In a Chinese book, I read about the relationship between the numerical model spatial resolution and the computation cost.
It states: when the spatial resolution of model is finer, the result will be preciser. But to achieve a fine grid resolution, the computation cost will increase. For example, when the grid resolution in a 3-D model framework halves (e.g. from 10 km to 5 km), the computation cost will increase by a factor 24.
Why is this? How can I determine the increase of computation costs when the spatial grid resolution changes?
The model here is a 3-d numerical model for weather forcasting like WRF, MM5, etc.