Development of Monthly Reference Evapotranspiration Machine Learning Models and Mapping of Pakistan—A Comparative Study

Abstract

Accurate estimation of reference evapotranspiration (ETo) plays a vital role in irrigation and water resource planning. The Penman–Monteith method recommended by the Food and Agriculture Organization (FAO PM56) is widely used and considered a standard to calculate ETo. However, FAO PM56 cannot be used with limited meteorological variables, so it is compulsory to choose an alternative model for ETo estimation, which requires fewer variables. This study built ten machine learning (ML) models based on multi-function, neural network, and tree-based structure against the FAO PM56 method. For this purpose, time series temperature data on a monthly scale are only used to train ML models. The developed ML models were applied to estimate ETo at different test stations and the obtained results were compared with the FAO PM56 method to verify and validate their performance in ETo estimation for the selected stations. In addition, multiple statistical indicators, including root-mean-square error (RMSE), coefficient of determination (R2), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and correlation coefficient (r) were calculated to compare the performance of each ML model on ETo estimation. Among the applied ML models, the ETo tree boost (TB) ML model outperformed the other ML models in estimating ETo in diverse climatic conditions based on statistical indicators (R2, NSE, r, RMSE, and MAE). Moreover, the observed R2, NSE, and r were the highest for the TB ML model, while RMSE and MAE were found to be the lowest at the study sites compared to other applied ML models. Lastly, ETo point data yielded from the TB ML model was used in an interpolation process to create monthly and annual ETo maps. Based on the ETo maps, this study suggests mainly a focus on areas with high ETo values and proper irrigation scheduling of crops to ensure water sustainability.