Parameterization of Drop Effective Radius for Drizzling Marine Stratus in Global Circulation Models

The cloud drop effective radius, Re, is one of the most important parameters in calculations of cloud radiative properties. Numerous formulations of the effective radius have been developed for use in numerical models (see, e.g., review in Gultepe et al. 1996); however, to the best of our knowledge, they all were designed for non-drizzling clouds. The objective of this paper is to derive a parameterization of Re for precipitating boundary layer clouds. The Re parameterization is necessarily a function of cloud prognostic variables used in a specific numerical model. To this regard, we note that the majority of current formulations of cloud processes in numerical models are based on partial moments of the drop distribution function: Qc, cloud water and Qr, rain water mixing ratios (Kessler 1969). Kogan and Belochitski (2000) argue that a better-posed problem can be formulated based on the total moments of the drop size distributions (DSD). In this paper, we describe Re parameterizations based on total, as well as partial moments of the DSD. In the latter case, we use the following set of variables: N total drop concentration, Q total liquid water content, and Qr drizzle liquid water content, while in the former case radar reflectivity Z is used instead of Qr. By using multiple nonlinear regression analysis, we seek Re in the form (Re)par =D N Q Z, where (Re)par is in microns, Q and Qr in g m, N in cm, and Z in dBZ.