In countries like Japan, particular solid precipitation particles
(PPs), such as unrimed PPs and graupel, often form a weak layer in snow,
which triggers slab avalanches. An understanding of weak PP layers is
therefore essential for avalanche prevention authorities to design a
predictive model for slab avalanches triggered by those layers. Specific
surface area (SSA) is a parameter that could characterize the physical
properties of PPs. The SSAs of solid PPs in Nagaoka – a city in Japan
experiencing the heaviest snowfall in the country – were measured for four
winters (from 2013/2014 to 2016/2017). More than 100 SSAs of PP
were measured during the study period using the gas absorption method. The
measured SSA values range from 42 to 153 m2 kg-1. Under melting
conditions, PPs showed comparatively smaller values. Unrimed and slightly
rimed PPs exhibited low SSA, whereas heavily rimed PPs and graupel exhibited
high SSA. The degree of PP riming depends on the synoptic meteorological
conditions. Based on the potential of weak PP layer formation with respect
to the degree of riming of PPs, the results indicate that SSA is a useful
parameter for describing the characteristics of PP, and consequently
predicting avalanches triggered by weak PP layers. The study found that the
values of SSA strongly depend on wind speed (WS) and wet-bulb temperature
(Tw) on the ground. SSA increases with increase in WS and decreases with
increase in Tw. An equation to empirically estimate the SSA of fresh PPs in
Nagaoka using WS and Tw was established. The equation successfully reproduced
the fluctuation of SSA. The SSA equation, along with the meteorological
data, is an efficient first step toward describing the development of weak
PP layers in the snow cover models.
Introduction
Individual snow crystals are made of ice structures with unique, intricate
geometries (Magono and Lee, 1966). The specific surface area (SSA) of snow
is defined as its surface area per unit mass or volume and includes
information on the size and shape of the snow particles. Therefore, SSA is a
key parameter in understanding the exchange of matter and energy between a
snow-covered surface and the atmosphere (Domine et al., 2006, 2007, 2008),
as well as in modeling the mass transfer of air or water in snow (e.g.
Arakawa et al., 2009; Calonne et al., 2012). To accurately simulate the
continuous change in the physical properties of snow, it is important to
formulate the temporal variations in the SSA. Several studies (Legagneux et
al., 2003, 2004; Legagneux and Domine, 2005; Taillandier et al., 2007) have
proposed empirical equations for the time variation in SSA, in which an
initial value of SSA was used. Therefore, the initial values of SSA, namely
SSA of fresh precipitation particles (PPs), are essential to simulate the
time variation in SSA in natural snow cover.
PPs have the potential to form a weak layer in a snowpack, which may trigger
slab avalanches (Akitaya and Shimizu, 1988; McClung and Schaerer, 1993). The
formation of weak PP layers should be considered to be dependent on the
degree of PP riming (LaChapelle, 1967). The degree of PP riming is hence a
key factor in designing a predictive model for slab avalanches triggered by
weak PP layers. To investigate the types of weak layers in a surface
avalanche, McCammon and Schweizer (2002) reported that the main cause of the
weak layer in the Swiss Alps and Canada is the recrystallization-type
layer with depth hoar, faceted crystal, and surface hoar. However, the main cause
of weak layers of snowpack in Japan is the PP type (Ozeki and Akitaya, 1995;
Matsumura, 2002; Ikeda, 2007). Therefore, forecast of
weak-PP-layer-triggered avalanche is necessary for avalanche prediction in
Japan. In recent times, several devastating avalanches have occurred in
Japan due to weak-PP-layer formation. In February 2014, hundreds of
avalanches occurred simultaneously in the Kanto region alone, which
typically receives limited snowfall during the winter. Due to the risk of
avalanche, many villages, some with over 9000 residents, were cut off from
accessing roads and services (Nakamura et al., 2014; Kamiishi and Nakamura,
2016). In March 2017, eight people, seven of whom were high school students,
lost their lives in an avalanche during an extracurricular outing (Nakamura
et al., 2017; Araki, 2018).
Akitaya and Shimizu (1988) reported that the large-size falling
broad-branched unrimed snow crystals form a weak layer due to low initial
density under windless conditions. From the perspective of the physical
characteristics of a PP layer, several studies (Shidei, 1953; Nakamura et
al., 2014; Ishizaka et al., 2018) reported that snow layers consisting of
unrimed snow crystals are fragile and trigger snow avalanches, even when the
weak PP layers in the snowpack are shallow. In fact, the measured repose
angles with the unrimed snow crystals were 35–45∘ (Ishizaka et
al., 2018; Kamiishi et al., 2016), much smaller than those of the rich-rimed
snow crystals (> 90∘) reported by Narita and Takeuchi (2009). These results indicate the potential relationship between avalanche
behavior and the weak-PP-layer characteristics. However, the dependence of
avalanche characteristics on PP, which is necessary to predict the potential
of a weak PP layer to trigger an avalanche, is still debated because of the
lack of any objective physical information on PP, such as shape, size, and
riming ratio. To solve this problem and record detailed information on PP,
the SSA of snow is considered an ideal parameter.
Several studies in the past have reported SSA measurements of fresh snow
(Legagneux et al., 2002; Cabanes et al., 2002; Domine et al., 2007; Schleef,
2014). Their measurement intervals after the snowfall period showed a wide
variation from several hours to a day. In general, SSA decreases with time due
to metamorphism (Legagneux et al., 2003; 2004; Cabanes et al., 2003;
Legagneux and Domine, 2005; Taillandier et al., 2007). Kerbrat et al. (2008)
implied that smoothing of the snow crystal surface due to the Kelvin effect
is expeditious; i.e., surface roughness of the size of several micrometers
disappears after a day, even at temperatures as low as -40∘C, and
the smoothing accelerates with increase in the temperature. In general, the
size of a riming droplet (cloud drop) is on the order of 1 to 10 µm, as reported by Harimaya (1975) and Mosimann et al. (1994).
Therefore, SSA measurement within short intervals is needed to model the
degree of PP riming, especially in a warmer environment, which is common in
Japan. Snow cover models, which are used for avalanche forecasting (e.g.
