Recalibration of four empirical reference crop evapotranspiration models using a hybrid Differential Evolution-Grey Wolf Optimizer algorithm

Accurate estimation of reference crop evapotranspiration (ET₀) is essential for water resource management and irrigation scheduling. A multitude of empirical models have been employed to estimate ET₀, yielding satisfactory outcomes. However, the performance of each model is contingent upon the empirical parameters utilized. This study examines the applicability of four empirical ET₀ models, namely the Makkink (Mak), Irmark-Allen (IA), improved Baier-Robertson (MBR), and Brutsaert-Stricker (BS) models. Meteorological data from 24 weather stations across various regions in China were procured and employed to assess the ET₀ simulation results. The study employed the Differential Evolution (DE) optimization algorithm, Grey Wolf Optimizer (GWO) algorithm, and a hybrid algorithm that combines DE and GWO algorithms (DE-GWO algorithm) to optimize the parameters of the four empirical models. The findings revealed that the optimization algorithms significantly enhanced the regional adaptability of the four models, particularly the BS model. The DE-GWO algorithm demonstrated superior optimization performance (RMSE=0.055-0.372, R²=0.912-0.998, MAE=0.037-0.311, and FS=0.864-0.982) compared to the DE (RMSE=0.101-2.015, R²=0.529-0.997, MAE=0.075-1.695, and FS=0.383-0.967) and GWO (RMSE=0.158-0.915, R²=0.694-0.987, MAE=0.111-0.701, and FS=0.688-0.947) algorithms. The DE-GWO-optimized BS model was the most accurate and improved, followed by the MBR model. The IA and Mak models also showed slightly better performance after optimization with the DE-GWO algorithm. The DE-GWO-optimized BS model performed better in the southern agricultural region than in other regions. It is recommended to utilize the DE-GWO to enhance the accurate prediction of empirical ET₀ models across the nine agricultural regions of China.