Estimation of reference evapotranspiration based on machine learning models and timeseries analysis: a case study in an arid climate

Abstract Water scarcity is a major challenge for irrigated agriculture, particularly in developing countries where access to meteorological data for calculating reference evapotranspiration (ET o ) is limited. Thus, this study explores the potential of two machine learning models (random forest (RF) and long short-term memory (LSTM)) and autoregressive integrated moving average (ARIMA) to forecast ET o . The investigation was conducted for four weather stations in Egypt, from 1982 to 2020. The machine learning models were evaluated using four combinations of inputs: maximum and minimum temperature, relative humidity, and wind speed. The best results for both RF and LSTM models were achieved with the first set of inputs that included all four variables at both regional and local scales. For the regional scale, RF and LSTM models achieved R 2 values of 0.85 and 0.86, respectively, with RMSE values of 0.69 and 0.68 mm/day. At the local scale, RF and LSTM models exhibited R 2 values ranging from 0.92 to 0.95 and 0.93 to 0.95, respectively, while RMSE ranged between 0.38 and 0.46 mm/day and 0.37–0.43 mm/day, respectively. Additionally, ARIMA models were employed for tim series analysis of the same ET o data. ARIMA (2,1,4) and ARIMA (2,1,3) were found to be the most suitable models for the local-scale analysis while ARIMA (2,1,4) was identified as the optimal model for the regional-scale analysis. For the local-scale analysis, R 2 values ranged from 0.86 to 0.91 and RMSE values ranged from 0.26 to 0.38. The regional scale analysis yielded an R 2 value of 0.89 and an RMSE value of 0.58 mm/day. The developed models can be used in places where meteorological data for forecasting ET o are limited.