...
In general, models cannot represent variability on scales smaller than those defined by the spacing between the discrete points, the grid scale. In fact, models don't represent the grid scale very well either, with the effective resolution of models being a small multiple of the grid scale.
Horizontal
In the horizontal the discrete points are arranged in a two dimensional grid and hence are referred to as grid points. The grid can be regular or irregular. An example of a regular latitude/longitude grid would be where the grid points are located every 1 degree of longitude in the east-west direction and every 1 degree of latitude in the north-south direction. Each grid point is associated with an area that either surrounds the grid point or lies between the grid points. This area is referred to as the "grid box".
...