# Common Spectral Model Grid Resolutions

Models which use spherical harmonics are called 'spectral models'.Spectral models have some advantages and disadvantages. An ECMWF workshop tutorial (which is no longer available online) stated the following:

• Space derivatives calculated exactly.
• Non-linear quadratic terms calculated without aliasing (if computed in spectral space or using the quadratic grid).
• For a given accuracy fewer degrees of freedom are required than in a grid-point model.
• Easy to construct semi-implicit schemes since spherical harmonics are eigenfunctions of the Helmholtz operator.
• On the sphere there is no pole problem.
• Phase lag errors of mid-latitude synoptic disturbances are reduced.
• The use of staggered grids is avoided.

• The schemes appear complicated, though they are relatively easy to implement.
• The calculation of the non-linear terms takes a long time unless the transform method is used.
• Physical processes cannot be included unless the transform method is used.
• As the horizontal resolution is refined, the number of arithmetic operations increases faster in spectral models than in grid-point models due to the Legendre transforms whose cost increases as N3.
• Spherical harmonics are not suitable for limited-area models.

Some commonly encountered spectral resolutions follow. A more extensive listing is at https://www.ecmwf.int/en/forecasts/documentation-and-support/data-spatial-coordinate-systems

 Common Model Spectral Resolutions Truncation lat x lon km at Eq deg at Eq T21 32x64 625 5.61 T42 64x128 310 2.79 T62 94x192 210 1.89 T63 96x192 210 1.88 T85 128x256 155 1.39 T106 160x320 125 1.12 T159 240x480 83 0.75 T255 256x512 60 0.54 T382 576x1152 38 0.34 T799 800x1600 25 0.22