Oct 19,1968 Gladys 28.8 82.9 235 97.7 28.8 82.9 101.1 39 19 120 120 1390 Aug 18,1969 Camille 30.3 89.5 160 90.8 28.2 88.8 100.8 15 Near 28�N, 89�W 30 219 224 482 Aug 3, 1970 Celia 27.9 97.2 115 94.4 27.9 97.2 101.0 17 Corpus Christi, TX 26 171 169 19 Sept 12,1970 Ella 23.9 97.7 100 96.7 23.9 97.7 100.8 39 13 133 130 630 Sept 10,1971 Fern 28.5 95.6 50 97.9 28.5 95.6 100.8 48 Palacios & Port 9 110 106 Comfort, TX 871 Sept 16,1971 Edith 29.4 93.2 230 97.8 29.4 93.2 100.9 50 Lake Charles, LA 28 113 117 1742 June 19,19'72 Agnes 30.1 85.6 195 97.8 28.5 85.7 101.0 37 Near 28�N, 86�W 20 117 118 1093 Sept 8,1974 Carmen 29.2 91.1 155 93.6 :28.0 90.7 101.3 19 Near 28�N, 91�W 17 186 179 | 74 Aug~31, 1975 Caroline 24.3 97.7 110 96.3' 24.3 97.7 101.2 19 Near 24�N, 97�W 9 149 141 1668 8 ep't 23,1975 Eloise 30.4 86.5 195 95.5 - 30.4 86.5 101.5. 33 Near 30�N, 86.5�W 41 162 165 | 19 ASepzt 2,1977 Anita 23.9 97.8 60 92.6 24.2 97.1 101.2 22 Near 24�N, 97�W 19 1918 |See notes preceding table 4.1. Table 4.2.--U.S. east coast hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronologicaZZlly (metric units). Approximate Track coastal ref. direction p + Locati at p Station(s) where T V V Station(s) where V Vx point (km)t Date (GMT)* Name Lat. Long." (8) (kVe) Lat. Long. (kPa) (kin) R was observed (kmlhr) (km/hr) (km/hr) 2780 Sept 12,1903 26.5 80.0 120 97.7 26.5 80.0 101.6 80 15 125 123 2863 June 17,1906 ex 27.3 80.2 220 97.9 25.1 81.1 101.3 48 22 120 121 3707 Sept 17,1906 33.6 78.9 105 98.1 33.6 78.9 101.8 82 Charleston, SC 30 118 122 2733 Oct 18,1906 ex 26.0 80.1 220 97.7 25.0 80.6 101.0 65 11 116 113 2595 Oct 11,1909 by 24.7 81.1 230 95.7 24.7 81.1 100.9 41 Key West, FL 19 151 147 3466 Aug 28 1911 32.1 81.0 100 97.9 32.1 81.0 101.6 50 Savannah, GA 15 123 121 3920 Sept.3,1913 34.7 76.4"~ 115 97.6 34.7 76.4 102.0 7.0 Hatteras, NC 30 131 134 2502 Sept.10,1919 by 24.7 82.9 110 92.9 24.7 82.9 101.2 28 15 193 184 3104 Oct 26,1921 ex 29.0 81.0 260 97.9 28.6 81.8 101.2 MSG 19 MSG MSG 4040 Aug 26,1924 by 35.0 75.0 210 97.2 35.0 75.2 101.4 63 Hatteras, NC 41 129 135 5022 �Aug 26,1924 by 41.1 69.8 220 97.2 41.1 69.8 101.4 122 Nantucket, MA 54 115 126 3920 Dec 2,1925 34.7 76.6 220 98.0 34.7 76.6 101.9 100 Wilmington, NC 26 118 121 2974 July 28,1926 28.2 80.4 150 96.0 28.2 80.4 101.6 26 15 158 152 2706 Sept 18,1926 25.8 80.1 110 93.4 25.8 80.1 101.4 44 32 187 186 2650 Oct 21,1926 by 25.1 80.1 220 93.2 23.6 81.8 100.8 39 30 183 181 2789 Sept 17,1928 26.7 80.0 120 93.5 26.7 80.0 101.2 52 24 182 178 2641 Sept 28,1929 25.1 80.4 90 94.8 25.1 80.4 100.9 52 19 162 158 4179 Aug 23,1933 36.8 75.9 145 97.0 36.8 75.9 101.4 67 Hatteras, NC 33 131 135 2836 Sept 4,1933 26.9 80.1 120 94.8 26.9 80.1 101.4 MSG 20 MSG MSG 4003 Sept 16,1933 35.0 76.2 180 95.7 35.0 76.2 101.7 74 Hatteras,NC 17 154 150 2613 Sept 3,1935 24.8 80.9 130 89.2 24.8 80.9 101.4 11 17 242 241 2706 Nov 4,1935 25.8 80.1 60 97.3 25.8 80.1 101.5 19 Miami, FL 22 138 137 4133 Sept 18,1936 by 36.1 75.4 160 96.6 35.2 74.6 102.0 63 30 147 148 4809 Sept 21,1938 40.7 72.7 180 94.0 38.7 72.5 101.5 93 87 168 182 3493 Aug 11,1940 32.4 80.9 100 97.5 32.4 80.9 101.8 50 Savannah, GA 17 135 131 4040 Sept 14,1944.. 35.2 75.5 195 94.4 35.2 75.5 101.1 32 Hatteras, NC 43 170 173 4874 �Sept 15,1944 40.9 72.2 220 95.9 40.9 72.2 101.3 67 Providence, RI 56 142 152 2669 Sept 15,1945 25.5 80.3 130 95.1 25.5 80.3 101.4 44 Miami, FL 19 166 161 See notes preceding table 4.1 00CO Ln Table 4.2.--U.S. east coast hurricanes Cmetric unitsl, continuled. o Approximate Track coastal Ref. direction o~ Location at Po Pw S ttns wh r Vgx Point (km)t Date (GM*T)" Namm Lat. Long.m (8) (k1)L a .LogPa) a(k)Rwsobsre :km/hr) (km/hr) (km/hr) 2733 Sept 17,1947 26.3 80.1 80 94.0 26.3 80.1 101.5 63 Miami, F L 19 179 173 3410 Oct 15,1947 31.8 81.1 '80 96.8 31.8 81.1 18113~ 24 32 140 142 2845 Sept 22,1945 8 es 27.3 80,1 230 96.2 26.6 81.0 100.7 30 20 141 139 2659 Oct 5,1948 ex 25.2 80.3 230 97.7 25.2 80.3 101.0 57 Miami, FL 24 117 119 4040 Aug 24,1949 by 35.0 75.1 220 97.7 35.1 75.3 101.8 44 41 130 136 2789 Aug 27,1949 26.7 80.0 130 95.4 26.7 80.0 101.5 43 W.Palm Beach, FL 26 163 161 2706 Oct 18,1950 King 25.8 80.2 150 95.5 25.8 80.2 101.4 11 Miami, FL 11 164 156 4059 Aug 31,1954 Carol 35.4 75.4 210 96.0 33.4 76.8 101.1 MSG 19 MSG MSG 4818 �Aug 31,1954 Carol 40.8 72.5 200 96.1 40.8 72.5 101.8 41 Many coastal stns. 61 151 161 4059 Sept 10,1954 by Edna 35.0 75.0 210 94.3 34.0 75.6 101.1 MSG 37 MSG MSG 5059 �Sept 11,1954 Edna 41.6 70.2 210 94.7 39.7 71.3 101,0 33 Nantucket, MA 74 161 173 3818 Oct 15,1954 Hazel 33.9 78.5 190 93.7 33.9 78.5 101.1 39 Myrtle Beach, SC 48 178 182 3920 Aug 12,1955 Connie 34.7 76.1 -;. 200� 96.2 34.7 76.1 101.1 83 13 137 132 3920 Sept 19,1955 lone 34.7 76.7 175 96.0; 34. 7 76.7 101.6 78 17 148 144 4021 Aug 28,1958 by Daisy 35.2 74.2 180 95.7 35.2 74.2 101.5 46 Near 35�N, 74�W 32 155 156 5041 � Aug 29,1958 by Daisy 40.6 69.1 240 97.9 40.6 69.1 101.4 93 Near 40.5�N, 69�W 39 109 116 3966 Sept 27,1958 by Helene 34.8 75.9 240 93.2 -32.4 78.5 101.2 39 26 185 181 3521 Sept 29,1959 Gracie 32.6 80.4 -`150 95.1 32.2 80.2 '101.6 19 Near 30�N, 78�W 22 169 166 2595 Sept 10,1966 ' Donna 24.7 80.9 140 93.0 24.3 80.5 11.37NaCohKeL 7 1918 3910 �Sept 12,1960v~ Donna 34.6 77.3 215 95.8 33.9 77.9 101.2 63 Wilmington, NC 48 147 154 4818 �Sept 12,1960 Donna 40.7 72.6 205` 96.1 40.7 72.6 101,0 89 Suffolk Co. AFB, 59 131 143 NY 2696 Aug 27,1964' Cleo 25.7 80.1 160 96.7 25.7 80.1 101.2 13 Miami, FL 17 14I 138 3178 Sept 10,1964 Dora 29.9 81.4 100 96.6 29.9 81.4 � 101.3 37 Near 30�N, 80�W 13 143 138 2632- Sept 8,1965 Betsy 25.0 80.6 90 95.2 '25.0; 80.6 .101.3 41 Plantation Key, FI 20 164 160 4188 Sept 17,1967 Doria 36,5 75.9 20 98.1 38.0 71.9 101.8 37 Near 38"N, 74�W 17 123 121 5680 Sept 10,1969 Gerda 44.7 67.3 195 :97.9 40.6 69.6 101.1 MSG 74 MSG MSG 4021 'VAug 9, 1976 Belle 35.2 74.4 -190 95.9 32.5 75.2 10i.5 15 Near 32.5�N. 75�W 39 157 161 4624 'LAug 10,1976 Belle 40.6 73.3 200 97.5 38,2 73,9 101,9 i56 39 130 _135 See notes preceding table 4.1. TalZe 4.3.--U.S. gulf coast hurricanes (1900-78) with centraZ pressure < 29.00 in. (98.2 kPa) listed chronoZogicaZly (English units). Approximate coastal reference point D ( (in. T(kt) V V (n.mi.) Date (GMT)* Name po(in.) R m 390 Sept 9, 1900 27.64 29.88 14 10 99 96 685 Aug 15, 1901 28.72 29.91 33 14 69 70 1395 June 17, 1906 28.91 29.91 26 10 65 65 780 Sept 27, 1906 28.50 29.91 43 16 75 76 1395 Oct 18, 1906 28.84 28.83 35 6 63 61 380 July 21; 1909 28.31 29.97 19 12 84 83 650 Sept 20, 1909 28.94 29.88 MSG 11 MSG MSG 1400 Oct 11, 1909 by 28.26 29.80 22 10 81 79 1330 Oct 18, 1910 27.80 29.77 16 11 93 91 380 Aug 17, 1915 28.01 29.88 29 11 88 86 660 Sept 29, 1915 27.53 29.80 26 10 98 95 770 July 5, 1916 28.38 29.86 45 25 76 80 185 Aug. 18, 1916 28.00 29.94 25 11 91 89 860 Oct 18, 1916 28.76 29.88 19 21 69 72 900 Sept 29, 1917 28.48 29.97 33 13 79 78 1350 Sept 10, 1919 by 27.44 29.88 15 8 104 99 220 �Sept 14, 1919 27.99 29.88 MSG 20 MSG MSG 610 Sept 21, 1920 28.93 29.91 28 28 63 69 320 June 22, 1921 28.17 29.94 17 11 88 86 1200 Oct 25, 1921 28.12 29.83 18 10 86 89 1350 Oct 21, 1924 28.70 29.88 19 8 71 70 600 Aug 26, 1926 28.31 29.97 27 10 83 81 845 Sept 20, 1926 28.20 29.94 17 7 87 83 1430 Oct 21, 1926 by 27.52 29.77 21 16 99 98 1220 Sept 17, 1928 28.30 29.88 MSG 12 MSG MSG See notes preceding table 4.1. -a Table 4.3.--U.S. gulf coast hurricanes [(English units), continued. Approximate coastal reference pointt R(n.mi.) T(kt) V V (n.mi.) Date (GMT)* Name p(in) p(in) n ) (kt) 300 June 28, 1929 28.62 29.80 13 15 72 73 970 Sept 30, 1929 28.80 29.91 55 6 64 62 390 Aug 14, 1932 27.83 29.91 12 15 96 95 130 Aug 5, 1933 28.80 29.91 25 10 69 68 1215 Sept 4, 1933 28.48 29.88 29 11 77 76 140 Sept 5, 1933 28.02 29.88 20 8 90 86 590 June 16, 1934 28.52 29.71 37 16 69 70 1410 Sept 3, 1935 26.35 29.94 6 9 131 130 1395 Nov 5, 1935ex 28.73 30.00 10 15 75 76 900 July 31, 1936 28.46 30.00 19 9 81 79 450 Aug 8, 1940 28.70 29.94 11 8 74 72 370 Sept 23, 1941 28.31 29.86 21 13 81 80 1015 Oct 7, 1941 28.98 30.00 18 11 66 66 330 Aug 30, 1942 28.07 29.83 18 14 87 86 425 July 27, 1943 28.78 29.94 16 8 70 69 1260 Oct 19, 1944 28.02 29.88 27 13 89 88 300 Aug 27, 1945 28.57 29.83 18 4 73 69 1440 Sept 15, 1945 28.09 29.94 24 10 89 87 1345 Sept 18, 1947 ex 28.03 30.00 34 7 91 87 740 �Sept 19, 1947 28.54 29.94 23 16 77 77 1380 Sept 21, 1948 27.62 29.83 7 8 100 95 1385 Oct 5, 1948 28.85 29.83 31 13 63 64 1250 Aug 27, 1949 28.37 29.97 23 14 83 82 360 Oct 4, 1949 28.45 29.88 20 11 79 78 820 Aug 31, 1950 Baker 28.92 29.65 21 23 55 61 See notes preceding table 4.1. Table 4.3.--U.S. gulf coast hurricanes (English units), continued Approximate coastal reference pointt Date (GMT)* Name po(in.) pw(in.) R(n.mi.) T(kt) () (n.mi.) 1150 Sept 5, 1950 Easy 28.30 29.80 15 3 81 76 1200 Oct 18, 1950 King 28.88 29.94 MSG 17 MSG MSG 905 Sept 24, 1956 Flossy 28.76 29.91 22 10 70 69 460 June 27, 1957 Audrey 27.95 29.74 19 14 87 87 1400 Sept 10, 1960 Donna 27.45 29.88 20 9 103 99 745 Sept 15, 1960 Ethel 28.70 29.97 18 10 74 73 295 Sept 11, 1961 Carla 27.49 29.77 30 6 98 93 595 Oct 3, 1964 Hilda 28.33 29.97 21 7 84 81 1350 Oct 14, 1964 Isbell 28.47 29.91 10 15 80 80 1375 Sept 8, 1965 Betsy 27.99 29.91 19 15 91 91 640 �Sept 10, 1965 Betsy 27.79 29.86 32 17 93 93 1030 June 9, 1966 Alma 28.65 29.97 23 9 75 73 1420 Oct 4, 1966 by Inez 28.85 29.91 19 7 68 66 150 Sept 20, 1967 Beulah 27.26 29.80 25 8 105 100 1140 Oct 19, 1968 Gladys 28.85 29.86 21 10 65 65 750 Aug 18, 1969 Camille 26.81 29.77 8 16 118 121 260 Aug 3, 1970 Celia 27.89 29.83 9 14 92 91 10 Sept 12, 1970 Ella 28.55 29.77 21 7 72 70 340 Sept 10, 1971 Fern 28.91 29.77 26 5 59 57 470 Sept 16, 1971 Edith 28.88 29.80 27 15 61 63 940 June 19, 1972 Agnes 28.88 29.83 20 11 63 64 590 Sept 8, 1974 Carmen 27.64 29.91 10 9 101 96 40 Aug 31, 1975 Caroline 28.44 29.88 10 5 80 76 900 Sept 23, 1975 Eloise 28.20 29.97 18 22 87 89 10 ISept 2, 1977 Anita 27.35 29.88 12 10 106 102 See notes preceding table 4.1. Table 4.4.--U.S. east coast hurricanes (1900-78) with central pressure < 29.00 in. (98.2 kPa) listed chronoZogicaZZy (English units). 0 Approximate coastal VX V reference pointt Date (GMT)* Name P(in.) p(nmi) R(n.mi.) T(kt) (kt) (kt) (n. mi.) Pwtn mit 1500 Sept 12, 1903 28.84 30.00 43 8 67 66 1545 June 17, 1906 ex 28.91 29.91 26 12 65 65 2000 Sept 17, 1906 28.98 30.06 44 16 63 66 1475 Oct 18, 1906 ex 28.84 29.83 35 6 63 61 1400 Oct 11, 1909 by 28.26 29.80 22 10 81 79 1870 Aug 28, 1911 28.92 30.00 27 8 66 65 2115 Sept 3, 1913 28.81 30.12 38 16 71 72 1350 Sept 10, 1919 by 27.44 29.88 15 8 104 99 1675 Oct 26, 1921ex 28.91 29.88 MSG 10 MSG MSG 2180 Aug 26, 1924 by 28.70 29.94 34 22 69 73 2710 �Aug 26, 1924 by 28.70 29.94 66 29 62 68 2115 Dec 2, 1925 28.95 30.09 54 14 64 65 1605 July 28, 1926 28.34 30.00 14 8 85 82 1460 Sept 18, 1926 27.59 29.94 24 17 101 100 1430 Oct 21, 1926 by 27.52 29.77 21 16 99 98 1505 Sept 17, 1928 27.62 29.88 28 13 98 96 1425 Sept 28, 1929 28.00 29.80 28 10 87 85 2255 Aug 23, 1933 28.63 29.94 36 18 71 73 1530 Sept 4, 1933 27.98 29.94 MSG 11 MSG MSG 2160 Sept 16, 1933 28.25 30.03 40 9 83 81 1410 Sept 3, 1935 26.35 29.94 6 9 131 130 1460 Nov 4, 1935 28.73 29.97 10 12 74 74 2230 Sept 18, 1936 by 28.52 30.12 34 16 79 80 2595 Sept 21, 1938 27.75 29.97 50 47 90 98 1885 Aug 11, 1940 28.78 30.06 27 9 72 70 2180 Sept 14, 1944 27.88 29.86 17 23 92 93 2630 �Sept 15, 1944 28,31 29.91 36 30 77 82 See notes preceding table 4.1. TabZe 4.4.--U.S. east coast hurricanes (English units), continued. Approximate coastal reference pointt Date (GMT)* Name pO(in.)T p(in.) R(n.mi.) T(kt) (kt) (n.mi.) P ) 1440 Sept 15, 1945 28.09 29.94 24 10 89 87 1475 Sept 17, 1947 27.76 29.97 34 10 97 93 1840 Oct 15, 1947 28.59 29.91 13 17 75 77 1535 Sept 22, 1948.ex 28.41 29.74 16 11 76 75 1435 Oct 5, 1948 ex 28.85 29.83 31 13 63 64 2180 Aug 24, 1949 by 28.86 30.06 24 22 70 74 1505 Aug 27, 1949 28.16 29.97 23 14 88 87 1460 Oct 18, 1950 King 28.20 29.94 6 6 88 84 2190 Aug 31, 1954 Carol 28.35 29.86 MSG 10 MSG MSG 2600 �Aug 31, 1954 Carol 28.38 30.06 22 33 82 87 2190 Sept 10, 1954by Edna 27.85 29.86 MSG 20 MSG MSG 2730 �Sept 11, 1954 Edna 27.97 29.83 18 40 87 93 2030 Oct 15, 1954 Hazel 27.66 29.86 21 26 96 98 2115 Aug 12, 1955 Connie 28.40 29.86 45 7 74 71 2115 Sept 19, 1955 Ione 28.35 30.00 42 9 80 78 2170 Aug 28, 1958by Daisy 28.26 29.97 25 17 84 84 2720 �Aug 29, 1958 by Daisy 28.91 29.94 50 21 58 63 2140 Sept 27, 1958by Helene 27.52 29.88 21 14 100 98 1900 Sept 29, 1959 Gracie 28.08 30.00 10 12 91 89 1400 Sept 10, 1960 Donna 27.45 29.88 20 9 103 99 2110 �Sept 12, 1960 Donna 28.29 29.88 34 26 80 83 2600 �Sept 12, 1960 Donna 28.38 29.83 48 32 71 77 1455 Aug 27, 1964 Cleo 28.57 29.88 7 9 76 74 1715 Sept 10, 1964 Dora 28.52 29.91 20 7 77 74 1420 Sept 8, 1965 Betsy 28.11 29.91 22 11 88 86 2260 Sept 17, 1967 Doria 28.97 30.06 20 9 66 65 3065 Sept 10, 1969 Gerda 28.91 29.86 MSG 40 MSG MSG 2170 %Aug 9, 1976 Belle 28.32 29.97 8 21 85 87 2550 %Aug 10, 1976 Belle 28.79 30.09 30 21 70 73 See notes preceding table 4.1. 92 : NOTES FOR TABLES 4.5 AND 4.6 p : central pressure R radius of maximum winds estimated at or near time of Po T forward speed based on a 6-hr average encompassing the time of Po 4 : track direction from which the hurricane moves measured clockwise from nortn at or near the time of po MSG : missing ..... [~~~~~-�~ 93 Table 4.5.--Western North Pacific typhoons (1960-74) with central pressure < 29. 10 in. (98.5 kPa) listed chronoZogicalZZy (metric units). Track Name Month Date Year Time Lat. Long. direction P R T (GMT) (�N) (0E) (C) (kPa) (km) (km/hr) Mary June 8 1960 1800 22.5 114.0 2000 97.5 MSG 9 Olive June 25 1960 0019 13.3 127.8 105� 95.0 6 22 Polly July 22 1960 0926 23.7 127.2 155� 95.0 20 6 Trix Aug. 6 1960 2050 23.4 129.8 125� 91.8 11 33 Virginia Aug. 10 1960 0800 31.4 136.3 1400 97.1 41 37 Bess Aug. 19 1960 2155 32.4 139.1 185� 98.0 17 15 Carmen Aug. 18 1960 2215 23.9 127.8 290� 97.0 93 9 Della Aug. 28 1960 0330 29.1 133.3 1550 96.8 46 13 Elaine Aug. 22 1960 0515 21.7 121.3 2150 97.6 11 19 Faye Aug. 30 1960 0825 31.8 141.0 195� 97.9 24 35 Kit Oct. 6 1960 0400 12.8 124.6 095� 96.6 20 13 Nina Oct. 26 1960 2300 32.9 142.7 2200 96.0 57 63 Lola Oct. 12 1960 0030 15.4 125.2 0800 97.8 35 7 Phyllis Dec. 18 1960 0330 17.2 124.3 1800 96.2 57 6 Alice May 17 1961 2230 17.2 114.0 1500 92.5 35 13 Betty May 25 1961 0315 17.8 124.0 1350 94.6 35 22 Elsie July 13 1961 0330 21.5 122.1 110� 97.4 41 7 Helen July 29 1961 0900 25.3 131.0 1600 97.1 24 15 June Aug. 6 1961 0845 22.0 121.8 1150 96.1 30 11 Kathy Aug. 16 1961 2130 30.8 133.8 140� 98.0 24 20 Lorna Aug. 23 1961 2215 19.4 124.2 130� 94.7 41 17 Nancy Sept. i3 1961 2200 22.7 129.4 1600 90.2 46 26 Pamela Sept. 11 1961 0700 23.7 125.7 0900 91.4 7 32 Tiida Oct. 1 1961 2210 25.3 130.7 1000 93.5 24 22 Violet Oct.. 8 1961 2145 27.2 136.7 1800 93.0 11 28 Ellen Dec. 9 1961 0300 14.2 124.2 1400 94.5 43 11 Hope May 20 1962 1006 20.7 127.6 2300 97.9 9 30 Kate July 22 1962 0333 21.1 120.6 2200 96.4 15 20 Louise July 26 1962 0340 31.0 136.5 1400 97.0 35 13 Nora July 30 1962 2200 23.3 127.8 1400 96.8 30 19 Opel Aug. 5 1962 0340 22.0 123.1 1450 91.0 20 26 Patsy Aug. 8 1962 2220 14.1 117.4 110� 98.0 17 30 Ruth Aug. 19 1962 0315 32.4 130.7 1850 95.4 17 6 Sarah Aug. 20 1962 1000 30.1 127.3 2400 97.8 30 13 Thelma Aug. 25 1962 0790 31.4 136.6 1800 94.7 19 20 Wanda Aug. 31 1962 0930 20.9 117.4 1100 94.9 6 22 Amy Sept. 3 1962 2150 20.6 125.5 1350 94.1 26 19 Dinah Oct. 1 1962 2221 20.7 126.1 0950 95.3 46 28 Gilda Oct. 27 1962 0040 18.0 125.6 1800 95.6 43 9 Jean Nov. 10 1962 0515 15.4 111.1 0950 96.0 24 4 Karen Nov. 15 1962 2225 27.0 132.0 2300 94.8 46 45 Lucy Nov. 28 1962 2200 10.3 114.8 0800 97.4 35 24 Shirley June 17 1963 0945 22.4 127.0 1500 96.2 35 20 Trix June 30 1963 0444 21.5 116.7 1800 98.1 17 17 Wendy July 15 1963 0400 20.9 125.7 1250 92.8 11 22 Bess July 7 1963 2202 28.7 133.2 1650 95.7 57 9 Carmen Aug. 12 1963 2145 13.4 124.7 130� 89.8 30 19 Della Aug. 26 1963 2200 30.4 132.1 2100 96.9 15 30 Faye Sept. 4 1963 0347 19.0 125.7 115" 97.6 30 30 Gloria Sept. 9 1963 2206 22.7 125.8 1250 91.2 43 13 Winnie June 29 1964 1020 14.5 122.6 0850 96.8 41 26 Betty July 5 1964 0400 26.8 123.7 1500 95.8 24 13 Flossie July 28 1964 2200 34.8 123.1 1950 97.4 24 24 Helen Aug. 1 1964 0400 29.6 131.6 1250 96.7 35 24 Ida Aug. 6 1964 0352 16.4 125.5 1100 92.7 46 24 Kathy Aug. 20 1964 2225 27.4 130.3 1600 94.5 15 4 Marie Aug. 17 1964 1000 24.7 134.3 160� 98.1 39 13 Ruby Sept. 4 1964 1000 20.7 117.8 125� 96.3 20 22 Sally Sept. 8 1964 1030 18.2 124.1 1000 89.4 15 24 Tilda Sept 20 1964 1015 18.6 112.4 060� 95.2 15 11 Wilda Sept 23 1964 0355 26.5 131.2 1400 93.5 44 15 Clara Oct 6 1964 0930 17.3 114.3 095� 97.9 24 22 Dot Oct. 12 1964 0300 20.2 115.2 1550 97.6 93 11 See notes preceding table 4.5. 94 Table 4.5.--Western North Pacific typhoons (metric units), continued. Name Month Date Year Time Lat. Long, Track direction R T Po (GMT) (�N) (�E) (e) (kPa) (km) (km/hr) Louise Nov. 18 1964 0300 8.6 129.8 090� 91.4 15 22 Opal Dec. 11 1964 2200 9.1 134.1 130~ 90.3 9 26 Amy May 26 1965 0900 25.7 132.1 220� 97.6 24 54 Dinah June 17 1965 0300 17.5 123.8 130� 93.2 9 19 Freda July 12 1965 2120 16.3 124.4 120� 92;2 11 32 Harriet July 25 1965 0910 21.5 125.2 110~ 97~3 24 32 Jean Aug. 4 1965 0300 25.7 126.8 175~ 94.0 35 13 Lucy Aug. 21 1965 0230 31.3 137.6 125� 95.3 41 11 Mary Aug. 17 1965 0310 21.2 129.0 125� 93~6 24 20 Rose Sept. 4 1965 1012 20.2 114.5 090� 96.8 20 20 Shirley Sept. 8 1965 2100 26.3 131.7 165� 93.6 t7 17 Trix Sept. 15 1965 0200 22.9 128.7 165� 93.0 70 6 Faye Nov. 23 1965 2142 17.9 127.1 170� 92.5 24 22 Irma May 17 1966 0300 12.4 122.2 ~120� 97.1 11 13 Judy May 29 1966 0914 20.9 117.1 245� 97.0 24 11 Kit June 26 1966 2110 24.3 132.3 205� 91.2 9 30 Tess Aug. 16 1966 0230 26.7 122.9 090� 97.4 11 32 Viola Aug. 21 1966 0325 29.1 146.2 140� 97.8 24 30 Alice Sept. 2 1966 0205 26.1 125.9 100� 93.8 24 20 Cora Sept. 4 1966 2200 24.6 125.2 175� 91.7 24 6 glsie Sept. 15 1966 0330 21.4- 117.8 225~ 94.3 20 9 Ida Sept. 24 1966 0207 27.5 138.1 170� 96.1 57 56 Pamela Dec. 26 1966 0830 11 126 110� 96.7 17 19 Violet April 7 1967 0900 16.1 125.8 110� 94.7 24 19 Anita June 28 1967 1600 19.2 121.8 120� 96.7 24 19 Clara July 10 1967 2103 23.5 123.2 110� 96.0 17 15 Marge Aug. 27 1967 0400 18.0 124.5 055v 93.7 i7 24 Nora Aug. 28 1967 2035 22.9 125.6 i10� 98.1 24 26 Opal Sept. 13 1967 1530 31.6 140.0 215" 96.3 6 19 Carla Oct. 16 1967 0400 16.3 125.6 120� 93.5 24 24 Oinah Oct. 24 1967 0257 22~9 129.1 085� 95.0 30 7 Emma Nov. 2 1967 2200 12.0 127.7 110" 90.8 17 26 Freda Nov. 9 1967 0940 11.8 111.7 105� 97.1 24 24 Gilda Nov. 15 1967 0300 17.0 131.8 110~ 91.9 46 28 I-ucy June 30 1968 1430 20.7 129.4 150" 96.8 17 13 Mary June 27 1968 2059 31.0 135.2 i55" 96.9 11 15 Shirley Aug. 21 1968 0558 21.6 114.7 145� 96.3 57 17 Wendy Sept. 2 1968 0234 22.7 133.3 095� 93.5 35 35 Della Sept. 21 1968 2359 22.8 125.5 160� ' 93.0 46 17 Carmen Sept. 22 1968 2100 34.8 144.9 200� 97.2 57 19 Elaine Sept. 27 1968 0300 16.8 124.7 120� 90.8 6 15 Mamie Nov. 20 1968 0300 9.6 119.4 090� 97.2 11 22 Nina Nov. 26 1968 0820 9.3 112.8 110� 95.9 30 24 Ora Nov. 28 1968 0815 15.2 126.4 085� 94.9 24 24 Susan April 21 1969 2130 8.2 129.0 115� 94.3 11 il Tess July 10 1969 0000 14.5 113.8 095� 96.9 24 28 Viola July 26 1969 2100 19.7 122.4 100�' 89.1 30 24 Betty Aug. 8 1969 0200 25.4 122.0 130� 96.2 17 22 Cora Aug. 19 1969 1135 25.4 127.4 175� 93.4 17 15 Elsie Sept. 24 1969 2150 22.1 132.4 ~ 1t0� ~ 91.8 33 26 Nancy Feb. 24 1970 0900 11.2 128.6 115~ 94.9 30 30 Olga July 2 1970 0015 21.6 125.6 i50~ 91.5 7 17 Wilda Aug. 13 1970 0300 27.5 129.0 185� 94.1 17 15 Anita Aug. 20 1970 0300 28.0 135.6 - 160� ~ 92.4 24 28 Billie Aug. 27 1970 2100 27.8 129.9 125� 94.6 41 16 Clara Aug. 28 1970 2100 35.6 142.2 220� 97.3 41 9 Georgia Sept. 10 1970 0600 15.2 125.2 115� 92.0 15 19 Iris Oct. 6 1970 0902 19.9 113.9 220Q 94.4 26 6 Joan Oct. 12 1970 2100 12.9 125.2 120� 90.1 30 20 Kate Oct. 17 1970 0300 4.4 130.3 090� 93.8 11~ 15 Patsy Nov. 18 1970 0957 t4.2 126.6 090� 91.6 20 28 See notes preceding table 4.5. 95 Table 4.5.--Western North Pacific typhoons (metric units), continued. Name Month Date Year Time Lat. Long. Track direction Po R T (GMT) (�N) (�E) (9) (kPa) (km) (km/hr) Wanda May 2 1971 0404 15.8 108.8 1700 97.6 44 15 Dinah May 25 1971 2200 12.4 125.5 100� 92.0 7 26 Freda June 15 1971 1603 17.6 121.3 110� 97.3 11 19 Gilda June 27 1971 0100 17.6 113.1 1200 97.5 24 24 Harriet July 5 1971 1310 16.2 110.8 1000 92.1 9 24 Jean July 16 1971 1900 16.6 111.8 1300 97.5 9 20 Lucy July 19 1971 1000 18.6 125.0 1150 92.0 11 15 Nadine July 24 1971 2215 20.9 124.9 1200 91.9 30 22 Olive Aug. 4 1971 2130 31.7 130.1 1800 93.5 15 26 Rose Aug. 15 1971 1500 19.3 114.8 135� 95.9 30 11 Trix Aug. 29 1971 0002 29.5 130.1 1800 91.4 11 11 Virginia Sept. 7 1971 0715 32.9 138.6 2100 97.6 30 30 Agnes Sept. 18 1971 0355 23.6 123.1 1200 97.4 46 17 Bess Sept. 21 1971 0955 22.8 127.6 105� 92.1 24 20 Della Sept. 28 1971 1810 19.1 113.3 0900 98.1 30 22 Elaine Oct. 6 1971 2330 16.4 115.6 1600 95.7 24 13 Faye Oct. 11 1971 0200 15.3 118.4 3200 98.4 30 13 Hester Oct. 22 1971 1900 14.3 110.2 1150 96.7 30 24 Irma Nov. 13 1971 1200 21.7 127.0 1750 93.8 6 15 Kit Jan.. 7 1972 0300 11.8 127.6 095� 93.3 6 22 Ora June 24 1972 0350 11.4 126.5 1100 98.1 17 24 Phyllis July 14 1972 1030 29.4 138.6 1350 98.0 30 22 Rita July 24 1972 0345 25.9 127.1 215� 95.4 57 13 Susan July 8 1972 0927 18.8 118.0 1800 98.5 9 17 Tess July 23 1972 0000 31.1 134.3 1250 97.0 46 30 Alice Aug. 6 1972 1705 32.8 140.9 160� 97.8 57 20 Betty Aug. 16 1972 1630 25.7 122.3 1250 93.7 15 19 Cora Aug. 27 1972 0632 18.5 114.0 115� 97.6 24 7 Elsie Sept. 3 1972 0600 15.5 109.9 0850 97.4 32 7 Flossie Sept. 14 1972 1026 15.1 112.0 0850 97.5 24 13 Helen Sept. 16 1972 0449 31.4 134.5 205� 95.9 46 54 Ida Sept. 24 1972 0030 32.3 142.7 215� 94.9 24 45 Pamela Nov. 7 1972 0645 16.0 112.5 1250 94.2 26 24 Therese Dec. 7 1972 1200 13.3 115.9 1100 94.4 35 11 Anita July 8 1973 1010 18.5 106.2 1050 98.0 35 15 Billie July 16 1973 1600 26.4 125.6 1800 92.9 15 15 Georgia Aug. 10 1973 0645 19.5 113.3 0850 97.6 17 11 Iris Aug. 15 1973 2112 30.0 126.6 130.0 97.2 57 17 Louise Sept 5 1973 1000 19..9 114.7 095� 97.4 15 17 Marge Sept. 13 1973 0900 18.9 113.1 0950 96.4 15 22 Nora Oct. 6 1973 1020 14.9 125.9 0900 89.4 15 17 Opal Oct. 5 1973 2340 13.1 112.0 175� 96.8 17 7 Ruth Oct. 15 1973 0947 15.1 122.9 120� 96.1 30 22 Dinah June 10 1974 0235 15.6 122.2 1150, 97.4 24 20 Gilda July 5 1974 0840 28.9 126.6 .1850 95.5 35 17 Ivy July 19 1974 2032 15.3 123.0 105� 94.6 9 28 Mary Aug. 24 1974 2141 26.6 132.1 2400 96.4 30 26 Polly Aug. 31 1974 2055 31.4 133.9 1500 95.6 35 13 Shirley Sept. 7 1974 0856 28.6 127.6 180� 97.2 46 7 Bess Oct. 10 1974 0907 17.2 125.2 1000 98.0 24 20 Della Oct. 25 1974 i 0456 18.2 114.4 100� 95.8 17 26 Elaine Oct. 27 1974 1430 17.3 123.7 0950 95.3 41 26 Gloria Nov. 6 1974 0916 17.0 126.2 105� 93.1 24 26 See notes preceding table 4.5. 96 Table 4.6.--Western North Pacific typhoons (1960-74) with central pressure < 29.10 in. (98.5 kPa) Zisted chronoZogicaZlly (EngZish units). Track Name Month Date Year Time Lat. Long. direction PO R T (GMT) (�N) (�E) (0) (in.) (n.mi.) (kt) Mary June 8 1960 1800 22.5 114.0 2000 28.79 MSG 5 Olive June 25 1960 0015 13.3 127.8 105� 28.05 3 12 Polly July 22 1960 0926 23.7 127.2 1550 28.05 11 3 Trix Aug. 6 1960 2050 23.4 129.8 1250 27.11 6 18 Virginia Aug. 10 1960 0800 31.4 133.6 140� 28.67 22 20 Bess Aug. 19 1960 2155 32.4 139.1 1850 28.94 9 8 Carmen Aug. 18 1960 2215 23.9 127.8 2900 28.64 50 5 Della Aug. 28 1960 0330 29.1 133.3 155� 28.59 25 7 Elaine Aug. 22 1960 0515 21.7 121.3 2150 28.82 6 10 Faye Aug. 30 1960 0825 31.8 141.0 1950 28.91 13 19 Kit Oct. 6 1960 0400 12.8 124.6 095� 28.52 11 7 Nina Oct. 26 1960 2300 32.9 142.7 2200 28.35 31 34 Lola Oct. 12 1960 0030 15.4 129.2 080� 28.89 19 4 Phyllis Dec. 18 1960 0330 17.2 124.3 180� 28.41 31 3 Alice May 17 1961 2230 17.2 114.0 150� 27.32 19 7 Betty May 25 1961 0315 17.8 124.0 1350 27.94 19 12 Elsie July 13 1961 0330 21.5 122.1 1100 28.76 22 4 Helen July 29 1961 0900 25.0 131.0 1600 28.67 13 8 June Aug. 6 1961 0845 22.0 121.8 1150 28.38 16 10 Katy Aug. 16 1961 2130 30.8 133.8 1400 28'.94 13 11 Lorna Aug. 23 1961 2215 19.4 124.2 1300 27.97 22 9 Nancy Sept. 13 1961 2200 22.7 129.4 1600 26.64 25 14 Pamela Sept. 11 1961 0700 23.7 125.7 0900 26.99 4 17 Tilda Oct. 2 1961 2210 25.3 130.7 1000 27.61 13 12 Violet Oct. 7 1961 2145 27.2 136.7 180� 27.46 6 15 Ellen Dec. 9 1961 0300 14.2 124.2 1400 27.91 23 ' 6 Hope May 20 1962 1006 20.7 127.6 2300 28.91 5 16 Kate July 22 1962 0333 21.1 120.6 2200 28.47 8 11 Louise July 26 1962 0340 31.0 136.5 1400 28.64 19 7 Nora July 30 1962 2200 23.3 127.8 1400 28.59 16 10 Opel Aug. 5 1962 0340 22.0 123.1 1450 26.87 11 14 Patsy Aug. 8 1962 2220 14.1 117.4 1100 28.94 9 16 Ruth Aug. 19 1962 0314 32.4 140.7 1850 28.17 9 3 Sarah Aug. 20 1962 1000 30.1 127.3 240� 28.88 16 7 Thelma Aug. 25 1962 0700 31.4 136.6 180� 28.97 10 11 Wanda Aug. 21 1962 0930 20.9 117.4 1100 28.02 3 12 Amy Sept. 3 1962 2150 20.6 125.5 1350 27.79 14 10 Dinah Oct. 1 1962 2221 20.7 126.1 0950 28.14 25 15 Gilda Oct. 27 1962 0040 18.Q 125.6 1800 28.23 23 5 Jean Nov. 10 1962 0515 15.4 111.1 0950 28.35 13 2 Karen Nov. 15 1962 2225 27.0 132.0 2300 27.99 25 24 Lucy Nov. 28 1962 2200 10.3 114.8 0800. 28.76 19 13 Shirley June 17 1963 0945 22.4 127.0 1500 28.41 19 11 Trix June 30 1963 0444 21.5 116.7 1800 28.97 9 9 Wendy July 15 1963 0400 20.9 125.7 125� 27.40 6 12 Bess July 7 1963 2202* 28.7 133.2 165� 28.26 31 5 Carmen Aug. 12 1963 2145 13.4 124.7 1300 26.52 16 10 Della Aug. 26 1963 2200 30.4 132.1 210� 28.62 8 7 Faye Sept. 4 1963 0347 19.0 125.7 115� 28.82 16 16 Gloria Sept. 9 1963 2206 22.7 125.8 1250;�, 26.93 23 7 Winnie June 29 1964 1020 14.5 122.6 0850 28.59 22 14 Betty July 5 1964 0400 26.8 123.7 1500 28.29 13 7 Flossie July 28 1964 2200 34.8 123.1 1950 28.76 13 13 Helen Aug. 1 1964 0400 29.6 131.6 1250 28.56 19 13 Ida Aug. 6 1964 0352 16.4 125.5 110� 27.37 25 13 Kathy Aug. 20 1964 2225 27.4 130.3 1600 27.91 8 2 Marie Aug. 17 1964 1000 24.7 134.3 1600 28.97 21 7 Ruby Sept. 4 1964 1000 20.7 117.8 1250 28.44 11 12 Sally Sept. 8 1964 1030 18.2 124.1 1000 26.40 8 13 Tilda Sept. 20 1964 1015 18.6 112.4 0600 28.11 8 6 Wilda Sept. 23 1964 0355 26.5 131.2 1400 27.61 24 8 Clara Oct. 6 1964 0930 17.3 114.3 095� 28.91 13 12 Dot Oct. 12 1964 0300 20.2 115.2 155� 28.82 50 6 See notes preceding table 4.5 97 Table 4.6.--Western North Pacific typhoons (English Units), continued. Track Name Month Date Year Time Lat. Long. Direction R Po T (GMT) (�N) (UE) (0) (in.) (n.mi.) (kt) Louise Nov. 18 1964 0300 8.6 129.8 090� 26.99 8 12 Opal Dec. 11 1964 2200 9.1 134.1 130� 26.67 5 14 Amy May 26 1965 0900 25.7 132.1 220� 28.82 13 29 Dinah June 17 1965 0300 17.5 123.8 130� 27.52 5 10 Freda July 12 1965 2120 16.3 124.4 120� 27.23 6 17 Harriet July 25 1965 0910 21.5 125.2 110� 28.73 13 17 Jean Aug. 4 1965 0330 25.7 126.8 175� 27.76 19 7 Lucy Aug. 21 1965 0230 31.3 137.6 125� 28.14 22 6 Ma~' Aug. 17 1965 0310 21.2 129.0 125� 27.64 13 11 Hose Sept. 4 1965 1012 20.2 114.5 090� 28.59 11 11 Shirley Sept. 8 1965 2100 26.3 131.7 165� 27.64 9 9 Trix Sept. 15 1965 0200 22.9 128.7 165� 27.46 38 3 Faye Nov. 23 1965 2142 17.9 127.1 170� 27.32 13 12 Irma May 17 1966 0300 12.4 122.2 120� 28.67 6 7 Judy May 29 1966 0915 20.9 117.1 245� 28.64 13 6 Kit June 26 1966 2110 24.3 132.3 205� 26.93 5 16 Tess Aug. 16 1966 0230 26.7 122.9 090� 28.76 6 17 Viola Aug. 21 1966 0325 29.1 146.2 140� 28.88 13 16 Alice Sept. 2 1966 0205 26.1 125.9 100� 27.70 13 11 Cora Sept. 4 1966 2200 24.6 125.2 175� 27.08 13 3 Elsie Sept. 15 1966 0330 21.4 117.8 225� 27.85 11 5 Ida Sept. 24 1966 0207 27.5 138.1 170� 28.38 31 30 Pamela. Dec. 26 1966 0830 11.6 126.6 110� 28.56 9 10 Violet April 7 1967 0900 16.1 125.8 110� 27.97 13 10 Anita June 28 1967 1600 19.2 121.8 120� 28.56 13 10 Clara July 10 1967 2103 23.5 123.2 110� 28.35 9 8 Marge Aug. 27 1967 0400 18.0 124.5 055� 27.67 9 13 Nora Aug. 28 1967 2035 22.9 125.6 110� 28.97 13 14 Opai Sept. 13 1967 1530 31.6 140.0 215� 28.44 3 10 Carla Oct. 16 1967 0400 16.3 125.6 120� 27.61 13 13 Dinah Oct. 24 1967 0257 22.9 129.1 085� 28.05 16 4 Emma Nov. 2 1967 2200 12.0 127.7 110� 26.81 9 14 Freda Nov. 9 1967 0940 11.8 111.7 105� 28.67 13 13 Gilda Nov. 15 1967 0300 17.0 131.8 110a 27.14 25 15 Lucy June 30 1968 1430 20.7 129.4 150� 28.59 9 7 Mary June 27 1968 2059 31.0 135.2 155� 28.62 6 8 Shirley Aug. 21 1968 0558 21.6 114.7 145� 28.44 31 9 Wemdy Sept. 2 1968 0234 22.7 1~3.3 095� 27.61 19 19 Della Sept. 21 1968 2359 22.8 125.5 160� 27.46 25 9 Carmen Sept. 22 1968 2100 34.8 144.9 200� 28.70 31 10 Elaine Sept. 27 1968 0300 16.8 124.7 120� 26.81 3 8 Mamie Nov. 20 1968 0300 9.6 119.4 090� 28.70 6 12 Nina Nov. 26 1968 0820 9.3 112.8 110� 28.32 16 13 Ora Nov. 28 1968 0815 15.2 ~26.4 085� 28.02 13 13 Susan April 21 1969 2130 8.2 129.0 115� 27.85 6 6 Tess July 10 1969 0000 14.5 113.8 095� 28.62 13 15 Viola July 26 1969 2100 19.7 122.4 100� 26.31 16 13 Betty Aug. 8 1969 0200 25.4 122.0 130� 28.41 9 12 Cora Aug. 19 1969 1135 25.4 127.4 175� 27.58 9 8 Elsie Sept. 24 1969 2150 22.1 132.4 110� 27.11 18 14 Nancy Feb. 24 1970 0900 11.2 128.6 115� 28.02 16 16 Ol�a July 2 1970 0015 21.0 125.6 150� 27.02 4 9 Wilda Aug. 13 1970 0300 27.5 129.0 185� 27.79 9 8 Anita Aug. 20 1970 0300 28.0 135.6 160� 27.29 13 15 Billie Aug. 27 1970 2100 27.8 129.9 125� 27.94 22 8 Clara Aug. 28 1970 2100 35.6 142.2 220� 28.73 22 5 Georgia Sept. 10 1970 0.600 15.2 125.2 115� 27.17 8 10 Iris Oct. 6 1970 0902 19.9 113.9 220� 27.88 14 3 Joan Oct. 12 1970 2100 12.9 129.2 120" 26.61 16 11 Kate Oct. 17 1970 0300 4.4 130.3 090� 27.70 6 8 Patsy Nov. 18 1970 0957 14.2 126.6 090� 27.05 11 15 Wanda May 2 1971 0404 15.8 108.8 170� 28.82 24 8 Dina May 25 1971 2200 12.4 125.5 100� 27.17 4 14 See notes preeeeding table 4.5 98 Table 4.6.--Western North Pacific typhoons (English units), continued. Track Name Month Date Year Time Lat. Long. direction po R T (GMT) (�N) (VE) (9) (in.) (n.mi.) (kt) Freda June 15 1971 1603 17.6 121.3 110� 28.73 6 10 Gilda June 27 1971 0100 i7.6 113.1 120� 28.79 13 13 Harriet July 5 1971 1310 16.2 110.8 100� 27.20 5 13 Jean July 16 1971 1900 16.6 111.8 130� 28.79 5 11 Lucy July 19 1971 1000 18.6 125.0 115� 27.17 6 8 Nadine July 24 1971 2215 20.9 124.9 120� 27.14 16 12 Olive Aug. 4 1971 2130 31.7 130.1 180� 27.61 8 14 Rose Aug. 15 1971 1500 19.3 114.8 135� 28.32 16 6 Trix Aug. 29 1971 0002 29.5 130.1 180� 26.99 6 6 Virginia Sept. 7 1971 0715 32.9 138.6 210� 28.82 16 16 Agnes Sept. 18 1971 0355 23.6 123.1 120� 28.76 25 9 Bess Sept. 21 1971 0955 22.8 127.6 105� 27.20 13 11 Della Sept. 28 1971 1810 19.1 113.3 090� 28.97 16 12 Elaine Oct. 6 1971 2330 16.4 115.6 160� 28.26 13 7 Faye Oct. 11 1971 0200 15.0 118.4 320� 29.06 16 7 Hester Oct. 22 1971 1900 14.3 110.2 115� 28.56 16 13 Irma Nov. 13 1971 1200 21.7 127.0 1750 27.70 3 8 Kit Jan. 7 1972 0300 11.8 127.6 095� 27.55 3 12 Ora June 24 1972 0350 11.4 126.5 110� 28.97 9 13 Phyllis July 14 1972 1030 29.4 138.6 135� 28.94 16 12 Rita July 24 1972 0345 25.9 127.1 215� 28.17 31 7 Susan July 8 1972 0927 18.8 118.0 180� 29.09 5 9 Tess July 23 1972 0000 31.1 134.3 125�- 28.64 25 15 Alice Aug. 6 1972 1705 32.8 140.9 160" 28.88 31 11 Betty Aug. 16 1972 1630 25.7 122.3 125� 27.67 8 10 Cora Aug. 27 1972 0632 18.6 114.0 115� 28.82 13 4 Elsie Sept. 3 1972 0600 15.5 109.9 085" 28.76 17 4 Flossie Sept. 14 1972 1026 15.1 112.0 085� 28.79 13 7 Helen Sept. 16 1972 0449 31.4 134.5 205� 28.32 25 29 Ida Sept. 24 1972 0030 32.3 142.7 215� 28.02 13 24 Pamela Nov. 7 1972 0645 16.0 112.5 125� 27.82 14 13 Therese Dec. 7 1972 1200 13.3 115.9 110� 27.88 19 6 Anita July 8 1973 1010 18.5 106.2 105" 28.94 19 8 Billie July 16 1973 1600 26.4 125.6 180� 27.43 8 8 Georgia Aug. 10 1973 0645 19.5 113.3 085� 28.82 9 6 Iris Aug. 15 1973 2112 30.0 126.6 130� 28.70 31 9 Louise Sept. 5 1973 1000 19.9 114.7 0950 28.76 8 9 Marge Sept. 13 1973 0900 18.9 113.1 095� 28.47 8 12 Nora Oct. 6 1973 1020 14.9 125.9 090� 26.40 8 9 Opal Oct. 5 1973 2340 13.1 112.0 175� 28.59 9 4 Ruth Oct. 15 1973 0947 15.1 122.9 120� 28.38 16 12 Dinah June 10 1974 0235 15.6 122.2 115� 28.76 13 11 Gilda July 5 1974 0840 28.9 126.6 185�' 28.20 19 9 Ivy July 19 1974 2032 15.3 123.0 105�. 27.94 5 15 Mary Aug. 24 1974 2141 26.3 132.1 2400 28.47 16 14 Polly Aug. 31 1974 2055 31.4 133.9 150� 28.23 19 7 Shirley Sept. 7 1974 0856 28.6 127.6 180� 28.70 25 4 Bess Oct. 10 1974 0907 17.2 125.2 100� 28.94 13 11 Della Oct. 25 1974 0456 18.2 114.4 100� 28.29 9 14 Elaine Oct. 27 1974 1430 17.3 123.7 095� 28.85 22 14 Gloria Nov. 6 1974 0916 17.0 125.2 105� 27.49 13 14 Irma Nov. 27 1974 0245 15.7 126.2 090� 27.76 19 11 See notes preceding table 4.5 99 5. METEOROLOGICAL AND OTHER PARAMETERS AND THEIR INTERRELATIONS 5.1 INTRODUCTION This chapter focuses on the interrelations of parameters which influence the strength and regional variation of hurricane wind fields. This is preceded by brief definitions of the meteorological parameters used in this study: peripheral pressure (Pw), central pressure (p0), radius of maximum winds (R), forward speed (T), track direction (0), and wind inflow angle (p). Two other parameters, latitude (i) and longitude (A), were also considered. To what extent parameters important to extreme hurricane wind fields are interrelated is of interest from two standpoints. One is from a broad aspect, in that a detailed study should show interrelations, even though they may not be sufficient to use in the SPH/PMH criteria. The other is to make use in this study of clear-cut relations shown in the tropical cyclone data. 5.2 DEFINITION OF METEOROLOGICAL PARAMETERS Peripheral pressure (Pw) - the sea-level pressure at the outer limits of the hurricane circulation. Pw in this study is the average pressure for the first anticyclonically turning isobar outward from the storm center. We averaged the pressure north, east, south, and west of the hurricane center. Central pressure (p) - the lowest sea-level pressure in a hurricane. Radius of maximum winds (R) - the radial distance from the hurricane center to the band of strongest winds within the hurricane wall cloud. Forward speed (T) - the rate of translation of the hurricane center from one geographical point to another. Track direction (0) - the path of forward movement along which the hurri- cane is coming measured in degrees clockwise from the north. Wind inflow angle (~) - the angle between true wind direction and a tangent to a circle concentric with the hurricane center. 100 5.3 INTERRELATIONS BETWEEN PAIRS OF PARAMETERS Interrelations between pairs of parameters were examined using linear correlation analyses. In most cases, these relations are curvilinear. How- ever, from plots of the data we determined that these curvilinear relations closely approximated linear relations. Differences between curvilinear and linear relations are least for more intense cyclones, our primary area of interest. In addition, statistical relations between pairs of parameters cannot be used to estimate SPH and PMH wind fields directly (we would be extrapolating beyond the data). Also, more than two parameters are involved in the development of wind fields. The developed linear relations and graphical plots were considered adequate for general guidance. Interrelations with pw and c were not considered. Pw varies slowly with time. c (a function of the other parameters) is difficult to measure with any precision. 5.3.1 ZERO-ORDER LINEAR CORRELATION COEFFICIENTS Linear correlation studies are based upon the assumption that the distribu- tion of values (x, y) is a two-variable normal distribution. If the assump- tion of normality is satisfied, it is possible to use the observed value of the sample zero-order linear correlation coefficient (r) to test for independence. If the two variables are independent, regression curves take the form of horizontal or vertical straight lines. This implies that the population correlation coefficient (p) is equal to zero. If r (which is an estimate of p ) is near zero, we shall say that we do not have sufficient reason to doubt the independence between x and y. However, if r is far from zero as determined by tests of significance, we shall reject the hypothesis that the two variables are independent (Dixon and Massey, Jr. 1957). Inde- pendence signifies that there is no relation between the variables, meaning that any conclusions drawn regarding one parameter in this report do not necessarily affect another parameter. 101 Table 5.1 summarizes the r's and standard errors of estimate (s yx between pairs of the five parameters (Po, R, T, e and i, A) for tropical cyclone data from each of three regions (east coast, gulf coast, and western North Pacific) and for three combinations of these regions (east and gulf coast, east coast and western North Pacific, and east and gulf coast and Western North Pacific). A storm is included for each region only when values were available for all parameters. Thus, some storms were not used, e.g., the gulf coast storm of September 20, 1909 for which R could not be determined; (see table 4.1). The table also indicates if the r is signi- ficant at the 1% or 5% level. The 5% level gives the values that would occur on the average once in 20 times in random sampling from uncorrelated material. The 1 % level is a more severe test. Four of the r's between the pairs of parameters shown in table 5.1 are >0.50. (The table shows eight but half of these are mirror images of the other half.) These four are significant at the 1% level. All have latitude as one of the pair. The highest r (0.68) is T for east coast hurricanes. The next highest (0.52) is the 9 for typhoons and with R for east coast hurricanes. The last (0.51) is with R for the combined set of east coast hurricanes and typhoons. These interrelations are guidance for establishing SPH and PMH criteria along the east coast (see chapters 9 to 11). 5.3.2 PLOTS OF DATA Trend lines are drawn on all seven figures discussed in this subsection. These lines are drawn through the data by eye and are shown for illustrative purposes. The linear regression lines are not shown because most of the interrelations shown in the seven figures are somewhat curvilinear. r and s t frpm Iable 5.1 are indicated in figures 5.1 to 5.7 for convenience. y-x *For both r and s we are assuming in a gross sense that all relations are y.x linear, For a loose definition of s see section 5.4. tHere again we are assuming in a gross sense that all relations are linear. 102 NOTES FOR TABLES 5.1 AND 5.2 p: central pressure R radius of maximum winds e : track direction T forward speed : latitude (east coast hurricanes and typhoons) X : longitude (gulf coast hurricanes) r linear correlation coefficient r' : multiple correlation coefficient '2 r : reduction of variance (square of the multiple correlation coefficient) s standard error of estimate y.x r sig, r' sig r, r' is significant at the 5 % level /* ; r, r' is significant at the 1 % level */* r, r' is neither significant at the 1% nor 5 % levels / N sample size vs. versus N/A not applicable . .: : r l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-� TabZe 3. 1. --Linear correlation coefficients between pairs of meteorological and other parameters. Independent riable R T X (X) Dependent r SYx r r ax r r ax r r SX r r SYx r Variable Sig Sig Sig Sig sig (.v) EAST COAST HURRICANES N = 49 p in. (kPa) - .39 .49(1.7) */* .02 .53(1.8) -.10 .53(1.8) / .27 .51(1.8) R n~mi. (km) .39 12.2(22.6) - - - .30 12.6(23.4) 1* .32 12.5(23.2) /* .52 11.3(20.9) * 6 deg. .02 55.3 .30 52.9 /* - .35 51.8 1* .35 51.9 1* T kt (km/hr) -.10 9.2(17.0) .32 8.7(16.1) /* .35 8.6(15.9) - - .68 6.7(12.4) *1* 1P deg. .27 5.4 .52 4.8 .35 5.3 1* .68 4.1 * - GULF COAST HURRICANES N = 67 pO in. (kPa) - - .33 .51(1.7) */" .14 .53(1.8) .09 .53(1.8) / -.02 .54(1.8) R n.ii. (km) .33 8.3(15.4) - - - .19 8.7(16.1) / .15 8.7(16.1) - .06 8.8(16.3) 8 deg. .14 50.2 .19 49.8 - - .02 50.7 / -.32 48.0 T kt(km/hr) .09 4.6(8.5) .15 4.6(8.5) .02 4.6(8.5) - - .02 4.6(8.5) X deg. -.02 6.1 -.06 6.1 /-.32 5.8 .02 6.1 - WESTERN NORTH PACIFIC TYPHOONS N = 178 pO in. (kPa) - - .20 .68(2.3) *1* .118 .68(2.3) * -.07 .69(2.3) / .18 .68(2.3) /* R n.mi. (km) .20 8.2(15.2) - - - .22 8.1(15.0) */* -.02 15.4(8.3) .26 8.0(14.8) */* G deg. .18 44.5 /* .22 44.1 1 - - + 0 N/A .52 *1* T kt (ki/hr) -.07 5.0(9.3) -.02 5.0(9.3) / �0 N/A - .10 5.0(9.3) deg. .18 6.4 1* .26 6.3 *1* .52 5.5 *1* .10 6.5 - H 0 Table 5.1.--Linear correlation coefficients between pairs of meteoroZogical and other parameters, 0 continued. Independent ariable \x) pC R 0 T i, A Dependent r s r r r r s r r s r Variable Y-x Y-x Y~x Y.X Y-x Variable sig sig yg sig sig EAST AND GULF COAST HURRICANES N = 116 pO in. (kPa) - - - .34 ;50(1.7) */* .09 .53(1.8) / -.02 .53(1.8) / R n.mi. (km) .34 10.6(19.6) */* - - - .23 11.0(20.4) /* .32 10.7(19.8) */* 0 deg. .09 52.5 / .23 51.3 /* - _ - .20 51.6 /* T kt (km/hr) -.02 7.3(13.5) / .32 6.9(12.8) */* .20 7.1(13.2) /* - - EAST COAST HURRICANES AND WESTERN NORTH PACIFIC TYPHOONS N = 227 p in. (kPa) - _ _ .26 .64(2.2) */* .16 .66(2.2) /* -.03 .66(2.2) / .22 .65(2.2) */* R n.mi. (km) .26 10.7(19.8) */* - - - .30 10.5(19.5 */* .27 10.6(19.6) */* .51 9.5(17.6) */* 9 deg. .16 47.9 /* .30 46.2 */* - - .19 47.6 */* .50 42.1 */* T kt (km/hr) -.03 6.6(12.2) / .27 6.3(11.7) */* .19 6.4(11.9)*/* - - .39 6.0(11.1) */* i deg. .22 7.4 */* .51 6.6 */* .50 6.6 */* .39 7.1 */* - - EAST AND GULF COAST HURRICANES AND WESTERN NORTH PACIFIC TYPHOONS N = 294 po in. (kPa) - - .28 .61(2.1) */* .17 .63(2.1)*/* -.02 .64(2.2) / R n.mi. (km) .28 10.3(19.1) */* - - - .30 10.3(19.1)*/* .24 10.4(19.3) */* 0 deg. .17 49.0 */* .30 47.4 */* - - .15 49.1 /* T kt (km/hr) -.02 6.2(11.5) / .24 6.0(11.1) */* .15 6.1(11.3) /* - - 105 Table 5.2.--Multiple correlation coefficients involving meteoroZogicaZ and other parameterst r' r'sig r'2 Sy'x EAST COAST HURRICANES N = 49 p0 vs. R .39 .15 0.49 in. (1.7 kPa) pO vs. R, T .45 */* .20 0.48 in. (1.6 kPa) pO vs. R, T, i .54 */* .30 0.45 in. (1.5 kPa) R vs. 4 .52 */* .27 11.3 n.mi. (20.4 km) R vs. p, P .58 */* .33 10.8 n.mi. (20.0 km) 0 vs. T .35 .12 51.8� T vs. 4 .68 */* .46 6.8 kt (12.5 km/hr) T vs. 4, po .74 */* .55 6.2 kt (11.5 km/hr) 4 vs. T .68 */* .46 4.1� r vs. T, po .76 .58 3.60 WESTERN NORTH PACIFIC TYPHOONS N = 178 pO vs. R .20 */* .04 0.68 in. (2.3 kPa) pO vs. R, 0 .24 */* .06 0.67 in. (2.3 kPa) R vs. 4 .26 */* .07 8.0 n.mi. (14.9 km) R vs. 4, po .30 */* .09 7.9 n.mi. (14.7 km) G vs. 4 .52 .27 38.5� T vs. 4 .10 / .01 5.0 kt (9.3 km/hr) T vs. 4, po .13 / .02 5.0 kt (9.3 km/hr) 4 vs. 0 .52 */* .27 5.60 tOnly ordinary zero-order correlation coefficients are listed where addi- tional combinations of parameters did not yield significant increases in r'. 106 5.3.2.1 INTERRELATIONS WITH CENTRAL PRESSURE (P0). Figure 5.1 is a composite plot of pO and R data for all hurricanes (tables 4.1-4.4) and typhoons (tables 4.5-4.6). The three data regions (east coast, gulf coast and western North Pacific) are distinguished by different plotting symbols. The conclusion from this plot is that R tends to be smaller and has a smaller range for lower po. This conclusion is supported by Myers (1954), Colon (1963), Sheets (1967), Shea and Gray (1972) and others. We also observe that the typhoon sample has nearly all R's <31 n.mi. (58 km) whereas quite a few hurricanes have R > 31 n.mi. Part of this may be explained by the hurricane sample extending into more northerly latitudes, where R's are generally larger, than the typhoon sample selected (see sec. 5.3.2.2). A plot of p vs 0 for all three regions (fig. 5.2) indicates that for the (kPal (kPal 90 92 94 96 98 90.0 92p 94.0 96. 0 9 .0 100.0 I I ' I j l360 I I I II I I - *EAST COAST o70- EAST COAST Y XGULF COAST �EAST COAST 1 32o- 0 oWESTERN 65- xGULF COAST 120 NORTH PACIFIC oWESTERN r = 0.17 0o- NORTH PACIFIC - Sy.x =49.0 DEG O r = 0.2 280- e I; _ Sy'x=10.3 N MI (19.1KMI X - .'- I5-O O _ 2 _ * - E - 0 � - z 50 - O - 240- O 0 - 0 0 4K k( 2)f1 Z 45- _ a -0 a 00 E: - aE 200- XK x 40 --- 0 o- x 00 - :- a 0 C DX X 00 ' S - 0 0 < 3-5 a � x a'> Zo* XI * * -60s: 160- o0 Y 8x. X- X oo-6 & AD 0 1 x 030- o X0 O X o'o 5 25- 0 oxO' 00 do - <120 O 00 cii o- 20- E r xo� � DO ��80 D O O o a D 9 00 aD ' _0 0.- o. - 0 * 20- 1o o5oo ooo5 c - oxo~80- o oo - �5 00 0� x _ 20 0 � x - 0 c)o . 000 0 00 * o -D o0- 027 28 29 0 27 28 29 CENTRAL PRESSURE (IN.I CENTRAL PRESSURE IINJ Figure 5.1.--Central pressure (po) vs. Figure 5.2.--Central pressure (po) vs. radius of maximum winds (R). track direction (0). 1I07 (kPo) 8 89 0 9 0.0 9 1.0 92~.0 93.0 94.0 9 5.0 9 6.0 97.0 9 8.0 9 9.0 - I I II I I IIII II IIIII1I11I. -50 26 EAST COAST 24- X GULF COAST c-45 0 WESTERN 22- NORTH PACIFIC X* *- r-.0 -40 SY = 6.2 KT I11 .5KM/HR) ~ 20 -* X0 0 0 -35 18- 0 0 0 x co * DX 2 2 ~ 30 '-16- X 0 0 >43K X22*OOO 0 0 0 0 0 OX 0 X M ~x X 14 - 0 C) 0 0 a 0 xxX xxoO 0 )< 00 - so W - 2 ::25~ 0 .0 0 XO O000 0 12~~~~~~~~~~~~~- .-v z; Z v rry-n 0e *00 - 0 0 0 OO O 0X '0 0 CK a-20 10 0 0 ~~~~~~~ ~~~~~0 xo. O)G 0.00 = 2 2D0 6 x OCC) 00 0 2K 0 2(C 6-~~~~~~~ ~~~~~~ ~~ ~ ~~ 0O x 0co 00 0 ) 10 4-~~~~~~~~~0 0 X0 0 00 0 0 0 C ) 00 x 0 - 2- 0 0 0 27 28 29 CENTRAL PRESSURE (INI Figure 5.3.--Central pressure (p ) vs. forward speed (T). ,45 - *EAST COA ST 8 oWESTERN * 40 - NORTH PACIFIC 35 -SY. 6. KT11 .1 KM/HRi 0t - 0**~~6 30- 0 M) 25- -0 _ 0~cc90 0 0 00 ~~~~~20 5- 0 0 S@S 0 0 05 10 15 20 25 30 35 40 45 LATITUDE ("N) Figure 5.4.--Latitude (i)vs. forward speed (T). 108 more extreme tropical cyclones [<27.46 in. (93.0 kPa)] the range of 0 is more restricted than it is for weaker storms. This indication supports restric- tions on the entry direction of extreme storms at the coast. Investigation of the interrelation between p and T (fig. 5.3) shows that storms with lower po0 move at slower speeds. Higher T's occur outside of tropical latitudes. Along the gulf coast, the most extreme storms (po < 27.46 in., 93.0 kPa) have moved between 8 and 16 kt (15 and 30 km/hr). Along the east coast, storms with p <27.75 in. (94.0 kPa) have traveled at T between 8 and 26 kt (15 and 48 km/hr). Western North Pacific typhoons have T between 3 and 18 kt (6 and 33 km/hr) for po < 27.46 in. (93.0 kPa). Weaker hurricanes and typhoons have a larger range of T. 5.3.2.2 INTERRELATIONS WITH LATITUDE (4). A composite plot of 4 vs. T data is shown in figure 5.4 for east coast hurricanes and typhoons of the western North Pacific. The general conclusion from this plot is that T tends to be lower and has a smaller range with lower 4. The storms with higher T's north of 25�N have recurved and have consequently accelerated. Po is higher at temperate latitudes than at tropical latitudes, partly because of warmer sea-surface temperatures to the south. Higher po0 at temperature latitudes is shown by a plot of 4 vs. p data (fig. 5.5), a trend line, and the enveloping minimum po curve for east coast hurricanes and western North Pacific typhoons. A plot of 4 vs. 0 is shown in figure 5.6 for east coast hurricanes and western North Pacific typhoons. r has a relatively high value of 0.50. This plot shows the well-known pattern of tropical cyclones moving from the east at lower 4 and changing to directions from the south and southwest as they move clockwise around the outer edge of the subtropical high. Figure 5.7 is a plot of 4 vs. R for east coast hurricanes and western North Pacific typhoons. r is again relatively high at 0.51. This plot supports what many meteorologists have observed as a characteristic of hurricanes and typhoons, i.e., storms expand in size as they move northward out of the tropics. 