Brun et al., 1992; Lehning et al., 1999), generally require input data with
high time resolution (e.g. 1 h) for avalanche forecasting. Therefore, if
information on PP is to be introduced in snow cover models using the SSA,
then a dataset of SSA information on fresh PPs with high time resolution must
be developed. Moreover, this information should contribute to the
improvement of the SSA of PP treatment in the snow cover models, which are
basically simplified in the model. For example, in the Crocus snowpack model
(Brun et al., 1992; Vionnet et al., 2012), the maximal SSA value of PP is 65 m2 kg-1 for low wind conditions, and it decreases with increasing wind speed down to 25 m2 kg-1 (Vionnet et al., 2012; Carmagnola et al., 2014).
The SSA measurements of fresh PPs were conducted over short intervals (1–2 h) in an area in Japan that receives heavy annual snowfall. The measurements
were compared to meteorological data and detailed falling snow data for
discussing the dependency of SSA on those parameters. Based on those
analyses, an empirical equation to estimate the SSA of fresh PPs using
surface meteorological data was proposed for introducing detailed
information on PP to the snow metamorphism models.
Falling snow observatory (FSO) and the device developed for the
methane adsorption method at the SIRC.
(a) Overview of FSO, which is protected by a defensive fence against wind. (b) Roof opening system for the cold room.
(c) Table in the cold room, on which snow samples are naturally deposited through the roof opening
(d) The system to automatically capture falling snow crystal photographs on
the conveyor belt with a close-up camera.
(e) Falling snow particle observation system using a CCD camera.
(f) Portable device developed for the methane adsorption method.
(g) Sample folder for measurement of SSA.
MethodologyObservation site
The SSA observations were conducted over four winters from 2013/2014 to
2016/2017, at the Snow and Ice Research Center (SIRC), National Research
Institute for Earth Science and Disaster Resilience (NIED), Nagaoka, Japan
(37∘25′ N, 138∘53′ E; 97 m a.s.l.). The SIRC is located in a coastal region facing the Sea of Japan,
where strong northwesterly monsoons blow from Siberia to the Japanese
islands, accumulating large amounts of water vapor when passing over the
warm sea and bringing heavy snowfall. The climatic conditions at the SIRC
include a typical maximum winter snow height greater than 1.4 m, but a mean
daily winter air temperature (December–February) higher than 2 ∘C
(Yamaguchi et al., 2018). Various types of solid PP (snow flake, graupel,
riming crystal, unrimed crystal, melting snow crystal, sleet, etc.) appear
at the SIRC and the type of PP frequently changes within a short interval
due to the change of precipitation mode (Ishizaka et al., 2013).
The falling snow observatory (FSO) (Fig. 1a) at the SIRC has a cold room
(-5∘C) with a 1.2×0.6 m roof opening (Fig. 1b)
(Ishizaka et al., 2013, 2016). This setup allows the accumulation of falling
snow on a flat table in the cold room under windless conditions (Fig. 1c).
The PP photographs are automatically captured with a close-up camera on a
conveyor belt system in the cold room (Fig. 1d). Additionally, the
characteristics of falling snowfall particles, including size and fall
speed, are automatically measured using a charge-coupled device (CCD) camera system (Fig. 1e), with
a particle size resolution of 0.25 mm for the width and 0.50 mm for the
height (Ishizaka et al., 2004). Using these characteristics, Ishizaka et al. (2013) presented a new parameter that quantitatively describes the main
types of snowfall hydrometeors and reflects the contribution of all
hydrometeors to precipitation. In their method, the dominant snowfall type
was represented by a pair of characteristics, size and fall speed, which
were obtained from the average size and fall speed and weighted by the mass
flux of all measured hydrometeors. This is termed the center of mass flux
(CMF) distribution. Because the size–fall–speed relationship of
hydrometeors is a good representation of particle types, the dominant snow
type in a snowfall event may be deduced from the location of the CMF in the
size–fall–speed coordinates. Based on the concept of CMF, Ishizaka et al. (2016) also established approximated relationships between the CMF density
and initial density. These data were used to check whether the measured SSA
fell under the single-PP-type conditions. Moreover, the detailed
characteristics of falling snow produced by the CMF were used when discussing
the relationship between the measured SSA of fresh PPs and the
characteristics of falling snow (Sect. 3.4).
The SIRC also acquires standard meteorological measurements at various
time resolutions (1 min, 10 min, and 1 h) in the field (Yamaguchi et al., 2018):
air temperature
(±0.1∘)
relative humidity (±2 %) at 3.5 m above
ground level
wind speed (±0.3 m s-1) and wind direction
(±3∘) at 8.7 m above ground level
precipitation
(3 %) at 3.1 m above ground level
incoming and outgoing shortwave
(±10 W m-2) and longwave (±10 W m-2) radiation at 6.5 m
above ground level
air pressure (±0.35 hPa) measured at 3.0 m above
ground level
surface temperature (±0.5∘)
snow height
(±1.5 cm)
snow water equivalents (±10 mm).
Here, the values in the parentheses signify the accuracy of each sensor.
These meteorological data were used with a 1 min resolution for conditioning
the SSA data (Sect. 3.2). The conditioned data were used to discuss the
relationship between the measured SSA of fresh PPs and near-surface
meteorological data (Sect. 3.5). This study uses these meteorological data
with a 10 min resolution for estimating the SSA, with an empirical equation
(Sect. 3.6). In addition to these measurements, the SIRC also operates a
Doppler radar on the rooftop of its building and gathers information on snow
clouds during the winter season (Nakai et al., 2019). This study used the
Doppler radar data when discussing the relationship between the SSA and
radar echo patterns related to the development of snow clouds (Sect. 3.3).
In addition to these data, weather charts produced by the Japan
Meteorological Agency (http://www.data.jma.go.jp/fcd/yoho/hibiten/index.html, last access: 20 April 2019) were used in the
discussions on the synoptic meteorological conditions (Sect. 3.3).
Measurement of specific surface area of fresh PPs
The methane gas adsorption method (Domine et al., 2001, 2007; Legagneux et
al., 2002) was used to measure the SSA of fresh PPs. Principles of the
methane gas adsorption method have been described in detail by Legagneux et
al. (2002). Recently, a portable device was developed for the methane
adsorption method (Fig. 1f) (Hachikubo et al., 2014, 2018). This device
allows us to measure the SSA of snow within a 1 h resolution
(measurement repeatability (standard deviation) of 3 %; Hachikubo et al.,
2012, 2013). The characteristics of this device make it
convenient for use in the current study of the SSA of fresh PPs with a short
interval measurement. The samples used in this study were made of fallen
snow deposited within 1–2 h on a table in a cold room (-5∘C) at
the FSO. The device requires a 30 mL sample for each measurement (Fig. 1g).
