Estimation of monthly reference evapotranspiration using novel hybrid machine learning approaches

In this research, five hybrid novel machine learning approaches, artificial neural network (ANN)-embedded grey wolf optimizer (ANN-GWO), multi-verse optimizer (ANN-MVO), particle swarm optimizer (ANN-PSO), whale optimization algorithm (ANN-WOA) and ant lion optimizer (ANN-ALO), were applied for modelling monthly reference evapotranspiration (ETo) at Ranichauri (India) and Dar El Beida (Algeria) stations. The estimates yielded by hybrid machine learning models were compared against three models, Valiantzas-1, 2 and 3 based on root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC) and Willmott index (WI). The results of comparison show that the ANN-GWO-1 model with five input variables (Tmin, Tmax, RH, Us, Rs) provides better estimates at both study stations (RMSE = 0.0592/0.0808, NSE = 0.9972/0.9956, PCC = 0.9986/0.9978, and WI = 0.9993/0.9989). Also, the adopted modelling strategy can build a truthful expert intelligent system for estimating the monthly ETo at study stations.