The dependence of equilibrium climate sensitivity on climate state: Applications to studies of climates colder than present



[1] We investigate the sensitivity of climate to a broad range of greenhouse gas forcing with coupled atmosphere-ocean general circulation models using atmospheric CO2 concentrations ranging from ~1400 to ~200 ppm. We show that climate sensitivity is greater when the base state climate is colder, a result noted previously but with models of much lower resolution and different parameterizations. The enhanced cold state sensitivity is more apparent in models coupled to dynamical versus slab oceans. The disproportionately large sensitivity for cold climates has applications to studies of climates colder than present.

1 Introduction

[2] The examination of the sensitivity of climate to changes in radiative forcing over a wide range of greenhouse gas (GHG) concentrations began with a very basic climate model [Arrhenius, 1896] and continued with increasingly realistic models. Manabe and Bryan [1985] were the first to use a coupled dynamical atmosphere-ocean model to study climates over a wide range of CO2 concentrations (8 × CO2 to 0.5 × CO2: 2400 to 150 ppm); they found increased climate sensitivity to GHG radiative forcing for cold climate states—a sensitivity they linked to cryosphere and dynamical ocean feedback processes. Subsequent papers continue to examine climate sensitivity using models [Boer and Yu, 2003; Meehl et al., 2007] and observations of past climates [Knutti and Hegerl, 2008].

[3] Here we use current high-resolution climate models to examine Equilibrium Climate Sensitivity (ECS: the increase in global mean surface temperature corresponding to a doubling of atmospheric CO2) as a function of climate state for a broad range of GHG concentrations (4 × CO2 to ~0.5 × CO2). We find that ECS is greater for cold than for warm climate states, but the degree of enhanced cold state ECS is less than that in the earliest studies. The enhanced cold state ECS is most apparent in models linked to dynamical oceans versus slab oceans and varies between models. Paleoclimate studies have produced estimates of ECS within the range of model-based estimates but have not identified a differential response between cold and warm states. We give examples of the relevance of enhanced cold climate ECS to studies of climates colder than present including glacials, interglacials, and glacial inceptions.

2 Climate Sensitivity as a Function of Climate State

[4] To identify the differential response of climate to changes of GHG radiative forcing for warm and cold base states, we analyzed simulations of the Community Climate System Model [Gent et al., 2011;Collins et al., 2006], versions 4 and 3 (CCSM4 and CCSM3). These CCSMs are fully coupled dynamical atmosphere-ocean models of relatively high resolution (CCSM4, 1° × 1° atmospheric resolution; CCSM3, T42 atmospheric resolution, approximately 2.8° × 2.8°; both models have oceans of correspondingly high resolution). The ECS of CCSM4 is 3.2 K (for CO2 doubling relative to preindustrial, PI) and that of CCSM3 is 2.8 K (for CO2 doubling relative to present day, PD) [Bitz et al., 2012]. These values, calculated with the slab ocean versions of the two models, are within the likely range of ECSs reported in the Intergovernmental Panel on Climate Change (IPCC): 2 to 4.5 K with median ~3 K [Meehl et al., 2007].

[5] We summarize climate responses to GHG forcing changes among six climate states associated with six levels of GHG forcing from ~1400 to ~150 ppm equivalent CO2 (CO2eq). CO2eq represents the combined radiative forcing effect associated with several greenhouse gases (CO2, CH4, N2O, and CFCs) and is referenced to the present-day GHG level of the CCSM3 control simulation. Two climate states are from our experiments with CCSM4 and CCSM3 [Kutzbach et al., 2010, 2011; He, F., et al., manuscript in preparation, 2013] for (i) PD, with CO2 level of 355 ppm, and (ii) NA, a hypothetical No Anthropogenic (NA) climate with CO2 level of 240–245 ppm (CO2eq of ~200 ppm) based upon GHG measurements from Antarctic ice cores in previous interglacials at times closest to the current orbital configurations [Ruddiman et al., 2011]. We augment these two climate states with four others: (iii) PI, the climate of ~1850 AD, with CO2 level of 285 ppm (CCSM4) [Gent et al., 2011] and 280 ppm (CCSM3) [Otto-Bliesner et al., 2006], i.e., a CO2eq of ~240 ppm; (iv, v) 2 × CO2 and 4 × CO2 (CCSM3 with CO2 referenced to PD, CCSM4 with CO2 referenced to PI) [Meehl et al., 2006, 2012]; and (vi) LGMCO2, with CO2 level of 185 ppm (CO2eq of ~160 ppm), the GHG level at the Last Glacial Maximum (LGM), but with no ice sheets (CCSM4) [Brady et al., 2012]. The simulations were typically several hundred years in length and close to equilibrium. Equilibrium global surface air temperature was estimated from a linear regression between top-of-the-atmosphere radiation budget and surface air temperature [Gregory et al., 2004], and a bootstrapping method [Andrews et al., 2012] provided uncertainty limits. (See Table S1 in the supporting information for GHG and CO2eq concentrations, radiative forcing, equilibrium surface air temperature, and climate sensitivity calculations.)

