In climate science, radiative forcing or climate forcing, is defined as the difference of insolation (sunlight) absorbed by the Earth and energy radiated back to space.[citation needed] Typically, radiative forcing is quantified at the tropopause in units of watts per square meter of the Earth's surface. A positive forcing (more incoming energy) warms the system, while negative forcing (more outgoing energy) cools it. Causes of radiative forcing include changes in insolation and the concentrations of radiatively active gases, commonly known as greenhouse gases and aerosols.

Atmospheric gases only absorb some wavelengths of energy but are transparent to others. The absorption patterns of water vapor (blue peaks) and carbon dioxide (pink peaks) overlap in some wavelengths. Carbon dioxide is not as strong a greenhouse gas as water vapor, but it absorbs energy in wavelengths (12-15 micrometers) that water vapor does not, partially closing the “window” through which heat radiated by the surface would normally escape to space. (Illustration NASA, Robert Rohde)[1]

Almost all of the energy which affects Earth's weather is received as radiant energy from the Sun. The planet and its atmosphere absorb and reflect some of the energy, while long-wave energy is radiated back into space. The balance between absorbed and radiated energy determines the average temperature. Because the atmosphere absorbs some of the re-radiated long-wave energy, the planet is warmer than it would be in the absence of the atmosphere: see greenhouse effect.

The radiation balance is altered by such factors as the intensity of solar energy, reflectivity of clouds or gases, absorption by various greenhouse gases or surfaces, emission of heat by various materials. Any such alteration is a radiative forcing, and causes a new balance to be reached. This happens continuously as sunlight hits the surface, clouds and aerosols form, the concentrations of atmospheric gases vary, and seasons alter the ground cover.

## IPCC usage

The IPCC AR4 report, defines radiative forcings as:[2]

"Radiative forcing is a measure of the influence a factor has in altering the balance of incoming and outgoing energy in the Earth-atmosphere system and is an index of the importance of the factor as a potential climate change mechanism. In this report radiative forcing values are for changes relative to preindustrial conditions defined at 1750 and are expressed in Watts per square meter (W/m2)."

In simple terms, radiative forcing is "...the rate of energy change per unit area of the globe as measured at the top of the atmosphere."[3] In the context of climate change, the term "forcing" is restricted to changes in the radiation balance of the surface-troposphere system imposed by external factors, with no changes in stratospheric dynamics, no surface and tropospheric feedbacks in operation (i.e., no secondary effects induced because of changes in tropospheric motions or its thermodynamic state), and no dynamically induced changes in the amount and distribution of atmospheric water (vapour, liquid, and solid forms).

## Climate sensitivity

Main article: Climate sensitivity

Radiative forcing can be used to estimate a subsequent change in equilibrium surface temperature (ΔTs) arising from that radiative forcing via the equation:

$\Delta T_s =~ \lambda~\Delta F$

where λ is the climate sensitivity, usually with units in K/(W/m2), and ΔF is the radiative forcing.[4] A typical value of λ is 0.8 K/(W/m2), which gives a warming of 3K for doubling of CO2.

## Example calculations

Radiative forcing for doubling CO2, as calculated by radiative transfer code Modtran. Red lines are Planck curves.
Radiative forcing for eight times increase of CH4, as calculated by radiative transfer code Modtran.

### Solar forcing

Radiative forcing (measured in Watts per square meter) can be estimated in different ways for different components. For the case of a change in solar irradiance (i.e., "solar forcing"), the radiative forcing is simply the change in the average amount of solar energy absorbed per square meter of the Earth's area. Since the cross-sectional area of the Earth exposed to the Sun (πr2) is equal to 1/4 of the surface area of the Earth (4πr2), the solar input per unit area is one quarter the change in solar intensity. This must be multiplied by the fraction of incident sunlight that is absorbed, F=(1-R), where R is the reflectivity, or albedo, of the Earth. The albedo of the Earth is approximately 0.3, so F is approximately equal to 0.7. Thus, the solar forcing is the change in the solar intensity divided by 4 and multiplied by 0.7.

Likewise, a change in albedo will produce a solar forcing equal to the change in albedo divided by 4 multiplied by the solar constant.

