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Climate sensitivity is a key measure in
climate science Climatology (from Greek , ''klima'', "slope"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. Climate concerns the atmospher ...
and describes how much Earth's surface will warm for a doubling in the atmospheric carbon dioxide () concentration. Its formal definition is: "The change in the surface temperature in response to a change in the atmospheric carbon dioxide (CO2) concentration or other radiative forcing."IPCC, 2021
Annex VII: Glossary
atthews, J.B.R., V. Möller, R. van Diemen, J.S. Fuglestvedt, V. Masson-Delmotte, C.  Méndez, S. Semenov, A. Reisinger (eds.) I
Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change
[Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 2215–2256, doi:10.1017/9781009157896.022.
This concept helps scientists understand the extent and magnitude of the
effects of climate change Effects of climate change are well documented and growing for Earth's natural environment and human societies. Changes to the climate system include an Instrumental temperature record, overall warming trend, Effects of climate change on the ...
. The Earth's surface warms as a direct consequence of increased atmospheric , as well as increased concentrations of other
greenhouse gases Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...
such as
nitrous oxide Nitrous oxide (dinitrogen oxide or dinitrogen monoxide), commonly known as laughing gas, nitrous, or factitious air, among others, is a chemical compound, an Nitrogen oxide, oxide of nitrogen with the Chemical formula, formula . At room te ...
and
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The abundance of methane on Earth makes ...
. The increasing temperatures have secondary effects on the
climate system Earth's climate system is a complex system with five interacting components: the Atmosphere of Earth, atmosphere (air), the hydrosphere (water), the cryosphere (ice and permafrost), the lithosphere (earth's upper rocky layer) and the biosphere ( ...
. These secondary effects are called climate feedbacks. Self-reinforcing feedbacks include for example the melting of sunlight-reflecting ice as well as higher
evapotranspiration Evapotranspiration (ET) refers to the combined processes which move water from the Earth's surface (open water and ice surfaces, bare soil and vegetation) into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of w ...
. The latter effect increases average atmospheric water vapour, which is itself a
greenhouse gas Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...
. Scientists do not know exactly how strong these climate feedbacks are. Therefore, it is difficult to predict the precise amount of warming that will result from a given increase in greenhouse gas concentrations. If climate sensitivity turns out to be on the high side of scientific estimates, the
Paris Agreement The Paris Agreement (also called the Paris Accords or Paris Climate Accords) is an international treaty on climate change that was signed in 2016. The treaty covers climate change mitigation, adaptation, and finance. The Paris Agreement was ...
goal of limiting
global warming Present-day climate change includes both global warming—the ongoing increase in global average temperature—and its wider effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes ...
to below will be even more difficult to achieve. There are two main kinds of climate sensitivity: the ''transient climate response'' is the initial rise in global temperature when levels double, and the ''equilibrium climate sensitivity'' is the larger long-term temperature increase after the planet adjusts to the doubling. Climate sensitivity is estimated by several methods: looking directly at
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
and greenhouse gas concentrations since the
Industrial Revolution The Industrial Revolution, sometimes divided into the First Industrial Revolution and Second Industrial Revolution, was a transitional period of the global economy toward more widespread, efficient and stable manufacturing processes, succee ...
began around the 1750s, using indirect measurements from the Earth's distant past, and simulating the climate.


Fundamentals

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 Radiative forcing (or climate forcing) is a concept used to quantify a change to the balance of energy flowing through a planetary atmosphere. Various factors contribute to this change in energy balance, such as concentrations of greenhouse gases ...
. 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

