Improving long-term water quality forecasting with limited data using hidden pattern extraction and explainable ensemble learning

This study focuses on enhancing long-term, multi-step forecasting of dissolved oxygen (DO), a key indicator of river water quality. We introduce a novel hybrid method, Hidden Pattern Feature Extraction–Statistical Mode Decomposition (HPFE–SMD), integrated with explainable ensemble learning models, namely Random Forest (RF) and Extra Trees Regressor (ETR), both in standalone and hybrid configurations (HPFE-RF and HPFE-ETR). The models were trained and evaluated using monthly DO data spanning 1974–2023 from two sites within the Mississippi River Basin, across forecasting horizons of 1, 3, 9, and 15 months. The hybrid models consistently outperformed their standalone counterparts. For instance, at a 15-month horizon for Site 1, the HPFE-ETR model reduced the Mean Absolute Error (MAE) by 98.1 % compared to standalone ETR. In comparison with TVF-EMD-based models, HPFE-SMD achieved a 10.8 % and 4.3 % reduction in Mean Absolute Percentage Error (MAPE) for RF and ETR, respectively, at the 9-month horizon. Overall, HPFE-RF and HPFE-ETR achieved high predictive performance with RMSE values below 0.25 mg/L and R² values exceeding 0.99, even for long-term forecasts. SHAP (SHapley Additive exPlanations) analysis revealed that key statistical features, such as vibration amplitude (RMS), energy, skewness, kurtosis, and crest factor, played a dominant role in model predictions. Additionally, the proposed method demonstrated strong generalizability by accurately forecasting other water quality parameters, including total nitrogen, pH, total dissolved solids, and sodium adsorption ratio. These results highlight the added value of the HPFE-SMD approach over traditional decomposition or standalone ML models, showcasing its potential for integration into advanced water quality monitoring and management systems.