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| [[Image:Frequency distribution of climate sensitivity, based on model simulations (NASA).png|thumb|350px|right |alt=Refer to caption and adjacent text|[[Frequency distribution]] of climate sensitivity, based on model simulations.<ref name="lindsey climate sensitivity frequency distribution">Edited quote from public-domain source: {{citation
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| | url=http://earthobservatory.nasa.gov/blogs/climateqa/what-if-global-warming-isnt-as-severe-as-predicted/
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| | title=What if global warming isn’t as severe as predicted? : Climate Q&A : Blogs
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| | publisher=[[NASA Earth Observatory]], part of the EOS Project Science Office, located at NASA Goddard Space Flight Center
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| | author=Lindsey, R.
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| | date=3 August 2010
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| }}
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| </ref> Few of the simulations result in less than 2 °C of warming—near the low end of estimates by the [[Intergovernmental Panel on Climate Change]] (IPCC).<ref name="lindsey climate sensitivity frequency distribution"/> Some simulations result in significantly more than the 4 °C, which is at the high end of the IPCC estimates.<ref name="lindsey climate sensitivity frequency distribution"/> This pattern (statisticians call it a "right-[[:en:skewness|skewed]] distribution") suggests that if carbon dioxide concentrations double, the probability of very large increases in temperature is greater than the probability of very small increases.<ref name="lindsey climate sensitivity frequency distribution"/>]]
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| '''Climate sensitivity''' is the [[radiative equilibrium|equilibrium]] temperature change in response to changes of the [[radiative forcing]].<ref>{{cite journal
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| |url= [http://www.nature.com/nature/journal/v491/n7426/full/nature11574.html Abstract] [http://academiccommons.columbia.edu/download/fedora_content/download/ac:162782/CONTENT/Paleosens_Project_Members_2012.pdf PDF]
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| |title=Making sense of palaeoclimate sensitivity
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| |author=PALAEOSENS
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| | volume = 491
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| |pages= 683–691
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| |doi=10.1038/nature11574
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| |publisher=Nature
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| |year=2012
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| }}</ref> Therefore climate sensitivity depends on the initial [[climate state]], but potentially can be accurately inferred from precise [[Proxy (climate)|palaeoclimate data]]. Slow feedbacks, especially change of ice sheet size and atmospheric CO2, amplify the total Earth system sensitivity by an amount that depends on the time scale considered.<ref name="Hansen et al 2013">{{cite journal | last = Hansen | first = James | authorlink = | coauthors = et al. |date=September 2013 | title = '''Climate sensitivity, sea level and atmospheric carbon dioxide''' | journal = Royal Society Publishing | volume = 371 | doi = 10.1098/rsta.2012.0294 | url = http://rsta.royalsocietypublishing.org/content/371/2001/20120294 }}</ref>
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| Although climate sensitivity is usually used in the context of radiative forcing by [[carbon dioxide]] (CO<sub>2</sub>), it is thought of as a general property of the climate system: the change in surface air temperature (ΔT<sub>s</sub>) following a unit change in [[radiative forcing]] (RF), and thus is expressed in units of °C/(W/m<sup>2</sup>). For this to be useful, the measure must be independent of the nature of the forcing (e.g. from [[greenhouse gases]] or [[solar variation]]); to first order this is indeed found to be so{{Citation needed|date=July 2012}}.
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| The climate sensitivity specifically due to {{CO2}} is often expressed as the temperature change in °C associated with a doubling of the concentration of [[carbon dioxide in Earth's atmosphere]].
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| For coupled atmosphere-ocean global climate models (i.e. [[Coupled model intercomparison project|CMIP5]]) the climate sensitivity is an emergent property: it is not a model parameter, but rather a result of a combination of model physics and parameters. By contrast, simpler energy-balance models may have climate sensitivity as an explicit parameter.
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| <blockquote>
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| <math>\Delta T_s = \lambda \cdot RF</math>
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| </blockquote>
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| The terms represented in the equation relate radiative forcing to linear changes in global surface temperature change.
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| It is also possible to estimate climate sensitivity from observations; however, this is difficult due to uncertainties in the forcing and temperature histories.
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| ==Equilibrium and transient climate sensitivity==
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| The '''equilibrium''' climate sensitivity (ECS) refers to the equilibrium change in global mean near-surface air temperature that would result from a sustained doubling of the atmospheric (equivalent) carbon dioxide concentration (ΔT<sub>x2</sub>). This value is estimated, by the [[IPCC Fourth Assessment Report]] (''AR4'') as ''likely to be in the range 2 to 4.5 °C with a best estimate of about 3 °C, and is very unlikely to be less than 1.5 °C. Values substantially higher than 4.5 °C cannot be excluded, but agreement of models with observations is not as good for those values''.<ref>{{Cite book
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| |author=IPCC
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| |editor = Pachauri, R.K and Reisinger, A.
