SPLASH (Special Program to List Amplitudes of Surges from Hurricanes)

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~~ ~ U.S. DEPARTMENT OF COMMERCE
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INFORMADiON CEENTER

SPLASH (Special Program To List
~~ Amplitudes of Surges
From Hurricanes)
I. Landfall Storms

CHESTER P. JELESNIANSKI

~QC
851
.U6
T3
if no .4 6

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WBTM TDL 12 Charts Giving Station Precipitation in the Plateau States from 700-Mb.
Lows During Winter. D. L. Jorgensen, A. F. Korte, and J. A. Bunce, Jr.,
October 1967. (PB-176 742)

WBTM TDL 13 Interim Report on Sea and Swell Forecasting. N. A. Pore and W. S.
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WBTM TDL 14 Meteorological Analysis of 1964-65 ICAO Turbulence Data. DeVer Colson,
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WBTM TDL 16 Objective Visibility Forecasting Techniques Based on Surface and Tower
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WBTM TDL 17 Second Interim Report on Sea and Swell Forecasting. N. A. Pore and
Lt. W. S. Richardson, USESSA, January 1969. (PB-182 273)

WBTM TDL 18 Conditional Probabilities of Precipitation Amounts in the Conterminous
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WBTM TDL 23 An Operational Subsynoptic Advection Model. Harry R. Glahn, Dale A.
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WBTM TDL 24 A Lake Erie Storm Surge Forecasting Technique. William S. Richardson
and N. Arthur Pore, August 1969. (PB-185 778)

WBTM TDL 25 Charts Giving Station Precipitation in the Plateau States From 850- and
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(Continued inside back cover)

U.S. DEPARTMENT OF COMMERCE
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COASTAL ZONE
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NOAA Technical Memorandum NWS TDL-46

SPLASH (SPECIAL PROGRAM TO LIST
AMPLITUDES OF SURGES FROM HURRICANES)
I. LANDFALL STORMS

Chester P. Jelesnianski

U. S. DEPARTMENT OF COMMERCE NOAA
COASTAL SERVICES CENTER
2234 SOUTH HOBSON AVENUE
ChARLESTON, SC 29405-2413

2om-------

..-.Q<~ <>-'Z� Property of CSC Library
19
~~~ ~ Systems Development Office
Techniques Development Laboratory

SILVER SPRING, MD.
April 1972

UDC 551 465 755 551.515.2(047)(75/76)

551.46 Oceanography
.465 Dynamics of sea
.755 Storm surges
551.5 Meteorology
515 2 Tropical hurricanes
(047) Case histories and reports
(75/76) (Southeast States and Gulf States)

CONTENTS

Abstract ............1.....................

1. Introduction ***... ..........................1

2. Symbols used . .. .. . .......................... 3

3. Developing a method to approximate the peak surge ......... 4
A. Preliminary number for peak surge ............... 5
B. Correcting for in situ (two-dimensional) sea depths . ......7
C. Correcting for in-s-itu vector storm motion ........... 10

4. Examples of peak surge approximation .............. ......12

5. Comments on approximating the peak surge ..... .. ...... . .. 17
A. Locating the peak surge on the coast . ............. I7
B. Correcting for variation of latitude . ..............18
C. Correction factors....................... is

6. Using the computer to display coastal storm surges * a. ...... . 19
A. Displaying storm surge envelopes by computer output . ....19

7. Further comments and conclusions .................. 23

Acknowledgments..............................24

References................................ 24

Appendix 1: empirical and nomogram surge models ............25
A. Correlations between precomputed and observed surges . . ....26
B. Composite nomogram and statistical model .. ...........29

Appendix 2: SPLASH ............................31
A. Mechanics of running the program .................31
B. Meteorological data deck for the program ...............32

Appendix 3: some do's, don'ts, and applications when fore-
casting storm surges.... .................... .. . 35
A. Meteorological parameters.. . . . ........... . .....36
B. Geographical features of basins and their coastlines . . ....40
C. Inundation ............................4 45
D. Continental Shelf width, depths, and grid spacing . . ..... 48
E. Astronomical tide .. .................... .. so

iii

SPLASH
(SPECIAL PROGRAM TO LIST AMPLITUDES OF SURGES FROM HURRICANES)
I. LANDFALL STORMS

Chester P. Jelesnianski
Techniques Development Laboratory,
Systems Development Office, NOAA, Silver Spring, Md.

ABSTRACT. Whenever a tropical storm threatens to
strike a coast, it is desirable to have at hand an
estimate of the height of the potential storm surge.
Two separate methods (based on dynamics) to estimate
or forecast the surge are developed. The first method
in which precomputed nomograms are used is designed
only to arrive at a peak surge value. Arguments for
the nomograms are simple meteorological parameters.

In the second method, a dynamic model is used to
compute surges along an entire coastline. Com-
putations are done by an electronic computer;
surface meteorological parameters are used as in-
put to the operational program.

Qualitative explanations for the surge phenomena are
interspersed throughout part I. The relative im-
portance of various meteorological parameters,
continental shelf topography, and coastal geography
are discussed.

1. INTRODUCTION

Coastal high waters generated by tropical storms often are the cause of a
significant fraction of total storm damage. Because the potential for de-
struction can be enormous, we should be familiar with the physics of these
tides as well as with the available forecasting procedures. When abnormal
situations not covered by forecasting techniques occur, an understanding of
the nature of the storm tide will serve to guide the forecaster.

The total storm tide is the sum of astronomical and meteorologically in-
duced tides or storm surges, the latter generated by storm-driving forces.
For practical purposes, these two tides are assumed superimposed with no
interaction between them. Thus, a mere addition of the astronomical tide to
the storm surge might be sufficient for storm tide prediction.

This paper (part I) continues and expands upon Harris' (1959) forecasting
guide. Two simple forecasting techniques are given herein. In the first, pre-
computed nomograms are employed to find quickly the expected peak surge onlyo
In the second, an off-the-shelf computer program, SPLASH, is used to compute
the expected surges along segments of the east and gulf coasts of the United

States. At present, only storms that are expected to cross coastlines will be
considered. A future paper (part 11) will deal with storms moving along a
coast.

Can the storm surge be predicted with an acceptable degree of accuracy and
confidence? The answer in most cases is yes--if we understand the limitations
of available models. One of the most serious limitations is meteorological.
Although simple input parameters are used, determining their values is not
always easy. One such parameter is the landfall point of storms; this is easy
to visualize but difficult to forecast. Another parameter is the storm's
central pressure, also used in the storm's size and vector motion. The fore-
cast of storm surges will stand or fall on how well these parameters are known
bef ore the storm strikes the coast. In addition, for planning, a climatology
of parameters can be used to form probability predictions of storm surges
(Myers 1970).

Prior to the computer age, solutions to tidal hydraulic problems such as
storm surges were arrived at by empirical means or by the use of simplified
mathematical models. Both procedures are limited, the empirical approach
because of a paucity of data, the other because of simplified assumptions.
Today, sophisticated dynamic models can be handled on the computer numerically.

A companion study to this paper, Jelesnianski (1967) describes the dynamic
model used h-ere. The model can and does use two-dimensional variable depth
basins and two-dimensional driving forces in motion. There are some severe
restrictions to the solutions since curvilinear boundaries, bays, estuaries,
islands., capes, spits, jetties, etc., are not considered. These geographical
formations give rise to unknown local perturbations on the open coast storm
surge. Best results occur for straight line coasts (with land elevations
sloping strongly upward).

The sea-surface response to meteorological forces gives -rise to surges on
and along the coast; the assemblage of these coastal surges, for any given
time, is called a storm surge profile. We regard this profile as a snapshot
of tide heights along the coast. It builds and abates with time; it also can
go through some erractic variations if storm motion is specialized or if the
forces vary strongly with time. In any profile, some points may be experi-
encing highest surge while others will not as yet have experienced it. The
curve made up of the highest (or upper) surges at each point over the entire
storm duration is called a storm surge envelope: in general, it is not a pro-
file but nevertheless is impportan't in assessing inland flood potential.

Usually, the significant profile or envelope length on the coast is not much
larger than the diameter of the storm. This means that affected coast lelagths
are generally small and could be represented by a tangent line meeting the
coast at or near the point of landfall. This is true only if the geographical
curvature of the coast relative to storm size is small; most of the east and
gulf coasts do have gentle curvature. Contrary examples would be the irregular
coasts of Japan, the Philippines, or East Pakistan.

To satisfy one objective (to forecast quickly an approximate value for the
peak surge), we prepared three precomputed nomograms. To satisfy the other

objective (to describe quantitatively the storm surge profile along the coast
and its peak surge value and position on the coast), we need access to a com-
puter.

For the present, the assessment of changes in the profile due to local irreg-
ularities in the geometry of the coast will depend on the experience and
artistry of the surge forecaster, In most cases, the local changes are not
overwhelmingly significant; the errors in meteorological parameters used will
most likely have a greater effect on the forecast. A substitute for experience
is a technical paper by Harris (1963) that gives accounts of many historical
surges; this reference should be in the library of all those engaged in storm
surge forecasting.

2. SYMBOLS USED

Only ordinary arithmetic is employed in this paper. Some symbolism, how-
ever, is required for terms in the figures and arithmetic statements; these
appear in table 1.

Table I.--Symbols and their meanings

S Surge on coast

Ss Peak surge on coast

Preliminary number for peak surge

Po Central pressure (in mb) of tropical storm

POO Peripheral or outside ambient pressure (in mb) of storm

AP Pressure drop (in mb) of storm (i.e., P0o--Po)

Variation of pressure drop (i.e., difference of two separate
choices for AP)
R Distance (in st.mi.) from storm's center to circle of maximum
winds

RC
RCRadius of curvature of coast

US Speed (in mi/hr) of storm's motion

Correction factor for local bathymetry along gulf coast

FE Correction factor for local bathymetry along east coast

FM Correction factor for vector storm motion

DS Distance to peak surge from landfall point

D Depth at any point on Continental Shelf

DO Finite sea depth at coast, obtained when general shelf pro-
file is extended to coast

Short length (<< R), running seaward and from coast, where
slope of depth profile greatly exceeds general slope of
Continental Shelf

Io Short length (<< R), running landward and from coast, up to
terrain heights that equal peak surge

p Correlation coefficient

Angular measure from coastline to track of storm, where
track terminates at landfall point

3. DEVELOPING A METHOD TO APPROXIMATE THE PEAK SURGE

Conner et al. (1957) designed a simple empirical model to forecast storm
surges. They plot observedI maximum tides against lowest observed2 central
pressure (P.) and then find the line of best fit. Their correlation coef-
ficient for 30 data points is 0.68. The data are for the Gulf of Mexico only,
where the astronomical tide is less than a foot above mean sea level (MSL)
and rarely exceeds 2 ft. Essentially, their model assumes that all storms are
the same except for central pressure, that all storms strike coasts in the same
relative way, and that the depth contours off all coasts are the same.

Harris (1959) expanded on this model to storms making landfall on the east
and gulf coasts. He removed the seasonal sea-level anomaly, whenever possible,
from the observed high waters. He also considered as parameters the peripheral
storm pressure (Poo), the size of the storm (R), the vector storm motion (UsO),
and the distance of the 50-fm line from shore. For the available data, he
found systematic variations of the surge with two parameters: the central pre�-
sure and the distance of the 50-fm line from shore. His correlation co-
efficient for 52 data points was 0.75.

Describing an objective forecasting scheme for the peak surge only, which
reflects the above empirical models, will be done through precomputations in
which our dynamic model is used. Here, the storm size R plays a minor role,
just as in Harris' model; but the bathymetry3 and vector storm motion play
significant roles. Qualitative explanation will be given for some of the
physics involved in surge generation.

For future reference, we make two definitions:

Standard basin. A basin with a straight coastline in which the depth profile
seaward is a linear slope. The slope is the same along the entire coast
(i.e., one-dimensional). Such a slope is shown in the inset of figure 2A.
The basin can be considered a hypothetical mean for all basins�

Standard storm motion. A storm motion with a speed of 15 mi/hr and a track
normal to the coast from sea to land. The storm must move onto land. This
motion can be considered a hypothetical mean motion for all storms.

1Hoover (1957) subjectively alters some of the surge data. His experience
suggests surge values higher than those reported. He arrives at an upper
maximum surge profile between observed values. This subjective analysis gives
him a correlation coefficient of 0.81. He does not alter surges for all storms,
nor does he consider as many storms as Conner et al. (1957).

2Lowest central pressures were rarely observed. Instead, estimates were used
(Weather Bureau 1957); and published data are scattered in the Monthly Weather
Review.

31n our use of bathymetry, we mean bottom topography. These depths are given
by marine coastal charts.

A. Preliminary Number for Peak Surge

Harris (1959) it his empirical model finds little variation of the surge with
the outside ambient air pressure P., and sets it as a constant. In our dynamic
model, P0 need not be constant. It is not difficult to obtain P00 One way
to do this is with a surface weather chart. Move outward from the storm center
to the first anticyclonically turning isobar and mentally record the pressure;
do this for several directions from the storm center. The mean of your several
pressure readings is P00 If the isobar patterns do not lend themselves to
this technique, then use any mean pressure for the area or even a constant
1012 mb.

To develop a scheme initially patterned on empirical models, we go to the
dynamic model (via computer) and ask it a preliminary question- -what maximum
surges do I obtain with the following constraints?

1. There are sets of storms; in each set, the radius of maximum wind R
is constant.

2. In each set of storms, only the pressure drop (AP =P0- PO) is varied.

3. All storms have a standard motion,

4. All storms traverse a standard basin.

5. All storms make landfall at 30'N.

The computer's answer to this question is shown in figure 1; it is our first
nomogram for quickly determining the expected peak surge.

Entering the nomogram with arguments AP and R gives a preliminary number.
Later, this number will be revised with relaxation of constraints 3 through
5. In its present form, however, the preliminary number can be used as a crude
estimate of the peak surge. When correlated with observed surges (appendix I)
it gives a correlation of 0.54 (i.e., the nomogram of fig. 1, which does not
use all the information available about the storms, is not as efficient a
predictor as the empirical models of Conner et al. 1957 and Harris 1959).
Understanding this nomogram, however, will give us a better physical insight
into surges.

For constant R, each curve is nearly a straight line passing through the
origin; this means the predicted surge has relative error = 5P/AP, where 6P is
a variation or error in the pressure drop. For example., a 1-mb error in pres-
sure drops of 100 and 50 mb gives a storm surg" error of I and 2 percent,
respectively. This immediately indicates how accurate- the pressure readings
should be.

If AP is constant, the surge is weakly or miildly dependent on R accordingly
as AP is small or large (i.e., the peak surge is quasi-conservative with re-

26 __

24 ~Y~

22 _ _ _ _

I20
W

W
LiJ

z. J
LiJ
1I4
CX

8I --
10
IL/

0
0 I0 20 30 40 50 60 70 80 90 100 110 120 L30 140
AP(PRESSURE DROP)
IN MILLIBARS

Figure I.--Nomogram of peak surge on the open
coast as a function of pressure drop and
radius of maximum winds (R in st.mi.). The
curves are computed for a standard storm
motion across a standard basin.

spect to R). This is a most useful property because R is difficult to as-
certain, especially for storms with double eye structures. For constant AP
in figure 1, the peak surge reaches its maximum value for R at or slightly
greater than 30 mi. We do not explain this behavior, except to state that,
in our model, there is a critical storm size for a given storm speed that
generates an upper maximum surge; similarly for a given storm size, there is
a critical storm speed that generates an upper maximum surge.

Figure 1 is for a hypothetical standard basin shelf width of 72 mi. If we
arbitrarily choose 50 fm (300 ft) to represent the shelf edge, the resulting
shelf width along the east and gulf coasts ranges from 2 to 100 mi. Now
noting that R rarely exceeds 50 mi for tropical storms, we have some clues for
the applicability of figure 1:

1. If the shelf width is much smaller than the storm diameter of 2R
(as occurs between the Florida Keys and Palm Beach) or if the shelf is much
steeper than standard, then figure 1 is strongly distorted with respect to
larger size storms.

2. If the shelf is much shallower than standard (as occurs at Eugene Isle,
La., or Cedar Keys, Fla.), then figure 1 may be distorted with respect to
medium to large size storms.

3. If an exceptionally large storm size occurs (i.e., Rs50 mi), then
figure 1 is out of range. This means that extratropical storms (in which R
is normally very large)are excluded.

Large R's present many technical difficulties not considered here; we will
only consider storms with R<50 mi. Here, we also take a pragmatic approach
and assume that maximum surge is nearly independent of R along most coasts
of the United States. One reason for restricting ourselves to the coasts of
the United States is that shelf widths are generally greater than the radius
of maximum winds for most tropical storms. In our model, the maximum wind4
is a function of AP and R; hence, direct reference to it is not required.

We will now continue to explore some ways in which the remaining information
about the storms can be used to improve forecasts. For the first of two cor-
rections on the preliminary number, we remove the constraint of standard basin
bathymetry; this is discussed in the next topic.

B. Correcting for In Situ (Two-Dimensional) Sea Depths

When a storm crosses a continental shelf, surges are not generated at once.
Initially, driving forces will impart momentum to the sea; and any surface
elevations are due mainly to static heights from pressure drop. To form
waves such as a storm surge requires factors to transform the variable mo-
mentum in the sea (i.e., vorticity) into divergence. One such factor is the
Coriolis force. However, it is not very effective for medium scale phenomena
occurring under hurricanes. A much more effective factor is the bathymetry or
sloping5 depths of the continental shelf.

Harris (1959) empirically found systematic variations in the surge with
variations in the distance of the 50-fm line from shore. Using this crude
parameter, however, he could not refine the variations caused by dramatic
changes in the bathymetry about the coast. Because the bathymetry along the
coastline of the United States varies considerably, we might expect pro-
nounced differences in storm surges at local coastal points, when all other
things are equal. To see how bathymetry in our model affects coastal surges
and also how to correct for it, we direct a second question to the dynamic
model via computer--if one is given two storms (one for the gulf coast and the
other for the east coast) with these constraints,

1. each storm has its own invariant AP and Rb and

2. both storms have the same standard motion,

what is the ratio of peak surge at any point along the coastline of the United

4The average wind on a circle around the storm at radius R, not the fastest
mile wind

5A limiting case is a vertical wall in a constant depth basin.

6For the gulf coast 55 mb and 15 mi. and for the east coast 68 mb and 30 mi.
These values were chosen strictly for convenience, but they roughly reflect
the differences in climatology between hurricanes in these areas.

. 2 3 4 5 6 7 8 9 10 1 12 13 14 IS

1.8 II1

L10 1.7

.0 -.3

Z 0.97-
<0.8 6 -_____ MILES FROM SHORE

o�� - ___U~ A% EA' 0 2 40 60
I)0.7 --B"o~ ____ ____

0.5 - I - __

0.4 -200

0.23 -tw I300 j___ _

0.0 Q 31
0.I -c- ---~ _ _ _ _ __- __ _ _ _ _9:
9 9: 9: ~ _
1 2 3 4 5 6 7 a 9- .0 II 12 13 14 IS
- � *..~~ MILES X 102
/0
~~~ ~Ii i
0 I

Ii r
30 ~~~~~ ~~~I '-.-- //

(0 41 0
w

Figure 2.--Nomogram for shoaling factors along-(A) the gulf coast and (B) the east coast

1 2 a 4 5 a 9 IC It 12 IS 14 15

1.4

ta~~~~~~

1.3 _

La..

