Development of multi-scalar standardized precipitation concentration index for the characterization of spatial distributions of precipitation

Understanding the spatio-temporal dynamics of precipitation is crucial for monitoring and managing natural hazards such as floods and droughts, which are strongly influenced by variability in precipitation patterns. Traditional precipitation indices often fall short in capturing both the intensity and concentration of precipitation events on multiple time scales. To address this gap, we introduce a new standardized index, the Multiscale Standardized Precipitation Concentration Index (MS–PCI) - designed to assess the spatio-temporal variability of precipitation in a robust and standardized manner. Unlike existing indices, the MS-PCI enables multiscalar characterization of precipitation concentration, allowing for effective comparison across spatial domains and temporal scales. In this study, we used monthly precipitation data collected from 1981 to 2021 in various locations in Pakistan. For the standardization process, we propose the use of K-Component Gaussian Mixture Models (KCGMMs), selected based on their superior performance over traditional univariate probability models as determined by the Bayesian Information Criterion (BIC). To assess spatial interpolation capability, we fit multiple variogram models to both the MS-PCI and the conventional Precipitation Concentration Index (PCI). The results reveal that the MS-PCI offers improved spatial predictive accuracy, outperforming the PCI in capturing the spatial distribution of precipitation at unobserved locations. In summary, MS-PCI provides a comprehensive and scalable tool to characterize spatial and temporal precipitation patterns, while also supporting data-driven decision making in water resource management, disaster preparedness, and climate adaptation planning, particularly in regions vulnerable to hydrometeorological extremes.