# Climate sensitivity

Frequency distribution of equilibrium climate sensitivity, based on model simulations.[1] Each model simulation has a different guess at processes that scientist don't understand sufficiently well. Few of the simulations result in less than 2 °C of warming or significantly more than 4 °C.[1] This pattern, which is also found in other studies,[2] suggests that if carbon dioxide concentrations double, the probability of very large increases in temperature is greater than the probability of very small increases.[1]

Climate sensitivity is the globally averaged temperature change in response to changes in radiative forcing, which can occur, for instance, due to increased levels of carbon dioxide (CO
2
).[3] Although the term climate sensitivity is usually used in the context of radiative forcing by CO2, it is thought of as a general property of the climate system: the change in surface air temperature following a unit change in radiative forcing, and the climate sensitivity parameter[note 1] is therefore 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); which is true approximately.[4] When climate sensitivity is expressed for a doubling of CO2, its units are degrees Celsius (°C).

In the context of global warming, different measures of climate sensitivity are used. The so-called equilibrium climate sensitivity (ECS) denotes the temperature increase in °C that would result from sustained doubling of the concentration of carbon dioxide in Earth's atmosphere relative to that of the initial state, after the climate system had reached a new steady state called equilibrium.[5] The transient climate response (TCR) is the amount of temperature increase that might occur at the time when CO2 doubles, having increased gradually by 1% each year (compounded). The earth system sensitivity (ESS) includes the effects of very-long-term Earth system feedback loops, such as changes in ice sheets or changes in the distribution of vegetative cover.[6]

Climate sensitivity is typically estimated in three ways; by using observations taken during the industrial age, by using temperature and other data from the Earth's past and by modelling the physical equations of the climate system in computers.[6] For coupled atmosphere-ocean global climate models the climate sensitivity is an emergent property; rather than being a model parameter it is a result of a combination of model physics and parameters. By contrast, simpler energy-balance models may have climate sensitivity as an explicit parameter.

## Different forms of climate sensitivity

Schematic of how different measures of climate sensitivity relate to one another

A component of climate sensitivity is directly due to radiative forcing, for instance by CO
2
, and a further contribution arises from climate feedback, both positive and negative. Without feedbacks, radiative forcing from doubling CO
2
(which equals approximately 3.7 W/m2) from the pre-industrial 280 ppm would eventually result in roughly 1 °C global warming. This is easy to calculate[note 2][7] and undisputed.[8] 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.[8] Due to climate inertia, the climate sensitivity depends upon the timescale in which one is interested. The transient response is defined by scientists as the temperature response over human time scales of around 70 years, the equilibrium climate sensitivity over centuries, and finally the Earth system sensitivity after multiple millennia.[9]

### Equilibrium 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 CO
2
concentration (ΔT). A comprehensive model estimate of equilibrium sensitivity requires a very long model integration; fully equilibrating ocean temperatures requires the integration of thousands of model years, although it is possible to produce an estimate more quickly using the method of Gregory et al. (2004).[10] As estimated by the IPCC Fifth Assessment Report (AR5), "there is high confidence that ECS is extremely unlikely less than 1°C and medium confidence that the ECS is likely between 1.5°C and 4.5°C and very unlikely greater than 6°C".[11]

#### Effective climate sensitivity

The effective climate sensitivity is an estimate of equilibrium climate sensitivity using data from a climate system, either in a model or real-world observations, that is not yet in equilibrium.[12] Estimation is done by using the assumption that the net effect of feedbacks as measured after a period of warming remains constant afterwards.[13] This is not necessarily true, as feedbacks can change with time, or with the particular starting state or forcing history of the climate system.[14][12]