Radiative forcings are generally quantified as
Watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
s per square meter (W/m2) and averaged over Earth's uppermost surface defined as the top of the atmosphere. The magnitude of a forcing is specific to the physical driver and is defined ''relative to'' an accompanying time span of interest for its application. In the context of a contribution to long-term climate sensitivity from 1750 to 2020, the 50% increase in atmospheric is characterized by a forcing of about +2.1 W/m2. In the context of shorter-term contributions to Earth's energy imbalance (i.e. its heating/cooling rate), time intervals of interest may be as short as the interval between measurement or simulation data samplings, and are thus likely to be accompanied by smaller forcing values. Forcings from such investigations have also been analyzed and reported at decadal time scales. Radiative forcing leads to long-term changes in global temperature. A number of factors contribute radiative forcing: increased downwelling radiation from the
greenhouse effect The greenhouse effect occurs when greenhouse gases in a planet's atmosphere insulate the planet from losing heat to space, raising its surface temperature. Surface heating can happen from an internal heat source (as in the case of Jupiter) or ...
, 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 Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...
from cloud cover), and changes in land use (deforestation or the loss of reflective ice cover).''Climate Change: The IPCC Scientific Assessment'' (1990), Report prepared for Intergovernmental Panel on Climate Change by Working Group I, Houghton JT, Jenkins GT, Ephraums JJ (eds.)
chapter 2, Radiative Forcing of Climate
, pp. 41–68
In contemporary research, radiative forcing by greenhouse gases is well understood. , large uncertainties remain for aerosols.


Key numbers

Carbon dioxide Carbon dioxide is a chemical compound with the chemical formula . It is made up of molecules that each have one carbon atom covalent bond, covalently double bonded to two oxygen atoms. It is found in a gas state at room temperature and at norma ...
() levels rose from 280
parts per million In science and engineering, the parts-per notation is a set of pseudo-units to describe the small values of miscellaneous dimensionless quantity, dimensionless quantities, e.g. mole fraction or mass fraction (chemistry), mass fraction. Since t ...
(ppm) in the 18th century, when humans in the
Industrial Revolution The Industrial Revolution, sometimes divided into the First Industrial Revolution and Second Industrial Revolution, was a transitional period of the global economy toward more widespread, efficient and stable manufacturing processes, succee ...
started burning significant amounts of fossil fuel such as coal, to over 415 ppm by 2020. As is a
greenhouse gas Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...
, it hinders heat energy from leaving the Earth's atmosphere. In 2016, atmospheric levels had increased by 45% over preindustrial levels, and radiative forcing caused by increased was already more than 50% higher than in pre-industrial times because of non-linear effects.The level in 2016 was 403 ppm, which is less than 50% higher than the pre-industrial concentration of 278 ppm. However, because increased concentrations have a progressively-smaller warming effect, the Earth was already more than halfway to doubling of radiative forcing caused by . Between the 18th-century start of the Industrial Revolution and the year 2020, the Earth's temperature rose by a little over one degree Celsius (about two degrees Fahrenheit).


Societal importance

Because the economics of climate change mitigation depend greatly on how quickly
carbon neutrality Global net-zero emissions is reached when greenhouse gas emissions and removals due to human activities are in balance. It is often called simply net zero. ''Emissions'' can refer to all greenhouse gases or only carbon dioxide (). Reaching net ze ...
needs to be achieved, climate sensitivity estimates can have important economic and policy-making implications. One study suggests that halving the uncertainty of the value for transient climate response (TCR) could save trillions of dollars. A higher climate sensitivity would mean more dramatic increases in temperature, which makes it more prudent to take significant climate action. If climate sensitivity turns out to be on the high end of what scientists estimate, the
Paris Agreement The Paris Agreement (also called the Paris Accords or Paris Climate Accords) is an international treaty on climate change that was signed in 2016. The treaty covers climate change mitigation, adaptation, and finance. The Paris Agreement was ...
goal of limiting global warming to well below 2 °C cannot be achieved, and temperature increases will exceed that limit, at least temporarily. One study estimated that emissions cannot be reduced fast enough to meet the 2 °C goal if equilibrium climate sensitivity (the long-term measure) is higher than . The more sensitive the climate system is to changes in greenhouse gas concentrations, the more likely it is to have decades when temperatures are much higher or much lower than the longer-term average.


