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Evaluating Cross-region Generalization for Wavelet-Diffusion Precipitation Downscaling

Weikang Qian, Yixin Wen, Chugang Yi, Zhi Li, Lingcheng Li, Haizhao Yang

arXiv:2609.28749v1cs.LGphysics.ao-ph

TL;DR

Precipitation downscaling’s generalization to geographically unseen regions remains insufficiently understood. This study compares WDM training settings with interpolation baselines in MRMS reflectivity super-resolution. The Oklahoma-trained model retains meaningful skill in unseen regions, with reported gains over nearest-neighbor interpolation.

  • Problem

    Whether precipitation downscaling generalizes to geographically unseen regions remains uncertain, despite high-resolution fields’ relevance to local hydrological modeling and flood-risk assessment.

    Source: §1 · p. 2

  • Method

    The study compares WDM-OK and WDM-ALL with nearest-neighbor and Bicubic interpolation for MRMS reflectivity super-resolution.

    Source: §2.2 · p. 4, §4.3 · p. 19, §5 · p. 20

  • Results

    WDM-OK preserves meaningful downscaling skill in five unseen regions; PSNR increases by 1.14–1.79 dB and RMSE decreases by 12.6–18.0% relative to NN.

    Source: §5 · p. 20

  • Takeaways & Limitations

    The findings support meaningful cross-region and cross-event generalization in the same-product MRMS downscaling setting.

    Source: §5 · p. 20

    The evaluation is bounded to same-product downscaling; cross-product correction also requires learning systematic source–target mismatches.

    Source: §4.3 · p. 19

Abstract

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Diffusion models have shown strong potential for kilometer-scale precipitation downscaling, but their performance in geographically unseen regions and event regimes remains insufficiently understood. Building on the wavelet diffusion model (WDM) framework, this study evaluates cross-region and cross-event generalization. Six 3 x 3 deg U.S. regions represent convective, winter, tropical, and atmospheric-river precipitation regimes. Low-resolution inputs are generated by block averaging NOAA Multi-Radar/Multi-Sensor (MRMS) composite reflectivity fields. A WDM trained only on Oklahoma (OK) samples and a WDM trained on all six regions are compared with nearest-neighbor and Bicubic interpolation. Model performance is evaluated using three metric families that measure image-domain reconstruction, spectral and distributional fidelity, and bin-wise precipitation detection. The OK-trained WDM remains competitive outside OK. Although the all-region WDM delivers the best and most consistent overall image-domain and detection performance, its gains are uneven across precipitation intensities. Bin-wise critical success index (CSI) over 5-dBZ reflectivity bins shows that WDM improvements concentrate in localized higher-reflectivity structures, which image-domain metrics partly obscure. In addition, the performance differences among samples are strongly associated with the spatial organization of the precipitation field, quantified by Moran's I as the spatial autocorrelation of each reflectivity bin. The sample-level Moran's I-CSI correlation stratified by sample intensity reaches 0.901 in all six regions, including regions unseen during training. Overall, these findings support future efforts to transfer downscaling models to regions with limited local training data and to generate globally consistent, high-resolution precipitation products.

1 Introduction

The introduction frames cross-region transfer as an unresolved issue for precipitation downscaling and motivates structure-aware evaluation. It presents a fixed-architecture study of regional transfer, multi-region training, and sample-level performance associations.

1 Introduction

  • Cross-region generalization remains insufficiently understood, motivating systematic evaluation of precipitation downscaling across geographic domains.The introduction notes that only a few studies have examined the issue, often through isolated cases rather than systematic cross-region evaluation.Source: §1 · p. 2
  • Image-similarity metrics can penalize small storm-core shifts while rewarding overly smooth predictions, motivating structure-aware evaluation.The study argues that evaluation should assess whether fine-scale structures persist across regions and help explain sample-level performance variation.Source: §1 · pp. 2–3
  • Prior WDM evaluation was confined to one region, leaving its performance on unseen regions and event conditions unresolved.This study keeps the model weights fixed and shifts focus from architecture development to cross-region generalization and sample characteristics associated with performance.Source: §1 · p. 3
  • The evaluation covers six heterogeneous precipitation regimes and compares regional and multi-region training across accuracy, spectral, distributional, detection, and spatial-structure measures.The introduction describes the study’s expanded MRMS-based dataset and its multiple evaluation dimensions.Source: §1 · p. 3
  • The study tests whether Oklahoma-trained WDM transfers to unseen regions and whether multi-region training improves robustness over region-specific training.It also seeks spatial characteristics associated with model performance.Source: §1 · p. 3

2 Data and Methods

The methods establish a same-product precipitation downscaling benchmark across six diverse MRMS regions, comparing WDM variants with interpolation baselines using image, spectral, distributional, and bin-wise detection metrics. Bin-wise Moran’s I diagnostics and CSI comparisons examine whether precipitation-field spatial organization conditions downscaling skill.

