Long-term shoreline evolution.  A combined cross-shore and long-shore model

Long-term modeling (decades) of shoreline changes cannot be easily challenged with physics based models. The best alternative is to use simple behavioral template models (Davidson & Turner, 2009), all the complex cross-shore erosion/accretion processes being encapsulated in a few parameters. Most of these cross-shore models draw on the phenomenological idea that a beach relaxes towards equilibrium (Wright & Short, 1984). Calibrated against reliable data series of cross-shore changes, this type of model reaches good predictive skills (Splinter et al., 2014; Castelle et al., 2014). However these shoreline models need to be improved by taking into account long-shore process (Robinet et al., 2018).This paper addresses the feasibility of a combined model that includes longshore sediment transport effects in a relaxation type cross-shore shoreline evolution model. Longshore transport produces long-term changes of the beach morphology and shoreline position. The longshore contribution is worked out on the basis of the one-line approach in which the shoreline position depends on the alongshore gradient of the volumetric sediment transport rate change. The analysis, which decomposes time dependent variables into averages and fluctuations (Reeve et al., 2014), provides (i) a relationship between the equilibrium beach angle and the wave forcing angle and (ii) a shoreline evolution equation for longshore transport only. This model is merged with the Splinter et al. (2014) behavioral model. This combined model is calibrated an tested on the Narrabeen (Australia) semi-embayed beach data (Turner et al., 2016). The combined model reproduces with good agreement the shoreline trends and variability. We show that the longshore component clearly contributes to the seasonal shoreline fluctuations. The model is also applied to low energetic beaches of the Vietnam coast (Nha Trang and Da Nang).Davidson, M., Turner, I., 2009. A behavioral template beach profile model for predicting seasonal to interannual shoreline evolution. Journal of Geophysical Research: Earth Surface 114.Wright, L., Short, A., 1984. Morphodynamic variability of surf zones and beaches: a synthesis. Marine geology 56, 93–118.Splinter, K., Turner, I., Davidson, M., Barnard, P., Castelle, B., Oltman-Shay, J., 2014. A generalized equilibrium model for predicting daily to interannual shoreline response. Journal of Geophysical Research: Earth Surface 119, 1936–1958.Castelle, B., Marieu, V., Bujan, S., Ferreira, S., Parisot, J., Capo, S., Sénéchal, N., Chouzenoux, T., 2014. Equilibrium shoreline modelling of a high-energy meso-macrotidal multiple-barred beach. Marine Geology 347, 85–94Robinet, A., Idier, D., Castelle, B., Marieu, V., 2018. A reduced complexity shoreline change model combining longshore and cross-shore processes: The LX-Shore model. Environmental Modelling & Software 109, 1–16.Reeve, D., Pedrozo-Acuña, A., Spivack, M., 2014. Beach memory and ensemble prediction of shoreline evolution near a groyne. Coastal Engineering 86, 77–87.Turner, I., Harley, M., Short, A., Simmons, J., Bracs, M., Phillips, M., Splinter, K., 2016. A multi-decade dataset of monthly beach profile surveys and inshore wave forcing at Narrabeen, Australia. Scientific Data 3.