A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator

Hira Saleem; Cormac Purcell; Steven Sherwood; Flora Salim

physics.ao-phOct 29, 2024

A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator

Authors: Hira Saleem, Cormac Purcell, Steven Sherwood, Flora Salim

Organizations: University of New South Wales, Sydney, NSW, Australia

Abstract

Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel, deep learning has delivered strong gains in short-range weather forecasting; however, auto-regressive roll-outs can accumulate error and become unstable when extended to decade-scale climate emulation. We introduce A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator, aimed at stable multi-year emulation across heterogeneous climate models and grid resolutions. A-UTE is trained on various physics-based models at varying spatial resolutions to emulate temperature fields over a 10-year horizon. A-UTE formulates climate emulation as a forward-time stochastic dynamical system. We propose an auto-regressive ODE-SDE surrogate in which transport dynamics are constrained by an advection consistent ODE component, while a learned neural SDE term models coarse-grained variability and cross-model discrepancy at monthly resolution. We train A-UTE under negative log-likelihood objective for principled uncertainty estimates and probabilistic evaluation. Experiments across 20 climate models show that A-UTE improves long roll-out stability and accuracy relative to relevant baselines, advancing data-driven climate emulation with explicit physical structure and uncertainty-aware predictions.

Figures & tables

Figure 1. GCM vs. A-UTE (emulation). General Circulation Models (GCMs) numerically solve the coupled atmosphere physics to simulate climate evolution under prescribed forcings, producing physically grounded trajectories at high computational cost. A-UTE is a hybrid data-driven emulator, it uses a forced advection-based dynamical core to provide a coarse-grained transport prior, and a latent Neural SDE residual trained with a likelihood objective to produce calibrated probabilistic roll-outs at a fraction of the runtime, enabling efficient long-horizon scenario analysis and cross-model evaluation.

Figure 2. Architectural pipeline of A-UTE. Forcing maps and the initial temperature field are used as input for the physics-informed backbone (left), where an initial pseudo-velocity is inferred and the forced-advection equation is integrated with the dopri5 ODE solver to produce a transport-shaped backbone trajectory. This trajectory is refined by the latent neural SDE (right): an encoder $\mathcal{E}_{\theta}$ maps it to a latent state, an Itô SDE with drift $f_{\theta}$ and diffusion $g_{\theta}$ evolves the latent trajectory, and a decoder $\mathcal{D}_{\theta}$ returns the refined temperature field. The full pipeline is trained end-to-end under the latitude-weighted Gaussian negative log-likelihood objective.

Hyperparameters	Value
Epochs	30
Conv2d kernel size	3x3
Integrator	srk
Noise type	diagnol
ODE solver	dopri5
Pooling No.1	AvgPool2d (2,2)

Table 1. A-UTE Training Details

ConvLayers	Value
Encoder	4
Latent SDE - Drift $f_{\theta}$	11
Latent SDE - Diffusion $g_{\theta}$	1
Decoder	4
Velocity Refiner	2

Table 2. A-UTE ConvLayer Details

	A-UTE		U-Net		ConvLSTM		SFNO		NADE
Climate Model	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS
AWI-CM-1-1-MR	0.369	0.251	0.916	0.842	0.543	0.441	0.406	0.316	0.412	0.327
BCC-CSM2-MR	0.381	0.263	0.950	0.871	0.549	0.451	0.412	0.323	0.435	0.355
CAS-ESM2-0	0.420	0.306	1.431	0.921	0.542	0.439	0.451	0.362	0.432	0.330
CESM2-WACCM	0.333	0.233	1.154	0.932	0.556	0.459	0.463	0.365	0.461	0.351
CESM2	0.353	0.248	0.926	0.811	0.557	0.457	0.475	0.397	0.387	0.291

Table 3. 10-year auto-regressive roll-outs on 19 ClimateSet models under the held-out SSP2-4.5 scenario. Latitude-weighted RMSE (K) and CRPS (K); lower is better. CRPS for the deterministic baselines is computed from a 5-seed empirical ensemble (Section 5.2 ). Best entry per metric in bold.

	A-UTE		U-Net		ConvLSTM		SFNO		NADE
Level	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS
$T_{1}$	0.437	0.347	0.924	0.876	0.653	0.598	0.466	0.354	0.452	0.342
$T_{3}$	0.408	0.274	0.865	0.772	0.656	0.582	0.482	0.392	0.492	0.398
$T_{4}$	0.355	0.222	0.796	0.622	0.592	0.462	0.491	0.365	0.382	0.323
$T_{5}$	0.349	0.221	0.899	0.731	0.536	0.401	0.379	0.399	0.421	0.392
$T_{6}$	0.379	0.240	0.738	0.598	0.582	0.421	0.459	0.387	0.451	0.372

Table 4. 10-year auto-regressive roll-outs on FV3GFS at six vertical levels. Latitude-weighted RMSE (K) and CRPS (K); lower is better. CRPS for the deterministic baselines is computed from a 5-seed empirical ensemble. Best entry per metric in bold.

Panel of Figure 3 — Figure 3. Time–mean maps for air temperature fields across vertical levels (2,3,4,5). Both the quantitative results in table 4 and visual results indicate stronger fidelity at higher levels (L4–L5) than at lower tropospheric levels (L2–L3), with reduced discretizations.

Source: AWI-CM-1-1-MR
	A-UTE		U-Net		ConvLSTM		SFNO		NADE
Target	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS	RMSE	CRPS
AWI-CM-1-1-MR	0.190	0.134	0.534	0.423	0.589	0.479	0.322	0.210	0.298	0.182
EC-Earth3	0.214	0.149	0.759	0.598	0.590	0.481	0.342	0.230	0.310	0.230
GFDL-ESM4	0.198	0.136	0.603	0.502	0.599	0.489	0.325	0.213	0.242	0.139
FGOALS-f3-L	0.225	0.155	0.659	0.553	0.587	0.477	0.351	0.240	0.336	0.215

Table 5. Zero-shot cross-model emulation at the 1-year roll-out horizon. Each block lists the source model in its first row (in-domain) and target models evaluated without fine-tuning. RMSE (K) and CRPS (K); lower is better. CRPS for the deterministic baselines reflects the 5-seed empirical construction. Best entry per metric in bold.

Figure 4. Ablation of the advection-forcing core across four CMIP6 models. Latitude-weighted RMSE for 10-year roll-outs comparing the full A-UTE (physics-informed) against the variant with the transport core removed and only the latent neural SDE retained (physics-uninformed). Removing the core raises RMSE on all four models, with the largest degradation on CAS-ESM2-0 and TaiESM1.

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Internal variability is a dominant contributor to the uncertainty of predictions at the interannual to decadal timescale. A typical approach to separating the internal variability from forced climate responses is to generate large ensembles of simulations under different initial conditions. Due to the complexity of Earth System Models, generating these large ensembles is computationally expensive. In this work, we present ArchesClimate, a deep learning-based climate model emulator designed to reduce the cost of exploring internal variability at timescales ranging from monthly to decadal. ArchesClimate is trained on decadal hindcasts of the IPSL-CM6A-LR climate model. We train a flow matching model following ArchesWeatherGen, which we adapt to predict near-term climate. Once trained, the model generates states at a one-month lead time from the states of the two preceding months, and can be used to auto-regressively emulate climate model simulations. We show that for up to 10 years, these generations are stable and physically consistent. We also show that for several important climate variables, ArchesClimate generates simulations that are interchangeable with the IPSL model. This work suggests that climate model emulators could reduce the cost of generating large ensembles with climate models.

Abstract

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