One consequence of 6(a) is that smaller spatial grids also require shorter time steps. This means that the computational resources required to implement simulations at a constant speed increase not arithmetically, but *geometrically* as the simulation becomes more precise^{[1]}. Smaller grid cells--and thus more precision--require not just *more* computation, but also *faster* computation; the model must generate predictions for the behavior of more cells, and it must do so more frequently^{[2]}.

Implementing either an atmospheric or oceanic general circulation model is a careful balancing act between these (and many other) concerns. However, the most sophisticated climate simulations go beyond even these challenges, and seek to couple different fully-fledged circulation models together to generate a comprehensive CGCM.

**6.2.1 Coupling General Circulation Models**

We can think of CGCMs as being “meta-models” that involve detailed circulation models of the atmosphere and ocean (and, at least sometimes, specialized terrestrial and cryosphere models) being *coupled* together. While some CGCMs do feature oceanic, atmospheric, cryonic, and terrestrial models that interface directly with one another (e.g. by having computer code in the atmospheric model “call” values of variables in the oceanic model), this direct interfacing is incredibly difficult to implement. Despite superficial similarities in the primitive equations underlying both atmospheric and oceanic models--both are based heavily on fluid

- ↑ In practice, halving the grid size does
*far*more than double the computational resources necessary to run the model at the same speed. Recall that in each grid, at least six distinct variables are being computed across three dimensions, and that doubling the number of cells doubles the number of each of these calculations. - ↑ Of course, another option is to reduce the output speed of the model--that is, to reduce the ratio of “modeled time” to “model time.” Even a fairly low-power computer can render the output of a small grid / short time step model given enough time to run. At a certain point, the model output becomes useless; a perfect simulation of the next decade of the global climate isn’t much use if it takes several centuries to output.

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