A Novel Framework for Predicting Daily Reference Evapotranspiration Using Interpretable Machine Learning Techniques

Elsayed Ahmed Elsadek, Mosaad Ali Hussein Ali, Clinton Williams, Kelly R. Thorp and Diaa Eldin M. Elshikha ()
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Elsayed Ahmed Elsadek: Biosystems Engineering Department, University of Arizona, Tucson, AZ 85721, USA
Mosaad Ali Hussein Ali: Mining and Metallurgical Engineering Department, Faculty of Engineering, Assiut University, Assiut 71511, Egypt
Clinton Williams: United States Department of Agriculture (USDA)—Agricultural Research Service (ARS), Arid Land Agricultural Research Center, Maricopa, AZ 85138, USA
Kelly R. Thorp: Grassland Soil & Water Research Laboratory, United States Department of Agriculture (USDA)—Agricultural Research Service (ARS), Temple, TX 76502, USA
Diaa Eldin M. Elshikha: Biosystems Engineering Department, University of Arizona, Tucson, AZ 85721, USA

Agriculture, 2025, vol. 15, issue 18, 1-29

Abstract: Accurate estimation of daily reference evapotranspiration (ET o ) is crucial for sustainable water resource management and irrigation scheduling, especially in water-scarce regions like Arizona. The standardized Penman–Monteith (PM) method is costly and requires specialized instruments and expertise, making it generally impractical for commercial growers. This study developed 35 ET o models to predict daily ET o across Coolidge, Maricopa, and Queen Creek in Pinal County, Arizona. Seven input combinations of daily meteorological variables were used for training and testing five machine learning (ML) models: Artificial Neural Network (ANN), Random Forest (RF), Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Support Vector Machine (SVM). Four statistical indicators, coefficient of determination (R 2 ), the normalized root-mean-squared error (RMSE n ), mean absolute error (MAE), and simulation error (S e ), were used to evaluate the ML models’ performance in comparison with the FAO-56 PM standardized method. The SHapley Additive exPlanations (SHAP) method was used to interpret each meteorological variable’s contribution to the model predictions. Overall, the 35 ET o -developed models showed an excellent to fair performance in predicting daily ET o over the three weather stations. Employing ANN10, RF10, XGBoost10, CatBoost10, and SVM10, incorporating all ten meteorological variables, yielded the highest accuracies during training and testing periods (0.994 ≤ R 2 ≤ 1.0, 0.729 ≤ RMSE n ≤ 3.662, 0.030 ≤ MAE ≤ 0.181 mm·day −1 , and 0.833 ≤ S e ≤ 2.295). Excluding meteorological variables caused a gradual decline in ET-developed models’ performance across the stations. However, 3-variable models using only maximum, minimum, and average temperatures (T max , T min , and T ave ) predicted ET o well across the three stations during testing (17.655 ≤ RMSE n ≤ 13.469 and S e ≤ 15.45%). Results highlighted that T max , solar radiation (R s ), and wind speed at 2 m height (U 2 ) are the most influential factors affecting ET o at the central Arizona sites, followed by extraterrestrial solar radiation (R a ) and T ave . In contrast, humidity-related variables (RH min , RH max , and RH ave ), along with T min and precipitation (P r ), had minimal impact on the model’s predictions. The results are informative for assisting growers and policymakers in developing effective water management strategies, especially for arid regions like central Arizona.

Keywords: arid climates; daily reference evapotranspiration (ET o ); ET o prediction; machine learning; SHapley Additive exPlanations (SHAP) (search for similar items in EconPapers)
JEL-codes: Q1 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 (search for similar items in EconPapers)
Date: 2025
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