< . 0a 7

0.3 - 1
LU~~~~~~~~~~~~~~~~~~~~ Co

0.2 q - z ~a n - __ _

U~~~~~~~~~~c LU LUU

0.5~~~~~~~~~~~~~~~~~~~~~t in i -

0.4 t
4 5 7 8 10 11 12 13 l;T~~~~~~~~~~~~~~~~~~~~~~~~~I
________ ________LE S 102 _ _ _
N,1.~~~~-FANOAII.. COOU,

30.3 ______ ______ _________-
T ~ ~ ~ ~ ~ a~L __L

~~~Fgr 2-Cnluded

States to that of the peak surge in a standard basin located at 300N?7 The
computer's answer to this question is broken into two parts,

1. the ratio FG for the gulf coast (fig. 2A on p. 8), and

2. the ratio FE for the eastern seaboard (fig. 2B).

In figure 2A, the vertical lines are 100 mi apart. Selected coastal cities
are shown along the abscissa. The inset compares the steepest and the shallowE
depth profiles in the gulf against the standard depth profile. The shoaling
curve varies inversely as the distance of the 10-fm curve from the coast. In
figure 2B, the shoaling curve between the Florida Keys and Vero Beach is
speculative because the Continental Shelf differs greatly from standard. The
factors are for the open coast surge and not for interior points.

Figure 2, our second nomogram, is used with figure 1 to determine the ex-
pected peak surge. For different constraints, the ratios or shoaling factor8
FG, FE will vary; but the variation in most casesbut not all, will be small.
We pragmatically accept the shoaling factors as a working tool to correct for
the local bathymetry. The preliminary number obtained from the nomogram of
figure 1 is multiplied by the shoaling factor obtained from figure 2. Note
in figure 2 that the distance of the 10-fm depth curve from the coast is a
rough inverse measure of the shoaling factor.

If we correlate the preliminary number, revised for shoaling, against the
data points of appendix 1, the correlation coefficient is 0.68, a significant
improvement in correlation. Note especially that some of the preliminary
numbers have been radically altered by the shoaling curve. The stage is now
set for another revision.

For the second of two corrections on the preliminary number, we remove the
constraint of standard storm motion; this is discussed in the next topic.

C. Correcting for In-Situ Vector Storm Motion

Harris (1959) found systematic variations of the surge for two parameters,
P. and a crude estimate of the bathymetry. His distribution of data points
was inadequate to permit him to derive systematic variations for vector storm
motion.

7We have incorporated corrections for latitude or Coriolis effects in the
ratios or shoaling factors.

8To develop the shoaling curve (fig. 2), we used the following procedure.
The same storm was made to reach land at equidistant points along the coast,
at the rate of three storms per 100 mi. The envelopes of the computed surges
were then drawn along the coast. Finally, the envelope of the envelopes was
drawn by hand. This hand-drawn envelope was then rescaled, for a non-dimensiol
ratio, using the computed peak surge in a standard basin. The shape of this
envelope, or shoaling curve, depends mildly on the storm size R.

MIj M2 O _ _ A /WSX \\ < ~0 ~STORM
TRACK 8

0.4
Z to

K 0 mph
0.7 --
0 1 I

04 � K e5

m Nr N Of� t {D 0 O N dw <0 0 0 (a m 0

Figure 3.--Nomogram of correction factors against the vector
storm motion. The factor corrects for motion other than
standard; standard motion is a vector track, 0900/15 mph,
relative to the coastline. The inset gives orientation
of the argument 0 and also gives some extreme tracks re-
lative to the coast.

In our model, the track of a storm influences surge generation. There exists
a critical motion relative to a coast that gives the highest possible surge
under any given set of conditions. The critical speed generally is greater
than 30 mi/hr; it will be less only with exceptionally small storms or in excep-
tionally shallow and wide basins. Storms reaching land rarely attain a
critical speed; thus, we will not consider it here.

To correct for the effect of different vector motions on coastal surges, we
direct a third question to the dynamic model via computer--if one is given storms
traveling at any direction and speed relative to a coast and these con-
straints,

1. all storms have R = 22.5 mi and AP = 62 mb and

2. all storms traverse a standard basin,
what is the ratio of the generated peak surge to that generated by a storm
with standard motion? The computer's answer to this question, in terms of the
ratio or motion factor FM, is given in figure 3; the insets define a direction
0 that is the angle of the storm's track relative to the coast. We mentally
orientate ourselves along the coast with the right side seaward, left side
landward, and facing 0� direction; 6 is then measured clockwise from shore
to track, where the track terminates at the landfall point.9 The figure is only

We arbitrarily assign a latitude of 30�N at this point and let the Coriolis
parameter be constant; latitude changes are accounted for in the shoaling
curve (fig. 2).

12
DATA PRECOMPUTED VALUES
STORM: name of storm - S : the preliminary number
DATE day, month, year enter figure 1 with arguments AP and R
HOUR: local time of landfall -FG FE : correction factor for shoaling
STAT: nearest station to landfall point enter figure 2 with argument STAT + MPR
see figure 5 for position of stations for location of peak surge on coast
MILES: distance to landfall from STAT ._FM : correction factor for vector storm motion
_ +MILES- M LES CO-AT' enter figure 3 with arguments Us end e
S'r~ ~~~~aSAT ,
SEA N'LES+R COMPUTATIONS

R : radius of man winds in miles, SS : the expected peak surge in feet
<SS ( )*( ) '( )
10 < R < 50
MPR~~~~~~~~~~~~~~~~~ FG FM gulf coast
- MPR : MILES + R, distance to peak surge from S FG FM gulf coast
STAT S FE FM east coast
Sp i
~~~~~~~~~~~~~~~~~~~~~Po:
P mean ambient air pressure about storm 1/P : relative surge error per mb error
: central pressure of storm example: AP = 50mb
AP : Poo-Po, the pressure drop of storm 1/AP = 0.02 = 2%
_US: speed of storm on shelf 5-mb error means 10% surge error
_ :angle from coast to storm track NOTE: SS should be superimposed with astronomical tide
at time of landfall. Use C&GS Tide Tables;
use MSL datum.

LAND

0 e, .e .

SEA e

g / ~~L AN Di

9 is measured from coast, seaward to track

Figure 4.--A form to obtain expected peak surge from precomputed
nomograms

speculative for storms crossing the coast with a small acute angle (i.e., for
0 = 0� or 9 = 180�). For different constraints, the motion factor FM will vary,
10
but in most cases only slightly ; we pragmatically accept the motion correction
as a working tool. This figure is our third and last nomogram to quickly
determine the expected peak surge. The product of Sp and FG (or FE) obtained

by use of the first two nomograms is multiplied by FM.

If we correlate the preliminary number, revised for shoaling and storm motion,
against the observed data points (appendix 1), the correlation coefficient is
0.85. i

4. EXAMPLES OF PEAK SURGE APPROXIMATION

To quickly construct the expected peak surge value, one must introduce three
nomograms; two of these require special orientation procedures. As an aid for
use with the nomograms, we suggest a computational form such as shown in figure
4. The form is broken into three parts. The first part, DATA, composes entry

0If basins have much steeper sloping depths than the standard basin -or the
vector storm motion is significantly different than standard, then FM as given
by figure 3 is exaggerated; the opposite is true if the basin slope is much
shallower than standard.

arguments for the nomograms. The second part, PRECOMPUTED VALUES, lists numbers
from the nomograms. The third part, CCMPUTATIONS, uses these numbers to compute
the peak surge value.

In the data part of the form, AP and R are self explanatory: these are
entry arguments for the first nomogram (fig. 1) to derive the preliminary number
Sp. This is then entered in the precomputed values part of the form.:

In the data part of the form, the geographical location of the expected peak
surge requires some explanation. We need this location for an entry argument
in the second nomogram (fig. 2) to extract the shoaling factor number FG or FE.
To find this location, we suggest.

1. Consider preselected geographical stations on the gulf and east coasts
(table 2 or fig.5); these stations are approximately 100 st.mi. apart.

2. Select the nearest station to the given landfall point; call it STAT.

3. Let the observer at sea face land with coastlines to his right and left.

4. Measure the distance in MILES from the station to the landfall point on
the coast.

a. Use negative MILES if landfall is left of STAT.
b. Use positive MILES if landfall is right of STAT.

5. Find MPR by adding MILES and R; this gives the approximate location of
the peak surge relative to STAT.

We enter the second nomogram at STAT; then move away from it the distance MPR
on the abscissa; if MPR is negative, then move to the left. Now move vertically
to the shoaling curve, then horizontally to the ordinate; read off the shoaling
factor number FG or FE* This is then entered in the precomputed values-part
of the form.

In the data part of the form, the angle e from coast to storm track requires
some explanation. We need this angle as an-entry argument for the third
nomogram (fig. 3); this is necessary to extract the correction factor FM for
arbitrary storm motion. We are not so much interested in the compass direction
of storm motion as we are in relative direction to the coast. The simplest way
to derive this direction is to measure it directly by protractor on a historical
or weather prognostic chart where the track is given; we remark that a tanget
line to the coast must be drawn at, say, landfall point. Here, the observer is
orientated so that sea is to his right and land to his left; he then measures
o clockwise from the coast to where the track terminates at the landfall point.
Note that the track can run from land to sea for exiting storms; in such cases,
* > 180�.

We enter the third nomogram with 0 and the storm speed US, and we read off
the correction factor number FM. This is then set in the precomputed values
part of the form. The remainder of the form is self explanatory.

Table 2.--Preselected coastal stations*

GULF STATIONS LATITUDE LOGITUDE EAST CST STATS LATITUDE LONGITUDE

PT ISABEL 26 05N 97 lOW MATCMB KEY 24 55N 80 39W
ARANSAS PS 27 5ON 97 03W FT LAUDRDL 26 07N 80 06W
MATAGORDA 28 21N 96 24W VERO BEACH 27 39N 80 21W
GALVESTON 29 16N 94 48W N SMYRNA BCH 29 02N 80 54W
CAMERON 29 46N 93 19W JACKSNVLLE 30 20N 81 24W
EUGENE ILE 29 21N 91 24W OSSABAW IS 31 46N 81 04W
GRAND ISLE 29 13N 90 01W CHARLESTON 32 44N 79 51W
GULFPORT 30 15N 89 00W MYRTLE BCH 33 41N 78 53W
PENSACOLA 30 20N 87 11W N RIVER IN 34 32N 77 20W
PANAMA CTY 30 07N 85 42W OCRCKE INL 35 04N 76 01W
PANACEA 29 59N 84 19W NAGS HEAD 36 01N 75 39W
CEDAR KEYS 29 IIN 83 02W ASSATEAGUE 37 54N 75 20W
CLEARWATER 27 59N 82 49W CAPE MAY 38 55N 74 54W
VORT MYERS 26 29N 82 10W SEA GIRT 40 08N 74 02W
EVRGLD CTY 25 45N 81 30W SHNNOK INL 40 51N 72 28W

*These location abbreviations are exactly as used for input to SPLASH.

T~~.- ~- ~D L I PE MA L

/ - - ~~~~~~~NAG NHA

Figure 5.-Selecte station on the glf and est coast

DATA PRECOMIPUTED VALUES
Cm&STORM: name of storm 2a_ S : the preliminary number
17f'/6?DATE : day, month, year enter figure 1 with argumentsAP and R
110" HOUR: local time of landfall /.2. FGIF : correction factor for shoaling
9 STAT: nearest station to landfall point enter figure 2 with argument STAT + MPR
see figure 5 for position of stations for location of peak surge on coast
-{6 MILES: distance to landfall from STAT 0.7 F : correction factor for vector storm motion
_ +MLE.... >|. Z -41<COAST enter figure 3 with arguments US and e
STAT SEA IeR* STAT
Is R radius of max Inds in miles, COMPUTATIONS
10 * R < 50 Y.Y 5S : the expected peak surge in feet
-I MPR : MILES + R, distance to peak surge from Ss = (20.).(I.23).(o.?7)
STAT SS FG FM gulf coast
/010 P mean ambient air pressure about storm S P east coast
sro p E
91O P.central pressure of storm 1/AP : relative surge error per mb error
_0 AP : Poo-Po, the pressure drop of storm example; AP = 50 mb
US : speed of storm on shelf AP = 0.02 = 2%
0 e- : angle from coast to storm track
5-omb error means 10% surge error
NOTE: SS should be superimposed with astronomical tide
at time of landfall. Use C&GS Tide Tables; use
MSL datum.

LAND

LAND
P, IudOmb Po- 9srab
e is measured from coast, seaward to track

Figure 6.--Completed computation form for the expected peak surge
value (hurricane Camille)

Hurricane Camille. One of the most devastatingll storms of record in the Gulf
of Mexico was hurricane Camille, 1969. For quickly computing the expected
peak surge for this storm, we used the form shown in figure 6. In the DATA
part of the form, the storm parameters were subjectively assembled from bulletins,
advisories, historical weather maps, etc.;12 official values for these parameters
may be somewhat different. In the lower right-hand corner of the figure, we
give a pictorial description of the meteorological parameters and geographical
orientation of the storm reaching land. The computed peak surge value on the
form is 24.4 ft; the astronomical tide at the time of landfall was negligible.
This compares favorably with the highest observed tide of 24.6 ft near Pass
Christian, La. We remark that different storm parameters may alter the computed
peak surge significantly; for example, a 5-mb change in the central pressure
means a 5-percent change in the expected peak surge.

11Hurricane Carla, 1961, might also share this dubious honor. Although not
as intense as Camille, its much larger size generated significant surges along
a remarkably long length of coast.

12The storm appeared to be filling as it approached the coast; hence, the
mean central pressure on the shelf was used.

16
DATA PRECOMPUTED VALUES
a STORM: name of storm /9.2 S : the preliminary number
!/Y-#DATE : day, month, year enter figure 1 with arguments AP and R
H8lo HOUR local time of landfall : 67 F"GPE correction factor for shoaling
ta.fS5 STAT: nearest station to landfall point enter figure 2 with argument STAT + MPR
see figure 5 for position of stations for location of peak surge on coast
MILES: distance to landfall from STAT 1__3 F : correction factor for vector storm motion
M LES l>|-----MILE COAST enter figure 3 with arguments U and
, ~COAST S anda
SEA " MILES+R
/ R : radius of max winds in miles, COMPUTATIONS
10 < R < 50 4. SS : the expected peak surge in feet
3 MPR : MILES + R, distance to peak surge SS = (/s.Z). (o.~T), (I.o)
S F
from STAT S FG FM gulf coast
/O/zP~ : mean ambient air pressure about storm S FE F east coast
Poo p E M
:c central pressure of storm O.X6 1A
i~ ~~PO~ : central pressure of storm I1/ AP: relative surge error per mb error
P oo =-Po, the pressure drop of storm /5 example; AP = 50 mb
U speed of storm on shelf I/ AP = 0.02 = 2%
/02 e: angle from coast to storm track 5-mb error means 10% surge error
NOTE: SS should be superimposed with astronomical tide
at time of landfall. Use C&GS Tide Tables; use
MSL datum.

