View source for Astronomy:Radiative forcing

{{short description|Difference between solar irradiance absorbed by the Earth and energy radiated back to space}}[[File:Physical Drivers of climate change.svg|thumb|300px|The assessment of radiative forcing and climate sensitivity shows contributions to temperature changes (increases or decreases) from those individual components that humans are influencing.<ref name=":1">IPCC, 2021: [https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_SPM.pdf Summary for Policymakers]. In: [https://www.ipcc.ch/report/ar6/wg1/ Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change] [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 3−32, doi:10.1017/9781009157896.001.</ref>{{rp|7}} Orange bars (due to positive radiative forcings) lead to a temperature increase, blue bars (to a negative radiative forcing) lead to a temperature decrease. |alt=Warming contributions of various GHGs, agents, factors [name the year that the contributions pertain to] [*correct reference given under the 'Talk' tab*]. Plus, the figure is inaccurate; at least wrt. to methane.]]'''Radiative forcing''' (or '''climate forcing'''<ref>{{cite web|url=https://earthobservatory.nasa.gov/Features/EnergyBalance/page7.php|title=Climate and Earth's Energy Budget: Feature Articles|first=Lindsey|last=Rebecca|date=14 January 2009|website=earthobservatory.nasa.gov|access-date=3 April 2018|archive-date=10 April 2020|archive-url=https://web.archive.org/web/20200410141354/https://earthobservatory.nasa.gov/features/EnergyBalance/page7.php|url-status=live}}</ref>) is a concept used in climate science to quantify the change in energy balance in the Earth's atmosphere caused by various factors, such as concentrations of greenhouse gases, aerosols, and changes in solar radiation. In more technical terms, it is "the change in the net, downward minus upward, radiative flux (expressed in W/m<sup>2</sup>) due to a change in an external driver of climate change."<ref name=":0" />{{rp|2245}}  These external drivers are distinguished from feedbacks and variability that are internal to the [[Earth:Climate system|climate system]], and that further influence the direction and magnitude of imbalance.
A planet in radiative equilibrium with its parent star and the rest of space can be characterized by net zero radiative forcing and by a [[Astronomy:Planetary equilibrium temperature|planetary equilibrium temperature]].<ref>{{Cite book|title=Fundamental planetary science: physics, chemistry, and habitability|last1=Lissauer |first1=Jack Jonathan|last2=De Pater |first2=Imke |isbn=9780521853309|location=New York City|oclc=808009225|date = 16 September 2013}}</ref>

Radiative forcing is not a "thing" in the sense that a single instrument has independently measured it.  Rather it is a useful scientific concept whose strength can be estimated from more fundamental [[Physics:Outline of physics#General concepts|physics principles]].  Radiative forcing can also be calculated based upon observation and analysis of other measurable parameters.<ref name="nrcrf">{{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 }}</ref>{{rp|1–4}}  

Radiative forcing on Earth is meaningfully evaluated at the [[Earth:Tropopause|tropopause]] and at the top of the [[Earth:Stratosphere|stratosphere]]. It is quantified in units of [[Watt|watt]]s per square meter, and often summarized as an average over the total surface area of the globe. Radiative forcing varies with solar insolation, [[Earth:Albedo|surface albedo]], and the atmospheric concentrations of radiatively active gases – commonly known as greenhouse gases – and [[Chemistry:Aerosol|aerosol]]s.

The [[Earth:IPCC Sixth Assessment Report|IPCC summarised the current scientific consensus]] about radiative forcing changes as follows: "Human-caused radiative forcing of 2.72 W/m<sup>2</sup> in 2019 relative to 1750 has warmed the climate system. This warming is mainly due to increased GHG concentrations, partly reduced by cooling due to increased aerosol concentrations".<ref name=":1" />{{rp|11}}

The atmospheric burden of greenhouse gases due to human activity has grown especially rapidly during the last several decades (since about year 1950).  For [[Chemistry:Carbon dioxide|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 (ΔF) 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 (ΔF) of +3.71 W/m<sup>2</sup>.

Radiative forcing can be a useful way to compare the growing warming influence of different anthropogenic greenhouse gases over time. The radiative forcing of long-lived and well-mixed greenhouse gases have been increasing in earth's atmosphere since the industrial revolution.<ref name="noaa aggi" /> {{CO2}} dominates the total forcing, with [[Chemistry:Methane|methane]] and chlorofluorocarbons (CFC) becoming relatively smaller contributors to the total forcing over time.<ref name="noaa aggi" /> The five major greenhouse gases account for about 96% of the direct radiative forcing by long-lived greenhouse gas increases since 1750. The remaining 4% is contributed by the 15 minor halogenated gases.

== Definition and fundamentals ==
''Radiative forcing'' is defined in the [[Earth:IPCC Sixth Assessment Report|IPCC Sixth Assessment Report]] as follows: "The change in the net, downward minus upward, radiative flux (expressed in W/m<sup>2</sup>) due to a change in an external driver of climate change, such as a change in the concentration of carbon dioxide (CO<sub>2</sub>), the concentration of volcanic aerosols or the output of the Sun."<ref name=":0">IPCC, 2021: [https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_AnnexVII.pdf Annex VII: Glossary] [Matthews, J.B.R., V. Möller, R. van Diemen, J.S. Fuglestvedt, V. Masson-Delmotte, C.  Méndez, S. Semenov, A. Reisinger (eds.)]. In [https://www.ipcc.ch/report/ar6/wg1/ Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change] [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 2215–2256, doi:10.1017/9781009157896.022.</ref>{{rp|2245}}

There are some different types of radiative forcing as defined in the literature:<ref name=":0" />{{rp|2245}}

* ''Stratospherically adjusted radiative forcing: "''when all tropospheric properties held fixed at their unperturbed values, and after allowing for stratospheric temperatures, if perturbed, to readjust to radiative-dynamical equilibrium."
* ''Instantaneous radiative forcing:'' "if no change in stratospheric temperature is accounted for". 
* ''Effective radiative forcing'': "once both stratospheric and tropospheric adjustments are accounted for".

The radiation balance of the Earth (i.e. the balance between absorbed and radiated energy) determines the average global temperature. This balance is also called [[Earth:Earth's energy budget|Earth's energy balance]]. Changes to this balance occur due to factors such as the intensity of [[Physics:Solar energy|solar energy]], reflectivity of clouds or gases, absorption by various [[Chemistry:Greenhouse gas|greenhouse gas]]es or surfaces and heat emission by various materials. Any such alteration is a ''radiative forcing'', which along with its [[Earth:Climate change feedback|climate feedbacks]], ultimately changes the balance. This happens continuously as sunlight hits the surface of Earth, clouds and aerosols form, the concentrations of atmospheric gases vary and seasons alter the [[Biology:Groundcover|groundcover]].

''Positive radiative forcing'' means Earth receives more incoming energy from sunlight than it radiates to space. This net gain of energy will cause [[Earth:Global warming|global warming]]. Conversely, ''negative radiative forcing'' means that Earth loses more energy to space than it receives from the Sun, which produces cooling ([[Earth:Global dimming|global dimming]]). 

=== Related metrics ===
The concept of radiative forcing has been evolving from the initial proposal, named nowadays ''instantaneous radiative forcing'' (IRF), to other proposals that aim to relate better the radiative imbalance with global warming (global surface mean temperature). For example, researchers explained in 2003 how the ''adjusted troposphere and stratosphere forcing'' can be used in [[Earth:General circulation model|general circulation models]].<ref>{{Cite journal |last1=Shine |first1=Keith P. |last2=Cook |first2=Jolene |last3=Highwood |first3=Eleanor J. |last4=Joshi |first4=Manoj M. |date=23 October 2003 |title=An alternative to radiative forcing for estimating the relative importance of climate change mechanisms |journal=Geophysical Research Letters |volume=30 |issue=20 |pages=2047 |bibcode=2003GeoRL..30.2047S |doi=10.1029/2003GL018141 |s2cid=59514371 |doi-access=free}}</ref> 

