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THE PHYSICAL EFFECTS OF VEGETATION ON COASTAL DUNE SYSTEMS IN FLORIDA Alan WM. Niedoroda and D. Max Sheppard December 1989 Funds for this proj ect were provided by the Department of Environmental Regulation, office of Coastal Management using funds made available through the National Oceanic and Atmospheric Administration under the Coastal Zone Management Act of 1972, as amended. THE PHYSICAL EFFECTS OF VEGETATION ON COASTAL DUNE SYSTEMS IN FLORIDA Alan Wm. Niedorodal and 2 D. Max Sheppard EXECUTIVE SUMMARY Although it has long been recognized that coastal plants serve to maintain and even develop sand dunes there has been surprisingly little study of the underlying aerodynamic processes. In regulating the development of Florida's coastal areas engineers in the Florida Department of Natural Resources Division of Beaches and Shores need to be able to ,make assessments of the relative roles of a wide range of vegetation types on the retention of sand. As a result of this need, a study has been conducted to establish the controlling physical relationships and to provide a quantitative method of determining the sand.trapping capacity of coastal vegetation. The study was intended to advance our understanding of these subjects quickly and effectively. Consequently, this first phase of the work was directed toward the development oftheory and methods of analysis using parameter measurements from the published literature. It is expected that subsequent research will provide other analyses and measurements based on the approach developed in this first phase. There are several theories and predictive equations for sand transport by wind (i.e. aeolian transport) for loose, dry sand on a flat horizontal surface; exposed to a fully developed turbulent shear boundary layer. All contain empirical constants and coefficients to some degree. Recent studies have demonstrated that most of the competing relationships produce similar results. As a result the theory developed by Bagnold was adopted as the method of computing sand transport by the wind provided that the sand grain size, density, and sorting are known. Bagnold's equation relates the mass flux of sand to the friction velocity of the wind and this must be known (measured, or calculated). Bagnold's equation is used to compute the sand transport on a flat open beach as a basis of comparison to changes caused by the interaction of vegetation with the air flow. These interactions are characterized by a three tiered boundary layer over and within the vegetated area. Above the plant .1 - Hunter Services, Gainesville, Florida, 32602 2 - Department of Coastal & oceanographic Engineering, University of Florida, Gainesville, Florida, 32611 canopy, a shear boundary layer similar to that over the open beach, is pictured. Typically the vegetation causes higher drag than bare ground so that there is a sharper vertical profile of the mean horizontal wind in this layer than the bare ground equivalent. The lowest portion of this velocity profile projects into-the upper portion of the vegetation canopy. Within the canopy the turbulence arises largely as a result of the air passing through the foliage. The vertical velocity profile is altered to an exponential shape matched at the top of the vegetation to the overlying shear boundary layer profile. Near the ground there is a third zone within which another .shear boundary layer is developed. Sand transport takes place in this layer. A series of equations are formulated to represent these physical processes. They are u.sed to compute the sand transported within, or beneath, a plant canopy for set wind conditions. These results are compared to corresponding bare ground results. Much of the approach is related to previous research concerning air flow above and within crops and forests. Many of the controlling relationships are constrained by simplifying assumptions. These relationships also depend on the evaluation of air flow parameters which can only be experimentally determined. These measurements have not been conducted for coastal plants. In order to provide working estimates of,these parameter values for coastal plant all accessible data concerning measurements made for all types of plants was assembled. The physical characteristics of both the measured and unmeasured types of plants were tabulated and used to assign aerodynamic coefficients to the coastal plants based on their similitude with the measured group.. The major portion of this study was devoted to developing a method of comparison of the sand transport in different types, sizes, and densities of coastal vegetation presuming a single plant type and a fully developed boundary layer for each analysis. However, the transitional boundary layer conditions were also considered and incorporated into a special'analysis. This analysis is appropriate to the case of narrow lines of vegetation, oriented across the wind. The case of mixed plant assemblages is also considered. Included in the recommendations for future work are: 1) Expansion of the approach to include larger horizontal scales and sloped terrain. 2) Development of better aerodynamic coefficients for coastal plants. THE PHYSICAL EFFECTS OF VEGETATION ON COASTAL DUNE SYSTEMS IN FLORIDA Alan Wm. Niedoroda and D.'Max Sheppard2 INTRODUCTION Natural coastal dune vegetation generally survives in an environment which requires special adaptation. Two features of this environment are the sandy, humus-poor soil and the high salt content of the air, soil and soil water. The plants which are adapted to this environment tend to stabilize its physical features by trapping and holding wind-blown sand. The beneficial nature of coastal vegetation in trapping and holding wind-blown sand has long been recognized and there are a large number of qualitative statements to this effect in the literature (Jagschitz and Bell 1966, Savage and Woodhouse 1968, Gage 1970, Dahl et al 1975), oftensupported by observations. However, the physics of the interaction of coastal plants and sand transport has remained poorly studied. Without a quantitative study of these effects it is not possible to understand how effective different types and distributions of plants are in causing deposition of wind-blown sand and in preventing erosion. For these reasons a study was conducted of the physical effects of vegetation on coastal dune systems in Florida. The study was proposed as an initial exploration of this subject and was therefore-based on existing literature as opposed to field or wind tunnel work. The objectives of the project were: 1 - Hunter Services, Gainesville, Florida, 32602 2 - Department of Coastal & oceanographic Engineering, University.of Florida, Gainesville, Florida, 32611 2 carry out a comprehensive literature search concerning-the natural dune plants of Florida, the role of vegetation in stabilizing sand dunes, and the theoretical understanding of the direct effects of vegetation on sand transport by'wind; -develop an understanding of the effect of the various physical attributes of plants in their relative abilities to trap and retain sand on, and near the beach; provide a basis of comparison for assessing the relative effectiveness of vegetation in promoting the stability and growth of coastal sand dunes; - develop a procedure to predict the potential magnitude and rate of change intle- 1178 sahdred in coastal dunes as the result of changes in the vegetation. The aim of this study is to provide coastal engineers and scientist working for the Division of Beaches and Shores with methods for assessing the effects of proposed changes in coastal vegetation on the natural functioning of the coastal systems. A major emphasis is on processes resulting in long-term sand storage which provides a buffer against erosion. It was soon discovered that a natural division of processes occurs based on the characteristic.coastal length scales under consideration. These generally divide into a local scale of features and processes acting over lengths on the order of los to 100s of feet and a coastal scale with lengths of thousands of feet to miles. Two factors influenced the study to concentrate on the local scale. First, most of the problems of interest to the Division of Beaches and Shores arise from individual lot permit issues and these lots are typically of the local length scale. Secondly, it proved feasible to develop an approach to evaluating the effects of vegetation on wind-blown sand transport at this scale in considerable detail. As a consequence, the major portion of this report is devoted to local scale processes, with coastal scale processes being treated only briefly towards the end. DESCRIPTION OF PROCESSES Near-Ground Atmospheric Flow The atmosphere flows in response to pressure gradients resulting in the wind. The frictional effects of the earth's surface are confined to a zone (or boundary layer) which is generally less 3 than a couple thousand feet in thickness. The major frictional processes occur in a subregion of this boundary layer where there is thought to be a constant mean horizontal shear stress. This layer is typically a few hundred feet thick. If the mean wind speed (u(z)) is measured at several heights (z) in the lower portion of the atmospheric boundary and plotted they tend to yield profiles of similar form to that shown in Figure la. The rate of increase of wind speed with height (au/az) is greatest near the ground and decreases with height. Such curves appear as straight lines when the wind speed is plotted against the log of the height (Figure 1b). The general form of this relationship is, u(z) = a ln(z) + b where a and b are independent of z. It is usual to replace b with -a ln(zo) where z is a roughness parameter equal to the small height at whichothe logarithmic equation predicts zero velocity. This is typically one order of magnitude smaller than the physical height of the surface roughness elements. From this it follows that, u(z) a ln(z/z.) Differentiation of this equation with respect to z yields, au a az z which shows that the vertical gradient of the wind is.inversely proportional to the height above the ground. This has been taken to indicate that the dimension of friction-driven turbulent eddies is directly related to the distance above the surface because larger eddies can be expected to be more effective in vertical mixing than smaller ones. Another useful parameter is the friction velocity (u.) which is defined as, U* CC/P) 0.5 where T is the vertical shear of horizontal momentum in the boundary layer and p is the air density. This quantity has the dimension of velocity which explains the name 'friction velocity'.. The parameter "all in the expression for velocity, is commonly assumed to be proportional to u. and both are independant of height. The constant.of proportionality is K, called von Karman's constant, and has a value of 0.4. a U./K Thom (1975) states that the product KZ can be identified with the mixing'length (1w) or effective eddy size at the level z, by the expression, 1W K Z. With the appropriate substitution for the parameter a, the equation for the velocity profile in the constant stress frictional boundary layer becomes, U(Z) = (U,/K) ln(z/z.) When.the value of von Karman's constant is included and the natural logarithm is replaced with the common logarithm this equation is written as, U(z) 5. 