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Relationship between spectral truncation and grid point resolution - linear, quadratic and cubic gridsThe relationship between the spectral resolution, governed by the truncation number T, and the grid resolution depends on the number of points on the grid at the equator, 4N, at which the shortest wavelength field is sampled: linear: each wavelength is sampled by 2 grid points → 4N = 2(TL + 1) quadratic: each wavelength is sampled by 3 grid points → 4N = 3(TQ + 1) cubic: each wavelength is sampled by 4 grid points → 4N = 4(TC + 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 TL notation. The linear grid has been used since then, up to and including IFS cycle 41r1. At IFS cycle 42r1, the cubic grid will be used and will be indicated by the TC notation. |
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By changing the number of points at which the shortest wavelength is sampled, the effective grid point resolution can be increased while keeping the spectral truncation number constant. Grid point computations, which are often non-linear, benefit from the higher resolution of the grid produced with cubic sampling. Such a grid has no aliasing, less numerical diffusion and more realistic surface fields. |
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