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| | title =Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change
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| | publisher = Intergovernmental Panel on Climate Change
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| | location =Geneva, Switzerland
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| | year = 2007
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| | chapter = 2.3 Climate sensitivity and feedbacks
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| | chapterurl = http://www.ipcc.ch/publications_and_data/ar4/syr/en/mains2-3.html
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| |accessdate=2010-07-03
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| |postscript=<!--None-->
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| }}</ref> This is a change from the [[IPCC Third Assessment Report]] (''TAR''), which said it was "likely to be in the range of 1.5 to 4.5 °C".<ref name="albritton 2001 climate sensitivity">{{Cite book |author=Albritton, D.L. ''et al'' |editor =Houghton J.T. ''et al''
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| | title = Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change
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| | publisher = Cambridge University Press
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| | year = 2001
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| | chapter = Technical Summary: F.3 Projections of Future Changes in Temperature
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| | chapterurl = http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/031.htm
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| |accessdate=2010-07-03 |postscript=<!--None-->
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| }}</ref> Other estimates of climate sensitivity are discussed later on.
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| A model estimate of equilibrium sensitivity thus requires a very long model integration; fully equilibrating ocean temperatures requires integrations of thousands of model years. A measure requiring shorter integrations is the '''transient''' climate response (TCR) which is defined as the average temperature response over a twenty-year period centered at {{CO2}} doubling in a transient simulation with {{CO2}} increasing at 1% per year.<ref>{{Cite book
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| |author=Randall, D.A., ''et al''
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| |editor = Solomon, S., D. ''et al''
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| | title =Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change
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| | publisher = Cambridge University Press
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| | year = 2007
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| | chapter = 8.6.2 Interpreting the Range of Climate Sensitivity Estimates Among General Circulation Models, In: Climate Models and Their Evaluation.
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| | chapterurl = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-2.html
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| |accessdate=2010-07-03
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| |postscript=<!--None-->
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| }}</ref> The transient response is lower than the equilibrium sensitivity, due to the "inertia" of ocean heat uptake.
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| Over the 50–100 year timescale, the climate response to forcing is likely to follow the TCR; for considerations of climate stabilization, the ECS is more useful.
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| An estimate of the equilibrium climate sensitivity may be made from combining the effective climate sensitivity with the known properties of the ocean reservoirs and the surface heat fluxes; this is the '''effective''' climate sensitivity. This "may vary with forcing history and climate state".<ref>{{Cite book
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| |author=Prentice, I.C. ''et al'' |editor =Houghton J.T. ''et al''
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| | title = Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change
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| | publisher = Cambridge University Press
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| | year = 2001
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| | chapter = 9.2.1 Climate Forcing and Climate Response, in chapter 9. Projections of Future Climate Change
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| | chapterurl = http://www.ipcc.ch/ipccreports/tar/wg1/345.htm
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| | accessdate=2010-07-03<!--, 2011-10-05(url)
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| -->| isbn=9780521807678
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| |postscript=<!--None-->
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| }}</ref>
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| <ref>{{Cite book
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| |editor=Solomon, S., D. ''et al''
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| | title = Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 2007
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| | publisher = Cambridge University Press
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| | year = 2007
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| | chapter = Glossary A-D, Climate sensitivity
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| | chapterurl = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/annex1sglossary-a-d.html
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| | accessdate=2011-10-05
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| |postscript=<!--None-->
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| }}</ref>
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| A less commonly used concept, the '''Earth system sensitivity''' (ESS), can be defined which includes the effects of slower feedbacks, such as the albedo change from melting the large ice sheets that covered much of the northern hemisphere during the [[last glacial maximum]]. These extra feedbacks make the ESS larger than the ECS — possibly twice as large — but also mean that it may well not apply to current conditions.<ref>{{cite web |url=http://www.realclimate.org/index.php/archives/2008/04/target-co2/ |title=Target {{CO2}} |work=RealClimate |year=2008 |month=April}}</ref>
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| == Sensitivity to carbon dioxide forcing ==
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| === Radiative forcing due to doubled {{CO2}} ===
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| {{CO2}} climate sensitivity has a component directly due to radiative forcing by {{CO2}}, and a further contribution arising from [[feedback]]s, positive and negative. "Without any feedbacks, a doubling of {{CO2}} (which amounts to a forcing of 3.7 W/m<sup>2</sup>) would result in 1 °C [[global warming]], which is easy to calculate and is undisputed. The remaining uncertainty is due entirely to feedbacks in the system, namely, [[Water vapor feedback#Role of water vapor|the water vapor feedback]], the [[ice-albedo feedback]], the [[cloud feedback]], and the lapse rate feedback";<ref name=rahmstorf2008/> addition of these feedbacks leads to a value of the sensitivity to {{CO2}} doubling of approximately 3 °C ± 1.5 °C, which corresponds to a value of λ of 0.8 K/(W/m<sup>2</sup>).
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| In the earlier 1979 NAS report<ref name=charney1979/> (p. 7), the radiative forcing due to doubled {{CO2}} is estimated to be 4 W/m<sup>2</sup>, as calculated (for example) in [[Veerabhadran Ramanathan|Ramanathan]] et al. (1979).<ref>{{cite journal
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| |url=http://www-ramanathan.ucsd.edu/publications/Ram%20Lian%20and%20Cess%20JGR%201979.pdf
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| |format=PDF|title=Increased Atmospheric {{CO2}}: Zonal and Seasonal Estimates of the Effect on Radiative Energy Balance and Surface Temperature
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| |author=V. Ramanathan, M.S. Lian, and R.D. Cess
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| |publisher=Journal of Geophysical Research
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| |year=1979
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| }}</ref> In 2001 the IPCC adopted the revised value of 3.7 W/m<sup>2</sup>, the difference attributed to a "stratospheric temperature adjustment".<ref>{{Cite book
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| |author=O. Boucher, ''et al''
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| |editor = Houghton J.T. ''et al'' (Eds).