The samples were directly taken from the snow deposited on the table during the
measurement interval. However, the PPs gathered by a broom were added to the
sample when the snow deposited on the table was not high enough. The
measured SSAs in this study were calculated by dividing the measured surface
area of the sample by its mass, which was in turn measured by an electronic
balance with a 0.01 g resolution. Therefore, units of square meters per kilogram are used.
Due to the short deposition time under the cold room conditions, the effect
of metamorphism on the sample, which requires longer deposition time, was
neglected in this study. The microphotographs of the sample using a
microscope were manually captured to determine the crystal types.
List of datasets.
NameConditionSample numberSect.All dataAll measured data102Sect. 3.1No-melt events (NMEs)Data without melting. Web-bulb temperature (Tw) < 0 ∘C72Sect. 3.2 Sect. 3.3Melt events (MEs)Data with melting. Web-bulb temperature (Tw) ≧ 0 ∘C30Sect. 3.2Uniform falling event (UFE)Data with a single PP type during the deposition period in NMEs.49Sect. 3.4 Sect. 3.5Data selection
In the study, several selected datasets (Table 1) were provided for each
analysis. In the discussion of the general characteristics of SSA of PPs in
Nagaoka (Sect. 3.1), all measured data were used. In the discussion of the
influence of melting effect (Sect. 3.2), all measured data were classified
into two datasets, no-melt events (NMEs) not affected by melt and melt events (MEs) affected by
melt, and then discussed. In the discussion of the relationship
between SSA and synoptic meteorological conditions (Sect. 3.3), only NME
was used. In Sect. 3.4 and 3.5, uniform falling events (UFEs), in which only data measured under
a single-PP-type condition during the deposition period, were selected from
the NMEs and used for the discussion. Information on data selection
conditions is detailed in each section.
Summary of datasets in Domine et al. (2007) and Schleef (2014).
NameMeasurement methodObservation sitesDom2007 (Domine et al., 2007)Methane gas adsorption methodFrench Alps, Arctic Canada, Alaska, SvalbardSch2014 (Schleef, 2014)X-ray microtomographyDavos in SwitzerlandResults and discussionMeasured SSA of fresh PPs
A total of 102 SSA measurements were collected from the samples acquired
from over four winters (from 2013/2014 to 2016/2017). For the methane
absorption method, the averaged heat of adsorption, which is an indicator of
the judgment of measurement quality, for the 102 measurements was 2472 ± 199 J mol-1, which is consistent with the value of 2540 ± 200 J mol-1 recommended by Domine et al. (2007). Therefore, the measurement results stand to reason. Figure 2a shows the comparison results between results of this study and SSA of natural, freshly fallen snow in previous studies (Domine et al., 2007; Schleef, 2014). Hereinafter, data of
Domine et al. (2007) will be referred to as Dom2007 and data of Schleef (2014) as Sch2014. Table 2 shows detailed information on Dom2007 and
Sch2014. Figure 2a also shows the optical radius (Ropt) for the
datasets, estimated from the SSA using the following equation (Grenfell and
Warren, 1999):
Ropt=3SSA×ρi.
Here, ρi is the density of ice (917 kg m-3).
The sample numbers of the SSA measurements in this study are larger than
those in the previous studies (Domine et al., 2007; Schleef, 2014), and they
present a wider range of SSA values. This could be explained by the larger
variety of PP types in this study. The average value of data in this study
(96 m2 kg-1) is much larger than that in Dom2007 (73 m2 kg-1). The average value in Sch2014 (93 m2 kg-1) is close to
that in this study. However, the number of samples in Sch2014 (8 cases) is
too small to discuss statistically. Therefore, we compare the results of
Dom2007 (68 cases) with those of this study (102 cases). Fassnacht et al. (1999) simulated the amount of change in the SSA of a dendritic snow crystal
caused by the presence of riming drops on the surface. They concluded that
the SSA could be doubled if 20 % of the surface of the snow crystal were
covered by needle- or plate-shaped rime. Therefore, one of the reasons the
averaged value in this study is larger than Dom2007 is that the measured data of
fresh PPs include many cases of graupel and richly rimed snow crystals.
Another reason could be the condition of the samples. The samples in this
study were measured within a short time (1–2 h) after deposition, so the
effect of metamorphism should be small. On the other hand, the samples in
Dom2007 were procured over a longer time span after deposition. Thus, the
effect of metamorphism on the samples in those studies should be larger than
on the samples in this study. For these reasons, the results of this study
show a more realistic value of the SSA of fresh PPs.
Measurement results of SSA.
(a) Comparison between the measurement results at Nagaoka and those of fresh snow reported in previous studies.
Red box plots show SSA values and pink box plots show optical grain radius
calculated for the datasets using Eq. (1).
Dom2007: data from Domine et al (2007).
Sch2014: data of natural snow from Schleef (2014).
This study: data at Nagaoka.
(b) Measurement results of SSA for each year;
2014: data measured in 2013/2014 winter;
2015: data measured in 2014/2015 winter;
2016: data measured in 2015/2016 winter;
2017: data measured in 2016/2017 winter.
Each box plot shows the median, 25 % and 75 % percentiles, 1.5× interquartile ranges, and outliers.
Values in parentheses are sample numbers
Large variations in the measured SSA values were observed every fourth
winter (2013/2014: 64–153 m2 kg-1; 2014/2015: 43–142 m2 kg-1; 2015/2016: 42–148 m2 kg-1; 2016/2017: 51–110 m2 kg-1) (Fig. 2b). These results indicate that the SSA of fresh PPs in the
winter season in Nagaoka usually varies by more than 2- or 3-fold.
Snow albedo is essentially a function of the physical parameters of snow
including SSA. To evaluate the effect of fluctuation in the SSA of fresh PPs
on its surface albedo, surface albedos in the UV (ultraviolet)–visible
spectral region and the near-infrared spectral region were simulated using
the measured maximum (77 µm) and minimum optical radii (22 µm) of
fresh PPs (Fig. 2), via the “physically based snow albedo model” (PBSAM)
developed by Aoki et al. (2011). These simulations were conducted for the
case of impurity-free snow under a clear-sky condition at a solar zenith
angle of 60∘. Previous studies (Wiscombe and Warren, 1980; Aoki
et al., 2011) show that the albedo at the near-infrared (NIR) wavelengths are affected more
significantly by the change in SSA than the albedo at the UV–visible
wavelength range. This is due to the spectral behavior of the imaginary part
of the complex refractive index of ice. In fact, the UV–visible (wavelength = 0.2–0.7 µm) albedo values simulated using the measured maximum and minimum optical radii show almost the same values (0.99), while the simulated NIR (wavelength = 0.7–3.0 µm) albedo values vary from
0.75 to 0.80. These results indicate that the information on SSA variation
in fresh PPs is important for the simulated evolution of the local surface
radiation budget. Therefore, parameterization of SSA fluctuations is
essential for the accurate simulation of NIR albedo in natural snow.
