The density of new snow is operationally monitored by
meteorological or hydrological services at daily time intervals, or
occasionally measured in local field studies. However, meteorological
conditions and thus settling of the freshly deposited snow rapidly alter the
new snow density until measurement. Physically based snow models and
nowcasting applications make use of hourly weather data to determine the
water equivalent of the snowfall and snow depth. In previous studies, a
number of empirical parameterizations were developed to approximate the new
snow density by meteorological parameters. These parameterizations are
largely based on new snow measurements derived from local in situ
measurements. In this study a data set of automated snow measurements at
four stations located in the European Alps is analysed for several winter
seasons. Hourly new snow densities are calculated from the height of new
snow and the water equivalent of snowfall. Considering the settling of the
new snow and the old snowpack, the average hourly new snow density is
68 kg m-3, with a standard deviation of 9 kg m-3. Seven existing
parameterizations for estimating new snow densities were tested against
these data, and most calculations overestimate the hourly automated
measurements. Two of the tested parameterizations were capable of simulating
low new snow densities observed at sheltered inner-alpine stations. The
observed variability in new snow density from the automated measurements
could not be described with satisfactory statistical significance by any of
the investigated parameterizations. Applying simple linear regressions
between new snow density and wet bulb temperature based on the measurements'
data resulted in significant relationships (r2 > 0.5 and p≤ 0.05)
for single periods at individual stations only.
Higher new snow density was calculated for the highest elevated and most
wind-exposed station location. Whereas snow measurements using ultrasonic
devices and snow pillows are appropriate for calculating station mean new
snow densities, we recommend instruments with higher accuracy e.g. optical
devices for more reliable investigations of the variability of new snow
densities at sub-daily intervals.
Introduction
In mountain regions there is an increasing demand for high-quality analysis,
nowcasting and short-range forecasts of the spatial distribution of
snowfall. Operational services, concerning avalanche warning, road
maintenance and hydrology, as well as hydropower companies and ski resorts,
need reliable information on the depth of new snow (HN) and the water
equivalent (HNW) of snowfall. Therefore the new snow density (ρHN) is needed to convert HN into HNW and vice versa. Information on HN
is especially relevant for cold and windy conditions, when measuring HNW is
a difficult task because conventional rain gauge measurements are prone to
large errors (e.g. Goodison et al., 1998). Recent results of the Solid
Precipitation Intercomparison Experiment (SPICE; Nitu et al., 2012) reveal
that these errors still exist in standard meteorological measurements (e.g.
Buisán et al., 2016; Pan et al., 2016). Many snow cover models calculate HN
from HNW at sub-daily time intervals, although reliable HNW input data are
difficult to obtain (Egli et al., 2009), and thus the new snow density is
needed in equal temporal resolution to convert between HNW and HN (e.g.
Lehning et al., 2002; Roebber et al., 2003; Olefs et al., 2013).
Additionally, ρHN has a considerable effect on the snow bulk
density of the total snowpack (e.g. Schöber et al., 2016).
Since the 1960s ultrasonic rangers have become more common for observing snow
depth changes automatically even at sub-hourly time intervals (e.g. Gubler,
1981; Goodison et al., 1984; Lundberg et al., 2010). They have the advantage
of a more objective method compared to subjective manual measurements of snow
depth (Ryan et al., 2008). Although high-accuracy optical snow depth sensors
have been more frequently used in practice over recent years (e.g. Mair and
Baumgartner, 2010; Helfricht et al., 2016), longer time series of snow depths
exist from ultrasonic measurements. Beside snow depth (HS), the water
equivalent of the snowpack (SWE) is observed operationally using weighing
devices such as lysimetric snow pillows (e.g. Serreze et al., 1999; Egli et
al., 2009; Lundberg et al., 2010; Krajči et al., 2017) and snow scales
(e.g. http://www.sommer.at/en/products/snow-ice/snow-scales-ssg-2, last
access: 3 May 2018). Upward-looking GPR (e.g. Heilig et al., 2009) and GPS
techniques (e.g. Koch et al., 2014; McCreight et al., 2014) and the
combination of both (Schmid et al., 2015) have been applied in scientific
studies to monitor the depth, SWE and liquid water content of the snowpack.
However, these techniques are rather expensive or not yet in use for
long-term observations by operational services. In general, automatic
measurements of SWE are prone to a high relative uncertainty and require a
certain degree of maintenance, which makes them complex and labour-intensive
(Smith et al., 2017). Due to such constraints, SWE measurement
instrumentation is installed at considerably fewer stations compared to HS
instruments, and only at sites with easy access for appropriate maintenance.
Recent studies present the performance of cosmic ray neutron sensors (e.g.
Schattan et al., 2017), which are partly used for long-term observations such
as e.g. from Col de Porte (Morin et al., 2012).