Factors that determine sensitivity

The radiative forcing caused by a doubling of atmospheric levels (from the pre-industrial 280 ppm) is approximately 3.7
watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
s per square meter (W/m2). In the absence of feedbacks, the energy imbalance would eventually result in roughly of
global warming Present-day climate change includes both global warming—the ongoing increase in global average temperature—and its wider effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes ...
. That figure is straightforward to calculate by using the
Stefan–Boltzmann law The Stefan–Boltzmann law, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...
The calculation is as follows. In equilibrium, the energy of incoming and outgoing radiation have to balance. The outgoing radiation F is given by the
Stefan–Boltzmann law The Stefan–Boltzmann law, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...
: F = -\sigma T^4. When incoming radiation increases, the outgoing radiation and therefore temperature must increase as well. The temperature rise \Delta T_ ''directly caused'' by the additional radiative forcing, \Delta F_ because of the doubling of is then given by :\Delta F_ = \frac \Delta T_ = 4 \sigma T^3 \Delta T_. Given an
effective temperature The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...
of , a constant lapse rate, the value of the Stefan–Boltzmann constant \sigma of 5.67 \times 10^W/m2 K−4 and \Delta F_around 4 W/m2, the equation gives a climate sensitivity of a world without feedback of approximately 1 K.
and is undisputed. A further contribution arises from climate feedbacks, both self-reinforcing and balancing. The uncertainty in climate sensitivity estimates is entirely from the modelling of feedbacks in the climate system, including water vapour feedback,
ice–albedo feedback Ice–albedo feedback is a climate change feedback, where a change in the area of ice caps, glaciers, and sea ice alters the albedo and surface temperature of a planet. Because ice is very reflective, it reflects far more solar energy back to spac ...
, cloud feedback, and lapse rate feedback. Balancing feedbacks tend to counteract warming by increasing the rate at which energy is radiated to space from a warmer planet. Exacerbating feedbacks increase warming; for example, higher temperatures can cause ice to melt, which reduces the ice area and the amount of sunlight the ice reflects, which in turn results in less heat energy being radiated back into space. Climate sensitivity depends on the balance between those feedbacks.


Types

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 increases is measured in the amount of temperature change for doubling in the atmospheric concentration. Although the term "climate sensitivity" is usually used for the sensitivity to radiative forcing caused by rising atmospheric , 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 parameterHere, 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. 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 Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. Unlike other gases, greenhouse gases absorb the radiations that a planet emits, resulting in the greenhouse effect. T ...
or solar variation). When climate sensitivity is expressed as the temperature change for a level of atmospheric double the pre-industrial level, its units are degrees Celsius (°C).


Transient climate response

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 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 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 and . A related measure is the transient climate response to cumulative carbon emissions (TCRE), which is the globally averaged surface temperature change after 1000 GtC of has been emitted. As such, it includes not only temperature feedbacks to forcing but also the
carbon cycle The carbon cycle is a part of the biogeochemical cycle where carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of Earth. Other major biogeochemical cycles include the nitrogen cycle and the water cycl ...
and carbon cycle feedbacks.


Equilibrium climate sensitivity

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 concentration (ΔT). It is a prediction of the new global mean near-surface air temperature once the 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 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
IPCC Sixth Assessment Report The Sixth Assessment Report (AR6) of the United Nations (UN) Intergovernmental Panel on Climate Change (IPCC) is the sixth in a series of reports which assess the available scientific information on climate change. Three Working Groups (WGI, II, ...
(''AR6'') stated that there is high confidence that ECS is within the range of 2.5 °C to 4 °C, with a best estimate of 3 °C. The long time scales involved with ECS make it arguably a less relevant measure for policy decisions around climate change.


Effective climate sensitivity

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.


Earth system sensitivity

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 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 Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...
from the melting of large continental ice sheets, which covered much of the Northern Hemisphere during the
Last Glacial Maximum The Last Glacial Maximum (LGM), also referred to as the Last Glacial Coldest Period, was the most recent time during the Last Glacial Period where ice sheets were at their greatest extent between 26,000 and 20,000 years ago. Ice sheets covered m ...
and still cover
Greenland Greenland is an autonomous territory in the Danish Realm, Kingdom of Denmark. It is by far the largest geographically of three constituent parts of the kingdom; the other two are metropolitan Denmark and the Faroe Islands. Citizens of Greenlan ...
and
Antarctica Antarctica () is Earth's southernmost and least-populated continent. Situated almost entirely south of the Antarctic Circle and surrounded by the Southern Ocean (also known as the Antarctic Ocean), it contains the geographic South Pole. ...
). 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 The carbon cycle is a part of the biogeochemical cycle where carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of Earth. Other major biogeochemical cycles include the nitrogen cycle and the water cycl ...
is not included in the definition of the ESS, but all other elements of the climate system are included.