75 u, logjO(z/zO) The Physics of Wind-Blown Sand our knowledge of aeolian, or wind-blown, sand transport dynamics has developed slowly as the result of research which has been of scattered intensity over the past 50 years. Much of what is presently known is based on empirical measurements and simplified dynamics. Recent field studies have shown that although there are competing theories they are similar and several produce results which show reasonable agreement with measured data (Horikawa et al 1986). The process of aeolian transport of loose sand on a large flat horizontal surface is easily described. Gravity stabilizes the surface grains in their places against fluid forces which tend to entrain and move.them. Therefore, there is a threshold wind intensity below which no sand transport occurs. Above this threshold individual grains are dislodged and put into various types of movement including upward and downwind displacement due to the fluid forces, downward movement due to gravity, and various bouncing, rolling and sliding motions. All this is generally called grain saltation. The presence of grains saltating in the lower portion of the boundary layer changes its behavior. Figure 2 shows profiles of the mean horizontal wind speed for conditions below and above the grain entrainment threshold. The height ordinate is a log scale so the profiles appear as straight lines. The three profiles (corresponding to three different mean wind speeds) for sub- threshold conditions intersect with the height axis at a common point above the ground surface. This is taken as the base of the constant stress portion of the turbulent boundary layer. Below this, the forces of molecular viscosity become increasingly important in the so-called laminar sublayer. The height of the zero intercept of these profiles is,the roughness height (z.). Figure 2 also shows profiles for three wind conditions which are- above the grain threshold conditions. These also intersect at a common point called the focal point. This point is displaced upward from zo to a new height designated as z The focal point is also displaced outward from the ordinate by a speed designated as ul. The change of z to z' as the grain movement threshold is exceeded indicates thal the vertical divergence of stress in the boundary layer increases and wind energy is dissipated more rapidly per unit area of the sand bed. A consequence of these changes in the structure of the boundary layer is that the:equation for mean wind speed as a function of height, u(z) 5.75 u. logjO(z/zO) (below threshold) is recast to, u(z) 5.75 u. logjO(z/z' + U, (above threshold). Various empirical relationships have been developed from wind tunnel experiments that relate these flow parameters to .characteristic sand grain parameters. Bagnold (1954) suggested, 6 zo d/30 and Zingg (1952) proposed, z' = 10 d and Ul = (894 cm/sec mm) d where d is the sediment grain diameter. Even though Zingg's equations are empirical they are based on extensive wind tunnel measurements. The above expression for z0f z', and ul are not well studied but they are commonly applied. Some comfort may be taken from a recent review of aeolian sand transport theories and measurements by Horikawa et al (1986) which indicates reasonable agreement between measurements and computed transports based, in part, on these empirical. relationships. These equations permit the velocity profile relationship to be rewritten to solve for u. in terms of a single wind speed determination at a known height and the mean sand grain size; U* = U(z)/ 5.75 logjO(z/zO) (no sand transpo rt), U* = (u(z) - u /5.75 loglo (Z/z (sand in transport). These expressions indicate that the wind conditions which define the threshold of grain movement should be expressed in terms of a critical value of the shear velocity (u*cri ) . The vertical profile of the wind changes depending on the condition of the sand bed so that the shear stress applied to the bed cannot be directly associated with a unique wind speed. Several investigators have developed methods to define and predict the values of the critical shear stress (u crit) needed to initiate grain transport (Bagnold 1941 and 1954 , I@agaki 1950, Horikawa and Shen 1960, Tsuchiya and Kawata 1975, and Nickling 1988). These relationships are also entirely based on empirical data. The one shown on Figure 3 from Horikawa and Shen (1960) is, in part, based on earlier observations by Iwagaki (1950) and Bagnold (1954), and provides an adequate summary of these observations. It relates u. crIt to a parameter comprised of the 7 square root of the product of the mean grain diameter and the. grain density. There-are also several expressions available to compute aeolian sand transport once the threshold conditions have been exceeded. These are also based largely on measured data but have varying degrees of associated physical explanations. Horikawa et al (1986) reviewed these relationships and conducted a comparison based on available measured data. They found that the various expressions derived by Bagnold (1941 and 1954), Nakashima (1979), Kawamura (1951), and Horikawa et al (1983) all produce similar results and are in reasonable agreement with measurements. The physics of Bagnold's equation for aeolian sand transport are readily explained. Figure 4 shows -a definition sketch of a control volume in which grain saltation occurs. The volume has a unit width and a length (L) defined by the average distance a saltating grain moves in a unit time increment (At). That is, L Us At where U. is the mean grain speed. Bagnold likened the aeolian sand transport process to the ordinary process of sliding friction and generalized the details of the various fluid forces acting on the grains by assuming that they are proportional to the shear stress per unit area (t ) . Thus the net downward force acting on the sum of the dispersA grains in the control volume is proportional to the fluid shear stress acting on the bed. The net downward force acting on the dispersed saltating grains (fd) is, fd Mg (QAt) 9' where Q is the mass flux of grains through the box. The fluid shear stress acting on the bed (f.) is the shear stress per unit area multiplied by the area of the base of the control volume, fS TO (USAt) If K is a constant of proportionality then Bagnold's relationship can be expressed as, (Q At) g K to (USAt) , 8 or Q K (Pa/9) where pa is the air density. Using the definition of the shear velocity (u.) this becomes, K (Pa/g) U.2us. If it is assumed that the average grain speed in the control volume is proportional to the shear.velocity us = k . u*' then Bagnold's relationship becomes, 3 K k (p./g) u* Bagnold (1954) used experimental data to show,. K k B (d/D)0*5 where B is a standard reference grain diameter of 0.25 mm. and B is a ;parameter controlled by the sand size gradation (sand size frequency distribution). He offers the following: B 1.5 uniformly graded sand, B = 1.8 naturally graded sand, and B = 2.8 broadly graded sand; to which Cooke and Warren (1979) have added, B.= 3.5 for pebbly sand. A substitution produces Bagnold's classic equation, 9 Q B (Pa/g) (d/D)"'U.' This equation is commonly used for computing aeolian sand transport but it must be kept in mind that it is derived for loose dry sand on a flat horizontal surface. Tsoat (1974), Hunter et al (1983), and Hotta (1984) report marked increases in threshold velocities and decreases in sand transport flux due to soil moisture in excess of 1%. Nickling (1984) has examined the effects of surface salt concentrations on the grain entrainment threshold values. He reports that even very low concentrations significantly increase the entrainment threshold. Small scale bedforms such as sand ripples also alter the threshold and transport relationships. Larger scale slopes, such as those associated with coastal dunes effect aeolian transport in several ways. First the slope can either increase or decrease the entrainment threshold values depending on their alignment relative to the wind. These slopes also create horizontal pressure gradients due to form drag and these gradients alter the structure of the near-ground vertical velocity gradient. As the profile of the lower turbulent boundary layer changes so does the magnitude of the shear stress applied to the sand bed. These complicating effects have been studied to varying degrees but there is no complete theory currently available which allows comprehensive treatment of their combined effect:�. In the absence of this it is usually best to evaluate problems using a simple theory such as Bagnold's while making allowances for the untreated factors. Air Flow in a Plant Canopy In a previous section the idea that the characteristic scale of turbulent eddies in a shear -flow is controlled by the proximity of the ground was presented. The logarithmic mean velocity profile follows as a consequence of this 'structure' to the turbulence. Air flow through a vegetated area is different because the plants create turbulent wakes which are the dominant eddies within most canopies. Both the intensity and the scale of the turbulence is changed by the plants. Clearly there must also be regions above the plants and very close to the ground where the structure of the turbulence is not dominated by the plants and resembles the basic shear flow conditions. This means that there should be at least three sub- regions in the turbulent boundary layer.