Sedimentation-Induced Errors in Bulk Microphysics Schemes

The computation of hydrometeor sedimentation in one-moment, two-moment, and three-moment bulk microphysics parameterizations is examined in the context of a 1D model, with no other microphysical processes active. The solution from an analytic bin model is used as a reference against which the bulk model simulations are compared. Errors in the computed (nonprognostic) moments from 0 to 7 from the bulk model runs are examined. In addition to the commonly used predicted variables (number concentration, mass, and reflectivity), bulk scheme configurations with alternative combinations of prognostic moments are considered. While the extra degree of freedom in a two-moment scheme adds realism to the simulation of sedimentation over a one-moment scheme, the standard practice of imposing a constant relative dispersion in the particle size distribution results in considerable errors in some of the computed moments. The error can be shifted to different moments by selecting different prognostic moments. For three-moment schemes, the error is considerably reduced over a wide range of computed moments and there is much less sensitivity to the choice of prognostic variables. Two alternative approaches are proposed for modifying the computation of sedimentation in two-moment schemes to reduce problems associated with excess size sorting. The first approach uses a diagnostic relative dispersion (shape) parameter, generalized for any pair of prognostic moments. The second involves progressively reducing the differential fall velocities between the moments and is therefore applicable for schemes that hold the shape parameter constant. Both approaches greatly reduce the errors in the computed moments, including those on which microphysical process rates depend, and are easily applied to existing two-moment schemes.