Statistical Analysis of Turbulence-Induced Fluctuations In In-Cloud Saturation Ratio and Rates of Cloud Droplet Growth

Abstract:

We develop methods that determine the influence of turbulence on the distribution of in-cloud water vapor saturation ratio and growth rates of cloud droplets. For this purpose, a moment-based cloud parcel model is used to translate Doppler cloud radar vertical velocity spectra and radiosonde measurements into a statistical distribution of in-cloud saturation ratio, S. Because cloud droplet growth/evaporation rates are proportional to S-1, the statistical analysis of fluctuations in S yields, among other quantities, direct information on the time correlation function of droplet growth rate. From this information a Green-Kubo relation is used to determine the diffusion coefficient for fluctuations along the coordinate of cloud droplet size, D, a key turbulence parameter used in the kinetic potential theory of drizzle formation. Measurements from the Azores, SGP, and TCAP sites are analyzed and compared. A significant finding is that the probability distribution function for fluctuations in S tends to be both highly symmetric about the equilibrium saturation ratio (S=1) and non-Gaussian. Indeed the distribution has much broader tails than the Gaussian and, for the cases we have studied, turns out to be in excellent agreement with the Voight lineshape.