LAND
NORTH

e 5- AND I -j= ARANSAS PASS

= SEA _
e - SEA ~~~~~~LAND I2/~p~\

:=945mb
SA

-oe: 1014mb
e is measured from coast, seaward to track

Figure 7.--Completed computation form for the expected peak surge

value (hurricane Celia)

Hurricane Celia. A noteworthy feature of this storm was strong deepening of
the central pressure prior to landfall. It is possible to program meteorological
parameters as functions of time if such complexity is desired. Forecasting them,
however, is problematical; and it is not easy to portray all combinations in
simple and convenient form. What must be understood is that parameters varying
strongly with time, in comparison with their mean values while the storm tra-
verses the shelf, sometimes can generate larger surges. Most storms reaching
land transverse the shelf quickly; thus, the parameters change insignificantly
with time except, possibly, the central pressure. Accordingly for deepening
storms, it is suggested that while the storm is on the shelf, the lowest central
pressure be used.

For quickly determining the expected peak surge for Celia, 1970, we used the
form shown in figure 7. In the data part of the form, the storm parameters
were subjectively assembled as for Camille. The computed peak surge value on
the form is 9.1 ft; the astronomical tide at the time of landfall was 0.3 ft,
thus making the expected peak surge 9.4 ft. This compares favorably with the
highest observed surge of 9.2 ft on the open coast. There were some higher
surges 7 mi inland from the open coast, but our model does not consider local
inland effects.

x/ /,////: / .. . 7/'//7J~D ~,/7/, ~/ 7///'7 ""

COAST

/ - -~ OCEAN DEPTH CONTOURS " '"..

/ N \
I\

S TORM TRACKM

e LOCATION OF PEAK SURGE R RADIUS OF MAX WINDS
- LANDFALL POINT Ds DISTANCE TO PEAK SURGE

Figure 8.--Qualitative illustration showing the varying poiatiOus of peak surge
on the coast as compared with two-dimensional bathymetry

5. COMMENTS ON APPROXIMATING THE PEAK SURGE

We should be aware of limitations when using precomputed nomograms to fore-
cast the peak surge. Some of the limitations are as follows.

A. Locating the Peak Surge on the Coast

If the storm track is about normal to the coast, then the peak surge will
occur at a distance roughly equal to R, to the right of landfall (as viewed
from the sea). We use this rule as a working criterion even though the peak
surge position will vary for two reasons.

1. The distance to peak surge from landfall (call it D.) is a function
of the vector motion of the storm relative to the coast.

2. If the local bathymetry varies considerably about the landfall point,
then DS also varies. Figure 8 describes this phenomena pictorially.

We make no attempt to apply these two phenomena (or other more subtle ones);
the interrelations are too complicated for convenient expression. We point out
that a landfall position on a steep portion of the shoaling curve of figure 2
will not only distort and stretch the surge profile but also relocate the peak
surge on the open coast. Thus whenusing nomograms, the peak surge determination
could be significantly in error. Generally, the absolute error IDs -R I is
not large compared with R. More important, the predicted landfall error in most
cases is much greater than [Ds - R 1. If there is a desire to locate the peak
surge and its value more precisely on the open coast for a particular storm,
then the dynamic model should be run on the computer directly to find the storm
surge profile.

B. Correction for Variation of Latitude

The variation of storm surges due to variations in latitude is generally
less than 10 percent for storms reaching land between 150 and 45'N. Because
of this rather small variation either side of latitude 30'N, it was, decided
to incorporate latitude corrections directly with the shoaling curves of figure
2. The incorporated correction i's not exact when the actual storm is greatly
different from the storm used in the figure, but the sign of the correction is
always proper.

We point out that for constant AlP and R, the wind speed decreases (increases)
with increasing (decreasing) latitude; similarly, for a constant wind profile,
the AP' increases (decreases) with increasing (decreasing) latitude. These
effects are due to variations of the Coriolis parameter with latitude.

It is of some consequence whether we used a fixed maximum wind or a fixed
pressure drop when computing the shoaling factors for a figure 2- type nomogram
that incorporates changes in latitude. This is because the small changes caused
by the Coriolis parameter can be opposite in sense. In most cases, pressures
are more readily ascertained than wind; therefore, we suggest that Al' be fixed
and the winds permitted to vary with latitude. The user need not concern him-
self with winds; insteadhe uses the pressure drop at or near the time of land-
fall--the wind effects are taken into account automatically.

C. Correction Factors

The three nomograms (figs. 1-3) form an ad-hoc system for quick determination
of useful numbers for the peak surge. -These nomograms are not independent. While
generally they are only weakly dependent, the dependency in isolated instances
is sufficiently significant to yield sizable errors in the expected peak surge.

Why are the nomograms interdependent? The shoaling factors FG, FE for non-
standard basins were computed using the convenient assumption that all storms
of a given size move with standard vector motion; but for the storm motion
factor FM for nonstandard motion, it was assumed that all storms have a given
size and traverse a standard basin. What this means is that the meteorolog y
and basin under consideration with a given storm must not be too far from
standard and that the storm size R must be between 10 and 50 mi.

if the correction factors are considered to be first order, then the dependency
between the nomograms is second order. We would like to give methods and values
for higher order corrections, but the relations are no longer simple.

Such a complication is now discussed. In the nomogram of figure 1, in which
all storms are assumed to travel with standard motion, we notice that, for a
givn A', he relminry umbr .p reaches a maximum at a critical of about
30 mi. This means that, for given travel speeds, we must concern ourselves with
critical storm sizes; similarly, for a given storm size, we must concern our-
selves with critical speeds. The critical situation, however, will vary as
the geography of the continental shelves varies. This type of torturous feed-
back--one of many--makes it difficult to arrive at simple generalized methods
f or higher order corrections.

One possible method is to eliminate the nomogram for shoaling factors.
This can be done by constructing particular nomograms for S p and FM at selected
points of interest on the coasts; of course, the motion factor charts of FM
should be constructed for storms of different sizes at each of the coastal
points.- Tn this way, the second-order corrections would be partially eliminated;
but the effort and cost of'doing this is staggering. Instead, we settle for
warning the user of where to expect weaknesses when using these nomograms.

A quick and easy but not foolproof way to spot suspicious situations is by
use of the shoaling curve. If you ascertain that the peak surge occurs near
one of the troughs or crests of the shoaling curve, the shoaling factor de-
vi ates significantly from 1.0, and the vector storm motion is significantly
different from standard, then the correction factors may be amiss.

We can avoid these uncertainties by direct machine computations that can be
made for particular storms reaching land at particular coastal points. A method
for doing this is described in section 6.

6. USING THE COMPUTER TO DISPLAY COASTAL STORM SURGES

The expected peak surge value, alone, gives no information as to how much
of the coast will be affected by surges. We need coastal storm surge profiles,
varying with time, to determine this. For operational conditions, direct com-
puter computation using SPLASH is suggested. The mechanism for running this
program is described in appendix 2; some limitations on the use of the re-
sulting open coast surge profiles are described in appendix 3. Note that
SPLASH is accessible for use in operational field forecasting.

Because local high water along An affected coast does not occur simulta-
*neously with the peak surge, we must consider time variations in the profile.
With the versatility of the computer, we can display the profile at successive
times before and after the time of peak surge or display surge history at
selected points on the coast, or both. For forecasting, we are more inter-
ested in high water heights along the affected coast than in time history;
therefore, when using the computer, we settle for the envelope of coastal high
water heights, disregarding the time of occurrence of local high water.

A. Displaying Storm Surge Envelopes by Computer Output

An example of a programmed computer output is shown in figure 9. The graph
displayed is the envelope of coastal high water heights for a storm reaching
land.

The printed message beginning the output is a resume" of storm parameters
selected by the programmer. For information, we also print out the maximum
wind of the storm. This is a sustained, average wind for a stationary storm;
as such, it should not be used for forecasting.13
The next message gives factors to update surges for a variation of the pres-
sure drop, AP. This factor corrects heights on the surge envelope if alternate

'3This wind should not be confused with the "fastest mile" wind tha t is
about 1.3 times greater.

pressure drops are used. The range of updated pressure is +10 mb; it is in-
cremented in 2-mb steps and added to the original pressure drop. We remark
that it is unnecessary to rerun the program for small errors in pressure drop;
the user merely multiplies the envelope surge heights with the correction
factor for the updated pressure estimate.

The vertical scale of the graph is 20 ft. If the peak surge exceeds this,
then the ordinate is rescaled to 40 ft.

The horizontal scale of the graph is 600 st.mi. long; it represents the coast
on a straight line. The dots on the scale are 4 mi apart. On alternate dots,
highest local surge heights are printed in feet. Just above, and near the
middle of the scale, is a symbol -*--.; this represents the landfall position
on the coast. Left and right of landfall, and below the dots, are linear
distances in statute miles; below this are selected cities as they lie along
the coast. The center of the horizontal scale is tangent to the natural coast;
as such, it distorts and compresses distances on the curvilinear coast. This
means that the printed distances away from the basin center are smaller than
the actual curvilinear distances along the coast.

The graph itself is portrayed with asterisks. Only positive surges are
printed. Negative surges do occur on the coast; if such information is desired,
it could be displayed by a snapshot of the surge profile against time (i.e.,
a time history of the coastal surge). With storms reaching land, however,
time surge profiles are less interesting operationally than the envelope of
high waters. We cannot give a complete envelope because computations are
terminated 3 to 9 hr (depending on storm speed) in real time after landfall
occurs. This means that heights computed along the trailing ends of the en-
velope are slightly smaller than those that would be obtained with an infinite
real-time run, especially for very slow storms traveling nearly parallel to
the coast. Note that the ends of the envelope occur some distance from land-
fall where the effects of curvilinear coasts can become significant.

For operational planning, without resort to extensive recomputations, it is
desirable to form an estimate of the surge if landfall occurs at a point other
than the one originally forecast. To do this, we assume the original storm
can strike anywhere on the coast, with the same constraints as for the original
landfall.l4 We only need to compare the relative shoaling factors given in
figure 2; the original envelope is then restructured with these relative
shoaling factors.

The three horizontal scales that appear below the column of cities all display
approximate surge heights. The first two give envelope surge heights for the
storm reaching land 100 mi to the right and left of the original landfall.
The last scale gives potential peak surge heights everywhere on the coast
(i.e., a worst case estimate for each point on the coast). Note that when
using the last scale, the peak surge is at about distance R to the right of
the assumed landfall; exceptionsl5 would be coastal areas where there are

14This means that the track orientation is always the same relative to
coastal orientation at landfall point (i.e., 9 of fig. 3 is constant).

5An example is given in appendix 3B, under the discussion of deltas and
hurricane Betsy, 1965.

YOU HAVE SPFCIFIED THE FOLLOWING STORM PARAMETERS
--LANIOFALL POINT IS�--------------------------6 MILES LEFT OF ---GULFPCRT-
THE STORM TS MEVING TO THE�--------------------NNW AT 12.0 MPH
THE PRESSURE OF[P IS�100--------------------- o )O0S.
-THE-RADIUS OF MAXIMUM WINO IS�-------------------15.0 STATUTE -l-LtES-
THE MAXIMUM (SUSTAINED) WIND IS�13-----------------6a.7 MPH
THE MAY WINO IS DERIVED FOR A (STATIONARY) STORM
N NUSING THE INPUT STIORM PARAMETERS ---

IF YOU WANT TO UPDATE YOUR 100 PR PRESSURE DROP, USE THE FOLLOWING CORRECTION FACTORS ON THE COMPUTED SURGE VALUES

UPFITEWVREPSSVWE DROP 90 92 194 96 98 ten 102 - 14 - -115 108 Ito11
CORRECTION FACTOR .89 .92 .93 .9A .97 1.10 1.01 1.04 1.05 1.08. 1.19

STORM SURGE HEIGHTS (FEET)
35 30 25 20 Is 10 5 0

______ .5 . . ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~26.0
1.2 0.0 n-.

1.4 0.0
.6 .. 21.8
2800 1.4 -.
4 .7 .. 21.2
1.5 - 0.
.7 .. 22:-2
1.0. 0 .0 2 -1
* .7 . . 23.1
* 7 . . 23.4
: 8 .. 22:9
24 0ST MARKS - 2.1 0.0
.7 .. 22.5
2.1 0.0
.7 CARRARELLE .. 21.1
2.0 0 :0
.7 .. 19.8
APPAL ACHI . 1.9 .4
.8 .. 18.2
1.8 .:4
2 00 1.7 .4 1 :

* 8 . . 13:2
PANAMA CTY 1.9 .4
.8 .: .3 11:8

.7 ~~~~~~~~~~2:5 10.
1O 4 .~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~8 *. 10.5
. 60 FREEPORT 3.2 .3
.8 . . ~~~~~~~~~10.1
4.3 .3
8 VALPARAISO 5.6 .3 .
.19 . . 94
6.9 .3
0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: 9.5

4 1.0 12. 10.1 : o3

1.2 PENSACOLA 5 11.3

i: 3 ~ ~~~~ 7.6 :6 i2
1.6 .. 12.9
M: IFLIN 4.1 .813
4~~~~~~~~~ 2. . 1.
4 2.5 . . ~~~~~~~~~~~13.5
* ~~~~~ ~~3.2 .. 13.9
* ~~~~ ~~~~~4.5 MOPILE . 4.4
0.0 1.1
4 6.6~~ ~ ~~~~ ~~~~~~~~~~~~~~ : o 1:4 1.
4 ~~~~ ~~~~~~~~~~~~9.9 PASCAGOULA .. 17.1
�40 40 0.0 1.6
14.~ ~ ~ ~ ~~00 1. i8.8
4 19.1 . .~~~~~~~~~~~~~~~~~~~~~e 21:9

25.0 .. 25.:0
GULFPORT 0.0, 2.7
24.6 .. 27.2
0.:0 2.93
22:3 PS OHRSTAN . . 28.7
4 1 1~~~~~ ~~~~~~~~~~~~~~~~~~8.2 . a. : 30:2
0.0 34.8
4 ~~~~~ ~ ~ ~ ~~~~~~~9.8 i . 1.

0.0 6.0 3.
0. a 30.0
HOPEDALE 0.0 6.4
- 0 40 0.0 7.125

PT PLEASNT 0.1' 8.4,

* 0.0 0.0 �1:4 �~~~~~~~5:1
. - . : 010 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~GRAND ISLE 0.0 12:93 14.

TIMBALP IS0.0 1.
0.0 ~~~~~0.0 1.
______~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-~ 0: 0. .2 1.

0.0 7.3 ~ 3i.

EUN IL20 0.0 0.2

C - ~~~~~~~~~~~~~~~ 0.0 ~~~~~~~~~~~~~~: a 30.5
(1 4 0.0 . . ~~~~~~~~~~~~~~~~~~~~310
YSWR PASS 0.0 0.

.3 * 0.0 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 0.

0.0 0.0
16~ ~ ~~~~ ~~20 0:0 0:0 3:

SWD PASSR 0.0 .
10 I, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.~~~~~~~~~~~~~~0 a 22.6-

4-.. 0.0~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~AE 0.0 a .0
.o~~~~a,,.os,~~~~~~~~~ . -~0 20 4. 00 25:2
a 00 2 i53.

SABIHNRE F S0.0 0.0
0.:0 .. 22.1

- 0240 0. .

HOURLY VALUE~~~~~~~~~~~~~~~~~~~~~~SAR9 INTE 12 0.0 BEOR.0 z
le "Kb AF TE~~~~~~~~~~~~~~~~~~~ 0.0MTE Tf F L ADFL.0
ESTIMATED~~~~~~~~ LADFL 01i 00 L0 ST TIM 1 7 AU 0.09 0.0ADTMEO ANFL

L~~~~~~:L~~~~ ~= 0.0: .Z .4i 2 7 4Li 5 i4 i; i 7 1 ; 20.8

PASC GOU A .3 .4 .4 .4 .~ ~ ~ 4 0.0 .-2 .2- A a : 04 :

10., -1K AE0 655 10 TI OFLNDAL

PRTsTJO .2 . .3 .4 .4 . 3 .3 . 2 .2 1 .1 .1 .1 . 2 .2 .3 .3 .3 3 .3 .3 .3 .3 .4 .4' :
P15 0A ENi .2 .2 .3 .3 .3 .3 .2 :2 .1 . .1 .1 .1 .2 .2 .2 .3 32 .3 .2 .2 .3 .3 .3 .16

LUbhNE 15 -5 . -.6 -.i .1 .,I .5 .b . .4 . L -.1 -.4 -.5 -.5 -.3 -.1 .1 .3 .5 .5 .5 .4 .2 .1
S OO--O TtrcUrI rn. Sr- IADU

Figure 9.--An example of the computer output by SPLASH. The graph is the computed envelope of open

coast high waters generated by hurricane Cami~lle, 1969.

severe changes in horizontal depth contours on the shelf.

In figure 9, for the particular basin used, the peak surge varies by more
than a factor of 3 on the last horizontal scale; this indicates the signi-
ficance of local bathymetry in surge generation and hence the importance of
landfall position.
Beneath the displayed graph, there is a printout of astronomical tide levels
for selected stations for 12 hr before and 12 hr after the predicted time of
landfall. The stations correspond to the cities listed on the graph above.
Tides are predicted in feet above MSL.16,17

In principle, we could combine astronomical and meteorological tide for a
total tide envelope. Although this appears to be a sensible procedure, such
an envelope would be misleading. A display of this nature is meaningful only
if we have an accurate knowledge of landfall in space and time and an accurate
knowledge of the meteorological parameters; we just cannot forecast meteoro-
logical occurrences to the accuracy required. Neither would it be meaningful
to display envelopes including highest and lowest expected values for a range
of meteorological accuracy with time; the range between the two envelopes
could be so large that the information would be almost useless.

