Skip to main content

Advertisement

Log in

Determination of Earth’s Transient and Equilibrium Climate Sensitivities from Observations Over the Twentieth Century: Strong Dependence on Assumed Forcing

Surveys in Geophysics Aims and scope Submit manuscript

Abstract

Relations among observed changes in global mean surface temperature, ocean heat content, ocean heating rate, and calculated radiative forcing, all as a function of time over the twentieth century, that are based on a two-compartment energy balance model, are used to determine key properties of Earth’s climate system. The increase in heat content of the world ocean, obtained as the average of several recent compilations, is found to be linearly related to the increase in global temperature over the period 1965–2009; the slope, augmented to account for additional heat sinks, which is an effective heat capacity of the climate system, is 21.8 ± 2.1 W year m−2 K−1 (one sigma), equivalent to the heat capacity of 170 m of seawater (for the entire planet) or 240 m for the world ocean. The rate of planetary heat uptake, determined from the time derivative of ocean heat content, is found to be proportional to the increase in global temperature relative to the beginning of the twentieth century with proportionality coefficient 1.05 ± 0.06 W m−2 K−1. Transient and equilibrium climate sensitivities were evaluated for six published data sets of forcing mainly by incremental greenhouse gases and aerosols over the twentieth century as calculated by radiation transfer models; these forcings ranged from 1.1 to 2.1 W m−2, spanning much of the range encompassed by the 2007 assessment of the Intergovernmental Panel on Climate Change (IPCC). For five of the six forcing data sets, a rather robust linear proportionality obtains between the observed increase in global temperature and the forcing, allowing transient sensitivity to be determined as the slope. Equilibrium sensitivities determined by two methods that account for the rate of planetary heat uptake range from 0.31 ± 0.02 to 1.32 ± 0.31 K (W m−2)−1 (CO2 doubling temperature 1.16 ± 0.09–4.9 ± 1.2 K), more than spanning the IPCC estimated “likely” uncertainty range, and strongly anticorrelated with the forcing used to determine the sensitivities. Transient sensitivities, relevant to climate change on the multidecadal time scale, are considerably lower, 0.23 ± 0.01 to 0.51 ± 0.04 K (W m−2)−1. The time constant characterizing the response of the upper ocean compartment of the climate system to perturbations is estimated as about 5 years, in broad agreement with other recent estimates, and much shorter than the time constant for thermal equilibration of the deep ocean, about 500 years.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. For reasons having to do with stratospheric adjustment that occurs rapidly (months) following an increase CO2, which has traditionally been used as a benchmark forcing in model studies of climate sensitivity, the forcing pertinent to climate change and to determination of climate sensitivity has long been considered to be the change in net absorbed radiation at the tropopause. Increasingly, however, it is becoming recognized (e.g., Gregory and Forster 2008) that the measure of forcing pertinent to the global energy balance is the change in net radiation at the top of the atmosphere, again following such rapid adjustment.

  2. Here the term "very likely" is used in the sense of the 2007 IPCC Assessment Report; that is, corresponding to the estimate of the central 90% of the PDF for the quantity. Likewise the term "likely" is used to denote the estimate of the central 66% of the PDF.

References

  • Allen MR, Frame DJ (2007) Call off the quest. Science 318:582–583. doi:10.1126/science.1149988

    Article  Google Scholar 

  • Andrews DG, Allen MR (2008) Diagnosis of climate models in terms of transient climate response and feedback response time. Atmos Sci Lett 9:7–12. doi:10.1002/asl.163

    Article  Google Scholar 

  • Andrews T, Forster PM, Gregory JM (2009) A surface energy perspective on climate change. J Clim 22(10):2557–2570. doi:10.1175/2008JCLI2759.1

    Article  Google Scholar 

  • Baker MB, Roe GH (2009) The shape of things to come: why is climate change so predictable? J Clim 22:4574–4589. doi:10.1175/2009JCLI2647.1

    Article  Google Scholar 

  • Boer GJ, Yu B (2002) Climate sensitivity and climate state. Clim Dyn 21:167–176. doi:10.1007/s00382-003-0323-7

