Importance of a proper treatment of ice crystal sedimentation for cirrus clouds in large-scale models

We investigate the effect of a dual-moment scheme for ice crystal sedimentation in an ice cloud microphysics scheme, namely using one terminal velocity for the ice crystal number density and a different terminal velocity for the ice mass concentration, which is always larger than the former. Both are derived from the flux density concept, which was introduced by Srivastava (1978) for raindrops. Traditionally, many microphysics schemes in large-scale models use only the mass weighted terminal velocity for ice crystals, which is usually dictated by computing time limitations. However, while computers get faster, it is possible to introduce more detailed microphysics schemes into these models.

We derive appropriate expressions for the two terminal velocities, and show how their implementation affects the simulated evolution of an ice cloud using a simple process study. In our study, we use the anelastic, non-hydrostatic model EuLag. Recently, a bulk scheme for ice microphysics was developed and implemented, including ice nucleation (homogeneous /heterogeneous), deposition growth/evaporation and sedimentation. In our present study, nucleation does not occur, we only regard sedimentation and evaporation of ice crystals.

Using the EuLag model we find the method with different terminal velocities for mass and number density superior to the simpler method with only one terminal velocity. In the dual-moment scheme larger crystals accumulate at cloud bottom while small crystals remain at the cloud top. In contrast, the single-moment scheme leads to a rather uniform crystal size distribution throughout the depth of the cloud, which is contrary to our physical understanding. The different treatment of sedimentation also leads to important differences in cloud vertical structure, cloud lifetime, and optical properties. Especially, the derived heating rates show differences up to few Kelvin per day. In particular the latter points indicate that use of a proper sedimentation scheme may be of great importance for climate models.