{{short description|Quantitative methods used to simulate climate}} {{about|the theories and mathematics of climate modeling|computer-driven prediction of Earth's climate|General circulation model}} {{Use dmy dates|date=November 2019}} {{broader|Atmospheric model|Oceanic model}} [[File:20250712 Climate model inputs and outputs.svg |thumb |upright=1.35 |Climate models apply knowledge in various [[Branches of science|sciences]] to process extensive sets of input climate data, executing [[differential equations]] among grid elements in a three-dimensional model of Earth's [[climate system]]. The models produce simulated climates having an array of climatic and weather elements, such as heatwaves and storms. Each element may be described by several attributes, including intensity, frequency, and impacts. Climate models support [[Climate change adaptation|adaptation]] to projected [[climate change]], and enable [[extreme event attribution]] to explain specific weather events.]] Numerical '''climate models''' (or '''climate system models''') are [[mathematical model]]s that can simulate the interactions of important drivers of [[climate]]. These drivers are the [[Earth's atmosphere|atmosphere]], [[ocean]]s, [[land surface]] and [[cryosphere|ice]]. Scientists use climate models to study the dynamics of the [[climate system]] and to make projections of future climate and of [[climate change]]. Climate models can also be qualitative (i.e. not numerical) models and contain narratives, largely descriptive, of possible futures.<ref>{{citation | author = IPCC | year = 2014 | title = AR5 Synthesis Report - Climate Change 2014. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change | page = 58 | url = https://www.ipcc.ch/site/assets/uploads/2018/02/SYR_AR5_FINAL_full.pdf#page=74 | quote = Box 2.3. ‘Models’ are typically numerical simulations of real-world systems, calibrated and validated using observations from experiments or analogies, and then run using input data representing future climate. Models can also include largely descriptive narratives of possible futures, such as those used in scenario construction. Quantitative and descriptive models are often used together. }}</ref>
Climate models take account of incoming [[energy]] from the Sun as well as outgoing energy from Earth. An imbalance results in a [[First law of thermodynamics|change in temperature]]. The incoming energy from the Sun is in the form of short wave [[electromagnetic radiation]], chiefly [[Visible spectrum|visible]] and short-wave (near) [[infrared]]. The outgoing energy is in the form of long wave (far) [[infrared]] electromagnetic energy. These processes are part of the [[greenhouse effect]].
Climate models vary in complexity. For example, a simple [[radiant heat]] transfer model treats the Earth as a single point and averages outgoing energy. This can be expanded vertically (radiative-convective models) and horizontally. More complex models are the coupled atmosphere–ocean–[[sea ice]] [[global climate model]]s. These types of models solve the full equations for mass transfer, [[energy transfer]] and radiant exchange. In addition, other types of models can be interlinked. For example [[Earth system model|Earth System Models]] include also [[land use]] as well as [[land use change]]s. This allows researchers to predict the interactions between climate and [[ecosystems]].
Climate models are systems of [[differential equation]]s based on the basic laws of [[physics]], [[Fluid dynamics|fluid motion]], and [[chemistry]]. Scientists divide the planet into a 3-dimensional grid and apply the basic equations to those grids. [[Atmospheric model]]s calculate [[winds]], [[heat transfer]], [[radiation]], [[relative humidity]], and surface [[hydrology]] within each grid and evaluate interactions with neighboring points. These are coupled with [[oceanic model]]s to simulate [[climate variability and change]] that occurs on different timescales due to shifting [[ocean current]]s and the much larger [[ocean heat content|heat storage capacity]] of the global ocean. [[climate forcing|External drivers]] of change may also be applied. Including an [[ice-sheet model]] better accounts for long term effects such as [[sea level rise]].
== Uses == [[File:Global Climate Model.png|thumb|right|350px|Climate models divide the planet into a 3-dimensional grid and apply [[differential equation]]s to each grid. Climate model equations are based on the basic laws of [[physics]], [[Fluid dynamics|fluid motion]], and [[chemistry]].]]