    Article  Google Scholar 

  • Boer GJ, Stowasser M, Hamilton K (2007) Inferring climate sensitivity from volcanic events. Clim Dyn 28:481–502. doi:10.1007/s00382-006-0193-x

    Article  Google Scholar 

  • Boucher O, Reddy MS (2008) Climate trade-off between black carbon and carbon dioxide emissions. Energy Policy 36:193–200. doi:10.1016/j.enpol.2007.08.039

    Google Scholar 

  • Brasseur GP, Roeckner E (2005) Impact of improved air quality on the future evolution of climate. Geophys Res Lett 32:L23704. doi:10.1029/2005GL023902

    Article  Google Scholar 

  • Brohan P, Kennedy JJ, Harris I, Tett SFB, Jones PD (2006) Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850. J Geophys Res 111:D12106. doi:10.1029/2005JD006548

    Article  Google Scholar 

  • Cleveland WS, Devlin SJ (1988) Locally-weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83(403):596–610. doi:10.2307/2289282

    Google Scholar 

  • Collins WD, Ramaswamy V, Schwarzkopf MD, Sun Y, Portmann RW, Fu Q, Casanova SEB, Defresne J-L, Fillmore DW, Forster PMD, Galin VY, Gohar LK, Ingram WJ, Kratz DP, Lefebvre M-P, Li J, Marquet P, Oinas V, Tsushima T, Uchiyama T, Zhong WY (2006) Radiative forcing by well-mixed greenhouse gases: estimates from climate models in the IPCC AR4. J Geophys Res 111:D14317. doi:10.1029/2005JD006713

    Article  Google Scholar 

  • Domingues CM, Church JA, White NJ, Gleckler PJ, Wijffels SE, Barker PM, Dunn JR (2008) Improved estimates of upper-ocean warming and multi-decadal sea-level rise. Nature 453:1090–1093. doi:10.1038/nature07080

    Article  Google Scholar 

  • Dufresne J-L, Bony S (2008) An assessment of the primary sources of spread of global warming estimates from coupled atmosphere-ocean models. J Clim 21:5135–5144. doi:10.1175/2008JCLI2239.1

    Article  Google Scholar 

  • Forster PMF, Gregory JM (2006) The climate sensitivity and its components diagnosed from earth radiation budget data. J Clim 19:39–52. doi:10.1175/JCLI3611.1

    Article  Google Scholar 

  • Forster PMD, Taylor KE (2006) Climate forcings and climate sensitivities diagnosed from coupled climate model integrations. J Clim 19:6181–6194. doi:10.1175/JCLI3974.1

    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:L09702. doi:09710.01029/02004GL022241

    Article  Google Scholar 

  • Gouretski V, Reseghetti F (2010) On depth and temperature biases in bathythermograph data: development of a new correction scheme based on the analysis of global ocean data. Deep-Sea Res I 57:812–833. doi:10.1016/j.dsr.2010.03.011

    Article  Google Scholar 

  • Gregory JM (2000) Vertical heat transports in the ocean and their effect on time-dependent climate change. Clim Dyn 16:501–515. doi:10.1007/s003820000059

    Article  Google Scholar 

  • Gregory JM, Forster PM (2008) Transient climate response estimated from radiative forcing and observed temperature change. J Geophys Res 113:D23105. doi:10.1029/2008JD010405

    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. doi:10.1175/1520-0442(2002)015<3117:AOBEOT>2.0.CO;2

    Article  Google Scholar 

  • Hansen J, Sato M, Ruedy R (1997) Radiative forcing and climate response. J Geophys Res 102:6831–6864. doi:10.1029/96JD03436

    Article  Google Scholar 

  • Hansen J, Nazarenko L, Ruedy R, Sato M, Willis J, DelGenio A, Koch D, Lacis A, Lo K, Menon S, Tovakov T, Perlwitz J, Russell G, Schmidt GA, Tausnev N (2005) Earth’s energy imbalance: confirmation and implications. Science 308:1431–1435. doi:1410.1126/science.1110252

