Climate sensitivity#Hot models

The rate at which energy reaches Earth as sunlight and leaves Earth as heat radiation to space must balance, or the total amount of heat energy on the planet at any one time will rise or fall, which results in a planet that is warmer or cooler overall. A driver of an imbalance between the rates of incoming and outgoing radiation energy is called radiative forcing. A warmer planet radiates heat to space faster and so a new balance is eventually reached, with a higher temperature and stored energy content. However, the warming of the planet also has knock-on effects, which create further warming in an exacerbating feedback loop. Climate sensitivity is a measure of how much temperature change a given amount of radiative forcing will cause.{{cite journal |author=PALAEOSENS Project Members |date=November 2012 |title=Making sense of palaeoclimate sensitivity |url=http://academiccommons.columbia.edu/download/fedora_content/download/ac:162782/CONTENT/Paleosens_Project_Members_2012.pdf |url-status=live |journal=Nature |volume=491 |issue=7426 |pages=683–691 |bibcode=2012Natur.491..683P |doi=10.1038/nature11574 |pmid=23192145 |s2cid=2840337 |archive-url=https://web.archive.org/web/20170815164923/https://academiccommons.columbia.edu/download/fedora_content/download/ac:162782/CONTENT/Paleosens_Project_Members_2012.pdf |archive-date=15 August 2017 |access-date=24 September 2013 |hdl=2078.1/118863}}

{{Main|Radiative forcing|Earth's energy imbalance}}

Radiative forcings are generally quantified as Watts per square meter (W/m²) and averaged over Earth's uppermost surface defined as the top of the atmosphere. The magnitude of a forcing is specific to the physical driver and is defined relative to an accompanying time span of interest for its application.{{cite book |title=Radiative Forcing of Climate Change: Expanding the Concept and Addressing Uncertainties |author=National Research Council |publisher=The National Academic Press |year=2005 |doi=10.17226/11175|isbn=978-0-309-09506-8 }} In the context of a contribution to long-term climate sensitivity from 1750 to 2020, the 50% increase in atmospheric {{chem|CO|2}} is characterized by a forcing of about +2.1 W/m².{{Cite web |url=https://www.esrl.noaa.gov/gmd/aggi/aggi.html |title=The NOAA Annual Greenhouse Gas Index (AGGI) |publisher=NOAA Global Monitoring Laboratory/Earth System Research Laboratories |author=Butler J. and Montzka S. |year=2020 }} In the context of shorter-term contributions to Earth's energy imbalance (i.e. its heating/cooling rate), time intervals of interest may be as short as the interval between measurement or simulation data samplings, and are thus likely to be accompanied by smaller forcing values. Forcings from such investigations have also been analyzed and reported at decadal time scales.{{cite web |url=https://phys.org/news/2021-03-humans-earth-energy.html |title=Direct observations confirm that humans are throwing Earth's energy budget off balance |website=phys.org |date=26 March 2021}}{{cite journal |url=https://www.nature.com/articles/nature14240 |title=Observational determination of surface radiative forcing by {{chem|CO|2}} from 2000 to 2010 |author=Feldman, D.R., W.D. Collins, P.J. Gero, M.S. Torn, E.J. Mlawer, and T.R. Shippert |journal=Nature |volume=519 |date=2015-02-25 |issue=7543 |pages=339–343 |doi=10.1038/nature14240 |pmid=25731165 |bibcode=2015Natur.519..339F |s2cid=2137527 }}

Radiative forcing leads to long-term changes in global temperature.{{Cite web|url=https://news.mit.edu/2010/explained-radforce-0309|title=Explained: Radiative forcing|website=MIT News|date=10 March 2010 |access-date=2019-03-30|archive-date=25 August 2019|archive-url=https://web.archive.org/web/20190825003553/http://news.mit.edu/2010/explained-radforce-0309|url-status=live}} A number of factors contribute radiative forcing: increased downwelling radiation from the greenhouse effect, variability in solar radiation from changes in planetary orbit, changes in solar irradiance, direct and indirect effects caused by aerosols (for example changes in albedo from cloud cover), and changes in land use (deforestation or the loss of reflective ice cover).Climate Change: The IPCC Scientific Assessment (1990), Report prepared for Intergovernmental Panel on Climate Change by Working Group I, Houghton JT, Jenkins GT, Ephraums JJ (eds.), [https://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_02.pdf chapter 2, Radiative Forcing of Climate] {{Webarchive|url=https://web.archive.org/web/20180808033533/http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_02.pdf|date=2018-08-08}}, pp. 41–68 In contemporary research, radiative forcing by greenhouse gases is well understood. {{As of|2019|df=}}, large uncertainties remain for aerosols.{{Cite journal|last1=Larson|first1=E. J. L.|last2=Portmann|first2=R. W.| name-list-style = vanc|date=2019-11-12|title=Anthropogenic aerosol drives uncertainty in future climate mitigation efforts|journal=Scientific Reports|language=en|volume=9|issue=1|pages=16538|doi=10.1038/s41598-019-52901-3|pmid=31719591|pmc=6851092|bibcode=2019NatSR...916538L|issn=2045-2322}}Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, 2013: [https://archive.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_Chapter08_FINAL.pdf Chapter 8: Anthropogenic and Natural Radiative Forcing]. In: [https://www.ipcc.ch/report/ar5/wg1/ Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change] [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

{{Further|Carbon dioxide in Earth's atmosphere|Instrumental temperature record}}

Carbon dioxide ({{CO2}}) levels rose from 280 parts per million (ppm) in the 18th century, when humans in the Industrial Revolution started burning significant amounts of fossil fuel such as coal, to over 415 ppm by 2020. As {{CO2}} is a greenhouse gas, it hinders heat energy from leaving the Earth's atmosphere. In 2016, atmospheric {{CO2}} levels had increased by 45% over preindustrial levels, and radiative forcing caused by increased {{CO2}} was already more than 50% higher than in pre-industrial times because of non-linear effects.{{Cite journal |last1=Myhre |first1=Gunnar |last2=Myhre |first2=Cathrine Lund |last3=Forster |first3=Piers M. |last4=Shine |first4=Keith P. |name-list-style=vanc |date=2017 |title=Halfway to doubling of CO2 radiative forcing |url=http://centaur.reading.ac.uk/72841/1/halfwayCO2doubling_revised_v2.pdf |journal=Nature Geoscience |volume=10 |issue=10 |pages=710–711 |doi=10.1038/ngeo3036 |bibcode=2017NatGe..10..710M |access-date=13 February 2020 |archive-date=26 April 2019 |archive-url=https://web.archive.org/web/20190426231756/http://centaur.reading.ac.uk/72841/1/halfwayCO2doubling_revised_v2.pdf |url-status=live }}The {{CO2}} level in 2016 was 403 ppm, which is less than 50% higher than the pre-industrial {{CO2}} concentration of 278 ppm. However, because increased concentrations have a progressively-smaller warming effect, the Earth was already more than halfway to doubling of radiative forcing caused by {{CO2}}. Between the 18th-century start of the Industrial Revolution and the year 2020, the Earth's temperature rose by a little over one degree Celsius (about two degrees Fahrenheit).{{cite news|last=Watts|first=Jonathan|name-list-style=vanc|url=https://www.theguardian.com/environment/2018/oct/08/global-warming-must-not-exceed-15c-warns-landmark-un-report|title=We have 12 years to limit climate change catastrophe, warns UN|date=2018-10-08|work=The Guardian|access-date=2020-02-13|language=en-GB|issn=0261-3077|archive-date=11 August 2019|archive-url=https://web.archive.org/web/20190811175157/https://www.theguardian.com/environment/2018/oct/08/global-warming-must-not-exceed-15c-warns-landmark-un-report|url-status=live}}

Because the economics of climate change mitigation depend greatly on how quickly carbon neutrality needs to be achieved, climate sensitivity estimates can have important economic and policy-making implications. One study suggests that halving the uncertainty of the value for transient climate response (TCR) could save trillions of dollars.{{cite journal | vauthors = Hope C | title = The $10 trillion value of better information about the transient climate response | journal = Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences | volume = 373 | issue = 2054 | page = 20140429 | date = November 2015 | pmid = 26438286 | doi = 10.1098/rsta.2014.0429 | bibcode = 2015RSPTA.37340429H | doi-access = free}} A higher climate sensitivity would mean more dramatic increases in temperature, which makes it more prudent to take significant climate action.{{cite journal | vauthors = Freeman MC, Wagner G, Zeckhauser RJ | title = Climate sensitivity uncertainty: when is good news bad? | journal = Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences | volume = 373 | issue = 2055 | page = 20150092 | date = November 2015 | pmid = 26460117 | doi = 10.1098/rsta.2015.0092 | bibcode = 2015RSPTA.37350092F | s2cid = 13843499 | url = http://eprints.whiterose.ac.uk/111971/1/For_repository.pdf | doi-access = free | access-date = 22 February 2020 | archive-date = 22 February 2020 | archive-url = https://web.archive.org/web/20200222153314/http://eprints.whiterose.ac.uk/111971/1/For_repository.pdf | url-status = live }} If climate sensitivity turns out to be on the high end of what scientists estimate, the Paris Agreement goal of limiting global warming to well below 2 °C cannot be achieved, and temperature increases will exceed that limit, at least temporarily. One study estimated that emissions cannot be reduced fast enough to meet the 2 °C goal if equilibrium climate sensitivity (the long-term measure) is higher than {{convert|3.4|C-change}}.{{Cite journal|last1=Tanaka|first1=Katsumasa|last2=O'Neill|first2=Brian C. | name-list-style = vanc |date=2018|title=The Paris Agreement zero-emissions goal is not always consistent with the 1.5 °C and 2 °C temperature targets |journal=Nature Climate Change|language=en|volume=8|issue=4|pages=319–324|doi=10.1038/s41558-018-0097-x|bibcode=2018NatCC...8..319T|s2cid=91163896|issn=1758-6798}} The more sensitive the climate system is to changes in greenhouse gas concentrations, the more likely it is to have decades when temperatures are much higher or much lower than the longer-term average.{{Cite web|url=https://www.independent.co.uk/voices/europe-heatwave-climate-change-europe-global-warming-science-a9018426.html|title=Opinion: Europe is burning just as scientists offer a chilling truth about climate change|last=Dyke|first=James|date=2019-07-24|website=The Independent|language=en|access-date=2019-07-26|name-list-style=vanc|archive-date=25 July 2019|archive-url=https://web.archive.org/web/20190725181005/https://www.independent.co.uk/voices/europe-heatwave-climate-change-europe-global-warming-science-a9018426.html|url-status=live}}{{Cite journal|last1=Nijsse|first1=Femke J. M. M.|last2=Cox|first2=Peter M.|last3=Huntingford|first3=Chris|last4=Williamson|first4=Mark S.|date=2019|title=Decadal global temperature variability increases strongly with climate sensitivity|url=http://nora.nerc.ac.uk/id/eprint/524582/1/N524582PP.pdf|journal=Nature Climate Change|language=en|volume=9|issue=8|pages=598–601|bibcode=2019NatCC...9..598N|doi=10.1038/s41558-019-0527-4|s2cid=198914522|issn=1758-6798|name-list-style=vanc|access-date=8 March 2020|archive-date=6 May 2020|archive-url=https://web.archive.org/web/20200506162654/http://nora.nerc.ac.uk/id/eprint/524582/1/N524582PP.pdf|url-status=live}}