Complex climate models enable [[extreme event attribution]], which is the science of identifying and quantifying the role that human-caused [[climate change]] plays in the frequency, intensity and impacts of [[Extreme weather|extreme weather events]].<ref name=UCS_20180604>{{cite web |title=The Science Connecting Extreme Weather to Climate Change |url=https://www.ucs.org/sites/default/files/attach/2018/06/The-Science-Connecting-Extreme-Weather-to-Climate-Change.pdf |date=4 June 2018 |archive-url=https://web.archive.org/web/20250610021624/https://www.ucs.org/sites/default/files/attach/2018/06/The-Science-Connecting-Extreme-Weather-to-Climate-Change.pdf |archive-date=10 June 2025 |publisher=Union of Concerned Scientists |url-status=live }}</ref><ref name=ClimateCentral_20241118>{{cite web |last1=McSweeney |first1=Robert |last2=Tandon |first2=Ayesha |title=Mapped: How climate change affects extreme weather around the world |url=https://interactive.carbonbrief.org/attribution-studies/index.html |publisher=Climate Central |archive-url=https://web.archive.org/web/20250610154758/https://interactive.carbonbrief.org/attribution-studies/index.html |archive-date=10 June 2025 |date=18 November 2024 |url-status=live}}</ref> Attribution science aims to determine the degree to which such events can be explained by or linked to human-caused global warming, and are not simply due to [[Climate variability and change|random climate variability]]<ref name=Conversation_20210825>{{cite web |last1=Zeng |first1=Zubin |title=Is climate change to blame for extreme weather events? Attribution science says yes, for some – here's how it works |url=https://theconversation.com/is-climate-change-to-blame-for-extreme-weather-events-attribution-science-says-yes-for-some-heres-how-it-works-164941 |website=[[The Conversation (website)|The Conversation]] |archive-url=https://web.archive.org/web/20250609064207/https://theconversation.com/is-climate-change-to-blame-for-extreme-weather-events-attribution-science-says-yes-for-some-heres-how-it-works-164941 |archive-date=9 June 2025 |date=25 August 2021 |url-status=live }}</ref> or natural [[weather|weather patterns]].<ref name=NOAA_20161215>{{cite web |last1=Lindsey |first1=Rebecca |last2=Herring |first2=Stephanie |last3=Kapnick |first3=Sarah |last4=van der Wahl |first4=Karin |title=Extreme event attribution: the climate versus weather blame game |url=https://www.climate.gov/news-features/understanding-climate/extreme-event-attribution-climate-versus-weather-blame-game |website=Climate.gov |publisher=National Oceanic and Atmospheric Administration (NOAA) |archive-url=https://web.archive.org/web/20250618004431/https://www.climate.gov/news-features/understanding-climate/extreme-event-attribution-climate-versus-weather-blame-game |archive-date=18 June 2025 |date=15 December 2016 |url-status=live}}</ref>
There are three major types of institution where climate models are developed, implemented and used: * National meteorological services: Most national weather services have a [[climatology]] section. * Universities: Relevant departments include atmospheric sciences, meteorology, climatology, and geography. * National and international research laboratories: Examples include the [[National Center for Atmospheric Research]] (NCAR, in [[Boulder, Colorado]], US), the [[Geophysical Fluid Dynamics Laboratory]] (GFDL, in [[Princeton, New Jersey]], US), [[Los Alamos National Laboratory]], the [[Hadley Centre for Climate Prediction and Research]] (in [[Exeter]], UK), the [[Max Planck Institute for Meteorology]] in Hamburg, Germany, or the [[Laboratoire des sciences du climat et de l'environnement|Laboratoire des Sciences du Climat et de l'Environnement]] (LSCE), France. Big climate models are essential but they are not perfect. Attention still needs to be given to the real world (what is happening and why). The global models are essential to assimilate all the observations, especially from space (satellites) and produce comprehensive analyses of what is happening, and then they can be used to make predictions/projections. Simple models have a role to play that is widely abused and fails to recognize the simplifications such as not including a water cycle.<ref>{{Cite journal |last1=Giardina |first1=Francesco |last2=Padrón |first2=Ryan S. |last3=Stocker |first3=Benjamin D. |last4=Schumacher |first4=Dominik L. |last5=Seneviratne |first5=Sonia I. |date=2025-06-16 |title=Large biases in the frequency of water limitation across Earth system models |url=https://www.nature.com/articles/s43247-025-02426-7 |journal=Communications Earth & Environment |language=en |volume=6 |issue=1 |pages=1–9 |doi=10.1038/s43247-025-02426-7 |issn=2662-4435|doi-access=free }}</ref><ref>{{Cite book |last=Trenberth |first=Kevin E. |url=https://www.cambridge.org/core/product/identifier/9781108979030/type/book |title=The Changing Flow of Energy Through the Climate System |date=2022 |publisher=Cambridge University Press |isbn=978-1-108-97903-0 |edition=1 |chapter=Chapter 1: Earth and Climate System |doi=10.1017/9781108979030}}</ref>
