Last Glacial Maximum pattern effects reduce climate sensitivity estimates

Here, we show that the Last Glacial Maximum (LGM) provides a stronger constraint on equilibrium climate sensitivity (ECS), the global warming from increasing greenhouse gases, after accounting for temperature patterns. Feedbacks governing ECS depend on spatial patterns of surface temperature (“pattern effects”); hence, using the LGM to constrain future warming requires quantifying how temperature patterns produce different feedbacks during LGM cooling versus modern-day warming. Combining data assimilation reconstructions with atmospheric models, we show that the climate is more sensitive to LGM forcing because ice sheets amplify extratropical cooling where feedbacks are destabilizing. Accounting for LGM pattern effects yields a median modern-day ECS of 2.4°C, 66% range 1.7° to 3.5°C (1.4° to 5.0°C, 5 to 95%), from LGM evidence alone. Combining the LGM with other lines of evidence, the best estimate becomes 2.9°C, 66% range 2.4° to 3.5°C (2.1° to 4.1°C, 5 to 95%), substantially narrowing uncertainty compared to recent assessments.


Supplementary Text
Text S1.Forcing Efficacy and Pattern Effects.
In this section, we briefly consider the relationship between "efficacy" and pattern effects, which has been investigated in a recent study (59).The efficacy framework (55) translates one unit of forcing by a non-CO2 agent, e.g., ice sheets, into the equivalent amount of CO2 forcing which would cause the same global-mean ΔT.While past research on forcing efficacy has considered that different forcings have different temperature impacts (55), analyses using the efficacy framework for the LGM have produced disparate results (22,23,42,43,48,56), possibly due to simplified physics of intermediate-complexity models (42,43).Because of these results, WCRP20 inflates uncertainty on LGM forcings.
The pattern effect, combined with temperature dependence, can equivalently explain forcing efficacy (59).We use the pattern-effect framework rather than efficacy because it allows for quantification of feedback changes in AGCMs using observational constraints on SST patterns from data assimilation and has strong theoretical underpinnings (12,18,59).The pattern-effect framework is oriented around the climate feedback, λ, which is the key uncertain parameter for climate sensitivity.We follow methods in WCRP20 (1) to account for Δλ for the LGM in estimates of modern-day climate sensitivity.We refer readers to Zhou et al. (2023) (59) for further explanation of the connection between efficacy and pattern-effect frameworks.
Text S2.LGM Pattern Effects in Coupled Models.
Simulations with mixed-layer ocean models coupled to AGCMs (known as slab ocean models (47), "SOM" hereafter) in CESM1-CAM5 (23), CESM2.1-CAM6(48), and CESM2-PaleoCalibr (49) illustrate pattern effects in coupled models.Note that feedbacks from ocean dynamics are excluded in the SOM, and models' SST/SIC patterns are not constrained by proxy data, hence we use the SOM only to support interpretation of the LGM pattern effect.Feedbacks in SOM simulations are calculated as λ=ΔERF/ΔT, where the effective radiative forcing (ERF) is determined from introducing forcings in separate simulations in the corresponding AGCMs (keeping SST/SIC fixed at pre-industrial values), and ΔT is the equilibrium change in globalmean near-surface air temperature in the SOM (also known as reference-height temperature, or "TREFHT" in CESM name conventions).The ERF is affected by changes in land-surface temperatures, which are not held constant in AGCM simulations due to practical limitations, and an adjustment (23,55) to the ERF can be made to account for land changes-see Zhu & Poulsen (2021) (23) for methods.
This adjustment, which is based on a climate sensitivity parameter (23) can also be applied to estimate an "adjusted ERF" for LGM ice sheets, although it is difficult to assess the validity of the adjustment for ice-sheet forcing, which affects not only land temperatures but also topography.Radiative kernels based on modern climate would typically be used to validate the ERF adjustment (23), but they cannot be applied with LGM topography.SI Appendix, Figure S11, shows feedbacks from coupled models using both ERF and adjusted ERF.Note that these values do not affect our quantification of Δλ for ECS calculations, which comes from AGCM simulations.
Text S3. Preparation of SST/SIC Boundary Conditions.
SST and SIC boundary conditions (BCs) for the LGM, Late Holocene baseline, and 2xCO2 are prepared to enable consistent calculation of the net feedback (λ) that is applicable to a modern-day doubling of CO2.When changing the surface BCs in AGCM simulations to compute λ, ΔF=0 in Eq. 1 only if there are no changes in land-sea distribution or ice-sheets.For the LGM and Late Holocene datasets, we adjust for differences in land-sea distribution, determined from refs.(89,90), compared to present day using kriging and extrapolation near coastlines in polar regions.While sea-level changes must be neutralized to preserve ΔF=0 in the AGCM simulations, infilling SST over the Sunda Shelf represents a notable uncertainty (28,91).The alternative option, holding all forcings constant at LGM rather than modern values, would require changing modern topography to include LGM ice sheets and inherit sea level of the LGM.Those changes could introduce more uncertainty in estimates of λ that are relevant to future warming.Here we only consider the framework with constant modern-day forcings.
For SST, kriging is performed across overlapping subset regions of radius≈3000 km spaced around the globe.Results for overlapping subset regions are merged using inverse-distance weighting from the center of each subset region.Kriging results are retained only where no preexisting SST value exists in a dataset.Over polar regions and inland waters, inverse-distance extrapolation populates the SST field.
