Snow aggregates evolve into a variety of observed shapes and densities. Despite this diversity, models and observational studies employ fractal or Euclidean geometric measures that are assumed universal for all aggregates. This work therefore seeks to improve understanding and representation of snow aggregate geometry and its evolution by characterizing distributions of both observed and Monte Carlo–generated aggregates. Two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations suggest the use of a bivariate beta distribution model for capturing aggregate shapes. Product moments of this model capture shape effects to within 4% of observations. This mathematical model is used along with Monte Carlo simulated aggregates to study how combinations of monomer properties affect aggregate shape evolution. Plate aggregates of any aspect ratio produce a consistent ellipsoid shape evolution whereas thin column aggregates evolve to become more spherical. Thin column aggregates yield fractal dimensions much less than the often-assumed value of 2.0. Ellipsoid densities and fractal analogs of density (lacunarity) are much more variable depending on combinations of monomer size and shape. Simple mathematical scaling relationships can explain the persistent triaxial ellipsoid shapes that appear in both observed and modeled aggregates. Overall, both simulations and observations prove aggregates are rarely oblate. Therefore, the use of the proposed bivariate ellipsoid distribution in models will allow for similar-sized aggregates to exhibit a realistic dispersion of masses and fall speeds.

This study evaluates ice particle size distribution and aspect ratio (φ) Multi-Radar/Multi-Sensor (MRMS) dual-polarization radar retrievals through a direct comparison with two legs of observational aircraft data obtained during a winter storm case from the Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) campaign. In situ cloud probes, satellite, and MRMS observations illustrate that the often-observed Kdp and ZDR enhancement regions in the dendritic growth layer can either indicate a local number concentration increase of dry ice particles or the presence of ice particles mixed with a significant number of supercooled liquid droplets. Compared to in situ measurements, MRMS retrievals on average underestimated mean volume diameters by 50% and overestimated number concentrations by over 100%. IWC retrievals using ZDR and Kdp within the dendritic growth layer were minimally biased compared to in situ calculations where retrievals yielded −2% median relative error for the entire aircraft leg. Incorporating φ retrievals decreased both the magnitude and spread of polarimetric retrievals below the dendritic growth layer. While φ radar retrievals suggest that observed dendritic growth layer particles were rather non-spherical (0.1 ≤ φ ≤ 0.2), in situ projected aspect ratios, idealized numerical simulations, and habit classifications from cloud probe images suggest that the population mean φ was generally much higher. Coordinated aircraft radar reflectivity with in situ observations suggests that the MRMS systematically underestimated reflectivity and could not resolve local peaks in mean volume diameter sizes. These results highlight the need to consider particle assumptions and radar limitations when performing retrievals.

Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework which couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m/s standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.