What can we conclude about the real aspect ratios of ice particle aggregates from two-dimensional images?

A simple numerical experiment was performed to investigate the result published in many papers that measurements indicate that aggregates may be well represented as oblate spheroids with mean aspect ratio (semiminor axis to semimajor axis length) of 0.6. The aspect ratio measurements are derived from two-dimensional projections of complex three-dimensional aggregates. Here, aggregates were modeled as ellipsoids with semiprincipal axes of length a, b, and c, which include oblate spheroids (a = b) as a class, and the projected aspect ratios of large numbers of two-dimensional projections of them were sampled. When sampling oblate spheroids with aspect ratio 0.6 over random orientations, the mean projected aspect ratio is 0.746. A mean projected aspect ratio of 0.6 is obtained for an oblate spheroid with aspect ratio of 0.33. When sampling randomly oriented ellipsoids with semiminor axes (b, c) varying from 0.10 to 1.00 in steps of 0.01, representing many complex shapes, the mean projected aspect ratio is 0.595, close to the measured mean projected aspect ratio of aggregates of 0.6. These experiments demonstrate that the conclusion one may safely draw from the projected aspect ratio measurements is that the mean aspect ratio of aggregates is lower than 0.6. Moreover, the projected aspect ratio distributions from measurements suggest a mixture of aggregate shapes, rather than only oblate spheroids as is often assumed.