Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology

This study investigates precipitation variability across the Mediterranean Basin (MB) with a specific focus on power-law relationships as a framework for understanding climatological patterns. Using National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) reanalysis monthly data from 1990 to 2024, the research employs statistical analyses and clustering techniques to unravel the spatial and temporal complexities of precipitation in the region. The findings highlight a strong power-law relationship between mean precipitation and its standard deviation, with an R² value of 0.75 demonstrating high explanatory power. This relationship indicates that variability increases nonlinearly with mean rainfall. This scaling behavior highlights how regions with higher precipitation experience greater absolute variability but proportionally less relative fluctuation. Such insights offer a quantitative framework for understanding precipitation dynamics in the MB and their dependence on climatic and physical geographic factors. The spatial analysis reveals a pronounced north-south gradient in precipitation distribution. Northern regions, influenced by orographic effects, receive annual precipitation exceeding 900 mm, while southern areas, dominated by subtropical high-pressure systems, often receive less than 300 mm. The study identifies seven distinct precipitation regimes through k-means clustering, with regimes varying in mean precipitation, variability, and skewness. Coastal clusters exhibit intermediate precipitation characteristics shaped by mesoscale systems, while arid regions display high interannual variability and increased propensity for extreme events. The analysis also shows a positive correlation between skewness and kurtosis. This indicates that regions with asymmetric rainfall distributions are prone to extreme precipitation events. Furthermore, the negative logarithmic relationship between mean precipitation and coefficient of variation (CV%) highlights increased variability in drier areas. Coastal North Africa and the eastern Mediterranean are identified as hotspots for intense, short-duration rainfall due to their elevated skewness values (> 2). This research integrates power-law scaling, statistical variability, and spatial clustering to provide a comprehensive climatological assessment of precipitation in MB. The findings advance our understanding of regional rainfall patterns and offer critical insights for water resource management, disaster risk reduction, and climate adaptation strategies.