Stress-Testing Dynamical and Generative Downscaling Using Subseasonal Extreme Precipitation Forecasts

1 Introduction

• Coarse subseasonal models poorly resolve local instability, wind shear, and updrafts, limiting their representation of deep convection and extreme precipitation.Global coverage supports large-scale information but comes at the expense of local resolution.Source: §1 · pp. 2–3
• Dynamical downscaling nests high-resolution physics-based models within coarser data, using the latter to provide large-scale boundary conditions.At fine grid resolutions, this approach can explicitly resolve convection while retaining physical consistency, but it is computationally demanding.Source: §1 · p. 3
• Statistical downscaling uses relationships between high- and low-resolution variables; generative models can provide ensembles representing a probability distribution.The paper adopts diffusion models, which have been used for downscaling and are becoming competitive in subseasonal prediction systems.Source: §1 · p. 3
• The study tests dynamical and generative downscaling on two severe convective events with different storm morphologies: multicells and supercells with upscale growth.Subseasonal extreme precipitation is a challenging and under-explored downscaling target.Source: §1 · pp. 3–4

2.1 Meteorological Description

• The 2018 multicellular event involved nearly stationary thunderstorms and torrential rain, whereas the 2021 event featured a supercell that developed into a bow echo and propagated across Switzerland.The 2018 event set the Swiss national 10-minute precipitation record; the 2021 event produced severe hail impacts.Source: §2.1 · p. 4

2.2 Datasets

• The study contrasts 2018 and 2021 CombiPrecip aggregates with a shared climatology and interpolated deterministic IFS forecasts at 0-day, 1-week, 2-week, and 3-week lead times.The 0-day forecasts show greater precipitation aggregation than forecasts at longer lead times.Source: §2.2 · p. 5, Figure 1 · p. 6
• CombiPrecip provides the high-resolution observational reference, combining radar and gauge data at 1-km spatial and 1-hour temporal resolution, aggregated to 6-hourly intervals.The study uses a Switzerland-focused domain and trims precipitation values between 0.0 and 0.1 mm/h to zero for metric computations.Source: §2.2 · p. 5
• The climatology baseline is the per-pixel empirical mean of the generative model’s CombiPrecip training data from June through August 2018–2023, excluding the two test dates.The same climatology is shown for both events.Source: Figure 1 · p. 6, §2.2 · p. 7

3 Model evaluation

• Most evaluation metrics are skill scores relative to climatology, with 1 indicating a perfect forecast and negative values indicating worse performance than climatology.The evaluation also accounts for differing ensemble sizes, which reflect the models’ computational costs.Source: §3 · p. 7

3.1 Continuous Ranked Probability Score

• CRPS evaluates ensemble forecasts against observations and rewards accurate representation of the true distribution; its fair formulation supports comparisons across different ensemble sizes.Its first term measures forecast-to-observation error and its second measures internal ensemble spread; for a deterministic forecast, CRPS equals mean absolute error.Source: §3.1 · p. 7

3.2 Member-Averaged Fraction Skill Score

• The member-averaged fraction skill score assesses spatial quality while tolerating displacement errors by comparing neighborhood precipitation fractions above a threshold.It ranges from 0 for no skill to 1 for a perfect forecast; neighborhood size and precipitation threshold are its two free parameters.Source: §3.2 · p. 8

3.3 Wasserstein Distance

• Wasserstein distance compares forecast and observation precipitation distributions aggregated across ensemble members, time, and space for each lead time.The study computes the distance over 0 to around 25 mm/h; although it measures the whole distribution, the analysis is especially interested in its right tail.Source: §3.3 · p. 8

3.4 Spectral Distance

• PSD distance evaluates whether downscaling reproduces spatial scales by comparing forecast and observed power spectral densities in the wavenumber domain.The deterministic metric uses the l1 norm, and its ensemble extension is member-averaged.Source: §3.4 · p. 9

3.5 Spread-Skill Ratio

• The spread-skill ratio evaluates probabilistic calibration by comparing ensemble dispersion with forecast error; a value of 1 indicates perfect dispersion.Values below 1 indicate under-dispersion and values above 1 indicate over-dispersion; SSR is not defined for deterministic forecasts.Source: §3.5 · p. 9

