Does wind shear cause hydrometeor size sorting?

Several recent studies have implicated vertical wind shear in producing steady-state size sorting of a distribution of hydrometeors falling at their terminal velocity, when such varies as a function of hydrometeor diameter. In particular, this mechanism has been invoked to explain both the strength and storm-relative orientation of the commonly observed Z_DR arc in supercell thunderstorms. However, the actual role of the shear has not been fully clarified. In this study, a simple analytical model is used to show that the fundamental source of size-sorting is the storm-relative wind field itself, and in particular, its mean taken over the depth of the sorting layer. Wind shear is only strictly required for producing sustained size sorting in the special but common case of a precipitation source having a motion that lies on the hodograph (such as with the environmental winds at the source level). In supercells, the precipitation source (the rotating updraft) does not necessarily move with the winds at any level. We show that this off-hodograph propagation and the associated storm-relative mean wind is responsible for the positive correlation of size sorting observables (such as Z_DR) and storm-relative helicity (SRH) that has been noted in previous work.