For SIC, all values are first required to be no less than the ice-sheet fraction at that location, i.e., modern seas that were covered by ice sheets at the LGM, such as the Hudson Bay, are assigned a minimum SIC that equals the LGM ice fraction at 21,000 years ago (89,90).For modern seas which were land but not ice sheet at the LGM, SIC is populated based on the SST.This step uses the SIC formula from the CAM boundary condition protocol (92), where SIC=100% if SST<-1.8°C,SIC=0% if SST>4.97°C, and otherwise the infilled SIC=0.729-((SST+1.8)/9.328) 1/3 .Gaussian smoothing is applied to the result, reducing any sharp boundaries caused by the infilling.The SIC formula above is also applied to maintain internally consistent values of SST and SIC (92) in the Late Holocene baseline.See SI Appendix, Text S4, for uncertainty tests regarding sea ice.
The Annan dataset includes only annual SST and no reconstruction of SIC.Because SIC is required in all AGCMs, we assign the SIC from Amrhein to the Annan data.In a CAM4 test using the LGMR SIC with Annan SSTs (instead of the Amrhein SIC), Δλ is marginally more negative (λLGM changes by < 0.1 Wm −2 K −1 ).This result suggests that uncertainty from assigning a SIC reconstruction to Annan SSTs is small compared to uncertainty in the SST reconstruction.We assign the Amrhein SIC for the Annan SST in our main results because this choice is more conservative in that it reduces the magnitude of the mean LGM pattern effect.For consistency, the Annan SST is assigned the annual cycle from the Amrhein data for SST/SIC.
HadCM3L results use years 500-700 due to an output error in the pre-industrial control run after year 700.All LongRunMIP results are regridded to a standard 1.9º x 2.5º lat-lon grid.For SIC, monthly output is available, and we compute a 200-yr climatology for each model and then a multi-model-mean climatology.For SST, annual output is available for each model and monthly output from MIROC3.2.We compute the 200-yr mean SST anomaly for each model and then apply the annual cycle from MIROC3.2 to the multi-model mean.We also show results in SI Appendix, Fig. S3-S4, which do not use the LongRunMIP-2xCO2 BC and instead use 150-year regressions (73) of abrupt-4xCO2 from parent coupled models corresponding to each AGCM used in this study, thereby sampling uncertainty in warming patterns because the 150-year regressions are produced from different models' warming patterns.
For the "pattern-only" simulations with SST anomalies normalized to −0.5 K, we make the following changes to the LGM and 2xCO2 BCs.For the LGM, we use the LGMR SST.For 2xCO2, we use the LongRunMIP SST.We compute the global-mean ΔSST for both datasets as ΔSST 0000000 , and we multiply all local SST anomalies by the scale factor −0.5/ΔSST 0000000 .This scaling causes the resulting global-mean ΔSST to become −0.5 K, but the spatial pattern of the SST anomalies is unchanged.We use −0.5 K for both the LGM and 2xCO2 so that there is no cooling-warming asymmetry, and ΔT is small enough that temperature dependence of λ is negligible (i.e., ΔλT≈0, and Δλ≈ΔλPatternOnly).ΔT is still large enough that we can compute λ=ΔN/ΔT without requiring an excessively long simulation to overcome noise in the denominator.We use the baseline SIC (Late Holocene) in all of the pattern-only simulations so there are no changes in sea ice, so this set of simulations also serves to check whether Δλ is attributable to SIC rather than SST changes.
To examine whether the pattern-only results are sensitive to the scaling method of separating pattern effects, we tested an alternative subtraction method in CAM4 (using the LGMR pattern for the LGM and the LongRunMIP pattern for 2xCO2).We ran alternative pattern-only simulations with global-mean SST anomalies set to zero by subtracting the global mean at all locations.These experiments produced consistent results for ΔλPatternOnly compared to scaling.
An additional simulation was run in HadGEM3-GC3.1-LLwith SIC held constant at the Late Holocene baseline while the SST field is varied with the full value of anomalies, using the LongRunMIP-2xCO2 and LGMR patterns of SST.Results from this simulation are shared in SI Appendix, Text S4.
This concludes the preparation steps for the main simulations (BCs from four dataassimilation reconstructions for the LGM, one Late Holocene, and one 2xCO2) and the "patternonly" simulations (two additional BCs: LGMR and LongRunMIP-2xCO2 scaled to −0.5 K).The final adjustment to each BC follows the standard boundary-condition protocol for CAM, known as "bcgen."This process ensures that SIC and SST are plausibly bounded (e.g., SIC between 0 and 1), and it transfers the monthly climatology to mid-month values which can be linearly interpolated in an AGCM.
To include the LGM pattern effect in the Bayesian framework of WCRP20, we must assign a statistical distribution to Δλ for the LGM (following WCRP20's method for Δλ in the historical record).In this section we provide additional detail on combining uncertainty from AGCM physics and LGM reconstructions with bootstrapping.
To evaluate the sensitivity of our uncertainty quantification to the size of our sample of AGCMs and reconstructions, we calculate a bootstrap confidence interval (CI) on our estimate, σ 6, of the standard deviation of Δλ as follows.First, we construct a sample where each AGCM is equally weighted and the spread from various LGM reconstructions is included in the sample (as described below).We then use bootstrapping of this sample to provide confidence bounds on our estimate (σ 6) of the population standard deviation from the sample standard deviation.
