Skip to main content

Advertisement

Log in

Climate sensitivity estimated from ensemble simulations of glacial climate

Climate Dynamics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  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.

Abbreviations

ΔT 2x :

Climate sensitivity

TCR:

Transient climate response

GCM:

General circulations model

IPCC:

Intergovernmental panel on climate change

LGM:

Last glacial maximum

GHG:

Greenhouse gas

CO2 :

Carbon dioxide

SST:

Sea surface temperatures

SAT:

Surface air temperature

References

  • Anderson TL, Charlson RJ, Schwartz SE, Knutti R, Boucher O, Rodhe H, Heintzenberg J (2003) Climate forcing by aerosol—a Hazy picture. Science 300(5622):1103–1104, DOI 10.1126/science.1084777

  • Andronova N, Schlesinger ME (2001) Objective estimation of the probability distribution for climate sensitivity. J Geophys Res 106:22605–22612

    Article  Google Scholar 

  • Annan J, Hargreaves J, Ohgaito R, Abe-Ouchi A, Emori S (2005) Efficiently constraining climate sensitivity with ensembles of paleoclimate simulations. SOLA 1:181–184, DOI 10.2151/sola. 2005-047

  • Bard E (2001) Comparison of alkenone estimates with other paleotemperature proxies. Geochem Geophys Geosyst 2, DOI 10.1029/2000GC000050

  • Barker S, Cacho I, Benway H, Tachikawa K (2005) Planktonic foraminiferal Mg/Ca as a proxy for past oceanic temperatures: a methodological overview and data compilation for the Last Glacial Maximum. Q Sci Rev 24(7–9):821–834

    Article  Google Scholar 

  • Bauer E, Claussen M, Brovkin V, Huenerbein A (2003) Assessing climate forcings of the Earth system for the past millennium. Geophys Res Lett 30(6):1276–1279, DOI 10.1029/2002GL016639

  • Berger AL (1978) Long-term variation of calcoric insolation resulting from the Earth’s orbital elements. Q Res 9:139–167

    Article  Google Scholar 

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Broccoli AJ (2000) Tropical cooling at the last glacial maximum: an atmosphere-mixed layer ocean model simulation. J Clim 13(5):951–976

    Article  Google Scholar 

  • Cavalieri DJ, Parkinson CL, Vinnikov KY (2003) 30-Year satellite record reveals contrasting Arctic and Antarctic decadal sea ice variability. Geophys Res Lett 30(18), DOI 10.1029/2003GL018031

  • Charney JG (1979) Carbon dioxide and climate: a scientific assessment. National Academy, Washington, DC, 22 pp

  • Claquin T, Schulz M, Balkanski Y, Boucher O (1998) Uncertainties in assessing radiative forcing by mineral dust. Tellus B Chem Phys Meteorol 50(5):491–505, DOI 10.1034/j.1600-0889.1998.t01-2-00007.x

  • Claquin T, Roelandt C, Kohfeld KE, Harrison SP, Tegen I, Prentice IC, Balkanski Y, Bergametti G, Hansson M, Mahowald N, Rodhe H, Schulz M (2003) Radiative forcing of climate by ice-age atmospheric dust. Clim Dyn 20(2–3):193–202, DOI 10.1007/s00382-002-0269-1

  • Colman R (2003) A comparison of climate feedbacks in general circulation models. Clim Dyn 20(7–8):865–873, DOI 10.1007/s00382-003-0310-z

  • Covey C, Sloan LC, Hoffert MI (1996) Paleoclimate data constraints on climate sensitivity: the paleocalibration method. Clim Change 32(2):165–184

    Article  Google Scholar 

  • Covey C, AchutaRao KM, Cubasch U, Jones P, Lambert SJ, Mann ME, Phillips TJ, Taylor KE (2003) An overview of results from the Coupled Model Intercomparison Project. Glob Planet Change 37(1–2):103–133