### Transient climate response

The transient climate response (TCR) is defined as the average temperature response over a twenty-year period centered at CO
2
doubling in a transient simulation with CO
2
increasing at 1% per year (compounded), i.e., 60 to 80 years following initiation of the increase in CO
2
.[15] The transient response is lower than the equilibrium sensitivity because the deep ocean, which takes many centuries to reach a new steady state after a perturbation, continues to serve as a sink for heat from the upper ocean.[16] The IPCC literature assessment estimates that TCR likely lies between 1 °C and 2.5 °C.[17] A related concept is the transient climate response to cumulative carbon emissions, which is the globally averaged surface temperature change per unit of CO
2
emitted.[18]

### Earth system sensitivity

The Earth system sensitivity (ESS) includes the effects of slower feedback loops, such as the change in Earth's albedo from the melting of large ice sheets that covered much of the northern hemisphere during the last glacial maximum. These extra feedback loops make the ESS larger than the ECS – possibly twice as large. Data from Earth's history is used to estimate ESS, but climatic conditions were quite different which makes it difficult to infer information for future ESS.[19] ESS includes the entire system except the carbon cycle.[20] Changes in albedo as a result of vegetation changes are included.[21]

Radiative forcing is the imbalance between incoming and outgoing radiation at the top of the atmosphere resulting from a change in atmospheric composition or other changes in radiation budget prior to long-term changes in global temperature resulting from forcing.[22] A number of inputs can give rise to radiative forcing; the extra downwelling radiation due to the greenhouse effect, solar radiation variability due to orbital changes, changes in solar irradiance, direct aerosol effects – for example changes in albedo due to cloud cover – indirect aerosol effects, and changes in land use.[23]

Radiative forcing as a consequence of greenhouse gases is well understood while, as of 2013, large uncertainties remain for aerosols.[24] In time-dependent estimates of climate sensitivity, the concept of the effective radiative forcing, which includes rapid adjustments in the stratosphere and the troposphere to the instantaneous radiative forcing, is usually used.[25]

## Sensitivity to nature of the forcing

Radiative forcing from sources other than CO
2
can cause a higher or lower surface warming than a similar radiative forcing due to CO
2
; the amount of feedback varies, mainly because these forcings are not uniformly distributed over the globe. Forcings that initially warm the northern hemisphere, land, or polar regions more strongly; are systematically more effective at changing temperatures than an equivalent amount of CO2 whose forcing is more uniformly distributed over the globe. Several studies indicate that aerosols are more effective than CO
2
at changing global temperatures while volcanic forcing is less effective.[26] Ignoring these factors causes lower estimates of climate sensitivity when using radiative forcing and temperature records from the historical period.[27]

## State dependence

While climate sensitivity is defined as the sensitivity to any doubling of CO
2
, there is evidence that the sensitivity of the climate system is not always constant. In the absence of sea ice, for instance, a positive ice-albedo feedback loop is lost, making the system less sensitive overall.[28] Because of this, the climate system may warm by a different amount after a first doubling of CO
2
than after a second doubling. The effect of this is small or negligible in the first century after CO
2
is released into the atmosphere.[28] Furthermore, climate sensitivity may change if tipping points are crossed. It is unlikely that climate sensitivity increases instantly; rather, it changes at the time scale of the subsystem that is undergoing the tipping point.[29]

## Estimating climate sensitivity

Climate sensitivity is often evaluated in terms of the change in equilibrium temperature due to radiative forcing caused by the greenhouse effect. The radiative forcing, and hence the change in temperature, is proportional to the logarithm of the concentration of infrared-absorbing ("greenhouse") gases in the atmosphere, as quantified by Arrhenius in the 19th century.[30] The sensitivity of temperature to atmospheric gasses, most notably CO
2
, is often expressed in terms of the change in temperature per doubling of the concentration of the gas.

