  We propose a number of variational regularisation methods for the estimation
and decomposition of motion fields on the $2$-sphere. While motion estimation
is based on the optical flow equation, the presented decomposition models are
motivated by recent trends in image analysis. In particular we treat $u+v$
decomposition as well as hierarchical decomposition. Helmholtz decomposition of
motion fields is obtained as a natural by-product of the chosen numerical
method based on vector spherical harmonics. All models are tested on time-lapse
microscopy data depicting fluorescently labelled endodermal cells of a
zebrafish embryo.