    Article  Google Scholar 

  • Crowley TJ (2000) CLIMAP SSTs re-revisited. Clim Dyn 16(4):241–255

    Article  Google Scholar 

  • Dahl-Jensen D, Mosegaard K, Gundestrup N, Clow GD, Johnsen SJ, Hansen AW, Balling N (1998) Past temperatures directly from the Greenland ice sheet. Science 282(5387):268–271

    Article  Google Scholar 

  • Farrera I, Harrison SP, Prentice IC, Ramstein G, Guiot J, Bartlein PJ, Bonnefille R, Bush M, Cramer W, von Grafenstein U, Holmgren K, Hooghiemstra H, Hope G, Jolly D, Lauritzen SE, Ono Y, Pinot S, Stute M, Yu G (1999) Tropical climates at the Last Glacial Maximum: a new synthesis of terrestrial palaeoclimate data. I. Vegetation, lake levels and geochemistry. Clim Dyn 15(11):823–856

    Article  Google Scholar 

  • Forest CE, Stone PH, Sokolov AP, Allen MR, Webster MD (2002) Quantifying uncertainties in climate system properties with the use of recent climate observations. Science 295(5552):113–117

    Article  Google Scholar 

  • Frame DJ, Booth BBB, Kettleborough JA, Stainforth DA, Gregory JM, Collins M, Allen MR (2005) Constraining climate forecasts: the role of prior assumptions. Geophys Res Lett 32(9), L09702, DOI 10.1029/2004GL022241

  • Ganachaud A, Wunsch C (2003) Large-scale ocean heat and freshwater transports during the World Ocean Circulation Experiment. J Clim 16(4):696–705, DOI 10.1175/1520-0442(2003)016<0696:LSOHAF>2.0.CO;2

  • Ganopolski A, Rahmstorf S (2001) Rapid changes of glacial climate simulated in a coupled climate model. Nature 409:153–158, DOI 10.1038/35051500

  • Ganopolski A, Rahmstorf S, Petoukhov V, Claussen M (1998) Simulation of modern and glacial climates with a coupled global model of intermediate complexity. Nature 391:351–356

    Article  Google Scholar 

  • Ganopolski A, Petoukhov V, Rahmstorf S, Brovkin V, Claussen M, Eliseev A, Kubatzki C (2001) CLIMBER-2 a climate system model of intermediate complexity. Part II. Model sensitivity. Clim Dyn 17:735–751

    Article  Google Scholar 

  • Gregory JM, Stouffer RJ, Raper SCB, Stott PA, Rayner NA (2002) An observationally based estimate of the climate sensitivity. J Clim 15(22):3117–3121

    Article  Google Scholar 

  • Hansen J, Lacis A, Ruedy R, Sato M, Wilson H (1993) How sensitive is the worlds climate. Res Explor 9(2):142–158

    Google Scholar 

  • Harrison SP, Kohfeld KE, Roelandt C, Claquin T (2001) The role of dust in climate changes today, at the last glacial maximum and in the future. Earth Sci Rev 54(1–3):43–80

    Article  Google Scholar 

  • Hewitt CD, Mitchell JFB (1997) Radiative forcing and response of a GCM to ice age boundary conditions: cloud feedback and climate sensitivity. Clim Dyn 13(11):821–834

    Article  Google Scholar 

  • Hewitt CD, Stouffer RJ, Broccoli AJ, Mitchell JFB, Valdes PJ (2003) The effect of ocean dynamics in a coupled GCM simulation of the Last Glacial Maximum. Clim Dyn 20(2–3):203–218

    Google Scholar 

  • Hoffert MI, Covey C (1992) Deriving global climate sensitivity from paleoclimate reconstructions. Nature 360(6404):573–576

    Article  Google Scholar 

  • Houghton JT et al. (2001) Climate change 2001: the scientific basis. Cambridge University Press, Cambridge p 944

    Google Scholar 

  • Houghton JT et al. (eds) (1996) Climate change 1995: the science of climate change. Cambridge University Press, Cambridge, pp 944

