The rate at which energy reaches Earth as sunlight and leaves Earth as heat radiation to space must balance, or the total amount of heat energy on the planet at any one time will rise or fall, which results in a planet that is warmer or cooler overall. A driver of an imbalance between the rates of incoming and outgoing radiation energy is called radiative forcing. A warmer planet radiates heat to space faster and so a new balance is eventually reached, with a higher temperature and stored energy content. However, the warming of the planet also has knock-on effects, which create further warming in an exacerbating feedback loop. Climate sensitivity is a measure of how much temperature change a given amount of radiative forcing will cause.
Radiative forcing leads to long-term changes in global temperature. A number of factors contribute radiative forcing: increased downwelling radiation from the greenhouse effect, variability in solar radiation from changes in planetary orbit, changes in solar irradiance, direct and indirect effects caused by aerosols (for example changes in albedo from cloud cover), and changes in land use (deforestation or the loss of reflective ice cover). In contemporary research, radiative forcing by greenhouse gases is well understood. As of 2019[update], large uncertainties remain for aerosols.
The radiative forcing caused by a doubling of atmospheric CO2 levels (from the pre-industrial 280 ppm) is approximately 3.7 watts per square meter (W/m2). In the absence of feedbacks, the energy imbalance would eventually result in roughly 1 °C (1.8 °F) of global warming. That figure is straightforward to calculate by using the Stefan–Boltzmann law and is undisputed.
Depending on the time scale, there are two main ways to define climate sensitivity: the short-term transient climate response (TCR) and the long-term equilibrium climate sensitivity (ECS), both of which incorporate the warming from exacerbating feedback loops. They are not discrete categories, but they overlap. Sensitivity to atmospheric CO2 increases is measured in the amount of temperature change for doubling in the atmospheric CO2 concentration.
Although the term "climate sensitivity" is usually used for the sensitivity to radiative forcing caused by rising atmospheric CO2, it is a general property of the climate system. Other agents can also cause a radiative imbalance. Climate sensitivity is the change in surface air temperature per unit change in radiative forcing, and the climate sensitivity parameter is therefore expressed in units of °C/(W/m2). Climate sensitivity is approximately the same whatever the reason for the radiative forcing (such as from greenhouse gases or solar variation). When climate sensitivity is expressed as the temperature change for a level of atmospheric CO2 double the pre-industrial level, its units are degrees Celsius (°C).
The transient climate response (TCR) is defined as "the change in the global mean surface temperature, averaged over a 20-year period, centered at the time of atmospheric carbon dioxide doubling, in a climate model simulation" in which the atmospheric CO2 concentration increases at 1% per year. That estimate is generated by using shorter-term simulations. The transient response is lower than the equilibrium climate sensitivity because slower feedbacks, which exacerbate the temperature increase, take more time to respond in full to an increase in the atmospheric CO2 concentration. For instance, the deep ocean takes many centuries to reach a new steady state after a perturbation during which it continues to serve as heatsink, which cools the upper ocean. The IPCC literature assessment estimates that the TCR likely lies between 1 °C (1.8 °F) and 2.5 °C (4.5 °F).
The equilibrium climate sensitivity (ECS) is the long-term temperature rise (equilibrium global mean near-surface air temperature) that is expected to result from a doubling of the atmospheric CO2 concentration (ΔT2×). It is a prediction of the new global mean near-surface air temperature once the CO2 concentration has stopped increasing, and most of the feedbacks have had time to have their full effect. Reaching an equilibrium temperature can take centuries or even millennia after CO2 has doubled. ECS is higher than TCR because of the oceans' short-term buffering effects. Computer models are used for estimating the ECS. A comprehensive estimate means that modelling the whole time span during which significant feedbacks continue to change global temperatures in the model, such as fully-equilibrating ocean temperatures, requires running a computer model that covers thousands of years. There are, however, less computing-intensive methods.
The long time scales involved with ECS make it arguably a less relevant measure for policy decisions around climate change.
