A Hybrid Deep Learning Approach: Constructing prediction intervals for Streamflow forecasting

Quantifying reliable uncertainty information in streamflow forecasts is essential for informed decision-making in water resources management and operation. Conventionally deterministic forecasts often fail in decision accuracy and overlook aleatoric uncertainty in the nonstationary hydrological behavior. While hydrological models (conceptual, process-based, empirical) can represent the underlying physical processes, deep learning models come with higher forecast accuracy, substituting the complex processes through complex neural structure. This paper presents a hybrid deep learning (DL) approach to construct reliable prediction intervals (PI) for streamflow predictions optimized through two novel objective functions. The paper applied the variational mode decomposition (VMD) technique on the target streamflow information to capture the underlying nonstationary feature and thus achieve improved predictive accuracy. Subsequently, prediction of each decomposed model are reconstructed using constrained particle swarm optimization (PSO). The developed approach is tested using Long Short-Term Memory (LSTM) model in Contiguous United States (CONUS) under various hydrological setting: i) PI-LSTM with dual objective functions (with and without Data Integration), ii) PI-LSTM-VMD with dual objective functions (with and without Data Integration). The proposed frameworks have yielded reliable predictions achieving median Nash Sutcliffe efficiency (NSE) 0.91 and 0.87 for PI-LSTM (with Data Integration) and PI-LSTM-VMD (with Data Integration) respectively along with the median coverage probability over 90% in both cases. The performances were robust across the basins with relatively minimum prediction width (relative average width) under 0.9 in both cases. Although the LSTM networks are largely beneficial with data integration (DI), the proposed frameworks showed relatively poor performance without DI which further emphasis the necessity to look on the guiding the deep learning models with promising data inputs.