Modelling daily reference evapotranspiration based on stacking hybridization of ANN with meta-heuristic algorithms under diverse agro-climatic conditions

Precise estimation of reference evapotranspiration (ET0) is crucial for efficient agricultural water management, crop modelling, and irrigation scheduling. In recent years, the data-driven models using Artificial Intelligence (AI)-based meta-heuristics algorithms have gained the attention of researchers worldwide. In this study, we have investigated the performance of five AI-based models for ET0 estimation, including Artificial Neural Networks-Additive Regression (ANN-AR), ANN-Random Forest (ANN-RF), ANN-REPtree, ANN-M5Pruning Tree (ANN-M5P), and ANN-Bagging at New Delhi (i.e., semi-arid climate), and Srinagar (i.e., humid climate) stations and the best yielded algorithms were evaluated at the third station i.e. Ludhiana (i.e., sub-humid climate) located in Northern India. The performances indicators (i.e., Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Nash-Sutcliffe Efficiency (NSE), and Willmott Index (WI)) of hybrid meta-heuristics algorithms were compared to FAO-56 Penman-monteith (P-M FAO-56). Results revealed that the M5P algorithm under limited climate variables (i.e., Model 1, 2, and 3) and Bagging (Model 4 and 5) acted as efficient tools in optimizing the ANN structure. Therefore, the algorithm ANN-M5P predicted ET0 values precisely under models 1, 2, and 3. While the ANN-Bagging algorithms gave better ET0 estimation under models 4 and 5 for both the selected stations. The evaluation of best hybrid algorithms under each constructed model for the Ludhiana station showed that the ANN-M5P algorithm under Model-3 outperformed the other four models (MAE = 0.730 mm/day, RMSE = 0.959 mm/day, NSE = 0.779, and WI = 0.935). The present study demonstrated that the AI-based hybrid meta-heuristics algorithms (ANN-M5P and ANN-Bagging) are promising pathways for ET0 estimation.