Influence of melting effect in SSA of fresh PPs
According to Yamaguchi et al. (2013), winter precipitation in Nagaoka
frequently occurs at an air temperature of approximately 0 ∘C. In
fact, the data in this study were partly measured at an air temperature of
approximately 0 ∘C. Thus, some of the samples were affected by
melting during the fall. To investigate the influence of melting on the
measured SSA data, the measured data were classified into two
categories – data without melting effect (no-melt events) and data with melting effect
(melt events) (Table 1). To classify these data, the wet-bulb temperature (Tw) during the
falling snow period was used, which is a good indicator of the melting event
(Matsuo et al., 1991); no-melt events (NMEs) followed the Tw<0∘C condition,
while melt events (EM) followed the Tw≧0∘C condition. In this study, the
interval of snowfall during the sample period was first determined using the
CMF data with a 1 min time resolution because falling snow did not always
occur continuously during the sample interval. Then, using the
meteorological data (1 min resolution), all the relevant meteorological
elements were averaged over the period in which snowfall was observed,
instead of averaging over all periods of the sample interval for calculation
(hereinafter, the averaged meteorological data will indicate data averaged
only over the period of snowfall). In this study, Tw was calculated based on the “forward” analytical psychrometric equations (Bohren and Albrecht, 1998) that employ an iterative approach using averaged air temperature, relative humidity, and air pressure.
Wet-bulb temperature (Tw) melting-based classification of SSA data classification.
NME (no-melt events): data with Tw<0∘C;
ME (melt events): data with Tw≧0∘C.
Each box plot shows the median, 25 % and 75 % percentiles, 1.5×
interquartile ranges, and outliers.
Values in parentheses are sample numbers.
Microphotographs of samples taken under melt events.
(a) Sample with Tw= 0.6 ∘C;
(b) sample with Tw= 0.03 ∘C.
Synoptic atmospheric pressure condition of falling snow events in
Nagaoka. Gray circles indicate the location of Nagaoka.
(a) Synoptic weather chart at 09:00 on 25 January 2016, as an example of the M type;
(b) synoptic weather chart at 09:00 on 29 January 2016, as an example of the C type;
(c) microphotograph of fresh PPs deposited on a table in a cold room under the conditions of (a);
(d) microphotograph of fresh PPs deposited on a table in a cold room under the conditions of (b).
Weather charts were produced by the Japan Meteorological Agency
(http://www.data.jma.go.jp/fcd/yoho/hibiten/index.html, last access: 20 April 2019).
Figure 3 shows the classified results (MEs and NMEs) using Tw. A total of 30 events were classified as MEs and 72 events as NMEs. The SSA averaged over the MEs (77±23 m2 kg-1) is smaller than that of NMEs (103±28 m2 kg-1). Here the values after “±” represent the standard deviation. The difference in the SSA values between MEs and NMEs
should be mainly due to the melting effect. Domine et al. (2007) reported an
SSA value of 50±11 m2 kg-1 for fresh PPs with melting
effect, i.e., PP falling at T>0∘C. Compared with the
results of this study, the values in their study are smaller. Moreover, the
SSA data under MEs in this study include higher values (> 100 m2 kg-1). Figure 4 shows the microphotographs of the two samples
taken under MEs with different Tw. The first sample, which showed the evidence of melting under high Tw (0.6 ∘C), had a small SSA (51 m2 kg-1) (Fig. 4a). The second sample, which falls under MEs with low Tw, slightly higher than 0 ∘C, did not reveal any substantial evidence of melting and had a large SSA (113 m2 kg-1) (Fig. 4b). These results indicate that the degree of melting depends on Tw.
Moreover, the results also imply that the Tw-based classification is not
sufficient to distinguish between melt and no melt. Basically, data under
NMEs show high SSA values but still include lower SSA values (< 77 m2 kg-1). These results indicate that fresh PPs can have a small SSA even without melting, and other factors, such as meteorological
conditions within the clouds and the atmosphere, for controlling the SSA of
fresh PPs ought to be considered.
Dependency of SSA of fresh PPs on synoptic-scale conditions.
M type: monsoon type; C type: cyclone type.
Each box plot shows the median, 25 % and 75 % percentiles, 1.5× interquartile ranges, and outliers.
Values in parentheses are sample numbers.
Relationship between SSA of fresh PPs and synoptic meteorological
condition
The measured SSA of fresh PPs sometimes reveals small values without melting
(Fig. 3). To investigate the cause of these small SSA values, the study will
focus on the synoptic meteorological conditions during snowfall. Snowfall
patterns in Japan can be roughly grouped into two categories (Nakamura et
al., 1987): monsoon-type snowfall, in which strong northwesterly monsoons
blow from Siberia to the Japanese islands, and cyclone-type snowfall, in
which cyclones blow from the south to the north along the archipelago. The
first type was named monsoon type (M type) (Fig. 5a) and the second
cyclone type (C type) (Fig. 5b). In Nagaoka, snowfall events under the
M type are dominant, while snowfall events under the C type rarely occur during
the winter season (Nakamura et al., 1987). Based on classifications using
the weather charts produced by the Japan Meteorological Agency (http://www.data.jma.go.jp/fcd/yoho/hibiten/index.html, last access: 20 April 2019), 60 events
resulted from the M type and 12 events from the C type in NMEs (a total of 72 events). Figure 6 presents the result of comparison of the SSA values
between the M type and C type and reveals a clear difference – SSAs during the
M type (average: 112 m2 kg-1) are much larger than those during the
C type (average: 60 m2 kg-1). These results indicate that the SSAs of fresh PPs in Nagaoka strongly depend on the synoptic-scale precipitation conditions. In general, the PPs during the M-type pattern generally allow aggregation and riming to be predominant (Fig. 5c). A previous study (Cabanes et al., 2002) reported dendritic snowfall with rich riming as
showing high SSA in the Canadian Arctic.
