Haixia et al. (2026) Multimodel ensemble heavy precipitation forecast with U-Net deep learning model integrating the spatial FSS loss function

Identification

• Journal: Atmospheric Research
• Year: 2026
• Date: 2026-04-01
• Authors: Qi Haixia, Xiefei Zhi, Tao Peng, Ji Yan, Yanhe Zhu, Shoupeng Zhu, Yue Zhou, Yiheng Xiang, Ke Liu, Hui Qiu
• DOI: 10.1016/j.atmosres.2026.108931

Research Groups

• Heavy Rainfall Research Center of China/China Meteorological Administration, Basin Heavy Rainfall Key Laboratory/Hubei Key Laboratory for Heavy Rain, Monitoring and Warning Research, Institute of Heavy Rain, China Meteorological Administration, Wuhan 430205, China
• Key Laboratory of Meteorology Disaster, Ministry of Education (KLME), Nanjing University of Information Science and Technology, Nanjing 210008, China
• Key Laboratory of Transportation Meteorology of China Meteorological Administration/Nanjing Joint Institute for Atmospheric Sciences, Nanjing 210041, China
• School of Atmospheric Science and Remote Sensing, Wuxi University, Wuxi 214105, China
• Ningbo Meteorological Observatory, Ningbo Meteorological Bureau, Ningbo 315012, China
• Bureau of Hydrology, Changjiang Water Resources Commission, Wuhan 430010, China

Short Summary

This study develops a U-Net deep learning model, incorporating a novel differentiable Spatial Fractional Skill Score (FSS) loss function, for multi-model ensemble post-processing to improve heavy precipitation forecasts, demonstrating enhanced skill in capturing spatial patterns and extreme intensities over the Middle and Lower Reaches of the Yangtze River.

Objective

• To develop and evaluate a U-Net deep learning model, trained with a novel differentiable Spatial Fractional Skill Score (FSS) loss function, for multi-model ensemble post-processing to optimize heavy precipitation forecasts by improving the representation of spatial patterns and extreme intensities.

Study Configuration

• Spatial Scale: Middle and Lower Reaches of the Yangtze River (MLYR), China.
• Temporal Scale: Daily precipitation forecasts, evaluated for lead times ranging from 24 hours to 240 hours.

Methodology and Data

• Models used: U-Net deep learning architecture. Performance was compared against the ensemble mean (MEAN) and the best individual numerical weather prediction (NWP) models.
• Data sources: Multi-model ensemble outputs (from NWP models, implied by TIGGE keyword) and daily precipitation observations for evaluation. A two-stage data-augmentation fine-tuning strategy was employed for heavy precipitation (≥25 mm/d).

Main Results

• The U-Net(FSS) model reduced the averaged Root Mean Square Error (RMSE) by 3–7% compared to the best individual model for daily precipitation forecasts within 24–240 hours lead time, with improvements increasing as lead time extended.
• For heavy precipitation (≥25 mm/d), the Fractional Skill Score (FSS) of U-Net improved by approximately 10% over the best individual model at 24–72 hours lead times, maintaining an improvement of over 5% through 168 hours.
• For extreme precipitation (95th percentile), the U-Net sustained a Threat Score (TS) around 0.28 at 168–240 hours lead times, improving by 10–20% compared to the ensemble mean (MEAN).
• A case study demonstrated that the U-Net model outperformed both individual models and the ensemble mean in capturing the spatial structure of rainbands and the intensity of extreme centers at 24, 168, and 240 hours lead times.

Contributions

• Introduces a novel differentiable Spatial Fractional Skill Score (FSS) as a loss function for deep learning models, specifically U-Net, to optimize for spatial patterns and extreme intensities in heavy precipitation forecasting.
• Develops a multi-model ensemble post-processing framework using U-Net with FSS loss, demonstrating significant improvements over traditional methods and individual models for heavy and extreme precipitation forecasts.
• Employs a two-stage data-augmentation fine-tuning strategy for heavy precipitation, further enhancing calibration.

Funding

[No funding information was provided in the article text.]

Citation

@article{Haixia2026Multimodel,
  author = {Haixia, Qi and Zhi, Xiefei and Peng, Tao and Yan, Ji and Zhu, Yanhe and Zhu, Shoupeng and Zhou, Yue and Xiang, Yiheng and Liu, Ke and Qiu, Hui},
  title = {Multimodel ensemble heavy precipitation forecast with U-Net deep learning model integrating the spatial FSS loss function},
  journal = {Atmospheric Research},
  year = {2026},
  doi = {10.1016/j.atmosres.2026.108931},
  url = {https://doi.org/10.1016/j.atmosres.2026.108931}
}