Minimal Impact of Parameter Estimation Methods on Drought Identification Using the Complementary Evaporation Principle

This paper investigates the relatively underexplored potential of the complementary relationship (CR) of evaporation as a tool for monitoring agricultural drought. The ratio of actual to potential evapotranspiration (r_ET), central to the CR theory, conceptually aligns with the water stress coefficient used in early bucket-type land surface models. Across the conterminous United States (CONUS), we derived r_ET from the power-function CR and converted it into the widely used evaporative stress index (ESI), without relying on remote sensing data or land surface schemes. In doing so, two physical parameters of the power-function CR were estimated using four previously proposed methods. We evaluated the CR-based ESI against soil moisture data from land surface models and vegetation indices from satellite observations. Results showed that the CR-based ESI effectively captured major drought events across the CONUS from 1981 to 2020, with Pearson correlations exceeding 0.8 against standardized soil moisture in most agricultural regions. While the two CR–Budyko combined methods outperformed the calibration-free approaches in reproducing basin-scale water balance, the ESI product from one of them (â and b 5 2) showed weaker correlations with soil moisture anomalies compared to the other three methods. Nonetheless, all CR-based ESI series exhibited strong agreement in identifying severe droughts linked to La Niña events. These findings suggest that the power-function CR provides a practical and physically grounded foundation for estimating ESI using only routine meteorological variables, with relatively minor sensitivity to parameter estimation methods. SIGNIFICANCE STATEMENT: This study evaluates the performance of the evaporative stress index derived from the complementary relationship (CR) of evaporation using four parameter estimation methods across the United States. Unlike traditional ESI approaches that rely on remote sensing or complex land surface models, the CR-based ESI can be computed using only routine atmospheric variables. The resulting products captured major drought events-including those associated with La Niña}with strong agreement against topsoil moisture, vegetation condition, and thermal stress indicators. While performance varied slightly depending on the parameterization method, all four approaches produced comparable drought detection patterns. These findings highlight the CR framework as a physically based, data-efficient alternative for agricultural drought monitoring, with broad applicability even in datasparse regions.