### Historical estimates

Svante Arrhenius was the first person to quantify global warming as a consequence of a doubling of CO
2
. In his first paper on the matter, he estimated that global temperature would rise by around 5 to 6 °C (9.0 to 10.8 °F) if the quantity of CO
2
was doubled. In later work he revised this estimate to 4 °C (7.2 °F).[31] Arrhenius used the observations of radiation emitted by the full moon made by the astronomer Samuel Pierpont Langley to estimate the amount of radiation that was absorbed by water vapour and CO
2
. He then assumed relative humidity would stay the same under global warming as a representation of the water vapour feedback.[32][33]

A committee on anthropogenic global warming convened in 1979 by the National Academy of Sciences and chaired by Jule Charney[34] estimated climate sensitivity to be 3 °C (5.4 °F) with a tolerance of 1.5 °C (2.7 °F). Only two sets of models were available; one, due to Syukuro Manabe, showed a climate sensitivity of 2 °C (3.6 °F) and the other, due to James E. Hansen, showed a climate sensitivity of 4 °C (7.2 °F). According to Manabe, "Charney chose 0.5 °C (0.90 °F) as a reasonable margin of error, subtracted it from Manabe's number, and added it to Hansen's, giving rise to the 1.5 to 4.5 °C (2.7 to 8.1 °F) range of likely climate sensitivity that has appeared in every greenhouse assessment since ..."[35]

In 2008 climatologist Stefan Rahmstorf wrote, regarding the Charney report's original range of uncertainty; "At that time, this range was on very shaky ground. Since then, many vastly improved models have been developed by a number of climate research centers around the world. Current state-of-the-art climate models span a range of 2.6 to 4.1 °C (4.7 to 7.4 °F), most clustering around 3 °C (5.4 °F)."[8]

#### Intergovernmental Panel on Climate Change

Historical estimates of climate sensitivity from the IPCC assessments. The first three reports gave a qualitative likely range, while the fourth and fifth assessment report formally quantified the uncertainty. The dark blue range is judged as being more than 66% likely.[36][37]

After the publication of the Charney report, despite considerable progress in the understanding of the climate system, further assessments reported a similar range in climate sensitivity.[38] The 1990 IPCC First Assessment Report estimated that equilibrium climate sensitivity to a doubling of CO
2
lay between 1.5 and 4.5 °C (2.7 and 8.1 °F), with a "best guess in the light of current knowledge" of 2.5 °C (4.5 °F).[39] This report used models that had simplified representations of ocean dynamics. The IPCC supplementary report, 1992, which used full-ocean GCMs, saw "no compelling reason to warrant changing" from this estimate;[40] and the IPCC Second Assessment Report said, "No strong reasons have emerged to change" these estimates.[41] In these reports, much of the uncertainty was attributed to cloud processes. The 2001 IPCC TAR also retained this likely range.[42]

Authors of the IPCC Fourth Assessment Report[36] stated that confidence in estimates of equilibrium climate sensitivity had increased substantially since the Third Annual Report.[43] IPCC authors concluded ECS is very likely to be greater than 1.5 °C (2.7 °F) and likely to lie in the range 2 to 4.5 °C (4 to 8.1 °F), with a most likely value of about 3 °C (5 °F). For fundamental physical reasons and data limitations, the IPCC stated a climate sensitivity higher than 4.5 °C (8.1 °F) cannot be ruled out but that agreement for these values with observations and "proxy" climate data is generally worse compared with values within the likely range.[43]

The IPCC Fifth Assessment Report reverted to the earlier range of 1.5 to 4.5 °C (2.7 to 8.1 °F) (high confidence) because some estimates using industrial-age data came out low.[6] They also stated that ECS is extremely unlikely to be less than 1 °C (1.8 °F) (high confidence), and is very unlikely to be greater than 6 °C (11 °F) (medium confidence). These values are estimated by combining the available data with expert judgement.[37]

### Using industrial-age data

Climate sensitivity can be estimated using observed temperature rise, observed ocean heat uptake, and modeled or observed radiative forcing. These data are linked though a simple energy-balance model to calculate climate sensitivity.[44] Radiative forcing is often modeled, because satellites that measure it have not existed for the entire period. Estimates of climate sensitivity calculated from global energy constraints have consistently been lower than those calculated using other methods;[45] estimates calculated using other methods have been around 2 °C (3.6 °F) or lower (e.g.[44][46][47][48][49]).