4.1 Dynamical Downscaling

• WRF uses three one-way nested domains at 9 km, 3 km, and 1 km resolution, with inner domains receiving boundary conditions from outer domains.Its setup also uses 35 terrain-following vertical levels and a 12-hour spin-up.Source: §4.1 · pp. 9–10
• Three IFS ensemble members are selected per lead time and event: those with the lowest, middle, and highest mean precipitation in the target domain.This selection is intended to maximize ensemble spread while limiting the computationally demanding WRF runs.Source: §4.1 · p. 11

4.2 Generative Downscaling

• The diffusion model is trained unpaired on CombiPrecip, with low-resolution forecasts imposed as conditions only after training, allowing one trained model to downscale different forecasts.The authors frame this design as enabling a fairer comparison with general-purpose WRF.Source: §4.2 · p. 11, §4.2.2 · p. 13

4.2.1 Denoising Diffusion Probabilistic Models

• The diffusion bridge progressively corrupts high-resolution data toward Gaussian noise, then reverses the process using a neural network trained to estimate the score.The reverse process moves from noise at t = 1 toward clean data at t = 0.Source: §4.2.1 · p. 12

4.2.2 Conditioning a Posteriori

• Posterior conditioning diffuses a low-resolution forecast to a selected time, then denoises it with the high-resolution score to add learned small-scale features.The spectral matching scale λ⋆ is set around 200 km; more noise allows more denoising steps but makes outputs less attached to the original forecast.Source: §4.2.2 · pp. 12–13

4.2.3 Pre-Processing Steps

• Before diffusion, low-resolution forecasts are interpolated onto the high-resolution grid and low-pass filtered at the original grid’s Nyquist limit.This removes spurious high-frequency content introduced by nearest-neighbor interpolation.Source: §4.2.3 · p. 14

5 Results

• The evaluation compares IFS forecasts, diffusion samples conditioned on deterministic or ensemble IFS forecasts, and WRF against CombiPrecip across lead times of 1–3 weeks.The 0-day forecast is also included for comparison.Source: §5 · pp. 14, 16
• For 2018, WRF leads Wasserstein skill at 1 and 3 weeks (0.88, 0.79), while DDPM ens leads at 2 weeks (0.43); diffusion models achieve the highest scores for 2021.Across both events and evaluated lead times, DDPM det and DDPM ens generally score higher than their corresponding IFS forecasts.Source: Table 3 · p. 16, §5 · pp. 16, 18
• At a 3-week lead, raw IFS forecasts visibly retain lower spatial resolution than diffusion and WRF outputs, which show variability near the 1-km scale.Source: §5 · p. 16, Figure 6 · p. 17
• 2018 avPSDd skill is highest for WRF at 1 and 3 weeks (0.49, 0.23) and DDPM det at 2 weeks (0.41).Source: Table 4 · p. 18, §5 · p. 18
• For 2021, avPSDd is more difficult, with negative skill more often; IFS det + NNI, WRF, and DDPM ens lead at 1, 2, and 3 weeks (0.15, 0.21, 0.01).Source: Table 4 · p. 18, §5 · p. 18
• Most models are under-dispersed; DDPM ens improves SSR over IFS ens and gives 2021's best spread, while WRF best calibrates 2018 (0.98 at 1 week; 1.04 at 3 weeks).DDPM ens combines diffusion-model variability with variability from the perturbed IFS forecast.Source: Table 5 · p. 18, §5 · p. 19
• At 3 weeks, all models diverge from CombiPrecip below 2 km; diffusion stays close to IFS above λ⋆ while adding information at lower scales.Source: §5 · p. 18, Figure 7 · p. 19
• Diffusion consistently improves avFSS over the original forecasts at all plotted thresholds, while WRF performs better at higher precipitation thresholds.The reported comparison uses a 15 km × 15 km moving window; changing window size to 30, 45, or 60 km does not qualitatively change the results.Source: §5 · p. 19, Figure 8 · p. 20