Sensitivity to nature of forcing

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 can cause a somewhat larger or smaller surface warming than a similar radiative forcing from . 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 The polar regions, also called the frigid geographical zone, zones or polar zones, of Earth are Earth's polar ice caps, the regions of the planet that surround its geographical poles (the North Pole, North and South Poles), lying within the pol ...
are more strongly systematically effective at changing temperatures than an equivalent forcing from , 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 at changing global temperatures, and volcanic forcing is less effective. When climate sensitivity to 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.


State dependence

Climate sensitivity has been defined as the short- or long-term temperature change resulting from any doubling of , but there is evidence that the sensitivity of Earth's climate system is not constant. For instance, the planet has
polar ice A polar ice cap or polar cap is a high-latitude region of a planet, dwarf planet, or natural satellite that is covered in ice. There are no requirements with respect to size or composition for a body of ice to be termed a polar ice cap, nor a ...
and high-altitude
glaciers A glacier (; or ) is a persistent body of dense ice, a form of rock, that is constantly moving downhill under its own weight. A glacier forms where the accumulation of snow exceeds its ablation over many years, often centuries. It acquires ...
. Until the world's ice has completely melted, an exacerbating
ice–albedo feedback Ice–albedo feedback is a climate change feedback, where a change in the area of ice caps, glaciers, and sea ice alters the albedo and surface temperature of a planet. Because ice is very reflective, it reflects far more solar energy back to spac ...
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 Ice–albedo feedback is a climate change feedback, where a change in the area of ice caps, glaciers, and sea ice alters the albedo and surface temperature of a planet. Because ice is very reflective, it reflects far more solar energy back to spac ...
. Volcanic atmospheric composition changes are thought to have provided the radiative forcing needed to escape the snowball state. Throughout the Quaternary period (the most recent 2.58 million years), climate has oscillated between
glacial period A glacial period (alternatively glacial or glaciation) is an interval of time (thousands of years) within an ice age that is marked by colder temperatures and glacier advances. Interglacials, on the other hand, are periods of warmer climate betw ...
s, the most recent one being the
Last Glacial Maximum The Last Glacial Maximum (LGM), also referred to as the Last Glacial Coldest Period, was the most recent time during the Last Glacial Period where ice sheets were at their greatest extent between 26,000 and 20,000 years ago. Ice sheets covered m ...
, and interglacial periods, the most recent one being the current
Holocene The Holocene () is the current geologic time scale, geological epoch, beginning approximately 11,700 years ago. It follows the Last Glacial Period, which concluded with the Holocene glacial retreat. The Holocene and the preceding Pleistocene to ...
, but the period's climate sensitivity is difficult to determine. The
Paleocene–Eocene Thermal Maximum The Paleocene–Eocene thermal maximum (PETM), alternatively ”Eocene thermal maximum 1 (ETM1)“ and formerly known as the "Initial Eocene" or “Late Paleocene thermal maximum", was a geologically brief time interval characterized by a ...
, about 55.5 million years ago, was unusually warm and may have been characterized by above-average climate sensitivity. 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 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 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 is released into the atmosphere.


