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Climate sensitivity estimated from ensemble simulations of glacial climate


The concentration of greenhouse gases (GHGs) in the atmosphere continues to rise, hence estimating the climate system’s sensitivity to changes in GHG concentration is of vital importance. Uncertainty in climate sensitivity is a main source of uncertainty in projections of future climate change. Here we present a new approach for constraining this key uncertainty by combining ensemble simulations of the last glacial maximum (LGM) with paleo-data. For this purpose we used a climate model of intermediate complexity to perform a large set of equilibrium runs for (1) pre-industrial boundary conditions, (2) doubled CO2 concentrations, and (3) a complete set of glacial forcings (including dust and vegetation changes). Using proxy-data from the LGM at low and high latitudes we constrain the set of realistic model versions and thus climate sensitivity. We show that irrespective of uncertainties in model parameters and feedback strengths, in our model a close link exists between the simulated warming due to a doubling of CO2, and the cooling obtained for the LGM. Our results agree with recent studies that annual mean data-constraints from present day climate prove to not rule out climate sensitivities above the widely assumed sensitivity range of 1.5–4.5°C (Houghton et al. 2001). Based on our inferred close relationship between past and future temperature evolution, our study suggests that paleo-climatic data can help to reduce uncertainty in future climate projections. Our inferred uncertainty range for climate sensitivity, constrained by paleo-data, is 1.2–4.3°C and thus almost identical to the IPCC estimate. When additionally accounting for potential structural uncertainties inferred from other models the upper limit increases by about 1°C.

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  1. It should be noted that those LGM simulations do not account for the forcing effects of dust and vegetation changes. If these forcings are included as further boundary conditions an additional global surface air temperature (SAT) cooling of about 1.5 to 2°C can be expected (Schneider von Deimling et al., in preparation).

  2. The parameter correlations neither cause the inferred quasi-linear relation between ΔT 2x and the magnitude of LGM cooling (Fig. 5), nor systematic differences in the model results, as can be seen in Fig. 6.

  3. For inference of consistency we compare PMIP-2 results with CLIMBER-2 simulations which are based on PMIP-2 boundary conditions (excluding forcing contributions by glacial dust and vegetation).

  4. Ice and sediment cores indicate a drastic increase of dust deposition rate at the MIS4/MIS3 boundary (around 60 kyr BP), while SST cooling in the tropics is rather moderate at that time. Multivariate analysis of tropical SST and Antarctic dust concentration (Lea 2004) provides an upper estimate for the impact of dust on glacial temperature. Moreover, when accounting for the fact that only part of the glacial SST signal should be attributed to the increase in dust concentration and that changes in dust concentration coincide with CO2 drop, ice sheet growth and sea level lowering, the effect of dust on LGM cooling is smaller than estimated by multivariate analysis (Lea 2004).

  5. This concentration yields the same radiative forcing as the sum of individual GHG forcings resulting from changes in CO2, CH4 and N2O concentrations.


ΔT 2x :

Climate sensitivity


Transient climate response


General circulations model


Intergovernmental panel on climate change


Last glacial maximum


Greenhouse gas

CO2 :

Carbon dioxide


Sea surface temperatures


Surface air temperature


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The authors are grateful to M. Werner and I. Tegen for providing and discussing the LGM radiative anomaly dust fields, to C. Schäfer-Neth and A. Paul for providing the SST paleo-data, to V. Petoukhov for assistance with the simulation design, to M. Flechsig, W.v. Bloh, A. Glauer and K. Kramer for providing the ensemble simulation framework. This work was supported by BMBF research grant 01LG0002, SFB555 and grant II/78470 by the Volkswagen Foundation.

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Correspondence to Thomas Schneider von Deimling.



