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Equilibrium Climate Sensitivity dependence on changing climate, geography, and ocean heat transportJuliaCampbell1✉Emailjuliacam@umich.edu
ChristopherJ.Poulsen2
1Earth and Environmental SciencesUniversity of MichiganAnn ArborMI)USA
2University of Oregon, (Earth Sciences)EugeneUSA
Julia Campbell1 & Christopher J. Poulsen2
1University of Michigan, (Earth and Environmental Sciences), Ann Arbor, (MI), USA
2University of Oregon, (Earth Sciences), Eugene, (OR), USA
Corresponding author: Julia Campbell (juliacam@umich.edu)
ORCID: Julia Campbell (0009-0002-8699-5194), Christopher J. Poulsen (0000-0001-5104-4271)
Abstract
Equilibrium climate sensitivity (ECS) – the global temperature response to doubling CO2 – can be better understood by examining past climate states and the feedback mechanisms regulating CO2-induced warming. While studies agree that ECS increases with higher CO2, the range of Earth’s historical ECS and its underlying drivers remain incompletely understood. Here, we use slab ocean Community Earth System Model simulations to analyze four distinct periods in Earth's climate history with substantially different continental configurations: the late Cretaceous, early Eocene, late Oligocene, and preindustrial. Our results show that ECS varies by over 2.5°C, ranging from 4.04°C to 6.66°C. We analyze the contributions of CO2 background, geography, and ocean heat transport to ECS variability and decompose the total climate feedback parameter into the water vapor, cloud, surface albedo, and temperature feedbacks. Using a consistent model framework across geological epochs, we provide new constraints on ECS sensitivity to boundary conditions and offer insights into its variability throughout Earth's history.
1 Introduction
As anthropogenic emissions continue to rise, global temperatures are increasing at an unprecedented rate in Earth’s known history (IPCC 2021). Despite efforts to narrow estimates, the range of modern-day equilibrium climate sensitivity (ECS) – the equilibrated surface warming due to a doubling of atmospheric CO2 – remains uncertain (Knutti et al. 2017; Zelinka et al. 2020). In the absence of long-term historical analogs for the rapid CO2 rise occurring today, past warm climates serve as valuable benchmarks for evaluating climate models (Tierney et al. 2020; Zhu et al. 2020). Climate feedbacks largely control the warming response to CO2 increases and are affected by model boundary conditions. ECS is traditionally understood in terms of the water vapor, cloud, surface albedo, and lapse-rate feedbacks (Farnsworth et al. 2019; Zhu et al. 2022; Landwehrs et al. 2021; Singh et al. 2022; Li et al. 2012; Hansen et al. 1984; Held and Soden 2000).
Although there is no completely comprehensive understanding of how ECS has varied throughout Earth’s history, several studies have advanced our knowledge of its potential variability. Model boundary conditions that influence climate feedbacks and therefore likely impact ECS include greenhouse gas levels, geographic configuration, and ocean heat transport (OHT) – the redistribution of heat from the equator to the poles, primarily driven by ocean currents and temperature gradients. Greenhouse gases, predominantly CO2, trap outgoing longwave radiation in the atmosphere, reheating the Earth’s surface and amplifying the water vapor feedback. There is broad agreement that ECS has likely varied across geologic time and, more specifically, increases with the CO2 background state and mean temperature (Caballero and Huber 2013; Eisenman and Armour 2024; Royer 2016; Köhler et al. 2015; Meraner et al. 2013; Shaffer et al. 2016; Zhu et al. 2020; Zhu and Poulsen 2020).
The continental configuration can significantly affect climate feedback systems. Recent work examining the Mesozoic (~ 252 to 66 million years ago) and the Last Glacial Maximum (~ 20,000 years ago) has shown that changes in geography and cloud feedbacks can meaningfully influence ECS (Landwehrs et al. 2021; Zhu et al. 2022). Farnsworth et al. (2019) analyzed HadCM3BL-modeled ECS through geologic time at a uniform CO2 level (560 ppm) with changes in continental configuration and solar luminosity. This study found that ECS is affected by geography, particularly total ocean surface area and ocean circulation, and varies between ~ 3.7℃ and 5.3℃ from the Cretaceous through the Eocene (Farnsworth et al. 2019).
The strength of the OHT determines the amount and rate at which oceanic heat is brought from the lower latitudes to the higher latitudes and can partly control spatial heating patterns. An increase in higher latitude marine warming may also lead to an increase in sea ice melt, which impacts climate feedbacks. OHT plays a key role in shaping the global climate; previous work has shown that OHT affects ECS and is sensitive to CO2 changes under pre-industrial (PI) conditions (Ferrari and Ferreira 2011; Danabasoglu and Gent 2009; Singh et al. 2022).
However, prior studies have typically investigated only one driver – CO2 background state, geography, or OHT – in isolation, often within a single climate state. In the paleoclimate context, an illuminating study by Farnsworth et al. (2019) examined ECS changes in response to solar luminosity and continental configuration changes across the Cretaceous, Paleocene, and Eocene using the HadCM3BL model. This study expands on their work by analyzing ECS changes across the Cretaceous, Eocene, Oligocene, and PI periods using the Community Earth System Model (CESM1.2). CESM1.2 is uniquely able to replicate the global temperatures and meridional temperature gradient of extreme past warming periods, like the Early Eocene (Zhu et al. 2019), and reproduce a Last Glacial Maximum climate sensitivity and temperature similar to proxy evidence (Zhu et al. 2021). Additionally, we further expand on previous work by quantitatively analyzing ECS variation through comparisons of individual climate feedback parameters – water vapor, clouds, surface albedo, and temperature. This also represents the first CESM simulations of the Late Oligocene and first modeled ECS for that time period. As a result, the model-dependency of ECS through Earth’s history, the ECS of the Oligocene, and the relative importance of each feedback mechanism in driving ECS differences between past climates can be better constrained.