To create the equally weighted sample, we assume that the spread around the LGMR feedback (of the feedbacks from Amrhein, Annan, and lgmDA) would be the same in GFDL-AM4, HadGEM3-GC3.1-LL,and CAM6 as they are in CAM4 or CAM5.We include the simulations using the extreme quartiles from Annan and LGMR in the sample.This assumption yields a sample of 40 values of Δλ based on ( 4LGM patterns + 2 extreme-quartile LGMR patterns + 2 extreme-quartile Annan patterns) x (5 AGCMs).We proceed with bootstrapping by sampling with replacement from the 40 values of Δλ.We generate 10 5 samples of size n=19, choosing this sample size for the bootstrap because there are 19 direct estimates of Δλ from simulations in the AGCMs.This process yields 10 5 bootstrapped values of σ 6 from which we derive the 95% CI: (0.15, 0.31) Wm −2 K −1 .Note that the upper bound of 0.31 Wm −2 K −1 is much less than two times the population standard deviation of 0.23 Wm −2 K −1 that we assign to Δλ, indicating that doubling the assumed standard deviation for Δλ is a more conservative uncertainty test (SI Appendix, Fig. S4) than using the bootstrapped 95% bound.
To determine the distribution of Δλ in SI Appendix, Figure S4, we repeat the bootstrap estimate using λ4x(150yr)/1.06instead of λ2x, where 1.06 represents WCRP20's central estimate (1) for the timescale adjustment between the 150-year feedback and the equilibrium feedback; this yields Δ!=−0.27Wm −2 K −1 and mean sample standard deviation of 0.20 Wm −2 K −1 .
Our method of combining uncertainty gives equal weight to the most-extreme quartiles and to the central estimates, but this overestimate of uncertainty is warranted given that paleoclimate data assimilation may underestimate the true uncertainty (35).The uncertainty estimate also gives more weight to the most recent reconstructions, LGMR (32) and Annan (33), by including three simulations (mean, 1 st quartile, and 4 th quartile) from these datasets.The weighting influences the bootstrap estimate and the distribution assigned to Δλ in our calculations of ECS.
Over the range of temperatures between the LGM and 2xCO2, all five AGCMs appear to have weaker temperature dependence of feedbacks than WCRP20 assumes, i.e., ΔλT appears smaller than in WCRP20.ΔλT could be underestimated in all models, so we include an uncertainty test where we use the pattern-only simulations in CAM4, CAM5, and CAM6 to estimate the mean ΔλPatternOnly contribution to the total ∆λ, and we retain WCRP20's estimate of ΔλT.In this uncertainty test, Δλ in Eq. 6 is calculated as the sum of ΔλT and ΔλPatternOnly: ΔλT=−αΔT/2 with α~N(0.1,0.1) Wm −2 K −2 as in WCRP20, while ΔλPatternOnly~N(−0.51,0.23) Wm −2 K −1 with μ based on CAM4, CAM5, and CAM6 results (SI Appendix, Table S3).The results of this uncertainty test are included in SI Appendix, Figure S9, indicating that accounting for pattern effects causes the dominant change to LGM evidence for ECS, while the revision to WCRP20's temperature dependence contributes a smaller portion of the update.
Sea-ice reconstructions, which are not well constrained, contribute to uncertainty in the LGM pattern effect.However, the uncertainty due to sea ice appears small compared to the uncertainty across AGCM physics and in the SST pattern.In an additional set of simulations with HadGEM3-GC3.1-LL, the SST anomalies are applied in full at the LGMR, Late Holocene, and LongRunMIP-2xCO2 values while the SIC is held constant at the Late Holocene values.These simulations make λ2x and λLGM more negative by eliminating the positive ice-albedo feedback, but the difference in the feedbacks, Δλ, is largely unaffected.Constant SIC produces Δλ = −0.28Wm −2 K −1 , compared to −0.27 Wm −2 K −1 in the main simulations for HadGEM3-GC3.1-LL.SIC is also held constant in the pattern-only simulations, which produce Δλ<0.While our results appear robust despite uncertainty in SIC, substantially different LGM reconstructions or SIC responses to modern-day 2xCO2 could change the resulting Δλ.Future work should continue investigating the role of sea ice in paleoclimate pattern effects.First column shows total Δλ=λ2x−λLGM from Figure 2, calculated in main simulations with full SST anomalies and SIC for 2xCO2 and LGM (using LGMR reconstruction).Second column shows pattern-only simulations with global-mean ΔSST scaled to −0.5 K, where ΔλPatternOnly≈λ 4@ %-./A − λ *+, %-./A .Third column shows temperature dependence, ΔλT, approximated as the residual difference between the main and pattern-only simulations, ΔλT≈Δλ-ΔλPatternOnly. Results in (A) CAM4, (B) CAM5, and (C) CAM6.LGM pattern effect (Δλ) calculated as difference in net feedbacks (λ) from 2xCO2 and LGM.λ2x is calculated in AGCM simulations with LongRunMIP (39) 2xCO2 pattern of SST/SIC.λLGM is calculated in AGCM simulations with LGMR (32) pattern.Alternative values for (Δλ) are shown using 150-year regression of abrupt-4xCO2 from coupled models corresponding to each AGCM (17).ζ is assumed to be 0.06 based on WCRP20's central estimate (1).Efficacy, ε, shown in right column.Note that CAM6 is an outlier in efficacy calculations.
LGM pattern effect and climate feedbacks from various SST patterns.LGM pattern effect (Δλ) from net feedbacks (λ) in 2xCO2 and with various LGM patterns of SST/SIC.λ2x is calculated in AGCMs with LongRunMIP (39) 2xCO2 pattern of SST/SIC.λLGM is calculated in AGCM simulations with four LGM patterns.Global-mean anomalies for SST, near-surface air temperature (T), and top-of-atmosphere radiative imbalance (N) are shown for reference.Values for LGM pattern effect are also shown using 150-year regression of abrupt-4xCO2 from coupled models (17).ζ is assumed to be 0.06 based on WCRP20 central estimate (1).Efficacy, ε, shown in right column.