- Well above the plant canopy the flow is such that the stress in constant, similar to that over bare ground but adjusted to a greater roughness height. 10 This sub-region is coupled to the boundary layer flow within the plant canopy whose turbulence is greatly influenced by the vegetation. Finally there is the near-ground sub-region where the scale of the turbulent eddies is again mainly controlled by the proximity of the ground and where a second constant stress layer occurs. Transition regions can be expected between these sub-regions. Inoue (1963), Cionco (1971), Thom (1975), and othershave examined the dynamics of turbulent flow in vegetation canopies. They have demonstrated that for a simple steady and fully developed flow with a neutrally-stable density structure, which is not influenced by adverse horizontal pressure gradients and is moving through a canopy with a nearly uniform vertical distribution of plant material, the vertical velocity profile has an exponential shape. This can be shown with the following explanation. There are two types of shear stresses acting on the fluid in the control volume. One at the boundary due to the surrounding fluid. The other is distributed through the control volume and is due to the vegetation. Because the shear forces on the fluid due to vegetation are distributed (assumed uniformly) throughout the canopy it is convenient to treat them as "body" forces. The force per unit volume is thus: Shear Force/unit vol. = Shear Stress/unit depth = 1/2 Cd p A u2 where Cd drag coefficient p mass density of air A vegetation surface area (all the leaves and branches) per unit volume u a horizontal velocity. A simple force balance on the fluid within the control volume (in the absence of horizontal pressure gradients) results in T + @_T AZ T C p Au 2 dz dz 2 d or dt 1 2 -- = - C p Au dz 2 d where t=the fluid shear stress acting on the fluid in the control volume at the lower boundary. If we now express t as du t = K -- w dz and K as W 2 du K = l -- W W dz where K = eddy viscosity and W l = mixing length in z-direction W then the above equation becomes dt d 2 du 2 -- = -- [l (--) ] dz dz w dz if lW is approximately constant as suggested by velocity and turbulence measurements within canopys 2 dt 2 d d u -- = l (2-) ---2 dz w dz dz 1 2 = - C p A U 2 d or C A du d u p d 2 -- (---) = ------ u dz 2 2 dz 4 l w Let C = C A p d and assume that C f (u,z) ------- 2 4 lw 12 Then du (d2u) = Cu2 dz 2 dz which is a second order, nonlinear, ordinary differential equation. The solution should be of the form, rz U = K'e Taking the appropriate derivatives, du rz d 2 u = 2 rz dz = k're and dz2 K' r e and substituting these into the ODE results in (K're rz) (K'r2e rz) = C(K'e rz)2 or K' 2 r3e2rz = CK' 2 e2rz or r = C 1/3 = (pCd2 A)1/3 4lw 2 so (1PC A 1 )1/3. t = 4 d 2 lw Thus u = K'e rz = K' exp (pCd A)1/3 z 2 4 lw The boundary conditions are, u(z=H) = u(H) u(z=H) = u(H) = K'e rH 13 or -rH KI u(H e and U U )e r(z-H) u )e rH(z/H-1) let rH =- a z a(-- U U(H )e H where a H P C A 1 )1/3 4 d 2 Zw In this analysis the leaf area density (A)'combined with the plant bulk aerodynamic drag coefficient (Cd) are used to parameterize the plant's frictional effects. The leaf area density can be determined from a more standard botanical (and agricultural) parameter known as the leaf area index (LAI) which is the sum of the area of one side of all of the leaves on a plant divided by the lot area (ie. total area of ground surrounding the plant). The leaf area density can be evaluated by dividing the LAI by the average plant height (H). This is also designated the PAI so that, PAI A/2. The presence of the vegetation and the air moving through it effects the overlying boundary layer conditions. AS illustrated on Figure 5 the vertical profile of the wind has a logarithmic profile starting a short distance above the top of the vegetation. Cionco (1971) performed regression analysis on numerous measured wind profiles above different types of vegetation and established that they could be fit with the same logarithmic function as an ordinary shear profile, provided that a zero plane displacement, d, is introduced. Using this parameter the equation of the mean horizontal velocity profile above the vegetation becomes, U(Z) (U,/K) ln((z-d)/zo)) 14 The zero plane displacement is typically a major fraction of the vegetation height. The roughness parameter (zo) tends to be considerably higher for vegetation than for bare ground indicating that the vertical divergence of horizontal momentum above the vegetation-is higher. Bruin-and Moore (1985) have developed an expression for the velocity profile.in the transition region between the top of the exponential wind profile in the vegetation canopy and the overlying logarithmic zone. This transition*zone is thought to extend to a distance of about twice the average plant height (H) above the ground over tall vegetation such as trees. However, this transition zone is not well studied and it is common practice to match the logarithmic and exponential velocity profiles presuming a sharp interface at the top of the vegetation. The near-ground constant shear sub-region of the boundary layer is poorly studied. No published measurements have been found for this zone. However, the measured velocity profiles within plant canopies given in Cionco (1971) indicate that the exponential profile extends from@the top of the vegetation to about 15% of its height. Although the relationship between the thickness of the near-ground logarithmic layer and plant parameters certainly contains planting density, vertical foliage distribution, and other factors in addition to plant height, this simple estimate is adequate as an initial estimate. In summary, the shear-dominated atmospheric boundary layer in a fully developed flow (remote from the boundaries of the vegetation) is characterized by three,sub-regions which can be described by either logarithmic or exponential velocity profiles which match at defined levels. The aerodynamic effects of the vegetation can largely be represented by three parameters: 1) the roughness length (zo) , 2) the zero plane displacement (d) , and 3) the attenuation parameter of the exponential profile (a). As will be discussed later, it is necessary to know these parameters.for the particular vegetation of interest because they vary significantly for different plants. There are no measurements in the literature for coastal vegetation so the principal of similarity, which is commonly used in studying flow phenomena, has been resorted to for estimates of values for coastal vegetation. A sensitivity analysis can be used to establish the relative importance of the vegetation aerodynamic parameters in evaluating changes in the shear stress applied to the ground and hence the. change in sand transport relative to bare ground. The wind profile equations are combined and'written so the wind speed at the top of the near-ground logarithmic layer (u9) is expressed in 15 terms of the vegetation parameters and the wind speed (u ref) at a reference height (z ref) high above the plant canopy. That is, ln ((H-d)/z 0) exp (-0.85a) ug = uref[ln((zref-d)/z0)] This is differentiated with respect to the vegetation aerodynamic parameters. dug = - 0.85 (M da u N) exp (-0.85a) ref dug zo [ln((u ref-d)/(H-d))] exp(-0. 85a) dZ o = - ur ef N2 dug = - exp (-0.85a) [(N/(H-d)) - (M/(u ref-d))] dd u ref N2 dug = - exp (-0.85a) dH uref (H-d) N where, M = ln ((H-d)/z 0) N = ln ((u ref-d)/z 0). When these partial derivatives are evaluated for extreme parameter values and a 50-m reference height, it was determined that the plant roughness parameter (z 0) is more important than the exponential velocity profile attenuation parameter (a). The zero plane displacement (d) and plant height (H) are less important than (a). This provides some guidance concerning the application of similarity-based comparisons between plants where measurements are available (generally crops and forests) and coastal plants. The process of estimating the vegetation aerodynamic parameters for the coastal plants of Florida, and the resulting values, are given in Appendix A. 16 METHODS OF ANALYSIS The role of vegetation in trapping sand and preserving sand storage within beach and dune systems can be analyzed using the concepts explained in the previous section. In many cases there is a rapid transition of near-ground wind velocity and boundary shear stress from bare sand to a vegetated zone. At the vegetation line there is a transition width in which the boundary layer exhibits nonuniform conditions as it adjusts to the - presence of the vegetation. This transition region has a length on the order of*10 to 30 times the average vegetation height. This may be a distance of only a few 10s of feet for short grass and considerably longer for coastal forests. Therefore, there are two major conditions to consider. Broad zones of coastal vegetation permit the re-establishment of uniform flow conditions. Narrow vegetation zones only exhibit non-uniform flow conditions. Fully Developed Flow The fully developed flow case provides a good beginning for the analysis of how vegetation brings about changes in aeolian sand transport for several reasons. First, it provides a relatively simple way to address such basic questions as: How great a change in sand transport is caused by-various types and densities of vegetation? What spacing or density of one vegetation type is equivalent to the'spacing of another vegetation type with respect to its.capacity to trap and retain wind blown sand? How do the sand trapping capacities of various vegetations change with wind speed and plant spacing? To what degree can a coastal forest be thinned out to provide a better view without seriously impacting the sand trapping capacity of the natural condition? A second reason