• Unpaired training makes diffusion reusable across reanalysis and subseasonal forecasts, and potentially climate projections, without tailoring it to specific events or boundary conditions.Source: §6 · p. 21
• After region-specific training (~10 h on one A100), diffusion generates 50-member ensembles in 10–20 min, versus ~24 h per WRF member; the comparison is wall-clock only.Source: §6 · p. 21
• For the 2018 multicell event, WRF generally leads at 1- and 3-week leads; at 2 weeks it remains above climatology across all skill metrics.Source: §6 · p. 21
• For the 2021 supercell, IFS ensemble and DDPM ensemble have the highest skill; DDPM ensemble leads dispersion, and diffusion models lead on W1.Source: §6 · pp. 21–22
• Performance does not clearly degrade with longer lead times; event nature and model type shape skill, and even 0-day forecasts begin hours before rainfall peaks.Source: §6 · p. 22
• Diffusion matches raw subseasonal ensemble CRPS and outperforms raw IFS on W1 and avPSDd; WRF excels when faster non-stationary dynamics require finer time-stepping.Source: §6 · p. 22

• The comparison stress-tests ensemble generation on two extreme Swiss precipitation events using observations and proper-score, spatial, distributional, and spectral diagnostics.Source: §7 · p. 22
• Downscaling generally improves raw subseasonal forecasts; diffusion offers lower computational cost and robust spatial and probability-distribution corrections, while WRF suits faster, more non-stationary convection.Source: §7 · pp. 22–23
• Adding soil moisture and topography, or training over wider geographical domains, is proposed as a potential way to enhance generative downscaling.Source: §7 · p. 23

Open Research Section

• ECMWF subseasonal prediction data were not open source at the date of last access, 14 November 2025.Source: Open Research Section · p. 23
• WRF is freely downloadable from NCAR, and the paper’s code is available through Zenodo.Source: Open Research Section · p. 23

Appendix A WRF inputs

• The appendix table describes inputs used by WRF that are supplied by the IFS subseasonal prediction product.Source: Appendix A · p. 29

• The noise schedule is used to gradually erase the original information.Source: Appendix B · p. 29
• The noise level follows a tangent schedule based on the cosine schedule introduced by Nichol and Dhariwal (2021).Source: Appendix B · p. 29
• The tangent schedule is scaled to produce noise levels in the range [0, 100].Source: Appendix B · p. 29

Appendix C Sampling procedure

• The backward SDE uses 256 Euler–Maruyama steps with an exponential noise schedule (ρ = 7), ending at σmin = 10−3.The schedule concentrates discretization near t ≈ 0 to spend more effort refining fine sample details.Source: Appendix C · p. 30

Appendix D Training details

• The score network sθ(xt, t) approximates ∇log p(xt), with the practical loss constructed using Gaussian noise and uniformly sampled diffusion time.The loss weights noise levels by λ(t) = 1/σ(t)^2, emphasizing low-noise levels.Source: Appendix D · p. 30
• Training noise is log-uniform and clipped at σmin = 10−4, with Karras weighting parameterized by σdata = 0.31.The weighting scheme balances the contribution of different noise levels to the overall loss.Source: Appendix D · p. 30
• The model is trained for 1,000,000 steps with batch size 2, Adam, and a learning rate that warms up to 10−4 before cosine decay to 10−6.An exponential moving average with decay 0.99 is used for generating samples.Source: Appendix D · p. 30

Appendix E Score architecture

• The score function is a U-Net that predicts denoised data from noisy input and is preconditioned by the training data’s standard deviation.It has four resolution levels, six residual blocks per level, and bottleneck self-attention with eight heads.Source: Appendix E · pp. 30–31

Appendix F Supporting figures

• Figures F1 and F2 compare mean aggregated precipitation for five models against CombiPrecip at 1- and 2-week leads for the 2018 and 2021 events.Rows show IFS deterministic and ensemble forecasts with NNI, DDPM deterministic and ensemble samples, and WRF; ensemble displays use the member with highest total accumulated precipitation over the event window.Source: Figure F1 · p. 33, Appendix F · pp. 33–34, Figure F2 · p. 34
• Figures F3 and F4 compare power spectral density for five models and CombiPrecip at 1- and 2-week leads across the two events.The spectral series are concatenated over the time axis.Source: Figure F3 · p. 35, Appendix F · pp. 35–36, Figure F4 · p. 36