Δλ=λ2x-λLGM Wm
Table S3.Climate feedbacks and temperature dependence from pattern-only simulations.Note: The posterior PDF from LGM evidence alone uses the uniform-S prior (0, 20) K, hence the shape of the posterior PDF matches that of the LGM likelihood.Methods follow WCRP20 (1).
Text S5.Zonal-mean Feedbacks.SI Appendix, FiguresS12-S22show zonal means (indicated by brackets as [λ]) of the global-mean feedbacks that appear in SI Appendix, FigureS6.The net feedback, clear-sky shortwave (SW), clear-sky longwave (LW), and cloud radiative effect are calculated directly from model output.The remaining feedbacks are from radiative kernel decomposition (Materials and Methods) using CAM5 kernels(77,100).GFDL-AM4's 2xCO2 simulation has error in the kernel-derived clear-sky feedback equal to 15.6% of the actual feedback, exceeding the 15% threshold commonly used as a test of clear-sky linearity(15,76,101); all other simulations have clear-sky feedback errors less than 10%.Total cloud feedback is also shown as the sum of kernel-derived SW and LW components.Each of the zonal-mean figures consists of: (A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in panel A. (C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in panel C. Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited availability of model output.

Fig. S1 .
Fig. S1.Differences in LGM sea-surface temperature (SST) patterns compared to 2xCO2 reference pattern.All local anomalies are normalized through division by global-mean anomaly, then differences between the 2xCO2 pattern and LGM pattern are taken.Red regions indicate where SST anomalies are relatively more amplified in 2xCO2, while blue regions indicate where SST anomalies are relatively more amplified at the LGM.(A-E), LGM patterns corresponding to Fig. 1A-E, and 2xCO2 reference pattern is Fig. 1F from LongRunMIP-2xCO2.(F) In CESM1-CAM5 (23) mixed-layer ocean model without data assimilation, difference between 2xCO2 and LGM patterns (shown in Fig. S5C-D).

