Extreme Rainfall Analysis in the Surabaya Metropolitan Region using Spatial Extreme Value Model with Kumaraswamy Generalized Inverse Lomax Distribution

Extreme weather events are natural phenomena that can cause significant losses across various sectors and have serious impacts on many aspects of life. These impacts can be minimized by analyzing the patterns and characteristics of extreme events. Extreme Value Theory (EVT) is one of the statistical techniques used to detect such events, and to capture extreme occurrences across multiple locations (multivariate), it has been extended into the Spatial Extreme Value (SEV) approach. This study applies the Peaks Over Threshold (POT) method to excessive rainfall using an extreme value model based on the Kumaraswamy Generalized Inverse Lomax (KumGIL) distribution, which combines the Kumaraswamy Generalized and Inverse Lomax distributions to provide high flexibility for modelling heavy-tailed and asymmetric data. The POT-KumGIL model is applied to monthly rainfall data from 1989-2024 in the Surabaya Metropolitan Area. Model suitability is tested using the Kolmogorov-Smirnov statistic and probability plots. If the model fits well, parameter estimation is performed using Maximum Likelihood Estimation (MLE) followed by BHHH numerical iteration. A trend surface model is then built to relate longitude, latitude, and elevation with parameter estimates, improving the robustness of spatial analysis. The best model, determined by the smallest Akaike Information Criterion (AIC), is used to calculate return levels for several future periods. This study aims to develop a POT-KumGIL spatial extreme value model and obtain return level estimates for the Surabaya Metropolitan Area to support future hydrometeorological disaster mitigation strategies.