Cirrus Crystal Terminal Velocities

Abstract

Cirrus crystal terminal velocities are of primary importance in determining the rate of transport of condensate from upper- to middle-tropospheric levels and profoundly influence the earth?s radiation balance through their effect on the rate of buildup or decay of cirrus clouds. In this study, laboratory and field-based cirrus crystal drag coefficient data, as well as analytical descriptions of cirrus crystal shapes, are used to derive more physically based expressions for the velocities of cirrus crystals than have been available in the past. Polycrystals?often bullet rosettes?are shown to be the dominant crystal types in synoptically generated cirrus, with columns present in varying but relatively large percentages, depending on the cloud. The two critical parameters needed to calculate terminal velocity are the drag coefficient and the ratio of mass to cross-sectional area normal to their fall direction. Using measurements and calculations, it is shown that drag coefficients from theory and laboratory studies are applicable to crystals of the types found in cirrus. The ratio of the mass to area, which is shown to be relatively independent of the number of bullets in the rosette, is derived from an analytic model that represents bullet rosettes containing one to eight bullets in 19 primary geometric configurations. The ratio is also derived for columns. Using this information, a general set of equations is developed to calculate the terminal velocities and masses in terms of the aspect ratio (width divided by length), ice density, and rosette maximum dimension. Simple expressions for terminal velocity and mass as a function of bullet rosette maximum dimension are developed by incorporating new information on bullet aspect ratios. The general terminal velocity and mass relations are then applied to a case from the First International Satellite Cloud Climatology Project (ISCCP) Research Experiment (FIRE) 2, when size spectra from a balloon-borne ice crystal replicator were acquired at the same time and close to measurements from a vertically pointing Doppler radar. The calculated and measured reflectivity-weighted terminal velocities and the radar reflectivities compare favorably, providing some indication that the approach developed in this study is appropriate for cirrus crystals. The utility of the approach developed in this study is further demonstrated through a series of sensitivity studies involving the replicator size spectra for this case. Aspect ratio and density are varied, and the corresponding changes in radar reflectivity, mean reflectivity-weighted velocity, and ice water content are derived.