Estimates of transient climate response (TCR) calculated from models and observational data can be reconciled if it is taken into account that fewer temperature measurements are taken in the polar regions, which warm more quickly than average. If only regions for which measurements are available are used in evaluating the model, differences in TCR estimates almost disappear.[6][50]

Rahmstorf (2008)[8] provides an informal example of the estimation of climate sensitivity using observations made since the pre-industrial era, 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 CO
2
(${\textstyle F_{2\times CO_{2}}}$ ; taken as 3.7 W/m2), as S °C. If Earth was to experience an equilibrium temperature change of ${\displaystyle \Delta T}$ (°C) due to a sustained forcing of ${\displaystyle \Delta F}$ (W/m2), then:

${\displaystyle S=\Delta T*F_{2\times CO_{2}}/\Delta F}$

The global temperature increase since the beginning of the industrial period (taken as 1750) is about 0.8 °C (1.4 °F), and the radiative forcing due to CO
2
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 (2.0 °F). However, ${\displaystyle \Delta F}$  also contains contributions from solar activity (+0.3 W/m2), aerosols (−1 W/m2), ozone (0.3 W/m2), and other smaller influences, bringing the total forcing over the industrial period to 1.6 W/m2 according to the best estimate of the IPCC AR4, with substantial uncertainty. The absence of equilibrium of the climate system must be accounted for by subtracting the planetary heat uptake rate H from the forcing; i.e.,

${\displaystyle S=\Delta T*F_{2\times CO_{2}}/(\Delta F-H).}$

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 S of 2.1 °C (3.8 °F).

#### Other strategies

The industrial-age temperatures can also be used to determine a timescale of the climate system, which is theoretically linked to climate sensitivity.[51] If the effective heat capacity of the climate system is known and the timescale estimated by using the autocorrelation of the measured temperature, an estimate of climate sensitivity can be derived. Determination of both the timescale and heat capacity has proven difficult.[52][53][54]

Attempts to use the 11-year solar cycle to constrain the transient climate response have been made.[55] Solar irradiance is about 0.9 W/m2 brighter during solar maximum than during solar minimum, which correlated with a variation of ±0.1 °C (0.18 °F) in measured average global temperature between the peak and minimum over the period 1959-2004.[56] The solar minima in this period coincided with volcanic eruptions, which have a cooling effect on the global temperature. Because this causes a larger radiative forcing than the solar variations, it is questionable whether much information can be derived from the temperature variations.[57]

### Using data from Earth's past

Climate sensitivity can be estimated by using reconstructions of Earth's past temperatures and CO
2
levels. Different geological periods, for instance the warm Pliocene and the colder Pleistocene, are studied.[58] Scientist seek periods that are in some sense analogous or informative to current climate change. As more information about the recent past becomes available, recent periods such as the Mid-holocene that occurred about 6,000 years ago and the Last Glacial Maximum (LGM) that took place about 21,000 years ago are often chosen.[59]

The LGM was a period with a significantly lower global mean temperature than present day, and with a relatively well-known CO
2
concentration and radiative forcing in general.[60] While orbital forcing was different from the present, this had little effect on mean annual temperatures.[61] Different approaches to the task of estimating climate sensitivity from the LGM are taken.[60] One approach is using estimates of global radiative forcing and temperature directly. The set of feedbacks active during the LGM, however, may be different than the feedbacks due to doubling CO
2
, introducing additional uncertainty.[61][62] In a different approach, a single model of intermediate complexity is run using a set of parameters so that each version has a different ECS. Those model versions that can best simulate the cooling during the LGM are thought to have the best ECS values.[63] Others use an ensemble of different models.[64][60]