The radiative forcing caused by a doubling of atmospheric {{CO2}} levels (from the pre-industrial 280 ppm) is approximately 3.7 watts per square meter (W/m²). In the absence of feedbacks, the energy imbalance would eventually result in roughly {{convert|1|C-change}} of global warming. That figure is straightforward to calculate by using the Stefan–Boltzmann lawThe calculation is as follows. In equilibrium, the energy of incoming and outgoing radiation have to balance. The outgoing radiation $F$ is given by the Stefan–Boltzmann law: $F\; =\; -\backslash sigma\; T^4$. When incoming radiation increases, the outgoing radiation and therefore temperature must increase as well. The temperature rise $\backslash Delta\; T\_\{2\; \backslash times\; CO\_2\}$ directly caused by the additional radiative forcing, $\backslash Delta\; F\_\{2\; \backslash times\; CO\_2\}$ because of the doubling of {{CO2}} is then given by

:$\backslash Delta\; F\_\{2\; \backslash times\; CO\_2\}\; =\; \backslash frac\{dF\}\{dT\}\; \backslash Delta\; T\_\{2\; \backslash times\; CO\_2\}\; =\; 4\; \backslash sigma\; T^3\; \backslash Delta\; T\_\{2\; \backslash times\; CO\_2\}$.

Given an effective temperature of {{convert|255|K|C F}}, a constant lapse rate, the value of the Stefan–Boltzmann constant $\backslash sigma$ of 5.67 $\backslash times\; 10^\{-8\}$W/m² K⁻⁴ and $\backslash Delta\; F\_\{2\backslash times\; CO\_2\}$around 4 W/m², the equation gives a climate sensitivity of a world without feedback of approximately 1 K.{{Cite journal|last=Roe|first=Gerard|s2cid=66109238| name-list-style = vanc|date=2009|title=Feedbacks, Timescales, and Seeing Red|journal=Annual Review of Earth and Planetary Sciences|volume=37|issue=1|pages=93–115|doi=10.1146/annurev.earth.061008.134734|bibcode=2009AREPS..37...93R}} and is undisputed.{{Cite book |last=Rahmstorf |first=Stefan |author-link=Stefan Rahmstorf |title=Global Warming: Looking Beyond Kyoto |publisher=Brookings Institution Press |year=2008 |editor-last=Zedillo |editor-first=Ernesto |pages=34–53 |chapter=Anthropogenic Climate Change: Revisiting the Facts |access-date=14 August 2008 |chapter-url=http://www.pik-potsdam.de/~stefan/Publications/Book_chapters/Rahmstorf_Zedillo_2008.pdf |archive-url=https://web.archive.org/web/20190714024054/http://www.pik-potsdam.de/~stefan/Publications/Book_chapters/Rahmstorf_Zedillo_2008.pdf |archive-date=14 July 2019 |url-status=live |name-list-style=vanc}}

A further contribution arises from climate feedbacks, both self-reinforcing and balancing.{{cite journal | vauthors = Lenton TM, Rockström J, Gaffney O, Rahmstorf S, Richardson K, Steffen W, Schellnhuber HJ | title = Climate tipping points - too risky to bet against | journal = Nature | volume = 575 | issue = 7784 | pages = 592–595 | date = November 2019 | pmid = 31776487 | doi = 10.1038/d41586-019-03595-0 | bibcode = 2019Natur.575..592L | doi-access = free | hdl = 10871/40141 | hdl-access = free }}{{Cite journal |last1=Armstrong McKay |first1=David I. |last2=Staal |first2=Arie |last3=Abrams |first3=Jesse F. |last4=Winkelmann |first4=Ricarda |last5=Sakschewski |first5=Boris |last6=Loriani |first6=Sina |last7=Fetzer |first7=Ingo |last8=Cornell |first8=Sarah E. |last9=Rockström |first9=Johan |last10=Lenton |first10=Timothy M. |date=2022-09-09 |title=Exceeding 1.5°C global warming could trigger multiple climate tipping points |url=https://www.science.org/doi/10.1126/science.abn7950 |journal=Science |language=en |volume=377 |issue=6611 |pages=eabn7950 |doi=10.1126/science.abn7950 |pmid=36074831 |hdl=10871/131584 |s2cid=252161375 |issn=0036-8075|hdl-access=free }} The uncertainty in climate sensitivity estimates is entirely from the modelling of feedbacks in the climate system, including water vapour feedback, ice–albedo feedback, cloud feedback, and lapse rate feedback. Balancing feedbacks tend to counteract warming by increasing the rate at which energy is radiated to space from a warmer planet. Exacerbating feedbacks increase warming; for example, higher temperatures can cause ice to melt, which reduces the ice area and the amount of sunlight the ice reflects, which in turn results in less heat energy being radiated back into space. Climate sensitivity depends on the balance between those feedbacks.

File:Schematic climate sensitivity.svgDepending on the time scale, there are two main ways to define climate sensitivity: the short-term transient climate response (TCR) and the long-term equilibrium climate sensitivity (ECS), both of which incorporate the warming from exacerbating feedback loops. They are not discrete categories, but they overlap. Sensitivity to atmospheric {{CO2}} increases is measured in the amount of temperature change for doubling in the atmospheric {{CO2}} concentration.{{Cite journal|last1=Gregory|first1=J. M.|last2=Andrews|first2=T.|date=2016|title=Variation in climate sensitivity and feedback parameters during the historical period|journal=Geophysical Research Letters|language=en|volume=43|issue=8|pages=3911–3920|doi=10.1002/2016GL068406|bibcode=2016GeoRL..43.3911G|issn=1944-8007|doi-access=free}}

Although the term "climate sensitivity" is usually used for the sensitivity to radiative forcing caused by rising atmospheric {{CO2}}, it is a general property of the climate system. Other agents can also cause a radiative imbalance. Climate sensitivity is the change in surface air temperature per unit change in radiative forcing, and the climate sensitivity parameterHere, the IPCC definition is used. In some other sources, the climate sensitivity parameter is simply called the climate sensitivity. The inverse of this parameter, is called the climate feedback parameter and is expressed in (W/m²)/°C. is therefore expressed in units of °C/(W/m²). Climate sensitivity is approximately the same whatever the reason for the radiative forcing (such as from greenhouse gases or solar variation).{{cite journal|last1=Modak|first1=Angshuman|last2=Bala|first2=Govindasamy|last3=Cao|first3=Long|last4=Caldeira|first4=Ken|date=2016|title=Why must a solar forcing be larger than a CO2forcing to cause the same global mean surface temperature change?|url=http://eprints.iisc.ac.in/53977/1/Env_Res_Let_11-4_044013_2016.pdf|journal=Environmental Research Letters|volume=11|issue=4|pages=044013|bibcode=2016ERL....11d4013M|doi=10.1088/1748-9326/11/4/044013|name-list-style=vanc|doi-access=free|access-date=22 February 2020|archive-date=13 July 2021|archive-url=https://web.archive.org/web/20210713214537/http://eprints.iisc.ac.in/53977/1/Env_Res_Let_11-4_044013_2016.pdf|url-status=live}} When climate sensitivity is expressed as the temperature change for a level of atmospheric {{CO2}} double the pre-industrial level, its units are degrees Celsius (°C).

{{Further|Transient climate response to cumulative carbon emissions}}

The transient climate response (TCR) is defined as "the change in the global mean surface temperature, averaged over a 20-year period, centered at the time of atmospheric carbon dioxide doubling, in a climate model simulation" in which the atmospheric {{CO2}} concentration increases at 1% per year. That estimate is generated by using shorter-term simulations.{{Cite book|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|vauthors=Randall DA|publisher=Cambridge University Press|year=2007|veditors=Solomon SD|chapter=8.6.2 Interpreting the Range of Climate Sensitivity Estimates Among General Circulation Models, In: Climate Models and Their Evaluation.|display-authors=etal|display-editors=etal|chapter-url=https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-2.html|access-date=1 July 2018|archive-date=30 June 2018|archive-url=https://web.archive.org/web/20180630193742/http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-2.html|url-status=live}} The transient response is lower than the equilibrium climate sensitivity because slower feedbacks, which exacerbate the temperature increase, take more time to respond in full to an increase in the atmospheric {{CO2}} concentration. For instance, the deep ocean takes many centuries to reach a new steady state after a perturbation during which it continues to serve as heatsink, which cools the upper ocean.{{Cite journal|last1=Hansen|first1=James|last2=Sato|first2=Makiko|last3=Kharecha|first3=Pushker|last4=von Schuckmann|first4=Karina|date=2011 | name-list-style = vanc |title=Earth's energy imbalance and implications|journal=Atmospheric Chemistry and Physics|volume=11|issue=24|pages=13421–13449|bibcode=2011ACP....1113421H|doi=10.5194/acp-11-13421-2011|arxiv=1105.1140|s2cid=16937940 |doi-access=free }} The IPCC literature assessment estimates that the TCR likely lies between {{convert|1|C-change}} and {{convert|2.5|C-change}}.{{Harvnb|Collins|Knutti|Arblaster|Dufresne|2013|loc=Executive Summary; p. 1033}}

A related measure is the transient climate response to cumulative carbon emissions (TCRE), which is the globally averaged surface temperature change after 1000 GtC of {{CO2}} has been emitted.{{Cite journal|last1=Millar|first1=Richard J.|last2=Friedlingstein|first2=Pierre|date=2018-05-13|title=The utility of the historical record for assessing the transient climate response to cumulative emissions|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=376|issue=2119|pages=20160449|doi=10.1098/rsta.2016.0449|pmc=5897822|pmid=29610381|bibcode=2018RSPTA.37660449M}} As such, it includes not only temperature feedbacks to forcing but also the carbon cycle and carbon cycle feedbacks.{{cite journal | vauthors = Matthews HD, Gillett NP, Stott PA, Zickfeld K | title = The proportionality of global warming to cumulative carbon emissions | journal = Nature | volume = 459 | issue = 7248 | pages = 829–832 | date = June 2009 | pmid = 19516338 | doi = 10.1038/nature08047 | bibcode = 2009Natur.459..829M | s2cid = 4423773 }}