2.1 MRMS dataset

  • Six approximately 3° × 3° regions represent severe convection, winter precipitation, heavy snow, tropical-cyclone precipitation, ice storms, and atmospheric rivers.Composite reflectivity represents precipitation structure and radar-reflectivity morphology rather than quantitative precipitation estimates.Source: §2.1 · pp. 3–4

2.2 High- and low-resolution sample construction

  • 300 × 300 high-resolution targets were paired with 30 × 30 inputs from 10 × 10 block averages; models trained and validated on 2022–2023 samples were tested on independent 2024 samples.Bmax25 defines sample intensity as the highest 5-dBZ bin containing at least 25 pixels, and the 2024 test set spans intensities whose distributions differ by region.Source: §2.2 · p. 4

2.3 Wavelet diffusion model (WDM) and interpolation baselines

  • WDM-ALL pools training samples across six regions, while WDM-OK trains only in Oklahoma; both use conditional wavelet diffusion and were trained on original-field and residual-field targets.The residual target is the difference between the high-resolution field and the upsampled low-resolution input, focusing generation on missing fine-scale structure.Source: §2.3 · p. 5
  • Residual-field WDMs were selected for the main evaluation because they converged faster and had comparable validation performance, with 1–4% higher MSE than original-field models.Nearest-neighbor and Bicubic served as interpolation benchmarks; other AI or generative baselines were not retrained.Source: §2.3 · pp. 5–6

2.4.1 General downscaling metrics

  • Evaluation used PSNR and SSIM for image quality, R² and RMSE for pointwise accuracy, Fourier-amplitude MAE for spatial-scale fidelity, and 1-D Wasserstein distance for pixel-value distributions.Source: §2.4.1 · p. 6

2.4.2 Bin-wise detection metrics and improvement cases

  • Bin-wise CSI evaluates binary detection within each 5-dBZ reflectivity interval from 0 to 70 dBZ, while improvement categories distinguish negative, normal, and significant gains over a baseline.A significant improvement occurs when a model detects a bin missed by the baseline or its gain exceeds 100%.Source: §2.4.2 · pp. 6–7

2.4.3 Spatial autocorrelation diagnostics

  • Moran’s I was computed on high-resolution targets at each 5-dBZ bin as a spatial-autocorrelation diagnostic, not a direct performance metric.The analysis also correlated bin-wise Moran’s I with CSI and calculated sample-level weighted averages over valid bins to test whether reconstruction skill depends on event morphology rather than only region or maximum intensity.Source: §2.4.3 · p. 7

3 Results

The results compare the WDM variants using image-domain, spectral and distributional, and bin-wise precipitation-detection metrics, alongside case studies of their fine-scale structures and errors. They examine how the models represent fragmented, filamentary features and organized rainbands.

3.1 General downscaling metrics

  • WDM-OK had the lowest 1D Wasserstein distance, but Bicubic remained slightly better on PSNR, R², and RMSE in external regions IL, MD, CA, and WA.In IL, amplitude MAE and Wasserstein distance decreased from 1.52 and 0.54 for Bicubic to 1.22 and 0.36 for WDM-OK.Source: §3.1 · p. 7
  • WDM-ALL had the highest PSNR and lowest RMSE in all six regions, improving PSNR by 1.14–1.79 dB and reducing RMSE by 12.6–18.0% versus NN, while WDM-OK retained lower amplitude MAE and Wasserstein distance.WDM-ALL did not outperform NN in amplitude MAE in four of six regions.Source: Table 1 · p. 8, §3.1 · p. 8

