  Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that
encodes information on the topology of magnetic field lines. It has long been
appreciated that magnetic topology is an important constraint for the evolution
of magnetic fields in MHD. In applications to the solar atmosphere,
understanding magnetic topology is crucial for following the evolution and
eruption of magnetic fields. At present, magnetic helicity flux can be measured
in solar observations but the interpretation of results is difficult due to the
combination of confounding factors. We propose that a renormalization of
helicity flux, the \emph{magnetic winding}, can be used to detect more detailed
topological features in magnetic fields and thus provide a more reliable
signature for predicting the onset of solar eruptions.
