Multimodel Ensemble Heavy Precipitation Forecast with U-Net Deep Learning Model Integrating the Spatial FSS Loss Function

Numerical models often systematically underestimate the intensity of heavy precipitation and struggle to accurately represent the spatial pattern of rainbands over MLYR. This study converts the Spatial Fractional Skill Score (FSS) into a differentiable loss function and the traditional loss function Mean Squared Error (MSE) trained the U-Net deep learning architecture to construct a multi-model ensemble post-processing model that optimizes for spatial pattern and extreme intensity. For heavy precipitation (≥ 25 mm/d), a two-stage data-augmentation fine-tuning strategy is employed to further calibrate the multi-model ensemble outputs. We evaluated the performance of four models, ensemble mean (MEAN), and the multi-model ensemble U-Net(FSS) and U-Net(MSE) for daily precipitation forecasts. The results demonstrate that within 24–240 h lead time, U-Net(FSS) reduces the  averaged RMSE by 3–7% compared to the best individual model, with the improvement increasing as the forecast lead time extends. For heavy precipitation(≥25 mm/d), the FSS of U-Net improvesby approximately 10% over the best individual model at lead times of 24–72 h, maintaining an improvement of over 5% through 168 h. For extreme precipitation (95th percentile), the U-Net sustains TS around 0.28 at  168–240h lead times, improving by 10–20% compared to MEAN. A case study of rainstorms in summer 2024 reveals that the U-Net outperforms both individual models and MEAN in capturing the spatial structure of rainbands and the intensity of extreme centers at lead times of 24, 168, and 240 h. The multi-model ensemble U-Net shows significant potential for optimizing the prediction of both the spatial and intensity of heavy precipitation forecasting.The applicability and improvement in heavy precipitation forecasting were discussed to inform future applications of multi-model ensemble techniques.

Key words: TIGGE,Multi-Model Ensemble Forecasting,Spatial FSS Loss Function，U-Net Deep Learning Model,Heavy Precipitation Forecasting