On the numerical treatment of hydrometeor sedimentation in bulk and hybrid bulk–bin microphysics schemes

Hybrid bulk--bin microphysics schemes discretize particle size distributions into bins for calculating microphysical process rates, while retaining a limited number of bulk prognostic quantities and assuming an underlying analytic functional form for the particle size distributions as in traditional bulk microphysics schemes. In this paper, the treatment of sedimentation in two-moment bulk and hybrid schemes is compared using different numerical methods.

Using the first-order upwind method for calculating sedimentation in conjunction with a widely used, two-step, time-splitting approach that updates model fields after transport by air motion followed by calculation of sedimentation, it is shown analytically that despite using a spectrum of fall speeds corresponding to different particle sizes, hybrid schemes converge with increasing bin resolution toward bulk schemes that utilize only characteristic moment-weighted particle fall speeds.