PERSPECTIVE doi:10.1038/nature11574 Making sense of palaeoclimate sensitivity PALAEOSENS Project Members* Many palaeoclimate studies have quantified pre-anthropogenic climate change to calculate climate sensitivity (equilibrium temperature change in response to radiative forcing change), but a lack of consistent methodologies produces a wide range of estimates and hinders comparability of results. Here we present a stricter approach, to improve intercomparison of palaeoclimate sensitivity estimates in a manner compatible with equilibrium projections for future climate change. Over the past 65 million years, this reveals a climate sensitivity (in K W21 m2) of 0.3–1.9 or 0.6–1.3 at 95% or 68% probability, respectively. The latter implies a warming of 2.2–4.8 K per doubling of atmospheric CO2, which agrees with IPCC estimates. haracterizing the complex responses of climate to changes in the radiation budget requires the definition of climate sensitivity: this is the global equilibrium surface temperature response to changes in radiative forcing (an alteration to the balance of incoming and outgoing energy in the Earth–atmosphere system) caused by a doubling of atmospheric CO2 concentrations. Despite progress in modelling and data acquisition, uncertainties remain regarding the exact value of climate sensitivity and its potential variability through time. The range of climate sensitivities in climate models used for Intergovernmental Panel for Climate Change Assessment Report 4 (IPCC-AR4) is 2.1–4.4 K per CO2 doubling1, or a warming of 0.6–1.2 K per W m–2 of forcing. Observational studies have not narrowed this range, and the upper limit is particularly difficult to estimate2. Large palaeoclimate changes can be used to estimate climate sensitivity on centennial to multi-millennial timescales, when estimates of both global mean temperature and radiative perturbations linked with slow components of the climate system (for example, carbon cycle, land ice) are available (Fig. 1). Here we evaluate published estimates of climate sensitivity from a variety of geological episodes, but find that intercomparison is hindered by differences in the definition of climate sensitivity C between studies (Table 1). There is a clear need for consistent definition of which processes are included and excluded in the estimated sensitivity, like the need for strict taxonomy in biology. The definition must agree as closely as possible with that used in modelling studies of past and future climate, while remaining sufficiently pragmatic (operational) to be applicable to studies of different climate states in the geological past. Here we propose a consistent operational definition for palaeoclimate sensitivity and illustrate how a tighter definition narrows the range of reported estimates. Consistent intercomparison is crucial to detect systematic differences in sensitivity values—for example, due to changing continental configurations, different climate background states, and the types of radiative perturbations considered. These differences may then be evaluated in terms of additional controls on climate sensitivity, such as those arising from plate tectonics, weathering cycles, changes in ocean circulation, non-CO2 greenhouse gases (GHGs), enhanced watervapour and cloud feedbacks under warm climate states. Palaeoclimate data allow such investigations across geological episodes with very different climates, both warmer and colder than today. Clarifying the dependence of feedbacks, and therefore climate sensitivity, on the background climate state is a top priority, because it is central to the utility of past climate sensitivity estimates in assessing the credibility of future climate projections1,3. Timescale Years Decades Centuries Millennia Multi-millennia // Myr Clouds, water vapour, lapse rate, snow/sea ice Upper ocean CH4 CH4 (major gas-hydrate feedback; for example, PETM) Vegetation Dust/aerosol Dust (vegetation mediated) Entire oceans Land ice sheets Carbon cycle Weathering Plate tectonics Biological evolution of vegetation types Figure 1 | Typical timescales of different feedbacks relevant to equilibrium climate sensitivity, as discussed in this work. Modified and extended from previous work98. Ocean timescales were extended to multi-millennial timescales99. Quantifying climate sensitivity ‘Equilibrium climate sensitivity’ is classically defined as the simulated global mean surface air temperature increase (DT, in K) in response to a doubling of atmospheric CO2, starting from pre-industrial conditions (which corresponds to a radiative perturbation, DR, of 3.7 W m–2; refs 1, 3). We introduce the more general definition of the ‘climate sensitivity parameter’ as the mean surface temperature response to any radiative perturbation (S 5 DT/DR; where DT and DR are centennial to multimillennial averages), which facilitates comparisons between studies from different time-slices in Earth history. For brevity, we refer to S as ‘climate sensitivity’. In the definition of S, an initial perturbation DR0 leads to a temperature response DT0 following the Stefan–Boltzmann law, which is the temperature-dependent blackbody radiation response. This is often referred to as the Planck response4, with a value S0 of about 0.3 K W21 m2 for the present-day climate5,6. The radiative perturbation of the climate system is increased (weakened) by various positive (negative) feedback processes, which operate at a range of different timescales (Fig. 1). Because the net effect of positive feedbacks is found to be greater than that of negative feedbacks, the end result is an increased climate sensitivity relative to the Planck response4. *Lists of participants and their affiliations appear at the end of the paper. 