Mass of different snow crystal shapes derived from fall speed measurements
Authors: Vázquez-Martín Sandra , Kuhn Thomas , Eliasson Salomon 
Published: December 2021

Abstract. Meteorological forecast and climate models require good knowledge of the
microphysical properties of hydrometeors and the atmospheric snow and ice
crystals in clouds, for instance, their size, cross-sectional area, shape,
mass, and fall speed. Especially shape is an important parameter in that it
strongly affects the scattering properties of ice particles and consequently
their response to remote sensing techniques. The fall speed and mass of ice
particles are other important parameters for both numerical forecast models
and the representation of snow and ice clouds in climate models. In the
case of fall speed, it is responsible for the rate of removal of ice from
these models. The particle mass is a key quantity that connects the cloud
microphysical properties to radiative properties. Using an empirical
relationship between the dimensionless Reynolds and Best numbers, fall speed
and mass can be derived from each other if particle size and cross-sectional
area are also known. In this study, ground-based in situ measurements of snow particle
microphysical properties are used to analyse mass as a function of shape and
the other properties particle size, cross-sectional area, and fall speed. The
measurements for this study were done in Kiruna, Sweden, during snowfall
seasons of 2014 to 2019 and using the ground-based in situ Dual Ice
Crystal Imager (D-ICI) instrument, which takes high-resolution side- and top-view images
of natural hydrometeors. From these images, particle size (maximum dimension),
cross-sectional area, and fall speed of individual particles are
determined. The particles are shape-classified according to the scheme
presented in our previous study, in which particles sort into 15 different
shape groups depending on their shape and morphology. Particle masses of
individual ice particles are estimated from measured particle size,
cross-sectional area, and fall speed. The selected dataset covers sizes from
about 0.1 to 3.2 mm, fall speeds from 0.1 to 1.6 m s−1,
and masses from 0.2 to 450 µg. In our previous
study, the fall speed relationships between particle size and cross-sectional
area were studied. In this study, the same dataset is used to determine the
particle mass, and consequently, the mass relationships between particle size,
cross-sectional area, and fall speed are studied for these 15 shape groups.
Furthermore, the mass relationships presented in this study are compared with
the previous studies. For certain crystal habits, in particular columnar shapes, the maximum
dimension is unsuitable for determining Reynolds number. Using a selection of
columns, for which the simple geometry allows the verification of an empirical
Best-number-to-Reynolds-number relationship, we show that Reynolds number and
fall speed are more closely related to the diameter of the basal facet than
the maximum dimension. The agreement with the empirical relationship is
further improved using a modified Best number, a function of an area ratio
based on the falling particle seen in the vertical direction.