Snowflakes are Not Spheres or Spheroids: What is the “True” Shape and Density Evolution of Snow Aggregates

Description

Snow precipitation rates, collection rates, and radiation properties are dependent on the geometry of each individual snow aggregate. Yet the literature on snowflake geometry presents many different and often contradictory claims as to their “true” shapes and densities. Some studies claim that snowflakes are approximately spheres while others claim that snowflakes are oblate spheroids with aspect ratios of 0.6. Still other studies use fractal geometry to claim that snowflakes exhibit a universal fractal dimension of 2.0 or 2.2. This study attempts to reconcile some of these claims by using both Multi-Angle Snowflake Camera (MASC) observations and Monte Carlo simulations to study how Euclidean and fractal geometric estimates of aggregate “shape” and “density” evolve throughout the aggregation process. MASC observations are used to derive estimates of best-fit tri-axial ellipsoids. We show that our Monte Carlo generated aggregates produce ellipsoid distributions that resemble the same shape as that observed from the MASC. The consistency of observed and modeled ellipsoid aspect ratio distributions with beta distributions allows us to construct a bivariate beta distribution model that can characterize the entire distribution of aggregate ellipsoids (see Figure). We show that this constructed bivariate distribution captures distribution moments related to the ellipsoid shapes to within approximately 4% of those observed. Furthermore, we show that while different initial monomer habits and aspect ratios always produce the same type of observed ellipsoid distribution, the estimates of density and fractal dimensions are much more variable. In particular, we show that aggregates composed of thin columns or needles exhibit significantly lower fractal dimensions than the often assumed value of 2.0. Estimates of other fractal quantities such as lacunarity (a measure of porosity) suggests that snowflake aggregates with the same fractal dimension can still exhibit different properties, such as mass and density. Therefore, our numerical studies illustrate that the current use of mass dimensional relationships should be modified to better estimate the prefactor components. Future work will incorporate the constructed bivariate ellipsoid aspect ratio model into the Ice-Spheroids Habit Model with Aspect-Ratio EvoLution (ISHMAEL) in WRF. Our proposed ellipsoid distribution will allow for particles of the same size to exhibit a realistic spectrum of mass and fall speeds.