The size of the boxes limits the resolution of the model just as the size of the dots in a newspaper photo limits the amount of detail the photo can represent. The problem is that making the boxes smaller requires more calculations, pushing even today s best computers to their limits. This is why climate scientists have more confidence in what models say about the broad global picture than about what the climate will be in a particular city. Some key atmospheric processes like clouds happen at scales too small to represent within the coarse resolution of models. Clouds are much smaller than 150 miles on a side, but they play a key role in shading or warming the earth.
Modelers represent such processes by making estimates.
Very well grounded estimates, perhaps but estimates nonetheless. Scientists are constantly testing and evaluating them to find out. One way to do this is to plug in a set of known historical conditions to start them off and then to see how accurately they reproduce the real climate that actually followed from those conditions. In many cases the models do quite well at such hindcasting, and they are getting better all the time. Whatever the disagreements among models or interpretations of them, one thing stands out.