Climate change metrics radiative forcing and climate sensitivity parameter

Historical climate metrics

·         1983—2013 was the warmest 30-year period for 1400 years.

·         The upper ocean warmed from 1971 to 2010.

·         Greenland and Antarctic ice sheets have been losing mass in the last two decades and that Arctic sea ice and Northern Hemisphere spring snow cover have continued to decrease in extent.

·         Sea level rise since the middle of the 19^th century has been larger than the mean sea level rise of the prior two millennia.

·         Concentration of greenhouse gases in the atmosphere has increased to levels unprecedented on earth in 800,000 years.

·         Total radiative forcing of the earth system, relative to 1750, is positive and the most significant driver is the increase in CO₂'s atmospheric concentration.

Radiative forcing

In climate science, radiative forcing is defined as the difference of 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 inconcentrations of radiatively active gases and aerosols.

IPCC usage

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. 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.

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

Radiative forcing can be used to estimate a subsequent change in equilibrium surface temperature (ΔT_s) arising from that radiative forcing.

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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.

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.

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. 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.

Changes in radiative forcing

The table below shows changes in radiative forcing between 1979 and 2012. The table includes the contribution to radiative forcing from carbon dioxide (CO₂), methane (CH₄),  nitrous oxide  (N
₂O); chlorofluorocarbons (CFCs) 12 and11; 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.

de 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 1979-2012

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

The table shows that CO₂ dominates the total forcing, with methane and the CFCs 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 (HCFCs and HFCs). Most of this increase is related to CO₂. For 2012, the AGGI was 1.32 (representing an increase in total direct radiative forcing of 32% since 1990). The increase in CO₂ forcing alone since 1990 was about 41%. The decline in the CFCs has tempered the increase in net radiative forcing considerably.

Climate sensitivity

Climate sensitivity is the equilibrium temperature change in response to changes of the radiative forcing. Therefore climate sensitivity depends on the initial climate state, but potentially can be accurately inferred from precis epalaeo climate data. Slow feedbacks, especially change of ice sheet size and atmospheric CO2, amplify the total Earth system sensitivity by an amount that depends on the time scale considered.

Although climate sensitivity is usually used in the context of radiative forcing by carbon dioxide (CO₂), it is thought of as a general property of the climate system: the change in surface air temperature (ΔT_s) following a unit change in radiative forcing (RF), and thus is expressed in units of °C/(W/m²). For this to be useful, the measure must be independent of the nature of the forcing (e.g. from greenhouse gases or solar variation); to first order this is indeed found to be so.

The climate sensitivity specifically due to CO₂ is often expressed as the temperature change in °C associated with a doubling of the concentration of carbon dioxide in Earth's atmosphere. For coupled atmosphere-ocean global climate models (i.e. CMIP5) the climate sensitivity is an emergent property: it is not a model parameter, but rather a result of a combination of model physics and parameters. By contrast, simpler energy-balance models may have climate sensitivity as an explicit parameter.

The terms represented in the equation relate radiative forcing to linear changes in global surface temperature change. It is also possible to estimate climate sensitivity from observations; however, this is difficult due to uncertainties in the forcing and temperature histories.

Equilibrium and transient climate sensitivity

The equilibrium climate sensitivity (ECS) refers to the equilibrium change in global mean near-surface air temperature that would result from a sustained doubling of the atmospheric (equivalent) carbon dioxide concentration (ΔT_x2). This value is estimated, by the IPCC Fourth Assessment Report (AR4) as likely to be in the range 2 to 4.5 °C with a best estimate of about 3 °C, and is very unlikely to be less than 1.5 °C. Values substantially higher than 4.5 °C cannot be excluded, but agreement of models with observations is not as good for those values. This is a change from the IPCC Third Assessment Report (TAR), which said it was "likely to be in the range of 1.5 to 4.5 °C". Other estimates of climate sensitivity are discussed later on.

A model estimate of equilibrium sensitivity thus requires a very long model integration; fully equilibrating ocean temperatures requires integrations of thousands of model years. A measure requiring shorter integrations is the transient climate response (TCR) which is defined as the average temperature response over a twenty-year period centered at CO₂ doubling in a transient simulation with CO₂ increasing at 1% per year. The transient response is lower than the equilibrium sensitivity, due to the "inertia" of ocean heat uptake.

Over the 50–100 year timescale, the climate response to forcing is likely to follow the TCR; for considerations of climate stabilization, the ECS is more useful.

An estimate of the equilibrium climate sensitivity may be made from combining the effective climate sensitivity with the known properties of the ocean reservoirs and the surface heat fluxes; this is the effective climate sensitivity. This "may vary with forcing history and climate state".

