On the Use of Helicity in Tornado Forecasting

Hodographs in proximity to violent tornadoes and idealized ones with different shapes and shear distributions are assessed for tornado threat, which is measured by the dynamical part of the significant tornado parameter (STP), namely, storm-relative helicity (SRH) from 0 to 1 km times the 0-6 km bulk wind difference (BWD).  The STP is a skillful predictor of tornadoes.  Here the SRH is computed across ground-based layers of different depths to assess the importance of different layers to updraft rotation.  The idealized hodographs are purely straight, straight apart from a right-angle bend at 1 km, and semicircular.  Storm motion for a right-moving supercell is customarily estimated as the mean 0-6 km wind plus a fixed propagation to the right of the 0-6 km shear vector of 7.5 m s^-1.  The propagation speed is amended herein to make it scale invariant, but this change has little bearing on the conclusions.

BWD is kept nearly constant at a high value to support supercells.  It is independent of storm motion so the effects of propagation on the STP are confined to the SRH factor.  Introduction of the storm-motion formula into the SRH expression decomposes SRH into a mean-wind helicity (MWH) and a propagation helicity (PH).  Limiting the SRH to the 0-1 km layer leaves PH mostly unrepresented in the STP for semicircular, bent, and proximity hodographs alike.  A storm need not propagate away from the mean wind for the updraft to ingest air with abundant helicity from the lowest kilometer of inflow.  Purely straight hodographs, which have no MWH and are unreal anyway, have the least tornado potential; semicircular hodographs with shear declining with height hold the greatest threat.  For semicircular hodographs, PH is smaller than MWH for all ground-based layers up to 6 km deep. In the most dangerous environments, updrafts would still rotate even if they moved simply with the mean wind and did not propagate at all.

The main contributor to 0-1 km SRH is MWH rather than PH.  This is true even for the bent hodographs, which appear almost straight.  The bend in the hodograph is crucial as it associates with near-ground streamwise vorticity and helicity in both the mean-wind and storm reference frames.  As far as the current tornado prediction method is concerned, propagation seems almost inconsequential.