Parameterizations for Clouds and Precipitation Based on the Kinetic Potential Theory for Drizzle Formation

Effects from turbulence-induced fluctuations in water vapor saturation on the growth of cloud droplets are examined using a Brownian-like diffusion model to represent the condensation growth/evaporation of droplets along the coordinate of droplet size. The model predicts a diffusive broadening of the droplet size distribution with time, tempered by enhanced evaporation-induced drift of droplets to smaller size from vapor depletion, and approach to a stationary size distribution determined by the balance between size-space diffusion and drift. This balance between diffusion and drift is shown to yield simple analytic expressions for the size distribution that are in good agreement with observed size distributions. Monte Carlo simulations of the approach to the stationary limit and of the distribution itself are presented. A key turbulence parameter required by the kinetic potential theory of drizzle formation (McGraw and Liu 2003, 2004) is estimated using the new results.