Incoming, reflected, and absorbed solar radiation. The actual (incoming Solar radiation) is an average of about 1360 W/m2 over a plane perpendicular to the incoming radiation from the Sun. The 340 W/m2 figure is a time-averaged and area-averaged reduction taken over the whole area of the Earth, including the night side. It is 1/4th of the 1360 W/m2 number because a disk has 1/4th the area of a sphere of the same diameter. The other numbers also have to be these kinds of averages in order to compare like to like. The 29% reflected is from an estimate of the Earth's albedo.

In climate modeling, radiative forcing or climate forcing is defined as the difference between insolation (sunlight) absorbed by the Earth and power radiated back to space, caused by any "forcing" effects of radiant heat transfer due to additional gas or dust.[1] Radiative forcing is usually quantified in units of watts per square meter (W/m2) of the Earth's surface, though it is often indexed at the tropopause in climate models. A positive forcing (more net incoming power) warms the system, while negative forcing (more outgoing energy per unit time) cools it. Possible causes of radiative forcing include changes in insolation as the Earth moves towards and away from the Sun, and the concentrations of radiatively active gases, commonly known as greenhouse gases and aerosols. The idea is to put various proposed radiative heat transfer drivers on a common scale to be able to compare them to one another.

Separating radiative heat transfer within a volume of gas or plasma from conductive and convective heat transfer is a very difficult theoretical and computational problem.[2] As with global temperatures, the published numbers for radiative forcings vary considerably and change from year to year even within individual, ongoing studies. This due in part to the need to make untested or untestable assumptions on many different parameters and the interactions between them.

Solar radiative forcing is also dependent on surface albedo, which in turn depends on the frequency of the radiation. When quoted unqualified, it usually refers to some calculated average across the spectrum of visible light and across the view angle, as emissivity varies. In general, the albedo also depends on the directional distribution of incident radiation, and so varies throughout the day at any given point on Earth.

The published numbers for global warming and the greenhouse effect rely on these theoretical radiative forcing numbers.

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. "The exact amount of the energy imbalance is very hard to measure, but it appears to be a little over 0.8 watts per square meter. The imbalance is inferred from a combination of measurements, including satellite and ocean-based observations of sea level rise and warming." (Illustration NASA, Robert Rohde)[3]
The absorbance of CO2 as presented at NIST. The spectrum is obtained from a laboratory setup. Light of a specific frequency and intensity passes through a 10 cm long optical path through a cylinder with a light detector at the end. The cylinder is filled with a gas (CO2) at a specific pressure. The resulting absorbance spectrum, found by sweeping the frequency, is in relative units. "Absorbance" should not be confused with "absorption". These terms are given different meanings by different authors.

Almost all of the energy that affects Earth's climate 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 global 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 and heat emission by various materials. Any such alteration is a radiative forcing, and changes the balance. This happens continuously as sunlight hits the surface, clouds and aerosols form, the concentrations of atmospheric gases vary and seasons alter the ground cover. These factors make it very difficult to calculate a global forcing constant. There are a wide range of published numbers, both from the IPCC and from other sources.

IPCC and other estimates

The Intergovernmental Panel on Climate Change (IPCC) AR4 report defines radiative forcings as:[4]

"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)."

There do not appear to be any radiative forcing measurements made in, or data from, the year 1750, it is simply being used as an assumed starting point. In 1750 the coal-fired steam engine was rare and used mostly for pumping water out of mines.

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."[5] 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).

There are many different estimates for the radiative forcing numbers. One NASA figure shows 0.6 W/m2. Another NASA estimate appears to be based on satellite data-

"The exact amount of the energy imbalance is very hard to measure, but it appears to be a little over 0.8 watts per square meter. The imbalance is inferred from a combination of measurements, including satellite and ocean-based observations of sea level rise and warming."[3]

