  This paper presents a method for the approximation of harmonic potentials
that combines downward continuation of globally available data on a sphere
$\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available
data on a sphere $\Omega_r$ of radius $r<R$ (e.g., the spherical Earth's
surface). The approximation is based on a two-step algorithm motivated by
spherical multiscale expansions: First, a convolution with a scaling kernel
$\Phi_N$ deals with the downward continuation from $\Omega_R$ to $\Omega_r$,
while in a second step, the result is locally refined by a convolution on
$\Omega_r$ with a wavelet kernel $\tilde{\Psi}_N$. Different from earlier
multiscale approaches, it is not the primary goal to obtain an adaptive spatial
localization but to simultaneously optimize the related kernels $\Phi_N$,
$\tilde{\Psi}_N$ in such a way that the former behaves well for the downward
continuation while the latter shows a good localization on $\Omega_r$ in the
region where data is available. The concept is indicated for scalar as well as
vector potentials.