Estimation


Using Industrial Age (1750–present) data

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 satellite An Earth observation satellite or Earth remote sensing satellite is a satellite used or designed for Earth observation (EO) from orbit, including spy satellites and similar ones intended for non-military uses such as environmental monitoring, me ...
s 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 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, (°C). Computation of the equilibrium climate sensitivity, ''S'' (°C), using the radiative forcing (W/m2) and the measured temperature rise, would then be possible. The radiative forcing resulting from a doubling of , , is relatively well known, at about 3.7 W/m2. Combining that information results in this equation: :S = \Delta T_ \times F_ / \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, (W/m2) and so climate sensitivity can be estimated: :S = \Delta T \times F_/(\Delta F-H). The global temperature increase between the beginning of the Industrial Period, which is ( taken as 1750, and 2011 was about . In 2011, the radiative forcing from and other long-lived greenhouse gases (mainly
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The abundance of methane on Earth makes ...
,
nitrous oxide Nitrous oxide (dinitrogen oxide or dinitrogen monoxide), commonly known as laughing gas, nitrous, or factitious air, among others, is a chemical compound, an Nitrogen oxide, oxide of nitrogen with the Chemical formula, formula . At room te ...
, and
chlorofluorocarbon Chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) are fully or partly Halogenation, halogenated hydrocarbons that contain carbon (C), hydrogen (H), chlorine (Cl), and fluorine (F). They are produced as volatility (chemistry), volat ...
) that have been emitted since the 18th century was roughly 2.8 W/m2. The climate forcing, , 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 The Fifth Assessment Report (AR5) of the United Nations Intergovernmental Panel on Climate Change (IPCC) is the fifth in IPCC#Assessment reports, a series of such reports and was completed in 2014.IPCC (2014The IPCC's Fifth Assessment Report (A ...
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 .


Other strategies

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 Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is a ...
of the climate system is known, and the timescale is estimated using
autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at differe ...
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. Attempts have been made to use the 11-year
solar cycle The Solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a periodic 11-year change in the Sun's activity measured in terms of Modern Maximum, variations in the number of observed sunspots on the Sun ...
to constrain the transient climate response. Solar irradiance is about 0.9 W/m2 higher during a
solar maximum Solar maximum is the regular period of greatest solar activity during the Sun's 11-year solar cycle. During solar maximum, large numbers of sunspots appear, and the solar irradiance output grows by about 0.07%. On average, the solar cycle take ...
than during a solar minimum, and those effect can be observed in measured average global temperatures from 1959 to 2004. Unfortunately, the solar minima in the period coincided with volcanic eruptions, which have a cooling effect on the global temperature. Because the eruptions caused a larger and less well-quantified decrease in radiative forcing than the reduced solar irradiance, it is questionable whether useful quantitative conclusions can be derived from the observed temperature variations. 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.


Using data from Earth's past

Historical climate sensitivity can be estimated by using reconstructions of Earth's past temperatures and levels.
Paleoclimatologists Paleoclimatology ( British spelling, palaeoclimatology) is the scientific study of climates predating the invention of meteorological instruments, when no direct measurement data were available. As instrumental records only span a tiny part of ...
have studied different geological periods, such as the warm
Pliocene The Pliocene ( ; also Pleiocene) is the epoch (geology), epoch in the geologic time scale that extends from 5.33 to 2.58Pleistocene The Pleistocene ( ; referred to colloquially as the ''ice age, Ice Age'') is the geological epoch (geology), epoch that lasted from to 11,700 years ago, spanning the Earth's most recent period of repeated glaciations. Before a change was fin ...
(2.6 million to 11,700 years ago), and sought periods that are in some way analogous to or informative about current climate change. Climates further back in Earth's history are more difficult to study because fewer data are available about them. For instance, past concentrations can be derived from air trapped in ice cores, but , the oldest continuous ice core is less than one million years old. Recent periods, such as the
Last Glacial Maximum The Last Glacial Maximum (LGM), also referred to as the Last Glacial Coldest Period, was the most recent time during the Last Glacial Period where ice sheets were at their greatest extent between 26,000 and 20,000 years ago. Ice sheets covered m ...
(LGM) (about 21,000 years ago) and the Mid-Holocene (about 6,000 years ago), are often studied, especially when more information about them becomes available. 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 The Paleocene–Eocene thermal maximum (PETM), alternatively ”Eocene thermal maximum 1 (ETM1)“ and formerly known as the "Initial Eocene" or “Late Paleocene thermal maximum", was a geologically brief time interval characterized by a ...
(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 , 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 A glacial period (alternatively glacial or glaciation) is an interval of time (thousands of years) within an ice age that is marked by colder temperatures and glacier advances. Interglacials, on the other hand, are periods of warmer climate betw ...
than in interglacial periods. As the name suggests, the Last Glacial Maximum was much colder than today, and good data on atmospheric 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 , 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.