Colle et al. (2014) reported consistent spatial patterns of habit and riming
intensity in the fallen snow during a cyclone at Stony Brook in New York on
the northeast coast of the United States relative to the cyclone structure.
Few to no riming snowfall crystals occurred within the outer comma head
to the north and northeast of the cyclone's eye and the western quadrant of
the comma head, while moderately rimed snow crystals were observed in the
middle of the comma head. In Japan, several studies with meteorological
condition analyses (Nakamura et al., 2013; Akitaya and Nakamura, 2013)
reported unrimed snow crystals falling at the warm front of the cyclone and
subsequently triggering avalanches. These studies corroborate each other,
namely in that unrimed snow crystals occurred with the cyclone event. In fact, all
observed crystals under the C type showed the unrimed snow crystal types as
shown in Fig. 5d. From these results, it was concluded that the
characteristics of PPs under the C type, namely unrimed snow crystal types,
reveal PPs with small SSA. To predict a weak-PP-layer avalanche, it is
necessary to have a description of PP-type information in numerical snow
models that can help reproduce the weak PP layer. This study considers the
riming conditions of PPs determined based on the SSA values to be a good
indicator of the potential of development of weak PP layer in snowpack for
numerical snow cover models.
Dependency of the SSA of fresh PPs on snowfall modes during the M type.
Each mode is described in Table 1. UD indicates data whose snowfall mode
could not be determined.
Each box plot shows the median, 25 % and 75 % percentiles, 1.5× interquartile ranges, and outliers.
Values in parentheses are sample numbers.
Classification of snowfall mode (modification of Table 1 in Nakai et
al., 2005).
L mode (longitudinal line)Bands running or cells aligned nearly parallel to the prevailing windT mode (transversal line)Bands running or cells aligned with a large angle relative to the prevailing windS mode (spreading precipitation)Widely spread, relatively uniform precipitationV mode (meso-β scale vortex)Vortices and associated curved bands with a significant change in the wind directionM mode (mountain-slope precipitation)Area of stationary precipitation around the windward slope of the mountainsD-mode (local-frontal band)A wide band is considered to form along a line of discontinuity
When the measurements of the M type were investigated, SSA values of fresh
PPs still showed a large variation in the range of 64–154 m2 kg-1. Nakai et al. (2005) reported that there were several snowfall
conditions corresponding to different snow cloud behaviors under the M-type
pattern. They investigated this behavior (snowfall modes) in the Niigata
Prefecture, including Nagaoka, using Doppler radar echo under the M type,
and then classified the snowfall according to six modes (Table 3).
Based on their method, in this study, data under the M type were classified
into several snowfall modes. A total of 53 out of 60 datasets under the M type
were classified into four modes (T mode: 20 events; L mode: 24 events; D
mode: 4 events; S mode: 5 events), while seven datasets could not be
determined due to the lack of radar data or difficulty in classification
resulting from the complexity of the snowfall mode. In this study, SSAs under
the V mode and the M mode were not measured. Figure 7 illustrates the
results of the SSA for each snowfall mode classification. For more
information on grain shape and riming, the reader is directed to the sample
microphotographs of PPs taken under each mode in Fig. 8. The values of SSA
under the T and L modes show larger values than the other two modes
(averaged SSA values of the T and L modes are 120 and 119 m2 kg-1,
respectively). A previous study (Harimaya and Nakai, 1999) reported that
falling snow crystals contain richly rimed types under the T and L modes. As a
matter of fact, the main types under the T and L modes in this study were
the graupel and richly rimed snow crystals (Fig. 8a and b). The values of SSA
measured under the D mode (averaged SSA value of the D mode is 93 m2 kg-1) show smaller values with those under the T and L modes. However,
these values showed large fluctuations from 60 to 120 m2 kg-1. This
result implies that a wide range of PP types – from slightly rimed snow
crystal to richly rimed snow crystal, should fall under the D mode. The
microphotographs in Fig. 8c also show that different crystal types can fall
under the D mode. Because of the small sample size of the D mode (only four
cases), the critical condition between the PPs with a large SSA and those
with a small SSA could not be established in this study. Although slightly
larger than the values under the C type, the measured values of SSA under
the S mode (averaged SSA value of the S mode is 75 m2 kg-1) are
smaller than those under other modes. Microphotographs of all samples under
the S mode revealed unrimed and slightly rimed snow crystals as the
classification of riming degree for a single crystal (Mosimann et al., 1993)
(Fig. 8d). The sample size of the S mode (only five cases) does not help to
confirm if all the cases under this mode have small SSA values, but the
results do indicate that the PPs with small SSAs (< 80 m2 kg-1) appeared even under the M type. Therefore, the risk of avalanche
caused by the weak PP layer, resulting from fallen unrimed snow crystals,
should not be neglected even under the monsoon type.
Microphotographs of samples for each snowfall mode.
Panels (a-1) and (a-2) were captured under T mode;
panels (b-1) and (b-2) were captured under L mode;
panels (c-1) and (c-2) were captured under D mode;
panels (d-1) and (d-2) were captured under S mode.
Values in the figures are the measured SSAs.
Distribution of CMF with 1 min resolution and the integrated CMFs
for events. (a) Example of uniform falling event (09:40–10:40: 25 January 2016);
(b) example of variant falling event (09:10–10:00: 10 February 2015). The x's: CMF of each minute. Black circle: averaged CMF.
Solid line: conical graupel (Locatelli and Hobbs, 1974);
broken line: densely rimed aggregate (Locatelli and Hobbs, 1974).
Relationship between SSA of fresh PPs and detailed characteristics of PPs produced by CMF analyses
In this section, the relationships between the SSA of fresh PPs and their
characteristics will be discussed in detail. The PP type sometimes varies
even for small observation periods (1–2 h) (Ishizaka et al., 2016).