1Q9 *EAST COAST OWESTERN NORTH PACIFIC r = 0.22 Sy*x= 0.65 IN. (2.2 kPa) O O 29.0 0 - 0O *O - 0.<~~~~~~~jO O �O -- ��� �OObL 2 j - 97.0 28.5 _ o * -9O.0 "i.' -- ^ r~ ~ O O 08O 00. 0U 0 0 0-- 96.0 06 0 - 95.0 o 25O o � 30 2 �8.� O / - 0 o �o - 94.0 0 0 Z27.0 0 0 - 93.0 - �8, 0oO O-/ 92.0 0 0 9.0 26.5 - |1 1 I I I I I I , I I 0.0 5 10 15 20 25 30 35 40 45 LATITUDE (ON) Figure 5.5.--Latitude (4p) vs. central pressure (po) 5.4 MULTIPLE INTERRELATIONS BETWEEN SETS OF PARAMETERS Multiple correlation coefficients (r'), using the same parameters as in table 5.1, were calculated for east and gulf coast hurricanes, and for typhoon data (table 5.2). In cases where only an ordinary zero-order correlation coefficient is listed for a pair of parameters, e.g., G vs. T (east coast), additional combinations of parameters did not yield signifi- cant increases in r'. For gulf coast hurricanes, the addition of a second parameter failed to yield significant increases in r' for all cases studied. Table VII of Mills (1955) was used to estimate significance. A screening technique selects the second, third, and fourth parameters which give the greatest increase in r' as each is added. A discussion of r' follows. If Y denotes the regression function of a random variable y with respect to certain other variables xl, x2, ..., xn, then the coefficient of multiple lip I.E II I I I ' " I I I "I I I I I I' I I I I I I I I I i I 320- 0 300 - *EAST COAST o 280- oWESTERN NORTH PACIFIC 260 r= 0.50 60 - Syox = 42.1 DEG. I ~~~~~~O 240- O O o o 0 roc Z 220- 0 o 0~~~~~~~~~~~~~~~~~~~0 Z~~~~~~~~ �� ~ 200 - O o 180o- 000 0 0000 O - UJ 0 0~~~~~~~~0 Om Io 00 160-- o o o 10 - C-,~~~~~~~~~~~3D3O,'[ 0~~~~~~~~~~ 0~~~~~ 1 100 - 0 00 * 10 - - 0 0 0e 0 C0 - ~J 0 0 O ~)J{~- . 0 00 �U 80 - O 60 -P 40 - 20 - 0 I I I I I I i - i I I I I I I I 0 5 10 15 20 25 30 35 40 45 50 LATITUDE (N) Figure 5.6.--Latitude (Ip) vs. track direction (6). correlation (r') between y and the x's is defined as the coefficient of simple linear correlation (r) between y and Y. However, the constants of the regression function automatically adjust the algebraic sign, with the result that the coefficient of correlation (r') between y and Y cannot be negative; in fact, its value is precisely equal to the ratio of their two standard deviations, i.e; a(Y)Ia(y).. Therefore, r' ranges from 0 to 1, and the square of r' is equal to the relative reduction, i.e.. the ratio of explained variance to total variance (Huschke 1959). table 5.2 lists the coefficient of multiple correlation (r'), significance tests on r' at the 5 and 1 percent levels (Mills 1955), the reduction of variance (ri'2 and the standard error of' estimate (s y.x 11' " ' I I' '' I I''" '' I I I I I I I I I I I I I I' I I I 65_ �EAST COAST oWESTERN 60- NORTH PACIFIC r = 0.51 Sy-x = 9.5N MI 117.6KM) *S~~~~~~ -100 50- 0 0 � � Z45 Z _ � -80 40 - DT~~~~~0 � 35 - 0O O O 0 0 O O 0 ~3O~~~ ~ 0 25 O _OD0 O0 00 O0 I a e 20 O O * o * -40 1 5 O . O o0 0 0 e 0 10 -- ao b 0 o O � ( 20 QD0 5 - 0 6D88O 0 �C' Si 0 sadr o o o o et o o s o o 0 5 10 15 20 25 30 35 40 45 50 LATITUDE (ON) Figure 5.7.--Latitude (9) vs. radius of maximum winds (R). The relation between reduction of variance (r'2), standard deviation (a), and standard error of estimate (sy.x) is given by: r2 1 2= 2 )/0 (5-1) where rel = reduction in variance a = standard deviation, or the positive square root y.x 112 Multiple correlations for the east coast hurricanes are higher than for the other two regions except for those involving e. The highest r' = 0.76 [between ip a-ad T, p occurs with east coast data. 5.5 SUMMARY The zero-order linear and multiple correlation coefficients, although often significant at the I % level, could not be used directly in developing criteria throughout this report. There are two reasons for this. First, the coefficients are derived from data for all hurricanes and typhoons from our period of record--not just the most extreme ones, which are too few in number - to develop meaningful interrelations. Second, though the results are signifi-1 cant they explain only about one quarter of the variance and the standard error of estimates are large in relation to the magnitude of the individual variables. The interrelations, however, were important guides in setting the along- coast variation of values for the SPH and PMH{. Extrapolation beyond the data (especially for the PMH) was based primarily on theory and experience, taking into account trends shown in extrapolation of the data. Meteorological parameters for western North Pacific typhoons blend in well with those of the east and gulf coast hurricanes for the common latitude span (250 to 35'N) in many of the interrelations shown (figs. 5.5, 5.6, and 5.7, for example). Some typhoon data fall out of the general limits of the hurri- cane data (fig. 5.1, for example). This is due to latitudinal and possibly other effects. Values of the typhoon parameters are less reliable than those of the hurricanes because of approximations, less detailed analyses, and fewer observations, particularly in earlier years. In general, however, the typhoon data support trends shown by the hurricane data; it is most helpful in supplementing data sparse areas on the plotted diagrams (for example, lower p0 and smaller R on fig. 5.1). 113 6, PRESSURE PROFILE FORMULA 6.1 INTRODUCTION We are interested in determining SPH and PMH wind field criteria along the coast from Texas to the Canadian border. In our approach, the hurricane wind field is related to the variations in the pressure field. Therefore, the profile of pressure through the storm must be a very good approximation to observed hurricane pressure profiles. A sea-level pressure profile was derived in Hydrometeorological Report No. 31 (Schloemer 1954), hereafter referred to as HMR 31. This formula has been used extensively in many hurricane studies-. Henceforth, we will refer to it as the Hydromet formula or H. Our objective is to test H and other formulas against data from recent hurricanes. 6.2 DEVELOPMENT AND EARLY USE OF THE HYDROMET FORMULA The Hydromet formula (H) is: P e-P (6.1) Pw Po where p is the sea-level pressure at distance r from the hurricane center. In the development of H, P Po was plotted against distance from the hurri- Pw Po cane center using observed pressure values from each of nine Florida hurri- canes. When the data were replotted on a semilog scale with the origin at P -Po = 1, the curves (fig. 6.1) suggested a family of rectangularhyperbolas Pw-po w 0 which have the general formula, xy = k. Substituting directly, Schloemer P -P obtained r in w = k, where y = r = distance from the center of the P -PO P -P hurricane and x = In - P -Po The distance from the hurricane center to the maximum winds (R) is important to the determination of these maximum winds. Schloemer assumed k would be some function of R. He examined the general relation k = kl R 114 (km) 1.0Oo 20 40 60 80 100 120 140 160 .90 n n n .80 - - - F i 1 T _____ .760 ..-i^5 -km..�5 Io�- 00I .0 . .. . .60 '5;'" o��~",...-"�'/'> " n O O' � � .50 /.woo' he ;ffiaxa ,91 SEP0T 0o o .40 / OO O .30 � o' o ' - .20 .. * I ::.o .08 1 ' :*- o0. 1� . :/, a o .04'; .03, 1 o .02 f o ' o 010 10 20 30 40 50 60 70 , 80 DISTANCE FROM CENTER (N MI) Figure 6.1.--Smoothed pressure profiles of FZorida hurricanes using observed pressure values (after SchZoemer 1954), Here, the restricted hurricane sample became a severe limitation. Examina- tion of the data indicated no consistent value for k and i. The values from his storm sample did not differ greatly from unity. The use of unity did not introduce appreciable error in hurricane wind computations. Replac- ing k by R and taking antilogarithms results in H (eq. 6.1). Schloemer believed that H was a reasonable representation of the sea-level pressure profile of a hurricane out to a distance of about 87 n.mi. (161 km). Myers (1954) used H to obtain sea-level pressure profiles for east and gulf coast hurricanes that occurred between 1900-50. At the time of that study R, po, and Pw for most of the hurricanes were not known. Myers did not check the validity of H. 115 6.3 PRESSURE PROFILE FORMULAS TESTED AND DATA SAMPLE HMR 31 gives a list of general formulas for replicating storm sea-level pressure profiles. The first seven formulas in table 6.1 are identical to those in HMR 31 if the values of i and j of that report are set equal to one. The last two formulas (I and II) in table 6.1 were developed for this study. We selected 19* of the more intense hurricanes during the period 1950-74 for testing against sea-level pressure profiles computed from the formulas in table 6.1. Some major hurricanes, such as Betsy (1965), were not tested since complete data were not available. We tested only hurricanes whose p0 s and R's could be determined from observations by reliable meteorological instruments. Table 6.2 chronologically lists by coast these hurricanes and their pertinent data. No attempt should be made to compare the revised data for King (1950) in table 6.2 to the pressure profile for the October 1950 hurricane in figure 6.1. The storms are one and the same, but the eye- fitted visual profile for King in this report was analyzed using information unavailable to Schloemer (1954). Figure 6.2 shows a data plot for Camille (f969) and an'eye-fitted visual profile to the data. Also shown are computed profiles using H, formula I and formula II. 6.4 COMPARISON OF EYE-FITTED HURRICANE PRESSURE PROFILES WITH PRESSURE PROFILES FROM FORMULAS 6.4.1 IN GENERAL A comparison of computations using the first seven formulas of table 6.1 (from HMR 31) with storm profiles showed they do not replicate observed events as well as H. The computed profiles would either shoot up too P -P0 rapidly toward -= 1 with distance away from the storm center or flatten Pw-po p -Po out much too rapidly toward- 0 with short distances near the storm : .. ~ ~~Pw-Po center. Initial computations with formulas I and II showed they gave more realistic~sea-level pressure profiles than the other seven formulas tested. *Although 19 hurricanes were selected, there were 22 profiles because Daisy (1958) was tested off North Carolina and Massachusetts and Donna (1960) was tested off Florida, North Carolina, and New York. 116 Table 6.1.--Pressure profile formuZas tested in dddition to the Hydromet formula P Po -Rr = l-e Pw -Po P -Po 1 P -P p - 2 1 (arctan Rr) P -Po 2 -1 - p(arccot -rr) P -Po 2 [arcsec (1 + Rr)] Pw-Po 2 p -p0 P = - [arccsc (1 + 1-)] P -Po = tanh Rr p -P W 0_ I: = C (arctan r/R), C is a constant Pw-Po P -Po R Pw-Po Note: Pw = Pn (see chapter 7) R = n from HMR 31, table 2 (Schloemer 1954) Numerous computations were made using different values of the constant of proportionality, C, in formulas I and II (table 6.1). Of course, in "fit- ting" a particular storm, a certain C value is best. Suitable values of C range from 0.50 to 0.65. The rounded average (0.6) from the above fittings was used in I and II for the pressure profile comparison in this study. Table 6.2--Comparison of storm and three pressure profile formulas Storm Hydromet Formula Formula profile Formula(eq. 6.1) I** II*** Storm Year P p * R P40 p 40 p80 P4040 P P40 P s4Ps80 Ps80 Ps80 (i.) (. (n.mi.)(in ,(in.) (in.) (in.) (in.) (in.) (in.) (in.) -PH40-PI40 I4 -PII40 -PH80 -PI8Q -PII80 (in.) (in.) (in.) (in.) (in.) (in.) East Coast King 1950 29.94 28.20 6 29.42 29.57 29.70 29.81 29.68 29.76 29.30 29.44 A -.28 -.26 +.12 -.24 -.19 +.13 Daisy (NC) 1958 29.97 28.26 25 -- 29.59 -- 29.51 -- 29.56 -- 29.15 A -- -- -- +.08 +.03 +.44 Daisy (NE) 1958 29.94 28.91 50 -- 29.67 -- 29.46 -- 29.54 -- 29.32 B -- -- -- +.21 +.13 +.35 Gracie 1959 30.00 28.08 10 29.24 29.55 29.57 29.77 29.61 29.75 29.15 29.34 A -.33 -.37 +.09 -.22 -.20 +.21 Donna (FL) 1960 29.88 27.55 20 28.99 29.47 28.96 29.37 29.10 29.40 28.57 28.85 A +.03 -.11 +.42 +.10 +.07 +.62 Donna (NC) 1960 29.88 28.29 34 28.91 29.25 28.97 29,33 29.12 29.41 28.83 29.03 A -.06 -.21 +.08 -.08 -.16 +.22 Donna (NE) 1960 29.83 28.38 48 28.66 28.99 28.82 29.18 28.99 29.28 28.80 28.97 B -.16 -.33 -.14 -.19 -.29 +.02 Cleo 1964 29.88 28.57 7 29.64 29.77 29,71 29.77 29.67 29.74 29.37 29.49 B -.03 -.03 +.27 0 +.03 +.28 Dora 1964 29.91 28.52 20 29.10 29.47 29.38 29.60 29.44 29.63 29.13 29.29 B -.26 -.34 -.03 -.13 -.16 +.18 Gulf coast Easy 1950 29.80 28.30 15 29.40 29.56 29.33 29.54 29.39 29.55 29.03 29.20 A +.07 +.01 +.37 +.02 +.01 +.36 Flossy 1956 29.91 28.80 22 -- 29.61 -- 29.64 -- 29.67 -- 29.40 B -- -- -- -,D3 -.06 +.21 Ethel 1960 29.97 28.98 18 29.62 29.81 29.61 29.77 29.66 29.78 29.43 29.55 B +.01 -.04 +.19 +.04 +.03 +.26 Carla 1961 29.77 27.49 30 28.59 29.08 28.57 29.06 28.76 29.15 28.32 28.60 A +.02 -.17 +.27 +.02 -.07 +.48 Isbell 1964 29.91 28.47 10 29.59 29.71 29.59 29.74 29.62 29.72 29.27 29.42 B 0 -.03 +.32 -.03 -.01 +.29 Alma 1966 29.97 28.65 23 29.34 29.59 29.39 29.64 29.48 29.67 29.19 29.35 B -.05 -.14 +.15 -.05 -.08 +.24 Beulah 1967 29.80 27.85 25 28.82 29.33 28.89 29.28 29.03 29.33 28.63 28.86 A -.07 -.21 +.19 +.05 0 +.47 Camille 1969 29.77 26.81 8 29.15 29.48 29.23 29.49 29.25 29.42 28.56 28.84 A -.08 -.10 +.59 -.01 + 06 +.64 Celia 1970 29.83 27.89 9 29.50 29.74 29.44 29.62 29.46 29.59 29.00 29.19 A +.06 +.04 +.50 +.12 +.15 +.55 Fern 1971 29.77 28.91 26 29.41 29.58 29.36 29.53 29.42 29.56 29.25 29.35 B +.05 -.01 +.16 +.05 +.02 +.23 Edith 1971 29.80 28.88 27 29.50 29.70 29.35 29.54 29.42 29.57 29.23 29.35 B +.15 +.08 +.27 +.16 +.13 +.35 Agnes 1972 29.83 28.88 20 29.26 29.41 29.46 29.62 29.51 29.64 29.30 29.41 B -.20 -.25 -.04 -.21 -.23 0 Carmen 1974 29.91 28.11 10 29.39 29.59 29.51 29.70 29.55 29.68 29.11 29.29 A -.12 -.16 +.28 -.11 -.09 +.30 *Pressure obtained at the coast - used in developing pressure profiles. In some cases it differs from po in tables 4.1 - 4.4. P-Po �*F ormula : p- = .6 (arctan ) P-P ***Formula I: p-p = .6 [arccsc (1+ )] 1 standard inch of Hg = 3.386 kPa w-Po r #A: po 28.30 in. (95.8 kIa) [see table 6.3] #B: p > 28.30 in. (95.8 kPa) [see table 6.3] ps40: storm pressure at a distance of 40 n.mi. (74 km) from the hurricane center; PH40: storm pressure computed from the Hydromet formula at a distance of 40 n.mi. (74 km) from the hurricane center. 118 IKMI 1.00 20 40 60 80 100 120 140 160 .9 0 I A I - I -I .80 .7~~~~ ~~~~~~ 0000000(0O000....o000( >00000000 .60 .40 ~~ r*X1~~-J~��~ _~iowo~a )0000000 )00000)00o0000U0o .50 j .40 ~s~t/ J _~Poo-" 430 LEGEND * 0 ~~~~~~~~~~~~~DATA POINTS P-P =e (HI o, i P ~ o=XX.6 ARCTAN r o�I~~~~~e~~~ .lo 13 1 Pw-~~~~~~~~~~ P, .oo 00000 =0.6 ARCCSC _1+ RI(I .08 - EYE - FITTED VISUAL PROFILE .07 _ _ _ P = 26.81 IN. 190.8 kPa) .06 P = 29.77 IN. 1100.8 kPa) DATA FROM TABLE 4.3 R =8N MI 114.8 KMW .04 .03 .02 .01 10 20 30 40 50 60 70 80 DISTANCE FROM CENTER (N MI) Figure 6. 2.--Eye-fitted and computed pressure profiles, Camille 1969. '2fTi 119 Figure 6.2 shows that H is a closer fit to the visual profile than I or II for hurricane Camille (1969). A different constant of proportionality in I would result in a better fit to the visual profile for Camille. However, C = 0.6, proved to be about the best overall fit for all the tested storms and was used in the comparisons of the three pressure profiles (table 6.2). A close study of figure 6.2 tells us the formula I curve rises more rapidly than the Hydromet formula, formula II, or the visual profile. This is a characteristic of the formula I pressure profile evident in all hurri- canes studied. 6.4.2 AT 40 AND 80 NAUTICAL MILES (74 AND 148 KILOMETERS) Pressures for distances of 40 and 80 n.mi. (74 and 148 km) from the storm center were taken from the "eye fit" hurricane sea-level pressure profiles and from computed formula pressure profiles. Farther out, the profiles tend to converge toward 1. Closer than 40 n.mi. (74 km) to the storm center, the storm data tend to become sparse for some storms, leading to less reliable comparisons. Table 6.2 shows these sea-level pressures for the eye-fitted storm profiles and the profiles for H, I, and II, in that order. We then give the dif- ferences in pressure(p s40-PH40 ), etc. ps40 is the storm pressure at a distance of 40 n.mi. (74 km). pH40 is the pressure computed from H at the same distance. p140' p1140' ps80' PIH80' p180, and pII80 are similarly defined. A plus difference means the storm profile pressure is greater. Table 6.3 summarizes the differences in sea-level pressures at the two distances. Hurricanes have been divided into two categories; those with central pressure (p <28.30 in. (95.8 kPa), Category A; those with p0 >28.30 in. (95.8 kPa), Category B. Beneath the sum of positive and negative differences are the number of profiles. There are only 19 profiles for the 40 n.mi. distance since data this close to the eye were not sufficient to define profiles for three hurricanes. Formula II is definitely biased toward giving lower pressures at both 40 and 80 n.mi. (74 and 148 km) for both storm categories. Therefore, it is not suitable for use as the pressure profile formula for this report. 120 Table 6. 3.--Summary of differences in pressure for formulas H, I and II for two categories of central pressure. Pressure from storm profiles minus pressure from computed pressure profiles (in.) At a distance of 40 n.mi. (74 km) H* I* II_*** (19 profiZes) Category A Po < 28.30 in. (95.8 kPa) (10 profiles) Sum of positive diff. .18 .05 2.91 No. of profiles 4 2 10 Sum of negative diff. .94 1.59 0 No. of profiles 6 8 0 No. of profiles with no diff. 0 0 0 Category B p > 28.30 in. (95.8 kPa) (9 profiles) Sum of positive diff. .21 .08 1.36 No. of profiles 3 1 6 Sum of negative diff. .70 1.17 .21 No. of profiles 5 8 3 No. of profiles with no diff. 1 0 0 At a distance of 80 n.mi. (148 km) (22 profiles) Category A p < 28.30 in. (95.8 kPa) (11 profiles) Sum of positive diff. .39 .32 4.42 No. of profiles 6 5 11 Sum of negative diff. .66 .71 0 No. of profiles 5 5 0 No. of profiles with no diff. 0 1 0 Category B po > 28.30 in. (95.8 kPa) (11 profiles) Sum of positive diff. .46 .34 2.41 No. of profiles 4 5 10 Sum of negative diff. .64 .83 0 No. of profiles 6 6 0 No. of profiles with no diff. 1 0 1 * Hydromet pressure profile formula (eq. 6.1) ** = .6 arctan r 1 standard inch of Hg = 3.386 kPa ** - = .6 arctan ( Pw-po *** P-P _=_ -.6 arccsc Pwd-Po 121 Differences between formulas H and I are very small. H is a slightly better overall fit at 40 and 80 n.mi. (74 and 148 km), particularly for the stronger category A hurricanes. 6.4.3 FOR FIVE INTENSE HURRICANES We selected the most intense hurricanes from table 6.2 [p <27.90 in. (94.5 kPa)] for special attention. Data from table 6.2 for these five hurri- canes [Donna (Fla.), 1960; Carla, 1961; Beulah, 1967; Camille, 1969; and Celia, 1970] are summarized in table 6.4. Table 6.4.--Summary of pressure differences from table 6.2 for formulas H and I for five intense hurricanes (po0 <27.90 in., 94.5 kPa) 40 n.mi. (74 km) 80 n.mi. (148 km) Storm pressure Storm pressure minus computed minus computed pressure pressure H I H I Z + diff. in 0.11 0.04 0.29 0.28 (kPa) (0.4) (0.1) (1.0) (0.9) No. of storms 3 1 4 3 Z - diff. in. -0.15 -0.59 -0.01 -0.07 (kPa) (-0.5) (-2.0) (-0.0) (-0.2) No.of storms 2 4 1 1 No difference 0 0 0 1 Results using the five most intense hurricanes (p <27.90 in., 94.5 kPa) 0 in table 6.2 again show only slight differences between formulas H and I with H being a better overall fit at 40 and 80 n.mi. (74 and 148 km). 6.4.4 HURRICANE CAMILLE Data from table 6.2 indicates that the Hydromet formula provides a better fit to the storm profile than formula I for extremely intense hurricane Camille (1969). 122 6.5 CONCLUSIONS Based upon comparisons in section 6.4, we conclude that the Hydromet formula gives a reasonably representative sea-level pressure profile of a hurricane and is therefore the best means of determining the maximum gradient wind speed (see chapter 12) for the SPH and PM-H. The reasons supporting this argument are as follows: a) Only formula I from table 6.1 replicates observed hurricane events with any degree of precision. b) For east and gulf coast hurricanes (1950-74) the Hydromet formula is a better overall fit than formula I for the entire storm sample of table 6.2, the five most intense hurricanes considered together, and hurricane Camille (1969). c) The formula I pressure profile, when fitted to po' rises too rapidly within a few miles of the pressure centers of hurricanes we studied. The Hydromet formula shows a more realistic gradual change in pressure in this short distance from po. d) The Hydromet formula has been used extensively in earlier studies. To justify a change, we would need to show significant improvement. We have not been able to do this. Can H be improved upon? As indicated by Schloemer in HMR 31, there may be a constant multiplier and an exponent of R other than unity. The problem is a reliable determination of other values for identifying these constants.* The results would be only as good as the pressure data and the tracks of the hurricanes. A refinement of the formula by employing two other constants might make it a better fit for the hurricane sample, but less applicable to the hurricane population. More than one set of constants varying with hurri- cane intensity or some other parameter might be the ultimate solution. We believe that such refinements would not improve the reliability of H at this time because of the rather large scatter of pressure data around most hurri- cane profiles (fig. 6.2). *See the work of Graham and Hudson (1960, pp. 89-90) for a discussion of fit- ting an exponential constant to develop a modified exponential equation for' hurricane Hazel (1954). 123 7. PERIPHERAL PRESSURE 7.1 INTRODUCTION Peripheral pressure (p ) is the sea-level pressure at the outer limits of the hurricane circulation. It is used to compute pressure drop (peripheral pressure minus central pressure), which is related to wind speed; see chapter 12. Prior to this report, the most complete listing of hurricane peripheral pressure (Pn) data was in National Hurricane Research Project Report No. 5 (NHRP 5), table 3-1(U.S. Weather Bureau 1957). P data are mostly values of asymptotic pressure (pn) and a few values read from weather maps (Pw). n is that value to which an exponential pressure profile defined by the Hydromet pressure profile formula is asymptotic. In NHRP 33 (Graham and Nunn 1959), a fixed peripheral pressure of 29.92 in. (101.3 kPa) was used to compute SPH winds. This is standard sea-level pres- sure and also an average of peripheral pressure for storms listed in NHRP 5. In HUR 7-97 (U.S. Weather Bureau 1968), peripheral pressure criteria are related to latitude by a curve that envelops the peripheral pressure (given in NHRP 5) of hurricanes within gulf and east coast zones. The highest peri- pheral pressure, used at 250N, is that required to produce the maximum cyclo- strophic wind for a central pressure of 26.00 in. (88.0 kPa) [see fig. 22, of NHRP 33]. The variation with latitude is based mainly on the p 's of record hurricanes. In HUR 7-120 (National Weather Service 1972), peripheral pressure is also related to latitude by an eye-fitted, least-error average curve through peripheral pressures for record hurricanes of table 3-1 of NHRP 5. These studies have used several techniques for evaluating peripheral pres- sure. In this chapter we will describe what we believe is the best approach. 7.2 METHODS OF DETERMINING PERIPHERAL PRESSURE pw is frequently considered as the average pressure around the hurricane where the isobars change from cyclonic to anticyclonic curvature. This pres- sure occurs at a distance from the storm center near where storm inflow 124 begins and, therefore, has physical meaning. In this study, Pw was deter- mined at four equally spaced points around the storm center (north, east, south, and west). Values of Pw were rounded off to the nearest 0.03 in. (0.1 kPa). Another method of obtaining weather map peripheral pressure uses the value of the last closed isobar. This value is designated by Pwi pwi's were also determined to the nearest 0.03 in. (b.01 kPa). Table 7.1 lists values of p and Pwi for gulf and east coast hurricanes. These values of Pw are the same as those listed in tables 4.1-4.4. All the values are at or near the time of lowest p within 150 n.mi. (278 km) of the coast. Also shown in table 7.1 are values of p given in NHRP 5, which are mostly Pn's except for a few p ws where the p nwas not available. 7.3 COMPARISON OF P AND P WITH P W WI NX We wish to use either p or Pwi and not pnx because peripheral pressure from weather maps is not based on how well the Hydromet pressure profile formula fits an individual storm profile of record. Before eliminating Pnx however, we would like to compare Pw and Pi to Pnx We stated earlier that the average of peripheral pressures (pnx) for storms listed in NHRP 5 is 29.92 in. (101.3 kPa). The average of Pw for all hurricanes in table 7.1 is 29.90 in. (101.3 kPa) and the average of Pwi for all hurricanes is 29.79 in. (100.9 kPa). P is comparable to Pn while Pwi is somewhat lower. 7.4 INTERRELATIONS AMONG PW' PWI' LATITUDE AND PO We have chosen to determine which peripheral pressure isbest suited for this study by evaluating the interrelations, if any, between the peripheral pressure, latitude, and central pressure. 7.4.1 PLOTS CONTAINING P A plot of ~ vs Pw for east coast hurricanes is shown in figure 7.1. Pw is plotted at the latitude for the location of Po (tables 4.1-4.2). The storms have been stratified into three groups. The 19 with central pressure (P.) <28.17 in. (95.4 kPa) are circled. The 17 with p > 28.64 in. (97.0 kPa) are boxed. There are 18 remaining storms with p between 28.18 and 28.63 in. (95.4 and 97.0 kPa). 125 Table 7.1.--Comparison of three peripheral pressures for gulf and east coast hurricanes, 1900-75. G U L F C O A S T H U R R I C A N E S Month Date Year Name Pwi Pw-Pwi P Pw P w Pw. Pnx (in.) (in.) i(in.) (i) (kPa) (a) PX P Sept. 9 1900 29.88 29.74 0.14 29.78 101.2 1Q.7 0.5 100.8 Aug. 15 1901 29.91 29.83 0.08 30.16 101.3 101.0 0.3 102.1 June 17 1906 29.91 29.83 0.08 29.98 101.3 101.0 0.3 101.5 Sept. 27 1906 29.91 29.77 0.14 30.07 101.3 100.8 0.5 101.8 Oct. 18 1906 29.83 29.74 0.09 29.80 101.0 100.7 0.3 100.9 July 21 1909 29.97 29.85 0.12 30.27 101.5 101.1 0.4 102.5 Sept. 20 1909 29.88 29.85 0.03 30.30 101.2 101.1 0.1 102.6 Oct. 11 1909 by 29.80 29.77 0.03 30.07 100.9 100.8 0.1 101.8 Oct. 18 1910 29.77 29.71 0.06 29.77 100.8 100.6 0.2 100.8 Aug. 17 1915 29.88 29.77 0.11 29.57 101.2 100.8 0.4 100.1 Sept. 29 1915 29.80 29.74 0.06 30.14 100.9 100.7 0.2 102.1 July 5 1916 29.86 29.74 0.12 30.03 101.1 100.7 0.4 101.7 Aug. 18 1916 29.94 29.83 0.11 30.77 101.4 101.0 0.4 104.2 Oct. 18 1916 29.88 29.85 0.03 30.20 101.2 101.1 0.1 102.3 Sept. 29 1917 29.97 29.88 0.09 29.88 101.5 101.2 0.3 101.2 Sept. 10 1919 by 29.88 29.77 0.11 29.73 101.2 100.8 0.4 100.7 �Sept. 14 1919 29.88 29.74 0.14 101.2 100.7 0.5 Sept. 21 .1920 29.91 29.85 0.06 29.90 101.3 101.1 0.2 101.3 June 22 1921 29.94 29.83 0.11 30.03 101.4 101.0 0.4 101.7 Oct. 25 1921 29.83 29.71 0.12 29.59 101.0 100.6 0.4 100.2 Oct. 21 1924 29.88 29.77 0.11 29.62 101.2 100.8 0.4 100.3 Aug. 26 1926' 29.97 29.88 0.09 30.35 101.5 101.2 0.3 102.8 Sept. 20 1926 29.94 29.77 0.17 30.13 101.4 100.8 0.6 102.0 Oct. 21 1926 by 29.77 29.68 0.09 29.97 100.8 100.5 0.3 101.5 Sept. 17 1928 29.88 29.74 0.14 30.38 101.2 100.7 0.5 102.9 June 28 1929 29.80 29.71 0.09 29.97 100.9 100.6 0.3 101.5 Sept. 30 1929 29.91 29.83 0.08 29.96 101.3 101.0 0.3 101.5 Aug. 14 1932 29.91 29.83 0.08 30.11 101.3 101.0 0.3 102.0 Aug. 5 1933 29.91 29.80 0.11 29.96 101.3 100.9 0.4 101.5 Sept. 4 1933 29.88 29.74 0.14 29.98 101.2 100.7 0.5 101.5 Sept. 5 1933 29.88 29.71 0.17 30.24 101.2 100.6 0.6 102.4 June 16 1934 29.71 29.59 0.12 29.94 100.6 100.2 0.4 101.4 Sept. 3 19.35 29.94 29.83 0.11 29.92 101.4 101.0 0.4 101.3 Nov. 5 1935 ex 30.00 29.83 0.17 101.6 101.0 0.6 July 31 1936 30.00 29.85 0.15 30.00 101.6 101.1 0.5 101.6 Aug. 8 1940 29.94 29.85 0.09 29.75 101.4 101.1 0.3 100.7 Sept. 23 1941 29.86 29.71 0.15 29.66 101.1 100.6 0.5 100.4 Oct. 7 1941 30.00 29.97 0.03 30.19 101.6 101.5 0.1 102.2 Aug. 30 1942 29.83 29.71 0.12 29.64 101.0 100.6 0.4. 100.4 July 27 1943 29.94 29.85 0.09 30.02 101.4 101.1 0.3 101.7 Oct. 19 1944 29.88 29.77 0.11 29.67 101.2 100.8 0.4 100.5 Aug. 27 1945 29.83 29.68 0.15 30.13 101.0 100.5 0.5 102.0 Sept. 15 1945 29.94 29.80 0.14 30.00 101.4 100.9 0.5 101.6 Sept. 18 1947 ex 30.00 29.88 0.12 29.83 101.6 101.2 0.4 101.0 �Sept. 19 1947 29.94 29.83 0.11 29.70 101.4 101.0 0.4 100.6 Sept. -21 1948 29.83 29.74 0.09 29.61 101.0 100.7 0.3 100.3 Oct. 5 194�8 29.83 29.77 0.06 29.77 101.0 100.8 0.2 100.8 Aug. 27 1949 29.97 29.85 0.12 30.12 101.5 101.1 0.4 102.0 Oct. 4 1949 29.88 29.74 0.14 30.13 101.2 100.7 0.5 102.0 Aug. 31 1950 Baker 29.65 29.53 0.12 29.71 100.4 100.0 0.4 100.6 Sept. 5 1950 Easy 29.80 29.71 0.09 100.9 100.6 0.3 Oct. 18 1950 King 29.94 29.77 0.17 101.4 100.8 0.6 Sept. 24 1956 Flossy 29.91 29.77 0.14 101.3 100.8 0.5 June 27 1957 Audrey 29.74 29.62 0.12 100.7 100.3 0.4 Sept. 10 1960 Donna 29.88 29.77 0.11 101.2 100.8 0.4 Sept. 15 1960 Ethel 29.97 29.88 0.09 101.5 101.2 0.3 126 TabZe 7.1.--Comparison of three peripheral pressures for gulf and east coast hurricanes, 1900-75, continued. G U L F C O A S T H u R R I C A N E S p w wi w-P Pwx P' Pwi Pw Pwi a Month Date Year Name (in.) ( in.) (in.) (kPa) (kPa) (kPa) (H.) Sept. 11 1961 Carla 29.77 29.65 0.12 100.8 100.4 0.4 Oct. 4 1964 Hilda 29.97 29.83 0.14 101.5 101.0 0.5 Oct. 14 1964 Isbell 29.91 29.77 0.14 101.3 100.8 0.5 Sept. 8 1965 Betsy 29.91 29.80 0.11, 101.3 100.9 0.4 �Sept. 10 1965 Betsy 29.86 29.77 0.09 101.1 100.8 0.3 June 9 1966 Alma 29.97 29.88 0.09 101.5 101.2 0.3 Oct. 4 1966 by Inez 29.91 29.80 0.11 101.3 100.9 0.4 Sept. 20 1967 Beulah 29.80 29.65 0.15 100.9 '100.4 0.5 Oct. 19 1968 Gladys 29.86 29.77. 0.09 101.1 100.8 0.3 Aug. 18 1969 Camille 29.77 29.65 '0.12 100.8 100.4 0.4 Aug. 3 1970 Celia 29.83 29.77 0.08 101.0 100.8 0.2 Sept. 12 1970 Ella 29.77 29.65 0.12 100.8 100.4 0.4 Sept. 10 1971 Fern 29.77 29.68 0.09 100.8 100.5 0.3 Sept. 16 1971 Edith 29.80 29.71 0.09 100.9 100.6 0:3 June 19 1972 Agnes 29.83 29.68 0.15 101.0 100.5 0.5 Sept. 8 1974 Carmen 29.91 29.80 0.11 101.3 100.9 0.4 Aug. 31 1975 Caroline 29.88 29.80 0.08 101.2 100.9 0.3 Sept. 23 1975 Eloise 29.97 29.80 0.17 101.5 100.9 0.6 EA S T C O A S T H U R R I C A N E S Sept. 12 1903 30.00 29.85 0.15 30.12 101.6 101.1 0.5 102.0 June 17 1906 ex 29.91 29.83 0.08 29.98 101.3 101.0 0.3 101.5 Sept. 17 1906 30.06 29.91 0.15 30.38 101.8 101.3 -0.5 102.9 Oct. 18 1906 ex 29.83 29.74 0.09 29.80 101.0 100.7 0.'3 100.9 Oct. 11 1909 by 29.80 29.77 0.03 30.07 100.9 100.8 0.1 101.8 Aug. 28 1911 30.00 29.85 0.15 30.10 101.6 101.1 0.5 101.9 Sept. 3 1913 30.12 30.00 0.12' 29.98 102.0 101.6 0.4 101.5 Sept. 10 1919 by 29.88 29.77 0.11 29.73 101.2 100.8 0.4 100.7 Oct. 26 1921 ex 29.88 29.74 0.14 29'.59 101.2 100.7 0.5 100.2 Aug. 26 1924 by 29.94 29.71 0.23 30.33 101.4 100.6 0.8 102.7 �Aug. 26 1924 by 29.94 29.71 0.23 29.62 101.4 100.6 0.8 100.3 Dec. 2 1925 30.09 29.88 0.21 29.90 101.9 101.2 0.7 101.3 July 28 1926 30.00 29.83 0.17 29.91 101.6 101.0 0.6 101.3 Sept. 18 1926 29.94 29.71 0.23 29.99 101.4 100.6 0.8 101.6 Oct. 21 1926 by 29.77 29.68 0.09 29.97 100.8 100.5 0.3 101.5 Sept. 17 1928 29.88 29.74 0.14 30.38 101.2 100.7 0.5 102.9 Sept. 28 1929 29.80 29.71 0.09 30.08 100.9 100.6 0.3 101.9 Aug. 23 1933 29.94 29.71 0.23 29.48 101.4 100.6 0.8 99.8 Sept. 4 1933 29.94 29.83 0.11 29.98 101.4 101.0 0.4 101.5 Sept. 16 1933 30.03 29.88 0.15 29.82 101.7 101.2 0.5 101.0 Sept. 3 1935 29.94 29.83 0.11 29.9.2 101.4 101.0 0.4 101.3 Nov. 4 1935 29.97 29.85 0.12 101.5 101.1 0.4 Sept. 18 1936 by 30.12 29.97 0.15 29.42 102.0 101.5 0.5 99.6 Sept. 21 1938 29.97 29.80 0.14 29.52 101.5 101;0 0.5 100.0 Aug. 11 1940 30.06 29.83 0.23 30.02 101.8 101.0 0.8 101.7 Sept. 14 1944 29.86 29.80 0.06 30.66 101.1 100.9 0.2 103.8 �Sept. 15 1944 29.91 29.85 0.06 29.39 101.3 101.1 0.2 99.5 127 Table 7.1.--Comparison of three peripheral pressures for gulf and east coast hurricanes, 1900-75, continued. EAST C O A S T H u R R I C A N E S Pw Pwi p _ Pw pwi PP Pnx Month Date Year Name (in.) (in.) ()n.Y' (i) (kPa) (kPa) YkaJ (ia) Sept. 15 1945 29.94 29.80 0.14 30.00 101.4 100.9 0.5 101.6 Sept. 17 1947 29.97 29.80 0.17 29.83 101.5 100.9 0.6 101.0 Oct. 15 1947 29.91 29.80 0.11 29.65 101.3 100.9 0.4 100.4 Sept. 22 1948 ex 29.74 29.68 0.06 29.83 100.7 100.5 0.2 101.0 Oct. 5 1948 ex 29.83 29.77 0.06 29.77 101.0 100.8 0.2 100.8 Aug. 24 1949 by 30.06 29.94 0.12 30.20 101.8 101.4 0.4 102.3 Aug. 27 1949 29.97 29.85 0.12 30.12 101.5 101.1 0.4 102.0 Oct. 18 1950 King 29.94 29.77 0.17 101.4 100.8 0.6 Aug. 31 1954 Carol 29.86 29.77 0.09 101.1 100.8 0.3 �Aug 31 1954 Carol 30.06 29.97 0.09 101.8 101.5 0.3 Sept. 10 1954 by Edna 29.86 29.83 0.03 101.1 101.0 0.1 �Sept. 11 1954 Edna 29.83 29.68 0.15 29.26 101.0 100.5 0.5 99.1 Oct. 15 1954 Hazel 29.86 29.77 0.09 29.32 101.1 100.8 0.3 99.3 Aug. 12 1955 Connie 29.86 29.80 0.06 29.77 101.1 100.9 0.2 100.8 Sept. 19 1955 Ione 30.00 29.88 0.12 29.87 101.6 101.2 0.4 101.2 Aug. 28 1958 by Daisy 29.97 29.77 0.20 101.5 100.8 0.7 �Aug. 29 1958 by Daisy 29.94 29.77 0.17 101.4 100.8 0.6 Sept. 27 1958 by Helene 29.88 29.83 0.05 101.2 101.0 0.2 Sept. 29 1959 Gracie 30.00 29.88 0.12 101.6 101.2 0.4 Sept. 10 1960 Donna 29.88 29.77 0.11 101.2 100.8 0.4 �Sept. 12 1960 Donna 29.88 29.77 0.11 101.2 100.8 0.4 �Sept. 12 1960 Donna 29.83 29.77 0.06 101.0 100.8 0.2 Aug. 27 1964 Cleo 29.88 29.77 0.11 101.2 100.8 0.4 Sept. 10 1964 Dora 29.91 29.88 0.03 101.3 101.2 0.1 Sept. 8 1965 Betsy 29.91 29.80 0.11 101.3 100.9 0.4 Sept. 17 1967 Doria 30.06 30.00 0.06 101.8 101.6 0.2 Sept. 10 1969 Gerda 29.86 29.68 0.18 101.1 100.5 0.6 �, ex, by: Defined in the notes preceeding tables 4.1 to 4.4. pw: Peripheral pressure-defined as the sea level pressure at the outer limits of the hurricane circulation determined by moving outward from the storm center to the first anticyclonically turning isobar in four equally spaced directions and averaging the four pressures thus obtained. Pwi: Peripheral pressure-defined as the sea level pressure at the outer limits of the hurricane circulation determined by moving outward from the storm center to the last closed isobar in four equally spaced directions and averaging the four pressures thus obtained. Pnx: A mixture of peripheral pressure defined as that value to which an exponen- tial pressure profile employing the Hydromet Pressure Profile formula becomes asymptotic and peripheral pressure defined by p . These values were published in NHRP 5, table 3-1 under p (in.) Some of the conversions to millibars were in error in table 3-1. These have been corrected in converting to kilopascals. 128 I I I I I I I I I I 8.7M J -8.581 30.10 - 8.94 8.79 N- B i8.97 M8.85 i8.97 8.38 - 101.8 30.05 - 88.26 z .85 8.35 891 88.o 101.6 30.00 me ' 4 *8.35- O_~ 7.76 8.73i �.8.17 .8.26 7.75 ,.95 8 .70 - ir 29.95 _- n6.34� (87.99 1 8.70 0 8.64 91 .70 -101.4 j) 8.08 LIJ a8.53 8.59 8.32 0L L8 76I .1 I 8.91 7.5 L 29.90 _- - 8.59 7.61 8.91 (7.55 �8.29 -101.2 < 7.46 7.43 L, 8.35. B.A I 8.9 I :: 29.85-- * @7.88 I 29.85 - 7.67 7.85 L a8.85 LEGEND 7.97 _ i) Po < 28.17 IN. 195.4kPa1 � .8.38 101.0 29.80- 8.26 )7.99 [ PO > 28.64 IN. 197.0kPa) * 28.17 < PO< 28.64 IN. .(_)7.52 195.4 < PO < 97.0 kP3) - 100.8 29.75-- NUMERALS DENOTE PO IN IN. WITH .8.4 1 THE NUMBER 2 (IN THE TEN'S PLACE) OMITTED. 25 30 35 40 LATITUDE (oN) Figure 7.1.--Latitude (v) vs. peripheral pressure p .) for east coast hurricanes stratified into three intensity groupizngs. An envelope of all the data (fig. 7.1) shows highest Pw near latitude 350N, near the average position of the subtropical high. North and south of 350N, enveloping Pw is less. The envelope, however, is made up of the weakest two groups of storms. An eye-fitted mean line through data for the strongest group (p < 28.17 in. or 95.4 kPa) shows a less pronounced latitudinal trend in Pw. Figure 7.2 is a plot of 4 vs. Pw for gulf coast hurricanes. The data do not show a latitudinal trend. Figure 7.3 is a plot of po vs. p for all hurricanes. The envelope indi- cates a higher Pw for storms with higher po with one outstanding exception. This is the extreme Labor Day hurricane of 1935, which struck the Florida Keys with a p of 26.35 in. (89.2 kPa). This exception warns us against overly restricting Pw for storms with low po. 7.4.2 PLOTS CONTAINING PWI Figure 7.4 is a plot of i vs Pwi for all hurricanes. Pwi is plotted at the latitude for the location of p (tables 4.1-4.2). If the data points were 129 labeled with values of po, they 101.8 would show essentially the same 30.05 I pattern as that indicated in 30.00 -3 8.03 8.90 6.6 _ 101.6 figure 7.1. Figure 7.5, a plot 8.37 33 48 of p vs. p . for all hurri- Z 8.6 8.20 wi 29.95 -- .35 8.09 8.00 8.17 8.78 8 20 - 'A�r~� -101.4 canes, shows essentially the X 8.5 .70 8.47 8.91 8.80 7.64 8.93 8.80 8.76 78.95, � , 7m80 . 47o same enveloping trend as figure 29.90- 7. 8.7 7.3. 7.45 7.44. 8.02 7.99 8.4 8457.64 8.76 c.o - 8.44 K 1� 8.94 - 101.2 7.3. 8.02 7030'0 8.0 "8.94 7.79 8.31 8.38 " 29.85 -- 6.88s5 - 7.4.3 PLOTS OF LATITUDE 762 8.85 7.89 8.07 VS. PW AND PWI FOR WESTERN - 8.84 8 8.5 -101.0 8.84 8.12 8.88 NORTH PACIFIC TYPHOONS I 29.80- .26 7.26 723 8.62 886 _ 8.30 L 7.52 7.8 0 6.81 .9? Pw was plotted against latia-2 8 .75. 7 -100.8 29.75 - LEGEND 7.95 tude (fig. 7.6) for typhoons , C2NTRA LEGEND * CENTRAL PRESSURE with p < 27.46 in. (93.0 kPa) _ NUMERALS DENOTE IN IN .52 0o ~~~~~~~~~~~~- WITH THE NUMBER 2 IIN THE- 00 29.70 - TEN'S PLACEI OMITTED. at the location given in tables I1.92 4.5-4.6. Pw and Pwi for these I 10 0.4 25 30 typhoons are listed in table LATITUDE (ON) 7.2. Data for all these ty- phoons were selected between phoons were selected between Figure 7.2--Latitude (fl) vs. peripheral 8� and 300N. Little if any pressure (pw) for gulf coast hurricanes. trend of latitude with Pw is apparent. Pwi was also plotted against latitude (not showr) for the same sample of intense typhoons and no obvious trend was present. The average difference between Pw and Pwi was about 0.11 in. (0.4 kPa). 7.5 CONCLUSIONS a. We decided to use Pw rather than Pwi for both the SPH and PMH criteria. pw can be understood in a physical sense as being near the region of a hurricane where storm inflow begins. Pwi would lie inward from this region. Trends shown by plots (sec. 7.4) are similar for Pw and Pwi' Also, Pw is the more accepted definition of peripheral pressure. b. We also decided not to vary the pw with 4 for either the SPH or PMH. While an envelopment of the data (fig. 7.1) would give the highest Pw near ,350N, with lower values to the north and south, the more intense storms 130 ' (kPa) 90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 30.10 - / -- LEGEND /� * -101.8 30.05 - / _ 1 SEP. 1935 2 SEP. 1938 30.00 3 AUG. 101.6 (CAMILLEI,9 z 2 STORMS / as D 29.950- 11.4 l) P9.9 -/ tv / � � en �. A - 101.2 C) as -101.2 0 LIU /0 29.75 - - 0~~~~~~~~~~~~~~~~~~- 100. 29.70- * _ 100.6 29.65- -- l i 26.50 27.00 27.50 28.00 28.50 29.00 CENTRAL PRESSURE (IN.) Figure 7.3.--Central pressure (po) vs. peripheral pressure (p,) for aZZll hurricanes. The dashed line envelops aZZ data except the Labor Day hurricane of 1935. [po < 28.17 in. (95.4 kPa)] indicate less of a trend. We may infer that this trend would be dampened out completely for SPH and PMH intensity storms. Typhoon data (fig. 7.6) do not show any significant latitudinal variation. c. The larger the Ap, the more intense the hurricane. We do not know of a theoretical approach for determining the upper bound of Pw for the PMH. Earlier studies have solved for Pn (using the Hydromet formula) which some- times resulted in unrealistically high values. For the SPH, we adopted a value of p = 29.77 in. (100.8 kPa) which is reasonably characteristic of extreme hurricanes, e.g., the October 21, 1926 Florida Keys hurricane with a po of 27.52 in'. (93.2 kPa). The Pw for .131 30.05~~ - 30.00-0 101.6 LEGEND 29. 95 - ~~~~~~~~~~~~1 SEP. 1935 -101.4 2 SEP. 1938 29.90- ~~~~~~~~~~~~~~3 AUG. 1969 2 STORMS - l01.2 LU29.85 - 0:: 1 *~~~~~~~~~~~~ ,, .~~~~~~2 -101.0 P 9.80 - ... ..*- em.. *g * g~~~~~3.. * *ee * @00 -~~~~~100.8 29.75 - - *... em.. . *. . 100.6 29.70 - 2,9.65=. *-0. ~~~~~~~~~~~~~~~~~00 29.60 -0 -100.2 29.55 - II I 0 25 30 35 40 LATITUDE (ON) Figure 7.4 Latitude (i)vs. peripheral pressure ( )for all hurricanes. (wi) --the most extreme hurricane on- record (Labor Day hurricane of 1935) was 29.94 in. (101.4 kPa). This suggests that p wfor the PMHi should be not less than 29.94 in. (101.4 kPa). We adopted 30.12 in. (102.0 kPa) for pw This is an upper bound for the data shown in figures 7.1 and 7.4. (kPa) 90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 ~~~'I I I 'I I I 'I I' * I I j I. '.1 29.95 - 101.4 LEGEND 1 SEP. 1935 2 SEP. 1938 0 � *� *� es** - 101.2 3 AUG. 1969 (CAMILLE) 29.85 -- *2 STORMS z -. *a 0 101.0 29.80- .. 0� ����� �� ��� -100.8 w 29.75 - -j / w * *� � -=100.4 w 29.70 - m:n 29.65'- j - 100.4 a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 29.50 - 29.55 100.0 ii III Iii ii 11 1 I ')� Ii ' 199.8 26.80 27.20 27.60 28.00 28.40 28.80 29.20 CENTRAL PRESSURE (IN.) Figure -7.5.--Central pressure (p ) vs. per:ipheral pressure (p .) for all hurricanes. The dashed tine enveZops aZZ daota excert the Labor Day hurrcane of 1935. 10.4 ''0[ ' I j I I I I I'' I t' 7 I14 I -I [10.4 29.90 7.14 - 101.2 7.46 29.85- 7.32 x, 6.81 7.17 7.11 6.99 8� � �7.20 101.0 6.81 D-'a ~ 6.67 7.17 6.6 29.80- * 6.61 � � 7.02 6.6 746 WL 6.99 6.40 6.52 6.40 7.40 6.93 ~~~cl)r,~~~~~~ ~6.93 LUI 29.75- ' Li 29.7.23 6.31 7.29 rL� � e7.32 � e 6.99 � D_ 7.05 7.11 S 7.43 as - 7.37 - 100.6 < 29.70- 7.20 7.14 a wL 7.17 D_ _ 6 *CENTRAL PRESSURE 6.82 7.08 ,, 29.65 _- 100.4 CL NUMERALS DENOTE P. IN 7.46 IN. WITH THE NUMBER 2 (IN THE TEN'S PLACE) OMITTED. 29.60 100.2 10 15 20 25 30 LATITUDE (ON) Figure 7.6.--Latitude (1p) vs. peripheral pressure (pS) for intense typhoons (p < 27.46 in. or 93.0 kPa), 1960-74 0- L 134 Table 7. 2.--Comparison of two peripheraZ pressures for typhoons with po < 27.46 in. (93.0 kPa), 1960-74 Month Date Year Name p P p P p - (in.) ( in.) in. a) a) kPa Aug. 6 1960 Trix 29.74 29.53 0.21 100.7 100.0 0.7 May 17 1961 Alice 29.74 29.62 0.12 100.7 100.3 0.4 Sept. 13 1961 Nancy 29.80 29.68 0.12 100.9 100.5 0.4 Sept. 11 1961 Pamela 29.74 29.62 0.12 100.7 100.3 0.4 Oct. 8 1961 Violet 29.86 29.71 0.15 101.1 100.6 0.5 Aug. 5 1962 Opel 29.65 29.56 0.09 100.4 100.1 0.3 July 15 1963 Wendy 29.77 29.68 0.09 100.8 100.5 0.3 Aug. 12 1963 Carmen 29.77 29.71 0.06 100.8 100.6 0.2 Sept. 9 1963 Clara 29.77 29.71 0.06 100.8 100.6 0.2 Aug. 6 1964 Ida 29.71 29.53 0.18 100.6 100.0 0.6 Sept. 8 1964 Sally 29.77 29.68 0.09 100.8 100.5 0.3 Nov. 18 1964 Louise 29.80 29.74 0.06 100.9 100.7 0.2 Dec. 11 1964 Opal 29.80 29.71 0.09 100.9 100.6 0.3 July 12 1965 Freda 29.74 29.56 0.18 100.7 100.1 0.6 Sept. 15 1965 Trix 29,65 29.56 0.09 100.4 100.1 0.3 Nov. 23 1965 Faye 29.86 29.80 0.06 101.1 100.9 0.2 June 26 1966 Kit 29.77 29.56 0.21 100.8 100.1 0.7 Sept. 4 1966 Cora 29.65 29.56 0.09 100.4 100.1 0.3 Nov. 2 1967 Emma 29.83 29.68 0.15 101.0 100.5 0.5 Nov. 15 1967 Gilda 29.88 29.80 0.08 101.2 100.9 0.3 Sept. 21 1968 Della 29.80 29.68 0.12 100.9 100.5 0.4 Sept. 27 1968 Elaine 29.83 29.77 0.06 101.0 100.8 0.2 July 26 1969 Viola 29.74 29.56 0.18 100.7 100.1 0.6 Sept. 24 1969 Elsie 29.83 29.68 0.15 101.0 100.5 0.5 July 2 1970 Olga 29.80 29.65 0.15 100.9 100.4 0.5 Aug. 20 1970 Anita 29.74 29.62 0.12 100.7 100.3 0.4 Sept. 10 1970 Georgia 29.83 29.77 0.06 101.0 100.8 0.2 Oct. 12 1970 Joan 29.80 29.68 0.12 100.9 100.5 0.4 Nov. 18 1970 Patsy 29.74 29.68 0.06 100.7 100.5 0.2 May 25 1971 Dinah 29.80 29.68 0.12 100.9 100.5 0.4 July 5 1971 Harriet 29.71 29.59 0.12 100.6 100.2 0.4 July 19 1971 Lucy 29.68 29.56 0.12 100.5 100.1 0.4 July 24 1971 Nadine 29.71 29.65 0.06 100.6 100.4 0.2 Aug. 29 1971 Trix 29.83 29.77 0.06 101.0 100.8 0.2 Sept. 21 1971 Bess 29.83 29.77 0.06 101.0 100.8 0.2 July 16 1973 Billie 29.71 29.56 0.15 100.6 100.1 .0.5 Oct. 6 1973 Nora 29.80 29.71 0.09 .100.9 100.6 0.3 pw: Peripheral pressure-defined as the sea-level pressure at the outer limits of the typhoon circulation determined by moving outward from the storm center to the first anticyclonically turning isobar in four equally spaced directions and averaging the four pressures thus obtained. Pwi: Peripheral pressure - defined as the sea-level pressure at the outer limits of the typhoon circulation determined by moving outward from the storm center to the last closed isobar in four equally spaced directions and averaging the four pressures thus obtained. 135 8. CENTRAL PRESSURE 8.1 INTRODUCTION Central pressure (p ) is a universally used index of hurricane intensity. Everything else being equal, the square of the wind speed varies directly with Ap (Ap = pw - p ). po is fundamental to the whole hurricane wind field. Reid and Wilson (1954), Harris (1959) and Jelesnianski (1972) demonstrated that storm surge height is approximately proportional to Ap, holding all other parameters constant. 