Our work builds on these previous studies by modeling ECS over the past ~ 100 million years with reconstructed shifts in CO2, geographic configuration, and OHT strength. Here, we use CESM1.2, a fully-coupled global climate model, to uniformly simulate four distinct periods in Earth’s history: the late Cretaceous (~ 90 million years ago), early Eocene (~ 55 million years ago), late Oligocene (~ 25 million years ago), and the PI era. These intervals capture a broad range of geographic configurations and climate states, allowing us to assess the effects of these boundary conditions. Testing the range of past ECS can also aid us in constraining the modern-day ECS, which remains highly uncertain (Meehl et al. 2020). We further decompose the total climate feedback parameter into water vapor, cloud, surface albedo, and temperature components, providing a multi-era paleoclimate analysis of feedback contributions to ECS. Evaluating ECS in past climate states – and clarifying how atmospheric CO2, geographic configuration, and OHT influence climate feedbacks – provides critical insights into how model boundary conditions shape global temperature and climate sensitivity during Earth’s recent geologic history.
2 Methods
This study uses CESM1.2 and combines fully coupled and slab ocean model (SOM) simulations in order to quantify ECS across multiple paleoclimate intervals with varied continental configurations. We employ published Cretaceous and Eocene simulations, along with new Oligocene simulations, to explore how changes in CO2, geography, and OHT influence ECS. For each climate state, we create SOM simulations from the equilibrated coupled simulations to efficiently calculate ECS. Finally, we estimate the relative contributions of major feedbacks – water vapor, clouds, surface albedo, and temperature – using model output and established empirical relationships to enable comparison of feedback changes with ECS across climate states.
2.1 Community Earth System Model
We use CESM1.2, a fully coupled global climate model that integrates atmosphere, land, ocean, and sea ice components. CESM1.2 consists of the Community Atmosphere Model (CAM) version 5.3, Community Land Model (CLM) version 4.0, Community Ice Code (CICE) version 4.0, River Transport Model (RTM), Parallel Ocean Program (POP) version 2, and a coupler to connect them (Hurrell et al. 2013). An advantage of CESM1.2 is that it aligns well with proxy records from past climate intervals, including Eocene proxies recording warming and a weakened meridional temperature gradient (DiNezio et al. 2016; Otto-Bliesner et al. 2016; Zhu et al. 2017; Zhu et al. 2019). Our configuration includes 30 vertical levels in the atmosphere, a resolution of 1.9° x 2.5° for atmosphere and land, and a nominal 1° for ocean and sea ice.
2.2 Paleoclimate simulations
Our study includes analysis of both existing and new paleoclimate simulations. We utilize two previously published late Cretaceous simulations: one at 3x PI CO2 (CRET3x) and one at 6x PI CO2 (CRET6x), as well as a published early Eocene simulation at 3x PI CO2 (EECO3x) (Sarr et al. 2025; Acosta et al. 2022; Zhu et al. 2019). We also utilize a new late Oligocene simulation at 2x PI CO2 (OLIG2x), using a published geographic configuration by Straume et al. (2020), and finally a PI simulation at 1x PI CO2 (PI1x), publicly available from the National Center for Atmospheric Research.
The fully-coupled 3x PI CO2 Cretaceous simulation (CRET3x) was branched from a 1x PI CO2 Cretaceous simulation that had been run for ~ 1500 model years, published in Acosta et al. (2022). Ocean temperatures were then uniformly raised by 6℃. A 6℃ increase was chosen based on the expected climate sensitivity for iCESM1.2 (Zhu et al. 2019). CRET3x was then run for ~ 800 more model years. The fully-coupled 6x PI CO2 Cretaceous simulation (CRET6x) was branched from an existing ~ 1500 model year-long run in iCESM1.2 published in Acosta et al. (2022), which used boundary conditions from Community Climate System Model (CCSM4) simulations published in Ladant et al. (2020). CRET6x was then run for an additional ~ 1200 model years.
The fully-coupled 3x PI CO2 Eocene simulation (EECO3x) has paleogeography, land-sea mask, and vegetation distribution following the Deep-Time Modeling Intercomparison Project (DeepMIP) protocol at ~ 55 million years ago (Herold et al. 2014). The simulation was run for ~ 2000 model years, and the ocean temperature and salinity were initialized from a Paleocene-Eocene Thermal Maximum (PETM) quasi-equilibrated state (Zhu et al. 2020).
The fully-coupled 2x PI CO2 Oligocene simulation (OLIG2x) was run using iCESM1.2 for ~ 1600 model years. The paleogeography and land-sea mask used has been published by Straume et al. (2020). The vegetation distribution used is based on a global BIOME4 model for the Chattian (26 million years ago) by the Bristol Research Initiative for the Dynamic Global Environment (BRIDGE 2022).
