LUCIE-3D: A three-dimensional climate emulator for forced responses

Guan, Haiwen; Arcomano, Troy; Chattopadhyay, Ashesh; Maulik, Romit

doi:10.5194/egusphere-2025-4305

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https://doi.org/10.5194/egusphere-2025-4305

Preprints

15 Sep 2025

| 15 Sep 2025

LUCIE-3D: A three-dimensional climate emulator for forced responses

Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, and Romit Maulik

Abstract. We introduce LUCIE-3D, a lightweight three-dimensional climate emulator designed to capture the vertical structure of the atmosphere, respond to climate change forcings, and maintain computational efficiency with long-term stability. Building on the original LUCIE-2D framework, LUCIE-3D employs a Spherical Fourier Neural Operator (SFNO) backbone and is trained on 30 years of ERA5 reanalysis data spanning eight vertical σ-levels. The model incorporates atmospheric CO₂ as a forcing variable and optionally integrates prescribed sea surface temperature (SST) to simulate coupled ocean atmosphere dynamics. Results demonstrate that LUCIE-3D successfully reproduces climatological means, variability, and long-term climate change signals, including surface warming and stratospheric cooling under increasing CO₂ concentrations. The model further captures key dynamical processes such as equatorial Kelvin waves, the Madden–Julian Oscillation, and annular modes, while showing credible behavior in the statistics of extreme events. Despite requiring longer training than its 2D predecessor, LUCIE-3D remains efficient, training in under five hours on four GPUs. Its combination of stability, physical consistency, and accessibility makes it a valuable tool for rapid experimentation, ablation studies, and the exploration of coupled climate dynamics, with potential applications extending to paleoclimate research and future Earth system emulation.

Received: 02 Sep 2025 – Discussion started: 15 Sep 2025

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Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, and Romit Maulik

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-4305', Anonymous Referee #1, 12 Nov 2025
The authors present LUCIE-3D, a machine learning emulator for predicting the time evolution of atmospheric variables. Compared to the original emulator, LUCIE, LUCIE-3D includes prognostic variables on 8 vertical levels. The emulator is stable in the long-term and trained on ERA5. One variant takes in SST as a forcing variable, and both variants use atmospheric CO2 concentrations as an additional forcing variables. Two relatively unique aspects of this emulator are that it has limited computational cost (35 GB training dataset, 20 GPU-hour training time) and that it uses CO2 as input.
I have included major comments, minor comments, and technical corrections.
Major comments:
In Figure 3, it appears that LUCIE-3d has a temperature bias of 0.5 K in its mean state. LUCIE-3d and LUCIE-3d SST have the right temperature trends, but the absolute global mean temperature is off by ~0.5-0.7 K for the surface. Why does this happen? This problem also exists in GCMs in AMIP, but in ML models, wouldn’t the expectation be that this bias does not exist since they are trained on ERA5 itself? NeuralGCM (https://research.google/blog/fast-accurate-climate-modeling-with-neuralgcm/) and ACE2 do not appear to have this mean state bias.

Pg. 7 Line 138: Why does the model prescribe land temperatures at 270 K? Land temperatures have a significant diurnal cycle and variability. Prescribing them at 270 K isn’t the correct value, and it seems like it would limit the ability to use LUCIE-3D for downstream applications. Either land temperatures should be prognosed (as in ACE2) or they should not be included at all (NeuralGCM), but why set them at 270 K? It also seems that this choice makes the model more brittle. It is worrying that the authors have to apply additional smoothing in order to get a reasonable response to +2K SST, and that without the smoothing, the model’s land response is of the wrong sign. (While other emulators have errors with +2K SST, they were not fundamentally of incorrect sign over land for temperature and moisture).

LUCIE-3D is trained with a spectral regularizer, which they say mitigates spectral bias and point to past literature. In order to validate this claim, I think the authors need to show that the spectra are the same in LUCIE-3D and ERA5. (I think past literature explores this, but it uses different models, not LUCIE-3D itself. ) Based on the PDFs in Fig 8, do the moisture and precip variables still have a spectral bias?

