Radiative forcing

Incoming solar radiation

Radiative forcing or climate forcing is the difference between insolation (sunlight) absorbed by the Earth and energy radiated back to space. Positive radiative forcing means Earth receives more incoming energy from sunlight than it radiates to space. This net gain of energy will cause warming. Conversely, negative radiative forcing means that Earth loses more energy to space than it receives from the sun, which produces cooling.

Typically, radiative forcing is quantified at the tropopause in units of watts per square meter of the Earth's surface. Positive forcing (incoming energy exceeding outgoing energy) warms the system, while negative forcing (outgoing energy exceeding incoming 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.

Radiation balance

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)

Main article: Radiative balance

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.

IPCC usage

Radiative forcings, IPCC 2007.

The Intergovernmental Panel on Climate Change (IPCC) AR4 report defines radiative forcings 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." 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 (ΔT_s) arising from that 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. 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 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 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. 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 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.

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. 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 changes in radiative forcing between 1979 and 2013. The table includes the contribution to radiative forcing from carbon dioxide (CO₂), methane (CH
₄), nitrous oxide (N
₂O); chlorofluorocarbons (CFCs) 12 and 11; and fifteen other minor, long-lived, halogenated gases. 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 (relative to 1750, in $~\mathrm {W} ~\mathrm {m} ^{-2}$), CO₂-equivalent mixing ratio, and the Annual Greenhouse Gas Index (AGGI) between 1979–2014

Year	CO2	CH 4	N 2O	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
2014	1.909	0.500	0.187	0.166	0.058	0.116	2.936	481	1.356	1.6

The table shows that CO₂ dominates the total forcing, with methane and chlorofluorocarbons (CFC) becoming relatively smaller contributors to the total forcing over time. 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. 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 considerably tempered the increase in net radiative forcing.

See also

• Climate sensitivity
• Anthropogenic heat
• Emission standard
• Global warming potential
• Sulfate

External links

• IPCC glossary
• CO2: The Thermostat that Controls Earth's Temperature by NASA's Goddard Institute for Space Studies, October, 2010, Forcing vs. Feedbacks
• Intergovernmental Panel on Climate Change’s Fourth Assessment Report (2007), Chapter 2, "Changes in Atmospheric Constituents and Radiative Forcing," pp. 133–134 (PDF, 8.6 MB, 106 pp.).
• U.S. EPA (2009), Climate Change – Science. Explanation of climate change topics including radiative forcing.
• United States National Research Council (2005), Radiative Forcing of Climate Change: Expanding the Concept and Addressing Uncertainties, Board on Atmospheric Sciences and Climate
• Small volcanoes add up to cooler climate; Airborne particles help explain why temperatures rose less last decade August 13, 2011; Vol.180 #4 (p. 5) Science News
• NASA: The Atmosphere’s Energy Budget
• Energy balance: the simplest climate model
• Explore Mann's climate projections from Scientific American