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Precipitation Downscaling Using Foundation Model-Conditioned Diffusion
Victor Nascimento Ribeiro, Jorge Guevara, Jorge Sebastian Moraga, Chris Lucas, Natalie Lord, Andrew Taylor, Edward Lockhart, Will Trojak, Johannes Schmude, Anne Jones
TL;DR
High-resolution precipitation is needed for hydrological impact assessment, but coarse and biased GCM outputs are unsuitable for direct use. The paper compares concatenation and cross-attention conditioning, including a pretrained Prithvi WxC encoder, in diffusion-based downscaling and finds a trade-off between point-wise accuracy and distributional realism, with foundation-model conditioning useful in data-limited settings.
Problem
Coarse, biased GCM precipitation outputs are unsuitable for hydrological impact assessment, while how predictors should condition probabilistic downscaling remains underexplored.
Method
The study compares channel concatenation and cross-attention conditioning with learned convolutional or frozen Prithvi WxC encoders under identical diffusion-downscaling experiments.
Results
Concatenation achieves the lowest point-wise CRPS and MSE, whereas cross-attention provides better distributional realism, spectral fidelity, and extreme-event representation.
Takeaways & Limitations
Cross-attention is advantageous when distributional realism and extremes matter, while Prithvi WxC conditioning may provide comparable performance with less training data.
Takeaways & Limitations
Results are limited to daily precipitation in the Colorado River Basin and rely on ERA5-based data, with extreme-event metrics uncertain because the evaluation period spans three years.
Abstract
from arXiv · showhide
High-resolution precipitation fields are essential for hydrological impact assessment, yet global climate model outputs are too coarse and biased for direct use. AI-based statistical downscaling with diffusion models offers a promising approach, but the mechanism by which large-scale atmospheric predictors condition generation remains largely unexplored. We investigate three conditioning strategies for a denoising diffusion probabilistic model applied to daily precipitation downscaling: channel concatenation of upsampled coarse predictors, cross-attention conditioning with a learned convolutional encoder, and cross-attention conditioning with the frozen encoder of the pretrained Prithvi WxC weather foundation model. All strategies are evaluated against an unconditioned baseline under identical conditions using probabilistic, distributional, spectral, and extreme-event metrics for the Colorado River Basin. Concatenation conditioning achieves the lowest point-wise CRPS and MSE, but tends to produce over-smoothed fields that suppress high-intensity events. In contrast, cross-attention conditioning provides substantially better distributional realism and modest improvements in spectral fidelity. Improvements are greatest for extremes: the Prithvi-WxC conditioned model retains over half of >100mm/day events, although estimates are uncertain due to limited samples. When trained on the full dataset, the learned convolutional model performs similarly to the foundation model-conditioned approach while requiring lower computational resources. However, the Prithvi-WxC-conditioned model achieves comparable performance with only five years of training data. These results indicate that cross-attention conditioning offers advantages over simple concatenation for probabilistic precipitation downscaling, and that pre-trained foundation model representations may offer benefits in data-limited settings.
1 Introduction
Global climate model precipitation is too coarse and biased for direct hydrological impact modeling, motivating statistical downscaling. This paper evaluates alternative diffusion-model conditioning mechanisms, including a pretrained weather foundation model, to address unresolved trade-offs in realism, extremes, and data efficiency.
- GCM precipitation outputs are unsuitable for flood modeling because their coarse resolution and biases inadequately represent small-scale effects and extremes.
- Climate downscaling requires learning a conditional distribution p(y|x), but the choice of conditioning mechanism for incorporating coarse predictors remains relatively unexplored.
- The study addresses three gaps: limited control from concatenation, underexplored foundation-model conditioning for probabilistic generation, and poorly quantified computational and data-efficiency trade-offs.
- The experiments compare channel concatenation with cross-attention using a learned convolutional encoder and the pretrained Prithvi WxC encoder under identical training and inference settings.
- Performance is assessed across spatial structure, distributional realism, probabilistic calibration, extreme-event behavior, and training-data efficiency.
2 Dataset
The study downscales daily precipitation over the Colorado River Basin using paired high-resolution targets and low-resolution climate predictors. Conditioning combines ERA5 atmospheric variables with high-resolution static physiographic information.
- The dataset focuses on daily total precipitation in the Colorado River Basin, using paired high-resolution targets and low-resolution conditioning climate variables.
- The target precipitation field comes from ERA5-Land at 0.1°, while dynamic conditioning variables come from 0.25° ERA5 reanalysis.
- Precipitation is excluded as a conditioning variable; instead, large-scale atmospheric state variables associated with precipitation processes are used.
- Five high-resolution static variables supplement the dynamic predictors, including ERA5-Land variables and terrain-derived variables from a 0.01° Copernicus GLO-90 digital elevation model.
- Vertical atmospheric variables are supplied at 500, 700, and 850 hPa, while static physiographic variables remain at native resolution.
3 Methods
The framework learns a conditional diffusion distribution for high-resolution precipitation from coarse atmospheric and high-resolution physiographic predictors. It compares concatenation and cross-attention mechanisms, including learned and pretrained encoders, to preserve large-scale context and fine-scale stochastic variability.
- Conditional diffusion formulation: The model learns p(y|x), generating high-resolution precipitation states conditioned on coarse atmospheric and physiographic predictors.The shared denoising architecture uses a UNet with EDM continuous-noise conditioning.
- Channel concatenation conditioning: Channel concatenation appends predictor fields to the noise input, requiring coarse surface and vertical variables to be interpolated onto the high-resolution grid.Static physiographic variables are included alongside the atmospheric predictors before UNet denoising.
