Climate model
From Academic Kids

Climate models use quantitative methods to simulate the interactions of the atmosphere, 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 talkedabout models of recent years have been those relating air temperature to emissions of carbon dioxide (see greenhouse gas). These models predict an upward trend in the 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 backoftheenvelope calculations of the radiative temperature treat the earth as a single point
 this can be expanded vertically (radiativeconvective models), or horizontally (energy balance models)
 finally, (coupled) atmosphereoceanseaice 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.
Contents 
Zerodimensional models
It is possible to obtain a very simple model of the radiative equilibrium of the Earth by writing
 <math>(1a)S \pi r^2 = 4 \pi r^2 sT^4<math>
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 StefanBoltzmann law assuming a constant radiative temperature, T, that is to be found,
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 6.371×10^{6}m
 π is well known, approximately 3.14159
 s is the StefanBoltzmann constant  approximately 5.67×10^{8} JK^{4}m^{2}s^{1}
Note that the factor of πr^{2} can be factored out, giving
 <math>(1a)S = 4sT^4<math>
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.
RadiativeConvective Models
The zerodimensional 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 radiativeconvective 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 troposphere).
The radiativeconvective 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.
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 zerodimensional 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.
EMIC's (Earthsystem 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, general circulation models operating at the highest spatial and temporal resolution currently feasible. Models of intermediate complexity bridge the gap. One example is the Climber3 model. Its atmosphere is a 2.5dimensional statisticaldynamical model with 7.5° × 22.5° resolution and time step of 1/2 a day; the ocean is MOM3 with a 3.75° × 3.75° grid and 24 vertical levels.
GCM's (Global Climate Models or General circulation models)
Main article: general circulation model
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 atmosphereocean 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/figspm4.htm) [2] (http://www.hadleycentre.gov.uk/research/hadleycentre/pubs/talks/sld017.html).
See also
Climate Models on the Web
 http://www.mmm.ucar.edu/mm5/mm5home.html  University Corporation for Atmospheric Research  NCAR MM5 Mesoscale model
 Hadley Centre  general info on their models (http://www.hadleycentre.gov.uk/research/hadleycentre/models/modeltypes.html)
 http://www.cgd.ucar.edu/csm/  NCAR/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://wwwpcmdi.llnl.gov/modeldoc/cmip/index.html)
http://ams.allenpress.com/amsonline/?request=getabstract&doi=10.1175%2F2786.1