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Weather and climate models do not represent the atmosphere in a continuous manner, but either at discrete points or averages around those points. This is the case in the horizontal (east-west and north-south), vertical and in time.

In general, models cannot represent spatial variability on scales smaller than those defined by the spacing between the discrete points, the grid scale. Model values described as representing values at the discrete points, actually represent some sort of average value over the grid scale. However, models don't represent the grid scale very well either, with the effective resolution of models being somewhat larger than the grid scale.

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(In addition to using grid points, the ECMWF model Integrated Forecasting System (IFS) also uses an additional mathematical concept, spectral space, to represent horizontal space. This concept uses a set of waveswavy basis functions, spherical harmonics, to describe variations in the horizontal. The IFS switches between spectral space and grid point space, in order to perform specific computations.)

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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.

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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 and its configuration.

So called "instantaneous" parameters, in fact, Model parameters cannot represent variability on short time scales smaller than the time step, but tend to evolve smoothly, for more information see the article "Parameters valid at the specified time".

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