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c Shore Response Modeling Methods INTRODUCTION This appendix reviews the characteristics and capabilities of several shore response models. Development and implementation of the {onger-term recommended methodology for predicting shoreline change would be based on improvements to and extensions of these and possibly new models. The presentation below is organized in terms of "Iongshore" and "cross-shore transport models, consistent with the general pattern of individual model development to represent shore response to one or the other of these transport components. [ONGSHOR1: TRANSPORT MODELS Longshore transport models include analytical models (applica- ble to limited situations of interest) and numerical models. Both analytical and numerical models can represent one contour (usually at the mean sea level) or several contours of interest. Analytical Models The one-line analytic mode! was developed by Peinard-Considere (1956) and applies to a number of cases of interest. The governing 151

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152 APPENDIX C equation Is the combined result of the linearized sediment trans- port equation and the continuity equation. Le Mehaute and Soldate (1978) and Larson et al. (1987) have summarized many of the avail- able analytical solutions. Two examples of application of the model to problems of interest are presented below and will serve to illustrate the general capabilities of analytical models. The interruption of longshore sediment transport by a littoral barrier wiD cause sed~rnent accumulation on the uplift side and erosion on the downdrift side. According to this model, bypassing does not commence until the shoreline reaches the tip of the struc- ture. Following that tune, sediment transport around the structure commences and approaches the ambient value. Figure C-1 compares the analytical mode} to experimental results obtained from tests in a wave basin. As Is evident, good agreement was found. A second example of interest is the planform evolution following placement of a rectangular beach nourishment project. Figure C-2 presents one example based on the solution of the PeInard-Considere equation. This solution demonstrates that the longevity of a nour- ishment project varies directly as the square of the project length and inversely as the 2.5 power of the representative wave height. Numerical ModeLs A number of investigators have developed one-~me numerical models to represent beach planform evolution as a result of natural effects or human-~duced alterations (Le Mehaute and Soldate, 1978 and 1980~. These models include the GENESIS model now used by the U.S. Army Corps of Engineers. Because one-line representations have inherent limitations, treatment of cross-shore transport, where necessary, must be by an ad hoc procedure. CROS~SHORE TRANSPORT MODELS A primary motivation for cross-shore transport models (also called onshore-offshore transport models) is associated with the es- tablishment of a zone of impact caused by elevated storm tides and high waves occurring during a severe storm. Some earlier models, based primarily on geometrical considerations, wiD not be discussed. Various models are reviewed briefly below.

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154 APPENDIX C Swart (1976) This empirical method is based on large-scale wave tank tests. The procedure is complex and involves numerous empirical expres- sions that, when programmed, make the method relatively straight- forward to apply. The only known application of Swart's theory to field conditions is by Swain and Houston (1984a,b) for storm erosion at Santa Barbara, California, and near Oregon Inlet, North Car- olina. Their modifications provided for time-varying tide and wave conditions. Vellinga (1983) This profile response mode! was developed to evaluate the in- tegrity of the Dutch dikes against storms and is based on a series of wave tank tests. The required parameters include wave height, storm tide, and grain size. The method predicts the profile for a storm du- ration of 5 hours; procedures are presented for storms differing from this duration. :Eriebe] and Dean (1985) This model allows time-varying input of storm tide and wave height and solves the equations governing cross-shore sediment trans- port and continuity using an efficient numerical method. The cross- shore sediment transport equation is based on the profile disequilib- rium caused by elevated storm tide and wave height conditions. The mode] has been evaluated against Hurricane Eloise (1975) for Bay County, Florida. A simplified modification of this method is cur- rently in use by the Florida Department of Natural Resources in its implementation of the Coastal Construction Control Tine program. Balsillie (1986) This is an empirical method that models relationships for the average and maximum expected erosion caused by a storm based on storm tide rise time raised to the 0.8 power and peak storm tide raised to the 1.6 power. Balsillie's approach provides encouraging correlation with numerous field data.