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| | title =Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change
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| | publisher = Cambridge University Press
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| | year = 2001
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| | chapter = 6.3.1 Carbon Dioxide in: Chapter 6 Radiative Forcing of Climate Change
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| | chapterurl = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-2.html
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| |accessdate=2010-07-03
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| |postscript=<!--None-->
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| }}</ref> More recently an intercomparison of radiative transfer codes (Collins et al., 2006)<ref>{{Cite journal
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| | author = Collins, W.D., ''et al''.
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| | title = Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4)
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| | journal = J. Geophys. Res.
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| | volume = 111
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| | issue = D14317
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| | year = 2006
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| | url = http://www.agu.org/pubs/crossref/2006/2005JD006713.shtml
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| | doi = 10.1029/2005JD006713
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| | accessdate = 2010-07-03
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| | pages = D14317
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| | bibcode=2006JGRD..11114317C}}</ref> showed discrepancies among climate models and between climate models and more exact radiation codes in the forcing attributed to doubled {{CO2}} even in cloud-free sky; presumably the differences would be even greater if forcing were evaluated in the presence of clouds because of differences in the treatment of clouds in different models. Undoubtedly the difference in forcing attributed to doubled {{CO2}} in different climate models contributes to differences in apparent sensitivities of the models, although this effect is thought to be small relative to the intrinsic differences in sensitivities of the models themselves.<ref>{{cite doi|10.1007/s00382-006-0111-2}}</ref>
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| [[Image:Frequency distribution of climate sensitivity, based on model simulations (NASA).png|thumb|350px|right |alt=Refer to caption and adjacent text|[[Frequency distribution]] of climate sensitivity, based on model simulations.<ref name="lindsey climate sensitivity frequency distribution">Edited quote from public-domain source: {{citation
| |
| | url=http://earthobservatory.nasa.gov/blogs/climateqa/what-if-global-warming-isnt-as-severe-as-predicted/
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| | title=What if global warming isn’t as severe as predicted? : Climate Q&A : Blogs
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| | publisher=[[NASA Earth Observatory]], part of the EOS Project Science Office, located at NASA Goddard Space Flight Center
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| | author=Lindsey, R.
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| | date=3 August 2010
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| }}
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| </ref> Few of the simulations result in less than 2 °C of warming—near the low end of estimates by the [[Intergovernmental Panel on Climate Change]] (IPCC).<ref name="lindsey climate sensitivity frequency distribution"/> Some simulations result in significantly more than the 4 °C, which is at the high end of the IPCC estimates.<ref name="lindsey climate sensitivity frequency distribution"/> This pattern (statisticians call it a "right-[[:en:skewness|skewed]] distribution") suggests that if carbon dioxide concentrations double, the probability of very large increases in temperature is greater than the probability of very small increases.<ref name="lindsey climate sensitivity frequency distribution"/>]]
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| === Consensus estimates ===
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| A committee on [[anthropogenic]] global warming convened in 1979 by the [[United States National Academy of Sciences|National Academy of Sciences]] and chaired by [[Jule Charney]]<ref name=charney1979/> estimated climate sensitivity to be 3 °C, plus or minus 1.5 °C. Only two sets of models were available; one, due to [[Syukuro Manabe]], exhibited a climate sensitivity of 2 °C, the other, due to [[James E. Hansen]], exhibited a climate sensitivity of 4 °C. "According to Manabe,
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| Charney chose 0.5 °C as a not-unreasonable margin of error, subtracted it from Manabe’s number, and added it to Hansen’s. Thus was born the 1.5 °C-to-4.5 °C range of likely climate sensitivity that has appeared in every greenhouse assessment since..."<ref>{{cite journal |journal=Science |volume=305 |issue=5686
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| |url=http://www.sciencemag.org/cgi/content/summary/305/5686/932
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| |title=Three Degrees of Consensus |author=Richard A. Kerr |date=13 August 2004 |pmid=15310873 |doi=10.1126/science.305.5686.932 |pages=932–4
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| }}</ref>
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| Chapter 4 of the "Charney report" compares the predictions of the models: "We conclude that the predictions ... are basically consistent and mutually supporting. The differences in model results are relatively small and may be accounted for by differences in model characteristics and simplifying assumptions."<ref name=charney1979>{{cite web
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| |url=http://www.atmos.ucla.edu/~brianpm/download/charney_report.pdf
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| |format=PDF|title=Carbon Dioxide and Climate: A Scientific Assessment
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| |author=Ad Hoc Study Group on Carbon Dioxide and Climate
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| |publisher=National Academy of Sciences
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| |year=1979
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| }}</ref>
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| In 2008 climatologist [[Stefan Rahmstorf]] wrote, regarding the Charney report's original range of uncertainty: "At that time, this range was on very shaky ground. Since then, many vastly improved models have been developed by a number of climate research centers around the world. Current state-of-the-art climate models span a range of 2.6–4.1 °C, most clustering around 3 °C."<ref name=rahmstorf2008>{{Cite book | |
| |last=Rahmstorf
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| |first=Stefan
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| |editor-last=Zedillo
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| |editor-first=E.