Using climate models

Climate model Numerical climate models (or climate system models) are mathematical models that can simulate the interactions of important drivers of climate. These drivers are the atmosphere, oceans, land surface and ice. Scientists use climate models to st ...
s simulate the -driven warming of the future as well as the past. They operate on principles similar to those underlying models that predict the weather, but they focus on longer-term processes. Climate models typically begin with a starting state and then apply physical laws and knowledge about biology to generate subsequent states. As with weather modelling, no computer has the power to model the complexity of the entire planet and so simplifications are used to reduce that complexity to something manageable. An important simplification divides Earth's atmosphere into model cells. For instance, the atmosphere might be divided into cubes of air ten or one hundred kilometers on a side. Each model cell is treated as if it were
homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
. Calculations for model cells are much faster than trying to simulate each molecule of air separately. A lower model resolution (large model cells and long time steps) takes less computing power but cannot simulate the atmosphere in as much detail. A model cannot simulate processes smaller than the model cells or shorter-term than a single time step. The effects of the smaller-scale and shorter-term processes must therefore be estimated by using other methods. Physical laws contained in the models may also be simplified to speed up calculations. The
biosphere The biosphere (), also called the ecosphere (), is the worldwide sum of all ecosystems. It can also be termed the zone of life on the Earth. The biosphere (which is technically a spherical shell) is virtually a closed system with regard to mat ...
must be included in climate models. The effects of the biosphere are estimated by using data on the average behaviour of the average plant assemblage of an area under the modelled conditions. Climate sensitivity is therefore an emergent property of these models. It is not prescribed, but it follows from the interaction of all the modelled processes. 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.


Testing, comparisons, and climate ensembles

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, Referred to by: 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 . The models with ECS slightly above 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 In climatology, the Coupled Model Intercomparison Project (CMIP) is a collaborative framework designed to improve knowledge of climate change. It was organized in 1995 by the Working Group on Coupled Modelling (WGCM) of the World Climate Research ...
(CMIP) has been running since the 1990s.


Historical estimates

Svante Arrhenius Svante August Arrhenius ( , ; 19 February 1859 – 2 October 1927) was a Swedish scientist. Originally a physicist, but often referred to as a chemist, Arrhenius was one of the founders of the science of physical chemistry. In 1903, he received ...
in the 19th century was the first person to quantify global warming as a consequence of a doubling of the concentration of . In his first paper on the matter, he estimated that global temperature would rise by around if the quantity of was doubled. In later work, he revised that estimate to . Arrhenius used Samuel Pierpont Langley's observations of radiation emitted by the full moon to estimate the amount of radiation that was absorbed by
water vapour Water vapor, water vapour, or aqueous vapor is the gaseous phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Water vapor ...
and by . To account for water vapour feedback, he assumed that
relative humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation (meteorology), precipitation, dew, or fog t ...
would stay the same under global warming. The first calculation of climate sensitivity that used detailed measurements of absorption spectra, as well as the first calculation to use a
computer A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
for
numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integr ...
of the radiative transfer through the atmosphere, was performed by Syukuro Manabe and Richard Wetherald in 1967. Assuming constant humidity, they computed an equilibrium climate sensitivity of 2.3 °C per doubling of , which they rounded to 2 °C, the value most often quoted from their work, in the abstract of the paper. The work has been called "arguably the greatest climate-science paper of all time" and "the most influential study of climate of all time." A committee on anthropogenic
global warming Present-day climate change includes both global warming—the ongoing increase in global average temperature—and its wider effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes ...
, convened in 1979 by the
United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
and chaired by Jule Charney, estimated equilibrium climate sensitivity to be , plus or minus . The Manabe and Wetherald estimate (), James E. Hansen's estimate of , and Charney's model were the only models available in 1979. According to Manabe, speaking in 2004, "Charney chose 0.5 °C as a reasonable margin of error, subtracted it from Manabe's number, and added it to Hansen's, giving rise to the range of likely climate sensitivity that has appeared in every greenhouse assessment since ...." In 2008, climatologist Stefan Rahmstorf said: "At that time t was published the harney report estimate'srange f uncertaintywas on very shaky ground. Since then, many vastly improved models have been developed by a number of climate research centers around the world."