A common approximation to ECS is the effective equilibrium climate sensitivity, is an estimate of equilibrium climate sensitivity by using data from a climate system in model or real-world observations that is not yet in equilibrium. Estimates assume that the net amplification effect of feedbacks, as measured after some period of warming, will remain constant afterwards. That is not necessarily true, as feedbacks can change with time. In many climate models, feedbacks become stronger over time and so the effective climate sensitivity is lower than the real ECS.
By definition, equilibrium climate sensitivity does not include feedbacks that take millennia to emerge, such as long-term changes in Earth's albedo because of changes in ice sheets and vegetation. It includes the slow response of the deep oceans' warming, which also takes millennia, and so ECS fails to reflect the actual future warming that would occur if CO2 is stabilized at double pre-industrial values. Earth system sensitivity (ESS) incorporates the effects of these slower feedback loops, such as the change in Earth's albedo from the melting of large continental ice sheets, which covered much of the Northern Hemisphere during the Last Glacial Maximum and still cover Greenland and Antarctica). Changes in albedo as a result of changes in vegetation, as well as changes in ocean circulation, are also included. The longer-term feedback loops make the ESS larger than the ECS, possibly twice as large. Data from the geological history of Earth is used in estimating ESS. Differences between modern and long-ago climatic conditions mean that estimates of the future ESS are highly uncertain. Unlike ECS and TCR, the carbon cycle is not included in the definition of the ESS, but all other elements of the climate system are included.
Different forcing agents, such as greenhouse gases and aerosols, can be compared using their radiative forcing, the initial radiative imbalance averaged over the entire globe. Climate sensitivity is the amount of warming per radiative forcing. To a first approximation, the cause of the radiative imbalance does not matter whether it is greenhouse gases or something else. However, radiative forcing from sources other than CO2 can cause a somewhat larger or smaller surface warming than a similar radiative forcing from CO2. The amount of feedback varies mainly because the forcings are not uniformly distributed over the globe. Forcings that initially warm the Northern Hemisphere, land, or polar regions are more strongly systematically effective at changing temperatures than an equivalent forcing from CO2, which is more uniformly distributed over the globe. That is because those regions have more self-reinforcing feedbacks, such as the ice–albedo feedback. Several studies indicate that human-emitted aerosols are more effective than CO2 at changing global temperatures, and volcanic forcing is less effective. When climate sensitivity to CO2 forcing is estimated by using historical temperature and forcing (caused by a mix of aerosols and greenhouse gases), and that effect is not taken into account, climate sensitivity is underestimated.
Climate sensitivity has been defined as the short- or long-term temperature change resulting from any doubling of CO2, but there is evidence that the sensitivity of Earth's climate system is not constant. For instance, the planet has polar ice and high-altitude glaciers. Until the world's ice has completely melted, an exacerbating ice–albedo feedback loop makes the system more sensitive overall. Throughout Earth's history, multiple periods are thought to have snow and ice cover almost the entire globe. In most models of "Snowball Earth", parts of the tropics were at least intermittently free of ice cover. As the ice advanced or retreated, climate sensitivity must have been very high, as the large changes in area of ice cover would have made for a very strong ice–albedo feedback. Volcanic atmospheric composition changes are thought to have provided the radiative forcing needed to escape the snowball state.
Climate sensitivity may further change if tipping points are crossed. It is unlikely that tipping points will cause short-term changes in climate sensitivity. If a tipping point is crossed, climate sensitivity is expected to change at the time scale of the subsystem that hits its tipping point. Especially if there are multiple interacting tipping points, the transition of climate to a new state may be difficult to reverse.
The two most common definitions of climate sensitivity specify the climate state: the ECS and the TCR are defined for a doubling with respect to the CO2 levels in the pre-industrial era. Because of potential changes in climate sensitivity, the climate system may warm by a different amount after a second doubling of CO2 from after a first doubling. The effect of any change in climate sensitivity is expected to be small or negligible in the first century after additional CO2 is released into the atmosphere.
Climate sensitivity can be estimated using the observed temperature increase, the observed ocean heat uptake, and the modelled or observed radiative forcing. The data are linked through a simple energy-balance model to calculate climate sensitivity. Radiative forcing is often modelled because Earth observation satellites measuring it has existed during only part of the Industrial Age (only since the late 1950s). Estimates of climate sensitivity calculated by using these global energy constraints have consistently been lower than those calculated by using other methods, around 2 °C (3.6 °F) or lower.