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| |url=http://www.pik-potsdam.de/~stefan/Publications/Book_chapters/Rahmstorf_Zedillo_2008.pdf
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| |format=PDF|contribution=Anthropogenic Climate Change: Revisiting the Facts
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| |title=Global Warming: Looking Beyond Kyoto
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| |pages=34–53
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| |publisher=Brookings Institution Press
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| |year=2008
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| }}</ref>
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| ====Intergovernmental Panel on Climate Change====
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| The 1990 [[IPCC First Assessment Report]] estimated that equilibrium climate sensitivity to {{CO2}} doubling lay between 1.5 and 4.5 °C, with a "best guess in the light of current knowledge" of 2.5 °C.<ref>''Climate Change: The IPCC Scientific Assessment (1990),'' Report prepared for Intergovernmental Panel on Climate Change by Working Group I, J.T. Houghton, G.J. Jenkins and J.J. Ephraums (eds.), [http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_05.pdf chapter 5, Equilibrium Climate Change — and its Implications for the Future], pp. 138–9</ref> This used models with strongly simplified representations of the ocean dynamics. The [[IPCC supplementary report, 1992]] which used full ocean [[General circulation model|GCM]]s nonetheless saw "no compelling reason to warrant changing" from this estimate <ref>IPCC '92 p118 section B3.5</ref> and the [[IPCC Second Assessment Report]] found that "No strong reasons have emerged to change" these estimates,<ref>IPCC SAR p 34, technical summary section D.2</ref> with much of the uncertainty attributed to cloud processes. As noted above, the IPCC TAR retained the likely range 1.5 to 4.5 °C.<ref name="albritton 2001 climate sensitivity"/>
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| Authors of the [[IPCC Fourth Assessment Report]] (Meehl ''et al.'', 2007)<ref name="meehl 2007 climate sensitivity">
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| {{citation
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| | at=[http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-5.html#box-10-2 Box 10.2: Equilibrium Climate Sensitivity]
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| | chapter=Ch. 10: Global Climate Projections
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| | author=Meehl, G.A., ''et al.''
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| }}, in {{harvnb|IPCC AR4 WG1|2007}}
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| </ref> stated that confidence in estimates of equilibrium climate sensitivity had increased substantially since the TAR. AR4's assessment was based on a combination of several independent lines of evidence, including observed climate change and the strength of known "[[climate change feedback|feedback]]s" simulated in [[global climate model|general circulation models]].<ref name="epa climate sensitivity">
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| {{Include-USGov
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| |agency=[[US Environmental Protection Agency]] (US EPA)
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| |source={{citation
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| | author=US EPA
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| | date=7 December 2009
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| | chapter=Ch. 6: Projected Future Greenhouse Gas Concentrations and Climate Change: Box 6.3: Climate sensitivity
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| | title=Technical Support Document for Endangerment and Cause or Contribute Findings for Greenhouse Gases under Section 202(a) of the Clean Air Act
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| | url=http://www.epa.gov/climatechange/Downloads/endangerment/Endangerment_TSD.pdf
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| | publisher=Climate Change Division, Office of Atmospheric Programs, US EPA
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| | location=Washington, DC, USA
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| }}, p.66 (78 of PDF file)
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| }}
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| </ref> IPCC authors concluded that the global mean equilibrium warming for doubling {{CO2}} (a concentration of approximately 540 [[parts per notation|parts-per-million]] (ppm)), or equilibrium climate sensitivity, very likely is greater than 2.7 °F (1.5 °C) and likely to lie in the range 4 to 8.1 °F (2 to 4.5 °C), with a most likely value of about 5 °F (3 °C). For fundamental physical reasons, as well as data limitations, the IPCC states a climate sensitivity higher than 8.1 °F (4.5 °C) cannot be ruled out, but that agreement for these values with observations and [[proxy (climate)|"proxy" climate data]] is generally worse compared to values in the 4 to 8.1 °F (2 to 4.5 °C) range.<ref name="epa climate sensitivity"/>
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| The TAR uses the word "likely" in a qualitative sense to describe the likelihood of the 1.5 to 4.5 °C range being correct.<ref name="meehl 2007 climate sensitivity"/> AR4, however, quantifies the probable range of climate sensitivity estimates:<ref name="solomon 2007 uncertainty">
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| {{citation
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| | at=[http://www.ipcc.ch/publications_and_data/ar4/wg1/en/tssts-2.html Box TS.1: Treatment of Uncertainties in the Working Group I Assessment]
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| | chapter=Technical summary
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| | author=Solomon, S., ''et al.''
