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.

随着水文气候非平稳性（hydroclimatic nonstationarity）与人类活动调控强度不断加剧，季节性径流峰值愈发难以捉摸，传统确定性预报方法的可靠性受到严重削弱。本研究提出一种峰值敏感型混合框架，将基于时变滤波的经验模态分解（time-varying filtering–based empirical mode decomposition，TVF-EMD）与深度学习方法相耦合。该框架将月度径流序列拆解为通用分量与复杂分量两类，其中确定性预测主干采用经贝叶斯优化（Bayesian optimization，BO）调参的卷积神经网络（convolutional neural network，CNN）-双向门控循环单元（bidirectional gated recurrent unit，BiGRU）结合自注意力机制（self-attention，SA）模型，并辅以观测关联误差校正（observation-linked error correction，OLEC）模块。经四项评价指标验证，该框架展现出更优异的点预测性能：威洛特指数（Willmott’s index，WI）取值介于0.9990至0.9997之间，纳什-萨特克利夫效率（Nash-Sutcliffe efficiency，NSE）介于0.9960至0.9988之间，平均绝对误差（mean absolute error，MAE）较低，百分偏差（percent bias，PBIAS）处于-1.1682%至0.7844%区间。针对复杂分量，研究采用带有误差敏感焦点损失（error-sensitive focal loss，ESFL）的分位数回归（quantile regression，QR）方法，生成经过校准且更紧致的预测区间。在90%名义覆盖率下，预测区间覆盖概率（prediction interval coverage probability，PICP）为98.6111%~100%，预测区间归一化平均宽度（prediction interval normalized average width，PINAW）介于6.8663%~23.9493%，且其温克勒得分（Winkler scores）始终低于BO-CNN-BiGRU-SA-QR基准模型。整体而言，该框架可生成更窄、校准良好且适配峰值特征的预测区间，可为基于风险研判的水资源管理提供坚实支撑。