On the Spatial Resolution of Homogeneous Isotropic Filters on the Sphere

Abstract

Interest in filtering on the sphere was rejuvenated by the necessity to filter GRACE data, which has led to the development of a variety of filters with a multitude of design methods. Nevertheless, a lacuna exists in the understanding of filters and filtered fields, especially signal leakage due to filtering and resolution of the filtered field. In this contribution, we specifically look into the latter aspect, where we take an intuitive and empirical approach instead of a rigorous mathematical approach. The empirical approach is an adaptation of the technique used in optics and photography communities for determining the resolving power of lenses. This resolution analysis is carried out for the most commonly used homogeneous isotropic filters in the GRACE community. The analysis indicates that a concrete number for the filters can only be specified as an ideal number. Nevertheless, resolution as a concept is described in detail by the modulation transfer function, which also provides some insight into the smoothing properties of the filter.