The density of new snow is influenced by the shape and size of the snow
crystals (e.g. Nakaya, 1951). Relationships between predominant snow crystal
type, riming properties and snowfall density were already reported by Power
et al. (1964) from snowstorm observations in Canada. Once the snow crystals
have accumulated at the snow surface, the density of the fresh snow starts to
increase depending on prevailing weather conditions and compaction caused by
overlaying of snow. A common mean ρHN used to convert between
HN and HNW is 100 kg m-3. Many studies analysed ρHN
values on a daily basis and confirmed this 10 : 1 rule as applicable for a
first estimate (e.g. Roebber et al., 2003; Egli et al., 2009; Teutsch, 2009).
However, ρHN values span a wide range, and values from 10 to
350 kg m-3 have been reported from American and European mountain
ranges, with mean values between 70 and 110 kg m-3 (e.g. Diamond and
Lowry, 1954; LaChapelle, 1962; Power et al., 1964; Judson, 1965; McKay et
al., 1981; Meister, 1985; Judson and Doesken, 2000; Valt et al., 2014). Most
of the ρHN data analysed in these studies were observed using
readings on a snow board. The density is calculated from HN measured with a
ruler and HNW is derived from an external precipitation device or from
weighing the new snow either in solid or melted form (Fierz et al., 2009).
Several studies have shown that measured ρHN can be related to
meteorological parameters, although with different time intervals and
different degrees of determination. Gold and
Power (1952) showed that the crystal type is related
to its estimated formation temperature. Diamond and Lowry (1954) and Simeral
et al. (2005) built an empirical calculation that ascertained relationships
between ρHN and air temperature at the 700 mb level.
Teutsch (2009) also concluded that ρHN of 12 h intervals at
valley stations is best correlated to the wet bulb temperature at mountain
stations in close vicinity (r2= 0.86). Judson and Doesken (2000)
found that near-surface air temperature and new snow density at mountain
stations could explain 52 % of the variance in snow density. Wetzel et
al. (2004) presented a similar degree of correlation of ρHN to
temperature at three high-elevation sites. Alcott and Steenburg (2010) showed
that ρHN is correlated with near-crest-level temperature and
wind speed particularly for high-SWE events. Wright et al. (2016) presented a
statistical analysis of data from 42 seasons of manual daily snow density
measurements along with air temperature and wind speed to derive
parameterizations to estimate new snow density. However, they end up with a
low coefficient of determination.
On the basis of data from seven stations in Switzerland located between 1250 and
1800 m a.s.l., Meister (1985) concluded that ρHN does not
correlate with the amount of new snow (HN), that it does not depend on
altitude and that air temperature does not accurately determine ρHN. Nevertheless, binning the data into temperature classes results in
a statistical equation with a correlation coefficient of 0.85. Further, he
recommended considering wind speed in addition to air temperature, at least
for stations higher than 1800 m a.s.l. On the basis of data sets from
Schmidt and Gluns (1991) and the US Army Corps of Engineers (1956), Hedstrom
and Pomeroy (1998) developed a power function using the air temperature, for
which they found a coefficient of determination of 0.84 and a standard error
of estimate of 9.3 kg m-3. Jordan et al. (1999) introduced an algorithm
for assigning ρHN within the SNTHERM snow cover model. They added
wind dependence to the temperature parameterization of Meister (1985). This
achieved a reduction of the error, but a significant scatter remained
between observed and parameterized ρHN values. Lehning et
al. (2002) built an empirical calculation for ρHN valid for a time
interval of 30 to 60 min in the framework of the snow model SNOWPACK. They
used air temperature, surface temperature, relative humidity and wind speed
for the regression analysis and achieved an approximate multiple coefficient
of determination of 0.83. Schmucki et al. (2014) used another empirical power
relation, including air temperature, wind speed and relative humidity, to
calculate the ρHN using SNOWPACK simulations for three
contrasting sites in Switzerland. ρHN was analysed in short
time intervals of 1–2 h by Ishizaka et al. (2016). They measured even lower
densities in comparison to ρHN estimates obtained using the
SNOWPACK density model, especially for aggregated snow crystal types. On the
basis of data from Col de Porte (1325 m altitude, French Alps), Pahaut et
al. (1976) developed a statistical relationship including the melting point
of water, air temperature and wind speed. This parameterization is used to
calculate the density of new snow in the snow cover model CROCUS (Vionnet et
al., 2012).
Settling of the new snow by its weight and destructive metamorphism may
reduce HN and hence increase ρHN between snowfall and the HN
reading and has to be considered when computing new snow density (e.g.
Anderson, 1976; Lehning et al., 2002; Steinkogler, 2009; Vionnet et al.,
2012). The contribution of settling to snow depth changes is highest in the
first hours after snowfall. Wind drift and radiation input to the snow
surface after the snowfall may increase ρHN in comparison to
ρHN at the time of snowfall. However, direct measurements of
ρHN at the time of snowfall are laborious and difficult to align
with the hours of peak snowfall rates.