The equilibrium climate sensitivity (ECS) is the long-term temperature rise (equilibrium global mean near-surface air temperature) that is expected to result from a doubling of the atmospheric {{CO2}} concentration (ΔT_2×). It is a prediction of the new global mean near-surface air temperature once the {{CO2}} concentration has stopped increasing, and most of the feedbacks have had time to have their full effect. Reaching an equilibrium temperature can take centuries or even millennia after {{CO2}} has doubled. ECS is higher than TCR because of the oceans' short-term buffering effects. Computer models are used for estimating the ECS.{{Cite book

|ref= {{harvid|IPCC SR15 Glossary|2018}}

|author= IPCC

|author-link= IPCC

|year= 2018

|chapter= Annex I: Glossary

|chapter-url= https://www.ipcc.ch/site/assets/uploads/sites/2/2019/05/SR15_AnnexI_Glossary.pdf

|title= {{Harvnb|IPCC SR15|2018}}

|access-date= 6 March 2020

|archive-date= 19 August 2019

|archive-url= https://web.archive.org/web/20190819230707/https://www.ipcc.ch/site/assets/uploads/sites/2/2019/05/SR15_AnnexI_Glossary.pdf

|url-status= live

}} A comprehensive estimate means that modelling the whole time span during which significant feedbacks continue to change global temperatures in the model, such as fully-equilibrating ocean temperatures, requires running a computer model that covers thousands of years. There are, however, less computing-intensive methods.{{cite journal | vauthors = Gregory JM, Ingram WJ, Palmer MA, Jones GS, Stott PA, Thorpe RB, Lowe JA, Johns TC, Williams KD |s2cid=73672483|date=2004|title=A new method for diagnosing radiative forcing and climate sensitivity|journal=Geophysical Research Letters|volume=31|issue=3|page=L03205|bibcode=2004GeoRL..31.3205G|doi=10.1029/2003GL018747|doi-access=free}}

The IPCC Sixth Assessment Report (AR6) stated that there is high confidence that ECS is within the range of 2.5 °C to 4 °C, with a best estimate of 3 °C.{{Cite web |url=https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_SPM.pdf |title=Archived copy |access-date=13 August 2021 |archive-date=11 August 2021 |archive-url=https://web.archive.org/web/20210811205522/https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_SPM.pdf |url-status=live }}

The long time scales involved with ECS make it arguably a less relevant measure for policy decisions around climate change.{{Cite journal|last1=Hawkins|first1=Ed|last2=Forster|first2=Piers|date=2019|title=Climate sensitivity: how much warming results from increases in atmospheric carbon dioxide (CO2)?|journal=Weather|language=en|volume=74|issue=4|pages=134|doi=10.1002/wea.3400|bibcode=2019Wthr...74..134H|issn=1477-8696|doi-access=free}}

A common approximation to ECS is the effective equilibrium climate sensitivity, is an estimate of equilibrium climate sensitivity by using data from a climate system in model or real-world observations that is not yet in equilibrium.{{Cite book|title=Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change|vauthors=Planton S|publisher=Cambridge University Press|year=2013|veditors=Stocker TF, Qin D, Plattner GK, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM|chapter=Annex III: Glossary|page=1451|chapter-url=https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_AnnexIII_FINAL.pdf|access-date=30 April 2019|archive-date=16 October 2021|archive-url=https://web.archive.org/web/20211016112637/https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_AnnexIII_FINAL.pdf|url-status=live}} Estimates assume that the net amplification effect of feedbacks, as measured after some period of warming, will remain constant afterwards.{{Cite journal|vauthors=Bitz CM, Shell KM, Gent PR, Bailey DA, Danabasoglu G, Armour KC, Holland MM, Kiehl JT|display-authors=6|date=2011|title=Climate Sensitivity of the Community Climate System Model, Version 4|journal=Journal of Climate|volume=25|issue=9|pages=3053–3070|doi=10.1175/JCLI-D-11-00290.1|citeseerx=10.1.1.716.6228|s2cid=7843257|issn=0894-8755|url=http://www.atmos.washington.edu/~bitz/CCSM4_climsens_preprint.pdf|access-date=22 February 2020|archive-date=8 August 2017|archive-url=https://web.archive.org/web/20170808234817/http://www.atmos.washington.edu/%7Ebitz/CCSM4_climsens_preprint.pdf|url-status=live}} That is not necessarily true, as feedbacks can change with time.{{Cite book|title=Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change| vauthors = Prentice IC |publisher=Cambridge University Press|year=2001|isbn=9780521807678|veditors=Houghton JT|chapter=9.2.1 Climate Forcing and Climate Response, in chapter 9. Projections of Future Climate Change|display-authors=etal|display-editors=etal|chapter-url=https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-09.pdf|url-access=registration|url=https://archive.org/details/climatechange2000000unse}} In many climate models, feedbacks become stronger over time and so the effective climate sensitivity is lower than the real ECS.{{Cite journal|last1=Rugenstein|first1=Maria|last2=Bloch-Johnson|first2=Jonah|last3=Gregory|first3=Jonathan|last4=Andrews|first4=Timothy|last5=Mauritsen|first5=Thorsten|last6=Li|first6=Chao|last7=Frölicher|first7=Thomas L.|last8=Paynter|first8=David|last9=Danabasoglu|first9=Gokhan|last10=Yang|first10=Shuting|last11=Dufresne|first11=Jean-Louis|date=2020|title=Equilibrium Climate Sensitivity Estimated by Equilibrating Climate Models|journal=Geophysical Research Letters|language=en|volume=47|issue=4|pages=e2019GL083898|doi=10.1029/2019GL083898|bibcode=2020GeoRL..4783898R|issn=1944-8007|url=http://centaur.reading.ac.uk/87462/1/rugenstein19ecs_authors.pdf|doi-access=free|access-date=18 September 2020|archive-date=30 August 2020|archive-url=https://web.archive.org/web/20200830000238/http://centaur.reading.ac.uk/87462/1/rugenstein19ecs_authors.pdf|url-status=live}}

By definition, equilibrium climate sensitivity does not include feedbacks that take millennia to emerge, such as long-term changes in Earth's albedo because of changes in ice sheets and vegetation. It includes the slow response of the deep oceans' warming, which also takes millennia, and so ECS fails to reflect the actual future warming that would occur if {{CO2}} is stabilized at double pre-industrial values.{{Cite journal|last1=Knutti|first1=Reto|last2=Rugenstein|first2=Maria A. A.|last3=Knutti|first3=Reto|date=2017|title=Beyond equilibrium climate sensitivity|journal=Nature Geoscience|language=en|volume=10|issue=10|pages=727–736|bibcode=2017NatGe..10..727K|doi=10.1038/ngeo3017|issn=1752-0908|hdl-access=free|name-list-style=vanc|hdl=20.500.11850/197761|s2cid=134579878 |url=https://www.research.ed.ac.uk/en/publications/6a35b333-b70d-4cc1-aa5c-3c68ba070fae }} Earth system sensitivity (ESS) incorporates the effects of these slower feedback loops, such as the change in Earth's albedo from the melting of large continental ice sheets, which covered much of the Northern Hemisphere during the Last Glacial Maximum and still cover Greenland and Antarctica). Changes in albedo as a result of changes in vegetation, as well as changes in ocean circulation, are also included.{{cite journal|display-authors=6|vauthors=Previdi M, Liepert BG, Peteet D, Hansen J, Beerling DJ, Broccoli AJ, Frolking S, Galloway JN, Heimann M, Le Quéré C, Levitus S|date=2013|title=Climate sensitivity in the Anthropocene|journal=Quarterly Journal of the Royal Meteorological Society|volume=139|issue=674|pages=1121–1131|bibcode=2013QJRMS.139.1121P|citeseerx=10.1.1.434.854|doi=10.1002/qj.2165|doi-access=free}}{{Cite journal|last1=Feng|first1=Ran|last2=Bette L.|first2=Otto-Bliesner|author-link2=Bette Otto-Bliesner|last3=Brady|first3=Esther C.|last4=Rosenbloom|first4=Nan A.|date=2020-01-04|title=Increasing Earth System Sensitivity in mid-Pliocene simulations from CCSM4 to CESM2|journal=Ess Open Archive ePrints |volume=105 |language=en|doi=10.1002/essoar.10501546.1|doi-access=free|bibcode=2020esoar.10501546F }} The longer-term feedback loops make the ESS larger than the ECS, possibly twice as large. Data from the geological history of Earth is used in estimating ESS. Differences between modern and long-ago climatic conditions mean that estimates of the future ESS are highly uncertain.{{cite web|url=http://www.realclimate.org/index.php/archives/2008/04/target-co2/|title=Target CO2|date=7 April 2008|work=RealClimate|archive-url=https://web.archive.org/web/20170824042512/http://www.realclimate.org/index.php/archives/2008/04/target-co2/|archive-date=24 August 2017|url-status=live}} Unlike ECS and TCR, the carbon cycle is not included in the definition of the ESS, but all other elements of the climate system are included.{{cite web|url=http://www.realclimate.org/index.php/archives/2013/01/on-sensitivity-part-i/|title=On sensitivity: Part I|date=3 January 2013 |publisher=RealClimate.org|access-date=30 July 2018|archive-date=30 July 2018|archive-url=https://web.archive.org/web/20180730080423/http://www.realclimate.org/index.php/archives/2013/01/on-sensitivity-part-i/|url-status=live}}