  • IPCC WG-I (2004) Workshop on Climate Sensitivity, Paris, 26–29 July 2004

  • Jones PD, New M, Parker DE, Martin S, Rigor IG (1999) Surface air temperature and its changes over the past 150 years. Rev Geophys 37:173–200, DOI 10.1029/1999RG900002

    Article  Google Scholar 

  • Jouzel J, Vimeux F, Caillon N, Delaygue G, Hoffmann G, Masson-Delmotte V, Parrenin F (2003) Magnitude of isotope/temperature scaling for interpretation of central Antarctic ice cores. J Geophys Res Atmos 108(D12), 4361, DOI 10.1029/2002JD002677

  • Kim SJ (2004) The effect of atmospheric CO2 and ice sheet topography on LGM climate. Clim Dyn 22:639–651, DOI 10.1007/s00382-004-0412-2

  • Kitoh A, Murakami S, Koide H (2001) A simulation of the last glacial maximum with a coupled atmosphere-ocean GCM. Geophys Res Lett 28(11):2221–2224

    Article  Google Scholar 

  • Knutti R, Stocker TF, Joos F, Plattner G-K (2002) Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature 416(6882):719–723

    Article  Google Scholar 

  • Kucera M, Rosell-Mele A, Schneider R, Waelbroeck C, Weinelt M (2005) Multiproxy approach for the reconstruction of the glacial ocean surface (MARGO). Q Sci Rev 24(7–9):813–819

    Article  Google Scholar 

  • Lea DW (2004) The 100 000-yr cycle in tropical SST, greenhouse forcing, and climate sensitivity. J Clim 17(11):2170–2179

    Article  Google Scholar 

  • Lea DW, Pak DK, Peterson LC, Hughen KA (2003) Synchroneity of tropical and high-latitude Atlantic temperatures over the last glacial termination. Science 301(5638):1361–1364

    Article  Google Scholar 

  • Legates DR (1995) Global and terrestrial precipitation—a comparative-assessment of existing climatologies. Int J Climatol 15(3):237–258

    Article  Google Scholar 

  • Lorius C, Jouzel J, Raynaud D, Hansen J, Le Treut H (1990) The ice-core record: climate sensitivity and future greenhouse warming. Nature 347:139–145

    Article  Google Scholar 

  • Murphy JM, Sexton DMH, Barnett DN, Jones GS, Webb MJ, Collins M, Stainforth DA (2004) Quantification of modelling uncertainties in a large ensemble of climate change simulations. Nature 430(7001):768–772

    Article  Google Scholar 

  • Niebler HS, Arz HW, Donner B, Mulitza S, Patzold J, Wefer G (2003) Sea surface temperatures in the equatorial and South Atlantic Ocean during the last glacial maximum (23–19 ka). Paleoceanography 18(3), DOI 10.1029/2003PA000902

  • Peltier WR (1994) Ice age paleotopography. Science 265:195–201

    Article  Google Scholar 

  • Peltier WR (2004) Global glacial isostasy and the surface of the ice-age earth: the ice-5G (VM2) model and grace. Annu Rev Earth Planet Sci 32:111–149, DOI 10.1146/annurev.earth.32.082503.144359

  • Petit JR, Jouzel J, Raynaud D, Barkov NI, Barnola JM, Basile I, Bender M, Chappellaz J, Davis M, Delaygue G, Delmotte M, Kotlyakov VM, Legrand M, Lipenkov VY, Lorius C, Pepin L, Ritz C, Saltzman E, Stievenard M (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399(6735):429–436

    Article  Google Scholar 

  • Petoukhov V, Ganopolski A, Brovkin V, Claussen M, Eliseev A, Kubatzki C, Rahmstorf S (2000) CLIMBER-2: a climate system model of intermediate complexity. Part I. Model description and performance for present climate. Clim Dyn 16:1–17

