In this paper we summarize the basic formulas of wavelet analysis
with the help of Poisson wavelets on the sphere. These wavelets have the nice property that all basic formulas of wavelet analysis as reproducing kernels, etc. may be expressed simply with the help of higher degree Poisson wavelets. This makes them numerically attractive for applications in geophysical modeling. We do not give any proofs and we refer to "M. Holschneider, I. Iglewska-Nowak, JFAA, 2007", where all proofs are published.