Editing Radiative forcing (section)

== Forcing due to changes in atmospheric gases ==
{{See also|Greenhouse gas#Radiative forcing}}
[[File:1750- Radiative forcing - greenhouse gases and aerosols.svg|thumb| Hansen ''et{{nbsp}}al.'' (2025) wrote that the IPCC had underestimated aerosols' cooling effect, causing it to also underestimate [[climate sensitivity]] (Earth's responsiveness to increases in greenhouse gas concentrations).<ref name=Envt_Hanson_20250203/> In what Hansen called a [[Deal with the Devil|Faustian bargain]], regulation of aerosols improved air quality, but aerosols' cooling effect became inadequate to temper the increasing warming effect of greenhouse gases—explaining unexpectedly large global warming in 2023-2024.<ref name=Envt_Hanson_20250203>{{cite journal |last1=Hansen |first1=James E. |last2=Kharecha |first2=Pushker |last3=Sato |first3=Makiko |last4=Tselioudis |first4=George |last5=Kelly |first5=Joseph |last6=Bauer |first6=Susanne E. |last7=Ruedy |first7=Reto |last8=Jeong |first8=Eunbi |last9=Jin |first9=Quijian |last10=Rignot |first10=Eric |last11=Velicogna |first11=Isabella |last12=Schoeberl |first12=Mark R. |last13=von Schuckmann |first13=Karina |last14=Amponsem |first14=Joshua |last15=Cao |first15=Junji |last16=Keskinen |first16=Anton |last17=Li |first17=Jing |last18=Pokela |first18=Anni |display-authors=4 |title=Global Warming Has Accelerated: Are the United Nations and the Public Well-Informed? |journal=Environment |date=3 February 2025 |volume=67 |issue=1 |pages=6-44 |doi=10.1080/00139157.2025.2434494|doi-access=free }} Figure 3.</ref>]]
For a well-mixed greenhouse gas, [[atmospheric radiative transfer codes|radiative transfer codes]] that examine each [[spectral line]] for atmospheric conditions can be used to calculate the forcing ΔF as a function of a change in its concentration. These calculations may be simplified into an algebraic formulation that is specific to that gas.

=== Carbon dioxide ===
[[File:ModtranRadiativeForcingDoubleCO2.png|thumb|200px|Radiative forcing for doubling {{CO2}}, as calculated by radiative transfer code Modtran. Red lines are [[Planck's law|Planck curves]].]]A simplified first-order approximation expression for [[carbon dioxide]] ({{CO2}}) is:<ref>{{cite journal |last1=Myhre |first1=G. |last2=Highwood |first2=E.J. |last3=Shine |first3=K.P. |last4=Stordal |first4=F. |year=1998 |title=New estimates of radiative forcing due to well mixed greenhouse gases |journal=[[Geophysical Research Letters]] |volume=25 |issue=14 |pages=2715–8 |bibcode=1998GeoRL..25.2715M |doi=10.1029/98GL01908 |s2cid=128895348 |doi-access=free}}</ref>

: <math>\Delta F = 5.35 \times \ln {(C_0+\Delta C) \over C_0} ~~(\mathrm{W}~\mathrm{m}^{-2}) \, </math>,

where ''C''<sub>0</sub> is a reference concentration in parts per million (ppm) by volume and ''ΔC'' is the concentration change in ppm. For the purpose of some studies (e.g. climate sensitivity), ''C''<sub>0</sub> is taken as the concentration prior to substantial anthropogenic changes and has a value of 278&nbsp;ppm as estimated for the year 1750.

{| class="wikitable" style="float:right style=" font-size:95%"
|+ {{CO2}} forcing (est. 10-yr changes)<ref name="noaa aggi" />
|-
!
! Baseline concentration, C<sub>0</sub>
! Concentration change, ΔC
! Radiative forcing change, ΔF (W m<sup>−2</sup>)
|-
! 1979–1989
| align="center" | 336.8
| align="center" | +16.0
| align="center" | +0.248
|-
! 1989–1999
| align="center" | 352.8
| align="center" | +15.0
| align="center" | +0.222
|-
! 1999–2009
| align="center" | 367.8
| align="center" | +18.7
| align="center" | +0.266
|-
! 2009–2019
| align="center" | 386.5
| align="center" | +23.6
| align="center" | +0.316
|}
The atmospheric burden of greenhouse gases due to human activity has grown especially rapidly during the last several decades (since about year 1950). For carbon dioxide, the 50% increase (''C/C<sub>0</sub>'' = 1.5) realized as of year 2020 since 1750 corresponds to a cumulative radiative forcing change (delta F) of +2.17 W/m<sup>2</sup>.<ref name="noaa aggi" />  Assuming no change in the emissions growth path, a doubling of concentrations (''C/C<sub>0</sub>'' = 2) within the next several decades would correspond to a cumulative radiative forcing change (delta F) of +3.71 W/m<sup>2</sup>.

