On the use of artificial smoothing in Galerkin and finite difference solutions of the primitive equations

Various techniques for smoothing numerical forecast integrations are compared for both finite difference and finite element Galerkin methods. The difference in the accuracy of finite element and finite difference methods is analysed to illustrate the removal of ‘aliasing’ by the Galerkin approach. This is then related to the appropriate choice of smoothing technique. The extra accuracy of finite elements allows the use of more selective methods. The use of filtering is shown to be suspect when significant energy is present in high wavenumbers and the Sadourny gravity‐wave smoothing is also discussed.