2.3 Slab Ocean Model simulations
We created SOM simulations using the climatological data from each equilibrated paleoclimate simulated ocean. A slab ocean is a simplified representation of the ocean, approximating a well-mixed ocean mixed layer at each grid point; SOM configurations have been traditionally used particularly for understanding the climate sensitivity of an environment through quicker, cost-effective means (Danabasoglu and Gent 2009; Singh et al. 2022; Zhu et al. 2019). SOM simulations use climatological data from fully-coupled, equilibrated oceans to prescribe spatially and seasonally varying ocean heat flux convergence (Qflux). The model includes a thermodynamic slab ocean with a prescribed mixed layer depth that varies spatially but does not simulate ocean currents. Surface salinity and temperature evolve prognostically, but there is no explicit advection or ocean dynamics (Kiehl et al. 2006). The Qflux is calculated using the density of seawater, ocean heat capacity, mixed layer depth, net heat flux into the ocean, and sea surface temperature (SST) (Bitz et al. 2012). A SOM simulation is still coupled with the other CESM components, but it only takes a few decades to equilibrate, even with an exceptionally high atmospheric CO2 level, and represents the foremost climatic processes that affect ECS (Danabasoglu and Gent 2009).
We ran five SOM simulations, each using one of the distinct slab oceans and geographic configurations (CRET3x, CRET6x, EECO3x, OLIG2x, and PI1x) for ~ 100 years each and produced climatological files at that original CO2 level. We then doubled the CO2 level of each simulation and ran them for another ~ 100 years to produce new climatological files at the doubled atmospheric CO2 level. For the CRET3x and PI1x simulations, we doubled CO2 a subsequent time to achieve a second ECS at a higher CO2 background state. The OHT experiment was conducted by cloning the CRET6x SOM simulation, swapping its ocean climatological data with the cooler CRET3x ocean, running the simulation for ~ 100 years, doubling CO2, and running it again (see “ECS sensitivity to ocean heat transport”). The atmospheric and land conditions of each simulation in the OHT experiment are identical to those of the fully-coupled paleoclimate simulation from which the ocean climatology was derived.
The climatological datasets from each simulation were created using the final 30 years of atmospheric output. Each simulation had a constant atmospheric CH4 concentration of 791.60 ppb and an atmospheric N2O concentration of 275.68 ppb. Unavoidable uncertainties lie within the boundary conditions, such as the geographic configuration, land ice extent, and global vegetation distribution. Other uncertainties lie in model-specific parameterizations associated with sub-grid processes, like cloud formation and evolution (Zhu and Poulsen 2020). We determine ECS by subtracting the grid-cell area weighted global mean surface temperature (GMST) of the initial SOM simulation from that of the simulation with doubled atmospheric CO2 (see Eq. 1).
1
Subscript 1 denotes the initial simulation and subscript 2 denotes the doubled CO2 simulation.
2.4 Feedback parameter estimation
To evaluate differences in ECS, we estimate the major climate feedbacks that control climate sensitivity. The dominant feedbacks controlling climate sensitivity include the water vapor feedback, cloud feedback, surface albedo feedback, and temperature feedback; the temperature feedback referenced in this study consists of the lapse-rate and Planck feedbacks (IPCC 2021; Held and Soden 2000). Radiative kernels, representative of the change in radiative flux caused by a change in a given variable, have been used to directly quantify climate feedback parameters in the modern system (Soden et al. 2008; Shell et al. 2008; Sanderson et al. 2010). However, paleoclimate simulations represent different past climates, and modern-day radiative kernels may not provide accurate estimates of the feedback parameters. Therefore, we estimate each feedback using climate model output and published empirical relationships.
The positive water vapor feedback amplifies warming and increases climate sensitivity by absorbing and trapping heat (Manabe and Wetherald 1967). We use the simulated column-integrated water vapor at each grid point, the Clausius-Clapeyron equation relating ~ 7% of water vapor increase to 1K of warming, and an observed radiative effect from Held and Soden (2000) that uses 2.0 W/m2/K as an empirical estimate for the radiative impact of water vapor to derive the water vapor feedback parameter (Eq. 2). Without radiative kernels, this is a reasonable first-order estimation of the water vapor feedback strength in different past climate states, although it is limited by assuming a fixed 2.0 W/m2/K scaling.
To calculate the net effect of the cloud feedback, we add the grid-cell area weighted negative (cooling) shortwave cloud forcing (SWCF) to positive (warming) longwave cloud forcing (LWCF) for each simulation and then find the difference and use the ECS to achieve the cloud feedback parameter (Eq. 3). The surface albedo feedback is also relatively simple to calculate from CESM output and uses the planetary energy balance approximation. We divide the total reflected albedo by the downward shortwave radiation at the surface and weight by grid-cell area to compute a global mean surface albedo, a, which is then used, along with the solar constant and ECS, to estimate the surface albedo feedback parameter (Eq. 4).
2
Qfrac is the global mean fractional increase in column water vapor and T is the GMST.
3
SWCF is shortwave cloud forcing, LWCF is longwave cloud forcing, T is the GMST, subscript 1 denotes the initial simulation, and subscript 2 denotes the doubled CO2 simulation.
4
S0 is the solar constant, a is the global mean surface albedo, A is the global mean planetary albedo, and T is the GMST.
