Increasing the accuracy and resolution of precipitation forecasts using deep generative models

1 INTRODUCTION

• Global forecasts use grid spacings of 10 km or larger despite heavy rain arising from small-scale motions, so they poorly resolve extreme precipitation.Regional high-resolution models are more accurate, but require substantial labor and computation and are maintained only by wealthy nations.Source: §1 · p. 1
• The proposed data-driven approach maps coarse, multivariable global forecasts to distributions over high-resolution precipitation fields, addressing bias correction, super-resolution, and probabilistic variability together.Source: §1 · p. 2
• The authors describe this as the first direct study evaluated against relevant baselines in a setup resembling operational forecasting.Source: §1 · p. 2
• The authors frame US results as preliminary evidence for questioning expensive regional models and ask whether the approach transfers to data-poor regions.The passage identifies established US radar-observation networks as the setting motivating the transfer question.Source: §1 · p. 2

2 RELATED WORK

• Univariate methods estimate separate distributions per pixel, whereas multivariate methods model conditional dependencies between pixels.Source: §2 · p. 2
• Pixelwise forecasts may be insufficient for risks involving large contiguous rainfall areas, such as catchments exposed to flooding.Source: §2 · pp. 2–3
• Post-hoc ensemble sampling methods such as Schaake Shuffle and Ensemble Copula Coupling rely on spatial information in the coarse input being reliable.The paper notes this reliability cannot always be assumed, especially for precipitation.Source: §2 · p. 3
• Earlier generative approaches include Gaussian random fields, normalizing flows for climate downscaling, and latent neural processes for temperature and precipitation.Source: §2 · p. 3
• Leinonen et al. (2020) super-resolve downsampled precipitation observations, unlike this paper's use of low-resolution forecasts requiring both bias correction and resolution refinement.Source: §2 · p. 3
• Ravuri et al. (2021) generate 90-minute nowcasts from recent radar observations, whereas this work processes forecasts with lead times of a few days.The paper also distinguishes its forecast inputs and finer-resolution outputs from that nowcasting setup.Source: §2 · p. 3

3 PROBLEM FORMULATION

• The formulation treats each low-resolution forecast and high-resolution observation pair as an input-output example, and assumes the true precipitation distribution can be modeled conditionally on the forecast.A conditional GAN is trained to approximate that distribution and generate high-resolution forecasts.Source: §3 · p. 3

3.1 Data

• MRMS radar estimates at 4 km resolution provide precipitation ground truth, while TIGGE supplies the global ensemble forecasts.Inputs include precipitation, 2 m temperature, convective available potential energy, and convective inhibition at 32 km resolution; precipitation is accumulated over 6–12 hours.Source: §3.1 · p. 3
• Training and validation use paired TIGGE and MRMS patches from 2018–2019, with the full year 2020 reserved for evaluation.Evaluation is restricted to patches with more than 90% of pixels having radar data quality above 0.5.Source: §3.1 · p. 3
• Each model input has 24 channels, including TIGGE precipitation ensemble members, total-column-water ensemble members, and deterministic weather variables.Source: §3.1 · p. 3
• The final input channel supplies surrounding precipitation context by extending the target patch with a larger forecast patch.It contains a downsampled 46 × 46 precipitation patch centered on the 16 × 16 target.Source: §3.1 · p. 4
• Training pairs receive a zero-preserving log transform followed by scaling to [0,1], while evaluation uses raw, untransformed data.Source: §3.1 · p. 4

4 MODEL

• The model is a GAN trained for stochastic forecast correction and super-resolution, with generator and discriminator components.Source: §4 · p. 4, §4.2 · p. 4

4.1 Network Architecture

• The generator first produces corrected stochastic low-resolution representations from ensemble forecasts, other weather variables, and surrounding context, then refines them into plausible high-resolution forecasts.Source: §4.1 · p. 4
• The Corrector injects noise into its intermediate representation and produces a proxy corrected low-resolution forecast, while the Super-resolver upsamples that representation to 128 × 128.The proxy error is jointly minimized with GAN and regularization losses.Source: §4.1 · p. 4
• The discriminator assesses whether a high-resolution field is plausible and whether it matches the ground truth given the low-resolution forecasts and context.Source: §4.1 · p. 4

4.2 Loss functions and training

• Stage 1 trains the Corrector with zero noise to improve low-resolution forecast skill, using precipitation-weighted error and a soft Fractional Skill Score term.The soft score term targets spatial distribution errors using patterns across ensemble inputs and contextual variables.Source: §4.2 · pp. 4–5
• Stage 2 adds a high-resolution L1 loss to pre-train the Super-resolver while retaining the low-resolution L1 error term and dropping the soft skill-score term.Source: §4.2 · p. 5
• Stage 3 trains the full GAN with a Wasserstein discriminator loss and a generator objective combining adversarial loss with low- and high-resolution loss terms.Additional terms compare the mean of generated ensembles with ground truth rather than penalizing each member individually.Source: §4.2 · p. 5