Therefore, it was necessary to select simpler cases with the same PP type
during the sample deposition period, to clarify the relationship between the
SSA of fresh PP and its characteristics. To examine the quality of PP type
variations, the CMF distribution of Ishizaka et al. (2016) during the sample
deposition period was considered. In the analyses, CMF was averaged over the
sample deposition period (averaged CMF) and over each 1 min interval (1 min
CMF). Figure 9 shows the representative CMF plots under different
conditions. In Fig. 9a, the pattern of a 1 min CMF can remain unchanged even
as the particle size differs during the sample deposition period. In such a
case, these events were regarded as uniform falling events (UFEs), which have a single PP type
during the deposition period. On the other hand, the pattern of a 1 min CMF
in Fig. 9b can also fluctuate in size–fall–speed coordinates, while the
averaged CMF in Fig. 9b is located in an intermediate area during the sample
deposition period. In such a case, these events were regarded as variant falling events, which
have mixed PP types during the deposition period. CMF distributions of all
cases in the NMEs were graphed and inspected visually based on these
analyses. A total of 49 UFEs were selected from the NMEs (Table 1). Figure 10
illustrates the results of comparison between data of NMEs (72) and data of
UFEs (49). Although the number of UFEs is two-thirds the number of NMEs, the
UFE dispersion still follows a trend similar to NME dispersion. For this
reason, only UFE data will be used for detailed analyses hereinafter.
As shown in Fig. 6, the SSA strongly depends on its synoptic-scale
conditions. Therefore, the relationship between SSA of fresh PPs and the
detailed characteristics of PPs should also depend on the synoptic-scale
conditions. For this reason, firstly UFE data were classified into the two
synoptic-scale conditions (M type and C type). In addition, M-type data were
classified into three groups based on the PP type (aggregate group, AGG;
graupel group, GRA; and small particle group, SMG) using the CMF analyses
reported by Ishizaka et al. (2016) (Fig. 11). Although Ishizaka divided a
small particle group (SMG) into two subgroups (S1 and S2), this study
treated S1 and S2 as one group (SMG) (Fig. 11). Finally, four data groups
(C type, AGG, GRA, and SMG) were used for analyses.
In this study, three physical characteristics obtained from the CMF analyses
were adopted – averaged fall speed (V) of PP and averaged apparent size
(D) of PP. These two elements were determined by the CCD image for each
particle and then averaged over all the particles during the sample
deposition period (Ishizaka et al., 2013). The third physical
characteristics is the initial density (ρ) after the deposition on the
ground, which was calculated based on 5 min averaged CMF data using
the method of Ishizaka et al. (2016). V and D were directly measured while ρ was estimated using V and D.
Figure 12 shows the relationship between the SSA of fresh PPs and the three
physical characteristics of PP produced for each data group. In the C-type
group, significant correlations (p value is smaller than 0.05) between the
measured SSA and all three physical characteristics could be obtained.
Parameters V and ρ decreased with increasing SSA (Fig. 12j and l), while D increased with the increase in SSA (Fig. 12k). The relationship
between the measured SSA and ρ under the C-type group shows a similar
trend as in Domine et al. (2007).
Comparison between data of no-melt events and uniform falling events.
NME indicates data of no-melt events and UFE indicates uniform falling events.
Each box plot shows the median, 25 % and 75 % percentiles, 1.5× interquartile ranges, and outliers.
Values in parentheses are sample numbers.
Categories used in snowfall event classification, showing their
location in terms of size–fall–speed coordinates.
The two curves represent size–fall–speed relationships for lump-type (red
curve) and hexagonal-type graupels (blue curve) (from Locatelli and Hobbs,
1974, denoted as L&H, 1974, on the graph).
Black circles are data under the M type in UFEs.
In the groups of AGG, GRA, and SMA under the M-type condition, only one
significant correlation (p value 0.05) between the SSA and D could be
obtained in the GRA. The p values for other combinations were not enough to
assure significant correlations (p value > 0.05). Basically, the
trends of GRA and SMA remain the same, while those of AGG differ from the
other two groups. The trend between D and SSA in the GRA, which is a positive
correlation, may result from the process of graupel growth. It is likely
that larger graupel collects a large number of small-rimed drops, and also
protects a larger number of small-rimed drops in its body from sublimation
during its fall. Therefore, a larger graupel stored a greater number of
small-rimed drops in its body. This is only a hypothesis, and further
investigation with more measurements is needed to prove it. Furthermore, a
simulation using a detailed cloud physics model, such as that of Hashimoto
et al. (2018a, b), will equip this study with some useful information to
understand the relationship between D and SSA in the GRA group.
Relationship between SSA of freshly fallen snow and detailed
characteristics of falling snow produced by the CMF.
(a–c) Data of aggregate group events in the M type (AGG);
(d–f) data of graupel type events in the M type (GRA);
(g–i) data of small particle type events in the M type (SMG);
(j–l) data in the C type (C type).
N: sample number, R: correlation coefficient, and p: p values.
Dotted lines indicate a SSA value of 90 m2 kg-1.
Relationships between meteorological elements and measured SSA.
(a) Relationship between air temperature and measured SSA;
(b) relationship between relative humidity and measured SSA;
(c) relationship between air pressure and measured SSA;
(d) relationship between wind speed and measured SSA;
(e) relationship between wet-bulb temperature and measured SSA.
Dashed lines are the linear least-square fit.
As shown in Fig. 6, all measured SSA values of an unrimed crystal in the
C-type group are less than 90 m2 kg-1 (the maximum value being 88 m2 kg-1). In addition, the measured SSA values in the S mode under
the M-type condition, which include unrimed and lightly rimed snow crystals,
are in the range of 70–78 m2 kg-1 (in the AGG). The relationships
between the SSA, D, and ρ of the AGG seem to be more complex than
those of the other two groups. These results may have resulted from the
different degrees of riming on the crystal. This study simply assumes that
the crystal having an SSA less than 90 m2 kg-1 is an unrimed
crystal type or lightly rimed snow crystal, while the crystal having an SSA
of over 90 m2 kg-1 is a rimed crystal; densely rimed, graupel-like, and graupel, are the classifications of riming degree for a single crystal
(Mosimann et al., 1993). In fact, a great majority of SSAs of graupels
(GRA), which have a large number of rimed drops in them, are larger than 90 m2 kg-1 (Fig. 12d–f). Moreover, SSAs in the SMA, which
should be made of small ice crystals with aggregated droplets, are also
mostly larger than 90 m2 kg-1 (Fig. 12g–i).