2 9 NO V E M B E R 2 0 1 2 | VO L 4 9 1 | N AT U R E | 6 8 3 ©2012 Macmillan Publishers Limited. All rights reserved RESEARCH PERSPECTIVE Table 1 | Summary of key studies. Label in Fig. 3 Source Time window Explicitly considered forcings Temperature data used S and 1s bounds (K W21 m2) 0.81 6 0.27 LGM compilation based (data); on ref. 15 z0:4 0:81{0:27 (models) z0:33 Scaling factor (0.85) for 0:72{0:23 smaller S at LGM compared to 2 3 CO2 (refs 12, 16) 0.80 6 0.14 Value after authors’ suggested correction of CLIMAP temperatures Model-based global estimate 0:62z0:08 1 Ref. 2 LGM Various Various 2 Ref. 6 LGM GHG (CO2, CH4, N2O), LI, AE, VG 3 Ref. 86 LGM GHG (CO2, CH4), LI, AE, VG DTglobal 5 25.8 6 1.4 K; GLAMAP extrapolated with model82 CLIMAP and DTaa&gld 4 Ref. 79 LGM 5 Ref. 76 GC GHG (CO2, CH4), LI, AE, VG GHG (CO2, CH4) MARGO81 SST based DT 5 {3:0z1:3 {0:7 K DTtrop 6 Ref. 74 GC GHG (CO2, CH4), LI, AE DTaa (with 1.5 3 polar amplification) 0.88 6 0.13 7 Ref. 52 GC GHG (CO2, CH4, N2O), LI DTaa (with 2 3 polar amplification) 0.75 6 0.13 8 Ref. 52 GC GHG (CO2, CH4, N2O) DTaa (with 2 3 polar amplification) 1.5 6 0.25 This work, GC (,800 kyr ago) based on ref. 6 GHG (CO2, CH4, N2O), LI, AE, VG 0.66 6 0.22 to 2.26 6 0.78 9 Ref. 85 GC GHG (CO2, CH4, N2O), LI DTNH 5 model-based deconvolution of benthic d18O (ref. 51), scaled to global DT using a NH polar amplification on land of 2.75 6 0.25 DTaa (with 2 3 polar amplification) and 1.5 3 DTds 10 Ref. 39 GC GHG (CO2, CH4, N2O), LI, AE 36-record global SST synthesis along with DTaa&gld. z0:25 0:85{0:2 11 Ref. 39 GC GHG (CO2, CH4, N2O), LI 1.05 6 0.25 12 Ref. 87 Early to Middle Pliocene (4.2–3.3 Myr ago) CO2, ESS 13 Ref. 65 Slow feedbacks 14 This work (compilation) 15 16 This work (compilation) Ref. 78 Miocene optimum to present day Eocene–Oligocene transition (,34 Myr ago) Late Eocene versus present Middle Eocene Climatic Optimum (,40 Myr ago) 36-record global SST synthesis along with DTaa&gld. Using model-based DT for Middle and Early Pliocene of 2.4–2.9 uC and 4 uC. DCO2 alkenone Deconvolution of benthic d18O (ref. 63) Model-based DT, with range of CO2 values Model-based DT, with range of CO2 values DTds (2 records) and DTmg (7 records). DCO2 from alkenones 17 Ref. 78 Mid to Late Eocene transition (41–35 Myr ago) 18 Ref. 88 Early Eocene (,55–50 Myr ago) 19 This work (compilation) PETM (,56 Myr ago) 23–32 CO2. ESS (in the sense of ref. 44) CO2. ESS (in the sense of ref. 44) CO2. Ice-free world. Event study (not affected by plate tectonics and evolution effects) CO2. Largely ice-free world. Event study (not affected by plate tectonics and evolution effects) CO2. Ice-free world. (potential influences of plate tectonics and biological evolution not considered) CO2. Ice-free world. Event study (not affected by plate tectonics and evolution effects) DTds (ref. 71) and DTmg. DCO2 5 difference mid Eocene alkenone and late Eocene d11B Notes {0:12 1.1 6 0.05 0.75 6 0.13 1.92 6 0.14 to 2.35 6 0.18 (3.3 Myr ago); 2.60 6 0.19 (4.2 Myr ago) 0.78 6 10% z0:9 1:72{0:54 z0:26 1:82{0:49 0.95 6 0.3 0.95 6 0.3 DTmg (refs 89–91). DCO2 0.65 6 0.25 based on modelling91 marine organic carbon isotope fractionation92 and soil nodules93 DTds (.6 records) and 1.0–1.8 DTmg (.11 records; equatorial to polar). DCO2 based on deep ocean carbonate chemistry72, 95 6 8 4 | N AT U R E | VO L 4 9 1 | 2 9 N O V E M B E R 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved Author’s linear regression case. Value based on single-site tropical SST, and representation of global changes will be more uncertain Author used a single value for polar amplification. If 2 3 were used52, then the central estimate is closer to 0.7 Authors used a single value for polar amplification. If 1.5 3 were used74, then the central estimate becomes 1.0 Authors used a single value for polar amplification. If 1.5 3 were used74, then the central estimate becomes 2.0 This covers the range of S[GHG,X] given in Table 2 Authors used a single value for polar amplification. If 1.5 3 were used73, then the central estimate becomes 1.0 Polar amplification diagnosed, not imposed. Estimates made both in a spatially explicit sense and as direct global means As above Forcing in ref. 44; temperature in ref. 87. Both derived in global sense from model experiments f 5 0.71, b 5 5.35, c 5 1.3. Details in Supplementary Information Details in Supplementary Information Details in Supplementary Information 500 kyr timescale. DTds 5 DTmg. Temperatures from subtropics to high latitudes; no tropical data. Hence biased to high-latitude sensitivity Multi-million-year timescale. Adding uncertainty of 61 uC to DT would enhance 1s limits to 60.45 K W21 m2 Central value recalculated in ref. 94. Note ref. 89 underestimated tropical SST Details in Supplementary Information. Assumes all warming due to C input, and range of background CO2 and C-injection scenarios. DTds 5 DTmg. Total range of S is 0.7–2.2 K W21 m2. PERSPECTIVE RESEARCH Table 1 j Continued Label in Fig. 3 Source Time window Explicitly considered forcings CO2. Largely ice-free world. (potential influences of plate tectonics and biological evolution not considered) CO2. Largely ice-free DT after refs 52, 71. DCO2 based on ref. 60. world. ESS in the sense of ref. 44 CO2. Ice-free situation. DTmg, DCO2 based (Potential influences on GEOCARBSULF of plate tectonics and biological evolution not considered). 20 Ref. 96 Cretaceous and early Palaeogene 21 Ref. 94 Cretaceous and early Palaeogene 22 Ref. 97 Phanerozoic Temperature data used S and 1s bounds (K W21 m2) Notes 1 Recalculated in ref. 94. No uncertainty range was reported, nor salient details for assessment. Figure 3b, c assumes 625% .0.8 No uncertainty range reported. This is a lower bound estimate only Model-based with extensive uncertainty analysis 0.8–1.08 These studies have empirically determined S for the Pleistocene and some deep-time periods from comparison between data-derived time series for temperature and for radiative change. Comparison of results between studies is greatly hindered by the different ‘versions’ of S used, as related to different notions of which processes should be explicitly accounted for, and by the different approaches taken to approximate global mean surface temperature. All uncertainties are as originally reported, but shown here at the level equivalent to 1s, estimated where necessary by dividing total range values by a factor of 2. All values for S are