In climate science, radiative forcing is defined as the difference between radiant energy received by the earth and energy radiated back to space. Typically, radiative forcing is quantified at the tropopause in units of watts per square meter of 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 (incident solar radiation) and in concentrations of radiatively active gases and aerosols.

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

2005 radiative forcings as estimated by the IPCC.

The term "radiative forcing" has been used in the IPCC Assessments with a specific technical meaning, to denote an externally imposed perturbation in the radiative energy budget of Earth’s climate system, which may lead to changes in climate parameters.[1] The exact definition used is:

The radiative forcing of the surface-troposphere system due to the perturbation in or the introduction of an agent (say, a change in greenhouse gas concentrations) is the change in net (down minus up) irradiance (solar plus long-wave; in Wm-2) at the tropopause AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.[2]

In a subsequent report,[3] the IPCC defines it as:

"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."[4] 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

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.[5] A typical value of λ is 0.8 K/(W/m2), which gives a warming of 3K for doubling of CO2.

## Example calculations

### 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.

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.

### 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.[6] 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.[7]

## 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.[8] 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.