Retrieving maximum dimension, aspect ratio, and orientation of ice particles from their two-dimensional projections

The maximum dimension, aspect ratio, and orientation of non-spherical particles cannot be truly determined by instruments that record only two-dimensional projections of the particles. In nature, ice crystals can present a large variety of shapes from very flat plates and dendrites to thin needles, and their aggregates. In this study, ice particles are represented by ellipsoids with different shapes. The relationships between the characteristics of 4186 ellipsoids and their projections at different orientations are studied by analysis of simulations of one (e.g. cloud imaging probes), two (e.g. two-dimensional video disdrometer) and three (e.g. multi-angle snowflake camera) simultaneous projections from different viewing directions. The particle maximum dimension is underestimated and aspect ratio overestimated from their projections, but using multiple projections reduces the biases. The maximum-dimension biases for oriented particles are larger than for randomly oriented particles, but their aspect-ratio biases are smaller. For oblate spheroids with aspect ratio 0.6, an oft-assumed shape for aggregates, the average retrieval aspect ratio is 0.75. A retrieved aspect ratio of 0.6 is obtained for an oblate spheroid with an actual aspect ratio of 0.33. Distributions of aspect ratios retrieval from two-dimensional projections are best matched from the complete set of ellipsoids, with each ellipsoid randomly oriented. Assuming an underlying oblate spheroid shape with the average observed aspect ratio produces approximately 100% bias in estimating volume by using the volume of the oblate spheroid for the measuring systems with one, two, or three projections. The standard deviation of the projection orientation angle (the angle between the major axis of the particle and the horizontal) distribution mainly depends on the standard deviation of a Gaussian distribution used to represent particle orientations, if the particles are assumed to be either oblate or prolate spheroids. For these spheroidal particles, the particle orientation can be accurately retrieved with the orientation angles from multiple cameras. A new measuring system, the Three Orthogonal (ThOr) cameras system, is proposed, which reduces the maximum dimension measurement bias to less than 4% for all shapes of ellipsoids and orientations.