The adjusted radiative forcing, in its different calculation methodologies, estimates the imbalance once the stratosphere temperatures has been modified to achieve a radiative equilibrium in the stratosphere (in the sense of zero radiative heating rates). This new methodology is not estimating any ''adjustment'' or ''feedback'' that could be produced on the troposphere (in addition to stratospheric temperature adjustments), for that goal another definition, named ''effective radiative forcing'' has been introduced.<ref>{{Cite journal |last1=Sherwood |first1=Steven C. |last2=Bony |first2=Sandrine |last3=Boucher |first3=Olivier |last4=Bretherton |first4=Chris |last5=Forster |first5=Piers M. |last6=Gregory |first6=Jonathan M. |last7=Stevens |first7=Bjorn |date=2015-02-01 |title=Adjustments in the Forcing-Feedback Framework for Understanding Climate Change |url=http://centaur.reading.ac.uk/38337/1/sherwood15forcefeed.pdf |url-status=live |journal=Bulletin of the American Meteorological Society |language=en |volume=96 |issue=2 |pages=217–228 |bibcode=2015BAMS...96..217S |doi=10.1175/bams-d-13-00167.1 |issn=0003-0007 |s2cid=12515303 |archive-url=https://web.archive.org/web/20190428115201/http://centaur.reading.ac.uk/38337/1/sherwood15forcefeed.pdf |archive-date=2019-04-28 |access-date=2019-12-16}}</ref> In general the ERF is the recommendation of the CMIP6 radiative forcing analysis <ref>{{Cite journal |last1=Forster |first1=Piers M. |last2=Richardson |first2=Thomas |last3=Maycock |first3=Amanda C. |last4=Smith |first4=Christopher J. |last5=Samset |first5=Bjorn H. |last6=Myhre |first6=Gunnar |last7=Andrews |first7=Timothy |last8=Pincus |first8=Robert |last9=Schulz |first9=Michael |date=2016-10-27 |title=Recommendations for diagnosing effective radiative forcing from climate models for CMIP6 |url=http://eprints.whiterose.ac.uk/111875/17/Forster_et_al-2016-Journal_of_Geophysical_Research__Atmospheres.pdf |url-status=live |journal=Journal of Geophysical Research: Atmospheres |language=en |volume=121 |issue=20 |pages=12,460–12,475 |bibcode=2016JGRD..12112460F |doi=10.1002/2016jd025320 |issn=2169-897X |s2cid=59367633 |archive-url=https://web.archive.org/web/20190925083723/http://eprints.whiterose.ac.uk/111875/17/Forster_et_al-2016-Journal_of_Geophysical_Research__Atmospheres.pdf |archive-date=2019-09-25 |access-date=2019-09-25}}</ref> although the stratospherically adjusted methodologies are still being applied in those cases where the adjustments and feedbacks on the troposphere are considered not critical, like in the well mixed greenhouse gases and ozone.<ref>{{Cite journal |last1=Stevenson |first1=D. S. |last2=Young |first2=P. J. |last3=Naik |first3=V. |last4=Lamarque |first4=J.-F. |last5=Shindell |first5=D. T. |last6=Voulgarakis |first6=A. |last7=Skeie |first7=R. B. |last8=Dalsoren |first8=S. B. |last9=Myhre |first9=G. |date=2013-03-15 |title=Tropospheric ozone changes, radiative forcing and attribution to emissions in the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP) |url=http://eprints.lancs.ac.uk/63025/1/Atmos._Chem._Phys._2013_Stevenson.pdf |url-status=live |journal=Atmospheric Chemistry and Physics |language=en |volume=13 |issue=6 |pages=3063–3085 |bibcode=2013ACP....13.3063S |doi=10.5194/acp-13-3063-2013 |issn=1680-7316 |s2cid=15347857 |archive-url=https://web.archive.org/web/20211121144029/http://eprints.lancs.ac.uk/id/eprint/63025/1/Atmos._Chem._Phys._2013_Stevenson.pdf |archive-date=2021-11-21 |access-date=2019-09-04 |doi-access=free}}</ref><ref>{{Cite journal |last1=Checa-Garcia |first1=Ramiro |last2=Hegglin |first2=Michaela I. |last3=Kinnison |first3=Douglas |last4=Plummer |first4=David A. |last5=Shine |first5=Keith P. |date=2018-04-06 |title=Historical Tropospheric and Stratospheric Ozone Radiative Forcing Using the CMIP6 Database |url=http://centaur.reading.ac.uk/75867/8/Checa-Garcia_et_al-2018-Geophysical_Research_Letters.pdf |url-status=live |journal=Geophysical Research Letters |language=en |volume=45 |issue=7 |pages=3264–3273 |bibcode=2018GeoRL..45.3264C |doi=10.1002/2017gl076770 |issn=0094-8276 |s2cid=53471515 |archive-url=https://web.archive.org/web/20190430055312/http://centaur.reading.ac.uk/75867/8/Checa-Garcia_et_al-2018-Geophysical_Research_Letters.pdf |archive-date=2019-04-30 |access-date=2019-12-16}}</ref> A methodology named ''radiative kernel approach'' allows to estimate the climate feedbacks within an offline calculation based on a linear approximation <ref>{{Cite journal |last1=Soden |first1=Brian J. |last2=Held |first2=Isaac M. |last3=Colman |first3=Robert |last4=Shell |first4=Karen M. |last5=Kiehl |first5=Jeffrey T. |last6=Shields |first6=Christine A. |date=2008-07-01 |title=Quantifying Climate Feedbacks Using Radiative Kernels |journal=Journal of Climate |language=en |volume=21 |issue=14 |pages=3504–3520 |bibcode=2008JCli...21.3504S |citeseerx=10.1.1.141.653 |doi=10.1175/2007jcli2110.1 |issn=0894-8755 |s2cid=14679991}}</ref>

== Calculations and measurements ==

=== Basic estimates ===
{{main|Earth:Earth's energy budget|Earth:Climate sensitivity}}

Radiative forcing can be evaluated for its dependence on different factors which are external to the climate system.<ref>{{cite web |url=https://climate.nasa.gov/nasa_science/science/ |title=The Study of Earth as an Integrated System |publisher=NASA |accessdate=2021-05-20 |archive-date=2016-11-02 |archive-url=https://web.archive.org/web/20161102022200/https://climate.nasa.gov/nasa_science/science/ |url-status=live }}</ref>  Except where necessary and noted, the basic estimates which follow do not include indirect feedbacks (positive or negative) which also occur via Earth system responses.  Forcings (ΔF) are expressed as changes over the total surface of the planet and over a specified time interval.  Estimates may be significant in the context of global climate forcing for times spanning decades or longer.<ref name="nrcrf" />

Radiative forcing can be used to estimate a subsequent change in steady-state (often denoted "equilibrium") surface temperature (Δ''T''<sub>s</sub>) arising from that forcing via the equation:

: <math>\Delta T_s =~ \tilde{\lambda}~\Delta F</math>

where <math>\tilde{\lambda}</math> is commonly denoted the [[Earth:Climate sensitivity|climate sensitivity]] parameter, usually with units K/(W/m<sup>2</sup>), and Δ''F'' is the radiative forcing in W/m<sup>2</sup>.<ref>{{cite web |title=IPCC Third Assessment Report - Climate Change 2001 |url=http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/222.htm |url-status=dead |archive-url=https://web.archive.org/web/20090630133202/http://www.grida.no/publications/other/ipcc_tar/?src=%2Fclimate%2Fipcc_tar%2Fwg1%2F222.htm |archive-date=30 June 2009}}</ref> An estimate for  <math>\tilde{\lambda}</math> is obtained from the inverse of the [[Earth:Climate change feedback|climate feedback]] parameter <math>\lambda</math> having units (W/m<sup>2</sup>)/K.  An estimated value of <math>\tilde{\lambda}\approx0.8</math> gives an increase in global temperature of about 1.6 K above the 1750 reference temperature due to the increase in {{CO2}} over that time (278 to 405 ppm, for a forcing of 2.0 W/m<sup>2</sup>), and predicts a further warming of 1.4 K above present temperatures if the {{CO2}} mixing ratio in the atmosphere were to become double its pre-industrial value.  Both of these calculations assume no other forcings.<ref>{{cite web |title=Atmosphere Changes |url=http://www.epa.gov/climatechange/science/recentac.html |url-status=dead |archive-url=https://web.archive.org/web/20090510053004/http://www.epa.gov/climatechange/science/recentac.html |archive-date=10 May 2009}}</ref>

