A novel multivariate decomposition-based hybrid model for interpretable multi-step-ahead daily reference evapotranspiration forecasting

The Yazd and Ramsar stations are located in hybrid arid and humid climates in Iran, respectively. This research study develops a complementary expert system for accurately forecasting reference evapotranspiration (ET0) over one, three, and seven-day horizons by integrating Machine Learning (ML) models with a novel multivariate decomposition technique. Initially, significant input predictor lags were established through cross-correlation, and the War Strategy Optimization (WSO) algorithm was used for optimal Feature Selection (FS) and determining Multivariate Variational Mode Decomposition (OMVMD) parameters. Each predictor was decomposed into Intrinsic Mode Functions (IMFs) to enhance the temporal characteristics of the data. The study introduced the FS-OMVMD-RF, FS-OMVMD-KNNR, and FS-OMVMD-ETE models, utilizing Random Forest (RF), K-Nearest Neighbors Regressor (KNNR), and Extra-Trees Ensemble (ETE) techniques for daily ET0 estimation. These hybrid models were benchmarked against alternatives combining Time-Varying Filter-based Empirical Mode Decomposition (TVF-EMD) with individual models. Results demonstrated that the developed models significantly enhance ET0 forecasting capabilities across multiple time scales. Notably, the FS-OMVMD-ETE model achieved the highest accuracy for ET0 (t + 7) at Yazd and Ramsar stations. The analysis indicated that in a hyper-arid climate, the U2 feature has the greatest impact on forecasting, while in a humid climate, T mean is the most influential factor. Graphical stages of ET 0 forecasting based on the proposed frameworks in two stations of Iran. • Utilizing the WSO algorithm to determine the optimal number of IMF for variable. • Developing an expert complementing system using the OMVMA and ML models. • A comparison was made between the proposed model and hybrid models. • Employing interpretability techniques to examine the impact of input parameters.