== General circulation models (GCMs) == {{excerpt|General circulation model}}
== Energy balance models (EBMs) ==
Simulation of the climate system in full 3-D space and time was impractical prior to the establishment of large computational facilities starting in the 1960s. In order to begin to understand which factors may have changed Earth's [[paleoclimate]] states, the constituent and dimensional complexities of the system needed to be reduced. A simple quantitative model that balanced incoming/outgoing energy was first developed for the atmosphere in the late 19th century.<ref name="sa1896" /> Other EBMs similarly seek an economical description of surface temperatures by applying the [[conservation of energy]] constraint to individual columns of the Earth-atmosphere system.<ref name="north06">{{citation |last1=North |first1=Gerald R. |last2=Stevens |first2= Mark J. |contribution=Energy-balance climate models |title=Frontiers in Climate Modelling |editor-last=Kiehl |editor-first=J. T. |editor-last2=Ramanathan |editor-first2=V. |page=52 |publisher=Cambridge University |date=2006 |isbn=9780511535857 |doi=10.1017/CBO9780511535857.004|hdl=2060/19810008165 |hdl-access=free }}</ref>
Essential features of EBMs include their relative conceptual simplicity and their ability to sometimes produce [[analytical solution]]s.<ref>{{citation |last1=North |first1=Gerald R. |last2=Kwang-Yul |first2=Kim |title=Energy Balance Climate Models |series=Wiley Series in Atmospheric Physics and Remote Sensing |publisher=Wiley-VCH |isbn=978-3-527-41132-0 |date=2017}}</ref>{{rp|19}} Some models account for effects of ocean, land, or ice features on the surface budget. Others include interactions with parts of the [[water cycle]] or [[carbon cycle]]. A variety of these and other reduced system models can be useful for specialized tasks that supplement GCMs, particularly to bridge gaps between simulation and understanding.<ref>{{cite journal |last=Held |first=Isaac M. |title=The gap between simulation and understanding in climate modelling |journal=Bulletin of the American Meteorological Society |volume=86 |issue=11 |pages=1609–1614 |date=2005 |doi=10.1175/BAMS-86-11-1609 }}</ref><ref>{{cite journal |last1=Polvani |first1=L. M. |last2=Clement |first2=A. C. |last3=Medeiros |first3=B. |last4=Benedict |first4=J. J. |last5=Simpson |first5=I. R. |title=When less is more: opening the door to simpler climate models |date=2017 |journal=Eos |issue=98 |doi=10.1029/2017EO079417|doi-access=free }}</ref>
=== Zero-dimensional models ===
Zero-dimensional models consider Earth as a point in space, analogous to the 1990 ''[[Pale Blue Dot]]'' photograph as viewed by ''[[Voyager 1]]'', or an astronomer's view of very distant objects. This [[zero-dimensional space|dimensionless]] view while highly limited is still useful in that the laws of physics are applicable in a bulk fashion to unknown objects, or in an appropriate [[lumped-element model|lumped manner]] if some major properties of the object are known. For example, astronomers know that most planets in our own solar system feature some kind of solid/liquid surface surrounded by a gaseous atmosphere.
==== Model with combined surface and atmosphere ====
A very simple model of the [[radiative equilibrium]] of the Earth is
:<math>(1-a)S \pi r^2 = 4 \pi r^2 \epsilon \sigma T^4</math>
where * the left hand side represents the total incoming shortwave power (in Watts) from the Sun * the right hand side represents the total outgoing longwave power (in Watts) from Earth, calculated from the [[Stefan–Boltzmann law]]. The constant parameters include * ''[[Solar constant|S]]'' is the [[solar constant]] – the incoming solar radiation per unit area—about 1367 W·m<sup>−2</sup> * ''[[Radius|r]]'' is Earth's radius—approximately 6.371 million meters (m) * ''[[pi|π]]'' is the mathematical constant (3.141...) * ''<math> \sigma </math>'' is the [[Stefan–Boltzmann constant]]—approximately 5.67×10<sup>−8</sup> J·K<sup>−4</sup>·m<sup>−2</sup>·s<sup>−1</sup>