8.2 CENTRAL PRESSURE FOR THE SPH 8.2.1 INTRODUCTION This study uses a less statistically bound approach than previous studies in setting the level of the SPH p along the east and gulf coasts. Statisti- cal results when using limited data are subject to considerable uncertainty, particularly when developing values for rare recurrence intervals. Reliable observations have been taken for only about 80 years and there has been an average of less than one hurricane per year for the period of record for either coast. This data sample (tables 4.1 to 4.4) must, therefore, be considered a limited sample. Since the criteria must stand the test of time, meteorological judgment was applied to the few extreme events rather than relying heavily on statistical analysis. Guides to this judgment were obtained by averaging several lowest p 's of record (for several lengths of coastline and various overlapping intervals). These averages emphasized two extreme p0os, that of Camille (1969) and the Labor Day hurricane of 1935. 8.2.2 �BASIC DATA Tables 8.1 and8.2 listed hurricanes by date, latitude and longitude, pos and milepost (the distance from a point on the Mexican coast at about 24�N, see fig. 1.1). These tables differ from tables 4.1 to 4.4 in that the milepost is for the lowest p.o In the Gulf of Mexico, the milepost is the shortest distance to the coast. In the North Atlantic, it is the latitude of Po. This procedure for the Atlantic easily relates p0 to the sea-surface temperature (Ts) at that latitude. Such a relation is useful when determin- ing PMH p0 in section 8.3. 136 8.2.3 HISTORICAL STORMS In order to supplement our limited sample of extreme hurricanes, we reviewed historical accounts of hurricanes occurring prior to the turn of this century. Table 8.3 lists dates and locations of some extreme hurricanes prior to 1900. For five of these storm reports (noted with an "S"), compar- isons with recent high surges in these locations allowed an appraisal of the Po's in the hurricanes. For two cases (noted with a "P"), the p was esti- mated from pressure readings given by Ludlum (1963). Because of the diffi- culty in determining p from surge observations, and uncertainty in pressure readings prior to the establishment of standardized instruments and observa- tional procedures, these data are used only in qualitative evaluations. 8.2.4 PROCEDURE Our general method for determining po for the SPH was to let the observed data be the control on the level of po. The data were grouped within over- lapping lengths. At the outset, we needed to decide on the best coastal zone length to use. We started with coastal zones 200, 400, 500 and 800 n.mi. (371, 741, 927 and 1483 km) in length covering both coasts. We averaged the three, five, seven, and ten lowest po's of record within each zone length and compared the averages with the lowest, or most extreme, of record. This was done a) for the original data set in tables 8.1 and 8.2; b) for the original data set plus the historical storm data (table 8.3); and c) for the original data set minus Camille (1969) and the Labor Day hurricane of 1935. These last two storms were given special treatment because their po0's are considerably lower than all other east and gulf coast hurricanes. Coastal lengths were overlapped by 50, 100 and 200 n.mi. (93, i85, and 371 km). One additional set was run with no overlapping. We thus prepared 192 plots (4 zone lengths x 4 averages x 3 data sets x 4 overlappings) of po0 averages and minimums. From a comparison of results we discarded those based on 200- and 800-n.mi. (371- and 1483-km) zone lengths; those with averages based on the three and ten lowest po's; those based on the original'data set plus historical values; and those based on no overlapping and 100- and 200-n.mi. (185- and 371-km) overlapping. The remaining sets were the only ones considered to give 137 Table 8.1.--Hurricane central pressure (po0 )-U.S. guf coast. lat. long. p milepost Date (�N) (�W) (in.) (kPa) (n.mi.) (km) 9-12-70 23.9 97.7 28.55 96.7 10 (19) 8-31-75 24.3 97.7 28.44 96.3 40 (74) 9-20-67 24.8 96.3 27.26 92.3 60 (111) 8-05-33 25.7 97.1 28.80 97.5 130 (241) 9-05-33 26.2 97.1 28.02 94.9 140 (259) 8-18-16 I 27.0 97.5 28.00 94.8 185 (343) 9-14-19 27.3 97.5 27.99 94.8 220 (403) 8-03-70 27.9 97.2 27.89 94.5 260 (482) 9-11-61 28.4 96.4 27.49 93.1 295 (547) 6-28-29 28.5 96.5 28.62 96.9 300 (556) 6-22-21 28.6 96.4 28.17 95.4 320 (593) 8-30-42 28.5 96.2 28.07 95.1 330 (612) 8-27-45 28.6 96.2 28.57 96.8 330 (612) 9-10-71 28.5 95.6 28.91 97.9 340 (630) 10-04-49 28.8 95.6 28.45 96.3 360 (667) 9-23-41 28.9 95.4 28.31 95.9 370 (686) 7-21-09 29.0 95.2 28.31 95.9 380 (704) 8-17-15 29.1 95.2 28.01 94.9 380 (704) 8-14-32 29.1 95.0 27.83 94.2 390 (723) 9-09-00 29.2 95.1 27.64 93.6 390 (723) 7-27-43 29.5 94.5 28.78 97.5 425 (788) 8-08-40 29.9 93.9 28.70 97.2 450 (834) 6-27-57 29.8 93.6 27.95 94.7 460 (852) 9-16-71 29.4 93.2 28.88 97.8 470 (871) 6-16-34 29.3 91.2 28.52 96.6 590 (1093) 10-03-64 29.5 91.4 28.33 95.9 595 (1103) 8-26-26 29.3 91.3 28.31 95.9 600 (1112) 9-08-74 28.0 90.7 27.64 93.6 605 (1121) 9-21-20 29.2 90.9 28.93 98.0 610 (1130) 9-20-09 29.2 90.2 28.94 98.0 650 (1205) 9-19-47 29.8 90.3 28.54 96.7 670 (1242) 8-15-01 29.3 89.7 28.72 97.3 685 (1269) 9-29-15 27.0 89.3 27.53 93.2 705 (1307) 9-15-60 26.6 89.3 28.70 97.2 705 (1307) 8-18-69 28.2 88.8 26.81 90.8 705 (1307) 9-10-65 28.2 89.2 27.79 94.1 710 (1316) 7-05-16 30.4 89.0 28.38 96.1 770 (1427) 9-27-06 30.4 88.5 28.50 96.5 780 (1445) 8-31-50 30.2 88.0 28.92 97.9 820 (1520) 9-20-26 30.3 87.5 28.20 95.5 845 (1566) 10-18-16 30.4 87.2 28.76 97.4 960 (1593) 9-24-56 30.3 86.5 28.76 97.4 890 (1649) 9-29-17 30.4 86.6 28.48 96.4 900 (1668) 7-31-36 30.4 86.5 28.46 96.4 900 (1668) 9-23-75 30.4 86.5 28.20 95.5 900 (1668) 138 Table 8.1.--Hurricane central pressure (pc) - U.S. gulf coast - continued. lat. long. p milepost (�N) (�W) (in.) (kPa) (n.mi.) (km) 9-30-29 29.7 85.4 28.80 97.5 970 (1798) 6-19-72 28.5 85.7 28.88 97.8 990 (1835) 10-07-41 29.9 84.7 28.98 98.1 1015 (1881) 6-09-66 29.1 84.3 28.65 97.0 1030 (1909) 9-05-50 29.1 83.1 28.30 95.8 1120 (2076) 10-19-68 28.8 82.9 28.85 97.7 1140 (2224) 10-25-21 28.1 82.8 28.12 95.2 1200 (2224) 10-18-50 28.0 81.6 28.88 97.8 1200 (2252) 9-04-33 27.8 81.6 28.48 96.4 1215 (2261) 9-17-28 27.7 81.7 28.30 95.8 1220 (2317) 8-27-49 27.2 81.2 28.37 96.1 1250 (2317) 9-18-47 26.3 81.3 28.03 94.9 1320 (2446) 9-08-65 25.2 82.1 27.99 94.8 1375 (2548) 10-05-48 24.7 81.3 28.85 97.7 1380 (2557) 6-17-06 25.1 81.1 28.91 97.9 1395 (2585) 10-18-06 25.0 81.0 28.84 97.7 1395 (2585) 10-11-09 24.7 81.1 28.26 95.7 1400 (2595) 9-03-35 24.8 80.9 26.35 89.2 1410 (2613) 9-10-60 24.3 80.5 27.45 93.0 1410 (2613) 11-05-35 25.6 80.4 28.73 97.3 1440 (2669) 9-15-45 25.5 80.3 28.09 95.1 1440 (2669) 9-21-48 24.5 81.5 27.62 93.5 1380 (2557) 10-21-26 23.6 81.8 27.52 93.2 1380 (2557) 10-14-64 24.3 82.7 28.47 96.4 1360 (2521) 10-17-10 24.5 82.9 27.80 94.1 1355 (2511) 9-10-19 24.7 82.9 27.44 92.9 1350 (2502) 10-20-24 24.7 82.9 28.70 97.2 1350 (2502) 10-19-44 24.7 82.9 28.02 94.9 1350 (2502) 10-04-66 24.1 84.2 28.85 97.7 1330 (2465) 139 Table 8.2.--Hurricane central pressure (po) - U.S. east coast Date lat. long. p milepost (DateN) (W) (in.) � (kPa) (n.mi.) (km) 9-10-19 24.7 82.9 27.44 92.9 1350 (2502) 10-21-26 23.6 81.8 27.52 93.2 1380 (2557) 6-17-06 25.1 81.1 28.91 97.9 1395 (2585) 10-18-06 25.0 80.6 28.84 97.7 1395 (2585) 10-11-09 24.7 81.1 28.26 95.7 1400 (2595) 9-10-60 24.3 80.5 27.45 93.0 1410 (2613) 9-03-35 24.8 80.9: 26.35 89.2 1410 (2613) 9-08-65 25.0 80.6 28.11 95.2 1420 (2632) 9-28-29 25.1 80.4 28.00 94.8 1425 (2641) 10-05-48 25.2 80.3 28.85 97.7 1435 (2659) 9-15-45 25.5 80.3 28.09 95.1 1440 (2669) 8-27-64 25.7 80.1 28.57 96.8 1455 (2695) 9-18-26 25.8 80.1 27.59 93.4 1460 (2706) 11-04-35 25.8 80.1 28.73 97.3 1460 (2706) 10-18-50 25.8 80.2 28.20 95.5 1460 (2706) 9-17-47 26.3 80.1 27.76 94.0 1475 (2733) 9-12-03 26.5 80.0 28.84 97.7 1500 (2780) 9-22-48 26.6 81.0 28.41 96.2 1500 (2780) -9-17-28 26.7 80.0 27.62 93.5 1505 (2789) 8-27-49 26.7 80.0 28.16 95.4 1505 (2789) 9-04-33 26.9 80.1 27.98 94.8 1530 (2836) 17-28-26 28.2 80.4 28.34 96.0 1605 (2974) 10-26-21 28.6 81.8 28.91 97.9 1630 (3021) 9-10-64 29.9 81.4 28.52 96.6 1715 (3178) 10-15-47 31.8 81.1 28.59 96.8 1840 (3410) 8-28-11 32.1 81.0 28.92 97.9 1870 (3466) 9-29-59 32.2 80.2 28.08 95.1 1875 (3475) 8-11-40 32.4 80.9 28.78 97.5 1885 (3493) 9-27-58 32.4 78.5 27.52 93.2 1885 (3493) 8-31-54 33.4 76.8 28.35 96.0 1980 (3669) 9-17-06 33.6 78.9 28.98 98.1 2000 (3707) 10-15-54 33.9 78.5 27.66 93.7 2030 (3762) 9-12-60 33.9 77.9 28.29 95.8 2030 (3762) 9-10-54 34.0 75.6 27.85 94.3 2035 (3771) 9-03-13 34.7 76.4 28.81 97.6 2115 (3920) 12-02-25 34.7 76.6 28.95 98.0 2115 (3920) 8-12-55 34.7 76.1 28.40 96.2 2115 (3920) 9-19-55 34.7 76.7 28.35 96.0 2115 (3920) 8-26-24 35.0 75.2 28.70 97.2 2160 (4003) 9-16-33 35.0 76.2 28.25 95.7 2160 (4003) 8-24-49 35.1 75.3 28.86 97.7 2165 (4012) 9-18-36 35.2 74.6 28.52 96.6 2170 (4021) 9-14-44 35.2 75.5 27.88 94.4 2170 (4021) 8-28-58 35.2 74.2 28.26 95.7 2170 (4021) 8-23-33 36.8 75.9 28.63 97.0 2255 (4179) 140 Table 8.2.--Hurricane central pressure (po) - U.S. east coast - continued. lat. long. p milepost Date (N) (�W) (in.) (kPa) (3. mi.) (kin) 9-17-67 38.0 71.9 28.97 98.1 2340 (4337) 9-21-38 38.7 72.5 27.75 94.0 2395 (4439) 9-11-54 39.7 71.3 27.97 94.7 2465 (4667) 9-09-69 40.6 69.6 28.91 97.9 2540 (4707) 8-29-58 40.6 69.1 28.91 9.7.9 2540 (4707) 9-12-60 40.7 72.6 28.38 96.1 2560 (4745) 8-31-54 40.8 72.5 28.38 96.1 2575 (4772) 9-15-44 40.9 72.2 28.31 95.9 2590 (4799) 8-26-24 41.1 69.8 28.70 97.2 2615 (4846) Table 8.3.--SeZected extreme hurricanes prior to 1900 Date Location Estimated po Origin (in.) (kPa) Aug. 31, 1837 nr. Apalachicola 27.46 93.0 S Oct. 5, 1842 nr. Cedar Key 28.26 95.7 S Sept. 25, 1848 nr. Tampa 28.05 95.0 P Oct. 11, 1846 Florida Keys 26.81 90.8 P Sept. 7-8, 1846 nr. Nags Head 27.96 94.7 S from central Conn. Sept. 23, 1815 } coast to coast be- 27.76 94,0 S Aug. 25, 1635 } tween Narragansett and Buzzards Bays S : surge reports P : pressure observations 141 realistic answers to the problem at hand, i.e., coastal zone lengths of 400 and 500 n.mi. (741 and 927 km); averages of the lowest five and seven p 's; original data sets with and without Camille (1969) and the Labor Day hurri- cane of 1935; and within the 400- and 500.-n.mi. zones overlapping by centering them at 50-n.mi. intervals along the coast. Figure 8.1 is an example of the plots. This one is for averages of the five lowest po's and the minimum p within 500-n.mi. (927 km) lengths centered at 50 -n.mi. (93 km) intervals and including Camille and the Labor Day hurricane of 1935. The next step was to introduce a method of smoothing. The procedure used by Ho et al. (1975) section 2.2.1.1, was adopted. The data for the two zone lengths were smoothed by weighted averaging of each successive 11 data points. These discrete values (A) may be considered as a continuous input series. The smoothed frequency value (Fi) for a point is obtained from the equation: n=5 z W A. n Ai+n n=-5 F. = (8.1) i n=5 Z W n n=-5 We used assigned weights for Wn, as in low pass filtering in time series analysis (after Craddock 1969) as follows*: W = 0.300, 0.252, 0.140, 0.028, -0.040, -0.030; for n n = 0, + 1, +2, +3, +4, +5, respectively. The weighting function adopted here is designed to maintain the frequency and phase angle of the original input series. These weights were applied to all successive discrete values from Texas to Maine, yielding a weighted mean storm p0 at each 50-n.mi. (93 km) milepost of the smoothed coastline. These values were connected to give a continuous smoothed curve. The two *An alternate smoothing procedure often applied in climatological analyses uses a running mean approach (W = 1). The results thus obtained may have n distortions in phase angle variation (shifting of maximum or minimum posi- tions) and in the total area under the curve. Clo r M� = z o 4 020~~~~~ ~DSAC E 0 ( KM X 1 >1 x - - o - C-. oP1 o > M P1 _ . I * _ t i DISTANCE (KM X]C02) 4 8 2 16 20 24 28 32 36 40 44 48 52 5697.0 28.50 - O C I' . I F 09 ' I - . '5 POJTAV R AGES 96.0 28.25 -\ 9.0 28.00- - ] . ~ I - - 27.75 - -o A. - 94.0 gm27.50 - 404 6 82 27.25- (PO() I I 92.0 I LI LEGE ND 27.00 - 27.00- ~I ~NIMU pJ POINT AVERAGES_ 91.0 26.75- 09 I I 0-MINIMUM PRESSURE 28.2.5 - 90.0 26.50 - 0 2 A 6 a 10 12 14 16 is 20 22 24 26 28 30 DISTANCE (N MI X 102) Figure 8.1.--Pzot showing averages of the five Lowest p Is (black dots) within 500-n.mi. (927 7cm) lengths overlapping by 50 n.mi. (93 kmn) for all hurricanes. Also shown are minimum p s (open circles) within 500-n.mi. lengths overlapping by 50 n.mi. The two curves were drawn using the smoothing technique described in section 8.2.4. 143 curves in the example of figure 8.1 are the results of this smoothing technique. We raised the solid curve near milepost 2600 to reflect the observed trend of increasing Po with latitude along the east coast. We compared the averages based on 400- and 500-n.mi. (741- and 927-km) zone lengths and concluded the averages for the 500-n.mi. (927-km) lengths were best. We also decided to use the averages of the seven lowest po's rather than the averages of the five lowest p 's. Figure 8.2 shows a smoothed curve based on the 7-point averages with and without Camille (1969) and the Labor Day hurricane of 1935. Also shown for comparison are data for all hurricanes with po < 28.41 in. (96.2 kPa). These data come from tables 4.1 to 4.4. The data are plotted along the gulf coast at the coastal location closest to the point where po was observed and along the east coast at the latitude where po was observed. We selected these two curves as the pair that give the better relative variation of p0 along both coasts. At this stage we decided the curve not considering Camille (1969) and the Keys (1935) storms should be used. Our decision was based on the idea that these two hurricanes contained extremely low p 's resulting in sustained wind speeds that were not reasonably characteristic of the northern gulf coast and the Florida Keys. The next question is, where should the relative variation be anchored? The decision was made to tie into the observed pressures in the 1938 New England hurricane and hurricane Helene (1958). Reasons for this decision are: a. So anchored (fig. 8.3) the level of p0 is less than for the two most extreme hurricanes along the gulf coast (Camille and Labor Day hurricane of 1935) while enveloping the rest of the data. These two hurricanes are much more severe than any other in the gulf and are therefore not "reasonably characteristic." b. The curve passes relatively close to p0 for Edna (1954) at milepost 2465 --the second most intense hurricane since 1900 north of the Chesapeake Bay area--and Hazel (1954) at milepost 2030. r o- - o 0 Z m m I" 0) '13 - 3> -- I - - -t 0 wH o m - 3> 3 M-I--~ 3> 3 � 3>-4 -3 Z o3 Z- U- o 0 -< 0 0 o 0 zP m z z > 0 ; --I C 0 iE~~~~~~~~~DSAC (K X 0 � -- - I 'Ti> z -q 3>c 28.50- 1 15 ;;I~~~~~~~~ m x C 28.00- 0'019' ~ .N~4~7 4~. I * .1 I 95.0 .x x '-n~~~~~~~~~~_ 4 a 12 16 2-0 24 1\ 2 18 312 36 / 40 44 48 5? 56 97 0 3> ' T I '1 � '~~' 27.75- ~ ~ ~ ~ / ~ 38~ -94.0-..:. 28.50 - / 2 6.75 50I-- 1~~ 55 69~~960 64"26 29. 28 950. 28.25- 28 0 24 21 3 28.00 **!*I I 57 N ___ a I z 1 6 -D (N M3 3102) a 0 7:0 3 I7 5% 44 27.75 a5 3 ulv, 27.50 -Y'L6000 28. LU 6 1 015 26* ./i�5 6 27.50 .60 y 158_ 95.0 a~~~~ AVERAGE OF 7 LOWEST lpAVERAGE OF 7 LOWEST 500 N _j67 M 97K)(IHU AIL 27.25 --e 500--N Ml 97 K) IHM (927 KM) (WITHOU AIL a ~~~~~~~~~~~~~~~~~~~~~~~AND LABOR DAY HURRICANE 92.0 z ~~~CAMILLE AND LABOR DAY- z ~~~~~~~~~~~~~OF 1935) 27.0 0 ~HURRICANE OF 1935)' 27.00 - ~~~~~~~~~~~~~~LEGEND 9 1.0 26.75 - 6�9 YEAR OF HURRICANE (FOR EXAMPLE, 60= 26.50 1960) /s II I II /o 1014 .L,~ /Q 54.0 7 2 4 6 a 10 12 14 16 is 20 22 2e 26 28 30 DISTANCE (N Ml X10 2 figure 8. 2 '--PZot showing smoothed curves through averages of the seven L owest p Is within 500- o-~~~~~~~~~~~~~ nm.927.k)5 n t h vrapigb 0- 6Jmi /588.Te rkncrv nZds ai n theLaor ayhuricneof195 .Teuboecuvomtthssor.Daapisae hurricanes of record with-�L~ po 'S84 in- (96.20 -3 G) r > -, 0- 0 z CD 1-i' M 3 ; > r r. 0 > * ~ ~ ~ -< � -I4~ X �3 > 3 "I -- CD rri > - > 0 , -- C" z m 0 o " > C rtl _~_ 11 ;0 c 0 _nIm > ' : C D 0 > P V) .z~~~~~~~~~~~~~~~V � Zr_ :> 'G m~~. �, 3> z 'm 3 >~ ~~I u, C~~~r I I _n 1 -TI I >. 6� DISTANCE (KM X 102) 4 8 12 16 20 24 28 32 36 40 44 48 52 56 28.50- I~~ I' ' 26 liii, 96.0 Z 28.25 ....~09 -4-260. 4 so 2 --~~Y-------- 96.0 Z 28.25- 64 1 21 0 ~75 2160 8,844 334 6214A5 334 ur~~~~~~~~~~2 97 (~.5 5 UA 4 -0 - 95.0 S1,75 544 c~ 26 6 11(074 0 28 58 54 4 < 27.501- 2I6* <~0~~~~~~~~~~ 3.58 lu 67 Q 27.2 5 1. 14 -1 ~ 92.0 AVERAGE OF 7 LOWEST 500 - 27.00 - N MI 927 KM) (WITHOUT CAMILLE AND LABOR DAY LEEN 2191 1 AND LABOR DAY HURRICANE 90.0 = 26.50 - j101' s 1935)l 351 I, 1 I 2I 1 1 960 I277- .II/1 /1I1I 1 m 67 67 ~u~~ 2746a. 25 I 6 is 20K22 2.4 26 28 309.0 AVERAGE OF 7 LOWEST 500- \ 27.00-- N MI (927 KM) (WITHOUT \ j __CAMILLE AND LABOR DAY - EGN DISTANCE (N M 9102) 26Figure 8..--PZot showing smoothed curves through averages of the seven est ps wihin 500-nm (927 km) Zengths oerapping by 50 n.mi. (93 KM) after(WITH CAMILLE (FOR EXAMPLE, 60=938 hurri- 26.sIII AN AoR-A URCN 1960) -9. I I I ~ ~i�I F 1935)1 I , I I /i i 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 308. DISTANCE (N MI X I02) Figure 8. 3.--Plot showing smoothed curves through averages of the seven lowest Pots5 within 500-n.mi. (927 kin) lengths overlapping by 50 n.mi. (93 kin) after anchoring the relative variation into the .2938 hurri- cane and Helene (1958). The broken curve includes Camille and the Labor Day hurricane of 1935. The unbroken curve omits these storms. Data points are hurricanes of record with po < 28.41 in. (96.2 kPa). 146 c. If the curve were extended, it would come close to hitting Beulah (1967)--the hurricane with the third lowest po in tables 4.1 to 4.4--near milepost 60. d. From extreme storm surges observed along'the New England coast prior to 1900 (table 8.3) we estimated that there have been two storms of about the same intensity as the 1938 hurricane. From about milepost 500 to milepost 1050, we then made an adjustment in our selected curve. We know of no valid meteorological reason for the SPH po in the Biloxi-Pensacola area (about milepost 800) to be higher than at Lake Charles, La. (about milepost 500). Camille entered the coast near Biloxi although it could have just as well entered 50 to 100 n.mi. (93 to 185 km) farther west with little, if any, loss of intensity. East of the Pensacola area, however, the Florida peninsula keeps an SPH from attaining the strength of an SPH farther west. Along this stretch of coast, a major portion of the eastern semicircle of an alongshore west Florida hurricane is overland. Therefore, a quantity of the storm's latent and sensible heat (cooling effect of falling rain) sources are reduced, the equivalent poten- tial temperature (0e) of the surface air is lowered, and the radial gradient of 0 at the surface is weakened. We also adjusted the curve downward near milepost 1400. The Florida Keys south of 25�N are more than a degree of latitude farther south than Port Isabel and should be represented by somewhat lower SPH po. We adjusted the curve downward to lower po along a portion of the nearly eastward oriented southern New England coast where SPH Po should not rise rapidly. We then raised the curve sharply between mileposts 2700 and 2800 where the coast resumes a basically north-south orientation. Figure 8.4 shows a) the adopted SPH po; b) the data for storms with po < 28.41 in.( 96.2 kPa), plotted in the same fashion as figures 8.2 and 8.3; c) the estimated pressure readings from historical data prior to the turn of this century (table 8.3); d) Po's from three previous studies. Tabular data from the adopted SPH Po's are presented in chapter 2. "~~~~ 0 0r 0 > z CD -4 r-' M 00 > -A M: r ~~ 0 0 Z ~~ Z Z 0 < 0 co0 0 z z Dn Z z P1 * 3' m Z DISTANCE (KM X 102) 4 a 12 16 2o0 24 PS 32 26 40 44 4R 52 56 2 6 54 A 060~ ; - 09 96.0 A 10,39 002 6~O 28.25- 6 ' @129 50 60 AA- 21. 64 21ree 18di1 : A 5 I ( W1 4 0 1 842 0 4 5 9 & *42 7 54 7 a ~95.0 z 28.00- ***5 @15 5,18 8 5 032 65..130 It 70 0 ~L855 5I47N 0IRI-33 uJ 3 881 94.0 27.75- 70 * W ..: - -94. N J 33 00 74 j-4 48 2 -- 4826.28 5 a 27.50 - 1s'7.~-7%.. Y'6 / ;1�I~~~cI V.. _L --r'. Ir~~~~~~~~~~75er 93.0 ~ \ *6C /-- /> . 93. 67 / - 3 7 \ 19 " 1 N 15(1%) 27.25;-; 'i- rx ~~~~~~~~~~~~~~~~~~~~~~~~~~~92.0 A\ ;r,,2, 7,' I/ IADOPTED SPH VARIATION 7 POINT LU 27.0- / HU 7-12 IAVERAGE ADJUSTED TO 1938 STORM / .00 NWS 15 ( I) &1846I/ -AND HELENE (WITHOUT-CAMILLE AND 00 ILABOR DAY HURRICANE OF 1935) 91.0 26.75- 69 I . YEAR OF HURRICANE (FOR EXAMPLE, 60=1960) 90.0 26.50 - ICOMPLETE YEAR LISTED 35 PRIOR TO 1900 I I I I i i I I I Ii ,I I ii ii l II Ii I I 9. 0 2 A 6 8 10 12 1I 16 18 20 22 24 26 28 30 DISTANCE (N MI X 102) Figure 8.4.--Plot showing the adopted SPH p0 and p Is from three previous studies. The adopted SPH pO is a modified version of the unbroken curve in figure 8.3. The basic data set (1900-75) and observed and estimated historical pols prior to the 20th century are shown. 148 8.3 CENTRAL PRESSURE FOR THE PMH 8.3.1 INTRODUCTION We first summarize the lowest observed central pressure in the North Atlantic and western North Pacific Oceans. Then we determine a tropical PMH sounding which is used in conjunction with equation 8.4 (one form of the hydrostatic equation) to determine PM1 p. 8.3.2 LOWEST OBSERVED Po 'S Over the North Atlantic, the lowest reported po, 26.35 in. (89.2 kPa), was in the Florida Keys from the Labor Day hurricane of 1935. The second lowest, 26.72 in. (90.5 kPa) occurred over the Gulf of Mexico more than 150 n.mi. (278 km) south of the Mississippi coast near 25�N, 87�W, during hurricane Camille (1969). Over the North Pacific, the lowest reported p is 25.87 in. (87.6 kPa), within the eye of typhoon June, in November 1975. The second lowest is 25.90 in. (87.7 kPa) reported in both typhoon Ida, September 1958, and in typhoon Nora, October 1973. During the last 17 years (1961-77), seven other typhoons have had po's lower than 26.35 in. (the lowest of record for North Atlantic hurricanes). These 10 typhoons occurred between late July and mid-November. All were south of the Florida Keys. 8.3.3 PMH Po0 SOUTH OF 250 N 8.3.3.1 HYDROSTATIC APPROXIMATION. One way to estimate the lowest probable po is to use the hydrostatic approximation to compute the surface pressure in the eye of a hurricane which has certain physical characteristics that can be optimized realistically. The hydrostatic equation between the vertical pressure force and the force of gravity is: dz :Pg' (8.2) dz pg where dp = incremental pressure dz = incremental height p = density of air g = acceleration of gravity 149 Another form of the hydrostatic equation: A = 29.289 T in PL (8.3) V P U [adapted from Smithsonian Meteorological Tables (List 1951), p.203, using natural logarithms, instead of common logarithms]. where A = difference in geopotential (in geopotential meters) between pL and PU T = mean adjusted virtual temperature (�K) [273�K = 32�F = 0�C] v and PU= pressures. PL is the pressure at the lower surface of PL L a layer and PU is the pressure at the upper surface. Computations of surface pressure in the eye of hurricanes are possible because we know that the eye is a vertical warm core. In his classical work, Haurwitz (1935) showed that subsidence of upper tropospheric air of high potential temperature is necessary to achieve the extremely low hydrostatic surface pressure inside the eye. The existence of this central core of subsidence and associated dry adiabatic warming is supported by high temperatures and an absence of significant clouds in the eye. Unusually warm dry eyes of hurricanes are almost always associated with intense or intensifying storms. Malkus (1958) and Kuo (1959) have proposed that subsidence inside the eye may be explained by the presence of supergradient winds in the vicinity of the eye wall within R. Supergradient winds within the inner region of hurricanes have also been stdied by Shea and Gray (1972). The outward acceleration that results ffdm the supergradient winds produces a mean out- ward radial acceleration and a compensating sinking of air in the eye. 8.3.3.2 CONSTRUCTION OF TROPICAL PMH SOUNDING The physical characteristics needed (not listed in order of importance) to compute the lowest po by using the hydrostatic approximation for the tropical North Atlantic are: 150 a. the lowest reasonable height of the 10 kPa (2.95 in.) level, which is the assumed height of the tropopause. b. a distribution of temperature between 70 kPa (20.67 in.) and the tropo- pause somewhere between the dry adiabatic and the moist adiabatic but nearer to the latter, and an isothermal layer from 70 kPa to near the sea surface. The temperature near 70 kPa should be at least 860F (30�C). c. reasonably high moisture content in the column. Details now follow: 8.3. 3.2.1 HEIGHT OF TROPOPAUSE. A hurricane is a system of inflow at low levels and outflow at high levels. In the inflow levels the pressure gradient must be directed inward and in the outflow levels mildly outward. Somewhere in transitioning from inward to outward there must be an approxi- mately horizontal constant pressure surface. Various analyses, e.g., Willett (1955) indicate that the outflow region of a typical hurricane lies near 10 kPa (2.95 in.). This approximately horizontal constant pressure surface could also be deduced from the location of the tropopause. In the PMH, by deduction, the outflow level might be forced a little higher than in the average hurricane but would still be near 10 kPa because this layer cannot extend far into the stratosphere. The hydrostatic computation is not unduly sensitive to the exact pressure given the height chosen for the level surface and 10 kPa appears to be representative. U.S. Weather Bureau Technical Paper No. 32 (Ratner 1957) lists average and extreme heights and temperatures at pressure levels from the surface to 1.5 kPa (0.44 in.) for the period 1946-55. Stations south of 26�N for which monthly data are published include Brownsville, Tex.; Havana, Cuba; Miami, Fla.; San Juan, Puerto Rico; and Isla del Cisne (Swan Island), Honduras (table 8.4). We chose August as the month of greatest potential for the PMH because the Labor Day hurricane of 1935 and hurricane Camille (1969) both developed during August. We believe that a PMH could occur anytime between July and early October. The lower the tropopause height, the lower the po when the hydrostatic approximation is used. To avoid compounding probabilities excessively, we decided to use an average height of the tropopause for the PMH po. The 151 Table 8.4.--August 10-kPa (2.95 in.) average heights (after Ratner 1957) during the period 1946-55 Mean Max. Min. August August August Station Latitude 10-kPa 10-kPa 10-kPa a* (nearest height height height (gpm) degree) (gpm) (gpm) (gpm) Gulf coast Brownsville, Tex. 26�N 16632 16852 16472 54 Lake Charles, La. 30�N 16633 16761 16487 58 Burrwood,La. 29�N 16642 16880 16522 52 Tampa,Fla. 28�N 16629 16825 16418 57 East coast Miami, Fla. 26�N 16613 16776 16474 56 Charleston, S.C. 33�N 16644 16802 16520 49 Hatteras, N.C 35�N 16643 16832 16495 62 Interior southeastern United States Atlanta, Ga. 34�N 16637 16781 16474 48 Caribbean Havana, Cuba 23�N 16634 16761 16485 55 Isla del Cisne 18�N 16586 16736 16416 49 (Swan Island) San Juan, P. R. 18�N 16595 16764 16471 54 *a = standard deviation of heights. 152 mean August 10 kPa (2.95 in.) Isla del Cisne height of 16,586 gpm* was used because it was the lowest mean of the five southernmost radiosonde stations listed by Ratner (1957). 8 3 3 2.2 DISTRIBUTION OF TEMPERATURE. Since we used the mean August 10 kPa (2 95 in.) Isla del Cisne height, we also used the correspond- ing 10kPa mean August temperature (T) of -74�C (-101.2�F). We did this because temperatures in the upper troposphere decrease with decreasing p [Gentry (1967) and Sheets (1969)], although via hydrostatic methods warmer temperatures yield lower p 's. The air temperature should be very warm and nearly isothermal from about 70 kPa (20.67 in.) down to near the sea surface. This is a pattern observed in extreme hurricanes and typhoons. We chose a temperature of 33�C (91.4�F). This is about 3�C (5.4�F) warmer than the warmest observed eye soundings at 70 kPa, e.g., typhoons Wllda (1964) and Nora (1973), and cor- responds to a temperature 10�C (1.9�F) warmer than the 99th percentile of the sea-surface temperature for the Florida Keys (U.S. Navy 1975). To obtain a temperature of 33�C (91.4�F), at 70 kPa, we warmed the air approxi- mately dry adiabatically between 10 kPa (2.95 in.) where T = -74�C (-101.2�F) and50 kPa (14.76 in.). We then warmed the air nearly moist adiabatically from 50 kPa where the temperature was set at 23�C (73.4�F) to 70 kPa. Warm- ing near the moist adiabatic rate would result from lateral mixing of the descending air with cooler moist air originating in the convective eye wall. The evaporation of liquid water reduces the compressional warming and increases the humidity of subsiding air (Malkus 1958). The sea-surface temperature (Ts) bounding the lower end of the tropical PMH sounding was chosen in the following way. Ninety-nlne percent frequency levels of T (U.S. Navy 1975) were plotted along the gulf coast from south- S ern Texas to the southern Florida coast. This consistently yielded *A geopotential meter (gpm) results from a hydrostatic computation in which gravity is assigned a value of 9.8 m (32.2 ft) s-2 throughout the world at all elevations rather than its true value which varies slightly with loca- tion and elevation. The gpm is the international standard for computing heights from radlosonde observations. 153 temperatures between 89.00 and 89.50F (31.70 and 31.90C). We chose to use 89.50F (-32�C) as the Ts, which allows the T to be 91.40F (33.00C), or about 2�F (~i�C) warmer than Ts 8. 3. 3.2.3 MOISTURE CONTENT. Maximum persisting 12-hr dew points (Td) used by the Hydrometeorological Branch of 780F (25.6�C) to compute upper limits of rainfall rates reach 780F (25.6�C) for much of the southeastern United States during the warmest months of the year. The 780F Td is set by higher Ts some distance offshore. Logic would lead us to believe that persisting 12-hr Td close to the sea surface around the center of a PMH in the tropics cannot be less than 780F. In addition, atany instant Td values can be substantially higher than persisting 12-hr Td's. We are not assuming saturation at the eye center so the dew-point tempera- ture at the eye center would have to be less than our assumed temperature of 91.4�F (33.00C). We have decided to let the Td = 82�F (27.8�C) between 85 kPa (25.10 in.) and the sea surface. This yields a mean relative humidity of about 75%. This is decreased slowly to 70% between 85 kPa and the top of the isothermal column or 70 kPa (20.67 in.). Further aloft relative humidity is decreased to 50% between 70 kPa and 50 kPa (14.76 in.), to 40% between 50 kPa and 40 kPa (11.81 in.) and to 5% between 20 kPa (5.91 in.)and 10 kPa (2.95 in.). Hawkins and Imbembo (1976) noted relative humidities falling under 50% at 65 kPa (19.19 in.) within the eye of hur- ricane Inez (1966). The mean relative humidities for the PMH in the Tropics are listed in table 8.5 along with T for seven layers of the troposphere. The mean relative humidities and T in table 8.5 were converted to Tv (List 1951). We used the preceding criteria to construct our adopted Tropical PMH sounding shown on a pseudoadiabatic chart in figure 8.5. An actual hurri- cane sounding for Inez (1966) at maximum intensity (27.37 in., 92.7 kPa) south of Puerto Rico is shown for comparison. The Inez sounding is the most complete sounding obtained from a hurricane of such great intensity. A partial typhoon sounding to about 50 kPa (14.76 in.) is presented for typhoon Marge on August 15, 1951, at 0155 GMT (Simpson 1952). This sounding .154 Table 8.5.--Computation of po for the tropical North Atlantic 10 kPa height of 16,586' gpm [Isla deZ Cisne (Swan Island) - August mean] (P U PL) T () T ( C) R. H. (%) A4 (gpm) Remarks (kPa) 20 kPa height 10 - 20 -56.5 -56.5 5 4399 20 kPa height 12187 gpm 30 kPa height 20 - 30 -28 -28 20 2912 30 kPa height 9275 gpm 40 kPa height 30 - 40 - 5.7 - 6 30 2253 7022gpm 7022 gpm 50 kPa height 40 - 50 +15.6 +14 40 1887 5135 gpm 5135 gpm 70 kPa height 50 - 70 +31.7 +28 50 3004 70 kPa height 2131 gpm 70 - 85 +38.4 +33 70 1770 85 kPa height 361 gpm > 85 +38.1 +33 75 = 16225 PU = pressure at a specified upper level L In = pressure at a specified lower level PU 29.289 () T = mean virtual temperature L 361 gpm 85 = 29.289 (311.3 OK) T = mean temperature = mean relative humidity P RH. PL 361 in - . 03959 85 9117.66609 A~ = difference between PU and PL (gpm) �K = �C + 273.20n Pi = .03959 + in 85 in PL =-.03959 + 4.44265 In PL = 4.48224 PL = Po = 26.11 in. (88.4 kPa) 155 6.0 8.0I I1 10.0 , ,-lISLA DEL CISNE (SWAN ISLAND) AUGUST T 10.0 12.5 -15.0 17.5 20.0 "'~ 25.0 30.0 35.0 40.0 45.0 50.0 -90 - 80 -70 -60 -50 -40 -30 -20 -10 0 TEMPERATURE (�C) 40.0 45.0 50.0 55.0 TYPHOON MARGE _ --60.0 \ AUGUST 15,1951 \ 0155 GMT U.L 65.0 P65.0 INEZ I | LU 70.0 --ADOPTED 75.0 TROPICAL - ~\ / PMH 80.0 Ah I SOUNDING 85.0 90.0 95.0 100.0 105.0 -50 -40 -30 -20 --10 0 10 20 30 40 50 TEMPERATURE (DC) Figure 8.5. - -Adopted tropical PMH sounding. AZso shown are soundings for hurricane Inez (1966) and typhoon Marge (1951). 156 is considerably warmer than the Inez sounding and is one of the warmest typhoon soundings on record. Marge's po was 26.43 in. (89.5 kPa). 8.3.3.3 CALCULATION OF PO. Values of A~ calculated from equation 8.3 for the upper six pressure layers are listed in table 8.5. Subtracting the accumulating sum of the Ac's from 16,586 gpm (assumed height of tropopause) gives the height at the respective PL'S. Thus, in our 'computation, the accumulated sum of Ac's is 16,225 gpm at the 85-kPa (25.10-in.) level; the 85-kPa height is 361 gpm (16,586-16,225). Now, if we wish to find the pressure at the surface of the sea, pL' we can rewrite equation 8.3 in the form: in PL = _ + in U (8.4) 29.289 T The 85-kPa level becomes PU' A~ = 361 gpm, and T = 38.10C (311.30�K). Then in pL = 4.48224; PL = 26.11 in. (88.4 kPa). Sensitivity of computed Po from soundings to changes in values of meteorological parameters is covered in section 8.3.6. 8.3.3.4 COMPARISON OF COMPUTED PMH PO WITH OTHER ESTIMATES The Hydrometeorological Branch (U.S. Weather Bureau 1968) decided on a value of 25.94 in. (87.8 kPa) for the PMH po based on a frequency approach to the problem. Prior to this, the Hydrometeorological Branch (U.S. Weather Bureau 1959b) made po computations using Tv from a'saturated moist adiabatic ascent around the eye from the surface to the 10-kPa (2.95 in.) level with a corresponding dry adiabatic descent inside the eye. Their computation gave a value near 26.00 in. (88.0 kPa). We may also estimate a PMH po for the North Atlantic by looking at data from the western North Pacific. Atkinson and Holliday (1977) have stated that peripherial pressure (Pw) is normally about 0.295 in. (1 kPa) lower over the western North Pacific than over the corresponding region of maxi- mum tropical cyclone activity over the tropical-North Atlantic. For the tropical North Atlantic, if we used the PMH Pw of 30.12 in. (102.0 kPa) with the lowest observed po of 26.35 in. (89.2 kPa), we have a pressure reduction of 12.5%. Lowering the Pw 0.295 in. (1 kPa) to 29.82 in. (101.0 kPa) over 157 the western North Pacific and using the lowest observed po0 of 25.87 in. (87.6 kPa) gives a reduction of 13.3%. If we increase the pressure reduc- tion of the North Atlantic from 12.5 to 13.3% our PMH po would equal 26.11 in. (88.4 kPa). We believe that a hurricane in an optimum tropical environment for at least 36 hours could in that time equal the explosive deepening of typhoon Irma (1971) even though the tropical North Atlantic is smaller in size than the tropical western North Pacific. Irma deepened from 28.97 in. (98.1 kPa) to 26.10 in. (88.4 kPa) in 24.5 hours. These considerations lend support to our estimate of PMH po0, 26.11 in. (88.4 kPa), for the Florida Keys south of 25�N. North of 25�N, we will increase PMH po0 as described later in this chapter. 8.3.4 PMH P AT CAPE HATTERAS Cape Hatteras was another location chosen for computing PMH po0. This location is still far enough south to be in a subtropical environment during a PMH situation. We followed a procedure similar to that given for the tropical sounding (secs. 8.3.3.1 to 8.3.3.3). Table 8.6 lists the values of parameters used and figure 8.6 shows the PMH sounding (solid line) on a pseudoadiabatic chart. We calculate the PMH p at Cape Hatteras at 26.40 in. (89.4 kPa). 8.3.5 PMH Po NEAR 45�N 8.3.5.1 FROM A SOUNDING. Since sea-surface temperatures (T ?s) at 5 45�N are too cool to nurture a PMH po0 the only recourse is to move a hurri- cane from south of Cape Hatteras at a fast forward speed, thereby avoiding excessive decay. We computed a po at 45�N from a sounding in much the same way as we did for the Cape Hatteras sounding. The major difference in the sounding (fig. 8.6) is that we must make modifications for a nontropical environment. Such modifications lead to less confidence because they do not consider weakening effects caused by entrainment of ambient air into the eye, strong T grad- s ients, and other factors. We therefore consider our computed po (table 8.7) as a lower limit for 45�N. 158 Table 8.6.--Computation of pO for Cape Hatteras 10 kPa height of 16,643 gpm (August mean) AP (PU- PL ) Tv (C) (�C) R.. (%) A (gpm) Remarks (kPa) 20 kPa height 10 - 20 -53 -53 5 4470 12173 gpm 30 kPa height 20 - 30 -29.5 -29.5 20 2893 30 kPa height 9280 gpm 40 kPa height 30 - 40 - 8.2 - 8.5 30 2232 40 kPa height 7048 gpm 40 - 50 +12.3 +11 40 1864a height 5184 gpm 71 kPa height 50 - 71 +28.6 +25.5 50 3097 2087 gpm 85 kPa height 71 - 85 +36.1 +31 75 1630 457 gpm > 85 +35.8 +31 80 = 16186 P PLA PU = pressure at a specified upper level n PU 29.289 (T) PL = pressure at a specified lower level ( -- PL 457 T = mean virtual temperature in 8 457 v85 29.289(309) T = mean temperature L457= .050,50 R.H. = mean relative humidity in 8- 9050.301 A~ = difference between PU and PL (gpm) ln P 0 .050 + ln 85 oK = �C + 273.20 in PL = 5050 + 4.44265 In PL = 4.49315 PL ) P = 26. 40 in. = (89.4. kPa) 159' 6.0 o.o0 CAPE HATTERAS AUGUST T 10.0 A. CARIBOU AUGUST T 12.5 15.0 - 17.5 20.0 - 25.0 30.0 35.0 40.0 _' 45.0 50.0 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 TEMPERATURE (OCI 40.0 45.0 CARIBOU %, 50.0 PMH 55.0 SOUNDIN\ CAPE HATTERAS 55.0 '% PMH SOUNDING 60.0 65.0 u. 70.0 75.0 80.0 85.0 90.0 95.0 100.0 105.0 -50 -40 -30 -20 -10 0 10 20 30 40 50 TEMPERATURE (�C) Figure 8.6.--Adopted PMH soundings for Cape Hatteras, N.C., and Caribou, Maine. 160 Table 8. 7.--Computation of po for Caribou, Maine (applied to 45�N) 12.5 kPa height of 15,110 gpm (August mean) Ap (PU -PL) Tv (C) T (0C) R. H. (%) A4 (gpm) Remarks (kPa) 15 kPa height 12.5 - 15 -55.5 -55.5 0 1162 13948 gpm 15 - 20 -48 -48 5 1883 20 kPa height 12065 gpm 30 kPa height 20 - 30 -29.5 -29.5 25 2895 90 gpm 9170 gpm 40 kPa height 30 - 40 - 9.2 - 9.5 30 2207 40 kPa height 6963 gpm 50 kPa height 40 - 50 + 3.2 + 2.5 40 1806 5157 gpm 50 - 70 +14.9 +13.5 50 2838 70 kPa height 2319 gpm 80 kPa height 70 - 80 +25.6 +22.5 75 1147 1172 gpm 1172 gpm 90 kPa height 80 - 90 +28.6 +25 85 1041 90 kPa height 131 gpm > 90 +24.4 +21.4 95 Y = 14979 PU = pressure at a specified upper level PL = PU 29.289 (T) = pressure at a specified lower level _PL~~~~~~~ ~PL 131 Tv = mean virtual temperature in 90 29.289 (297.6) T = mean temperature 131 in 9- = .01503 90 8716.40T R.H. = mean relative humidity Ac = difference between PU and PL (gpm) Pl = .01503 + ln.90 OK = �C + 273.20P = .01503 + 4.49981 i PL = 4.51484 PL = po = 26.98 in. (91.4 kPa) 161 In constructing the sounding, we used data from Caribou (47�N) rather than two other New England radiosonde stations (Nantucket, 41�N and Portland, 43.5�N) because for the months of August and September, Caribou had the lowest tropopause heights and warmest temperatures (yielding lower po). We elected to use the August height rather than September because T 's are s highest off the Maine coast during this month. This height is near 12.5 kPa (3.69 in.), 15,110 gpm, rather than 10 kPa (2.95 in.) used for the other two soundings. The values of parameters selected are given in table 8.7. The computed p is 26.98 in. (91.4 kPa). 8.3.5.2 FROM HISTORICAL STORMS. We studied storms north of 40�N along the Atlantic coast and those near Japan. 8.3.5.2.1 AFFECTING NEW ENGLAND, NOVA SCOTIA, AND NEWFOUNDLAND. The two lowest po'S along the New England coast since 1900 are listed in table 8.8. Record low po 's from hurricanes affecting Sydney and Halifax (Nova Scotia) and Gander (Newfoundland) are also indicated. The po0 at Gander from Ione approximates the lowest p in that hurricane on the given date. The lowest p over Nova Scotia is undoubtedly lower than 28.63 in. (97.0 kPa) because the centers of Helene and the 1927 storm did not pass directly over Sydney nor Halifax. The 27.86 in. (94.3 kPa) po0 along the Connecticut coast during the New England hurricane of 1938 is a record low po for New England from either a hurricane or winter-type storm. For Nova Scotia and Newfoundland, however, winter storms have had lower po0 's. Newfoundland has reported an all-time low po of 27.94 in. (94.6 kPa) and Nova Scotia 28.06 in. (95.0 kPa). 8.3.5.2.2 AFFECTING JAPAN. It is of interest to examine the lowest recorded po's from other midlatitude land areas other than the North American east coast. We used Climatic Table of Japan, Part 3 (Japan Meteorological Agency 1972) to study po's over the western North Pacific. Table 8.9 lists these lowest po's from Japan occurring within designated 5� latitude bands. Comparing this table with table 4.1, we see that the Labor Day hurricane of 1935 (24.8�N) with a po0 of 26.35 in. (89.2 kPa) and 162 Table 8.8.--Lowest observed p 's from New England, Nova Scotia and New- foundland during hurricane passages. Lati- PO Place p recorded Hurricane Date tude (in.) (kPa) or estimated New England New England Sept. 21, 1938 41.30N 27.86 94.3 Just west of New Haven, CT Edna Sept. 11, 1954 41.70N 28.05 95.0 Chatham, MA Nova Scotia Helene Sept. 29, 1958 46.10N 28.63 97.0 Sydney --- Aug. 25, 1927 44.60N 28.69 97.2 Halifax Newfoundland Ione Sept. 22, 1955 49.00N 28.26 95.7 Gander Table 8.9.--Lowest observed pO for selected latitude bands (Japan) Latitude p Location and Band (�N) (in.) (kPa) Date latitude <25 26.82 (90.8) Sept. 15, 1959 Miyakojima (24047') 25-30 27.11 (91.8) Sept. 15, 1961* Naze (28023') 30-35 26.92 (91.2) Sept. 21, 1934 Murotchisaki (33�15') 35-40 27.68 (93.7) Sept. 16, 1961* Kyoto (35001') 40-45 28.24 (95.6) Mar. 18, 1912** Nemuro (43020') >45 28.37 (96.1) Sept. 17, 1961* Wakkanai (45025') *Typhoon Nancy **Extratropical cyclone hurricane Camille while offshore (28.20N) with a po of 26.81 (90.8 kPa) were more intense than the typhoons of 1959 and 1961,respectively. Ho et al. (1975) gave a po of 26.85 in. (90.9 kPa) for Camille north of 300N, which is lower than the typhoon of 1934. Tables 8.8 and 8.9 indicate that the New England hurricane of 1938 (41.3�N) and hurricane Ione (49.0�N) were stronger than any typhoons affecting Japan north of 400N. Only between 350 and 40�N has a po been recorded that was lower on land in Japan than along the U.S. east coast. 163 8.3.5.3 FROM PREVIOUS ESTIMATES, The only earlier estimate of PMH p along the east coast near 45�N is 27.66 in. (93.7 kPa) (U,S. Weather Bureau 1968) based on an estimated'1000-yr return period po developed from extrapola- tion of observational data north of 38�N. 8.3.5.4 RECOMMENDED VALUE OF PMH PO NEAR 45 N. The computed p for the PMH from a sounding'based on the hydrostatic approximation is highly dependent on the assumptions that go into setting the sounding. For example, if the height of the 12.5 kPa (3.69 in.) level were raised 1 a away from the mean height for Caribou (Ratner 1957) to 15,202 gpm, the computed po would increase from 26.98 in. (91.4 kPa) to 27.25 in. (92.3 kPa). It would not be too hard to raise the computed po to 27.46 in. (93.0 kPa) by revising the values of other input factors. A po of 27.86 in. (94.3 kPa) has occurred near 41�N only once in this century and possibly twice'before that (see sec. 8.2.4). We shall assume that a p lower than 27.86 in. could occur at 45�N. We have decided to adopt 27.46 in. (93.0 kPa) as the PMH po at 45�N. This is a rounded metric value about halfway between the values from the sounding and the 1938 hurricane in New England. 8.3.6 SENSITIVITY OF ADOPTED PMH PO COMPUTATIONS TO CHANGES IN INPUT FACTORS Important to any computation of p from an assumed sounding is the sensi- tivity of the'results to variations in the input factors. Such sensitivity tests were made for the adopted tropical and Cape Hatteras soundings. Results are shown in table 8.10. The most important factor-in-table 8.10 is the temperature of the column in the layer between about'70 and 40 kPa (20.67 in. and 11.81 in.). In the lower portion of this layeY<, the lapse rate of temperature was assumed to be approximately equal to the midst adiabatic rate, and in the upper portion, the dry adiabatic rate was 'approximated. For the tropical sounding, we chose to reduce the Tv in this layer by 4.9�F (2.7�C) from 74.7�F (23.7�C) to v 69.8�F-(21.0�C). This is the T if we connect the temperatures near 70 and v 40'kPa with a straight line, thereby bypassing the temperature shown at 50 kPa (14.76 in.) in figure 8.5. The lower Tv raises our tropical pMH p 164 Table8.1O--Sensitivity of computed PMH p0to changes in input factors Tropical sounding Cape Hatteras sounding po 26.11 in. (88.4 kpa) Po 26.40 in. (89.4 kPa) Change Input factor Change in value AP i nAPu 1.. Height of *+ a =49 gpm � 0.15 in. tropopause - ~~(+ 0.48 kPa) +a =62 gpm + 0.19 in. (+ 0.62 kPa) 2. T emperature at + a =4.5-OF + 0.08 in. +.a .=-5.0"F + 0.09 in. tropopause .(2. 5 0 C) (+0.2.8 kPa) (2. 