Machine-Learning Models to Improve Accuracy of Real-Time Reference Evapotranspiration Estimates in an Arid Environment

Studies of the estimation of reference evapotranspiration (${\mathrm{ET}}_0$) in Iran are mostly related to areas with humid and semiarid climates and less related to arid areas. On the other hand, few studies in arid regions have reported high root-mean square error (RMSE) values. However, these regions make an important contribution to agricultural production, and thus, water management of these regions is crucial. It motivated the implementation of such a study in an arid environment of Karaj, Iran, as a case study, in order to estimate daily ${\mathrm{ET}}_0$ with as much accuracy as possible. To achieve this purpose, the performance of 21 known models estimating ${\mathrm{ET}}_0$, including 9 empirical models and 12 machine learning (ML) models, were evaluated. The method provided by the food and agriculture organization (FAO) known as FAO-56 Penman-Monteith (FPM) was regarded as the main reference method for measuring ${\mathrm{ET}}_0$. A new climate data set related to the period of 2005–2020 (April–September) was used to calibrate and cross-validate models. In fact, this study intended to develop an approach for simulating day-to-day variations in ${\mathrm{ET}}_0$ in arid environments by benefitting minimal weather data (i.e., temperature, humidity, and wind speed) for practical purposes because most regions suffer from a lack of weather data, especially radiation data. Therefore, the performance of the best models calibrated in Karaj station was also validated based on data recorded in a research field with a similar climate during 2020–2021. The cross-validated results showed that the deep-learning (DL) model had the lowest RMSE as well as the highest $R^2$ compared with other models. As averaged over all months in Karaj, the DL model exhibited a RMSE 64% less than the best-calibrated empirical model (i.e., Valiantzas-VTS), which is a solar radiation–based model. Furthermore, the improvements arising from using the DL model were more considerable in the extremes than in the middle values. The findings of the field research also demonstrated that the approach developed in the current study would be beneficial at locations other than the calibration station. This approach requires few inputs, is independent of solar radiation data, and also has the lowest RMSE compared with that of other studies. For future studies, the combination of the daily ${\mathrm{ET}}_0$ estimator developed in this study with a recently developed empirical approach to estimate crop coefficients is suggested to manage irrigation on croplands if arid regions.