Examining Fast Radiatively Driven Responses Using Machine-Learning Weather Emulators
Authors: Ankur Mahesh, William D. Collins, Travis A. O'Brien, Paul B. Goddard, Sinclaire Zebaze, Shashank Subramanian, James P. C. Duncan, Oliver Watt-Meyer, Boris Bonev, Thorsten Kurth, Karthik Kashinath, Michael S. Pritchard, Da Yang
Organizations: Earth and Planetary Science, University of California, Berkeley, Berkeley, CA, USA. · Earth and Environmental Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. · Earth and Atmospheric Sciences, Indiana University, Bloomington, IN, USA. · Computational Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. · Allen Institute for Artificial Intelligence (Ai2), Seattle, WA, USA. · NVIDIA Corporation, Santa Clara, CA, USA. · Department of Geophysics, Stanford University, Stanford, CA, USA.
The response of the climate system to increased greenhouse gases and other radiative perturbations is governed by a combination of fast and slow feedbacks. Slow feedbacks are typically activated in response to changes in ocean temperatures on decadal timescales and manifest as changes in climatic state with no recent historical analogue. However, fast feedbacks are activated in response to rapid atmospheric physical processes on weekly timescales, and they are already operative in the present-day climate. This distinction implies that the physics of fast radiative feedbacks is present in the historical meteorological reanalyses used to train many recent successful machine-learning-based (ML) emulators of weather and climate. In addition, these feedbacks are functional under the historical boundary conditions pertaining to the top-of-atmosphere radiative balance and sea-surface temperatures. Together, these factors imply that we can use historically trained ML weather emulators to study the response of radiative-convective equilibrium (RCE), and hence the global hydrological cycle, to perturbations in carbon dioxide and other well-mixed greenhouse gases. Without retraining on prospective Earth system conditions, we use ML weather emulators to quantify the fast precipitation response to reduced and elevated carbon dioxed concentrations with no recent historical precedent. We show that the responses from historically trained emulators agree with those produced by full-physics Earth System Models (ESMs). In conclusion, we discuss the prospects for and advantages from using ESMs and ML emulators to study fast processes in global climate.
Figures & tables
Figure 1: Response of CMIP Models to Abrupt CO 2 Quadrupling. The response of 8 ESMs to the abrupt4xCO2 experiment from the Coupled Model Intercomparison Project (CMIP) v6 ( Eyring et al., 2016 ) . Lead time is shown as days since CO 2 was quadrupled. Listed in Table 3 , models were selected based on availability of data at daily resolution and sufficient metadata to determine the branch points of the instantaneous quadrupling simulations from the corresponding pre-industrial control simulations. Panel (a) shows the response of ocean surface temperature, and panel (b) shows the response of precipitation. For precipitation and temperature, the Δ refers to the global-mean differences between the abrupt4xCO2 simulations and the pre-industrial control simulations from which these were branched. Shading denotes ±1 standard deviation across the multi-model ensemble.
Figure 2: Diagram of ACE-RRTMG Rollout . Panel (a) shows the standard rollout of ACE with no perturbations for CO 2 applied. The instantaneous model states are depicted at times t0,t1,andt2 with stylized maps depicting various prognosed variables. Panel (b) shows ACE-RRTMG with modifications to simulate the effects of different levels of CO 2 . Q is the net clear-sky radiative heating [ ∘ K], and Qnet is the sum of the clear-sky longwave and shortwave heating rates [ ∘ K/s]. At each timestep, RRTMG is used to calculate ΔQ , the heating perturbation due to an instantaneous change in CO 2 from 1× to N× its concentration at 2010 CE. The heating rate perturbations are applied to the temperature fields at each pressure level in the ACE rollout.
Figure 3: Heating Rate Perturbations from 1 × CO 2 & 4 × CO 2 . The longwave, shortwave, and net heating rate perturbations are shown for the E3SM Atmosphere Model EAMv2 in panel (a) and ACE coupled to RRTMG in panel (b). The net heating rate perturbation (4 × CO 2 - 1 × CO 2 ) is shown for EAMv2 and ACE in (c). Note the different scales in the x axis in (c) compared to (a) and (b).
Figure 4: Global Mean Fast Response to Instantaneous Changes in CO 2 Concentrations . Panel (a): the fast response to increased CO 2 from the E3SM Atmosphere Model; panel (b): the corresponding response from our modified ACE architecture including column diagnosis and prognosis. See Section 4.6.2 and Figure 6 for a description of these modifications. Colors denote the response to instantaneous multiplicative changes in CO 2 concentration relative to a 1× baseline. Dashed lines denote latent heat flux, and solid lines denote precipitation. Responses are calculated using 96-member ensembles of 1-month-long simulations from EAMv2 and columnwise ACE.