for concentrating on the analysis of uniform flow conditions is that they have been more fully studied in agricultural and military applications so that there is a body of' knowledge that can be adapted for application to coastal .engineering problems. There is also a substantial difference in the approach that agricultural scientists have taken to uniform and non-uniform conditions with the former having more rigor. Figure 6 illustrates a simplified version of the envisioned conditions. As the air flow enters the zone of vegetation the near-ground flow is changed as the boundary layer (b.l.) establishes a new equilibrium. If the wind is strong enough to transport sand on the beach, and the vegetation causes this transport to cease, then deposition will occur in the transition zone. A similar, but reversed pattern develops on the downwind side of the vegetation zone. Here erosion can occur when the 17 upwind sand supply is blocked by the vegetation. Clearly these general patterns will reverse for an offshore wind. In order to address the types of questions examplified in the introduction to this section a straightforward method of analysis can be applied. Figure 7 provides a definition sketch. The problem is started by specifying a 10-m wind speed. This wind speed, either measured at, or corrected to, the height of 10 m above the ground is used because it is a standard measurement used by most meteorologists. The mean sand grain size, the sand size gradation,and the sand grain density must also be specified as environmental inputs. Several vegetation parameters must also be known. These include the average height, characteristic plant spacing, spacing or density of plant in the area of interest, and the vegetation aerodynamic parameters (ie. z , d, and a). The vegetation aerodynamic parameters are nA available from the literature or previous studies but estimates for these are available in Appendix A of this report for most of Florida's common coastal plants. The 10-m,wind and sediment information are used to compute the fluid shear stress applied to the sand bed by the wind and to compare this to the critical shear stress for grain entrainment.' If this is not exceeded then the.analysis is not of further interest. If the threshold is exceeded then a second computation is made using the new roughness parameter (zl) to compute the ' friction velocity (u,) . This is used to compute the sand mass transport flux using Bagnold's equation. This provides the bare sand transport rate as a basis of comparison. The logarithmic velocity profile equation is then used to calculate a reference wind speed (Uret) high. above the ground surface (a reference height of 50 m is convenient) based on the .10-m value. It is reasonable to assume that this value will remain unchanged over the vegetation, at least for local scale analyses. The 50-m wind speed provides a starting point for the analysis of air flow over and within the vegetation canopy. The vegetation parameters zo and d are used with the modified velocity profile equation to compute the wind speed at the top of the vegetation (UH). This can be used with the exponential velocity profile and the vegetation attenuation parameter (a) to calculate the velocity at the level of the top of the near-ground log layer (z = 0.15H). Finally, the shear velocity can be calculated with another application of the logarithmic velocity profile so that Bagnold's equation can be used to compute the mass flux of wind blown sand in the vegetated area. 18 Transitional Flow Although the procedures for analyzing the effects of coastal vegetation using vertical wind profiles and uniform flow conditions are quite useful in quantifying the effects of different plant types and densities on aeolian sand transport, deposition and erosion, it is clear that the width of many coastal vegetation zones is not sufficient for this type of analysis to be entirely satisfactory. This is particulary true for taller vegetation as the width of the transition regions is typically 20 to 30 times the plant height. For these reasons a method has been developed to account for long narrow vegetation zones, generally parallel to the coast. These zones may be either natural or planted. They tend to look and function like .the windbreaks and shelter belts common in inland agricultural areas. Again, there is no published information regarding the physical effects of these narrow zones on the coastal environment and the information which has been used is adapted from the agricultural engineering literature. The use of vegetation as windbreaks and shelter belts dates from the time of the ancients and is still widely used in agriculture to shelter crops from strong winds that inhibit growth. They are also used to reduce evapo-transpiration losses or to enhance 02 and C02 exchange, the former by reducing the turbulence in the sheltered area and the latter by increasing it with appropriately designed windbreaks. Consequently, there have been many studies of windbreaks and different types of optimizations have been sought. one common definition of an optimized windbreak in agricultural engineering is that which provides the greatest near-ground reduction of wind speed over the longest downwind distance. This is a definition which promotins sand retention in the coastal environment and thus, is adopted for these analyses. In order to understand why a narrow line of vegetation (or a single sand or snow fence) is quite effective in trapping wind blown sand it is necessary to understand its effect on the atmospheric boundary layer. The actual effects are complex and no analytic solution of the governing equations has been developed. As a result, a combination of wind tunnel experiments, field measurements, and some numerical modeling have been used to develop a descriptive understanding of the underlying processes. Figure 8 shows the pattern of developing boundary layers which form as the result of a low narrow, wedge- shaped non-porous barrier in a thick boundary layer flow (ie. the thickness of the boundary layer is many times the height of the barrier). Plate (1971), and many others, have pointed out that the flow disturbance is very dependant on the upstream velocity profile, well before it encounters the barrier. A simple uniform logarithmic velocity profile is pictured in Figure 8 as an initial condition. 19 The flow disturbance begins a distance upstream of the barrier (typically 3 to 5 times the height of a non-porous barrier). A persistent counter7flowing eddy often forms upwind of the barrier. A zone of flow'separation begins at the top of the barrier and'extends many times the height of the barrier downstream. This zone of separation is outlined by a streamline defined by, Ub/Uinf 0.5, where ub is the velocity in the lee of the barrier and ulnf is the velocity at a corresponding height in the undisturbed boundary layer upstream of the barrier (Plate, 1971). There is a transition region, centered on this bounding streamline, between the region of barrier influence (#2 on Figure 8) and a 'bubble' of sheltered air flow (#6 on Figure 8) in the lee of the barrier. The point where the bounding streamline intersects the land .surface is defined as the reattachment point. This marks the downwind limit of most zones of interest in agricultural engineering because most of the sheltering occurs upwind of the reattachment point. However, from the point of view of understanding coastal processes it must be noted that the region of the re-establishing boundary layer (#3 on Figure 8) is still an area where the near-ground wind field is substantially altered from the undisturbed upwind reference condition. This means that the barrier can exert an influence on the sand transport patterns on the downwind lengths comparable to the coastal length scale. Several other-features shown on Figure 8 are significant. As the air flow encounters the region of influence of the barrier it is deflected upward and over the sheltered.lbubblel. Indeed, most non-porous barriers create a counter-flowing eddy on their upwind sides which has a near-ground flow opposite the regional wind direction. In strong winds the sand transport is arrested with the deposition taking place several barrier heights upwind. Downwind of a non-porous barrier another counter-flowing eddy forms in the sheltered bubble. In extreme cases this flow is strong enough to transport sand in the direction opposed to the regional wind and to form a blow-out depression. It has also been noted that the reattachment point is relatively close to the barrier (about 10 H) if it is non-porous. Narrow belts of vegetation such as windbreaks and shelter belts can be very dense and thus approach the condition of a non-porous barrier. However,.more generally, they have varying degrees of porosity and therefore provide 'leaky barriers'. Although the overall pattern of boundary layer disturbances shown on Figure 8 20 is generally also valid for porous barriers, there are some important differences. one difference is that the air flow leaking through the barrier reduces the velocity contrast above and below the streamline bounding the sheltered bubble and thus the amount of shear-driven turbulence in the transition region is reduced. This has the effect of actually reducing the turbulent exchange of horizontal momentum across the bounding streamline and stretching out the downwind extent of the sheltered region. Furthermore, the porous barrier substantially reduces the magnitude of the pressure difference across the barrier which further contributes to the lengthening of the sheltered region. This also promotes the breaking down of the counter-flowing eddy in the sheltered bubble. The counter-flowing eddy upwind of the barrier also vanishes as the pressure difference across the barrier is reduced. Plate (1971) quotes classic field studies by Nageli (1941) and wind tunnel experiments by Blenk and Trienes,,(1956) which showed that, for a maximization.of near-ground wind speed over the longest downwind distance, a medium barrier porosity (30 - 50%) i,s needed. The zone of at least 20% reduction in wind speed near the ground extends about 25 H in these conditions (Robinette 1972). As the