An IPCC estimate from 2001-

"The radiative forcing due to all well-mixed greenhouse gases since pre-industrial times was estimated to be 2.45 Wm-2 in the SAR with an uncertainty of 15%. This is now altered to a radiative forcing of 2.43 Wm-2 with an uncertainty of 10%, based on the range of model results and the discussion of factors leading to uncertainties in the radiative forcing due to these greenhouse gases. The uncertainty in the radiative forcing due to CO2 is estimated to be smaller than for the other well-mixed greenhouse gases; less than 10%...(see also Hansen et al., 1998)...Compared to IPCC (1990) and the SAR and for similar changes in the concentrations of well-mixed greenhouse gases, the improved simplified expressions result in a 15% decrease in the estimate of the radiative forcing by CO2 "[6]

The bar chart for the IPCC 2007 estimates appears to show about 1.7 Wm-2 for CO2, about 1.0 Wm-2 for miscellaneous other gasses, and another 0.4 Wm-2 for ozone, for an approximate total of 3.1 Wm-2.

Climate sensitivity

Main article: Climate sensitivity

Radiative forcing is a simplified method used to estimate a change in equilibrium surface temperature (ΔTs) arising from the assumed effect of a greenhouse gas as

ΔTs = λΔF

where λ is the assumed climate sensitivity, usually with units in K/(W/m2), and ΔF is the radiative forcing factor.[7] A typical proposed 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 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 Earth's cross-sectional area 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 (albedo), of the Earth. The albedo 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 proposed 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 are often simplified into an algebraic formulation that is specific to that gas.

For each gas, several different forcing factor equations and values have been proposed. For instance, one simplified first-order approximation expression for carbon dioxide is:

ΔF = 5.35 • ln(C/Co) W m-2

where C is the CO2 concentration in parts per million by volume and C0 is the reference concentration.[8] The relationship between carbon dioxide and radiative forcing is logarithmic[9] and thus increased concentrations have a progressively smaller warming effect.

A different formula applies for 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.[10] When two or more gasses are present, the single-gas radiative forcing factor is not valid.

Related measures

Radiative forcing is 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.[11] 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.

History

The table below (derived from atmospheric radiative transfer models) shows calculated estimates of changes in radiative forcing between 1979 and 2013.[12] The table includes the contribution to radiative forcing from carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O); chlorofluorocarbons (CFCs) 12 and 11; and fifteen other minor, long-lived, halogenated gases.[13] The table includes the contribution to radiative forcing of long-lived greenhouse gases. It does not include other forcings, such as the cooling effects of aerosols, changes in solar activity, and in particular from water vapor and cloud cover.

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 (in watts per square meter), CO2-equivalent mixing ratio, and the Annual Greenhouse Gas Index (AGGI) between 1979-2014[12]
Year CO2 CH4 N2O CFC-12 CFC-11 15-minor Total CO22-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
2014 1.909 0.500 0.187 0.166 0.058 0.116 2.936 481 1.356 1.6

In part because it leave out water vapor (H2O), the table shows that CO2 dominates the total forcing in this model, with methane and chlorofluorocarbons (CFC) becoming relatively smaller contributors to the total forcing over time.[12] It is claimed that 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.[12] 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 (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 is claimed to have considerably tempered the increase in net radiative forcing.

References

1. Shindell, Drew (2013). "Radiative Forcing in the AR5" (PDF). Retrieved August 2015. Check date values in: `|access-date=` (help)
2. http://qs.mc-computing.com/qs/Global_Warming/Atmospheric_Analysis.html
3. "NASA: Climate Forcings and Global Warming". January 14, 2009.
4. Climate Change 2007: Synthesis Report
5. Rockström, Johan; Steffen, Will; Noone, Kevin; Persson, Asa; Chapin, F. Stuart; Lambin, Eric F.; Lenton, Timothy F.; Scheffer, M; et al. (2009). "A safe operating space for humanity". Nature. 461 (7263): 472–475. Bibcode:2009Natur.461..472R. PMID 19779433. doi:10.1038/461472a.
6. "6.3.4 Total Well-Mixed Greenhouse Gas Forcing Estimate". April 1, 2001.
7. 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
8. Huang, Y., and M. Bani Shahabadi (2014) Why logarithmic?, J. Geophys. Res. Atmos., 119, 13,683–13,689
9. IPCC WG-1 report
10. 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
11.  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
12. CFC-113, tetrachloromethane (CCl4), 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)