The separate displays of surge envelope and tide forecasts allows the surge
forecaster to correct for revisions in meteorology (i.e., he can update the
surge prediction as his input data improves with time without constant re-
running of the program).

Hurricane Camille. This storm was discussed previously when we computed the
peak surge only with precomputed nomograms. To illustrate the envelope of
high water heights, with peak surge and its position on the coast, we compose
the data deck of figure 13 (appendix 2) and let SPLASH print out the computer
display of figure 9. In the figure, we have transferred the storm surge
envelope to the inset of actual observed high water for comparison. At the
time of landfall, the astronomical tide was miniscule; its diurnal range was
less than a foot. For this reason, it is ignored.

The observed and computed curve seem to fit reasonably well except in the
vicinity of peak surge. One could argue that the landfall position was slightly
to the left of the computed position, that the storm size could be smaller,
that observed values are not on the open coast, etc. We leave it to the reader
to judge the results of the computed envelope.

16By "above MSL," we mean the tidal computations--for the rise and fall of
the tide plus the annual variations of sea level--are with respect to a zero
"datum"; thus, the computations can be added to any other datum. The datum
used in the tide tables for the east and gulf coast stations is MLW (mean low
water). The datum for contours on terrain charts is usually geodetic MSL; this
does not always coincide with local MSL. For practical purposes, we can
assume that the difference between geodetic and local MSL is very small; hence,
our total tide--meteorological plus astronomical--can be compared directly with
land contours for a measure of inland inundation.

17We use a tide program developed by Pore and Cummings (1967). The specific
application here was developed by Lt. R. Garwood, NQAA Commissioned Corps.

Because Camille caused a record peak surge on the coast of the United States,
it is interesting to know what the computed peak surge could be in surrounding
coastal regions. The last horizontal line of figure 9 is a printout of po-
tential peak surges on the coast if Camille had struck elsewhere on the coast
and in the same relative way.

Hurricane Gracie. This particular storm is discussed to show the importance
of the astronomical tide. The surge computed by SPLASH, tide predictions,
and observed high-water marks are shown in figure 10. Meteorological data for
this storm were supplied by the Hydrometeorology Branch, Water Managepnent In-
formation Division, NWS, NOAA.

The storm made landfall at Charleston, S.C., at 1100 LST when a low astro-
nomical tide of -2.3 ft MSL existed in the landfall area. This means that
the total peak surge was computed to be about 13.5 ft MSL (15.8 ft computed
plus a low tide of -2.3 ft). The highest observed high-water mark was 11.9 ft
30 mi southwest of Charleston, but there may have been higher, unobserved
surges to the northeast. The nearest tide gage to the landfall point was
Charleston, and the highest surge of 5.9 ft occurred there at low tide; thus,
computed surge becomes 9.3 -2.3, or 7.0 ft MSL. This agrees reasonably well
with observed values in the Charleston area.

Consider now the observed values of 8+ ft in the Myrtle BeachS.C., area.
Note, particularly, that these values were measured by tide gages at 1700 hr,
the time of high astronomical tide. Our computed values plus astronomical
tide were about 4 ft lower than those observed. We will always have such
problems at the ends of the envelope because:

1. Our model is designed to be most effective in the area of landfall
and during landfall time.

2. Our computations, for economic and computational reasons, are terminated
3-9 hr after landfall, depending on storm speed. Hence, the ends are not
completely representative.

3. The ends of the envelope, such as the area near Myrtle Beach in figure
10, are about 150 mi from the landfall point. Hence,

a. curvilinear coastlines become significant, and

b. the ends of the envelope are close to a fictitious lateral boundary
in the basin where false wave reflections may play a part.

4. The surges at the ends of the envelope are sensitive to storm size R,
a length difficult to observe.

The point is that high and low astronomical tides can superimpose separately
on sections of the storm surge envelope.

.- 40 0.0 -.1
9 .3 C:H~R ST N Ii 16.1

14.8 5 157
15 .8 .: 5 158
* )~~~~~~~~~~~~~~~~~~~~~~~~I :115 .. 16.0

3.:9 ... 16 .2
HUNTING is 0.0 1.9
1.7 FRPPS INL . . 164
0.:0 2.3
.1 PARIS IS .: .: 16.7

a 0. 0 0 17.1i
0~ ~ ~ ~ ~~ ~. 3.is

-40 BA IS REN 0:0 4i:4 1:
0 0 0 : a I 5:0.0 6.0
0.0 .LBDC : .'~ 8.7 .
0 0.0 2 6 2 6 1.4
0 0. . 201

-80 BRUNSWICK 0.0 4 19.9.
0.:0 I 8 206
0:0 JEKYLL PT ~00 a 20.6 7:
-12 0.0 i i:20.
FRNNON BCH 0.0 14.5
*~~~~~~~~APR 0.0 0. i4:i 9.
JARUNSWICK 0.0 C : 4.7
* ~ ~~~~~ ~ ~ ~ ~~~~~~~ 0. 0 . 8.
- 16D n a o .0 1.
0.0 JEYS T A U I 17.3
-120~~~~~ ~~~~ 0. 0 .1
* 00 . 0 1.2 :
FLGRNN BCH 0.0 0.0
0.0 a.: i t 5.9
MaYP 0. 0.09
0.0 9 a 14.10
a0.0 it :73.
a 0 ~~~~~~0.0 a 0.0 i:
a 0. 0 a 12.8

-140 0.0 0.'0
0.0 STAG N:..12.
* ~ ~~~~~ ~ ~ ~ ~~~~~~~~ 0. : . 2.
0 o ~~~~~~0.0 :0.0

N ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . V . 1.
H(UPLY~~~~~~~ ~ ~ ~ ~ ~ ~ ~ 0.0UF E. PRNE 121.9PPRFT
12 MRS AFTER ESTIMATED TI-M E O F L A N D F A L L ~ ~~~~-2000.0 .0
ESTTMATCO LAN)OFALL TTAF ~ ~ ~ ~ ~ 10.0 LO S IE,2.E 11.7ETMAE IEOFLNFL

LCL S~n TIMP 23 ?1+ 1 2 3 4 5 6 7 8 9 1 It i2 13 14 i5 16 17 18 19 20 0.022.2
NEWRV NL-1. -7 -1 6 1 21 .6 . 1. 4 .8 .1 . -1. -ti . 8- 0.0 12 .32.018 . 2 44 . 0 11.3
GP FER - . 6 -13 . 1. I1. 82. 22. 1 . 67 - 3-i.3-I~q-1. 9-1 .3 3 . i.92. 52.7 23 1. 4 -0.0.7-0.0
MYRL CH-18 - . 0t. 2 U .5 .41 . 93 i. - . -2.2 i. 4 2i .90.0 .7 1 8 6 -8 �1.3- .
WNYH ENT- t 7 - . I 0 1 I i~ 9 2 2 2 2 i7 8 -i.3-I~q-2 .0 - . 4 39 1. 2.62.8 .4 i. 5 0.01 020
CHRSTN* -.V- 1.13 5 .7 . 72 .4 2. 2 2 . 3-1 0 -.9 2 3 2. 0.0 4 .63 02 .2 .2 105 2.2
FRPPSINL -.5 -20 -. .7 20 2.93.1 27 i. .4 -.0 -22 -2. -2. -1.4.2 1. 3.1 .7 35 2.71.4 -a0.0. 020
SA PEN- 2. -2 4 I. 52.0 .i .5 .1 . .7 .9-2. - .0 29 1. - I1 70.0 4 04.0 . 1810.1I. -.
BL~qD C ? 5 2 5 -.8 i 2 . 3.2 3. 22. 1 4 0 1 . -?6 -2. -2 4 . .72 .4 3 5 -2405 .50.00 -.7.0.

TPIDE R HE TTF APREFT AOVT ON S ET F A LVALAL

MOU~~LY V8LUFigr IO.-Sm PaIsE fiur 9OS Bexcep tiisf o r h r i a e Ga ,15

YOU HAVE SPECICIEO THE FOLLOWING STORM PARAMETERS
LANDFALL POINT 1�------------------------36 MILES LEFT OF CHARLESTON
THE STORM IS MOVING TO THE ------------------- NW AT 14.0 MPH
THE PRESSURF DRIP IS ----------------------------------------75 MS.
THE AOTIUS OF jXINIUN W~IND4 IS------------- - i2.0 STATUTE MILES
THF MAXIMUM (SUSTAINEO) WINO IS 121.8 MPH
THE MAX WINDO IS DERIVEO FOR A (STATIONARY) STORM
ON USING THE INPUT STORM PARAMETERS

IF YOU WANT TO UJPONTE YOUP 75 M9 PRESSURE DROP, USE THE FOLLOWING CORRECTION FACTORS ON THE COMPUTED SURGE VALUES

UPOATEO PPESSURE DROP 65 67 69 71 73 75 77 79 81 83 85
CORPFCTIDN FACTIP .86 .8q .91 .94 .97 1.00 1.03 1.05 1.08 1.12 1.13

STORM SURGE HEIGHTS (FEET)
15 10 5 0
� .2 .0.8
.2 ~~.3 0.0
32 *9.2
d .3 0.0

� * .2 o.9
1013. .3 0.0
4 .2 � 8:9
03 0:0

0~~~~~~ .~~~~~2 4 a . ' 9.0
.4 0.0
I,~~~~. . . 9.2
/�e~~~~~ .280 .4 0.0
4l~s i g .2 OP LOOKOUT :0 9
.5 .
.2 9 7

.6 0.0
.3 10t.
SWANSODRO .7 0.0
.3 ii~.
.3 NEW RV INL 12.0
.9 .2
.4 12.5
1.0 .2
.4 13I1
44 13.1
1.1 :2
* .4 . . 13.1
n. ~~~~~~~~~~~~~~~~~~~~~1.2 .2
.5 13.0
200 1.3 .3
.5 WILMINGTON 13.0
1.8 .3
.6 .. 13.0
d ~ 1.8 .3
CP FEAR 2.2 .3

,7~~~~~~~~~: 134
i t .7 ia~~~~~~~~~~~~~~~~~~~~~~i1.
2.7 13
1:2 Y.8 B C 13.5
. 160 3.4 .4
.8 13.8
MURRLS INL t4.6 .4
.9;. 14.3
6.3 .4
1.0 14.7
8.7 .4
*1.1 .. 1.
11.8 .
1.2 MYRTL BCH 16.0
120 15.5 .5
41.4 .. 16.6
MURPLS INL 16.8 .6
1.6 17.0
) 12.4 .6
1.8 4 . 17.5
C 4.3 .7
2.1 WNYH B ENT . 17.6
1.A .8
2.5 . 17.6
29 .2 .9
CP ROMAIN 0.0 .9
3.5 17.3
0.n0 n,

7. FURTHER COMMENTS AND CONCLUSIONS

Our dynamic storm surge model is only a first approximation for coastal
surge phenomena. It is designed specifically for the open coast surge and
assumes idealized conditions. These meteorological, geographical, and math-
ematical idealizations limit the model both for operations and research.
The meteorology for our storm model presupposes a moving steady-state
storm; we describe it with parameters that are invariant in space and time
(as the storm moves). It is a rather naive, simplistic model that needs im-
provement. Even so, a plethora of dynamic surge activity was extracted by
using the storm model of this study. Operationally, it is pointless to use
variable or changing storm parameters because currently they cannot be measured,
much less forecast reliably. We can, however, easily incorporate variant
parameters in the model for special studies, if so desired.
There are many interesting surge phenomena to be explored by means of pa-
rameters that vary in space or time. Meteorological observations, however,
are just not available that describe wind and pressure changes on the entire
sea surface while following the storm . There are some gross indications such
as central pressure changes with time, forming or decaying double eye structures,
etc.; but none of these are directly useful for description on the entire sea
surface affected by the storm. It is tempting to extend the surge model by
experimenting with variant storm parameters to see if the storm surge pre-
diction would be significantly different. We are, however, in no position at
this time to specify continuous dynamic changes in a storm as it moves within
surrounding meteorological systems, across land surfaces, or across sea-surface
temperature changes, or for more exotic situations such as cloud-seeding
operations.

We point out that improvements in surge forecasting rest on improvements in
meteorological data input. More sophisticated models for surge dynamics will
not help operational forecasting if the meteorological data are not of the
same quality. As an example, consider what a missed landfall point means for
an unbroken versus a broken coastline:

1. On the unbroken coast, the surge envelope Is merely translated to the
new landfall point, with a relative amplitude correction for shoaling. The
distortion of the envelope is not great unless the bathymetry about the new
landfall point is drastically different.

2. On the broken coast--say, for a bay or estuary--the dynamics are entirely
different, depending on which side of the broken coast the storm lands. it
would not pay to make elaborate computations of the surge inside a bay or es-
tuary for a storm forecast to move onto one side of the broken coast, but
which in fact moves onto the opposite side.

For storms moving alongshore, no operational scheme has been designed for
surge computations. We prefer to delay development at this time because the
techniques required are much more complicated than for storms reaching land.
Moreover, the results are quite sensitive to meteorologiczal parameters (i.e.,
storm tracks are difficult to ascertain even in a climatological sense). These
storms, moving at or nearly parallel to the coast, can generate specialized
wave phenomena that, under certain circumstances,, could be threatening if not

disastrous. The surge dynamics generated by these storms sometimes can be ex-
ceedingly complex compared with storms reaching land; however, such surges
generally will be smaller in amplitude. Before going operational with these
storms in the surge model, it is advisable for the surge forecaster to learn
something about wave mechanics. He then can select storm parameters with a
practiced eye on how they generate wave phenomena in a particular basin.

The surge model is neutral on the selection of storm parameters by the user;
it makes no protest unless certain bounds are exceeded. This means that almost
any number (for, say, the peak surge) can be computed depending upon meteor-
ological input data. Because data from past storms at any selected point on
the coast are sparse or even nonexistent, the way is open by any individual to
supply processed data from climatology. We point out that the model is no
better than the quality of the data used. The user should be careful and sus-
picious of broad, highly smoothed data from long stretches of space about the
coastal area of interest; these may no longer be representative of meteorological
conditions for particular problems under study.
ACKNOWLEDGMENTS

I am deeply indebted to Dr. Albion Taylor for his many helpful suggestions,
technical help in designing the computer program, and the many friendly hours
of discussion on storm surge hydraulics. Appreciation is expressed to Lt.
Roland Garwood, NOAA Commissioned Corps, who developed the astronomical tide
program used in this paper. Special thanks are in order to Mr. Herman Perrotti
for the graphic arts. Work on this project was supported in part by the
National Science Foundation (NSF) under Grant AG-253, "NOAA Participation in
the International Decade of Ocean Exploration (IDOE)."

REFERENCES

Conner, W. C., Kraft, R. H., and Harris, D. Lee, "Empirical Methods for Fore-
casting the Maximum Storm Tide due to Hurricanes and Other Tropical Storms,"
Monthly Weather Review, Vol. 85, No. 4, Apr. 1957, pp. 113-116.

Cry, George W., "Tropical Cyclones of the North Atlantic Ocean: Tracks and
Frequencies of Hurricanes and Tropical Storms, 1871-1963," Technical Paper
No. 55, Weather Bureau, U.S. Dept. of Commerce, Washington, D.C., 1965,
148 pp.

Graham, Howard E., and Hudson, Georgina N., "Surface Winds Near the Center
of Hurricanes (and other Cyclones)," National Hurricane Research Project
Report No. 39, Weather Bureau, U.S. Dept. of Commerce, Washington, D.C.,
Sept. 1960, 200 pp. (see p. 123). i

Harris, D. Lee, "Hurricane Audrey Storm Tide," National Hurricane Research
Project Report No. 23, Weather Bureau, U.S. Dept. of Commerce, Washington,
D.C., Oct. 1958, 19 pp.
Harris, D. Lee, "Characteristics of the Hurricane Storm Surge," Technical
Paper No. 48, Weather Bureau, U.S. Dept. of Commerce, Washington, D.C.,
1963, 139 pp.
Harris, D. Lee, "An Interim Hurricane Storm Surge Forecasting Guide," National
Hurricane Research Project Report No. 32, Weather Bureau, U.S. Dept. of
Commerce, Washington, D.C., Aug. 1959, 24 pp.

Holliday, Charles, "On the Maximum Sustained Winds Occurring in Atlantic
Hurricanes," ESSA Technical Memorandum WBTM-SR-45, Weather Bureau Southern
Region, Environmental Science Services Administration, U.S. Dept. of Commerce,
Fort Worth, Tex., May 1969, 6 pp.

Hoover, Robert A., "Empirical Relationships of the Central Pressures in
Hurricanes to the Maximum Surge and Storm Tide," Monthly Weather Review,
Vol. 85, No. 5, May 1957, pp. 167-174.

Jelesnianski, Chester P., "Numerical Computations of Storm Surges With
Bottom Stress," Monthly Weather Review, Vol. 95, No. 11, Nov. 1967,
pp. 740-756.

Jelesnianski, Chester P. (Techniques Development Laboratory, National Ocean-
ographic and Atmospheric Administration, U.S. Dept. of Commerce, Silver
Spring, Md.), "Resonance Phenomena in Storm Surges" (unpublished manuscript),
1970, 30 pp.