Is the precipitation climatology believable, and is the spectra precipitation blurred? Precip is validated in Figure 6 and Figure 9 (bottom right), which shows that the precip tail is heavily underestimated. Given the underestimation in Figure 9, does the climatology of precip have a sufficiently low bias? And are the precipitation results significantly blurred as measured by the spectra?

To me, this emulator appears to be very similar to ACE2. They both use the same model architecture (SFNO), they both input atmospheric CO2 forcing in the same way, they both have 8 vertical levels with a 6hour timestep, and they both inherit the same stratospheric biases. The main difference is that ACE2 has more diagnostic variables (e.g. turbulent and radiative fluxes) and trains on 1 degree data. LUCIE is coarser resolution, on a T30 grid (~3.8 degree data). This is likely the major reason why LUCIE trains faster than ACE2. Would it be fair to characterize LUCIE-3D as a coarse-resolution version of ACE2?

Even if LUCIE-3D is similar to ACE2, I think LUCIE-3D is still valuable: it shows that coarse-resolution emulators can start from climatological conditions, just like PanGu (Hakim and Masanam) and SFNO (Peings et. al.).
I have the following minor comments:
NeuralGCM displays a property where some initial conditions are stable and others are not. Does LUCIE-3D show signs of instability if initialized with different initial conditions? Or does LUCIE-3D fully solve this problem?

In Figures 12 and 13, from the caption, I don’t understand what the ERA5 data corresponds to, since the x axis is year 0,1,2,3. Is the ERA5 data initialized at 1981 (is it a climatology?) Furthermore, it would be helpful if the Figure 12 and Figure 13 captions stated explicitly if they correspond to the LUCIE-3D variant with SSTs or without. Is the result robust across these 2 LUCIE 3-D variants?

The authors should clarify the approximate resolution in degrees of the T30 grid. This would be helpful for readers.

I was confused by the title and think that there should be a clarification in the text. Based on the title, I thought that LUCIE-3D included 3D architectural components, like PanGu’s 3D Earth-specific transformer (many of the readers will likely be familiar with PanGu). However, from the Zenodo codebase, I think the authors are adding the vertical fields as additional 2D fields, and the SFNO operates on the 2D fields with spherical harmonic transforms.

Missing citation: I think the paper should cite ArchesWeather and ArchesClimate. These are another class of emulators that is designed to be efficient (and accessible to academic labs).

A surprising result and contribution of this paper is that it shows that models cannot extrapolate out of sample for boundary conditions, but they can extrapolate out of sample for initial conditions (e.g. all zero initial conditions). Do the authors have an explanation for this behavior? It’s of course hard to say why because of the overparameterized nature of ML which can be a black box, but if the authors have any reason why this might be the case, I would welcome more discussion on this in the Discussion section.

Technical correction
Typo: Line 113 on page 5 should be “polar amplification” not “olar amplification”

Typo: Figure 7 caption “Annualr” should be “Annular”

Sometimes the authors refer to a figure without actually stating the figure number. This is a small thing but it would be helpful to ensure the figures are referred to in the text directly by number. For example, page 8 and 9 should say “Fig. 6” explicitly.

Figure 5 caption itself wasn’t sufficiently explanatory. It should clarify that the interpolated SST output refers to the Gaussian convolution to smooth land and sea discontinuities, and it should point to the relevant section in the text.
Citation: https://doi.org/10.5194/egusphere-2025-4305-RC1
RC2: 'Comment on egusphere-2025-4305', Anonymous Referee #2, 19 Nov 2025

Comments are highlighted in the attached document.

Citation: https://doi.org/10.5194/egusphere-2025-4305-RC2

Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, and Romit Maulik

Model code and software

LUCIE-3D: A three-dimensional climate emulator for forced responses Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, Romit Maulik https://doi.org/10.5281/zenodo.17032360

Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, and Romit Maulik

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Short summary

LUCIE-3D is a fast machine learning climate model that simulates the atmosphere in 3D using 30 years of ERA5 data across eight levels. It takes changing CO₂ and optional SST to reflect ocean effects. LUCIE-3D reproduces means, variability, and long-term signals like surface warming and stratospheric cooling, and captures patterns such as equatorial Kelvin waves, the MJO, and annular modes. It trains in under five hours on four GPUs, supporting quick studies and coupled climate exploration.


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