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| }}, in {{harvnb|IPCC AR4 WG1|2007}}
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| </ref>
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| *2-4.5 °C is "likely", = greater than 66% chance of being correct
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| *less than 1.5 °C is "very unlikely" = less than 10% " " "
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| These are [[Bayesian probability|Bayesian]] probabilities, which are based on an expert assessment of the available evidence.<ref name="solomon 2007 uncertainty"/>
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| ==Calculations of {{CO2}} sensitivity from observational data==
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| === Sample calculation using industrial-age data ===
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| Rahmstorf (2008)<ref name=rahmstorf2008/> provides an informal example of how climate sensitivity might be estimated empirically, from which the following is modified. Denote the sensitivity, i.e. the equilibrium increase in global mean temperature including the effects of feedbacks due to a sustained forcing by doubled {{CO2}} (taken as 3.7 W/m<sup>2</sup>), as ''x'' °C. If [[Earth]] were to experience an equilibrium temperature change of ΔT (°C) due to a sustained forcing of ΔF (W/m<sup>2</sup>), then one might say that ''x''/(ΔT) = (3.7 W/m<sup>2</sup>)/(ΔF), i.e. that ''x'' = ΔT * (3.7 W/m<sup>2</sup>)/ΔF. The global temperature increase since the beginning of the industrial period (taken as 1750) is about 0.8 °C, and the radiative forcing due to {{CO2}} and other long-lived greenhouse gases (mainly methane, nitrous oxide, and chlorofluorocarbons) emitted since that time is about 2.6 W/m<sup>2</sup>. Neglecting other forcings and considering the temperature increase to be an equilibrium increase would lead to a sensitivity of about 1.1 °C. However, ΔF also contains contributions due to solar activity (+0.3 W/m<sup>2</sup>), aerosols (-1 W/m<sup>2</sup>), ozone (0.3 W/m<sup>2</sup>) and other lesser influences, bringing the total forcing over the industrial period to 1.6 W/m<sup>2</sup> according to best estimate of the [[IPCC Fourth Assessment Report|IPCC AR4]], albeit with substantial uncertainty. Additionally the fact that the climate system is not at equilibrium must be accounted for; this is done by subtracting the planetary heat uptake rate H from the forcing; i.e., ''x'' = ΔT * (3.7 W/m<sup>2</sup>)/(ΔF-H). Taking planetary heat uptake rate as the rate of ocean heat uptake, estimated by the [[IPCC Fourth Assessment Report|IPCC AR4]] as 0.2 W/m<sup>2</sup>, yields a value for ''x'' of 2.1 °C. (All numbers are approximate and quite uncertain.)
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| === Sample calculation using ice-age data ===
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| In 2008, Farley wrote: "... examine the change in temperature and solar forcing between [[glaciation]] (ice age) and [[interglacial]] (no ice age) periods. The change in temperature, revealed in [[ice core]] samples, is 5 °C, while the change in solar forcing is 7.1 W/m<sup>2</sup>. The computed climate sensitivity is therefore 5/7.1 = 0.7 K(W/m<sup>2</sup>)<sup>−1</sup>. We can use this empirically derived climate sensitivity to predict the temperature rise from a forcing of 4 W/m<sup>2</sup>, arising from a doubling of the atmospheric {{CO2}} from pre-industrial levels. The result is a predicted temperature increase of 3 °C."<ref>{{cite web
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| |url=http://monthlyreview.org/080728farley.php
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| |title=The Scientific Case for Modern Anthropogenic Global Warming
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| |author=John Farley
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| |publisher=Monthly Review
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| |year=2008
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| }}</ref>
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| Based on analysis of uncertainties in total forcing, in Antarctic cooling, and in the ratio of global to Antarctic cooling of the [[last glacial maximum]] relative to the present, Ganopolski and Schneider von Deimling (2008) infer a range of 1.3 to 6.8 °C for climate sensitivity determined by this approach.<ref>{{Cite journal | author = Ganopolski, A., and T. Schneider von Deimling | title = Comment on "Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition" by Petr Chylek and Ulrike Lohmann | journal = Geophys. Res. Lett.
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| | volume = 35 | year = 2008 | url = http://www.agu.org/pubs/crossref/2008/2008GL033888.shtml
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| | doi = 10.1029/2008GL033888 | pages = L23703 | bibcode=2008GeoRL..3523703G}}</ref>
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| A lower figure was calculated in a 2011 ''[[Science (journal)|Science]]'' paper by Schmittner ''et al.'', who combined temperature reconstructions of the [[Last Glacial Maximum]] with climate model simulations to suggest a rate of global warming from doubling of atmospheric carbon dioxide of a median of 2.3 °C and uncertainty 1.7–2.6 °C (66% probability range), less than the earlier estimates of 2 to 4.5 °C as the 66% probability range. Schmittner et al. said their "results imply less probability of extreme climatic change than previously thought." Their work suggests that climate sensitivities >6 °C "cannot be reconciled with paleoclimatic and geologic evidence, and hence should be assigned near-zero probability."<ref name=Schmittner11>{{cite journal |author=Schmittner, A.; Urban, N.M.; Shakun, J.D.; Mahowald, N.M.; Clark, P.U.; Bartlein, P.J.; Mix, A.C.; Rosell-Melé, A. |title=Climate Sensitivity Estimated from Temperature Reconstructions of the Last Glacial Maximum |journal=Science |volume=334 |issue=6061 |pages=1385–8 |date=9 December 2011 |doi=10.1126/science.1203513 |url=http://www.sciencemag.org/content/334/6061/1385.abstract?sid=a7ab01bf-f2e5-413d-bbf0-c2c5ac2362df|bibcode = 2011Sci...334.1385S }}</ref><ref>[http://www.innovations-report.de/html/berichte/geowissenschaften/climate_sensitivity_limited_extreme_projections_186483.html Climate sensitivity to CO2 more limited than extreme projections], news article re Schmittner et al., ''Innovations Report'', 25.11.2011.</ref>
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| === Other experimental estimates ===
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| Idso (1998)<ref name="idso98">{{cite journal |doi=10.3354/cr010069 |last1=Idso |first1=Sherwood |title=CO2-induced global warming: A skeptic’s view of potential climate change |journal=Climate Research |volume=10 |pages=69–82 |year=1998 |url=http://www.int-res.com/articles/cr/10/c010p069.pdf }} (reprinted in {{cite journal |last1=Gerhard |first1=L.C. |last2=Harrison |first2=W.E. |last3=Hanson |first3=W.E. |title=Geological perspectives of global climate change |journal=AAPG Special Publication |volume=SG47 |pages=317–336 |year=2001 |url=http://dpa.aapg.org/gcc/index.cfm }})</ref> calculated based on eight natural experiments a λ of 0.1 °C/(Wm<sup>−2</sup>) resulting in a climate sensitivity of only 0.4 °C for a doubling of the concentration of {{CO2}} in the atmosphere.
