MARS modelling for spatial analysis of coastal erosion susceptibility

Abstract

This study assessed the susceptibility of the entire Tuscan coastline to coastal erosion using Multivariate Adaptive Regression Splines (MARS), a flexible yet interpretable non-parametric regression technique that explicitly models nonlinear relationships and variable interactions through physically meaningful thresholds. Unlike machine learning approaches commonly used in coastal erosion studies (e.g. SVMs, ANNs or logistic regression), MARS offers high predictive performance combined with enhanced transparency. This enables the controlling factors and their critical ranges to be interpreted more clearly. The coastline was segmented into transects spaced at 50 m intervals, and shore- line change was quantified for three periods (2000–2010, 2011–2020, and 2000–2020) using Net Shoreline Movement (NSM). To reduce uncertainty, two datasets were created: CUT2 (excluding transects with changes within ±2 m) and CUT4 (excluding those within ±4 m) according to shoreline digitalisation accuracy. The dependent variable was binarized to represent either eroding (1) or advancing (0) coastlines. The independent variables included coastal slope, number of storms, storm energy, depth of closure, geomorphology, and main longshore sediment transport directions, which are known to control coastal morpho dynamics at regional scale. Model calibration was conducted on 70% of the CUT4 dataset, with validation performed using both internal (30% of CUT4) and external (100% of CUT2) strategies. The performance of the MARS models was evaluated using ROC curves and AUC values, achieving good results (AUC > 0.8) in most cases. The resulting susceptibility maps classified the coastline into four susceptibility levels (from low to very high) and showed strong agreement with observed shoreline trends. The identification of erosion hotspots was statistically supported by the MARS model outcomes and their associated variable contributions, while the relationship between persistently eroding sectors and limited sediment supply from river basins was derived from an integrated interpretation combining model results with geomorphological and observational evidence. Overall, the proposed MARS-based framework provides a robust, interpretable, and data-driven tool to support integrated coastal management, enabling the identification of critical erosion hotspots and the definition of targeted adaptation measures.