The snowflake microstructure determines the microwave scattering properties of individual snowflakes and has a strong impact on snowfall radar signatures. In this study, individual snowflakes are represented by collections of randomly distributed ice spheres where the size and number of the constituent ice spheres are specified by the snowflake mass and surface-area-to-volume ratio (SAV) and the bounding volume of each ice sphere collection is given by the snowflake maximum dimension. Radar backscatter cross sections for the ice sphere collections are calculated at X-, Ku-, Ka-, and W-band frequencies and then used to model triple-frequency radar signatures for exponential snowflake size distributions (SSDs). Additionally, snowflake complexity values obtained from high-resolution multi-view snowflake images are used as an indicator of snowflake SAV to derive snowfall triple-frequency radar signatures. The modeled snowfall triple-frequency radar signatures cover a wide range of triple-frequency signatures that were previously determined from radar reflectivity measurements and illustrate characteristic differences related to snow type, quantified through snowflake SAV, and snowflake size. The results show high sensitivity to snowflake SAV and SSD maximum size but are generally less affected by uncertainties in the parameterization of snowflake mass, indicating the importance of snowflake SAV for the interpretation of snowfall triple-frequency radar signatures.

Snowfall retrievals from radar remote sensing of snow clouds are highly
sensitive to the applied characterization of the snowflake microstructure,
i.e., of snowflake mass and shape

In recent years, several studies have found that the “soft” spheroidal
particle model, where the volume, density, and complex index of refraction of
a homogeneously mixed ice–air spheroid are derived from the
snowflake size, mass, and aspect ratio, yields a realistic description of
microwave backscatter only for small snowflakes and at low frequencies

Due to the large variety of (visually distinct) snow types defined by
characteristic geometric shapes resembling the snowflake microstructure, such
as planar dendrites or aggregates of plates

In materials science, four basic characteristics play a central role for an
objective and quantitative description of 3-D microstructures: volume fraction
or equivalently (mass) density, surface area per volume, integrated mean
curvature per volume, and integrated Gaussian curvature per volume

In this study, snowflake density and surface-area-to-volume ratio (SAV) are
used to model snowflake backscatter cross sections at X-, Ku-, Ka-, and
W-band frequencies and then derive snowfall triple-frequency radar signatures
for realistic snowflake size distributions. The impact of snowflake SAV on
snowfall triple-frequency radar signatures is analyzed based on
high-resolution snowflake imaging data collected with the Multi-Angle
Snowflake Camera

First, MASC measurements are presented in Sect.

First, the Multi-Angle Snowflake Camera (MASC) and the derived snowflake
microstructural properties are described briefly

Estimates of near-surface snowflake microstructural properties are obtained
from MASC photographs taken at Alta (UT, USA) and at Barrow (AK, USA)
during winter 2013–2014 and spring 2014. The MASC provides
multi-view snowflake images from three cameras that are separated by

(left) MASC single-view images of two snowflakes: (top) aggregate snowflake and (bottom) heavily rimed graupel snow.
(right) Illustration of the corresponding projection images of
perimeter

In this study, MASC images are used to derive the snowflake diameter

The applied definition of

One MASC was installed at Alta Ski Resort at 2590

Figure

Snowflake (frequency) size distributions

The distributions of snowflake diameters and complexities in
Fig.

Similar to previous studies that have used exponential snowflake size
distributions to describe snowfall

Exponential snowflake size distributions

For uniform visualization in Fig.

For each analyzed snowstorm, the sampled snowflakes were also divided into 20 bins
according to their complexity

To illustrate the correlation between snowflake diameter

Logarithmic 2-D histogram for all MASC data of snowflake
diameter

As already seen in Fig.

Based on the mean snowflake complexity values

Figure

In this study, snowflakes are specified by their diameter, mass, and
surface-area-to-volume ratio (SAV). Snowflake diameters were derived from a
large set of MASC observations in Sect.

No coincident measurements of snowflake mass are available for the analyzed
MASC data in Sect.

With Eqs. (

The normalized snowflake surface-area-to-volume ratio

Snowflake SAV is quantified from the total range of

The impact of snowflake SAV on snowfall radar signatures is analyzed based on
synthetically generated expressions

Synthetically generated

Constant

The method for relating

Schematic representation of the modeling approach described in
Sect.

High values of

Microwave backscatter by a snowflake is modeled at X-, Ku-, Ka-, and W-band
frequencies of 10, 14, 35, and 94

A snowflake defined by the diameter

Equation (

The MASC observations presented in Sect.

Sets of 500 realizations were chosen for averaging because mean values of

To analyze the impact of snowflake surface-area-to-volume ratio on modeled
backscatter cross sections for a given snowflake diameter

For comparison, the analysis also includes mass-equivalent soft (mixed
ice–air) oblate spheroids and snowflakes modeled according to the
self-similar Rayleigh–Gans approximation

In this study, snowfall triple-frequency radar signatures are defined by the
two dual-wavelength ratios of modeled snowfall radar reflectivity factors at
(i) Ka and W band and at (ii) either X and Ka band or Ku and Ka band, where
X, Ku, Ka, and W band refer to frequencies of 10, 14, 35, and 94

To derive snowfall triple-frequency radar signatures at X, Ka, and W band and
at Ku, Ka, and W band, snowflake (radar) backscatter cross
sections

Snowfall triple-frequency radar signatures are then given by dual-wavelength ratios

Modeled snowflake backscatter cross
sections

Radar reflectivity factors

In Sect.

Figure

For soft spheres, Figs.

In Fig.