Relationship between SSA of fresh PPs and meteorological data on the ground
The SSA of PPs should be governed by synoptic conditions and meteorological
conditions in the clouds; however, meteorological conditions in the clouds
cannot be fully characterized at present. The parameterization of SSA of
fresh PPs should be useful to introduce the fresh PP characteristics in the
snow cover models, which are essential to predict the avalanche resulting
from weak PP layers. A previous study (Domine et al., 2007) concluded that
the relationship between measured SSA of fresh PPs and meteorological data on
the ground in their data was not legible. One of the reasons for this
conclusion originates from the PP samples collected from different sites
characterized by different snow climate and synoptic conditions. We propose
their SSA values include the influence of different environments. The second
reason originates from the presence of various sample measurement intervals,
which were longer than those in this study. Their fresh PP samples must have
changed due to metamorphism before the measurements, and the metamorphism
degrees must have varied depending on their measurement interval. Moreover,
meteorological conditions and falling snow types must have varied during the
sample deposition because of the longer interval. For these reasons, their
conditions complicate the understanding of the relationship between SSA of
fresh PPs and meteorological data on the ground. On the other hand, in this
study, the SSAs of fresh PPs were measured at the same place with a short time
interval (1–2 h), to avoid the effects of pre-measurement metamorphism and
meteorological fluctuations. Therefore, in this section, the possibility of
parameterizing the SSA of fresh PPs using the meteorological data on the ground
is explored. As mentioned in Sect. 3.4, the PP type sometimes varied even
for short observation periods (1–2 h) (Ishizaka et al., 2016). Therefore,
only the UFE data were used for the analyses (Table 1), to focus on the
relationship between the SSA of the uniform PP type and meteorological
conditions. The following elements, averaged only over the period of
snowfall (see Sect. 3.2), were chosen – air temperature (Ta), relative humidity (RH), wind speed (WS), air pressure (p), and wet-bulb temperature (Tw) calculated using Ta, RH, and p. The reasons for selecting these
meteorological elements are that Ta, RH, WS, and Tw are often used for the
parameterization of new snow density, as summarized by Helfricht et al. (2018). Although WS is also strongly affected by the local topography and
roughness, WS and p should share a relation with the synoptic-scale conditions.
Figure 13 shows the correlations between the measured SSA and each
meteorological variable (Ta, RH, WS, p, and Tw). Although all variables show a
significant correlation with the measured SSA (p value < 0.05), the
relationships vary with each variable. A strong, positive relationship
between the measured SSA and WS was obtained with a high correlation
coefficient, R (R=0.74); SSA increases with increasing WS (Fig. 13d). The results of this study correspond to those of Harimaya and Nakai (1999), in which the mass proportion of rime reportedly increased with an increase in
the wind speed under the T and L modes. Tw shows a strong negative correlation with SSA (R=-0.60); SSA decreases with an increase in Tw (Fig. 13e). Ta and RH show relatively low negative correlations (Ta: R=-0.44; RH: R=-0.48) (Fig. 13a and b). On the other hand, the relationship between SSA and p shows a small negative correlation (R=-0.30) (Fig. 13c). Based on these analyses, WS and Tw were selected for the parameterization of the SSA of fresh PPs because of their high R values. Moreover, Tw indirectly
involves the influences of Ta, RH, and p fluctuations because it is
calculated using those parameters. To deduce an estimation equation for SSA
using WS and Tw, SSA was assumed to be linearly dependent on WS and Tw. Equation (2) is this parameterization with the least-squares method:
SSA=17.6WS-9.4Tw+58.5(R=0.81).
Here, the valid range in Eq. (2) is from 0 to 4 m s-1 for WS and from
-4 to 0 ∘C for Tw.
Comparison between measured SSA and calculated SSA using Eq. (2)
Dotted line indicates 1 : 1 line.
Synoptic atmospheric pressure conditions during the period from 27 January to 1 February 2015.
Red circles indicate the location of Nagaoka.
Each weather chart shows the condition at 09:00 (JST).
Weather charts were produced by the Japan Meteorological Agency
(http://www.data.jma.go.jp/fcd/yoho/hibiten/index.html, last access: 20 April 2019).
Figure 14 shows the comparison between the measured SSA and the calculated
SSA, using Eq. (2) with WS and Tw. The residual standard error is 16.8 m2 kg-1. These results indicate that the SSA of fresh PPs can be calculated using meteorological data of Nagaoka. Although the equation
includes the limitation of its parameterization, which is strongly
site-specific, especially due to the introduction of wind speed as a
parameter, this idea is the first step to introducing falling snow crystals
into the snow cover models using SSA. To investigate the adaptable ratio to
the valid range in Eq. (2) during winter in Nagaoka, the data of winter 2015
(December 2014–March 2015) were analyzed using meteorological data with
1 h resolution: 445 snowfall events occurred during the winter of 2015
(here, a snowfall event is defined as an event where the snow height
increases within 1 h), and 374 cases of 445 snowfall events (84 % cases of snowfall events) were in the valid range of Eq. (2). In the case of outrange in Eq. (2), Tw≧0∘C (59 cases) and WS > 4 m s-1 (14 cases) (the case of Tw≧0∘C and WS > 4 m s-1: three cases). Therefore, there is still room for improvement to treat SSA under the melting effect simulation in Eq. (2).
Calculation of time evolution of SSA of fresh PPs
Here, the time-evolution estimation of the SSA of fresh PPs for the period
of 27 January to 1 February 2015, in which the synoptic meteorological
conditions periodically changed (Fig. 15), is presented using Eq. (2).
Figure 16 shows the meteorological conditions (WS: wind speed; Tw: wet-bulb temperature; HS: height of snow; and P: precipitation) during this period. Values of the SSA of fresh PPs calculated using Eq. (2) with 10 min
meteorological data (WS and Tw) are also shown in Fig. 16. In this figure, SSA is calculated only for the conditions where Tw<0∘C and P>0 mm, based on the 10 min meteorological data, and are then averaged over each hour to obtain hourly data. In the figure, the ranges of fluctuations in the calculated SSA during each hour and the values of the measured SSA are also shown in the figure.
Simulation results of SSA fluctuations using meteorological data
during the period from 27 January to 1 February 2015 (JST).
WS: wind speed; Tw: wet-bulb temperature; Ta: air temperature; HS: height of
snow; P: precipitation. Blue bars with circles are the fluctuation of
simulated SSA during each hour, and green triangles are the measured SSA.
Unrimed precipitation particles observed at Nagaoka (11:00 JST on
30 January 2015).
On 27 January, the synoptic precipitation condition was the C type (Fig. 15a).
