Tracking magnetic footpoints with the magnetic induction equation

The accurate estimation of magnetic footpoint velocities from a temporal sequence of photospheric magnetograms is critical for estimating the magnetic energy and helicity fluxes through the photosphere. A new technique for determining the magnetic footpoint velocities from a sequence of magnetograms is presented. This technique implements a variational principle to minimize deviations in the magnitude of the magnetic induction equation constrained by an affine velocity profile, which depends linearly on coordinates, within a windowed subregion of the magnetogram sequence. The variational principle produces an overdetermined system that is solved directly by linear least-squares or total least-squares methods. The resulting optical flow field and associated uncertainties are statistically consistent with the magnetic induction equation and the affine velocity profile within this aperture. The general technique has potential for application to other solar data sets where a physical model for the underlying image dynamics can be applied.