8 0C). (� 0.30 kPa) 3. Height and + a (item 1) +'a (item 14) temperature + 0.22 in. + 0.27 in. at tropo- 1-.0.75 kPa) (+ 0.91 kPa) pause - ar (item .2) - a (item 2) - a (itemi1) - a (item 1) - 0.22 in. -0.27 in. (-0.75 kPa) (-0.91 kPa), -i a (item 2) + a (item 2 4. Cooling the T for column + 0.21 in. T for column + 0.19 in. column be- from 74.70F (+ 0.70 kPa) from 68.9F (+ 0.62 kPa) tween 40 (23.7-C) to (20.5"C) to and about 69.8-F (21.0-C) 164.80F (18.2oCJj 70 kPa 5. Relative Lowered 10% Lowered 10% humidity below 50 kPa below 50 kPa and 20% above + 0.11 in. and 20% above + 0.09 in. 50 kPa (+ 0.36 kPa).50 ka (+ 0.29 kPa) 165 from 26.11 in. (88.4 kPa) to 26.32 (89.1 kPa). The reduced T results in v only about a 1% change in po. In our computations we used a mean August height for the tropopause. If the values are normally distributed, approximately 2/3 of them will be within + a of the mean value. A variation of the tropopause height by this amount results in a less than 1% change in po. The sensitivity tests shown in table 8.10 indicate that by using + a from the mean August tropopause heights and temperatures our estimate of PMH p could be too high or too low by as much as 0.22 in. (0.75 kPa). The indi- cated changes in items 4 and 5 would increase not lower PM1H po. We did not add changes in item 4 to those of item 3 to raise po even more. Although meteorologically realistic, such an approach would raise the p0 of the tropical sounding to a level higher than what was observed at Long Key, Florida Keys, in September 1935. For the Cape Hatteras sounding, which used the same technique of construction, we believe the effect of adding changes in items 3 and 4 together would also underestimate the PMH po. Adding changes of items 3 and 5 or 4 and 5 would also underestimate PMH p for both locations. 8.3.7 GENERALIZED ALONGSHORE VARIATION OF PO FOR THE PMH 8.3.7.1 EAST COAST. The tropical PMH p of 26.11 in. (88.4 kPa) is applied south of 25�N (milepost 1400) and the po of 26.40 in. (89.4 kPa) at Cape Hatteras, near milepost 2180. Between these two points we increased the po in proportion to the decrease in sea-surface temperatures (Ts) at the 99% level along the east coast (fig. 8.7). We are not implying a dynamical relation between the Ts and minimum po0, but are using observational data which have shown that the lower the Ts the higher the po, everything else being equal. Between Cape Hatteras and 45�N (near Eastport, Maine), a first approximation to the coastal variation of p was obtained by increas- ing p in proportion to the decrease in T at the 99% level. Amodification to this general procedure was made between mileposts 2550 (near New York City)and milepost 2700 (near Martha's Vineyard). Here T indicated p should rise faster than the adopted variation shown in indicated Po should rise faster than the adopted variation shown in O 0 > H 0 0 C H~~~~~~~~~~~~~~~~~~m _ 0 >l -U < m c Io r- m > 0 ((3 cir C) C Z 0 z m . H 0 H 3 0 H c o P P1 z o > z - P1- OlP Io *m Ut! vo 7Z i DISTANCE (KMX10 4 a 1 16 PO 24 28 32 136 40 44 48 52- 56 90 -32 U,~of , LU 86 3 30 I.- 82-2 _ LU IS 7 -26 - -~~~~~~~~~~~~~~~~~~~~~~~~~24 U- 70 - N...... ~~~~~~~~~~~~~~~~~~~~~20 6 6 I~~ ~ i I ,Iii lii Ili 0 2 A 6 a 10 1 2 14 16 is 20 -22 24 26 2 8 30 DISTANCE (N Ml X 102) Figure. B. 7. --99th percentile sea-surf'ace temperatures along the gulf' and east coasts,. 167 figure 8.8. We did not accept a faster rate of increase because of the nearly east-west orientation of the coast in this region. Figure 8.8 shows data for all storms with po0 <28.05 in. (95.0 kPa) [including estimated pressure readings from historical data prior to the turn of this century (table 8.3)]; the adopted po0 curve; and the curve from HUR 7-97 (U.S. Weather Bureau 1968). The p data are plotted using the same format as used in figures 8.2 to 8.4. PMH po tabular data for the east coast are presented in chapter 2. 8.3. 7.2 GULF COAST. All the 10-kPa (2.95 in.) August mean heights along the gulf coast are lower than the height at Cape Hatteras, implying that PMH p0 along the gulf coast is less than that at Cape Hatteras. Ts (99th percentile) is also warmer everywhere in the Gulf of Mexico than at Cape Hatteras, also implying a lower PMH po0 along the gulf coast. This suggests a range of PMH p along the gulf coast somewhere between the 26.11 in. (88.4 kPa) p computed from the tropical sounding and the 26.40 in. (89.4 kPa) po computed at Cape Hatteras. In contrast,the PMH po's for the Texas coast should be slightly higher than similar latitudes (26�-30�N) along the east coast because comparable 10 kPa (2.95 in.) heights are higher over the western gulf than along this portion of the east coast (see table 8.4). Figure 8.7 also shows the 99% level of T for the gulf coast. From the S middle Texas coast (milepost 300) to the Florida Keys (milepost 1400), Ts has a small range [between 89.0�F (31.7�C) and 89.5�F (31.9�C)]. 8.3. 7.2.1 NORTHEAST GULF COAST. Reasons for PMH p0 being higher along the northeastern gulf coast than anywhere else in the gulf are: a. The influence of the Florida peninsula (see sec. 8.2.4). In order for the PMH to enter near normal to the coast at full intensity, it would have to be a recurved storm yielding a p0 higher than if the Florida peninsula did not exist and it had not recurved; (see sec. 8.3.7.2.1,2). b. The difficulty of gaining entrance to the concave coast without weakening. c. Observational data and analysis suggest a higher po; (see fig.8.8). W ~~z M C M -0 > - - I M z z -~~~~~c -- I- o P1 0.0 -(P 0 -( 0 a W 0 > W 0 -4 ~~> < CO m* -n c c~zao CD ; '~~~~~~~~- CE -< 0 P1 Z ~~~~~~~~~~~~~~~~~~~~~~ _ z P1 -4 z I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F mMzU x z 4,~~ I I I DISTANCE (KM X 102) 4 8 12 16 20 A 24r. 28 32 36 40 44 48 52 56 95.0 28.00 -33 'I5 1 5 1 I7 118 8476s I 4 L618 461 I 1 1 33 54 1457 * 65 4li 70 @32 6 .5 40 AAAI' 27.75 - 72 61 0 2 58 9380 27.50 - 0 2 6 - 2 8 6 1837 160 LU 67 .19 a:~~~~~~~-/ 27.25 9. ByRE~~~~~~U. fl A~~~~~~~~~l ~92.0 LU U.25 WEATF-ER BUR ivlhU PiA (196 3) - 27.00 "N / 91.0 1846 ~~~~~~6 ADOPRTED FIMF 26.75- 69 I 'el-, LU .0F R 90.0 26.506-0 35 E 7 ~-.-- / LEGL~ND 26.25- .. '/.�~---- -.-- _ 89.0 26. . YEAR OF HURRICANE -~ (FOR EXAMPLE, 60= 1960) 26.00=-- -P-RELIMI-t4A.tY---2 JJR4E - A COMPLETE YEAR LISTED 88.0 PRIOR TO 1900 25.75- I I . I I I I II i , I 1i 87.0 0 2 4 6 8 10 12 14 16 is 20 22 24 26 28 30 DISTANCE (N MI X 102), Figure 8.8.--Plot showing the adopted PMH p a preliminary p for the eastern Gulf of Mexico. and the p from a study completed in 1968. The Basic data set (1900-75) and observed or estimated histori- cal p 's prior to the 20th century are shown. 169 8.3.7.2.1.1 PRELIMINARY PO' One would expect the PMH p0 near mile- post 1100 to be higher than the PMH po0 of 26.21 in. (88.8 kPa) along the east coast at the same latitude (milepost 1700) because mean 10 kPa (2.95 in.) heights are higher over the Gulf of Mexico during the warmer part of the year. Yet, the milepost 1100 p should be lower than the PMH po at Cape Hatteras (26.40 in. or 89.4 kPa) because of higher heights at Cape Hatteras. The PMH poat Burrwood, La. (near milepost 700), based on 10 kPa height considerations (table 8.4) should be about 26.22 in. (88.8 kPa). A slightly higher PMH p farther east based on slightly cooler T yields a p �~~~~~~~~~~~~~ of about 26.25 in. (88.9 kPa) which is 0.04 in. (0.1 kPa) higher than east coast PMH po0 near milepost 1700. We set the PMH po near milepost 1100 at 26.25 in. (88.9 kPa) before con- sidering recurvature and subsequent filling considerations. The dropoff in p southward from near milepost 1100 to the Florida Keys (see preliminary PMH curve fig. 8.8) is consistent with the dampening effect of the peninsula. 8.3.7.2.1.2. DETERMINATION OF FINAL PO. The northeastern gulf coast near milepost 1100 will have higher PMH po than the 26.25 in. (88.9 kPa) indicated above. The Florida peninsula prevents an extreme steady state hurricane from entering a coastal area centered near milepost 1100 from the east through south. Also, intense storms moving from the north are not meteorologically realistic. Therefore, the PMH over this part of the northeastern gulf must be a recurved hurricane. We assume based on the discussion which follows that this recurved PMH will also be filling. During a survey of 256 typhoons, which will follow, we found that 94 recurved with a po <29.00 in. (98.2 kPa). Eighty-nine of these storms either recurved while filling or deepened with a po0 >27.46 in. (93.0 kPa)-- the upper limit of PMH po for the east coast. Riehl (1972) states "virtually all typhoons reached their peak intensity at or a little before the point of recurvature and subsequently decrease at some variable rate." Point of recurvature is defined as the point where the 0 of the storm just exceeds 180� (movement from just west of due south). For all practical 170 purposes point of recurvature may be considered to equal 1800 for a recurving storm moving from 1800 for less than a few hours. The hurricane data show the trend for larger p0 s for recurving storms. Only two of them approach the severity of the PMH. One of these, the Labor Day hurricane of 1935, recurved west of Cedar Key after it had filled about 2 in. (-7 kPa) in 36 hours. Camille (1969), the other storm, did not recurve until after she made landfall along the Mississippi coast. Janet (1955), an extreme hurricane (27.00 in., 91.4 kPa) over the western Carib- bean, did not recurve. Another extreme western Caribbean hurricane (Nov. 1932) did recurve after reaching a minimum p0 of 27.01 in. (91.5 kPa) but its filling rate is not known. Hattie (1961), still another extreme western Caribbean hurricane, followed an unusual track. After moving northward for a couple of days, she turned westward and devastated the country of Belize I day after attaining a minimum p0 of 27.17 in. (92.0 kPa). To estimate the p along the coastal section under discussion (Florida panhandle to Cape Sable), we shall analyze the filling rates of recurved typhoons, and assume the results can be applied to hurricanes. There is no apparent reason why there would be a difference in filling rates in the western North Pacific and North Atlantic. Chin (1972) evaluated reconnaissance eye-fix typhoon data gathered by air- craft of the U.S. AirForceand U.S. Navy for the period 1961-70. He summa- rized positions of all typhoons for this 10-year period by month, date and 6-hourly synoptic time, and gave values of sea-level p0. The location and the p0 of the typhoons are often estimates. The positions are based on the best storm track produced by the Royal Observatory, Hong Kong. If available, the two fixes before and the two after each synoptic hour were used to interpolate coordinates for intermediate times. When data were not quite so abundant, Chin estimated positions only if there was at least one fix less than 12 hours from a synoptic hour. Weighting factors were also introduced by Chin to allow for time differences between the fixes and the reference hour. We made extensive use of Chin's data and raw data extracted from the Annual 21yphoon Reports (U.S. Dept. of Defense 1971-74) in determining filling rates for typhoons. 171 We categorized all typhoons during the 14-yr period (1961-74), using 10 years of Chin's data and 4 years of typhoon reports, with the aim of identi- fying the filling rates of intense typhoons that had recurved. In order to do this, we started with all 256 typhoons during this period, not just those near the coasts of Japan, Taiwan, and the Philippines. Figure 8.9 gives a schematic summary of these 256 typhoons. Sixteen were discarded because their p was >29.00 in. (98.2 kPa)--a po considered to be too high throughout this report for PMH guidance. Of the 240 remaining typhoons, 137 were discarded because they moved from an easterly direction for their entire lives prior to striking the Asian Mainland and, therefore, were not considered to have recurved. Another nine typhoons were rejected because they moved from the south or southwest from inception. The lowest Po for these nine was 27.64 in. (93.6 kPa). After throwing out the last two groups of typhoons we were left with 94 that recurved before reaching the mainland. Of these 94, 76 had a p at the time of recurvature that was >27.76 in. (94.0 kPa)--a relatively high p about 1.65 in. (5.6 kPa) higher than the p0 for the PMH in'tropical regions and not considered favorable for 0 further study. This left 18 typhoons still under consideration. We determined that 15 of these 18 were affected appreciably by colder Ts, colder and drier air associated with extratropical weather systems, stalling, and/or filling interrupted by deepening within 24 hours of the point of recurvature. Only three typhoons [Nancy (1961), Violet (1961) and Trix (1971)], or about 1% of the original sample, remained to provide possible guidance to a PMH filling rate after recurvature. Data for these three typhoons are shown in table 8.11. Violet had a relatively high p at the time of recurvature (compared to 0 Nancy and Trix) but gave us some support. Trix had an incomplete p record following recurvature but helped substantiate pertinent findings. Nancy turns out to be the best typhoon to work with since it met all the following criteria: a. extremely intense at the time of recurvature; b. moved over a small sea-surface temperature gradient; TYPHOONS 11961 - 741 LOWEST p LOWESTp 29 00 IN > 2900N 198 2 kPal (9 2 POI I_ i ,9e I I MOVED FROM EASTERLY MOVED FROM THE DIRECTION AND DID SOUTH OR SOUTHWEST NOT RECURVE FROM INCEPTION po At POINT OF o AT POINT OF RECURVATURE < RECURVATURE > 2776 IN 1940 kPal 2776 IN 1940 kPaI ( NOTAFFECED APPRECIABLY BY AFFECTED APPRECIABLY BY COLDER COLDER TS EXTRATROPICAL WX T EXTRATROPICAL WX SYSTEMS SYSTEMS STALLING AND/OR FILLING STALLING AND/ OR FILLING INTERRUPTED INTERRUPTED BY DEEPENING WITHIN BY DEEPENING WITHIN 24 HOURS OF BY DEEPENING WITHIN 24 HOURS OF 24 HOURS OF THE POINT OF THE POINT OF RECURVATURE RECURVATURE I I I OVIOLET 119611 - USED TRIX 119711 - INCOMPLETE NANCY 119611- USED TO IN SUPPORT OF FILLING RATE p0 RECORD AFTER POINT OF DEVELOP PMH FILLING RATE DEVELOPED FROM NANCY RECURVATURE BUT HELPED TO DUE TO RECURVATURE 119611 SUBSTANTIATE FINDINGS FROM NANCY 11961) TS = SEA-SURFACE TEMPERATURE WX = WEATHER Figure 8.9.--Schematic swmary of typhoons used for guidance on fzzling rate of PMH after recurvature over the northeast gulf coast. 173 Table 8. 11.--Smoothed typhoon data used as guidance to recurvature filling [after Chin (1972) and U.S. Dept. of Defense 1961-74]. Hour Lat. Long. PO Po Date (GMT) (�N) (�E) (in.) (kPa) Typhoon Nancy (Sept. 1961) 13 00 18.7 132.2 26.28 89.0 13 06 19.7 131.3 26.16 88.6 *13 08 20.0 131.1 26.05 88.2 13 12 20.7 130.7 26.13 88.5 13 18 21.9 129.8 26.40 89.4 13 22 22.7 129.7 26.64 90.2 14 00 23.1 129.2 26.67 90.3 14 06 24.8 128.9 26.70 90.4 14 12 26.2 128.8 26.78 90.7 **14 15 26.7 128.7 26.84 90.9 14 18 27.2 128.8 26.90 91.1 15 00 28.2 129.1 27.05 91.6 15 04 28.7 129.6 27.17 92.0 15 06 29.2 129.9 27.17 92.0 15 12 30.0 130.8 27.20 92.1 Typhoon Violet (Oct. 1961) 7 06 20.1 140.8 26.10 88.4 * 7 07 20.3 140.7 26.04 88.2 7 12 21.2 140.0 26.10 88.6 7 18 22.0 139.2 26.49 89.7 8 00 22.8 138.7 26.90 91.1 8 04 23.4 138.3 27.05 91.6 8 06 23.8 138.0 27.08 91.7 8 12 25.0 137.3 27.20 92.1 8 18 26.3 136.9 27.34 92.6 ** 8 22 27.3 136.7 27.46 93.0 9 00 27.8 136.8 27.58 93.4 9 06 29.4 137.0 27.94 94.6 9 12 31.3 137.7 28.23 95.6 9 18 33.7 138.8 28.56 96.7 10 00 35.8 140.0 28.73 97.3 10 06 38.5 142.0 28.85 97.7 Typhoon Trix (Aug. 1971) 28 19 29.4 130.3 27.20 92.1 28 22 29.5 130.2 27.05 91.6 *29 00 29.6 130.1 26.99 91.4 29 04 29.8 130.0 27.02 91.5 29 07 30.2 130'.0 27.05 91.6 **29 09 30.5 130.0 27.11 91.8 29 12 30.7 130.3 - - *Lowest central pressure **Point of recurvature (movement from west of south begins) 174 c. moved through Gulf of Mexico latitudes; d. remained tropical in character; e. did not fill unevenly (sinusoidally); f. traveled near the middle of the range of specified PMH forward speeds for the Gulf of Mexico (chapter 10). The lowest po in typhoon Nancy was 26.05 in. (88.2 kPa), fig. 8.10a, near 20.00N, 131.10E, at about 0800 GMT September 13, 1961. At the time ofrecurv- ature, 31 hours later, her po was 26.84 in. (90.9 kPa). Nancy moved to 26.70N over mean monthly Ts of 840 to 830F [28.90 to 28.30C (U.S. Navy 1969a)] during these 31 hours. During the succeeding 21 hours Nancy, still possess- ing tropical characteristics, moved 230 n.mi. (426 km) to 300N [Ts = 82�F (27.80C)] at an average speed of 11 kt (20 km/hr), while filling 0.36 in. (1.2 kPa) to 27.20 in. (92.1 kPa). The rate of filling after this is not known accurately, but we do know that about 36 hours after recurvature, Nancy's po stood at 27.68 in. (93.7 kPa) at Kyoto, Japan (35�N) where Nancy was becoming extratropical. Figure 8.10a depicts the filling -93.0 27.40 - of Nancy from the time of lowest 27.20 --- po. This figure clearly shows a 27.0 -92.0 27.00 - 14-hr period ending about 2200 - so MONTaFRCUoVRE -910 '' D 26.80 - OF SOUTH BEGINS) GMT September 13, 1961, when Nancy . 2 INTERNAL ADJUSTMENT ENDS - 90.0 filled quite rapidly (section a- I -90.0 : - X 26.40 - x DATA POINT of curve). We theorize that this (1961) -9.0 NANCY (1961) rapid filling [0.60 in. (2.0 kPa) 2/ ---INTERNAL ADJUSTMENT BEGINS 6.00- I 88.0 00Z 12 00 12 00 12 00 in 14 hours] was an "internal SEP. 13, 1961 SEP. 14, 1961 SEP. 15. 1961 adjustment" to the slightly TIME (GMT) cooler Ts [falling below 84�F (28.90C)] Nancy was passing over. Figure 8.10a.--Variation of centraZ pressure with time, typhoon Nancy We speculate [based not only on (1961). Nancy but other typhoons including Dot and Violet (1961), Bess (1965), Irma (1971), and Ida (1972)] that a very intense steady state typhoon (hurricane) will begin to fill when the Ts drops below about 840F (-290C). Such an internal adjustment is shown for typhoon Violet in figure 8.10b. 175 Nancy's rate of filling follow- I I I I I I 98.0 28.80 - ing recurvature (0.36 in., 1.2 28.0- / - 97.0 kPa/21 hours) shown by section c 28.40 A/ -96.0 // ~~~96.0 of figure 8.10a, is due partly to 28.20- - the fact that she was moving over a 28.00-950 slight mean monthly T gradient of 27.80- -940 s~~~~~~ 94.0 <2�F (-~lC). The additional fill- 27.60 POINT OF RECURVATURE lS_ IMOVEMENT FROM WEST - - -r / oF SOUTH bEO~NS, - 93.0 ing evident in section c compared 27.40 OF SOUTH BEGINSI -J/ X 2'7. 2 0 , to section b (time between the 27.20 92.0 27.00 -- internal adjustment termination INTERNAL ADJUSTMENT ENDS_ --91.O and the point of recurvature) is 26.60 - a/ x DATA POINT 90.0 most likely a result of recurva- 6-E/ 26.40- a/ VIOLET (1961) _ ture. We assume that the overall 89.0 26.20 / INTERNAL ADJUSTMENT BEGINS filling rate indicated by section 26.00 ADJUSTMENT 26.00~~~~I I I I I I I --. 12Z 00 12 o00 12 288.0 b of 0.20 in./17 hr (0.7 kPa/17 hr) OCT. 7, 1961' OCT. 8, 1961 OCT. 9, 1961 OCT. 10, 1961 between 2200 GIT September 13 and TIME (GMT) 1500 GT September 14 would have Figure 8.10b.--Variation of central 1.500 GMT September 14 would have pressure with time, typhoon Violet continued if Nancy had not (1961). recurved. Such a filling rate would result in a 0.25 in. (0.8 kPa) increase in p during the next 21 hours ending at 1200 GMT September 15. In other words, we are saying that 0.11 in. (0.4 kPa) of the 0.36 in. (1.2 kPa) filling in 21 hours, or about one-third, results from recurvature. We examined typhoon Violet (table 8.11). Violet's filling rate is shown in figure 8.10b. At the time of recurvature (about 2200 GMT October 8, 1961) her p was 27.46 in. (93.0 kPa). Violet's lowest p was 26.04 in. (88.2 kPa), 39 hours earlier. Her internal adjustment filling rate (sec. a of curve) was 0.86 in. (2.9 kPa) in 17 hours or, 0.71 in. (2.4 kPa) in 14 hours (compared to Nancy's 0.60 in., 2.0 kPa, in 14 hours). Thus, Violet's internal adjustment filling rate was greater than Nancy's. During the 22 hours between the end of the internal adjustment and the time of recurva- ture (sec. b of curve) Violet filled 0.56 in. (1.9 kPa). This is again a much faster rate than Nancy's comparable rate (section b, fig. 8.10a). Violet's p at 0600 GMT October 10 would have been about 28.26 in. (95.7 kPa) had the filling rate of 0.56 in./22 hours continued without 176 interruption. However, Violet filled at a much faster rate (sec. c of curve) than the above to 28.85 in. (97.7 kPa) at 0600 GMT October 10. Violet's assumed filling rate due to recurvature was 0.59 in. (2.0 kPa) in 32 hours or, comparing with Nancy, 0.39 in. (1.3 kPa) in 21 hours--over three times as fast, We would certainly not want to adopt such a fast filling rate after recurvature for the PMH in the northeastern Gulf of Mexico. We mentioned earlier that Trix (1971), table 8.11 (the last of the three typhoons selected for guidance) had an incomplete po record following recurvature. Trix's filling rate prior to recurvature, however, of 0.12 in. (0.4 kPa) in 9 hours to 27.11 in. (91.8 kPa) is close to Nancy's 0.20 in. (0.7 kPa)/17 hr filling rate prior to recurvature. This correspondence lends support to the assumed filling rate for Nancy. For the PMH in the Gulf of Mexico, we have adopted Nancy's filling rate (0.11 in./21 hours or about 0.4 kPa/21 hours) to adjust from a PMH po0 near 25�N with a track direction >190� to coastal po near milepost 1100. This angle (1.90�) is 10� greater than the angle defining the point of recurvature and is the maximum value of track direction allowed a PMH over all areas except the northeast Gulf of Mexico; (see chapter 11). Before we can determine the PMH po near milepost 1100, we need to deline- ate PMH tracks into the Florida west coast. We cannot pattern these tracks after the Labor Day hurricane of 1935 because it recurved too close to land and filled rapidly. Camille did not recurve and apparently was not too close to land (Florida peninsula) since she filled <0.15 in. (0.5 kPa) between 25� and 30�N. The problem is that we do not know how close "too close" is. We will blend two assumed PMH tracks into the Camille track (which extended across the gulf from extreme western Cuba to Bay St. Louis, Miss.) (fig. 8.11). These two tracks enter the northern portion of the west Florida coast after passing through the Yucatan Channel, thereby avoiding the west coast of Cuba. One track, labeled 8, is perpendicular to the coastline near milepost 1100 and the other track, labeled 9, is perpendi- cular to the Florida coastline between Cape Sable and-Tampa Bay even though it is shown entering the coast near milepost 1170. The latter track is shorter than a track would be if drawn perpendicular to the coastline 177 at milepost 1170. Tracks 8 and 9 are 85� 800 sample tracks shown to give the user . a feel for what a PMH track over the northeastern Gulf of Mexico might 3"00 N Ml -- ' Q ' oio o look like. We realize that a PMH 9 could follow tracks slightly dif- � 2 ferent from those in figure 8.11. a The lengths of the two tracks to thea 250 coast from the time 9 exceeds 190� .1400 I 5 are about 280 n.mi. (-520 km). \ 0N If we move the PMH at the same speed as typhoon Nancy (11 kt, 20 km/hr) it would take about 25.5 90o 850 hours to reach the coast after LONGITUDE (�W) recurvature and using Nancy's Figure 8.11.--Likely paths of the PMH into northeastern gulf coast. Also filling rate would fill approxi- shown is a portion of the Camille mately 0.13 in. (0.4 kPa). This (969) storm track. would yield a p0 of 26.38 in. (89.3 kPa) because the PMH po before consider- ing recurvature has already been set at 26.25 in. or 88.9 kPa (sec. 8.3.7.2.1.1). If the PMH moved at its upper limit of 20 kt (37 km/hr) in this region (chapter 10), it would fill about 0.07 in. (0.2 kPa) in the 14 hours required to travel the 280 n.mi. (~520 km). The po near milepost 1100 is then 26.32 in. (89.1 kPa). 8.3.7.2.1.3 FINAL P . Higher po in this concave portion of the Florida coast means adjoining coastal reaches will be affected. Near milepost 700 at Burrwood, La., we have left the theoretically-derived p (26.22 in., 88.8 kPa) unchanged. From there eastward, it is raised to a peak of 26.32 in. (89.1 kPa) northwest of milepost 1100. The increase in po is slow at first, becoming steeper between mileposts 900 and 1000. The p near Cape Sable, Fla. (fig. 8.8), remains unchanged (26.12 in., 88.5 kPa). North- northwestward up to the coast, PMH po rises slowly to 26.16 in. (88.6 kPa) at Fort Myers and then more rapidly to nearly 26.28 in. (89.0 kPa) at Tampa. 178 Figure 8.8 shows po data including values estimated from historical data readings prior to the turn of this century, the adopted PMt po0 curve and the curve from HUR 7-97 (U.S. Weather Bureau 1968). The PMH p tabular data are presented in chapter 2. 8.4 COMPARISON OF SPH AND PMH PRESSURE DROP Now that we have SPH po and PMH po, it would pay to look at the pressure drop (Pw - Po) relation between the SPH and PMH. A comparison is particularly needed since the p 's were derived using different methods. Figure 8.12 shows Ap for the PMH (top curve) and the SPH (bottom curve). The curves are separated by as much as 1.80 in. (6.1 kPa) northwest of mile- post 1100 and as little as 1.15 in. (3.9 kPa) at milepost 3100. The dif- ference between the curves from milepost 0 to 2700 ranges from 1.36 in. (4.6 kPa) near mileposts 0 and 1400 to 1.80 in. (6.1 kPa). The rather rapid dropoff in the PMH Ap between mileposts 2700 and 2800 is attributed to the inability of the PMH north of Cape Cod to maintain itself over the colder water of that area. The SPH, being a weaker storm, has a higher po to begin with; it does not lose strength as rapidly in this area. There is a relative minimum in Ap for the SPH between mileposts 1700 and 1900. The fact that the coast in this area does not intersect the tracks of severe hurricanes of record is the probable cause of this small minimum. This dip is not present on the PMH curve because there are no theoretical reasons for having a noticeably weaker PMH in this area. In other words, for the SPH, lower Ap in this area is reasonably characteristic of record storms whereas the potential for the most extreme event (the PMH) remains. Along the gulf coast, the two Ap curves are similar with minimum values of Ap over the northeastern gulf coast. In other words, observations used in determining the SPH curve back up the more theoretical arguments employed in developing the PMH curve. C) ED >1 -O 0 o ~ ~ * 3: zo m Z > 0~~~~~~I 0 - > -r-= m r o ("~~~~~~~~~ mC -1 ri * I . z -lr 3J C , --t CO cnr ; co rl~~~~~~ I I~ I M~~~~~~~~~~~~ DISTANCE (KM X 102) 4 8 12 16 20 24 28 32 36 40 44 4$ 52 56 14.0 4.0 - !3.M5 - 12.0 3.5 - 3.0 - ---,- 2.0o.o d~~~~~ 1.5- (~~~~~~~~~~~~~~~~~~~~~SPI- 6.0 1.5 4.0 1.0 - 2.0 0.5- 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~. 0,5 - 0 11 1 1 i i1 1 1 i i I 0 2 4 6 8 10 12 IA 16 18 20 22 24 26 28 30 DISTANCE (N MI X 102) Figure 8.12. --Comparison of pressure drop (Ap) for the PMH and SPH. '-I 180 9. RADIUS OF MAXIMUM WINDS 9.1 INTRODUCTION The radius of maximum winds (R) is the radial distance from the hurricane center to the band of strongest winds within the hurricane wall cloud, just outside the hurricane eye. It is used as a measure of the lateral extent or size of hurricanes and is one important factor in the generation of storm surge. The peak surge that a hurricane can produce is dependent upon R, other factors being held constant. The larger the R the larger the surge until a critical value of R is reached; thereafter, the peak surge decreases with increasing R (Jelesnianski and Taylor 1973). This critical value of R (for peak surge generation) for a hurricane of given intensity is a function of the storm's forward speed (T) and track direction (0) relative to the coast. It also varies with the width and steepness of the continental shelf and the curvature of the coast. A hurricane that is both large and intense would have enormous destructive power. Myers (1954) applied a kinetic energy evaluation to coastal hurri- canes and found an inverse relation between size (R) and intensity (p0). An, analysis of hurricane R vs p0 in NOAA Technical Report NWS 15 (Ho et al. 1975) also showed this inverse relation. The two hurricanes of record (Labor Day hurricane of 1935 and Camille) with central pressure below 26.87 in. (91.0 kPa) had well-formed vortices associated with small R's. 9.2 DATA Values of R at or near the time of lowest p within 150 n.mi. (278 km) of the coast for record hurricanes are given in tables 4.1 to 4.4. In addi- tion, data from western North Pacific typhoons were used in this study. These data are listed in tables 4.5 and 4.6. We also made use of studies on typhoon eye diameter by Ito (1962) and Bell (1974). 9.3 RANGE IN R FOR THE SPH Figure 9.1 shows the R observed in hurricanes with p0 <28.35 in. (96.0 kPa) plotted along the gulf coast at the coastal location closest to the point 0 CDI > -z CD z o > > 1= > ' ~~ > _ C1 - ,a V 2' it 0x 0 r- A ~~~ Z K - P 0 5 En > z M M:~ ~ z v 0 m z DISTANCE (KM X 02) ~ 4 8 12 16 20 24 281 32 36 A0 44 48 52 56 IZ~~~~~~~~~~~~ I 'T II I I z~~~~~~~~~ >- - --i --iP 0 r- 91 7.75 : o8.311 771 803 * 8.29 7;149 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~9 I� 8.00 8.31 I~~8200 - 118.O 20 248.3 . 36 8.26 25 I.1 7.53 8.G 8o� .�7.59 7.26 8. - 8.3 083 8. 8.7 18l 7.5125 I -401 320 5 .2. 7876 7.99 7.88 I. 6 8.17` 8120 -7.79 0LE3ENDI 15 3I 8.29 834 0 HURRICANES (P0 o~~~~~~80 004 7.6 2:3 1.0-- * 7'~3 28.35 IN. OR 8.00 8 8 N R D ON 7.89 .1 7,62 * IN. WITH THE NUMBER 16811 8*2 8.811 - 8.31 1 82I 7 5 1 * 2 (IN THE TENS PLACE)- OMITTED. I0 I 2 I I I I I ii I l II I II I 0 Oo 2 4 6 8 10 12 1* 16 18 20 22 24 26 28 30 DISTANCE (N MIX102) Figure 9.1.,--Radius of maximwn w~inds for hurricccnes With central! pressure <28. 35 in. (96.0 kPa)l<isted beside each data point. 7.6 I73-I 1 8.08NUMERAS DENOE POI 182 (KM) 0 10 20 30 40 50 60 70 80 90 96.0 ,, I �219.5 *29.3 I I 29.1 30.329.0 x24. 28.2- 28.6 X28.1 25.5 / 28.5 X 95.0 27.02 278.0- 8. 29.2 2X 2 , 27.46- 28.0 225.2x :26 2.2 0 1 LJ ;124.7 29.1 � 27.2- e 92.0 - / X GULF HURRICANES ?WITH 0 - 27.0 - <229.2.351N. OR 96.0 kPa) Li 28.2 -@ WESTERN NORTH PACIFIC -91.0 268 - x TYPHOONS IPQ5 27.461N. !C) �3 a/ <3 TWO TYPHOONS WITH 26.6- | SAME R.AND P0 -_0.0 W/00 267.4 - ~~~~~ 8 O ~~~~~~~~~~~~~~~~~~24.8 i 92~~~~~~~~~~.. for western North Pacific typhoons and gulf coast hurricanes. SoZid ines are smoothed curves joining the 5th and 95th percentiles of R. Latitude 0 020 TYPHOONS (Po4 19.0 Values of R for intense typhoons [p < 27.46 in. (93.0 kPa)] of the west- Z6.4 - x0- <28.35 in. (96.0 kPa)] since 1900 are plotted against p in figure 9.2a. Figure 9.2b is a similar plot of the same typhoon data and east coast hurri- canes. In both of these figures the latitude of each hurricane location is given. The diagrams reveal that for extreme storms [p < 26.58 in. (90.0 (93 kmn) was observed in the New England hurricane of 1938 [po = 27.75 in. (94.0 kPa)]. .l( 183 (KM) 0 10 20 30 40 50 60 70 80 90 960 2.2 35.2 I _ 11- ,: 40.9 , I /33.9- 28.2- 24.7 35.0 32 2 / 2.0 5.5 28.0 - /. 9 *29* 20 - 39.7 297j5 a$ 35* 2 27.8 - 3 26.3 9 276 - 247324 27.4.- 235 I 26.6- | -% /O- 27.2- | 3 / 99.0 2e~~~~~~~~~o~C-J | 27.0 - o W r 91.0 26.48- o CD *EAST COAST HURRICANES IWITH - ~~~~~~I I I I I I LATITUDE INDICATED) (Po 1 0 1 28.35 IN. OR 96.0 kPQ4 - 26.6- J WESTERN NORTH PACIFIC TYPHOONS IF 27.46 IN. - 90.0 forID~~~ w e o Ptp s e OR 93.0 kPoI 2TWO TYPHOONS WITH SAME 26.4- R4.24.8 ,R AND P- LIJ RADIUS OF MAXIMUM WINDS (N MI) are smoothed curves joining the 5th and 95th percentiZes of R. Dashed portion of the 5th percentile curve is a preliminary curve which does not refZect the increase in R with Zatitude shown by the soZid curve. Percentiles of R occurrences with hurricanes and typhoons were determined for selected p intervals. These selected intervals are: p <27.08 in. (91.7 kPa); <27.76 in. (94.0 kPa); p between 27.46 and 28.05 in. (93.0 to 95.0 kPa);and p between 27.76 and 28.35 in. (94.0 to 96.0 kPa). Several small R values are reported in typhoons with pO <27.08 in. (91.7 kPa). The R's in these typhoons were given less weight than that given gulf hurricanes when calculating the 5th percentile values in figure 9.2a because these po's are lower than that of the SPH. Gulf hurricanes and typhoons were given equal weight when we determined the 95th percentiles. The 5th and 95th percentile curves shown on figure 9.2a are drawn through the calculated values. 184 A nearly similar procedure was followed for the east coast hurricane and typhoon data. The outermost curves of fig. 9.2b, the 5th and 95th percen- tiles of east coast hurricanes and typhoons, do not reflect variations with latitude. Generally speaking, the R's observed in hurricanes in northerly latitudes are larger than those of southerly latitudes. The analysis discussed in chapter 5 supports this contention (see sec. 5.3.2.2). There- fore, the hurricanes north of 38�N were analyzed separately. Data for this region are scarce, so Carol (1954) and Donna (1960), table 4.2, with po's of 28.38 in. (96.1 kPa) were added to the sample. The solid portion of the 5th percentile curve above about 27.'08 in. (91.7 kPa) includes hurricanes north of 38�N and takes into account the increase in R with latitude. The 95th percentile curve was unaltered by the separate analysis north of 38�N. We have adopted the 95th percentile curves of figures 9.2a and 9.2b for the upper limit to values of R for the SPH for the gulf and east coasts. The lower limit of R comes from the 5th percentile curves of these figures. The 5th percentile curve used for the east coast is the one modified for lati- tude. The limited latitudinal range for the gulf coast suggested an adjust- ment for latitude was not required. This is supported by plots (not shown), of R vs. i for hurricanes in the Gulf of Mexico. By entering figures 9.2a and 9.2b with SPH p0 (chapter 8), we obtain the range in R for the entire coast. The results are shown in figure 9.3. This figure also includes the hurricane R data from figure 9.1 plotted again along the gulf coast at the coastal location closest to the point where Po was observed and along the east coast at the latitude where p0 was observed. The upper and lower limits of R shown in figure 9.3 give the permis- sible range at all points of interest on the open coast. Any value within this range may be considered to be characteristic of an SPH at a given loca- tion. As indicated earlier, a critical R may vary with a combination of other factors. Our results for larger R's may be compared with other studies that list the frequency of eye diameters of typhoons. Since the maximum winds of intense hurricanes are observed within the eye wall, we may approximate R from the eye diameter (Shea and Gray 1972). This distribution of eye 0~~~~~~ -> -M 0 0 > r- - -u - CO) CO <rrl (a 0 _1 -- M 0 > -0 co CO > z - -1 0 M " j2U0 M I 50- *n -n ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 7.75( t< DISTANCE (KM X 10 2)I 40 a 12 16 20 24 28 32 36 AO 44 48 /S 56 40 I8 I ' Ii iF z 7~9. .778.29 . 83 V) - 7. 98. 03 -60 3 0 80 08.01 I.~ .62 8.- -50 25 ~~~~~~8.3 1 80 .6~~e75 257.2 6 -B X ~~~~~~~~~~~~8.11. 18.16 <- 8.03 81 8.~2 2I 91 7.66 4 40 2 20 7 .; *T9 - o 3~~~~~.0!0 * 81179 .50 81 7 - o20~ 7.8 8 --30 Io 7.640 7.44 * 8.2 P 8.3 4 * .783 -..7.64 8-20 7.89 4j*5~20.81-0 0 2 4 6 a 10 12 14 16 is 20 22 24 26 28 300 DISTANCE (N Ml X 102) Figure 9.3. --Adopted upper and lower limits of radius of maximum winds for the S-PH. Data are identical to that in figure 9.1. co. Ln 186 diameters for-the period 1958-68 (Bell 1974), gives a 95th percentile level of 38 n.mi. (70 km). Dividing by two and multiplying the result by 0.25 gives an approximate R of 24 n.mi. (44 km). This is for typhoons with po <27.76 in. (94.0 kPa). Another researcher (Ito 1962) gave the frequency distribution of eye diameters in typhoons for the period 1950-61. This 95th percentile R for typhoons having pc <27.17 in. (92.0 kPa) is 34 n.mi. (63 km). Dividing by two and multiplying the result by 0.25 gives an approximate R value of 21 n.mi. (39 km). Our data show a 95th percentile R of 30 n.mi. (56 km) for hurricanes and typhoons having po <27.76 in. and 25 n.mi. (46 km) for hurricanes and typhoons having pc <27.17 in. 9.4 RANGE IN R FOR THE PMH The determination of the range in R for the PMH must use a different approach compared to the method just described for the SPH because of the limited number of storms with extreme values ofPo. The two hurricanes with pO less than 26.87 in. (91.0 kPa) were observed along the northern gulf coast and over the Florida Keys. Both of these extreme hurricanes had small R's. 9.4.1 LOWER LIMIT OF R FOR THE PMH The existence of a central core and spiral cloud bands associated with converging low-level inflow currents are well known phenomena in tropical cyclones. In a study of the dynamics of tropical cyclone eye formations, Kuo (1959) showed that there exists a limiting radius beyond which the converging current cannot penetrate. This agrees with the observations of a calm near the center and maximum winds some distance away at R. The con- verging current, which reaches its maximum speed at the limiting radius (Rlim), must therefore turn upward and then outward at upper levels. The surface defined by these innermost streamlines is identified as the eye wall. Kuo has estimated Rlim as a function of other variables. His formula is: R = [( 2 fr / -] 1- (9.1) where, Rlim = limiting radius of maximum winds f = coriolis parameter 187 r = an outer radius from which inflow air starts with negligible momentum relative to the earth. V = maximum wind at Rlim. max li (3 = fraction of tangential component of momentum generated in the inflow layer, between r0 and Rlim, that is dissipated by surface stress. E1 = a similar.coefficient expressing stress opposition to coriolis force. Kuo made computations to show the effects of various friction factors. A B of 0.5 and a 13 of 0.4 give the smallest �im. The B value of 0.5 is comparable to the magnitude of frictional effects implicitly expressed in the Hydromet gradient wind equation 9.4. These small Rlim values are comparable to small R values observed in western North Pacific typhoons. We (KM/HR) 200 220 240 260 280 300 I. I I I 'I I I I I' ' I' 30- VMAxAT 20�N=159KT 1295KM/HRI 2 - ' 2 I35 VMAXAT 30'N=138KT 1256KM/HR) 18- \ k450N VMAX AT 40AN=117KT (217KM/HRIJ -50 40N 25- - 16- 30 ro=270N MI \ \ N 1500 KM) 40 '4 \.26 ~~~~20 /- 35�N \@$b88kK~4 -1 25 30 15- / / - , 10- 20 14 - 105 02 I 300I � 2 3042-0 IN50 LATITUDE (0N) I I X | | I i I I I 00 KM) 120 140 150 160 Figure 9.4.--Latitude vs. Rz1. The VMAX (KT) to v2 . two curves are computed from equa- tion 9.1 (after Kuo 1959). Figure 9.5.--V vs. R.im. Dashed line determines Rev computed from FMH po at selecte5Uatitudes using equations 9.1 and 9.4 and an r of 216 n.mi. (400 m).150 10 216 n.mi. (400 kmn). assumed V values of 159, 138, and 117 kt (295, 256 and 217 km/hr) at max latitudes 20�, 30� and 40�N, respectively, and then obtained the variation of Rlim with latitude for r o's of 270 n.mi. (500 km) and 216 n.mi. (400 km). These variations are shown in figure 9.4. The two curves indicate the combined effects of Vmax and latitude on Rlim for a storm of fixed ro. The diagram also reveals the variation with ro, i.e., a storm with a smaller r ~ 0 would have a smaller Rlim than one with a larger r0. Hereafter, we will make use of an r of 216 n.mi. (400 km). In order to lend support to this o choice, we approximated r for the Labor Day hurricane of 1935 and Camille O (1969) by letting r0 be the closest distance Pw is to the center of each hurricane. For the Labor Day storm, r0 is slightly more than 300 n.mi. (556 km) and for Camille, r is about 180 n.mi. (334 km). In estimating Rlim for the PMH, whose intensity is defined in terms of po it is necessary to establish the variation of R with respect to po; (see sec. 9.1). This can be accomplished by applying a wind-pressure relation at various latitudes. Since the coriolis parameter (f) is a constant at a given latitude, and if we prescribe f = 0.5 and set r and B, to any arbi- trary constant, Rlim in equation 9.1 can be expressed as a function of Vma constant Rlim = 2 (9.2) max 2 Since Vmax varies with Ap we have: max constant 93) Rlim Ap The relation between Ap and V is obtained from the gradient wind max equation: V K (P P)1/2 - Rf (94) gx - 2 max' where K e ; e ' 2.71828 A small R of 10 n.mi. (19 km) and p of 30.12 in. (102.0 kPa) for the PMH were used in the computations of Vgx. Values of K are derived in chapter 12. 189 On figure 9.5 we show computed points relating Vmax, latitude, PMH pO and Rlim that were computed from equations 9.1 and 9.4. The smoothed curve (dashed line), joining these points, gives the variation of Rlim with lati- tude for the PMH. This is adopted as the Rlim for the PMH. 9.4.2 UPPER LIMIT OF R FOR THE PMH Figure 9.6 shows the variation of R with respect to p0 for the western North Pacific typhoons and gulf and east coast hurricanes with pO <27.46 in. (93.0 kPa) for the typhoons and 27.76 in. (94.0 kPa) for the hurricanes. The solid line envelops the largest observed or estimated R's of the typhoons and east coast hurricanes. Large R for gulf coast hurricanes were- much smaller than those for east coast hurricanes and typhoons and had no effect in determining this line. The dashed line intersecting the lower (KM) 0 10 20 30 40 50 60 70 80 90 27.8 - 20 26.73 27.6 - 2 25.8 38.7 -- 27.6- ' 2 3.6 X27.0 . CD: 1"7~28.4,,,' x21 1.. -93.0 27.4- 32.4 Z8 o ;24.8 27.2 - X 27,0- 8 " 9 2 /9.0 ) 29.2 '91.0 26.8- o x0 X GULF AND * EAST COAST HURRICANES- (WITH LATITUDE INDICATEDI IP, -ir~~~: ( 27.76 IN. OR 94.0 kPal 26.6- o T WESTERN NORTH PACIFIC TYPHOONS 900 Li j (P0 < 27.46 IN. OR 93.0 kPql) � // TWO TYPHOONS WITH SAME R AND 26.4 - / - 24.8 t I / -- 89.0 26.2- 26.0- I I88 .0 0 5 10 15 20 25 30 35 40 45 50 RADIUS OF MAXIMUM WINDS (N MI) Figure 9.6.--Variation of radius of maximum winds (R) with central pressure for western North Pacific typhoons and hurricanes. SoZid curve is an envelopment of the stormn data. Dashed curve is a modification of the solid curve; it sets the upper limit of R at 20 n.mi. (37 km) for the PMH for the Florida Keys. Hurricane latitudes are also shown. 190 portion of the envelope sets the limit of large R at 20'n.mi. (37 km) for the most intense hurricane at po = 26.11 in. (88.4 kPa). Ito (1962) shows that an R of 20 n.mi. (37 km) has a frequency of occurrence of 1% for typhoons with po <27.17!in. (92.0 kPa) while Bell (1974)shows this value of R to be 3.1% for typhoons with p <27.17 in. (92.0 kPa). These values lend support to our adopted value. Figure 9.7 shows variations of R with latitude for the PMH: The dashed curve is obtained by entering figure 9.6 with the PMH po (chapter 8) at various latitudes along the east coast to obtain values of the upper limit of R [e.g., po for the PMH is 26.11 in. (88.4 kPa) at 250N, 26.38 in. (89.3 kPa) at 35�N and 26.71 in. (90.4 kPa) at 400N]. These R values are 20 40 (KM) 60 80 45- II I I I I I I 45 --- I i........./ -- / 0;/ a' 40 - /7, 9.7- :/ ,' O X GULF AND * EAST COAST HURRICANES 788 Po VALUE IN INCHES WITH THE NUMBER Z 35-/ 7- 2 (IN THE TEN'S PLACE) OMITTED .9 6t/ 6.gWxg [Po< 28.05 IN. (95.0 kPo)] .1- < 30- f1 -J/ 6X81. 7X87X64 7X95 8X0I 6XII 7X83 3 7X64 ~~~~7Xv4 802 8Xo~ 7*62 7.76 7X 7,59 8,00 25 - 6x35 74 745 75 7X62 7 7652 2,I ,III .1 *I iI I. Ii( II I 200 10 20 30 40 50 RADIUS OF MAXIMUM WINDS '(N MI) Figure 9.7.--Variation of the lower limit and upper limit of PMH radius of maximum winds (R) with latitude. The lower limit of R curve is from figure 9.5. Dashed curve is the upper limit of R using figures 9.6 and 8.8. The upper limit of R curve (final) is obtained after modifying the dashed curve for latitude. 191 then plotted against latitude in figure 9.7 and a smoothed dashed line fitted by eye. The lower limit of R curve is similarly obtained from figure 9.5. Figure 9.7 also shows data for east and gulf coast hurricanes with values of po next to each point. A casual inspection of the plotted data clearly indicates that some R values are greater than the envelope shown by the dashed line. These R's [obtained from hurricanes with po <--28.05 in. (95.0 kPa)] should be larger than PMH R's because R decreases as the p0 of a hurricane decreases (see fig. 5.1). That is, the R for the PMH would have smaller values at each latitude than those observed in less severe hurri- canes. At first glance, the dashed upper limit of R curve appears to be drawn far away from the data point for the New England hurricane of 1938. However, the PMH p is 1.09 in. (3.7 kPa) lower than the 1938 hurricane at the latitude of the 1938 storm. The difference is slightly too large since we have not yet considered the variation of R with k. R values for intense western North Pacific typhoons were used to supple- ment sparse hurricane data with low po. These R values for typhoons with p0 <27.46 in. (93.0 kPa) were all observed south of 30�N at an average latitude of 19.40N, while the PMH of these intensities will occur at higher latitudes (25�-45�N) along the east and gulf coasts. Therefore, the variation of R with latitude has to be considered in assessing the upper limit of R for the PMH. The variation of R with t of western North Pacific typhoons as well as that of east coast hurricanes was used to obtain the solid curve to the right of the dashed curve (preliminary upper limit of R) shown on figure 9.7. This variation of R with 1 was not used for the upper portion of the curve (north of 43�N) where the solid line is superimposed on the dashed line. Even larger R's at these northern latitudes would be more representa- tive of hurricanes becoming extratropical, e.g., the New England hurricane of 1938. For the PMH, we therefore have increased the upper limit of R to the values shown by the solid line of figure 9.7. This curve gives a maximum increase of <5 n.mi. (-9 km) from the earlier enveloping curve (dashed line). 