Use of Doppler radar to assess ice cloud particle fall velocity-size relations for remote sensing and climate studies

Knowledge of ice crystal terminal velocities, both for individual crystals and for size distributions, is important for an adequate representation of ice particle sedimentation in climate models. While the terminal velocities (nu(t)) of individual crystals of simple shapes have been measured, theoretical relations of the form nu(t) = AD(B) (where D is the maximum particle dimension), obtained using expressions for the aerodynamic drag force, are often more useful because they can be applied to a wide range of particle sizes and heights and temperatures in the atmosphere. For high tropospheric ice clouds the coefficient A has been found to vary over 1 order of magnitude; the exponent B is generally within the range 0.7-1.4. Aerodynamic drag force calculations show that A and B are related. A and B can also be used to characterize terminal-velocity-particle characteristic size relations for size distributions. In this study we use collocated, vertically pointing measurements of ice cloud radar reflectivity, Doppler velocity, and IR brightness temperatures to estimate the vertical profiles of cloud particle characteristic size, cloud ice water content, and vertically averaged value of the coefficient A, emphasizing cirrus clouds. We analyze variations in terminal-velocity-size relations for individual particles and corresponding variations for ensembles of particles: for example, in relations between the reflectivity-weighted terminal velocity and the median volume size and between the mass-weighted terminal velocity and the median volume size. The retrievals indicate that A ranges from similar to 250 to almost 4000 legs units), similar to the range found from the theoretical calculations. The coefficient A tends to decrease as a characteristic particle size (e.g., median size) increases. As a simplification for climate modeling efforts, we present an empirical relation between median size and A, although there is a fair amount of variability about this relation. Using the Doppler measurements and retrieval data, we also derive relations between the mass-weighted terminal velocity and cloud ice water content. Such relations are useful for representing fallout of ice particles in climate and cloud-resolving models.