Optimization of extreme learning machine model with biological heuristic algorithms to estimate daily reference crop evapotranspiration in different climatic regions of China

Abstract

Accurate prediction of reference crop evapotranspiration (ET0) is important for regional water resources management and optimal design of agricultural irrigation system. In this study, three hybrid models (PSO-ELM, GA-ELM and ABC-ELM) integrating the extreme learning machine model (ELM) with three biological heuristic algorithms, i.e., PSO, GA and ABC, were proposed for predicting daily ET0 based on daily meteorological data from 2000 to 2019 at twelve representative stations in different climatic zones of China. The performances of the three hybrid ELM models were further compared with the standalone ELM model and three empirical models (Hargreaves, Priestley-Talor and Makkink models). The results showed that the hybrid ELM models (R2 = 0.973–0.999) all performed better than the standalone ELM model (R2 = 0.955–0.989) in four climatic regions in China. The estimation accuracy of the empirical models was relatively lower, with R2 of 0.822–0.887 and RMSE of 0.381–1.951 mm/d. The R2 values of PSO-ELM, GA-ELM and ABC-ELM models were 0.993, 0.986 and 0.981 and the RMSE values were 0.266 mm/d, 0.306 mm/d and 0.404 mm/d, respectively, indicating that the PSO-ELM model had the best performance. When setting Tmax, Tmin and RH as the model inputs, the PSO-ELM model presented better performance in the temperate continental zone (TCZ), subtropical monsoon region (SMZ) and temperate monsoon zone (TMZ) climate zones, with R2 of 0.892, 0866 and 0.870 and RMSE of 0.773 mm/d, 0.597 mm/d and 0.832 mm/d, respectively. The PSO-ELM model also performed in the mountain plateau region (MPZ) when only Tmax and Tmin data were available, with R2 of 0.808 and RMSE of 0.651 mm/d. All the three biological heuristic algorithms effectively improved the performance of the ELM model. Particularly, the PSO-ELM was recommended as a promising model realizing the high-precision estimation of daily ET0 with fewer meteorological parameters in different climatic zones of China.