Genetic Algorithm-Optimized Extreme Learning Machine Model for Estimating Daily Reference Evapotranspiration in Southwest China

Reference evapotranspiration (ET0) is an essential component in hydrological and ecological processes. The Penman-Monteith (PM) model of Food and Agriculture Organization of the United Nations (FAO) model requires a number of meteorological parameters; it is urgent to develop high-precision and computationally efficient ET0 models with fewer parameter inputs. This study proposed the genetic algorithm (GA) to optimize extreme learning machine (ELM), and evaluated the performances of ELM, GA-ELM, and empirical models for estimating daily ET0 in Southwest China. Daily meteorological data including maximum temperature (T-max), minimum temperature (T-min), wind speed (u(2)), relative humidity (RH), net radiation (R-n), and global solar radiation (R-s) during 1992-2016 from meteorological stations were used for model training and testing. The results from the FAO-56 Penman-Monteith formula were used as a control group. The results showed that GA-ELM models (with R-2 ranging 0.71-0.99, RMSE ranging 0.036-0.77 mm center dot d(-1)) outperformed the standalone ELM models (with R-2 ranging 0.716-0.99, RMSE ranging 0.08-0.77 mm center dot d(-1)) during training and testing, both of which were superior to empirical models (with R-2 ranging 0.36-0.91, RMSE ranging 0.69-2.64 mm center dot d(-1)). ET0 prediction accuracy varies with different input combination models. The machine learning models using T-max, T-min, u(2), RH, and R-n/R-s (GA-ELM5/GA-ELM4 and ELM5/ELM4) obtained the best ET0 estimates, with R-2 ranging 0.98-0.99, RMSE ranging 0.03-0.21 mm center dot d(-1), followed by models with T-max, T-min, and R-n/R-s (GA-ELM3/GA-ELM2 and ELM3/ELM2) as inputs. The machine learning models involved with R-n outperformed those with R-s when the quantity of input parameters was the same. Overall, GA-ELM5 (T-max, T-min, u(2), RH and R-n as inputs) outperformed the other models during training and testing, and was thus recommended for daily ET0 estimation. With the estimation accuracy, computational costs, and availability of input parameters accounted, GA-ELM2 (T-max, T-min, and R-s as inputs) was determined to be the most effective model for estimating daily ET0 with limited meteorological data in Southwest China.