Historically, radiative forcing displays the best predictive capacity for specific types of forcing such as greenhouse gases.<ref name="Nauels-2019">{{Cite journal |last1=Nauels |first1=A. |last2=Rosen |first2=D. |last3=Mauritsen |first3=T. |last4=Maycock |first4=A. |last5=McKenna |first5=C. |last6=Rogelj |first6=J. |author6-link=Joeri Rogelj |last7=Schleussner |first7=C.-F. |last8=Smith |first8=E. |last9=Smith |first9=C. |date=2019-12-02 |title=ZERO IN ON the remaining carbon budget and decadal warming rates. The CONSTRAIN Project Annual Report 2019 |url=https://constrain-eu.org/ |url-status=live |language=en |doi=10.5518/100/20 |archive-url=https://web.archive.org/web/20191209110854/https://constrain-eu.org/ |archive-date=2019-12-09 |access-date=2020-01-20 |website=constrain-eu.org}}</ref> It is less effective for other anthropogenic influences like [[Earth:Soot|soot]]. Another metric called ''effective radiative forcing'' or ERF removes the effect of rapid adjustments within the atmosphere that are unrelated to longer term surface temperature responses.<ref name="Nauels-2019" /> ERF means different factors driving climate change can be placed onto a level playing field to enable comparison of their effects and a more consistent view of how [[Earth:Global surface temperature|global surface temperature]] responds to various types of human forcing.<ref name="Nauels-2019" />

=== Direct observation ===
Earth's global radiation balance fluctuates as the planet rotates and orbits the Sun, and as global-scale thermal anomalies  arise and dissipate within the terrestrial, oceanic and atmospheric systems (e.g. ENSO).<ref>{{cite web |last=Rebecca |first=Lindsey |date=14 January 2009 |title=Climate and Earth's Energy Budget |url=https://earthobservatory.nasa.gov/features/EnergyBalance/page1.php |url-status=live |archive-url=https://web.archive.org/web/20210121082936/https://earthobservatory.nasa.gov/features/EnergyBalance/page1.php |archive-date=21 January 2021 |access-date=15 April 2021 |website=earthobservatory.nasa.gov}}</ref>  Consequently, the planet's 'instantaneous radiative forcing' (IRF) is also dynamic and naturally fluctuates between states of overall warming and cooling. The combination of [[Periodic function|periodic]] and [[Complex system|complex]] processes that give rise to these natural variations will typically revert over periods lasting as long as a few years to produce a net-zero average IRF.  Such fluctuations also mask the longer-term (decade-long) forcing trends due to human activities,  and thus make direct observation of such trends challenging.<ref name="kramer">{{cite journal |author=Kramer, R.J., H. He, B.J. Soden, L. Oreopoulos, G. Myhre, P.M. Forster, and C.J. Smith |date=2021-03-25 |title=Observational Evidence of Increasing Global Radiative Forcing |url=https://doi.org/10.1029/2020GL091585 |url-status=live |journal=Geophysical Research Letters |volume=48 |issue=7 |pages=e91585 |bibcode=2021GeoRL..4891585K |doi=10.1029/2020GL091585 |s2cid=233684244 |archive-url=https://web.archive.org/web/20211121144045/https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020GL091585 |archive-date=2021-11-21 |access-date=2021-04-17 |hdl-access=free |hdl=11250/2788616}}</ref>

[[File:NASA Earth Science Division Operating Missions.jpg|thumbnail|300px|right|NASA Earth Science Division Operating Missions<ref>{{cite web |title=NASA's Earth Observing System homepage |url=https://eospso.gsfc.nasa.gov/ |url-status=live |archive-url=https://web.archive.org/web/20210318000130/https://eospso.gsfc.nasa.gov/ |archive-date=2021-03-18 |accessdate=2021-04-16 |publisher=NASA EOS Project Science Office}}</ref>]]
Earth's radiation balance has been continuously monitored by NASA's [[Astronomy:Clouds and the Earth's Radiant Energy System|Clouds and the Earth's Radiant Energy System]] (CERES)  instruments since year 1998.<ref>{{cite journal |author=Loeb, N.G., S. Kato, K. Loukachine, and N. Manalo-Smith |date=2005-04-01 |title=Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Terra Satellite. Part I: Methodology |journal=Journal of Atmospheric and Oceanic Technology |volume=22 |issue=4 |pages=338–351 |bibcode=2005JAtOT..22..338L |doi=10.1175/JTECH1712.1 |doi-access=free}}</ref><ref>{{cite journal |author=Loeb, N.G., F.G. Rose, S. Kato, D.A. Rutan, W. Su, H. Wang, D.R. Doelling, W.L. Smith, and A. Gettelman |date=2020-01-01 |title=Toward a Consistent Definition between Satellite and Model Clear-Sky Radiative Fluxes |journal=Journal of Climate |volume=33 |issue=1 |pages=61–75 |bibcode=2020JCli...33...61L |doi=10.1175/JCLI-D-19-0381.1 |doi-access=free}}</ref>  Each scan of the globe provides an estimate of the total (all-sky) instantaneous radiation balance.  This data record captures both the natural fluctuations and human influences on IRF; including changes in greenhouse gases, aerosols, land surface, etc.  The record also includes the lagging radiative responses to the radiative imbalances; occurring mainly by way of Earth system feedbacks in temperature, surface albedo, atmospheric water vapor and clouds.<ref>{{cite journal |author=Sherwood, S.C., S. Bony, O. Boucher, C. Bretherton, P.M. Forster, J.M. Gregory, and B. Stevens |date=2015-02-01 |title=Adjustments in the Forcing-Feedback Framework for Understanding Climate Change |journal=Bulletin of the American Meteorological Society |volume=96 |issue=2 |pages=217–228 |bibcode=2015BAMS...96..217S |doi=10.1175/BAMS-D-13-00167.1 |s2cid=12515303 |doi-access=free |hdl-access=free |hdl=11858/00-001M-0000-0015-79FA-A}}</ref><ref>{{cite journal |author=Wielicki, B.A., R.D. Cess, M.D. King, D.A. Randall, and E.F. Harrison |date=1995-11-01 |title=Mission to Planet Earth: Role of Clouds and Radiation in Climate |journal=Bulletin of the American Meteorological Society |volume=76 |issue=11 |pages=2125–2154 |bibcode=1995BAMS...76.2125W |doi=10.1175/1520-0477(1995)076<2125:MTPERO>2.0.CO;2 |doi-access=free}}</ref>

Researchers have used measurements from CERES, [[Engineering:Atmospheric infrared sounder|AIRS]], [[Engineering:CloudSat|CloudSat]] and other satellite-based instruments within NASA's [[Astronomy:Earth Observing System|Earth Observing System]] to parse out contributions by the natural fluctuations and system feedbacks.  Removing these contributions within the multi-year data record allows observation of the anthropogenic trend in top-of-atmosphere (TOA) IRF. The data analysis has also been done in a way that is computationally efficient and independent of most related [[Earth:Climate model|modelling]] methods and results.  Radiative forcing was thus directly observed to have risen by +0.53&nbsp;W&nbsp;m<sup>−2</sup>&nbsp;(±0.11&nbsp;W&nbsp;m<sup>−2</sup>) from years 2003 to 2018.  About 20% of the increase was associated with a reduction in the atmospheric aerosol burden, and most of the remaining 80% was attributed to the rising burden of greenhouse gases.<ref name="kramer" /><ref>{{cite web |author=Sarah Hansen |date=12 April 2021 |title=UMBC's Ryan Kramer confirms human-caused climate change with direct evidence for first time |url=https://news.umbc.edu/umbcs-ryan-kramer-confirms-human-caused-climate-change-with-direct-evidence-for-first-time/ |url-status=live |archive-url=https://web.archive.org/web/20210417044742/https://news.umbc.edu/umbcs-ryan-kramer-confirms-human-caused-climate-change-with-direct-evidence-for-first-time/ |archive-date=17 April 2021 |access-date=17 April 2021 |publisher=University of Maryland, Baltimore County}}</ref><ref>{{cite web |date=26 March 2021 |title=Direct observations confirm that humans are throwing Earth's energy budget off balance |url=https://phys.org/news/2021-03-humans-earth-energy.html |url-status=live |archive-url=https://web.archive.org/web/20210418072159/https://phys.org/news/2021-03-humans-earth-energy.html |archive-date=18 April 2021 |access-date=17 April 2021 |website=phys.org}}</ref>

