Statistical analysis of turbulence induced fluctuations in in-cloud saturation ratio and rates of cloud droplet growth

Description

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 analysis 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 Kubo-Nyquist 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. (1) Environmental Sciences Department, Brookhaven National Laboratory, Upton, NY 11973. (2) Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, QC, Canada.