A gridpoint model's horizontal resolution is defined as the average distance between adjacent grid points with the same variables. For example, if all of a model's forecast variables are predicted at each of its grid points, the model is considered to have a resolution equal to the minimum spacing between adjacent grid points at a specific latitude and longitude.
In this example, all of the variables are computed at each grid point so the resolution is 50 km. A similar model with 10 km between adjacent grid points is considered to have 10-km horizontal resolution. However, that does not mean it can resolve features which are only 10 km across!
If the horizontal resolution of a model is increased from 50 km to 10 km, how much will the memory requirements increase by?
The correct answer is c.
The increase in memory is a factor of 5 for an increase in resolution in each horizontal direction, hence 5 x 5 = 25. It is at least this much because a horizontal resolution will typically be accompanied by an increase in vertical resolution, and an increase in timestep.