The constant <math> \pi\,r^2 </math> can be factored out, giving a nildimensional equation for the equilibrium
:<math>(1-a)S = 4 \epsilon \sigma T^4</math>
where * the left hand side represents the incoming shortwave energy flux from the Sun in W·m<sup>−2</sup> * the right hand side represents the outgoing longwave energy flux from Earth in W·m<sup>−2</sup>. The remaining variable parameters which are specific to the planet include * ''<math>a</math>'' is Earth's average [[albedo]], measured to be 0.3.<ref>{{cite journal |last=Goode |first=P. R. |year=2001 |title=Earthshine Observations of the Earth's Reflectance |journal=Geophys. Res. Lett. |volume=28 |issue=9 |pages=1671–4 |doi=10.1029/2000GL012580 |bibcode=2001GeoRL..28.1671G|s2cid=34790317 |display-authors=etal|url=https://authors.library.caltech.edu/50838/1/grl14388.pdf |archive-url=https://web.archive.org/web/20180722192421/https://authors.library.caltech.edu/50838/1/grl14388.pdf |archive-date=2018-07-22 |url-status=live }}</ref><ref>{{cite web |title=Scientists Watch Dark Side of the Moon to Monitor Earth's Climate |url=http://www.agu.org/sci_soc/prrl/prrl0113.html |work=American Geophysical Union |date=17 April 2001 |access-date=1 March 2010 |archive-date=27 February 2009 |archive-url=https://web.archive.org/web/20090227182139/http://www.agu.org/sci_soc/prrl/prrl0113.html |url-status=dead }}</ref> * ''<math> T </math>'' is Earth's [[global surface temperature|average surface temperature]], measured as about 288 [[Kelvin]] (K) as of year 2020<ref>{{cite web |url=https://www.climate.gov/news-features/understanding-climate/climate-change-global-temperature |archive-url=https://web.archive.org/web/20130615053036/http://www.climate.gov/news-features/understanding-climate/climate-change-global-temperature |url-status=dead |archive-date=15 June 2013 |title=Climate Change: Global Temperature |publisher=NOAA |accessdate=6 July 2023}}</ref> * ''<math> \epsilon </math>'' is the [[Emissivity#Effective emissivity due to atmosphere|effective emissivity]] of Earth's combined surface and atmosphere (including clouds). It is a quantity between 0 and 1 that is calculated from the equilibrium to be about 0.61. For the zero-dimensional treatment it is equivalent to an average value over all viewing angles.
This very simple model is quite instructive. For example, it shows the temperature sensitivity to changes in the solar constant, Earth albedo, or effective Earth emissivity. The effective emissivity also gauges the strength of the atmospheric [[greenhouse effect]], since it is the ratio of the thermal emissions escaping to space versus those emanating from the surface.<ref>{{cite web |url=http://eospso.gsfc.nasa.gov/ftp_docs/lithographs/CERES_litho.pdf |title=Clouds and the Earth's Radiant Energy System |publisher=NASA |archive-url=https://web.archive.org/web/20130218204711/http://eospso.gsfc.nasa.gov/ftp_docs/lithographs/CERES_litho.pdf |archive-date=18 February 2013 |year=2013 |url-status=dead}}</ref>
The calculated emissivity can be compared to available data. Terrestrial surface emissivities are all in the range of 0.96 to 0.99<ref>{{cite web|url=http://www.icess.ucsb.edu/modis/EMIS/html/seawater.html|title=Seawater Samples - Emissivities|work=ucsb.edu}}</ref><ref>{{cite journal |doi=10.1175/JCLI3720.1 |vauthors=Jin M, Liang S |title=An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations |journal=J. Climate |volume=19 |issue=12 |pages=2867–81 |date=15 June 2006 |url=http://www.glue.umd.edu/~sliang/papers/Jin2006.emissivity.pdf |archive-url=https://web.archive.org/web/20070604185622/http://www.glue.umd.edu/~sliang/papers/Jin2006.emissivity.pdf |archive-date=2007-06-04 |url-status=live |bibcode = 2006JCli...19.2867J }}</ref> (except for some small desert areas which may be as low as 0.7). Clouds, however, which cover about half of the planet's surface, have an average emissivity of about 0.5<ref>{{cite conference |author1=T.R. Shippert |author2=S.A. Clough |author3=P.D. Brown |author4=W.L. Smith |author5=R.O. Knuteson |author6=S.A. Ackerman |title=Spectral Cloud Emissivities from LBLRTM/AERI QME |book-title=Proceedings of the Eighth Atmospheric Radiation Measurement (ARM) Science Team Meeting March 1998 Tucson, Arizona |url=http://www.arm.gov/publications/proceedings/conf08/extended_abs/shippert_tr.pdf |archive-url=https://web.archive.org/web/20060925194147/http://www.arm.gov/publications/proceedings/conf08/extended_abs/shippert_tr.pdf |archive-date=2006-09-25 |url-status=live }}</ref> (which must be reduced by the fourth power of the ratio of cloud absolute temperature to average surface absolute temperature) and an average cloud temperature of about {{convert|258|K|abbr=on}}.