A Climate-Informed Multi-Model Framework for Probabilistic Intensity–Duration–Frequency Curves Using CMIP6 Projections and Probabilistic Uncertainty Analysis: A Case Study of Makkah, Saudi Arabia

Abstract

Reliable intensity–duration–frequency (IDF) curves are essential for the design of stormwater drainage systems and flood mitigation infrastructure; however, conventional IDF relationships assume stationarity and may underestimate future rainfall extremes under climate change. This study developed climate-informed IDF curves for Makkah, Saudi Arabia, using hourly observed rainfall records (1985–2025) and projections from five CMIP6 Global Climate Models (EC-Earth3-CC, CNRM-CM6-1, GFDL-ESM4, MPI-ESM1-2-LR, and UKESM1-0-LL) under the SSP245 and SSP585 scenarios. Spatial downscaling was first carried out using bilinear interpolation, after which the resulting data were corrected for systematic bias using the Delta Change method. Daily precipitation projections were subsequently disaggregated to an hourly timescale using an enhanced KNN-MOF approach. Annual maximum precipitation series were then derived for durations of 1, 2, 3, 6, 12, and 24 h and fitted to a range of candidate probability distributions. The goodness of fit was evaluated using the log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Across the five CMIP6 models, two emission scenarios, and six rainfall durations, the Log-Pearson Type III distribution consistently yielded the most satisfactory fit. Historical analysis estimated 100-year rainfall depths ranging from 7.84 mm (1 h) to 38.29 mm (24 h), while future projections indicated substantially higher design rainfall intensities under several climate models. For example, under the SSP585 scenario, the 100-year 1 h rainfall intensity reached 29.73 mm h−1 for EC-Earth3-CC, whereas MPI-ESM1-2-LR projected a 102% increase in the 6 h 100-year intensity relative to SSP245. Sherman equations were successfully fitted to develop continuous IDF relationships, while bootstrap resampling and Bayesian inference quantified projection uncertainty. The multi-model ensemble indicated increasing uncertainty with return period, particularly for the 100-year event, highlighting the importance of incorporating uncertainty into engineering design. The proposed framework provides robust climate-informed IDF curves for supporting resilient urban drainage design, flood-risk assessment, and water resources planning in arid environments.