Enhancing Reference Evapotranspiration Prediction Using Deep Learning Transformer Models and Multivariate Variational Mode Decomposition in Arid Regions

Accurate estimation of reference evapotranspiration (ETo) is fundamental for irrigation scheduling, hydrological modeling, and sustainable water-resources management, particularly in arid and semi-arid regions where strong climatic variability challenges predictive reliability. This study investigates the performance of advanced Transformer-based deep learning architectures and their hybrid extensions for daily ETo prediction at two climatically distinct inland stations—Nizwa and Rustaq in northern Oman. Three state-of-the-art single models, namely Autoformer, Informer, and FEDformer, were evaluated and further integrated with Multivariate Variational Mode Decomposition (MVMD) to develop hybrid frameworks capable of explicitly disentangling multi-scale temporal patterns and cross-variable dependencies. Meteorological data spanning 2018–2025 were used to train and test the models under five input scenarios: (i) temperature only, (ii) temperature with wind speed (U2), (iii) temperature with net radiation (Rn), (iv) temperature with vapor pressure deficit (es–ea), and (v) all available meteorological variables. Model performance was assessed using the coefficient of determination (R²), root mean square error (RMSE), and the RMSE–standard deviation ratio (RSR). Results indicate that hybrid MVMD-based models consistently outperform their single-model counterparts across all input scenarios and both stations, with the most pronounced improvements observed under multi-variable configurations. FEDformer-MVMD model demonstrated superior generalization, particularly under high evaporative demand conditions, highlighting its effectiveness in capturing long-term dependencies and non-stationary climatic signals. Scenario-based analysis further reveals that incorporating radiation and vapor pressure deficit substantially enhances prediction accuracy in inland arid environments. Overall, the findings confirm that combining Transformer architectures with multivariate signal decomposition significantly improves ETo prediction accuracy and robustness. The proposed frameworks provide a scalable and climate-adaptive solution for operational irrigation management and drought-risk assessment in data-scarce arid regions.