A novel approach for representing ice microphysics in models: Description and tests using a kinematic framework

This paper documents the development of a novel approach for representing ice microphysics in numerical models. In this approach, the ice particle mass-dimension and projected-area-dimension relationships vary as a function of particle size and rimed mass fraction. All ice microphysical processes and parameters are calculated in a self-consistent manner in terms of these mass-dimension and area-dimension relationships. The rimed mass fraction is predicted locally by separately predicting the ice mixing ratios acquired through water vapor deposition and through riming. The third predicted variable is the number concentration of ice particles. This approach allows representing in a natural way the gradual transition from small to large ice particles due to growth by water vapor deposition and aggregation and from unrimed crystals to graupel due to riming. In traditional approaches, these processes are treated by separating ice particles into predefined categories (such as cloud ice, snow, and graupel) using fairly arbitrary thresholds and conversion rates. With some modifications, the new approach can be employed in either bin or bulk microphysical models. In this paper, the new approach is implemented in a bulk two-moment microphysical scheme representing both warm-rain and ice processes and it is applied to an idealized 2D kinematic framework mimicking a shallow mixed-phase cumulus. The size distributions of cloud droplets, drizzle/rain drops, and ice particles are represented using gamma distributions. The new scheme is compared to a version of the scheme that uses the traditional approach for ice microphysics; that is, unrimed ice/snow and graupel are separate species, with threshold-based conversion rates between the former and the latter. The new and traditional schemes produce similar results, although the traditional scheme, unlike the new scheme, produces a distinct double maximum in the surface precipitation rate, corresponding to precipitation shafts consisting of either ice/snow or graupel. The relative magnitude of these peaks, as well as the ice water path and optical depth of the simulated cloud, is highly sensitive to the threshold for converting unrimed ice to graupel. In contrast, the new scheme does not require any conversion threshold and predicts formation of ice particles with wide range of rimed fractions.