Performance Evaluation of Five Machine Learning Algorithms for Estimating Reference Evapotranspiration in an Arid Climate

The Food and Agriculture Organization recommends that the Penman–Monteith Method contains Equation 56 (PMF) as a widely accepted standard for reference evapotranspiration (ET_o) calculation. Despite this, the PMF cannot be employed when meteorological variables are constrained; therefore, alternative models for ET_o estimation requiring fewer variables must be chosen, which means that they perform at least as well as, if not better than, the PMF in terms of accuracy and efficiency. This study evaluated five machine learning (ML) algorithms to estimate ET_o and compared their results with the standardized PMF. For this purpose, ML models were trained using monthly time series climatic data. The created ML models underwent testing to determine ET_o under varying meteorological input combinations. The results of ML models were compared to assess their accuracy and validate their performance using several statistical indicators, errors (root-mean-square (RMSE), mean absolute error (MAE)), model efficiency (NSE), and determination coefficient (R²). The process of evaluating ML models involved the utilization of radar charts, Smith graphs, heatmaps, and bullet charts. Based on our findings, satisfactory results have been obtained using RBFFNN based on M12 input combinations (mean temperature (T_mean), mean relative humidity (RH_mean), sunshine hours (Sh)) for ET_o estimation. The RBFFNN model exhibited the most precise estimation as RMSE obtained values of 0.30 and 0.22 during the training and testing phases, respectively. In addition, during training and testing, the MAE values for this model were recorded as 0.15 and 0.17, respectively. The highest R² and NSE values were noted as 0.98 and 0.99 for the RBFNN during performance analysis, respectively. The scatter plots and spatial variations of the RBFNN and PMF in the studied region indicated that the RBFNN had the highest efficacy (R², NSE) and lowest errors (RMSE, MAE) as compared with the other four ML models. Overall, our study highlights the potential of ML models for ET_o estimation in the arid region (Jacobabad), providing vital insights for improving water resource management, helping climate change research, and optimizing irrigation scheduling for optimal agricultural water usage in the region.