WADEPre: A Wavelet-based Decomposition Model for Extreme Precipitation Nowcasting with Multi-Scale Learning

The heavy-tailed nature of precipitation intensity impedes precise precipitation nowcasting. Standard models that optimize pixel-wise losses are prone to regression-to-the-mean bias, which blurs extreme values. Existing Fourier-based methods also lack the spatial localization needed to resolve transient convective cells. To overcome these intrinsic limitations, we propose WADEPre, a wavelet-based decomposition model for extreme precipitation that transitions the modeling into the wavelet domain. By leveraging the Discrete Wavelet Transform for explicit decomposition, WADEPre employs a dual-branch architecture: an Approximation Network to model stable, low-frequency advection, isolating deterministic trends from statistical bias, and a spatially localized Detail Network to capture high-frequency stochastic convection, resolving transient singularities and preserving sharp boundaries. A subsequent Refiner module then dynamically reconstructs these decoupled multi-scale components into the final high-fidelity forecast. To address optimization instability, we introduce a multi-scale curriculum learning strategy that progressively shifts supervision from coarse scales to fine-grained details. Extensive experiments on the SEVIR and Shanghai Radar datasets demonstrate that WADEPre achieves state-of-the-art performance, yielding significant improvements in capturing extreme thresholds and maintaining structural fidelity. Our code is available at https://github.com/sonderlau/WADEPre.

💡 Research Summary

WADEPre addresses three fundamental challenges in extreme precipitation nowcasting: (1) regression‑to‑the‑mean bias caused by the heavy‑tailed distribution of rainfall intensities, (2) the lack of spatial localization in Fourier‑based spectral models, and (3) spectral‑physical inconsistency and training instability when high‑frequency components are learned independently. The authors propose to move the prediction task into the wavelet domain by applying a Discrete Wavelet Transform (DWT) to each input radar sequence, thereby decomposing it into a low‑frequency approximation (A) and high‑frequency detail (D) sub‑bands.

The architecture consists of three modules. The Approximation Network (A‑Net) processes the low‑frequency coefficients. It first encodes the sequence with a 2‑D convolutional encoder, then injects temporal dynamics using a 3‑D convolutional Temporal Injector. The encoded features are fed into a stack of Spatio‑Temporal Blocks (STBlocks) built on Dilated ResNet, which expands the receptive field exponentially while preserving resolution. After N blocks, a decoder reconstructs the future approximation coefficients. To generate the background flow in image space, the authors adopt a stationary texture assumption, repeating the last observed detail frame across the prediction horizon.

The Details Network (D‑Net) handles the three high‑frequency detail sub‑bands (horizontal, vertical, diagonal) using a multi‑scale Feature Pyramid Network (FPN). Each level applies dedicated convolutional layers to capture fine‑grained textures and stochastic convective cells that are typically lost in pixel‑wise regression.

A Refiner module then merges the predicted approximation and detail coefficients via an inverse DWT (IDWT) and applies additional convolutional residual blocks to enforce physical consistency and correct any spatial misalignments.

Training stability is enhanced through a Multi‑Scale Curriculum Learning strategy. Early epochs assign higher weight to coarse‑scale losses (e.g., L1, SSIM on the approximation), allowing the model to first learn large‑scale advection patterns. As training progresses, the weight of high‑frequency losses (gradient‑based detail loss, perceptual loss) is gradually increased, mitigating the instability that typically arises when learning fine details from scratch.

Experiments on the SEVIR dataset and a real‑world Shanghai radar dataset demonstrate that WADEPre outperforms state‑of‑the‑art baselines—including ConvLSTM, PredRNN, AlphaPre, NowcastNet, and DGMR—across multiple metrics. Notably, Critical Success Index (CSI) at high thresholds (30 mm/h and 50 mm/h) improves by 8–15 percentage points, and Structural Similarity Index (SSIM) gains 0.02–0.04 over the best competing method. Visual inspection shows that WADEPre preserves sharp boundaries of intense convective cells while maintaining smooth background flow, avoiding the blurring typical of pixel‑wise models and the ghosting artifacts seen in Fourier‑based approaches.

Ablation studies confirm that (i) removing the wavelet decomposition and using a single network degrades performance, and (ii) omitting the curriculum learning leads to unstable training and poorer high‑frequency reconstruction.

The paper’s contributions are: (1) explicit wavelet‑based disentanglement of precipitation into deterministic low‑frequency advection and stochastic high‑frequency convection, (2) a dual‑branch architecture with a physics‑aware Refiner that bridges the spectral barrier, (3) a curriculum learning scheme that stabilizes multi‑scale optimization, and (4) state‑of‑the‑art results on extreme event forecasting.

Limitations include the lack of analysis on how different wavelet families or decomposition levels affect performance, and the absence of latency benchmarks for real‑time deployment. Future work could explore lightweight variants, alternative wavelet kernels, and integration with numerical weather prediction models to further enhance operational applicability.