3.2 Bin-wise CSI for precipitation detection

  • For WDM-OK over Bicubic, mean positive CSI improvement in normal cases rose from 4.5–8.3% at 5–15 dBZ to 41.4–69.6% at 45–55 dBZ and above 90% at 60–65 dBZ.These normal-improvement cases indicate added skill when the target bin remains partly recoverable by Bicubic.Source: §3.2 · p. 9, Figure 3 · p. 10
  • Across 40–55 dBZ, significant-improvement cases averaged 26.0% for WDM-ALL and 25.0% for WDM-OK, versus 3.0% for Bicubic; WDM-OK improved in 86.4% of external-region cases at 5–20 dBZ.The higher external-region percentages may partly reflect differences in precipitation regimes across regions.Source: §3.2 · pp. 10–11, Figure 4 · p. 12

3.3 Case studies

  • Case studies showed blocky NN fields and blurred Bicubic cores, while WDM recovered coherent fine-scale structures; WDM-ALL appeared smoother and WDM-OK retained sharper texture.Errors concentrated near sharp transitions, small isolated cells, and intense cores whose locations were difficult to infer from the coarse input.Source: §3.3 · pp. 12–13
  • Both WDM variants better recover fragmented, filamentary precipitation features, while WDM-OK has the lowest Wasserstein distance; WDM outputs also broaden and smooth organized rainband structure.The case studies therefore show why image-domain and precipitation-specific metrics are both needed.Source: §3.3 · p. 13, Figure 5 · p. 14

4 Discussion

The discussion examines cross-region WDM performance and how spatial autocorrelation relates to detection skill, while noting limitations of full-field metrics and the bounded robustness finding. It also distinguishes reflectivity downscaling from area-averaged precipitation estimation and identifies bias correction, ensemble calibration, and impact-relevant evaluation as needed considerations.

4.1 Spatial autocorrelation helps explain within-bin variability in downscaling performance

  • Moran’s I and bin-wise CSI are broadly positively related, but the correlation weakens in the highest reflectivity bins, where sparse pixels make CSI sensitive to missed or displaced cores.Across 5–20 dBZ bins, all-case CC is about 0.92–0.95; at 60, 65, and 70 dBZ it falls to about 0.60, 0.49, and 0.18, respectively.Source: §4.1 · p. 15, Figure 6 · p. 16

4.2 General metrics are necessary but insufficient for precipitation downscaling

  • Full-field image metrics can hide errors in localized high-reflectivity structures, and metric rankings diverge because reconstruction measures reward different model behaviors.WDM-ALL has higher PSNR and lower RMSE in OK, while WDM-OK has lower amplitude MAE and Wasserstein distance; bin-wise CSI exposes Bicubic’s loss of skill in higher-reflectivity bins.Source: §4.2 · p. 17
  • 0.901 is the pooled correlation between WDM-OK sample-level CSI and Moran’s I across all six regions, with regional correlations from 0.861 in Oklahoma to 0.925 in California.The relationship persists across weak and intense samples, including the five regions outside Oklahoma that are out-of-distribution for WDM-OK.Source: §4.2 · p. 18, Figure 8 · p. 18

4.3 Regional robustness depends on the task boundary

  • In the controlled same-product setting, WDM-ALL has the most stable image-domain performance, while WDM-OK remains competitive outside OK and in spectral and distributional fidelity.This cross-region result should not be assumed to transfer directly to cross-product correction-and-downscaling, where models must also learn source-target mismatches.Source: §4.3 · p. 19
  • Because rain rate depends quasi-exponentially on reflectivity in dBZ, averaging reflectivity over an area is not equivalent to averaging precipitation.The study chose MRMS composite reflectivity to represent precipitation patterns amid uncertainties in quantitative precipitation estimation.Source: §4.3 · p. 19
  • Future work should couple downscaling with explicit bias correction for real low-resolution products and evaluate probabilistic calibration of generated ensembles.Source: §4.3 · p. 19
  • Future work should extend reflectivity-bin detection toward impact-relevant hydrological and warning metrics.Source: §4.3 · p. 19

5 Conclusion

In a controlled same-product MRMS reflectivity downscaling setting, WDM generalizes across regions and event regimes, but performance varies with precipitation intensity and spatial organization. The findings support evaluating event-relevant structures alongside average image similarity.