192 9.4.3 COASTAL ANALYSIS OF LOWER AND UPPER LIMITS OF R FOR THE PMH The lower and upper limits of R curves shown in figure 9.8 give the range of R's for the PMH at points of interest on the open coast. The user should select any value of R within these limits that is critical for his applica- tion. Figure 9.8 also shows the hurricane R data from figure 9.1 plotted in the same manner. The lower limit is from the curve on the left side of figure 9.7. Along the east coast, the upper limit is from the solid (final) curve on the right side of this figure. We could have used this same curve to show the upper limit of R along the gulf coast. If we had done this our range of the upper limit of R along the entire gulf coast would be <2 n.mi. (-3 km). Instead of using this curve from figure 9.7, we chose to vary the upper limit of R along the gulf coast with central pressure and indirectly with latitude. The reasons for making this choice are as follows: a. The solid (final) upper limit curve was developed from east coast hurricanes and western North Pacific typhoons. b. In chapter 5, we state that on the average the meteorological para- meters for the gulf coast are better related to longitude than latitude. However, from table 5.1 we see that for gulf coast hurricanes the p0 vs. R correlation coefficient (.33) is significant at the 1 % level whereas the X vs. R correlation coefficient (-.06) is much smaller and is not significant at the 5 % level. Based on the above, we decided to relate the upper limit of R along the gulf coast to PMH po along the gulf coast (chapter 8, fig. 8.8) and then relate this po to the upper limit of R value for the same PMH p0 along the east coast. For example, the PMH p near milepost 1100 (n.mi.) is 26.32 in. (89.1 kPa). From figure 8.8, we see that along the east coast a PMH po of 26.32 in. lies near milepost 2000 (n.mi.). From figure 9.8, the upper limit of R at milepost 2000 is about 23 n.mi. (42.6 km). Therefore, the upper limit of R near milepost 1100 is also 23 n.mi. -u C) I- W~~L -V >' _n-' 0 c o m o ~~~> I,, M. H > > m0 m L< W m ~~~~~0Zm m' W 0U OD r- ~ ~ ~ ~ ~ ~ ~ ~ ~ > X n rn~ ~~ z n m in~~~~~~~~~~~~~~~~~~~~~~~~~~82 I 0 m _n 7.7 7.7 3 z~~ ~~ 30 ~~~~~~~~~~~~~~~~~~~8.01 8.0 AO~~~~~~~~~~~0 I II 112 8.3'1~~~~~~~~~~~~~~~~~~~~~~. S _I jO z 25~~~~~~ - 8.Q8.~~~~~~.E".5 8.9 ' ~ ~* - -.~ 7.549@ 7r to~~ 8.02 8. 820 *5T 7_2 81 8.11 9r / 3 - 8100 15~~~~~~~~~~~~~~~~~~. .2) ~~~~~~~~~~~~~~~~~~~~~~~I ~I 0 *el i76 8. 29Y 0 7.830 7.6A 2.08 10I 0~@ 2 _ 'ml 6.81 ~~~~~~~~~17.66 17.8~~~~~~~~~~~~ 8.1 1 0 2 A 6 8 10 12 1 4 16 18 20 2 2 2 4 26 2 8 300 DISTANCE (N Ml X 1O2) Figure 9.8. --Adopted upper and Lower limits of radius of maximum winds for the FMH. Data are identical to that of figure 9. 1. 194 9.4 4 APPLICATION OF R CRITERIA As indicated earlier (sec. 9.1), the critical R for a PMH with a given forward speed that would produce the maximum peak surge on the coast is dependent upon geographical features of the coast (e.g., the configuration of the slope of the continental shelf and the curvature of the coast) and other factors. An example of such effects is given by hurricane Camille (1969) which struck the coast where the shelf topography becomes steeper with distance east of the storm center. Hurricane Camille (R = 8 n.mi., 15 kin) gave a record surge in the Gulfport area. If the size of the storm had been larger with maximum winds farther from the storm center, the peak surge would have occurred in a steep shelf area where the surge would have a different potential. Thus, the critical R of a hurricane striking a particular location may be smaller than the R value given by the upper limit of R curve in figure 9.8. In applying R to a particular coastal location, the user should consider these and other more subtle effects of variations in R on the storm surge. A -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 195 10. FORWARD SPEED 10.1 INTRODUCTION 10.1.1 USE OF FORWARD SPEED The rate of translation', or forward sipeed (T), of the hurricane center is an important meteorological parameter. Taken together with track direction (8) (chapter 11), it enables us to determine where a hurricane has been, is now, and may go. T makes up part of an asymmetry factor used in the deter- mination of 10-m (32.8 ft) overwater winds. In simulating storm surge, the location of the hurricane can be determined at selected times if we know T and 0. Depending on the specific coastal location for storm surge simulation or other wind field application, either a low or a high T could be most critical. Lower and upper limits of T will be set for the SPH and the PMH. Any value of T within these bounds may be used, and the user must evaluate the most critical T for a particular application. 10.1.2 FORWARD SPEEDS. OF HISTORICAL HURRICANES Forward speeds of hurricanes with p0 <29.00 in. (98.2 kPa) during the period 1900-78 are listed in tables 4.1 to 4.4. 10.1.3 RANGES OF T Hurricane or typhoon data were used to develop portions of the PMH and SPH lower and upper coastal profiles of T. The profiles were completed by applying various meteorological concepts. PMH curves are developed first in section 10.2. The SPH curve development in section 10.3 makes use of the PMH results, particularly for the upper limit of T. 10.2 FORWARD SPEED FOR THE PMH 10.2.1 UPPER LIMIT OF T 10.2.1.1 RIO GRANDE TO MAYPORT, FLA. (LATITUDE 30.50 N). Figure 10.1 shows the T for hurricanes plotted against approximate coastal refer- ence points. South of latitude 30;5�N (mileposts 0 to 1750 n.mi.), only six hurricanes moved faster than 18 kt (33 km/hr). These storms were weak Co, Z m m C O z A 2 61~~~~~ --I rn r- -0coa 2~~~~~~~~~~~ a ~ ~ j4 _;In 0) x 4. DISTANCE (KM X 102) 4 ~ 2 16 20 24 28 32 36 40 44 52 56 SELECTED POINTS LABELED WITH P0 (2 OMITTED.e.g. 27.53 - 100 LISTED AS 7.53) 50 9 CIRCLED POINTS P05. lIPP:R LIWIT -9 27.761N. (94.0 kPci O 7.97 80 4d0 -I3 - / 8.9170 a. / 8.3 6 - A--60 30 7. 0o 67 o 8.38 8.92 752 3 1 . 50 420 B.7* *4l8.20y.99 7.39 7 .I .8.91 -40 im 2 0 7 .83 7 79. 7.4 F 70) - * O'W -R LIMIT 0 6. 8 1 10 ~~~~~~~~I7 x2 7 - P 7.795 * ft-7 62 13 9 5 04% 0 _ * ~& 9 z I - U 897 -20 -AIL s ' 4 - - M 10, 6 ~ 79~ '08.9 1 RI8 812 -8 2 1 8.44726 8 76 7168.EO/'. 1Li 8.40 8.44 -8.7 O N 6 .35 0 I IB 8.8B54 jE4 0 2 4 6 a 10 12 14 16 18 20 22 24 26 28 30 DISTANCE (N MIX 102) Figure 10.1.--Adopted PMH upper and lower limits of T. Data are from tables 4.1 to 4.4. All data points falling outside the two curves are labeled with lowest central pressure (p ). All circled data points faZZing inside the two curves are labeled with lowest p0 0tIer data points (except those between mileposts 1300 and 1500) are labeled with lowest p0 if this p is < 28. 00 in. (94.8 kPa). 197 compared to the PMH -- none had a po0 lower than 27.99 in. (94.8 kPa). The remainder of the data (T < 18 kt) up to about milepost 1800 does not exhibit any noticeable latitudinal variation. The east coast data plotted against latitude in figure 5.4 show novariation in T south of 30.5�N. We conclude that the fast T for the PMH is constant to milepost 1750. Data from hurricanes in the central Gulf of Mexico, Caribbean Sea, and western North Atlantic were investigated in support of this conclusion. Three hurricanes were identified which had a p <27.26 in. (92.3 kPa) -- po of hurricane Beulah (1967), the third most intense hurricane in tables 4.1 to 4.4. These storms were over the western Caribbean Sea and are: the Nov. 5, 1932, hurricane (p = 27.01 in., 91.5 kPa); Janet, 1955 (po = 27.00 in., 91.4 kPa); and Hattie, 1961 (p = 27.17 in., 92.0 kPa). Of these three, Janet had the highest T (20 kt, 37 km/hr) near 18�N, 86�W. We also examined data for typhoons (table 10.1) having po 's < that of Camille, 1969 -- the second most intense hurricane (po = 26.81 in., 90.8 kPa) in tables 4.1 to 4.4 -- in order to determine how fast extremely intense typhoons can move across the western North Pacific. Table 10.1 extends T data for extreme typhoons beyond the spatial limitations imposed in tables 4.5 and 4.6 which show nine typhoons with po <26.81 in. The high- est T for these nine typhoons is 15 kt (28 km/hr) associated with typhoon Emma of 1967 (po = 26.81 in., 90.8 kPa). Figure 10.2 is a plot of T vs. po at the time of lowest po for the 31 typhoons of table 10.1. By increas- ing d6i �4mple of extreme typhoons, highest T's increase from 15 to 18 kt (28 to J3 khi/hr). Typhoon Gilda (1967) is the storm traveling at 18 kt; it was fdVitig west-northwestward with a p0 of 26.28 in. (89.0 kPa). Gilda latel filed to 27.14 in. (91.9 kPa) and its T decreased to 15 kt (28 km/hr) near 1706N, 131.8�E, as it drew closer to the Philippines (tables 4.5 and 4.6); We have adopted 20 kt (37 km/hr) as the upper limit of T for the PMH for the efittId coastal region south of 30.5�N. Looking at all extreme hurricane and typhbbfi data-supported our selection of 20 kt rather than a higher value. 198 Table 10.1 .--Forward speeds of western North Pacific typhoons (1961-75) with po < 26.81 in. (90.8 kPa) at time of lowest p.. T Po Typhoon Year (kt) (km/hr) (in.) (kPa) Nancy 1961 14 26 26.05 88.2 Violet 1961 10 19 26.05 88.2 Emma 1962 6 11 26.67 90.3 Karen 1962 15 28 26.48 89.7 Carmen 1963 10 19 26.52 89.8 Judy 1963 13 24 26.78 90.7 Sally 1964 13 24 26.40 89.4 Wilda 1964 9 17 26.73 90.5 Louise 1964 11 20 26.31 89.1 Opal 1964 14 26 26.67 90.3 Bess 1965 7 13 26.46 89.6 Kit ! 1966 15 28' - -26.49- 89.7 Carla 1967 11 20 26.61 90.1 Emma 1967 14 26 26.81 90.8 Gilda 1967 18 33 26.28 89.0 Agnes 1968 9 17 26.70 90.4 Elaine 1968 8 15 26.81 90.8 Viola 1969 13 24 26.31 '-89.1 Elsie 1969 16 30 26.28 '89.0 Olga 1970 13 24 26.70 90.4 Georgia 1970 .11 20 26.70 90..4 Hope 1970 14 26 26.43 89.5 Joan 1970 11 20 26.61 90.1 Amy 1971. 13 24 26.43 89.5 Nadine 1971 11 20 26.52 89.8 Irma 1971 16 30 26.11 88.4 Nora 1973 8 15 25.90 87.7 Patsy 1973 11 20 26.37 89.3 Nina 1975 15 28 26.70 90.4 Elsie 1975 12 22 26.58 90.0 June 1975 10 19 25.87 87.6 199 (KM/HR) 5 10 15 20 25 30 35 ' 1 ' I I '1 1 I 1 * SINGLE DATA POINT _ ~@DOUBLE DATA POINT 0i ~~~~~~~- 91.0 Z * � 26.75- . a.. EMMA 11962] 0 � UO - ' @ * -90.0 ,, 26.50- .- a 'J_ * * * �RANGE OF PMH Po - 89.0 c,< 26.25- GILDA (1967) SOUTH OF 30.5N- z ) 26.00 * 0 SPEEDS FROM ANNUAL TYPHOON REPORTS (1961-75) -88.0 NORA E1973) 5 P0 FROM ANNUAL TYPHOON JlNE 11975) REPORTS AND CHIN 119721 25.75- . I , I |I I I I II I FORI TE rEARS 1961-70 _ 0 2 .4 6 8 10 12 14 16 18 20 7.0 FORWARD SPEED (KT) Figure 10.2.--Forward speed (T) vs. central pressure (pc) for typhoons listed in table 10.1. 10.2.1.2 MAYPORT, FLA. TO LATITUDE 450N. A T envelope along the east coast passes through the data point for the New England hurricane of 1938, which had a T of 47 kt (87 km/hr) near milepost 2600 (fig. 10.1). We have adopted a T of 47 kt at this location as an upper limit for the PMH. The PMH p0 is about an inch (3.4 kPa) lower than the 1938 hurricane at mile- post 2600. Speeds faster than 47 kt near milepost 2600 would make the storm increasingly asymmetrical leading to higher po. Therefore, such speeds are reserved for points farther north. We have adopted an upper limit for T of 50 kt (93 km/hr) at 450N. 10.2.2 LOWER LIMIT OF T 10.2.2.1 RIO GRANDE TO SAVANNAH, GA. We recommend a lower limit of T for the PMH of 6 kt (11 km/hr) over most of the Gulf of Mexico and the east coast to near Savannah, Ga. (near milepost 1860, fig. 10.1). Of the typhoons, Emma (1962) had the slowest T [6 kt (11 km/hr)] (fig. 10.2) at the time of lowest po. In the next 24 hours, Emma slowed to 4 or 5 kt (-8km/hr), 200 started to recurve and filled 0.56 in. (1.9 kPa). Environmental factors were favorable for intensification. The filling was most probably the result of both the slow movement and recurvature. Based on the typhoon sample (fig. 10.2), 6 kt (11 km/hr) is considered the minimum stable speed for the PMH in a tropical region. The Labor Day hurricane of 1935 had a T of 9 kt (17 km/hr) and Camille the much higher T of 16 kt (30 km/hr). We consider T below 6 kt to be a stalling speed for the PMH along the gulf and east coasts. Near milepost 1100 the minimum T is increased to 15 kt (28 km/hr) because of particular characteristics of this area (described in chapter 8). Along this area of the coast and extending west and south a PMH must recurve and move quickly because it is a filling, nonsteady state hurricane. 10.2.2.2 SAVANNAH, GA. TO LATITUDE 450 N. The adopted lower limit of T increases slowly from 6 kt (11 km/hr) to 10 kt (19 km/hr) at a point near Cape Hatteras. North of there slow T's for the PMH are not considered meteorologically reasonable because of lowering sea-surface temperatures. Therefore, the lower limit curve (fig. 10.1) increases rapidly until it is 9 kt (17 km/hr) less than the PMH upper limit of T curve at 45�N. Slower- moving hurricanes all have po0 > 28,31 in. (95.9 kPa). Faster T's are necessary over the colder New England waters for the PMH to have the lowest possible po. Over warmer waters farther south, a PMH can exist at slower T. 10.3 FORWARD SPEED FOR THE SPH 10.3.1 UPPER LIMIT OF T 10.3.1.1 GULF COAST. The SPH, although an intense hurricane, is substantially weaker than the PMH. Weaker hurricanes in general are known to travel within a broader range of T. Therefore, the SPH should have a larger overall range in T than the PMH. Thus, we are justified in setting the upper limit of T for the SPH higher than the upper limit of T for the PMH. We recommend a value of 25 kt (46 km/hr) for the SPH upper limit of T for the Gulf coast (fig. 10.3). This is 5 kt (9 km/hr) faster than the upper limit of PMH T along the Gulf coast. _~~~~~~~~~~~~~~~~~~~~~1 2 ;3 -- -- > '-Z O l r- 0 Z : r- co 0 rl z M x 0') Co CD m , o . r- m z rn G3 I K --I ;Z - C '~~~~~~~c r- 3> P SEECE POINTST D ; ' ~ ' m ~ z P o ' = x x r- . . > r- ' DISTANCE (KM X 102) 4 a 1 1 1 6 20 24 28 32 36 40 44 4R 52 56 SELECT:D POINTS LABELED WITH P0 (2 OMITTED, e.g.27.53 LISTED AS 7.53 ~~~~~~~~~~~~~50--~~~~~~~~~~0 CIRCLED POINTS P < : - (94.0~~~~~~~~~~~~~~ 'k-P07 _o~~/ 27.76 IN. (94.0 kPa)97 -- 7.97--8 ,o /- -~ / 70 W 30 n n? ~~~~/ � J.I -60 - "' 30 "-*2 a~~~ - 30 � 8.38 UPPER IMIT '/ -6-50 UIL"99 ....7 - -5" - 7.99 * " I 7.66 -.. - 20 -7' 0 7,521 * 40 ..7.99--13Y 7 . -3 7.� � .,,=73~i ;;6'81 /-�..7 176 7- 3 76' 6 2:,s - 0 -77.64 -.2 O 10-7 -2 7 2 64 7A" WT- 'PT 714\,.; - 10 ~~~~:0 ' nLOW6R IMIT , I , I , ~~I, I , I II 30 0 2 A 6 8 10 12 14 16 18 20 22 24 26 28 30 DISTANCE (N MIX 102) Figure 10.3.--Adopted SPH upper and lower limits of T. Data is from tables 4.1 to 4.4. All data points falling outside the two curves are labeled with lowest central pressure (p ). All circled data points falling inside the two curves are labeled with lowest p 0tAer data points (except those between mileposts 1300 and 1500) are labeled with lowest Po if this po is < 28.00 in. (94.8 kPa). 202 10.3.1.2 EAST COAST. Along the east coast (fig. 10.3), we have adopted the 25-kt (46 km/hr) value from the Keys northward to Savannah. From there northward the upper limit of T curve exceeds an envelope of the data and is parallel to and 5 kt (9 km/hr) more than the PMH upper limit of T in figure 10.1. 10.3.2 LOWER LIMIT OF T 10.3.2.1 RIO GRANDE TO CAPE HATTERAS, N.C. Geisler (1970) has stated that there is a gradual transition from upwelling to no upwelling of cold subsurface sea water as hurricanes increase their T beyond 4 kt (7 km/hr). Upwelling weakens hurricanes. Others such as Black and Mallinger (1972) have spoken in support of Geisler's theory. We adopted 4 kt as the lower limit of T for the SPH over southern latitudes to a point just north of Cape Hatteras. This envelops the storm data except for the 28.30 in. (95.8 kPa) hurricane (fig. 10.3) moving at 3 kt (6 km/hr). This is reasonable because the storm was too weak to meet the SPH po criteria anywhere along the U.S. coast to latitude 45�N. 10.3.2.2 CAPE HATTERAS TO LATITUDE 45 N. The adopted SPH lower limit of T envelops the data of figure 10.3 over these northern latitudes and envelops the lower 5 percentile T north of milepost 2500 from Ho et al. (1975) for landfalling hurricanes. 203 11. TRACK DIRECTION 11.1 INTRODUCTION Peripheral pressure (pw), central pressure (po), radius of maximum winds (R)and forward speed (T), the subjects of chapters 7 to 10, are all used in computing 10-m (32.8-ft) overwater 10-min winds. Track direction (0) is not used to compute wind speeds, but it is an important parameter because it is used to determine from what directions an SPH or a PMH may approach the coast. For example, a section of the coast that can be affected by an SPH from a wide range of directions is more likely to include a critical track to the coast than a coastal section accommodating only a narrow range of permissible directions. 11.2 DEFINITION OF TRACK DIRECTION (0) In this report, G for the SPH and PMH is defined as the path of forward movement or track from which the hurricane is coming. 0 is measured in degrees clockwise from north. We must remember that the SPH and PMH are steady state hurricanes (see definition in sec. 1.2.3). As steady state hurricanes, we assume they do not change course during the last several hours before making landfall. Exiting hurricanes are not considered except along capes or the tip of peninsulas, e.g., Cape Hatteras, Cape Cod and the Mississippi Delta where the SPH and the PMH are permitted to exit after passing over a small land area. 11.3 VARIATIONS IN 0 SHOWN BY HURRICANES OF RECORD Figure 11.1 shows the track direction for hurricanes of record for the period 1900-75 for the gulf and east coasts. The direction was plotted at the point of landfall or the point at which bypassing hurricanes were nearest the coast (from tables 4.1 and 4.2). The scatter is large for the entire sample. New England hurricanes have not entered the coast from directions east of south. In figure 11.2, the storm sample is restricted to hurricanes with p < 28.05 in. (95.0 kPa) to milepost 2200 and to hurricanes with po0 "' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' G3 > ~ 3' O4 - z w P 5" P r cn~~~~~~~~~~ X r ~~~r- M~ > C O CA~ r-A -' z z co 8 z T m 0 CI) I 0 3' P1 zF - r~~ ~ ~~~~~~~~ I" cn cn Cn I W~~~~~~~~~~~~~~~~~~~ DISTANCE (KM X 102) 4 i 12 16 20 24 28 32 36 40 44 48 52 56 260 ~ 230 z 4 200 - U) *4 0I U3 170 o - - 140 - * z O ~ o 04 'S1 0 0 - 80 u �TW p:~~~~~~~~~~ HURRICANES C 50 -j 0_ 2 4 8 10 12 14 16 18 20 22' 24 26 28 30 DISTANrCE (N MI X102) Figure 11.1. --Track direction for lanndfalling or bypassing hucrricanes atong the gulf and east coasts of the Uni~tedZ States. mI m 0o wn o zo z 00 - z m z 0~~~~~~~~~~~~~ 0 0 r~~~~~~~ F - P1~~~~~C i;I~ ~ ~ ~ ~ ~ I x 'V DISTANCE (KM X 10') 4 8 12 16 0 24 28 32a36 40 44 48 52 56 260 I~~~~~~~~~~I o 230 z SO o200 =4 U. 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 LU LU 170-- W~~~~~~~ O LIJ 140 z I 0' 4 110 LU Ye 80 U ex I.- 50 0 2 A 6 8 10 12 14 16 1l 20 22 24 26 28 30 DISTANCE (N MIX102) Figure 11.2.--Track direction for landfalling or bypassing hurricanes along the gulf and east coasts of the United States with p0 <28.05 in. (95.0 kPa) to miZepost 2200 or with P. <28.41 in. (96.2 kPa) north of milepost 2200. 206 <28.41 in. (96.2 kPa) north of milepost 2200. Three regions'have several storms each: western gulf, south Florida, and the Carolinas to New England. The scatter in 0 is quite large except from the Carolinas to New England where all severe hurricanes had 0 between 180� and 240�. 11.4 GENERALIZED COASTAL ORIENTATIONS We divided the gulf and east coasts into 21 straight line segments in order to study the variation of 0 along the coast for the PMH and the SPH. These segments stretch from the Rio Grande, clockwise to Cape Sable, Fla. just west of milepost 1400. The other 11 extend from the vicinity of Cape Sable to the Canadian border (~45�N). The segments (fig. 11.3) range in length from about 45 n.mi. (83 km) to about 335 n.mi. (621 km). Table 11.1 contains geographical and meteorological data by segment. Track direc- tions are listed for hurricanes (1900-75) entering or bypassing the coast with central pressure < 28.05 in. (95.0 kPa) for segments 1 to 15, and with central pressure < 28.41 in. (96.2 kPa) for segments 16 to 21 (from milepost 2200 to the Canadian border). The permissible PMH and SPH limits of 0 defined in sections 11.5 and 11.6 and ranges of forward speed discussed in chapter 10 make up the right side of the table. 11.5 TRACK DIRECTION FOR THE PMH 11.5.1 RANGE OF 4 OVER THE OPEN OCEAN Initially, let us consider a PMH over the open ocean. From what direc- i tions can this PMH travel? Experience tells us that it will not be moving from the north. Should the range of 8 be even more restricted? We know that hurricane Camille (1969) with a po of 26.81 in. (90.8 kPa) entered the Mississippi coast from 0 = 160� without showing signs of weakening. If Camille had entered the coast from 180� instead of 160�, the typhoon data for storms moving from the south or southwest from inception (discussed in chapter 8, sec. 8.3.7.2.1.2) suggest to us that the pO at landfall might have been higher. However, in this report we will not be quite so restric- tive because this indication stemmed from typhoon data and not hurricane data. We assume that PMH 0 over the open ocean will be limited to angles < 190� but not to angles near 0�. 207 950 900 950 80 ' 0' 650 SC~~~~~~~~~~~~ ' N. Sao z 3~~~~~~~~~~~~~~~~~~~~~~~AD 8PQ CHARLU _ b4Q]~~I AN CI~~~ 32 DAYCHONA R 200 PORT ISABE ~ ~ ~ ~ ~ ~ ~ A 0 25~~~~~~~~~~~~~~~~~~~VM Figure11.3. -Generlizedstraijt linesegmens depcting rientaion o gulf LAnd eas cost ofteUntdSAt. Table 11.1.--Coastal segments, observed severe hurricane direction and permissible track direction Zimits oo before smoothing for the PMP and SPH. Severe Severe hurricane Permissible ranges of Permissible limits Coastal Direction Cities or hurricane central pres. forward speed (T) before smoothing t Segment & orientation normal to other Severe hurricane direction within 150 n.mi. length (from north) coast landmarks (date) (name) (from north) (278 km) of coast PMH SPH PMH SPP 1 A A 110 n.mi. (360�-180�) (900) Mex.brder. 18 Aug.1916 115� 28.00 in. slow 6 kt slow 4 kt 70�-1400 50�-1500 (204 km) to Corpus (94.8 kPa) (11 km/hr) (7 km/hr) Christi,TX 14 Sep.1919 105� 27.99 in. (94.8 kPa) 5 Sep.1933 0900 28.02 in. fast 20 kt fast 25 kt B B (94.9 kPa) (37 km/hr) (46 km/hr) 70�-150' 50�-160� 20 Sep.1967 (Beulah) 1550 27.26 in. (92.3 kPa) Near intersection of segments 1-2 3 Aug.1970 (Celia) 1150 27.89 in. (94.4 kPa) 2 A A 195 n.mi. (55�-2350) (1450) Corpus 9 Sep.1900 130� 27.64 in. slow 6 kt slow 4 kt 95�-190� 85�-195� (361 km) Christi (93.6 kPa) (11 km/hr) (7 km/hr) to vic. 17 Aug.1915 130' 28.01 in. fast 20 kt fast 25 kt B B Sabine,TX (94.9 kPa) (37 km/hr) (46 km/hr) 850-1900 75o-200� 14 Aug.1932 135� 27.83 in. (94.2 kPa) 11 Sep.1961 (Carla) 170� 27.49 in. (93.1 kPa) 3 A A 75 n.mi. (850-2650) (175') Vic.Sabine 27 Jun.1957 (Audrey) 200� 27.95 in. slow 6 kt slow 4 kt 1500-1900 140�-2050 ' (139 km) to vic. (94.7 kPa) (11 km/hr) (7 km/hr) Tigre Pt., fast 20 kt fast 25 kt B B LA. (37 km/hr) (46 km/hr) 140�-1900 1300-215� 4 A A 15 n.mi. (110�-290�) (200')* Vic. Tigre 8 Sep.1974 (Carmen) 155� 27.64 in. slow 6 kt slow 4 kt 150�-190' 140�-250� (213,kmV Pt. to (93.6 kPa) (11 km/hr) (7 km/hr) Isle Der- fast 20 kt fast 25 kt B B niere (37 km/hr) (46 km/hr) 1400-190� 130�-250� 5 A A 75 n.mi. (900-2700) (1800) Isle Der- 29 Sep.1915 170� 27.53 in. slow 6 kt slow 4 kt 130�-1900 120�-240� (139 km) niere to (93.2 kPa) (11 km/hr) (7 km/hr) Port Eads, 10 Sep.1965 (Betsy) 135' 27.79 in. fast 20 kt fast 25 kt B B LA. (94.1 kPa) (37 km/hr) (46 km/hr) 1200-1900 110�-2500 6 A A 75 n.mi. (360�-1800) (90�)*# Port Eads, 18 Aug.1969 (Camille) 1600 26.81 in. slow 6 kt slow 4 kt 135�-140� 125�-150� (139 km) LA., to vic. (90.8 kPa) (11 km/hr) (7 km/hr) Long Beach; fast 20 kt fast 25 kt B B MS. (37 km/hr) (46 km/hr) 125�-150� 115�-160" Table 11.1.--Coastal segments, observed severe hurricane direction and permissible track direction Zimits before smoothing for the PMH and SPH - continued. Severe Severe hurricane Coastal Direction Cities or hurricane central pres. Permissible ranges of Permissible limits Segment & orientation normal to other Severe hurricane direction within 150 n.mi. forward speed (T) before smoothing t length (from north) coast landmarks (date) (name) (from north) (278 km) of coast PMH SPII PMH SPH 7 (950-2750) (185�) Vic. Long No severe A A 265 n.mi. Beach to hurricanes slow 6-14 kt slow 4 kt 135�-190� 125�-245� (491 km) mouth of (11-26 km/hr) (7 km/hr) Aucilla R., fast 20 kt fast 25 kt B B FL (37 km/hr) (46 km/hr) 125�-190� 115�-2500 8 A A 90 n.mi. (130�-310�) (2200) Mouth of No severe slow 14-15 kt slow 4 kt 2153-2450 (167 km) Aucilla R. hurricanes (26-28 km/hr) (7 km/hr) to Homo- fast 20 kt, fast 25 kt B B sassa, FL (37 km/hr) (46 km/hr) 215�-245� 205�--250� 9- A A 75 n.mi. (185�-5�) (2750)*# Homosassa No severe slow13-14 kt slow 4 kt 215�-2500 (139 km) to Indian hurricanes (24-26 km/hr) (7 km/hr) Rocks fast 20 kt fast 25 kt B B Beach, FL (37 km/hr) (46 km/hr) 215�-2450 2050-2500 10 A A 190 n.mi. (150�-3300) (240')* Indian 18 Oct.1910 2000 27.80 in. slow 6-13 kt slow 4 kt 180�-1900 1800-2500 (352 km) Rocks Beach (94.1 kPa) (11-24 km/hr) (7 km/hr) to Cape 21 Sep.1948 2100 27.62 in. fast 20 kt fast 25 kt B B Sable (East (93.5 kPa) (37 km/hr) (46 km/hr) 180�-190 1700�-2500 Cape), FL Near intersection of segments 10-11 3 Sep.1935 1300 26.35 in. (89.2 kPa) 10 Sep.1960 (Donna) 1400 27.45 in. (93.0 kPa) ~~~~11 . ~A A 45 n.mi. (80o-260�) (170�) Cape Sable 28 Sep.1929 0900 28.00 in. slow 6 kt slow 4 kt 120�-1900 1100-230� (83 km) (East Cape) (94.8 kPa) (11 km/hr) (7 km/hr) to Key Largo, fast 20 kt fast 25 kt B B FL (37 km/hr) (46 km/hr) 110�-1900 100�-2400 Severe hur- 10 Sep.1919 110� 27.44 in. canes whose (92,9 kPa) p0 values 21 Oct.1926 220� 27.52 in. were applied (93.2 kPa) to the 19 Oct.1944 1950 28.02 in. Florida Keys (94.9 kPa) '8 Sep.1965 (Betsy) 0900 27.99 in. (94.8 IcPa) [. Table 11.1.--CoastaZ segments, observed severe hurricane direction and permissible track direction Zimits before smoothing for the PMH and SPH - continued. Severe Severe hurricane Coastal Direction Cities or hurricane central pres. Permissible ranges of Permissible limits Segment & orientation normal to other Severe hurricane direction within 150 n.mi. forward speed (T) before smoothing t length (from north) coast landmarks (date) (name) (from north) (278 km) of coast PMH SPH PMH SPH 12 A A 90 n.mi. (100-190�) (1000) Key Largo 18 Sep.1926 110� 27.59 in. slow 6 kt slow 4 kt 70�-150� 50�-1600 (167 km) to Palm (93.4 kPa) (11 km/hr) (7 km/hr) Beach 17 Sep.1947 0800 27.76 in. fast 20 kt fast 25 kt B B Harbor,FL. (94.0 kPa) (37 km/hr) (46 km/hr) 700-160� 500-1700 Near intersection of segments 12-13 17 Sep.1928 1200 27.62 in. (93.5 kPa) 13 A A 250 n.mi. (3400-160�) (700) Palm Beach 4 Sep.1933 1200 27.98 in. slow 6 kt slow 4 kt 70�-120� 50�-130� (463 km) Harbor to (94.8 kPa) (11 km/hr) (7 km/hr) Amelia Is., fast 20 kt fast 25 kt B B FL (37 km/hr) (46 km/hr) 70�-130� 50�-1400 14 A A 90 n-mi. (20o-200�) (110�) Amelia Is., No severe slow 6 kt slow 4 kt 90�-120� 800-130� (167 km) FL to GA - hurricanes (11 km/hr) (7 km/hr) SC line fast 20-21 kt fast 25-26 kt B B (37-39 km/hr) (46-48 km/hr)80'130" 70�-1400 15 A A 335 n.mi. (500-230�) (1400) GA-SC 15 Oct.1954 (Hazel) 190� 27.66 in. slow 6-10 kt slow 4 kt 90�-190� 80�-200" (621 km) line to (93.7 kPa) (11-18 km/hr) (7 km/hr) Cape Hat- fast 21-36 kt fast 26-41 kt B B teras,NC (39-67 km/hr) (48-76 km/hr)800-1900 70022100 Severe 10 Sep.1954 (Edna) 2100 27.85 in. hurricanes (94.3 kPa) C whose ctr. 28 Aug.1958 (Daisy) 1800 28.26 in. 600-220� bypassed (95.7 kPa) NC Outer 27 Sep.1958 (Helene) 2400 27.52 in. Banks (93.2 kPa) Near intersection of segments 15-16 14 Sep.1944 195� 27.88 in. (94.4 kPa) 16 A 110 n.mi. (350�-170�) (800) Cape Hat- No severe slow 10-17 kt slow 4-5 kt 50�-140� (204 km) teras to hurricanes (18-32 km/hr) (7-9 km/hr) B B Cape fast 36-43 kt fast41-48 kt 700-140' 500-150� Charles, VA (67-80 km/hr) (76-89 km/hr) C C 70�-150� 500-160� Table 11.1.--CoastaZ segments, observed severe hurricane direction and permissible track direction limits before smoothing for the PMH and SPH - continued. Severe Severe hurricane Coastal Direction Cities or hurricane central pres. Permissible ranges of Permissible limits Segment & orientation normal to other Severe hurricane direction within 150 n.mi. forward speed (T) before smoothing t length (from north) coast landmarks '(date) (name) (from north) (278 km) of coast PMH SPH PMH SPH 17 A 225 n.mi. (25o-205�) (115�) Cape No severe slow 17-33 kt slow 5-15 kt 70�- 1750 (417 km) Charles,VA hurricanes (32-61 km/hr) (9-28 km/hr) B B to Brooklyn, fast 43-48 kt) fast 48-53 kt 80�-175� 70�-185� NY (80-89 km/hr) (89-98 km/hr) C C 80�-1850 70�-195" B B 140 n.mi. (70�-250�) (160�) Brooklyn to 21 Sep.1938 180� 27.75 in. slow 33-38 kt slow 15-19 kt 90�-190� 80�-190� (260 km) vic. (94.0 kPa) (61-70 km/hr) (28-35 km/hr) C C Martha's 15 Sep.1944 2200 28.31 in. fast 48-49 kt fast 53-54 kt 900-190� 80�-200' Vineyard,MA (95.9 kPa) (89-91 km/hr) (98-100 km/hr) 31 Aug.1954(Carol) 200" 28.38 in. 96.1 kPa) 12 Sep.1960(Donna) 2050 28.38 in. (96.1 kPa) Near intersection of segments 18-19 11 Sep.1954(Edna) 2100 27.97 in. (94.7 kPa) 19 B 90 n.mi. (3500-170�) (80�)*# Vic. No severe slow 38-40 kt slow 19-22 kt 90�-1500 (167 km) Martha's hurricanes (70-74 km/hr) (35-41 km/hr) C C Vineyard fast 49 kt fast 54 kt 1006�-150� 90�-1600 to MA-NH (91 km/hr) (100 km/hr) line 20 B 60 n.mi. (30�-210�) (1200) MA-NH No severe slow 40-41 kt slow 22-23 kt 110 �-1700 (111 km) line to hurricanes (74-76 km/hr) (41-43 km/hr) C C Casco Bay, fast 49-50 kt fast 54-55 kt 120�-1700 110�-1800 ME (91-93 km/hr) (100-102 km/hi 21 B 165 n.mi. (60�-24G�) (150' Casco Bay, No severe slow 41 kt slow 23-24 kt 130�-2000 (306 km) ME to Vic. hurricanes (76 km/hr): (43-44 km/hr) C C 450N fast 50 kt fast 55 kt 1400-190' 1300-2100 (93 km/hr) (102 km/hr) * Segments where PMH cannot enter normal to coast (before smoothing). # Segments where SPH cannot enter normal to coast (before smoothing). t For definitions of categories A, B, and C see tables 11.2 and 11.3. "'3L 212 We also need to know if a PMH can travel from the east-northeast or even northeast. During the time period between their lowest po's and 12 hours before their lowest po 's, all typhoons (1960-75) with po < Camille's were moving from e > 90�. Typhoon Nora (1973), one of the three most severe typhoons on record in terms of po' moved from the east (0 = 90�) at latitude 14.8�N for more than 3 hours while its p varied between 25.90 in. (87.7 kPa) and 25.93 in. (87.8 kPa). None of this sample of great typhoons moved from north of due east around the time of minimum po. The question now is can a PMH do so? In the Northern Hemisphere a direction of movement from <90� is not common for a hurricane (typhoon). Riehl (1954) states, "motion toward the southwest occurs under a deep northeasterly flow. Preferred regions are the western parts of the Gulf of Mexico and the China Sea, where such upper (air) currents are common, especially in August." Only the hurricanes of August 5, 1933 (0 = 70�) and Fern of 1971 (0 = 50�) followed a course from between the north and east over the western Gulf of Mexico during our period of record (1900-78). These two hurricanes had po > 28.79 in.(97.5 kPa). However, on Sept. 2, 1977, extreme hurricane Anita (not included on figs. 11.1 and 11.2 or table 11.1) entered a sparsely populated region of Mexico about 145 n.mi. south of Brownsville, Tex., from a 0 = 60�. A po0 of 27.34 in. (92.6 kPa) was measured by aircraft reconnais- ance just prior to landfall. This po is within 0.15 in. (0.5 kPa) of SPH po for this portion of the coast. Over the eastern gulf, the only hurricane traveling from between north and east that did not cross the Florida Peninsula was Inez of 1966 (0 = 65�). This storm's po was 28.85 in. (97.7 kPa). In the Atlantic, the strongest hurricane following a course from between north and east was the storm of September 17, 1947 (0 = 80�), which entered the Florida east coast near Fort Lauderdale with po = 27.76 in. (94.0 kPa). The number of typhoons moving from the northeasterly quadrant over the South China Sea is also small (Crutcher and Quayle 1974). A typhoon of hurricane Camille intensity (26.81 in. [90.8 kPa]) or stronger has never intensified or developed over the China Sea as far as we can ascertain. 213 Typhoons such as Viola (1969) have passed through the Formosa Strait between Taiwan and Luzon, moving generally from the east or east-southeast, with p < Camille's, but have then filled. The only way a typhoon can enter the China Sea without crossing land is through the Formosa Strait. In addition, typhoons will weaken over the China Sea since sea-surface temperatures are cooler than over the Philippine Sea where the world's tropical cyclones have achieved maximum intensity. Only weak typhoons have moved from the northeast over the Philippine Sea. Thus, we have learned not only that movement from <90� is uncommon for a hurricane, and occurs under a deep northeasterly flow, but also that none of the typhoons or hurricanes of near PMH intensity have followed tracks from the northeast. We conclude initially that hurricane movement from <450 will not lead to PMH intensity. Since movement from the east is possible (the extreme typhoon Nora), it also seems likely that a PMH could move from a direction slightly north of east, while maintaining its PNH po' Probably, Nora could have moved from slightly north of east. We therefore assume that a PMH can travel from a direction between east and east-northeast, limiting o to > 70�. We have thus set the limits of 0 for the PMH over the open ocean to between 70� and 1900 (measured clockwise). We must now determine how the orientation of the 21 coastal segments affect this generalization. Throughout much of the rest of this chapter we will refer to maximum 0 and minimum 0 (or maximum permissible 0 and minimum permissible 0). Maximum 0 is simply the largest numerical value of 0 considered, and minimum 0 is the smallest numerical value. For example, in discussing the open ocean criterion for the PMH, minimum 0 = 70�. 11.5.2 RANGE IN0G AOl-O THE.COAST BEFORE SMOOTHING 11.5.2.1 DEPENDENCY ON FORWARD SPEED AND ANGLE OF APPROACH. At this point, we wish to make two basic assumptions: a. A PMH cannot travel close and parallel to a coast without weakening. b. If a PMH is traveling close and parallel to a coast, the faster it moves the less it weakens. 214 The following discussion is meant to convey to the reader our concept for the minimum track angle permissible between 'the PMH 'and a random stretch of coast without filling. Figure 11.4 is a schematic that shows the percent- age of the storm over the coast when the hurricane tracks have various entrance angles to the same location. A line labeled 900 is perpendicular to the coast. Three other lines are drawn at angles of 200, 30� and 0O% 20% 45�. Let the four circles represent the same PMH I // /COAST/ moving toward the coast. When the PMH, following the track perpendicular to the coast, is a dis- 201 tance equal to the radius of the circle from the 30. coast (r) the land is not affecting the PMH winds. 450 If, however, the PMH follows the 450 track, about 9Oo 10% of the circle will be overland when the distance along the track is equal to r; simi- FIGURE11;4 SCHEMATIC REPRESENTATION OF PMH NEAR THE COAST larly, if it follows the 300 track about 20% will be overland, and if it follows the 20� track, Figure 11.4.--Schematic about 30% (nearly one-third of its circulation) representation of PH near the coast. will be overland. (Of course, if tracks were drawn at 135�, 150�, and 1600, the results would be identical, except that the effect would be on the other half of the PMH).' From the discussion of the percent of the storm's circulatidn overland for selected angles to the coast, we have adopted allowable angles between the coast and 4 related to the minimum speed a hurricane can have without weak- ening (table 11.2). We make the additional assumption that a PMH following a track with an angle <200 to the coast will Vweaken regardless- of its forward speed. ' In table 11.2 our three speed categories range from slowest (category A) to fastest (category C). The speeds within these categories were decided arbitrarily. In category A, 6 kt (11 km/hr) is the lowest limit of PMH forward speed criteria. The 10-kt (18 km/hr) speed is an arbitrary 5 kt (9 km/hr) greater than the allowable speed of a stalling hurricane (< 5 kt). ,, - - .~~~~~~~ 215 Table 11.2.--Relation between forward speed (T) and the aZZllowable angles between the coast and track direction (0) for the PMH. Allowable angles between Speed category Forward speeds (T) the coast and 0 A 6 kt < T < 10 kt 40� - 140� (11 km/hr < T < 18 km/hr) B 10 kt < T < 36 kt (18 km/hr < T < 67 km/hr) 30� - 150� C T > 36 kt 20� - 160� (T > 67 km/hr) Thus, for any coastal location, the allowable range in angles between the coast and 0 for the PMH are determined by the forward speeds specified in chapter 10. We are assuming the size (R) of the hurricane (see sec. 11.7) will not be a major factor in limiting Q. 11.5.2.2 RANGE IN 0 FOR INDIVIDUAL COASTAL SEGMENTS. We have given an open ocean criterion in section 11.5.1 and a general coastal criterion dependent on forward speed in section 11.5.2.1. Some of the 21 coastal segments (fig. 11.3 and table 11.1) use only these two criteria in setting the permissible PMH limits before smoothing. Other segments have additional criteria, e.g., cool sea-surface temperatures and their effect on 0. We will first look at the segments using only the open ocean and general coastal criteria. Permissible 0 limits for segments 1, 2, 4, 5, 7, 11-13, 15 and 16 are based on our open ocean criterion and the criterion indicated in table 11.2. For example, segment 16 has a coastal orientation (from north) of 350�-170�. The open ocean criterion gives PMH 0 limits of 70� to 190�. Table 11.1, however, gives 0 limits of 70� to 140� for category B and 70� to 150� for category C. The minimum 0 of 70� in each category is from the open ocean criterion. The maximum 0 for each category comes from the allowable angles given in table 11.2. For example, for category B, we may move 150� clock- wise from 350� (350� + 150� = 500� or 140�) or 30� counterclockwise from 170� (170� - 30� = 140�) and obtain 140�. A similar method is used for category C, which is associated with higher forward speeds. This increase in the value of minimum 0 (from 80� for segment 17 to 140� for segment 21), although somewhat arbitrary, is considered reasonable when compared with available data. A glance at east coast hurricanes (tables 4.2 and 4.4) indicates that of the eight hurricanes traveling at speeds > 25 kt or 46 km/hr (median slow speed for segment 17) the minimum 9 was 180�. Also, maximum sea-surface temperature data during late summer and early autumn lend support to our minimum 9's for segments 17-21 before smoothing (U.S. Navy 1975). 11.5.3 RANGE IN 9 ALONG THE COAST AFTER SMOOTHING. The curves of figure 11.5 show the permissible limits of 9 for the PMH after smoothing across coastal segments. The maximum allowable range of 90 within the segments before smoothing is shown by hatching. Figure 11.6 shows these curves plotted with these data of figure 11.1. Points falling outside the curves are labeled with central pressure. Smoothing in figure 11.5 was accomplished by connecting limits for the 21 individual coastal segments with smooth curves, making sure that the curves show realistic 9 near segment intersections and also within portions of the segments where there are large departures in actual coastal orientation from the generalized segment orientation. The smooth outer curves represent the maximum allowable range of 9 after smoothing. The smooth inner curves represent the decrease of the allowable range for the lower speed category A (< 10 kt [< 18 km/hr]) for segments 1-7 and 10-15 and category B (10 kt < T < 36 kt or 18 km/hr < T < km/hr) for segments 16-18. Only category C (T > 36 kt or 67 km/hr) applies to segments 19-21 and only category B applies to segments 8-9. A single minimum 9 curve is analyzed for segments 16-21 even though two forward speed categories apply in segments 16, 17 and` a portion of 18. Milepost 1800 (3336 km) provides an example of a point along the coast crossed by two inner and two outer curves. The two outer curves indicate that for forward speeds >10 kt or 18.5 km/hr (speed category B), the allow- able range of 0 is 75� to 130�. The two inner curves tell us that for for- ward speeds < 10 kt or 18.5 km/hr (category A), the allowable range of O decreases to 85� to 125�. Along some stretches of the coast such as near CO -0 I-~~~j M CD 00 0 Zj 0 w o ~~~~~~~~' 0 ~ ~ _ CD) CD -~~~r P1 M, z 260 dI~~~~~~~~~~~STANCE (KM X 12 4 I i I I'LbE2DI I 16 20 24 28 32 36 40 44 4t 5 56 I ~~~---CATEGORY A 230 CATEGORY B 200 Ill~~~~~~~..-.... CATEGORY C 170 2 1 . ...... e-rI *1Ii ~~~~~~~~~~~~~~~~~~~~~~~~~L>~~~~~~~~.. ..~. ....:.. se o CC)A,"TAL SEGM-NN1 NO. I 2 3. 56 7 I 190l I1V112 1,3 I1, I 15, 16 17, 18 19~21, 2~1 0 2 14 6 8 I10 1 2 14A 16 18 2 0 2 2 2 4 2 6 2 8 3 0 DISTANCE IN Ml X 102) Figure 11.5.--Permissible Limits of 0 for the PMH. The maximum limits before smoothing are shown by hatching. Allowable limits after smoothing for forward speed categories A, B, and C (see table 11.2) are shown by smooth curves. 0 z a M P H ' o m > --I 3> M 0 r-A Z I> . 3> -< co <- P C O -- 0 -4 -4 > 0 z m 0 o 0 co z M 0G~ X 0 z M z 03o - 0 H PI P z > DISTANCE (KM X 102) 240 8 12 1 6 20 24 a s .32 36 40 44 48 52 56 260 1 8.70 1 7.g12 -8884I I I. .91I I I I 8.88 \88 8 230 9 8 86 XO.700 f ) XX8X.91 8.29VxI X8 2 \~-B. ~ 4 B-35 8 3X C"8.317 7. 58.10CO fX76 W:8.7 2 6 7.52 7..85 8,38,, 200 -8-0- ~ x "':~X7.86 z 8.10:! 170 7, 726 w~ 7xJ - ./ 8.88K \ LI X 88 4IU~~~~~~~~~i 5 0.3 LEGEND~ A 140 V/3 I - AA Nd 't .,*x 35 -- CATEGORY 0. oil 1 'J1 11 A\30.'A *- CATEGORY B 11 11 E.E 3OXX 8L%_�3 -- CATEGORY C~ 8.793 87.11 810 8.C' - 8. T33%iT 1.91-, CC)AZTA. SEGME14T NC. .S 50 1 23 4156 1819110 1 13 I4 I 15 16I 17 18 19121 21 I II Ii I 11181 81 7I 0 2 A 6 a 10 12 14 16 19 20 22"- 24 26 28 30 DISTANCE (N MI X 102) Figure 16. --Maximum allowable range of PMH 0 after smoothing is represented by the area between the outermost curves. Data points are the same as those in figure 11.1. Those inside the outermost curves are indicated by a dot and those outside these curves by an X. Two hurricanes plotted at the same position are indicated by a 0 . Plotted vaZues (shown for data falling outside the curves) are central pressure. n inches of Hg (exanrple: 8.72 28.72 in.) 221 milepost 250 (463 km), an outermost and an innermost curve merge into a single curve. Here, the permissible maximum limits of 0 are the same (160�) for the entire range of forward speeds. 11.6 TRACK DIRECTION FOR THE SPH Track directions(O)for the SPH given in this section are considered to be "reasonably characteristic." The data show that storms weaker than the SPH have a wider range of 0. 11.6.1 RANGE IN 0 OVER THE OPEN OCEAN In section 11.5.1, we set the limits of 0 for the PMH over the open ocean between 70� and 190� (measured clockwise from north). The limits of 0 for the SPH should cover a wider range of angles. We have adopted limits between 50� and 250� (measured clockwise from north) for the SPH over the open ocean. We believe that movement from 0 < 50� of a hurricane will not lead to SPH intensity. Hurricane Anita of September 1977, (see sec. 11.5.1) entered the coast of Mexico from a 0 = 60� Its 27.34 in. (92.6 kPa) p was near SPH intensity. Therefore, we need to include 0 = 60� in our SPH range. An angle of 50� is therefore a reasonable minimum permissible 4 for the SPH. Recurved hurricanes (g225�)are a rather common phenomenon (figs. 11.1 and 11.2), especially in more northerly lati- tudes. In fact, these storms will often move at 0>225�, although only one hurricane with po <28.05 in. (95.0 kPa) has exceeded this value (fig. 11.2). This is bypassing hurricane Helene with po of 27.52 in. (93.2 kPa) and 0 of 240� near Cape Hatteras. We wish to exceed the 0 of Helene and also be able to bring an SPH normally into most of the west Florida coast. For the maximum SPH 0 over the open ocean 0 - 250� meets these requirements. 11.6.2 RANGE IN 0 ALONG THE COAST BEFORE SMOOTHING 11.6.2.1 DEPENDENCYbN FORWARD SPEED AND ANGLE OF APPROACH. Our constraints in 0 for the SPH are not as restrictive as they are for the PMH. For each of our speed categories (category A now includes speeds as low as 4 kt or 7 km/hr), we have increased our range of allowable angles between the coast and 0 by 20�. These angles are shown in table 11.3. 222 Table 11.3.--ReZation between forward speed (T) and the alzbwable angles between the coast and track direction (9) for the SPH. Allowable angles between Speed category Forward speeds (T) the coast and 0 A 4 kt < T < 10 kt (7 km/hr < T < 18 km/hr) 30� - 1500 B 10 kt < T < 36 kt (18 km/hr< T < 67 km/hr)' 20� -.1600 C T > 36 kt - (T > 67 km/hr) 100 - 1700 11.6.2.2 RANGE IN 9 FOR INDIVIDUAL COASTAL SEGMENTS. The permissible SPH limits of segments 1, 4, 5, 7, 9-13, 15 and 16 agree with our open ocean criterion and the criterion listed in table 11.3. Additional criteriawere imposed on the remaining segments (2, 3, 6, 8, 14, and 17-21) before permissible SPH limits were set (table 11.1). The reasons for additional criteria for segments 3, 6, and 14 are identical to the reasons given for the PMH in section 11.5.2.2. Reasons for imposing' additional criteria on segments 2, 8, and 17-21 follow. In segment 2, SPH category A has a maximum G of 1950 and category B has a maximum 0 of 2000. These O's keep the SPH from traveling over southern Texas and northeastern Mexico. Because of the coastal orientation, only an SPH that has recurved may enter segment 8. Segment 8 takes its minimum 9 from segment 9 and its maximum from segment 7. Maximum 9 is determined by the coastal criterion (table: 11.3) for seg- ments 17 and 19. For the PMH, we gave a range of 90� to 1900 for segment 18 even though segment 17 would tend to limit'G to angles less than 1850 over Long Island and Connecticut. We did this because 18 is relatively long, juts out from the coast, and is not' Concave' like' segment '14', for example. For the SPH, we increase the range from 1900 to 200� for category C and leave 9 at 190� for category B". Along segment 20, we increase the range for category C from 1700 for the PMH to 1800 for the SPH to allow the SPH a larger range. An SPH with 9 = 1800 will pass over 223 the western portion of the Cape Cod peninsula. In segment 21, the SPH maximum 0 is 2100. Angles >2100 are not permissible because the hurricane would pass over southern New England. Minimum e for the northernmost five segments (17-21) is determined by subtracting 100 from the PMH minimum 0 for these segments. 