Fig. S3 .
Fig. S3.LGM pattern effect (Δλ) based on LGM climate feedbacks in AGCMs and CO2 climate feedbacks from 150-yr regression of abrupt-4xCO2 in coupled models.Similar to Fig. 2, except λ2x is replaced by λ4x(150yr)/1.06,the feedback from regression in abrupt-4xCO2 simulations (73) using parent coupled models corresponding to each AGCM; a timescale adjustment of 1/1.06 is applied based on the WCRP20 central estimate (1) to make 150-year 4xCO2 feedbacks comparable with λLGM equilibrium feedbacks.Different models (all using the LGMR pattern for the LGM) are indicated by symbols.Different LGM patterns (in CAM5 and CAM4) are indicated by colors.(A) Scatter plot of 4xCO2 feedbacks (including adjustment factor of 1/1.06) versus LGM feedbacks, with λ4x(150yr)/1.06=λLGMshown as dashed line.(B) LGM pattern effect, Δλ= λ4x(150yr)/1.06−λLGM,using feedbacks shown in (A), with Δλ=0 shown as dashed line.Note that Δλ includes SST pattern effects and contributions from temperature dependence.

Fig. S5 .
Fig. S5.Spatial patterns of sea-surface temperature (SST) response and effective radiative forcing (ERF) in CESM1-CAM5 model simulations from Zhu & Poulsen (23).Spatial patterns here are shown as zonal means in Fig. 2. All local anomalies are normalized through division by absolute value of global-mean anomaly.(A-B) SST patterns in quasiequilibrium from fully coupled atmosphere-ocean model with LGM ice-sheet and greenhousegas forcings (23) compared to abrupt-4xCO2.(C-E) Equilibrium SST patterns from mixed-layer ocean model coupled to CAM5, including a simulation with only LGM ice-sheet forcing (23).(F-H) ERF patterns from corresponding AGCM simulations in CAM5.

Fig. S6 .
Fig. S6.Feedback decomposition of Last Glacial Maximum (LGM) and 2xCO2 climate feedbacks in atmospheric general circulation models (AGCMs).Left column uses direct model outputs in scatter plots of 2xCO2 feedbacks (λ2x) versus LGM feedbacks (λLGM), with λ2x=λLGM denoted by dashed line.Cloud radiative effect (CRE), shortwave clear-sky (SWcs), longwave clear-sky (LWcs), and net feedbacks are shown.(A) Results from various AGCMs, all using the LGMR reconstruction for the LGM.(B) Results from various LGM reconstructions in CAM4 and CAM5, with different reconstructions indicated by colors.Right column shows decomposition of Δλ using CAM5 radiative kernels (100), with residual equal to the net feedback in models minus the sum of kernel-derived feedbacks.(C) Results from various AGCMs (note that only net λ is available for HadGEM3).(D) Results from various LGM reconstructions in CAM4 and CAM5.Lapse rate and water vapor feedbacks are combined (LR+WV) given their anti-correlation across models (102).Note that Δλ includes SST pattern effects and contributions from temperature dependence.