The total climate feedback parameter, denoted by λtotal, balances positive and negative feedbacks, with the residual accounted for by the temperature feedback. λtotal is estimated as the magnitude of the radiative response to a change in GMST in W/m2/K (Eq. 5). The feedback parameters must then sum to λtotal, as shown in Eq. 6. The λtotal is near 0, as the climate system is equilibrated in each simulation, so there must be a negative residual component to balance the positive water vapor, clouds, and surface albedo components. The residual is largely accounted for by the lapse-rate and Planck feedbacks, or the combined ‘temperature feedback’, and is a negative cooling feedback parameter. The Planck feedback is the dominant and strongly negative feedback here, estimated at -3.2 W/m2/K for modern-day, and is combined with a weaker lapse-rate feedback (Soden et al. 2008). Without radiative kernels, we are unable to confidently untangle the Planck feedback from the lapse-rate feedback. For that reason, here we report the residual as the combined temperature feedback.
5
R is the top-of-atmosphere net radiative flux, λtotal is the total climate feedback parameter, and T is the GMST.
6
3 Results
3.1 ECS and climate feedback comparisons
Simulation Name | ECS | Initial GMST | Initial % Ocean | Initial % High Latitude (> 60°) Ocean |
|---|---|---|---|---|
CRET3xSOM3x◊CRET3xSOM6x | 5.57 | 25.57℃ | 73.0% | 40.5% |
CRET3xSOM6x◊CRET3xSOM12x | 6.14 | 31.14℃ | 73.1% | 41.3% |
CRET6xSOM6x◊CRET6xSOM12x | 6.66 | 30.71℃ | 73.1% | 41.4% |
EECO3xSOM3x◊EECO3xSOM6x | 6.57 | 25.24℃ | 73.6% | 48.1% |
OLIG2xSOM2x◊OLIG2xSOM4x | 5.06 | 21.95℃ | 72.1% | 46.9% |
PI1xSOM1x◊PI1xSOM2x | 4.04 | 14.73℃ | 66.6% | 22.0% |
PI1xSOM2x◊PI1xSOM4x | 4.62 | 18.77℃ | 68.6% | 35.7% |
CRET3xOHT6x◊CRET3xOHT12x | 5.77 | 31.08℃ | 73.1% | 41.3% |
While doubling CO2 increases GMST across all simulations, ECS varies by more than 2.5°C (Table 1). The highest ECS of 6.66°C occurs in the Cretaceous 6x PI CO2 case while the lowest, 4.04°C, is in the PI 1x PI CO2 case. The Cretaceous and Eocene ‘greenhouse’ climate simulations with higher initial GMST exhibit higher ECS than the Oligocene and PI ‘icehouse’ simulations. However, initial GMST alone does not determine ECS: for example, the CRET3xSOM6x simulation has the highest initial GMST at 31.14°C, yet only the third highest ECS at 6.14°C (Table 1, Fig. S7).
Fig. 1
The four key climate feedbacks affecting ECS in each simulation are shown as W/m2/K contribution to the total climate feedback parameter. The positive water vapor, clouds, and surface albedo feedbacks warm, while the negative temperature feedback cools. The right-hand plot illustrates ECS (°C) for each climate state
In our simulations, a lower ECS generally corresponds to a smaller water vapor feedback, smaller cloud feedback, and larger surface albedo feedback (Fig. 1). The water vapor feedback, governed by the Clausius-Clapeyron relationship, contributes the most to global warming. However, the range in water vapor feedback parameters across simulations is just 0.44 W/m2/K, indicating other feedbacks play a similarly substantial role in explaining variations in ECS.
SWCF, the cooling effect of reflective clouds, and LWCF, the warming effect of heat-trapping clouds, have significant impacts on climate. A reduction in SWCF indicates less shortwave radiation is reflected back to space, leading to warming, while a reduction in LWCF means less longwave radiation is trapped, lessening warming. Although both SWCF and LWCF weaken with warming in our simulations, the decline in SWCF exceeds that of LWCF in every simulation, resulting in a net amplification of warming (Figs. 1, S4). Earth’s surface albedo declines more in lower ECS simulations, driven by greater snow and sea ice melt. While the Antarctic ice sheet is prescribed in the Oligocene and PI and remains fixed, land snow cover and sea ice are free to melt, reinforcing the ice-albedo feedback, especially near the poles (Dickinson et al. 1987). In contrast, the Cretaceous and Eocene simulations exhibit less albedo-driven feedback due to limited sea ice coverage and less snow. Temperature feedbacks show a weaker correlation with ECS and greater uncertainty, as they are estimated residually from the total feedback parameter. However, the Planck feedback parameter may be generally weaker in warmer climates due to increased emission from higher, cooler, and drier atmospheric layers, which radiate less efficiently per degree of surface warming (Pithan and Mauritsen 2014; IPCC 2021).
All simulations show more intense warming on land than ocean, an omnipresent pattern linked to drier air over land causing a drop in land relative humidity which feeds back on the warming contrast, and greater warming at higher latitudes due to polar amplification (Fig. 2; Byrne and O’Gorman 2018). The Cretaceous and Eocene simulations without a prescribed Antarctic ice sheet experience enhanced warming over Antarctica, while the Oligocene and PI simulations with a prescribed Antarctic ice sheet show greater warming in the Arctic, where sea ice melting is pronounced. The ice sheet on Antarctica suppresses some of the warming that would occur in that region in the Oligocene and PI simulations. Antarctic warming in the Cretaceous and Eocene is partly due to a decrease in snow cover (Fig. S2). There are some areas of localized warming as well, especially in the Cretaceous. A reduction in low reflective clouds, seen by increased outgoing longwave radiation in Antarctica, the southern tips of Africa and South America, and part of southeast Asia, partially accounts for localized warming in the Cretaceous (Fig. S5). A decrease in Cretaceous southeast Asian monsoonal activity, caused by a slight southern shift in the ITCZ, may contribute to this warming by reduced cloud cover and reduced evaporative cooling (Fig. S6).
