A unified theory for computing surface kinetic effects on ice vapor growth in cloud models

We present a simple, unified theory for ice crystal vapor growth that includes the influences of surface kinetics. The method is developed with a view to improving computation of ice vapor growth in cloud models, which require relatively simple techniques. Our method improves the traditional capacitance model for ice crystal growth, which fails at low ice supersaturations and small particle sizes when surface kinetics dominate the growth process. The theory makes use of two separate, but inter-related methods. Diffusion of vapor to within a small vapor jump length of the surface is computed using the capacitance model for crystal growth. The effects of surface kinetics are included in a similar fashion to that for spherical drops. However, for non-spherical particles we allow for the prediction of different deposition coefficients for each crystal axis (a and c) depending on the vapor flux over each axis based on crystal growth theory. Matching the total mass flow to the particle from both theories yields a kinetically-modified capacitance model which is computationally simple enough to include in cloud models. Comparisons of the instantaneous growth rates derived from the new model compare well with those from detailed ice crystal growth models. Furthermore, parcel model simulations with the new theory shows that our method predicts similar evolution of temperature, supersaturation and ice mass as compared to models that include detailed computations of ice crystal growth. This new method provides a suitable framework upon which to build parameterizations for numerical models.