A cross-shore beach profile evolution model

Developing an accurate and reliable time-averaged beach profile evolution model under storm and nonstorm conditions is a challenging task. Over the last few decades, a number of beach deformation models have been developed under limited experimental conditions and uncertainties, and sometimes they required a long computation time. It is quite evident that a large amount of wave, current, sediment and beach profile data is available today. The present study leads to the development of a simple two-dimensional beach profile evolution model with on-offshore sand bar formation under nonstorm and storm conditions based on the time-averaged suspended sediment concentration models of Jayaratne and Shibayama [Jayaratne, M. P. R. and Shibayama, T. [2007] "Suspended sediment concentration on beaches under three different mechanisms," Coastal Eng. J., JSCE 49(4), 357-392.] and Jayaratne et al. [Jayaratne, M. P. R., Sritharan, S. and Shibayama, T. [2011] "Examination of the suspended sediment concentration formulae using full-scale rippled bed and sheet flow data," Coastal Eng. J., JSCE 53(4), 451-489.]. These models were formulated for computing sediment concentration in and outside the surf zone under three different mechanisms: (1) suspension due to turbulent motion over sand ripples, (2) suspension from sheet flow layer and (3) suspension due to turbulent motion under breaking waves. The suspended load is calculated by the product of time-averaged sediment concentration and undertow velocity from edge of the wave boundary layer to wave trough and mass transport velocity from wave trough to crest (bore-like wave region). Sediment transport in wave boundary layer is computed from the modified Watanabe [Watanabe, A. [1982] "Numerical model of nearshore currents and beach deformation model," Coastal Eng. Jpn., JSCE 25, 147-161.] model. Rattanapitikon and Shibayama [Rattanapitikon, W. and Shibayama, T. [1998] "Energy dissipation model for regular and irregular breaking waves," Coastal Eng. J., JSCE 40(4), 327-346.] wave model is used to calculate the average rate of energy dissipation due to wave breaking. The beach deformation is calculated from the conservation of sediment mass while the avalanching concept of Larson and Kraus [Larson, M. and Kraus, N. C. [1989] SBEACH: Numerical model for simulating storm induced beach change, Report 1, Technical Report CERC-89-9, US Army Eng. Water. Exp. Station.] is used to re-distribute the sediment mass in neighboring grids for a steady solution. Published field-scale experimental and natural beach profiles from five high-quality data sources from 1983-2009 [Kajima et al., 1983; Kraus and Larson, 1988; Port and Airport Research Institute, Japan, 2005, 2009; Hasan and Takewaka, 2007, 2009; Ruessink et al., 2007] are used to verify the performance of the proposed numerical model. The key feature in this process-based model is that it takes about a couple of minutes to simulate beach profiles of a 2-3 days storm qualitatively at a fairly satisfactory level using a standard personal computer. It is found that the present numerical predictions are not better than the null hypothesis as the model is in a stage of ongoing development. Therefore, it is believed that the final model is often of more value to a practical coastal engineer than a very detailed study of hydrodynamics and sediment transport study, however an incorporation of swash dynamics, more precise evaluation of offshore sand bar formation and continuation to a longer time scale with precise beach deformation are recommended as the next stage of the model.