Journal of Geophysical Research: Atmospheres
Snowﬂake Melting Simulation Using Smoothed
and Annakaisa von Lerber
Joint Institute for Regional Earth System Science and Engineering, University of California, Los Angeles, CA, USA,
Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA,
Earth Observation, Finnish Meteorological
Institute, Helsinki, Finland,
School of Electrical Engineering, Aalto University, Espoo, Finland
Motivated by the need to understand the microphysics and improve the remote sensing of
the melting layer of precipitation, we have developed a numerical 3-D model for the melting of single
snowﬂakes. The model uses the smoothed particle hydrodynamics method and is forced by surface
tension that controls the ﬂow of meltwater on the ice surface. Heat transfer from the environment to the
snowﬂake is simulated with a Monte Carlo scheme. In model experiments with snowﬂakes of various sizes
and densities, we observed that the meltwater tends to initially gather in concave regions of the snowﬂake
surface. These liquid water regions merge as they grow, and as meltwater is added, they form a shell of
liquid around an ice core. This eventually develops into a water drop. The observed features during melting
are consistent with experimental ﬁndings from earlier research, which suggests that the model is adequate
for exploring the physics of snowﬂake melting. The principal remaining uncertainties arise from the
omission of aerodynamic forces from the model. The results suggest that the degree of riming has a
signiﬁcant inﬂuence on the melting process: During initial melting, liquid water is apparent on the surface
of unrimed or lightly rimed particles, while rime provides a porous structure that can absorb a relatively
large amount of meltwater. Riming also strengthens the connections between diﬀerent parts of the
snowﬂake, making rimed snowﬂakes less prone to breakup during melting, while unrimed ones break up
Plain Language Summary
Rain often starts as snow higher in the atmosphere, where it is colder.
The snowﬂakes melt as they fall into above-freezing temperatures. The layer of melting snowﬂakes can,
among other things, aﬀect weather patterns, block radio signals, and be a hazard to aircraft. Our study
was the ﬁrst to simulate the melting of snowﬂakes in 3-D by reproducing the physical processes involved
on a computer. The behavior of meltwater on the simulated snowﬂakes is very similar to that seen in
observations of real ones. The simulation can help us better understand the details of the melting process
and how the snowﬂake type aﬀects it, as well as create better models for the interaction of melting
snowﬂakes with radar and telecommunication signals.
The melting layer of precipitation occurs near the 0
C isotherm, where snowﬂakes fall to temperatures above
freezing and gradually melt, eventually becoming raindrops. Globally, the majority of rainfall is initially pro-
duced as snow (Mülmenstädt et al., 2015), and thus the melting layer occurs commonly nearly everywhere on
Earth, although its altitude varies considerably.
Despite its relatively small vertical extent, typically a few hundred meters (Fabry & Zawadzki, 1995), the melt-
ing layer has signiﬁcant eﬀects on the physics of the atmosphere, as well as societal impacts. The microphysics
of melting snow is particularly complex, with characteristics distinct from those of either rain or dry snow,
which has prompted a body of research devoted to it (e.g., Szyrmer & Zawadzki, 1999, and references thereof).
It has also long been known that the melting layer aﬀects atmospheric dynamics through the cooling of air
caused by absorption of latent heat by melting particles (Wexler et al., 1954). In everyday life, the most tan-
gible eﬀects of the melting layer are felt when it touches the ground and is observed as wet snow (sleet),
which happens routinely in regions where surface temperatures near 0
C occur. The impacts of wet snow
• The melting of falling snowﬂakes was
simulated in three dimensions
• The model is based on the smoothed
particle hydrodynamics method
• The simulation reproduces the
key features of snowﬂake melting
observed in nature
• Supporting Information S1
Leinonen, J., & von Lerber, A. (2018).
Snowﬂake melting simulation using
smoothed particle hydrodynamics.
Journal of Geophysical Research:
Atmospheres, 123, 1811–1825.
Received 19 OCT 2017
Accepted 19 JAN 2018
Accepted article online 6 FEB 2018
Published online 13 FEB 2018
©2018. American Geophysical Union.
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LEINONEN AND VON LERBER