porosity of the barrier is decreased the magnitude of the reduction of near-ground wind speed tends to increase, and eventually a counter-flowing eddy develops in the sheltered - bubble. At the same time, the increased pressure gradients due to the reduction in barrier porosity cause the point of reattachment to move closer to the barrier and the inclination of the separation streamline, as it approaches the ground near the point of reattachment, also increases. The downwind length of the sheltered zone is reduced. On the other hand, if the porosity of the barrier is increased from the optimum 30-50% level, the downwind length of the sheltered zone increases to a maximum at about 35 H but the reduction of the near-ground velocity becomes increasingly negligible. These patterns are shown in a general way on Figure 9. The bottom panel (D) of-Figure 9 illustrates another feature of vegetation wind barriers. If they are quite narrow and lack near-ground foliage, they can cause a near-ground jet to form. When this effect is strong it can lead to scour of the sand surface beneath the vegetation and may even threaten the health of the vegetation. These observations of the behavior of vegetation windbreaks are' in general agreement with studies of sand, and snow fences. Hotta et al. (1987) provide a good review of the literature on both field and wind tunnel experiments with snow fences. No 21 really comprehensive study has been carried out in a way that permits identification of the optimum porosity to create the greatest near-ground wind reduction over the longest downwind length. Different investigators used fences with different discrete slat arrangements along with various sand sizes, wind regimes, fence alignments, experiment durations, and measurement methods (Tani-1958, Kimura 1957, Nishi and Kimura 1966, Jagschitz and Bell 1966, Monchar and Bruun 1970, Savage 1963, Woodhouse and Savage 1969, Gage 1970, Dahl et al. 1975, Phillips and Willetts 1979, and Iversen 1981). These studies show that sand fences (and snow fences,) act like vegetation wind barriers so that the most protection is effected when the counter-flow eddies are minimized, the width of the sheltered area is long and the effective wind reduction is acceptibly high to promote dune growth. This occurs when the fence porosities are in the 30-50%' range. As noted earlier, there is a problem in combining the approach used for analyzing the uniform flow conditions to that used for transitional flows because the researchers.studying crop air exchanges and windbreaks have taken different approaches. Although there are scattered detailed studies of specific conditions that have been carried out with rigor (eg..the application of numerical models) there is no consistent basis of comparison. In the absence of an established common basis for quantifying the attenuation of wind on sand transport by continuous and narrow vegetation belts, a combined approach was developed. The basis of this approach rests on the.common observation that greatest'sheltering is developed by a wind break with a 30-50% porosity and this is similar to the vegetation density which causes maximum attenuation in a large field of vegetation. This provides a link to combining the largely judgement-based assessment of a wind barrier's porosity used.by one group of agricultural scientists with the more quantitative measures developed in the numerical model of Pereira and Shaw (1982) which associates the drag parameters with the product of the plant drag coef f icient and the leaf area density (C,. PAI) The ratios of the vegetation aerodynamic parameters zo/H and d/H are used to estimate the product of C PAI for the observed spacing of plants in a wind break. TEs value is then compared to the value associated with the greatest drag (ie. the highest zo/H). When the estimated product for the observed spacing is above the point of greatest drag then the length of the sheltered zone is reduced proportionally from 20H to 10H depending on the ratio of the difference between observed and maximum common spacing to the maximum common spacing. On the other hand, if the estimated product Cd*PAI is less than that for maximum drag then the wind attenuation is adjusted in the same way that it is for 22 the fully developed flow case and the maximum sheltered length is lengthened towards a maximum of 35H. The result of the 'analysis is a sand transport rate calculated for the sheltered area and compared to the bare sand case. The length of the sheltered area is also calculated. Some auxillary information is of value in using the results of the above calculations. If a line of vegeation parallel to the beach is shown to be an effective windbreak then the effects of natural or man-made gaps should be carefully considered. Such gaps will only degrade the effectiveness of.the vegetation line and if they are wider than several times the average plant spacing, they can cause a funneling of the near ground wind speed. Robinette (1972) indicated that such funneling can increase the wind speed immediately upwind of the gap by about 20%. This can be sufficient to cause a local scour hole with a width approximately equal to the gap in the line of vegetation. All of this shows that even narrow zones of vegetation can be quite significant in contributing to long sand retention on the upper beach and in the dune system. Effects of Local Slopes and Terrain Up to.this point there has not been mention of how slopes and terrain effect the analysis of the physical effects of vegetation on sand transport and dune systems. The effects are rather complex. Furthermore, these effects have been routinely avoided by researchers concerned with the attenuation of the wind by crop and forest canopies because they needlessly complicate .experiments. It is, however, necessary.to discuss these effects, at least qualitatively so that proper judgement can be used in applying the methods of analysis described in this report. If a wind is directed onshore across a broad and flat beach it will develop a logarithmic velocity profile. When the air flow encounters a slope behind the beach the vertical structure of the boundary layer changes. The slope introduces form drag which is realized as a pressure gradient. As the air flows upslope the streamlines converge,'the flow accelerates, and the pressure falls. Hence, there is a pressure gradient in the direction of the upslope flow which tends to further accelerate it. This favorable pressure gradient exists close to the ground so that the increase in velocity is not uniform with height. The vertical velocity profile is no longer a simple logarithmic function and the methods for analyzing wind attenuation in plant canopies and aeolian sand transport, which depend on a simple, predictable form of the vertical velocity profile, can no longer be rigorously applied. 23 Figure 10, taken from Bowen and Lindley (1974) illustrates the near-ground over-speeding effect from measurements made on a 13 m high slope of 260 and a nearly vertical cliff 9.5 m tall. The over-speeding was confined to a height of about twice the ground level difference (z'') and extends about 12 z'' downwind of the slope top. These results are qualitatively similar to what can be,expect for other forms of local relief but accurate predictions depend on many factors including the wind speed, the roughness of the ground upwind of the toe of the slope, the density stability of the boundary layer, whether the slope is vegetated, etc. There are many other effects. of local topography which affect the wind speed and its vertical-profile. The wind is often funneled into gullies and low areas, it is disturbed by large obstructions such as buildings, and the air flow can become detached at the crest of dunes causing a counter-flowing eddy in the lee. All of these factors are too complex to be treated in a comprehensive analytical method. The engineer or scientist is left to use the analysis techniques presented in this report along with good judgement in applying them to complex real problems. Coastal Scale Effects In evaluating the p hysical effects of vegetation in coastal areas it can be important to consider large scale processes which may be alteAd as aresult of changes in vegetation. Ideally, there should be an analytic method which predicts sand transport, ' erosion, and deposition by the wind over zones with length scales of several thousand of feet. This method would be able to account for the changes in the near-ground air flow brought about by both the topography and the differences in the vegetation. of course, the development of this procedure constitutes a rather large undertaking and is not available at this time. However, there have been many studies which address elements of this procedure and which provide insight into the results that are possible. A starting point involves considerations as simple as: "From the point of view of preserving the coasts against long term erosion, what physical features should be considered a dune"? "What combinations of winds and sand transport cause and maintain coastal dunes"? "How does vegetation in one part of a dune field effect the air flow long distances downwind"? A reconnaissance was made to evaluate the type of features which can be designated as dunes as a first step in addressing these coastal scale processes. The viewpoint adopted was not purely that of a coastal engineer or coastal geomorphologist who might tend to restrict the term dune to only those features which originate solely as a result of aeolian processes. Instead, the consideration was based on the idea that any feature which tends 24 to collect and retain wind-blown sand can be included in the pragmatic definition of the term 'dune'. Florida Department of Natural Resources beach topographical profiles were obtained and plotted for Walton, Manatee, Charlotte, Collier, Dade, St Lucie, Brevard, Flagler, and Nassau counties as a sample of the general coastal environments around Florida. A detailed description of the analyses of these data is. presented in Appendix D. The analysis supported a classification of the dune, and dune-like, features as being represented in five general categories which bear little resemblence to the classical dunb forms common to desert areas. These five classes are: 1) multiple parallel to sub-parallel sand ridges generally aligned with the shoreline, 2) a-single very elongated ridge parallel to the beach, 3) one or more elongated ridges atop the low wave-cut cliff or bluff behind an active beach prism, 4) low hummocky sand hills, often with nearly irregular plan-view patterns, 5) coastal relief highly modified by roads, structures, and other unnatural features. The characteristic dimensions and"sIopes of these features were tabulated as a first step-in determining methods for rigorous study of air flow and vegetation-distributions on the coastal length scale. These data are included in Appendix D. The analysis of coastal scale processes was delayed for a future phase of this work in agreement with the Division of Beaches and Shores contract technical representative to allow substantial effort to be directed at the local scale processes. 