Myers, Vance A., "Joint Probability Method of Tide Frequency Analysis Applied
to Atlantic City and Long Beach Island, N.J.," ESSA Technical Memorandum
WBTM HYDRO 11, Office of Hydrology, Weather Bureau, Environmental Science
Services Administration, U.S. Dept. of Commerce, Silver Spring, Md., Apr. 1970,
109 pp.

Pore, N. A., and Cummings, R. A., "A FORTRAN Program for the Calculation of
Hourly Values of Astronomical Tide and Time and Height of High and Low Water,"
ESSA Technical Memorandum WBTM TDL-6, Techniques Development Laboratory,
Weather Bureau, Environmental Science Services Administration, U.S. Dept. of
Commerce, Silver Spring, Md., Jan. 1967, 17 pp.

U.S. Army Corps of Engineers, "Report on Hurricane Betsy, 8-11 September 1965,"
Engineer District, New Orleans, La., Nov. 1965, 47 pp.

Weather Bureau, "Survey of Meteorological Factors Pertinent to Reduction ot
Loss of Life and Property in Hurricane Situations," National Hurricane
Research Project Report No. 5, U.S. Dept. of Commerce, Washington, D.C.,
Mar. 1957, 87 pp.

APPENDIX 1: EMPIRICAL AND NCMOGRAM SURGE MODELS

Connor et al. (1957) and Harris (1959) developed empirical statistical models
to predict peak storm surges. The first of these papers was based on data from
30 hurricanes in the Gulf of Mexico. Because of the small size of the data
sample, storm intensity was the only predictor considered. A correlation co-
efficient of 0.68 was obtained between observed and predicted surges when
dependent data were used. In the second paper, data from 52 storms that occurred
on both the Atlantic and gulf coasts were available for analysis. This time,
it was possible to consider the slope of the Continental Shelf in a very crude
way. The correlation coefficient was then increased to 0.75. The effect of
storm size was found to be trivial. The data set was inadequate for a con-
sideration of such dynamic effects as storm motion.

We want to see if the end product of our nomograms in the present paper does
as well or better. To this end, we compare and correlate the observed peak
surge values--adjusted for seasonal sea-level anomaly--against our peak surge
approximations from nomograms.

A. Correlations Between Precomputed and Observed Surges

We have compared the observed peak surges reported for 43 of the 52 storms18
used by Harris (1959) with predictions from the precomputed nomograms in this
study (table 3). Seven of the tabulated storms have R greater than 50 mi,
thus; they are not covered by the nomograms. Two entered New England where
shoaling factors have not been developed. Missing in several of the tabulated
storms are Poo and R; where this occurs, values of Poo = 1012 mb and R = 15
and 30 st.mi. have been assumed for the gulf and east coasts, respectively.
For the vector storm motion parameters (Us, 0), we extracted from Cry (1965)
the values19 given while the storms were on the Continental Shelf.

In the first panel of figure 11, the peak observed surge is plotted against
the predicted preliminary number Sp derived from figure 1; thus, storm in-
tensity and size of storm only are considered. The correlation coefficient,
o, for the line of best fit for these data is 0.54 and loosely corresponds to
the empirical model of Conner et al. (1957). For reference, a perfect fore-
cast line slanted at 450 is drawn on each'of the panels; this line could
represent the conceptually ideal case when predictions and observations are
identical; however, we view it as the line we want to approach with our issued
forecasts. Comparing the difference in vertical or y values between the two
lines gives a crude estimate for the reliability of our nomogram s.chenie.
The second panel gives a plot of the observed peak surge against a prediction
by the nomogram method when the effects of storm intensity, storm size, and
local bottom topography from figure 2 are considered. The prediction here is
the product of Sp . FG,E. The correlation coefficient for the line of best
fit with this data is 0.68. The panel corresponds loosely to the empirical
model given by Harris (1959).
The third panel gives a plot of the observed peak surge against a prediction
by the nomogram method when the effects of storm intensity, storm size, local
bottom topography, and storm motion from figure 3 are considered. The pre-
diction here is the product of Sp.FG E.FM The correlation coefficient for the
line of best fit is 0.85.
Note that speed and direction of storm motion just might be correlated with
the storm intensity and that both could be correlated with the location or
landfall point of the storm. Although these secondary correlations may have

18Most of the meteorological data given by Harris comes from page 29 of the
report by'the Weather Bureau (1957). Note that Poo given by this reference
does not always agree with historical weather maps; this is because meteor-
ological parameters were derived quasi-empirically and random errors were
allowed to accumulate in the ambient air pressure.

19The values extracted are somewhat subjective. This occurs because coast
and track lines, which are curvilinear, are subjectively represented by straight
lines.

Table 3.--Comparison of the observed peak surges reported for 43 of the 52
storms used by Harris (1959) with predictions from the precomputed nomograms
in this study

storm[ Date Peak tide Poo P0 AP R Spt uFGE SpU F SS

1 2 Oct. 1893 Mobile, Ala. 1016 956 60 20 12.8 1.18 15.1 11 14010.72 10.9 9.3 MSL M 9.3
227 Sept. 1894 Charleston, S. C. 1012 986 26 30 5.6 1.17 6.6 12 120 0.79 5.2 5.3 AN M 5.3
3 8 Sept. 1900 Galveston, Tex. 1009 936 73 16 15.1 1.02 15.- 13 080 0.98 15.1 14.6 MSL M 14.6
4 14 Aug. 1901 Mobile, Ala. 1021 973 48 38 10.5 0.79 8.3 8 090 0.82 6.8 7.4 MSL M 7.4
5 27 Sept. 1906 Pt. Barrancas, Fla. 1018 965 53 75 radius greater than 50 mi, storm out of range
6 21 July 1909 Galveston, Tex. 1025 959 66 22 14.211.02114.51 9106010.80111.6110.0IMSLI MI10.0
7 20 Sept. 1909 'Timbalier I. , La. 1026 980 46102 radius greater than 50 mi, storm out of range
8 18 Oct. 1910 Everglades, Fla. 1008 959 49 55 radius greater than 50 mi, storm out of range
913 Sept. 1912 Mobile, Ala. 1012 993 19 15 3.9 0.79 3.1 13 080 0.96 3.0 14.4 MSL[ M 4.4
10 16 Aug. 1915 High I., Tex. 1oo0 953 48 37 10.3 1.09 11.2116 080 1.05 11.8 13.9 MSL M 13.9
11 29 Sept. 1915 Grand Isle, La. 1021 944 77 34 17.0 0.76 12.9 12 100 0.87 11.2 9.0 MSL M 9.0
12 5 July 1916 Ft. Morgan, Ala. 1017 961 56 57 radius greater than 50 mi, storm out of range
13 18 Oct. 1916 Pensacola, Fla. 1023 974 49 50 9.510.61 5.8 15 110 0.90 5.2 3.0 MSL M 3.0
14 28 Sept. 1917 Ft. Barrancas, Fla. 1012 964 48 37 10.5 0.59 6.2 12 090 0.93 5.8 7.1 MSL M 7.1
15 9 Sept. 1919 Key West, Fla. 1007 929 78 17 16.3 0.53 8.6 9 040 0.85 7-3 6.6 MSL 0.1 6.5
16 25 Oct'. 1921 Punta Rassa, Fla. 1002 958 44 21 9.! 1.28 12.0 12 070 0.90 10.8 11.0 MSL 0.1 10.9
17 26 Aug. 1926 Timbalier I. , La. 1028 959 69 31 15.9 0.75 11.9 9 070 0.83 9.9 10.0 MSL 0.2 9.8
18 18 Sept. 1926 Miami Beach, Fla. 1016 934 82 28 18.3 0.70 12.8 13 100 0.91 11.7 10.5 MSL 0.1 10.4
19 20 Sept;. 1926 Pensacola, Fla. 1020 955 65 24 14.5 0.61 8.8 9 060 0.81 7.2 9.4 MSL 0.4 9.0
20 16 Sept. 1928 West Palm Beach, Fla. 1029 935 94 32 22.2 0.47 10.1, 15 120 0.86 9.0 9.8 AN 0.1 9.7
21 28 Sept. 1929 Key Largo, Fla 1019 953 66 32 15.2 0.54 8.2 12 070 0.89 7.3 8.8 MSL 0.0 8.8
22 23 Aug. 1933 Hampton Roads, Va. 998 970 28 62 radius greater than 50 mi, storm out of range
23 7 Sept'. 1933 Brownsville, Tax. 1024 949 75 35 17.2 0.64 11.011 090 0.90 9.9113.0 MSL M 13.0
24 25 July' 1934 Galveston, Tex. 1012 975 37 15 7.3 1.02 7.4 13 040 0.91 6.8 5.9 MSL M| 5.9
25 4 Nov. 1935 Miami Beach, Fla. 1012 973 39 30 8.7 0.70 6.1 18 070 1.09 6.6 9.3 MSL 0.3 9.0
26 31 July 1936 Panama City, Fla. 1016 964 52 22 11.3 0.601 6.8 10 060 0.82 5.6 6.0 MSL 0.0 6.0
27 21 Sept. 1938 Moriches, N.Y. 1000 943 57 58 radius greater than 50 mi, storm out of range
28, 7 Aug. 1940 Colcasieu Pass, La. 1008 974 34 13 6.4 1.16 741 5 03010.71 5.3 4.8 MSL 0.1 5.3
29 11 Aug. .1940 Beaufort, S. C. 1017 975 42 30 9.3 1.15 10.7 8 060 0.75 8.0 8.5 AN 0.5 8.0
30 23 Sept. 1941 Sargent, Tex. 1004 959 45 24 9.9 0.88 8.7 13 1110 0.88 7.7 9.9 MSL 1.4 8.5
31 7 Oct. 1941 St. Marks, Fla. 1022 981 41 21 8.4 1.32 11.1 13 100 0.91 10.1 6.4 MSL 0.3 6.1
32 30 Aug. 1942 Matagorda, Tex. 1004 951 53 21 11.5 0.791 9.1 161080 1.04 9.5 14.8 MSL 0.8 14.0
33 27 July 1943 Galveston, Tax. 1017 975 42 19 8.6 1.02 8.8 4 060 0.66 5.8 4.0 MSL 0.4 3.6
34 14 Sept. 1944 Newport, R.I. 992 959 36 26 shoaling factor unavailable
35 19 Oct. 1944 Naples, Fla. 1004 962 42 39 8.6 9.24 10.7 16 060 1.00 10.7 11.0 MSLIO.4 10.6
36 20 Oct. 1944 Charleston, Fla. 1012 991 21 30 4.2 1.17 4.9 16 140 0.81 4.0 4.4 AN 0.4 4.0
37 27 Aug. 1945 Matagorda, Tex. 1020 968 52 21 11.3 0.79 8.9 7 140 0.69 6.2 7.3 AN 0.9 6.4
38 24 Aug. 1947 Sabine Pass, La. 1012 992 20 15 3.9 1.11 4.3 4 080 0.68 2.9 3.6 MSL 1.1 2.5
39 17 Aug. 1947 Hillsboro Beach, Fla.1010 940 70 22 15.3 0.b7 7.2 11 080 0.89 6.4 9.8 MSL 0.3 9.5
40 19 Sept. 1947 Biloxi, Miss. 1006 968 38 32 8.3 1.20 10.0 23 040 1.12 11.2 11.1 MSL 0.2 10.9
41 15 Oct- 1947 Quarantine Sta., Ga. 1004 968 36 15 7.1 1.22 8.7 10 060 0.81 7.0 6.5 AN 0.7 5.8
42 4 Sept. 1948 Biloxi, Miss. 1012 987 25 15 4.9 1.20 5.9 14 110 0.88 5.2 5.6 MSL 0.5 5.1
43 26 Aug. 1949 New Jupiter In., Fla. 1020 954 66 25 14.5 0.48 7.0 14 130 0.77 5.4 4.2 MSL 0.1 4.1
44 4 Oct. 1949 Freeport, Tex. 1020 978 42 32 9.4 0.89 8.4 20 110 1.05 8.8 10.4 AN 1.4 9.C
45 30 Aug. 1950 Pensacola, Fla. 1006 979 27 24 5.6 0.61 3.4 18 080 1.10 3.8 5.5 MSL 0.4 5.1
46 5 Sept. 1950 St. Petersburg, Fla. 1012 958 54 15 10.8 1.28 13.8 10 270 0.50 6.9 7.2 MSL 0.9 6.3
47 31 Aug. 1954 Sakonnet Pt., R.I. 1012 961 51 30 shoaling factor unavailable
48 15 Oct. 1954 South Port, N.C. 993 937 56 16 11.510.95 10.9 261120 1.14112.5112.71 ANI0.2112.8
4917 Aug. 1955 Holden Beach, N.C. 1012 986 26 30 5 .511.00 5.51131090 0.961 5.31 6.0 ANI0.6 5.4
50 19 Sept. 1955 Morehead City, N.C. 1012 966 46 58 radius greater than 50 mi, storm out of range
51 24 Sept. 1956 Laguna Beach, Fla. 1012 974 38 30 8.5 0.59 5. 13 10010.941 4.71 7.4 AN 0.3 7.1
52 27 June 1957 Calcasieu Pass, La. 1006 947 59 22 13.0 1.17 1.2 160811.04115.8 13.9 AN 1.4 12.5

Poo Outside ambient pressure (in mb) US Speed of storm (in mph)
P Central pressure (in mb) e Direction of storm traverse relative
Po Central pressure (in mb)
4,P Poo - PO to coast
R Radius of maximum winds (in st.mi.) FM Correction factor for vector storm
Sp Preliminary number for peek surgeputed storm surge
FG E Shoaling factor for gulf or east coast SS Computed storm surge (Sp-FG,E FM)
Us' Speed of storm (in mph) h Observed high tide (in t
UM M issi ng mhSLA Seasonal sea-level anomaly (in ft)
h* High tide adjusted for SLA
AN Above normal

contributed to the skill obtained with the purely empirical models, they were
deliberately rejected in the construction of our nomograms from dynamic cal-
culations. This is presumed to be the major reason why the correlation co-
efficients of the first two panels in figure 11 are smaller than those obtained
in the corresponding empirical models.

The data in table 3 leave much to be desired. Although some of the peak
surge values came from tide-gage records, most were from post-storm surveys

PRELIMINARY NUMBER /S SHOALING CORRECTION SI;FGE STORM SURGE SS=SPF,'FM
20 y 20- 0 / - /

y = 0.4x + 3.73 / y = 0.662x+ 2.04 / y = 0.868x + 1.12 //
p = .0.54 1p = 0.68 / t = 0.85
16 - / /S /
i032 / la / .1 o3/
/,o 52-1|4i /j 4"/<-;31 4 /8#60d~
12 / 12- /12 -
/31 "~~~~ ~~~..20 //
.o,- B FI
8- am- x c-
7ee1 14/l "2
� 4,
.33 13 4,-,4.
.13 33,,13
/ 46 .- .dd / I I

x X X
LEGEND:

--- PERFECT FORECAST

Figure 1l.--Correlation between the nomogram-computed x coordinate and the observed y coordinate peak surges.
See table 3 for the data used. The number on the data points represents the storm number in table 3. The
first panel correlates the preliminary number Sp derived from the nomogram of figure 1. The second panel
corrects for local bathymetry. The third panel further corrects for the vector storm motion and gives the
final product SS the computed storm surge.

Table 4.--Mean square differences between nomogram-computed and reported peak
surges

Including a cor-
Considering size Including a rection for speed
and intensity of correction for and direction of
storm only local topography storm motion

Departure from 4.56 ft 2. 74 f t 1.68 ft
perfect forecast line;
no statistical ad-
justment

Departure from 2.62 ft 2.30 ft 1.63 ft
least-squares(best fit)
regression line

of high water marks. In general, it was not possible to take the stage of
the astronomical tide into consideration in evaluating the effects of the
storm. It is unlikely that the actual peak surge would coincide with one of
the small number of high water marks measured. It is likely that purely local
factors have contributed to most of the high water marks listed; and it is un-
likely that the storm parameters P. and P., and the speed and direction of the
storm were sufficiently correct in all cases, particularly for the earlier
storms. It should be noted that the only fitting between the predictions and
the reported peak surges permitted in this evaluation are the regression co-
efficients and line of best fit shown in figure 11.

B. Composite Nomogram and Statistical Model

We want to combine our predictions from nomograms with available statistics
to arrive at a possible better peak surge estimate. To this end, let the
abscissa x'in figure 11 represent a forecast from our nomograms and let the
ordinate y represent the forecast issued. If we use nomograms only f or our
forecast, then the perfect forecast line must be used; however, there are
times when we can correct the nomogram prediction with available statistics.
To combine statistics with our nomograms, we should use the line of best fit
(fig. 11) to issue a forecast.

To show how the two lines in figure 11 differ, we will consider the mean
square differences between the reported peak surge values and those pre-
dicted by:

1. The nomogram scheme only (i.e., using the perfect forecast line).

2. The best fit regression line.

These are given in table 4. It is seen that the least-squares regression line
gives no significant improvement over our nomogram scheme when all of the meteox-
ological. data are'used.
One might suspect that individual computations with the dynamic model
(instead of nomograms) fitted directly to the local bathymetry and to the in-
dividual storm parameters might give even smaller average differences between
reported and computed values.

