Toward Spatially Sharper Precipitation Prediction via Global-Local Frequency Guidance

Precipitation prediction is critical for water-related hazard preparedness, and deep learning has shown strong potential. However, conventional mean squared error (MSE) training oversmooths high-frequency variability, producing blurred precipitation fields. Although frequency-domain losses such as Fourier Amplitude and Correlation Loss (FACL) enhance global spectral consistency, they lack constraints on local phase coherence. To address this, we develop the Wavelet-Fourier Composite Loss (WFCL), integrating Wavelet Amplitude and Correlation Loss (WACL) based on the Dual-Tree Complex Wavelet Transform with FACL to jointly enforce global spectral alignment and localized phase coherence. Experiments with a U-Net show WFCL consistently outperforms MSE and FACL, maintaining stable performance across 1–3 day lead times (2018–2023). It reduces lead-time-averaged Learned Perceptual Image Patch Similarity from 0.1980 to 0.1067 relative to MSE and improves Local Phase Coherence by about 21%. In addition, for 1-day prediction, WFCL reduces Regional Histogram Distance by approximately 24% locally and 52% globally compared with FACL.