Daily reference evapotranspiration prediction based on hybridized extreme learning machine model with bio-inspired optimization algorithms: Application in contrasting climates of China

Abstract Reliable and accurate prediction of reference evapotranspiration (ETo) is a precondition for the efficient management and planning of agricultural water resources as well as the optimal design of irrigation scheduling. This study evaluated the performances of four bio-inspired algorithm optimized extreme learning machine (ELM) models, i.e. ELM with genetic algorithm (ELM-GA), ELM with ant colony optimization (ELM-ACO), ELM with cuckoo search algorithm (CSA) and ELM with flower pollination algorithm (ELM-FPA), for predicting daily ETo across China by using a five-fold cross-validation approach. These models were further compared with the classical ELM model parameterized by the grid search method to demonstrate their capability and efficiency. Daily maximum and minimum ambient temperatures, wind speed, relative humidity and global solar radiation data during 2001–2015 collected from eight meteorological stations in contrasting climates of China were utilized to train, validate and test the models. The results showed that ETo values predicted by all ELM models agreed well with the corresponding FAO-56 Penman–Monteith values, with R2, RMSE, NRMSE and MAE ranging 0.9766–0.9967, 0.0896–0.2883 mm day−1, 3.2910%-11.7653% and 0.0708–0.1998 mm day−1, respectively. The ELM-FPA model (R2 = 0.9930, RMSE = 0.1589 mm day−1, NRMSE = 5.5406% and MAE = 0.1188 mm day−1) slightly outperformed the ELM-CSA model (R2 = 0.9922, RMSE = 0.1619 mm day−1, NRMSE = 5.6864% and MAE = 0.1200 mm day−1) during testing, both of which were superior to the ELM-ACO (R2 = 0.9912, RMSE = 0.1730 mm day−1, NRMSE = 6.0816% and MAE = 0.1254 mm day−1) and ELM-GA (R2 = 0.9889, RMSE = 0.1895 mm day−1, NRMSE = 6.7197% and MAE = 0.1310 mm day−1) models, followed by the standalone ELM model (R2 = 0.9856, RMSE = 0.2104 mm day−1, NRMSE = 7.1693% and MAE = 0.1408 mm day−1). The four hybrid ELM models exhibited higher improvements in daily ETo prediction in the temperate monsoon and (sub)tropical monsoon climates (with average decrease in RMSE of 14.0%, 25.1%, 31.4% and 33.1%, respectively), compared with those in the temperate continental and mountain plateau climates (with average decrease in RMSE of 5.2%, 9.8%, 12.9% and 14.1%, respectively). The results advocated the capability of bio-inspired optimization algorithms, especially the FPA and CSA algorithms, for improving the performance of the conventional ELM model in daily ETo prediction in contrasting climates of China.