A rising trend in the radiative imbalance due to increasing global {{CO2}} has been previously observed by ground-based instruments.  For example, such measurements have been separately gathered under clear-sky conditions at two Atmospheric Radiation Measurement (ARM) sites in Oklahoma and Alaska.<ref>{{cite web |title=ARM Capabilities - Atmospheric Observatories |url=https://www.arm.gov/capabilities/observatories/ |url-status=live |archive-url=https://web.archive.org/web/20210425162041/https://www.arm.gov/capabilities/observatories/ |archive-date=2021-04-25 |accessdate=2021-04-25 |publisher=U.S. Department of Energy - Office of Science}}</ref>  Each direct observation found that the associated radiative (infrared) heating experienced by surface dwellers rose by +0.2&nbsp;W&nbsp;m<sup>−2</sup>&nbsp;(±0.07&nbsp;W&nbsp;m<sup>−2</sup>) during the decade ending 2010.<ref>{{cite journal |author=Feldman, D.R., W.D. Collins, P.J. Gero, M.S. Torn, E.J. Mlawer, and T.R. Shippert |date=2015-02-25 |title=Observational determination of surface radiative forcing by CO2 from 2000 to 2010 |url=https://www.nature.com/articles/nature14240 |url-status=live |journal=Nature |volume=519 |issue=7543 |pages=339–343 |bibcode=2015Natur.519..339F |doi=10.1038/nature14240 |pmid=25731165 |s2cid=2137527 |archive-url=https://web.archive.org/web/20210405161008/https://www.nature.com/articles/nature14240 |archive-date=2021-04-05 |access-date=2021-04-25}}</ref><ref>{{cite web |author=Robert McSweeney |date=2015-02-25 |title=New study directly measures greenhouse effect at Earth's surface |url=https://www.carbonbrief.org/new-study-directly-measures-greenhouse-effect-at-earths-surface |url-status=live |archive-url=https://web.archive.org/web/20210418151415/https://www.carbonbrief.org/new-study-directly-measures-greenhouse-effect-at-earths-surface |archive-date=2021-04-18 |access-date=2021-04-25 |publisher=Carbon Brief}}</ref>  In addition to its focus on [[Earth:Outgoing longwave radiation|longwave radiation]] and the most influential forcing gas ({{CO2}}) only, this result is proportionally less than the TOA forcing due to its buffering by atmospheric absorption.

== Forcing due to changes in atmospheric gases ==
[[File:ModtranRadiativeForcingDoubleCO2.png|thumb|left|200px|Radiative forcing for doubling {{CO2}}, as calculated by radiative transfer code Modtran. Red lines are [[Physics:Planck's law|Planck curves]].]]

For a well-mixed greenhouse gas, [[Engineering:Atmospheric radiative transfer codes|radiative transfer codes]] that examine each [[Physics:Spectral line|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 ===
A simplified first-order approximation expression for [[Chemistry:Carbon dioxide|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=[[Earth:Geophysical Research Letters|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>

=== Other trace gases ===
Somewhat different formulae apply for other trace greenhouse gases such as [[Chemistry:Methane|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 [[Organization: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, and in the [[Chemistry:IPCC list of greenhouse gases|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: [[Physics:Clausius–Clapeyron relation|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>

== Forcing due to changes in solar irradiance ==

The intensity of [[Astronomy:Solar irradiance|solar irradiance]] including all wavelengths is the Total Solar Irradiance (TSI) and on average is the [[Astronomy:Solar constant|solar constant]].  It is equal to about 1361&nbsp;W&nbsp;m<sup>−2</sup> at the distance of Earth's annual-mean orbital radius of one [[Astronomy:Astronomical unit|astronomical unit]] and as measured at the top of the atmosphere.<ref>{{cite journal |title=A new, lower value of total solar irradiance: Evidence and climate significance |journal=Geophysical Research Letters |author1=Gregg Kopp | author2=Judith L. Lean |volume=38 |issue=1 |date=2011-01-14 |pages=n/a |doi=10.1029/2010GL045777 |bibcode=2011GeoRL..38.1706K |s2cid=8190208 |doi-access=free }}</ref>  Earth TSI varies with both solar activity and planetary orbital dynamics.  Multiple satellite-based instruments including [[Engineering:Nimbus 7|ERB]], [[Engineering:ACRIMSAT|ACRIM 1-3]], [[Astronomy:Solar and Heliospheric Observatory|VIRGO]], and [[Astronomy:Solar Radiation and Climate Experiment|TIM]]<ref>{{cite web |url=https://lasp.colorado.edu/home/sorce/ |title=Solar Radiation and Climate Experiment |publisher=University of Colorado, Laboratory for Atmospheric and Space Physics |accessdate=2021-05-15 |archive-date=2021-05-19 |archive-url=https://web.archive.org/web/20210519020104/https://lasp.colorado.edu/home/sorce/ |url-status=live }}</ref><ref>{{cite web |url=https://www.nasa.gov/content/goddard/tsis-1-mission-overview |title=TSIS-1 Mission Overview |date=28 November 2017 |publisher=NASA |accessdate=2021-05-20 |archive-date=2021-07-18 |archive-url=https://web.archive.org/web/20210718123934/https://www.nasa.gov/content/goddard/tsis-1-mission-overview/ |url-status=live }}</ref> have continuously measured TSI with improving [[Accuracy and precision|accuracy and precision]] since 1978.<ref name="kopp">{{cite journal |url=https://www.swsc-journal.org/articles/swsc/full_html/2014/01/swsc130036/swsc130036.html |title=Solar variability, solar forcing, and coupling mechanisms in the terrestrial atmosphere |author=Gregg Kopp |journal=Journal of Space Weather and Space Climate |date=2014-04-24 |doi=10.1051/swsc/2014012 |volume=4 |number=A14 |pages=1–9 |bibcode=2014JSWSC...4A..14K |access-date=2021-05-24 |archive-date=2021-05-06 |archive-url=https://web.archive.org/web/20210506134317/https://www.swsc-journal.org/articles/swsc/full_html/2014/01/swsc130036/swsc130036.html |url-status=live |doi-access=free }}</ref>

Approximating Earth as a [[Sphere|sphere]], the cross-sectional area exposed to the Sun (<math display="inline">\pi r^2</math>) is equal to one quarter the area of the planet's surface (<math display="inline">4\pi r^2</math>). The globally and annually averaged amount of solar irradiance per square meter of Earth's atmospheric surface (<math display="inline">I_0</math>) is therefore equal to one quarter of TSI, and has a nearly constant value of <math display="inline">I_0=340~~\mathrm{W}~\mathrm{m}^{-2}</math>.

=== Annual cycles ===
{{Main|Astronomy:Solar irradiance|Astronomy:Solar constant|Astronomy:Sunlight}}
Earth follows an elliptical orbit around the Sun such that TSI received at any instance fluctuates between about 1321&nbsp;W&nbsp;m<sup>−2</sup> (at aphelion in early July) and 1412&nbsp;W&nbsp;m<sup>−2</sup> (at perihelion in early January), or thus by about ±3.4% during each year.<ref name="apperi">{{cite web |url=https://www.msn.com/en-us/weather/topstories/earth-reaches-perihelion-closer-to-the-sun-than-any-other-day/ar-BB1cpVCF |title=Earth reaches perihelion, closer to the sun than any other day |date=2021-01-02 |author=Sophie Lewis |publisher=CBS News |access-date=2021-05-24 |archive-date=2021-05-24 |archive-url=https://web.archive.org/web/20210524165821/https://www.msn.com/en-us/weather/topstories/earth-reaches-perihelion-closer-to-the-sun-than-any-other-day/ar-BB1cpVCF |url-status=live }}</ref>  This change in irradiance has minor influences on Earth's seasonal weather patterns and its climate zones, which primarily result from the annual cycling in Earth's relative tilt direction.<ref>{{cite web |url=https://www.weather.gov/cle/seasons |title=The Seasons, the Equinox, and the Solstices |publisher=National Weather Service |accessdate=2021-05-20 |archive-date=2021-05-24 |archive-url=https://web.archive.org/web/20210524165823/https://www.weather.gov/cle/seasons |url-status=live }}</ref>  Such repeating cycles contribute a net-zero forcing (by definition) in the context of decades-long climate changes.