A less commonly used concept, the Earth system sensitivity (ESS), can be defined which includes the effects of slower feedbacks, such as the albedo change from melting the large ice sheets that covered much of the northern hemisphere during the last glacial maximum. These extra feedbacks make the ESS larger than the ECS — possibly twice as large — but also mean that it may well not apply to current conditions.

Sensitivity to carbon dioxide forcing

Radiative forcing due to doubled CO₂

CO₂ climate sensitivity has a component directly due to radiative forcing by CO₂, and a further contribution arising from feedbacks, positive and negative. "Without any feedbacks, a doubling of CO₂ (which amounts to a forcing of 3.7 W/m²) would result in 1 °C global warming, which is easy to calculate and is undisputed. The remaining uncertainty is due entirely to feedbacks in the system, namely, the water vapor feedback, the ice-albedo feedback, the cloud feedback, and the lapse rate feedback"; addition of these feedbacks leads to a value of the sensitivity to CO₂ doubling of approximately 3 °C ± 1.5 °C, which corresponds to a value of λ of 0.8 K/(W/m²).

The radiative forcing due to doubled CO₂is estimated to be 3.7  W/m², as calculated by IPCC in 2001. IPCC authors concluded that the global mean equilibrium warming for doubling CO₂ (a concentration of approximately 540 parts-per-million (ppm)), or equilibrium climate sensitivity, very likely is greater than 2.7 °F (1.5 °C) and likely to lie in the range 4 to 8.1 °F (2 to 4.5 °C), with a most likely value of about 5 °F (3 °C). For fundamental physical reasons, as well as data limitations, the IPCC states a climate sensitivity higher than 8.1 °F (4.5 °C) cannot be ruled out, but that agreement for these values with observations and "proxy" climate data is generally worse compared to values in the 4 to 8.1  °F (2 to 4.5 °C) range.

The TAR uses the word "likely" in a qualitative sense to describe the likelihood of the 1.5 to 4.5 °C range being correct. AR4, however, quantifies the probable range of climate sensitivity estimates:

·         2-4.5 °C is "likely", = greater than 66% chance of being correct

·         less than 1.5 °C is "very unlikely" = less than 10% " " "

These are Bayesian probabilities, which are based on an expert assessment of the available evidence.

Calculations of CO₂ sensitivity from observational data

Sample calculation using industrial-age data

Rahmstorf (2008) provides an informal example of how climate sensitivity might be estimated empirically, from which the following is modified. Denote the sensitivity, i.e. the equilibrium increase in global mean temperature including the effects of feedbacks due to a sustained forcing by doubled CO₂ (taken as 3.7 W/m²), as x °C. If Earth were to experience an equilibrium temperature change of ΔT (°C) due to a sustained forcing of ΔF (W/m²), then one might say that x/(ΔT) = (3.7 W/m²)/(ΔF), i.e. that x = ΔT * (3.7 W/m²)/ΔF. The global temperature increase since the beginning of the industrial period (taken as 1750) is about 0.8 °C, and the radiative forcing due to CO₂ and other long-lived greenhouse gases (mainly methane, nitrous oxide, and chlorofluorocarbons) emitted since that time is about 2.6 W/m². Neglecting other forcings and considering the temperature increase to be an equilibrium increase would lead to a sensitivity of about 1.1 °C. However, ΔF also contains contributions due to solar activity (+0.3 W/m²), aerosols (-1 W/m²), ozone (0.3 W/m²) and other lesser influences, bringing the total forcing over the industrial period to 1.6 W/m² according to best estimate of the IPCC AR4, albeit with substantial uncertainty. Additionally the fact that the climate system is not at equilibrium must be accounted for; this is done by subtracting the planetary heat uptake rate H from the forcing; i.e., x = ΔT * (3.7 W/m²)/(ΔF-H). Taking planetary heat uptake rate as the rate of ocean heat uptake, estimated by the IPCC AR4 as 0.2 W/m², yields a value for x of 2.1 °C. (All numbers are approximate and quite uncertain.)

Sample calculation using ice-age data

In 2008, Farley wrote: "... examine the change in temperature and solar forcing between glaciations (ice age) and interglacial (no ice age) periods. The change in temperature, revealed in ice core samples, is 5 °C, while the change in solar forcing is 7.1 W/m². The computed climate sensitivity is therefore 5/7.1 = 0.7 K(W/m²)⁻¹. We can use this empirically derived climate sensitivity to predict the temperature rise from a forcing of 4 W/m², arising from a doubling of the atmospheric CO₂ from pre-industrial levels. The result is a predicted temperature increase of 3 °C."

Based on analysis of uncertainties in total forcing, in Antarctic cooling, and in the ratio of global to Antarctic cooling of the last glacial maximum relative to the present, Ganopolski and Schneider von Deimling (2008) infer a range of 1.3 to 6.8 °C for climate sensitivity determined by this approach.

