Frequency-Gated Wavelet-LSTM for Probabilistic Streamflow Forecasting

Extreme streamflow forecasting remains challenging because hydrological time series are highly imbalanced and meteorological forcings are non-stationary. These characteristics can cause conventional data-driven models to underestimate flood peaks. While wavelet-coupled LSTM models can extract multi-scale hydrological features to boost forecasting performance, their static feature fusion limits the model’s ability to balance peak-flow and baseflow prediction, limiting adaptive forecasting for variable flow scenarios. Moreover, the Gaussian Mixture Model (GMM) adopted for probabilistic prediction suffers from gradient explosion and numerical collapse when fitting heavy-tailed extreme hydrological data, degrading prediction. To address these limitations, we propose a Frequency-Gated Wavelet Transform LSTM (FG-WT-LSTM) framework. The model uses the stationary wavelet transform (SWT) to decompose the input into multiple frequency components. A frequency-domain gating mechanism then assigns time-varying weights to these components, enhancing rainfall-related high-frequency signals while reducing flood-induced high-frequency features noise and suppressing redundant spectral noise. A LogSumExp stabilization strategy is further embedded into GMM to eliminate numerical instability. Validated on the CAMELS dataset, the proposed model achieves a median NSE of 0.872 and reduces FHV bias to −1.108%, with probabilistic prediction intervals reaching 93.9% coverage. These results indicate that the proposed framework can improve peak-flow prediction while maintaining stable baseflow simulation for accurate extreme flood forecasting and hydrological uncertainty quantification.