Physics-guided interpretable ensemble learning for daily reference evapotranspiration estimation in arid regions

Abstract

Dependable estimates of reference evapotranspiration (ETo) are fundamental to managing water sustainably across arid regions, yet conventional empirical methods have limited capacity to represent the complex non-linear interactions among meteorological variables governing ETo dynamics. This study develops a physics-guided interpretable ensemble learning framework that integrates rule-based (RuleFit) modeling, Support Vector Machines (SVMs), Generalized Simulated Annealing (GenSA) optimization, and SHapley Additive exPlanations (SHAP). Twenty-one RuleFit models were systematically developed across three variable groups, meteorological (air and moisture), solar and radiation, and derived thermodynamic (temperature-vapor), using ten years (2015–2024) of daily observations from two stations (Bahla and Sunaynah) in Oman. The best configuration from each group was integrated into a hierarchical ensemble in which an SVM fuses the group-level predictions as meta-features, with hyperparameters tuned via GenSA. The RuleFit-SVM-GenSA framework achieved exceptional test performance at Bahla (coefficient of determination (R 2 ) = 0.982, Root Mean Square Error (RMSE) = 0.216 mm/d) and Sunaynah (R 2 = 0.989, RMSE = 0.19 mm/d), outperforming benchmark Hargreaves-Samani method (R 2 = 0.932–0.958, RMSE = 0.379–0.42 mm/d). SHAP analysis identified maximum temperature, solar radiation, and saturation vapor pressure as dominant predictors, confirming physically consistent behavior. Results demonstrate that the developed framework simultaneously achieves high predictive accuracy while retaining a transparent, rule-based model structure at the base-learner level, providing water resource managers with a reliable tool for precision irrigation and hydrological applications in water-scarce arid environments.