reported in K W21 m2, where necessary after transformation using 3.7 W m–2 per doubling of CO2, bearing in mind the caveats for this at high CO2 concentrations as elaborated in the main text. GC, glacial cycles; LGM, Last Glacial Maximum; PETM, Palaeocene/Eocene thermal maximum; SST, sea surface temperature. See main text for details of forcings. Subscripts: aa, Antarctica; gld, Greenland; trop, tropical; ds, deep sea; global, global mean; mg, Mg/Ca; NH, Northern Hemisphere. We emphasize that all feedbacks, and thus the calculated climate sensitivity, may depend in a—largely unknown—nonlinear manner on the state of the system before perturbation (the ‘background climate state’) and on the type of forcing7–15. The relationship of S with background climate state differs among climate models12,16–18. A suggestion of state dependence is also found in a data comparison (Table 2)6, where climate sensitivity for the past 800,000 years (800 kyr) shows substantial fluctuations through time (Fig. 2). In contrast, its values for the Last Glacial Maximum (LGM) alone occupy only the lower half of that range (Fig. 2). That evaluation also suggests that the relationship of S with the general climate state may not be simple. ‘Fast’ versus ‘slow’ processes Climate sensitivity depends on processes that operate on many different timescales, from seconds to millions of years, due to both direct response to external radiative forcing, and internal feedback processes (Fig. 1). Hence, the timescale over which climate sensitivity is considered is critical. An operationally pragmatic decision is needed to categorize a process as ‘slow’ or ‘fast’, depending on the timescale of interest, the resolution of the (palaeo-)records considered and the character of changes therein19. If a process results in temperature changes that reach steady state slower than the timescale of the underlying radiative perturbation, then it is considered ‘slow’; if it is faster or coincident, then it is ‘fast’. Present-day atmospheric GHG concentrations and the radiative perturbation due to anthropogenic emissions increase much faster than observed for any natural process within the Cenozoic era20–22. For the present, the relevant timescale for distinguishing between fast and slow processes can be taken as 100 yr (ref. 23). Ocean heat uptake plays out over multiple centuries. Combined with further ‘slow’ processes, it causes climate change over the next few decades to centuries to be dominated by the so-called ‘transient climate response’ to radiative changes that result from changing GHG concentrations and aerosols5,19,24. After about 100 yr, this transient climate response is thought to amount to roughly two-thirds of the equilibrium (see below) climate sensitivity5,25. Climate models account for the fast feedbacks from changes in watervapour content, lapse rate, cloud cover, snow and sea-ice albedo26, and the resulting response is often referred to as the ‘fast-feedback’ or ‘Charney’ sensitivity23. To approximate the ‘equilibrium’ value of that climate sensitivity, accounting for ocean heat uptake and further slow processes, models might be run over centuries with all the associated computational difficulties27–30, or alternative approaches may be used that exploit the energy balance of the system for known forcing or extrapolation to equilibrium31. In palaeoclimate studies, an operational distinction has emerged to distinguish ‘fast’ and ‘slow’ processes relative to the timescales of temperature responses measured in palaeodata, where ‘fast’ is taken to apply to processes up to centennial scales, and ‘slow’ to processes with timescales close to millennial or longer. Thus, changes in natural GHG concentrations are dominated by ‘slow’ feedbacks related to global biogeochemical cycles (Fig. 1). Similarly slow are the radiative influences of albedo feedbacks that are dominated by centennial-scale or longer changes in global vegetation cover and global ice area/volume (continental ice sheets) (Fig. 1). Table 2 | Common permutations of S that may be encountered in palaeostudies Label in Fig. 3 S definition Explicitly considered radiative perturbation Period in which it is practical to use the definition S 6 1s for 800 kyr (K W21 m2) S 6 1s for LGM (K W21 m2) S for Pliocene (K W21 m2) 23 S[CO2] DR[CO2] 3.08 6 0.96 2.63 6 0.57 1.2 24 25 26 27 28 29 30 31 32 S[CO2, LI] S[CO2, LI, VG] S[CO2, LI, AE] S[CO2, LI, AE, VG] S[GHG] S[GHG, LI] S[GHG, LI, VG] S[GHG, LI, AE] S[GHG, LI, AE, VG] DR[CO2, LI] DR[CO2, LI, VG] DR[CO2, LI, AE] DR[CO2, LI, AE, VG] DR[GHG] DR[GHG, LI] DR[GHG, LI, VG] DR[GHG, LI, AE] DR[GHG, LI, AE, VG] All (especially pre-35 Myr ago when LI < 0) ,35 Myr ago ,35 Myr ago ,35 Myr ago, but mainly ,800 kyr ago ,35 Myr ago, but mainly ,800 kyr ago ,800 kyr ago ,800 kyr ago ,800 kyr ago ,800 kyr ago ,800 kyr ago 1.07 6 0.40 0.86 6 0.27 0.90 6 0.42 0.75 6 0.29 2.32 6 0.76 0.96 6 0.36 0.78 6 0.23 0.82 6 0.36 0.68 6 0.24 0.95 6 0.22 0.80 6 0.19 0.72 6 0.18 0.63 6 0.15 1.97 6 0.41 0.85 6 0.19 0.73 6 0.16 0.66 6 0.16 0.58 6 0.14 0.97 0.82 S (second column) is presented with a subscript that identifies the explicitly considered radiative perturbations DR (third column, same subscripts as for S); all other processes are implicitly resolved as feedbacks within S. The period in which the various definitions of S are practical is determined by the availability of data for the explicitly considered processes. Subscript CO2 indicates the radiative impact of atmospheric CO2 concentration changes; LI represents the radiative impact of global land ice-volume changes; VG stands for the radiative impact of global vegetation cover changes; AE indicates the radiative impact of aerosol changes; GHG stands for the impact of changes in all non-water natural greenhouse gases (notably CO2, CH4 and N2O). Columns 5 and 6 give calculated values for all suggested permutations of S for the past 800 kyr or the LGM, respectively, based on a previous data compilation6. Mean values of all S[X] for the LGM are about 13% smaller than for the whole 800 kyr, but lie well within the given uncertainties. This offset illustrates the state-dependence of S (see Supplementary Information). Column 7 gives examples for the Pliocene13,44; Fig. 3b, c assumes 625% uncertainty in these. In these values the effects of orographic changes have been taken into account (see Supplementary Information section B2). 