Hybrid VMD-EMD Enhanced Machine Learning Models for Daily Reference Evapotranspiration Forecasting

Getting accurate daily estimates of reference evapotranspiration (ET₀) is essential for hydrological modeling, irrigation planning, and climate research. This study evaluated the performance of four machine learning models: Adaptive Boosting (AdaBoost), Categorical Boosting (CatBoost), Deep Neural Network (DNN), and Light Gradient Boosting Machine (LGBM) for daily ET₀ prediction. Feature selection was implemented using Partial Autocorrelation (PACF) and Autocorrelation (ACF) analysis on the basis of an 8-day lag structure, while the CatBoost feature importance framework was implemented to identify the most important inputs. Moreover, the methodologies of decomposition-based preprocessing, Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) were implemented on the lagged inputs to build the hybrid models augmented with intrinsic constituents. These augmented hybrid models were created to improve the data representation as well as predictive capability. Model performance was evaluated using key statistical metrics, including RMSE, MAE, NSE, KGE, R2, and bias-related indicators. CatBoost produced the lowest RMSE (1.57 mm/day) and MAE (1.13 mm/day), and the highest NSE (0.67), KGE (0.78), and R2 (0.67), along with the lowest AIC score (627.15), indicating strong and reliable predictive performance. Furthermore, the VMD based CatBoost model yielded even greater improvements, highlighting the added value of decomposition enhanced learning. On the contrary, DNN showed the weakest results, with the highest RMSE (2.39 mm/day) and lowest NSE (0.23). These findings suggest that CatBoost and its hybrid variants are highly effective and reliable tools for daily ET₀ prediction, particularly in data limited environments and mountainous regions.