[6] We use selected CCSM4 results to describe the differential responses of eight climatic indices for cold (PI-NA), intermediate (PD-PI), and warm (4 × CO2-PD) states and compare these responses to the corresponding change in GHG radiative forcing (Figure 1). We use PI-NA rather than PI-LGMCO2 to illustrate the cold state response, even though the latter has a greater GHG forcing difference, because NA was simulated with CCSM3 thus allowing intermodel comparisons, and because the radiative forcing for NA is based on conditions observed in previous interglacials whereas LGMCO2 is a sensitivity experiment related to an LGM experiment, both of which have been compared to PI by Brady et al. [2012]. By comparing the climatic responses to the change in radiative forcing (Figure 1) rather than the change in GHG concentration, we take into account the logarithmic relation between concentration change and radiative forcing change [Ramaswamy et al., 2001]. For the cold state change, NA to PI, the GHG radiative forcing increased 1.05 W/m2 (12% of the range between NA and 4 × CO2; Figure 1). However, the surface air temperature (SAT) increase, the Northern Hemisphere (NH) sea ice and snow cover decrease, the Southern Hemisphere (SH) sea ice cover decrease, the global ocean temperature increase, and the global surface specific humidity and global precipitation increase are all larger in percent, ~20–30%, than the radiative forcing change (12%). In contrast, for the warm state change, PD to 4 × CO2, the radiative forcing increased 5.40 W/m2 (64% of the full range), but the changes in the eight climate indices are all smaller in percent, ~50–55%, than the radiative forcing change (64%). For the intermediate climate state change, PI to PD, the percentage changes for the eight climate indices are approximately equal to the percentage change in GHG radiative forcing (24% of the full range). In summary, the cold state climate response is consistently increased relative to the GHG radiative forcing and the warm state response is correspondingly decreased.

Figure 1.

Annual average changes of GHG radiative forcing and climatic response of eight climate indices for the differences between four climate simulations with CCSM4-dynamical ocean. The three differences are warm state, 4 × CO2-PD (red), intermediate state, PD-PI (yellow), and cold state, PI-NA (blue). Numbers inside each bar are percent change (in parentheses—relative to the full range of 100% from NA to 4 × CO2) and magnitude of change (see Table S2 in the supporting information).

[7] Another index of hydrologic response, the change in global precipitation relative to the change in global SAT, also varies between cold and warm states. This hydrologic response is 1.8%/K over the entire range NA to 4 × CO2, close to the average response of a large sample of climate models for two climatic warming scenarios [Held and Soden, 2006]. However, the hydrologic response is greater for NA to PI (2.2%/K) than for PD to 4 × CO2 (1.5%/K). The decreases in precipitation (P) and precipitation-evaporation (P-E) with cooling occur in equatorial and polar regions [Held and Soden, 2006; Kutzbach et al., 2005; Manabe and Bryan, 1985] (see Table S2 in the supporting information).

3 Comparisons With Other Models

[8] We summarize the ECS for cold, intermediate, and warm climate state changes for CCSM4 (section 2 and Figure 1) and CCSM3, both coupled to dynamical oceans, and compare our results with others in Figure 2a. For CCSM4, ECS is 5.3 K for PI-NA and 4.2 K for PI-LGMCO2 [Brady et al., 2012], compared with 3.2 K for 4 × CO2-PD and 2.9 K for 2 × CO2-PD. The ECS is larger for the two cold states (~4–5 K ) than for the two warm states (~3 K). In this brief report, we do not attempt to explain the relatively small differences in ECS between individual “cold state/warm state” simulations—for example, why the ECSs for the two warm state simulations are slightly different or why the ECS for PI-NA is greater than that for PI-LGMCO2. However, as noted by Brady et al. [2012], the ECS for PI-LGMCO2 (4.2 K) is not equivalent to their ECS for PI-LGM (3.1 K), a difference they ascribe to the role of LGM ice sheets in producing downslope winds that moderate temperatures along the ice margins causing significantly less expansion of sea ice cover and increased Atlantic meridional overturning circulation—i.e., changes opposite to those in PI-LGMCO2.

