Comprehensive Probabilistic Analysis and Practical Implications of Rainfall Distribution in Pakistan

Accurately selecting an appropriate probability distribution model is a critical challenge when predicting extreme rainfall in arid and semi-arid regions, especially in countries with diverse climatic conditions. This study presents a comprehensive methodology for evaluating rainfall probability distributions across Pakistan, and aims to create a probabilistic zoning map that could serve as a valuable resource to inform the development of strategies for efficient water resource management and improved flood resilience in diverse climatic and geographic conditions. Precipitation data from the Pakistan Meteorological Department (PMD) over 42 years were compared with CHIRPS, confirming their accuracy. Nine probability distributions were assessed, with five models—log Pearson type-III (LP3), Weibull (W2), log normal (LN2), Generalized Extreme Value (GEV), and gamma (GAM)—deemed most suitable for the region’s climatic variability. The spatial applicability of these distributions was identified as follows: LP3 (30%), LN2 (30%), W2 (15%), GEV (10%), and GAM (15%). The central and southern regions of Punjab were predominantly characterized by LN2, while GAM was prevalent in the coastal areas of Sindh. Balochistan exhibited a heterogeneous distribution of W2, LP3, and LN2, while the mountainous Gilgit-Baltistan region was exclusively associated with GEV. Khyber Pakhtunkhwa demonstrated a mix of GEV and LP3 distributions. Beyond provincial variations, distinct patterns emerged: GEV dominated high-altitude, cold-temperate areas; LP3 was common in mountainous regions with variable temperature profiles; and W2 was prevalent along the flood-prone Indus River. This study provides a robust framework for region-specific disaster preparedness and contributes to sustainable development initiatives by offering tailored strategies for managing extreme rainfall events across Pakistan’s diverse climatic zones.