Evaluating empirical and machine learning approaches for reference evapotranspiration estimation using limited climatic variables in Nepal

Accurate estimation of reference evapotranspiration (ET0) is essential for optimizing water resource management. The widely accepted Penman-Monteith (FAO-56PM) model is commonly used for ET0 estimation but relies on numerous weather variables that are often unavailable in developing countries like Nepal. The suitability of both empirical and machine learning (ML) models with limited climatic variables for estimating ET0 in Nepal remains unexplored. We used 19 meteorological stations across Nepal that measured climatic variables, including maximum and minimum temperatures, wind speed, relative humidity, and sunshine hours. We assessed the performance of six widely used empirical models (Hargreaves Samani, modified Hargreaves Samani, Romanenko, Schendel, Priestley-Taylor, and Makkink) and four ML models (random forest, extreme gradient boosting, deep neural network, and long short-term memory) to estimate ET0 with limited climatic variables in Nepal. Two strategies were applied: (1) the proposed ML models were tested at each weather station using leave- one-out cross-validation (LOOCV), (2) meteorological stations were grouped into three clusters using the Kmeans clustering and model performance were evaluated on each cluster. Results indicate that radiation-based models outperformed humidity and temperature-based models, with R2 increasing from 23 to 38 % and RMSE decreasing by 27 to 41 % across empirical and ML models. Notably, all ML models outperformed empirical models, with clustering of weather stations further reducing prediction error in ET0 estimation by 10 to 18 %. These findings demonstrate the potential of ML models for accurate ET0 estimation with limited data, supporting agricultural water management and enhancing resilience in water-stressed areas.