Climate models use quantitative methods to simulate the interactions of the Earths atmosphere is the layer of gases surrounding the planet Earth and retained by the Earths gravity. ...atmosphere, Ocean (Okeanos, a Greek god of sea and water; Greek ωκεανός) covers almost three quarters (71%) of the surface of the Earth. ...oceans, land surface, and ice. They are used for a variety of purposes: from study of the dynamics of the weather and climate system, to projections of future climate.

The most talked_about models of recent years have been those relating air temperature to emissions of Carbon dioxide is an atmospheric gas composed of one carbon and two oxygen atoms. ...carbon dioxide (see Greenhouse gases are gaseous components of the atmosphere that contribute to the greenhouse effect. ...greenhouse gas). These models predict an upward trend in the The historical temperature record shows the fluctuations of the temperature of the atmosphere and the oceans throughout history, and in particular since 1850. ...surface temperature record, as well as a more rapid increase in temperature at higher altitudes.

Models can range from relatively simple to quite complex:

• Simple The phrase back_of_the_envelope refers to rough calculations that, while not rigorous, test or support a point. ...back_of_the_envelope calculations of the radiative temperature treat the earth as a single point
• this can be expanded vertically (radiative_convective models), or horizontally (energy balance models)
• finally, (coupled) atmosphere_ocean_seaice global climate models discretise and solve the full equations for fluid motion.

This is not a full list; for example "box models" can be written to treat flows across and within ocean basins.

Zero_dimensional models

It is possible to obtain a very simple model of the radiative equilibrium of the Earth by writing

(1 − a)Sπr² = 4πr²sT⁴

where

• The left hand side represents the incoming energy from the Sun
• The right hand side represents the outgoing energy from the Earth, calculated from Stefan_Boltzmann law (also Stefans law) states that the total energy radiated per unit surface area of a black body in unit time (black_body irradiance), (or the energy flux density (radiant flux) or the emissive power), j* is directly proportional to the fourth power of its thermodynamic temperature...Stefan_Boltzmann law assuming a constant radiative temperature, T, that is to be found,

and

• S is the The solar constant is the amount of incoming solar radiation per unit area, measured on the outer surface of Earths atmosphere, in a plane perpendicular to the rays. ...Solar constant _ the incoming solar radiation per unit area _ about 1367 Wm^_2
• a is the Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ...Earth's average This article discusses the physical or planetological property of albedo. ...albedo, approximately 0.37 to 0.39
• r is Earth's radius _ approximately 6.371×10⁶m
• The title given to this article is incorrect due to technical limitations. ...π is well known, approximately 3.14159
• s is the The Stefan_Boltzmann constant (also Stefans constant), denoted with a Greek letter σ, is a derivable physical constant, the constant of proportionality between the total energy radiated per unit surface area of a black body in unit time and the fourth power of the thermodynamic temperature, as per the...Stefan_Boltzmann constant _ approximately 5.67×10^_8 JK^_4m^_2s^_1

Note that the factor of πr² can be factored out, giving

(1 − a)S = 4sT⁴

which gives a value of 246 to 248 The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. ...kelvin _ about _27 to _25 °C _ as the Earth's average temperature T. This is approximately 35 degrees colder than the average surface temperature of 282 K. This is because the above equation attempts to represent the radiative temperature of the earth, and the average radiative level is well above the surface. The difference between the radiative and surface temperatures is the natural The greenhouse effect first discovered by Jean Baptiste Joseph Fourier in 1824 is the process by which an atmosphere warms a planet. ...greenhouse effect.

This very simple model is quite instructive, and the only model that could fit on a page. But it produces a result we are not really interested in _ the radiative temperature _ rather than the more useful surface temperature. It also contains the albedo as a specified constant, with no way to "predict" it from within the model.

Radiative_Convective Models

The zero_dimensional model above predicts the temperature of an imaginary layer where long wave radiation is emitted to space. This can be extended in the vertical to a one dimensional radiative_convective model, which simplifies the atmosphere to consider only two processes of energy transport:

• upwelling and downwelling radiative transfer through atmospheric layers
• upwards transport of heat by convection (especially important in the lower The troposphere is the lowermost portion of Earths atmosphere and the one in which most weather phenomena occur. ...troposphere).

The radiative_convective models have advantages over the simple model: they can tell you the surface termperature, and the effects of varying Greenhouse gases are gaseous components of the atmosphere that contribute to the greenhouse effect. ...greenhouse gas concentrations on the surface temperature. But they need added parameters, and still represent by one point the horizontal surface of the earth.

