On the Geometry of Aggregate Snowflakes

Snowflakes play a crucial role in weather and climate. A significant portion of precipitation that reaches the surface originates as ice, even when it ultimately falls as rain. Contrary to the popular image of symmetric, dendritic crystals, most large snowflakes are irregular aggregates formed through the collision of primary ice crystals, such as hexagonal plates, columns, and dendrites. These aggregates exhibit complex, fractal-like structures, particularly at large sizes. As a result of this structural complexity, each aggregate snowflake is unique, with properties that vary significantly around the mean—variability that is typically neglected in weather and climate models. Using a physically based aggregation model, we generate millions of synthetic snowflakes to investigate their geometric properties. The resulting dataset reveals that, for a given monomer number (cluster size) and mass, the maximum dimension follows approximately a lognormal distribution. We present a parameterization of aggregate geometry that captures key statistical properties, including maximum dimension, aspect ratio, cross-sectional area, and their joint correlations. This formulation enables a stochastic representation of aggregate snowflakes in Lagrangian particle models. Incorporating this variability in the Monte-Carlo super-particle model McSnow improves the realism of simulated fall velocities, enhances growth rates by aggregation, and broadens Doppler radar spectra in closer agreement with observations.