Precipitation exhibits significant localized characteristics within the complex terrain of small watersheds and serves as a key factor in runoff processes. Fine-resolution precipitation estimates are crucial for the refined runoff simulations in mountainous catchments. We propose a novel, refined method for rainfall-runoff simulation that combines a modified downscaling model with a two-dimensional hydrodynamic model. By introducing an attention mechanism focusing on topographical features, the proposed Terrain-based Attention U-Net model (TAUNet) achieves efficient and convenient downscaling of Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG GPM) data from 0.1 degrees to 0.02 degrees. TA-UNet's robustness and accuracy were systematically evaluated, demonstrating improvements of 34.0 %, 29.9 %, 4.4 %, and 0.6 % in the mean squared error (MSE), mean absolute error (MAE), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), respectively, compared with bilinear interpolation. Additionally, it outperformed meteorological forecasting indices such as the volumetric hit index (VHI), volumetric miss index (VMI), volumetric false alarm ratio (VFAR), and volumetric critical success index (VCSI). Validated against ground observations from 156 national meteorological stations in Sichuan Province and eight rain gauges in the Jiangjia Gully, TA-UNet effectively performed spatial downscaling of the IMERG GPM products, delivering higher precision in localized precipitation estimates. The fine-resolution downscaled precipitation demonstrated high sensitivity to runoff responses in rainfall-runoff simulations for the Jiangjia Gully. This refined method captures enhanced spatial precipitation characteristics in mountainous catchments and details rainfall-runoff propagation, providing an innovative and efficient forecasting strategy for hydrological management.