=== Sunspot activity ===
{{Main|Astronomy:Solar cycle}}
[[File:Sunspot Numbers.png|thumb|right|350px|400 year sunspot history, including the [[Astronomy:Maunder Minimum|Maunder Minimum]]|alt=Line graph showing historical sunspot number count, Maunder and Dalton minima, and the Modern Maximum]]
Average annual TSI varies between about 1360&nbsp;W&nbsp;m<sup>−2</sup> and 1362&nbsp;W&nbsp;m<sup>−2</sup> (±0.05%) over the course of a typical 11-year sunspot activity cycle.<ref name="lean">{{cite journal |url=https://link.springer.com/article/10.1007%2Fs00159-004-0024-1 |title=Solar radiative output and its variability: evidence and mechanisms |author=Claus Fröhlich & Judith Lean |journal=The Astronomy and Astrophysics Review |date=2004-12-01 |volume=12 |issue=4 |pages=273–320 |doi=10.1007/s00159-004-0024-1 |bibcode=2004A&ARv..12..273F |s2cid=121558685 |access-date=2021-05-24 |archive-date=2021-05-25 |archive-url=https://web.archive.org/web/20210525175238/https://link.springer.com/article/10.1007%2Fs00159-004-0024-1 |url-status=live }}</ref>  Sunspot observations have been recorded since about year 1600 and show evidence of lengthier oscillations (Gleissberg cycle, Devries/Seuss cycle, etc.) which modulate the 11-year cycle (Schwabe cycle).  Despite such complex behavior, the amplitude of the 11-year cycle has been the most prominent variation throughout this long-term observation record.<ref>{{cite journal |author=David H. Hathaway |url=https://link.springer.com/content/pdf/10.1007%2Flrsp-2015-4.pdf |title=The Solar Cycle |journal=Living Reviews in Solar Physics |date=2015-09-21 |volume=12 |issue=12 |page=4 |issn=1614-4961 |doi=10.1007/lrsp-2015-4 |pmid=27194958 |pmc=4841188 |arxiv=1502.07020 |bibcode=2015LRSP...12....4H |access-date=2021-05-24 |archive-date=2021-05-23 |archive-url=https://web.archive.org/web/20210523045126/https://link.springer.com/content/pdf/10.1007%2Flrsp-2015-4.pdf |url-status=live }}</ref>

TSI variations associated with sunspots contribute a small but non-zero net forcing in the context of decadal climate changes.<ref name="kopp"/> Some research suggests they may have partly influenced climate shifts during the [[Earth:Little Ice Age|Little Ice Age]], along with concurrent changes in volcanic activity and deforestation.<ref>{{Cite journal |title=Evaluating sun–climate relationships since the Little Ice Age |url=https://www.sciencedirect.com/science/article/abs/pii/S1364682698001138 |journal=Journal of Atmospheric and Solar-Terrestrial Physics |date=1999-01-01 |volume=61 |issue=1–2 |pages=25–36 |doi=10.1016/S1364-6826(98)00113-8 |issn=1364-6826 |last1=Lean |first1=Judith |last2=Rind |first2=David |bibcode=1999JASTP..61...25L |access-date=2021-05-24 |archive-date=2021-05-10 |archive-url=https://web.archive.org/web/20210510195659/https://www.sciencedirect.com/science/article/abs/pii/S1364682698001138 |url-status=live }}</ref>  Since the late 20th century, average TSI has trended slightly lower along with a downward trend in [[Astronomy:Sunspot|sunspot]] activity.<ref name="jones">{{cite journal |title=What influence will future solar activity changes over the 21st century have on projected global near-surface temperature changes? |author=Gareth S. Jones, Mike Lockwood, Peter A. Stott |journal=Journal of Geophysical Research: Atmospheres |date=2012-03-16 |volume=117 |issue=D5 |pages=n/a |doi=10.1029/2011JD017013 |bibcode=2012JGRD..117.5103J |doi-access=free }}</ref>

=== Milankovitch shifts ===
Climate forcing caused by variations in solar irradiance have occurred during Milankovitch cycles, which span periods of about 40,000 to 100,000 years.   Milankovitch cycles consist of long-duration cycles in Earth's orbital eccentricity (or ellipticity), cycles in its orbital obliquity (or [[Astronomy:Axial tilt|axial tilt]]), and [[Physics:Precession|precession]] of its relative tilt direction.<ref name="buis">{{cite web |url=https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/ |title=Milankovitch (Orbital) Cycles and Their Role in Earth's Climate |publisher=NASA Jet Propulsion Laboratory |author=Alan Buis |date=2020-02-27 |access-date=2021-05-24 |archive-date=2020-10-30 |archive-url=https://web.archive.org/web/20201030105553/https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/ |url-status=live }}</ref>  Among these, the 100,000 year cycle in eccentricity causes TSI to fluctuate by about ±0.2%.<ref name="loutre">{{cite journal |url=https://www.sciencedirect.com/science/article/abs/pii/S0012821X04001086 |title=Does mean annual insolation have the potential to change the climate? |author=Marie-France Loutre, Didier Paillard, Françoise Vimeux, Elsa Cortijo |journal=Earth and Planetary Science Letters |issue=1–4 |volume=221 |date=2004-04-30 |pages=1–14 |doi=10.1016/S0012-821X(04)00108-6 |bibcode=2004E&PSL.221....1L |access-date=2021-05-24 |archive-date=2021-05-14 |archive-url=https://web.archive.org/web/20210514155008/https://www.sciencedirect.com/science/article/abs/pii/S0012821X04001086 |url-status=live }}</ref>  Currently, Earth's eccentricity is nearing its least elliptic (most circular) causing average annual TSI to very slowly decrease.<ref name="buis"/>  Simulations also indicate that Earth's orbital dynamics will remain stable including these variations for least the next 10 million years.<ref>{{cite journal |url=https://www.nature.com/articles/338237a0/ |title=A numerical experiment on the chaotic behaviour of the Solar System |author=J. Laskar |journal=Nature |date=1989-03-16 |volume=338 |issue=6212 |pages=237–238 |doi=10.1038/338237a0 |bibcode=1989Natur.338..237L |s2cid=4321705 |access-date=2021-05-24 |archive-date=2021-03-11 |archive-url=https://web.archive.org/web/20210311142810/https://www.nature.com/articles/338237a0 |url-status=live }}</ref>

=== Sun aging ===
{{Main|Astronomy:Formation and evolution of the Solar System|Astronomy:Sun}}
The Sun has consumed about half its hydrogen fuel since forming approximately 4.5 billion years ago.<ref name="sunage">{{cite web |url=https://solarsystem.nasa.gov/solar-system/sun/in-depth/#otp_formation |title=NASA Solar System Exploration - Our Sun |publisher=NASA |accessdate=2021-05-15 |archive-date=2021-05-15 |archive-url=https://web.archive.org/web/20210515174830/https://solarsystem.nasa.gov/solar-system/sun/in-depth/#otp_formation |url-status=live }}</ref>  TSI will continue to slowly increase during the aging process at a rate of about 1% each 100 million years.   Such rate of change is far too small to be detectable within measurements and is insignificant on human timescales.

=== Total Solar Irradiance (TSI) forcing summary ===
{| class="wikitable" style="float:right style="font-size:95%"
|+ TSI forcing (est. 10-yr change)
|-
!
! Δ''τ''
! Radiative forcing change Δ''F'' (W m<sup>−2</sup>)
|-
! Annual cycle
| align=center | ±0.034 <ref name="apperi"/>
| align=center | 0 (net)
|-
! Sunspot activity
| align=center | ±5{{e|-4}} <ref name="lean"/>
| align=center | ±0.1 <ref name="jones"/><ref>{{cite web |url=https://climate.nasa.gov/blog/2953/there-is-no-impending-mini-ice-age/ |title=There Is No Impending 'Mini Ice Age' |publisher=NASA Global Climate Change |date=2020-02-13 |access-date=2021-05-28 |archive-date=2021-05-28 |archive-url=https://web.archive.org/web/20210528020538/https://climate.nasa.gov/blog/2953/there-is-no-impending-mini-ice-age/ |url-status=live }}</ref>
|-
! Orbital shift
| align=center | {{val|-4|e=-7}} <ref name="loutre"/>
| align=center | {{val|-1|e=-4}}
|-
! Sun aging
| align=center | +1{{e|-9}} <ref name="sunage"/>
| align=center | +2{{e|-7}}
|}
The maximum fractional variations (Δτ) in Earth's solar irradiance during the last decade are summarized in the accompanying table.  Each variation previously discussed contributes a forcing of: 
: <math>\Delta F =  ~I_0 \times (1-R) \times \Delta \tau ~~ = ~ 238 \times \Delta \tau ~~(\mathrm{W}~\mathrm{m}^{-2}) \, </math>,
where R=0.30 is Earth's reflectivity.  The radiative and climate forcings arising from changes in the Sun's insolation are expected to continue to be minor, notwithstanding some as-of-yet undiscovered [[Physics:Solar physics|solar physics]].<ref name="jones"/><ref>{{cite web |url=https://climate.nasa.gov/blog/2910/what-is-the-suns-role-in-climate-change/ |title=What Is the Sun's Role in Climate Change? |publisher=NASA |date=2019-09-06 |access-date=2021-05-24 |archive-date=2021-05-26 |archive-url=https://web.archive.org/web/20210526005417/https://climate.nasa.gov/blog/2910/what-is-the-suns-role-in-climate-change/ |url-status=live }}</ref>

