Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation

TL;DR

This work addresses global data assimilation by seeking the posterior trajectory p(x^{1:L} | y) given observations y. Appa introduces a latent diffusion framework that compresses atmospheric states x^i to latent z^i via a learned autoencoder with z^i ∼ N(Eψ(x^i), σ_z^2 I) and uses a diffusion transformer to model trajectories in latent space. Conditioning on observations is achieved by inserting the posterior score ∇_{z^{1:L}_t} log p(z^{1:L}_t | y) = ∇_{z^{1:L}_t} log p(z^{1:L}_t) + ∇_{z^{1:L}_t} log p(y | z^{1:L}_t) and approximating the likelihood p(y^{1:L} | z^{1:L}) through the decoder Dψ and a measurement operator M, yielding p(y^{1:L} | z^{1:L}) ≈ N(y^{1:L} | A(z^{1:L}), Σ_y) with A(z^{1:L}) = (M^1(Dψ(z^1)) … M^L(Dψ(z^L)))^T. Empirical results on ERA5 (1993–2021) show RMSEs below 0.1 after standardization, preservation of energy spectra, and physical relationships such as altitude estimation and geostrophic balance, with short-lead forecasts achieving skill comparable to IFS and better than GraphDOP, demonstrating the utility of a probabilistic, unified latent DA framework.

Abstract

Deep learning has advanced weather forecasting, but accurate predictions first require identifying the current state of the atmosphere from observational data. In this work, we introduce Appa, a score-based data assimilation model generating global atmospheric trajectories at 0.25\si{\degree} resolution and 1-hour intervals. Powered by a 565M-parameter latent diffusion model trained on ERA5, Appa can be conditioned on arbitrary observations to infer plausible trajectories, without retraining. Our probabilistic framework handles reanalysis, filtering, and forecasting, within a single model, producing physically consistent reconstructions from various inputs. Results establish latent score-based data assimilation as a promising foundation for future global atmospheric modeling systems.

Figures (14)

• Figure 1: (Left) Standardized autoencoder reconstruction RMSEs. Lower-frequency fields (temperature, geopotential) are reconstructed more accurately than volatile fields (humidity, winds). Near-surface fields benefit from altitude-weighting. (Right) Power spectral density comparison of ground truth, autoencoder reconstructions, and samples generated from Appa’s prior. Median and percentile ranges show close alignment across scales, with deviations below 100 km (3 to 4 grid cells).
• Figure 2: Skill and Continuous Ranked Probability Score (CRPS) for representative variables in January 2023. Detailed experimental setup can be found in \ref{['app:forecast-details']}. Reanalysis scores are averaged over assimilation windows $x^{1:L}$, while filtering reports the last reanalyzed state. Both improve with longer assimilation windows, but eventually stagnate. Forecasts gradually lose skill over lead time but remain superior to persistence and unconditional baselines. The initial skill level of the full-state forecast matches the compression error level. IFS ifs and GraphDOP alexe2024graphdop are shown for reference.
• Figure 3: Power spectral density across wavelengths for atmospheric variables at selected pressure levels. Lines show median values and error bars indicate the 5th to 95th percentiles. The close alignment between the curves demonstrates that both the autoencoder and the diffusion model preserve the energy distribution across most spatial scales. Deviations begin to appear at wavelengths around 1000km, which corresponds to roughly 40 grid cells at our 0.25-degree resolution at the equator. These differences become more pronounced at smaller scales, suggesting that while large-scale atmospheric patterns are well-preserved, features spanning fewer than 40 grid cells show some energy loss in the compression and generation processes. Deviations become more pronounced at lower pressure levels, as the model prioritizes surface and low-altitude variables.
• Figure 4: Physical consistency analysis of generated atmospheric states. (Top row) Analysis of altitude consistency at 500 hPa showing the difference $\Delta H$ between two independent altitude estimators, and geostrophic balance assessment through the cosine and sine of the angle $\theta$ between wind direction and geopotential gradients, demonstrating angles concentrated around 90°. (Bottom row) Same metrics at 1000 hPa demonstrating the presence of a significant ageostrophic component near the surface. (Right) Correlation coefficient between wind magnitude and geopotential gradient magnitude across pressure levels, showing strong correlation at upper levels (near 1) with a consistent decrease toward the surface in both ERA5 data (blue) and generated samples (black dots), confirming Appa's ability to capture complex physical relationships.
• Figure 5: Signed reconstruction errors for surface variables (top) across all grid points and atmospheric variables (bottom) across all pressure levels. Shaded gray area for surface variables corresponds to error spread. In both cases, the concentrated distributions centered around zero demonstrate unbiased and precise predictions. Given $721 \times 1440 = 1,038,240$ grid points, a $0.01 \%$ fraction on the y-axis corresponds to approximately 100 grid points, indicating that large errors are rare.