Whereas most of the studies have analysed daily and sub-daily, manual ρHN measurements, to the best of our knowledge no extensive analysis of automated
ρHN measurements in hourly intervals over several winter seasons
exists. The aim of this study is to assess the value of automated
measurements of hourly HN and HNW for the calculation of ρHN at
different stations and at hourly time intervals. Therefore we examine the
following questions.
Are automated measurements of HN and HNW suitable for the calculation of
ρHN at hourly intervals?
How do the mean and the variability of observed ρHN differ
between distinct study sites?
How well do established density parameterizations represent observed hourly
ρHN values?
To this end, we calculated ρHN from hourly snow depth changes
(HN) and hourly SWE changes (HNW). The mean values and the variability of
hourly ρHN are discussed for observations at four different
meteorological stations and compared to calculations using established ρHN parameterizations. A critical assessment with an outlook for
next-generation measurement techniques is given in the discussion.
Data and methods
Data from four automatic weather stations (AWSs) were used in this study
(Fig. 1, Table 1). A prerequisite for the station selection was the combined
measurement of HS and SWE at each station in addition to the standard
meteorological measurements of air temperature, relative humidity,
precipitation, wind speed and global radiation. HS data are measured using
ultrasonic rangers. SWE data are recorded using snow pillows. Details
regarding the instruments at each AMS and the exact location of each AWS, as well as
the start and end dates of the available data coverage, are presented in
Table 1.
Map of the station locations. Pictures are given for
(a) Weissfluhjoch station, (b) Kühtai station,
(c) Wattener Lizum station and (d) Kühroint station.
Coordinates and data availability are
given for the four snow stations. The instrumentation for measuring snow depth (HS), snow water
equivalent (SWE), temperature (T), relative humidity (RH), precipitation
(P), wind speed (u) and global radiation (r) is listed.
Station abbreviation KührointKühtaiWattener LizumWeissfluhjochKROKTAWALWFJLocationEast12∘57′35.5′′11∘00′21.6′′11∘38′18.6′′9∘48′35.7′′North47∘34′12.4′′47∘12′25.6′′47∘10′05.5′′46∘49′46.4′′z (m a.s.l.)1420197019942540Data 1 Jan 2011–27 Feb 1987–1 Oct 2010–1 Oct 2013–2 Dec 201520 May 201530 Dec 201629 Sep 2015InstrumentsHSSommer USH 8Sommer USH 8Sommer USH 8Campbell Scientific SR50ASWESommer Snow Scale SSGOTT Thalimedes Shaft Encoder, Endress + Hauser Deltapilot MSommer SnowpillowSommer SnowpillowTRotronic MP408Kroneis NTCVaisala HMP45CRotronic Hydroclip S3RHRotronic MP408Pernix hair hygrometerVaisala HMP45CRotronic Hydroclip S3PSommer NIWA/Med-K505Ott Pluvio since 2001, custom built tipping bucket beforeSommer NIWA/Med-K505Lambrecht Pluvio 1518 H3uYoung 05103Kroneis cup anemometer + vaneYOUNG Wind MonitorYoung 05103rSchenk 8101Schenk 8101Kipp&Zonen CM21Kipp&Zonen CM21Comments Data gap winter 2012/13, wind regionalized from 1999Meteorological measurements at 2041 m a.s.l.
The Kühroint station (Germany) is operated by the Bavarian Avalanche
Warning Service. It is a well-equipped and maintained station for snow
climate at the northern fringe of the eastern Alps. It is located in a
meadow below the tree line.
The Kühtai station (Austria) is operated by the Tiroler Wasserkraft AG
(TIWAG). It is located south of the Inntal valley, but north of the Alpine
main ridge, and it is situated in a wind-sheltered location.
The station at Wattener Lizum (Austria) is operated by the Austrian Research
Centre for Forests (BFW) of the Federal Ministry of Agriculture, Forestry,
Environment and Water Management. This station is situated in a
south–north-oriented high alpine valley above the tree line near to the
Alpine main ridge. This station has an exceptionally long time series of
snow-hydrological measurements (Krajči et al., 2017; Parajka, 2017).
The station at Weissfluhjoch (Switzerland) is operated by the Institute for
Snow and Avalanche Research (SLF), which is part of the Swiss Federal
Institute for Forest, Snow and Landscape Research (WSL). The station is
presented in more detail by Marty and Meister (2012). Weissfluhjoch is the
highest elevated station considered in this study.
On the basis of coinciding data availability we consider four time periods as
presented in Table 1. Data outputs of the AWSs are logged at time intervals
ranging from 2 to 30 min. Hourly values were computed for global radiation,
relative humidity, air temperature and wind speed. The hourly value is the
mean of the previous hour. For precipitation it is the sum of the previous
hour. To account for noise in the ultrasonic signal, HS and SWE were smoothed
using a centred moving average over three values in the original data
resolution. The hourly values for HS and SWE are the values from the
smoothed time series.