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| Andronova and Schlesinger (2001) found that the climate sensitivity could lie between 1 and 10 °C, with a 54 percent likelihood that it lies outside the IPCC range.<ref>{{cite journal |last1=Andronova |first1=N. |last2=Schlesinger |first2=M. E. |title=Objective Estimation of the Probability Distribution for Climate Sensitivity |journal=J. Geophys. Res. |volume=106 |issue=D19 |pages=22605 |year=2001 |url=http://www.agu.org/pubs/crossref/2001/2000JD000259.shtml |doi=10.1029/2000JD000259 |bibcode=2001JGR...10622605A}} [http://crga.atmos.uiuc.edu/publications/Objective_Est_dT2x.pdf as PDF] [http://crga.atmos.uiuc.edu/publications/Climate.html data]</ref> The exact range depends on which factors are most important during the instrumental period: "At present, the most likely scenario is one that includes anthropogenic sulfate aerosol forcing but not solar variation. Although the value of the climate sensitivity in that case is most uncertain, there is a 70 percent chance that it exceeds the maximum IPCC value. This is not good news," said Schlesinger.
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| Forest, ''et al.'' (2002)<ref>{{cite journal |last1=Forest |first1=C.E. |first2=P.H. |last2=Stone |first3=A.P. |last3=Sokolov |first4=M.R. |last4=Allen |first5=M.D. |last5=Webster |title=Quantifying uncertainties in climate system properties with the use of recent observations |journal=Science |volume=295 |issue=5552 |year=2002 |url=http://www.sciencemag.org/cgi/content/abstract/295/5552/113 |pmid=11778044 |doi=10.1126/science.1064419 |pages=113–7|bibcode = 2002Sci...295..113F }} [https://dspace.mit.edu/bitstream/1721.1/3567/1/MITJPSPGC_Rpt78.pdf as PDF]</ref> using patterns of change and the MIT EMIC estimated a 95% confidence interval of 1.4–7.7 °C for the climate sensitivity, and a 30% probability that sensitivity was outside the 1.5 to 4.5 °C range.
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| Gregory, ''et al.'' (2002)<ref>{{cite journal |last1=Gregory |first1=J.M. |first2=R.J. |last2=Stouffer |first3=S.C.B. |last3=Raper |first4=P.A. |last4=Stott |first5=N.A. |last5=Rayner |title=An observationally based estimate of the climate sensitivity |journal=Journal of Climate |volume=15 |pages=3117 |year=2002 |url=http://ams.allenpress.com/perlserv/?request=get-abstract&issn=1520-0442&volume=015&issue=22&page=3117 |doi=10.1175/1520-0442(2002)015<3117:AOBEOT>2.0.CO;2 |issue=22|bibcode = 2002JCli...15.3117G }} [http://www.gfdl.gov/reference/bibliography/2002/jmgregory0201.pdf as PDF]</ref> estimated a lower bound of 1.6 °C by estimating the change in Earth's radiation budget and comparing it to the global warming observed over the 20th century.
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| Shaviv (2005)<ref>{{cite journal |last1=Shaviv |first1=N.J. |title=On climate response to changes in the cosmic ray flux and radiative budget |journal=J. Geophys. Res. |volume=110 |pages=A08105 |year=2005 |url=http://www.agu.org/pubs/crossref/2005/2004JA010866.shtml |doi=10.1029/2004JA010866 |bibcode=2005JGRA..11008105S|arxiv = physics/0409123 }} ([http://www.phys.huji.ac.il/~shaviv/articles/sensitivity.pdf preprint]), and a [http://www.sciencebits.com/OnClimateSensitivity discussion] about it.</ref> carried out a similar analysis for 6 different time scales, ranging from the 11-yr solar cycle to the climate variations over geological time scales. He found a typical sensitivity of 0.54±0.12 K/(W m<sup>−2</sup>) or 2.1 °C (ranging between 1.6 °C and 2.5 °C at 99% confidence) if there is no cosmic-ray climate connection, or a typical sensitivity of 0.35±0.09 K/(W m<sup>−2</sup>) or 1.3 °C (between 1.0 °C and 1.7 °C at 99% confidence), if the [[Solar variation|cosmic-ray climate link]] is real. (Note Shaviv quotes a radiative forcing equivalent of 3.8Wm<sup>−2</sup>. [ΔT<sub>x2</sub>=3.8 Wm<sup>−2</sup> λ].)
