Achieving accuracy and efficiency in spherical modelling of real data

In this paper, a hybrid approximation method on the sphere is analysed. As interpolation scheme, we consider a partition of unity method, such as the modified spherical Shepard method, which uses zonal basis functions plus spherical harmonics as local approximants. The associated algorithm is efficiently implemented and works well also when the amount of data is very large, as it is based on an optimized searching procedure. Locality of the method guarantees stability in numerical computations, and numerical results show good accuracy. Moreover, we aimed to discuss preservation of such features when the method and the related algorithm are applied to experimental data. To achieve this purpose, we considered the Magnetic Field Satellite data. The goal was reached, as efficiency and accuracy are maintained on several sets of real data.