The thermodynamic wet bulb temperature (Tw) was computed applying the
psychrometric equation (Sonntag, 1990) and an exact iterative approach
presented by Olefs et al. (2010). A standard barometric equation was used to
determine air pressure based on the station elevation. Air pressure
dependency of Tw is generally minor and only relevant for air
temperatures larger than +2 ∘C (Olefs et al., 2010).
A necessary condition for all further analysis of the time series was the
presence of a precipitation signal at the heated precipitation gauges in
combination with positive snow depth changes. Then, the hourly height of new
snow (HN) and the water equivalent of snowfall (HNW) were computed as the
change in HS and SWE. Within the next filtering step, only HN and HNW values
with Tw less than 0 ∘C and a wind speed (u) of less than 5 m s-1 were considered.
Constraints have to be set in order to avoid low values of HNW and HN,
which are prone to large relative errors due to random and systemic
measurement uncertainties in HN and SWE, but a minimum of approx. 100
remaining samples for statistical analysis must be ensured.
To investigate the influence of different minimum HNW and HN limits, a
distribution matrix was calculated by varying the minimum HNW and HN limits
in steps of 0.5 mm for HNW and 0.5 cm for HN, respectively. To account for
settling during ongoing snowfall, the compaction correction described in
Anderson (1976) was applied. The approach was simplified with respect to HS,
SWE and snow density by considering only two layers of the snowpack: the new
snow and the total snowpack of the previous time step. Destructive settling
(S) of HN is considered for each time step in which the snow depth increases
(Eq. 1). The destructive settling of the new snow (SHN) for each time
step is calculated by
1aSHN=-0.000002777⋅e0.04⋅TρHN≤150kgm-31bSHN=SHN⋅e0.046⋅T⋅(ρHN-150)ρHN≥150kgm-3,
where T is the air temperature. Settling of the new snow layer caused by the
weight of the ongoing snow accumulation is not taken into account.
Settling within the old snowpack is computed considering the total snow
depth (HS). The destructive settling within the old snow layer (SHS) is
calculated using Eq. (1), substituting HS for HN and using the bulk density
of the old snowpack (ρHS) calculated from HS and total SWE of the
previous time step. Settling within the old snowpack caused by the weight of
the snowpack (SwHS) is given as
SwHS=-248.976⋅HN3600000⋅e0.8⋅T⋅e-0.021⋅ρHS.
The resulting settling factors of SHN, SHS and SwHS are
multiplied by HS and HN to adjust HN accordingly.
New snow density (ρHN) was obtained from the ratio of HN to HNW.
Outliers below the 5 % percentile and higher than the 95 % percentile
were excluded. The ρHN data were grouped by wet bulb temperature
and wind speed, using bins of 1 ∘C and 0.5 ms-1 respectively.
A least squares regression was carried out using both the ungrouped data and
the median of the grouped data to quantify possible correlations of ρHN with Tw and u.
The ρHN values were compared to the following parameterizations
developed in previous studies. In these parameterizations, ρHN is
a function of meteorological parameters such as air temperature (T), wind
speed (u) and relative humidity (RH). The time interval for ρHN
readings of the respective study is given in brackets.
ρHP=67.92+51.52⋅eT2.59(Hedstrom and Pomeroy 1998,3event/daily)ρD=119+6.48T(Diamond and Lowry 1954,4frequent interval during event)5ρLC=50+1.7⋅(T+15)1.5(LaChapelle 1962, event)ρJ=500⋅1-0.951⋅e-1.4⋅5-T-1.15-0.008u1.76a-13∘C<T≤2.5∘CρJ=500⋅1-0.904⋅e-0.008u1.7T≤13∘C6b(Jordan et al., 1999, event/daily)ρV=109+6⋅T-Tf+26u0.57(Vionnet et al., 2012, event/daily)ρS=103.28+0.03T-0.36-0.75⋅arcsin(0.01RH+0.03⋅log10u)8aT≥-14∘CρS=103.28+0.03T-0.75⋅arcsin(0.01RH+0.03⋅log10u)8bT<-14∘C(Schmucki et al., 2014, event/hourly)ρL=70+6.5T+7.5Ts+0.26RH+13u-4.5TTs-0.65Tu-0.17RHu+0.06TTsRH9(Lehning et al., 2002, event/hourly)
The melting point of snow (Tf) in Eq. (7) was approximated
as 0 ∘C (Vionnet et al., 2012). Following Schmucki et al. (2014), we
limited the parameter range and set RH to a constant value of 0.8 (80 %)
during snowfall and the lower boundary for the wind speed to 2 ms-1.
The temperature of the snow surface (Ts) is required in Eq. (9). As
this was not available for each station, we used the approximation
Ts=T. We argue that Ts could not considerably exceed
0∘ because of the maximum Tw of 0 ∘C. Since only
precipitation events are considered, RH can be expected to be high, and thus
the difference between Tw and T is small.
