Modeling beach profile evolution at centennial to millennial scales

The proposed model allows the satisfactory reproduction of the changes in the profile geometry in each time step depending on the sediment budgets in a given morphodynamic system. The applied modification to the general Bruun rule governing the conservation of mass must account for the effect of the sediment transport, which is described in terms of the erosion and accretion rates (Er and and Ac, respectively). The scale of the erosion is a function of the total annual wave energy flux reaching the beach. The accretion is governed by the Er, on the one hand, and by the sediment budget in the morphodynamic system, on the other hand. The equilibrium profile obtained for the case of a balanced sediment budget (Er = Ac) shows good agreement with the observed profiles. A deficit or surplus in the sediment budget results in the shoreline's retreat or advance accompanied by either a decrease or increase in the slope of the bottom profile. The model accounts for different types of shoreline responses to changes in the sea level (the Bruun rule, the development of a coastal barrier, and abrasion). Sediment budget imbalances can be a factor in the profile's evolution due to changes in the sea level, while the combination of both factors will produce a variety of behaviors of the shoreline, as was shown by our calculations. The model was verified using historical data on the behavior of the Central Holland coast and the Abkhazian coast during the Late Holocene. It was shown that the model satisfactory reproduces the progradation of coastal barriers. An example of a relatively short-term forecast (over a 100-year period) is given.