Terminal Velocity Is Not Enough: A New Parametrization for the Settling of Hydrometeors in Turbulent Air

Various parameterizations exist for the fall speed of frozen hydrometeors such as graupel and aggregate snowflakes, perhaps most notably that of Locatelli and Hobbs (1974) based on a measurements of 376 particles sampled in the Cascade Mountain range. What has been less explored is how turbulence impacts how snow falls, and generally it is assumed in numerical modeling that it doesn't. This is somewhat surprising given that it is readily observed that snow swirls, and there is extensive fluid dynamics literature discussing the non-linearities introduced by turbulence on particle trajectories: it has been extensively discussed how, even for isotropic turbulence, the average effect of varying fluid motions on heavy inertial spherical particles is non-zero. The atmosphere is a particularly challenging example of this problem given that hydrometeors can have highly irregular shapes and turbulence is non-uniform.

To address this question, we developed a unique experimental setup including a new instrument for the direct measurement of hydrometeor mass, density, and size - the Differential Emissivity Imaging Distrometer (DEID) - which was placed it below a laser light sheet for tracking hydrometeor motions and adjacent to turbulence measurements obtained from a 3D sonic anemometer. Our observations, for an unprecedentedly wide range of turbulence conditions and snowflake types, with Stokes numbers between 0.11 and 5.0, confirm that snow swirls. As expected, individual particles that are dense tend to fall through turbulent eddies while more porous snowflakes undergo both "sweeping" and "loitering" as they are accelerated upward and downward. Viewed as an ensemble, we observed a wide range of settling velocities ranging from -2.63 to 5.17 m/s based on millions of particles, where a negative settling velocity represents particles moving upwards. Terminal velocities derived from DEID measurements for the same particles were not the same, ranging from 0.09 to 2.50 m/s owing to large variations in particle density from 5 kg/m³ to 225 kg/m³ and effective diameters between 0.8 mm and 12.2 mm. Thus, both enhancement and reduction of snowflake settling velocity is shown relative to their still air terminal velocity, which we observe can be expressed as a function of the intensity of the turbulence and an expression of the porosity of the hydrometeor. Notably, aggregate type snowflakes are those that are most likely to experience both loitering and sweeping depending on the turbulence level. Despite the complexity of the phenomenon, we find that hydrometeor acceleration distributions can be described probabilistically as an exponential function that is a sole function of the hydrometeor Stokes number. The observations presented offer a path forward for developing new parameterizations for hydrometeor settling that account for turbulence levels in the atmosphere.