The uncertainty of ultrasonic measurements on snow can be assumed to be in
the range of ±1 cm, which is partly a consequence of changes in
signal velocity due to meteorological conditions. However, we used the
original HS data logged in millimetre resolution to avoid the effects caused by
rounding to full centimetre when calculating HN. Likewise, we used the tenths of millimetre SWE
data logged at the pillows. Another documented error source of the HS
measurement is signal blocking by e.g. dense snowfall or drifting snow,
which causes peaks of the HS. However, with the filtering procedure applied
in this study, no such spikes were left in the analysis.
A source of uncertainty is the spatial offset between the HS measurements
and the SWE measurements. HS is measured directly above the SWE measurement
at Kühtai station, Kühroint station and Wattener Lizum station
(Fig. 1). However, the footprint of the snow depth sensor may be smaller
than the surface area of the pillow, and it decreases with increasing
HS. A spatial variability of HS on the pillow can be caused by snow drift
and differing snow settling or snowmelt.
For the calculations within this study we used the changes in HS and SWE
over the time period of snowfall only. Errors due to spatial variability in
HS and SWE caused by spatial differences in energy consumption and snow
drift between precipitation events are reduced. This is especially valid for
the HS and SWE measurements at the stations with matching HS and SWE
measurements. The snow depth sensor and the snow pillow of Weissfluhjoch
station are separated by 9 m. Schmid et al. (2014) suggest a
small-scale variability in HS of ±4.3 % at the Weissfluhjoch
station. Again, the error may be smaller due to using temporally limited
changes of HS, but an additional uncertainty of ±5 % can be
assumed here.
A well-known issue with snow pillows is bridging effects (e.g. Serreze et
al., 1999; Johnson and Schaefer, 2002). Dense snow layers and crusts within
the snowpack sustain the weight of the new snow so that HNW, and thus ρHN, are underestimated. We cannot exclude such data explicitly.
However, all filtering conditions have to be fulfilled to include values
in the analysis, so that data without or with lagged HN increase were not
considered. Additionally, the chosen snow stations are well maintained in
case of implausible data due to their overall good accessibility; e.g.
trenches are dug out around the base area of the snow pillow at Kühtai
station to cut off the measured part of the snowpack to avoid bridging
effects.
Nevertheless, the measurement uncertainty is ±1 cm for HN and 0.1 cm
for HNW. Considering mean HN (Table 2) and HNW values, the uncertainty is
±25 kg m-3 or 37 % of the mean density. This value is lower
considering higher HN, but increases to 80 % for the combination of
minimum HN and minimum HNW of 1.6 and 0.2 mm respectively.
Time periods analysed in this study with the mean and the median of
hourly values for the height of new snow (HN), wet bulb temperature
(Tw), wind speed (u), calculated densities from observed values (ρ) and calculated densities corrected for settling of the snowpack (ρHN). The results are valid for the filtered data values (nth) with
HN > 2 cm, HNW > 1.5 mm, Tw < 0 ∘C
and u < 5 ms-1 as a subset of all data
that have a precipitation signal and positive HS change (nP).
StationPeriod Count data HN (cm) Tw (∘C) u (m s-1) ρ (kg m-3) ρHN (kg m-3) no.npnthmeanmedianmeanmedianmeanmedianmeanmedianmeanmedianKRO11 Oct 2013–20 May 20151139913.23.1-3.9-3.01.10.98273736721 Oct 2011–30 Sep 201315761183.43.1-4.2-4.21.00.987777469KTA11 Oct 2013–20 May 2015579533.83.3-3.4-3.40.80.87069616121 Oct 2011–30 Sep 2013506363.32.8-4.8-4.00.80.77566605431 Oct 1999–30 Sep 201152932523.53.2-3.5-3.20.80.874746464427 Feb 1987–30 Sep 199979583873.73.3-3.6-3.40.80.774756159WAL11 Oct 2013–20 May 201512481113.63.4-4.3-4.81.31.37672686621 Oct 2011–30 Sep 201315881263.93.5-4.3-3.61.71.771696258WFJ11 Oct 2013–20 May 201516191003.02.7-4.9-4.02.22.095869183Results and discussionData filtering, correction of settling and evaluation
Figure 2 presents the median new snow density (ρHN) data calculated from all filtered HN and HNW values
exceeding the respective minimum HN and HNW limits. This presentation
highlights the variability of ρHN by using different
minimum limits with respect to the high relative uncertainty of low HN and
HNW values. Changing the minimum limits for HN and HNW affects the resulting
ρHN considerably. However, increasing the minimum limits for HN
and HNW results in a distinct lowering of the number of data remaining for
the subsequent analysis (Fig. 2). There are certain differences between the
stations for high minimum HNW limits. Calculated ρHN decrease
when low minimum HN and high minimum HNW limits are applied at Kühtai
and Wattener Lizum station. In contrast, ρHN values increase for equal
minimum limits at Kühroint and Weissfluhjoch stations. At Kühtai and
Wattener Lizum stations, high HNW values of more than 3 mm HNW are
accompanied by a rather high HN (Fig. 2). In contrast, a low HN occurring with
a high HNW at Kühroint and Weissfluhjoch causes a high ρHN.