2 9 NO V E M B E R 2 0 1 2 | VO L 4 9 1 | N AT U R E | 6 8 5 ©2012 Macmillan Publishers Limited. All rights reserved RESEARCH PERSPECTIVE a and process modelling, especially because dust forcing may account for some 20% of the glacial–interglacial change in the radiative budget6,39. So for comparison of results between studies, it is most effective to consider only the classical ‘Charney’ water-vapour, cloud, lapse rate, and snow and sea-ice feedbacks23 as ‘fast’, and all other feedbacks as ‘slow’. In addition, results from palaeoclimate sensitivity studies generally do not address the transient climate response that dominates present-day changes, but capture a more complete longer-term system response comparable with equilibrium climate sensitivity in climate models. 2 ΔT (K) 0 –2 –4 –6 –8 2 0 –2 –4 –6 ΔR[CO2, LI] (W m–2) b –8 c 3.0 2.8 2.6 2.4 S[CO2, LI] (K W–1 m2) 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 800 Mean of Si ± σ0 Si ± σ1 at LGM σ1 100-kyr running mean of Si 700 600 500 400 300 200 100 0 Time (kyr BP) Figure 2 | Illustration of variability of climate sensitivity using a calculation of S[CO2,LI], as defined in this work, for the past 800 kyr. a, Changes in global temperature. b, Changes in radiative forcing due to changes in CO2 and surface albedo due to land ice. c, Calculated S[CO2,LI], which is only considered robust and calculated when DT , 21.5 K and DR[CO2,LI] , 20.5 W m–2, as indicated by the dotted red lines in a and b. In c, mean of Si 6 s0 (dashed black lines indicate s0, the uncertainty of averaging) and 100-kyr running mean (blue line) are shown. Magenta marker in c denotes Si 6 s1 for the LGM only (23–19 kyr ago) (s1 is the square root of the sum of squares of individual uncertainties connected with different processes contributing to Si). The grey areas in a–c denote s1 (standard deviation) uncertainties of Si for single points in time (points themselves are omitted for clarity). Details of data and the definition of the calculated uncertainties presented in this figure are available in Supplementary Information. In a and b, the dashed black lines indicate the preindustrial reference case (DT 5 0 K, DR[CO2,LI] 5 0 W m–2). Other processes clearly have both fast and slow components. For example, palaeorecords of atmospheric dust deposition imply important aerosol variations on decadal to astronomical (orbital) timescales32–36, reflecting both slow controlling processes related to ice-volume and land-surface changes, and fast processes related to changes in atmospheric circulation. A further complication arises from the lack of adequate global atmospheric dust data for any geological episode except the LGM37,38, even though that is essential because the spatial distribution of dust in the atmosphere tends to be inhomogeneous and because temporal variations in some locations tend to take place over several orders of magnitude32–36. Moreover, palaeoclimate models generally struggle to account for aerosols, with experiments neither prescribing nor implicitly resolving aerosol influences. So far, understanding of aerosol/dust feedbacks remains weak and in need of improvements in both data coverage Forcing and slow feedbacks The external drivers of past natural climate changes mainly resulted from changes in solar luminosity over time40, from temporal and spatial variations in insolation due to changes in astronomical parameters41–43, from changes in continental configurations14,44, and from geological processes that directly affect the carbon cycle (for example, volcanic outgassing). However, the complete Earth system response to such forcings as recorded by palaeodata cannot be immediately deduced from the (equilibrium) ‘fast feedback’ sensitivity of climate models, because of the inclusion of slow feedback contributions. When estimating climate sensitivity from palaeodata, agreement is therefore needed about which of the slower feedback processes are viewed as feedbacks (implicitly accounted for in S), and which are best considered as radiative forcings (explicitly accounted for in DR). We employ an operational distinction31,45 in which a process is considered as a radiative forcing if its radiative influence is not changing with temperature on the timescale considered, and as a feedback if its impact on the radiation balance is affected by temperature changes on that timescale. For example, the radiative impacts of GHG changes over the past 800 kyr may be derived from concentration measurements of CO2, CH4 and N2O in ice cores46–48, and the radiative impacts of land-ice albedo changes may be calculated from continental ice-sheet estimates, mainly based on sea-level records49–51. Thus, the impacts of these slow feedbacks can be explicitly accounted for before climate sensitivity is calculated. This leaves only fast feedbacks to be considered implicitly in the calculated climate sensitivity, which so approximates the (equilibrium) ‘Charney’ sensitivity from modelling studies6,39,52. Operational challenges All palaeoclimate sensitivity studies are affected by limitations of data availability. Below we discuss such limitations to reconstructions of forcings and feedbacks, and of global surface temperature responses. First, however, we re-iterate a critical caveat, namely that the climate response depends to some degree on the type of forcing (for example, shortwave versus longwave, surface versus top-of-atmosphere, and local versus global). The various radiative forcings with similar absolute magnitudes have different spatial distributions and physics, so that the concept of global mean radiative forcing is a simplification that introduces some (difficult to quantify) uncertainty. Astronomical (orbital) forcing is a key driver of climate change. In global annual mean