Evaluation of Data-driven Hybrid Machine Learning Algorithms for Modelling Daily Reference Evapotranspiration

Reference evapotranspiration (ET0) is one of the crucial variables used for irrigation scheduling, agricultural production, and water balance studies. This study compares six different models with sequential inclusion of six meteorological input variables such as minimum temperature (Tmin), maximum temperature (Tmax), mean relative humidity (RH), wind speed (SW), sunshine hours (HSS), and solar radiation (RS), which are necessarily used in physical or empirical-based models to estimate ET0. Each model utilized three variants of machine learning algorithms, i.e. Additive Regression (A(d)R), Random Subspace (RSS), M5 Pruning tree (M5P) independently and four novel permutated hybrid combinations of these algorithms. To evaluate the efficacy of these hybridizations and the stability of machine learning models, a comprehensive evaluation of independent and hybrid models was performed. With more input variables, the model performances were found to be superior in terms of prediction accuracies. The model A(d)R6 that included all the 6 selected meteorological variables outperformed other models during the testing period, exhibiting statistical performance of MAPE (1.30), RMSE (0.07), RAE (2.41), RRSE (3.10), and R-2 (0.998). However, the A(d)R algorithm, alone, was found to capture about 86% of variance in the observed data conforming to the 95% confidence band across all models irrespective of the number of input variables used to predict ET0. The RSS algorithm, in comparison to other algorithms, failed to capture the observed trends even with all the input variables. The hybrid combinations of algorithms with A(d)R as a constituent were better performers in terms of their prediction accuracies but remained inferior to A(d)R as an individual performer. All the algorithms are better predictors of the higher values of ET0 that included values beyond the 75% quartile.

Automated summary

This study compares different models and algorithms for estimating reference evapotranspiration (ET0). The model performances were found to be superior with the inclusion of more meteorological input variables. The A(d)R6 model, which included all selected variables, outperformed other models during testing. The A(d)R algorithm alone captured about 86% of the observed data's variance, while hybrid combinations with A(d)R as a constituent showed better prediction accuracies but still inferior to A(d)R as an individual performer.