However, these results are based on a small number of values only. In
general, the calculated median ρHN values are rather constant following
the 1 : 1 line of minimum HNW and HN limits (Fig. 2).
Median new snow densities (colour scale) calculated using all data
exceeding different minimum limits of the height of new snow (HN) and the
water equivalent of snowfall (HNW) for period 1 (1 October 2013–20 May
2015). Note that multiples of 25 kg m-3 are highlighted with red
contour lines. The labelled black dashed lines give the count of the hourly
data remaining after filtering. The straight dotted and dashed lines show results
for equal minimum limits of HN (cm) and HNW (mm).
In order to avoid low values of HNW and HN, but ensuring an appropriate
number of approx. 100 samples and with respect to the results of the
Fig. 2, we decided to use a minimum limit of 1.5 mm in HNW and 2.0 cm in
HN. This leads to the exclusion of on average 94 % of all data points
that have a precipitation signal and positive snow depth changes (Table 2).
Frequency distributions for HN, HNW, Tw and u of the unfiltered and
filtered data are presented for each station and for each time period in the
Supplement Figs. S01 to S09.
The exclusion of high wind speeds only has a small effect at the lower
stations and is more noticeable at the more wind-exposed stations of
Wattener Lizum and Weissfluhjoch. Considering period 1 comprising all
stations, the filtering process causes the highest filtering rate for
Weissfluhjoch station, with 6 % of data remaining after applying the
filtering. The overall highest amount of data reduction is found at
Kühtai station, with 5 % of the data remaining after filtering of the
longer periods 3 and 4 (Table 2). There was a considerable fraction of data
with positive HS changes, a precipitation signal and positive Tw. Most
of these data seem to be paired with very small HS changes and are
eliminated for the final data set when the HN minimum limit is applied.
The correction of the HN underestimation caused by settling of the snowpack
during snowfall leads to an average reduction of mean ρHN of
10.2 kg m-3, with a standard deviation (σ)
of 2.6 kg m-3 (Table 2). This corresponds to 13.5 % with a σ of 3.7 %. The compaction correction causes noticeably less change in
ρHN at Weissfluhjoch in period 1 (5 % reduction of mean
ρHN) than in the other time periods and other stations. The
next closest is Kühroint, also in period 1, with a reduction in
ρHN of 7 %. Unless otherwise stated in the text,
ρHN always refers to the corrected densities hereafter.
Based on a 15-year data set of Weissfluhjoch (WSL Institute for Snow and
Avalanche Research SLF, 2015, 10.16904/1) from 1 September 1999 to 31
December 2015, the contribution of settling relative to HN was calculated
using the multi-layer SNOWPACK model (e.g. Lehning et al., 2002) and the
approach from Anderson (1976) to compare the results of this study to a more
physically based estimate. Results are presented in Fig. 3. While a median
relative contribution of settling to HN by 19 % was calculated with
SNOWPACK, the approach of Anderson (1976) resulted in lower values of 5 %
in median and 9 % in mean. Thus, the settling considered for the
presented data can be assumed to be a lower estimation. However, higher
contributions of settling would result in lower ρHN values,
with an increased HN assuming a fixed HNW.
Box plots (median, 25 and 75 % percentiles, 1.5 × interquartile
ranges, outliers) of settling relative to hourly new snow
heights (HN) modelled with SNOWPACK and using the approach presented by
Anderson (1976).
Figure 4 shows the distribution of ρHN values obtained from the
filtered data at Kühroint station as representative of all stations
and periods (Figs. S10 to S17). In general, the ρHN values show high variability at all stations. Nevertheless, ρHN
values are within a reasonable range of less than 200 kg m-3. The
histograms of ρHN show one-tailed distribution towards
higher ρHN. Median ρHN values of the different stations and
for different periods range between 66 and 86 kg m-3for uncorrected
values and between 54 and 83 kg m-3 for ρHN
corrected for settling (Table 2).
Distribution of calculated new snow densities at Kühroint
station for period 1 (1 October 2013–20 May 2015). (a) All data
have a precipitation signal and positive HS change, all data are filtered with
HN > 2 cm, HNW > 1.5 mm, Tw < 0 ∘C
and u < 5 ms-1) and filtered data are reduced by
cutting off at 5 and 95 % percentiles. (b) Histogram of all filtered
densities. (c) The box plot showing the median and 25 and 75 % interquartile
range of uncorrected densities and densities corrected for settling of the
snowpack. Note that similar figures are available in the Supplement
(Figs. S10–S17) for all stations and all time periods considered in this study.
Station-dependent differences
The distributions of ρHN, Tw and u during all filtered
snowfall data are presented in Figs. 5 and 6 and in Table 2. The lowest
Tw and highest wind speeds were observed during snowfall at
Weissfluhjoch station. However, the range and distribution of Tw at
Weissfluhjoch station result in a higher median Tw during snowfall
compared to Tw at Wattener Lizum station. With respect to wind speeds,
Wattener Lizum is second. The lowest wind speeds at Kühtai station occur
together with the lowest ρHN. Weissfluhjoch station has the highest
median ρHN by a large margin with 83 kg m-3 in period 1
compared to, respectively, 67, 61 and 66 kg m-3 at Kühroint,
Kühtai and Wattener Lizum stations.
