Characteristic updrafts for computing distribution-averaged cloud droplet number and stratocumulus cloud properties

A computationally effective framework is presented that addresses the contribution of subgrid-scale vertical velocity variations in predictions of cloud droplet number concentration (CDNC) in large-scale models. Central to the framework is the concept of a "characteristic updraft velocity" w*, which yields CDNC value representative of integration over a probability density function (PDF) of updraft (i.e., positive vertical) velocity. Analytical formulations for w* are developed for computation of average CDNC over a Gaussian PDF using the Twomey droplet parameterization. The analytical relationship also agrees with numerical integrations using a state-of-the-art droplet activation parameterization. For situations where the variabilities of vertical velocity and liquid water content can be decoupled, the concept of w* is extended to the calculation of cloud properties and process rates that complements existing treatments for subgrid variability of liquid water content. It is shown that using the average updraft velocity w* (instead of w*) for calculations of Nd, re, and A (a common practice in atmospheric models) can overestimate PDF-averaged Nd by 10%, underestimate re by 10%-15%, and significantly underpredict autoconversion rate between a factor of 2-10. The simple expressions of w* presented here can account for an important source of parameterization "tuning" in a physically based manner. Copyright 2010 by the American Geophysical Union.