Different forcing agents, such as greenhouse gases and aerosols, can be compared using their radiative forcing, the initial radiative imbalance averaged over the entire globe. Climate sensitivity is the amount of warming per radiative forcing. To a first approximation, the cause of the radiative imbalance does not matter whether it is greenhouse gases or something else. However, radiative forcing from sources other than {{CO2}} can cause a somewhat larger or smaller surface warming than a similar radiative forcing from {{CO2}}. The amount of feedback varies mainly because the forcings are not uniformly distributed over the globe. Forcings that initially warm the Northern Hemisphere, land, or polar regions are more strongly systematically effective at changing temperatures than an equivalent forcing from {{CO2}}, which is more uniformly distributed over the globe. That is because those regions have more self-reinforcing feedbacks, such as the ice–albedo feedback. Several studies indicate that human-emitted aerosols are more effective than {{CO2}} at changing global temperatures, and volcanic forcing is less effective.{{Cite journal|last1=Marvel|first1=Kate|last2=Schmidt|first2=Gavin A.|last3=Miller|first3=Ron L.|last4=Nazarenko|first4=Larissa S. | name-list-style = vanc |date=2016|title=Implications for climate sensitivity from the response to individual forcings|journal=Nature Climate Change |language=en |volume=6 |issue=4 |pages=386–389 |doi=10.1038/nclimate2888 |issn=1758-6798|bibcode=2016NatCC...6..386M|hdl=2060/20160012693|hdl-access=free}} When climate sensitivity to {{CO2}} forcing is estimated by using historical temperature and forcing (caused by a mix of aerosols and greenhouse gases), and that effect is not taken into account, climate sensitivity is underestimated.{{Cite journal| first1 = Robert | last1 = Pincus | last2 = Mauritsen | first2 = Thorsten | name-list-style = vanc |date=2017|title=Committed warming inferred from observations|journal=Nature Climate Change|language=en|volume=7|issue=9|pages=652–655|doi=10.1038/nclimate3357|issn=1758-6798|bibcode=2017NatCC...7..652M|hdl=11858/00-001M-0000-002D-CBC9-F|hdl-access=free}}

File:Fictional Snowball Earth 1 Neethis.jpg

Climate sensitivity has been defined as the short- or long-term temperature change resulting from any doubling of {{CO2}}, but there is evidence that the sensitivity of Earth's climate system is not constant. For instance, the planet has polar ice and high-altitude glaciers. Until the world's ice has completely melted, an exacerbating ice–albedo feedback loop makes the system more sensitive overall.{{Cite journal|last1=Pfister|first1=Patrik L.|last2=Stocker|first2=Thomas F.|name-list-style=vanc|date=2017|title=State-Dependence of the Climate Sensitivity in Earth System Models of Intermediate Complexity|journal=Geophysical Research Letters|language=en|volume=44|issue=20|pages=10643–10653|doi=10.1002/2017GL075457|issn=1944-8007|bibcode=2017GeoRL..4410643P|url=https://boris.unibe.ch/112659/1/Pfister_et_al-2017-Geophysical_Research_Letters.pdf|doi-access=free|access-date=22 February 2020|archive-date=22 February 2020|archive-url=https://web.archive.org/web/20200222153313/https://boris.unibe.ch/112659/1/Pfister_et_al-2017-Geophysical_Research_Letters.pdf|url-status=live}} Throughout Earth's history, multiple periods are thought to have snow and ice cover almost the entire globe. In most models of "Snowball Earth", parts of the tropics were at least intermittently free of ice cover. As the ice advanced or retreated, climate sensitivity must have been very high, as the large changes in area of ice cover would have made for a very strong ice–albedo feedback. Volcanic atmospheric composition changes are thought to have provided the radiative forcing needed to escape the snowball state.{{cite journal|vauthors=Hansen J, Sato M, Russell G, Kharecha P|date=October 2013|title=Climate sensitivity, sea level and atmospheric carbon dioxide|journal=Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences|volume=371|issue=2001|page=20120294|doi=10.1098/rsta.2012.0294|pmc=3785813|pmid=24043864|arxiv=1211.4846|bibcode=2013RSPTA.37120294H}}

File:Hansen & Sato, Climate Sensitivity Estimated From Earth's Climate History Figure 7.svgThroughout the Quaternary period (the most recent 2.58 million years), climate has oscillated between glacial periods, the most recent one being the Last Glacial Maximum, and interglacial periods, the most recent one being the current Holocene, but the period's climate sensitivity is difficult to determine. The Paleocene–Eocene Thermal Maximum, about 55.5 million years ago, was unusually warm and may have been characterized by above-average climate sensitivity.{{Cite journal|last1=Hansen|first1=James|last2=Sato|first2=Makiko|last3=Russell|first3=Gary|last4=Kharecha|first4=Pushker|date=2013-10-28|title=Climate sensitivity, sea level and atmospheric carbon dioxide|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=371|issue=2001|pages=20120294|doi=10.1098/rsta.2012.0294|pmc=3785813|pmid=24043864|arxiv=1211.4846|bibcode=2013RSPTA.37120294H}}

Climate sensitivity may further change if tipping points are crossed. It is unlikely that tipping points will cause short-term changes in climate sensitivity. If a tipping point is crossed, climate sensitivity is expected to change at the time scale of the subsystem that hits its tipping point. Especially if there are multiple interacting tipping points, the transition of climate to a new state may be difficult to reverse.{{Cite journal|last1=Lontzek|first1=Thomas S.|last2=Lenton|first2=Timothy M.|last3=Cai|first3=Yongyang | name-list-style = vanc |date=2016|title=Risk of multiple interacting tipping points should encourage rapid CO2 emission reduction|journal=Nature Climate Change|language=en|volume=6|issue=5|pages=520–525|doi=10.1038/nclimate2964|issn=1758-6798|bibcode=2016NatCC...6..520C|hdl=10871/20598|s2cid=38156745 |hdl-access=free}}

The two most common definitions of climate sensitivity specify the climate state: the ECS and the TCR are defined for a doubling with respect to the {{CO2}} levels in the pre-industrial era. Because of potential changes in climate sensitivity, the climate system may warm by a different amount after a second doubling of {{CO2}} from after a first doubling. The effect of any change in climate sensitivity is expected to be small or negligible in the first century after additional {{CO2}} is released into the atmosphere.

Climate sensitivity can be estimated using the observed temperature increase, the observed ocean heat uptake, and the modelled or observed radiative forcing. The data are linked through a simple energy-balance model to calculate climate sensitivity.{{cite journal| vauthors = Skeie RB, Berntsen T, Aldrin M, Holden M, Myhre G |s2cid=55652873|date=2014|title=A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series|journal=Earth System Dynamics|volume=5|issue=1|pages=139–175|bibcode=2014ESD.....5..139S|doi=10.5194/esd-5-139-2014|doi-access=free}} Radiative forcing is often modelled because Earth observation satellites measuring it has existed during only part of the Industrial Age (only since the late 1950s). Estimates of climate sensitivity calculated by using these global energy constraints have consistently been lower than those calculated by using other methods,{{Cite journal|last=Armour|first=Kyle C.| name-list-style = vanc |date=2017|title=Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks|journal=Nature Climate Change|language=en|volume=7|issue=5|pages=331–335|doi=10.1038/nclimate3278|issn=1758-6798|bibcode=2017NatCC...7..331A}} around {{Convert|2|°C-change}} or lower.{{cite journal|vauthors=Forster PM, Gregory JM|author-link=Piers Forster|date=2006|title=The Climate Sensitivity and Its Components Diagnosed from Earth Radiation Budget Data|journal=Journal of Climate|volume=19|issue=1|pages=39–52|bibcode=2006JCli...19...39F|doi=10.1175/JCLI3611.1|url=https://zenodo.org/record/918270|access-date=17 July 2019|archive-date=17 July 2019|archive-url=https://web.archive.org/web/20190717125922/https://zenodo.org/record/918270|url-status=live}}{{cite journal|last1=Lewis|first1=Nicholas|last2=Curry|first2=Judith A. | name-list-style = vanc |date=2014|title=The implications for climate sensitivity of AR5 forcing and heat uptake estimates|journal=Climate Dynamics|volume=45|issue=3–4|pages=1009–1023|bibcode=2015ClDy...45.1009L|doi=10.1007/s00382-014-2342-y|s2cid=55828449}}{{Cite journal |vauthors=Otto A, Otto FE, Boucher O, Church J, Hegerl G, Forster PM, Gillett NP, Gregory J, Johnson GC, Knutti R, Lewis N |display-authors=6 |date=2013 |title=Energy budget constraints on climate response |journal=Nature Geoscience |language=en |volume=6 |issue=6 |pages=415–416 |doi=10.1038/ngeo1836 |issn=1752-0908 |bibcode=2013NatGe...6..415O |url=http://eprints.whiterose.ac.uk/76064/7/ngeo1836%281%29_with_coversheet.pdf |access-date=4 December 2019 |archive-date=26 September 2019 |archive-url=https://web.archive.org/web/20190926002536/http://eprints.whiterose.ac.uk/76064/7/ngeo1836(1)_with_coversheet.pdf |url-status=live }}

Estimates of transient climate response (TCR) that have been calculated from models and observational data can be reconciled if it is taken into account that fewer temperature measurements are taken in the polar regions, which warm more quickly than the Earth as a whole. If only regions for which measurements are available are used in evaluating the model, the differences in TCR estimates are negligible.{{Cite journal |last1=Stolpe |first1=Martin B. |last2=Ed Hawkins |last3=Cowtan |first3=Kevin |last4=Richardson |first4=Mark |name-list-style=vanc |date=2016 |title=Reconciled climate response estimates from climate models and the energy budget of Earth |journal=Nature Climate Change |language=en |volume=6 |issue=10 |pages=931–935 |doi=10.1038/nclimate3066 |issn=1758-6798 |bibcode=2016NatCC...6..931R |s2cid=89143351 |url=http://centaur.reading.ac.uk/65992/1/RichardsonTCR_accepted.pdf |access-date=23 September 2019 |archive-date=28 April 2019 |archive-url=https://web.archive.org/web/20190428015243/http://centaur.reading.ac.uk/65992/1/RichardsonTCR_accepted.pdf |url-status=live }}

A very simple climate model could estimate climate sensitivity from Industrial Age data by waiting for the climate system to reach equilibrium and then by measuring the resulting warming, {{math|ΔT_eq}} (°C). Computation of the equilibrium climate sensitivity, S (°C), using the radiative forcing {{math|ΔF}} (W/m²) and the measured temperature rise, would then be possible. The radiative forcing resulting from a doubling of {{CO2}}, {{math|F_{2$\backslash times$CO2}}}, is relatively well known, at about 3.7 W/m². Combining that information results in this equation:

:$S\; =\; \backslash Delta\; T\_\{eq\}\; \backslash times\; F\_\{2\backslash times\; CO\_2\}\; /\; \backslash Delta\; F$.

