Representation errors in various grid and spectral truncations for a symmetric feature on the sphere

Abstract

A smooth Gaussian bell-shaped feature is used for a test case to examine the accuracy properties of finite spectral representations on the sphere. Firstly, the effect of different degrees of thinning of the number of longitudes in the Gaussian grid in the vicinity of the poles is illustrated. Secondly, it is shown that the inhomogeneity of the Gaussian grid leads to variations in accuracy as the feature location is changed, despite the fact that the triangular truncation spectral representation is homogeneous. Thirdly, the accuracy of triangular, rhomboidal and other spectral truncations are compared, with triangular truncation proving the most accurate for this type of feature.