Fig. 2
Surface temperature anomaly minus ECS at each grid-cell, emphasizing polar amplification and spatial heating trends. One example from each time period is shown here – Cretaceous from 6x to 12x PI CO2, Eocene from 3x to 6x PI CO2, Oligocene from 2x to 4x PI CO2, and PI from 1x to 2x PI CO2
3.2 ECS sensitivity to state-dependence
Warmer background states result in feedback changes that lead to higher ECS, as evident in two experiments where CO2 is the only variable: (a) CRET3xSOM3x compared to CRET3xSOM6x and (b) PI1xSOM1x compared to PI1xSOM2x. In the Cretaceous simulations, the cooler background state has an ECS that is 0.57°C lower, while in the PI scenarios, the difference is 0.58°C with the warmer climate background prompting a higher ECS. These results indicate that warmer baseline climates amplify ECS through enhanced feedbacks.
Fig. 3
The relationship between ECS and W/m2 feedback changes in (a) specific humidity, (b) clouds, and (c) surface albedo with doubled CO2. ECS and specific humidity show a strong positive correlation (r = 0.99), as well as ECS and clouds (r = 0.97). ECS and surface albedo have a weaker negative relationship (r=-0.81), but the temperature response is larger
Simulations exhibiting larger changes in water vapor and clouds between CO2 levels show higher ECS (Fig. 3). Warmer background climates have greater water vapor content, and rising temperatures lead to exponentially higher saturation vapor pressure. Since water vapor is a greenhouse gas, elevated humidity levels are strongly correlated with ECS. The warmer Cretaceous simulation, which also has an initial GMST 5.57℃ higher, has a stronger water vapor feedback by 1.08 W/m2 (Fig. 3a). Similarly, the warmer PI simulation, with an initial GMST 4.04℃ higher, exhibits a stronger water vapor feedback by 1.57 W/m2 (Fig. 3a).
Changes in the balance between LWCF and SWCF drive stronger cloud feedbacks. Although both forcings decrease with a doubling of CO2 due to an overall reduction in total cloud coverage, SWCF decreases more than LWCF, leading to net warming (Fig. S4). This imbalance is even more pronounced with a higher CO2 background state, where the net cloud feedback is 0.65 W/m2 greater in the warmer Cretaceous simulation and 0.22 W/m2 greater in the warmer PI simulation (Fig. 3b).
The warmer cloud feedbacks are primarily driven by increasing background CO2 which leads to relatively more high clouds and fewer low clouds. Every doubled CO2 simulation experiences a decrease in total cloud coverage from the surface to ~ 250 hPa and an increase in coverage above ~ 250 hPa. This shift is due to a heightened tropopause, reflecting changes in the atmospheric lapse rate, which diminishes lower cloud cover (Fig. S1, Lorenz and DeWeaver 2007). Additionally, every doubled CO2 simulation, with the exception of PI1xSOM2x, exhibits greater cloud ice crystal amounts, primarily around 250 hPa, due to cloud tops forming at higher altitudes (Fig. S5, Harrison 2000). CRET3xSOM6x reports a 7% greater shift toward ice crystal composition than CRET3xSOM3x. The higher CO2 PI background state reports a 5.7% increase in in-cloud ice composition, while the lower CO2 PI background state reports a 4.6% decrease in global cloud ice composition. Interestingly, doubling CO2 from PI1xSOM1x is the only case where cloud composition shifts in favor of liquid water droplets.
Lastly, surface albedo change is weakly negatively correlated with ECS, but contributes more to ECS variation in cooler climates due to the greater amount of snow and ice (Fig. 3c). Still, the warmer Cretaceous and warmer PI simulations compared here exhibit a slightly stronger surface albedo feedback than their lower CO2 counterparts (Fig. 3c). Surface albedo feedback is relatively more important to ECS in cooler climates with substantial snow to melt, while the water vapor and cloud feedbacks grow in importance in warmer climates.
3.3 ECS sensitivity to geography
Tectonically-induced continental drift drives changes in paleogeography that influence the ECS, mainly through changes in global ocean surface area. While our simulations do not independently isolate geography, much of the variation in ECS between periods can be attributed to geographic differences. We compare simulations with similar CO2 levels and ice sheet scenarios: CRET3xSOM3x to EECO3xSOM3x and OLIG2xSOM2x to PI1xSOM2x.