25 FIGURES ZO zo I U (Z) U (Z) I a 1 b Figure 1 The logarithmic velocity profile as a linear (a) and a semi-log plot (b) 1 2 3 4 5 6 Below Threshold = 1,2,3 ZI Above Threshold = 4,5,6 zo U, U (Z) Figure 2 velocity profiles before and after the grain transport threshold is exceeded 70 60- 50- Fluid Threshold ( 40- D 30- .01P Oe 20- %% 00 Impact Threshold 10- w 0 -j 0 0.50 1.00 1.50 2.00 ip? Figure 3 Threshold shear velocities (u. crit) Ou T @hr.,es h 0 1 Zd impact jjnIt L idt Mass Flux fS fd Figure 4 Definition sketch of a sand transport control volume. Log u (H) -- -------- Js ntial x one H d Log U Figure 5. Definition sketch of velocity profiles and a plant canopy LOCAL SCALE STEADY NON-UNIFORM FLOW Wind Wind Deposition Erosion Established b.l. Established b.l. b.l. Establishment b.l. Establishment Figure 6 Definition sketch of wind moving from bare sand to vegetation U (50M) U (50M) U (10M) U (10M) H d= 0.7 H 1 do @--O.l 5H t Figure 7 Uniform flow analysis definition sketch UNDISTURBED BOUNDARY LAYER (OUTER LAYER) REGION OF HILL INFLUENCE (MIDDLE LAYER) REGION OF REESTABLISHING BOUNDARY LAYER INNER LAYER BLENDING REGION BETWEEN MIDDLE AND OUTER LAYER BLENDING REGION BETWEEN INNER AND MIDDLE LAYER STANDING EDDY ZONE POTENTIAL OUTER FLOW 1!0 MM h 0 L Figure. 8 Diagram of flow disturbances and boundary layer development around a non-porous barrier (from Plate 1971) A 2-5H 10-30H 22 18 6 10 19 22@ MPH .10H C 2-2 19 19 22 MPH 25H lot D Figure 9 Typical sheltering by vegetation strips. A: non-porous barrier, B: barrier with low porosity, C: barrier with moderate porosity, D: wind jetting under barrier foliage (from Robinette 1972) roference upst PC r*am 1h I local oneen rnean virlocity profile ity Pircollif err#. wind direction IOU louret. E -hu CF I III in cl Iff heights distance in Cliff heights f ram top edge. I rarn W"r edge. 1.0 I-S 1.0 I-S .1-0 I-S 1.0 14 1.0 I-S 1.0 VS S 2z 0. 1-0 I-S as 1-0 1-5 f 2Z z z z 2z 3z &Z Gz 4z 12 z S'Z 2Z IOOOk 10 I's 1-0 I-S VO I-S 1.0 I-S VO I-S It I-S 1-5 2 Z zz z z 2 22 4 z 6z Oz 12 z FIELD RESULTS 5 z WIND TUNNEL RESULTS Figure 10 Variation of mean wind-speed over a sloping and cliff escarpment relative to the upstream wind speed at I Hit 10 m above the ground from Bowen and Lindley 1974) p APPENDICES Appendix A -- Vegetation Aerodynamic Parameters Appendix A -- vegetation Aerodynamic Parameters The previous discussion of air flow through plant canopies shows that vegetation is effective in reducing the near-ground wind and consequently the associated sand transport. The present theories for predicting the effect of the vegetation canopy on the wind profile depend on aerodynamic parameters which must be measured for each plant type and community. These measurements must be performed carefully in the correct conditions to provide general results and therefore very few measurements are available in the literature. Furthermore, the understanding of the roles of many of the aerodynamic parameters in defining air flow was not recognized in the early stages of this research. Thus, several years went by with only incomplete data sets being produced, many with key parameters omitted. The intent of this study is to understand the role of coastal vegetation in modifying the air flow and sand transport regime. The research on winds in plant canopies was motivated by agricultural and forestry concerns. Therefore, there are no direct measurements of the aerodynamic parameters for coastal vegetation typical of Florida. In order to provide a rational basis for analysing these questions before such measurements for coastal vegetation become available we have applied the concept of similitude, which is often used in problems of fluid flow, and estimated the aerodynamic parameters for the coastal plants based on the largest amount of measured data for non-coastal plants that could be assembled. Although there have been several published attempts to relate some of the aerodynamic parameters to physical properties of the plants (or somewhat predictable flow scales such are the mixing length amid the foliage), none have proved successful. As a result, the estimates were based on judgement, guided by a good understanding of the underlying physics and assisted by the results of the numerical model developed by Shaw and Pereira (1982). Their results associate z /H and d/H with the product of the plant drag coefficient and theoleaf area density as adjusted for the vertical distribution of foliage. Table A-1 shows the total collection of measured data which were assembled. Almost all of the data are for crop plants or forest trees but some trees are the same as those found close to the beach in some places in Florida. Table A-2 lists the common dune plants of Florida and many of their physical characteristics. These characteristics were obtained for the literature where @possible or estimated by experienced botanists. The physical characteristics such as typical plant height, diameter, spacing, leaf area, leaf area index, etc., and photographs where available, were used to assess the similarity of the unmeasured coastal plants to the plants with measured aerodynamic parameters. The assigned values of ZO/H, d/H, a, and the typical close spacing are shown on Table A-2. A method was developed to provide for different spacing of the coastal vegetation in computing its effect on sand transport. Shaw and Pereira (1982) provide graphical results that relate zo/H and d/H to the product of the leaf area density and the drag coefficient for the plant type. The leaf area density is easily adjusted for changes of the plant spacing and functions fit to the graphs were used to adjust zo/H and d/H. The modification of the exponential profile attenuation coefficient was accomplished in a similar way. Cionco (1978) provides the only published data. The attenuation coefficient is related to a planting density which is poorly defined. The data are available only for different planting densities of corn, in a set of field measurements and for different densities of wooden pegs, in a series of wind tunnel measurements. The data show similar trends to each other with the maximum attenuation occurring at about 1.5 times the closest spacing. At closer spacing the canopy is relatively impenetrable and the air flow tends to slide over the canopy as if it were a 'new' surface. Although these data are very limited they-are the only source available and therefore were used as the basis of an equation which was fitted to the experimental results. This equation is used to adjust the attenuation coefficient for different plant spacings. TABLE A-1 AERODYNAMIC PARAMETERS AND VEGETATION DATA Page 1/4 S ROUGHNESS P! A --------- k@@ --------- PAI (to N @ n@ --@ t area) ELEMENT DRAG COEF. VEEGETAT I ON VV; .'CE NOTES 171 r, D ri A! C. V down LAI (LAIA) SA (HA) SA/s (cm) Cd Cld Zmax/h SO, ------------------- corn or Ess 0.56 0.012 5-10 Inoue & Uchkima (79) crowing plants @ 59,000/HA crass 140 40,i.4o 2 2.56 0.018 5-10 6 4.2 0.019 5-10 Grass 225 *Y0 -10 GFEES 4.2 0.011 5 crass 5 2.9 25 0.17 Wilson, etal (82) f total area index total surf. 2rea/unit ground aTea Grass plantsi'"A grass (various) 1695 sq. cm/pI ant or a SF 5-10 r)Q 0, 1 era=r 0. 00 Cionco (Cw@ from Inoue (63) Grass 5 0.036 0.61 0 Uchijiaa & Wright (63) unpublished, 4.2 Cooper (75)i 'IT as 5 0. 22 Wilson @ S6Y (77) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 0.0 Raynor (71)@ crass Grass LJ U Grass 70 JL 0.74 Fritschen, etal (B5) 7- - - - - - - - - - - - - - - - --- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Kochea Grass 20 to 0.50 Frit5Chen, etal (85) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 7 -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- I - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - O.-ts 0 T 2 SS 90 6.5 60 0.072 0.67 -2.B 0.22 Cionco (83)1 press 4.2 Cooper (75) grass 30-100 1.0 (Various) *leaf length = 25 cm -------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------- --------------------------- ----------- rice grass 5 Tsenq & Teng, f booting stage grass 4.5 1 heading 5taqe grass 3.6 1 oil k-ripe staqe Grass 3.2 1 douqh-ripe stage Orass 85 6 50 0.071 0.5j Maitani (78), * ear emeroence stage grass 60 9.4 35 0. 157 0. 58 f young ear formation stage grass 122 1.0 (various) I leaf lenqth = 30 cm Grass 76 2 0 x 2 0 0, 000 3.65 1.0 Inoue & Uchi.jima (79) 1 240,000/HA in 30 CM TOWS; spacing 1400 cm Grass 85 25 50 0. 2,1- @9 Maitani (77) J VESS 60 0 1 21 i 1 01.67 1.18 0.24 Nakagawa (5@6 L Gr2ss Cionco 0 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- rush Crass 130 16 80 0 . 1, 2 3' 0.62 Maitani (78 1 harvest stage ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ i ------------------------------------ ------------ I-------------------------------- sunfiower crasc- 1.89 Cox & jolifi (87) iTTigated-early 4.5 irriqated-late class I . '27 dryland-early Grass 2.05 f dryland-I ate crass 5 1 J. artichoke (various) I leaf length = 5-18 cm Grass @ij ij.! i [A. 7 0.53 Cionco (83) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Q0 ----- i-------------------------------------------------------------------- wheat Glass 89 0. 63 Flaitani (78.), t T10en1nQ staoe Grass 100 818 60 0. 088 0. 60 t riDenin- Stage 3 4 Grass 14"q -4 0. 