calculations of radiative change, astronomical forcing is very small and often ignored39,52. Although this obscures its importance, mainly concerning seasonal changes in the spatial distribution of insolation over the planet41,42,53–55, we propose that the contribution of the astronomical forcing to DR may be neglected initially. When other components of the system respond to the seasonal aspects of forcing, such as Quaternary ice-sheet variations, these may be accounted for as forcings themselves. GHG concentrations from ice cores are not available for times before 800 kyr ago, when CO2 levels instead have to be estimated from indirect methods. These employ physico-chemical or biological processes that depend on CO2 concentrations, such as the abundance of stomata on fossil leaves56, fractionation of stable carbon isotopes by marine phytoplankton57, boron speciation and isotopic fractionation in sea water as a function of pH and preserved in biogenic calcite58, and the stability fields of minerals precipitated from waters in contact with the atmosphere59. 6 8 6 | N AT U R E | VO L 4 9 1 | 2 9 N O V E M B E R 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved PERSPECTIVE RESEARCH Considerable uncertainties remain in such reconstructions, but improvements are continually made to the methods, their temporal coverage and their mutual consistency60. Recent work has synthesized a high-resolution CO2 record for the past 20 million years (Myr; ref. 61), but new data and updated syntheses remain essential, particularly for warmer climate states. Also, proxies are needed for reconstruction of CH4 and N2O concentrations in periods pre-dating the ice-core records62. Regarding the assessment of land-ice albedo changes, good methods exist for the generation of continuous centennial- to millennial-scale sea-level (ice-volume) records over the past 500 kyr (refs 49–51), but such detailed information remains scarce for older periods. A modelbased deconvolution of deep-sea stable oxygen isotope records into their ice-volume and deep-sea temperature components51 was recently extended to 35 Myr ago63, but urgently requires independent validation, especially to address uncertainties about the volume-to-area relationships that would be different for incipient ice sheets than for mature ice sheets64,65. Before 35 Myr ago, there is thought to have been (virtually) no significant land-ice volume66, but this does not exclude the potential existence of major semi-permanent snow/ice-fields67,68, and there remain questions whether these would constitute ‘fast’ (snow) or ‘slow’ (land-ice) feedbacks. The contribution of the sea-ice albedo feedback also remains uncertain, with little quantitative information beyond the LGM. Similar examples of uncertainties and limited data availability could be listed for all feedbacks. However, a ‘deep-time’ (before 1 Myr ago) geological perspective must be maintained because it offers access to the nearest natural approximations of the current rate and magnitude of GHG emissions69,70, and because only ancient records provide insight into climate states globally warmer than the present. Given that no past perturbation will ever present a perfect analogue for the continuing anthropogenic perturbation, it may be more useful to consider past warm climate states as test-beds for evaluating processes and responses, and for challenging/validating model simulations of those past climate states. Such data–model comparisons will drive model skill and understanding of processes, improving confidence in future multi-century projections. For such an approach, palaeostudies may minimize the impacts of very long-term influences on climate sensitivity (for example, due to changes in orography, or biological evolution of vegetation) through a focus on highly resolved documentation of specific perturbations that are superimposed upon different long-term background climate states. An example is the pronounced transient global warming and carbon-cycle perturbation during the Palaeocene/Eocene thermal maximum (PETM) anomaly71,72, which punctuated an already warm climate state73. Note that deep-time case studies need to consider one further complication, namely that the radiative forcing per CO2 doubling may be about 3.7 W m–2 when starting from pre-industrial concentrations, but increases at higher CO2 levels11. Data-led studies may help with a first-order documentation of this dependence. Calculation of S from CO2 and temperature measurements using a constant 3.7 W m–2 per CO2 doubling would (knowingly) overestimate S for high-CO2 episodes. The difference with other, identically defined, S values for different climate background states may then be used to assess any deviation from 3.7 W m–2 per CO2 doubling. Regarding the reconstruction of past global surface temperature responses (that is, DT in equation (1) below), again much remains to be improved. Most work to date (see Table 1) relies on one or more of the following: polar temperature variations from Antarctic ice cores (since 800 kyr ago) with a multiplicative correction for ‘polar amplification’ (usually estimated at 1.5–2.0; refs 74, 75); deep-sea temperature variations from marine sediment-core data with a correction for the ratio between global surface temperature and deep-sea temperature changes (often estimated at 1.5); single-site sea surface temperature (SST) records from marine sediment cores; or compilations of SST data of varying geographic coverage from marine sediment cores6,39,52,76–78. So far, few studies have included terrestrial temperature proxy records other than those from ice cores79, yet better control on land-surface data is crucial because of seasonal and land-sea contrasts. Continued development is needed of independently validated (multi-proxy) and spatially representative (global) data sets of high temporal resolution relative to the climate perturbations studied. Uncertainties in individual reconstructions of temperature change may in exceptional cases be reported to 60.5 K, but more comprehensive uncertainty assessments normally