Field-Space Autoencoder for Scalable Climate Emulators

TL;DR

The paper tackles the challenge of scale and data volume in kilometer-scale climate emulation by introducing the Field-Space Autoencoder (FS-AE), which compresses spherical climate fields on the HEALPix grid using Field-Space Attention to avoid projection distortions. It achieves high-fidelity compression that preserves physical structure and enables zero-shot super-resolution across resolutions. A diffusion model trained in the compressed field space (Compressed Field Diffusion) combines abundant low-resolution statistics with sparse high-resolution detail to generate ensembles that reflect internal variability and sharpen fine-scale features. This framework offers a scalable, physics-aware pathway to bridge large low-resolution ensembles and scarce high-resolution data, with broad implications for probabilistic risk assessment and climate emulation.

Abstract

Kilometer-scale Earth system models are essential for capturing local climate change. However, these models are computationally expensive and produce petabyte-scale outputs, which limits their utility for applications such as probabilistic risk assessment. Here, we present the Field-Space Autoencoder, a scalable climate emulation framework based on a spherical compression model that overcomes these challenges. By utilizing Field-Space Attention, the model efficiently operates on native climate model output and therefore avoids geometric distortions caused by forcing spherical data onto Euclidean grids. This approach preserves physical structures significantly better than convolutional baselines. By producing a structured compressed field, it serves as a good baseline for downstream generative emulation. In addition, the model can perform zero-shot super-resolution that maps low-resolution large ensembles and scarce high-resolution data into a shared representation. We train a generative diffusion model on these compressed fields. The model can simultaneously learn internal variability from abundant low-resolution data and fine-scale physics from sparse high-resolution data. Our work bridges the gap between the high volume of low-resolution ensemble statistics and the scarcity of high-resolution physical detail.

Figures (11)

• Figure 1: Field-Space Autoencoder: overview and multi-scale processing. (a) The Encoder $E$ compresses multi-scale inputs on the HEALPix sphere at a target coarse HEALPix level. The Decoder $D$ reconstructs fields at the original input HEALPix level. We denote native inputs by $x^{(n)}$, residuals by $r^{(n)}$, and compressed fields by $c^{(n)}$, where $n$ is the HEALPix level (resolution). (b) Schematic Field-Space Autoencoder block combining Field-Space Attention and Field-Space Compression/Decompression (details in methods). (c–d) Examples of a single Field-Space Compression/Decompression block: coarse base grid $x^3$ and residuals $r^6$/$r^7$ are aggregated and forwarded through a linear layer to produce the output at the requested residual level $r^{6'}$/$r^{7'}$.
• Figure 2: Reconstruction performance and compressed space visualization. (a) Dual-axis plot showing root-mean-square error (RMSE; left vertical axis, °C) and peak signal-to-noise ratio (PSNR; right vertical axis, dB) as functions of compression ratio for both the Field-Space Autoencoder (FS-AE) and CNN-VAE models. The effective compression ratios of our models are slightly lower compared to the corresponding CNN-VAE models, because we additionally maintain an average field at the coarsest resolution (see Fig. \ref{['fig:setup']}). (b) Two-dimensional t-SNE projection of the compressed/latent representations (for $f=16$) of the full daily ERA5 near-surface air temperature (tas) dataset covering 1940–2024, computed with a fixed random seed for reproducibility. The same projection is shown in two views: colored by month (top) and by year (bottom). Each point corresponds to one encoded daily field.
• Figure 3: Multi-variable reconstruction evaluation. (a-b) Radar plot showing per-variable RMSE at respective compression for five ERA5 variables: surface air temperature (tas), eastward and northward wind at 10m (uas, vas), surface pressure (ps), and precipitation (pr). Values closer to the center of the radar chart correspond to lower RMSE. (c) Global reconstruction error of a selected sample at 64× compression. Positive values indicate too warm predictions, negative too cold. (d) Ground Truth and reconstructions of global precipitation of a selected sample at 64× compression.
• Figure 4: Compression and Zero-shot super-resolution on the MPI-ESM historical simulations. Left: Original snapshots of surface temperature ($tas$) from the MPI-ESM historical simulation (HEALPix level 6). Right: The corresponding output from the Field-Space Autoencoder ($64\times$ compression) after compressing the input and decoding to level HEALPix 8.
• Figure 5: Evaluation of generative fidelity and ensemble variability. a. Global spherical power spectral density of a subset of the output variables ($tas$ and $uas$) of a single simulation over a year. b. Maps of internal variability (standard deviation) for the original 10-member MPI-ESM1.2-HR ensemble (left) and the synthetic 10-member ensemble generated via Compressed Field Diffusion (right). The standard deviation was calculated over the 10 ensemble members and then averaged over a full year.