Consistent treatment of diffusional growth in mixed-phase clouds

Diffusional growth is the most important growth mechanism for small water particles in clouds. Two non-linear diffusion equations control the transport of water vapor and energy. In a mixed-phase cloud the situation becomes more complicated due to the presence of ice particles, being the new stable phase. The correct representation of this situation will lead to a correct description of the Wegener-Bergeron-Findeisen (WBF) process. This process describes the growth of ice particles at the expense of present water droplets but is usually not well represented in cloud models, neither in bin nor bulk microphysics parameterizations.

We developed a reference model based on single particles to investigate the diffusional growth. In this model we solve the non-linear time-dependent diffusion equations for vapor and energy transport by a finite element approach. The shape of the ice particles is approximated by ellipsoids, including a space dependent saturation pressure at the surface of the particles. The background water vapor field is time-dependent in order to mimic the impact of turbulence. Different geometrical distributions of droplets and ice particles are prescribed in order to investigate effects of inhomogeneous droplet and crystal distributions.

Additionally we used a bulk-model approach with potential functions to represent the WBF process and solved the evolution equation for the time-dependent mass distribution function with a Galerkin method.