    Article  Google Scholar 

  • Pflaumann U, Sarnthein M, Chapman M, d’Abreu L, Funnell B, Huels M, Kiefer T, Maslin M, Schulz H, Swallow J, van Kreveld S, Vautravers M, Vogelsang E, Weinelt M (2003) Glacial North Atlantic: sea-surface conditions reconstructed by GLAMAP 2000. Paleoceanography 18(3), 1065, DOI 10.1029/2002PA000774

  • Pinot S, Ramstein G, Harrison SP, Prentice IC, Guiot J, Stute M, Joussaume S (1999) Tropical paleoclimates at the Last Glacial Maximum: comparison of Paleoclimate Modeling Intercomparison Project (PMIP) simulations and paleodata. Clim Dyn 15(11):857–874

    Article  Google Scholar 

  • Rosell-Mele A, Bard E, Emeis KC, Grieger B, Hewitt C, Muller PJ, Schneider RR (2004) Sea surface temperature anomalies in the oceans at the LGM estimated from the alkenone-U-37(K′) index: comparison with GCMs. Geophys Res Lett 31(3), L03208, DOI 10.1029/2003GL018151

  • Sarnthein M, Gersonde R, Niebler S, Pflaumann U, Spielhagen R, Thiede J, Wefer G, Weinelt M (2003) Overview of Glacial Atlantic Ocean Mapping (GLAMAP 2000). Paleoceanography 18(2), 1030, DOI 10.1029/2002PA000769

  • Schäfer-Neth C, Paul A (2003) Gridded global LGM SST and salinity reconstruction, IGBP PAGES/World Data Center for paleoclimatology. Boulder, NOAA/NGDC Paleoclimatology Program, Boulder, CO

  • Schäfer-Neth C, Paul A, Mulitza S (2004) Perspectives on mapping the MARGO reconstructions by variogram analysis/kriging and objective analysis. Q Sci Rev 24:1095–1107

  • Shin SI, Liu Z, Otto-Bliesner B, Brady EC, Kutzbach JE, Harrison SP (2003) A simulation of the last glacial maximum climate using the NCAR-CCSM. Clim Dyn 20(2–3):127–151, DOI 10.1007/s00382-002-0260-x

  • Sokolik IN, Toon OB (1999) Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths. J Geophys Res Atmos 104(D8):9423–9444

    Article  Google Scholar 

  • Stainforth DA, Aina T, Christensen C, Collins M, Faull N, Frame DJ, Kettleborough JA, Knight S, Martin A, Murphy JM, Piani C, Sexton D, Smith LA, Spicer RA, Thorpe AJ, Allen MR (2005) Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature 433(7024):403–406

    Article  Google Scholar 

  • Stier P, Feichter J, Kinne S, Kloster S, Vignati E, Wilson J (2004) The aerosol-climate model ECHAM5-HAM. Atmos Chem Phys Discuss 4:5551–5623

    Article  Google Scholar 

  • Talley LD, Reid JL, Robbins PE (2003) Data-based meridional overturning stream functions for the global ocean. J Clim 16:3213–3226, DOI 10.1175/1520-0442(2003)016<3213:DMOSFT>2.0.CO;2

  • Vimeux F, Cuffey KM, Jouzel J (2002) New insights into Southern Hemisphere temperature changes from Vostok ice cores using deuterium excess correction. Earth Planet Sci Lett 203(3–4):829–843, DOI 10.1016/S0012-821X(02)00950-0

    Article  Google Scholar 

  • Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, London

    Google Scholar 

  • Watanabe O, Jouzel J, Johnsen S, Parrenin F, Shoji H, Yoshida N (2003) Homogeneous climate variability across East Antarctica over the past three glacial cycles. Nature 422(6931):509–512, DOI 10.1038/nature01525

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Schneider von Deimling.

Appendices

Appendices

1.1 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.

1.2 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.

1.3 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.

1.4 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).

Rights and permissions

Reprints and permissions

About this article

Cite this article

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). https://doi.org/10.1007/s00382-006-0126-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00382-006-0126-8

Keywords

Navigation