Weather and climate models do not represent the atmosphere in a continuous manner, but at either discrete points or "area" averages. This is the case in the horizontal (east-west and north-south), vertical and in time. In general, models cannot represent variability on scales smaller than those defined by these discrete points or "area" averages.
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".
(In addition to using grid points, the ECMWF model (IFS) also uses an additional mathematical concept, spectral space, to represent horizontal space. This concept uses a set of waves, spherical harmonics, to describe variations in the horizontal. The IFS switches between spectral space and grid point space, in order to perform specific computations.)
A description of the grid used for ERA5 data is given at:
ERA5: What is the spatial reference
A description of the grid used for ERA-Interim data is given at:
ERA-Interim: What is the spatial reference
Vertical
In the vertical, models can use levels, located at discrete points, and/or averages over layers.
Time
Weather and climate models usually represent time at discrete points, with a spacing that is called the time step. The time step typically varies between a few minutes and half an hour, depending on the model.