Despite similar CO2 levels and ice sheet conditions, the Eocene (EECO3xSOM3x) exhibits a higher ECS than the Cretaceous (CRET3xSOM3x) due to geographic differences. The Eocene ECS is 1.00°C higher than the Cretaceous. The Eocene experiences greater changes in water vapor, clouds, and surface albedo with a CO2 doubling than the Cretaceous (Figs. 3, S2). Although the Eocene has only 0.59% more global ocean surface area than the Cretaceous, it has a higher proportion of ocean at higher latitudes (> 60°), which alters the spatial pattern of warming and moisture increases (Table 1; Farnsworth et al. 2019). Because high-latitude ocean areas tend to warm strongly under CO2 forcing due to polar amplification, they can contribute disproportionately to increases in atmospheric specific humidity in those regions. While the local fractional increase in water vapor is primarily governed by temperature via the Clausius-Clapeyron relation, changes in the spatial distribution of warming and moisture can amplify the global mean water vapor radiative feedback (Held and Soden 2000). The Eocene’s water vapor feedback is 3.11 W/m2 greater and the cloud feedback is 0.57 W/m2 greater than the Cretaceous simulation’s at the same CO2 level (Fig. 3). The Eocene also has less sea ice coverage than the Cretaceous and experiences 24.7% more snow melt than the Cretaceous at high latitudes (Fig. S2). Therefore, EECO3xSOM3x appears to exhibit a higher climate sensitivity than CRET3xSOM3x in part because high-latitude ocean regions enhance warming where water vapor changes have a large radiative effect.
Geographic differences also influence ECS in lower CO2 background climates. The PI1xSOM2x and OLIG2xSOM2x represent cooler climates, with CO2 levels of 560 ppm and prescribed Antarctic ice sheets. Their ECS values are more similar than the warm case comparison, as colder climates have dampened sensitivities, with the OLIG2xSOM2x ECS 0.44°C higher. The Oligocene simulation experiences greater changes in water vapor and cloud feedbacks and has 3.55% more total ocean surface area, as well as more high-latitude ocean surface area, again altering the warming and moisture patterns (Table 1; Fig. 3). The Oligocene experiences 44.5% more snow melt than the PI, though the difference in surface albedo feedback between simulations is very small (Figs. 3c, S2). The Oligocene also has a higher initial GMST than the PI simulation, but the Eocene does not have a higher initial GMST than the Cretaceous, meaning initial GMST does not exactly indicate relative ECS (Fig. S7). Geographic differences, especially the distribution of ocean surface area at high latitudes, can significantly influence ECS through their effect on the spatial pattern of warming and the resulting water vapor radiative feedback.
3.4 ECS sensitivity to ocean heat transport
To evaluate the influence of OHT on ECS, we compare Cretaceous simulations at 6x PI CO2: CRET6xSOM6x using OHT from an equilibrated 6x PI CO2 ocean, and CRET3xOHT6x using OHT from an equilibrated 3x PI CO2 ocean. The poleward heat transport in the 6x PI CO2 case is 21.1% stronger in the Northern Hemisphere and 22.6% stronger in the Southern Hemisphere, leading to an ECS of 6.66°C for CRET6xSOM6x, which is 0.89°C higher than CRET3xOHT6x (Fig. S3). Singh et al. (2022) also found that stronger OHT results in higher ECS under cooler PI conditions. The initial GMST for the stronger OHT and higher ECS simulation is slightly cooler than for the lower ECS simulation, signaling that initial GMST does not indicate relative ECS.
The greater OHT leads to polar amplification, increasing surface evaporation and latent heat flux at mid- and high-latitudes. The CRET6xSOM6x experiences a water vapor feedback that is 2.68 W/m2 stronger than CRET3xOHT6x. Surface warming causes some destruction of low-level stability and low cloud formation and increases convection. This leads to a greater reduction in lower clouds than higher clouds, or a stronger SWCF reduction. The stronger OHT simulation experiences a greater drop in SWCF by 2.2% compared to the weaker OHT simulation, as well as higher cloud formation and a 12% increase in cloud ice composition with CO2 doubling. Overall, the net cloud feedback is 0.79 W/m2 stronger in the CRET6xSOM6x simulation. High-latitude warming in the stronger OHT simulation leads to slightly more snow melt (by 0.6%); this small change is a product of a very warm climate background with little snow. The ~ 20% increase in OHT notably amplifies ECS, with the water vapor feedback contributing the most and the surface albedo feedback contributing the least.
4 Discussion
In this study, we compare ECS between past climate intervals reconstructed with different CO2 levels, geographies, and OHT strengths. We additionally decompose the total climate feedback parameter and estimate the contribution of each feedback to global temperature change under CO2-doubling. We find the water vapor feedback contributes the most to warming, and through our geography experiment, that high latitude ocean surface area has a significant impact on moisture availability and thereby the water vapor feedback amplification (Fig. 1). Moreover, the surface albedo feedback exhibits the greatest range, ~ 0-1.1 W/m2/K, in total climate feedback parameter contribution through past climates (Fig. 1). The substantial difference in surface albedo feedback between simulations confirms that differences in reflective surfaces, like land and sea ice, play a key role in the fluctuation of global temperatures and ECS through time. These results highlight that state-dependent feedbacks, particularly water vapor and surface albedo, are primary drivers of variations in climate sensitivity across past Earth states, emphasizing the importance of accurately representing high-latitude processes and surface properties in CESM simulations.
Validating model ECS estimates with proxy evidence can be difficult, as it requires a large amount of warming to occur on a short time-scale with small geographic changes, and the Cretaceous and Oligocene warming rate and proxy abundance limits ECS validation. However, the PETM was a relatively short time interval of extreme warming about 55 million years ago, and the Eocene CESM1.2 simulated ECS between 3x and 6x PI CO2 has been validated with temperature proxy evidence in Zhu et al. (2019). Thus, the PETM provides a valuable benchmark for evaluating model-derived ECS against proxy-based temperature reconstructions in deep-time warming events.