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| Frame, ''et al.'' (2005)<ref>{{cite journal |last1=Frame |first1=D.J. |first2=B.B.B. |last2=Booth |first3=J.A. |last3=Kettleborough |first4=D.A. |last4=Stainforth |first5=J.M. |last5=Gregory |first6=M. |last6=Collins |first7=M.R. |last7=Allen |title=Constraining climate forecasts: the role of prior assumptions |journal=Geophysical Research Letters |volume=32 |pages=L09702 |year=2005 |doi=10.1029/2004GL022241 |url=http://www.agu.org/pubs/crossref/2005/2004GL022241.shtml |bibcode=2005GeoRL..3209702F |issue=9}}</ref> noted that the range of the confidence limits is dependent on the nature of the prior assumptions made.
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| Annan and Hargreaves (2006)<ref>{{cite journal |last1=Annan |first1=J.D. |last2=Hargreaves |first2=J. C. |title=Using multiple observationally-based constraints to estimate climate sensitivity |journal=Geophysical Research Letters |volume=33 |pages=L06704 |year=2006 |doi=10.1029/2005GL025259 |url=http://www.agu.org/pubs/crossref/2006/2005GL025259.shtml |bibcode=2006GeoRL..3306704A |issue=6}} [http://www.jamstec.go.jp/frcgc/research/d5/jdannan/GRL_sensitivity.pdf as PDF]</ref> presented an estimate that resulted from combining prior estimates based on analyses of paleoclimate, responses to volcanic eruptions, and the temperature change in response to forcings over the twentieth century. They also introduced a triad notation (L, C, H) to convey the probability distribution function (pdf) of the sensitivity, where the central value C indicates the maximum likelihood estimate in degrees Celsius and the outer values L and H represent the limits of the 95% confidence interval for a pdf, or 95% of the area under the curve for a likelihood function. In this notation their estimate of sensitivity was (1.7, 2.9, 4.9)°C.
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| Forster and Gregory (2006)<ref>{{cite journal |last1=Forster |first1=Piers M. de F. |last2=Gregory |first2=Jonathan M. |title=The Climate Sensitivity and Its Components Diagnosed from Earth Radiation Budget Data |journal=Journal of Climate |volume=19 |issue=1 |pages=39–52 |year=2006 |doi=10.1175/JCLI3611.1 |url=http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175%2FJCLI3611.1|bibcode = 2006JCli...19...39F }}</ref> presented a new independent estimate based on the slope of a plot of calculated greenhouse gas forcing minus top-of-atmosphere energy imbalance, as measured by satellite borne radiometers, versus global mean surface temperature. In the triad notation of Annan and Hargreaves their estimate of sensitivity was (1.0, 1.6, 4.1)°C.
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| Royer, ''et al.'' (2007)<ref>{{cite journal |first1=Dana L. |last1=Royer |first2=Robert A. |last2=Berner |first3=Jeffrey |last3=Park |title=Climate sensitivity constrained by {{CO2}} concentrations over the past 420 million years |journal=Nature |volume=446 |pages=530–2 |date=29 March 2007 |doi=10.1038/nature05699 |url=http://www.nature.com/nature/journal/v446/n7135/full/nature05699.html |pmid=17392784 |issue=7135|bibcode = 2007Natur.446..530R }}</ref> determined climate sensitivity within a major part of the [[Phanerozoic]]. The range of values—1.5 °C minimum, 2.8 °C best estimate, and 6.2 °C maximum—is, given various uncertainties, consistent with sensitivities of current climate models and with other determinations.<ref>Sceptics as [[Jan Veizer]] have pointed out that while data for the whole Phanerozoic are available <!-- (and have been mentioned in the 2001 IPCC Mitchell report), --> Royer ''et al.'' left out the time span younger than 420 Ma with an ice age and extremely high carbon dioxide content during the [[Hirnantian]].</ref>
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| ''[[ScienceDaily]]'' reported on a study by Fasullo and Trenberth (2012),<ref name="fasullo 2012 climate sensitivity estimate">
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| {{citation
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| | title=A Less Cloudy Future: The Role of Subtropical Subsidence in Climate Sensitivity
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| | author=Fasullo, J.T., and K.E. Trenberth
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| | journal=Science
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| | volume=338
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| | issue=6108
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| | pages=792–794
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| | doi=10.1126/science.1227465
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| | url=http://www.sciencemag.org/content/338/6108/792.abstract
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| | date=9 November 2012
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| |bibcode = 2012Sci...338..792F }}. Referred to by: {{citation
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| | title=Future warming likely to be on high side of climate projections, analysis finds
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| | date=8 November 2012
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| | author= ScienceDaily
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| | url=http://www.sciencedaily.com/releases/2012/11/121108142746.htm
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| | publisher=ScienceDaily
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| }}
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| </ref> who tested model estimates of climate sensitivity based on their ability to reproduce observed relative [[humidity]] in the [[tropics]] and [[subtropics]]. The best performing models tended to project relatively high climate sensitivities, of around 4 °C.<ref name="fasullo 2012 climate sensitivity estimate"/>
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| Previdi et al. 2013 reviewed the 2×CO2 Earth system sensitivity, and concluded it is higher if the [[Ice-albedo feedback|ice sheet]] and the vegetation albedo feedback is included in addition to the fast feedbacks, being ∼'''4–6'''◦ C, and higher still if climate–GHG feedbacks are also included.<ref name="Previdi et al 2013">
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| {{citation
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| | title= '''Climate sensitivity in the Anthropocene'''
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| | author= Previdi et al.