    Article  Google Scholar 

  • Hansen J, Ruedy R, Sato M, Lo K (2010) Global surface temperature change. Rev Geophys 48:RG4004. doi:10.1029/2010RG000345

    Article  Google Scholar 

  • Hansen J, Sato M, Kharecha P, von Schuckmann K (2011) Earth’s energy imbalance and implications. Atmos Chem Phys 11:13421–13449. doi:10.5194/acp-11-13421-2011

    Article  Google Scholar 

  • Held IM, Winton M, Takahashi K, Delworth T, Zeng F, Vallis GK (2010) Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. J Clim 23:2418–2427. doi:10.1175/2009JCLI3466.1

    Article  Google Scholar 

  • Hoffert MI, Callegari AJ, Hsieh CT (1980) The role of deep sea heat storage in the secular response to climate forcing. J Geophys Res 85:6667–6679. doi:10.1029/JC085iC11p06667

    Article  Google Scholar 

  • IPCC (2007) Climate change 2007: the physical science basis. In: Solomon S, Qin D, Manning M (eds) Intergovernmental panel on climate change, Geneva. http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html

  • Ishii M, Kimoto M (2009) Reevaluation of historical ocean heat content variations with time-varying XBT and MBT depth bias corrections. J Oceanogr 65:287–299. doi:10.1007/s10872-009-0027-7

    Article  Google Scholar 

  • Jarvis A, Li S (2011) The contribution of timescales to the temperature response of climate models. Clim Dyn 36:523–531. doi:10.1007/s00382-010-0753-y

    Article  Google Scholar 

  • Jones GS, Christidis N, Stott PA (2011) Detecting the influence of fossil fuel and bio-fuel black carbon aerosols on near surface temperature changes. Atmos Chem Phys 11:799–816. doi:10.5194/acp-11-799-2011

    Google Scholar 

  • Joshi M, Shine K, Ponater M, Stuber N, Sausen R, Li L (2003) A comparison of climate response to different radiative forcing in three general circulation models: towards and improved metric of climate change. Clim Dyn 20:843–854. doi:10.1007/s00382-003-0305-9

    Google Scholar 

  • Kiehl JT (2007) Twentieth century climate model response and climate sensitivity. Geophys Res Lett 34:L22710. doi:10.1029/2007GL031383

    Article  Google Scholar 

  • Kloster S, Dentener F, Feichter J, Raes F, Lohmann U, Roeckner E, Fischer-Bruns I (2010) A GCM study of future climate response to aerosol pollution reductions. Clim Dyn 34:1177–1194. doi:10.1007/s00382-009-0573-0

    Article  Google Scholar 

  • Knutti R (2008) Why are climate models reproducing the observed global surface warming so well? Geophys Res Lett 35:L18704. doi:10.1029/2008GL034932

    Article  Google Scholar 

  • Knutti R, Plattner G-K, (2012) Comment on “Why Hasn’t earth warmed as much as expected?” by Schwartz et al. 2010. J Clim 25:2192–2199. doi:10.1175/2011JCLI4038.1

  • Knutti R, Krähenmann S, Frame DJ, Allen MR (2008) Comment on ‘‘Heat capacity, time constant, and sensitivity of Earth’s climate system’’ by S. E. Schwartz. J Geophys Res 113:D15103. doi:10.1029/2007JD009473

    Article  Google Scholar 

  • Levitus S, Antonov J, Boyer T (2005) Warming of the world ocean, 1955–2003. Geophys Res Lett 32:L02604. doi:10.1029/2004GL021592

  • Levitus S, Antonov JI, Boyer TP, Locarnini RA, Garcia HE, Mishonov AV (2009) Global ocean heat content 1955–2008 in light of recently revealed instrumentation problems. Geophys Res Lett 36:L07608. doi:10.1029/2008GL037155

