## 3 Results
### Basic Performance  
Figure 3 displays the RMSEs for various models at different lead times. The results indicate that the RMSE increases with longer lead times, potentially attributed to the increased uncertainty associated with longer forecasts. Specifically, the VGG model has the highest overall RMSE, followed by the GFS model. Notably, the median RMSEs of the two ensemble models, AVR and PM, are consistently the lowest at each lead time. Figure 4 illustrates the mean RMSEs for various models used to forecast precipitation induced by TC points with varying intensities. The mean RMSEs of all TC points are presented in Figure 4a. The VGG model produces the highest average RMSE across all TC levels, followed by the GFS model. Figure 4b-f demonstrate that UNet-based models consistently produce lower RMSEs than GFS models at different TC levels. Specifically, the GFS models have mean RMSEs of 20.51 mm, 32.29 mm, and 41.07 mm at lead times of 24 h, 48 h, and 72 h, respectively. In contrast, the UNet-based models exhibit lower mean RMSEs at the same lead times: U-Net 19.25 mm, 29.65 mm, 37.78 mm; UNet3+ 18.61 mm, 29.10 mm,  
37.30 mm; SE-UNet 18.31 mm, 29.11 mm, 37.93 mm; SE-UNet3+ 18.24 mm, 28.93 mm, 37.56 mm; AVR 18.17 mm, 28.74 mm, 36.87 mm; PM 18.16 mm, 28.72 mm, 36.84 mm. On average, the RMSEs of precipitation forecasts by U-Net, UNet3+, SE-UNet, SE-UNet3+, AVR, and PM are lower by 8.7%, 10.1%, 9.7%, 10.0%, 11.4%, and 11.5%, respectively, compared with the GFS model's precipitation forecasts. This result suggests that the neural network model based on the U-Net structure effectively reduces the RMSE of precipitation predictions compared with the GFS model. Notably, the UNet3+, SE-UNet, and SE-UNet3+ models with improved U-Net structures reduce the RMSE more effectively than the standard U-Net model. Additionally, the ensemble models, AVR and PM, exhibit lower RMSE than any separate precipitation prediction models. Based on Figure 4, the PM model has a lower average RMSE compared with other models, and therefore we use it for comparison with the GFS model. Figure 5 illustrates the spatial distribution of RMSEs for both PM and GFS models at different lead times. Comparing Figure 5a-c with Figure 5d-f, we observe that the high RMSE areas for both models are concentrated near the TC center, which may be associated with heavy precipitation in that area. The RMSEs for PM models at lead times of 24 h, 48 h, and 72 h are  
Figure 4: RMSEs of different models for various TC levels: (**a**) all TC points, (**b**) TD, (**c**) TS, (**d**) STS, (**e**) TY, and (**f**) SSTY. Figure 3: Boxplots of RMSEs for different models with various lead times. The box plot shows the median (line inside the box) and the upper and lower quartiles (top and bottom of the box), while the whiskers extend to the minimum and maximum non-outlier values. Outliers are indicated by dots beyond the whiskers. 18.16 mm, 28.72 mm, and 36.84 mm, respectively, lower than the RMSEs for GFS models at the same lead times, which are 20.51 mm, 32.29 mm, and 41.07 mm, respectively. Figure 5g-i illustrate the difference between the average RMSEs for PM and GFS models, consistently showing lower RMSEs for PM models in most regions. The average differences are 2.35 mm, 3.57 mm, and 4.33 mm at lead times of 24 h, 48 h, and 72 h, respectively, increasing with longer lead times. The higher RMSE difference between PM and GFS models near the TC center, as shown in Figure 5g-i, implies that the PM model primarily optimizes precipitation prediction RMSE in that area. Similar to the RMSE analysis, the MAE analysis (Figures S2 and S3 in the Supplementary Materials) reveals that the UNet-based models outperform the GFS model in reducing MAE. The PM models consistently exhibit the lowest average MAE compared with other models, aligning with the RMSE calculation results. The spatial distribution of MAE further emphasizes the PM model's effectiveness in reducing MAE in precipitation prediction, particularly near the TC center.