[jokabrink]

Such simulations usually consist of three major systems (atmosphere, land, and ocean) that are coupled together at their geometric boundaries by a coupler that 'communicates' values like temperature from one domain to another. The coupler is needed because of different grid geometries, time step size differences and other aspects.

You initialize the system at some known state (I.e. set the temperature, pressure, etc. at all grid points to real world measurements) and then integrate a complex differential equation for the next time step and so forth. So it is not like a automaton. Finite elements analysis comes closer, but I think they use a different scheme like finite volume methods.

A lot of insight can be gained by [this](https://pure.mpg.de/rest/items/item_3379183/component/file_3...) paper. The first 10 pages should give you a rough overview.