Radiative forcing

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 W m⁻² at the distance of Earth's annual-mean orbital radius of one astronomical unit and as measured at the top of the atmosphere.[10] Earth TSI varies with both solar activity and planetary orbital dynamics. Multiple satellite-based instruments including ERB, ACRIM 1-3, VIRGO, and TIM[11][12] have continuously measured TSI with improving accuracy and precision since 1978.[13]

Approximating Earth as a sphere, the cross-sectional area exposed to the Sun (${\textstyle \pi r^{2}}$) is equal to one quarter the area of the planet's surface (${\textstyle 4\pi r^{2}}$). The globally and annually averaged amount of solar irradiance per square meter of Earth's atmospheric surface (${\textstyle I_{0}}$) is therefore equal to one quarter of TSI, and has a nearly constant value of ${\textstyle I_{0}=340~~\mathrm {W} ~\mathrm {m} ^{-2}}$.

Earth follows an elliptical orbit around the Sun such that TSI received at any instance fluctuates between about 1321 W m⁻² (at aphelion in early July) and 1412 W m⁻² (at perihelion in early January), or thus by about ±3.4% during each year.[14] 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.[15] Such repeating cycles contribute a net-zero forcing (by definition) in the context of decades-long climate changes.

400 year sunspot history, including the Maunder Minimum

Average annual TSI varies between about 1360 W m⁻² and 1362 W m⁻² (±0.05%) over the course of a typical 11-year sunspot activity cycle.[16] 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.[17]

TSI variations associated with sunspots contribute a small but non-zero net forcing in the context of decadal climate changes.[13] Some research suggests they may have partly influenced climate shifts during the Little Ice Age, along with concurrent changes in volcanic activity and deforestation.[18] Since the late 20th century, average TSI has trended slightly lower along with a downward trend in sunspot activity.[19]

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.[20] Among these, the 100,000 year cycle in eccentricity causes TSI to fluctuate by about ±0.2%.[21] Currently, Earth's eccentricity is nearing its least elliptic (most circular) causing average annual TSI to very slowly decrease.[20] Simulations also indicate that Earth's orbital dynamics will remain stable including these variations for least the next 10 million years.[22]

The Sun has consumed about half its hydrogen fuel since forming approximately 4.5 billion years ago.[23] 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.

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:

${\displaystyle \Delta F=~I_{0}\times (1-R)\times \Delta \tau ~~=~238\times \Delta \tau ~~(\mathrm {W} ~\mathrm {m} ^{-2})\,}$,

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.[19][25]

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 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%).[26]

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 the planet's crust. Global patterns in cloud formation and circulation are highly complex phenomena with couplings to ocean heat flows, and with jet streams 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.[27]

Multiple satellite-based instruments including MODIS, VIIRs, and CERES have continuously monitored Earth's albedo since 1998.[28] Landsat imagery available since 1972 has also been used in some studies.[29] Measurement accuracy has improved and results have converged in recent years, enabling more confident assessment of the recent decadal forcing influence of planetary albedo.[27] Nevertheless, the existing data record is still too short to support longer-term predictions or to address other related questions.

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.[27] This repeating cycle contributes net-zero forcing in the context of decades-long climate changes.

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 water storage and irrigation to arid lands may lower it. Likewise considering feedbacks, ice loss in arctic regions decreases albedo while expanding 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.[27] 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 volcanic eruptions can significantly perturb the planetary albedo for several years or longer.[30]

The measured fractional variations (Δα) 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 (Δα) is:

${\displaystyle \Delta F=~-I_{0}\times R\times \Delta \alpha ~~=~-102\times \Delta \alpha ~~(\mathrm {W} ~\mathrm {m} ^{-2})\,}$.

Satellite observations show that various Earth system feedbacks have stabilized planetary albedo despite recent natural and human-caused shifts.[28] On longer timescales, it is more uncertain whether the net forcing which results from such external changes will remain minor.

Radiative forcing for doubling CO₂, as calculated by radiative transfer code Modtran. Red lines are Planck curves.

For a well-mixed greenhouse gas, 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.

A simplified first-order approximation expression for carbon dioxide (CO₂) is:[31]

${\displaystyle \Delta F=5.35\times \ln {(C_{0}+\Delta C) \over C_{0}}~~(\mathrm {W} ~\mathrm {m} ^{-2})\,}$,

where C₀ 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), C₀ is taken as the concentration prior to substantial anthropogenic changes and has a value of 278 ppm as estimated for the year 1750.

The atmospheric burden of greenhouse gases due to human activity has grown especially rapidly during the last several decades (since about year 1950). For CO₂, the 50% increase (C/C₀ = 1.5) realized as of year 2020 since 1750 corresponds to a cumulative ${\textstyle \Delta F=+2.17~~\mathrm {W} ~\mathrm {m} ^{-2}}$.[32] Assuming no change in the emissions growth path, a doubling (C/C₀ = 2) within the next several decades would correspond to a cumulative ${\textstyle \Delta F=+3.71~~\mathrm {W} ~\mathrm {m} ^{-2}}$.

The relationship between CO₂ and radiative forcing is logarithmic at concentrations up to around eight times the current value.[33] 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.[34]

Somewhat different formulae apply for other trace greenhouse gases such as methane and N
₂O (square-root dependence) or CFCs (linear), with coefficients that may be found for example in the IPCC reports.[35] A year 2016 study suggests a significant revision to the methane IPCC formula.[36] Forcings by the most influential trace gases in Earth's atmosphere are included in the section describing recent growth trends, and in the IPCC list of greenhouse gases.

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).[37] 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.[38][39]