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 for developing crop irrigation schemes and rational allocation of regional water 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 Optimization (PSO-ELM), Whale Optimization Algorithm (WOA-ELM), and besides three types of empirical models (temperature-, radiation-, and mass transfer-based), and Penman model (P-M) were also applied to estimate the daily ETo in the Hetao irrigation district (HID). The results demonstrated that GWO-ELM obtained the highest estimation accuracy (R-2 = 0.945-0.955; RRMSE = 14.52-15.29%; MAE = 0.124-0.141 mm d(-1), and NSE = 0.942-0.952) at all stations when using mass transfer combination (Tmax, Tmin, RH, u(2)) as models input, and the GWO-ELM hybrid model outperformed other models. Herein, the biogenic heuristic algorithm can effectively enhance the ELM performance in ETo estimation, it was strongly recommended for estimating daily ETo in the HID using the hybrid GWO-ELM model and mass transfer combination as input. The optimized hybrid algorithms, especially GWO-ELM, can accurately estimate daily ETo with limited meteorological data, which can provide scientific guidance for the development of precision agriculture in the HID.

Automated summary

In this study, biological heuristic algorithms were used to optimize the Extreme Learning Machine (ELM) for estimating daily reference evapotranspiration (ETo) in the Hetao irrigation district. The results showed that the GWO-ELM model had the highest estimation accuracy at all stations, and the hybrid model outperformed others, providing scientific guidance for precision agriculture development.