<ref>{{cite conference |author1=A.G. Gorelik |author2=V. Sterljadkin |author3=E. Kadygrov |author4=A. Koldaev |title=Microwave and IR Radiometry for Estimation of Atmospheric Radiation Balance and Sea Ice Formation |book-title=Proceedings of the Eleventh Atmospheric Radiation Measurement (ARM) Science Team Meeting March 2001 Atlanta, Georgia |url=http://www.arm.gov/publications/proceedings/conf11/extended_abs/gorelik_ag.pdf |archive-url=https://web.archive.org/web/20060925174423/http://www.arm.gov/publications/proceedings/conf11/extended_abs/gorelik_ag.pdf |archive-date=2006-09-25 |url-status=live }}</ref> Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature {{convert|285|K|abbr=on}}).{{cn|date=July 2023}}
==== Models with separated surface and atmospheric layers ==== [[file:greenhouse slab model.png|thumb|upright=1|right|One-layer EBM with blackbody surface]]
Dimensionless models have also been constructed with functionally distinct atmospheric layers from the surface. The simplest of these is the [[idealized greenhouse model|zero-dimensional, one-layer model]],<ref>{{cite web |url=https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/singlelayermodel.html |title=ACS Climate Science Toolkit - Atmospheric Warming - A Single-Layer Atmosphere Model |publisher=[[American Chemical Society]] |accessdate=2 October 2022}}</ref> which may be readily extended to an arbitrary number of atmospheric layers. The surface and atmospheric layer(s) are each characterized by a corresponding temperature and emissivity value, but no thickness. Applying radiative equilibrium (i.e conservation of energy) at the idealized interfaces between layers produces a set of coupled equations which are solvable.<ref>{{cite web |url=https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/multilayermodel.html |title=ACS Climate Science Toolkit - Atmospheric Warming - A Multi-Layer Atmosphere Model |publisher=[[American Chemical Society]] |accessdate=2 October 2022}}</ref>
These multi-layered EBMs are examples of [[multi-compartment model]]s. They can estimate average temperatures closer to those observed for Earth's surface and troposphere.<ref>{{cite web |url=https://www.e-education.psu.edu/meteo469/node/198 |title=METEO 469: From Meteorology to Mitigation - Understanding Global Warming - Lesson 5 - Modelling of the Climate System - One-Layer Energy Balance Model |publisher=[[Pennsylvania State University]] College of Mineral and Earth Sciences - Department of Meteorology and Atmospheric Sciences |accessdate=2 October 2022}}</ref> They likewise further illustrate the radiative [[heat transfer]] processes which underlie the greenhouse effect. Quantification of this phenomenon using a version of the one-layer model was first published by [[Svante Arrhenius]] in year 1896.<ref name="sa1896">{{Cite journal | author=Svante Arrhenius | year=1896 | title=On the influence of carbonic acid in the air upon the temperature of the ground | journal=Philosophical Magazine and Journal of Science | volume=41 | issue=251 | pages=237–276 | language=en| doi=10.1080/14786449608620846 | url=https://zenodo.org/record/1431217 }}</ref>
=== Radiative-convective models === {{See also|Radiative-convective equilibrium}}
[[Water vapor]] is a main determinant of the emissivity of Earth's atmosphere. It both influences the flows of radiation and is influenced by convective flows of heat in a manner that is consistent with its equilibrium concentration and temperature as a function of elevation (i.e. [[relative humidity]] distribution). This has been shown by refining the zero dimension model in the vertical to a one-dimensional radiative-convective model which considers two processes of energy transport:<ref name="manwether">{{cite journal |last1=Manabe |first1=Syukuro |author1-link=Syukuro Manabe |last2=Wetherald |first2=Richard T. |title=Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity |journal=Journal of the Atmospheric Sciences |volume=24 |issue=3 |pages=241–259 |date=1 May 1967 |bibcode=1967JAtS...24..241M |doi=10.1175/1520-0469(1967)024<0241:TEOTAW>2.0.CO;2 |doi-access=free}}</ref> * upwelling and downwelling radiative transfer through atmospheric layers that both absorb and emit infrared radiation * upward transport of heat by air and vapor convection, which is especially important in the lower [[troposphere]].
