Comparative assessment of empirical and hybrid machine learning models for estimating daily reference evapotranspiration in sub-humid and semi-arid climates

Abstract

Improving the accuracy of reference evapotranspiration (RET) estimation is essential for effective water resource management, irrigation planning, and climate change assessments in agricultural systems. The FAO-56 Penman-Monteith (PM-FAO56) model, a widely endorsed approach for RET estimation, often encounters limitations due to the lack of complete meteorological data. This study evaluates the performance of eight empirical models and four machine learning (ML) models, along with their hybrid counterparts, in estimating daily RET within the Gharb and Loukkos irrigated perimeters in Morocco. The ML models examined include Random Forest (RF), M5 Pruned (M5P), eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), with hybrid combinations of RF-M5P, RF-XGBoost, RF-LightGBM, and XGBoost-LightGBM. Six input combinations were created, utilizing Tmax, Tmin, RHmean, Rs, and U2, with the PM-FAO56 model serving as the benchmark. Model performance was assessed using four statistical indicators: Kling-Gupta efficiency index (KGE), coefficient of determination (R2), mean squared error (RMSE), and relative root squared error (RRSE). Results indicate that the Valiantzas 2013 (VAL2013b) model outperformed other empirical models across all stations, achieving high KGE and R2 values (0.95–0.97) and low RMSE (0.32–0.35 mm/day) and RRSE (8.14–10.30%). The XGBoost-LightGBM and RF-LightGBM hybrid models exhibited the highest accuracy (average RMSE of 0.015–0.097 mm/day), underscoring the potential of hybrid ML models for RET estimation in subhumid and semi-arid regions, thereby enhancing water resource management and irrigation scheduling.