    Article  Google Scholar 

  • Lohmann U, Rotstayn L, Storelvmo T, Jones A, Menon S, Quaas J, Ekman AML, Koch D, Ruedy R (2010) Total aerosol effect: radiative forcing or radiative flux perturbation? Atmos Chem Phys 10(7):3235–3246. doi:10.5194/acp-10-3235-2010

    Article  Google Scholar 

  • Lucarini V, Ragone F (2011) Energetics of climate models: net energy balance and meridional enthalpy transport. Rev Geophys 49:RG1001. doi:10.1029/2009RG000323

    Article  Google Scholar 

  • Lyman JM (2011) Estimating global energy flow from the global upper ocean. Surv Geophys. doi: 10.1007/s10712-011-9167-6

  • Lyman JM, Johnson GC (2008) Estimating annual global upper ocean heat content anomalies despite irregular in situ ocean sampling. J Clim 21:5629–5641. doi:10.1175/2008JCLI2259.1

    Article  Google Scholar 

  • Matthews HD, Caldeira K (2007) Transient climate-carbon simulations of planetary geoengineering. Proc Natl Acad Sci USA 104:9949–9954. doi:10.1073/pnas.0700419104

    Article  Google Scholar 

  • Meehl GA, Washington WM, Wigley TML, Arblaster JM, Dai A (2003) Solar and greenhouse gas forcing and climate response in the twentieth century. JClim 16:426–444. doi:10.1175/1520-0442(2003)016<0426:SAGGFA>2.0.CO;2

    Google Scholar 

  • Meinshausen M, Smith S, Calvin K, Daniel JS, Kainuma M, Lamarque J-F, Matsumoto K, Montzka SA, Raper SCB, Riahi K, Thomson AM, Velders GJM, van Vuuren D (2011) The RCP greenhouse gas concentrations and their extension from 1765 to 2300. Clim Chang. doi:10.1007/s10584-011-0156-z

  • Murphy DM, Solomon S, Portmann RW, Rosenlof KH, Forster PM, Wong T (2009) An observationally based energy balance for the Earth since 1950. J Geophys Res 114:D17107. doi:10.1029/2009JD012105

    Article  Google Scholar 

  • Myhre G, Highwood EJ, Shine KP, Stordal F (1998) New estimates of radiative forcing due to well mixed greenhouse gases. Geophys Res Lett 25:2715–2718. doi:10.1029/98GL01908

    Article  Google Scholar 

  • Myhre G, Myhre A, Stordal F (2001) Historical evolution of radiative forcing of climate. Atmos Environ 35:2361–2373. doi:10.1016/S1352-2310(00)00531-8

    Article  Google Scholar 

  • Padilla LE, Vallis GK, Rowley CW (2011) Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability. J Clim 24:5521–5537. doi:10.1175/2011JCLI3989.1

    Article  Google Scholar 

  • Palmer MD, Haines K, Tett SFB, Ansell TJ (2007) Isolating the signal of ocean global warming. Geophys Res Lett 34:L23610. doi:10.1029/2007GL031712

    Article  Google Scholar 

  • Palmer M, Antonov J, Barker P, Bindoff N, Boyer T, Carson M, Domingues C, C. SG, Gleckler P, Good S, Gouretski V, Guinehut S, Haines K, Harrison DE, Ishii M, Johnson G, Levitus S, Lozier S, Lyman J, Meijers A, Schuckmann Kv, Smith D, Wijffels S, Willis J (2010) Future observations for monitoring global ocean heat content. In: Hall J, Harrison DE, Stammer D (eds) Proceedings of the “OceanObs’ 09: Sustained ocean observations and information for society” Conference (vol 2), Venice, Italy, 21–25 September 2009. ESA Publication WPP-306. doi:10.5270/OceanObs09.cwp.68

  • Pilewskie P (2011) Measurements of solar spectral irradiance. ISSI Workshop on Observing and Modeling Earth’s Energy Flows. Bern, 10--14 January 2011

  • Scafetta N (2008) Comment on “Heat capacity, time constant, and sensitivity of Earth’s climate system” by S. E. Schwartz. J Geophys Res 113:D15104. doi:10.1029/2007JD009586