### Forcing due to atmospheric gas

For a greenhouse gas, such as carbon dioxide, radiative transfer codes that examine each spectral line for atmospheric conditions can be used to calculate the change ΔF as a function of changing concentration. These calculations can often be simplified into an algebraic formulation that is specific to that gas.

For instance, the simplified first-order approximation expression for carbon dioxide is:

$\Delta F = 5.35 \times \ln {C \over C_0}~\mathrm{W}~\mathrm{m}^{-2} \,$

where C is the CO2 concentration in parts per million by volume and C0 is the reference concentration.[5] The relationship between carbon dioxide and radiative forcing is logarithmic, and thus increased concentrations have a progressively smaller warming effect.

A different formula applies for some other greenhouse gases such as methane and N2O (square-root dependence) or CFCs (linear), with coefficients that can be found e.g. in the IPCC reports.[6]

## Related measures

Radiative forcing is intended as a useful way to compare different causes of perturbations in a climate system. Other possible tools can be constructed for the same purpose: for example Shine et al.[7] say "...recent experiments indicate that for changes in absorbing aerosols and ozone, the predictive ability of radiative forcing is much worse... we propose an alternative, the 'adjusted troposphere and stratosphere forcing'. We present GCM calculations showing that it is a significantly more reliable predictor of this GCM's surface temperature change than radiative forcing. It is a candidate to supplement radiative forcing as a metric for comparing different mechanisms...". In this quote, GCM stands for "global circulation model", and the word "predictive" does not refer to the ability of GCMs to forecast climate change. Instead, it refers to the ability of the alternative tool proposed by the authors to help explain the system response.

The table below (derived from atmospheric radiative transfer models) shows changes in radiative forcing between 1979 and 2013.[8] The table includes the contribution to radiative forcing from carbon dioxide (CO2), methane (CH
4
), nitrous oxide (N
2
O
); chlorofluorocarbons (CFCs) 12 and 11; and fifteen other minor, long-lived, halogenated gases.[9] The table includes the contribution to radiative forcing of long-lived greenhouse gases. It does not include other forcings, such as aerosols and changes in solar activity.

Changes in radiative forcing of long-lived greenhouse gases between 1979 and 2012.
Radiative forcing, relative to 1750, due to carbon dioxide alone since 1979. The percent change from January 1, 1990 is shown on the right axis.

