Predicting coastal profiles evolution from a diffusion model based on real data

Abstract

A diffusion model is considered to represent the time evolution of coastal profiles, over the time span of several years ahead. This is important in view of both, natural and anthropic activities, which affect and tend to modify the environment near the sea coastal lines, river’s estuaries, and harbors. The final aim is to make useful predictions for the depth profile evolution, basing on real available data, so that suitable actions might be planned. From the mathematical standpoint, the problem takes on the form of an inverse problem for a parabolic model equation, and thus the minimization of a suitable cost functional was accomplished to calibrate the model. An open source version of a genetic algorithm is used to identify the desired model parameters. To effectively reduce the overall computational cost, the code was parallelized. The computed and the measured depth profiles have been compared estimating the integrated relative error (IRE), using only ten years of measurements, each of them having been taken once a year. A regression analysis was carried out exploiting a machine learningalgorithm, provided by a support vector machine, to predict the evolution of the model parameters over one, two, and three years ahead. Predicted and measured depth profiles were compared in terms of IRE.