Box plot (median, 25 and 75 % percentiles, 1.5 × interquartile
ranges, outliers) of calculated new snow densities
(ρHN) based on observations, wet bulb
temperature (Tw) and wind speed (u) for filtered snowfall events
(Table 2) at all four stations within period 1 (1 October 2013–20 May 2015).
Box plots (median, 25 and 75 % percentiles, 1.5 × interquartile
ranges, outliers) of calculated new snow densities
(ρHN) based on observations, wet bulb
temperature (Tw) and wind speed (u) for filtered snowfall events
(Table 2) at three stations within period 2 (1 October 2011–1 October 2013) and
at Kühtai station within period 3 (index*, 1 October 1999–30 September 2011)
and period 4 (index**, 27 February 1987–30 September 1999).
Wind influence may be the reason for higher ρHN at Weissfluhjoch
station. Snow grains are fragmented by snow drift (e.g. Sato et al., 2008),
and thus more packed into the layer of new snow during windy conditions even
over the course of only 1 h. The Kühtai station shows the lowest ρHN, and the difference of the mean ρHN is 17 kg m-3 between
Weissfluhjoch and Kühtai stations for period 1. Median ρHN and
median Tw of the different periods show a relationship between the
periods at Kühtai station, with a higher ρHN for a higher Tw
(Fig. 6, Table 2).
The overall mean hourly ρHN of all stations and time periods is
68 kg m-3, with a standard deviation of 9 kg m-3. In general, this
is considerably lower than new snow densities from daily measurements (e.g.
Roebber et al., 2003; Egli et al., 2009; Teutsch, 2009). Meister (1985)
measured ρHN lower than 100 kg m-3 on a daily basis,
analysing data with a HN of more than 0.1 m. In contrast, the presented
ρHN values are closer to the time of the snowfall event, and density
changes over several hours due to e.g. energy exchanges and wind drift at
the uppermost snow layer can be excluded. On the basis of ρHN
in situ measurements in hourly resolution Lehning et al. (2002) emphasized
that at sub-daily time intervals, lower densities in comparison to daily new
snow densities have to be applied. Comparatively low ρHN values
close to 50 kg m-3 were also presented by Ishizaka et al. (2016), with
an average ρHN of 52 kg m-3 for aggregated snowflakes and
55 kg m-3 for small hydrometeors. They further found a mean ρHN of 72 kg m-3 for a second group of smaller crystals and
99.4 kg m-3 for graupel-type hydrometeors.
The observed inter-station variability shows the importance of differing
ρHN between more windy mountain stations and less windy stations
in the valleys.
Density parameterizations
A simple linear regression analysis showed that the short-term variability
of ρHN cannot be explained with corresponding changes in Tw
or u (Table 3, Figs. 7 and S18 to S26). An increase of ρHN with
increasing Tw can be identified in the figures, and the slopes of the
least squares regressions show an increase of ρHN with an
increase of wet bulb temperature for all stations (Table 3). However, no
consistent relationship between ρHN and u could be found, either
for single stations or for different periods at one station. The binned
analysis based on Tw showed a considerable r2 of more than 0.5 on
a 0.01 significance level at Kühroint and Kühtai station, with
intercepts of 70 to 80 kg m-3 and gradients of about 3 to 4 kg m-3
per 1 ∘C.
Results of a single linear regression between the corrected
densities (ρHN) as a dependent variable and wet bulb temperature
(Tw) and wind speed (u) as explanatory variables for the class
median values based on all filtered data points binned into 0.5∘ K
classes and classes of 0.5 ms-1, respectively. The corresponding
coefficient of determination (r2) and the p value are
presented.
Although the regressions generally show the expected trends, it must be
noted that the variability of ρHN remains unexplained. This could
partly be attributed to the measurement uncertainties. However, the
variability caused by measurement uncertainties is assumed to be equalized, only
considering the mean and median of ρHN values for
total time periods. Relationships between ρHN and Tw
were recognized for distinct periods and stations only, but with similar
coefficients of determination in comparison to the results of e.g. Judson
and Doesken (2000), Wetzel et al. (2004) or Wright et al. (2016).
Box plots (median, 25 and 75 % percentiles, 1.5 × interquartile
ranges, outliers) of calculated new snow densities
(ρHN) based on observations and
densities calculated using parameterizations developed in previous studies
(Eqs. 3–9) at all four stations within period 1 (1 October 2013–20 May
2015).
