> That means it has to treat the globe as a grid of 18 mile cubes
Although this is made somewhat easier in that the vertical component is done in pressure "levels", somewhat simplifying the equations to be solved. However that shouldn't underestimate the scale of the problem. IIRC a model with a surface resolution of 100km means solving for something of the order of 30 million variables for each time step.
Full scale climate models can get even harder, as you need to couple an ocean circulation model to a atmospheric circulation model - ocean circulation is less important for a weather model as its time scale is of the order of up to 1000 years.
Although this is made somewhat easier in that the vertical component is done in pressure "levels", somewhat simplifying the equations to be solved. However that shouldn't underestimate the scale of the problem. IIRC a model with a surface resolution of 100km means solving for something of the order of 30 million variables for each time step.
Full scale climate models can get even harder, as you need to couple an ocean circulation model to a atmospheric circulation model - ocean circulation is less important for a weather model as its time scale is of the order of up to 1000 years.