Radiative-convective models typically use a [[distributed element model|distributed model]] of the atmosphere versus elevation. This has advantages over the lumped models and also lays a foundation for more complex models.<ref>{{cite web |url=https://www.nobelprize.org/prizes/physics/2021/manabe/facts/ |title=Syukuro Manabe Facts |website=nobelprize.org |access-date=14 November 2023}}</ref> They can estimate both surface temperature and the temperature variation with elevation in a more realistic manner. In particular, they properly simulate the observed decline in upper atmospheric temperature and the rise in surface temperature when [[trace gas|trace]] amounts of other non-condensible greenhouse gases such as [[carbon dioxide]] are included.<ref name="manwether" />
Other parameters are sometimes included to simulate localized effects in other dimensions and to address the factors that move energy about Earth. For example, the effect of ice-albedo feedback on global [[climate sensitivity]] has been investigated using a one-dimensional radiative-convective climate model.<ref>{{cite web|url=http://pubs.giss.nasa.gov/cgi-bin/abstract.cgi?id=wa03100m|archive-url=https://archive.today/20120730021359/http://pubs.giss.nasa.gov/cgi-bin/abstract.cgi?id=wa03100m|url-status=dead|archive-date=2012-07-30|title=Pubs.GISS: Wang and Stone 1980: Effect of ice-albedo feedback on global sensitivity in a one-dimensional...|work=nasa.gov}}</ref><ref>{{Cite journal | last = Wang | first = W.C. | author2 = P.H. Stone | title = Effect of ice-albedo feedback on global sensitivity in a one-dimensional radiative-convective climate model | journal = J. Atmos. Sci. | volume = 37 | issue = 3 | pages = 545–52 | year = 1980 | doi = 10.1175/1520-0469(1980)037<0545:EOIAFO>2.0.CO;2 | bibcode = 1980JAtS...37..545W | doi-access = free }}</ref>
=== Higher-dimension models === The zero-dimensional model may be expanded to consider the energy transported horizontally in the atmosphere. This kind of model may well be [[Zonal and meridional|zonally]] averaged. This model has the advantage of allowing a rational dependence of ''local'' albedo and emissivity on temperature – the poles can be allowed to be icy and the equator warm – but the lack of true dynamics means that horizontal transports have to be specified.<ref>{{cite web|url=http://www.shodor.org/master/environmental/general/energy/application.html|title=Energy Balance Models|work=shodor.org}}</ref>
Early examples include research of [[Mikhail Budyko]] and [[William D. Sellers]] who worked on the ''Budyko-Sellers model''.<ref>{{cite journal|title=The effect of solar radiation variations on the climate of the Earth|author=M.I. Budyko|journal=Tellus|year=1969|volume=21|issue=5|pages=611–619|doi=10.3402/tellusa.v21i5.10109 |doi-access=free}}</ref><ref>{{cite journal|title=A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System|year=1969|doi=10.1175/1520-0450(1969)008<0392:AGCMBO>2.0.CO;2|author=William D. Sellers|journal=Journal of Applied Meteorology|volume = 8|issue=3|pages=392–400|bibcode=1969JApMe...8..392S|doi-access=free}}</ref> This work also showed the role of [[climate change feedbacks|positive feedback]] in the climate system and has been considered foundational for the energy balance models since its publication in 1969.<ref name="north06" /><ref>{{cite journal|title=Twenty-five years of physical climatology|year=1990|author=J. Graham Cogley|doi=10.1016/0921-8181(90)90001-S|journal=Global and Planetary Change|volume=2|issue=3–4|pages=213–216|doi-access=}}</ref>
== Earth systems models of intermediate complexity (EMICs) == {{Main|Earth systems model of intermediate complexity}} Depending on the nature of questions asked and the pertinent time scales, there are, on the one extreme, conceptual, more inductive models, and, on the other extreme, [[general circulation model]]s operating at the highest spatial and temporal resolution currently feasible. Models of intermediate complexity bridge the gap. One example is the Climber-3 model. Its atmosphere is a 2.5-dimensional statistical-dynamical model with 7.5° × 22.5° resolution and time step of half a day; the ocean is MOM-3 ([[Modular Ocean Model]]) with a 3.75° × 3.75° grid and 24 vertical levels.<ref>{{cite web|url=http://www.pik-potsdam.de/emics/|title=emics1|work=pik-potsdam.de}}</ref>
==Box models== {{See also|Multi-compartment model}} [[File:Simple box model.png|thumb|upright=1|right| Schematic of a simple box model used to illustrate [[flux]]es in geochemical cycles, showing a source ''(Q)'', sink ''(S)'' and reservoir ''(M)'']]
Box models are simplified versions of complex systems, reducing them to boxes linked by fluxes. The boxes contain reservoirs (i.e. [[inventories]]) of species of matter and energy that are assumed to be mixed homogeneously. The concentration of any species is therefore uniform at any time within a box. However, the abundance of a species within a given box may vary as a function of time due to input flows or output flows; and may also vary due to the production, consumption or transformation of a species within the box.<ref>{{cite web |url=https://institutebishop.org/Enviro_6.pdf |title=Box Models: Stocks, Flows, and Residence Times |author=Mark Bishop |website=institutebishop.org |access-date=2025-10-26}}</ref><ref>{{cite web |url=https://www.gfdl.noaa.gov/wp-content/uploads/files/user_files/pag/lecture2008/lecture13.pdf |title=Mathematical models |author=NOAA GFDL |access-date=2025-10-26}}</ref>
