A Spatial Extreme Value Modelling with Fused Lasso and Fused Ridge Regularization

Case Study of Extreme Rainfall in North Sumatera Province

Abstract

Extreme rainfall is a hydrometeorological phenomenon that can cause disasters such as floods and landslides, especially in North Sumatera Province, which has a complex geographical and topographical character. The purpose of this study is to model extreme rainfall spatially using the Extreme Value Theory (EVT) approach through the Generalized Pareto Distribution (GPD) model with the Peaks Over Threshold (POT) method, as well as to compare the performance of regularization using fused lasso and fused ridge in stabilizing spatial parameter estimation. The data used is daily rainfall data from 2014 to 2024 from five BMKG stations in North Sumatera Province. Thresholds were determined using a combination of the percentile method and the Mean Residual Life Plot (MRL). The parameter estimates were calculated using Maximum Likelihood Estimation (MLE). Model evaluation was performed using the Takeuchi information criterion (TIC). The results show that both regularization methods are capable of modeling spatial extreme rainfall effectively and produce return levels that increase with longer return periods. The highest return levels for both models were observed in Central Tapanuli. Based on the TIC values, fused ridge outperformed fused lasso with a TIC value of 100,913.9 and was therefore selected as the best model for spatial extreme rainfall modeling in North Sumatra Province. This study is expected to contribute to the development of spatial extreme value modeling and support data-driven hydrometeorological disaster risk mitigation.