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| | journal= Wiley
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| | volume=139
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| | issue=674
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| | pages=1121–1131
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| | doi= 10.1002/qj.2165
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| | year=2013
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| | bibcode =
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| | publisher= Quarterly Journal of the Royal Meteorological Society
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| }}</ref>
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| ===Literature reviews===
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| A literature review by Knutti and Hegerl (2008)<ref>{{Cite journal
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| | last = Knutti
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| | first = Reto
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| | last2 = Hegerl
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| | first2 = Gabriele C.
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| | title = The equilibrium sensitivity of the Earth's temperature to radiation changes
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| | journal = Nature Geoscience
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| | volume = 1
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| | pages = 735–743
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| | date = 2008-10-26
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| | url = http://www.nature.com/ngeo/journal/v1/n11/abs/ngeo337.html
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| | doi = 10.1038/ngeo337
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| | accessdate = 2010-07-03
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| | issue=11|bibcode = 2008NatGe...1..735K }}. This paper can be freely [http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf downloaded] from Prof. Reto Knutti's [http://www.iac.ethz.ch/people/knuttir webpage] at the Institute for Atmospheric and Climate Science, Zürich, Switzerland.
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| </ref> concluded that "various observations favour a climate sensitivity value of about 3 °C, with a likely range of about 2-4.5 °C. However, the physics of the response and uncertainties in forcing lead to difficulties in ruling out higher values."
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| ==Radiative forcing functions==
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| A number of different inputs can give rise to radiative forcing. In addition to the downwelling radiation due to the greenhouse effect, the [[IPCC First Assessment Report|IPCC First Scientific Assessment Report]] listed solar radiation variability due to orbital changes, variability due to changes in solar irradiance, direct aerosol effects (''e.g.,'' changes in albedo due to cloud cover), indirect aerosol effects, and surface characteristics.<ref>''Climate Change: The IPCC Scientific Assessment (1990),'' Report prepared for Intergovernmental Panel on Climate Change by Working Group I, J.T. Houghton, G.J. Jenkins and J.J. Ephraums (eds.), [http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_02.pdf chapter 2, Radiative Forcing of Climate], pp. 41–68</ref>
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| ==Sensitivity to solar forcing==
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| [[Solar luminosity]] is about 0.9 W/m<sup>2</sup> brighter during [[solar maximum]] than during [[solar minimum]]. Analysis by Camp and Tung shows that this correlates with a variation of ±0.1°C in measured average global temperature between the peak and minimum of the 11-year solar cycle.<ref name="solar-climate">{{cite journal |author=C. D. Camp and K. K. Tung |journal=Geophysical Research Letters |volume=34 |pages= L14703 | title=Surface warming by the solar cycle as revealed by the composite mean difference projection |url=http://depts.washington.edu/amath/research/articles/Tung/journals/GRL-solar-07.pdf |year=2007 |doi= 10.1029/2007GL030207 | accessdate=20 January 2012 |bibcode=2007GeoRL..3414703C}}</ref> From this data (incorporating the Earth's albedo and the fact that the solar absorption cross-section is 1/4 of the surface area of the Earth), Tung, Zhou and Camp (2008) derive a transient sensitivity value of 0.69 to 0.97 °C/(W/m<sup>2</sup>).<ref>{{cite journal |author=Tung, K.K.; Zhou, J.; Camp, C.D. |title=Constraining model transient climate response using independent observations of solar-cycle forcing and response |journal=[[Geophysical Research Letters]] |volume=35 |pages=L17707 |year=2008 |doi=10.1029/2008GL034240 |url=http://www.calpoly.edu/~camp/Publications/Tung_etal_GRL_2008.pdf |format=PDF|bibcode = 2008GeoRL..3517707T }}</ref> This would correspond to a transient climate sensitivity to carbon dioxide doubling of 2.5 to 3.6 K, similar to the range of the current scientific consensus. However, they note that this is the transient response to a forcing with an 11 year cycle; due to lag effects, they estimate the equilibrium response to forcing would be about 1.5 times higher.
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| ==See also==
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| {{Portal|Global warming}}
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| * [[Climate change feedback]]
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| * [[Climate state]]
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| * [[Runaway climate change]]
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| * [[Tipping point (climatology)]]
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| == References ==
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| {{Reflist|2}}
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| ==References==
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| * {{Citation
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| |year = 2007
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| |author = IPCC AR4 WG1
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| |author-link = IPCC
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| |title = Climate Change 2007: The Physical Science Basis
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| |series = Contribution of Working Group I to the [[IPCC Fourth Assessment Report|Fourth Assessment Report]] of the Intergovernmental Panel on Climate Change
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| |editor = Solomon, S.; Qin, D.; Manning, M.; Chen, Z.; Marquis, M.; Averyt, K.B.; Tignor, M.; and Miller, H.L.
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| |publisher = Cambridge University Press
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| |url = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html
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| |isbn = 978-0-521-88009-1
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| }} (pb: {{ISBNT|978-0-521-70596-7}}).
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| {{global warming}}
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| {{DEFAULTSORT:Climate Sensitivity}}
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| [[Category:Climate change science]]
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| [[Category:Climate feedbacks]]
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| [[Category:Paleoclimatology]]
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