11.6.3 RANGE IN 0 ALONG THE COAST AFTER SMOOTHING The curves of figure 11.7 show the permissible limits of 0 for the SPH after smoothing across coastal segments. Figure 11.8 shows these curves plotted with the data of figure 11.1. Points falling outside the curves are labeled with central pressure. Smoothing in figure 11.7 was accomplished in the same way as the smooth- ing for the PMH (see sec. 11.5.3). The SPH curves in figure 11.7 always envelop the corresponding PMH curves; i.e., an SPH being a weaker hurricane than the PMH has a wider range of allowable 0 at any coastal point. The smooth outer curves represent the maximum allowable range of 9 after smoothing. The smooth inner curves represent the decrease of the allowable range for the lower speed category A (< 10 kt or < 18 km/hr) for segments 1-17 and category B (10 kt < T < 36 kt or 18 km/hr < T < 67 km/hr) for segments 17-21. A single minimum 0 curve is analyzed for segments 16-21. This is done even though three forward speed categories apply to an SPH entering segment 16 and portions of segments 15 and 17, and segments 18-21 are represented by two forward speed categories. 11.7 INTERPRETATION OF RESULTS OF SECTIONS 11.5 AND 11.6 Some readers may find it paradoxical for the SPH, the weaker storm, to have a larger range in direction than the PMH, the stronger storm. After all, the PMH is what probably can happen, while the SPH is what is likely to happen within some undefined but long period of time. However, the truth is that the rarer the hurricane, the more ideal or favorable the ambient conditions must.be which lead to a narrower range of 9. To put it another way, P111 O's are more limited than the SPH because the lower central pressure of the PMH can only be accommodated by a smaller range of Q. -~~~~~ - WU ~~~~~~~~~~~~ -4 m 0 0 ~~~~~~~~~~~~~~~~ 0 0 z C D r o i m D 4 - 3~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~> M P1 0 > ~ Cl) CI) 0 ~~~~ ~~~~~~ ~~0 Z z 3>~ ~~~~~~~~~~~~~~ - 3> -4 -i m G) f- Pco DISTANCE (KM X 102) 260~~ ~ ~ ~ a 812 16 20 24 28 39 36 40 44 48 59 6 260 '' ...Il i ' IG&I.DI5 I ~~~~~~~~~~ ., :. - ~~~~~~~~~~~~~~~~~~~~~~~~~-CATEGORY .::*: -ATEOYB -- 200 *_XCATEGORYC U0Z~~~~~~~~~~~~~~~~... 170 1 50 ~ ICCA~TA $EGMI~N1 I. . ..... ..... 80~~~~~~~~~~~~~~~~~... . 20 -----K..... rI6I~~~~~~I1O 111121131141 15, ~~~~~~~~~~~~Misui s1h 1J0 j DISTANCE~~~~~~~~~~~~~~~~~~Z (N .....02 0~~~ ~~ ~~ ~~~~~~~~~~... I2 .. . . ... 12 1. 16 1.20 22 24 26 28 3 Fi~~~~~~~'ure~~~~.... 11. ...risil ....t o. . for t.e ..Thmaiulmtsbfrsotin are~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. .hw ... htin. ......A ...llowable llmt .fe ...tin ....I .owr ...........i~e A, B,~~~~~~~~~~~~~~~~~~~~~~~~~X. ... .. ....... ..... 1..3). -r shon-b-smothcures Ho WV > - Z 0 C Dz -:~ r * F~ F Z *, - D O - 0 0 1-1 it;1 ;I ' I DISTANCE (KM X 102) 2 60 ,B 2 16 20 24 28 O,32 36 . 40 44 4 52 56 230 888 .- 8.41 X 0 zol3o r' . "-,_ 'q ' f'a t ' ' 14rr, l / 0 * ",xsl -q_ ' 8.8i -CE 3_z 8 -''n co,3 1? � I1 � 0 DISTANCE (KM X 10'2 *SIO I I'>13 outermost s D pea 50 C TA S LEGEND L"CATEGEORY ,-' 110 = � /4 71.99 as 8.0 3xX/I .,/091 CCASTA- SEGMEI1IT NC). It , I ,1 I ,, I 1I , j 8.97 I , I 0 2 4 6 8 10 12 1' 16 18 20 22" 24 26 28 30 DISTANCE (N MIX 102) Figure 11.8.--Maximum aZZowable range of SPH 0 after smoothing is shown by the area between the outermost curves. Data points are the same as those in figure 11.1. .Those inside the outermost curves are indicated by a dot and those outside these curves by an X. Two hurricanes plotted at the same position are indicated by aO . Plotted vaZueskshawn for data falling outside the curves) are central pressure in inches of Hg (examplZe: 8.88 = 28.88 in.). 226 The developed ranges of 0 are dependent on forward speed (T). Radius of maximum winds (R) is not employed in developing the 0 ranges. One reason R was not used is because it shows little correlation (0.19) with 0 for gulf coast storms. East coast recurved hurricanes (0 > 1800) have larger R, which could indicate that these storms may require a smaller range of 0 with respect to the coast to remain steady state, but not enough is known about the interrelation between 0 and R under nonrecurvature conditions to have R dependent on 4 in this report. '1. .. .. . 227 12. OVERWATER WINDS 12.1 THE MAXIMUM GRADIENT WIND SPEED EQUATION 12.1.1 INTRODUCTION The meteorological parameters Pw' Po and R, discussed in chapters 7, 8, and 9, respectively, are used in determining maximum theoretical gradient wind speed (V gx). Gradient wind is defined as a wind blowing under condi- tions of circular motion, parallel to the isobars, in which the centripetal and coriolis accelerations together exactly balance the horizontal pressure- gradient force per unit mass. Gradient wind is independent of duration. The maximum gradient wind speed in a hurricane is the maximum gradient wind at the radius of maximum winds. The larger the pressure drop (Ap = Pw - Po), the larger the gradient wind speed (everything else being equal). The maximum gradient wind speed in this study is computed from the equation: 1l/2 Rf = p - -. (12.1) Vgx K(Pw o (12.1) where Pw = peripheral pressure from weather maps Po = central pressure R = radius of maximum winds f = coriolis parameter* 1/2 K = (i~ 1/2 = density of the air (p) computed from sea-surface temperatures; e g 2.71828 12.1.2 DERIVATION In order to derive the maximum gradient wind speed equation, we should first define the cyclostrophic wind. Cyclostrophic wind is that horizontal wind for which the centripetal acceleration exactly balances the horizontal *Twice the component of the Earth's angular velocity about the local verti- cal, 20 sin 4,where 0 is the angular speed of the earth and ~ is the lati- tude. Since the earth is in rigid rotation, the coriolis parameter is equal to the component of the Earth's vorticity about the local vertical. 228 pressure-gradient force per unit mass. Cyclostrophic wind approximates gradient wind best in hurricanes under conditions when R and f are small, i.e., small-size hurricanes at low latitudes. Maximum winds occur at R when winds are cyclostrophic. The maximum winds for the SPH and PMH are nearly in cyclostrophic balance since the second term on the right side of eq. 12.1 is much smaller than the first term. We will show that: Vx K (Pw )12 (12.2) cx w 0 where Vcx = maximum cyclostrophic wind speed. cx A standard formula for the cyclostrophic wind speed is: 2 v -c I dpa (12.3) r p dr where V = cyclostrophic wind speed c p = the pressure at radius r p = air density A standard formula for the gradient wind speed is: 2 ~~~~ ~~~~~ ~~(12.4) 2 + fVg p dr where V gradient wind speed. g Equating the left hand members of eq. 12.3 and 12.4 we obtain: 2 2 V V g + fV = c (12.5) r g r 229 which may be solved for VC - Vg: 2 2 V - V = rfV c g g (Vc + Vg) (Vc - Vg) = rfVg rfV grf (12.6) c g V + V c g Over the range of hurricane wind speeds of interest to this study, the difference between the quantities Vc and Vg is small compared with the quanti- ties themselves. The approximation is made in the right hand member of eq. 12.6 that V and V are equal. c g This yields: ~ rf V Vg -f (12.7) c g 2 and v -V - Rf cx gx 2 Neglecting the approximation, we have Rf V g V 2 (12.8) gx cx 2 From chapter 6, the Hydromet Pressure Profile Formula is: -R/r P Po = e Pw Po or -R/r P -Po= (Pw -P) e (12.9) Equatidi T2.9 may be solved for the pressure gradient (p - po) by taking deriVaitiw : -R/r dp (P- po)Re (12.10) dr 2 r 230 From eq. 12.3 dp PVc dr r So Pv (P po) Re r 2 r and -R/r 2 (Pw - Po) Re pr For V r R; CX then V (Pw - Po) (12.12) ex pe and V P- P cx 1/2 (12.13) 1/2 Since K p , we have derived eq. 12.2: V = K (Pw Po) /2 Substituting equation 12.2 into eq. 12.8, we obtain eq. 12.1: Vgx= K (Pw - Po) 2 Eq. 12.1, the maximum gradient wind speed equation, has now been rigorously derived. The next task is to determine suitable values of the K coefficient for the SPH and the PMH. 231 12.1.3 DETERMINATION OF THE K COEFFICIENT 12.1.3.1 BACKGROUND. Eq. 12.13 shows that the magnitude of the maximum gradient wind is dependent not only on the pressure difference, but also on the air density at R, which has been included in K. We should not overlook a significant fact. The kinetic energy of the 2 hurricane wind, proportional to pV , is responsible both for exerting stress on a water surface (thereby producing surges and waves) and wind damage. In comparing thin air (large value of K) with dense air (small value of K), !both experiencing the same travel from high to low pressure, the thin air will be moving faster but the kinetic energy will be identical. From the above discussion, it appears that we have two options. We can assume a standard p, hence a standard value of K, because the kinetic energy will be identical anyway, or we can justify a latitudinal variation of density as a matter of convenience and realism. In NHRP 33 (Graham and Nunn 1959) a standard value of 73 was used for K along both coasts for the SPH. This is based on the air density at 68�F (20�C) and a pressure of 29.53 in. (100.0 kPa). The numerical value of K depends on the units used; in this case the wind speed is in miles per hour ~and the pressure is in inches of mercury. Given K in the above units, we can convert it for use with either knots and inches of mercury or kilo- meters/hour and kilopascals by multiplying by 0.868 or 0.8805. HUR 7-97 used a latitudinal variation of K (in the same units as in NHRP 33) ranging from 76.8 at latitude 24�N to 72.8 at latitude 42�N. This variation was based on the variation inmaximum sea-surface temperatures along the east coast, using what is now out of date data. The draft revision of NHRP 33 (HUR 7-120) used the same values of K for computation of maximum gradient winds as those used in HUR 7-97. 12.1.3.2 ADOPTED VARIATION IN K. In this report, we recommend that K be varied with latitude. We base the latitudinal variation of K on the variation of the 0.99 probability level sea-surface temperature (a rare event) for the PMH and the 0.75 probability level (above average but not rare) for the SPH, making the assumption that the air temperature is the 232 same as the sea-surface temperature. This assumption is less likely in northern latitudes where the hurricane transports warmer tropical air over colder water. A recent publication (U.S. Navy 1975) gives sea-surface temperature (Ts) frequencies by blocks over coastal waters of the North Atlantic Ocean and Gulf of Mexico (fig. 12.1). Figure 12.2 is a plot of the 99% and 75% frequency levels of Ts for August, the month of highest temperatures, r1'00� 90 80�o 70 600 50o 40 against coastal reference points from '/' tables 4.1 to 4.4. For the gulf coast, the variation is very slight, the 99% frequency level varying be- tween 89.00 and 89.50F (31.70 and a 31.9�C). For the east coast, the variation is large, the 99% level is d - about 89.5�F (31.9�C) near milepost 1400 and about 68.06F (20.0�C) at milepost 3100. Figures 12.3 and 12.4 show smoothed \d- values of the K factor for three \s units of measurement for the SPH and - the PMH, respectively. These values were computed for a number of loca- 2d tions along the east coast using 90� as" Be 75 70 J the central pressure (po) determined Figure 12.1.--BZocks used to calcuZate in chapter 8. Values of K between sea-surface temperatures in deter- mining ZatitudinaZ variation of K 240 and 30�N may also be applied to mining latitudinal variation of K coefficient (after U.S. Navy 1975). the gulf coast with little loss of accuracy. Temperatures were taken from the 75% frequency level values of figure 12.2 for the SPH and the 99% frequency level values for the PMH. These temperatures are adjusted to virtual temperature (assuming saturation) in order to determine air density. W 3 1r rE o z - o > I m 0 ti- z Oz*ZoC o,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ec O~~ ~~~ 0 8 - z 0 m z* z DISTANCE (KM X 102) 4 8 12 16 20 24 28 32 36 40 44 48 52 56 00 90 32 I- 0.. 82 -8.. LU .Lu 28 u 78 - U - LEGEND -24 L~74 99% FREQUENCY - --- 775% FREQUENCY LU 70 K20 66 a 2 A 6 8 10 12 14 16 18 20 22 24 26 28 30 DISTANCE (N MI X 102) Figure 12.2.--Sea-surface temperatures, 99th percentile and 75th percentile, along the gulf and east coasts during August. 234 K IMP-l. IN) 78 -_ _ / MPH. NHJ - 78 -_ 76 - 76- - 74 - 74- W' E 72 - 72- - o 8~~~~~~~~~~~~~~K IKWHR. kP) (METRIC ~68 - 2 /KIKM/NI{ hP.IIM C s - 68- X~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IE INJ IENGLISH) 66 - 66- X DATA POINT K I E. IN.) IINGI XDATA POINT 64 .1 I , ,, ,i I , ,I,,,,,, ,,lI 84 30 22 40 42 64 'I 'I~I 64 530 240 45 64 25 30 35 40 45 LATITUDE C'I LATITUDE CM Figure 12.3.--Vatlues of latitude- Figure 12.4.--Values of latitude- dependent K coefficient for three dependent K coefficient for three units of measurement for the SPH. units of measurement for the PMH. The difference in the numerical values of K at 24"N and 45�N is about 4% for the SPH and 5% for the PMH. If the user does not wish to vary K with latitude, a constant could be applied. Maximum wind speeds would differ by a few percent by employing such a constant. 12.2 TEN-METER, 10-MINUTE OVERWATER WINDS 12.2.1 INTRODUCTION Observed maximum 10-m (32.8-ft), 10-min winds (V)over open water in hur- ricanes of above average intensity have been found to vary from about 75 to 100% of Vgx (Myers 1954). Occasionally, however, V over open water in gx x hurricanes of above average intensity exceeds Vgx. When this happens, supergradient winds result. These winds are especially prevalent in the right semicircle of a hurricane (Shea and Gray 1972). We see from the above thatthe Vg can be equal or even less than Vx in gxx some cases. The value of Vx will exceed Vg in fast-moving hurricanes. The x ~~~ gx applicable asymmetry factor will be discussed in section 12.2.3.1. Empirical equations have been used in previous reports to estimate the maximum 10-m, 10-min overwater wind speed. This maximum wind will occur at 235 some point around the circle defined by R. These equations take the form: V = F (Vgx) +A (12.14) x ~gx where V = maximum 10-m, 10-min overwater wind speed. x F = reduction factor to convert from maximum gradient wind speed to 10-m, 10-min overwater wind speed. V = maximum gradient wind speed defined by eq. 12.1. gx A = asymmetry factor resulting from the forward speed (T) of the hurricane. 12.2.1.1 RECOMMENDED REDUCTION FACTORS (F) FOR SPH AND PMH. A factor, F, of 0.865 (to convert from Vgx to V ) was developed from data observed in the 1949 hurricane that crossed Lake Okeechobee, Fla. It was used as the standard in previous reports because it not only was from this well-documented hurricane, but also because it lay about half way between the 0.75 to 1.00 ratios cited in section 12.2.1 (Myers 1954). Supergradient winds (F factor >1.00) were not considered in these reports. Since super- gradient winds in intense hurricanes (Shea and Gray 1972) now appear to be more prevalent than earlier reports indicated, some slight increase in the 0.865 value would be appropriate. Additionally, because of the accuracy implied by this value (which is not justified by the data), it should be rounded. For these reasons, we have adopted 0.9 for the SPH. We have adopted'0.95 for the PMH on the grounds of representing a more extreme condition. 12.2.2 WINDS IN A STATIONARY HURRICANE For a stationary hurricane, equation 12.14 reduces to: V = 0.9 V , for the SPH (12.15) x gx V = 0.95 Vgx, for the PMH, (12.16) xg' since A, the asymmetry factor, equals zero. Vx for a stationary hurricane we shall call Vxs. 236 Knowing Vs, we can use relative wind profile information in chapter 13 to determine 10-m, 10-min overwater winds at any distance from the hurricane center. 12.2.3 WINDS IN A MOVING HURRICANE 12.2. 3.1 THE ASYMMETRY FACTOR. Equation 12.14 includes an asymmetry factor A, which is added on the right of the storm track and subtracted on the left, which when combined with F (V gx) gives Vx--the maximum 10-m, 10-min overwater wind in a moving hurricane. The general equation for A is: A yT cos (12.17) where y and x are two empirical constants, T is the forward speed of the hurricane, and B is the angle between track direction (9) and the surface wind direction (a), measured counterclockwise from Q. 12.2.3.1.1 CONSTANTS Y AND X. In previous studies (Graham and Nunn 1959, U.S. Weather Bureau 1968), y was assumed to be 0.5 and x to be 1.0. In the present study, we have reviewed this assumption. It appears to yield results that are unreasonable with T. Consideration of the energy imparted to the storm's circulation by a factor of 0.5 when T is large, suggests a lesser adjustment. Also, when T is small, there is not enough asymmetry across the hurricane. These concepts were tested with several values of both y and x. When T is expressed in knots, a value of y = 1.5 and x = 0.63 yielded satisfactory results. At T = 6 kt, the asymmetry factor would add a maximum of 4.6 kt to speeds in the right semicircle; at T = 50 kt, the maximum additive value would be 17.6 kt. At approximately 20 kt, the maximum additive value would be 10 kt. The value of y is independent of the units of measure, while x depends on the forward speed units of the storm. Similar factors of x and y could have been developed for other units. We chose instead to expand eq. 12.17 as follows: A = yTx T (l-x) cos B (12.18) 0o 237 where TO is a parameter in speed units and the other factors are as previ- ously defined. We have already chosen to use y = 1.5, x = 0.63 when T is in knots. In this case, eq. 12.18 reduces to eq. 12.17 by definition, i.e., To 1 kt. T equals 0.514791 when units are in m s , 1.853248 when in km -1 -1. hr and 1.151556 when in mi hr 12.2.3.1.2 THE ANGLE S. The angle B varies: a. Around the hurricane at any constant radial distance (r), and b. Along a radial at varying distances from the hurricane center. 12.2.3.2 ADOPTED SPH AND PMH MAXIMUM 10-M, 10-MIN OVERWATER WIND EQUATIONS. Equation 12.14 has provided a general form for these equations. Values of F are defined in section 12.2.1.1 and the asymmetry factor is evaluated in section 12.2.3.1. Using this information, Vx for the SPH can be determined from: 0.63 0.37 V = 0.9 V + 1.5 (T 63) (T o37 s (12.19) x gx o and for the PMH from: V = 0.95 V + 1.5 (T '63) (T 037) cos (12.20) x gx. o V is defined as occurring at the point along the circumference of maximum x winds where the actual wind direction is parallel to the track direction (0). Here, S = 0 and cos 5 = 1. The inherent relation between B and inflow angle (9) requires the point at which Vx occurs to fall in the right-rear quadrant of a hurricane. Chapter 13 will set allowable limits of rotation for this point. 12.2.3.3 SPH AND PMH 10-M, 10-MIN OVERWATER WIND EQUATION AT ANY r. The equation for 10-m, 10-min overwater winds at any distance (r) from the hurricane center is: V = V + 1.5 (T 0.63) (T 0'37) cos 5 (12.21) where Vis the wind speed at radius r and Vs is the wind speed in a stationary hurricane at radius r. Relative wind profiles for computing V ~are developed in chapter 13. are developed in chapter 13. 238 12.2.3.3.1 ALONG A RADIAL THROUGH V (RAD I AL M). The procedure for x computingV along any radial is most easily understood by first computing V along the radial M through the point of maximum wind. The variation of with r along this radial is illustrated schematically in figure 12.5. For better understanding we are let- ing R = 15 n.mi. (28 km). Since the inflow angle (4) (see chapter 14) e r<R r>R varies with r, B must also vary with \ e 9 r. The tangential wind direction (St) \ T '.,5H. t 25OI'DO is normal to the radial as shown in 1 \a W\ the diagram. 0t at any point along E this radial is a constant. Since the track direction (0) is a constant, -% the angle between 0 and t at any point along this radial is a constant. Figure 12.5.-Iustation of the Figure 12.5.--Illustration of the At r = R, B = 0 by definition because relation between track direction (0), radial M passes through V . Thus, cos tangential wind direction (0t), and x actual surface wind direction (Ga) B = 1. along the radial through point of maximum wind (radial M) B is given The right side of figure 12.5 for r = 10, 15, and 25 n.mi. (19, 28 illustrates that at some point where and 46 k) for this exa mple of a PMH with R =15 n.mi. (28 kmn). r >R, B is the difference between i at this point and c at r = R, where = R-R MR =0. Therefore: -6~~~~ (�r fR(12.22) For example, from figure 14.7 (PMH) for an R of 15 n.mi. (28 km), = 7.2� at r = 15 n.mi. and 20.6� for r = 25 n.mi. (46 km). Then: B = (~25 - 15) 3 = 20.6� -7.2� = 13.4� The left side of figure 12.5 indicates how at some point where r <R, B is the difference between c at this point and c at r = R. Therefore, we may again make use of eq. 12.22: 239 = (-r R) From figure 14.7, 4 = 3.0� if we let r = 10 n.mi. (19 km). Therefore: S = (010 - ~15) = 3.0� - 7.2� =-4.2� = 355.8� 12.2.3.3.2 ALONG ANY OTHER DESIRED RADIAL. The 6's along any other radial are determined by modifying the 8M's computed along radial M. The angles ~ along other profiles are computed by adding the number of degrees counterclockwise between radial M and the desired radial to the computed IMs. For example, at r = 25 n.mi. (46 km) in sec. 12.2.3.3.1, B would equal 103.4� not 13.4� if our desired radial lay 90� counterclockwise from radial M. At r = 10 n.mi. (19 km), B would equal 85.80, not 355.8�. 12.3 VALUES OF Vgx AND VX FOR RECORD HURRICANES Tables 4.1 and 4.2 list values of V and V in kilometers/hour and tables gx x 4.3 and 4.4 in knots for the gulf and east coasts of the United States for hurricanes with central pressure < 29.00 in. (98.2 kPa) during the period 1900-78. Values of K and the coriolis parameter (f) are evaluated at the latitude of the minimum po. K values were taken from figure 12.3 for all but two hurricanes, the Labor Day hurricane of 1935 and hurricane Camille (1969), whose po's are much lower than the SPH. For these two, the K of figure 12.4 was used. The values of V and V were computed using equa- gx x tions 12.1 and 12.19 for all hurricanes except the Labor Day hurricane of 1935 and Camille (1969). Equations 12.1 and 12.20 were used for these two storms. For Vx, cos 8 = 1. Vx, the maximum 10-m, 10-min sustained overwater wind speed, is not the wind normally reported as the maximum sustained wind in a hurricane by reconnaissance aircraft. They normally report sustained 1-min winds, not 10-min winds. Sometimes, sustained winds of shorter duration are reported. Therefore, these reconnaissance winds have the tendency to be 15% or more higher than V . Also, the winds are measured at flight level and only estimated near the surface. In addition, many wind reports in the litera- ture are gusts or sustained winds of short duration. 240 Hurricane Camille's (1969) V is 121 kt or 224 km/hr (tables 4.3 and 4.1). x This compares with highest SPH V of about 106 kt (196 km/hr) near milepost X 700 (tables 2.3 and 2.4) and a highest PMH V of 139 kt (258 km/hr) foundin X tables 2.5 and 2.6). The Labor Day hurricane of 1935 had a Vx of 130 kt (241 km/hr), or the highest V of any record hurricane. The highest SPH V X ~~~~~~~~~~x at milepost 1400 is 110 kt (204 km/hr) while the highest PMH V is 141 kt x (261 km/hr). Camille and the Labor Day hurricane are therefore stronger than the SPH and weaker than the PMH. In contrast, the less intense New Orleans hurricane of 1915 has a V of 95 kt (176 km/hr) which is less than x the SPH V of about 106 kt (196 km/hr) near milepost 700. The results X presented above are true even if we had used SPH K and F for Camille and the Labor Day hurricane and PMH K and F for the 1915 hurricane. 12.4 Vgx AND V FOR THE SPH AND PMH gX X Maximum computed values of V and V for the SPH and the PMH are listed gx x by 100-n.mi. (185-km) intervals in both metric and English units (tables 2.3 to 2.6). Figures 2.22 to 2.27 show a comparison of these winds with maximum computed winds for hurricanes of record using observed or estimated values of meteorological parameters or factors for each hurricane. All wind computa- tions are based on equations 12.1, 12.19 and 12.20. 12.5 COMPARISON WITH OTHER RESEARCH Comparisons between this report and other research are not overly benefi- cial because other studies have not tried to define upper limits in the same way we have. Nevertheless, a comparison with another recent study should indicate whether or not our winds are very much "out of line." A recent study by Atkinson and Holliday (1977) using actual measurements of peak gusts in western North Pacific tropical cyclones with a wide range of po between 27.11 and 29.35 in. (91.8 and 99.4 kPa), yielded a central pressure-maximum 1-min sustained wind speed relation. The authors state this relation has "proved suitable for both high and low wind speeds, a feature not found in previous relationships." The authors state, "Hope- fully, this wind pressure relationship can be refined and improved in future years as more cases are added to this sample and more accurate techniques for measuring surface winds in tropical cyclones are developed." 241 Atkinson and Holliday's sample of 76 storms over a 28-year period was restricted to cases where they were reasonably certain that a coastal or island station experienced the cyclone's maximum winds during its passage. Extrapolation of their mean relation (between p0 and wind speed from these 76 storms) beyond the data allows a comparison of their winds with the winds from this report. po's corresponding to the range of PMH po along the east coast were selected to compare the Atkinson and Holliday winds to the PMH VLU and VUL level winds. These are the strongest and weakest PMH winds (tables 2.5 and 2.6). To make this comparison, our PMH 10-min winds were converted to 1-min winds using the formula given by Thom (1973). Table 12.1 lists these converted winds and those from Atkinson and Holliday's extra- polated relation. We see from table 12.1 that our estimated PMH winds are everywhere higher than Atkinson and Holliday's for the same po. At the least, we feel com- fortable that the PMH winds exceed those of Atkinson and Holliday's. Any evaluation must be tempered by the assumptions that: a. Atkinson and Holliday's procedure for estimating 1-min sustained winds from peak gusts and our use of Thom's relation for adjusting 10-min sus- tained winds to 1-min sustained winds are both reasonable. b. Atkinson and Holliday's choice of pw (29.83 in., 101.0 kPa) permits a direct comparison of winds for the same p0; (sec. 8.3.3.4). c. The mean curve fitted to the 76 data points, expressed by the non- linear equation (Atkinson and Holliday 1977), V = 6.7 (1010 -pc) 0.644 (12.23) m C where V is the maximum sustained surface wind speed (kt) and p c is the mean sea-level pressure (mb), can be extrapolated to 26.11 in. (88.4 kPa) extending the relation 1.00 in. (3.4 kPa) beyond their most intense storm. d. East coast PMH winds should be larger than winds developed from eq. 12.23 because extrapolation using this equation requires average rather than upper limit winds. [An envelopment of their data (not shown) gives wind values closer to but not exceeding PMH VLU and VUL winds]. 242 Table 12.1.--Comparison of maximum sustained 1-min, 10-m winds (Atkinson and HoZZiday 1977) 10-min, 10-m PMH winds adjusted to 1-min, 10-m winds for seZected common po levels. Use caution in interpreting this table; see text. Estimated PMH Estimated PMH maximum sustained maximum sustained 1-min*, 10-m l-min*, 10-m winds from VLU winds from VUL Atkinson and Holliday's column, tables column, tables maximum sustained l-min PMH Po 2.5 and 2.6 2.5 and 2.6 10-m winds (east coast) (east coast) (east coast) (in.) (kPa) (kt) (km/hr) (kt) (km/hr). (kt) (km/hr) 27.46 93.0 134 248 128 237 113 209 27.17 92.0 143 265 137 254 122 226 26.87 91.0 150 278 143 265 130 241 26.58 90.0 157 291 149 276 138 256 26.28 89.0 160 296 151 280 146 271 26.11 88.4 164 304 156 289 i51 280 *Obtained from tables 2.5 and 2.6 by dividing the 10-min values by 0.863 (see notes for tables 4.1 to 4.4). e. Other less recognizable differences between our winds and those of Atkinson and Holliday would have a negligible effect on values in table 12.1. 243 13. RELATIVE WIND PROFILES 13.1 INTRODUCTION In the last chapter we developed equations for computing 10-m (32.8-ft), 10-min overwater winds at any point around the circumference of maximum winds. We also need to determine how the winds should decrease with distance both inward and outward from R so that we may define the entire hurricane wind field for the SPHland the PMH. We have already mentioned in the last chapter that wind profiles both in- ward and outward from R could have been determined from the adopted pressure profile (eq. 6.1). We chose instead to shape the profile after wind observations from hurricanes of record. Profiles were derived that relate the relative wind (V/Vx) to distance (r) outward from the hurricane center and the radius of maximum wind (R). These profiles were then adjusted to remove the effect of forward speed (T). The results, termed "standardized" profiles, insure continuity in wind fields outward and inward from R. 13.2 DEVELOPMENT OF STANDARDIZED PROFILES FOR WINDS OUTWARD FROM R 13.2.1 DATA Wind fields constructed for severe hurricanes of record were the primary source of data for developing standardized profiles for relative winds out- ward from R. These wind fields are representative of average 10-m, 10-min overwater values for nonstationary hurricanes. A wind profile was con- structed through the region of maximum winds. A secondary data source was wind profiles constructed for severe hurricanes for which no analyzed wind fields were available. Wind records at stations or ships in or near the path of the storm were used in constructing partial wind fields that were then used in constructing wind profiles through the region of maximum winds. Table 13.1 lists the hurricanes used for determining the standardized pro- files along with other pertinent information. Analyzed wind fields were not available for storms identified with a plus (+). The central pressure (po) listed in most cases is the minimum occurring within 150 n.mi. (278 km) of Table 15.1.--Available hurricane wind profile data Wind speed (kt) and stationary storm rel. Central Radius of wind speed (Vs/ Vxs) @ Stationary storm Date of pressure1 Max. winds Forward Max. wind 60 n.mi. 200 n.mi. tel. wind speed (Vs/Vx~ @ wind (pc) (R) speed speed (Vx)2 (111km) (371 km) tel. distances (r/~ of: Hurricane No. profile (in.) (kPa) (n.mi.) (km) (kt) (km/hr) (kt) (km/hr) 2 4 from storm center 8 12 Donna (hr. S. Carolina) la 9/11/60 28.67 97.1 34 63 20 37 85 158 0.65 0.43 0.28 (0.11) 63 0.71 35 0.33 Donna (nr. New Eng.) lb 9/12/60 28.38 96.1 48 89 33 61 85 158 .68 .45 .... 81 .94 44 .43 Carla (oentral gulf) 2a 9/10/61 27.61 93.5 20 37 8 15 104 193 .93 .79 .49 .39 90 .86 48 .43 Carla (nr. land) 2b 9/11/61 27.49 93.1 30 56 5 9 102 189 .81 ,56 .33 .19 84 .82 43 .40 Gracie 3 9/29/59 28.08 95.1 10 19 10 18 105 195 .91 .63 .36 .28 44 .38 26 .20 lone 4 9/18/55 28.35 96.0 20 37 16 30 93 172 .89 .71 .42 .27 76 .80 37 .33 Camille 5 8/17/69 26.81 90.8 12 23 13 24 120 222 .89 .66 .45 .36 75 .60 39 .28 Florida Keys (+) 6 9/03/35 26.34 89.2 6 11 7 13 122 226 .90 .67 .45 .31 34 .25 .... New England 7 9/14/44 28.32 95.9 23 43 30 56 82 152 .68 .35 .15 -- 50 .54 .... Pensacola (+) 8 10/19/16 28.76 97.4 19 35 15 28 69 128 .62 .50 .12 -- 48 .65 .... Celia (+) 9 8/03/70 27.88 94.4 9 17 13 24 95 176 .67 .44 .23 .15 33 .29 -- -- Florida (+) 10 8/27/49 28.17 95.4 20 37 13 24 81 150 .68 .39 .... 41 .46 .... Relene 11 9/27/58 27.52 93.2 20 37 14 26 95 176 .83 .55 .28 .i7 67 .68 27 .22 Audrey 12 6/27/57 27.94 94.6 19 35 18 33 110 204 .68 .44 .25 .13 60 .50 .... Galveston 13 9/09/00 27.64 93.6 14 26 10 18 77 143 .78 .47 .26 -- 37 .43 .... New Orleans (+) 14 9/19/47 28,53 96.6 18 33 20 37 97 180 .78 .43 (.22) -- 54 .51 .... Central gulf 15 9/13/19 27.99 94.8 32 59 10 18 91 167 .80 .55 .29 -- 76 .82 .... New England 16 9/21/38 27,76 94.0 50 93 40 74 85 158 .49 .27 .... 78 .90 -- -- Hilda 17 10/01/64 28.23 95~6 21 39 5 9 96 178 .77 .56 .39 .27 64 .65 36 .35 Carol 18 8/31/54 28.38 96.1 22 41 33 61 84 156 77 .58 .31 .14 62 .69 30 .23 Debra 19 7/24/59 29.06 98.4 14 26 5 9 72 133 .76 .58 .39 (.18) 42 ,56 -- -- New Orleans 20 9/29/15 27.52 93.2 23 43 11 20 92 171 .73 .46 .... 61 .64 .... Betsy 21 9/10/65 27.79 94.1 32 59 14 26 101 187 .74 .46 .18 -- 80 .77 32 .26 Texas 22 10/03/49 28.44 96.3 20 37 12 22 75 139 .77 (.64) .... 62 .81 -- -- Flossy 23 9/24/56 28.76 97.4 22 41 10 18 73 135 .75 .59 .45 .32 60 .80 -- -- Hazel 24 10/15/54 27.67 93.7 18 33 23 43 84 156 .71 ,57 .46 .37 55 .60 ~39 .39 S. Carolina coast (+) 25 8/11/40 28.79 97.5 20 37 10 18 85 158 .91 .54 .25 .19 60 .68 23 ,21 Note: 1Underlined central pressures are at time of wind field analysis; otherwise, they are minimum central pressures as lis~ed in tables 4.1 - 4.4. 2V from w~nd f~eld or wind profile analysis. ( ~ =, exD~apotated; -- = beyond extent of wind field or wind profile analysis. (+) = wind, profile determined from a partial analysis based on nearby wind records; otherwise from a detailed wind field analysis. 245 the coast as found in tables 4.1 to 4.4. Exceptions are the underlined cen- tral pressures, which were observed at the time of each wind field analysis. Examples of wind profiles are shown in figure 13.1 for Donna (1960) when she was off the South Carolina and the New England coasts. Similar wind profiles were constructed for all hurricanes listed in table 13.1. 13.2.2 ANALYSIS Hurricane wind profiles for nonstationary storms, e.g., those in table 13.1 and figure 13.1, contain asymmetry. This asymmetry is dependent on forward speed (T) and yields stronger winds in the right semicircle of (KM) (KM) 50 Io00 ISO 200 250 300 350 400 450 500 550 Ann osr a storm than would be observed in I I ' a stationary hurricane; (see sec. .- 12.2.3.1).*S -- 1100 GIT SIPT. 12, 1960 1 O_ NEW ENGLAND COAST) We wish to develop standardized .6- profiles for stationary hurri- > 2OFF OUTH CAI 196 .4 - canes and then in application J add the asymmetry due to the 20 ZU 40 60 o Ioo I120o 140 IbO I0 Eoo Zo40 260zE0300 320 340360 selected T. The value of V DISTANCE FROM CENTER (N. MI) x for each hurricane in table Figure 13.1.--Relative wind speed pro- 13.1 is often an approxima-. fiZes outward from R vs. distance tion, being most correct when from center for Donna (1960). the wind field analysis fits the true wind field of the hurricane. We will treat Vx as a known quantity located at a point at a distance R from the hurricane center in the right semicircle of each nonstationary hurricane. From chapter 12 (eq. 12.14, 12.19 and 12.20), we recall 0.63 V = F (Vg ) + 1.5 (T ) cos (13.1) when T is expressed in k6ibts and cos = 1. Knowing the forward speed (T) for each hurricane at the given analysis time, we can subtract the effects of T from the wind profiles at distances outward from R by making use of the asymmetry term [1.5 (T 063)] in eq. 13.1. This exercise results in stationary hurricane relative wind profiles for the hurricanes in table 13.1. Removing the asymmetry, eq. 13.1 then becomes 246 Vxs g gx r (13.2) where V = maximum 10-m, 10-min overwater wind speed for a stationary hurri- xs cane. Values of Vs/Vxs (where Vs is the overwater wind speed at distance r in a stationary storm) were extracted from the storm profiles at discrete values of r. Examples are shown in table 13.1 at r = 60 n.mi. (111 km) and 200 n.mi. (371 km). Plots were made of Vs/Vxs for various relative distances (r/R) vs.R.- Four such plots are shown in figures 13.2 to 13.5. These plots were obtained from the final standardized profiles. Preliminary curves (not shown)were drawn to provide a best "eye fit" to the storm data by weighting the extreme (KM) 10 20 30 40 50 .60 . 70 . 80 90 ,., .0 N.9 25 7- - . - .6- NOTE: THE NUMBER BESIDE EACH DATA POINT REFERS TO Lbi ARE IDENTIFIEDOBY 0 FOR MAXIMUM WINDS IWx( GREATER _ .5 THAN 100 KT (185 KM/HR) AND BYOFOR CENTRAL PRESSURE I P.,) LESS THAN 27.76 IN. (94.0 kPa .16 40 .II 1 , i 1 .1. I. RADIUS OF MAXIMUM WINDS (N MI) Figure 13. 2.--VI/V s for r/R of 2 vs.- radius of maximum winds. 13Xs�1. (KM) 10 09 30 40 50 60 70 80 90 �1 .8 - IF �21a NOTE: THE NUMBER BESIDE EACH DATA POINT REFERS TO THE NUMBER ON TABLE 13.1. THE MORE INTENSE STORMS I 0 - *4 ARE IDENTIFIED BY 0 FOR MAXIMUM WINDS IVx) GREATER .7 5 THAN 100 KT (185 KM/HR) AND BYO FOR CENTRAL - - 3 4 *22 ~PRESSURE (Ph) LESS THAN 27.76 IN. 194.0 kPal. 0 .4 - . 3 J - - ,II [ I I, i I ., I , I I - .*20 5 10 15 20 25 30 35 40 45 50 RADIUS OF MAXIMUM WINDS (N MI) Figure 13.3.--Vs/Vxs for r/R of 4 vs. radius of maximum winds. 247 storms more heavily. These curves were used to determine a first approxima- tion family of curves (standardized profiles) of Vs/Vxs versus r for a set of R's. This first approximation set was then checked and adjusted when necessary by numerous cross plots and by comparing the results with individual hurri- cane wind profiles. The objective was to determine a consistent set of standardized profiles that best fit the data. 13.2.3 RESULTS After checking numerous cross plots and nmaking use of hand smoothing tech- niques, a set of standardized profiles was adopted. This is shown in (KM) 06 10 20 30 40 50 60 70 80 90 DI *I II l l l l NOtE: THE IIUMBER BESIbE EACH DATA POINT REFERS TO THE NUMBER ON TABLE 13.1 . THE MORE INTENSE STORM � .5-- r2a ARE IDENTIFIED BY 0 FOR MAXIMUM WINDS IV) GREATER Ux u 6135s 24i *23 THAN 100 KT (185KM/HRI AND BYO-FOR CENTRAL 4-1 4 PRESSURE (Po) LESS THAN 27.76 IN. 194.0 kPa). .4-- 1 9 '17 ', ,�-- 1 2 i1e2b _ a *3o113 i 2 Oi .2- 14 e 9 �2 1 .I - II I I I I , I I t CO 5 10 15 20 25 30 35 40 45 50 RADIUS OF MAXIMUM WINDS (N MI) Figure 13.4.--Vs/Vxs for r/R of 8 vs. radius of maximwn winds. Nc (KM) 'L7' 10 20 30 40 50 60 70 80 90 II I I I I NOIE: THE NUABER BESIDE' EACH DATA POINT REFERS TO l O THE NUMBER ON TABLE 13.1 . THE MORE INTENSE STORMS � .4- '2a ARE IDENTIFIED BY O FOR MAXIMUM WINDS IV) GREATER - . _ L 915 2r4 ITHAN I00KT (185 KM/HRI AND BY 0 FOR CENfRAL god~~- e 23 PRESSURE fPo) LESS THAN 27.76 IN. (94.0 kPa). o .2- - *18 .I - -- II 1 I I , I I l I i I I I I I &0 5 10 15 20 25 30 35 40 45 50 _J W,-"' RADIUS OF MAXIMUM WINDS (N MI) Figure 13.5.--Vs/VIs for r/R of 12 vs. radius of maximum winds. X~~~~~~ais o a'.rr ons 248 figure 13.6 where Vs/Vxs is plotted against r. The curves shown on figures 13.2 to 13.5 were obtained from figure 13.6. They indicate that the stand- ardized profiles are a reasonable fit to the hurricane data. (KM) 0 50 100 150 200 250 300 350 400 450 5I0 550 .9 - W .7 - o .6-r .5 - z .4 - R26 \ R=10 ~Re15~-R=20 R=3 R=50iN MI} Li 7.4) 111.1) l18.51 i7.8) f37.0o 1 r556stac(92.6) ( KM) .3- n- .2- 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 DISTANCE,r (N. MI) Figure 13.6. --Adopted standardized wind profiles outward from R. Whether or not the standard iz e d profiles of figure 13. 6 may be used for both the SPH and the PMH can be assessed by referring to figures 13.7 and 13.8. Here, the relative wind (V /V ) for relative distances (r/R) of 4 and 8, respectively, are plotted against hurricane central pressures. While there appears to be a small trend to higher values of V s/Vxs for lower central pressures, there is insufficient data to judge whether the trend is significant. We will use the relative wind profiles of figure 13.6 for both the SPH and the PMH wind fields. 249 (kPa) 89.0 90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0. 99.0 ."8 02a .4 _ -0 .7 -- @6 @3 *22 < .6- 1 24 -7 18 23 19 v I11 *15 *1725 Z .5- J3 21 lb 3 4 NOTE: THE NUMBER BESIDE EACH DATA 20 � 012 014 �la WLI .4 POINT REFERS TO THE NUMBER ON TABLE 10 -> 13.1. THE MORE INTENSE STORMS ARE 07 - IDENTIFIED BY O FOR MAXIMUM WINDS ._J .3 (VX) GREATER THAN 100 KT (185 KM/HRI. .16 rrA.) IiI ii hI I I ~ I i I 26.50 26.75 27.00 27.25 27.50 27.75 28.00 28.25 28.50 28.75 29.00 CENTRAL PRESSURE (IN.) Figure 13.7.--VsI/Vs for r/R = 4 vs. central pressure CD 11(kPa ' 8R.0 90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 99.0 >:x .5 -- o2a . (6 t5 �24 e23 .4 ~' .4 - *17 *19 - Z (2b 12 .3 - NOTE: THE NUMBER BESIDE EACH DATA I 18 POINT REFERS TO THE NUMBER ON TABLE *11 15 *la LI 13.1 . THE MORE INTENSE STORMS ARE 913 �25 2 DENTIFIED BY O FOR MAXIMUM WINDS9 14 > .2 -(Vx) GREATER THAN 100 KT (185 KM/HR) O�21 26.50 26.75 27.00 27.25 27.50 27.75 28.00 28.25 28.50 28.75 29.00 CENTRAL PRESSURE (IN.) Figure 13.8.--V /Vxs for r/R = 8 vs. central pressure 13.3 DEVELOPMENT OF A STANDARDIZED PROFILE FOR WINDS WITHIN R 13.3.1 DATA Wind profiles were constructed from wind records of Weather Bureau (now National Weather Service) reconnaissance aircraft by Colon (1963) in his study on the evolution of wind fields during the life cycle of tropical cyclones. This same data source extended through 1969 was used by Shea and Gray (1972) in their study on the structure and dynamics of the hurricane's inner core region. Shea and Gray subtracted the forward speed from the data. Using these data, we selected the most severe hurricanes from the cited 250 references for analysis. The po and R for these severe hurricanes of record are listed in table 13.2. Table 13.2.--Selected severe hurricane data for development of a wind profile within the radius of maximum winds (R) Radius of Central maximum pressure (p0) winds (R) Hurricane Date Latitude (in.) (kPa) (n.mi.) (kmn) Helene Sept. 26, 1958 30�N 27.82 94.2 15 27.8 Donna Sept. 9, 1960 23�N 27.46 93.0 15 27.8 Carla Sept. 10, 1961 27�N 27.61 93.5 20 37.1 Esther Sept. 16, 1961 23�N 27.61 93.5 12 22.2 Flora Oct. 3, 1963 17�N 27.64 93.6 8 14.8 13.3.2 ANALYSIS Figure 13.9 shows the variation of stationary hurricane relative wind speed(Vs/Vxs) within R for the storms in table 13.2. The wind profiles were constructed from winds obtained at flight levels [between the 80- and 56-kPa or 23.62-and the 16.54-in. levels.] Because of the similarity of the wind profiles in the lower half of the troposphere (Shea and Gray 1972), no attempt has been made to normalize the observed values to a standard height. Figure 13.9 shows that,in general, in intense storms the wind drops off rapidly inward from R. Esther is an exception to this generalization. Figure 13.10 shows mean wind profiles constructed from hurricane wind data compiled by Shea and Gray (1972) for the 900- to 700-mb (26.58-to 20.67-in.) level for intense hurricanes (p <27.91 in. or 94.5 kPa), weaker hurricanes (po >28.50 in. or 96.5 kPa), and hurricanes centered north of 30�N, regard- less of intensity. The mean profile constructed by the same authors from all data considered (22 hurricanes) is also shown. In general, hurricane wind profiles inside R indicate a gradual decrease in magnitude for weak storms and a much sharper drop in wind speed for intense storms. 251 I I I i I I I I I 1.0- TO~~~~~~~~~~~~~~~~~~~~~. 8-.-. 0.8-/ �ts~-ADPE STNDRIZERFL // - X - - - ///L'7A w-- ~~~~~~IL C I I I I I I I~~~~~~~~/i/:I /~~~~~~A 0.2~~~~~~~~~~ -, 0.2- , .- - - ~~ADOPTED STANDARDIZED PROFILE 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RELATIVE DISTANCE Ir/R) Figure 13.9.--Relative wind speed profiles within the radius of maximum winds for stationary hurricanes [after Shea and Gray (1972)]. The solid curve is the adopted standardized profile from figure 13.11. 13.3.3 RESULTS For the SPH and the PMH, we have adopted the relative wind profile within R given in figure 13.11. This profile is a slight envelopment of the intense hurricanes of figure 13.10. The upper portion of the adopted pro- file was modified to avoid being discontinuous with the adopted standard- ized profile from R outward. Figures 13.9 and 13.10 compare the adopted standardized profile with the other wind profiles. 13.4 CONCLUDING REMARKS ON RELATIVE WIND PROFILES The relative wind profiles shown in figures 13.6 and 13.11 enable us to determine values of Vs at various r's given Vxs [Vxs = F(VgX); see sec. 13.2.2]. Once we have determined Vs. we can compute actual winds (V) in a moving hurricane by using the following equation: 252 I-..I I I I 1 -0 0.1- 0..7.8 . 0.Fu- .3.1.-- -Rea.. wew ndm - " ~- A0= 1 . 63 0 371.0 Figure 3..--Reative wind speed rofies witin the radius of mam(13.3) I3.T 1. The other four curves were constructed from data compied by Shea Note: T = 1 when T, V and V are in k nots. T = 0.514791 when T, V and V� are in ms -1 TO T = 1.853248 when T, V and V are in km hr 253 I I I I I I I I 1.0- 0.9- 0.8- L 0.7 - z0.6- 3/ 0.4- uJ 0.3- 0.2 - 0.1- 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RELATIVE DISTANCE I r/R) Figure 13.11. Variation of relative wind speed with relative distance (r/R) within the radius of maximnum winds for the stationary SPH and PMH. 13.5 LIMITS OF ROTATION OF WIND FIELDS 13.5.1 INTRODUCTION The orientation of the isotach pattern (lines of equal wind speed) with respect to track direction (chapter 11) needs to be determined in order to construct reasonable wind fields. Are there constraints to the angle between the direction (0) and the location of the region of maximum winds? The computational scheme developed in section 12.2.3 will result in the region of maximum winds falling in the right rear quadrant (as related to the storm motion). We have reviewed observational data to ascertain if this restric- tion is realistic. 