Consistency criteria

For our interval method simulated climate characteristics have to lie within the ranges of all seven data-constraints to be regarded as consistent with the data (see Appendix 7.2). This prerequisite leads to an extensive rejection of parameter combinations (about 90%). Further constraints, which account for latitudinal model characteristics, have not proven to further constrain ΔT 2x (not shown). Application of paleo-data-constraints to this strongly constrained ensemble (123 out of 1,000 model runs) results in even fewer paleo-consistent model realizations. To derive statistically robust estimates of ΔT 2x we therefore approximate the inferred relationship between ΔT 2x and LGM SST cooling by a linear regression (Fig. 6, solid red curve). The fit uses the simulation results of the correlated ensemble (blue dots), which covers a broad range of ΔT 2x . We read the consistent ΔT 2x range from the fit-curve (pink asterisks). Then we account for the additional uncertainty on ΔT 2x caused by deviations from the fit. This is realized by choosing the 5–95% of the deviation spread (represented as red dashed lines), estimated from the uncorrelated ensemble (orange dots), as it provides larger deviations than for the correlated ensemble and thus yields a more conservative uncertainty measure. Using the fit and the spread estimate, we then determine ΔT 2x ranges (green asterisks), which are consistent with the assumed LGM cooling.

The same methodology cannot be applied for constraining TCR, as the linear relationship between LGM cooling and equilibrium warming does not hold for the transient model response. Therefore, for TCR, we replace the linear fit by the more general function type \( f(x) = a(x - x_{0} )^{b} \) (with f↔TCR, x↔LGM cooling) and furthermore allow the standard deviation σ of the residuals to vary with x as a quadratic function σ(x). In fact we observe σ to mildly expand at the tails of the fit. We determine the coefficients of that function as a maximum likelihood estimate, assuming a Gaussian distribution of the residuals for each x. Both fitting procedures (the one for f(x) as well as for σ(x)) are performed with the correlated ensemble that is more informative in the tails of σ(x). However, as for the linear fitting procedure, we would like to obtain a conservative estimate in the sense that the uncorrelated ensemble displays larger values of σ. Hence we assume the same shape σ(x) for the uncorrelated ensemble, but allow for an overall upscaling (x), c being estimated from a quadratic fit. In summary, we have generalised the linear fitting f(x) including constant σ(x) to a non-linear fit f(x), σ(x), yet ensuring that the average σ(x) is obtained from the uncorrelated ensemble.

One may ask what would be the consequences if one applied this non-linear procedure to the estimates of ΔT 2x as well. We have tested for that and found only minor changes in the derived intervals. The bounds of the intervals are shifted at maximum by 0.2°C to the extremes in one case (for tropical constraints) and much less otherwise. Hence we conclude that our results derived for ΔT 2x are very robust against the choice of fitting curve. As a final remark on our results for TCR we would like to stress that this study is designed to constrain a characteristic of equilibrium temperature change. To effectively constrain the range of TCR, transient data information should be included in the analysis.

As a final remark on our interval method we would like to discuss its relation to a more formal procedure that would independently sample (“IS-scheme”) the error distribution of the paleo-constraint and the error distribution of the fit (the latter generated from the deviation of the uncorrelated ensemble from the fit). Intervals derived from the IS-scheme could strictly be interpreted as quantiles. However, the interval transparently derived from our method is more conservative (larger) than the interval derived from the IS-scheme. In order to clarify this we would like to discuss a linear relation f (that we suppose to hold for climate sensitivity) first: there, our scheme simply adds the paleo and the fitting error, while IS would add according to Pythagoras (in the Monte Carlo scheme, the variances would add), as the paleo and the fitting error are statistically independent. Our scheme can be interpreted as choosing the worst case of perfect correlation of paleo and fitting error, leading to strictly larger error bars than the IS-scheme. As the relation f between TCR and LGM cooling is only slightly non-linear, the same statement holds for TCR as well. Finally, both schemes lead to identical results for vanishing fitting error, even for very non-linear, however, monotonous relations.

