Inferring Fall Attitudes of Pristine Dendritic Crystals from Polarimetric Radar Data

Abstract

Single pristine planar ice crystals exhibit some flutter around their preferential horizontal orientation as they fall. This study presents estimates of flutter and analyzes predominant fall attitudes of pristine dendritic crystals observed with a polarization agile Ka-band cloud radar. The observations were made in weakly precipitating winter clouds on slopes of Mt. Washington, New Hampshire. The radar is capable of measuring the linear depolarization ratios in the standard horizontal?vertical polarization basis (HLDR) and the slant 45°?135° polarization basis (SLDR). Both HLDR and SLDR depend on crystal shape. HLDR also exhibits a strong dependence on crystal orientation, while SLDR depends only weakly on orientation. The different sensitivities of SLDR and HLDR to the shape and orientation effects are interpreted to estimate the angular flutter of crystals. A simple analytical expression is derived for the standard deviation of angular flutter as a function of the HLDR to SLDR ratio assuming perfect radar system characteristics. The flutter is also assessed by matching theoretical and observed depolarization patterns as a function of the elevation of the radar?s beam. The matching procedure is generally more robust since it accounts for the actual polarization states and imperfections in the radar hardware. The depolarization approach was used to estimate flutter of falling pristine dendrites that were characterized by Reynolds numbers in a range of approximately 40?100. Using the matching approach, this flutter was found to be about 9° ± 3°, as expressed by the standard deviation of the crystal minor axes from the vertical direction. The analytical expression provides a value of flutter of about 12°, which is at the high end of the estimate obtained by the matching procedure. The difference is explained by the imperfections in the polarization states and radar hardware, so the analytical result serves as an upper bound to the more robust result from matching. The values of flutter estimated from the experimental example are comparable to estimates for planar crystals obtained in laboratory models and by individual crystal sampling.