Dynamics of complex snowflakes in a broad range of surface-atmosphere turbulence*

We present the first direct measurements of Lagrangian snowflake trajectories and their microphysical properties, mass, and density in surface-layer atmospheric turbulence. We deployed three primary instruments at the Alta-Collins snow study plot at a high elevation site in Utah: a 3-D sonic anemometer, a snowflake velocity laser-tracking system, and the Differential Emissivity Imaging Disdrometer (DEID), which provides precise estimates of hydrometeor mass, density, and size. The particle tracking system measured the actual fall velocity of snowflakes in a turbulent atmosphere. In contrast, the snowflake terminal velocity in still air was derived from DEID microphysical measurements using well-known aerodynamic formulations. We observed a broad range of turbulence and particle conditions covering Kolmogorov-scale Stokes numbers ($St$) and Reynolds numbers $R_{\lambda}$ ranging from 0.12 to 3.50 and from 400 to 70,000, respectively. The actual fall velocity is found to be greater and less than the associated terminal velocity in still air, indicating that turbulence enhances (sweeping) and reduces (loitering) settling, depending on conditions.  We find for a very broad range of turbulence where the probability distribution function of normalized individual Lagrangian snowflake accelerations follows a Laplacian distribution ($exp(-3/2 a/a_{rms}$)) with a nearly constant slope -3/2, which is independent of $St$ and $R_{\lambda}$.Surprisingly, an identical Laplacian distribution applied to pseudo-accelerations was calculated from Eulerian temporal variability in both observed snowflakes mean vertical velocities and the mean terminal fall velocity expected in still air. Furthermore, fat tails compose 1\% of acceleration distribution with values as high as 142\,m\,s$^{-2}$  However, the question remains to be determined why the value of the coefficient is $3/(2 a_{\rm{rms}})$ in the distribution of Lagrangian and Eulerian