Figure 2.

Equilibrium Climate Sensitivity (ECS) (K) for three climate states for eight climate models. (a) Models linked to dynamical oceans—CCSM4, CCSM3, GFDL, and GISS; (b) models linked to slab oceans—CCSM4, CCSM3, CCM3, and ABMRC. See text for the references to each of these model simulations. The ECSs are for cold (blue), intermediate (yellow), and warm (red) climate states. The dashed line indicates the average ECS for each model.(see Table S1 in the supporting information).

[9] For CCSM3, ECS is 3.3 K for PI-NA, compared with 2.8 K for 2 × CO2-PD (Figure 2a). The differences in ECS between cold and warm climate states are larger for CCSM4 than for CCSM3. The cold climate state ECSs for both CCSM models are not as large as that simulated by a Geophysical Fluid Dynamics Laboratory (GFDL) model of lower resolution and different parameterizations [Stouffer and Manabe, 2003]: an ECS of 7–8 K (coldest state) and 3–4 K (warmest state) (Figure 2a)—results similar to those of the earlier study by Manabe and Bryan [1985]. Hansen et al. [2005] used a relatively low-resolution Goddard Institute for Space Studies (GISS) model and found a very slight increase in ECS from cold to warm states (Figure 2a); however, they noted that the relatively short length of the simulations might not have allowed a close approach to equilibrium for the colder states and that earlier versions of their models with stronger sea ice feedbacks had been more sensitive to “colder” forcing.

[10] Figure 2b illustrates ECSs for climate models coupled to slab oceans rather than dynamical oceans. Three of the four slab ocean models do not exhibit enhanced cold climate sensitivity: for CCSM4, ECSs are similar for cold and warm states; for CCM3 [Kothavala et al., 1999] there are only slight differences in ECS; for the Australian Bureau model (ABMRC) [Colman and McAvaney, 2009], there is no ECS difference between warm and cold states over the range of CO2 considered here (Figure 2b), although they found greatly enhanced cold climate ECSs relative to warm climate ECSs for more extreme low and high GHG forcing (not shown). Only CCSM3 [Vavrus et al., 2008] simulated enhanced ECS for cold climate states.

[11] The enhanced ECS of cold climate states is more pronounced in the simulations coupled to dynamical oceans versus slab oceans, a result we find linked to decreased ocean heat transport in high latitudes and cryosphere (albedo-temperature) feedbacks, the same explanation proposed earlier by Manabe and Bryan [1985] to account for similar differences in cold climate response for their models with dynamical versus slab ocean. In the CCSM4 simulations with dynamical ocean, comparing PI to NA, the maximum of the Atlantic Meridional Overturning Circulation decreased from 26 to 23 Sv (Sverdrup (106 m3/s)) and shifted several degrees latitude south (and contracted vertically), the northward ocean heat transport at 50 N decreased from 0.91 to 0.74 PW, and the southward ocean heat transport at 60S decreased from 0.60 to 0.56 PW. Likewise, NH annual sea ice cover increased from 11.7 to 15.3 × 106km2, SH annual sea ice cover increased from 16.9 to 20.0 × 106km2, and NH permanent snow cover almost doubled from 5.2 to 9.2 × 106km2 (Figure 1). In the simulations with slab ocean, ocean heat transport is essentially fixed.

[12] Compared to the large difference in cold state ECSs between the dynamical and slab ocean versions of CCSM4 (Figure 2), the corresponding differences in warm state ECSs are small (Figure 2). The difference in warm state ECSs for the dynamical and slab oceans versions of CCSM3 is also small (Figure 2), a result noted earlier by Danabasoglu and Gent [2009] who found that the warm state ECS (2 × CO2-PD) for CCSM3 with dynamical ocean was only slightly larger (0.1 K) than that with slab ocean.