However, the climate system is not in equilibrium since the actual warming lags the equilibrium warming, largely because the oceans take up heat and will take centuries or millennia to reach equilibrium. Estimating climate sensitivity from Industrial Age data requires an adjustment to the equation above. The actual forcing felt by the atmosphere is the radiative forcing minus the ocean's heat uptake, {{math|H}} (W/m²) and so climate sensitivity can be estimated:

:$S\; =\; \backslash Delta\; T\; \backslash times\; F\_\{2\backslash times\; CO\_2\}/(\backslash Delta\; F-H).$

The global temperature increase between the beginning of the Industrial Period, which is (taken as 1750, and 2011 was about {{Convert|0.85|°C-change}}. In 2011, the radiative forcing from {{CO2}} and other long-lived greenhouse gases (mainly methane, nitrous oxide, and chlorofluorocarbon) that have been emitted since the 18th century was roughly 2.8 W/m². The climate forcing, {{math|ΔF}}, also contains contributions from solar activity (+0.05 W/m²), aerosols (−0.9 W/m²), ozone (+0.35 W/m²), and other smaller influences, which brings the total forcing over the Industrial Period to 2.2 W/m², according to the best estimate of the IPCC Fifth Assessment Report in 2014, with substantial uncertainty.{{sfn|IPCC AR5 WG1 Technical Summary|2013|p=53-56}} The ocean heat uptake, estimated by the same report to be 0.42 W/m²,{{sfn|IPCC AR5 WG1 Technical Summary|2013|p=39}} yields a value for S of {{Convert|1.8|°C-change||abbr=}}.

In theory, Industrial Age temperatures could also be used to determine a time scale for the temperature response of the climate system and thus climate sensitivity:{{Cite journal|last=Schwartz|first=Stephen E.|author-link=Stephen E. Schwartz| name-list-style = vanc |date=2007|title=Heat capacity, time constant, and sensitivity of Earth's climate system|journal=Journal of Geophysical Research: Atmospheres|volume=112|issue=D24|page=D24S05|bibcode=2007JGRD..11224S05S|citeseerx=10.1.1.482.4066|doi=10.1029/2007JD008746}} if the effective heat capacity of the climate system is known, and the timescale is estimated using autocorrelation of the measured temperature, an estimate of climate sensitivity can be derived. In practice, however, the simultaneous determination of the time scale and heat capacity is difficult.{{cite journal| vauthors = Knutti R, Kraehenmann S, Frame DJ, Allen MR |year=2008|title=Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz|journal=Journal of Geophysical Research: Atmospheres |volume=113 |issue=D15 |page=D15103 |doi=10.1029/2007JD009473 |bibcode=2008JGRD..11315103K |doi-access=free }}{{cite journal| vauthors = Foster G, Annan JD, Schmidt GA, Mann ME |s2cid=17960844|year=2008|title=Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz|journal=Journal of Geophysical Research: Atmospheres |volume=113 |issue=D15 |page=D15102 |doi=10.1029/2007JD009373 |bibcode=2008JGRD..11315102F |doi-access=free }}{{cite journal| vauthors = Scafetta N |year=2008|title=Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz.|journal=Journal of Geophysical Research: Atmospheres |volume=113|issue=D15|page=D15104|doi=10.1029/2007JD009586|bibcode=2008JGRD..11315104S|doi-access=free}}

Attempts have been made to use the 11-year solar cycle to constrain the transient climate response.{{cite journal |vauthors=Tung KK, Zhou J, Camp CD |date=2008 |title=Constraining model transient climate response using independent observations of solar-cycle forcing and response |url=https://www.calpoly.edu/~camp/Publications/Tung_etal_GRL_2008.pdf |journal=Geophysical Research Letters |volume=35 |issue=17 |pages=L17707 |bibcode=2008GeoRL..3517707T |doi=10.1029/2008GL034240 |s2cid=14656629 |access-date=1 July 2018 |archive-date=1 February 2017 |archive-url=https://web.archive.org/web/20170201232022/http://www.calpoly.edu/~camp/Publications/Tung_etal_GRL_2008.pdf |url-status=live }} Solar irradiance is about 0.9 W/m² higher during a solar maximum than during a solar minimum, and those effect can be observed in measured average global temperatures from 1959 to 2004.{{cite journal| vauthors = Camp CD, Tung KK |date=2007|title=Surface warming by the solar cycle as revealed by the composite mean difference projection |journal=Geophysical Research Letters|volume=34|issue=14|page=L14703|bibcode=2007GeoRL..3414703C|doi=10.1029/2007GL030207|doi-access=free}} Unfortunately, the solar minima in the period coincided with volcanic eruptions, which have a cooling effect on the global temperature. Because the eruptions caused a larger and less well-quantified decrease in radiative forcing than the reduced solar irradiance, it is questionable whether useful quantitative conclusions can be derived from the observed temperature variations.{{Cite journal|last=Rypdal|first=K. | name-list-style = vanc|date=2012|title=Global temperature response to radiative forcing: Solar cycle versus volcanic eruptions|journal=Journal of Geophysical Research: Atmospheres|language=en|volume=117|issue=D6|pages=|doi=10.1029/2011JD017283|issn=2156-2202|bibcode=2012JGRD..117.6115R|doi-access=free}}

Observations of volcanic eruptions have also been used to try to estimate climate sensitivity, but as the aerosols from a single eruption last at most a couple of years in the atmosphere, the climate system can never come close to equilibrium, and there is less cooling than there would be if the aerosols stayed in the atmosphere for longer. Therefore, volcanic eruptions give information only about a lower bound on transient climate sensitivity.{{cite journal| vauthors = Merlis TM, Held IM, Stenchikov GL, Zeng F, Horowitz LW |date=2014|title=Constraining Transient Climate Sensitivity Using Coupled Climate Model Simulations of Volcanic Eruptions |journal=Journal of Climate |volume=27 |issue=20 |pages=7781–7795 |doi=10.1175/JCLI-D-14-00214.1 |issn=0894-8755 |bibcode=2014JCli...27.7781M |hdl=10754/347010|hdl-access=free }}

Historical climate sensitivity can be estimated by using reconstructions of Earth's past temperatures and {{CO2}} levels. Paleoclimatologists have studied different geological periods, such as the warm Pliocene (5.3 to 2.6 million years ago) and the colder Pleistocene (2.6 million to 11,700 years ago),{{Cite web|url=https://www.carbonbrief.org/what-a-three-million-year-fossil-record-tells-us-about-climate-sensitivity|title=What a three-million year fossil record tells us about climate sensitivity|last=McSweeney|first=Robert|name-list-style=vanc|date=2015-02-04|website=Carbon Brief|language=en|access-date=2019-03-20|archive-date=31 March 2019|archive-url=https://web.archive.org/web/20190331131232/https://www.carbonbrief.org/what-a-three-million-year-fossil-record-tells-us-about-climate-sensitivity|url-status=live}} and sought periods that are in some way analogous to or informative about current climate change. Climates further back in Earth's history are more difficult to study because fewer data are available about them. For instance, past {{CO2}} concentrations can be derived from air trapped in ice cores, but {{As of|2020||df=|lc=y}}, the oldest continuous ice core is less than one million years old.{{Cite news|last=Amos|first=Jonathan|url=https://www.bbc.com/news/science-environment-47848344|title=European team to drill for 'oldest ice'|date=2019-04-09|work=BBC News|access-date=2020-03-04|language=en-GB|archive-date=31 March 2020|archive-url=https://web.archive.org/web/20200331145213/https://www.bbc.com/news/science-environment-47848344|url-status=live}} Recent periods, such as the Last Glacial Maximum (LGM) (about 21,000 years ago) and the Mid-Holocene (about 6,000 years ago), are often studied, especially when more information about them becomes available.{{Cite journal |last1=Hargreaves |first1=Julia C. |last2=Annan |first2=James D. |name-list-style=vanc |date=2009 |title=On the importance of paleoclimate modelling for improving predictions of future climate change |url=https://www.clim-past.net/5/803/2009/cp-5-803-2009.pdf |journal=Climate of the Past |volume=5 |issue=4 |pages=803–814 |doi=10.5194/cp-5-803-2009 |bibcode=2009CliPa...5..803H |doi-access=free |access-date=31 March 2019 |archive-date=2 December 2017 |archive-url=https://web.archive.org/web/20171202220504/https://www.clim-past.net/5/803/2009/cp-5-803-2009.pdf |url-status=live }}{{cite journal| vauthors = Hargreaves JC, Annan JD, Yoshimori M, Abe-Ouchi A |s2cid=15222363 |date=2012 |title=Can the Last Glacial Maximum constrain climate sensitivity? |journal=Geophysical Research Letters |language=en |volume=39 |issue=24 |page=L24702 |doi= 10.1029/2012GL053872 |issn=1944-8007 |bibcode=2012GeoRL..3924702H |doi-access=free}}

A 2007 estimate of sensitivity made using data from the most recent 420 million years is consistent with sensitivities of current climate models and with other determinations.{{cite journal | vauthors = Royer DL, Berner RA, Park J | title = Climate sensitivity constrained by CO2 concentrations over the past 420 million years | journal = Nature | volume = 446 | issue = 7135 | pages = 530–532 | date = March 2007 | pmid = 17392784 | doi = 10.1038/nature05699 | bibcode = 2007Natur.446..530R | s2cid = 4323367 | author-link2 = Robert Berner | author-link = Dana Royer }} The Paleocene–Eocene Thermal Maximum (about 55.5 million years ago), a 20,000-year period during which massive amount of carbon entered the atmosphere and average global temperatures increased by approximately {{Convert|6|°C-change}}, also provides a good opportunity to study the climate system when it was in a warm state.{{cite journal | vauthors = Kiehl JT, Shields CA | title = Sensitivity of the Palaeocene-Eocene Thermal Maximum climate to cloud properties | journal = Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences | volume = 371 | issue = 2001 | page = 20130093 | date = October 2013 | pmid = 24043867 | doi = 10.1098/rsta.2013.0093 | bibcode = 2013RSPTA.37130093K | doi-access = free}} Studies of the last 800,000 years have concluded that climate sensitivity was greater in glacial periods than in interglacial periods.{{cite journal| vauthors = von der Heydt AS, Köhler P, van de Wal RS, Dijkstra HA |date=2014|title=On the state dependency of fast feedback processes in (paleo) climate sensitivity|journal=Geophysical Research Letters |language=en |volume=41 |issue=18 |pages=6484–6492 |doi=10.1002/2014GL061121 |issn=1944-8007 |arxiv=1403.5391|s2cid=53703955}}