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156 APPENDIX C [arson et al. (1988) This mode] is based on extensive correlations of wave, sediment, and profile characteristics. The beach/nearshore profile is subdi- vided into four zones, each with different transport rate properties. The model has been applied to erosion of natural and seawalled pro- files. It is capable of predicting single and multiple bar formations. Comparisons/evaluations have been conducted with wave tank data and with field data from Duck, North Carolina. The model also was compared with the Kriebe} and Dean (1985) model. Good agreement was found with the laboratory case and the Kriebel/Dean model, but only fair agreement was obtained with the field data. Federal Emergency Management Agency (FEMA) Method The method adopted by FEMA (Hallermeier and Rhodes, 1988) for the 100-year storm event references all eroded volumes to the portion of the dune above the 100-year still water flood level (SWFL). The method is illustrated graphically in Figure ~3. The first step evaluates whether at least 50 m3/m of sand per meter of beach length is contained in the dune reservoir above the SWFL and seaward of the dune crest (Figure ~3A). If this reservoir contains at least 50 m3/m, then the dune is considered to not erode through and the geometry of the eroded profile is as follows. The landward portion of the eroded profile is at a 1:1 slope and extends landward from the SWFL to intersection with the dune profile. Seaward from the SWFI., the profile extends seaward at a slope of 1:40. The final seaward segment of the profile is at a slope of 1:12.5 and extends downward to intersection with the prestorm profile. The eroded volume above the SWFI. is 50 m3/m, and the 1:40 slope extends seaward the required distance to obtain a balance between eroded and deposited volumes. We return now to the case presented in Figure C-3C in which the dune reservoir does not contain the 50 m3/m, and it is therefore assumed that the dune will be eroded through. The eroded profile is at a 1:50 slope and extends landward from the dune toe defined as the slope transition between the seaward limit of the dune and the milder beach berm. For this case a portion of the eroded sand is considered to be transported landward; thus, there is no basis (or requirement) for balancing eroded and deposited volumes.

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APPENDIX C A. Cross section to ~ be compared to / ///// 50 s uare meters q / Em/ Frontal ~ / ~ Dune ~: ~~/~ - SWFL- (Defined by existing profile and vertical line from upper limit of steep rear slope to horizontal line at stillwater elevation) B. Eroded profile / . for case of duneface retreat J / 1 on 1 ~ Slope 1. Place t on 1 slope for Som2 erosion above SWFL 2. Determine additional erosion, shown domed 3. Place 1 on 12.5 slope for erosion/deposition balance C. Eroded profile for case of ; dune removal / 1. Locate dune toe at lower limit to steep front slope 2. Remove dune above 1 on 50 slope through dune toe 157 \ \ lon40 Slope \ SWFL - SWFL Movable I 1 on 12.5 Slope FIGURE C-3 Treatment of sand dune erosion in l00-year event for a coastal good insurance study. SOURCE: Hallermeier and Rhodes, 1988.

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158 APPENDIX C Brunn Rue Bruun (1962) was the first to evaluate quantitatively the role of slowly changing water levels on shore erosion. His formulation is based on the concept of an equilibrium profile, defined as an average profile that maintains its form, apart from small fluctuations, at a particular water level. The Bruun rule provides a profile of equilibrium with the mate- rial removed during shoreline retreat transferred onto the adjacent shoreface, thus maintaining the original nearshore shallow-water pro- file relative to the increased water level. Hence, the formulation represents an on/offshore sediment balancing between eroded and deposited volumes without consideration of longshore transport. The Bruun rule can be expressed as dy_ {dS~ ~ w* ~ at \`dtJ \`h*+B)' where y is the shoreline position, ads represents the average rate of sea level rise, h* + B is the vertical extent of active profile motion, and w* is the associated width of active motion. Thus, the milder the nearshore slope [(h* + B)/w*] of the active profile, the greater the erosion rate. An offshore limit of sediment activity is assumed, thus precluding the possibility of shoreward sediment transport. Bruun's concept is intuitively appearing but difficult to confirm or quantify without precise bathymetric surveys and documentation of complex nearshore profiles over a long period of time. A problem with the Bruun rule is that it always predicts shore recession with offshore transport through time as sea levels have gradually risen. However, this is not the case along all shorelines. For example, some barrier islands along the west coast of Florida have obviously accreted over the last few thousand years from the onshore movement of sand (Evans et al., 1985~. Sandy material from the shallow shoreface and inner shelf have been moved onshore by waves to form "perched" barrier islands atop of Pleistocene limestone highs. There is no other source of the beach sediment, indicating a reverse product from that predicted by a cursory application of the Bruun rule. The Dutch also have argued that large-scare coastal accretion (thousands of feet of beach and dune) has occurred dur- ing the late Holocene (last 6,000 years) during a period of ostensible sea level rise. Finally, there are direct indications of onshore sediment