Links:

• http://www.giss.nasa.gov/gpol/abstracts/1980/WangStone.html
• http://members.fortunecity.com/yhu/paper/scat/node4.html
• http://www.grida.no/climate/ipcc-tar/wg1/258.htm

Energy Balance Models

Alternatively, the zero_dimensional model may be expanded horizontally to consider the energy transported _ ahem _ horizontally in the atmosphere. This kind of model may well be zonally averaged. This model has the advantage of allowing a plausible dependence of albedo 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.

• http://www.shodor.org/master/environmental/general/energy/application.html

EMIC's (Earth_system Models 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, A general circulation model (GCM) aims to describe geophysical flow by integrating a variety of fluid_dynamical, chemical, or even biological equations that are either derived directly from physical laws (e. ...general circulation models 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 1/2 a day; the ocean is MOM_3 with a 3.75° × 3.75° grid and 24 vertical levels.

• http://www.pik_potsdam.de/emics/

GCM's (Global Climate Models or A general circulation model (GCM) aims to describe geophysical flow by integrating a variety of fluid_dynamical, chemical, or even biological equations that are either derived directly from physical laws (e. ...General circulation models)

Three (or more properly, four) dimensional GCM's discretise the equations for fluid motion and integrate these forward in time. They also contain parametrisations for processes _ such as convection _ that occur on scales too small to be resolved directly.

Atmospheric GCMs (AGCMs) model the atmosphere and impose sea surface temperatures. Coupled atmosphere_ocean GCMs (AOGCMs, e.g. HadCM3) combine the two models. AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. However, they are still under development and uncertainties remain.

Most recent simulations show "plausible" agreement with the measured temperature anomalies over the past 150 year, when forced by observed changes in "Greenhouse" gases and aerosols, but better agreement is achieved when natural forcings are also included [1]  (http://www.grida.no/climate/ipcc_tar/wg1/figspm-4.htm) [2] (http://www.hadleycentre.gov.uk/research/hadleycentre/pubs/talks/sld017.html).

See also

• Climate forcing is the overall term for the various theories of the methods by which phenomena exert an effect on a climate. ...climate forcing
• The term climate change is used to refer to changes in the Earths climate. ...climate change
• Global Mean Temperatures 1880_2005 Global warming is a term used to describe an increase over time of the average temperature of Earths atmosphere and oceans. ...global warming

Climate Models on the Web

• http://www.mmm.ucar.edu/mm5/mm5_home.html _ University Corporation for Atmospheric Research _ The National Center for Atmospheric Research (NCAR), in Boulder, Colorado, was established in 1960 to serve as a focus for United States research on atmospheric and related science problems, including climate change, atmospheric chemistry, changes in atmospheric composition, mesoscale and microscale meteorology, Earth_Sun interactions, weather formation and forecasting, and...NCAR MM5 Mesoscale model
• The Hadley Centre for Climate Prediction and Research, which is part of the Met Office, provides a focus in the United Kingdom for the scientific issues associated with climate change. ...Hadley Centre _ general info on their models (http://www.hadleycentre.gov.uk/research/hadleycentre/models/modeltypes.html)
• http://www.cgd.ucar.edu/csm/ _ The National Center for Atmospheric Research (NCAR), in Boulder, Colorado, was established in 1960 to serve as a focus for United States research on atmospheric and related science problems, including climate change, atmospheric chemistry, changes in atmospheric composition, mesoscale and microscale meteorology, Earth_Sun interactions, weather formation and forecasting, and...NCAR/ UCAR is a nonprofit corporation formed in 1959 by research institutions with doctoral programs in the atmospheric and related sciences. ...UCAR Community Climate System Model (CCSM)
• http://www.climateprediction.net _ do it yourself climate prediction

References

• (IPCC 2001 section 8.3) (http://www.grida.no/climate/ipcc-tar/wg1/313.htm) _ on model hierarchy
• (IPCC 2001 section 8) (http://www.grida.no/climate/ipcc-tar/wg1/308.htm) _ much information on coupled GCM's
• Coupled Model Intercomparison Project (http://www_pcmdi.llnl.gov/modeldoc/cmip/index.html)

http://ams.allenpress.com/amsonline/?request=get_abstract&doi=10.1175%2F2786.1