Figure 5: Spatial Pattern of Precipitation and Latent Heat Flux Fast Response to 8 × CO 2 . Spatial patterns are calculated from the first seven days after CO 2 is instantaneously octupled. Panels (a) and (b): response from the physics-based E3SM Atmosphere Model; panels (c) and (d): response from our modified ACE architecture with column diagnostics and prognostics. Panels (a) and (c): spatial pattern of the response of precipitation; panels (b) and (d): corresponding response of latent heat flux converted to equivalent precipitation units.
Symbol
Description
Units
Time
Variable Type
Tk
Air temperature
K
Snapshot
Prognostic
Ts
Skin temperature of land or sea ice
K
Snapshot
Prognostic
qkT
Specific total water (vapor + condensates)
kg/kg
Snapshot
Prognostic
Uk
Wind speed in eastward direction
m/s
Snapshot
Prognostic
Vk
Wind speed in northward direction
m/s
Snapshot
Prognostic
ps
Atmospheric pressure at surface
Pa
Snapshot
Prognostic
Table 1: List of variables used in ACE. Forcing variables are input-only, diagnostic variables are output-only, and prognostic variables are both input and output by ACE.
k
ak [Pa]
bk [unitless]
Ik
pkref [hPa]
0
10.0
0.0
0
0.1
1
4943.694
0.0
19
49.4
2
13913.118
0.0
30
139
3
16254.503
0.10464
38
267
4
12435.282
0.31152
44
436
5
8945.939
0.50053
48
590
Table 2: Hybrid vertical coordinate parameters and reference pressures for ACE model level interfaces Duncan et al. (2024) . Ik indexes EAMv2 model interfaces. Pressure p=ak+bkps where ps is the surface pressure. pkref is computed for ps=1000 hPa.
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Diagram of ACE Architecture Changes for Columnwise Diagnostics . ACE has input-only variables (called forcing variables), output-only variables (called diagnostic variables), and variables that are both input and output (called prognostic variables). Panel (a): the default ACE architecture uses the Spherical Fourier Neural Operator (SFNO) architecture for all variables Duncan et al. (2024) . SFNO is not a column-local architecture; rather, it is a global architecture that makes predictions using nonlocal information via a spherical harmonic transform. Panel (b): our proposed ACE architecture has two modifications depicted in red relative to the default ACE architecture. First, the diagnostic variables are diagnosed solely based on a column-local neural network architecture. Second, the prognostic variables are calculated from the sum of two networks: the SFNO and another column-local architecture.
Figure 7: Global Mean Fast Response to Instantaneous Changes in CO 2 Concentrations . Same as Figure 4 but for the default ACE architecture Duncan et al. (2024) . This architecture does not contain the columnwise modifications described in Section 4.6 .
Figure 8: Spatial Pattern of Fast Responses of Precipitation and Latent Heat Flux to 8 × CO 2 . Same as Figures 5 (a) and (b) but for the default ACE architecture Duncan et al. (2024) . This architecture does not contain the columnwise modifications described in Section 4.6 .
Figure 9: Visualization of Heating Rate Perturbations . Longwave clear-sky heating rate perturbations for concentrations of CO 2 set to 0.5, 2, 4, and 8 × its concentration in 2010 CE. Heating rate perturbations are calculated from RRTMG using Equation 1 . Heating rates are shown for a single representative timestep and apply to temperatures T7 in layer 7 of ACE (Table 2 ), i.e., the temperatures at the model level closest to the surface. The global means are shown in the boxes in the bottom left of each panel.
Figure 10: Ensemble Spread as a Function of Lead Time . Same as the 2 × CO 2 simulation shown in Figure 4 , but the shading denotes the standard deviation of the ensemble response as a function of the number of hours from initialization.
Figure 11: ACE Response to Idealized Heating Rate Perturbations . The response to the idealized heating rate perturbation in Equation 2 is shown for the default ACE and the columnwise ACE. The expected response to the perturbation is calculated assuming a global-mean Bowen ratio of 0.23 obtained from EAMv2. The shading denotes the expected range of the response, based on water vapor only condensing to liquid water (in which case Lv is used) or exclusively depositing as ice and snow (in which case Lv+Lf is used). See Section 4.5 for the derivations.
Figure 12: Spatial Pattern of Precipitation and Latent Heat Flux Fast Response to 8 × CO 2 . Same as Figures 5 and 8 but the spatial patterns are averaged over 28 days of simulation.