Over the last 800,000 years, climate sensitivity has been found to be larger in cold periods than in warm periods.[65] Climates further back in Earth's history are also used; an additional difficulty is that CO
2
concentrations cannot be readily obtained from ice cores so they must be estimated less directly. An estimate made using data from a major part of the Phanerozoic is consistent with sensitivities of current climate models and with other determinations.[66] The Paleocene–Eocene Thermal Maximum provides a good opportunity to study the climate system when it is in a warm state.[67]

### Using climate models

Climate models of earth, for example the Coupled model intercomparison project (CMIP), are used to simulate the quantity of warming that will occur with rising CO
2
concentrations. The models are based on physical laws and represent the biosphere. Because of limited computer power, the physical laws have to be approximated, which leads to a wide range of estimates of climate sensitivity. Because the physical laws are programmed in a bottom-up way, climate sensitivity is an emergent property of these models.[6]

#### Constrained models

Bottom-up modelling of the climate system can lead to a wide range of outcomes. Models are often run using different plausible parameters in their approximation of physical laws and the behaviour of the biosphere; a so-called perturbed physics ensemble. Alternatively, structurally different models developed at different institutions are put together, creating an ensemble. By selecting only those simulations that can simulate some part of the historical climate well, a constrained estimate of climate sensitivity can be made. One strategy is the placing of more trust in climate models that perform well in general.[68]

Alternatively, specific metrics that are directly and physically linked to climate sensitivity are sought; examples of this are the global patterns of warming,[69] the ability of the models to reproduce observed relative humidity in the tropics and sub-tropics,[70] patterns of radiation,[71] and the variability of temperature about long term historical warming.[72][73][74] When using ensemble climate models developed in different institutions, many of these constrained estimates of ECS are slightly higher than 3 °C (5.4 °F); the models with ECS slightly above 3 °C (5.4 °F) perform better in these metrics than models with a low climate sensitivity.[75]

As of 2019 many CMIP phase 6 (CMIP6) models are being developed for the United Nations's next major assessment of global warming, due in 2021: some show climate sensitivity around 5 °C (9.0 °F), however the CMIP6 models have yet to be thoroughly independently analysed and researchers do not yet understand why some show this higher sensitivity.[76]

## Economics

Because the economics of climate change mitigation depend a lot on how quickly carbon neutrality needs to be achieved, climate sensitivity is very important economically: one study suggests that halving the uncertainty of the transient climate response could save trillions of dollars.[77]

## References

Notes

1. ^ Here the IPCC definition is used. In some other sources, the climate sensitivity parameter is simply called the climate sensitivity. The inverse of this parameter, is called the climate feedback parameter and is expressed in (W/m2)/°C.
2. ^ This calculation goes as follows. In equilibrium, the energy of incoming and outgoing radiation have to balance. The outgoing radiation ${\displaystyle F}$  is given by the Stefan-Boltzmann law: ${\displaystyle F=-\sigma T^{4}}$ . When incoming radiation increases, the outgoing radiation, and therefore temperature has to increase as well. The temperature rise ${\displaystyle \Delta T_{2\times CO_{2}}}$  for the additional radiative forcing ${\displaystyle \Delta F_{2\times CO_{2}}}$  due to doubling of CO2 is then given by
${\displaystyle \Delta F_{2\times CO_{2}}={\frac {dF}{dT}}\Delta T_{2\times CO_{2}}=4\sigma T^{3}\Delta T_{2\times CO_{2}}}$ .
Given an effective temperature of 255 K, a constant lapse rate, the value of the Stefan-Boltzmann constant ${\displaystyle \sigma }$  of 5.67 ${\displaystyle \times 10^{-8}}$ W/m2 K-4 and ${\displaystyle F_{2\times CO_{2}}}$ around 4 W/m2, this gives a climate sensitivity of a world without feedbacks of approximately 1 K.

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