Editing Radiative forcing (section)

=== 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>