find them to be larger80,81. Compilation of such records to determine changes in global mean surface temperature involves the propagation of further assumptions/uncertainties, for example due to interpolation from limited spatial coverage, and the end result is unlikely to be constrained within narrower limits than 61 K even for well-studied intervals. Finally, comparisons between independent reconstructions for the same episode reveal ‘hidden’ uncertainties due to differences between each study’s methodological choices, uncertainty determination, and data-quality criteria, which are hard to quantify and often poorly elucidated. Take the LGM for example, which for temperature is among the best-studied intervals. The MARGO compilation81 inferred a global SST reduction of –1.9 6 1.8 K relative to the present. Another spatially explicit study79 used that range to infer a global mean surface air temperature anomaly of {3z1:3 {0:7 K. The latter contrasts with a previous estimate of 25.8 6 1.4 K (ref. 82), which is consistent with tropical (30u S to 30u N) SST anomalies of 22.7 6 1.4 K (ref. 83). However, that tropical range itself is also contested; the MARGO81 study suggested such cooling in the Atlantic Ocean, but less in the tropics of the Indian and Pacific Oceans (giving a global tropical cooling of only 21.7 6 1.0 K). Clearly, even a well-studied interval gives rise to a range of estimates for temperature, and therefore for climate sensitivity. It is evident that progress in quantifying palaeoclimate sensitivity will not only rely on a common concept and terminology that allows like-for-like comparisons (see below); it will also rely on an objective, transparent and hence reproducible discussion in each study of the assumptions and uncertainties that affect the values determined for change in both temperature and radiative forcing. A way forward Here we propose a new terminology to help palaeoclimate sensitivity studies adopt common concepts and approaches, and thus improve the potential for like-for-like comparisons between studies. First we outline how our concept of ‘equilibrium’ S for palaeo-studies relates to ‘equilibrium’ S for modern studies. Then, we present a notation system that is primarily of value to data-based palaeo studies to clarify which slow feedbacks are explicitly accounted for. We finish with an application of the new framework, calculating climate sensitivity from a representative selection of palaeoclimate sensitivity estimates over the past 65 Myr, with a fair balance of climates warmer than the present to those colder than the present. When the DT response to an applied GHG radiative forcing DR is small relative to ‘pre-perturbation’ reference temperature, the ‘equilibrium’ climate sensitivity Sa (where a indicates actuo, for present-day) takes the form (see, for example, refs 4, 84): Sa ~ DT ~ DR {1 N P lfi lP z ð1Þ i~1 Here lP is the Planck feedback parameter (23.2 W m22 K21) and lfi (in W m22 K21) represents the feedback parameters of any number (N) of fast (f ) feedbacks. We define feedback parameters in the form lfi 5 DRi/DT. Sa is the ‘Charney’ sensitivity calculated by most climate models in ‘2 3 CO2’ equilibrium simulations, with a range of 0.6–1.2 K W21 m2 in IPCC-AR4. However, the Earth system in reality responds to a perturbation according to an equilibrium climate sensitivity parameter Sp (where p indicates palaeo), but the timescales to reach this equilibrium are long, so that the forcing normally changes before equilibrium is reached. To obtain Sa from palaeoclimate sensitivity Sp, a correction is therefore needed for the slow feedback influences. Using lsj to represent any number (M) of slow (s) feedbacks, we derive the general expression (see Supplementary Information): 2 9 NO V E M B E R 2 0 1 2 | VO L 4 9 1 | N AT U R E | 6 8 7 ©2012 Macmillan Publishers Limited. All rights reserved RESEARCH PERSPECTIVE 0 B B Sa ~Sp B1z @ M P lsj 1 C j~1 C C N P fA lP z li ð2Þ i~1 This approach is contingent on the above-mentioned caveats of statedependence, linearization (small DT ), changes in slow feedbacks, and transient effects, where the last is relevant only in records of exceptionally high temporal resolution. Knowledge of slow (ls) and fast (lf) feedbacks can be combined into a factor F 5 ls/(lf 1 ls) that may then be used to back-calculate fast feedbacks out of palaeoclimate sensitivity Sp. A recent study44 defined the term ‘Earth system sensitivity’ (ESS) to represent the long-term climate response of Earth’s climate system to a given CO2 forcing, including both fast and slow processes. In our notation, ESS 5 DR23CO2 Sp, where DR23CO2 is the forcing due to a CO2doubling (3.7 W m–2). Here we introduce a more explicit notation regarding what was (not) included in the climate sensitivity diagnosis. It is the ‘specific climate sensitivity’ S[A,B…], expressed in K W21 m2, where slow feedback processes A, B, and so on, are explicitly accounted for (that is, included in the forcing term, DR[A,B…]). We use ‘LI’ to denote albedo forcing due to land-ice volume/area changes, ‘VG’ for vegetation-albedo forcing, ‘AE’ for aerosol forcing and ‘CO2’ for atmospheric CO2 forcing (see also Table 1). This approach requires from the outset that a comprehensive view is taken of the various causes of change in the radiative balance. b 0.05 12a 12b 12c 14 15 23plei 23plio 28plei 5 8 19 16 17 18 20 21 22 24plei 24plio 26plei 27plei 25plei 25plio 7 9 29plei 11 6 31plei 10 3 13 32plei 4 2 30plei 1b 1a 0 0.82 0.58 Frequency 1.23 0.28 0.04 1.70 0.03 0.02 0.01 0 –0.5 c 0 1 0.5 1.5 2 2.5 0.79 0.06 0.65 1.27 0.48 1.91 0.05 Frequency Row identifier in Tables 1 and 2 a The most practical version of S to be estimated from palaeodata is S[CO2,LI], because S[CO2,LI] 5 S[CO2] during times (pre-35 Myr ago) without ice volume, and because global vegetation cover changes, atmospheric dust fluctuations, and both CH4 and N2O fluctuations (the two important non-CO2 GHGs) generally remain poorly constrained by proxy data. Common reporting of S[CO2,LI] would bring results closer in line with the model-based