Fig. S7 .
Fig. S7.Spatial decomposition of Last Glacial Maximum (LGM) and 2xCO2 local climate feedbacks in atmospheric general circulation models (AGCMs).Local feedbacks represent local change in top-of-atmosphere radiation (ΔNlocal) divided by global-mean change in near-surface air temperature (ΔTglobal); global integrals of the local feedbacks equal the global-mean feedbacks.Top row shows net feedback (λNet) from total all-sky changes in ΔN, second row shows λClearSky from changes in ΔN attributable to clear-sky radiation, third row shows cloud radiative effects (λCRE); rows 1-3 use direct model output.Fourth row shows radiative-kernel estimates of shortwave cloud feedbacks (λ 9:;<= >? ).(A) 2xCO2 multi-model mean based on five AGCM simulations using LongRunMIP (39) pattern.(B) LGM multi-model mean based on five AGCM simulations using LGMR (32) pattern.(C) LGM multipattern mean in CAM5 using four LGM reconstructions.Note that radiative-kernel results for λ 9:;<= >? exclude HadGEM3 due to output limitations.

Fig. S10 .
Fig. S10.Patterns of SST anomalies from Annan (33) ensemble members in quartile with strongest negative climate feedback (λ).19 ensemble members are ranked by estimated λ, which is produced from CAM5 Green's functions (18), and 5 members shown comprise the quartile with most-negative estimated λ. (A-E) Data-assimilation posterior SST using model priors specified in subtitles.(F) Pattern of the quartile-mean SST.To show SST patterns, local SST anomalies are normalized into patterns through division by absolute value of global-mean SST anomaly (consistent with feedbacks being radiative responses divided by global-mean temperature anomalies).All panels show annual means.LGM reconstructions are infilled to modern coastlines (Materials and Methods).

Fig. S11 .
Fig. S11.Feedbacks and Δλ using either effective radiative forcing (ERF) or adjusted ERF from previously published simulations in mixed-layer ocean models.(A)Scatter plot of λ2x vs. λLGM in mixed-layer ocean models; λLGM is shown for simulations using only the LGM ice-sheet forcing (dark blue), which includes LGM sea-level changes, and for simulations using LGM ice-sheet forcing and greenhouse-gas (GHG) forcings (royal blue).Dashed markers indicate corresponding results using "adjusted ERF" to calculate feedbacks.(B) Δλ based on feedbacks shown in panel A. Note that in LGM simulations using CESM2.1-CAM6(48) and CESM2-PaleoCalibr (49), the LGM ice-sheet forcing and GHG forcing are applied in separate simulations, and their sums are shown as LGM Ice & GHG.This linearity assumption was validated in CESM1-CAM5(23).

Fig. S12 .
Fig. S12.Zonal-mean net feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S13 .
Fig. S13.Zonal-mean shortwave clear-sky feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S14 .
Fig. S14.Zonal-mean longwave clear-sky feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S15 .
Fig. S15.Zonal-mean cloud radiative effect and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S16 .
Fig. S16.Zonal-mean Planck response and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S17 .
Fig. S17.Zonal-mean lapse rate feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S18 .
Fig. S18.Zonal-mean water vapor feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S19 .
Fig. S19.Zonal-mean surface albedo feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S20 .
Fig. S20.Zonal-mean shortwave cloud feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S21 .
Fig. S21.Zonal-mean longwave cloud feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.

Fig. S22 .
Fig. S22.Zonal-mean total (shortwave + longwave) cloud feedback and Δλ.(A) In CAM5, mean and range of feedbacks across four LGM reconstructions and 2xCO2 from LongRunMIP.(B) In CAM5, mean and range of the difference in feedbacks (Δλ = λ2x − λLGM) across four LGM reconstructions from results in (A).(C) Feedbacks across various AGCMs, using the LGMR reconstruction of the LGM and 2xCO2 from LongRunMIP.(D) Mean and range of Δλ across various AGCMs from results in (C).Note that HadGEM3 is not included in the kernel-derived feedbacks due to limited model output.