Chen et al. (2026) SSPP: a Novel Flood Probabilistic Forecasting Model Based on Synergistic Seq2Seq Framework and Peak-Enhanced Loss Function

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Chang Chen, Dawei Zhang, Fan Wang, Xin Qi, Kang Zheng, Liyun Xiang
• DOI: 10.1007/s11269-025-04478-y

Research Groups

• State Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, China
• Research Center on Flood & Drought Disaster Prevention and Reduction, Ministry of Water Resources, Beijing, China

Short Summary

This paper proposes SSPP, a novel flood probabilistic forecasting model combining a synergistic Seq2Seq framework and a peak-enhanced loss function. The model demonstrates superior accuracy in deterministic and probabilistic flood predictions, especially for peak flows, compared to existing advanced models.

Objective

• To overcome limitations in existing neural network-based flood forecasting models, such as the lack of targeted feature extraction, inadequate emphasis on peak flows in loss functions, and deterministic outputs, by proposing a Synergistic Seq2Seq and Peak-enhanced Probabilistic model (SSPP) for accurate and reliable flood forecasting with uncertainty quantification.

Study Configuration

• Spatial Scale: Xiaoqing River basin above the Huangtaiqiao hydrological station in Jinan City, China, with a catchment area of 321 square kilometers.
• Temporal Scale: Hydrological data from 1998 to 2021. Input time series of 6-hour rainfall and runoff are used to forecast streamflow for 3-hour lead times.

Methodology and Data

• Models used:
  • Proposed: SSPP (Synergistic Seq2Seq framework with CNN and BiGRU Encoder, Diffusion Model for uncertainty quantification, and Peak-enhanced Loss function).
  • Comparative (Deterministic): Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Bidirectional Long Short-Term Memory (BiLSTM), Bidirectional Gated Recurrent Unit (BiGRU), Transformer.
  • Comparative (Probabilistic): Quantile Regression (QR), Lower and Upper Bound Estimation (LUBE), DeepAR.
• Data sources: Hydrological data collected from 1998 to 2021, including rainfall data from five stations (Liujiazhuang, Wujiapu, Donghongmiao, Xinglong, Yanzishan) and runoff data from the Huangtaiqiao hydrological station.

Main Results

• Deterministic Forecasting:
  • SSPP achieved the highest predictive precision, with RMSE values of 4.52–6.47, MAE values of 3.95–4.47, and NSE values of 0.893–0.962 for 1-hour to 3-hour lead times.
  • SSPP demonstrated the most precise peak flow fitting, with the smallest average Relative Peak Error (|δRPE|avg) of 4.67%–9.64% and average Peak Time Error (|ΔPTE|avg) of 0.33–0.83.
  • Ablation studies showed the synergistic mechanism reduced RMSE by an average of 25.78% and MAE by 10.75%, while the Peak-enhanced Loss reduced |ΔPTE|avg by 51.26% and |δRPE|avg by 39.32% compared to MSE.
• Probabilistic Forecasting:
  • SSPP achieved a high Prediction Interval Coverage Probability (PICP) of 90.3%–94.0% for a 90% confidence interval, indicating high reliability.
  • SSPP produced the narrowest prediction intervals, with the smallest Prediction Interval Normalized Averaged Width (PINAW), reducing it by 0.029–0.214 compared to other probabilistic models.
  • SSPP exhibited superior overall probabilistic forecasting skill with the lowest Continuous Ranking Probability Score (CRPS) values of 3.87–4.30.

Contributions

• Probabilistic Modeling: Introduces a diffusion model to bridge the Encoder and Decoder, quantifying hydrological uncertainties and providing a more expressive and robust representation of hydrological sequences, overcoming limitations of unstable training and quantile crossing in methods like MVE and QR.
• Feature Extraction: Employs a synergistic mechanism within the Encoder, integrating Convolutional Neural Network (CNN) for local transient features and Bidirectional Gated Recurrent Unit (BiGRU) for temporal global features, enabling complementary and comprehensive capture of hydrological characteristics.
• Optimization Objective: Proposes a novel peak-enhanced loss function that dynamically assigns greater weight to peak errors, compelling the model to prioritize and improve the accuracy and reliability of flood peak predictions.

Funding

• National Key Research and Development Program of China (Grant No. 2024YFC3214802)
• IWHR Research & Development Support Program (WH0145B022021)

Citation

@article{Chen2026SSPP,
  author = {Chen, Chang and Zhang, Dawei and Wang, Fan and Qi, Xin and Zheng, Kang and Xiang, Liyun},
  title = {SSPP: a Novel Flood Probabilistic Forecasting Model Based on Synergistic Seq2Seq Framework and Peak-Enhanced Loss Function},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04478-y},
  url = {https://doi.org/10.1007/s11269-025-04478-y}
}