Further, we compare the decomposition of the total climate feedback parameter between our PI1xSOM1x and PI1xSOM2x simulations and the kernel-derived feedbacks reported by Pendergrass et al. (2018) for the CESM1 large ensemble. The modern-day radiative kernels they provide cannot be directly applied to our CESM-SOM simulations of the Cretaceous, Eocene, Oligocene, and PI climate states due to substantial differences in mean climate and model configuration. Nonetheless, a qualitative comparison between our PI 280 ppm to 560 ppm slab ocean equilibrated simulations and their 1976–2005 versus 2071–2100 transient response provides useful context. In our simulations, the water vapor feedback is approximately 2.0 W/m2/K, closely matching their ensemble-mean value of 2.1 W/m2/K. Our residual temperature feedback is -3.1 W/m2/K, similar in magnitude to their Planck component (-3.2 W/m2/K), though smaller when their Planck is combined with the lapse-rate contribution (-0.58 W/m2/K). Larger differences arise in the surface albedo and cloud feedbacks: our surface albedo feedback (1.1 W/m2/K) exceeds their estimate of 0.51 W/m2/K; whereas our cloud feedback (0.08 W/m2/K) is substantially smaller than their 0.66 W/m2/K estimate. Importantly, these two feedbacks combine to produce a total planetary albedo feedback that is broadly consistent between the two studies, indicating that the differences lie in partitioning between surface and cloud contributions rather than in the net radiative effect. The larger surface albedo sensitivity in our PI simulations likely reflects the colder reference climate and more extensive snow and sea ice, which amplify the radiative response to warming relative to the modern baseline in Pendergrass et al. (2018).
Cloud feedback remains one of the most uncertain components of the climate feedback system, with published global mean estimates ranging from near-zero to well above 0.5 W/m2/K depending on methodology (Dessler 2010; Zelinka et al. 2020; Ceppi and Nowack 2021; Myers et al. 2021; Chao et al. 2024). Therefore, several methodological differences help explain why our estimated cloud feedback is smaller than that obtained by Pendergrass et al. (2018). First, our cloud feedback is estimated as the change in cloud radiative effect (CRE) per degree of global warming (ΔCRE/ΔT). This metric provides a useful proxy but is not equivalent to the kernel-residual cloud feedback used in Pendergrass et al. (2018). Radiative kernel methods explicitly subtract the radiative impacts of temperature, water vapor, surface albedo, and effective radiative forcing, including rapid cloud adjustments to CO2, before attributing the remaining top-of-atmosphere flux change to cloud feedback (Shell et al. 2008; Soden et al. 2008). In contrast, CRE methods conflate true cloud feedback changes with cloud adjustments and with differences between all-sky and clear-sky non-cloud feedbacks. As a result, they often produce a smaller global-mean cloud feedback than kernel-residual approaches (Colman 2003; Soden et al. 2004; Soden et al. 2008). Second, our equilibrated slab ocean experiments feature more uniform SST warming patterns and lack the transient ocean-atmosphere coupling and regional SST pattern effects present in fully-coupled RCP8.5 simulations, both of which can influence the magnitude of low cloud SWCF (Ceppi and Gregory 2017; Zhou et al. 2017; Andrews and Webb 2018). Third, the colder PI climate state alters inversion strength, cloud phase distribution, and the sensitivity of low clouds to warming, further reducing the magnitude of the cloud feedback relative to modern conditions (McCoy et al. 2015; Frey and Kay 2018). Taken together, differences in diagnostic methodology, baseline climate state, SST pattern, and model configuration provide a coherent explanation for our smaller cloud feedback estimate, even though the combined planetary albedo response agrees closely with that derived from the modern climate simulations.
Most modeling studies agree that climate sensitivity increases as the climate warms (Zhu and Poulsen 2020; Caballero and Huber 2013; Meraner et al. 2013). A key contributor to this trend is the increase in atmospheric water vapor under higher CO2 levels, as warmer air supports higher saturation vapor pressure. Our simulations also support this mechanism, showing enhanced water vapor feedback when CO2 is doubled. In particular, increased moisture in the subtropics – likely driven by changes in atmospheric circulation – may further amplify ECS (Bloch-Johnson et al. 2020; Henry et al. 2023). We also find that global cloud cover declines under higher CO2, reducing both SWCF and LWCF. However, the decrease in SWCF is larger, diminishing the cooling effect of clouds (Fig. S4; Zhu et al. 2019). Additionally, warming is enhanced by an increase in high-altitude ice clouds, which are less reflective and more emissive in the longwave spectrum. These simulated microphysical changes, such as more efficient fallout of ice crystals and fewer reflective liquid droplets, shift cloud radiative effects in ways that amplify warming (Zhu and Poulsen 2020; Pruppacher et al. 2007). While cloud feedbacks remain highly uncertain and model-dependent, especially in non-cloud-resolving models like ours, our results reinforce previous findings that ECS increases with CO2 due to coupled changes in water vapor, cloud properties, and surface albedo. Unlike other studies, we compare experiments between cooler PI climates and warmer Cretaceous climates and found that the resulting ECS varied more than 2.5℃, indicating a wide range in global temperature response to CO2-induced warming across Earth’s history.