concept of ‘equilibrium’ fast-feedback sensitivity. The above-mentioned issues with aerosol influences mean that it would currently be best for estimates from palaeodata to report both S[CO2,LI] and S[CO2,LI,AE]. Table 2 lists example estimates for S following the main potential permutations of the definition of S in our approach (for detailed breakdowns, see Supplementary Information). The first example uses records of palaeodata since 800 kyr ago. The second example uses the same input data series6, but focuses only on the LGM; the contrast between examples one and two thus highlights state-dependence. The third example lists estimates for S[CO2], S[CO2,LI] and S[CO2,LI,VG] from a more modelbased assessment for the mid-Pliocene (,3–3.3 Myr ago)13, with DT 5 3.3 K relative to the present and DRCO2 5 1.9 W m–2 due to CO2 increase from 280 to 400 parts per million by volume (p.p.m.v.; ref. 44). The broad range of S values found within each example illustrates that comparison across different definitions unrealistically widens the range of values reported, notably towards high values, because omission of ‘forcing’ due to the action of any slow feedbacks will cause overestimation of S (see also Fig. 3). For a first-order estimate of the range of S from palaeodata that approximates compatibility with the centennial timescale ‘equilibrium’ LGM Pleistocene Pliocene Miocene Eocene PETM Cretaceous Phanerozoic 1 2 3 S[X] (K W–1 m2) 4 0.04 0.03 0.02 0.01 CO2 GHG LI Figure 3 | Evaluation of results from Tables 1 and 2. y-Axis labels refer to numbered rows in these Tables. a, Data summary by table row. b, Probability assessment using normal distributions (shifted where relevant). c, Probability assessment using lognormal distributions. S[X] refers to the climate sensitivity as defined in detail by the subscript X in Tables 1 and 2. For b and c, we assume a relative uncertainty of 25% for entries that lacked uncertainty estimates in the source studies. In a, rows from Table 2 are identified with either ‘plei’ or ‘plio’ to distinguish between the past 800 kyr and the Pliocene entries, respectively. The colour coding refers to broad geological intervals, as shown in the key. Boxes at right indicate which conditions were explicitly accounted for; that is, as ‘forcings’ (in the CO2/GHG column, filled squares indicate GHG and open AE VG 0 –0.5 0 0.5 1 S[X] (K W–1 m2) 2 2.5 squares CO2). Circles (data points in a) show central values where reported, error bars represent uncertainties as outlined in the Tables, at the 1s equivalent level. Arrow (case 21) indicates a value reported only as .0.8 K W21 m2. Black dashed lines in a show 68% probability limits for all estimates that account for at least ‘CO2’ and ‘LI’, based on thick dashed lines in b and c, taking whichever 68% value offers the widest (more conservatively estimated) margin. In b and c, the solid black line indicates the mode value (maximum), and the thin dashed lines the 95% probability limits. All distributions in b and c are given as individual normalized frequencies (grey lines), and as mean normalized frequencies (red line). 6 8 8 | N AT U R E | VO L 4 9 1 | 2 9 N O V E M B E R 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved PERSPECTIVE RESEARCH 10 Equilibrium ΔT (K) 8 10 a This work 8 6 6 4 4 2 2 0 0 –2 –2 Fast+slow feed backs Only fast feedbacks –4 –6 200 250 300 350 400 450 500 550 10 Equilibrium ΔT (K) 8 Fast+slow feedbacks Only fast feedbacks –4 –6 200 250 300 350 400 450 500 550 10 c JH_12 8 6 6 4 4 2 2 d All Only fast feedbacks Fast+slow 0 feedbacks 0 –2 –2 Fast+slow feedbacks Only fast feedbacks –4 –6 b RW_11 200 250 300 350 400 450 500 One study Two studies Three studies –4 550 –6 CO2 (p.p.m.v.) 200 250 300 350 400 450 500 550 CO2 (p.p.m.v.) Figure 4 | Equilibrium response of the global temperature as a function of CO2 concentrations, based on three different approaches. a, This work, using data from the late Pleistocene of the past 800 kyr (ref. 6). b, Using data of the past 20 Myr (RW_11; ref. 61). c, Based on JH_12 (ref. 85) using similar data of the past 800 kyr as in a. d, Combination of all three approaches. Plotted areas include uncertainty estimates of one standard deviation. Because this work and JH_12 developed their approach only on Pleistocene data (climate being mainly colder than today), extrapolation of the impact of slow feedbacks to 2 3 CO2 is not meaningful (we show only extrapolation with fast feedbacks). RW_11 in contrast also includes warmer climates with CO2 up to 450 p.p.m.v., so that the applicable range with slow feedbacks extends to 450 p.p.m.v. For future climate with 2 3 CO2 and a short time horizon (,100 yr), only fast feedbacks are of interest (see d). Approaches partly disagree because of different assumptions. Uncertainties in this work (a) are estimated to be larger than they were in RW_11 (b) and JH_12 (c). For details of the equations and values used, see Supplementary Information. values of the IPCC-AR41, values need to be used that account for ‘CO2’ or ‘GHG’ as well as ‘LI’, and preferably also ‘AE’ and/or ‘VG’ (Tables 1, 2; Fig. 3). Such an assessment, excluding the case of row 21 in Table 1, yields a likely1 (68%) probability range of 0.6–1.3 K W21 m2, and a 95% range of 0.3–1.9 K W21 m2 (Fig. 3). These represent the widest margins out of two assessments, using either normal distributions with shifts when relevant (Fig. 3a), or lognormal distributions that inherently allow asymmetry2 (Fig. 3b). These assessments include uncertainties as outlined in the source studies, as well as any unaccounted-for dependence on different background climate states, but exclude potential additional uncertainties highlighted in this study. Inclusion of ESS values (approximated by S[CO2]) would extend the upper limit beyond 3 K W21 m2 (Fig. 3a). Future work following a strict framework for reporting and comparison of palaeodata may refine the observed asymmetry. Finally, following our conceptual framework, we can make a projection of equilibrium temperature change over a range of CO2 concentrations while considering either slow and fast (or only fast) feedbacks (Fig. 4; see Supplementary Information for details). Including the known uncertainties associated with palaeoclimate sensitivity calculations, and comparing with two previous approaches61,85, we find overlap in the 68% probability envelopes that implies equilibrium warming of 3.1–3.7 K for 2 3 CO2 (Fig. 4), equivalent to a fast feedback (Charney) climate sensitivity between 0.8 and 1.0 K W21 m2. For longer, multi-centennial projections, some of the slow feedbacks (namely vegetation-albedo and aerosol feedbacks) may need further consideration. However, their impact is difficult to estimate from palaeodata, because uncertainties are large, and because responses during climates colder than present may differ from responses during future warming. 