What are general circulation models ?

B. Geerts and E. Linacre


Differences with NWP models

A general circulation model (also known as a global climate model, both labels are abbreviated as GCM) uses the same equations of motion as a numerical weather prediction (NWP) model, but the purpose is to numerically simulate changes in climate as a result of slow changes in some boundary conditions (such as the solar constant)or physical parameters (such as the greenhouse gas concentration). Numerical weather prediction (NWP) models are used to predict the weather in the short (1-3 days) and medium (4-10 days) range future. GCM's are run much longer, for years on end, long enough to learn about the climate in a statistical sense (i.e. the means and variability). A good NWP model accurately predicts the movement and evolution of disturbances such as frontal systems and tropical cyclones. A GCM should do this as well, but all types of models err so much after some time (e.g. 2 weeks), that they become useless from a perspective of weather foresight. The quality of a GCM is judged, amongst others, by the quality of the statistics of tropical or extratropical disturbances.

An error in the sea surface temperature by a few ºC, or a small but systematic bias in cloudiness throughout the model, matter little to a NWP model. For a GCM these factors are important, because they matter over a long term. GCMs ignore fluctuating conditions when considering long-term changes, whereas NWP models take no notice of very slow processes.

State-of-the-art GCMs are coupled atmosphere-ocean models, i.e. a model simulating surface and deep ocean circulations is 'coupled' to an atmospheric GCM. The interface is the sea surface: that is where the transfers of water (evaporation/precipitation) and momentum occur. An accurate coupling of the fast atmosphere to the slow ocean (with long memory) is essential to simulate the ENSO, for instance (Note 11.A). GCM's can further be coupled to dynamic models of sea ice and conditions on land. Short to medium range NWP models are usually not coupled to a dynamic ocean model. The GCM-NWP comparison is summarised in Table 1.

Table 1. A comparison between NWP models and GCMs





to predict weather

to predict climate

spatial coverage

regional or global


temporal range



spatial resolution

variable (20-100 km)

usually coarse

relevance of initial conditions



relevance of clouds, radiation



relevance of surface (land, ice, ocean...)



relevance of ocean dynamics



relevance of model stability



time dimension







equations of motion (plus radiative transfer equations, water conservation equations ..)


Finite difference expression of continuous equations, or spectral representation; run prognostically


state variables and motion of the atmosphere in 3 dimensions

maximum time step

controlled by spatial resolution (CFL condition)


A key problem in GCM (not NWP) modelling is long-term stability, and sensitivity to small changes in surface conditions or radiation input. The atmosphere may be ‘almost transitive’. This means that it is neither invariant (i.e. intransitive) nor transitive (1). An ‘almost transitive’ system can flip between alternative patterns. The flipping to and from Ice Age conditions is an example. An increase of solar radiation will lead to a rising temperature, to an extent depending on the amount of ice on the surface; an ice cover will reflect much of the extra radiation away, causing less heating, until eventually the heating is sufficient to melt the ice. Conversely, reduced radiation will lower temperatures more if the surface is free of ice, accelerating the formation of ice. The difference between the reluctance of ice melting and the rapidity towards ice formation leads to ‘hysteresis’: when there is a difference between the radiation inputs at which ice comes and goes, two distinctly different global mean temperatures can arise under the same intermediate radiation inputs, depending on whether the input was waxing or waning (1).

 What GCMs and NWP models have in common...

  1. GCMs, as well as NWP models, numerically simulate the 'state' of the atmosphere, using a finite expression of the equations of motion (Note 15.G)(Table 1).
  2. The time-step of any numerical simulation of the atmosphere or ocean is constrained by the Courant-Friedrich-Levy (CFL) criterion (Table 1). According to this criterion, the time-step must be too small for the fastest-travelling disturbance to have time to traverse the distance of the grid spacing. Noise travels fastest of course, Noise travels as waves of expanding and contracting air, therefore models assume that the air is incompressible (the density varies only with height). The fastest meteorologically significant disturbances are large gravity waves, or the air in jet streaks, and their speed rarely exceeds 100 m/s (take 200 m/s as a maximum speed, to be safe). Then for a model resolution of 100 km, the maximum time-step is 100,000 m/ (200 m/s) = 500 s or about 8 minutes. Higher-resolution models require shorter time-steps, so that more calculations are needed to simulate climate over the same period. [Note: a ‘gravity wave’ is a wave disturbance in which buoyancy acts as the force restoring hydrostatic equilibrium. There is an oscillatory conversion to and from potential and kinetic energy. In the atmosphere such undulations are internal, rather than at a surface. They may be induced by mountains ranges, thunderstorms, or the jet stream.]
  3. Sub-grid scale processes are those that have dimensions smaller than the model resolution. Certainly cloud microphysical processes are in this category, therefore they need to be ‘parameterised’,i.e. the aggregate effect of the clouds on the resolved scale (in terms of changes in the radiation fluxes or moisture and mass transport, etc) is calculated. Parameterizations are empirical approximations based on large-scale (resolved) variables. Global models do not resolve cumulus clouds (even thunderstorms), so their presence and effects are parameterised: for instance, when the atmosphere is conditionally unstable and (gridscale) moisture convergence occurs, thunderstorms are assumed which stabilise and the atmosphere deposit rain. Parameterizations may have a theoretical justification but always need to be tested experimentally. For instance, one can assume that the surface albedo depends solely on surface temperature (i.e. the likelihood of ice), or that the planetary albedo is simply related to cloud amount. All state-of-the-art models somehow parameterise atmospheric radiation, sub-gridscale motion, chemistry, and cloud physics. Clearly, some parameterizations are specific to GCMs, such as very slow land surface changes, or slow chemical processes.
  4. Global NWP models and GCMs are generally spectral in design, for two reasons: spectral models assume that the model domain continuously repeats itself, and this applies to the Earth: after travelling 360 degrees around the globe we have returned to the initial point. In other words, a sphere lends itself to a spectral approach. More importantly, spectral models are up to 10 times faster than grid models, especially if complex derivatives are involved (e.g. a Laplacian operator must be solved in the diagnosis of pressure perturbations).
  5. As computer processing units (CPUs) become less expensive, models are refined to allow for closer spatial resolution, more accurate parameterisations, and more runs (tweaking parameters or initial conditions, as in ensemble forecasting). Fortunately the speed of computers has been increasing almost a hundredfold each decade since 1950 (1). Atmospheric predictions have been at the forefront of computer development ever since John von Neumann used one of the world's first computers, the EDVAC, to run a weather simulation at Princeton University's Institute for Advanced Study, in 1945.



  1. McGuffie, K. and A. Henderson-Sellers 1997. A Climate Modelling Primer (John Wiley & Sons) 253pp.