Simple box models, i.e. box model with a small number of boxes whose properties (e.g. their volume) do not change with time, are often useful to derive [[analytical formula]]s describing the dynamical and steady-state abundances of a species. The formulae are called [[governing equations]] and are derived from [[conservation laws]] (e.g. conservation of energy, conservation of mass, etc.). Larger sets of interacting species and equations are evaluated with numerical techniques to describe behavior of the system.<ref>{{cite book |last=Calvetti |first=Daniela |last2=Somersalo |first2=Erkki |title=Computational Mathematical Modeling: An Integrated Approach Across Scales |publisher=Society for Industrial and Applied Mathematics |ISBN=978-1-61197-247-4 |doi=10.1137/1.9781611972481 |year=2012 |chapter=Compartment models |chapter-url=https://epubs.siam.org/doi/pdf/10.1137/1.9781611972481.ch2}}</ref>
Box models are used extensively to simulate environmental systems and ecosystems. In 1961 [[Henry Stommel]] was the first to use a simple [[Multiple equilibria in the Atlantic meridional overturning circulation#Stommel box model|2-box model]] to study the stability of large-scale [[ocean circulation]].<ref>{{Cite journal|last=Stommel|first=Henry|date=May 1961|title=Thermohaline Convection with Two Stable Regimes of Flow|journal=Tellus|volume=13|issue=2|pages=224–230|doi=10.3402/tellusa.v13i2.9491|doi-access=free|issn=0040-2826}}</ref> A more complex model has examined interactions between ocean circulation and the [[carbon cycle]].<ref name="Sarmiento1984">{{cite journal |author=Sarmiento, J.L. |author2=Toggweiler, J.R. |year=1984 |title=A new model for the role of the oceans in determining atmospheric P CO 2 |journal=Nature |volume=308 |issue=5960 |pages=621–24 |bibcode=1984Natur.308..621S |doi=10.1038/308621a0 |s2cid=4312683}}</ref>
== Networked data models == {{See also|Data model}} {{excerpt|Climate as complex networks}}
==History== {{See also|History of climate change science}} {{excerpt|Atmospheric model#Climate modeling}}
=== Increase of forecasts confidence over time === [[File:CMIP climate model progress.jpg|thumb|upright=1|right|The pattern correlation between global climate models and observations has improved over sequential CMIP phases 3, 5, and 6.<ref>{{cite journal |last1=Bock |first1=L. |last2=Lauer |first2=A. |last3=Schlund |first3=M. |last4=Barreiro |first4=M |last5=Bellouin |first5=N. |last6=Jones |first6=C. |last7=Meehl |first7=G.A. |last8=Predoi |first8=V. |last9=Roberts |first9=M.J. |last10=Eyring |first10=V. |title=Quantifying Progress Across Different CMIP Phases With the ESMValTool |journal=Journal of Geophysical Research: Atmospheres |volume=125 |issue=21 |year=2020 |doi=10.1029/2019JD032321 |doi-access=free|hdl=20.500.12008/30864 |hdl-access=free }}</ref>]]
The [[Coupled Model Intercomparison Project]] (CMIP) has been a leading effort to foster improvements in GCMs and climate change understanding since 1995.<ref>{{cite web |title=Coupled Model Intercomparison Project |url=https://wcrp-cmip.org |publisher=World Climate Research Program |access-date=11 November 2024}}</ref><ref>{{cite journal |last1=Meehl |first1=Gerald A. |last2=Boer |first2=George J. |last3=Covey |first3=Curt |last4=Latif |first4=Mojib |last5=Stouffer |first5=Ronald J. |title=Intercomparison makes for a better climate model |journal=Eos, Transactions American Geophysical Union |volume=78 |number=41 |date=14 October 1997 |doi=10.1029/97EO00276 |doi-access=free}}</ref>
The IPCC stated in 2010 it has increased confidence in forecasts coming from climate models:<blockquote>"There is considerable confidence that climate models provide credible quantitative estimates of future climate change, particularly at continental scales and above. This confidence comes from the foundation of the models in accepted physical principles and from their ability to reproduce observed features of current climate and past climate changes. Confidence in model estimates is higher for some climate variables (e.g., temperature) than for others (e.g., precipitation). Over several decades of development, models have consistently provided a robust and unambiguous picture of significant climate warming in response to increasing greenhouse gases."<ref>{{cite web |title=Climate Models and Their Evaluation |url=http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter8.pdf |url-status=dead |archive-url=https://web.archive.org/web/20100922124304/http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter8.pdf |archive-date=22 September 2010 |access-date=29 August 2010 |df=dmy-all}}</ref></blockquote>
== Coordination of research == The [[World Climate Research Programme]] (WCRP), hosted by the [[World Meteorological Organization]] (WMO), coordinates research activities on climate modelling worldwide.