[13] This increased ECS for climates colder than present (Figure 2) is illustrated in Figure 3a by plotting SAT as a function of CO2eq radiative forcing. The expected linear relation between these variables fits well for climates warmer than present; however, for climates colder than present, the responses of the three models with dynamical oceans tend to depart from the linear regression line (as determined between 4 × CO2 and PD), indicating increased ECS for the colder states.

Figure 3.

Equilibrium annual-average global surface air temperature (SAT) (C) as a function of (a) CO2eq radiative Forcing (W/m2) and (b) CO2eq concentration (ppm). There are six (five) simulations with CCSM4 (CCSM3) and four simulations with a GFDL model, all coupled to dynamical oceans, and four simulations with CCSM4-slab ocean (CCSM4 SOM). The different CO2eq concentrations for 2 and 4 × CO2 among the three models occur because the base level CO2 is referenced to PI (285 ppm) for CCSM4, to PD (355 ppm) for CCSM3, and to PD (300 ppm) for GFDL. The dashed lines in the top panel indicates the linear regression slope based on results from PD to 4 × CO2 and extrapolated beyond PD to show the departures of colder simulations from the linear fit based on warmer simulations. The stippled triangles highlight the different slopes between NA-PI versus PI-PD (see text). The simulated SAT for the GFDL model for 0.5 × CO2 is 3.2 C (off-scale, see arrow) (see Table S1 in the supporting information).

4 Climate Sensitivity Estimates From Paleoclimate Observations

[14] Paleoclimate data have been used to estimate climate sensitivity. Hansen and Sato [2012] found ECSs of ~3 K but noted that climate sensitivity could be considerably larger (for both cold and warm states) if slow, long-term feedbacks (e.g., ice sheet growth or decay) were considered. Others [Rohling et al., 2012; Knutti and Hegerl, 2008] find ECSs within the range of model-based IPCC estimates for future CO2 doubling (median ~3 K, with a likely range of 2 to 4.5 K); see also Zeebe [2011] and Skinner [2012].

[15] Several studies, beginning with Hansen et al. in the 1980s, have tried to estimate ECS using observations from the Last Glacial Maximum (LGM), a cold climate with relatively large observational databases. Crucifix [2006] used four models to study the climate response to LGM boundary condition forcing, compared to 2 × CO2 forcing. He concluded that ECS could not be directly scaled from glacial ECS because the LGM forcing is not known accurately enough and because of complications arising from nonlinear temperature-dependent feedback processes, mainly involving clouds. Hargreaves et al. [2012] used seven PMIP2 model simulations of the LGM and a new analysis of LGM ocean temperature (the MARGO data set) to estimate ECS. They found a near-linear relation between ECS and simulated LGM tropical ocean temperature and then used the observed LGM tropical ocean data to estimate a median ECS of ~2.5 K with a high likelihood that ECS was less than 4 K. Their approach takes advantage of a near-linear relation between ECS and tropical ocean temperature (a relationship they find plausible because GHG forcing could be a dominant cause of tropical ocean temperature change whereas ice sheet boundary condition forcing would contribute to middle and polar latitude temperature change), but it has the limitation of calibrating only against LGM tropical ocean temperature rather than global temperature, and the linear relation used is dependent on the choice of models (ECS varies between models). Schmittner et al. [2011] used a somewhat analogous method to estimate ECS by comparing multiple LGM simulations with a low-resolution climate model of intermediate complexity (adjustable to produce a range of climate sensitivities) to global LGM surface temperature (temperatures over ocean, land, and ice). They found a median ECS of ~2.3 K.

[16] In summary, the various estimates of ECS based upon paleoclimate studies do not yet clearly isolate cold versus warm state differences. ECSs are either in the range of the IPCC estimates (median ~3 K with a likely range from 2 K to 4.5 K) or, as in the latter two studies of the LGM, have slightly lower medians of ~2.5 K. Estimates of ECS from paleoclimates are subject to the caveats of incomplete knowledge of the forcing (GHGs, ice, aerosol, and insolation) and the observations. The model-simulated estimates of ECS based only upon GHG changes have the advantage of precise knowledge of the forcing but the response still differs between models (section 3 and Figure 2).

5 Applications to Studies of Colder Climates

[17] An enhanced cold climate ECS has applications to studies of climates of the past.

[18] Some of these applications were discussed by Manabe and Bryan [1985] in the first paper identifying an enhanced cold climate ECS, which they related to the observed greatly extended LGM sea ice cover, and linked to the simulated reduced poleward ocean heat transport and weaker and vertically contracted thermohaline circulation.