Figure 13: Histogram and Zonal Spectra of Precipitation . Panel (a): the histogram of daily mean precipitation for the default ACE, columnwise ACE, and EAMv2 training dataset. Panel (b): the meridional-mean zonal power spectrum of daily mean precipitation across all grid points over 10 years.
Figure 14: ACE Precipitation Hovmöller Diagram . Hovmöller diagrams of 1×CO2 daily mean tropical-mean precipitation are shown over two years with a bandpass filter to retain 20–100 day periods. Diagrams use the default ACE, columnwise ACE, and EAMv2 training dataset in the left, center, and right columns, respectively. D
Figure 15: Spatial Pattern of Bias . Bias maps comparing the columnwise ACE (left column) to the default ACE (right column). Bias is calculated by comparing an 8-year ACE rollout to the corresponding mean values of the EAMv2 out-of-sample test set. Bias maps are shown for precipitation (“Precip”), latent heat flux (“LHFLX”), outgoing shortwave at the top of the atmosphere (“SW ↑ TOA”), and outgoing longwave at the top of the atmosphere (“LW ↑ TOA”). Values in the bottom left corner of each figure denote the global latitude-weighted root mean squared bias (RMSB).
Abrupt4xCO2
piControl
Variant
Variant
Model
and Grid Label
and Grid Label
ACCESS-CM2
r1i1p1f1_gn
r1i1p1f1_gn
CMCC-CM2-SR5
r1i1p1f1_gn
r1i1p1f1_gn
CNRM-ESM2-1
r1i1p1f2_gr
r1i1p1f2_gr
CanESM5
r1i1p1f1_gn
r1i1p1f1_gn
Appendix
Table 3: The following lists the CMIP models and the model variants used to create Figure 1 .
Figure 16: Fast Responses in the Default ACE Architecture with Moisture Constraints . The response of precipitation (“P”) and latent heat flux(“LHFLX”) to 4× CO 2 is shown in the default ACE architecture with moisture and dry air conservation Watt-Meyer et al. (2025) added during training. Left (right) panels: Moisture conservation imposed by Equations 19 ( 20 ). The response is calculated only using the two years in the validation set (simulation years 0064-0065).
Figure 17: Fast Responses in the Columnwise ACE Architecture with SFNO and the Column Diagnostic Network Trained Separately . The response of precipitation (“P”) and latent heat flux (“LHFLX”) to 4×CO2 is shown in a columnwise ACE architecture with a modified training setup. First, SFNO is trained for the prognostic variables. Then, the weights of SFNO are frozen and the column diagnostic network is trained. The fast response is calculated only using the two years in the validation set (simulation years 0064-0065).
Figure 18: 10-year Bias using Planar Convolutions for Columnwise Diagnostics. Same as Figure 15 but for a model that uses planar 3×3 diagnostics.
Figure 19: Fast Responses in a Columnwise ACE Architecture with Column Diagnostics but No Column Prognostics . The response of precipitation (“P”) and latent heat flux (“LHFLX”) to 4×CO2 is shown in a columnwise ACE architecture with a column diagnostic network but no column prognostic network. See Figure 6 for a description of these two networks. The fast response is calculated only using the two years in the validation set (simulation years 0064-0065).
Figure 20: Fast Responses in a Columnwise ACE Architecture with No Position Embedding for Diagnostics . The response of precipitation (“P”) and latent heat flux (“LHFLX”) to 4×CO2 is shown in a columnwise ACE architecture with no position embedding used in the diagnostic network. The position embedding is a learnable vector added to each grid cell in the latent space of ACE. The fast response is calculated only using the two years in the validation set (simulation years 0064-0065).
Figure 21: 10-year Bias using Purely Local Column Diagnostics. The diagnostic architecture presented in Figure 15 uses a 3×3 convolution kernel in its first layer, which implies that the diagnostic variables are predicted using a 3×3 window. This figure shows the bias maps of a 10-year rollout on the validation set, with no nonlocal window.
Figure 22: Precipitation Response to Increased CO 2 in NeuralGCM Panel (a) shows the response from a version of NeuralGCM that predicts precipitation and diagnoses evaporation as a residual. Panel (b) shows the response from the other version of NeuralGCM, which predicts evaporation and diagnoses precipitation as a residual.
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Shan Zhao, Ilija Trajkovic, Julia Kaltenborn +4
Technical University of Munich Munich, Germany · Karlsruhe Institute of Technology Karlsruhe, Germany · McGill University & Mila Montreal, Canada +1
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1INRIA, Paris, France · 2MILA, Montreal, Canada · 3Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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