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Geologic constraints on the glacial amplification of Phanerozoic climate sensitivity. Am. J. Sci. 311, 1–26 (2011). 98. Schmidt, G. A. Climate sensitivity — how sensitive is Earth’s climate to CO2; past. PAGES News 20, 11 (2012). 99. Wunsch, C. & Heimbach, P. How long to oceanic tracer and proxy equilibrium? Quat. Sci. Rev. 27, 637–651 (2008). Supplementary Information is available in the online version of the paper. Acknowledgements This Perspective arose from the first PALAEOSENS workshop in March 2011. We thank the Royal Netherlands Academy of Arts and Sciences (KNAW) for funding and hosting this workshop in Amsterdam, PAGES for their support, and J. Gregory for discussions. This study was supported by the UK-NERC consortium iGlass (NE/I009906/1), and 2012 Australian Laureate Fellowship FL120100050. D.J.B., E.J.R. and P.V. were supported by Royal Society Wolfson Research Merit Awards. A.S. thanks the European Research Council for ERC starting grant 259627, and M.H. acknowledges NSF P2C2 grant 0902882. Some of the work was supported by grant 243908 ‘Past4Future’ of the EU’s seventh framework programme; this is Past4Future contribution number 30. Author Contributions E.J.R., A.S. and H.A.D. initiated the PALAEOSENS workshop, and led the drafting of this study together with P.K., A.S.v.d.H. and R.S.W.v.d.W. The other authors contributed specialist insights, discussions and feedback. Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper. Correspondence and requests for materials should be addressed to E.J.R. (e.rohling@noc.soton.ac.uk). PALAEOSENS Project Members E. J. Rohling1,2, A. Sluijs3, H. A. Dijkstra4, P. Köhler5, R. S. W. van de Wal4, A. S. von der Heydt4, D. J. Beerling6, A. Berger7, P. K. Bijl3, M. Crucifix7, R. DeConto8, S. S. Drijfhout9, A. Fedorov10, G. L. Foster1, A. Ganopolski11, J. Hansen12, B. Hönisch13, H. Hooghiemstra14, M. Huber15, P. Huybers16, R. Knutti17, D. W. Lea18, L. J. Lourens3, D. Lunt19, V. Masson-Demotte20, M. Medina-Elizalde21, B. Otto-Bliesner22, M. Pagani10, H. Pälike1,23, H. Renssen24, D. L. Royer25, M. Siddall26, P. Valdes19, J. C. Zachos27 & R. E. Zeebe28 Affiliations for participants: 1School of Ocean and Earth Science, University of Southampton, National Oceanography Centre, Southampton SO14 3ZH, UK. 2Research School of Earth Sciences, The Australian National University, Canberra, Australian Capital Territory 0200, Australia. 3Department of Earth Sciences, Faculty of Geosciences, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, The Netherlands. 4Institute for Marine and Atmospheric Research Utrecht, Utrecht University, 3584 CC Utrecht, The Netherlands. 5 Alfred Wegener Institute for Polar and Marine Research (AWI), PO Box 12 01 61, 27515 Bremerhaven, Germany. 6Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK. 7Georges Lemaitre Centre for Earth and Climate Research, Earth and Life Institute–Université catholique de Louvain, Chemin du Cyclotron 2, Box L7.01.11, 1348 Louvain-la-Neuve, Belgium. 8Department of Geosciences, 611 North Pleasant Street, 233 Morrill Science Center, University of Massachusetts, Amherst, Massachusetts 01003-9297, USA. 9Royal Netherlands Meteorological Institute, PO Box 201, 3730 AE De Bilt, The Netherlands. 10Department of Geology and Geophysics, Yale University, PO Box 208109, New Haven, Connecticut 06520-8109, USA. 11Potsdam Institute for Climate Impact Research (PIK), PO Box 601203, 14412 Potsdam, Germany. 12 NASA Goddard Institute for Space Studies, 2880 Broadway, New York, New York 10025, USA. 13Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York 10964, USA. 14Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands. 15Earth and Atmospheric Sciences Department, Purdue University, West Lafayette, Indiana 47907, USA. 16Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA. 17Institute for Atmospheric and Climate Science, ETH Zurich, Universitätstrasse 16, 8092 Zurich, Switzerland. 18Department of Earth Science, University of California, Santa Barbara, California 93106-9630, USA. 19School of Geographical Sciences, University of Bristol, University Road, Bristol BS8 1SS, UK. 20LSCE (IPSL/CEA-CNRS-UVSQ), UMR 8212, LCEA Saclay, 91 191 Gif sur Yvette Cedex, France. 21 Centro de Investigación Cientı́fica de Yucatán, Unidad Ciencias del Agua, Cancún, Quintana Roo, 77500, México. 22National Center for Atmospheric Research, PO Box 3000, Boulder, Colorado 80307-3000, USA. 23MARUM, University of Bremen, Leobener Straße, 28359 Bremen, Germany. 24Department of Earth Sciences, Faculty of Earth and Life Sciences, Free University Amsterdam, De Boelelaan 1085, NL1081HV Amsterdam, The Netherlands. 25Department of Earth and Environmental Sciences, Wesleyan University, Middletown, Connecticut 06459, USA. 26Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen’s Road, Bristol BS8 1RJ, UK. 27Earth and Planetary Sciences, University of California, Santa Cruz, California 95064, USA. 28 School of Ocean and Earth Science and Technology, Department of Oceanography, University of Hawaii at Manoa, 1000 Pope Road, MSB 629 Honolulu, Hawaii 96822, USA. 2 9 NO V E M B E R 2 0 1 2 | VO L 4 9 1 | N AT U R E | 6 9 1 View publication stats ©2012 Macmillan Publishers Limited. 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