Optimization of extreme learning machine model with biological heuristic algorithms to estimate daily reference evapotranspiration in Hetao Irrigation District of China

Due to frequent drought events, increased water demand for agricultural production and limited, accurate estimation of reference evapotranspiration (ETo) is necessary developing crop irrigation schemes rational allocation regional resources. The extreme learning machine (ELM) was optimized using four biological heuristic algorithms, namely, Grey Wolf Optimizer (GWO-ELM), Moth-Flame Optimization (MFO-ELM), Particle Swarm (PSO-ELM), Whale Algorithm (WOA-ELM), besides three types empirical models (temperature-, radiation-, mass transfer-based), Penman model (P-M) were also applied estimate the daily ETo in Hetao district (HID). results demonstrated that GWO-ELM obtained highest accuracy (R2 = 0.945–0.955; RRMSE 14.52–15.29%; MAE 0.124–0.141 mm d?1, NSE 0.942–0.952) at all stations when transfer combination (Tmax, Tmin, RH, u2) as input, hybrid outperformed other models. Herein, biogenic algorithm can effectively enhance ELM performance estimation, it strongly recommended estimating HID input. especially GWO-ELM, accurately with limited meteorological data, which provide scientific guidance development precision agriculture HID.Abbreviations: ANN: artificial neural network; BP: back propagation CMA: China Meteorological Administration; D-T: Dalton; EL: elevation; ELM: machine; ETo: evapotranspiration; GEP: gene expression programming; GP: genetic GWO: gray wolf optimization; H-S: Hargreaves-Samani; MFO: moth flame ML: learning; P-M model: FAO-56 Penman-Monteith model; P-T: Priestley-Taylor; PSO: particle swarm RF: random forest; R-O: Rohwer; SVM: support vector SVR: regression; WOA: whale optimization