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 talked-about 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 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.
It is possible to obtain a very simple model of the radiative equilibrium of the Earth by writing
- (1 - a)Sπr2 = 4πr2sT4
- 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 assuming a constant radiative temperature, T, that is to be found,
- 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
- π 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:
- upwelling and downwelling radiative transfer through atmospheric layers
- upwards transport of heat by convection (especially important in the lower troposphere).
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 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.
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  . 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)
- 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.
Early generations of AOGCMs required a somewhat ad hoc process of "flux correction" to achieve a stable climate. More recent models do not require this. "Flux correction" was always felt to be an undesirable feature of the models by those that wrote them (as well as by those that did not like them) and was resorted to out of necessity. One of the principle (valid) objections to flux corrections was that they amounted to a "tuning" of the models towards the current climate and made future projections less reliable. The model improvements that now make flux corrections unnecessary are various, but include improved ocean physics, improved resolution in both atmosphere and ocean, and a better fit between atmosphere and ocean models. Most recent simulations show a close agreement with the measured temperature anomalies over the past 150 year, when forced by observed changes in "Greenhouse" gases and aerosols   .
Coupled ocean-atmosphere GCMs are used to project/predict future temperature changes under various scenarios. The IPCC TAR figure 9.3 shows the global mean response of 19 different coupled models to an idealised experiment in which CO2 is increased at 1% per year  . Figure 9.5 shows the response of a smaller number of models to more realistic forcing - although the forcings used depend on projections of future CO2 emissions, which are themselves uncertain.
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.
Accuracy of models that predict global warming
Whether these models are sufficiently "correct" to be useful or not is a matter of dispute. GCMs are certainly capable of reproducing the observed global temperature over the past century  . Thousands of climate researchers around the world use climate models to understand the climate system, and publish thousands of papers about this in peer reviewed journals - and a part of this research is work improving the models. A rather more complete discussion of climate models is provided by the IPCC TAR chapter 8, Model Evaluation .
There is a debate over how to reconcile climate model predictions that upper air (tropospheric) warming should be greater than surface warming, with observations that appear to show otherwise (see also satellite temperature record)  . Possible explanations include errors in the surface or upper-air records; a problem with the model; or just the shortness of the observed record. This problem is no longer as intense as it used to be a few years ago, because (1) all versions of the satellite record now show warming; (2) there are now multiple versions of the satellite temperature record, some of which show warming greater than that observed at the surface.
Climate Models on the Web
- http://www.mmm.ucar.edu/mm5/mm5-home.html - University Corporation for Atmospheric Research - NCAR MM5 Mesoscale model
- Hadley Centre - general info on their models
- http://www.cgd.ucar.edu/csm/ - NCAR/UCAR Community Climate System Model (CCSM)
- http://www.climateprediction.net - do it yourself climate prediction
- (IPCC 2001 section 8.3) - on model hierarchy
- (IPCC 2001 section 8) - much information on coupled GCM's
- Coupled Model Intercomparison Project