Analytical Estimation of Precipitation Anomalies Based on the Standardized Precipitation Index: An Improvement for Drought Estimation in Vulnerable Semi-Arid Regions

Quantifying rainfall variability is essential for understanding hydroclimatic behavior in vulnerable semiarid regions characterized by strong spatial and temporal variability. This study proposes Math-SPI-Pro as an alternative computational framework for precipitation anomaly standardization assessing drought. The approach retains the conventional gamma/mixed-gamma probabilistic basis used in SPI, including Thom’s approximation for gamma parameter estimation, while applying a direct standardization of the resulting cumulative probability H(x). Consequently, the Math-SPI-Pro standardized scale is mathematically related to, but numerically distinct from, the conventional inverse-normal SPI transformation. The approach incorporates an analytical treatment of the gamma distribution, including the evaluation of scale-dependent changes in the shape of the fitted gamma distribution and the explicit consideration of the precipitation series with and without zero values, enabling a more robust probabilistic representation across the time scales. The method was implemented for spatial–temporal drought characterization in a semiarid basin of Mexico and compared with three commonly SPI models used (SPI_SL_6, Climpact, and Variclim). Results show that the proposed Math-SPI_Pro formulation achieved high agreement with the reference models, with a Pearson correlation coefficient close to 0.98 and generally small pairwise discrepancies according to the error metrics. These findings demonstrate that the proposed analytical framework provides an explicit and reproducible alternative framework for standardized precipitation anomaly for drought assessment for sustainable water management in applications such as reservoirs, aquifers, and surface water; disaster prevention; agriculture; and socioeconomic issues.