5 Conclusion

  • The study compares WDM-OK and WDM-ALL with NN and Bicubic across six U.S. regions using image-domain, spectral, distributional, bin-wise CSI, case-study, and Moran’s I analyses.Low-resolution inputs and high-resolution targets come from the same MRMS fields, isolating spatial super-resolution from product-to-product bias correction.Source: §5 · pp. 19–20
  • In the same-product MRMS downscaling setting, WDM trained only on Oklahoma cases preserves downscaling skill across five geographically unseen regions, with PSNR 1.14–1.79 dB higher and RMSE 12.6–18.0% lower than NN.Source: §5 · p. 20
  • Bin-wise CSI shows that image-domain averages do not fully reveal intensity-specific skill: low-reflectivity structures can be easier to interpolate, while higher-reflectivity structures distinguish WDM from baselines.CSI evaluates non-overlapping reflectivity bins separately.Source: §5 · p. 20
  • Stronger spatial autocorrelation is generally associated with greater detectability, while fragmented structures are harder to reconstruct; this relationship persists across regions and intensity strata.For WDM-OK, the weighted Moran’s I–CSI correlation is 0.901 across regions, ranging from 0.861 in Oklahoma to 0.925 in California.Source: §5 · p. 20
  • Cross-region generalization cannot be characterized solely by whether a target region appeared in training: its apparent strength depends on the target field’s spatial organization.In the controlled same-product setting, WDM learns precipitation-structure information that transfers across regions.Source: §5 · p. 20
  • The authors conclude that evaluation should consider intensity-specific skill and morphology-dependent difficulty, not only improvements in average image similarity.The bin-wise metrics and diagnostics distinguish cross-region generalization, intensity-specific reconstruction skill, and morphology-dependent difficulty.Source: §5 · p. 20

Data and code availability

The paper identifies public sources for MRMS and storm-event data and reports that WDM code is available in Zenodo.

Data and code availability

Supporting Information

The supporting information provides supplementary methodological details, dataset tables, and additional model-training results for evaluating regional robustness and spatial-structure performance.

Supporting Information

  • The supporting information provides supplementary methodological details.Source: Introduction · p. 24
  • It includes tabulated dataset information.Source: Introduction · p. 24
  • It reports additional model-training results for evaluation of regional robustness and spatial-structure performance in wavelet-diffusion precipitation downscaling.Source: Introduction · p. 24

Text S1

Text S1 defines the study’s reconstruction, spectral, and distributional metrics and states that all metrics use the main evaluation’s preprocessing, masking, and normalization settings.

Text S1

  • All metrics were computed after the same preprocessing, masking, and normalization used in the main evaluation.The target is the high-resolution field, the prediction is the predicted field, and N denotes the number of pixels.Source: Text S1 · p. 24
  • RMSE measures the error between the prediction and target, while R squared measures how well observed outcomes are replicated by the model.The section also provides definitions for PSNR and SSIM.Source: Text S1 · p. 24
  • Amplitude MAE is computed in the frequency domain after transferring the image-domain field with a fast Fourier transform.The section also defines one-dimensional Wasserstein distance using cumulative distribution functions of the target and prediction.Source: Text S1 · p. 25

Table S 1. Study regions, crop windows and event-selection rules used to construct event-centered MRMS samples.

The supplement compares original-field and residual-field WDM variants, finding faster convergence for residual-field models and comparable validation-sample MSE; the residual variants were selected for the main evaluation.

Table S 1. Study regions, crop windows and event-selection rules used to construct event-centered MRMS samples.

  • The sample-count table reports counts by region and year; each sample represents one 10-minute MRMS time interval.Train and validation counts are approximate because 2022–2023 data were randomly split 80/20.Source: Table S 1. Study regions, crop windows… · p. 25

Figures

  • Residual-field models were selected for the main evaluation because they converged faster while achieving comparable validation accuracy.The best-checkpoint comparisons use minimum validation-sample MSE.Source: Figures · p. 26
  • Converged validation-sample MSE values were 7.71 vs. 7.63 (all-region) and 8.32 vs. 8.02 (random-split), indicating comparable performance between variants.The figure’s bottom panel reports sampled-output MSE in dBZ space, directly comparable across variants; its other loss and MSE panels use each variant’s own target space.Source: Figures · pp. 26–27
  • Residual-field models reached best checkpoints at epochs 460 (ALL-trained) and 1220 (OK-trained), versus 1900 and 2980 for original-field models.Residual models reached their validation-sample MSE plateau before epoch 1000, roughly three to four times faster.Source: Figures · pp. 26–27
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