As the name suggests, the Last Glacial Maximum was much colder than today, and good data on atmospheric {{CO2}} concentrations and radiative forcing from that period are available.{{Harvnb |Masson-Delmotte |Schulz |Abe-Ouchi |Beer |2013}} The period's orbital forcing was different from today's but had little effect on mean annual temperatures.{{Cite journal |last1=Hopcroft |first1=Peter O. |last2=Valdes |first2=Paul J. |name-list-style=vanc |date=2015 |title=How well do simulated last glacial maximum tropical temperatures constrain equilibrium climate sensitivity?: CMIP5 LGM TROPICS AND CLIMATE SENSITIVITY |journal=Geophysical Research Letters |language=en |volume=42 |issue=13 |pages=5533–5539 |doi=10.1002/2015GL064903 |url=https://research-information.bris.ac.uk/files/51793503/Hopcroft_et_al_2015_Geophysical_Research_Letters.pdf |doi-access=free |access-date=22 February 2020 |archive-date=22 February 2020 |archive-url=https://web.archive.org/web/20200222153315/https://research-information.bris.ac.uk/files/51793503/Hopcroft_et_al_2015_Geophysical_Research_Letters.pdf |url-status=live }} Estimating climate sensitivity from the Last Glacial Maximum can be done by several different ways. One way is to use estimates of global radiative forcing and temperature directly. The set of feedback mechanisms active during the period, however, may be different from the feedbacks caused by a present doubling of {{CO2}},{{Cite journal |last1=Cooper |first1=Vincent T. |date=17 April 2024 |title=Last Glacial Maximum pattern effects reduce climate sensitivity estimates |journal=Science Advances |language=en |volume=10 |issue=16 |doi=10.1126/sciadv.adk9461 |doi-access=free |pmc=11023557 }} which introduces additional uncertainty.{{Cite journal |last1=Ganopolski |first1=Andrey |last2=von Deimling |first2=Thomas Schneider | name-list-style = vanc |date=2008 |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=Geophysical Research Letters |volume=35 |issue=23 |page=L23703 |bibcode=2008GeoRL..3523703G |doi=10.1029/2008GL033888|doi-access=free }} In a different approach, a model of intermediate complexity is used to simulate conditions during the period. Several versions of this single model are run, with different values chosen for uncertain parameters, such that each version has a different ECS. Outcomes that best simulate the LGM's observed cooling probably produce the most realistic ECS values.{{cite journal | vauthors = Schmittner A, Urban NM, Shakun JD, Mahowald NM, Clark PU, Bartlein PJ, Mix AC, Rosell-Melé A | display-authors = 6 | title = Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum | journal = Science | volume = 334 | issue = 6061 | pages = 1385–1388 | date = December 2011 | pmid = 22116027 | doi = 10.1126/science.1203513 | bibcode = 2011Sci...334.1385S | citeseerx = 10.1.1.419.8341 | s2cid = 18735283}}

File:Frequency distribution of climate sensitivity, based on model simulations (NASA).png of equilibrium climate sensitivity based on simulations of the doubling of {{chem2|CO2}}.Edited quote from public-domain source: {{cite web|last=Lindsey|first=Rebecca|name-list-style=vanc|title=What if global warming isn't as severe as predicted? : Climate Q&A : Blogs|date=3 August 2010|url=https://earthobservatory.nasa.gov/blogs/climateqa/what-if-global-warming-isnt-as-severe-as-predicted/|publisher=NASA Earth Observatory, part of the EOS Project Science Office, at NASA Goddard Space Flight Center|access-date=1 July 2018|archive-date=27 May 2019|archive-url=https://web.archive.org/web/20190527192026/https://earthobservatory.nasa.gov/blogs/climateqa/what-if-global-warming-isnt-as-severe-as-predicted/|url-status=live}} Each model simulation has different estimates for processes which scientists do not sufficiently understand. Few of the simulations result in less than {{Convert|2|°C-change||abbr=}} of warming or significantly more than {{Convert|4|°C-change||abbr=}}. However, the positive skew, which is also found in other studies,{{cite journal | vauthors = Roe GH, Baker MB | s2cid = 7325301 | title = Why is climate sensitivity so unpredictable? | journal = Science | volume = 318 | issue = 5850 | pages = 629–632 | date = October 2007 | pmid = 17962560 | doi = 10.1126/science.1144735 | bibcode = 2007Sci...318..629R }} suggests that if carbon dioxide concentrations double, the probability of large or very large increases in temperature is greater than the probability of small increases.]]

Climate models simulate the {{CO2}}-driven warming of the future as well as the past. They operate on principles similar to those underlying models that predict the weather, but they focus on longer-term processes. Climate models typically begin with a starting state and then apply physical laws and knowledge about biology to generate subsequent states. As with weather modelling, no computer has the power to model the complexity of the entire planet and so simplifications are used to reduce that complexity to something manageable. An important simplification divides Earth's atmosphere into model cells. For instance, the atmosphere might be divided into cubes of air ten or one hundred kilometers on a side. Each model cell is treated as if it were homogeneous. Calculations for model cells are much faster than trying to simulate each molecule of air separately.{{Cite web|url=https://www.carbonbrief.org/qa-how-do-climate-models-work|title=Q&A: How do climate models work?|last1=McSweeney|first1=Robert|last2=Hausfather|first2=Zeke|date=2018-01-15|website=Carbon Brief|language=en|access-date=2020-03-07|archive-date=5 March 2019|archive-url=https://web.archive.org/web/20190305004530/https://www.carbonbrief.org/qa-how-do-climate-models-work|url-status=live}}

A lower model resolution (large model cells and long time steps) takes less computing power but cannot simulate the atmosphere in as much detail. A model cannot simulate processes smaller than the model cells or shorter-term than a single time step. The effects of the smaller-scale and shorter-term processes must therefore be estimated by using other methods. Physical laws contained in the models may also be simplified to speed up calculations. The biosphere must be included in climate models. The effects of the biosphere are estimated by using data on the average behaviour of the average plant assemblage of an area under the modelled conditions. Climate sensitivity is therefore an emergent property of these models. It is not prescribed, but it follows from the interaction of all the modelled processes.

To estimate climate sensitivity, a model is run by using a variety of radiative forcings (doubling quickly, doubling gradually, or following historical emissions) and the temperature results are compared to the forcing applied. Different models give different estimates of climate sensitivity, but they tend to fall within a similar range, as described above.

Modelling of the climate system can lead to a wide range of outcomes. Models are often run that use different plausible parameters in their approximation of physical laws and the behaviour of the biosphere, which forms a perturbed physics ensemble, which attempts to model the sensitivity of the climate to different types and amounts of change in each parameter. Alternatively, structurally-different models developed at different institutions are put together, creating an ensemble. By selecting only the simulations that can simulate some part of the historical climate well, a constrained estimate of climate sensitivity can be made. One strategy for obtaining more accurate results is placing more emphasis on climate models that perform well in general.{{Cite journal|last1=Sanderson|first1=Benjamin M.|last2=Knutti|first2=Reto|last3=Caldwell|first3=Peter|s2cid=51583558|date=2015|title=Addressing Interdependency in a Multimodel Ensemble by Interpolation of Model Properties|journal=Journal of Climate|volume=28|issue=13|pages=5150–5170|bibcode=2015JCli...28.5150S|doi=10.1175/JCLI-D-14-00361.1|osti=1840116 |issn=0894-8755|name-list-style=vanc}}

A model is tested using observations, paleoclimate data, or both to see if it replicates them accurately. If it does not, inaccuracies in the physical model and parametrizations are sought, and the model is modified. For models used to estimate climate sensitivity, specific test metrics that are directly and physically linked to climate sensitivity are sought. Examples of such metrics are the global patterns of warming,{{cite journal | vauthors = Forest CE, Stone PH, Sokolov AP, Allen MR, Webster MD | title = Quantifying uncertainties in climate system properties with the use of recent climate observations | journal = Science | volume = 295 | issue = 5552 | pages = 113–117 | date = January 2002 | pmid = 11778044 | doi = 10.1126/science.1064419 | url = https://dspace.mit.edu/bitstream/1721.1/3567/1/MITJPSPGC_Rpt78.pdf | bibcode = 2002Sci...295..113F | citeseerx = 10.1.1.297.1145 | s2cid = 5322736 | access-date = 4 February 2006 | archive-date = 4 June 2007 | archive-url = https://web.archive.org/web/20070604184427/http://dspace.mit.edu/bitstream/1721.1/3567/1/MITJPSPGC_Rpt78.pdf | url-status = live }} the ability of a model to reproduce observed relative humidity in the tropics and subtropics,{{cite journal | vauthors = Fasullo JT, Trenberth KE |title=A Less Cloudy Future: The Role of Subtropical Subsidence in Climate Sensitivity |date= 2012 |journal=Science |volume=338|issue=6108 |pages=792–794 |bibcode=2012Sci...338..792F |doi=10.1126/science.1227465 |pmid=23139331|s2cid=2710565 }} Referred to by: {{cite web |author=ScienceDaily |title=Future warming likely to be on high side of climate projections, analysis finds |date=8 November 2012 |url=https://www.sciencedaily.com/releases/2012/11/121108142746.htm |website=ScienceDaily |access-date=9 March 2018 |archive-date=1 July 2018 |archive-url=https://web.archive.org/web/20180701164952/https://www.sciencedaily.com/releases/2012/11/121108142746.htm |url-status=live }} patterns of heat radiation,{{cite journal | vauthors = Brown PT, Caldeira K | title = Greater future global warming inferred from Earth's recent energy budget | journal = Nature | volume = 552 | issue = 7683 | pages = 45–50 | date = December 2017 | pmid = 29219964 | doi = 10.1038/nature24672 | bibcode = 2017Natur.552...45B | s2cid = 602036 }} and the variability of temperature around long-term historical warming.{{cite journal | vauthors = Cox PM, Huntingford C, Williamson MS | title = Emergent constraint on equilibrium climate sensitivity from global temperature variability | journal = Nature | volume = 553 | issue = 7688 | pages = 319–322 | date = January 2018 | pmid = 29345639 | doi = 10.1038/nature25450 | url = http://nora.nerc.ac.uk/id/eprint/519612/1/N519612PP.pdf | bibcode = 2018Natur.553..319C | hdl = 10871/34396 | s2cid = 205263680 | access-date = 17 July 2019 | archive-date = 29 August 2019 | archive-url = https://web.archive.org/web/20190829015124/http://nora.nerc.ac.uk/id/eprint/519612/1/N519612PP.pdf | url-status = live }}{{cite journal | vauthors = Brown PT, Stolpe MB, Caldeira K | title = Assumptions for emergent constraints | journal = Nature | volume = 563 | issue = 7729 | pages = E1–E3 | date = November 2018 | pmid = 30382203 | doi = 10.1038/s41586-018-0638-5 | bibcode = 2018Natur.563E...1B | s2cid = 53190363}}{{cite journal | vauthors = Cox PM, Williamson MS, Nijsse FJ, Huntingford C | title = Cox et al. reply | journal = Nature | volume = 563 | issue = 7729 | pages = E10–E15 | date = November 2018 | pmid = 30382204 | doi = 10.1038/s41586-018-0641-x | bibcode = 2018Natur.563E..10C | s2cid = 53145737 }} Ensemble climate models developed at different institutions tend to produce constrained estimates of ECS that are slightly higher than {{Convert|3|°C-change}}. The models with ECS slightly above {{Convert|3|°C-change}} simulate the above situations better than models with a lower climate sensitivity.{{cite journal| vauthors = Caldwell PM, Zelinka MD, Klein SA |date=2018|title=Evaluating Emergent Constraints on Equilibrium Climate Sensitivity |journal=Journal of Climate |volume=31 |issue=10 |pages=3921–3942 |doi=10.1175/JCLI-D-17-0631.1 |issn=0894-8755|bibcode=2018JCli...31.3921C|osti=1438763|doi-access=free }}

