Estimation reference crop evapotranspiration (ET0) using artificial intelligence model in an arid climate with external data

Abstract Water resource management and crop growth control require the calculation of reference evapotranspiration (ET0), but meteorological data can often be incomplete, necessitating models with minimal inputs. This study was conducted in Iran’s arid synoptic stations of Sirjan and Kerman, where data scarcity is severe. Penman–Monteith FAO-56 was selected as the target data for modeling artificial neural network (ANN), fuzzy neural adaptive inference system (ANFIS), and ANN-gray wolf optimization (ANN-GWO). The performance of these models was evaluated using an input dataset consisting of the current station’s minimum and maximum temperatures, ET0, and the wind speed of the nearby station (external data) in three different combinations. The models’ accuracy was assessed using two widely used criteria: root mean square error (RMSE) and coefficient of determination ( R 2 ), as well as the empirical Hargreaves equation. In the absence of climatic data, the ANFIS, ANN, and ANN-GWO methods using minimum and maximum temperatures, which are relatively easier to estimate, outperformed the empirical Hargreaves equation method in both stations. The results demonstrate that the ANFIS method performed better than ANN and ANN-GWO in all three input combinations. All three methods showed improvement when external data (wind speed and ET0 of the adjacent station) were used. Ultimately, the ANFIS method using minimum and maximum temperatures and the adjacent station’s ET0 in Kerman and Sirjan yielded the best results, with an RMSE of 0.33 and 0.36, respectively.