[19] An enhanced cold climate ECS also has applications to understanding interglacial climates and interglacial terminations (glacial inceptions) of the past several hundred thousand years, and to climatic changes of the past several thousand years. Yin and Berger [2012] examined interglacial climates of the past 800,000 years using a series of simulations with a climate model of intermediate complexity with both orbital and GHG forcing. The nine interglacials had concentrations of CO2eq ranging from 234 to 300 ppm (all lower than present), and, in simulating the equilibrium climates of each interglacial, they found that ECS generally increased with decreasing temperature—a result in agreement with the CCSM experiments (section 3) and useful for helping understand differences between interglacials.

[20] Enhanced cold climate ECS related to albedo-temperature feedbacks has also been found in studies of glacial inception (the termination of interglacials), a phenomenon shown to be caused by a combination of reduced summertime orbital insolation forcing and by GHG forcing lower than present day (generally the PI level or lower), along with possible vegetation feedbacks in high latitudes [Mysak, 2008; Jochum et al., 2012; Vavrus et al., 2008].

[21] In the current interglacial, there has been a small but significant upward trend in GHG concentrations, beginning several thousand years ago, which is opposite to the GHG trends of previous interglacials; see Ruddiman [2003] and Ruddiman et al. [2011]. Ruddiman linked this upward trend to early agriculture—farming and associated land clearance (deforestation), rice cultivation, and livestock herding—an effect amplified by the relatively large per capita “footprint” of early agriculture [Ruddiman, 2013; Ruddiman and Ellis, 2009; Ellis et al., 2013]. The absolute magnitude of the change in CO2eq attributed to early agriculture is small, but, as illustrated by the triangles associated with the CCSM4 results (Figure 3), small increases in CO2eq radiative forcing and CO2eq concentration in cold climates can have a relatively large effect on temperature because of high-latitude albedo-temperature feedbacks. Referring to Figures 3a and 3b, the simulated SAT increase in CCSM4 from NA to PI, 1.5 K, is almost identical to the SAT increase from PI to PD, 1.6 K, even though the increases of CO2eq radiative forcing and CO2eq concentration from NA to PI (1.05 W/m2 and 45 ppm (200 to 245 ppm)) are approximately half that from PI to PD (2.02 W/m2 and 110 ppm (245 to 355 ppm)).

6 Conclusions

[22] The climatic response to changes in GHG radiative forcing, as simulated with CCSM4 and CCSM3 with dynamical oceans over a wide range of GHG concentrations, supports and extends the findings of much earlier studies, namely, that the climatic response is larger if the base state climate is cold. Changes in heat transport by the dynamical oceans, interacting with high-latitude albedo-temperature feedbacks, are implicated as a major contributor to the enhanced cold climate sensitivity, because the increased ECS for cold climates is generally smaller or absent in models with slab oceans.

[23] It would be useful to examine this cold state enhancement of ECS with other models and in greater detail. It would also be useful to further test this model-based result using paleoclimatic observations. Some progress is being made in estimating ECS from paleoclimates, but there are still uncertainties because the paleoclimatic forcing is not known accurately enough, including the roles of different components of forcing (GHGs, ice sheets, insolation, and aerosols), and different feedbacks might operate with different forcings. Paleoclimatic studies generally find ECSs within the range of current IPCC estimates (median ECS ~ 3 K, with a likely range from 2 to 4.5 K), and some recent studies of the LGM find a slightly lower median ECS of ~ 2.5 K.

[24] Studies of colder climates of the past, including glacials, interglacials, and glacial inceptions, and the climatic changes of the late Holocene attributed in part to early agriculture, would all benefit from improved understanding of enhanced cold climate ECS.


[25] This research has been supported by National Science Foundation grants ATM-0602270, ATM-0902802, and AGS-1203430 to the University of Wisconsin-Madison and ATM-0902982 and AGS-1203965 to the University of Virginia. Computational support was provided by NCAR’s Climate Simulation Laboratory, which is supported by the National Science Foundation. We thank Jerry Meehl, Gary Strand, Bette Otto-Bliesner, Gokhan Donabasoglu, and Esther Brady at NCAR for facilitating access to the data files of various CCSM3 and CCSM4 simulations. We thank two anonymous reviewers for their helpful comments.

[26] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.