Fewer studies address the impact of geographic changes on ECS. Farnsworth et al. (2019) found that ECS varied by up to 1.6°C, from 3.7°C to 5.3°C, due to changes in solar luminosity and continental configuration from 145 million years ago to 35 million years ago. Our study covers 90 million years ago to PI and our ECS results span a broader range, approximately 1.0°C more, partly due to the inclusion of multiple CO2 levels and the use of CESM instead of HadCM3B. This likely reflects differences in model physics, particularly cloud parameterizations. The simulations in Farnsworth et al. (2019) also result in lower ECS than our simulations at every comparable time interval, including a lower ECS by ~ 0.3°C in the PI at equivalent CO2 levels (280 ppm to 560 ppm), which can be attributed to model differences between CESM and HadCM3B. In our geographic experiment, we found ECS to change by up to 1.0°C between 90 million years ago and 55 million years ago at equivalent CO2 levels, and Farnsworth et al. (2019) found ECS to change by up to 0.6°C over the same time interval. However, Farnsworth et al. (2019) set the simulations at 2x and 4x PI CO2, while our simulations are set at 3x and 6x PI CO2 for those time intervals, and other than model differences, our higher CO2 background state may explain the greater change in ECS between those periods. Solar luminosity had little effect on ECS in our simulations, unlike in Farnsworth et al. (2019), though this is unsurprising given the smaller luminosity differences we tested. Farnsworth et al. (2019) determined total ocean surface area and ocean circulation to influence the changes in ECS spanning the Cretaceous, Paleocene, and Eocene. We also show that changes in geography affect ECS, but particularly that a greater high-latitude (> 60°) ocean surface area enhances the potential for moisture availability and strengthens the water vapor feedback, thus raising ECS.
Our findings reveal that an average difference in OHT strength of ~ 20% affects ECS by ~ 0.9°C. Singh et al. (2022) used CESM-SOM to test OHT influence under low CO2 conditions and similarly concluded that stronger OHT causes a higher ECS through amplified water vapor feedback and increased sea ice melt. While Singh et al. (2022) associated stronger OHT with a lower CO2 ocean, our results link a stronger OHT with a higher CO2 ocean. Despite this difference, both studies find that stronger OHT leads to higher ECS, primarily due to the water vapor feedback. Surface albedo changes contribute relatively more to sensitivity variations in cooler climates, as seen in Singh et al. (2022), while this warmer climate experiment does not find high significance in surface albedo change. Since CO2 changes alter OHT strength, SOM simulations are particularly useful for disentangling the physical mechanisms driving GMST responses, even if they lack the detailed ocean dynamics needed for the most complete estimation.
5 Conclusions
We present CESM1.2 SOM simulations of Earth’s climate over the past ~ 100 million years to analyze mechanisms controlling global warming. ECS varies by up to 2.5℃, ranging from 4.04℃ to 6.66℃. Our findings suggest that the reshaping of Earth’s CO2 levels, tectonics, and ocean circulation through time modulated the intensities of the water vapor, cloud, and surface albedo feedbacks, which govern the Earth's climate sensitivity. The water vapor feedback contributes the most to warming, while the surface albedo feedback heavily impacts the range of ECS through Earth’s history. We examine ECS across varying CO2 background states, geographic configurations, and OHT strengths, finding each of these boundary conditions to significantly impact ECS. The novel findings of our study suggest that a greater high-latitude ocean surface area may increase warming by amplifying the water vapor feedback, the feedback that contributes most to warming, through polar moisture availability. Further, our findings suggest that the surface albedo feedback covers the greatest range between climates, suggesting that a lack of polar ice significantly increases ECS. These surface albedo changes affect climate sensitivity more in cooler climates, while water vapor changes amplify global heating more in warmer climates. Our changes in CO2 level and OHT strength showed similar differences in ECS, with higher CO2 and greater OHT strength increasing warming, while our change in geography, particularly high-latitude ocean surface area, between the Cretaceous and Eocene resulted in the largest ECS difference between our experiments. Future directions could include specific high-latitude and low-latitude ocean surface area experiments on global temperature and ECS, as well as quantifying radiative kernels for past climate states and re-examining individual feedback contribution to the total climate feedback parameter.
Electronic Supplementary Material
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Statements and Declarations
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Funding
The research was funded by the National Science Foundation, Directorate for Geosciences (grant no. 2309580), the National Science Foundation, Division of Graduate Education (grant no. 2241144), and the National Science Foundation, Frontier Research in Earth Sciences (grant no. 2325048). We are grateful to the National Center for Atmospheric Research for providing supercomputing resources.
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Competing InterestsThe authors have no competing interests to declare that are relevant to the content of this article.
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Author Contributions
Both authors designed the experimental approach. Julia Campbell performed the model simulations, analyzed the results, and prepared the figures. Julia Campbell prepared the manuscript and Christopher J. Poulsen provided comments. Both authors read and approved the final manuscript.
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Data Availability Statement
This work utilized data from published CESM1.2 Cretaceous and Eocene climate simulations, as well as a publicly available CESM1.2 pre-industrial climate simulation. The Oligocene climate simulation is unpublished – requests may be sent to the authors for additional information or data. The model data used for ECS evaluations and figures in the study are publicly available at Zenodo via 10.5281/zenodo.17673703 (Campbell 2025).