Evaluation of bio-inspired optimization algorithms hybrid with artificial neural network for reference crop evapotranspiration estimation

Reference crop evapotranspiration (ETo) is a determinant factor in agricultural water resource management. Therefore, accurate ETo information is critical to quantify crop water requirements for precision agriculture management. This study coupled bio-inspired optimization algorithms with artificial neural network (ANN), i.e., ANN with bat algorithm (BA-ANN), ANN with cuckoo search algorithm (CSA-ANN), and ANN with whale optimization algorithm (WOA-ANN), and developed three hybrid ANN models for daily ETo modeling with limited inputs. The models were trained and evaluated using a k-fold test approach and long-term daily climatic data from 2001 to 2018 at six climatic stations in the Loess Plateau of north China. Three input scenarios were used, including temperature-based inputs, radiation-based inputs, and mass transfer-based inputs. The statistical comparison showed that the hybrid WOA-ANN offered better estimates than BA-ANN and CSA-ANN in all three input scenarios. In general, the radiation-based WOA-ANN provided the most accurate ETo estimations, with regional average relative root mean square error and Nash-Sutcliffe efficiency coefficient of 13.3% and 0.959, respectively. The temperature-based WOA-ANN offered acceptable and reasonable ETo estimates. Thus, it is a reliable tool for ETo modeling, given that air temperature is available in many regions. Overall, the bio-inspired optimization algorithms are robust tools for enhancing ANN performance in ETo simulation, and thus they are highly recommended to estimate ETo in the study region. Our study proposed powerful models for accurately estimating ETo with limited inputs, offering practical implications for the development of precision agriculture.