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APPENDIX C 159 transport by using natural tracers. Millions and Meisburger (1987) reported that glaucionitic sands, which are only available by wave quarrying of offshore sediments, are found on the Rockaway beaches in significant quantities and geographic positions to indicate such a transport process. REFERENCES Balsillie, J. H. 1986. Beach and storm erosion due to extreme event impact. Shore Beach 54~4~:22-36. Bruun, P. 1962. Sea level rise as a cause of shore erosion. J. Waterways Harbors Division, ASCE 88:117-130. Dean, R. G. 1988. Sediment interaction at modified coastal inlets: Processes and policies. In Hydrodynamics and Sediment Dynamics of Tidal Inlets, D. Aubrey, ed. Woods Hole, Mass.: Woods Hole Oceanographic Institution. Evans, M. W., A. C. Hine, D. F. Belknap, and R. A. Davis, Jr. 1985. Bedrock controls on barrier island development: West-central Florida coast. Marine Geol. 63:263-283. Hallermeier, R. J., and P. E. Rhodes. 1988. Generic Treatment of Dune Erosion for 100-Year Event. Proceedings, Twenty-First International Conference on Coastal Engineering, ASCE, pp. 1121-1197. Kriebel, D. L., and R. G. Dean. 1985. Numerical simulation of time-dependent beach and dune erosion. Coastal Eng. 9:221-245. Larson, M., H. Hanson, and N. C. Kraus. 1987. Analytical Solutions of the One-Line Model of Shoreline Change. Technical Report CERC-87-15, U.S. Army Engineer Waterways Experiment Station, Coastal Engineering Research Center. Larson, M., N. Kraus, and T. Sunamura. 1988. Beach Profile Change: Morphol- ogy, Transport Rate and Numerical Simulation. Proceedings, Twenty-First International Conference on Coastal Engineering, ASCE, pp. 1295-1309. Le Mehaute, B., and M. Soldate. 1978. Mathematical Modelling of Shoreline Evolution. Proceedings, Sixteenth International Conference on Coastal Engineering, ASCE, pp. 1163-1179. Le Mehaute, B., and M. Soldate. 1980. A Numerical Modelling for Predicting Shoreline Change. U.S. Army Corps of Engineers, Coastal Engineering Research Center (CERC), No. 80-6. Pelnard-Considere, J. 1956. Essai de Theorie de ['Evolution des Formes de Rivate en Plages de Sable et de Galets. 4th Journees de l'Hydraulique, Les Energies de la Mar, Question III, Rapport No. 1. Swain, A., and J. R. Houston. 1984a. Onshore-OfEshore Sediment Transport Numerical Model. Proceedings, Nineteenth International Conference on Coastal Engineering, ASCE, pp. 1244-1251. Swain, A., and J. R. Houston. 1984b. Discussion of the Proceedings Paper 17749 by Richard J. Seymour, The Nearshore Sediment Transport Study. ASCE, Port, Coastal and Ocean Engineering Division. Swart, D. H. 1976. Predictive Equations Regarding Coastal Transports. Proceed ings, Fifteenth International Conference on Coastal Engineering, Honolulu ASCE, pp. 1113-1132. ,

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160 APPENDIX C Vellinga, P. 1983. Predictive Computational Modelling for Beach and Dune Erosion During Storm Surges. Proceedings of ASCE Specialty Conference Coastal Structures '83, pp. 806-819. Williams, S. J., and E. P. Meisburger. 1987. Sand sources for the transgressive barrier coast of Long Island, New Yorkevidence for landward transport of shelf sediments. Pp. 1517-1532 in Proceedings, Coastal Sediment. New York: ASCE.