Multi-step daily forecasting of reference evapotranspiration for different climates of India: A modern multivariate complementary technique reinforced with ridge regression feature selection

Accurate ahead forecasting of reference evapotranspiration (ET_o) is crucial for effective irrigation scheduling and management of water resources on a regional scale. A variety of methods are available for ET_o simulation, but the most trending is complementary artificial intelligence (AI) paradigms. In this research, a novel Multivariate Variational Mode Decomposition technique (MVMD) integrated with the Ridge Regression (RR) feature selection algorithm and Kernel Extreme Learning Machine (KELM) model (i.e., M_VMD-RR-K_ELM) was adopted to multi-step ahead (t + 3, and t + 7) forecasting of daily ET_o in different climate of India. Here, the complementary expert system hybridized with the Boosted Regression Tree (BRT) and Extreme Gradient Boosted (XGBoost) along with the standalone counterpart models (KELM, BRT, and XGBoost) were examined to validate the robustness of the primary model. The complementary (i.e., M_VMD-RR-K_ELM, M_VMD-RR-B_RT, & M_VMD-RR-X_GBoost) and their standalone counterpart models were trained and tested using daily climatic data of Hisar (located in Haryana State), Bathinda, and Ludhiana (located in Punjab State) sites. The forecasting accuracy of standalone and hybrid AI models was assessed using six goodness-of-fit metrics, i.e., R (Correlation Coefficient), RMSE (root mean square error), MAPE (mean absolute percentage error), NSE (Nash-Sutcliffe Efficiency), I_A (Index of Agreement), U_95% (Uncertainty Coefficient with 95% level) along with visual interpretation. According to the testing results, the hybrid M_VMD-RR-K_ELM models had superior performance than other AI models for forecasting three and seven days ahead ET_o. The KELM model optimized using the MVMD-RR technique provides promising and robust results with higher forecasting accuracy and minimum error for multi-step ahead forecasting of ET_o in semi-arid and sub-humid regions.