Regional modeling of zero-inflated precipitation in Pakistan by classical and Bayesian approaches

Study region: Pakistan exhibits pronounced spatial and seasonal variability in rainfall patterns, with extreme precipitation posing major challenges for flood risk management, agriculture, and infrastructure planning. Accurate estimation of return levels remains difficult due to sampling variability, threshold selection, and the presence of zero-inflation associated with dry days. The present study analyzes daily precipitation data from 135 districts across Pakistan for the period 2001–2023, encompassing diverse climatic changes. Study focus: A zero-inflated Extended Generalized Pareto Distribution (ziEGPD) model is introduced to characterize the full precipitation spectrum, including dry days, within a regional modeling framework. Within the regional model setting, homogeneous regions based on upper-tail behavior were constructed using the Δ ˆ ratio method. To capture spatial variation in the region, the parameters of ziEGPD were modeled as functions of covariates using Generalized Additive Models (GAMs). The developed model was estimated through maximum-likelihood and Bayesian frameworks and evaluated via cross-validation using accuracy and robustness measures. New hydrological insights: Results indicate that the Bayesian GAM–ziEGPD model with covariates provides the highest accuracy and consistently outperforms the MLE-based approach across all seasons and clusters. This model is therefore adopted as the optimal framework for estimating regional quantiles across a range of return periods. Regional analysis further shows that the monsoon period exhibits the highest 100-year return levels, with intense rainfall concentrated in southern and southeastern Pakistan. • Comprehensive modeling of rainfall including zero values and extremes. • Integration of regional frequency analysis and spatial GAM framework. • MLE along with Bayesian inference for robust and accurate estimation. • Return levels for climate resilience and flood risk management.