Grid models vs. spectral models

Grid models vs. spectral models

The three dimensions of space can be accounted for in various ways in numerical weather or climate prediction models. Most models are grid models, in which variables are computed at discrete grid points in the horizontal and vertical directions. The model resolution refers to the (horizontal) spacing between gridpoints. The grid spacing is not necessarily equidistant. For instance, some models use a longitude difference as zonal grid spacing, so near the poles the zonal grid spacing becomes zero. In the vertical direction the spacing is usually variable, the model resolution typically is highest just above sea level.

Other models, in particular those whose domain is global, are spectral models (Note 15.H): these transform the variation of some variable (e.g. temperature) with latitude and longitude into a series of waves; the highest wave number retained in the Fourier transform is a measure of the model resolution.

Numerical prediction models are based on the equations of motion (Note 15.G), and these involve many partial derivatives in space. Partial derivatives of wave fields (as used in spectral models) can be calculated exactly, rather than by means of a finite difference approach (used in grid models). This is the main advantage of spectral models. Of course the wave form is converted back into a spatial form after the calculations, in order to analyze the forecasts.