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Causal Climate Emulation with Bayesian Filtering
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Proposes PICABU, a causal representation learning climate emulator built on CDSD with CRPS and spectral losses plus a particle-style Bayesian filter for stable 100-year autoregressive rollouts of NorESM2 and CESM2-FV2 surface temperature.
Problem
Climate model emulators are fast but lack physically grounded causal structure and often become unstable or diverge during long autoregressive climate rollouts.
Approach
Extends CDSD causal representation learning with a sparsity constraint (instead of penalty), orthogonality constraint, CRPS and Fourier spectral losses, and a Bayesian filter that weights latent samples by how well the decoded spatial spectrum matches a fixed observed spectrum.
Key results
- On 12 SAVAR datasets, PICABU achieves F1 of 1 on 4-latent easy/med-easy/med-hard and 0.84 on the hardest 100-latent case, slightly above CDSD and well above V-PCMCI.
- On NorESM2 GMST, PICABU's standard deviation is 0.277 vs 0.177 ground truth, and its LSD is 0.444 for GMST; CDSD diverges, and PICABU without the Bayesian filter or sparsity term diverges.
- On out-of-distribution SSP5-8.5 initial conditions, PICABU has MAE 0.75 and LSD 0.031, outperforming the ablations without sparsity or orthogonality.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the spectral loss (ablation) | PICABU · NorESM2 pre-industrial, GMST | LSD: 0.658 -> 0.444 | Helped |
| add the spectral loss (ablation) | PICABU · NorESM2 pre-industrial, Niño3.4 | LSD: 0.334 -> 0.191 | Helped |
| add the CRPS loss (ablation) | PICABU · NorESM2 pre-industrial, GMST | Range: 3.65 -> 2.02 | Helped |
| add the orthogonality constraint (ablation) | PICABU · NorESM2 pre-industrial, GMST | Std. Dev.: 0.527 -> 0.277 | Helped |
| add the sparsity constraint (ablation) | PICABU · NorESM2 pre-industrial, GMST | Mean | Helped |
| add the Bayesian filter (ablation) | PICABU · NorESM2 pre-industrial, GMST | Mean | Helped |
| enforce the sparsity constraint (ablation) | PICABU · Out-of-distribution next-step prediction, SSP5-8.5 | MAE: 0.81 -> 0.75 | Helped |
| enforce the orthogonality constraint (ablation) | PICABU · Out-of-distribution next-step prediction, SSP5-8.5 | MAE: 0.84 -> 0.75 | Helped |
| use the inferred variance instead of constant observation-based variance (ablation) | PICABU Bayesian filter · NorESM2 pre-industrial, Niño3.4 | Range: 5.99 -> 7.70 | Hurt |
| increase the number of latent variables (ablation) | PICABU · NorESM2 pre-industrial, Niño3.4 | power spectrum | Helped |
| vary the sparsity coefficient (ablation) | PICABU · NorESM2 pre-industrial rollouts | power spectra | No clear effect |
| use PICABU instead of V-PCMCI | climate emulation · NorESM2 pre-industrial, Niño3.4 | LSD: 0.180 -> 0.191 | Helped |
Surprising findings
- CDSD diverges on climate model data, showing the additional losses are essential for real climate emulation.
- Using the model's inferred variance in the Bayesian filter degrades predictions relative to a constant observed variance.
Limitations
- Single-parent decoding assumption requires a high latent dimension for complex fields and may cause high-frequency noise in GMST.
- Emulator has too much power at high frequencies for GMST and AMO and too little spatial variability over some land regions.
- No anthropogenic emissions are included as inputs, so the model cannot directly represent forced climate change.
Experimental setup
Datasets: NorESM2 pre-industrial monthly surface temperature CESM2-FV2 surface temperature SAVAR synthetic datasets
Benchmarks: SAVAR synthetic causal graphs NorESM2 pre-industrial emulation CESM2-FV2 emulation SSP2-4.5, SSP3-7.0, SSP5-8.5 out-of-distribution initial conditions
Metrics: F1 score mean standard deviation range log-spectral distance MAE R^2 power spectral density
Baselines: CDSD V-PCMCI ViT + pos. encoding PICABU without Bayesian filter PICABU without sparsity PICABU without orthogonality PICABU without spectral loss PICABU without CRPS
Builds on: CDSD PCMCI ClimaX augmented Lagrangian method
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