== Forcing due to changes in albedo and aerosols ==
A fraction of incident solar radiation is reflected by clouds and aerosols, oceans and landforms, snow and ice, vegetation, and other natural and man-made surface features.  The reflected fraction is known as Earth's [[Physics:Bond albedo|bond albedo]] (R), is evaluated at the top of the atmosphere, and has an average annual global value of about 0.30 (30%).  The overall fraction of solar power absorbed by Earth is then (1-R) or 0.70 (70%).<ref>{{cite journal |title=The Impacts of Atmospheric and Surface Parameters on Long-Term Variations in the Planetary Albedo |author=Bida Jian, Jiming Li, Guoyin Wang, Yongli He, Ying Han, Min Zhang, and Jianping Huang |journal=Journal of Climate |date=2018-11-01 |doi=10.1175/JCLI-D-17-0848.1 |volume=31 |issue=21 |pages=8705–8718 |bibcode=2018JCli...31.8705J |s2cid=133651731 |doi-access=free }}</ref>

Atmospheric components contribute about three-quarters of Earth albedo, and clouds alone are responsible for half.  The pronounced roles of clouds and water vapor are linked with the majority presence of liquid water covering [[Earth:Earth's crust|the planet's crust]].  Global patterns in cloud formation and circulation are highly complex phenomena with couplings to ocean heat flows, and with [[Earth:Jet stream|jet stream]]s assisting their rapid transport.  Moreover, the albedos of Earth's northern and southern hemispheres have been observed to be essentially equal (within 0.2%). This is noteworthy since more than two-thirds of land and 85% of the human population are distributed north.<ref name="stephens">{{cite journal |url=https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014RG000449 |title=The albedo of Earth |author=Graeme L. Stephens, Denis O'Brien, Peter J. Webster, Peter Pilewski, Seiji Kato, Jui-lin Li |journal=Reviews of Geophysics |doi=10.1002/2014RG000449 |date=2015-01-25 |pages=141–163 |volume=53 |issue=1 |bibcode=2015RvGeo..53..141S |s2cid=12536954 |access-date=2021-05-24 |archive-date=2021-05-24 |archive-url=https://web.archive.org/web/20210524165822/https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014RG000449 |url-status=live }}</ref>

Multiple satellite-based instruments including [[Astronomy:Moderate Resolution Imaging Spectroradiometer|MODIS]], [[Physics:Visible Infrared Imaging Radiometer Suite|VIIRs]], and [[Astronomy:Clouds and the Earth's Radiant Energy System|CERES]] have continuously monitored Earth's albedo since 1998.<ref name="nalb">{{cite web |url=https://earthobservatory.nasa.gov/images/84499/measuring-earths-albedo |title=Measuring Earth's Albedo |date=21 October 2014 |publisher=NASA Earth Observatory |accessdate=2021-05-15 |archive-date=2021-05-06 |archive-url=https://web.archive.org/web/20210506163414/https://earthobservatory.nasa.gov/images/84499/measuring-earths-albedo |url-status=live }}</ref>  [[Astronomy:Landsat program|Landsat]] imagery available since 1972 has also been used in some studies.<ref>{{cite web |url=https://www.usgs.gov/center-news/landsat-science-teams-crystal-schaaf-discusses-albedo-its-importance-and-how-it-can?qt-news_science_products=1#qt-news_science_products |title=Landsat Science Team's Crystal Schaaf Discusses Albedo, Its Importance, and How It Can Affect Climate |publisher=U.S. Geological Survey |date=2021-01-12 |access-date=2021-05-24 |archive-date=2021-05-24 |archive-url=https://web.archive.org/web/20210524171333/https://www.usgs.gov/center-news/landsat-science-teams-crystal-schaaf-discusses-albedo-its-importance-and-how-it-can?qt-news_science_products=1#qt-news_science_products |url-status=live }}</ref>  Measurement accuracy has improved and results have converged in recent years, enabling more confident assessment of the recent decadal forcing influence of planetary albedo.<ref name="stephens"/>   Nevertheless, the existing data record is still too short to support longer-term predictions or to address other related questions.

=== Annual cycles ===
Seasonal variations in planetary albedo can be understood as a set of system feedbacks that occur largely in response to the yearly cycling of Earth's relative tilt direction.  Along with the atmospheric responses, most apparent to surface dwellers are the changes in vegetation, snow, and sea-ice coverage.  Intra-annual variations of about ±0.02 (± 7%) around Earth's mean albedo have been observed throughout the course of a year, with maxima occurring twice per year near the time of each solar equinox.<ref name="stephens"/>  This repeating cycle contributes net-zero forcing in the context of decades-long climate changes.

=== Interannual variability ===
[[File:CERES Global albedo anomaly.png|thumb|right|350px|Measured global albedo anomaly from CERES (2000-2011).]]
Regional albedos change from year to year due to shifts arising from natural processes, human actions, and system feedbacks.  For example, human acts of deforestion typically raise Earth's reflectivity while introducing [[Earth:Water storage|water storage]] and [[Earth:Irrigation|irrigation]] to arid lands may lower it. Likewise considering feedbacks, [[Earth:Ice–albedo feedback|ice loss]] in arctic regions decreases albedo while expanding [[Earth:Desertification|desertification]] at low to middle latitudes increases it.

During years 2000-2012, no overall trend in Earth's albedo was discernible within the 0.1% standard deviation of values measured by CERES.<ref name="stephens"/>   Along with the hemispherical equivalence,  some researchers interpret the remarkably small interannual differences as evidence that planetary albedo may currently be constrained by the action of complex system feedbacks.  Nevertheless, historical evidence also suggests that infrequent events such as major [[Earth:Volcanic winter|volcanic eruptions]] can significantly perturb the planetary albedo for several years or longer.<ref>{{cite journal |last1=Robock |first1=Alan |title=Volcanic eruptions and climate |journal=Reviews of Geophysics |date=2000-05-01 |volume=38 |issue=2 |pages=191–219 |doi=10.1029/1998RG000054 |bibcode=2000RvGeo..38..191R |s2cid=1299888 |doi-access=free }}</ref>

=== Albedo forcing summary ===
{| class="wikitable" style="float:right style="font-size:95%"
|+ Albedo forcing (est. 10-yr change)
|-
!
! Fractional variations (Δ''α'') in Earth's albedo
! Radiative forcing change Δ''F'' (W m<sup>−2</sup>)
|-
! Annual cycle
| align=center | ± 0.07<ref name="stephens"/>
| align=center | 0 (net)
|-
! Interannual variation
| align=center | ± 0.001<ref name="stephens"/>
| align=center | ∓ 0.1
|}   
The measured fractional variations (Δ''α'') in Earth's albedo during the first decade of the 21st century are summarized in the accompanying table.  Similar to TSI, the radiative forcing due to a fractional change in planetary albedo (Δ''α'') is:  
: <math>\Delta F =  ~-I_0 \times R \times \Delta \alpha ~~ = ~-102 \times \Delta \alpha ~~(\mathrm{W}~\mathrm{m}^{-2}) \, </math>.
Satellite observations show that various Earth system feedbacks have stabilized planetary albedo despite recent natural and human-caused shifts.<ref name="nalb"/>  On longer timescales, it is more uncertain whether the net forcing which results from such external changes will remain minor.