Choice of tolerable intervals for “realistic” model versions

It is still not well understood how model biases in simulation of modern climate affect climate sensitivity. Yet results from models, which produce a “realistic” modern climate state, might be preferable to “unrealistic” models. The strict and objective criteria of realistic model performance would be a requirement for model simulations to fall within the range of uncertainties of observed climate characteristics. However, even state-of-the-art climate models (GCMs) have systematic errors in simulation of different climate characteristics, which are often much larger than observations uncertainties (Covey et al. 2003). A more subjective way to assess the degree of model realism is to accept as tolerable the magnitude of errors typical for other climate models. Because this is an implicit target for any climate model development and tuning, the selection of such subjective criteria mimics a suite of models, which will be treated by other modellers as suitable for climate studies. To constrain models with empirical data we use seven global climate characteristics, which are listed below. All of these characteristics (except for the ocean temperature) have been used in SAR and TAR IPCC (Houghton et al. 1996; 2001) reports for model-data inter-comparison: we considered as tolerable the following intervals for the annual means of the following climate characteristics which encompass corresponding empirical estimates: global SAT 13.1–14.1°C (Jones et al. 1999); area of sea ice in the Northern Hemisphere 6–14 mil km2 and in the Southern Hemisphere 6–18 mil km2 (Cavalieri et al. 2003); total precipitation rate 2.45–3.05 mm/day (Legates 1995); maximum Atlantic northward heat transport 0.5–1.5 PW (Ganachaud and Wunsch 2003); maximum of North Atlantic meridional overturning stream function 15–25 Sv (Talley et al. 2003), volume averaged ocean temperature 3–5°C (Levitus 1982). Thus the chosen ranges—while being somewhat subjective—represent to the first approximation typical scattering of simulations with different AOGCMs (e.g. SAR and TAR IPCC reports) (Houghton et al. 1996; 2001) and encompass observational data of key present day climate characteristics.

Parameter choice

In our study the range of simulated ΔT 2x is affected by accounting for uncertainty in 11 model parameters, nine representing atmospheric characteristics (affecting parametrisations of cloud optical depth, height of clouds, lapse rate, tropopause height) and two describing mixing processes in the ocean. For each run all parameters have been simultaneously perturbed over the following expert derived ranges (values in {brackets} denote the standard setting for CLIMBER-2.3):

  • Ocean parameters: horizontal and vertical ocean diffusivity k H=200–5,000 {2000} m2/s, k V=0.1–1.0×10−4 {0.3×10−4} m2/s at top, 1.1–2.0×10−4 {1.3×10−4} m2/s at ocean bottom (vertical profile after Bryan Lewis).

  • Optical depth of cloudiness: \( {\text{ODc}} = (1 - {\text{Rcc}}) \times ({\text{OD}}_{1} - {\text{OD}}_{2} \times {\text{cos}}({\text{latitude}})^{2} ) + {\text{Rcc}} \times {\text{OD}}_{3} \), with Rcc relative amount of cumulus clouds, OD1=9.0–11.5 {10.2}, OD2=6.6–8.4 {7.7}.

  • Tropopause height: C t=0.74–0.76 {0.75} (see Eq. (3) from Petoukhov et al. 2000); a further parameter (A CO21=0.3–0.65 {0.5}) has been perturbed, which affects the value of integral transmission function of atmosphere (D) in Eq. (3).

  • Lapse rate: a q=625–4440 {1,110} (kg/kg)−2; Γ0=4.7–5.2×10−3 {5.0×10−3} K/m; Γ1=3.6–4.4×10−5 {4.0×10−5} m−1 (Eq. (2) of Petoukhov et al. 2000).

  • Height of stratiform clouds: c 1=0.165–0.200 {0.185} (Eq. (34) of Petoukhov et al. 2000).

  • Radiative forcing of CO2: \( A^{}_{{{\text{CO}}_{2} }} = 0.70{\text{--}}0.76\,\{ 0.755\} \) (Eq. (6.7) from V. Petoukhov, A. Ganopolski, M. Claussen 2003, PIK report No. 81).