When the approximate nature of the parameters assigned to many of the early
storms is considered, it appears that the individual calculations could be
justified for only a very few of the early storms. Individualized computer
runs with the dynamic model are currently being made for all hurricanes
entering the mainland of the United States.

Using the Composite Model for Initial Planning Purposes

When a tropical storm is first discovered, we have either very limited or
no meteorological information. With time, the information dribbles in--in the
form of observations, forecasts, climatology, or even speculation. Never-
theless, for incomplete meteorological information, the composite model can
be useful. What we have in mind here is to use whatever information is
available for the best possible forecast.

Initially, we know a storm exists, confirmed, say, by satellite observations.
This in itself is not sufficient information to proceed with the nomogram com-
putations for storm surges. We might, however, ascertain information indirectly
from cloud pictures, climatology, or experience. Generally though, we must
be content to wait for in-situ observations, such as ship reports and drop-
sondes.

The first--and most useful--piece of information is the pressure drop;
it allows us to determine from our first nomogram the preliminary number20
Sp. At this stage, the history of the storm is unknown; and we do not know
the landfall point or storm motion. Therefore, the number Sp is the best
we can do with our nomograms.21 We can, however, revise this crude number
with available statistics. This is done with the line of best fit on the
first panel of figure 11.; we enter with Sp on the x axis and issue a revised
preliminary number from the y axis through the line of best fit. The re-
vised number, a general number for the entire coast, is the best that can
be done until more information becomes available.

Suppose, for the next piece of information, we determine (or assume) a land
fall point; we then appraise surges locally (rather than generally) on the
open coast. This is done by multiplying the preliminary number Sp with the
shoaling factor of our second nomogram and forming the product of S .FGE.
We enter this product on the x axis of the second panel of figure 1 and
use the line of best fit to issue a locally revised preliminary number for
our prediction. This number is the best we can do until the last piece of
information (storm motion) becomes available.

Suppose we now ascertain the last piece of information (storm motion). We
then formulate the final product of Sp.FGE.FM, where FM is the motion factor
from our third nomogram. This new product, call it SS, is entered on the x

20
R can be chosen arbitrarily. The peak surge is not unduly sensitive to
this parameter.

21We remind you that these nomograms were designed only for the gulf and
east coasts.

axis of the third panel of figure 11; in this case, the issued forecast is
just as good whether we use the line of best fit or the perfect forecast line
(i.e., we need not revise the number SS to issue a forecast). When we have
sufficient information to enter the third panel, available statistics no longer
help to improve our forecast.

APPENDIX 2: SPLASH

Our purpose here is not to give a detailed description of the program, but
to describe a simple procedure to run it with minimal effort. This procedure
can be used by part-time limited-experience programmers such as operational
weather forecasters. Access to a computer, at least by terminal drop, is
assumed.

A. Mechanics of Running the Program

The approach adopted here is to store SPLASH onto tape; the program is called
for an operational run by a small program of only a few cards, followed by a
data deck of pertinent meteorological parameters. The tape is divided into
three files composed of:

1. A program deck in binary.

2. Thirty basins and their geography, each basin separated by an EOR
card.22

3. A program deck in FORTRAN (formula translator).

The program is run with the binary deck; the FORTRAN deck is present in case
a listing of the program is desired.

rn ~ The tape program is written for the NOAA CDC 6600 computer; it is not com-
patible with the software of other computers. To call and run the taped
program, one needs a small program of several cards. This is shown in figure
12.

The. first card of the small program, JOB card, is self-explanatory. For a
given storm, it usually takes about 2 min of CP or central processing time to
run the program. For exceptionally large or slow-moving storms, it may take
4 min of CP time. The T400 on the card represents 400 octal seconds (or about
4 min decimal) needed for CF.

The second card requests the program tape. MXXXXX is used to designate the
tape number. The tape is physically located at the CDC Computer Center,
FOB-4, Suitland, Md.; it is administered by NHC, the National Hurricane Center
at Miami, Fla., where numbers are assigned to the five X's. The tape will be
revised as time goes by; to run it, the user will have to make periodic ar-
rangements with the NHC.

22 A CDC 6600 EOR (end of record) card is one with the 7, 8, and 9 holes
punched in column 1.

SMALL PROGRAM DECK TO CALL PROGRAM TAPE (SINGLE JOR)
JOBNO.CM770001T4On,TPl.
REQUEST.TAPEIHI.E. USE MXXIXX
REWINDTAPEI.
RFL,150nO.
CKLBL(TAPEI ,MXXXXX)
REWIND TAPE1.
COPYRF(TAPEI SPLASH)
COPYBF(TAPEI.TAPF9)
RETURN,TAPEI.
RFL.770nn.
SPLASH.
EXIT.
RETURN TAPEI.
7-8-9 (END OF RECORD CARD)
(DATA DECK. SEE FIGURE 13)
6-7-8-9 (END OF FILE CARD)

OBTAINING A FORTRAN LISTING WITH A JOB RUN (MULTI JOBS)
JOBNOCM77000,T400,TP1.
REQUEST.TAPEI.HI,E. USE MXXXXX
REWIND,TAPEI.
RFL,15OnO.
CKLBL(TAPEI .MXXXXX)
REWIND TAPEF.
COPYBF(TAPEI,SPLASH)
COPYBF(TAPEI,TAPF9]
COPYBF(TAPEI.OLDPL) -
RETURN,TAPEI.
RFL,770n0.
SPLASH.
SPLASH.

SPLASH.
RFL,B00n. - DELETE THESE FIVE CARDS IF
UPDATE(P,F.L=0)4 A LISTING OF THE FORTRAN
COPYSBF(COMPILE,OUTPUT) ---- PROGRAM IS NOT DESIRED
EXIT.
RETURN TAPEI.
7-8-9
(FIRST DATA DECK)
7-8-9
(SECOND DATA DECK)
7-8-9

7-8-9
(LAST DATA nFCK)
7-8-9
6-7-8-9

Figure 12.--Program decks for use with SPLASH

The small program deck in figure 12 will run only one job. If one desires
to run several consecutive jobs (ay, for other landfall points on either side
of predicted landfall), then insert the card

SPLASH. 2d job
SPLASH. 3d job

after SPLASH and repeat the last card for any following jobs. Of course,
meteorological data--the data deck--must be supplied separately for each job;
data decks will be discussed in the next topic. Also, TXXXX in the job card
must be revised to accomnodate a longer run time. If a listing of the FORTRAN
program is also desired, the procedure shown in figure 12 can be used.

B. Meteorological Data Deck for the Program

To predict storm surges by computer, one must describe the tropical storm
prior to landfall. This is done with simple meteorological parameters that
can be prepunched on data cards. Forecasters at weather stations are best
equipped to handle this; for this reason, the program is designed for their
use.

33
The data dedk for the program consists of two title cards (followed by six
storm data cards) and is terminated by four tme cards for astronomical tide.
The two title cards are self-explanatory. The form and style of the storm
and tide data cards require some explanation; they represent the parameters
given in figure 13.

The first two storm data cards give landfall position. Although latitude
and longitude would seem likely coordinates for this position, we follow
common usage instead and refer landfall position relative to a geographical
landmark or stationi Stations used in the program are listed in table 2.
The geographical locations of the stations are shown in figure 5; they are
approximately 100 mi apart.

For the first storm data card, use the nearest station to landfall. The
station letters begin on the first space of the card, never exceed 10 spaces,
and are punched exactly as printed in table 2, spaces and all; any spaces
beyond the 10th space can be used for comments. We use an AlO format here.

For the second storm data card, use the distance (in st.mi.) for the land-
fall point lying to the right or left of the station as viewed from sea by
one facing land. Use a negative sign only if landfall is left of the station.
Use the first five spaces of the card; any spaces beyond can be used for
comments. We use an I5 format23 here. Note that the first two storm data
cards are used by the machine to position local two-dimensional bathymetry in
the basin and to orientate the coast relative to north.

For the third storm data card, use the pressure drop (in mb) while the storm
traverses the Continental Shelf. Note, 10 < AP < 140 in the program. Use the
first five spaces of the data card; any spaces beyond can be used for comments.
We use an 15 format here.

For the fourth storm data card, use the mean compass direction (meteor-
ological sense) in which the storm will traverse the Continental Shelf just
prior to landfall. The admissible directions inthe program are 16 points
boxed on the compass. They are in letters, not degrees. Use the first three
spaces of the card, always ending on the third space; any spaces beyond can
be used for comments. We use an A3 format here.

For the fifth storm data card, use the average storm speed (in mi/hr)
during traverse over the Continental Shelf just prior to landfall. Note,
6.0 < speed < 60.0 in the program. Use the first five spaces of the card;
any spaces beyond can be used for comments. The speed can be in decimals if
desired. We use an F5.1 format here.

For the sixth storm data card, use the average storm size (in st.mi.) during
its traverse over the Continental Shelf. The storm size is R, the radius of

23For all 15 formats, punch the number right justified. That is, the units
digit is in the fifth space, the 10's digit in the fourth space, etc. Other-
wise, the number will not be read in properly; and the computer will supply a
zero for each blank space (e.g., 10 mi/hr is punched-^^^10, where ' 'means a
blank space.

first title card4h
second title card
GULFPORT
-16
100
NNW
12.
15.
1000
17
AUG
1969

