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 resolve/specify real-world states using a grid 1,000 meters to a side).

The link between time-step length and grid size, though, is perhaps slightly less obvious. In general, the shorter the time-steps in the simulation--that is, the smaller Δt is in the difference equations underlying the simulation--the smaller the grid cells must be. This makes sense if we recall that the simulation is supposed to be modeling a physical phenomenon, and is therefore constrained by conditions on the transfer of information between different physical points. After all, the grid must be designed such that during the span between one time-step and the next, no relevant information about the state of the world inside one grid cell could have been communicated to another grid cell. This is a kind of locality condition on climate simulations, and must be in place if we’re to assume that relevant interactions--interactions captured by the simulation, that is--can’t happen at a distance. Though a butterfly’s flapping wings might eventually spawn a hurricane on the other side of the world, they can’t do so instantly: the signal must propagate locally around the globe (or, in the case of the model, across grid cells). This locality condition is usually written:

In the context of climate modeling, $$c$$ refers not to the speed of light in a vacuum, but rather the maximum speed at which information can propagate through the medium being modeled Its value thus is different in atmospheric and oceanic models, but the condition holds in both cases: the timesteps must be short enough that even if it were to propagate at the maximum possible speed, information could not be communicated between one cell and another between one time step and the next. 194