0., Cionco (831) Grass 1.0 (various) leaf length = 41 cm OT2S= fl, 140 3 7 Cooper (75) Or 2 55 7. "1 0. i E, 2;5 t 0.25 Legg (74) sc-E@@-.j is between rows crass o.-) Pain-es (71) ------------------------------ ----------------- ---------- .................. 77 ------------ TABLE A-1 AERODYNAMIC PARAMETERS AND VEGETATION DATA Page 2/4 5 ROUGHNESS PLANT h SPACING Z o D --------- RC --------- PAI (lot area.) ELEMENT DRAG COEF. VEGETATION TYPE Q 11) (Cm.) (C 01) (CA) Zo/h D/h ALPHA up Canopy down LAI (LAI/h! SA (HA) SA/5 (Cm) Cd r1d Zmax/h SOURCE NOTES alfalfa '2'a' shrub 80 52, 0.000 0.65 Fritschen, eta] (85) alfalfa 'a' Shrub 1). 000 0. 5" ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------- bean chrub 118 10.8 88,@ 0.092 0.75 6.25 (1. 1- Thom (71) J bean sprouts shrub 100 6 0.000 0.60 Rider (56) all plants @ mature ht --------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------- ------------------------------------------------------ cotton shrub 1321 - 3 13.8 co 0.104 0.38 Stanhill & Fuc@s (67) * mature plants shrub 126.8 12.6 62 0.099 0.49 shrub 47 25x8O 14 45 0.298 0.96 1.1 3.4 0.01 Jarmam (59) * irriqated olants shrub 72 50x8O 14 45 0.194 0.63 3 0.01 * 3 plants/hole shrub 80 50x8O 14 45 0.175 0.56 3.8 4.6 0.01 rows were 80 cm aoaTt shrub 69 25x8O 14 45 0.203 0.65 2.5 3.4 0.01 not fUIIY Mature shrub -77 50x8O 14 4 5 0.182 0.58 3.5 4.1. 0.01 shrub 91 50x8O 14 45 0.154 0.49 6.1 7 0.01 ------------------------------------------------------------------------------------------------------------------------------------ -------------------------------------------------------------------------------- -------------------------------------------------------------------- Creosote bush shrub 200 150 0.000 0.75 Fritschen, et@ (85) --------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------- peas shrub 60 25 0.000 0.42 Rider (56) 7 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------- sagebrush shrub 53 73%139 6.4 12.2 0.121 0.23 0.25 Haqen & Lyles (80) shrub 68 73x139 5.4 54.4 0.079 0.80 0.25 --------------------------------------------------------------------------------------------------------------------------------------- I----------------------------------------------------------------------- ----- - ----------- ----------------------------------- soybean shrub too 4.4 76 0.044 0.76 0.5 0.23 Cionco (83) shrub 0.87 Cox & Joliff (97) * irTiqated-early shrub * irriqated-late shrub 0.77 * dryland-early shrub 2.2 * dryland-lite shrub 7.5-183 (various) I leaf lenoth = 7.5-15 cm shrub 0.12 Baldocchi (82) in Meyers & Paw (86) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------- yucca shrub 44 73x218 5.3 7 0.120 0.16 2.0 Haaen & Lylesl11-8-8-) ------ F--d--and --- Zo --- va-1-ues are taken from figures showinq these to shrub 79 73x218 6.3 39.5- 0.080 0.50 be functions of PAI & Cd -------------- TABLE A-1 AERODYNAMIC PARAMETERS AND VEGETATION DATA Page 3/4 S ROU6HNESS PLANT h lb@pAcltqb Z c. 11 --------- Pr --------- PAI (lot area) ELEMENT DRA6 COEF. VEGETATION TYPE (rm) 1'rm) (cm) Q@) Zo/h D/h ALPHA U0 cancloy down LAI (LAIA) SA tHA) SAIr Cd C'd Zmax/h so CE NOTES i- @Fll ----------- -------------- citrus tree '360 730x610 0.000 0.49 2.54 Brooks @. Shultz (55) * distance between canopies 90 - 180 coi citrus qrove tree 8.9 Hirano, et@l (81) * 13 Yrs. old @ 10,000 trees/HA tree 7.6 * 5 YTS. old @ 10,000 trees/HA tree 4.7 1 13 Yrs. old @ 1250 trees/HA tree 0.9 * 5 vr5. old @ 14150 tree5/HA tree 7.1 f 1-3000 trees/HA; most common plantinq tree 370 0.60 0.'T4 orange tree 425 400x4OO 40.4 286 0.095 0.67 6.5 4.5 0.04 0.71 Kalma & Sta ,nhill (71) * trees 35 yrs. old ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ -------------------------------------------------------------------- 7 Douqlas Fir tree 2300-3000 Hiqht5hoe 0 8) # leaf lenoth = 2.5-4 cm; tvoical spread = 6-10 m tree lEJ50 9 0.006 * 60 vrs. old tree 70 7.7 0.11 Cooper (75)1 * 5 yrs. old tree 000 9 0,009 * 25 yrs. old tree 1420 9.31 0.007 BOTQhEtti (86) * plantation fir tree 3000 2100 01000 0.70 Frit5chen? Ietal (85) --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------- Qum tree 1500-2000 7.5 Hightshoe (78) leaf lenqth = 7.5-15 cm; typical spread = 10-15 m Qum-MaDle tree 4.4 0.07 Cionco (83)' --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ----------------------------- --------------------------------------------------------- larch tree 1040 3000100 57.1 809 0.055 0.78 9.36 0.013 Allen (68) * 2/3 of needles dropped but rest well spaced tree 126.8 633 * data for fully dropped needles ignored tree B1.3 750 tree 39.2 704 tree 206.7 494 tree 52.2 733 tree 112.4 635 tree ------------------ tree ave 96.8 691 tree 4.1 larch plantation tree 1040 54 726 0.052 0.70 1 0.16 Cooper (75)) tree 1500-2300 Hiqhtshoe (78) 1 leaf lenoth 1-4 ca -- ------------------------------------------ ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- maple-fir tree 4 Cionco (83)i -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------- I Oak tree 150 6.5 0.043 Cooper (75) saplinq tree 1000 5.8 0,006 tree 2000-3200 Hiahtshoe (78) fleaf lenoth = 4-10 cm; typical spread = 15-23) m Oak-G.Um @ree 0.19 Cionco (83) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- TP,'EES, continued... TREES, continued... TABLE A-1 AERODYNAMIC PARAMETERS AND VEGETATION DATA Page 4/4 S ROUGHNESS PLANT h SPACING 11, 11 --------- Rc --------- PAI (lot area) ELEMENT DRAG COEF. VEGETATION TYPE (c 11) ico) (cm) (cm) Zo/h D/h ALPHA up canopy down LAI (LAI/h) SA (HA) SA/s (cm) Cd C'd Zmax/h SOURCI NOTES pine tree 1050 120xI50 100 Soo 0.095 0.76 0.68 0.15 6 Raynor (71) * forest tree tree * 1474 trees/ha tree * trunk dist. @ breast ht, 3.8 - 1Z.3 cm tree * lowest livinq branches 2 - 4 m above oround tree f spacinq is as Planted in 1939 2.5 0.3 Halldin & Lin roth (85)f projected needle area 2.5 (thin) tree 1850 1270 0.069 0.69 DeRruin (84) tree 1850 1@9 1310 0.075 0.71 Molion & Moore (83) I tree 700 490 0.000 0.70 FTitschen. etal (85) tree 700 460 0.000 0.66 Red Pine tree 2200 19.1 0.000 0.0087 Martin (71) density 60 -70% tree 2200 19.3 A. 006 0.0088 bottom of canopy @ 10 m tree 2200 20.0 0.000 forest tree 2200 19.9 0.000 0.0090 tree - 2200 20.2 0.0010 0.0092 tree 2200 19.8 0.000 0.0090 tree 2200 19.7 0.000 0.0090 tree 2200 20.2 0.000 0.0092 tree 2200 ------- 0.000 tree 2200 ave. 17.275 0.0079 0.23 12.1 Scot Pine tree 0.14 Cionco (83) Southern Pine tree 0.2 -------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------- T-------- ---------------------------------------------------------- Red Maple tree 2300-3000 5-10 Hightshoe (78)@ leaf lenqth = 5-10 ca; typical spread = 15-22 m tree 1300 5.13 0.004 Wang & Miller; (87) 30 yrs, old ----------------------------------------------------------------------------------------------------------------------------------------- 7 ------------------------------------------------------------------------- L----------------------------------------------------------------- SaItcedar tree 200 .150 0.000 0.75 Fritschen, etJ41 (85) tree 600 3056 0.000 0.5B ; I ----------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------ spruce tree 9.7 Cooper (75) F 25 yrs. old tree 10.6 * 60 yrs, old tree. 1500-3000 0.5 Hiahtshoe (78f) t leaf lenQth 1-2 cm; typical spread 6-10 N tree 2'. 7 0.13 Cionco (83) tree 1050 136. U2 0.130 0.64 1.8 10 0.14 Landsberq & ilames (71) TABLE A-2 COASTAL VEGETAT-ION AEROI)YNAMIC PARAMETERS s LEAF LEAF PLANT PLANT h SPACIN6 PAII (lot area) LENGTH AREA DIA. SIMILAP h ALPKA. LAI (.LAI./h) S A tso. cm) SA/s (cm) (sq. c a) (cm) FLEXIBILITY 4ARDINESS PLANT NOTES VEGETATiON TYPE Mro Dune Prairie Grass crass 150 46 0:640 0.80 2'. 4 4.60 . 0.0311 01010 2090 1.440 137 250 2 5. 3 high hiah corn * corn values used Saltmeadow CoTdqTas5 orass 90 12.2 0.1215 0. 60 2.21 5,00 0.056 372 145 21. 4 9 7 fil 37 12.2 h i ah rich rice * riCe Values used Sea Oats grass 183 60 0.120 0.60 2. 511 4.00 0.022 560 1860 0.301 60 46 15 hiah hiah wheat * wheat values used ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Beach Dean herb 15 1212 0.070 0.50 1 3.84 0. '156 620 14860 0.042 7.6 37 15 mod hiah ;au2sh * sunflower values used _0 Beach Croton herb 70 0. 1"20 0.56 0. J 1.68 0,024 117 3750 0.031 5.2 13 15 Pod god bushel basket-s * shrub default values use Beach Mornina Glorv herb 15 27 0. 070 0.53 1. 4.32 0.28B 1630 752 2.168 10 65 6.1 mod high Watermelon * sunflower values used Dune Sunflower herb 90 76 0.070 0.53 1.3 1.60 0.018 2930 5850 0.501 7.6 59 60 mod hioh watermelon * sunflower values used Railroad Vine herb 15 21 0.070 0.50 1.3 4.90 0.327 1115 460 2.424 10 74 7.6 mod hich watermelon * sunflower values used O.C use Sea Blite herb 76 61 0.120 0.56 1) 2.40 0.032 557 3720 0.150 5.2 2.8 15 low mod wooden petis * shrub default values - d Sea Purslane herb 15 30 0.120 0.56 0.5 1.20 0.080 280 940 0.298 3.8 2.8 15 nod high wooden peQs * shrub default values used@ ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ----------------------------- Camphorweed shrub 70 90 0.125 0.56 0.5 1.25 0.018 500 8430 0.059 5.2 8.4 37 nod hioh sovbean * shrub default values used Cocoplum shrub 300 460 0.060 0180 1.5 10.00 0.033 93000 186000 0.500 5.1 !93 460 low hiah junale * Door comparison-adjustments made to default values ConT adina shrub 90 150 0.125 0.56 0.5 1.20 0,013 2443 23200 0.105 1.2 0.93 60 mod mod * default shrub values use Gray Nicker Bean shrub 150 0.125 0.56 0.5 7.10 0.047 111500 5.2 A 460 mod high citrus * poor comparison--shrub default values used Prickly Pear Cactus shrub 90 30 0.120 0.50 0.4 2.40 0.027 2150 930 2.312 21 1430 24 low high bushel baskets * erect plants with fir flat Daddle-shaped leaves m' I Rosemary shrub 90 180 0.125 0.56 0.5 1.20 3500 33400 0.105 1,2 3.7 76 mod low plastic strips * poor comparison--shrub default values used Saw Palmetto shrub 150 15 0.120 0.50 0.6 4.20 0.028 17400 23400 0.744 76 5800 90 mod high bushel baskets * coaparison based on Yucc and cottontalfalfa Sea Grape shrub 240 240 0.100 0.70 1.5 10.00 0.042 93000 186000 0.500 20 410 244 low high Jungle * Spreads hor.; much wind hear across surf; comp. data, med Sea Myrtle shrub 200 150 0,125 0.56 0.5 3.60 16900 23200 0.728 3.8 9.3 107 mod high sunflower * medium level of comparable data 'Spanish Bayonet shrub 215 300 0.100 0.50 1.0 3.20 0.015 13500 93656 0.144 52 269 90 low high yucca * qood comparison with yucca data ---------------------------------------------------------------------------------------------------------------------- w------------------------------------------------------------------------------------------ ------------------------ Australian vine tree 3000 600 0.090 .0.70 2.7 23.60 836000 371600 2.250 21 900 low high spruce * d/H and Zo/H reasonable oaparison; alpha, poor Bay Cedar tree 2400 150 0.120 0.64 2.5 10.60 0.004 37200 23200 1.603 3,8 3.7 150 low sod Spruce * values for Spruce used Cabbage Pala tree 2300 600 0.070 0.50 1.3 7.10 146300 371600 0.394 75 460 low high oak * values for sunflower usel Chapman's Oak tree 600 180 0.060 0.70 2. 