Galerkin's formulation of the finite elements method to obtain the depth of closure

Abstract

Coastal erosion and lack of sediment supply are a serious global problem. It is therefore necessary to determine the depth of closure (DoC) of a beach—key parameter in the calculation of the sand volume and the location of the beach protection elements—in a precise way. For this reason, this work generates a numerical model based on Galerkin's formulation of finite elements that provides sufficient precision for the determination of DoC with a minimum investment. Thus, after the generation of three models in which the difference was the dependent variables, the least complex has been chosen. It is composed of the variables: median sediment size, wave height and period associated with the mean flow, as well as the angle that the mean flow forms with respect to the studied profile in absolute value (α). The selected model has been compared with the most commonly used models currently in use, having an average absolute error of 0.36 m and an average MAPE of <7.5%, which represents an improvement of >70% over current models. In addition, it presents a high stability, since after the random disturbance of all the input variables (up to 5%), the model error remains stable, increasing the MAPE by a maximum of 7.4% and the average absolute error by 0.15 m. Therefore, it is possible to use the model to infer the DoC in other study areas where the values of the variables are similar to those studied here, although the selected method can be extrapolated to other parts of the world.