On Averaging Aspect Ratios and Distortion Parameters over Ice Crystal Population Ensembles for Estimating Effective Scattering Asymmetry Parameters

Abstract

he use of ensemble-average values of aspect ratio and distortion parameter of hexagonal ice prisms for the estimation of ensemble-average scattering asymmetry parameters is evaluated. Using crystal aspect ratios greater than unity generally leads to ensemble-average values of aspect ratio that are inconsistent with the ensemble-average asymmetry parameters. When a definition of aspect ratio is used that limits the aspect ratio to below unity for both hexagonal plates and columns, the effective asymmetry parameters calculated using ensemble-average aspect ratios are generally consistent with ensemble-average asymmetry parameters, especially if aspect ratios are geometrically averaged. Ensemble-average distortion parameters generally also yield effective asymmetry parameters that are largely consistent with ensemble-average asymmetry parameters. In the case of mixtures of plates and columns, it is recommended to geometrically average the aspect ratios and to subsequently calculate the effective asymmetry parameter using a column or plate geometry when the contribution by columns to a given mixture?s total projected area is greater or less than 50%, respectively. In addition, it is shown that ensemble-average aspect ratios, distortion parameters, and asymmetry parameters can generally be retrieved accurately from simulated multidirectional polarization measurements based on mixtures of varying columns and plates. However, such retrievals tend to be somewhat biased toward yielding columnlike aspect ratios. Furthermore, generally large retrieval errors can occur for mixtures with approximately equal contributions of columns and plates and for ensembles with strong contributions of thin plates.