Extreme Rainfall Modelling Using Time-Varying Threshold Generalised Pareto Regression Trees

Abstract

The escalating frequency and intensity of extreme rainfall events driven by climate change threaten infrastructure resilience and societal safety, underscoring the urgent need for robust models to predict these events. Previous studies on the integration of Extreme Value Theory (EVT) and machine learning in modelling extreme rainfall events have not explored the use of a time-varying threshold. This study introduces a novel time-varying threshold Generalised Pareto (GP) regression tree for modelling extreme rainfall in Durban, South Africa. The proposed hybrid model combines EVT with covariate-driven regression tree partitioning, allowing the threshold to evolve dynamically with meteorological conditions. Using daily rainfall and meteorological covariate data from 1981 to 2025, the model was developed, pruned, and benchmarked against a static-threshold GP regression tree and a time-varying threshold Generalised Pareto Distribution (GPD). Evaluation based on the Bayesian Information Criterion (BIC) and log-likelihood demonstrated the superior performance of the proposed model in capturing covariate-driven heterogeneity and temporal variability of rainfall extremes. Four distinct climatic regimes with different tail behaviours and return levels were identified. This study provides the first meteorological application of a time-varying threshold GP regression tree and offers practical insights into flood risk assessment and climate resilience planning in the city of Durban.