Estimates of transient climate response (TCR) that have been 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 the Earth as a whole. If only regions for which measurements are available are used in evaluating the model, the differences in TCR estimates are negligible.
A very simple climate model could estimate climate sensitivity from Industrial Age data by waiting for the climate system to reach equilibrium and then by measuring the resulting warming, ΔTeq (°C). Computation of the equilibrium climate sensitivity, S (°C), using the radiative forcing ΔF (W/m2) and the measured temperature rise, would then be possible. The radiative forcing resulting from a doubling of CO2, F2
×
{\displaystyle \times }
CO2, is relatively well known, at about 3.7 W/m2. Combining that information results in this equation:
S
=
Δ
T
e
q
×
F
2
×
C
O
2
/
Δ
F
{\displaystyle S=\Delta T_{eq}\times F_{2\times CO_{2}}/\Delta F}
.
However, the climate system is not in equilibrium since the actual warming lags the equilibrium warming, largely because the oceans take up heat and will take centuries or millennia to reach equilibrium. Estimating climate sensitivity from Industrial Age data requires an adjustment to the equation above. The actual forcing felt by the atmosphere is the radiative forcing minus the ocean's heat uptake, H (W/m2) and so climate sensitivity can be estimated:
S
=
Δ
T
×
F
2
×
C
O
2
/
(
Δ
F
−
H
)
.
{\displaystyle S=\Delta T\times F_{2\times CO_{2}}/(\Delta F-H).}
The global temperature increase between the beginning of the Industrial Period, which is (taken as 1750, and 2011 was about 0.85 °C (1.53 °F). In 2011, the radiative forcing from CO2 and other long-lived greenhouse gases (mainly methane, nitrous oxide, and chlorofluorocarbon) that have been emitted since the 18th century was roughly 2.8 W/m2. The climate forcing, ΔF, also contains contributions from solar activity (+0.05 W/m2), aerosols (−0.9 W/m2), ozone (+0.35 W/m2), and other smaller influences, which brings the total forcing over the Industrial Period to 2.2 W/m2, according to the best estimate of the IPCC Fifth Assessment Report in 2014, with substantial uncertainty. The ocean heat uptake, estimated by the same report to be 0.42 W/m2, yields a value for S of 1.8 °C (3.2 °F).
In theory, Industrial Age temperatures could also be used to determine a time scale for the temperature response of the climate system and thus climate sensitivity: if the effective heat capacity of the climate system is known, and the timescale is estimated using autocorrelation of the measured temperature, an estimate of climate sensitivity can be derived. In practice, however, the simultaneous determination of the time scale and heat capacity is difficult.
Observations of volcanic eruptions have also been used to try to estimate climate sensitivity, but as the aerosols from a single eruption last at most a couple of years in the atmosphere, the climate system can never come close to equilibrium, and there is less cooling than there would be if the aerosols stayed in the atmosphere for longer. Therefore, volcanic eruptions give information only about a lower bound on transient climate sensitivity.
A 2007 estimate of sensitivity made using data from the most recent 420 million years is consistent with sensitivities of current climate models and with other determinations. The Paleocene–Eocene Thermal Maximum (about 55.5 million years ago), a 20,000-year period during which massive amount of carbon entered the atmosphere and average global temperatures increased by approximately 6 °C (11 °F), also provides a good opportunity to study the climate system when it was in a warm state. Studies of the last 800,000 years have concluded that climate sensitivity was greater in glacial periods than in interglacial periods.
As the name suggests, the Last Glacial Maximum was much colder than today, and good data on atmospheric CO2 concentrations and radiative forcing from that period are available. The period's orbital forcing was different from today's but had little effect on mean annual temperatures. Estimating climate sensitivity from the Last Glacial Maximum can be done by several different ways. One way is to use estimates of global radiative forcing and temperature directly. The set of feedback mechanisms active during the period, however, may be different from the feedbacks caused by a present doubling of CO2, which introduces additional uncertainty. In a different approach, a model of intermediate complexity is used to simulate conditions during the period. Several versions of this single model are run, with different values chosen for uncertain parameters, such that each version has a different ECS. Outcomes that best simulate the LGM's observed cooling probably produce the most realistic ECS values.