  • Schwartz SE (2004) Uncertainty requirements in radiative forcing of climate change. J Air Waste Manag Assoc 54:1351–1359. doi:10.1080/10473289.2004.10471006

    Article  Google Scholar 

  • Schwartz SE (2007) Heat capacity, time constant, and sensitivity of Earth’s climate system. J Geophys Res 112(D24):D24S05. doi:10.1029/2007JD008746

    Article  Google Scholar 

  • Schwartz SE (2008a) Reply to comments by G. Foster et al., R. Knutti et al., and N. Scafetta on “Heat capacity, time constant, and sensitivity of Earth’s climate system”. J Geophys Res 113:D15105. doi:10.1029/2008JD009872

    Article  Google Scholar 

  • Schwartz SE (2008b) Uncertainty in climate sensitivity: causes, consequences, challenges. Energy Environ Sci 1:430–453. doi:10.1039/B810350J

    Article  Google Scholar 

  • Schwartz SE, Charlson RJ, Kahn RA, Ogren JA, Rodhe H (2010) Why hasn’t Earth warmed as much as expected? J Clim 23:2453–2464. doi:10.1175/2009JCLI3461.1

    Article  Google Scholar 

  • Smith TM, Reynolds RW, Peterson TC, Lawrimore J (2008) Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006). J Clim 21:2283–2296. doi:10.1175/2007JCLI2100.1

    Article  Google Scholar 

  • Stevens B, Schwartz SE (2012) Observing and modeling Earth’s energy flows. Surv Geophys. doi:10.1007/s10712-012-9184-0

  • Sutton P, Roemmich D (2001) Ocean temperature climate off north-east New Zealand. N Z J Marine Freshw Res 35:553–565. doi:10.1080/00288330.2001.9517022

    Article  Google Scholar 

  • Takemura T, Tsushima Y, Yokohata T, Nozawa T, Nagashima T, Nakajima T (2006) Time evolutions of various radiative forcings for the past 150 years estimated by a general circulation model. Geophys Res Lett 33:L19705. doi:10.1029/2006GL026666

    Article  Google Scholar 

  • Watterson G, Dix MR (2005) Effective sensitivity and heat capacity in the response of climate models to greenhouse gas and aerosol forcings. Q J R Meteorol Soc 131:259–279. doi:10.1256/qj.03.232

    Article  Google Scholar 

  • Webb MJ, Senior CA, Sexton DMH, Ingram WJ, Williams KD, Ringer MA, McAvaney BJ, Colman R, Soden BJ, Gudgel R, Knutson T, Emori S, Ogura T, Tsushima Y, Andronova N, Li B, Musat I, Bony S, Taylor KE (2006) On the contribution of local feedback mechanisms to the range of climate sensitivity in two GCM ensembles. Clim Dyn 27:17–38. doi:10.1007/s00382-006-0111-2

    Google Scholar 

  • Willis JK, Roemmich D, Cornuelle B (2004) Interannual variability in upper ocean heat content, temperature, and thermosteric expansion on global scales. J Geophys Res 109:C12036. doi:10.1029/2003JC002260

Download references

Acknowledgments

I thank the several modeling groups for providing the forcing data sets employed in this analysis. An earlier version of this paper was presented at the Workshop on Observing and Modelling Earth’s Energy Flows organized and sponsored by the International Space Science Institute in Bern Switzerland, January, 10–14, 2011, and I thank Lennart Bengtsson for his encouragement of this study. This study benefited from comments by Bjorn Stevens and a second, anonymous reviewer. This work was supported by the U.S. Department of Energy’s Atmospheric System Research Program (Office of Science, OBER) under Contract No. DE-AC02-98CH10886.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stephen E. Schwartz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwartz, S.E. Determination of Earth’s Transient and Equilibrium Climate Sensitivities from Observations Over the Twentieth Century: Strong Dependence on Assumed Forcing. Surv Geophys 33, 745–777 (2012). https://doi.org/10.1007/s10712-012-9180-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10712-012-9180-4

Keywords

Navigation