Many projects and groups exist to compare and to analyse the results of multiple models. For instance, the Coupled Model Intercomparison Project (CMIP) has been running since the 1990s.{{Cite web|url=https://pcmdi.llnl.gov/mips/cmip5/history.html|title=CMIP - History|website=pcmdi.llnl.gov|publisher=Program for Climate Model Diagnosis & Intercomparison|access-date=2020-03-06|archive-date=28 July 2020|archive-url=https://web.archive.org/web/20200728161046/https://pcmdi.llnl.gov/mips/cmip5/history.html|url-status=live}}

Svante Arrhenius in the 19th century was the first person to quantify global warming as a consequence of a doubling of the concentration of {{Co2}}. In his first paper on the matter, he estimated that global temperature would rise by around {{Convert|5|to|6|°C-change|°F-change}} if the quantity of {{Co2}} was doubled. In later work, he revised that estimate to {{Convert|4|°C-change|°F-change}}.{{Cite journal |last=Lapenis |first=Andrei G. |name-list-style=vanc |date=1998 |title=Arrhenius and the Intergovernmental Panel on Climate Change |journal=Eos, Transactions American Geophysical Union |language=en |volume=79 |issue=23 |page=271 |bibcode=1998EOSTr..79..271L |doi=10.1029/98EO00206 |issn=2324-9250}} Arrhenius used Samuel Pierpont Langley's observations of radiation emitted by the full moon to estimate the amount of radiation that was absorbed by water vapour and by {{Co2}}. To account for water vapour feedback, he assumed that relative humidity would stay the same under global warming.{{Cite news |last=Sample |first=Ian |name-list-style=vanc |date=2005-06-30 |title=The father of climate change |url=https://www.theguardian.com/environment/2005/jun/30/climatechange.climatechangeenvironment2 |access-date=2019-03-18 |work=The Guardian |language=en-GB |issn=0261-3077}}{{cite journal |vauthors=Anderson TR, Hawkins E, Jones PD |date=September 2016 |title=2, the greenhouse effect and global warming: from the pioneering work of Arrhenius and Callendar to today's Earth System Models |url=http://centaur.reading.ac.uk/66238/1/anderson_etal_2016_Callendar.pdf |url-status=live |journal=Endeavour |volume=40 |issue=3 |pages=178–187 |doi=10.1016/j.endeavour.2016.07.002 |pmid=27469427 |archive-url=https://web.archive.org/web/20190819082714/http://centaur.reading.ac.uk/66238/1/anderson_etal_2016_Callendar.pdf |archive-date=19 August 2019 |access-date=22 February 2020 |doi-access=free}}

The first calculation of climate sensitivity that used detailed measurements of absorption spectra, as well as the first calculation to use a computer for numerical integration of the radiative transfer through the atmosphere, was performed by Syukuro Manabe and Richard Wetherald in 1967.{{cite journal |vauthors=Manabe S, Wetherald RT |date=May 1967 |title=Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity |journal=Journal of the Atmospheric Sciences |volume=24 |issue=3 |pages=241–259 |bibcode=1967JAtS...24..241M |doi=10.1175/1520-0469(1967)024<0241:teotaw>2.0.co;2 |s2cid=124082372 |doi-access=free}} Assuming constant humidity, they computed an equilibrium climate sensitivity of 2.3 °C per doubling of {{CO2}}, which they rounded to 2 °C, the value most often quoted from their work, in the abstract of the paper. The work has been called "arguably the greatest climate-science paper of all time"{{cite journal |vauthors=Forster P |date=May 2017 |title=In Retrospect: Half a century of robust climate models |url=https://aos.princeton.edu/sites/aos/files/manabewetherald_retro-1.pdf |url-status=live |journal=Nature |volume=545 |issue=7654 |pages=296–297 |bibcode=2017Natur.545..296F |doi=10.1038/545296a |pmid=28516918 |s2cid=205094044 |archive-url=https://web.archive.org/web/20191019033610/https://aos.princeton.edu/sites/aos/files/manabewetherald_retro-1.pdf |archive-date=19 October 2019 |access-date=2019-10-19 |doi-access=free}} and "the most influential study of climate of all time."{{cite web |last=Pidcock |first=Roz |name-list-style=vanc |date=July 6, 2015 |title=The most influential climate change papers of all time |url=https://www.carbonbrief.org/the-most-influential-climate-change-papers-of-all-time |url-status=live |archive-url=https://web.archive.org/web/20191019033559/https://www.carbonbrief.org/the-most-influential-climate-change-papers-of-all-time |archive-date=19 October 2019 |access-date=2019-10-19 |work=CarbonBrief}}

A committee on anthropogenic global warming, convened in 1979 by the United States National Academy of Sciences and chaired by Jule Charney,{{cite book |author=Ad Hoc Study Group on Carbon Dioxide and Climate |url=http://www.atmos.ucla.edu/~brianpm/download/charney_report.pdf |title=Carbon Dioxide and Climate: A Scientific Assessment |publisher=National Academy of Sciences |year=1979 |isbn=978-0-309-11910-8 |doi=10.17226/12181 |archive-url=https://web.archive.org/web/20110813231807/http://www.atmos.ucla.edu/~brianpm/download/charney_report.pdf |archive-date=13 August 2011 |url-status=dead}} estimated equilibrium climate sensitivity to be {{Convert|3|°C-change|°F-change}}, plus or minus {{Convert|1.5|°C-change|°F-change}}. The Manabe and Wetherald estimate ({{Convert|2|°C-change|°F-change}}), James E. Hansen's estimate of {{Convert|4|°C-change|°F-change}}, and Charney's model were the only models available in 1979. According to Manabe, speaking in 2004, "Charney chose 0.5 °C as a reasonable margin of error, subtracted it from Manabe's number, and added it to Hansen's, giving rise to the {{Convert|1.5|to|4.5|°C-change|°F-change}} range of likely climate sensitivity that has appeared in every greenhouse assessment since ...."{{cite journal |vauthors=Kerr RA |date=August 2004 |title=Climate change. Three degrees of consensus |journal=Science |volume=305 |issue=5686 |pages=932–934 |doi=10.1126/science.305.5686.932 |pmid=15310873 |s2cid=129548731}} In 2008, climatologist Stefan Rahmstorf said: "At that time [it was published], the [Charney report estimate's] range [of uncertainty] was on very shaky ground. Since then, many vastly improved models have been developed by a number of climate research centers around the world."

File:ECS assessments IPCC.svg

Despite considerable progress in the understanding of Earth's climate system, assessments continued to report similar uncertainty ranges for climate sensitivity for some time after the 1979 Charney report.{{cite journal | vauthors = Forster PM |date=2016|title=Inference of Climate Sensitivity from Analysis of Earth's Energy Budget|journal=Annual Review of Earth and Planetary Sciences|volume=44|issue=1|pages=85–106|doi=10.1146/annurev-earth-060614-105156|bibcode=2016AREPS..44...85F|doi-access=free}} The First Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), published in 1990, estimated that equilibrium climate sensitivity to a doubling of {{CO2}} lay between {{Convert|1.5|and|4.5|°C-change}}, with a "best guess in the light of current knowledge" of {{Convert|2.5|°C-change}}.Climate Change: The IPCC Scientific Assessment (1990), Report prepared for Intergovernmental Panel on Climate Change by Working Group I, Houghton JT, Jenkins GJ, Ephraums JJ (eds.), [https://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] {{Webarchive|url=https://web.archive.org/web/20180413062807/http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_05.pdf |date=2018-04-13 }}, pp. 138–139 The report used models with simplified representations of ocean dynamics. The IPCC supplementary report, 1992, which used full-ocean circulation models, saw "no compelling reason to warrant changing" the 1990 estimate;IPCC '92 p. 118 section B3.5 and the IPCC Second Assessment Report stated, "No strong reasons have emerged to change [these estimates],"IPCC SAR p. 34, technical summary section D.2 In the reports, much of the uncertainty around climate sensitivity was attributed to insufficient knowledge of cloud processes. The 2001 IPCC Third Assessment Report also retained this likely range.{{Cite book|title=Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change| vauthors = Albritton DL |publisher=Cambridge University Press|year=2001|veditors=Houghton JT|chapter=Technical Summary: F.3 Projections of Future Changes in Temperature|display-authors=etal|display-editors=etal|chapter-url=http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/031.htm|archive-url=https://web.archive.org/web/20120112213930/http://www.grida.no/publications/other/ipcc_tar/?src=%2Fclimate%2Fipcc_tar%2Fwg1%2F031.htm|archive-date=12 January 2012|url-status=dead}}

Authors of the 2007 IPCC Fourth Assessment Report{{cite book|vauthors=Meehl GA|title=IPCC Fourth Assessment Report WG1 2007|chapter-url=https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-5.html#box-10-2|chapter=Ch. 10: Global Climate Projections; Box 10.2: Equilibrium Climate Sensitivity|display-authors=etal|access-date=1 July 2018|archive-date=9 June 2018|archive-url=https://web.archive.org/web/20180609121732/http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-5.html#box-10-2|url-status=live}} stated that confidence in estimates of equilibrium climate sensitivity had increased substantially since the Third Annual Report.{{Include-USGov |agency=US Environmental Protection Agency|date=7 December 2009| chapter=Ch. 6: Projected Future Greenhouse Gas Concentrations and Climate Change: Box 6.3: Climate sensitivity| title=Technical Support Document for Endangerment and Cause or Contribute Findings for Greenhouse Gases under Section 202(a) of the Clean Air Act| chapter-url=http://www.epa.gov/climatechange/Downloads/endangerment/Endangerment_TSD.pdf| publisher=Climate Change Division, Office of Atmospheric Programs, US EPA| location=Washington, DC, USA| access-date=15 December 2012| archive-date=1 December 2012| archive-url=https://web.archive.org/web/20121201041155/http://www.epa.gov/climatechange/Downloads/endangerment/Endangerment_TSD.pdf| url-status=live|comment=p.66 (p. 78 of PDF file)}} The IPCC authors concluded that ECS is very likely to be greater than {{convert|1.5|C-change}} and likely to lie in the range {{convert|2|to|4.5|C-change}}, with a most likely value of about {{convert|3|C-change}}. The IPCC stated that fundamental physical reasons and data limitations prevent a climate sensitivity higher than {{convert|4.5|C-change}} from being ruled out, but the climate sensitivity estimates in the likely range agreed better with observations and the proxy climate data.

