Sedimentation in bulk microphysics schemes—considering alternatives to the standard two-moment approach

In the last decade, two-moment bulk microphysics schemes have become increasing popular in mesoscale modeling research and will likely become common in high-resolution operational numerical weather prediction models in the very near future. The standard approach for two-moment schemes is to assume a functional form of the particle size distribution (PSD) for each hydrometeor category and predict the mass mixing ratio and total number concentration (the third and zereoth moments, respectively),with two corresponding free parameters of the PSD. Relatively little attention has been given to exploring alternatives to this standard approach. Recently, it has been shown that alternatives to assuming a fixed relative dispersion of the distribution can alleviate problems associated with sedimentation in standard two-moment schemes and that the choice of prognostic moments can have important consequences on the computation of other important moments, such as those on which the microphysical growth rates depend.

In this study, we explore alternatives to the standard bulk method and we examine and quantify the errors associated with the choice of prognostic moments in one-moment, two-moment, and three-moment bulk schemes for the treatment of pure sedimentation (with all other microphysical processes shut off) in the context of a 1D column model. While highly simplified, this approach has the advantage of having available an exact analytic solution for a given set of prescribed conditions. In addition to quantifying the relative benefits of predicting additional moments, it will be shown that by appropriately choosing the prognostic moments used to compute sedimentation, errors in the computation of the moments on which the microphysical growth rates depend most strongly can be minimized. Further, error that results from uncontrolled size-sorting in standard two-moment schemes can be can be reduced considerably by modifying the ratio of the bulk fall velocities, based on the values of the prognostic moments, or by allowing a variable relative dispersion in the PSD. While the least error for the largest range of computed moments comes from using three-moment schemes, the error in the important moments can be minimized in a two-moment scheme through careful considerations of the treatment of sedimentation.