== Recent growth trends ==
{{Multiple image
| direction = horizontal | align =  center | total_width = 650

| image1 = 1979- Radiative forcing - climate change - global warming - EPA NOAA.svg
| caption1 = Radiative forcing (warming influence) of long-lived atmospheric greenhouse gases has nearly doubled since 1979.<ref name=NOAA_AGGI_2022>{{cite web |title=The NOAA Annual Greenhouse Gas Index (AGGI) |url=https://gml.noaa.gov/aggi/aggi.html |website=NOAA.gov |publisher=National Oceanic and Atmospheric Administration (NOAA) |archive-url=https://web.archive.org/web/20230524133553/https://gml.noaa.gov/aggi/aggi.html |archive-date=24 May 2023 |date=Spring 2023 |url-status=live }}</ref>
| width1 = 340

| image2 = Global climate forcing of the industrial era.png
| caption2 = The industrial era growth in CO2-equivalent gas concentration and AGGI since year 1750.<ref>{{cite web |year= 2020 |title= The NOAA Annual Greenhouse Gas Index - Figure 5 |publisher= NOAA |url= http://www.esrl.noaa.gov/gmd/aggi/ |access-date= 2009-07-30 |archive-date= 2009-08-25 |archive-url= https://web.archive.org/web/20090825000732/http://www.esrl.noaa.gov/gmd/aggi/ |url-status= live }}</ref>
| width2 = 340

| image3 = Greenhouse gas radiative forcing growth since 1979.svg
| caption3 = The annual growth in overall gas forcing has held steady near 2% since 1979.<ref name="noaa aggi"/>
| width3 = 340
}}
The [[Earth:IPCC Sixth Assessment Report|IPCC summarised the current scientific consensus]] about radiative forcing changes as follows: "Human-caused radiative forcing of 2.72 [1.96 to 3.48] W/m<sup>2</sup> in 2019 relative to 1750 has warmed the climate system. This warming is mainly due to increased GHG concentrations, partly reduced by cooling due to increased aerosol concentrations".<ref name=":1" />{{rp|11}}

Radiative forcing can be a useful way to compare the growing warming influence of different anthropogenic greenhouse gases over time.

The radiative forcing of long-lived and well-mixed greenhouse gases have been increasing in earth's atmosphere since the industrial revolution.<ref name="noaa aggi">{{Include-USGov |agency=NOAA |url=https://gml.noaa.gov/aggi/aggi.html |title=THE NOAA ANNUAL GREENHOUSE GAS INDEX (AGGI) |publisher=NOAA/ESRL |author=Butler, James H. and Montzka, Steven J. |date=2022| access-date=7 March 2023}}</ref> The table includes the direct forcing contributions from [[Chemistry:Carbon dioxide|carbon dioxide]] ({{CO2}}), [[Chemistry:Methane|methane]] ({{chem|CH|4}}), [[Chemistry:Nitrous oxide|nitrous oxide]] ({{chem|N|2|O}}); [[Earth:Chlorofluorocarbon|chlorofluorocarbon]]s (CFCs) 12 and 11;{{failed verification|date=March 2023|reason=The table does not appear to give values for CFC-12 and CFC-11, specifically, only for CFCs as a whole. This may be because the information in the source changed since this paragraph was added in 2013.}} and fifteen other [[Chemistry:Halogen|halogen]]ated gases.<ref>
CFC-113, tetrachloromethane ({{chem|CCl|4}}), 1,1,1-trichloroethane ({{chem|CH|3|CCl|3}}); hydrochlorofluorocarbons (HCFCs) 22, 141b and 142b; [[Chemistry:Hydrofluorocarbon|hydrofluorocarbon]]s (HFCs) 134a, 152a, 23, 143a, and 125; [[Chemistry:Sulfur hexafluoride|sulfur hexafluoride]] ({{chem|SF|6}}), and halons 1211, 1301 and 2402)
</ref> These data do not include the significant forcing contributions from shorter-lived and less-well-mixed gases or aerosols; including those indirect forcings from the decay of methane and some halogens.  They also do not account for changes in land use or solar activity.

{{collapse top |title=Click at right to show/hide table }}


{| class="wikitable" style="text-align:right; font-size:0.8em; width:650px"
|+ Global radiative forcing (relative to 1750, in <math>~\mathrm{W}~\mathrm{m}^{-2}</math>), [[Physics:Carbon dioxide equivalent|{{CO2}}-equivalent]] mixing ratio, and the Annual Greenhouse Gas Index (AGGI) since 1979<ref name="noaa aggi"/>
! Year !! {{CO2}} !! {{chem|CH|4}} !! {{chem|N|2|O}} !! CFCs !! HCFCs !! HFCs !! Total !! {{CO2}}-eq<br/>[[Physics:Parts-per notation|ppm]] !! AGGI<br/>1990 = 1 !! AGGI<br/>% change
|-
| 1979 || 1.025 || 0.500 || 0.088 || 0.175 || 0.008 || 0.001 || 1.798 || 388 || 0.787 || 
|-
| 1980 || 1.058 || 0.509 || 0.088 || 0.185 || 0.009 || 0.001 || 1.850 || 392 || 0.810 || 2.3
|-
| 1981 || 1.076 || 0.517 || 0.091 || 0.195 || 0.010 || 0.001 || 1.890 || 395 || 0.827 || 1.8
|-
| 1982 || 1.088 || 0.525 || 0.095 || 0.205 || 0.011 || 0.001 || 1.924 || 397 || 0.842 || 1.5
|-
| 1983 || 1.114 || 0.528 || 0.097 || 0.215 || 0.012 || 0.001 || 1.967 || 400 || 0.861 || 1.9
|-
| 1984 || 1.138 || 0.532 || 0.100 || 0.225 || 0.013 || 0.002 || 2.009 || 403 || 0.879 || 1.8
|-
| 1985 || 1.161 || 0.538 || 0.101 || 0.236 || 0.014 || 0.002 || 2.051 || 407 || 0.898 || 1.8
|-
| 1986 || 1.182 || 0.544 || 0.105 || 0.247 || 0.015 || 0.002 || 2.095 || 410 || 0.917 || 1.9
|-
| 1987 || 1.208 || 0.550 || 0.104 || 0.260 || 0.016 || 0.002 || 2.140 || 413 || 0.937 || 2.0
|-
| 1988 || 1.247 || 0.555 || 0.106 || 0.275 || 0.017 || 0.002 || 2.201 || 418 || 0.963 || 2.7
|-
| 1989 || 1.271 || 0.560 || 0.110 || 0.287 || 0.018 || 0.003 || 2.248 || 422 || 0.984 || 2.0
|-
| 1990 || 1.290 || 0.564 || 0.112 || 0.296 || 0.020 || 0.003 || 2.285 || 425 || 1.000 || 1.6
|-
| 1991 || 1.310 || 0.569 || 0.114 || 0.304 || 0.021 || 0.003 || 2.321 || 428 || 1.016 || 1.6
|-
| 1992 || 1.321 || 0.574 || 0.116 || 0.311 || 0.022 || 0.003 || 2.348 || 430 || 1.027 || 1.2
|-
| 1993 || 1.332 || 0.574 || 0.117 || 0.314 || 0.024 || 0.004 || 2.364 || 431 || 1.034 || 0.7
|-
| 1994 || 1.354 || 0.577 || 0.119 || 0.315 || 0.025 || 0.004 || 2.394 || 434 || 1.048 || 1.3
|-
| 1995 || 1.381 || 0.580 || 0.119 || 0.317 || 0.027 || 0.005 || 2.428 || 436 || 1.063 || 1.5
|-
| 1996 || 1.408 || 0.581 || 0.122 || 0.317 || 0.028 || 0.005 || 2.461 || 439 || 1.077 || 1.5
|-
| 1997 || 1.424 || 0.582 || 0.125 || 0.317 || 0.030 || 0.006 || 2.484 || 441 || 1.087 || 1.0
|-
| 1998 || 1.462 || 0.587 || 0.127 || 0.317 || 0.031 || 0.007 || 2.531 || 445 || 1.108 || 2.1
|-
| 1999 || 1.493 || 0.590 || 0.129 || 0.317 || 0.033 || 0.008 || 2.570 || 448 || 1.125 || 1.7
|-
| 2000 || 1.511 || 0.591 || 0.133 || 0.316 || 0.035 || 0.008 || 2.593 || 450 || 1.135 || 1.0
|-
| 2001 || 1.533 || 0.590 || 0.135 || 0.315 || 0.036 || 0.010 || 2.619 || 452 || 1.146 || 1.1
|-
| 2002 || 1.562 || 0.590 || 0.137 || 0.314 || 0.038 || 0.011 || 2.652 || 455 || 1.161 || 1.5
|-
| 2003 || 1.599 || 0.592 || 0.139 || 0.312 || 0.039 || 0.012 || 2.694 || 459 || 1.179 || 1.8
|-
| 2004 || 1.625 || 0.592 || 0.141 || 0.311 || 0.040 || 0.013 || 2.723 || 461 || 1.192 || 1.3
|-
| 2005 || 1.654 || 0.591 || 0.143 || 0.309 || 0.042 || 0.015 || 2.753 || 464 || 1.205 || 1.3
|-
| 2006 || 1.684 || 0.591 || 0.146 || 0.308 || 0.043 || 0.016 || 2.789 || 467 || 1.220 || 1.5
|-
| 2007 || 1.709 || 0.594 || 0.148 || 0.306 || 0.045 || 0.018 || 2.820 || 469 || 1.234 || 1.4
|-
| 2008 || 1.739 || 0.597 || 0.151 || 0.304 || 0.048 || 0.019 || 2.857 || 473 || 1.250 || 1.6
|-
| 2009 || 1.759 || 0.599 || 0.153 || 0.302 || 0.049 || 0.021 || 2.884 || 475 || 1.262 || 1.2
|-
| 2010 || 1.791 || 0.602 || 0.156 || 0.299 || 0.051 || 0.023 || 2.921 || 478 || 1.278 || 1.6
|-
| 2011 || 1.816 || 0.604 || 0.159 || 0.297 || 0.053 || 0.024 || 2.954 || 481 || 1.293 || 1.4
|-
| 2012 || 1.845 || 0.606 || 0.161 || 0.295 || 0.054 || 0.026 || 2.987 || 484 || 1.307 || 1.5
|-
| 2013 || 1.882 || 0.608 || 0.164 || 0.293 || 0.056 || 0.028 || 3.031 || 488 || 1.326 || 1.9
|-
| 2014 || 1.908 || 0.612 || 0.168 || 0.291 || 0.057 || 0.030 || 3.066 || 492 || 1.342 || 1.5
|-
| 2015 || 1.939 || 0.617 || 0.171 || 0.289 || 0.058 || 0.032 || 3.107 || 495 || 1.359 || 1.8
|-
| 2016 || 1.986 || 0.621 || 0.173 || 0.288 || 0.059 || 0.034 || 3.161 || 500 || 1.383 || 2.4
|-
| 2017 || 2.014 || 0.624 || 0.175 || 0.286 || 0.060 || 0.037 || 3.195 || 504 || 1.398 || 1.5
|-
| 2018 || 2.046 || 0.627 || 0.179 || 0.284 || 0.060 || 0.039 || 3.235 || 507 || 1.416 || 1.7
|-
| 2019 || 2.079 || 0.631 || 0.182 || 0.282 || 0.061 || 0.041 || 3.275 || 511 || 1.433 || 1.7
|-
| 2020 || 2.110 || 0.636 || 0.185 || 0.279 || 0.061 || 0.044 || 3.316 || 515 || 1.451 || 1.8
|-
| 2021 || 2.140 || 0.643 || 0.189 || 0.276 || 0.061 || 0.046 || 3.356 || 519 || 1.469 || 1.8
|-
| 2022 || 2.170 || 0.650 || 0.193 || 0.274 || 0.061 || 0.049 || 3.398 || 523 || 1.487 || 1.8
|}
{{collapse bottom}}

