Models which use spherical harmonics are called 'spectral models'. The following contains a tutorial:**http://www.ecmwf.int/newsevents/training/rcourse_notes/NUMERICAL_METHODS...**

Spectral models have some advantages and disadvantages as listed at the above URL. They are quoted here for convenience:

(a) Advantages

- Space derivatives calculated exactly.
- Non-linear quadratic terns 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.

(b) Disadvantages

- 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.

National Center for Atmospheric Research Staff (Eds). Last modified 29 Aug 2017. **"The Climate Data Guide: Common Spectral Model Grid Resolutions."** Retrieved from https://climatedataguide.ucar.edu/climate-model-evaluation/common-spectral-model-grid-resolutions.

**Funding:** NSF | National Science Foundation

**Based at:** NCAR | National Center for Atmospheric Research

**A Project of:** Climate Analysis Section in Climate and Global Dynamics Laboratory

**Created by:** Climate Data Guide PIs and Staff