Editing Radiative forcing (section)

== Forcing due to changes in solar irradiance ==
{{Main|Solar activity and climate|Solar irradiance}}

=== Variations in total solar irradiance (TSI) ===
The intensity of [[solar irradiance]] including all wavelengths is the [[Total Solar Irradiance]] (TSI) and on average is the [[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 [[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 |author2-link=Judith 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 [[Nimbus 7|ERB]], [[ACRIMSAT|ACRIM 1-3]], [[Solar and Heliospheric Observatory|VIRGO]], and [[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]] 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]], 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>.

Earth follows an [[elliptical orbit]] around the Sun, so that the TSI received at any instant 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), and thus by about ±3.4% over 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 zone]]s, 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|Solar cycle}}
[[File:Sunspot Numbers.png|thumb|right|350px|400 year sunspot history, including the [[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 cycle|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 |url-access=subscription }}</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 [[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 |url-access=subscription }}</ref> Since the late 20th century, average TSI has trended slightly lower along with a downward trend in [[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 ===
{{Main|Milankovitch cycles|Orbital forcing|Ice age}}
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 [[axial tilt]]), and [[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 |url-access=subscription }}</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 [[stability of the solar system|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 |url-access=subscription }}</ref>

=== Sun aging ===
{{Main|Formation and evolution of the Solar System|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 [[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>