A comparison of the

The N13 and W04 snowflake parameterizations according to the SSRGA used in
this study were originally derived for snowflake 3-D shape models with
diameters

Diameters of

Notably, snowfall triple-frequency radar signatures modeled according to the
SSRGA for N13 and W04 snowflake parameterizations and snowflake size
distributions truncated at

An overview of the snowfall radar reflectivity factors

Modeled snowfall triple-frequency radar signatures given
by dual-wavelength ratios of DWR Ka/W and either
DWR X/Ka or DWR Ku/Ka. DWRs are determined
according to Sect.

Triple-frequency curves for soft spheres and spheroids with aspect ratios of

Modeled triple-frequency radar signatures for the N13 and W04 snowflake
parameterizations according to the SSRGA roughly follow the shape of the
curves determined for soft spheres and spheroids for high values of

For collections of randomly distributed ice spheres inside the (spherical)
snowflake bounding volume, triple-frequency curves in
Fig.

The hook shape of triple-frequency curves derived for intermediate and high
normalized surface-area-to-volume ratios

Modeling snowfall triple-frequency radar signatures for collections of
randomly distributed ice spheres inside the snowflake bounding volume also
leads to a much wider range of triple-frequency radar signatures in
Fig.

The total range of triple-frequency radar signatures modeled for collections
of randomly distributed ice spheres in Fig.

Modeled triple-frequency radar signatures in
Fig.

In contrast, snowfall triple-frequency radar signatures that were modeled by

Modeled snowfall triple-frequency radar signatures for
exponential size distributions with snowflake diameters of

Triple-frequency curves determined for soft spheres and spheroids and for the
N13 and W04 snowflake parameterizations according to the SSRGA cover a much
smaller region of the indicated range of observed snowfall triple-frequency
radar signatures in Fig.

Comparing radar reflectivity measurements and in situ snowflake observations,

Modeled snowfall triple-frequency radar signatures based on the MASC
measurements of snowflake complexity

Thus far, all snowfall radar signatures have been determined for exponential
snowflake size distributions with snowflake diameters of

Impact of snowflake maximum diameter

In general, truncation at smaller

For snowflake size distributions limited to diameters of

Combining the hook shape of triple-frequency curves derived for high
normalized surface-area-to-volume ratios in
Figs.

All presented results have been determined for only one parameterization of
snowflake mass

Impact of the parameterization of snowflake mass on
modeled snowfall radar reflectivity factors

The analyzed

Nonetheless, even high differences of

In this study, snowflake (radar) backscatter cross sections were modeled at
X-, Ku-, Ka-, and W-band radar frequencies of 10, 14, 35, and 94

Snowfall triple-frequency radar signatures were then determined from
dual-wavelength ratios (DWRs) of the snowfall equivalent radar
reflectivity factors

The analysis focused on the impact of snowflake SAV on modeled snowfall
triple-frequency radar signatures. Additionally, snowflake complexity values
obtained from the snowflake images and averaged over one winter season were
used as an indicator of snowflake SAV to derive snowfall triple-frequency
radar signatures at Alta and at Barrow. Finally, the effect of truncating
snowflake size distributions at

Important findings are as follows:

Average snowflake complexity increases with increasing snowflake size.

Modeled snowflake backscatter cross sections generally decrease with increasing snowflake surface-area-to-volume ratio (SAV).

Modeled snowfall triple-frequency radar signatures cover a wide range of snowfall triple-frequency signatures previously determined from radar reflectivity measurements.

Snowflake SAV and truncated snowflake size distributions offer a physical interpretation of snowfall triple-frequency radar signatures that is consistent with previously observed differences in snowfall triple-frequency radar signatures related to the presence of large aggregate snowflakes and rimed snowflakes and that may explain why some snowfall triple-frequency radar signatures apparently point to a spheroidal snowflake shape.

While modeled

The analyzed impact of the parameterization of snowflake mass on modeled snowfall triple-frequency radar signatures is generally much smaller than the analyzed impact of snowflake SAV.

Accordingly, current and future databases of microwave scattering properties determined for detailed snowflake 3-D shape models would benefit from incorporating snowflake surface area as an additional microstructural parameter (besides snowflake size and mass). Common features and differences in modeled scattering properties could then be related not only to visually distinct snow types (and snowflake size and mass) but also to snowflake surface-area-to-volume ratio, providing a quantitative description of the snowflake microstructure across all snow types and thereby helping to further constrain snowflake shape for snowfall remote sensing.

Based on a more comprehensive quantification of snowflake
surface-area-to-volume ratio that reflects characteristic differences among
snow types, the outlined approach for relating normalized snowflake
surface-area-to-volume ratio

Modeled snowflake backscatter cross sections and dual-wavelength ratios of snowfall equivalent radar reflectivity factors are included in the Supplement. Additional data may be obtained by contacting the corresponding author.

In this study, snowflakes defined by the maximum dimension or diameter

To generate collections of non-overlapping ice spheres inside

To determine radar reflectivity factors

At 10 and 14

As

TJG is a member of the editorial board of the journal and has a financial interest in Particle Flux Analytics, which sells the MASC.

Mathias Gergely's work was supported through NASA grant NNX14AP78G and by the German Research Foundation (DFG) through DFG research fellowship GE 2658/1-1; Steven J. Cooper acknowledges support from the National Science Foundation (NSF) under grant 1531930; Timothy J. Garrett was supported through NSF grant 1303965 and US Department of Energy grant DE-SC0016282. The authors thank Henning Löwe at the WSL Institute for Snow and Avalanche Research SLF and two anonymous referees for their comments that helped improve this study. Edited by: Ari Laaksonen Reviewed by: two anonymous referees