A 2012 [[U.S. National Research Council]] report discussed how the large and diverse U.S. climate modeling enterprise could evolve to become more unified.<ref>{{cite web | title=U.S. National Research Council Report, ''A National Strategy for Advancing Climate Modeling'' | url=http://dels.nas.edu/Report/National-Strategy-Advancing-Climate/13430 | access-date=18 January 2021 | archive-date=3 October 2012 | archive-url=https://web.archive.org/web/20121003043232/http://dels.nas.edu/Report/National-Strategy-Advancing-Climate/13430 | url-status=dead }}</ref> Efficiencies could be gained by developing a common software infrastructure shared by all U.S. climate researchers, and holding an annual climate modeling forum, the report found.<ref>{{cite web | title=U.S. National Research Council Report-in-Brief, ''A National Strategy for Advancing Climate Modeling'' | url=http://dels.nas.edu/Materials/Report-In-Brief/4291-Climate-Modeling | access-date=3 October 2012 | archive-date=18 October 2012 | archive-url=https://web.archive.org/web/20121018071324/http://dels.nas.edu/Materials/Report-In-Brief/4291-Climate-Modeling | url-status=dead }}</ref>
== Issues ==
=== Electricity consumption === Cloud-resolving climate models are nowadays run on high intensity [[Supercomputer|super-computers]] which have a high power consumption and thus cause CO<sub>2</sub> emissions.<ref name=":0">{{Cite journal |last=Loft |first=Richard |date=2020 |title=Earth System Modeling Must Become More Energy Efficient |url=https://eos.org/opinions/earth-system-modeling-must-become-more-energy-efficient |journal=Eos |issue=101 |doi=10.1029/2020EO147051 |issn=2324-9250|doi-access=free }}</ref> They require [[exascale computing]] (billion billion – i.e., a quintillion – calculations per second). For example, the [[Frontier (supercomputer)|Frontier exascale supercomputer]] consumes 29 MW.<ref>{{Cite web |last=Trader |first=Tiffany |date=2021 |title=Frontier to Meet 20MW Exascale Power Target Set by DARPA in 2008 |url=https://www.hpcwire.com/2021/07/14/frontier-to-meet-20mw-exascale-power-target-set-by-darpa-in-2008/ |access-date=2023-12-08 |website=HPCwire |language=en-US}}</ref> It can simulate a year’s worth of climate at cloud resolving scales in a day.<ref>{{Cite web |title=Cloud-resolving climate model meets world's fastest supercomputer |url=https://www.sandia.gov/labnews/2023/04/06/cloud-resolving-climate-model-meets-worlds-fastest-supercomputer/ |access-date=2023-12-08 |website=LabNews |language=en-US}}</ref>
Techniques that could lead to energy savings, include for example: "reducing floating point precision computation; developing machine learning algorithms to avoid unnecessary computations; and creating a new generation of scalable numerical algorithms that would enable higher throughput in terms of simulated years per wall clock day."<ref name=":0" />
=== Parametrization === {{excerpt|Parametrization (climate modeling)}}
== See also == * [[Atmospheric reanalysis]] * [[Chemical transport model]] * [[Atmospheric Radiation Measurement]] (ARM) (in the US) * [[Climate Data Exchange]] * [[Climateprediction.net]] * [[Numerical Weather Prediction]] * [[Static atmospheric model]] * [[Tropical cyclone prediction model]] * [[Verification and validation of computer simulation models]] * [[CICE (sea ice model)|CICE sea ice model]]
== References == {{Reflist|30em}}
==External links==
{{Wikibooks|Historical Geology|Climate models}}
* [https://www.carbonbrief.org/timeline-history-climate-modelling/ Timeline: The History of Climate Modelling] CarbonBrief, 16 January 2018 * [https://www.carbonbrief.org/guest-post-why-results-from-the-next-generation-of-climate-models-matter Why results from the next generation of climate models matter] CarbonBrief, Guest post by Belcher, Boucher, Sutton, 21 March 2019 '''Climate models on the web:''' * [https://www2.cesm.ucar.edu/models/ccsm4.0/ NCAR/UCAR Community Climate System Model] (CCSM) * [https://www.climateprediction.net/ Do it yourself climate prediction] * [http://www.giss.nasa.gov/tools/modelE/ Primary research GCM developed by NASA/GISS (Goddard Institute for Space Studies)] * [https://web.archive.org/web/20150323033013/http://edgcm.columbia.edu/ Original NASA/GISS global climate model] (GCM) with a user-friendly interface for PCs and Macs * [https://web.archive.org/web/19981212023617/http://www.cccma.bc.ec.gc.ca/ CCCma model info and interface to retrieve model data]
{{Climate change}} {{Atmospheric, Oceanographic and Climate Models}} {{Computer modeling}} {{Portal bar|Energy|Global warming}}
[[Category:Numerical climate and weather models]] [[Category:Climate modeling| ]]