254 13.5.2 LOCATION OF REGION OF MAXIMUM WINDS IN SEVERE HURRICANES Hawkins (1971) states, "It is a well-known' fact that wind speeds on the right-hand side of the storm (looking in the direction toward which the storm is heading) are stronger than the winds on the left. This phenomenon can be associated with greater radius of trajectory curvature associated with parcels moving cyclonically on the right of the storm than on the left." Myers and Malkin (1961) have also discussed thiS. They attributed greater speeds on the right-hand side mostly to the smaller effects of asymmetry in the horizontal pressure gradient rather than to differences in the radius of trajectory curvature between the right and left-hand side of the hurricane. Simpson and Pelissier (1971) relate, however, "Sometimes when a hurricane is intensifying and its circulation is not in a quasi-steady state, the ' isotach maximum ... apparently tends to migrate ... around the vortex center .... The maximum convection in the eyewall rotates with the isotach maximum, and the eyewall sometimes breaks open in those quadrants that are normally the strongest in steady-state hurricanes.'" This was the case with Celia (1970) as she moved from 115� and underwent rapid deepening 1.27 in. (4.3 kPa) during the 15-hr period before landfall near Corpus Christi, Texas. Lowest central pressure was 27.89 in. (94.4 kPa)*. Figure 13.12 shows the track of Celia across southern Texas and wind reports (fastest mile and peak gusts)from stations to the north and south of the track. The figure shows that at the Corpus Christi Weather Service Office (CRPWSO) the fastest mile, SW 109 kt (202 km/hr) and peak gusts, SW 140 kt (260 km/hr),'occurred at 2228 GMT on August 3. These gusts were the highest of any observed near Corpus Christi Bay. From the storm track, this means that the location of maximum winds was over 2000 from the direction the-storm was moving. This agrees with reconnaissance reports which located-the.maximum winds at a point 2150 clockwise from the direction Celia was-:gaing at 1856 GMT, August 3 and 250� from that direction at 2228 GMTAuigust 3. Hawkins and Imbembo (1976) studied hurricane: Inez '(1966) over the north- eastern Caribbean Sea during the 24-hr period when she was intensifying from 28.41 in. (96.2 kPa) to 27.37 in. (92.7 kPa). At the end of the deepening period, "Streamlines at 28.05 in. (95.0 kPa) indicated the strongest winds, in excess of 130 kt (241 km/hr) were located anomalously in an area to the 255 9800 97�45 97�30 97� 15 97�00 96�45 96�30 96�15 28.45+ + + + + + + 2 A- 2830+- + + + + + -f BEEVILLE INE 65) �103001 NWSED CHASE FIELD NE 40 o 2300-0000 E 59) (00111 REFUGIO 35 / NNE 104 o 2815+ + + + + + + +28�15 MATHIS @ AYSIDv IN I0 E 96 ol3 28"oo+ 4+ - '-J " LEGEND o� -q8I~EGORY IREYNOLDS MET STATION NAM oW o 21 20 FASTES MLI.I ' OF FASTESTMILE(GMT 1 11 AS CG (MM MEK GUT) (TIM OF PEAK GUST) 2033 CRP=CORPUS CHRISTI ~CRPW5~ ( ~IN 1 20331 WSO-WEATHER SERVICE OFFICE h~ 5 W )~109.,2228W NAS-NATIONAL AIR STATION ~27' 45+ (SW I! 4g(222I A $SW amqOiss~J Of 1 KNOT=1.85325 KM/HR (SWII 27030 + + + / + + + 2 7 030 98�00 97045 PADRE I$. 'SEASHORE 97000 96045 96030 B 96�15 -'W 5/2050 [SW I 2050) Figure 13.12.--Track of hurricane Celia (Aug. 1970) and wind reports near point of ZandfaZZ. Time in GMT. Wind speed in knots. rear of the moving storm. Except for an open section in the front portion, winds in excess of 120 kt (222 km/hr) were recorded in all quadrants." The isotach maximum migrated slightly with time in Inez too, increasing from a 200� angle (clockwise from the track direction) measured from 8090 ft (2466 m) at the beginning of the 24-hr period to 210� measured at 1770 ft (540 m) at the end of the period. The difference in the angle may have been > 10� since the isotach maximum in Inez was observed to rotate clock- wise with increasing height at both times. 256 13.5.3 ADOPTED LIMITS OF ROTATION FOR THE SPH AND THE PMH In this report and in previous SPH and PMH studies, the SPH and the PMH are considered to be in a steady state; (see definition in sec. 1.2.3). A PMH deepening as it approaches the coast conflicts with the definition of the PMH. Our assumption of steady state is somewhat more arbitrary for the SPH, since SPH p0 can theoretically become lower. We recognize from the discus- sion in section 13.5.2 that a deepening SPH would have wider limits of rota- tion of its wind field. Celia and Inez were rapidly deepening nonsteady state hurricanes. We propose to allow the region of maximum winds for a PMH or an SPH to have limits of rotation between 0� and 1800 clockwise from track direction as defined in chapter 11. These limits are an expansion of the limits allowed in previous studies and the theoretical constraints mentioned in section 13.5.1 to acknowledge a broader range of possibilities than were previously thought to be reasonable. The steady state SPH and PMH will be barred from having their isotach maximum in the left semicircle with respect to track direction. Sometimes the isotach maximum will remain over water after landfall. The location of the isotach maximum is then set by the position of the SPH or PMH with respect to the water. It may fall outside of the 00-through-1800 limits imposed on the SPH and PMH prior to landfall'. iri~~~~~~~~~~~~~~~~~~~~~r 257 14. WIND INFLOW ANGLE 14.1 INTRODUCTION Hurricane winds blow spirally inward and not along circles of equal wind speed concentric with the hurricane center. The angles between the true wind direction and tangents to these circles have been known by many names. Deflection angle, angle of incurvature, crossing angle, and inflow angle have all been used. We will use the term inflow angle (4). In this chapter, we will determine a range of reasonable ~'s that can be used for the SPH and the PMH. 14.2 RESULTS OF OTHER STUDIES The earliest SPH study (Graham and Nunn 1959) specified a value of 0 of 20� from the hurricane center to the radius of maximum winds (R), a transition from 20� to 25� between R and 1.2 R, and 25� beyond 1.2R. Later studies for the PMH (U.S. Weather Bureau 1968) and for the SPH (National Weather Service 1972) varied this somewhat. Although 25� continued to be used from 1.2 R outward, angles from 0� at the (KM) hurricane center increasing to 10� KM) 10 20 30 40 50 60 70 80 9G 100 110 120 at R were specified. A transition I' ' I' I' ' l ' 'I { 30 - from 10� to 25� was used between R and 1.2R. These criteria are shown 25-- 2:~~~~~.: graphically in figure 14.1. 20 .- / ~; 20 . / - ~1 I* ' / '"' '~y Hughes (1952) used a median J of 100 v cane" from weather reconnaissance 0~~~~~~~ to is� to construct a "mean hurri- l:'-'iz /~1 196: missions at low levels. Ausman ~1 ~ ~ ~ ~ -P I"=HMAN UN 99 (1959) found a mean surface rang- - -PH WGRAHAM AN D NUNNREU 19968) - AND $PH (NATIONAL WEATHER ing from 300 to -5� with the J ' SERVICE 1972) oSl 1, , I, , I, I I, ,I , ,1 , median near 16� based on ship reports o 10 20 30 40 50 60 70 around s xhriaeDISTANCE FROM HURRICANE CENTER (N MI) around six hurricanes (a minus sign means the true wind blows outward from the hurricane center). Malkus Figure 14. 1.--InfZoW angles from earlier and Riehl (1960) assumed ~ constant SPH and PMH studies applied to smallest and largest R values (figs. for distances >54 n.mi. (100 km) 9.3 and 9.8) of the present study. 258 from the center, decreasing inward linearly to 0� at the eyewall. For moder- ate hurricanes (po = 28.53 in., 96.6 kPa), 4 reached a maximum value of 20�. For intense and extreme hurricanes (p < 26.87 in., 91.0 kPa), 4 had a maxi- mum value of 250. Figure 14.2 shows the �'s of Malkus and Riehl for intense and extreme hurricanes applied to the R's of this study. Jelesnianski (1967) related inflow angle to maximum surface winds, R and pressure drop (Pw - PO). Nomograms can be constructed at a given latitude at prescribed distances from the hurricane center. He gives an example at 30�N of the range of c at 87 n.mi. (161 km) from the center of a hypothetical stationary hurricane (figure 14.3). Frank (1976) shows mean 4 for three distances of 120 to 360 n.mi. (222 to 667 km), or 2� to 60 of latitude, from the typhoon center (fig. 14.4a). IMean , is not shown any closer to the center. The basis for his study is a composite of 10 years (1961-70) of western North Pacific rawinsonde data (-18,000 soundings) from 30 stations most of which are near sea level. The (KM) IKM) 10 20 30 40 50 60 70 90 90 100 110 120 0 10 20 30 40 50 60 70 B0 90 100 I'0 I '''- 13 0 I 1 I I2 A 240 e _ k -80 120 - 220 25 - 1I o Figure 110- a from - - ~ V' -'',00 -o A 70- 5� III II, I, A, -~ 8' :i 0 5 0o 15 20 25 30 35 (f0 45 50 55 00d,~~~~~4 1 20 30 30 50 60 76 RADIUS, OF MAXIMUM WINDS (N MI! DISTANCE FROM HURRICANE CENTER (N MI) Figure 14.2.--Inflow angles from Malkus and Riehi (1960) appg ied to Figure 14.3.--Nomogram for determining smallest and largest R values (figs. inflow angles (given radius of max- 9. 3 and 9. 8) of the present study. mum winds, pressure drop, and maximum surface winds) at a distance of 87 n.mi. (1261 km) from the hurricane' center (after Jelesnianski 1967). 259 120 240 360N MI DISTANCE FROM TYPHOON .222) 445) f667 KM) CENTER=120N MI (222 KM) 70.0 2 70.0 x 75.0 - 75.0 -; - x 50. '1 - ~' --r~ l, ! LEFT LU 85.- 85.0 Ix x" 95.0- 95.0 1a BACK , RIGHT SFC SFC I -5 0 5 10 15 20 25 10 0 10 20 30 40 50 INFLOW ANGLE (DEG.I INFLOW ANGLE (DEG.) Figure 14.4a.--InfZow angles at 120, 240, and 360 n.mi. (222, 445 and Figure 14.4b.--Inflow angles at 120 n. 667 kmin) from the typhoon center mi. (222 km) from the typhoon center (after Frank 1976). for four storm quadrants (after Niuiez and Gray 1978). mean 4 at the surface was almost iden- DISTANCE FROU RICANE CENTER =120 N MI 1222 KM) tical for the three distances and ave- 70.C0 _ En ~raged about 240. His value at 95.0 kPa (28.05 in.) agreed with the 16 reported 75.0 by Ausman (1959) at the ocean's surface. 80.0 x Nuiez and Gray (1978) have utilized LU :x .X mFrank's compositing technique and 90 _ I \ Xx RIGHT ' ~ typhoon data set and also studied 14 90.0 X - x ; years (1961-74) of hurricane data \ x (4650 soundings). Figure 14.4b shows 95.0 \ j X X-X! FRONT LEFT B A K mean F for four quadrants of a mean SFC 0 10 20 30 40 5 typhoon at a distance of 120 n.mi. 10 0 1 0 220 30 40 50 (222 km) from the eye center. Figure INFLOW ANGLE: (DEG.) 14.4c is for a mean hurricane and fol- Figure --Ino angles at 120 lows the same format as 14.4b. The Figure 14.40. -~Infow angles at 120 n.mi. (222 km) from the hurricane center for four storm quadrants (after NiViez and Gray 1978). 260 quadrants are labeled front, left, back and right. The front quadrant is defined as being centered around track direction (0). Nuniez and Gray state, "La the boundary layer the front and right quadrants have a greater inflow angle than the left and back. The relationship is true at 4� and 60 also (not shown). For the hurricane, at all three radii, the boundary layer's inflow angle magnitude decreases from quadrant to quadrant in the following order: right, front, back, left. For the typhoon the order is different: front, right, left, back." At the surface, mean 4 in figure 14.4b (typhoons) is about 300, or about 60 larger than what Frank calculated over three distances while averaging around a belt of octants. Mean 4 at the surface in figure 14.4c (hurricanes) is about 27�. 14.3 ESTIMATION OF INFLOW ANGLES USING SHIP DATA We attempted to use ship data* as guidance for the SPH/PMH 4's. Using ship reports, plots were made for 4 vs. distance from the hurricane center for hurricanes Carla (September 9-11, 1961) and Celia (August 3, 1970). As expected, the data for both storms exhibited high scatter. Figure 14.5 shows the plot for Celia. We concluded that data from ship reports would not be very helpful in setting �'s for this study. 14.4 RECOMMENDED INFLOW ANGLES FOR THE SPH AND THE PMH Jelesnianski (1967, 1972) and Chow (1971) varied 4 with R. Jelesnianski and Taylor (1973) have given dynamic justification for such a variation based on the equations of motion. 14.4.1 ASSUMPTIONS OR CONSTRAINTS In our analysis, we have decided to rely heAVilY 5h the results of Jelesnianski but we simplify them based on the fliibwitig additional assump- tions or constraints. * Data from operational reconnaissance flights Ifito huiricanes were not used to calculate 4 near sea level because such flights do not obtain wind reports precise enough to use for 4 studies. Doppler winds are measured under the assumption that the reference plane below, in this case the ocean, is stationary (Hawkins 1975). It is unlikely that any such condition prevails' during an SPH/P1H. 261 a. The SPH is modeled after Jelesnianski's nomogram (fig. 14.3) for a Ap of 2.08 in. (7.0 kPa). This Ap is a mean between that at the Florida Keys and at 450N. b. For the PMH we used the same model but with a Ap of 3.34 in. (11.3 kPa. This Ap is halfway between the PMH Ap for the Florida Keys and the PMH Ap for 450N [(13.6 kPa + 9.0 kPa)/2 = 11.3 kPa]. c. Maximum 0 will occur at a distance of 3R. d. 0 will decrease outward but remain positive from 3R to the outer periphery of the hurricane circulation, i.e., ro where Pw is found. e. ~ will have a constant value for a given R at a given distance in any horizontal direction from the hurricane center. f. 0 does not vary with forward speed (T). g. 0 does not vary with latitude (24� to 450N.) These simplifying assumptions or constraints may occasionally lead to over- simplified results. However, we think that in the mean sizable errors will not occur. 220 I I I I I I 400 14.4.2 ANALYSIS - 380 200 - .00 .06 - 360 Jelesnianski's nomogram (fig. 14.3) IS0- .12 -340 gives values of 0 for a distance of 00 - 320 z 160 --.00 .09 300 87 n.mi, (161 km) from the hurricane .12 .0 -280 , 140- .12 6 260 centet7. 'or other distances out to . --240 20 = 220 130 n.mi. (241 km), comparable - -=~, - 200 .18 -- 180 values were obtained indirectly from '00 -06 1800 c: ~~~~~~~- .03 - 160 compittatiorii of storm surge heights. , 80- -00 06.15 -140 0 ' 0%1,2 .06 -120 Using thtse values and the nomogram, So - *03 *-12 SPH 4's (fig. 14.6) and PMH 's 40- LEENDso (figs i4.7) were determined for 20- - 40 selected values of R for a continuum i i I -040 -20 0 20 40 60 80 100 120 of dist-Ate� from the hurricane center INFLOW ANGLE (DEG.) out to 130 ii.mi. Figure 14.5.--InfZow angZes based on ship reports from the vicinity of Although the two figures were hurricane CeZia (R = 9 n.mi 7 km) hurrivedane Celia (R = 9 n.m.,17 km)SPH on August 3 derived using median Ap's for the SPH on August 3, 1970. 262 (KM) (KM) ,3535 20 40 60 80 100 120 140 160 180 200 220 240 35 20 40 60 80 100 120 140 160 180 200 220 240 45 (83) 38 (70) 3C_" -' 40 (74) 30 35 (65) 35 (65) ; ie-30 (56) - 5 25 (46) v 25 (46) 20 ,-20(37) , * ~.P 20 (37) z 2 0 20 P 0 0 - 15 (28)~ z 15 7 1 l5(28) 3 5 (95 ' ,I I I I I I i I0 I I '""-4 I(7) I20 40 60 80 100 120 20 40 60 80 100 120 DISTANCE FROM HURRICANE CENTER (N MI) DISTANCE FROM HURRICANE CENTER (N MI) Figure 14.7.--Same as figure 14.6 Figure 14.6.--Adopted SPH inflow except for the PMH. angles vs. distance from the hurri- cane center at selected R values. - � 220 Open circles denote maximum inflow -400 angle at each R. Closed circles 200- .00 0 -80 are points taken from the nomogram -360 on figure 14.3. 180- .12 .00 -320 160 --00 09 00 and PMH, they may be used at all - .12 .00 -280 .06 40 12 .18 -260 coastal locations with little loss of .00 -24 .0 -240 .12 accuracy. The points plotted on the I 21 - 0220 0 7- 6 ISO-200' two figures at 87 n.mi. (161 km) are ' oo--06 18. .00 -180 . 03 -16o taken from the nomogram and can be 80- .00 L,. 06_15 -140 used to interpolate � between 5-n.mi. 60 .03 9 6 60- 03 I-U,~ _-~~ 7 * I ~LEGEND - 100 (9-kin) intervals. The dashed line on X-- SPH SP8 402- 0--0 PMH TIME IN GMT 106 - 60 each figure connecting the other E6O0GMT. T -o 20 -- points delineates a line of maximum 2 -20 -040 -20 0 20 40 60 80 IOO 120 which is also helpful in interpolating INFLOW ANGLE (DEG.) for intermediate R values. Figure 14.8 is a replot of figure Figure 14.8.--Same as figure 14.5 with SPH/PMH curves (obtained from figures 14.5 with SPH/PMH curves, obtained 14.6 and 14.7) superimposed. from figures 14.6 and 14.7, 263 superimposed. The R in Celia (1970) was 9 n.mi. (17 km). Our theoretical approach is a reasonable fit to this highly scattered data. 14.5 COMPARISON OF RESULTS WITH OTHER RESEARCH We believe that from the standpoint of dynamics, 0 values from figures 14.6 and 14.7 are an improvement over previous inflow angle criteria given in NHRP 33, HUR 7-97, and HUR 7-120 (fig. 14.1). Curves of R are continuous and do not have sharp breaks as before. Maximum 0 is no longer a constant numerical value for all R's. Our results agree with the work of Jelesnianski and Taylor (1973) which indicates increasing 0 as hurricanes become more intense. Lastly, maximum 0 does not extend out to the outer periphery of the hurricane, which is in agreement with Chow (1971). SPH 0 ranges from 0� to a maximum of 30.5� and PMH 0 from 0� to 32�. Chow gives a maximum d of 34� at a distance of 3R from the hurricane center. Thus, a median ~ is in good agreement with both Hughes (1952) and Ausman (1959). Figure 14.2, from Malkus and Riehl (1960), is much like figure 14.1 except that 4 reaches 0� at R. Although �'s in some hurricanes reach 0� at R, other hurricanes would have inflow extending inward beyond R. However, most hurricanes have slight outflow rather than inflow very near their centers (Malkus 1958). Nevertheless, we contend that a continuous decrease of d from maximum 4 to 0� at the hurricane center is a justifiable simpli- fying assumption for the SPH and the PMH. At and near the surface, the mean O's (fig. 14.4a) of Frank (1976) are within 2� of each other between 120 and 360 n.mi. (222 and 667 km) from the storm center. Thus, we have support for assuming a nearly constant (but slightly decreasing) ~ beyond 130 n.mi. (241 km). Frank (1976) and Nu'nez and Gray (1978) give mean l between 240 and 300 at the surface. One would expect their data to show larger mean d than our results because they used a number of elevated land stations, resulting in greater surface friction and more inflow. 264 15. ADJUSTMENTS OF WIND SPEED FOR FRICTIONAL EFFECTS AND FOR: FILLING OVERLAND 15.1 INTRODUCTION When a hurricane moves toward the coast eventually to make landfall, more and more of its wind field moves overland. The rougher character of the land compared to the water results in a reduction of wind speed. When the eye of the storm later moves ashore, further weakening takes place because of a reduction in energy since the surface air is no longer warmed by the ocean. This leads to a cooling of the eye and eventual loss of tropical character- istics (Dunn and Miller 19 64). In this chapter, we will develop criteria for adjusting wind speeds when the SPH and PMH approach shore and for filling when overland. 15.2 ADJUSTMENT OF WIND SPEED FOR FRICTIONAL EFFECTS 15.2.1 BACKGROUND Winds near the surface of the earth depend on a number of factors, includ- ing the winds above the surface boundary layer, the thickness of the boundary layer, the surface roughness, the surface stress, and the elevation of measurement. We seldom know all these factors. The effect of an abrupt change in surface roughness on the airflow close to the ground has been studied, both theoretically and experimentally, in recent years (e.g., Peterson 1971). In studies of dynamic processes near the coast, the modification in surface boundary layer wind structure with onshore winds was discussed by Echols (1970) and Echols and Wagner (1972) and the shear stress on a beach and on an awash zone by Hsu (1970a and 1970b). Panofsky and Peterson (1972) point out that measured wind profiles on a narrow cape varied with the wind direction in a manner consistent with effects of upwind terrain features. Reiso and Vincent (1976) reported on the estimation of winds over the Great Lakes and proposed a ratio of over- lake wind speed to overland wind speed approaching 1.2 for moderate overland wind speeds of 30-42 kt (56-78 km/hr) under conditions of neutral stability. Since a portion of the hurricane circulation will be overland as it ap- proaches the coast, a conversion from overwater to overland wind speeds is required in order to describe the hurricane winds. In earlier studies by the 265 National Weather Service (e.g., Graham and Nunn 1959), the adjustment factors for wind speed near shore were derived from limited observations on Lake Okeechobee (Myers 1954) during the hurricanes of August 1949 and October 1950. By studying wind observations on and near Lake Ontario, we attempted to improve on the Lake Okeechobee adjustment factors. 15.2.2 LAKE ONTARIO DATA FROM IFYGL During the International Field Year for the Great takes (IFYGL) , detailed wind observations were made on and around Lake Ontario. Towers were used for near shore observations and buoys served as observation platforms on the lake (Foreman 1976). The period of observations from buoys was from May I to October 15, 1972. We selected winds that were greater than 20 kt (37 kin! hr) for 6 hours or longer. The daily (24-hr) resultant and average winds obtained in this manner tended to cancel out diurnal land and sea breeze effects. Eleven cases were selected for further analysis and led to the following results: a. Onshore w inds show a sharp decrease upwind within I n.mi. (1-2 kmn) of shore. b. Offshore winds increased with distance up to about 22 n.mi. (40 kin) from shore; wind speeds seemed to remain steady at distances greater than 22 n.mi. from shore. Results from both the Lake Ontario data and the Lake Okeechobee data indicate that onshore winds should reduce sharply at or very close to the coast and offshore winds should increase more gradually out to some distance offshore and then remain steady. Two important differences exist, however. First, the Lake Ontario wind speeds are much lower than those observed over Lake Okeechobee. Second, the terrain near Lake Ontario is rough as compared to the marshy lowlands near Lake Okeechobee. These differences make the Lake Ontario data less desirable for application along most of the U.S. east and gulf coasts than the Lake Okeechobee data. Therefore, we used the Lake Okeechobee results. 266 15.2.3 DEFINITION OF FRICTION CATEGORIES The effect of friction on winds is complex. The varied physical form of the Earth's surface requires involved studies just to determine relations over a specified area. For this generalized study, we identified four cate- gories of friction surfaces: a) water, b) awash, c) land, and d) rough terrain. Definitions of the four categories are: Water--an open water surface with no significant obstructions to surface winds, e.g., oceans (including all tidewater to the indicated coastline) and large inland water bodies. Awash-- normally dry ground with tree or shrub growth, hills, or dunes, which are inundated during a storm surge. Land--flat or rolling terrain and buildings, not inundated. Rough terrain--major urban areas, dense forest areas and mountains or ridges with abrupt changes in elevation over short distances. 15.2.4 ADOPTED ADJUSTMENT OF WIND SPEED FOR FRICTIONAL EFFECTS 15.2.4.1 ONSHORE WINDS. Figure 15.1 shows the adopted variation of the onshore to overwater wind speed ratio (KM/HRI (k ) at the coast for awash, land, 6 0 0 20 o 200 220 C 60 80 100 120 140 160 180 200 220 and rough terrain. We also show data I 1.00 - (scattered large black dots) from . .90- �% FOR LAND Lake Okeechobee which suggest an -- - - - FOR ROUGH TERRAIN .80 -- F�OR ROUGHTERRAIN average ratio for land of 0.89 .70 - (fig. 27 of Myers 1954). The 0.95 6-- for awash areas is approximately O .50 - _ half-way between the value for land I I '%20 30 40 50 60 70 80 90 100 110 120 and 1.0. The adopted ratio of 0.83 OVERWATER WIND1S IKT) for rough terrain was based on observations of high winds in severe Figure 15..--Onshore to overwater winds ratio (k C). hurricanes. The above three ratios, which do not vary with wind speed and apply at the immediate coast or boundary from water to some other friction category, are shown in table 15.1. 267 Table 15.1.--Onshore to overwater winds ratio (kC) Water to land : 0.89 Water to awash : 0.95 Water to rough terrain : 0.83 15.2.4.2 OFFSHORE WINDS. Figure 15.2 shows the adopted variation of the offshore to overwater wind speed ratio (ke) for awash, land, and rough terrain areas. In addition, a curve and data are shown (fig. 30 of Myers 1954) for Lake Okeechobee which indicate that the reduction of wind speed due to friction is larger for lower wind speeds. (KM/HR) 20 40 60 80' 100 120 140 160 180 200 220 r1.00 I ' ll lll illlIll II .90 FOR AWASH FOR LAND .70 ,, , .60- - u LU .50 - ,,, 3 "_" - FOR ROUGH TERRAIN U. .40 .30--. 0 .20 /MYERS 119541 .10 10 20 30 40 so50 60 70 80 90 100 110 120 OVERWATER WINDS (KT) Figure 15.2.--Offshore to overwater winds ratio (ke) e 268 We recommend using adjustments from the solid heavy curve (land) of figure 15.2 for a comparatively smooth shoreline (see definition of land in sec. 15.2.3). For awash areas, we recommend the dashed-dotted curve, which lies halfway between the land curve and 1.0. For rough terrain, we recommend the dashed curve. This is based on a 0.4 factor observed at Brookhaven National Laboratory (Myers and Jordan 1956), considered a rough site. In previous studies, the offshore to overwater wind ratio was allowed to increase to unity 10 n.mi. (19 km) offshore based on the Lake Okeechobee data. Although Lake Ontario data indicate that lower wind speeds would require a longer distance to reach equilibrium, we feel this is a refinement we are not able to justify. We therefore assume the ratio reaches unity 10 n.mi. (19 km) offshore for all wind speeds. The adjustments given in this chapter are not applicable at places where the surface friction category changes at inland locations far from the coast. For example, our methods are applicable over the coastal plain of Virginia, but not over the Blue Ridge Mountains farther inland. 15.2.4.3 THE SURFACE FRICTION COEFFICIENT. In prescribing the wind field of a hurricane approaching the coast, the wind path crosses the coast from the sea at a point (see sec. 15.2.4.1), traverses land for some distance, and then exits the coast at another point downstream (see sec. 15.2.4.2). We know that the ratios in table 15.1 must be further reduced to the ratios given in figure 15.2 as the wind traces this path. The process by which we make this computational reduction is described below. In a general sense, the 10-mi (32.8-ft), 10-min frictionally reduced wind speed near shore is: Vk = kV (15.1) where, V = the 10-mi (32.8-ft), 10-min overwater wind speed for a given location. Vk = the 10-mi (32.8-ft), 10-min wind speed adjusted for underlying terrain. k = the surface friction coefficient at a given location. 269 We assume that the surface friction coefficient (k) will reach equilibrium after the wind has been over a specific friction category for 10 n.mi. (19 km). That is k will vary for the first 10 n.mi. downwind from aboundary between two surface friction categories, after which it reaches equilibrium. This criterion holds for onshore and offshore winds. The surface friction coefficient (k) can be computed from: k = k + Q (ki - k) (15.2) e e where, k = the equilibrium surface friction coefficient at a point. e This is dependent on wind speed as well as the sur- face friction category {KM) (see sec. 15.2.4.2) 2 3 4 5 6 7 8 9 1011 121314 15 16 1718 ' ji' I' ' I' I '1' '1 Ij I I ' I ki = the previous surface friction coefficient 09\ at the last upwind 0.8- boundary between surface 07 0.7?- friction categories. 0.6 - ki = k at the boundary I IC between water and other 0.5- surfaces. 0.4 - Q = a coefficient ranging in 0 0.3 - value from 1.0 to 0. 0.2- - Q is simply an interpolation Q-1-0.195s+ 0.0095S 2 0.1 - x- device and is computed from: 0 1,, ,11 , ,I , ,I ,.1, 1, Q = 1 - 0.195s + 0.0095s2 (15.3) IN. MIJ s(DISTANCE ALONG WIND PATH) where s is the distance from sur- face friction categoryboundaries. > 10 n.mi. Figure 15.3.--Graphical solution for Q Q is defined as 0 when s > 10 n.mi. (eq. 15.3). (19 km). At the initial boundary of any surface friction category, Q is 1.0. The solution of equation 15.3 is shown graphically in figure 15.3. Similar equations could be developed for a faster or slower approach to equilibrium. 270 A schematic portrayal of adjustments is shown in figure 15.4. the ke values shown are for overwater wind speeds > 73 kt (135 km/hr). Figure 15.2 shows that ke varies with wind speed < 73 kt. (KM) 0 5 10 15.20 0 5 IC 15 20 I I 7 I ' ' I WIND PATH BOUNDARY WATER TO BOUNDARY NONWATER XNONWATER SURFACE ,T WATER SURFACE LL- Ke (WATER) NE K KeK : KeWTR 0,1. j~~ .8 Ki1 Kcoe Ke (LAND)O7/ .6 K(RUH INOTE: Ke VALUES FOR W eIOIH WIND SPEEDS >73 TERRAIN) =0.45 fKT (I135 KM/HR) LJ_ L~ .4 a~~~~~~~~~~~~~ KKe+Q (Ki -Ke) FROM WATER NONWATER TO WATER- 0 5 10 0 IC1 (N MI) DISTANCE ALONG WIND PATH(S Figure 15.4. Schematic of nearshore frictional adjustments. 271 15.3 ADJUSTMENT OF WIND SPEED FOR FILLING OVERLAND 15.3.1 INTRODUCTION It is a well-known fact that hurricanes begin to fill after their center crosses from sea to land. Central pressure (p ) rises and winds start droppingoff. Hubert (1955) was one of the first to note that filling is most pronounced in the innermost portion of the hurricane, with less pro- nounced effects farther from the center. 15.3.2 REASONS FOR AND EFFECTS OF FILLING OF HURRICANES OVERLAND Palmen and Newton (1969) state "Filling results because the heat flux from the Earth's surface becomes negligibly small when a storm moves inland, resulting in a reduction of the temperature excess of the core." This decrease of heat leads to a decrease in the production of kinetic eiLrgy. Miller (1963) confirmed the earlier work of Bergeron (1954) in stating that filling stems principally from the reduction of equivalent potential tempe- ture'(0 ) of the rising air around the hurricane core. Miller also noted that filling due to surface friction was of minor importance compared to the removal of the oceanic heat source. Palmen and Newton (1969) have summarized the effects of filling overland. "Owing to the removal of the oceanic heat source in the inner region, the baroclinity is reduced since the air ascending in the inner cloud wall now has somewhat lower 0 . As a result, the outward radial wind component in e upper levels is reduced. The previous balance between the mass inflow in low levels and mass outflow in upper levels is thus temporarily disturbed, leading to an integrated net mass convergence and pressure rise. During this phase, the cyclone tends to approach a depth around 1000 mb, according to Malkus and Riehl (1960), determined only by the release of latent heat intrinsic to the moist surface layer in its outer parts." 15.3.3 DATA; We selected 16 extreme hurricane events (table 15.2). Eight of these events from the period 1928-55 with p0 <28.41 in. (96.2 kPa) were analyzed by Malkin (1959). The other eight were extreme hurricanes since 1957. The 272 criterion for choosing these latter eight was that they made landfall with p <27.99 in. (94.8 kPa) along the Gulf of Mexico coast and p < 28.38 in. 0- o0 (96.1 kPa) along the east coast. We accepted Malkin's data and analysis after checking for consistency by constructing a central pressure-time pro- file (graph showing the increase of central pressure with time) after land- fall for the 1938 hurricane and comparing this profile with Malkin's profile for this storm. Figures 15.5 and 15.6 show tracks of all 16 hurricanes. LEGEND .� **.TROPICAL DEPRESSION (DEVELOPMENT STAGE : ----TROPICAL STORM STAGE (WINDS 34 TO 63 KT, 63 TO 117KM/HRo HURRICANE STAGE (WINDS 264KT (1119KM/HR +++EXTRATROPICAL STAGE - ***TROPICAL DISSIPATION STAGE * 0000 GMT POSITION 22 X O 1200 GMT POSITION !: c J6 '- I.S 24 1949 Figure 15.5.--Partial tracks of hurricanes of September 1928, August 1932, September I938, Sptember 19941, August 1949, Cara (1954), Betsy (1965) Camille (1969), and Celia (1970). 273 00' 50 .,,g,}*-An 3F/@$5sziy ~*-......*TROPICAL DEPRESSION (DEVELOPMENT STAGE) 9 y \/ ~"_ do } ~' I ,5 r t ---TROPICAL STORM STAGE (WINDS 34 TO 63 KT, ".'a /J 2gQ . - HURRICANE STAGE IWINDS Z 64 KT 11 9KM/HR) All, -. . . Smas+++-EXTRATROPICAL STAGE / 8 \ no Z / / St~r>L2Z~co *** TROPICAL DISSIPATION STAGE ,i 0 80 i 0 0000 GMT POSITION , 6RA 0 1200 GMT POSITION |"\xls __t..SET. j 1550" 1 Figure 15.6.--Partia tracks of hurricanes of September 1945, Connie (1955), Audrey (1957), Gracie (1959), Donna (2960) and Carla (1961). 15.3.4 ANALYSIS Adjustment factors (ff) for estimating the decrease of the overwater wind speeds after landfall may be computed using the classical assumption that the speeds are directly proportional to the square root of the pressure drop (Ap = Pw - PO). ff is defined here as the square root of Ap at some speci- fied time after landfall divided by the square root of Ap at landfall (APt), or (Ap/APt) /2 Therefore, we first need to analyze the change in Ap with time after landfall for the 16 hurricanes. 274 Table 15.2.--Classification of hurricanes Geograph- Number Forward Forward ical of speed State of Description region hurricanes Hurricane (kt) (km/hr) landfall of region Aug. 14, 1932 15 28 Texas Gulf coast Sep. 23, 1941 13 24 Texas from Missis- Audrey (1957) 14 26 Louisiana sippi west- A 7 Carla (1961) 6 11 Texas ward Betsy (1965) 17 32 Louisiana Camille (1969) 16 30 Mississippi Celia (1970) 14 26 Texas Sep. 17, 1928 13 24 Florida Florida south Sep. 15, 1945 10 19 Florida of 27�N B 4 Aug. 27, 1949 14 26 Florida Donna (1960) 9 17 Florida Sep. 21, 1938 47 87 New York East coast Carol (1954) 33 61 New York from S. Caro- C 5 Connie (1955) 7 13 N. Carolina lina northward Gracie (1959) 12 22 S. Carolina Donna (1960) 32 59 New York Graphs were constructed showing sea-level pressure readings from stations with available continuous pressure records during the time period when a hurricane passed by that station after landfall vs. distance of the stations from the hurricane center for seven of the eight hurricanes not previously considered and the New England hurricane of 1938. [For hurricane Donna over Florida, we dispensed with these graphs and used the pressure-time profile given by Miller (1964)]. The data on each graph were for different times, varying in the extreme by 3 or 4 hours. Composite pressure-distance profiles were then analyzed at 3- or 4-hour intervals from a few hours after landfall (t)out to t + 24 hours. These profiles were then extrapolated to distance = 0 to give estimated p. In drawing these pressure-distance profiles, data from some stations were given less weight because it didn't appear to fit well into the overall data mass. The next step was to construct central pressure-time profiles. These were constructed using: a. The estimated po0 values from the pressure-distance profiles. b. Single point lowest pressure-time after landfall data from other stations and some of those in a. that were close to the hurricane center. 275 c. National Meteorological Center weather map analyses of po. d. Estimates of pO at landfall from other studies e.g., Ho et al. (1975). These profiles were subjectively weighted to the data and eye-fitted. Figures 15.7a and 15.7b are examples of these central pressure-time profiles. The letters next to each data point correspond to the lettered items in this paragraph. Gracie hit the east coast and Camille the gulf coast. 30.0c - 29.70 - c - 100.5 -01.0 29.75 29.60 - 29.50 - a 100.0 29.50 "00.0 29.40 C a - 99.5 29.25 99.0 29.40 - c 29.00- ~~2 ~ ~ ~ ~ ~p"99 29.250- a ^ 29.10= b@ -=98.5 .-97.0 W 28.50 29.00- a- :-L - 98.0 2.- b - 96.0 a 28.90- - 22 5 - 28.80- 9 5 / 2 95.0 Z 28.70 - Lu - 97.0 94.0 28.60 - CAMILLE 1969 28.50 -- -- 96.5 9/.0 28.40 - 27.25 - LANDFALL 0430 GMT 2 . -a- 96.0 27 0 -A U G . IS - 92.0 29.30- 27.00 - LANDFALL 1615 GMT 9.0 28.20 - / SEPT. 29 _ 955 - d - 9X.0 28.10- I I 00 I2 I15 20 25 90 0 8 10 5 0 15 20 25 309- cane Gracie ?1959) after she crossed CamiZZe (199) after she crossed the the South Carolina coast. Data Mississippi coast. Data marked with marked with an "a" are from pres- an "a" are from pressure-distance sure-distance profiles; "b" data profiles; "b' data are Zowest pres- are lowest pressure data at a sure data at a station close to the station close to the hurricane hurricane center; "c" data are from center; "c" data are from weather weather maps; "d" data are estimates maps; "d" data are estimates of p of at Zandfa from other studies. at ZandfaZZ from other studies. 0 An analysis of pw with time after landfall was also needed for the nine hurricanes. Values of pw were taken from 3-hourly weather maps. Figures 276 15.8a and 15.8b show eye-fitted curves of the change of Pw with time after landfall for Gracie and Camille. I I I I I I I I I I I I 1i2. - 102.0 30.20 _ Z 30.10- 102.0 x 000 - 11: 30.00 -- 02 30.10 - 101.5 29.70 - GRCIE 1 29.80- - .- - 101.0 .3 L 29.960-0 10 2 2AFTER LANDFALL HOURS AFTER LANDFALL Figure 15.8b.--Variation of peripheral pressure (pu) with time for hurri- Figure 15. 8a. --Variation of pern- cane CamiZe (1969) after she pheraZ pressure (p ) with time for crossed the Mississippi coast. hurricane Gracie 1(959) after she crossed the South CaroZina coast. We broke our sample of 16 hurricanes into three groups based on the coastal region where each entered land. These regions are shown in figure 15.9. Region A is the coast between Corpus Christi, Tex., and Mississippi; region B, the coast of Florida south of 270N; and region C, the coast from South Carolina to Long Island, N.Y. Storms in these regions are in table 15.2. We did not attempt to incorporate forward speed (T) into our determination of ff because we did not have a full range of T in our sample (table 15.2). Thirteen of the 16 hurricanes had forward speeds between 6 and 17 kt (11 and 32 km/hr), while the other three storms (all affecting New England) had speeds of 32, 33 and 47 kt (59, 61 and 87 km/hr). Figure 15.10 is a graph of average ff vs. time after landfall for hurri- canes it regions A, B and C. Rather large regional differences are seen in the adjustment factors. We calculated the region B adjustment curve for the four hurricanes (table 15.2) using the mainland (between Marco a diEverglades City) as Donna's landfall point rather than Conch Key in the Florida'Keys. The difference in Donna's filling rate following landfall at either of these 277 .20 - .30 - J I'�-. - I .40 .80- r .70 .; .90 / Figure 15.9.--Map showing extended boundaries of regions A, B, and C. 0 5 10 15. 20 25 30 two points was small enough not to HOURS AFTER LANDFALL have an effect on the mean curve for region B. Figure 15.10.--Variation in adjustment factors with time for three geo- 15. 3.5 DISCUSSION OF ANALYSIS graphic regions. Region A (o- o) includes the gulf coast states of We need to assess the adjustment Texas, Louisiana, and Mississippi. curves (fig. 15.10) for meteorological Region B .-- ) is Florida south of 270N. Region C (x- x) represents reasonableness. First, we would the east coast from South CaroZina expect the adjustment for the Florida northward. peninsula (region B) to be the least, i.e., slowest filling,of the three regions because more of a to:It's circulation can be over water while the center is inland. We find this is so. Next, we might expect hurricanes to fill the fastest along ifif .iid'ale and northern east coast (region C) because hurricanes there travel the fastest away from the oceanic heat source. How- ever, our results show that the Gulf coast storms (region A) fill the fastest. This is probably because they do not take on extratropical characteristics as often as east coast (region C) hurricanes. Our data sample bears this out. Fifty-seven percent of the region A hurricanes became extratropical before dissipating whereas 80 percent of the region C hurricanes dissipated as 278 extratropical cyclones. We would expect this to be true because region C storms often penetrate to more northerly latitudes where the air is cooler and drier. 15.3.6 RESULTS Figure 15.11 shows smoothed curves from figure 15.10. These are to be used" for the designated areas only. Region A has been extended to the Mexican border and region C to the Canadian border in order to include the entire coastline. Figure 15.12 illustrates the coast- I I I I al boundaries of the three curves .20 - and, by way of the dashed lines, coastal sections where linear inter-- - .30- polation should be used to develop W =e(-.O35t+.0O03t - intermediate curves. .40- W WI (-.026t +.0001812A Curves A and C (fig. 15.11) can be w -.026+.000 .so --- expressed by the following equation: < WI = WC e (t + (15.4) ' .60 - C where, .70 - WI = the overland wind speed at some specified time after landfall (friction effects not considered). = I. WC = the overwater wind speed at 5 10 15 20 25 30 landfall. HOURS AFTER LANDFALL t = time Figure 15.11.--Smoothed adjustment factor curves for reducing hurricane a and B are coefficients. wind speedsw'hen center is overZland for three geographic regions defined For the gulf coast from Mississippi for thregeographic regions defined in figure 15.9. westward (curve A) a = -0.035 and 1 = 0.00013 and for the east coast north of Savannah, Georgia (curve C) a = -0.026 and 8 = 0.00018. Or > -O I -4 pT P1 0 -U 0 0 z 0D 0 r~io 0 > M T~~~~~~~Tl Z0 0) 0) .Z ~I I! IU H, I 1' DISTANCE (KM X 10') 4 a 12 16 20 24 28 32 36 40 44 4S 52 56 ~~I I I I ) I i�I I I j I ~I I I 1 1 1 'I 'I ' 0 2 A 6 8 10 12 14 16 18 20 22 24 26 28 30 DISTANCE (N MI X 101) Figure 15.12.--Limits of the three geographic regions (A, B, and C). The dashed lines delineate where linear interpolation should be used to develop intermediate curves in figure 15.11. 280 Curve B (fig. 15.11) for the Florida coast south of 27�N can be expressed by a linear regression line in terms of t: W = W (1.0 -0.013t) (15.5) 15.3.7 DISCUSSION OF RESULTS 15.3.7.1 COMPARISON OF SPH AND PMH ADJUSTMENT FACTORS. The adjustments in figure 15.11 are to be applied directly as a percent of the overwater wind field isotachs. They provide an estimate of the reduction in wind speed due to filling anywhere in the hurricane, if we assume only slight variations in the shape of the overwater and overland wind speed profiles with time. Our hurricane sample indicates that there is a trend for the more intense hurricanes to fill faster except over the Florida peninsula where there is a slight tendency for the more intense to fill more slowly. These trends are seen in table 15.3. In this table the Apt 's of hurricanes within each region are ranked (rank 1, the largest). We also have ranked the adjustment for each storm for t + 6, t + 14 and t + 22 hours (rank 1, the lowest number, or greatest filling). Correlation coefficients were computed for various times, t, between Apt at the coast and the adjustments of table 15.3. The results (significant at the 5-percent level) support the idea that the more intense hurricanes fill faster. Correlation coefficients of -0.79,-0.75 and -0.60 were computed for 6 hours after landfall for: 1) gulf coast hurricanes (region A), 2) hurricanes north of 27� (regions A and C), and 3) all hurricanes (regions A, B, and C), respectively. Correlation coefficients for the other time periods (t + 14 and t + 22) were nearly of the same order of magnitude. From table 15.3 we see that the somewhat lower correlation for group 3) probably results because intense Florida peninsula hurricanes tend to fill more slowly than less intense storms and because there is more scatter in the larger sample. Table 15.3.--Hurricane pressure drop at ZandfaZZ and computed wind speed adjustments Adjustment Adjustment Adjustment Geographic Apt Apt factor (ff) ff factor (ff) ff factor (ff) ff region Hurricane (in.) (kPa) Rank at t + 6* Rank at t + 14* Rank at t + 22* Rank Aug.14,1932 2.10 7.1 3 .77 2 .55 2 .37 1 Sep.23,1941 1.54 5.2 7 .94 7 .81 7 .62 7 Audrey 1.79 6.05 6 .85 4 .60 4 .43 4 A Carla 2.27 7.7 2- .88 5 .68 5 .61 6 Betsy 1.86 6.3 5 .93 6 .73 6 .52 5 Camille' 2.92 9.9 1 .67 1 .46 1 .37 1 Celia 1.93 6.55 4 .79 3 .56 3 .41 3 Sep.17,1928 2.27 7.7 1 .92 3 .86 4 .76 Sep.15,1945 1.86 6.3 3 .95 4 .83 3 .70 B Aug.27,1949 1.80 6.1 4 .89 1 .80 1 .68 Donna1 2.02 6.85 2 .91 2 .80 1 - - Sep.21,1938 2.13 7.2 1 .77 1 .65 3 .51 1 Carol 1.68 5.7 3 .80 2 .64 2 .55 3 C Connie 1.45 4.9 4 .98 5 .90 5 .81 5 Gracie 1.92 6.5 2 .83 3 .62 1 .53 2 Donna 1.45 4.9 4 .87 4 .83 4 .75 4 *t + 6 = 6 hours after landfall, etc. 282 Another set of correlation coefficients was computed for the same three storm groups, leaving out the most severe storm, Camille. These correlation coefficients for t + 6 hours are -0.46, -0.55 and -0.30 for groups 1), 2) and 3), respectively. The new coefficients are not significant at the 5-percent level. The significance of the correlation coefficients using Camille are clearly a result of the effect of one hurricane on a small sample. The addition of more storms over the next few decades could result in a loss of significance. Therefore, we have decided to use the same adjustment factors for both the SPH and PMH wind fields. 15.3.7.2 OTHER RESEARCH INVOLVING OVERLAND FILLING. Malkin (1959) also showed that the square root of the average pressure gradient (Ap/Dw*) when used in a similar procedure to ours gave wind speeds that were reason- ably consistent with some observations. This procedure results in a faster drop-off of wind speed with time than is indicated by using only Ap. Goldman and Ushijima (1974) determined decreases in wind speed inland for hurricanes Carla, Camille and Celia. They studied the extent of damaging winds at landfall and inland up to 78 n.mi. (145 km) and compared observed peak gusts (not Ap) at the coast when the storm entered with peak gusts in- land at some later time. Near the strongest portion of the eyewall 6 hours after landfall, Goldman and Ushijima calculated the percentage reduction from peak gusts at 0..66 for Carla and 0.70 for Camille and Celia. By contrast, the adjustment factor (ff) at t + 6 (6 hours after landfall), listed in table 15.3, gives a percentage reduction from 10-m, 10-min winds of 0.88 for Carla, 0.67 for Camille, and 0.79 for Celia. In making this comparison, we note that 1) Goldman and Ushijima are considering frictional effects in addition to filling effects while we are not and 2) they are using peak gusts while we deal with sustained winds. *D is the average distance from the pressure center to the points where Pw w is calculated. 283 15 3.7 3 PMH OR SPH CROSSING FLORIDA PENINSULA FROM EAST TO WEST. A hurricane approaching from the sea produces a much higher surge than a hurricane of equal intensity exiting the coast. However, of possible importance is whether a PMH or SPH can enter the Florida peninsula from the east, cross the peninsula, and be stronger than a PMH or SPH entering the peninsula from the west. Such a question would be most critical for the area just north of the 29th parallel where the distance from the east coast to the west coast is only about 100 n.mi. (185 km) and where the central pressure difference between the two coasts is the largest. We have made computations based on filling rates while overland which show that the winds on the west coast of Florida from an east coast PMH or SPH striking milepost 1700 (fig. 1.1) and crossing the peninsula cannot be stronger than the winds from a gulf coast PMH or SPH striking milepost 1100 directly from the sea. This would also be the case at points along the central and southern portions of the peninsula because the difference in p0 between the two coasts increases with latitude. 