Linking deterministic and probabilistic paradigms: a peak-sensitive prediction framework for heterogeneous runoff processes

With intensifying hydroclimatic nonstationarity and human regulation, seasonal runoff peaks have become erratic, undermining conventional deterministic forecasts. A peak-sensitive hybrid framework is introduced by coupling time-varying filtering–based empirical mode decomposition (TVF-EMD) with deep learning. Monthly runoff is split into general and complex components. The deterministic backbone uses Bayesian optimization (BO)-tuned convolutional neural network (CNN)-bidirectional gated recurrent unit (BiGRU) with self-attention (SA), plus an observation-linked error correction (OLEC). Across four metrics it delivers superior point predictions, with Willmott’s index (WI) ranging from 0.9990 to 0.9997, Nash-Sutcliffe efficiency (NSE) from 0.9960 to 0.9988, low mean absolute error (MAE), and percent bias (PBIAS) between −1.1682% and 0.7844%. For the complex component, quantile regression (QR) with an error-sensitive focal loss (ESFL) produces calibrated yet sharper intervals. At 90% nominal coverage, prediction interval coverage probability (PICP) spans 98.6111−100% and prediction interval normalized average width (PINAW) spans 6.8663−23.9493%, with consistently lower Winkler scores than the BO-CNN-BiGRU-SA-QR baseline. Overall, the framework yields narrower, well-calibrated, peak-aware prediction intervals that support risk-informed water-resources management.