To estimate climate sensitivity, a model is run by using a variety of radiative forcings (doubling quickly, doubling gradually, or following historical emissions) and the temperature results are compared to the forcing applied. Different models give different estimates of climate sensitivity, but they tend to fall within a similar range, as described above.
Modelling of the climate system can lead to a wide range of outcomes. Models are often run that use different plausible parameters in their approximation of physical laws and the behaviour of the biosphere, which forms a perturbed physics ensemble, which attempts to model the sensitivity of the climate to different types and amounts of change in each parameter. Alternatively, structurally-different models developed at different institutions are put together, creating an ensemble. By selecting only the simulations that can simulate some part of the historical climate well, a constrained estimate of climate sensitivity can be made. One strategy for obtaining more accurate results is placing more emphasis on climate models that perform well in general.
A model is tested using observations, paleoclimate data, or both to see if it replicates them accurately. If it does not, inaccuracies in the physical model and parametrizations are sought, and the model is modified. For models used to estimate climate sensitivity, specific test metrics that are directly and physically linked to climate sensitivity are sought. Examples of such metrics are the global patterns of warming, the ability of a model to reproduce observed relative humidity in the tropics and subtropics, patterns of heat radiation, and the variability of temperature around long-term historical warming. Ensemble climate models developed at different institutions tend to produce constrained estimates of ECS that are slightly higher than 3 °C (5.4 °F). The models with ECS slightly above 3 °C (5.4 °F) simulate the above situations better than models with a lower climate sensitivity.
Many projects and groups exist to compare and to analyse the results of multiple models. For instance, the Coupled Model Intercomparison Project (CMIP) has been running since the 1990s.
Remaining deficiencies in the simulation of clouds may have led to overestimates, as models with the highest ECS values were not consistent with observed warming. A fifth of the models began to 'run hot', predicting that global warming would produce significantly higher temperatures than is considered plausible. According to these models, known as hot models, average global temperatures in the worst-case scenario would rise by more than 5 °C above preindustrial levels by 2100, with a "catastrophic" impact on human society. In comparison, empirical observations combined with physics models indicate that the "very likely" range is between 2.3 and 4.7 °C. Models with a very high climate sensitivity are also known to be poor at reproducing known historical climate trends, such as warming over the 20th century or cooling during the last ice age. For these reasons the predictions of hot models are considered implausible, and have been given less weight by the IPCC in 2022.
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The calculation is as follows. In equilibrium, the energy of incoming and outgoing radiation have to balance. The outgoing radiation
F
{\displaystyle F}
is given by the Stefan–Boltzmann law:
F
=
−
σ
T
4
{\displaystyle F=-\sigma T^{4}}
. When incoming radiation increases, the outgoing radiation and therefore temperature must increase as well. The temperature rise
Δ
T
2
×
C
O
2
{\displaystyle \Delta T_{2\times CO_{2}}}
directly caused by the additional radiative forcing,
Δ
F
2
×
C
O
2
{\displaystyle \Delta F_{2\times CO_{2}}}
because of the doubling of CO2 is then given by
Δ
F
2
×
C
O
2
=
d
F
d
T
Δ
T
2
×
C
O
2
=
4
σ
T
3
Δ
T
2
×
C
O
2
{\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 (−18 °C; −1 °F), a constant lapse rate, the value of the Stefan–Boltzmann constant
σ
{\displaystyle \sigma }
of 5.67
×
10
−
8
{\displaystyle \times 10^{-8}}
W/m2 K−4 and
Δ
F
2
×
C
O
2
{\displaystyle \Delta F_{2\times CO_{2}}}
around 4 W/m2, the equation gives a climate sensitivity of a world without feedback of approximately 1 K. /wiki/Stefan%E2%80%93Boltzmann_law
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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.
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