- Cross-attention conditioning: Static physiographic variables remain at native high resolution and use concatenation because spatial coarsening would discard fine-scale information critical for downscaling.The cross-attention encoder is applied to coarse atmospheric predictors rather than these static fields.
- Cross-attention conditioning: Cross-attention encodes coarse predictors into latent embeddings that are injected into UNet feature maps at multiple spatial resolutions.UNet feature maps act as queries, while predictor embeddings provide keys and values.
- Foundation-model conditioning: Prithvi WxC supplies frozen, high-dimensional spatiotemporal embeddings that are compressed by convolutional layers before cross-attention injection into the diffusion UNet.Only the preprocessing adapter, projection head, and diffusion UNet are trainable.
- Evaluation rationale: The evaluation uses multiple quality dimensions because precipitation has high spatial heterogeneity and complex distributional tails.The study assesses distributional realism, spatial structure, extremes, uncertainty, and related downscaling behavior.
4 Results and Discussion
Under identical evaluation settings, conditioning strategies trade pixel-level accuracy against distributional, spectral, and extreme-event fidelity. Cross-attention models generally better preserve realistic precipitation structure and extremes, while Prithvi-WxC shows a data-efficiency advantage.
- Probabilistic accuracy: CC achieves the lowest raw CRPS (0.511) and MSE (4.282), indicating the strongest pixel-level accuracy.CA-CE and CA-PWC have raw CRPS values of 0.581 and 0.557, respectively.
- Bias: CA-PWC achieves the lowest time-averaged absolute bias (0.095 mm/day) and absolute relative bias (0.097).These outperform CC values of 0.185 and 0.169 and CA-CE values of 0.107 and 0.112.
- Distribution and spectral fidelity: CA-PWC achieves the lowest distribution bias (0.065), while both cross-attention models improve spatial spectral metrics over CC.RAPSD CRPS is 2.632 for CA-CE and 2.598 for CA-PWC, versus 2.763 for CC and 7.011 for UNC; RALSD is also lower for cross-attention models.
- Spatial and distributional behavior: CC produces smoother fields and underestimates high-intensity events, whereas CA-CE and CA-PWC more faithfully reproduce the reference precipitation right tail and peak values.The contrast appears in mean and maximum precipitation fields, marginal histograms, and spatial bias maps.
- Extreme events: For 100–200 mm/day events, CA-PWC retains over 50% of reference counts, compared with approximately 17% for CA-CE and nearly 0% for CC.Models perform comparably below 20 mm/day, where conditioning strategy has little effect.
5 Conclusions
Cross-attention conditioning improved distributional realism, spectral fidelity, and extreme-event representation relative to concatenation, while concatenation achieved better pixel-level CRPS and MSE. The results are promising for impact assessment but remain limited by domain, data, and sampling constraints.
- Overall comparison: Concatenation achieved the lowest pixel-level CRPS and MSE, whereas cross-attention produced more accurate precipitation distributions and better extreme-event representation.These comparisons were made under identical training and inference conditions.
- Distributional and spectral realism: Distribution biases from cross-attention were up to five times lower than Concatenation, with more faithful high-scale spectra and annual-maximum precipitation distributions.Annual-maximum statistics were based on only three observation years and therefore have substantial sampling uncertainty.
- Extreme events: For intensities above 100 mm/day, CA-PWC retained over 50% of observed event counts while CC produced virtually none.The limited number of observed tail events makes this extreme-event comparison uncertain.
- Encoder comparison: CA-PWC and CA-CE performed broadly similarly, with CA-PWC favoring annual-maximum distributional and spectral metrics while CA-CE favored some error and spatial-realism metrics.CA-CE is described as lightweight and operationally practical, whereas CA-PWC offers advantages in limited-training-data regimes.
- Implications and scope: Cross-attention conditioning may be particularly advantageous for climate-impact applications where extreme precipitation frequency and intensity are primary concerns.The study evaluated a single regional domain and daily precipitation, so transferability remains uncertain.
A.1 Evaluation Metrics
The evaluation uses complementary metrics to assess probabilistic accuracy, calibration, distributional bias, spatial spectral fidelity, and neighborhood-based precipitation skill. Together, these metrics separate point-wise error from distributional and spatial realism.
- Probabilistic accuracy: CRPS measures the distance between the predicted ensemble CDF and reference data, including pixel-wise, aggregated-field, and histogram variants.Histogram CRPS evaluates overall value-distribution consistency independently of spatial structure.
- Distributional realism: Distribution Bias is the integrated absolute difference between model and reference empirical CDFs, capturing systematic intensity-frequency errors independent of temporal synchronization.The metric assesses climatological distributional agreement across grid points and time steps.
- Bias metrics: Absolute bias measures mean absolute prediction-reference differences, while relative bias normalizes pointwise error by observed precipitation and excludes zero observations.Relative bias is especially informative where low mean precipitation makes small absolute errors proportionally large.
- Calibration: Calibration Error measures consistency between predicted probabilities and observed frequencies, with a uniform rank histogram corresponding to zero error.For ensemble size M, the error uses the frequency pk with which observations fall in predictive-distribution bins.
- Spatial fidelity and skill: RAPSD evaluates spatial realism by azimuthally averaging the two-dimensional power spectrum, while FSS measures neighborhood agreement for threshold exceedances on a 0-to-1 scale.RAPSD comparisons use log-spectral distance, and FSS is averaged across samples.