Estimating reference crop evapotranspiration using optimized empirical methods with a novel improved Grey Wolf Algorithm in four climatic regions of China

Accurate estimation of reference crop evapotranspiration (ETo) is crucial for agricultural water management. As the simplified alternatives of the Penman-Monteith equation, empirical methods have been widely recommended worldwide. However, its application is still limited to parameters localization varied with geographical and climatic conditions, therefore developing an excellent optimization algorithm for calibrating parameters is very necessary. Regarding the above requirement, the present study developed a novel improved Grey Wolf Algorithm (MDSL-GWA) to optimize the most recommended ones among three types of ETo methods. After the optimization performance comparison among Least Square Method (LSM), Genetic Algorithm (GA), Grey Wolf Algorithm (GWA), and MDSL-GWA in four climatic regions of China, this study found that the Priestley-Taylor (PT) method was the best radiation-based (Rn-based) method and achieved better performance in temperate continental region (TCR), mountain plateau region (MPR), and temperate monsoon region (TMR) than other types. While the temperature-based (T-based) Hargreaves-Samani (HS) method performed best in subtropical monsoon region (SMR), further attaching better performance among the same type in TMR and TCR, while the Oudin method was the best T-based method in MPR. Moreover, the Romanenko method was better humidity-based (RH-based) in TCR and MPR, whereas the Brockamp-Wenner method exhibited higher in SMR and TMR. Furthermore, despite intelligence optimization algorithms significantly enhancing original ETo methods, the MDSL-GWA achieved best performance and outperformed other algorithms by 4.5–29.6% in determination coefficient (R2), 4.7–27.3% in nash-sutcliffe efficient (NSE), 3.7–44.4% in relative root mean square error (RRMSE), and 3.1–56.2% in mean absolute error (MAE), respectively. After optimization, the MDSL-GWA-PT was the most recommended ETo method in TMR, TCR, and MPR, and the median values of R2, NSE, RRMSE, and MAE ranged 0.907–0.958, 0.887–0.925, 0.083–0.103, and 0.115–0.162 mm, respectively. In SMR, the MDSL-GWA-HS produced the best ETo estimates, with median values of R2, NSE, RRMSE, and MAE being 0.876, 0.843, 0.112, and 0.146 mm, respectively. In summary, this study recommended the best ETo method and algorithms using accessible data in four climatic regions of China, which is helpful for decision-making in effective management and utilization of regional agricultural water resources.