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



[1] 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” equation image, which yields CDNC value representative of integration over a probability density function (PDF) of updraft (i.e., positive vertical) velocity. Analytical formulations for equation image 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 equation image 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 equation image (instead of equation image) 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 equation image presented here can account for an important source of parameterization “tuning” in a physically based manner.