5.1 Metrics

• Probabilistic evaluation targets both reliability and sharpness because precipitation forecasts are intermittent and users may value different aspects of forecasts.No single metric captures the full spectrum of skill.Source: §5.1 · p. 5
• Reliability diagrams bin thresholded events by forecast probability; a perfectly reliable forecast lies on y = x.The described thresholds are 1 mm, 5 mm, and 10 mm.Source: §5.1 · p. 5
• The Brier Score evaluates thresholded events, while CRPS integrates the Brier Score across thresholds.Source: §5.1 · pp. 5–6

5.2 Baselines

• Baselines include interpolated TIGGE, univariate BG-CNN, a pure super-resolution GAN, and 10-member HREF, combining five regional models with lagged members.Source: §5.2 · p. 6
• CorrectorGAN is evaluated with 10 predictions for fairness, though its ensemble can be enlarged; its trained forecasts are described as essentially free.The comparison frames HREF as computationally and labor intensive.Source: §5.2 · p. 6

• CorrectorGAN matches or outperforms interpolated TIGGE, Pure-SR GAN, and BG-CNN on CRPS and Brier Scores at all thresholds, while HREF tends to be slightly better.Source: §6 · p. 6
• CorrectorGAN’s reliability is similar to HREF and generally better at 10mm and 30mm thresholds; TIGGE’s flatter slope indicates overconfidence.Source: Figure 2 · p. 7, §6 · p. 7
• CorrectorGAN adds small-scale detail and extremes resembling MRMS and HREF, approaching regional-model skill at much reduced cost and effort.Source: §6 · pp. 7, 9
• In selected rainy patches, CorrectorGAN corrects large-scale TIGGE biases toward MRMS, with the input variables offering evidence of information beyond super-resolution.Source: §6 · p. 7, Figure 3 · p. 8

7 CONCLUSION AND FUTURE WORK

• The two-stage architecture first maps coarse precipitation to a weather-informed corrected distribution, then maps it to high-resolution plausible predictions.This addresses both forecast correction and downscaling.Source: §7 · p. 9
• CorrectorGAN matches or outperforms interpolation, super-resolution GAN, and CNN baselines across probabilistic metrics, and is close to the regional model while exceeding its extreme-rainfall reliability.The method is fast and cheap compared with regional weather models.Source: §7 · p. 9
• Some predictions retain wavy artifacts, and the GAN sometimes fails to correct large-scale TIGGE errors.Longer training, an improved GAN architecture, additional weather inputs, or more local and surrounding weather information are proposed avenues for improvement.Source: §7 · p. 9
• Future work could add recent radar observations for temporal high-resolution context, evaluate forecast times beyond 12 hours, and use recurrent blocks for temporally coherent realizations.The beyond-12-hour evaluation would test whether skill improvements persist.Source: §7 · p. 9
• The results tentatively suggest similar extreme-precipitation skill to a regional model using data rather than expensive physics simulations, while transfer to regions without high-resolution data remains an open question.Proposed tests include radar observations in Europe or station observations in high-risk regions such as West Africa.Source: §7 · p. 9

B ARCHITECTURES

• Figure 4 diagrams the Generator and Discriminator, with layers annotated by output-channel counts or linear-layer row counts and their internal nonlinearities when applicable.The text identifies the diagrams as summaries of the CorrectorGAN architectures.Source: Figure 4 · p. 11, B ARCHITECTURES · p. 11
• The architecture diagrams distinguish the Generator from the Discriminator.The caption identifies both networks but does not describe their individual layer sequences.Source: Figure 4 · p. 11
• For linear layers, the displayed layer size is given as the number of rows rather than output channels.The diagrams also indicate internal nonlinearities where applicable.Source: Figure 4 · p. 11

C TRAINING HYPERPARAMETERS

• Stage 1 uses Adam at learning rate 5e-05 with β1 = 0 and β2 = 0.9 for five epochs and batch size 128.Source: C TRAINING HYPERPARAMETERS · p. 11
• Stage 2 uses Adam at learning rate 5e-05 with β1 = 0 and β2 = 0.9 for seven epochs and batch size 128.Source: C TRAINING HYPERPARAMETERS · p. 11
• Stage 3 trains for 35 epochs with batch size 256, selects the final model by validation CRPS, and uses five discriminator steps per generator step.It uses Adam at 5e-05 with β1 = 0 and β2 = 0.9 for both networks, γ1 = 20, γ2 = 20, λ = 10, and six ensemble members for LLR and LHR expectations.Source: C TRAINING HYPERPARAMETERS · p. 11
• Training runs on four Tesla T4 GPUs using mixed precision.Source: C TRAINING HYPERPARAMETERS · p. 12

