# Linear, quadratic and cubic grids

The relationship between the spectral resolution, governed by the truncation number T, and the grid resolution depends on the number of grid points at which the shortest wavelength field is represented. For a grid with 2N points between the poles (so 4N grid points in total around the globe) the relationship is:

**linear grid:** the shortest wavelength is represented by 2 grid points → 4N
\( \simeq \)
2(T_{L} + 1)

**quadratic grid:** the shortest wavelength is represented by 3 grid points → 4N
\( \simeq \)
3(T_{Q} + 1)

**cubic grid:** the shortest wavelength is represented by 4 grid points → 4N
\( \simeq \)
4(T_{C} + 1)

Until the implementation of IFS cycle 18r5 on 1 April 1998, the IFS used a quadratic grid. The introduction of the two-time level semi-Lagrangian numerical scheme at IFS cycle 18r5 made possible the use of a linear Gaussian grid reflected by the T_{L} notation. The linear grid has been used since then, up to IFS cycle 41r1. For the planned resolution upgrade, the cubic representation is used with the notation T_{C} used to indicate the spectral truncation.