A hierarchy of ice cloud models

Ice clouds, as all clouds, are important components of the Earth-Atmosphere system, influencing Earth’s energy budget and the hydrological cycle. For the representation of ice clouds in models on different scales, we have to design meaningful cloud schemes based on the relevant process (as, e.g., nucleation, growth/evaporation, or sedimentation). Since most of these processes are quite complex, we have to derive simple (or even much simpler) schemes, adapted adequately to the scales as resolved in the respective model. The derivation of bulk schemes from the underlying population balance equation is a typical example for such model reduction; this procedure typically results into a set of ordinary differential equations for averaged quantities. Even for such bulk models, simplification of these complex schemes is often necessary for the use in weather models. However, further reduction of the dynamical systems might alter their qualitative properties, i.e. the quality of solutions.

In this contribution, a consistent hierarchy of models for ice clouds at low temperatures is developed. Using several consistent approximations and simplifications, complex (bulk) schemes can be reduced to simpler models, allowing a better understanding of the represented processes. These models are analyzed in terms of qualitative behavior of solutions. It can be shown, that certain reduction steps, as, e.g., the change to a constant sedimentation velocity of cloud particles suppresses oscillatory solutions, as recently determined. During the reduction process, the ability of the resulting simpler models to represent measurements at least qualitatively is addressed.