D DATA; D.2 Input patch

• The paper uses an approximate conversion of 0.01° to 1 km, and Figure 5 shows the generator input-channel breakdown.The supplied input-patch caption gives no further channel values.Source: D DATA · p. 12, §D.2 · p. 12, Figure 5 · p. 12

D.1 Weighted sampling during training

• Training preferentially samples patches with more precipitation, using the fraction of grid points above 0.025 mm to calculate weights bounded by 0.02 and 0.4 with exponent 4.Source: §D.1 · p. 12

D.3 TIGGE Ensemble

• TIGGE data uses ECMWF operational ensemble forecasts regridded from about 0.13° to 0.32°, with initializations at 00 and 12 UTC.Source: §D.3 · p. 12

D.4 Multi-Radar/Multi-Sensor (MRMS) Observations

• MRMS radar-only six-hour precipitation estimates are regridded from 0.01° to 0.04°, and evaluation retains patches with quality above 0.5 in more than 90% of pixels.Source: §D.4 · p. 13, Figure 6 · p. 13

D.5 HREF High-resolution Ensemble

• The HREF comparison ensemble stacks five models with lagged forecasts, while differing precipitation accumulation formats require checks and conversions when assembling its data.The constructed ten-member ensemble's lagging differs slightly from operational HREF for HRRR.Source: §D.5 · p. 13

F.1 Rank Histogram

• CorrectorGAN and HREF have flatter rank histograms than TIGGE interpolation, while CorrectorGAN retains some heavy-rainfall localization misses.The comparison also reports drizzle bias in TIGGE interpolation and Pure-SR GAN, and slight over-forecasting bias in BG-CNN.Source: §F.1 · p. 14

F.2 Full TIGGE Ensembles

• CorrectorGAN achieves large-scale correction in some instances when its predictions are compared with the full TIGGE ensembles.Source: §F.2 · p. 14, Figure 8 · p. 15

F.3 Deterministic metrics

• CorrectorGAN and TIGGE interpolation perform similarly on RMSE and FSS at a 4 mm threshold, outperforming the other methods on RMSE but underperforming HREF on FSS.The text notes that deterministic metrics are not the most appropriate for evaluating probabilistic forecasts and calls BG-CNN's higher FSS a notable outlier.Source: §F.3 · p. 16, Table 2 · p. 16

G ABLATION STUDY

• The ablations compare staged CorrectorGAN with end-to-end CorrectorGAN (NPT) and single-variable LeinGAN, which removes other TIGGE inputs.LeinGAN uses one precipitation input channel and the loss proposed by Leinonen et al. (2020).Source: G ABLATION STUDY · p. 16
• CorrectorGAN’s design, added TIGGE variables and ensemble members, and staged training improve CRPS and Brier Scores over LeinGAN across thresholds.The staged procedure adds gains beyond the other design elements.Source: G ABLATION STUDY · p. 16
• Except at 1mm, CorrectorGAN matches or exceeds other methods in reliability, although LeinGAN mostly outperforms CorrectorGAN (NPT).The reliability comparison therefore differs from the CRPS and Brier Score pattern.Source: G ABLATION STUDY · p. 16

4.1 Weighted sampling during training

• To address patches with little or no precipitation, the dataset is balanced by preferentially sampling patches with more precipitation, using the fraction of grid points exceeding 0.025 mm.Sample weights have enforced bounds of 0.02 and 0.4, with exponent a = 4.Source: §4.1 · p. 19

4.2 Input patch

• For the HREF comparison, a 10-member ensemble is created by stacking the five original models with each model’s lagged forecast, initialized 12 hours earlier; data are downloaded for 00 and 12 UTC initialization times.Source: §4.5 · p. 19

5 Supplementary definitions

• FSS evaluates forecast accuracy using threshold-exceedance fractions in windows and avoids over-penalizing small spatial shifts; its approximation trains Stage 1 correction.The approximation uses sigmoid-transformed predictions and observations as its learning signal.Source: §5 · p. 21

6.1 Rank Histogram

• CorrectorGAN and HREF have flatter rank histograms than TIGGE interpolation, but HREF better localizes some heavy-rain pixels.The larger far-right peak for CorrectorGAN indicates remaining cases of heavy rainfall that it misses in the correct pixels.Source: §6.1 · pp. 21–22

6.2 Full TIGGE Ensembles

• Full TIGGE ensembles confirm that CorrectorGAN achieves large-scale correction in some cases.The deterministic comparison finds CorrectorGAN and TIGGE interpolation perform similarly, both outperforming HREF on RMSE but under-performing it on FSS.Source: §6.2 · p. 22, §6.3 · p. 22