A lower figure was calculated in a 2011 Science paper by Schmittner et al., who combined temperature reconstructions of the Last Glacial Maximum with climate model simulations to suggest a rate of global warming from doubling of atmospheric carbon dioxide of a median of 2.3 °C and uncertainty 1.7–2.6 °C (66% probability range), less than the earlier estimates of 2 to 4.5 °C as the 66% probability range. Schmittner et al. said their "results imply less probability of extreme climatic change than previously thought." Their work suggests that climate sensitivities >6 °C "cannot be reconciled with paleoclimatic and geologic evidence, and hence should be assigned near-zero probability."

Other experimental estimates

Idso (1998) calculated based on eight natural experiments a λ of 0.1 °C/(Wm⁻²) resulting in a climate sensitivity of only 0.4 °C for a doubling of the concentration of CO₂ in the atmosphere.

Andronova and Schlesinger (2001) found that the climate sensitivity could lie between 1 and 10 °C, with a 54 percent likelihood that it lies outside the IPCC range. The exact range depends on which factors are most important during the instrumental period: "At present, the most likely scenario is one that includes anthropogenic sulfate aerosol forcing but not solar variation. Although the value of the climate sensitivity in that case is most uncertain, there is a 70 percent chance that it exceeds the maximum IPCC value. This is not good news," said Schlesinger.

Forest, et al. (2002) using patterns of change and the MIT EMIC estimated a 95% confidence interval of 1.4–7.7 °C for the climate sensitivity, and a 30% probability that sensitivity was outside the 1.5 to 4.5 °C range.

Gregory, et al. (2002) estimated a lower bound of 1.6 °C by estimating the change in Earth's radiation budget and comparing it to the global warming observed over the 20th century.

Shaviv (2005) carried out a similar analysis for 6 different time scales, ranging from the 11-yr solar cycle to the climate variations over geological time scales. He found a typical sensitivity of 0.54±0.12 K/(W m⁻²) or 2.1 °C (ranging between 1.6 °C and 2.5 °C at 99% confidence) if there is no cosmic-ray climate connection, or a typical sensitivity of 0.35±0.09 K/(W m⁻²) or 1.3 °C (between 1.0 °C and 1.7 °C at 99% confidence), if the cosmic-ray climate link is real. (Note Shaviv quotes a radiative forcing equivalent of 3.8Wm⁻². [ΔT_x2=3.8 Wm⁻² λ].)

Frame, et al. (2005) noted that the range of the confidence limits is dependent on the nature of the prior assumptions made.

Annan and Hargreaves (2006) presented an estimate that resulted from combining prior estimates based on analyses of paleoclimate, responses to volcanic eruptions, and the temperature change in response to forcings over the twentieth century. They also introduced a triad notation (L, C, H) to convey the probability distribution function (pdf) of the sensitivity, where the central value C indicates the maximum likelihood estimate in degrees Celsius and the outer values L and H represent the limits of the 95% confidence interval for a pdf, or 95% of the area under the curve for a likelihood function. In this notation their estimate of sensitivity was (1.7, 2.9, 4.9)°C.

Forster and Gregory (2006) presented a new independent estimate based on the slope of a plot of calculated greenhouse gas forcing minus top-of-atmosphere energy imbalance, as measured by satellite borne radiometers, versus global mean surface temperature. In the triad notation of Annan and Hargreaves their estimate of sensitivity was (1.0, 1.6, 4.1)°C.

Royer, et al. (2007) determined climate sensitivity within a major part of the Phanerozoic. The range of values—1.5 °C minimum, 2.8 °C best estimate, and 6.2 °C maximum—is, given various uncertainties, consistent with sensitivities of current climate models and with other determinations.

Science Daily reported on a study by Fasullo and Trenberth (2012), who tested model estimates of climate sensitivity based on their ability to reproduce observed relative humidity in the tropics and subtropics. The best performing models tended to project relatively high climate sensitivities, of around 4 °C.

Previdi et al. 2013 reviewed the 2×CO2 Earth system sensitivity, and concluded it is higher if the ice sheet and the vegetation albedo feedback is included in addition to the fast feedbacks, being ∼4–6◦ C, and higher still if climate–GHG feedbacks are also included.

Literature reviews

A literature review by Knutti and Hegerl (2008) concluded that "various observations favour a climate sensitivity value of about 3 °C, with a likely range of about 2-4.5 °C. However, the physics of the response and uncertainties in forcing lead to difficulties in ruling out higher values."

Radiative forcing functions

A number of different inputs can give rise to radiative forcing. In addition to the down welling radiation due to the greenhouse effect, the IPCC First Scientific Assessment Report listed solar radiation variability due to orbital changes, variability due to changes in solar irradiance, direct aerosol effects (e.g., changes in albedo due to cloud cover), indirect aerosol effects, and surface characteristics.