Multivariate Regionalization of Rainfall Stations in Saudi Arabia Using Rainfall Concentration, Short-Duration Intensity, and Physiographic Descriptors

Reliable rainfall regionalization underpins hydrological design and the transfer of rainfall information to ungauged or short-record sites, yet it is especially difficult in arid regions with strong spatial and temporal variability and short, uneven records. This study develops a multivariate, stability-validated framework for classifying rain gauges into candidate homogeneous rainfall regions across Saudi Arabia. A national database of 274 stations was screened for 2015–2023, and 202 stations were retained. Ten descriptors representing annual rainfall, interannual variability, L-skewness of annual maxima, within-day rainfall concentration, short-duration intensity, elevation, and distance from the coast were constructed from 5 min records; correlated concentration and intensity descriptors were compressed by block-wise principal component analysis into a seven-variable, robustly scaled feature matrix. Partitions from K = 2 to 10 were evaluated using internal-validity indices, the gap statistic, minimum cluster size, repeated-subsample stability, cross-algorithm agreement, and sensitivity to alternative feature representations. The diagnostics supported several low-order structures: the four-region K-means solution showed the highest subsample stability (median adjusted Rand index: 0.977) and best consensus rank, whereas Ward clustering and Gaussian mixture modeling favored a parsimonious three-region solution. At four regions, cross-algorithm agreement was moderate (adjusted Rand index: 0.526–0.663) and the partition was strongly reproduced under the robust original-variable and global principal component analysis-(PCA)PCA representations (0.804). The regions comprised a widespread arid interior, a small near-coastal group, a wetter western–southwestern group, and a coastal-foothill group, with distance from the coast, elevation, and short-duration intensity providing the strongest contrasts. The framework offers a reproducible basis for regional rainfall-frequency analysis, station pooling, and hydrological transfer, pending verified completeness data and formal homogeneity testing.