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Climate models are quantitative methods of representing the interactions of the atmosphere, oceans, land surface, and ice. Models can range from relatively simple to quite comprehensive.

Climate models can be ordered into a rough hierarchy of complexity:

• Simple 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 discretize and solve the full equations for fluid motion.

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

 Table of contents 1 Zero-dimensional models 2 Radiative-Convective Models 3 Energy Balance Models 4 GCM's (Global Climate Models or General Circulation Models) 5 See also 6 References

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

and

• S is the Solar Constant - the incoming solar radiation per unit area - about 1367 Wm-2
• a is the Earth's average albedo, approximately 0.37 to 0.39
• r is Earth's radius - approximately 6.371×106m
• &pi is well known, approximately 3.14159
• s is 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 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 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.

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:

The radiative-convective models have advantages over the simple model: they can tell you the surface termperature, and the effects of varying greenhouse gas concentrations on the surface temperature. But they need added parameters, and still represent by one point the horizontal surface of the earth.

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 meaned. 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.

GCM's (Global Climate Models or 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. More sophisticated models may include representations of the carbon and other cycles.

Atmospheric GCMs (AGCMs) model the atmosphere (and typically contain a land-surface model as well) and impose sea surface temperatures. A large amount of information including model documentation is available from AMIP [1]. They may include atmospheric chemistry. AGCMs consist of a dynamical core, which integrates the equations of fluid motion for, typically:

• surface pressure
• horizontal components of velocity in layers
• temperature and moisture in layers

and parametrisations which handle other processes: these include

• radiation (solar/short wave and terrestrial/infra-red/long wave)
• convection
• land surface processes and hydrology

The method by which AGCMs discretise the fluid equations may be the familiar finite difference method or the somewhat harder to understand spectral method. Typical AGCM resolution is between 1 and 5 degrees in latitude or longitude: the Hadley Centre model HadAM3, for example, uses 2.5 degrees in latitude and 3.75 in longitude, giving a grid of 73 by 96 points; and has 19 levels in the vertical.

Oceanic GCMs (OGCMs) model the ocean (with fluxes from the atmosphere imposed) and may or may not contain a sea ice model.

Coupled atmosphere-ocean GCMs (AOGCMs) combine the two models. They thus have the advantage of removing the need to specify fluxes across the interface of the ocean surface. These models are the basis for sophisticated model predictions of future climate, such as are discussed by the IPCC.

AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. They are the only tools that could provide detailed regional predictions of future climate change. However, they are still under development. The simpler models are generally susceptible to simple analysis and their results are generally easy to understand. AOGCMs, by contrast, are often as hard to analyse as the real climate system.

The most modern AOGCMs simulate the observed warming over the past 150 years, when forced by observed changes in "Greenhouse" gases and aerosols [1] [1].

Note that global climate models, whilst very similar in structure to (and often sharing computer code with) numerical weather prediction models are nonetheless logically distinct: see weather vs climate for details.