196.9 CARD TEN--- YEAR FOR LANDFALL OCCURRENCE
AUGIST CARD NINE--MONTH OF THE YEAR FOR LANDFALL OCCURRENCE
1? CARD EIGHT-DAY OF THE MONTH FOR LANDFALL OCCURRENCE
1000 CARD SEVEN-ESTIMATED LANDFALL TIME TO NEAREST HOURLCL STD TM
0 15, CARD SIX---SJZE OF STORM (RADIUS OF MAXIMNUM WINDS)PSTAT.NILES
0 12. CARD FIVE--SPEED OF STORM IN MPH
0 INW CARD FOUR--DIRECTION OF STORM MOTION IN LETTERS
2 - 0 100 CARD THREE-PRESSURE DROP 0F STORM IN NPS
2 oi -16 CARD TWO---LANDFALL DISTANCE TO NEAREST STATlON,(-)LFTP(+)RT
2 0 GULFPORT CARD ONE---NEAREST STATION TO LANDFALL
4 2 0 SECOND TITLE CARD
4 2 1 FIRST TITLE CARD
4 2
5 3 1
6~~~~~~~~~~~~~~~~ 0
6 .4 3 2

~~~~6 4 2 22222 222222222222 ''C,227??722172272223
7 5
I: 3 2 a 0 a 0 0 00 0 a 0 ' 0 0 a 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 090 0 0 0 10 0 0 0 a10 0 a 0 0 0 0 0 66660 0 6 0 0 6 0 0 6 0 0 6 6 0 0 0 0 66
5 4 3 2 1 1.2 345 6I0I 611 12 1 14 15 19 7 18 9 2 212223 2425 2 2728 2930 3132 3334 5 3 3 3339 0 1 424 44 G4 805 ' 25 15 i5 85 06 28 16 6 a6 In91 13 74 1 16nl 19 g
:I j I, 6 r 4 3 2 64 22 1 11 1111 11 111 111 1 1 ~l I I IIIII I'lllrllltl I I I I I I I I I11111 I IIIIIIIIIIIIIIIIIIII
91 7 31 V N o

9 5~aO~ 33333 3335333.333 33 333333 333 133
1 7 4 3 3 3 3 3 333 3 3 3 3 3 3 13 3 3 33 333333
9 7 ~6 5 44 .4444444444444444~4444 ,4444444 44 44 44 4 444 4 4 4 4 4 4 4 44 4 4444044P

JI 66666666666666666666666666.666646

'I 999239990'9999"9009999999999999999999999999og99gg9g999g99g99
1 2 3 ; 5 6 I a 9 T 11 12 13 14 1511 16 1718 9 N21 22 2314 926 2f 28 29 301 32 33 4 35 3 37 3839 40 41 4 43 4 45 6 47 49 50 51 52 53 4 5 560 50 5 60 6162 63 6465 66 7 60 E 70 7 12 73 7 75 7 71 7 79 5

Figure 13.--An example of a data deck. It is inserted inmmediatelyafter the small program deck of
figure 12.

maximum winds. Note, 10.0 < R < 60.0 in the program.24 Use the first five
spaces of the card; any spaces beyond can be used for comments. The size can
be in decimals if desired. We use an F5.1 format here.

The program constraints for storm data cards 3, 5, and 6 can be changed,
if so desired, only by updating the taped FORTRAN deck through UPDATE pro-
cedures; we do not discuss this operation here and refer the user to CDC
manuals.

The next four data cards are optional; they are used for astronomical tide
predictions. If not presented in the data deck, the program will ignore tide
computations.
For the seventh data card, use the nearest integer hour of landfall, from
0100 to 2400. Use the first four spaces of the card and let the last two
spaces be zeros; any spaces beyond can be used for comments. We use an 14
format here.
For the eighth data card, use the day of landfall, from day 01 to day 31.
Use the first two spaces of the card; any spaces beyond can be used for
comments. We use an 12 format here.
For the ninth data card, use the month of landfall. Use the first three
letters of the month in the first three spaces of the data card; any spaces
beyond can be used for comments, including the complete spelling of the month.
We use an A3 format here.
For the 10th data card, use the year of landfall. The years can lie be-
tween 1900 and 1999 for past-present-future predictions of astronomical tide.
Use the first four spaces of the data card; any spaces beyond can be used for
comments. We use the 14 format here.
An example of a punched data deck is shown in figure 13; the deck is set
in the small program as shown in figure 12. The cards must be in sequence.
If N jobs are to be executed, then set N data decks in the small program;
separate each data deck with an EOR card. Behind the last data deck, in-
sert an end of file (EOF) card.25
It is suggested that data cards be prepunched to reflect all ranges of
meteorological and time parameters. In this way, the user can assemble cards
that best describe tropical storms and their landfall times without punching
errors.

APPENDIX 3: SOME DO'S, DON'TS, AND APPLICATIONS WHEN FORECASTING STORM SURGES

The operational computer output developed in this study is a useful tool.
As such, it should be considered only an aid for the prediction of, or plan-
ning for, storm surges. It is not a substitute for experience and judg-
ment. We advise that there are inherent weaknesses in the dynamic model used
here and there will always be uncertainties in the meteorological input data;

It is doubtful if such a large-sized storm as 60 mi can be adequately re-
presented by our model.

25A CDC 6600 EOR card is one with the 7, 8, and 9 holes punched in column 1.
An EOF card has the 6, 7, 8, and 9 holes punched.

the user must judiciously apply his knowledge to shore up and buttress these
inadequacies.

It is a fact that forecasters will extrapolate the limited range of any
model well beyond physical constraints. Therefore, we want to discuss and
develop some criteria for evaluating the output surge computations. We will
want to adjust the computer product, at least qualitatively, for inherent
weaknesses and uncertainties.

The discussions inthis appendix will be mostly qualitative, even speculative;
they are intended to guide and warn the user engaged in storm surge prediction.
First, meteorological parameters and their relative importance will be con-
sidered. Next, we will consider coastal geographical features and how they
alter the surge locally.
A. Meteorological Parameters

When tropical storms threaten a coast, much interest is centered on the
value of the meteorologically forecast maximum wind--fastest mile(Holliday
1969). This physical number is readily assimilated by communities, planners,
and others. The tendency then is to use it as a direct measure for potential
damage.

For storm surge generation, we must strongly resist the temptation to use
the forecast maximum wind26 as a direct measure of the peak surge. Instead,
we should pay strict attention to parameters directly accessible and amenable
to measurements.

Pressure Drop

What we need paramountly to concentrate on is the pressure drop of the storm.
The peak surge value varies almost linearly with the pressure drop; and this
value is quasi-conservative with respect to storm size.

1. Errors in pressure drop (6p) are significant only when significant in
comparison to the pressure drop Ap (i.e., the ratio between 6p and Ap is the.
deciding factor).

a. For small pressure drops, we must have quite accurate readings
(forecasts) of the storm's central pressure.

b. For large pressure drops, such as that of hurricane Camille, we can
afford more error in the central pressure readings.

2. The relative error of pressure drop is a measure of the corresponding
relative error of peak surge value.

3. If the storm is deepening while traversing the Continental Shelf, use
the central pressure at the time of landfall.

a. If the central pressure deepens dramatically with time, there will
be some overshooting of surge amplitudes. This is why the lowest central

26We can use an average maximum wind around the circle of radius R. This
is significantly smaller than the fastest mile wind.

pressure at the time of landfall is used rather than a mean central pressure.

4. If the storm is filling while traversing the Continental Shelf, use
the mean central pressure of the storm during traverse.

a. If the central pressure fills dramatically with timel, there will be
a lag in surge amplitude adjustments. This is why we use a higher central
pressure thanthat.,expected at landfall.

Size of Storms

Of secondary importance for peak surge values is the storm size. Although
large variations in storm size (say, by a factor of 2) generally have only
a mild effect on the peak surge value, we should not be too cavalier about
choosing its value. We point out that larger storm. cause surges along a larger
length of coast; also-, the potential for inland inundation is greater.

Direction of Storm Motion Relative to the Coast

For operational and illustrative convenience, let the coast and storm
track be straight lines. There are two extreme positions of these lines with
respect to each other, either normal (a landfall storm) or parallel (along
shore-moving storm). Each extreme has two particular orientations:

1. Landfall storms.

a. Storm m.v~es from sea to land.

b. Storm moves from land to sea (exiting storm).

2. Storms moving alongshore.

a. Storms moving up the coast.

b. Storms moving down the coast.

Fov the particular orientations within each extreme, the surge profile and
peak surge value are significantly different.

The varieties of dynamical behavior for each extreme are vastly different,
all dependent on the meteorological parameters and basin used. For storm
tracks between the two extremes, the storm surge profile undergoes tran-
sitional changes.

Herein lies one advantage for direct machine computations with the dynamic
model; dynamic effects for particular situations are directly incorporated in
the coimputations.

Storms Reachn Land. Storms reaching land, traveling near normal to the coast,
generate surge profiles that grow with time. The position of the highest
surge on the profile remains nearly stationary; eventually, it reaches peak
surge amplitude at approximately the time of landfall. Exiting storms (i.e.,
storms traveling from land to sea) follow a similar pattern, but with a
smaller peak surge.

- ENVELOPE Or aGHEST
SURGES
SURGE PROFILE AT TIME
OF PEAK SURGE
SURGE PROFILE SOME
TIME AFTER PEAK
SURGE OCCURS,

LI.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

� ' -' -------- COAST
N'~ '" // MILES

Figure 14.--Envelope of coastal high water heights
for coastal surge profiles

For conceptual purposes, we can view the coastal surge profile at the time
of peak surge as a string that is held or plucked by the storm at or near the
time of landfall. Of course, things are not quite so simple as the mechanics
of a plucked string; but the illustration is informative. An example of such
a profile is shown in figure 14. Note that there are negative surges to the
left of the storm; furthermore, these negative values are larger for exiting
storms. With passage of the storm, we now view the profile as a released
string that forms two waves moving to the right and left, respectively. The
form and speed of propagation of these two waves depend on the input mete-
orological parameters and basin used. To portray a convenient end product of
this phenomena, we consider the envelope of all high water heights on the
coast and call it the storm surge envelope. The form of the envelope along
the coast represents the observed high water heights, without respect to time
of occurrence.

If the storm travels other than normal to the coast, then the highest surge
on the'profile prior to landfall is no longer stationary in space; the highest
surge moves along the coast following the storm on its track. This continues
until peak surge occurs. The net result is that the envelope of high water
heights is elongated along the component of track direction on the coast; this
can mean a long length of coast will be affected by surges for storms that move
nearly parallel to the coast. Only one end of the surge envelope can become
elongated, but only for storms traveling nearly parallel to the coast.

Storms Moving Alongsliore. These storms generate interesting assortments of
complicated wave phenomena. It is not easy to summarize all these wave phe-
nomena for ordinary forecasting.

One problem in forecasting these surges, possibly insurmountable at this
time, is the lack of advance knowledge of meteorological parameters. Not only
do we need to know the track of the storm--which can easily exceed 500 mi--but
also the possible or probable large variations of storm parameters along the
track with time. The art of weather forecasting has not yet advanced to the
point where these parameters can be predicted reliably for 2 or 3 days in
advance.

Storms moving alongshore generally cause significantly smaller surges than
storms reaching land,. An exception could occur with storms traveling at
particular speeds in particular basins so. as to generate a resonance con-
dition (Jelesnianski 1970); the direction of travel must be down the coast,
that is 9 is 00 (see fig. 3 for orientation). Fortunately, this case will
almost never occur except possibly with a storm traveling northward along the
west coast of Florida. Generally, storms move alongshore only on the eastern
seaboard.

The portrayal of storm surge profiles for storms moving alongshore will be
deferred to a later paper.

Landfall Position and Storm Track

For operational procedures, such as evacuation decisions, we must know the
length of coast threatened with significant surges. This length is roughly
the diameter of the storm where surges are greater than one-half the peak surge
value The 24-hr-forecast error in landfall position is about the same order of
magnitude; hence, it is desirable to ascertain the landfall point as precisely
as possible. Another reason for precise positioning is the effect of local
bathymetry on surges; more will be said about this later.

In connection with landfall point, we need to appraise how vector storm
motion affects surges. For the following, use figure 3 as applicable.

1. Storms traveling from sea to land generate larger surges than those
traveling from land to sea.

a. The opposite holds for negative surges (an observer positioned at
sea while facing land will find negative surges to the left of landfall at
the time of peak surge).

2. For storms traveling near normal to the coast, small variations in
storm speed can affect peak surge values significantly. The opposite is
true for small variations in storm direction.

a. For storms traveling from sea to land, the peak surge increases
with increased speed until a critical speed is reached. Critical speed is
rarel~y reached; exceptions can occur with very small storms or on wide and
shallow shelves.

b. For storms traveling from land to sea, the peak surge decreases
with increasing storm speed. There is no critical speed.

3. For storms traveling nearly parallel to the coast, small variations
in storm direction can affect peak surge values significantly. The opposite
is for small variations in storm speed. Here, we need to know the storm
track and landfall rather precisely.

4. When determining the storm track, use the direction of the mean vector
motion of the storm during its traverse across the shelf.

B. Geographical Features of Basins and Their Coastlin~es

The dynamic model assumes an ideal basin (shown in fig. 15A). Its pro-
perties are:

1. A straight unbroken coastline.

2. Land elevations rising vertically on the coast, with

a. finite sea depths (D.) on the coast.

3. A wide shallow shelf where the width is greater than R, but of the same.
order of magnitude.

Real basins do not satisfy all of these properties; but for basins along
the United States and attendant coasts, conditions do not deviate too much
from the model basin. What we will need to do is to consider the ratios of
several scale sizes for particular basins against storm size R.. These ratios
will help to guide us in selecting a range of nonidealism that is tolerable
in our storm surge model. In what follows, only the sense (not magnitude)
of corrective action on our open coast surge forecasts will be discussed for
natural basins.

Unbroken Coastlines

At this point, we consider coastlines that are unbroken by bays, estuaries,
and inlets. No natural coastline is straight; all are curvilinear to some
extent. In figure 15B, we show a curvilinear coast with a radius of cur-
vature RC at the landfall point. For operational convenience when faced with
the problem of determining RC, we suggest a visual estimate by first drawing
a circle of radius R. for the storm, tangent to the coast at the landfall
point. If the direction of RC is toward the sea, as shown in the figure, we
call the coast "concave downward." If the direction of RC0 is toward land
because of opposite curvature, we call the coast "concave upward."

We now formulate some criteria of a qualitative nature for a range of
applicability with the storm surge model.

1. if RC >>R, then consider the coast a straight line and do not correct
for curvature. (The symbol �> can be interpreted as an order of magnitude
greater.)

2. If RC0 > R, then the curvature of the coast can have a significant
effect on surges. (The symbol > can be interpreted as greater than, but
of the same order of magnitude.

a. If RC0 is concave downward, the generated surge will be greater
than on a straight line coast.

b. if R. is concave upward, the generated surge will be smaller than
on a straight line coast.

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Figure 15.--(A) idealized model of the open coast surge generated by a traveling tropical storm reaching
-Ti

Figure 15.--(A) idealized model of the open coast surge generated by a traveling tropical storm reaching
land. The area immediately adjacent to the straight line coast is represented by a vertical wall. (B)
same as (A), except this is for a more realistic basin. The coast is curvilinear and borken by bays
and estuaries; the areas immediately adjacent to the coast form a slanted surface rather than a vertical
wall.

3. If R C< R, then we are out of range for the model. Some examples are:

a. Capes that prominently mark a change in or interrupt the coastal
trend and on which the curvature is concave upward.

b. Corner points that prominently mark the meeting of two separate
coasts at an angle (e.g., Long Island and the mainland; Florida Keys
and Florida) and on which the curvature is concave downward.

4. If RC �< R, but the surrounding coast also is equally irregular, then
we still consider the coastline as being nearly straight. What we have in
mind here is a ragged coastline where each localized feature is much smaller
in scale than the storm. We realize that ragged coastlines will generate
surge profiles that are ragged in appearance.

Broken Coastlines

Coastlines are broken by bays, estuaries, deltas, and inlets. There are
no precise definitions for these coastal indentations. We will consider only
indentations with widths or lengths of the same magnitude as our storm sizes.

Bays. A bay is somewhat oval shaped with its longest axis more or less
parallel to the coast. A bay differs from a closed lake in that part of its
boundary, the mout~h,,is exposed to the sea; at most, there is a barrier, island
on the seaward side of the bay. The following may be applicable.

1. For a bay to the right (as viewed from the sea) of an exiting storm
or one reaching land, the surge on the landward sides of the bay will be
larger than surges computed for the open coast. By "sides," we also mean
portions of the lateral sides of the bay.

2. For a bay to the left of an exiting storm or one reaching land, the
surge on the seaward sides of the bay (not including the mouth) will be
larger than that on the landward sides and that computed by the model for
the open coast.

3. The left lateral side of the bay will have higher surges than those
along the right lateral side.

The surges at the mouth of the bay may be much smaller than those computed
by the numerical model for the unbroken coast.

Hurricane Carla. For an example of the bay effect, see figure 16 that gives
surges for hurricane Carla, 1961, an exceptionally large and slow-moving
storm.27 The inset gives observed surges for comparison with the computed
surge envelope. Available tide gage readings (Harris 1958) show a re-
markably long duration for the higher surges. Since landfall occurred near
the time of high astronomical tide, peak meteorological and astronomical
tides were nearly simultaneous. The astronomical tide was about 0.5+ ft

27 Meteorological data were subjectively determined from the Monthly Weather
Review, bulletins, advisories, etc.

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above MSL; if we add this to the computed surges from just to the left of
landfall to Galveston, then the computed surges agree with observed values
to almost the nearest foot along the unbroken open coast. We do not make
such comparisons for the ends of the envelope, especially to the left of
landfall, where coastal boundaries curve significantly.
On the inset, to the left of landfall, all bays appear to have larger surges
on the seaward sides. Because of the lack of open coast surge measurements
and dynamic effects of coastal curvature, we cannot make comparisons 'With the
model envelope. To the right of landfall, all bays appear to have larger
surges on the landward sides. The ratio of landward to seaward surges appears
to be greater in Galveston than Matagorda Bay; we suggest this may be attributed
in part to the more rapidly changing driving forces about the storm'sa core
as it crossed Matagorda Bay.

The barrier islands about Matagorda Bay were inundated, and there are no
surge measurements to compare with the computed envelope. If we assu~me that
the maximum surge on the model envelope is representative for the open coast,
then the bay effect increased the maximum surge. The highest measured surge
of 22 ft appears to be an extreme local effect; the next highest still-water,
high-water mark is 19 ft. This is not too far from the computed maximum surge
of 15.9 ft (astronomical tide28 added) on the model envelope.

The surges in Sabine Lake do not appear to have any preferred areas for
higher surges. Note that the lake has no significant exposure to the sea.

Estuaries. An estuary is usually rather long and narrow, somewhat like a
canal, with its axis more or less normal to the coast. Usually, a large
river discharges into the head of an estuary at the end opposite its mouth;
several smaller rivers also may discharge into the sides. On marine charts,
estuaries often are listed or named as bays. Estuarine effects are less
known than bay effects; at this stage, we are nearly helpless in specifying
surge characteristics for estuaries. Exceptions are specialized studies for
idealized canals that do not directly concern us here. We speculate that
estuarine effects are as follows.

1. If the axis of an estuary is smaller than R, then estuarine effects are
similar to bay effects, but possibly smaller in ratio. Mobile Bay on the
Alabama coast is an example of such an estuary.

2. If the axis length is larger than the storm's diameter, then the
situation is indeed complicated. The surge will depend in part on vector
storm motion relative to the axis. We are in no position to list all possible
phenomena, but we can speculate qualitatively and warn for the following:

a. If the axis is to the right (as viewed from the sea) of an exiting
storm or one reaching land and if the track parallels the axis, then conditions
could be ripe to generate a substantial surge. By "ie"we mean a critical
storm speed for a given estuary. However, we do not as yet know the critical
speed for particular estuaries.

28 High astronomical tide occurred 2 to 3 hr after landfall; high storm
surge changed slightly duringthis period because of slow storm motion. No
attempt was made to correct for SLA, the seasonal sea-level anomoly.

b. If the axis is to the left of an exiting storm or one reaching land
and if the track parallels the axis, then the surges at the mouth and head
of the estuary are reversed (i.e.,the mouth will have positive surges while the
head will have negative ones).

c. If the storm track crosses the axis, there will be many variations
of the surge in space and time within the estuary.

We remark that the surge at the mouth of an estuary may be much smaller than
that computed by the model for the unbroken coast.

Inlets. An inlet is a short, narrow waterway connecting an inland feature
(e.g., bay, lagoon, or inner coast) with the sea. What we have in mind here
is a long barrier island parallel to the coast and broken by inlets; the
island has high vertical dunes, and there is a narrow sound or intracoastal
waterway between the coast and island. An example of this is along the
northeast coast of Florida. A storm reaching land on this coast may generate
surges that do not overtop the dunes, but can and do enter the inlets.
Currently, we are in no position to discuss the dynamics of this situation
or to give operational rules for forecasting. Presumably, if the inlet length
is larger than R, then the surge can be expected to reach the segment of the
coast inland from the inlet. We can even ignore a sound much smaller in width
than R. We do not know, however,. how far the surge moves into the sound on
either side of the inlet.

For large-scale sounds with inlets such as Long Island Sound between Long
Island and Connecticut,we are completely helpless. These features are similar
in many respects to the estuary.

Deltas. A delta is an alluvial deposit surrounding the mouth of a river or