Global radiative forcing, CO2-equivalent mixing ratio, and the Annual Greenhouse Gas Index (AGGI) between 1979-2013[8]
Year CO2 CH
4
N
2
O
CFC-12 CFC-11 15-minor Total CO2-eq
ppm
AGGI
1990 = 1
AGGI
% change
1979 1.027 0.419 0.104 0.092 0.039 0.031 1.712 383 0.786
1980 1.058 0.426 0.104 0.097 0.042 0.034 1.761 386 0.808 2.8
1981 1.077 0.433 0.107 0.102 0.044 0.036 1.799 389 0.826 2.2
1982 1.089 0.440 0.111 0.108 0.046 0.038 1.831 391 0.841 1.8
1983 1.115 0.443 0.113 0.113 0.048 0.041 1.873 395 0.860 2.2
1984 1.140 0.446 0.116 0.118 0.050 0.044 1.913 397 0.878 2.2
1985 1.162 0.451 0.118 0.123 0.053 0.047 1.953 401 0.897 2.1
1986 1.184 0.456 0.122 0.129 0.056 0.049 1.996 404 0.916 2.2
1987 1.211 0.460 0.120 0.135 0.059 0.053 2.039 407 0.936 2.2
1988 1.250 0.464 0.123 0.143 0.062 0.057 2.099 412 0.964 3.0
1989 1.274 0.468 0.126 0.149 0.064 0.061 2.144 415 0.984 2.1
1990 1.293 0.472 0.129 0.154 0.065 0.065 2.178 418 1.000 1.6
1991 1.313 0.476 0.131 0.158 0.067 0.069 2.213 420 1.016 1.6
1992 1.324 0.480 0.133 0.162 0.067 0.072 2.238 422 1.027 1.1
1993 1.334 0.481 0.134 0.164 0.068 0.074 2.254 424 1.035 0.7
1994 1.356 0.483 0.134 0.166 0.068 0.075 2.282 426 1.048 1.3
1995 1.383 0.485 0.136 0.168 0.067 0.077 2.317 429 1.064 1.5
1996 1.410 0.486 0.139 0.169 0.067 0.078 2.350 431 1.079 1.4
1997 1.426 0.487 0.142 0.171 0.067 0.079 2.372 433 1.089 0.9
1998 1.465 0.491 0.145 0.172 0.067 0.080 2.419 437 1.111 2.0
1999 1.495 0.494 0.148 0.173 0.066 0.082 2.458 440 1.128 1.6
2000 1.513 0.494 0.151 0.173 0.066 0.083 2.481 442 1.139 0.9
2001 1.535 0.494 0.153 0.174 0.065 0.085 2.506 444 1.150 1.0
2002 1.564 0.494 0.156 0.174 0.065 0.087 2.539 447 1.166 1.3
2003 1.601 0.496 0.158 0.174 0.064 0.088 2.580 450 1.185 1.6
2004 1.627 0.496 0.160 0.174 0.063 0.090 2.610 453 1.198 1.1
2005 1.655 0.495 0.162 0.173 0.063 0.092 2.640 455 1.212 1.2
2006 1.685 0.495 0.165 0.173 0.062 0.095 2.675 458 1.228 1.3
2007 1.710 0.498 0.167 0.172 0.062 0.097 2.706 461 1.242 1.1
2008 1.739 0.500 0.170 0.171 0.061 0.100 2.742 464 1.259 1.3
2009 1.760 0.502 0.172 0.171 0.061 0.103 2.768 466 1.271 1.0
2010 1.791 0.504 0.174 0.170 0.060 0.106 2.805 470 1.288 1.3
2011 1.818 0.505 0.178 0.169 0.060 0.109 2.838 473 1.303 1.2
2012 1.846 0.507 0.181 0.168 0.059 0.111 2.873 476 1.319 1.2
2013 1.884 0.509 0.184 0.167 0.059 0.114 2.916 479 1.338 1.5

The table shows that CO2 dominates the total forcing, with methane and the CFCs becoming relatively smaller contributors to the total forcing over time.[8] 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.

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.[8] 1990 was chosen because it is the baseline year for the Kyoto Protocol. This index is a measure of the inter-annual changes in conditions that affect carbon dioxide emission and uptake, methane and nitrous oxide sources and sinks, the decline in the atmospheric abundance of ozone-depleting chemicals related to the Montreal Protocol. and the increase in their substitutes (HCFCs and HFCs). 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 the CFCs has tempered the increase in net radiative forcing considerably.

## References

1. ^ "NASA: Climate Forcings and Global Warming". January 14, 2009.
2. ^ http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr.pdf
3. ^ Rockström, Johan; Steffen, Will; Noone, Kevin; Persson, Asa; Chapin, F. Stuart; Lambin, Eric F.; Scheffer, M et al. (2009). "A safe operating space for humanity". Nature 461 (7263): 472–475. Bibcode:2009Natur.461..472R. doi:10.1038/461472a. PMID 19779433.
4. ^ http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/222.htm
5. ^ Myhre et al., New estimates of radiative forcing due to well mixed greenhouse gases, Geophysical Research Letters, Vol 25, No. 14, pp 2715–2718, 1998
6. ^ IPCC WG-1 report
7. ^ Shine et al., An alternative to radiative forcing for estimating the relative importance of climate change mechanisms, Geophysical Research Letters, Vol 30, No. 20, 2047, doi:10.1029/2003GL018141, 2003
8. ^ a b c d  This article incorporates public domain material from the NOAA document: Butler, J.H. and S.A. Montzka (1 August 2013). "THE NOAA ANNUAL GREENHOUSE GAS INDEX (AGGI)". NOAA/ESRL Global Monitoring Division
9. ^ CFC-113, tetrachloromethane (CCl
4
), trichloromethane (CH
3
CCl
3
); hydrochlorofluorocarbons (HCFCs) 22, 141b and 142b; hydrofluorocarbons (HFCs) 134a, 152a, 23, 143a, and 125; sulfur hexafluoride (SF
6
), and halons 1211, 1301 and 2402)