Application of Bayesian Techniques and L-Moments I Regional Frequency Analysis of Rainfall Extremes: Insight from Northern Pakistan

Abstract

Accurate estimation of rainfall extremes is critical for flood risk management, infrastructure design, and climate adaptation particularly in data-scarce, mountainous regions like northern Pakistan, where hydro-meteorological hazards are intensifying due to climate change. This study presents a robust regional frequency analysis (RFA) framework that integrates L-moment-based regionalization with Bayesian hierarchical modeling to improve the estimation of extreme rainfall quantiles. Using annual maximum rainfall data (2006–2023) from seven stations across the Hindu-Kush and Karakoram ranges, the analysis identifies the Generalized Logistic (GLO) distribution as the optimal model, as determined by L-moment ratio diagrams and the ZDIST statistic. The region is confirmed to be acceptably homogeneous (H < 1), with no discordant sites (Di < 1.91), allowing for the reliable pooling of data. Both L-moment and Bayesian MCMC methods are employed for parameter and quantile estimation, with the Bayesian approach yielding more conservative and uncertainty-aware predictions, particularly for long return periods. At-site quantiles derived from regional growth curves show strong alignment with observed rainfall in 2022–2023, validating the model’s predictive accuracy. The Bayesian framework, with its superior handling of small-sample uncertainty and parameter variability, is shown to outperform classical methods, offering a more resilient tool for hydrological risk assessment. These findings underscore the value of integrating Bayesian inference into RFA for climate-resilient water resources planning in vulnerable high-mountain environments.