inlet. Deltas have various shapes and sizes. An extreme example is the
triangular shaped delta on the coast of East Pakistan. It consists of
several rivers, inlets, and islands juxtaposed about the coast. For effects
of deltas on the open coast surge, we admit to almost complete helplessness
in specifying any characteristics.

Our main concern in the United States is the Mississippi Delta that has a
digitate shape extending into the sea; its length is the same magnitude as
storm sizes. In part, it resembles a cape. The coast on either side of the
delta is confused and choatic with bays and many lakes not too far inland.
All these irregularities destroy the reliability of the open coast computations
in a delta area. We cannot formulate firm guides for the surge forecaster;
reference to past storms and subjective comparison of observed or computed
surges might be helpful here. We warn, however, that vector storm motions
in the future may be different from those observed in the past, which may
radically alter the dynamics of surge generation about the delta.

Hurricane Betsy. For an example of a storm striking in this area, consider
hurricane Betsy, 1965. Figure 17 gives computed and observed surges for
this storm; meteorological data were subjectively extracted from such sources
as the Monthly Weather Review, bulletins, and advisories. Note that the
observed surges about the mouth of the delta are significantly smaller than
those at the head of the delta; this could be attributed to the steepness of
the Continental Shelf at the mouth and its shallowness on either side of the

delta. In our model, we ignore the delta and substitute shallow water to
connect the shelves on either side of delta; we also ignore the islands be-
tween Chandeleur Sound and the gulf and between Mississippi Sound and the
gulf.

Except for the delta Itself, the model shows some skill. The observed and
computed surges show fair agreement on the open coast at Grand Isle, Pt.
Pleasant:, Gulfport, Biloxi, etc. The highest computed surges, off Hopedale
on the open coast, are for an area devoid of observations; thus, it may be
that we do not know how high the actual surges29 were for this storm.

We remark on a subtle interplay (in this geographical area) that could be
important. Notice that peak surge was computed to lie 52 mi to the right of
the landfall point, a distance significantly larger than R = 32 mi for the
storm. This seeming discrepancy in placement of peak surge relative to the
landfall point is caused by severe horizontal changes of the ocean depth con-
tours to the right of the landfall point. For an explanation of this dynamic
phenomena, see figure 8. Had the same storm made landfall several miles to
the right of the observed landfall, then the shoaling phenomena could have
produced more dramatic peak surge; this is shown in the last horizontal line
of figure 17 where the potential peak surge on the coast is given. Note that
there can be sizeable differences between potential and computed peak surge
heights for any particular point on the coast. The message here is that, in
geographical areas with severe horizontal changes in the ocean depth contours,
the peak surge and its placement on the coast are sensitive not only to the
landfall point but also to the size of the storm.

C. Inundation

A storm moving across a sloping continental shelf builds a mound of water
that eventually impinges on the coast. Momentum then forces the mound of
water to charge up the coast, a situation we call "runup" (Harris 1963).
Runup is a complicated nonlinear phenomena; but for long gravity waves such
as storm surges, we can make approximations. Consider the vertical and
horizontal components of runup; these are S and go is shown in figure 15B
where S is the open coast surge and I1, is length of inundation normal to the
coast. Along Ii,, the heights of the inland surges vary in a complicated
fashion in space and time; these variations are not considered in th&model..

In the model, a vertical130 wall is used to represent the lafidward terrain.
How well does a vertical wall represent the near-horizontal terrain? Well, it
does not exactly, but it does approximately. We use this approximation when
10 is small compared to some length normal to the coast. For convenience,

29 The terrain in question is very shallow; inundation effects may have de-
creased the open coast surge. See the next topic for a description of in-
undation effects.

30 The inland slope of the terrain from the coast usually is about two orders
of magnitude greater than the slope of the surge normal to the coast; this
means that the long gravity wave (storm surge) sees the inland terrain ap-
proximately as a vertical wall, even though the inland slope may be numerically
quite small.

measure Io as the inland distance where the land contour (elevation) and com-
puted peak surge are equal. The following may be applicable.

1. If to < R along the open coast, then computed surges are a good re-
presentation for the open coast surge.

2. If 10 > R, then our computed surges are larger than the natural open
coast surges.

Our model tells us nothing about inland inundation. We cannot say analyt-
ically whether the surges decrease or increase inland. However, this situation
becomes critical only when item 2 occurs. In practice, it is usually assumed
that surges decrease inland.31

Hurricane Audrey. For an example of inundation effects, consider hurricane
Audrey, 1957. This was a storm of ordinary intensity compared to Carla or
Camille. Figure 18 shows a comparison of computed and observed surges for
this storm.32 Note that the inland area,,about and to the east of landfall,
is very flat except for several low-lying ridges paralleling the coast; in
fact, one must proceed 20 to 30 mi inland before the terrain rises to as
much as 10 ft. This flat terrain virtually guarantees that 10 > R; ex-
ceptions would occur only with weak storms.

The observed surges for this storm were extensively studied by Harris
(1958); we use his data in the following discussion. To compare observed
and computed surges, we note that landfall occurred at high tide of about
0.5 ft; Harris (1958) gives a seasonal sea-level anomaly of 1.4 ft in the area
affected by this storm. Hence for comparisons, we will have to add about
2 ft to the computed surge.

The nearest observation, with respect to position of computed peak surge,
showed 12.1 ft just west of Cameron; this was not a strict measurement but
rather a reconstruction of partial data from a tide gage destroyed by the
storm. We note a ap in observations just east of Cameron where highest tide
may have occurred.53 The computed surge envelope (plus a 1-to 2-ft correction)
gives 1 to 5 ft higher surges than observations inland from the open coast;
this is for the core of the envelope between Sabine and Southwest Passes.
Overall, the observed surges tended to decrease inland; but there are ex-
ceptions, especially about Calcasieu Lake. We remark that inland surges, at

31We would emphasize that observed, inland, high-water marks are not water
above terrain but rather above MSL. As an example, a 15-ft high-water mark on
terrain 10 ft above MSL means that there is 5 ft of water above the terrain in
question. Sometimes rain will flood pockets of land in high terrain. This
may give the illusion of runup from a very high open coast surge. Similarly,
rivers overflowing their banks should not be confused with runup of the surge.

32Meteorological data for this storm were extracted from Graham and Hudson
(1960). These data were accepted as is.

33The landfall position and storm size are best estimates from available
meteorological data, formulation, etc. (see footnote 32). Thus, there is
some uncertainty as to the position of the computed peak surge.

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distances comparable to storm size R, may and no doubt are significantly
smaller than the open coast surge.

For another example of the inundation phenomena, consider the large-sized
storm Carla, 1961 (fig. 12). Here, 1c, < R; and the computed surges plus the
astronomical tides are representative for the obs-erved open coast surge. The
observed surge heights do not always decrease inland, and they do not follow
any easily discernible pattern.

In both examples, the effects of curvilinear coasts, bays, lakes, etc.,,
follow patterns similar to those discussed in previous topics.

Wave setup. When a wave breaks on a coast, the chaotic mass of water runs up
the coast; this occurs because the water mass has energy to dispose. After
runup, the mass of water should flow back to the sea but is prevented from
completing the action by succeeding breaking waves. After some time, an
equilibrium pattern is formed in which the mean water level inland and sea-
ward from the coast is other than normal. This situation is called "wave
setup";this can be negative or positive in the area influenced by breaking
waves.

Our empirical knowledge of wave setup comes mostly from laboratory wave
tanks under idealized conditions, not from natural basins during hurricane
conditions. Note especially that wave setup is an equilibrium state with
short gravity waves breaking periodically.

The storm surge is a long gravity wave. It too runs up the coast but does
not break. The surge also runs down the coast after the storm passes; but
because there are no following long waves, it cannot form wave setup. During
runup, the elevated surge can act as a pathway for short-gravity, breaking waves
(e.g., surf and swell) farther inland; but in almost all cases, the breaking
activity does not extend much beyond the normal coast. One should remember
that the slope of inland terrain is considerably different from the seaward
slope in the wave-breaking zone. A large surge occurring in flat terrain
will inundate the land for several miles inland; it is possible that the wind
pattern in a slow-moving storm may form short-gravity, breaking waves in the
inundation area; but it takes time to do this, sometimes a lot of time. We
cannot assume a priori that wave setup, in the positive sense, automatically
takes place; nor can we assume it acts more favorably in a given area merely
because the surge measurements are higher than expected. The phenomena is
just too complex to give operational rules at this time; we need an extensive
and exhaustive study on generation of short-gravity, breaking waves during
surge inundation before speaking authoritatively about wave setup.

We do not consider wave setup in our computations because it is a nonlinear
phenomena not too well understood during transient surge states. It is possible
that wave setup is partially, and indirectly, accounted for in our model
through the drag coefficient in our wind stress formulation. The surge
forecaster should have sound physical reasons before applying corrections for
wave setup onto surge computations.

D. Continental Shelf Width, Depths, and Grid Spacing

In the dynamic model, the computational grid spacing must be small enough
to detect a passing storm of given size. The spacing serves equally well
for computing the generated surge wave becaus~e its length34 under the storm
is directly related to storm size. A 4-mi grid spacing is sufficient for
most storms reaching land; exceptions would be for storms with R < 10 mi.
For economic and operational reasons, the entire ocean cannot be used in the
model; therefore, we use only a segment of the Continental Shelf. This
necessitates the introduction of open boundaries in our truncated basin. We
must also contend with the wide variations of shelf width along the United
States and improvise when shelves are not compatible with the surge model.

We require a shelf width in the model. On the basis of empirical com-
putations, this width must be at least of size R.35 For operational con-
venience, we set our shelf width as 72 mi, larger than any R used in the model.
The coastal surge computations are not sensitive to the exact width of the
shelf edge, even if it is much wider than 72 mi.

It is difficult to define precisely the edge of the Continental Shelf.
The depths on the edges vary considerably along the United States. For
the constant invariant grid size used in the model, we dare not allow the
depths to become too large because of economic and computational limits;
hence, we must improvise. From results wish empirical computations, we
find that the coastal storm surge is not asensitive to depths greater than
300 ft; accordingly, no depth on the Continental Shelf is allowed to exceed
this limit. What is so magical about 300 ft? Well, our model incorporates
some of mkman's concepts in linking driving forces with momentum. This means
that the transfer of momentum downward into the sea by wind stress is con-
strained to an Ekman depth36 of about 300 ft. Also, for a time invariant
surface stress, it takes more than a day for momentum to reach equilibrium at
the Ekman depth; but the storm traverses the Continental Shelf in less than a
day, except possibly for exceptionally slow storms.

34 An exception could be resonant or trapped waves a short distance from
land (Jelesnianski 1970).

35 The computed coastal surge begins to vary significantly only when the
shelf width becomes smaller than R. On the deep water open boundary, the
model uses static heights. This boundary condition is useful but not completely
accurate; hence., we want the boundary as far removed from the coast as pos-
sible to reduce the effects of errors..

361In a homogeneous sea, pressure gradient effects reach the basin's bottom
immediately; however, coastal surges resulting from the wind stress driving
force are greater than surges from the pressure gradient driving forces, at-
least for tropical storms. Also, mass adjustments in a stratified sea, plus
thermoclines, limit dynamic effects from driving forces to shallow surface
layers not too great in depth~at least during the transient state of surge
generation.

Small Shelf Widths

There are some areas along the United States where the Continental Shelf
is almost nonexistent, notably between the Florida Keys and West Palm Beach.
The dynamic model, limited in its present state, would prefer to neglect these
areas. However, from the viewpoint of the operational surge forecaster, this
attitude is unacceptable. So, we here are forced to compromise as well as to
improvise.

To form a usable shelf for the basin, we begin with the depth profiles off
the Continential Shelf, as they exist for the first few miles from shore,
until the 300-ft depth curve is reached. We then compromise our basin with
a false, constant shelf depth of 300 ft for the remainder of the basin's
length. Such severe depth changes at the coast, however, create special
problems at one or both of the two false lateral boundaries that truncate our
basin on the oceanside. The lateral boundary condition admits ref lected37
waves in the basin; with severe depth changes these reflected waves reach
large amplitudes and move rapidly to the middle of the basin. To alleviate
this situation, we improvise a platform or shallow depth profile normal to
the coast at the lateral boundary and taper38 the platform down to extreme
depth values along the coast well before arriving at the basin's center.
But false tapering depths along the shore and near a lateral boundary can
form their own system of trapped waves which eventually corrupts the numerical
solution. To prevent this effect, we limit the computation, stopping it well
before the solution can be corrupted with these waves; empirical computations
give a usable span of 10 to 12 hr in real time. This means that the com-
putations here are less reliable for very slow storms.

We remark that the axis of Biscayne Bay, along the southeast coast of
Florida, is larger than the diameter of most storms. It is a shallow area
abutting a shelf of small width. The adjacent coastal areas are densely
populated. Because of these factors,, an attempt is made to incorporate the
bay in the model; of course, we cannot do this precisely because of cur-
vilinear coasts and the surrounding islands. It is unnecessary to apply a
qualitative bay correction onto the computations here, but the model cannot
account for local variations in the surge due to abrupt, local terrain changes.

The above techniques are provisional and have not been fully tested for all
conceivable situations. So., we can expect unforseen problems to arise. The
model tries to accommodate a variety of situations, but unusual conditions
may precipitate an untenable state; the model then gives up in despair and
produces instability. If or when this arises, the following guides will help
for a new computation attempt.

37 Clearly, we need here a radiation type boundary condition that is trans-
parent for a group of traveling waves. This would be an interesting research
project for the future.

38 The tapering depths have a shoaling effect on waves traveling toward the
shallow platform, and bottom stress dampens the shoaled waves. The trick here
is to taper the shallow platform so that dampening effects are significant on
all the shoaled waves; we do this by empirical tests with the model.

1. Let the storm track strike the coast at a less acute angle, con-
sistent with meteorological accuracy.

2. Let the speed of the storm be as large as possible, consistent with
meteorological accuracy.

3. Let the size of the storm be as large as possible, consistent with
meteorological accuracy.

E. Astronomical Tide

The tide tables, issued by the National Ocean Survey (NOS), give times and
heights of high and low waters with respect to a datum. This datum, along
the United States coasts of our interest, is MLW. We note that nautical
charts published by the NOS for this area give depth soundings below MLW.
This system is used by mariners for navigation purposes in which the lowest
expected waters are of great interest.

The surge forecaster has a slightly different outlook; to him, highest
expected waters are of great interest. His datum is MSL. The charts he uses
'give land contour elevations39 above geodetic MSL; for this reason, we pre-
pare astronomical tide predictions with respect to local MSL rather than MLW.
The predicted tide plus computed surge (i.e., total storm tide) can then be
directly compared with land contours to determine areas of inundation along
the coast.

It would be better if we could always be this direct, but there are two
anomolies here that sometimes can be significant.

1. Local MSL is not invariant with time.

2. The constituents Sa and SSa (annual and semiannual variations of the
astronomical tide) are not always representative of actual conditions.

In almost all cases, local MSL changes slightly with the years; hence,
land-contoured charts should be representative of the coast regardless of
the year of issue. However, there are some special areas where changes in
local MSL may be significant through the years. Thus, it may be wise for the
surge forecaster to check the survey year of his chart and correct its sea-level
datum to current or local MSL. Information on the relationship between geo-
detic and local tidal datum can be obtained from the NOS.

Sa and SSa presumably are measures of the seasonal changes of the sea-
surface height at a tide station, caused by seasonal changes of the earth's
meteorology. Figure 19 illustrates the amplitudes of these changes at a
selected station for I yr; note that the peak amplitude occurs during the U.S.
hurricane season. The curve is a best fit average with significant variance;
it does not always represent the current state of affairs. For safety, it
is suggested that normal predicted tide, in the coastal area of expected land-

39 The NOS charts give some land elevations with respect to MHW (mean
high water).

5."~~~~~~~~~~~~~~~~5

Fiu0 19*00al vaiaio of0 sea level at00 MaYP0000. 0000
6.000 -.000

10.000 -.111

(slrana)tiecnttet. 000 = -.400S A
40.^,o -.174 '

?l0.aa0 -.103

??%^0 0 .. 0?

1.00 -.0))

fall, be compared with observed tide for several days before landfall (Harris
1958). If there is a trend in the comparison, then it can be incorporated
with the predicted tide at the time of landfall.

A potentially dangerous situation occurs when both the peak meteorological
and astronomical tides occur at or nearly at the same time. This situation
generates larger total surges. From tide tables,, we do know when peak semi-
diurnal or diurnal astronomical tides occur; but peak meteorological tide is
another story. Because of the state of the art in weather forecasting, we are
not certain to the nearest hour when landfall will occur; also, we have given
no criteria for the arrival time of peak meteorological tide with respect to
landfall time. This arrival time depends in a complex manner on meteorological
parameters, especially vector storm motion and the sea's bathymetry about the
landfall point. In general we can say:

1. The peak meteorological surge occurs before landfall with slower moving
storms (storms moving at speeds less than 20 mi/hr).

2. The peak meteorological surge occurs after landfall for faster moving
storms (storms moving at speeds greater than 20 mi/hr).

3. In almost all cases, the time interval between peak surge and landfall
is less than 1 hr.

For practical operational purposes, we can assume that peak surge and land-
fall occur simultaneously.

The probability of simultaneous occurrence of the two peaks is the same no
matter what the storm speed, providing the storm is not stationary. We re-
mark on a property of slow-moving storms; the duration of upper surges on the
surge profile is long, sometimes even longer than a tidal period. Thus when
dealing with very slow storms (speeds less than 10 mi/hr), the highest com-
bined surge is virtually guaranteed to be larger than peak meteorological
surge. But with fast-moving storms (speeds greater than 20 mi/hr), the
duration of high surges is short, sometimes much shorter than a tidal period.
Therefore, if astronomical tide is to be appended to meteorological tide with
any reliability, we must have a reliable landfall time--say, to within +2 hr
for a semidiurnal tide and +3 hr for a diurnal tide.

(Continued from inside front cover)

WBTM TDL 27 An Operational Method for Objectively Forecasting Probability of Precipi-
tation. Harry R. Glahn and Dale A. Lowry, October 1969. (PB-188 660)

WBTM TDL 28 Techniques for Forecasting Low Water Occurrences at Baltimore and Norfolk.
Lt. (jg) James M. McClelland, USESSA, March 1970. (PB-191 744)

WBTM TDL 29 A Method for Predicting Surface Winds. Harry R. Glahn, March 1970.
(PB-191 745)

WBTM TDL 30 Summary of Selected Reference Material on the Oceanographic Phenomena of
Tides, Storm Surges, Waves, and Breakers. Arthur N. Pore, May 1970.
(PB-193 449)

WBTM TDL 31 Persistence of Precipitation at 108 Cities in the Conterminous United
States. Donald L. Jorgensen and William H. Klein, May 1970. (PB-193 599)

WBTM TDL 32 Computer-Produced Worded Forecasts. Harry R. Glahn, June 1970. (PB-194 262)

WBTM TDL 33 Calculation of Precipitable Water. L. P. Harrison, June 1970. (PB-193 600)

WBTM TDL 34 An Objective Method for Forecasting Winds Over Lake Erie and Lake Ontario.
Celso S. Barrientos, August 1970. (PB-194 586)

WBTM TDL 35 A Probabilistic Prediction in Meteorology: A Bibliography. A. H. Murphy
and R. A. Allen, June 1970. (PB-194 415)

WBTM TDL 36 Current High Altitude Observations--Investigation and Possible Improvement.
M. A. Alaka and R. C. Elvander, July 1970. (Com-71-00003)

NOAA Technical Memoranda

NWS TDL 37 Prediction of Surface Dew Point Temperatures. R. C. Elvander, January
1971. (Com-71-00253)

NWS TDL 38 Objectively Computed Surface Diagnostic Fields. Robert J. Bermowitz,
February 1971. (Com-71-00301)

NWS TDL 39 Computer Prediction of Precipitation Probability for 108 Cities in the
United States. William H. Klein, February 1971. (Com-71-00249)

NWS TDL 40 Wave Climatology for the Great Lakes. N. A. Pore, J. M. McClelland, and
C. S. Barrientos, February 1971. (Com-71-00368)

NWS TDL 41 Twice-Daily Mean Monthly Heights in the Troposphere Over North America
and Vicinity. August F. Korte, June 1971. (Com-71-00826)

NWS TDL 42 Some Experiments With A Fine-Mesh 500-Millibar Barotropic Model. Robert
J. Bermowitz, August 1971. (COM-71-00958)

NWS TDL 43 Air-Sea Energy Exchange in Lagrangian Temperature and Dew Point Forecasts.
Ronald M. Reap, October 1971. (COM-71-01112)

NWS TDL 44 Use of Surface Observations in Boundary-Layer Analysis. H. Michael Mogil
and William D. Bonner, March 1972.

NWS TDL 45 The Use of Model Output Statistics (MOS) To Estimate Daily Maximum
Temperatures. Lt. (jg) John R. Annett, NOAA, Harry R. Glahn, and Dale
A. Lowry, March 1972.

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