These data show that {{CO2}} dominates the total forcing, with [[Chemistry:Methane|methane]] and chlorofluorocarbons (CFC) becoming relatively smaller contributors to the total forcing over time.<ref name="noaa aggi"/> The five major greenhouse gases account for about 96% of the direct radiative forcing by long-lived greenhouse gas increases since 1750. The remaining 4% is contributed by the 15 minor halogenated gases.

It might be observed that the total forcing for year 2016, 3.027 W m<sup>−2</sup>, together with the commonly accepted value of climate sensitivity parameter λ, 0.8 K /(W m<sup>−2</sup>), results in an increase in global temperature of 2.4 K, much greater than the observed increase, about 1.2 K.<ref>{{cite web |first=J.E. |last=Hansen |display-authors=0 |url=https://data.giss.nasa.gov/gistemp/graphs/ |title=GISS Surface Temperature Analysis: Analysis Graphs and Plots |publisher=Goddard Institute for Space Studies, National Aeronautics and Space Administration |access-date=2018-01-25 |archive-date=2018-01-18 |archive-url=https://web.archive.org/web/20180118174622/https://data.giss.nasa.gov/gistemp/graphs/ |url-status=live }}</ref>{{failed verification|date=November 2023|reason=The value (3.027) is different from that given in the table above, and the source doesn't seem to mention it, or the conclusion drawn here.}} Part of this difference is due to lag in the global temperature achieving steady state with the forcing. The remainder of the difference is due to negative aerosol forcing (compare [[Earth:Particulates#Climate effects|climate effects of particulates]]), climate sensitivity being less than the commonly accepted value, or some combination thereof.<ref>{{cite journal|last1=Schwartz|first1=Stephen E.|last2=Charlson|first2=Robert J.|last3=Kahn|first3=Ralph A.|last4=Ogren|first4=John A.|last5=Rodhe|first5=Henning|year=2010|title=Why hasn't Earth warmed as much as expected?|journal=Journal of Climate|publication-date=15 May 2010|volume=23|issue=10|pages=2453–64|bibcode=2010JCli...23.2453S|doi=10.1175/2009JCLI3461.1|s2cid=14309074 |url=https://digital.library.unt.edu/ark:/67531/metadc930353/m2/1/high_res_d/978306.pdf|access-date=24 September 2019|archive-date=8 March 2021|archive-url=https://web.archive.org/web/20210308053854/https://digital.library.unt.edu/ark:/67531/metadc930353/m2/1/high_res_d/978306.pdf|url-status=live}}</ref>

The table also includes an "Annual Greenhouse Gas Index" (AGGI), which is defined as the ratio of the total direct radiative forcing due to long-lived greenhouse gases for any year for which adequate global measurements exist to that which was present in 1990.<ref name="noaa aggi"/> 1990 was chosen because it is the baseline year for the [[Chemistry:Kyoto Protocol|Kyoto Protocol]]. This index is a measure of the inter-annual changes in conditions that affect [[Earth:Greenhouse gas emissions|carbon dioxide emission]] and uptake, methane and nitrous oxide sources and sinks, the decline in the atmospheric abundance of [[Earth:Ozone depletion|ozone-depleting]] chemicals related to the Montreal Protocol. and the increase in their substitutes (hydrogenated CFCs (HCFCs) and hydrofluorocarbons (HFC). Most of this increase is related to {{CO2}}. For 2013, the AGGI was 1.34 (representing an increase in total direct radiative forcing of 34% since 1990). The increase in {{CO2}} forcing alone since 1990 was about 46%. The decline in CFCs considerably tempered the increase in net radiative forcing.

An alternative table prepared for use in climate model intercomparisons conducted under the auspices of IPCC and including all forcings, not just those of greenhouse gases.<ref>{{Cite book |last=Stocker |first=Thomas |url=http://worldcat.org/oclc/1120509660 |title=Climate change 2013 : the physical science basis : Working Group I contribution to the Fifth assessment report of the Intergovernmental Panel on Climate Change|date=24 March 2014|isbn=978-1-107-66182-0|oclc=1120509660|access-date=18 April 2021|archive-date=19 April 2021|archive-url=https://web.archive.org/web/20210419134709/https://www.worldcat.org/oclc/1120509660|url-status=live}} [http://www.climatechange2013.org/images/report/WG1AR5_AIISM_Datafiles.xlsx datafile] {{Webarchive|url=https://web.archive.org/web/20170930161009/http://www.climatechange2013.org/images/report/WG1AR5_AIISM_Datafiles.xlsx |date=2017-09-30 }}</ref>

==See also==
* [[Earth:Global dimming|Global dimming]]
* [[Physics:Global warming potential|Global warming potential]]

== References ==
{{reflist|30em}}

== External links ==
* United States National Research Council (2005), ''[http://www.nap.edu/openbook/0309095069/html/ Radiative Forcing of Climate Change: Expanding the Concept and Addressing Uncertainties]'', Board on Atmospheric Sciences and Climate
*[http://www.sciencenews.org/view/generic/id/332612/title/Small_volcanoes_add_up_to_cooler_climate Small volcanoes add up to cooler climate; Airborne particles help explain why temperatures rose less last decade] {{Webarchive|url=https://web.archive.org/web/20121003145119/http://www.sciencenews.org/view/generic/id/332612/title/Small_volcanoes_add_up_to_cooler_climate |date=2012-10-03 }} August 13, 2011; Vol.180 #4 (p.&nbsp;5) ''Science News'' 
*[http://earthobservatory.nasa.gov/Features/EnergyBalance/page6.php NASA: The Atmosphere's Energy Budget]


{{DEFAULTSORT:Radiative Forcing (Calculation and Measurement)}}
[[Category:Atmospheric radiation]]

{{Sourceattribution|Radiative forcing}}