Assessment reports of IPCC

Despite considerable progress in the understanding of Earth's
climate system Earth's climate system is a complex system with five interacting components: the Atmosphere of Earth, atmosphere (air), the hydrosphere (water), the cryosphere (ice and permafrost), the lithosphere (earth's upper rocky layer) and the biosphere ( ...
, assessments continued to report similar uncertainty ranges for climate sensitivity for some time after the 1979 Charney report. The First Assessment Report of the
Intergovernmental Panel on Climate Change The Intergovernmental Panel on Climate Change (IPCC) is an intergovernmental body of the United Nations. Its job is to "provide governments at all levels with scientific information that they can use to develop climate policies". The World Met ...
(IPCC), published in 1990, estimated that equilibrium climate sensitivity to a doubling of lay between , with a "best guess in the light of current knowledge" of . The report used models with simplified representations of ocean dynamics. The IPCC supplementary report, 1992, which used full-ocean circulation models, saw "no compelling reason to warrant changing" the 1990 estimate; and the IPCC Second Assessment Report stated, "No strong reasons have emerged to change hese estimates" In the reports, much of the uncertainty around climate sensitivity was attributed to insufficient knowledge of cloud processes. The 2001 IPCC Third Assessment Report also retained this likely range. Authors of the 2007 IPCC Fourth Assessment Report stated that confidence in estimates of equilibrium climate sensitivity had increased substantially since the Third Annual Report. The IPCC authors concluded that ECS is very likely to be greater than and likely to lie in the range , with a most likely value of about . The IPCC stated that fundamental physical reasons and data limitations prevent a climate sensitivity higher than from being ruled out, but the climate sensitivity estimates in the likely range agreed better with observations and the proxy climate data. The 2013
IPCC Fifth Assessment Report The Fifth Assessment Report (AR5) of the United Nations Intergovernmental Panel on Climate Change (IPCC) is the fifth in IPCC#Assessment reports, a series of such reports and was completed in 2014.IPCC (2014The IPCC's Fifth Assessment Report (A ...
reverted to the earlier range of (with high confidence), because some estimates using industrial-age data came out low. The report also stated that ECS is extremely unlikely to be less than (high confidence), and it is very unlikely to be greater than (medium confidence). Those values were estimated by combining the available data with expert judgement. In preparation for the 2021
IPCC Sixth Assessment Report The Sixth Assessment Report (AR6) of the United Nations (UN) Intergovernmental Panel on Climate Change (IPCC) is the sixth in a series of reports which assess the available scientific information on climate change. Three Working Groups (WGI, II, ...
, a new generation of climate models was developed by scientific groups around the world. Across 27 global climate models, estimates of a higher climate sensitivity were produced. The values spanned and exceeded in 10 of them. The estimates for equilibrium climate sensitivity changed from 3.2 °C to 3.7 °C and the estimates for the transient climate response from 1.8 °C, to 2.0 °C. The cause of the increased ECS lies mainly in improved modelling of clouds. Temperature rises are now believed to cause sharper decreases in the number of low clouds, and fewer low clouds means more sunlight is absorbed by the planet and less reflected to space. 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.


See also

* Climate risk * Charney Report


Notes


References


Sources

* (pb: ) * (pb: ). * ** ** *


External links


What is 'climate sensitivity'?
Met Office The Met Office, until November 2000 officially the Meteorological Office, is the United Kingdom's national weather and climate service. It is an executive agency and trading fund of the Department for Science, Innovation and Technology and ...

How scientists estimate 'climate sensitivity'
Carbon Brief {{DEFAULTSORT:Climate Sensitivity Climate change feedbacks Paleoclimatology