284 16. THE STALLED PMH 16.1 INTRODUCTION For some problems it is necessary to evaluate the degree of scouring or erosion of beaches from intense hurricanes. Naturally, the slower the storm moves, the greater the beach damage. In this chapter we estimate the proper- ties of a slow moving PMH. We assume that a PMH moving at 5 kt or less for a period of at least 24 hours is particularly critical to the beaches. We classify storms meeting this criteria as stalZing. A study by the Florida Power and Light Company (1975) using data between 1901 and 1973 for the Gulf of Mexico and the Atlantic south of 35�N classified 2 hurricanes as stalling. In that study, a hurricane was so classified if its average forward speed (T) was < 5 kt (9 km/hr) for a period of 2 days or longer. North of the Virginia-North Carolina border (milepost 2260), where the lower limit of forward speed begins to significantly exceed stalling speed, we need to consider how much a PMH will weaken before it reaches stalling speed. For this region, numerous assumptions must be made concerning the transition from a slow speed PMH storm to the storm just before it reaches stalling speed. Discussion of these assumptions and resulting procedures begin with section 16.5. 16.2 BACKGROUND Stalled hurricanes weaken because in an environment of slight steering winds, warm air cannot be transported away from the hurricane core quickly enough (Beebe and Simpson 1976). Thus, the mechanism of lower-level inflow combined with upper-level outflow which is essential to a mature hurricane, begins to break down. In addition, cooling of surface water due to upwelling in the wake of a hurricane leads to weakening of a stalled hurricane (Geisler 1970). Leipper (1967) reported that, in hurricane Hilda (1964), stalling and an outbreak of cold air behind the storm caused the sea-surface tempera- ture (Ts) to fall 10.8�F (6�C). Hilda then filled 0.61 in. (2.1 kPa) and, after striking the coast, became extratropical. Using airborne infrared thermometers and airborne expendable bathythermographs, Black and Mallinge�'"' X"�i; . =': ....- '- 285 (1972) documented the presence of cold surface water beneath slow-moving weakening hurricane Ginger in 1971. Smith (1975) reported that the movement of hurricane Celia (1970) over colder Ts's and shallower mixed-layer* depths probably contributed to its filling. The storm initially deepened to 28.50 in. (96.5 kPa), then filled to 29.12 in. (98.6 kPa). When air and sea-surface temperatures are about the same, evaporation and conduction of heat are minimized and little energy is extracted from the sea by the hurricane. Leipper and Volgenau (1972) computed the hurricane heat potential of the Gulf of Mexico for four summers and identified areas of low- heat potential where a storm could be supported for only one or two days. The sea-surface temperature in the gulf is normally about 81�F (27-280C) in summer. We conclude that a hurricane stalled for longer than 2 days over waters a few degrees colder than this would weaken and would not extract enough heat energy from the ocean to reintensify. 16.2.1 EFFECTS OF SEA-SURFACE TEMPERATURE ON "CROSSOVER" TYPHOONS The influence of cool sea-surface temperatures on the intensity of hurri- canes may be studied statistically by examining the intensities of tropical cyclones crossing the wake of a recent tropical cyclone. Brand (1971) extracted 57 "crossover" typhoons from 12 years of typhoon data in the western North Pacific Ocean (1958-69). He defined crossover typhoons as those that crossed the track of a previous typhoon within 30 days. He con- cluded that both the movement and the intensity of a tropical cyclone may be affected by the cooler water left in the wake of an earlier storm. Thirty- eight of the 57 cases he studied indicated an intensity decrease in the later storm. He also pointed out that a larger percentage of storms showed a decrease of intensity at high latitudes than at low latitudes. This could be related to the latitudinal variation of mixed-layer depth. *The mixed layer extends downward from the ocean surface, is virtually iso- thermal, and frequently exists above the thermocline. The thermocline is a vertical temperature gradient which is appreciably steeper than the gradient above it. Below the thermocline, temperatures continue to decrease but at a slower rate. 286 16.2.2 GEOGRAPHIC VARIATION IN SEA-SURFACE TEMPERATURE DROPS Table 16.1 lists some hurricanes for which T dropped following the passage of the storm. The storm tracks'and approximate locations of thes' events are shown in figure 16.1. The average change in T for 7 gulf hurricanes was -4.00F (2.2�C) and for 5 Atlantic hurricanes -3.70F (2.10C). (-6.30F or -3.5�C was used for Carla in the gulf, while -5.4�F or -3.00C was used for Betsy and -5.9�F or -3.3�C for Ginger in the Atlantic. Betsy is included in the counts of both gulf and Atlantic hurricanes.) The difference between the two regions is negligible. Most of the T drops on figure 16.1 fall between 250 and 300N; therefore, no conclusions can be made on the latitudinal varia- tion of Ts drops. However, the mixed layer depth decreases to the north, enhancing the ability of a hurricane to produce a colder wake at higher than at lower latitudes. 16.3 DATA We studied Atlantic hurricanes that occurred west of 40�W for 1955- 75* and western North Pacific typhoons for 1961-75. The criterion used for selection of cases was p _29.00 in. (98.2 kPa) for hurricanes and po < 28. 20. in. (95.5 kPa) for typhoons at the time stalling began. Also, a storm could not have its eye over land during a stall and could not have reached its maxi- mum intensity more than 24 hours prior to the time stalling began. The- storm sample is listed in table 16.2. Central pressure and other data'were obtained from aircraft reconnaissance reports. 'The reports for typhoons are published in the AnnuaZ Typhoon Reports by the Joint Typhoon Warning Center, Guam (U.S. Department of Defense 1961-72). The data for hurricanes came from the unpublished records of NOAA. The storm tracks are shown in figures 16.:2a and 16.2b. All storms meeting our criteria began their stall at or south of 36.50N. We shall cover characteristics of stalling storms for this region first. For the region north of 36.50N, our results are more subjective and are discussed separately. *Reconnaissance data prior to 1955 are not considered to be as reliable as subsequent data. '; g r~i: -, 287 Tabte 16.1.--Sea-surface temrperature (T%) changes associated with the passage of various hurricanes Maximum AT S Hurricane (�F) (�C) Source Donna, Sept. 1960 -2.7 -1.5 Hazelworth, 1968 (ff Carolinas) Ethel, Sept. 1960 -4.5 -2.5 Hazelworth 1968 (mid-Gulf) Carla, Sept. 9, 1961 -9 -5 Hazelworth, 1968 (western Gulf) Carla, Sept. 10, 1961 -3.6 -2 Stevenson and Armstrong, 1965 (off Texas coast) Arlene, Aug. 1963 -1.8 -1 Hazelworth, 1968 (near Bermuda) Cleo, Aug. 1964 -2.7 -1.5 Hazelworth, 1968 (near south Florida) Hilda, Oct. 1964 -10.8 -6 Leipper, 1967 (mid-Gulf) Betsy, Sept. 1, 1965 -4.5 -2.5 Landis and Leipper, 1968 (north of Puerto Rico) Betsy, Sept. 4, 1965 -6.3 -3.5 Landis, 1966 (NE of Bahamas) Betsy, Sept. 9, 1965 -1.8 -1 McFadden, 1967; Taylor, 1966 (Gulf) Camille, Aug. 1969 -1.8 -1 Jensen, 1970 (northern Gulf) Celia, Aug. 1970 0 0 Molinari and Franceschini, (mid-Gulf) 1971 Ginger, Sept. 27, 1971 -7.2 -4 Black and Mallinger, 1972 (NE of Bahamas) Ginger, Sept. 28, 1971 -4.5 -2.5 Black and Mallinger, 1972 (NE of Bahamas) Eloise, Sept. 1975 -2.7 -1.5 Price, 1976 (northern Gulf) 288 Ace 1~~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~5 NO. STORM DATE h ~' ':k 2", 6 HILD./A 1964 a" ' 2 o*,..._.T 7 BETSY 1965 8 CAMILLE 1969 j p ~ v, 9 CELIA 1970 6s 10 GINGER 1970 s sf >- t ~~~~~~~~~T 1.1 ELOISE 1975 Figure 16.1.--Partial hurricane tracks and approximate locations of reported sea-surface tenmperature drops (�F). See table 16. 1. Table 16.2.--Most intense stalled hurricanes and typhoons selected for analysis. Lowest po near the Duration of time stalling began* stalling (in.) (kPa) (hr) Hurricanes Betsy, Sept. 1961 27.91 94.5 54 Hilda, Oct. 1964 27.99 94.8 36 Betsy, Sept. 1965 27.85 94.3 24 Faith, Aug. 1966 28.26 95.7 36 Heidi, Oct. 1967 28.97 98.1 72 Typhoons Ellen, Dec. 1961 27.91 94.5 36 Emma, Oct. 1962 26.61 90.1 60 Trix, Sept. 1965 27.46 93.0 ' 24 Harriet, Nov. 1967 28.11 95.2 36 Agnes, Sept. 1968 26.67 90.3 30 Faye, Oct. 1968 26.90 91.1 ' 30 June, Nov. 1969 27.61 93.5 24 Wendy, Sept. 1971 27.02 91.5 30 Rita, July 1972 26.84 90.9 60 *These po'ts occurred between 18 hours before stalling began to 8 hours after for hurricanes and between 21 hours before stalling began to 6 hours after for typhoons. 289 24 P SITIONS 0000 GMT 4 2 POSITIONS DURING STALL NO. STORM D 2 21 I BETSY 2 HILDA 1 3 BETSY 4 FAITH 3 HE(DI Figure-16.2a.-Partiat t-racks of selected hurricanes (table 16.2). Dots denote store positions at 0000 GMT; circled dots are approximate positions where the storm stalled. NO. STORMDATIE 'OF STALL I ELLEN 12/1961, 2 EMMA 10/1962' a TRIX 9/1963 4 HARRIET 1111967 5 AGNES $11968 6 FAYE 1011960, 7 JUNE 11/1969 a WENDY 9/IP71, 9 RITA 7/1972 ID 2 9 0 0 POSITIONS 0000 GMT POSITIONS DURING STALL Figure 16.2b.-Same as figure 16.2a except for selected typhoons, 290 16.4 STALLED PMH SOUTH OF 36.50N 16.4.1 VARIATION IN INTENSITY 16.4.1.1 AP BEFORE AND AFTER TIME OF STALL. The variation of inten- sity, Ap, (Pw - Po), before and after stalling for the selected storms (table 16.2) is shown in figures 16.3a and 16.3b. Central pressure values(po) are from aircraft reconnaissance reports and peripheral pressure values (pw are from daily weather maps from the Northern Hemisphere map series (Environmen- tal Data Service 1961-72). Time zero in figures 16.3a and 16.3b indicates the time at which the storm begins a stall (moves at a forward speed < 5kt or 9 km/hr). Arrows indicate the end of the stalling period. The storms reached their maximum intensity preceding stalling, with three exceptions. Two hurricanes (Faith and Heidi) and one typhoon (Trix) were at their maximum intensity 6 to 8 hours after stalling commenced. Since maximum intensity is reached at different times relative to the beginning of a stall, we will use as reference the time of maximum intensity rather than the time of the beginning of the stall. 16.4.1.2 VARIATION OF AP OVER APMA X WITH TIME AFTER APMAX Figures 16.4a and 16.4b show the variation in intensity with time from maximum intensity (t = 0) for the selected stalled hurricanes and typhoons, respectively. The variation is in terms of the ratio of the intensity to the maximum intensity. Arrows indicate the end of the stalling period. In general, during the first 30 to 40 hours after reaching maximum intensity, the more intense storms weaken at a faster rate. After stalling for 30 hours, typhoon Wendy (fig. 16.4b) reintensified to near her original strength as her forward speed picked up to 13 kt (24 km/hr). Wendy's intensity decreased by about 40 percent in 36 hours* whileishe moved at a T of about 4 kt (7 km/hr). Stalling in this case can be traced to the light steering currents associated with a breakdown of the subtropical high to the north- west. The subsequent deepening of the typhoon was linked to a strengthening of these currents after a rebuilding of the high to the northeast. *Wendy began her stall at the time of maximum intensity. 291 2.5 -f~~. t _~~~~~ _BETSY '65 - 6.0 0 '- * >1 . o ~ ~ ~ t~~ 5lro - END OF ST ** _.0 r .DOD .oo ..oo~, BETSY '65 1 I I .o ;j~ C* * -3.0 -.0 -12 0 12 24 36 48 60 72 84 96 108 120 0 32 0 -9.0 TIE BEFORE AND AFTER STALL COMMENCED T.'S I I I I I I I I I 3_'0 - 10.0 -.0 � JUNE _2.5 '. - 2.0 -:\ � \.. .. .0 TRIXME BEFORE AND AFTER STALL COMMENCED Fgr1632.0 f iur .xc -- .%-2.0 Figure 16.3b.--Same as figure 16.3a except for selected stalling typhoons. 292 I.e \.. 0.9-\ o. HILDA oe e FAITH 127.991 (128.26) ~*~~ ~e* *55* BETSY 65 TY6 ** *~~**9 **5 127.911 0.74- * * HEIDI *I28.97) 0 12 24 36 48 60 72 84 96 108 120 TIME AFTER MAXIMUM INTENSITY IHRI Figure 16.4a.--Variation in pressure drop pw - p) from the maximum pressure drop reached in seZected staZZing hurricanes. Arrows indicate the end of the stalZing period. Time = O marks the time of maximum intensity. The data next to each storm Zists the centraZ pressure at time = O in inches (Hg). o 0 0.6 - to 0.7 - Q4~ \ / * HARRIET 127.84) .7 I I 2.111 ��.(28 9 7) 0' 12 24 36 4H 60 72 84 96 108 120 TIME AFTER MAXIMUM INTENSITY IHRI Figure 16.4b.--Samoe as figure 16.4a except for selected staZZlling typhoons. :IEATRMXMMITNIY(R E~igure26.4b.-Same asfigure16.4a ecept fo se~ectd stal�in yhos 293 16.4.1.3 VARIATION OF AP MAx WITH AP AFTER MAXIMUM INTENSITY Figures 16.5a, 16.5b, and 16.5c show the maximum storm intensity (Apa) max plotted against the intensity (Ap) 24, 36, and 48 hours, respectively, after the maximum intensity is reached. A line of best fit is drawn by eye on each of the diagrams. The deviation of each line of best fit from the 450 line indicates that the decrease in Ap from the maximum Ap is greatest at the upper end of the curve corresponding to storms with the greatest intensities. We note that the three plots show good agreement between stalled hurricanes and typhoons. 16.4.1.4 VARIATION IN PMH WIND SPEED WITH TIME AFTER STALL. Two curves of figure 16.6 show the average rates of weakening for the stalled hurricanes and typhoons of table 16.2. An average of the two (solid curve) indicates a 23% and 33% decrease in pressure drop 24 hours and 48 hours, respectively, after the storms began to stall. The top and bottom curves give the full range in intensity variation of the storms studied. Figures 16.5 a, b, and c indicate that the decrease in Ap after stalling begins is greatest for the more intense storms. Since the PMH has a greater intensity than any recorded hurricane, we may expect an even greater decrease in intensity when it stalls. However, in view of the uncertainties inherent in a study of this kind, we have adopted the average decrease in storm intensity given by the solid curve in figure 16.6 for the rate of decrease for the PMH south of latitude 36.5�N (Virginia - North Carolina border). This curve has been expressed in terms of the decrease in wind speed for the PMH through the classical pressure-wind relation: APf (16.1) APmax The resulting stalling adjustment factor (sf) is shown in figure 16.7 by a solid curve out to 60 hours after the time of stall, and by a dashed curve to 120 hours. The dashed curve is based partially on hurricane Heidi. Hur- ricane Carol (1965) stalled for 120 hours over the open North Atlantic but diminished to tropical storm strength for about 12 hours during that period. We think a former PMH can stall for 120 hours south of Virginia and maintain hurricane strength. 294 (kEPoa) r(kPo), 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8. 9.0 10 . 2. 3 .0 . . 7. 9.0 1 TRI00 1.0 2.0 3.0 .0 0 . 1.50- - E 10 5.0 . 3_ 25 H EMMA - 11.0 3.25 _NE Of D EST F1 EYE L INE O f REST FIT Y A S NE .0 3.00 - / 2.0 /- . NE 10.0 2.2- 2 0 .25- - BET1SY. 1 1ETTl. . T IX 0I E1.TT . I7.0 2.00- JULNE X 200 BETSY'65IY UNE ELLEN ELLEN ,HILDAt 1.71 6 a ARiIET o HxD .6.0 a .5 E a 4 t 1.75 HARRIE 6.0 ~~~~~~~~~~1.25~~~~~~0 1.0 FAGNE h i.0 an ty n. eAITH -.0 1.22 - HEIDI f by HEIV I A O.R 101.00 OHUERICANE - .0 0 HURRICANE -3.0 0.75 - TYPHOON - N TYPHOON -2.0 2.0 0.50- / 2. 0.25 - 1TRI0.25 - 0. . e C. 1.I5 /I ./I.*i. I 1 1 .1 I 1.- 2.250- END0 'O 0.25 0.20 0.75 1.00 1.25 1.20 1.72 2.00 2.25 2.50 2.75 0 % 0.22 0.50 0.72 1.00 .25 1.50 1.75 2.00 2.25 2.50 2.75 IIN.J IIN.I AP AT t - 94 HE AFTER MAXIMUM INTENSITY IS BEACHED AP A i t-36 HR AFTER MAXIMUM INTENSITY IS REACHED Figure� 16.5a.--Var-iation of maximum Figure 16.5b.--Same as figure 26.5a pressure drop with pressure drop 24 except abscissa refers to time 36 hours lZater for selected staling - thors m alterh . f hurricanes -and typhoons. Note the line of best fit by eye. 16.4.2 VARIATION IN FORWARD SPEED TRX. 20 3. 4. 7.0 Fi 1~o 6 .--Same~~ as o fgr 16.5..a OFigures 16.8a and 16.8b show the 4.80 h Zae r I Ia I1 3.22 - LINE OF BEST PIT BY EYE -11.0 variation with time of the forward EMMA 3.00 - ONES FAY2E .7- speed (T) of selected stalled storms. WENDY9.0 These T's are 6-hr averages. All T's 2.50 - 22.0 <5 kt (9 kmjhr) are shown as 5 kt. The 2.25 RI - -70 ~2.00 - J IUN~LEN 7.0hurricanes and typhoons generally moved 1.75 HIL 6.0 . HARRIET - at speeds between 6 and 16 kt (11 to 0 1.20- FAITH o. 5.0 30 kmhr) during the 24 hours prior to 1stalling. This does not exclude the ~~~0.50do - ~storms.. -'-The -diagrams also show that 0.25 - . 1.0 0.2050072 0 1.25 0 2. 2.20'the storms moved at T's ranging from ' 01 0.50 0.75 1.001.25 1.50 1.7- 2.00 2.25 2.50 2.7 IIN.I F P AT ti48 HR AFTER MAXIMUM INTENSITY IS REACHED 6 to 30 kt (11 to 56 km/hr) 36 hours after the end of their last stall. Figure 16.5c.--Same as fiure 6.5a On the average, the T increased to except abscissa refers to time 48 hours Later. about 10 kt (19 km/hr) 24 hours 295 I.O / UPPER LIMIT / -.9 - 0.1.\ \ <,_ AVERAGE FOR HURRICANES 0.7 - 0 ~ AVERAGE ALL ..~ .~ ~- STORMS 0.6 AVERAGE FOR - TYPHOONS LOWER LIMIT- 0 . I I I I I I I 0 12 24 36 48 60 ASSUMED TIME FROM BEGINNING OF STALL (HR) Figure 16.6.--Ratio of pressure drop (pW - Po) to the maximum pressure drop. Time = 0 represents the assumed time stalling begins corresponding to the time of maximum pressure drop. The upper and Zower Zimit curves are enve- Zopes of observed data for the seZected stalling hurricanes and typhoons. after stalling ceased, and to 14 kt ,.o ., , , , , , , , , , , , , , , , , (26 km/hr) 48 hours after. The T after ~-~- -WOIo r LWI Lo IT .. ., -_ stalling seems to be independent of S - - --- the storm's initial intensity. Two 0.6 - ~- -~ typhoons which moved slowly after Q - - stalling (Harriet and Ellen) continued 0.2- 3, _ to weaken to tropical storm strength. ,'12 24 '6 48 60 72 84 96 108 ,20 Other slow-moving storms (Betsy of TIME FROM BEGINNING OF STALL (HR) 1965, Agnes, and Rita) maintained hurricane or typhoon intensity (figs. Figure 16.7.--StaZZting adjustment factor (sf) curve for the PMH to be 16.3a and 16.3b). used south of the Virginia - North Carolina border (36.5�N). 296 40 BETSY'61 40 -DA ....... B0 ETSY'6 -70 T for a stalled hurricane -60 - 60 30 30 - - s o -50 -50 is given by definition, i.e., 20 4 0 20 40 30 - -30 < 5 kt (9 km/hr). Prior to v 10 _20 10 20 : v --,o --10 c'= - o stalling a PMH can have the a �24 0 24 48 72 96 120 2 024 0 s 72 96 12 0 aj ~ CT~ I range of T given in chapter a 10. The rate of increasing - - - FAITH -70 - HEDI -670 T after stalling for a former - - 60 - -60 D30- -- 30 - - -50 - -50 PMH has been left unanswered. 20 -40 20- -40 -30 - -30 ,1OL_ _20 1 _20 16.4.3 TRACK DIRECTION _-10 - -10o %, ; ' ; ' ;6 ' o ' | Since looping and other, %24 0 24 48 72 96 120 4 024 48 72 96 120 ' TIME BEFORE AND AFTER BEGINNING OF STALL (HR) erratic storm motions may accompany a stalled hurri- Figure 16.8a.--Variation of forward speed (T) with time for seZected staZZling hurricane, no limiting values are Time = 0 indicates the beginning of stall assigned to 0 for a stalled (T < 5 kt, 9 km/hr) -MH. 40 N- 40LEMMA - OEMAt 403_ ELEEN - 70 .,vR l A .,- _7T70 16.4.4 RADIUS OF MAXI- - _ 60 -30 _ , ,,"60- MUM WINDS AND INFLOW 30~- 3~-50 - -o0 20o ~'-ANGLE 20- 40 20-- 40 -30 - 30 2o- 1 20 lo>.O _0 The increase in pO because -24 2'4 4 2 9 120 24 4 8 72 6 1 of stalling would indicate -HARRIET -70 --FAYE 70 larger R's for the stalled ...... AGNES - ". -JUNE -60 -60 30 -- - 30 .. .. Lm - ,o -0 50 case, but because this in- .. 20 A O -40 2 _ I.I- 2o 2 ,2- ' -3o30 1- crease is often small south T 1''-20 0_,__L,., " 20 " ":. of the Virginia - North o �24 0 24 48 712 96 120 4 0 24 4' 72 96 120 0 Carolina border, we recom- Lu. 40- - mend no change, i.e., use -WENDY -70 0- RITA -60 figure 9.8. From Virginia - so 20- -40 northward we recommend a - 30 10- .. 20 variation in R prior to and _.- -10 .%4 ; 2'48 72 '6 120 after stalling; (see sec. 0 24 48 72 96 120 TIME BEFORE AND AFTER BEGINNING OF STALL (HR) 16.5. 7) Figure 16.8b.--Same as figure 16.8a except for selected stalling typhoons. 297 We recommend that figure 14.7 continue to be used to compute inflow angle (c) for the former PMH after it stalls. 16.4.5 LENGTH OF STALL The length of stall (figs. 16.8a and 16.8b, table 16.2) for the selected hurricanes and typhoons varies from 24 hours (3 storms) to 72 hours for hur- ricane Heidi, which was weak when it stalled (fig. 16.3a). The length of stall for the selected hurricanes and typhoons (omitting Heidi) varies from 24 to 60 hours (typhoons Emma and Rita.)* We think a former PMH can stall and maintain hurricane strength for 120 hours south of Virginia. 16.4.6 REINTENSIFICATION WHEN THE STALL IS OVER The reintensification of a storm after stalling ceases is restrained by sea- surface temperatures. Thirty years ago, Palmen (1948) postulated that a tropical storm cannot develop into hurricane intensity over waters with sur- face temperatures of 78.80F (26�C) or less. This critical limit is still accepted today. The mean August sea-surface temperature, lowering with increasing latitude, drops to about 64.40F (180C) off the New England coast near 43�N (U.S. Navy 1969b). After stalling is over and T again exceeds 5 kt (9 km/hr), a former PMH south of 36.50N may reintensify to the maximum intensity it had before stalling. The time required for a storm to regain PMH intensity and the rate of this reintensification has notbeen studied extensively but is linked to the length of the stall and also, therefore, to the degree of weakening. In our storm sample, the only storm to regain its maximum intensity was typhoon Wendy. It regained this intensity 30 hours after stalling ended (fig. 16.3b). The length of Wendy's stall was also 30 hours. A PMH as a stronger storm would probably require a reintensification period longer than its stall period. *Intense hurricanes have stalled for longer periods near land. Hurricane Flora stalled over eastern Cuba for 4 days in October 1963. 298 16.5 STALLED PMH NORTH OF 36.50N 16.5.1 INTRODUCTION Examination of our sample of stalled hurricanes and typhoons shows only one north of 36�N and none north of 39�N. Nevertheless, this does not preclude a hurricane stalling or looping from Delaware Bay (39�N) northward. Since this report is developed to provide comprehensive guidelines for the PMH along the gulf and east coasts of the United States, it is necessary to develop criteria for a stalled PMH for the entire region. The criteria are exten- sions of those prepared for south of Virginia (36.5�N) and are based on meteorological reasoning which includes indications from more southerly hurricanes. 16.5.2 RATE OF DECREASE OF WIND SPEED The rate of decrease of the wind speed south of 36.5�N (fig. 16.7) was developed from storms over sea-surface temperatures at or above 79�F (26�C). From southern Florida to Cape Hatteras, the sea-surface temperature decreases slowly. North of about 36.5�N the decrease becomes more rapid (see fig. 12.2) with considerably less potential energy from the sea-surface. It is reasonable for a stalled hurricane to have a more rapid rate of decrease in wind speed over cold water. Since some energy is still available from the water surface, the rate of decrease should be less than that for decreasing winds for overland filling along the east coast (curve C, fig. 15.11). For the region north of Cape Cod (42�N), a curve was interpolated one-fourth the distance between the warmer water curve (fig. 16.7) and the overland filling curve. Figure 16.9 shows these three curves and several interpolated curves. All curves are dashed beyond 60 hours. For the coast between 36.5�N and Cape Cod, the rate of decrease in wind speed may be obtained by using the curves on figure 16.9 and, if necessary, linearly interpolating between them. 16.5.3 DECREASE IN T FOR A PMH NORTH OF THE VIRGINIA-NORTH CAROLINA BORDER North of 36.50 the lower limits of T for a PMH are too fast (13 kt, 24 km/hr) for a storm to reach stall speed(< 5 kt, 9 km/hr) in a few'hours or less. Some intermediate limits must be set on the rate of decrease of T for a PMH in order to approach stalling speed at a logical rate. During this 299 0.9- LOWER LIMIT OF PMH, T 0.8-' SOUTH OF VIRGINIA-NORTH i~ 0.8 \2 39 -_ -'-_ --CAROLINA BORDER (36.5 N) ig0.7 0.- --_ -3 _ -3 Z UPPER EAST COAST OVERLAND 0. 5 FILLING CURVE (REGION Cl ..._ _ 0.4 - I~ NORTH OF CAPE COD (42'N) 0.3 - 42-_ _ 0.2 - 0.1 I I I I I I I I I I I I I I I I I 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 TIME FROM BEGINNING OF STALL (HR) Figure 16.9.--StaZZlling adjustment factor (sf) curves for the PMH to be used north of the Virginia - North Carolina border. The upper straight line shows the Zower Zimit of PMH T (no weakening). period, the storm must weaken, but at a lesser rate than during a stalled condition. 16.5.3.1 MAXIMUM AND MINIMUM RATES OF DECREASING FORWARD SPEED (T). We need to set maximum and minimum rates of decrease of T for the former PMH. Figure 16.8a shows that Betsy's (1961) T dropped 7 kt (13 km/hr) in 6 hours prior to stalling. This is the greatest decrease in T of the storms examined, but our data sample is very small. We have decided to allow a former PMH to decrease at a maximum rate of 15 kt (28 km/hr) during the first 6 hours after its T falls below the lower limits, and to decrease an additional 10 kt (19 km/hr) during each additional 6-hr period until the stalled T of 5 kt (9 km/hr) is achieved. We set a minimum rate of decrease of T for-the storm at 10 kt (19 km/hr) during the first 6 hours and at 8 kt (15 km/hr) for each additional 6-hr period. 300 16.5.3.2 CHOOSING S. Once a 1pMH drops below the limiting T and begins to weaken, it is no longer bound by the permissible limits of 0 given in figure 11.6. However, we will require that the 0 chosen be within the per- missible limits for the SPH (fig. 11.8) over the distance between the LT point [where T first falls below the minimum T (TL)], and the stall point. This is reasonable since, though weaker than a PMH, the hurricane is still of greater than SPH intensity. The user should select a 0 at the latitude of the LT point and then determine if this direction remains within permissible limits between the LT point and the stall point. 16.5.3.3 DEFINITION OF THE POINT WHERE T DECREASES BELOW THE MINIMUM LIMIT. The LT point pertains to the point where the PMH first falls below the minimum speed (TL) permissible for maintaining PMH intensity. It does not pertain to the point where the former PMH reaches the 5 kt (9 km/ hr) stall speed. The distance between these two points is dependent on a) the magnitude of TL, i.e., the larger the TL, the larger the distance traveled between these two points, and b) the rate of speed decrease selected between the maximum and minimum rates of decreasing T given in section 16.5.3.1. We will see in section 16.5.4.2 that former PMH's moving from the south or near south must start dropping off from PMH TL south of New England or the hurricane will cross the coast before reaching stall speed (5 kt or 9 km/hr). 16.5.3.4 DETERMINATION OF LT POINT KNOWING POINT OF STALL. In order to determine the point where the PMH first drops below the TL, we must choose a 0 (sec. 16.5.3.2) that a former PMH will follow to the stall point. We must also choose the rate of decreasing.forward speed (sec. 16.5.3.1). This will not present much of a problem for a hurricane moving toward the stall point from the east (possible south of milepost 2800) because the lati- tude for the stall and the LT points is the same. In that unioue case, we would arrive at the LT point by taking an average T [TL + 5 kt (9 km/hr) . 2] and multiply the result by the time it takes to decrease from the TL'to 5 kt (depends on chosen rate of decreasing speed). This will give a distance eastward of the stall point where the LT point is located. In all other cases, the LT point is located with more difficulty. A helpful first guess at the location of the LT point may be made by taking average T 301 (as explained earlier), using the TL for the stall point, and then multiplying that average T by the time it takes to decrease to 5 kt. This distance measured along the chosen 0 will be greater than the distance to the LT point for 0 >900 because TL decreases with decreasing latitude. (For 0 between 50� and 90. the reverse is true.) The user can then choose LT at an arbitrary point closer to (farther from) the stall point and compute a shorter (longer) distance to the stall point using an average T (using the TL at this arbitrary point) and the chosen rate of decrease in T. If required, additional LT points should be selected until a point is found that permits the storm to reach a stall point at or very near the selected stall point. If the stall point selected is some distance offshore, this distance must be considered in selecting the LT point. 16.5.4 DECREASE OF INTENSITY FOR A NONSTALLED FORMER PMH MOVING SLOWER THAN THE LOWER LIMITS OF T (TL) Once a PMH begins to move at a speed less than the lower limits of T (TL) it will begin to decrease in intensity. As the storm continues to slow, it will continue to weaken until it reaches its stalled speed (5 kt or 9 km/hr) where further weakening will occur as described in section 16.5.2. The rate of weakening prior to stall should be less than the rate of weakening after the hurricane stalls. This is so because a stalled storm will be affected more by upwelling of cold water than will a nonstalled storm, even one approaching stall speed (Geisler 1970). 16.5.4.1 GENERAL CONSIDERATIONS INVOLVING P0. In developing quanti- tative loss of intensity with time for a former PMH after T has dropped below TL, we must weaken the storm fast enough so that its p0 at the stall point is less than that of the PMH at that point. The former PMH should not weaken at such a rapid rate that the decrease in intensity before reaching stall speed is greater than the weakening rate of a stalled PMH. 16.5.4.2 PROCEDURE FOR DECREASING WIND SPEED AT LT POINT TO WIND SPEED AT STALL POINT. Once the LT point has been located, the milepost or latitude of this point is determined and then an overwater wind field for that milepost is reduced using the following procedure and the curves of figure 16.9: 302 a. Enter the abscissa of figure 16.9 with the time from when the T of the hurricane fell below LT to when it reached the stall T. Draw a vertical line up to the curve marked with the latitude of the stall point. b. Read off the percentage adjustment at that point on the y-axis. This would be the percentage by which the whole wind field would be multiplied if a former PMH had actually stalled for this period of time. c. Since our storm has not stalled it would weaken at a lesser but unknown rate. We have elected to assume that the storm would decrease at a rate only 70 percent of a stalled PMH. Thus, we increase the value of (b) by 30 per- cent of 1.0 - the value of (b) to give a lesser reduction. d. Multiply the entire wind field by the percentage in (c) to obtain a reduced wind field. After stalling, this wind field will be further reduced by using the method given in section 16.5.2 with the curves of figure 16.9. e. If a portion of the wind field is over land, it will need to be reduced further on account of friction; (see chapter 15). The average rate of decrease of wind speed from the PMH wind speed computed for a slowing PMH should be used with caution. For example, a former P1MH traveling from the south or near south and stalling just north of Cape Cod may have originally dropped below T south of the Virginia - North Carolina L border if its T is decreasing at the minimum rate or a slightly faster rate. During the early part of its passage from North Carolina to Massachusetts, therefore, the hurricane would probably be weakening at a lesser rate than the given average rate of weakening to the stall point north of Cape Cod. Such differences in rates would become smaller as we rotate 0 toward 90�. If the user wishes to approximate a decrease in intensity not too long after T drops below PMH TL it is probably appropriate to use a rate of decrease less than an average curve would indicate. 16.5.5 FORWARD SPEED T for a stalled hurricane is given by definition, i.e. < 5 kt (9 km/hr). Prior to stalling, a PMH can have the range of T given in chapter 10. The rate of increasing T after stalling for a former PM1 has been left unanswered 303 16.5.6 TRACK DIRECTION Since looping and other erratic storm motions may accompany a stalled hurricane, no limiting values are assigned to 0 for a stalled PMH. 16.5.7 RADIUS OF MAXIMUM WINDS AND INFLOW ANGLE North of the Virginia - North Carolina border, we recommend that R be increased as a former PMH weakens while slowing down and stalling. This increase should relate to the variation in p. The initial R should be from within the limits of R (fig. 9.8) at the milepost corresponding to the LT point. The R after T falls below TL and during the stall should be deter- mined by increasing the R in proportion to the upper and lower limits of figure 9.8. Enter that figure at the milepost corresponding to a higher p0 associated with the amount of decrease of wind speed obtained from figure 16.9. This higher P is determined using equation 16.1. Knowing the original APmaxVmax and the maximum wind speed at the end of the stall period, we compute a new Ap at the stall point. Seeing that p is constant with lati- tude*, a higher p0 can be determined (Ap = Pw - Po)' This p0 will correspond to an east coast milepost in figure 8.8. R is then read at that milepost. If the higher p0 exceeds 27.46 in. (93 kPa), R may be increased at the rate of 1 n.mi. (1.9 ki) for every 0.12 in. (0.4 kPa) increase in P0 at the upper limit of R and 1 n. mi. (1. 9 km) for every 0.42 in. ( 1. 4 k Pa ) increase in p0 at the lower limit of R. For R's between these limits, interpolate. As R varies, so will inflow angle (0). Continue to use figure 14.7 to compute 0 north of 36.5�N. If R exceeds 38 n.mi. (70 km) use figure 14.6 [for R >45 n.mi. (83 kin), use the R = 45 n.mi. curve]. 16.5.8 REINTENSIFICATION WHEN THE STALL IS OVER North of the Virginia - North Carolina border a former PMH cannot reinten- sify to the maximum intensity it had before stalling. The colder water at these latitudes would prevent the full regeneration of the storm to its initial PMH intensity at the LT point. We believe this would be the case *We consider Pw to be constant with latitude for the PMH. As a former PMH weakens, especially during a stall, Pw would probably decrease toward SPH Pw' We will neglect this. 304 everywhere, even for a former PMH which moved at 0 = 50� to a stall point off the Virginia capes where the water is the warmest and PMH p is lower than the PMH p at the LT point. The actual rate of reintensification of a former PMH to an intensity less than its PMH po at the LT point was not addressed in this report. 16.5.9 LIMITATIONS These procedures are approximate and are based on several assumptions. Curves and procedures were developed to maintain maximum intensity for the stalled storm within a logical framework. Only additional knowledge and data can support our conclusions. The procedures developed in this section are subject to the following limitations: a. An LT point cannot be located north of 45�N. b. An LT point may not be more than 300 n.mi. (556 km) from any point on the U.S. east coast, including capes. c. The procedure is undefined if a former PMH crosses land between the LT point and the stall point. Limitation (a) is called for because we have defined the PMH to only 45�N. Limitation (b) is adopted because our east coast data sample extended outward 150 n.mi. (278 km) from the coast. We will assume that additional data between 150 and 300 n.mi. (278 and 556 km) from the coast would be of the same family as the "closer in" data. We are unwilling to make this assumption beyond 300 n.mi. (556 km). Limitation (c) is given because a former PMH would also be filling and, therefore, weakening more rapidly if it crossed land between the LT and stall points. 16.5.10 ADDITIONAL REMARKS The problem of p at the stall point being lower than the stall point PMH p0 will not occur. Tests made with Po and wind speeds given in tables 2.3 to 2.6, for several stall points along the east coast, showed this to be so. The manner in which the slopes of the wind curves (fig. 16.9, then increased by 30 percent; see sec. 16.5.4.2), used from the Virginia-North Carolina border northward, roughly vary with cooler sea-surface temperatures,-prevent this problem. 305 By employing a percentage of the weakening rate for stalling as the storm moves from the LT point to the stall point (sec. 16.5.4), we are assured by definition of lesser weakening prior to stalling than after stalling. 16.5.11 EXAMPLE OF CALCULATION OF DECREASE IN PMH WINDS NORTH OF 36.50N The following is an example of how to decrease PMH winds for stalling north of 36.50N. We will assume: a. A former PMH stalls just south of the Rhode Island coast near 41.30N. b. The hurricane moves from 0 = 180�. c. The hurricane decreases its T at the maximum rate (sec. 16.5.3.1). The initial TL would be taken at the Rhode Island coast near milepost 2650 and would equal 37 kt (69 km/hr). Using this TL as a first guess (sec. 16.5.3.4) we obtain an average T of 21 kt (39 km/hr), or 37 kt + 5 kt . 2. It takes 16.2 hours for a PMH to slow down from 37 kt to 5 kt (69 km/hr to 9 km/hr) at the assumed maximum rate of decrease in T. Multiplication of 21 kt by 16.2 hours gives a distance of 340 n.mi. (630 km) or 5.7� due south of 41.30N. This gives an LT point at 35.60N, or about 200 n.mi. (370 km) east of Cape Hatteras. Here TL is only 10 kt (19 km/hr). This is not our final LT point because a former PMH would slow down to 5 kt (9 km/hr) from 10 kt (19 km/hr) in just 2 hours using the maximum rate. This would obviously not be enough time to travel 340 n.mi. (630 km). As a second guess, we will arbitrarily put an LT point east of the New Jersey coast near milepost 2460 (39.50N) where TL = 30 kt (56 km/hr). In this case, we obtain an average T of 17.5 kt (32.5 km/hr), or 30 kt + 5 kt - 2. Twelve hours will pass before a PMH with a TL of 30 kt (56 km/hr) slows down to 5 kt (9 km/hr) at the maximum rate. Multiplication of 17.5 kt by 12 hours gives a distance of 210 n.mi. (389 km) due north of 39.50N, or 3.50 north of 39;.5�N, giving a stall point at 43.00N in southern New Hampshire, or 1.70 north of the required stall point. Our guess of 39.50N for the LT point was too far north. We know that 35.60N is too far south (first guess) and 39.5�N is too far north (second guess) for the LT point. As a third guess, we will select a point east of Delaware Bay near milepost 2400 (38.80N) where TL 26 kt (48 km/hr). Here, we obtain an average T of L 306 15.5 kt (28.8 km/hr), or 26 kt + 5 kt - 2. It takes 9.6 hours for a PMH to slow down from 26 kt to 5 kt (48 km/hr to 9 km/hr) at the maximum rate. Multiplication of 15.5 kt by 9.6 hours gives a distance of 149 n.mi. (276 km) due north of 38.8�N or 2.5� north of 38.8�N, giving a stall point at 41.3�N. This is the required stall point. The LT point is therefore 38.8�N. The wind speed of the PMH at the LT point is decreased to the wind speed at the stall point by using the procedure given in section 16.5.4.2 and refer- ring to figure 16.9. Interpolate a curve for 41.3� (between the 41� and 42�N curves). Draw a vertical line up from 9.6 hours on the abscissa (the time from when the T of the hurricane fell below T to when it reached 5 kt, or L 9 km/hr) to the interpolated curve. Read 0.851 on the y-axis; this is the adjustment to the winds due to stalling for 9.6 hours. The designated stalling factor (sf) is 0.851. The percentage reduction over the whole wind field if a former PMH had actually stalled for 9.6 hours would be 14.9%; or (1 -0.851) x 100. Since, in this example, the hurricane was slowing down to 5 kt (9 km/hr) during the 9.6 hours it took to travel from the LT point to the stall point, its winds would decrease at only 70 percent of 14.9% or 10.4%. Subtracting 10.4% from 100% gives 89.6%, the percentage to be applied over the entire PMH wind field corresponding to the LT point at 38.8�N (due south of milepost 2650) after the hurricane has moved to 41.3�N, just south of the Rhode Island coast. This adjusted wind field will be further reduced after stalling by using the procedures given in section 16.5.2 with the curves of figures 16.9. For example, if the former PMH stalls near 41.3�N for 12 hours, this new wind field will be reduced by 18% by employing an sf of 0.82. Since the storm stalled just south of the Rhode Island coast, most of its northern semicircle will be over land and a portion of its wind field will have to be reduced further to account for friction (see chapter 15). 16.6 EFFECT OF LAND ON STORM WEAKENING One would expect stalled hurricanes with a part of their circulation over land to weaken more rapidly than those whose circulation is entirely over water, all other things being equal. We are unable to find an adequate number of hurricanes which stalled close to land or whose eyes drifted over land during a stall to verify this idea. A larger sample of typhoons was available. However, western North Pacific land masses (Philippines, Taiwan, and Japan) would not be representative of the U.S. east and gulf coasts. 307 Lacking data, we recommend the use of a constant weakening rate for a stalled hurricane over the western North Atlantic or Gulf of Mexico, whether or not it is close to land. 16.7 OTHER RESEARCH Beebe and Simpson (1976) have studied the hydrometeorological aspects of stalling and meandering hurricanes. Their investigation indicated that after stalling to a forward speed of < 4 kt (7 km/hr), a hurricane with the strength of Camille (1969) would be able to maintain its intensity for only a very short period. Such a storm would have potential for causing much greater coastal erosion than has been observed historically. We allow an SPH (weaker than Camille) to travel at 4 kt whereas a PMH (stronger than Camille along the gulf coast and most of the east coast) is allowed to move at speeds of 6 kt (11 km/hr) or more. 308 ACKNOWLEDGMENTS The authors wish to thank the many members of the Water Management Information Division (WMID), Office of Hydrology, National Weather Service (NWS), NOAA, for their help in preparing this report. The guidance and critical review of the manuscript given by John T. Riedel, Chief, Hydro- meteorological Branch, WMID; John F. Miller, Chief, Water Management Information Division; and Dr. Vance A. Myers, Chief, Special Studies Branch, WMID, were both needed and appreciated. Keith Bell, Marion Choate, Roxanne Johnson, Teresa Johnson and Ray Evans provided valuable research support at various stages throughout our study. Roxanne Johnson also prepared most of the camera-ready illustrations seen within these pages. Clara Brown typed the final version of this substantialreport. Virginia Hostler helped in typing several draft versions. Conversations with Dr. Harry F. Hawkins, now retired from the National Hurricane and Experimental Meteorology Laboratory (NHEML), and Paul Hebert, National Hurricane Center (NHC), Coral Gables, Fla., were extremely helpful during the formative stages of our study. Periodic meetings with the staff of our supporting agencies (U.S. Army Corps of Engineers and the Nuclear Regulatory Commission) and their consultants provided us with additional insights throughout the preparation of this report. We especially wish to thank Dwight E. Nunn, consultant, and coauthor of NHRP Report No. 33 on the SPH, for his valuable suggestions. Lastly, we would like to thank researchers at the NHC; NHEML; the Systems Development Office, NWS; and the Coastal Engineering Research Center, U.S. Department of the Army, for a critical but extremely helpful review of the manuscript during the later stages of its preparation. l: 309 REFERENCES American Meteorological Society, 1974-78: Monthly Weather Review, Boston, Mass. Atkinson, G.D. and C. R. Holliday, 1977: Tropical cyclone minimum sea-level pressure/maximum sustained wind relationship for the western North Pacific. Monthly Weather Review, Vol. 105, No. 4, pp. 421-27. Ausman, M., 1959: Some Computations of the Inflow Angle in Hurricanes near the Ocean Surface. Department of Meteorology Report on Research, Univer- sity of Chicago, Chicago, Ill., 19 pp. Beebe, R. C. and R. H. Simpson, 1976: Hydrometeorological aspects of stalling and meandering hurricanes. 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Inter-Regional Insurance Conference, New York, N.Y., 63 pp. 317 CONVERSIONS To CONVERT FROM TO USE THE FOLLOWING EQUATION TEMPERATURE degrees, Fahrenheit degrees, Celsius tc = (tf - 32)/1.8 degrees, Fahrenheit degrees, Kelvin tk = (tf - 32)/1.8 + 273.16 degrees, Celsius degrees, Kelvin tk = t + 273.16 TO CONVERT FROM To MULTIPLY BY DISTANCE feet meters 0.305 miles (nautical) kilometers 1.853 miles (statute) kilometers 1.609 miles (statute) miles (nautical) 0.868 PRESSURE inches (Hg) kilopascals 3.386 millibars inches (Hg) 0.030 millibars kilopascals 0.100 SPEED knots kilometers/hour 1.853 knots miles/hour 1.152 miles/hour kilometers/hour 1.609 '*U.S. GOVERNMENT PRINTING OFFICE: 1979-281-067/266 (Continued from inside front cover) NWS 16 Storm Tide Frequencies on the South Carolina Coast Vance A Myers, June 1975, 79 p (COM-75- 11335) NWS 17 Estlmation of Hurricane Storm Surge in Apalachlcola Bay, Florida James E. Overland, June 1975. 66 p. (COM-75-11332) NWS 18 Joint Probability Method of Tide Frequency Analysis Applied to Apalachicola Bay and St George Sound, Florida Francis P Ho and Vance A. Myers, November 1975, 43 p. (PB-251123) NWS 19 A Point Energy and Mass Balance Model of a Snow Cover. Eric A. Anderson, February 1976, 150 p. (PB-254653) NWS 20 Precipltable Water Over the United States, Volume 1 Monthly Means George A Lott, November 1976, 173 p. (PB-264219) NWS 20 Preclpltable Water Over the United States, Volume II Semimonthly Maxima Francis P Ho and John T Rledel, July 1979, 359 p NWS 21 Interduration Preclpltation Relations for Storms - Southeast States Ralph H Frederick, March 1979, 66 p. (PB-297192) NWS 22 The Nested Groin Model. Norman A Phillips, March 1979, 85 p ,r nv _ -c NOAA SCIENTIFIC AND TECHNICAL PUBLICATIONS The National Oceanic and Atmospheric Administration was established as part of the Department of Commerce on October 3, 1970. 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