Evaluation of Machine Learning versus Empirical Models for Monthly Reference Evapotranspiration Estimation in Uttar Pradesh and Uttarakhand States, India

Abstract

Reference evapotranspiration (ETo) plays an important role in agriculture applications such as irrigation scheduling, crop simulation, water budgeting, and reservoir operations. Therefore, the accurate estimation of ETo is essential for optimal utilization of available water resources on regional and global scales. The present study was conducted to estimate the monthly ETo at Nagina (Uttar Pradesh State) and Pantnagar (Uttarakhand State) stations by employing the three ML (machine learning) techniques including the SVM (support vector machine), M5P (M5P model tree), and RF (random forest) against the three empirical models (i.e., Valiantzas-1: V-1, Valiantzas-2: V-2, Valiantzas-3: V-3). Three different input combinations (i.e., C-1, C-2, C-3) were formulated by using 8-year (2009–2016) climatic data of wind speed (u), solar radiation (Rs), relative humidity (RH), and mean air temperature (T) recorded at both stations. The predictive efficacy of ML and the empirical models was evaluated based on five statistical indicators i.e., CC (correlation coefficient), WI (Willmott index), EC (efficiency coefficient), RMSE (root mean square error), and MAE (mean absolute error) presented through a heatmap along with graphical interpretation (Taylor diagram, time-series, and scatter plots). The results showed that the SVM-1 model corresponding to the C-1 input combination outperformed the other ML and empirical models at both stations. Moreover, the SVM-1 model had the lowest MAE (0.076, 0.047 mm/month) and RMSE (0.110, 0.063 mm/month), and highest EC (0.995, 0.999), CC (0.998, 0.999), and WI (0.999, 1.000) values during validation period at Nagina and Pantnagar stations, respectively, and closely followed by the M5P model. Consequently, the ML model (i.e., SVM) was found to be more robust, and reliable in monthly ETo estimation and can be used as a promising alternative to empirical models at both study locations.