  We present an asymptotic approach for the systematic investigation of the
effect of gravity waves (GW) on ice clouds formed through homogeneous
nucleation. In particular, we consider high- and mid-frequency GW in the
tropopause region driving the formation of ice clouds, modeled with a
double-moment bulk ice microphysics scheme. The asymptotic approach allows for
identifying reduced equations for self-consistent description of the ice
dynamics forced by GW including the effects of diffusional growth and
nucleation of ice crystals. Further, corresponding analytical solutions for a
monochromatic GW are derived under a single-parcel approximation. It is
demonstrated that the asymptotic solutions capture the dynamics of the full ice
model and provide a simple expression for the nucleated number of ice crystals.
The present approach is extended to allow for superposition of GW, as well as,
for variable mean mass in the ice crystal distribution. Implications of the
results for an improved representation of GW variability in cirrus
parameterizations are discussed.
