Evaluation of Empirical and Machine Learning Approaches for Estimating Monthly Reference Evapotranspiration with Limited Meteorological Data in the Jialing River Basin, China

The accurate estimation of reference evapotranspiration (ET(0)) is crucial for water resource management and crop water requirements. This study aims to develop an efficient and accurate model to estimate the monthly ET(0) in the Jialing River Basin, China. For this purpose, a relevance vector machine, complex extreme learning machine (C-ELM), extremely randomized trees, and four empirical equations were developed. Monthly climatic data including mean air temperature, solar radiation, relative humidity, and wind speed from 1964 to 2014 were used as inputs for modeling. A total comparison was made between all constructed models using four statistical indicators, i.e., the coefficient of determination (R(2)), Nash efficiency coefficient (NSE), root mean square error (RMSE) and mean absolute error (MAE). The outcome of this study revealed that the Hargreaves equation (R(2) = 0.982, NSE = 0.957, RMSE = 7.047 mm month(−1), MAE = 5.946 mm month(−1)) had better performance than the other empirical equations. All machine learning models generally outperformed the studied empirical equations. The C-ELM model (R(2) = 0.995, NSE = 0.995, RMSE = 2.517 mm month(−1), MAE = 1.966 mm month(−1)) had the most accurate estimates among all generated models and can be recommended for monthly ET(0) estimation in the Jialing River Basin, China.