The relationship between {{CO2}} and radiative forcing is [[logarithmic scale|logarithmic]] at concentrations up to around eight times the current value.<ref>{{cite journal |last1=Huang |first1=Yi |last2=Bani Shahabadi |first2=Maziar |date=28 November 2014 |title=Why logarithmic? |journal=J. Geophys. Res. Atmos. |volume=119 |issue=24 |pages=13,683–89 |bibcode=2014JGRD..11913683H |doi=10.1002/2014JD022466 |s2cid=129640693 |doi-access=free}}</ref> Constant concentration increases thus have a progressively smaller warming effect. However, the first-order approximation is inaccurate at higher concentrations and there is no saturation in the absorption of infrared radiation by {{CO2}}.<ref>{{Cite journal |last1=Zhong |first1=Wenyi |last2=Haigh |first2=Joanna D. |date=27 March 2013 |title=The greenhouse effect and carbon dioxide |journal=Weather |volume=68 |issue=4 |pages=100–5 |bibcode=2013Wthr...68..100Z |doi=10.1002/wea.2072 |issn=1477-8696 |s2cid=121741093}}</ref> Various mechanism behind the logarithmic scaling has been proposed but the spectrum distribution of the carbon dioxide seems to be essential,<ref>{{Cite journal |last1=Romps |first1=David M. |last2=Seeley |first2=Jacob T. |last3=Edman |first3=Jacob P. |date=2022-07-01 |title=Why the Forcing from Carbon Dioxide Scales as the Logarithm of Its Concentration |url=https://journals.ametsoc.org/view/journals/clim/35/13/JCLI-D-21-0275.1.xml |journal=Journal of Climate |volume=35 |issue=13 |pages=4027–4047 |doi=10.1175/JCLI-D-21-0275.1 |bibcode=2022JCli...35.4027R |issn=0894-8755}}</ref> particularly a broadening in the relevant 15-''μ''m band coming from a [[Fermi resonance#CO2|Fermi resonance]] present in the molecule.<ref>{{Cite journal |last1=Shine |first1=Keith P. |last2=Perry |first2=Georgina E. |date=July 2023 |title=Radiative forcing due to carbon dioxide decomposed into its component vibrational bands† |url=https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4485 |journal=Quarterly Journal of the Royal Meteorological Society |language=en |volume=149 |issue=754 |pages=1856–1866 |doi=10.1002/qj.4485 |bibcode=2023QJRMS.149.1856S |issn=0035-9009}}</ref><ref>{{Cite journal |last1=Wordsworth |first1=R. |last2=Seeley |first2=J. T. |last3=Shine |first3=K. P. |date=2024-03-01 |title=Fermi Resonance and the Quantum Mechanical Basis of Global Warming |journal=The Planetary Science Journal |volume=5 |issue=3 |pages=67 |doi=10.3847/PSJ/ad226d |doi-access=free |arxiv=2401.15177 |bibcode=2024PSJ.....5...67W |issn=2632-3338}}</ref><ref>{{Cite web |last=Howlett |first=Joseph |date=2024-08-07 |title=Physicists Pinpoint the Quantum Origin of the Greenhouse Effect |url=https://www.quantamagazine.org/physicists-pinpoint-the-quantum-origin-of-the-greenhouse-effect-20240807/ |access-date=2024-08-12 |website=Quanta Magazine |language=en}}</ref>

=== Other trace gases ===
Somewhat different formulae apply for other trace greenhouse gases such as [[methane]] and {{chem|link=nitrous oxide|N|2|O}} (square-root dependence) or [[CFCs]] (linear), with coefficients that may be found for example in the [[Intergovernmental Panel on Climate Change|IPCC]] reports.<ref>[http://www.grida.no/climate/ipcc_tar/wg1/222.htm IPCC WG-1] {{webarchive|url=https://web.archive.org/web/20071213215142/http://www.grida.no/climate/ipcc_tar/wg1/222.htm|date=13 December 2007|title=}} report</ref> A year 2016 study suggests a significant revision to the methane IPCC formula.<ref>{{Cite journal |last1=Etminan |first1=M. |last2=Myhre |first2=G. |last3=Highwood |first3=E. J. |last4=Shine |first4=K. P. |date=2016-12-27 |title=Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing |journal=Geophysical Research Letters |language=en |volume=43 |issue=24 |pages=12,614–12,623 |bibcode=2016GeoRL..4312614E |doi=10.1002/2016gl071930 |issn=0094-8276 |doi-access=free}}</ref> Forcings by the most influential trace gases in Earth's atmosphere are included in the section describing [[#Recent growth trends|recent growth trends]], and in the [[IPCC list of greenhouse gases]].

=== Water vapor ===
Water vapor is Earth's primary greenhouse gas currently responsible for about half of all atmospheric gas forcing. Its overall atmospheric concentration depends almost entirely on the average planetary temperature, and has the potential to increase by as much as 7% with every degree (°C) of temperature rise (see also: [[Clausius–Clapeyron relation]]).<ref>{{cite web |author=Gavin Schmidt |date=2010-10-01 |title=Taking the Measure of the Greenhouse Effect |url=https://www.giss.nasa.gov/research/briefs/2010_schmidt_05/ |url-status=live |archive-url=https://web.archive.org/web/20210421003101/https://www.giss.nasa.gov/research/briefs/2010_schmidt_05/ |archive-date=2021-04-21 |access-date=2021-05-24 |publisher=NASA Goddard Institute for Space Studies - Science Briefs}}</ref> Thus over long time scales, water vapor behaves as a system feedback that amplifies the radiative forcing driven by the growth of carbon dioxide and other trace gases.<ref>{{cite web |title=It's Water Vapor, Not the CO2 |url=https://www.acs.org/content/acs/en/climatescience/climatesciencenarratives/its-water-vapor-not-the-co2.html |url-status=live |archive-url=https://web.archive.org/web/20210511111642/https://www.acs.org/content/acs/en/climatescience/climatesciencenarratives/its-water-vapor-not-the-co2.html |archive-date=2021-05-11 |accessdate=2021-05-20 |publisher=American Chemical Society}}</ref><ref>{{cite journal |last1=Lacis |first1=Andrew A. |last2=Schmidt |first2=Gavin A. |last3=Rind |first3=David |last4=Ruedy |first4=Reto A. |date=15 October 2010 |title=Atmospheric CO2: Principal Control Knob Governing Earth's Temperature |journal=Science |volume=330 |issue=6002 |pages=356–359 |doi=10.1126/science.1190653 |pmid=20947761 |s2cid=20076916}}</ref>