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

Abstract

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 (Tmax), minimum temperature (Tmin), wind speed (u2), relative humidity (RH), net radiation (Rn), and global solar radiation (Rs) 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 R2 ranging 0.71–0.99, RMSE ranging 0.036–0.77 mm·d−1) outperformed the standalone ELM models (with R2 ranging 0.716–0.99, RMSE ranging 0.08–0.77 mm·d−1) during training and testing, both of which were superior to empirical models (with R2 ranging 0.36–0.91, RMSE ranging 0.69–2.64 mm·d−1). ET0 prediction accuracy varies with different input combination models. The machine learning models using Tmax, Tmin, u2, RH, and Rn/Rs (GA-ELM5/GA-ELM4 and ELM5/ELM4) obtained the best ET0 estimates, with R2 ranging 0.98–0.99, RMSE ranging 0.03–0.21 mm·d−1, followed by models with Tmax, Tmin, and Rn/Rs (GA-ELM3/GA-ELM2 and ELM3/ELM2) as inputs. The machine learning models involved with Rn outperformed those with Rs when the quantity of input parameters was the same. Overall, GA-ELM5 (Tmax, Tmin, u2, RH and Rn 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 (Tmax, Tmin, and Rs as inputs) was determined to be the most effective model for estimating daily ET0 with limited meteorological data in Southwest China.

Keywords

• reference evapotranspiration
• extreme learning machine
• optimization algorithm
• empirical model
• solar radiation