The modification of all feedback parameters results in changes of the sum of all feedbacks (water vapour, cloud, lapse rate and albedo), spanning a minimum–maximum range of 71% (63%) of the mean value for the correlated (uncorrelated) ensemble. Parameter variations, which affect the CO2 radiative forcing, result in a range of 16% (28%) of the mean forcing.

Quantification of paleo-data uncertainties

To estimate the uncertainty range (2σ) for mean tropical SST cooling, we consider the error contributions from (a) large-scale patterns in the ocean data temperature field, which hamper a direct comparison with a coarse-resolution model, and (b) the statistical error for each reconstructed paleo-temperature value.

We refer to an interpolated data set (Schäfer-Neth and Paul 2003) from which we use the variance V=(1.41°C)2 as the starting point to estimate an uncertainty range for the spatial mean of the data field. In order to do so, we need to consider the correlation structure of the individual error sources. The data were interpolated using a kriging method (Schäfer-Neth et al. 2005), which basically takes into account data points in the vicinity of a location to be reconstructed, weighted by the ocean correlation structure. This results in a spatially smoothed correlation structure of the interpolated oceanic temperature field, with only (b) being affected by the smoothing. The most extreme version of smoothing (compatible with the requirement that (a) is not affected) would result in a spatial clustering of (b) on the same scale as (a). That simplifies the discussion as then we can estimate \( 2\sigma \approx 2{\sqrt {V/(N - 1)} } \), where N is given by the number of uncorrelated Atlantic ocean areas between 20°N and 20°S. With a correlation length of ∼10–15° we obtain a rough estimate of N≈12 for the tropical Atlantic sector. For less extreme versions of smoothing we were allowed to use larger values of N as more independent sources within (b) had entered V. In that sense \( 2\sigma \approx 2{\sqrt {V/(N - 1)} } \) with N≈12 provides a conservative estimate. We thus derive an estimate of 2.96±0.85°C of the 2σ range for mean tropical Atlantic SST cooling.

We cannot address, however, systematic errors in paleo-temperature reconstructions beyond the quality tests of TF methods, as, e.g. described in Pflaumann et al. (2003). Reconstructed temperature anomalies from GCs agree with TF based LGM cooling estimates for most regions of low latitudes (Bard 2001; Niebler et al. 2003; Barker et al. 2005). Yet some systematic bias arises for regions of pronounced cooling (especially in the eastern tropical Atlantic). To account for this bias we confine maximum cooling in our used data set to 4°C (which corresponds to the upper limit of tropical Atlantic SST cooling derived by GC methods; Rosell-Mele et al. 2004; Barker et al. 2005). This shifts the mean about 0.2°C to less cooling and at the same time narrows the standard deviation of mean SST cooling. Thus this revised data estimate, which might be regarded as more representative for GC reconstructions, is included in the range of 2.96±0.85°C of our FT-based estimate and is not separately discussed for constraining ΔT 2x .

Given pronounced spatial inhomogeneities we emphasize that by describing mean tropical Atlantic SST anomalies, we discuss the mean annual cooling averaged from 20°N to 20°S over the whole Atlantic sector. Thus the effect of sediment cores, which show strong local effects (e.g. in upwelling regions) is minimized, and the mean SST anomaly should be more representative for large scale tropical conditions (dominated by large scale forcings, such as lowered CO2 concentrations). Modelling and data-analysis studies show that the mean cooling for the tropical Atlantic section is slightly larger than comparable estimates from the Pacific and Indian sector. When considering a global tropical SST data-constraint, an average tropical cooling of about 2.5°C would have to be considered to constrain the same ΔT 2x range (as derived from tropical Atlantic).

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Schneider von Deimling, T., Held, H., Ganopolski, A. et al. Climate sensitivity estimated from ensemble simulations of glacial climate. Clim Dyn 27, 149–163 (2006).

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  • Last Glacial Maximum
  • Climate Sensitivity
  • Water Vapour Feedback
  • Transient Climate Response
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