Optimized empirical model based on whale optimization algorithm for simulate daily reference crop evapotranspiration in different climatic regions of China.

• The accuracy of the temperature, radiation and hybrid models improved by 12.05 %, 11.06% and 10.46% after being optimized by WOA. • The estimation accuracy of the temperature, radiation and hybrid models optimized by the whale algorithm were higher than the prediction result of the ELM model. • The empirical model with more input parameters has higher estimation accuracy than the empirical model with fewer parameters. The accurate estimation of reference crop evapotranspiration (ET 0) is of great significance to improve agricultural water use efficiency and optimize regional water resources management. At present, the applicability evaluation system of ET 0 models is still lacking in several climate regions in China, leading to the confusion in application of the ET 0 model in some specific regions. In this study, the daily meteorological data of 84 representative stations in four climate regions of China during the past 30 years (1991–2019) were selected to evaluate the ET 0 simulation results of twelve empirical models (four temperature models, five radiation models, and three hybrid models) on the daily scale, and the optimal models suitable for each climate region were screened. Whale optimization algorithm (WOA) was used to optimize the optimal model to improve the simulation accuracy, and the ET 0 results were compared with those predicted by extreme learning machine (ELM). The results showed that the estimation accuracy of the hybrid model was the best throughout China, followed by the radiation model, and the temperature model was relatively poor, with R2 ranges of 0.77–0.88, 0.60–0.86, and 0.58–0.82, respectively. Among the temperature-based models, Hargreaves-Samani and Improve Baier-Robertson model had the highest accuracy, with R2 of 0.80 and 0.79. Among the radiation-based models, Priestley-Taylor and Jensen-Haise models had the best accuracy, with R2 of 0.82 and 0.79. Among the hybrid models, Penman model had the highest accuracy, with R2 of 0.84. The accuracy of Hargreaves-Samani and Improve Baier-Robertson model in SMZ climate region was higher than TCZ, TMZ, and MPZ, and the accuracy of Jensen-Haise model in TCZ was the highest. The estimation accuracy of Priestley-Taylor and Penman models was similar in SMZ, TCZ, TMZ and MPZ. Using WOA to optimize the optimal temperature, radiation, and hybrid models, the prediction accuracy was improved by 12.05 %, 11.06 %, and 10.46 %, which were higher than the result of ELM model, with R2 of 0.90, 0.91, 0.95 and 0.90, respectively. Therefore, it is recommended to adopt WOA to optimize the empirical model to estimate the ET 0 all over China. [ABSTRACT FROM AUTHOR]