The 2013 IPCC Fifth Assessment Report reverted to the earlier range of {{Convert|1.5|to|4.5|°C-change}} (with high confidence), because some estimates using industrial-age data came out low.{{Cite web|url=https://www.carbonbrief.org/explainer-how-scientists-estimate-climate-sensitivity|title=Explainer: How scientists estimate climate sensitivity|last=Hausfather|first=Zeke|name-list-style=vanc|date=2018-06-19|website=Carbon Brief|language=en|access-date=2019-03-14|archive-date=1 April 2020|archive-url=https://web.archive.org/web/20200401044606/https://www.carbonbrief.org/explainer-how-scientists-estimate-climate-sensitivity|url-status=live}} The report also stated that ECS is extremely unlikely to be less than {{Convert|1|°C-change}} (high confidence), and it is very unlikely to be greater than {{Convert|6|°C-change}} (medium confidence). Those values were estimated by combining the available data with expert judgement.

In preparation for the 2021 IPCC Sixth Assessment Report, a new generation of climate models was developed by scientific groups around the world.{{Cite journal|last=|date=2019-09-25|title=The CMIP6 landscape (Editorial)|journal=Nature Climate Change|language=en|volume=9|issue=10|page=727|doi=10.1038/s41558-019-0599-1|issn=1758-6798|bibcode=2019NatCC...9..727.|doi-access=free}}{{Cite web|url=https://www.france24.com/en/20200114-new-climate-models-suggest-paris-goals-may-be-out-of-reach|title=New climate models suggest Paris goals may be out of reach|date=2020-01-14|website=France 24|language=en|access-date=2020-01-18|archive-date=14 January 2020|archive-url=https://web.archive.org/web/20200114083228/https://www.france24.com/en/20200114-new-climate-models-suggest-paris-goals-may-be-out-of-reach|url-status=live}} Across 27 global climate models, estimates of a higher climate sensitivity were produced. The values spanned {{Convert|1.8|to|5.6|°C-change}} and exceeded {{Convert|4.5|°C-change}} in 10 of them.{{Cite journal| vauthors = Zelinka MD, Myers TA, McCoy DT, Po-Chedley S, Caldwell PM, Ceppi P, Klein SA, Taylor KE |date=2020|title=Causes of Higher Climate Sensitivity in CMIP6 Models|journal=Geophysical Research Letters|language=en|volume=47|issue=1|page=e2019GL085782|doi=10.1029/2019GL085782|bibcode=2020GeoRL..4785782Z|issn=1944-8007|doi-access=free|hdl=10044/1/76038|hdl-access=free}}{{Cite web|date=2020-07-23|title=International analysis narrows range of climate's sensitivity to CO2|url=https://newsroom.unsw.edu.au/news/science-tech/international-analysis-narrows-range-climate%E2%80%99s-sensitivity-co2|access-date=2020-07-23|website=UNSW Newsroom|archive-date=23 July 2020|archive-url=https://web.archive.org/web/20200723221955/https://newsroom.unsw.edu.au/news/science-tech/international-analysis-narrows-range-climate%E2%80%99s-sensitivity-co2|url-status=live}} The estimates for equilibrium climate sensitivity changed from 3.2 °C to 3.7 °C and the estimates for the transient climate response from 1.8 °C, to 2.0 °C.{{cite journal |title=Increased warming in latest generation of climate models likely caused by clouds: New representations of clouds are making models more sensitive to carbon dioxide. |journal=Science Daily |date=24 June 2020 |url=https://www.sciencedaily.com/releases/2020/06/200624151600.htm |access-date=26 June 2020 |archive-date=26 June 2020 |archive-url=https://web.archive.org/web/20200626005318/https://www.sciencedaily.com/releases/2020/06/200624151600.htm |url-status=live }} The cause of the increased ECS lies mainly in improved modelling of clouds. Temperature rises are now believed to cause sharper decreases in the number of low clouds, and fewer low clouds means more sunlight is absorbed by the planet and less reflected to space.{{Cite journal|last=Palmer|first=Tim|date=2020-05-26|title=Short-term tests validate long-term estimates of climate change|journal=Nature|language=en|volume=582|issue=7811|pages=185–186|doi=10.1038/d41586-020-01484-5|pmid=32457461|bibcode=2020Natur.582..185P|doi-access=free}}{{Cite news|last=Watts|first=Jonathan|date=2020-06-13|title=Climate worst-case scenarios may not go far enough, cloud data shows|language=en-GB|work=The Guardian|url=https://www.theguardian.com/environment/2020/jun/13/climate-worst-case-scenarios-clouds-scientists-global-heating|access-date=2020-06-19|issn=0261-3077|archive-date=19 June 2020|archive-url=https://web.archive.org/web/20200619083126/https://www.theguardian.com/environment/2020/jun/13/climate-worst-case-scenarios-clouds-scientists-global-heating|url-status=live}}

Remaining deficiencies in the simulation of clouds may have led to overestimates, as models with the highest ECS values were not consistent with observed warming.{{cite web|url=https://www.vice.com/en_uk/article/9393jd/climate-change-predictions-have-suddenly-gone-catastrophic-this-is-why|title=Climate Change Predictions Have Suddenly Gone Catastrophic. This Is Why|last=Bender|first=Maddie|name-list-style=vanc|date=2020-02-07|website=Vice|language=en|access-date=2020-02-09|archive-date=10 February 2020|archive-url=https://web.archive.org/web/20200210021549/https://www.vice.com/en_uk/article/9393jd/climate-change-predictions-have-suddenly-gone-catastrophic-this-is-why|url-status=live}} A fifth of the models began to 'run hot', predicting that global warming would produce significantly higher temperatures than is considered plausible.{{cite journal |last1=Voosen |first1=Paul |title=New climate models forecast a warming surge |url=https://www.science.org/doi/10.1126/science.364.6437.222 |journal=Science |date=19 April 2019 |volume=364 |issue=6437 |pages=222–223 |language=en |doi=10.1126/science.364.6437.222|pmid=31000644 |bibcode=2019Sci...364..222V }}{{cite journal |last1=Hausfather |first1=Zeke |last2=Marvel |first2=Kate |last3=Schmidt |first3=Gavin A. |last4=Nielsen-Gammon |first4=John W. |last5=Zelinka |first5=Mark |title=Climate simulations: recognize the 'hot model' problem |journal=Nature |date=May 2022 |volume=605 |issue=7908 |pages=26–29 |doi=10.1038/d41586-022-01192-2 |pmid=35508771 |bibcode=2022Natur.605...26H |url=https://www.nature.com/articles/d41586-022-01192-2 |language=en}} According to these models, known as hot models, average global temperatures in the worst-case scenario would rise by more than 5{{nbsp}}°C above preindustrial levels by 2100,{{Cite web |last=Voosen |first=Paul |date=2021-07-27 |title=U.N. climate panel confronts implausibly hot forecasts of future warming |url=https://www.science.org/content/article/un-climate-panel-confronts-implausibly-hot-forecasts-future-warming |access-date=2025-01-12 |website=www.science.org |language=en}} with a "catastrophic" impact on human society.{{cite news |last1=Berardelli |first1=Jeff |title=Some new climate models are projecting extreme warming. Are they correct? |url=https://yaleclimateconnections.org/2020/07/some-new-climate-models-are-projecting-extreme-warming-are-they-correct/ |work=Yale Climate Connections |publisher=Yale University |date=1 July 2020}} In comparison, empirical observations combined with physics models indicate that the "very likely" range is between 2.3 and 4.7{{nbsp}}°C. Models with a very high climate sensitivity are also known to be poor at reproducing known historical climate trends, such as warming over the 20th century or cooling during the last ice age. For these reasons the predictions of hot models are considered implausible, and have been given less weight by the IPCC in 2022.{{Cite web |last=Voosen |first=Paul |date=4 May 2022 |title=Use of ‘too hot’ climate models exaggerates impacts of global warming |url=https://www.science.org/content/article/use-too-hot-climate-models-exaggerates-impacts-global-warming |access-date=2025-01-12 |website=www.science.org |language=en}}

• Climate risk
• Charney Report

{{reflist|group=note}}

{{Reflist}}

{{commons category}}

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• {{cite book |year = 2007 |ref = {{harvid|IPCC AR4 WG1|2007}} |collaboration = IPCC AR4 WG1 |title = Climate Change 2007: The Physical Science Basis |series = Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change |veditors = Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL |publisher = Cambridge University Press |url = http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html |isbn = 978-0-521-88009-1 |access-date = 15 December 2012 |archive-date = 5 June 2012 |archive-url = https://web.archive.org/web/20120605025550/http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html |url-status = live }} (pb: {{ISBNT|978-0-521-70596-7}})
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• {{Cite book | chapter = Chapter 12: Long-term Climate Change: Projections, Commitments and Irreversibility | chapter-url = https://archive.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_Chapter12_FINAL.pdf | vauthors = Collins M, Knutti R, Arblaster J, Dufresne JL, Fichefet T, Friedlingstein P | display-authors = etal | year = 2013 | title = {{Harvnb|IPCC AR5 WG1|2013}} | pages = 1029–1136 | access-date = 24 September 2019 | archive-date = 19 December 2019 | archive-url = https://web.archive.org/web/20191219013928/https://archive.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_Chapter12_FINAL.pdf | url-status = live }}
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{{refend}}

• [https://www.metoffice.gov.uk/research/climate/understanding-climate/climate-sensitivity-explained What is 'climate sensitivity'?] Met Office
• [https://www.carbonbrief.org/explainer-how-scientists-estimate-climate-sensitivity How scientists estimate 'climate sensitivity'] Carbon Brief

{{global warming}}

{{DEFAULTSORT:Climate Sensitivity}}

Category:Climate change feedbacks

Category:Paleoclimatology