7 15.10 66900 33400 2.003 7.6 12 183 low high oak * grows w/Myrtle Oak; dens 3 thickets; values like Live Oak Coconut Palo tree 900 750 0.070 0,50 1.3 12.60 410000 580600 0.720 ' 460 900 mod god * values for sunflower usei Myrtle Oak tree 300 120 0.100 0.70 2.0 9.80 0. 033 37200 19500 1.908 7.6 12 152 low hiah oak. * dense thickets: soacina mailer than plant dia; poor comp. Sand Live Oak tree 900 460 0.060 0.70 2.7 18,90 445900 209000 2.133 5,2 13 600 low hiQh oak * Door @Iata Sand Pine tree 900 460 0.090 0.70 2. 5 11-11.60 334400 210700 1.587 7.6 90 low hioh Dine * d/H and Zo/H reasonable 2ta;alpha, poor Slash Pine tree 1830 900 0.090 0.70 2.5. 18.80 891800 836000 1.067 25 120 1 r@w hich FQTuce * d/H and Zo,H reasonable ata;alDha. Door Southern Maonolia tree 180 900 0.09 0.60 1.5 14.10 1170500 836000 1.400 15 900 low hiah OUM * not often in coastal sit ations; bnlv in panhandle Southern Red Cedar tree 760 600 0.07 0.70 2, 7 15.70 464500 371600 1.250 6 600 low hiGh ChFiStHS tree * nine. Salt Ceoar. and Ila ni values used Wax Myrtle tree 520 2 8 0.11 0,60 1.0 3. 0 0.007 79000 75240 1.050 10 21 21 13 low hiQh c. a I., -------------- Appendix B -- Recommendations for Future Work Appendix B -- Recommendations for Future Work There are clearly two major areas of future work that are essential to the successful application of the results of this study to the permit review procedures of the Division of Beaches and Shores. One is to develop and experimental program, including both field and wind tunnel measurements to verify and extend the methods which have so far been entirely based on literature values and relationships. The other major need is to extend this work to the coastal scale so that the larger scale effects of changes in coastal vegetation can be identified and quantified. It was not possible to accomplish this until there was a proper understanding of the role of coastal vegetation on the local scale and-the results of this study largely provide this. 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Appendix D -- Dune Forms of Florida Coast W f 2 -@scarp ib hscarp hi h2 h3 hbb -Wb Type 1 Multiple Parallel Sand Ridges IN f @scar b 1b hscarp hi hbb h low - - - - - - - - - - - - - - - - - - - - - - Th__ b Type 2 Single Long Sand Ridge .kW 4 @-q J5 f slope -@scarp 1b hslope hi h max hscarp IF . hplateau/hiow - - - - - - - - - - - - - - - --j- - - - - - - - - - - - - - Ft7b b f t@b Type 3 - One or More Ridges on a Coastal Bluff ' fW f 2 b-@ 4 h @m ,..,/h s I p e' b-@ @ZFb b t@b Wf @bb 3 ---------- Type 4 - Low and Irregular Sand Hills FLORIDA COASTAL DUNE PARAMETERS FLACLER (CLASS-2) lb hb lbb hbb l.. h.c l.f ilf 11 12 h, h2 h3 is, h3l h.. hl.. 50 2 0 0 0 0 80 240 0' 0 16 0 0 0 0 0 7.5 R-7 50 5 50 10 0 0 20 208 0 0 12 0 0 0 0 0 2.5 R-14 100 7 45 12 0 0 8 256 0 0 14 0 0 0 0 0 5.0 R-16 48 5 55 11.5 0 0 10 208 0 0 16 0 0 0 0 0 7.0 R-22 50 1 50 3.5 50 6.5 48 176 0 0 25 0 0 0 0 0 8.0 R-47 50 1.5 50 5.5 32 4.5 48 82 0 0 23.50 0 0 0 0 9.0 R-48 50 3 50 5 50 3 80 72 0 0 26 0 0 0 0 0 20 R-55 FLAGLER (CIASS-3) lb hb lbb hbb h3c lf llf 11 12 h, h2 h3 1.1 hal h. hl.. 100 9 50 12 16 7 20 52 0 0 24 0 0 16 21.5 20.5 '19 R-65 72 7 80 10 0 0 32 44 0 0 24 0 0 0 0 23 18 R-67 50 2 50 3 50 2 24. 96 0 0 20.5 0 0 50 9 20 19 R-80 50 3.5 50 10 32 2.5 16 88 0 0 21.5 0 0 0 0 21.5 19 R-82 50 2.5 50 9 56 2.5 16 176 0 0 27 0 0 32 18 27 26 R-91 50 5.2 40 10.5 24 2 20 65 0 0 21.5 0 0 16 17 22.5 19 R-97 72 9 30 9.5 24 28 16 24 0 0 22 0 0 12 15 22 20 R-98 FLORIDA COASTAL DUNE PARAMETERS (CONTINUED) ST. LUCIE.(CLASS-1) lb hb lbb hbb l.c h,. lf llf 11 12 h, h2 h3 1,1 h31 hmax hlow 50 4.8 50 11.5 0 0 16 0 40 40 14.5 13.5 14.5 0 0 0 0 R-15 50 5 48 10 0 0 20 0 68 40 12 14 11.5 0 0 0 0 R-16 24 1.6 56 8 32 4.4 12 0 52 24 14 12.8 13.6 0 0 0 0 R-19 48 4.5 0 0 0 0 72 0 96 96 12.5 12.4 14 0 0 0 0 R-21 48 3.5 50 8 28 2.5 40 0 52 80 14 10.8 11.2 0 0 0 0 R-31 100 7.2 32 8.8 16 0.4 48 0 104 64 15.5 10 15.5 0 0 0 0 R-32 48 5.6 24 8.8 0 0 40 0 152 124 11 7.2 7.2 0 0 0 0 R-35 ST. LUCIE (CIASS-2) lb hb lbb hbb l.. h.. lf llf 11 12 h, h2 h3 1.1 h., h. hlo .w 32 2 55 8.4 0 0 32 225 0 0 15.4 0 0 0 0 0 4 R-58 50 3.2 50 10 0 0 8 240 0 0 11.2 0 0 0 0 0 4.8 R-59 50 2.4 0 0 0 0 80 192 0 0 11.2 0 0 0 0 0 3.2 R-60 40 4.5 40 11.2 0 0 8 274 0 0 12.4 0 0 0 0 0 2.8 R-70 50 4 50 9.2 12 3.2 10 208 0 0 15.0 0 0 0 0 0 3.6 R-75 40 3.2 56 9.6 0 0 36 152 0 0 10.0 0 0 0 0 0 4.5 R-86 0 0 0 0 0 0 100 100 0 0 13.2 0 0 0 0 0 8 R-99 FLORIDA COASTAL DUNE PARAMETERS (CONTINUED) NASSAU (CLASS-1) lb hb lbb hbb is. h. c lwf llf 11 12 h, h2 h 3 is, hs, h.. hlow 50 2 45 3.5 155 8.5 25 0 75 25 16.5 20.5 23 0 0 0 0 R-33 50 4. 50 3.5 50 1 150 0 100 17 17 20.5 22 0 0 0 0 R-36 50 1 40 1.5 110 2 90 0 35 50 15.5 16 13.5 0 0 0 0 R-42 50 1.5 100 3.5 50 2.5 65 0 62 58 16 17.5 14.5 0 0 0 0 R-46 100 4 100 6 45 2.5 60 0 85 85 19.5 16.5 24 0 0 0 0 R-53 100 1 50 3 110 4.5 55 0 45 75 16 20.5 26.5 0 0 0 0 R-63 50 2 50 2.5 50 1 65 0 80 230 8.5 17.5 26.5 0 0 0 0 R-73 NASSAU (CIASS-2) lb hb lbb hbb is. h.,. lwf 'If 11 12 h, h2 h3 I., h., h. hl,. 100 3.5 65 7.5 35 2 140 110 0 0 21 0 0 0 0 0 8.5 R-10 50 2 50 3.5 40 5 160 65 0 0 16.5 0 0 0 0 0 10.5 R-11 50 1.5 25 2 25 2 85 80 0 0 9.5 0 0 0 0 0 8.5 R-12 50 2 60 7 50 3 55 75 0 0 14 0 0 0 0 0 9.5 R-17 50 2.5 48 7 25 1.5 150 125 0- 0 14 0 0 0 0 0 9.5 R-18 80 5 36 5 40 3.5 90 115 0 0 11.5 0 0 0 0 0 13.5 R-19 50 2 50 3.5 50 3 30 90 0 0 11.5 0 0 0 0 0 9.5 R-20 6 FLORIDA COASTAL DUNE PARAMETERS (CONTINUED) MANATEE (CLASS-2) lb hb lbb hbb 1.r h.c l.f lif 11 12 h, h2 h3 lrl h., 1-@.. hl.. 50 2 30 6 20 1 90 100 0 0 11 0 0 0 0 0 7 R-57 25 4 0 0 15 2 80 42 0 0 8.5 0 0 0 0 0 7.5 R-58 10 2 44 6 20 2.5 50 90 0 0 10.5 0 0 0 0 0 10 R-59 25 2 30 4 20 2 48 28 0 0 12 0 0 0 0 0 10.5 R-63 50 3.5 0 0 20 1 18 80 0 0 10 0 0 0 0 0 8 R-64 82 7.5 0 0 0 0 17 60 0 0 11 0 0 0 0 0 9 R-65 25 2 0 0 0 0 25 150 0 0 11 0 0 0 0 0 8.5 R-67 MANATEE (CLASS-4) lb hb lbb hbb l.. h.. lf llf 11 12 h, h2 h3 1.1 h., hhl. 5 2 25 4 0 0 150 0 1.25 94 6 9 8 0 0 0 0 R-3 50 4.5 16 4 0 0 40 0 175 115 4.5 9.5 6 .0 0 0 0 R-4 25 2.5 25 4 0 0 65 0 60 65 10 10.5 7.5 0 0 0 0 R-5 35 2 15 2 0 0 30 0 25 100 5 5.5 8.5 0 0 0 0 R-36 80 4 20 3 0 0 110 0 65 88 12 10 8 0 0 0 0 R-41 55 4 225 4.5 0 0 40 0 155 0 12.5 2.5 0 0 0 0 0 R-44 50 5 30 6.5 0 0 48 0 150 120 7.5 7.5 8 0 0 0 0 R-52 CHARLOTTE (CLASS-1) lb hb lbb hbb l.. h.. l.f llf 11 12 h, h2 h3 1.1 h.j. h..hlow 24 2 32 4.5 16 0.8 16 0 168 200 7.2 6.4 4.8 0 0 0 0 R-49 20 2.5 32 4.8 16 1 40 0 88 160 8 9.6 4.4 0 0 0 0. R-50 0 0 0 0 0 0 64 0 120 80 5.2 6.6 7.2 0 0 0 0 R-51 25 2.8 50 3.6 32 6 28 0 104 36 6 7.2 7 0 0 0 0 R-53 24 2.4 20 3.6 0 0 80 0 85 32 6 8.4 10 0 0 0 0 R-54 16 0.4 36 4 112 2.4 16 0 164 72 10.8 2.4 2.6 0 0 0 0 R-55 FLORIDA COASTAL DUNE PARAMETERS (CONTINUED) CHARLOTTE (CLASS-2) lb hb lbb hbb l.. h.. l.f llf 11 12 h, h2 h3 1,sl hsl h.. hl. 0 0 0 0 0 0 40 36 0 0 4.4 0 0 0 0 0 3.2 R-32 48 6 36 5.6 32 1.2 12 248 0 0 8.4 0 0 0 0 0 3.6 R-35 50 7.2 36 '4. 8 36 2 44 80 0 0 9.2 0 0 0 6 0 6 R-36 40 3.2 32 4.8 20 1 24 88 0 0 7.2 0 0 0 0 0 5.8 R-39 44 3.2 28 5 32 1.6 28 260 0 0 8.4 0 0 0 0 0 2 R-40 24 2.8 36 4 32 2 24 96 0 0 8.4 0 0 0 0 0 5 R-41 48 4.8 40 3.6 20 0.8 0 164 0 0 4.8 0 0 0 0 0 2 R-47 CHARLOTTE (CLASS-4) lb hb lbb hbb l.. h.. lf llf 11 12 h, h2 h3 1.1 h., h. hl. 50 4.4 50 4.4 0 0 36 0 240 0 9 7.6 0 .0 0 0 0 R-6 48 4 64 4.2 0 0 96 0 160 116 11 6 6 0 0 0 0 R-7 44 4.8 64 4.8 0 0 80 0 152 96 11.2 10 4.6 0 0 0 0 R-8 32 4 44 3.6 0 0 84 0 120 100 8.8 5.6 6.8 0 0 0 0 R-11 16 3 64 8 0 0 52 0 32 52 11.6 11.6 11.2 0 0 0 0 R-12 16 1.2 0 0 0 0 24 0 128 196 4 8.6 5.6 0 0 0 0 R-27 8 1.4 32 5.6 0 0 52 0 100 160 6.4 11 6 0 0 0 0 R-29 WALTON (CLASS-1) lb hb lbb hbb l.. h.. 1-,f llf 11 12 h, h2 h3 1.1 h., li.. hlow 60 6 82 9 25 4.5 42 0 75 100 23.5 26.5 25.5 0 0 0 0 R-35 0 0 0 0 0 0 45 0 140 50 6 8.5 8 0 0 0 0 R-46 30 5 20 3.5 100 5 50 0 150 250 25.5 11.5 13 0 0 0 0 R-53 30 3 20 0.5 0 0 30 0 180 75 5.5 8.:@ 12.5 0 0 0 0 R-69 12.5 2 25 5 0 0 48 0 165 110 8 19 13 0 0 0 0 R-70 0 0 0 0 0 0 60 0 135 100 7 7.5 8.5 0 0 0 0 R-72 0 0 0 0 0 0 42 0 155 100 5 14 24 0 0 0 0 R-103 FLORIDA COASTAL DUNE PARAMETERS (CONTINUED) WALTON (CLASS-2) lb hb lbb hbb l3c h3c 1,,f 'If 11 12 hi h2 h3 1.1 h., h.. hl.. 75 5.5 95 11.5 25 5.5 85 90 0 0 28 0 0 0 0 0 24.5 R-4 90 7 60 9 50 11.5 50 250 0 0 29.50 0 0 0 0 26.5 R-5 50 2.5 35 4.5 110 3 60 50 0 0 19 0 0 0 0 0 13 R-14 25 3.5 120 7 64 8.5 13 90 0 0 25.50 0 0 0 0 6.5 R-19 25 1.5 45 5 92 5 85 70 0 0 28 0 0 0 0 0 6 R-23 40 4 20 7 60 2.5 95 65 0 0 31 0 0 0 0 0 5.5 R-27 25 2 40 6 26 1.5 70 100 0 0 27 0 0 0 0 0 7 R-31 WALTON (CIASS-3) lb hb lbb hbb l.. h.. 1.f 'If 11 12 h, h2 h3 1.1 h., h.. hl. 50 3.5 0 0 100 7.5 75 200 0 0 33.5 0 0 50 34 36.5 0 R-85 50 4 60 6.5 65 15.5 35 280 0 0 38 0 0 45 30 38 36 R-86 50 4 80 8.5 42 7 65 155 0 0 29.5 0 0 0 0 29.5 27 R-89 90 5 125 9.5 50 14.5 0 350 0 0 50 0 0 50 8 35 0 R-90 40 5 25 5 0 0 0 180 0 0 6.5 0 0 0 0 13 8 R-94 40 5 60 7 15 0.5 70 100 0 0 28 0 0 60 14 15 0 R-105 12 2.5 317 5 55 2.5 30 25 0 0 32.5 0 0 30 13 31 30 R-114 Nassau Sept-Dec 81 Control Line R-46 R-42 R-41 R-36 R-33 R-31 Scale: X 1 in 125 ft; Y 1 in 20 ft R-26 (Profiles Cut at IVISL) Flagler 1987 Control Line R-48 R-47 R-46 R-41 R-36 R-31 R-26 Scale: X 1 in 125 ft; Y I in 20 ft (Profiles Cut at IVISL) Flagler 1987 Control Line R-71 R-67 R-66 R-65 3 R-61 R-56 R-55 R-51 2 Scale: X I in 125 ft; Y 1 In 20 ft (Profiles Cut at IVISL) IQN ST. LUCIE COUNTY BEACH TERRAIN HUNTER/ESE ST LUCIE COUNTY BEACH TERRAIN HUNTER/ESE ST. LUCJE COUNTY BEACH TER RAJN HUNTER/ESE I I HOAA COASTAL SERVICES CTR LIBRARY i 3 6668 14111413 1, ,