Although precipitation had occurred, the temperature was above
0 ∘C and most of the precipitations should have been in the liquid
phase. In fact, the HS did not increase on 27 January. The synoptic
meteorological condition changed from the C type to M type during the night of
27 January to the morning of 28 January (Fig. 15b). During this period, the
temperature dropped during the period, the precipitation changed from a liquid
to solid state, and the HS increased. The calculated SSA also gradually
increased (Fig. 16). The M-type condition continued from the morning of 28 January to 29 January (Fig. 15c). During this period, the temperature remained low and the precipitation occurred in a solid state, and the HS increased continuously. In addition, the calculated SSA remained large (Fig. 16). The temperature gradually increased as the cyclone lashed from the south to the north along the Japanese archipelago on 30 January (Fig. 15d). Although no precipitation occurred during the morning of 30 January, solid precipitation occurred in the evening of the same day with small values of the calculated SSA. On 31 January, the synoptic meteorological condition gradually changed from C type to M type (Fig. 15e). Because the temperature was high, only liquid
precipitation occurred, and the HS decreased during this period. On 1 February,
the condition was M type (Fig. 15f) and the temperature dropped. Therefore,
solid precipitation occurred with large values of the calculated SSA. A
comparison of the calculated and the measured SSAs reveals that the former
can reproduce the fluctuation in the measured SSA (SSA increased after the
morning of 28 January and SSA decreased on 30 January), although some difference
between the absolute values exists. As discussed in Sect. 3.4, if the PPs
with SSA < 90 m2 kg-1 are considered to be unrimed snow
crystals, which should transform into a weak PP layer, the results imply two
possibilities (28 and 30 January) of weak-PP-layer development during the
study period. In fact, the unrimed PPs were observed in Nagaoka on 30 January 2015 (Fig. 17). For these reasons, this study has considered that
calculating the SSA using Eq. (2) with meteorological data is an efficient
first step toward describing the development of a weak PP layer in the snow
cover model.
Conclusions
A total of 102 SSAs of fresh PPs were measured shortly after their deposition
(1–2 h) at the SIRC in NIED during four winters (2013/2014, 2014/2015,
2015/2016, 2016/2017) in Nagaoka – one of the regions in Japan (located in a
coastal region on Honshu Island facing the Sea of Japan) that receives the
heaviest snowfall. The measured SSA values ranged widely between 42 and 153 m2 kg-1. To investigate the cause of variation in the SSA of fresh
PPs, the influence of melting during snowfall was analyzed. The SSAs of fresh
PPs under melting conditions are smaller than those without melting.
In addition, the relationship between the measured SSA and synoptic
meteorological conditions – monsoon type (M type) and cyclone type (C type)
– was also analyzed. The measured SSAs under the C type are smaller than those
of the M type because the snow crystals under the C type are unrimed, while those
under the M type are mostly richly rimed snow crystals and graupels. Furthermore,
a detailed investigation of SSA under the M type was conducted with various
snowfall modes determined using radar data. The results indicate the
possibility that unrimed and slightly rimed snow crystals occurred at a
specific snowfall mode (S mode) even under the M type. This result implies that
the weak PP layer with unrimed/slightly rimed snow crystals can develop not
only under the C-type but also under M-type snowfalls. The analysis of
comparisons between the SSA values of PPs and their properties (averaged fall
speed, averaged apparent size, and initial deposited density) confirms that
the SSA of PPs is strongly influenced by its physical properties.
Based on the analyses using the measured on-ground meteorological data, the
values of SSA were found to be strongly dependent on wind speed (WS) and
wet-bulb temperature (Tw); SSA increases with an increase in WS, while SSA decreases with an increase in Tw. Using WS and Tw, the equation to estimate the
SSA of fresh PPs was derived. This equation helped simulate the fluctuation
of SSA of fresh PPs during the period in which the C type and M-type snowfall
appeared periodically. Regardless of the limiting site-dependent
parameterization, the equation to simulate the SSA with meteorological data
is an efficient first step towards describing the weak PP layer in the new
snow cover model, especially due to introduction of wind speed as a
parameter in the empirical equation.
This study focuses on estimating the SSA of fresh PPs, which will help in
designing a predictive model for slab avalanche caused by a weak PP layer.
However, to implement the development process of the weak PP layer in the
snow cover model with SSA, the dependency of physical characteristics of the
PP type on SSA should be investigated in future studies. Moreover, this
study discussed the SSA of fresh PPs only under one climatic condition.
Additional similar measurements of SSA of fresh snow in other climatic
conditions are required to further understand the SSA of fresh snow. For
further parameterizing of the SSA of fresh PPs, it is necessary to use the
meteorological conditions of the cloud on which the SSA of fresh PPs strongly
depends. To promote this parameterization, future studies should compare the
results of this study with the detailed information on precipitation
particles from numerical meteorological models, such as the Japan
Meteorological Agency's non-hydrostatic model (JMA-NHM; Saito et al., 2006),
with the option of double-moment bulk cloud microphysics scheme (Hashimoto
et al., 2018a, b) or the WRF model (Skamarock et al., 2008), which
includes the P3 scheme (predicted particles properties; Morrison and
Milbrandt, 2015).
Data availability
Measured SSA data including meteorological data and microphotographs of each precipitation particle are available at 10.1594/PANGAEA.907148 (Yamaguchi et al., 2019).
Author contributions
SY performed measurement of specific surface area (SSA) of PPs. MI, HM, and KY performed measurement of precipitation particle properties. SN analyzed the doppler radar data. TA calculated the albedo using his model (PBSAM). VV and AH discussed the results from the viewpoint of cloud science. AH prepared the device for the methane adsorption method and gave advice on the measurement SSA of PPs using the devise. SY prepared the manuscript with the contribution of all coauthors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We would like to acknowledge members of the Snow and Ice Research Center
(SIRC) for their participation in useful discussions. We also appreciate
helpful comments and suggestions from Florent Domine, Leena Leppänen and one
anonymous reviewer. This study was part of the project “Research on
combining risk monitoring and forecasting technologies for mitigation of
diversifying snow disasters” and was supported by JSPS KAKENHI, grant
numbers JP23221004 (SIGMA PJ), JP15H01733 (SACURA PJ) and JP16K01340.
Financial support
This research has been supported by the JSPS KAKENHI (grant no. JP23221004), the JSPS KAKENHI (grant no. JP15H01733), and the JSPS KAKENHI (grant no. JP16K01340).
Review statement
This paper was edited by Florent Dominé and reviewed by Leena Leppänen and one anonymous referee.
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