Box plots (median, 25 and 75 % percentiles, 1.5 × interquartile
ranges, outliers) of calculated new snow densities
(ρHN) based on observations and
densities calculated using parameterizations developed in previous studies
(Eqs. 3–9) at three stations within period 2 (1 October 2011–1 October
2013) and at Kühtai station within period 3 (index*, 1 October 1999–30
September 2011) and period 4 (index**, 27 February 1987–30 September 1999).
Testing multiple regressions using additional meteorological parameters
did not increase the statistical significance. Instead, a comparison to
existing parameterizations of ρHN was performed for all stations
and periods.
Considering the various parameterizations, which use meteorological
parameters to approximate new snow density (Eqs. 3 to 9), it is evident that
the observed variability of ρHN is not correlated to the
variability of parameterized new snow densities (Table 4). Most of the seven
parameterizations overestimate the median of the observed ρHN
values (Figs. 3, 7 and 8 and Table 4). However, some parameterizations produce
considerably better results than others for median ρHN values.
The parameterizations of LaChapelle (1962), Diamond and Lowry (1954) and
Vionnet et al. (2012) consistently overestimate ρHN. The
parameterization of Hedstrom and Pomeroy (1998) overestimates ρHN
at Kühroint, Kühtai and Wattener Lizum stations (Figs. 7 and 8), but
converges with the median ρHN at Weissfluhjoch station for period
1 (Fig. 7, Table 4). In general, the ρHN values simulated using the
parameterization of Jordan et al. (1999) are closer to calculated ρHN, but median ρHN values are underestimated for Weissfluhjoch
station. Median ρHN values and the range of ρHN at
Weissfluhjoch are well simulated using the parameterization of Schmucki et al. (2014),
but it overestimates median ρHN of Kühroint,
Kühtai and Wattener Lizum stations (Figs. 3 and 7 and Table 4). However, this
parameterization was fitted to original density data from Weissfluhjoch.
Comparison of corrected density values (ρHN,
(kg m-3)) and parameterizations, applying Eqs. (3) to (9) presented in
Sect. 2. Median values (m, (kg m-3)) are shown together with the
Pearson correlation coefficient (r) and the root mean squared error (RMSE,
(kg m-3)) between the respective calculations and ρHN.
Best values of the performance measures are highlighted for each station and
time period using bold and italic numbers.
The lowest root mean squared error (RMSE) was achieved for Weissfluhjoch
station with the parameterization of Diamond and Lowry (1954). The
parameterizations of Lehning et al. (2002) and Jordan et al. (1999) result
in the lowest RMSE (Table 4) compared to ρHN at Kühroint, Kühtai
and Wattener Lizum stations, with slightly lower density values using the
parameterization of Lehning et al. (2002) fitting best to the low median
ρHN values of the Kühtai station.
Thus, the parameterization of Lehning et al. (2002) appears to be the first
choice regarding the calculation of hourly new snow densities for high
elevations and inner-alpine regions. This parameterization requires multiple
input parameters. Where such data are not available, the parameterization of
Jordan et al. (1999), requiring temperature and wind data only, might be a
good alternative. Even though correlations are low in general, some of the
highest Pearson correlation values (r, Table 4) were achieved by applying
the simpler, linear equations by Diamond and Lowry (1954), LaChapelle (1962)
and Vionnet et al. (2012). In addition to the regressions presented in
Table 3, this shows again the identifiable relation between snow density and
temperature.
Mair et al. (2016) evaluated some of the parameterizations also considered in
this study. Using a distinctly larger time window for smoothing their HS data
(5 h average), they calculated median ρHN between 75 and
100 kg m-3 using the parameterizations of Jordan et al. (1999) and
Hedstrom and Pomeroy (1998), which is close to the results presented in this
study. They also found that using the parameterization of LaChapelle (1962)
results in a mean ρHN higher than 100 kg m-3. In
general they concluded that using a constant ρHN of
100 kg m-3 caused an overestimation of seasonal precipitation by up to
30 %. Conversely, a mean ρHN of 70 kg m-3 will
result in better SWE estimations. This is in accordance with the resulting
average ρHN of 68 kg m-3 calculated from automated
measurements within our study.
Conclusion
The aim of this study was to assess the value of automated measurements of
snow depth (HS) and snow water equivalent (SWE) to compute new snow density
(ρHN) on an hourly time interval. Complementary data sets of HS
and SWE measurements using ultrasonic devices and snow pillows from four
mountain stations were used to calculate the height of new snow (HN) and the
water equivalent of snowfall (HNW). Subsequently, ρHN was
calculated from HN and HNW, considering potential underestimation of HN by
settling of the snowpack.
The snow measurements using ultrasonic devices and snow pillows were found
to be appropriate for the calculation of station average hourly ρHN values. However, the observed variability in ρHN from
the automated measurements could not be described with appropriate
statistical significance by any of the investigated algorithms. An average
ρHN of 68 kg m-3 with a standard deviation of 9 kg m-3
was calculated considering all stations and time periods. The average ρHN for individual stations in a common period ranged from
61 to 83 kg m-3, with a higher ρHN at more windy
locations. Thus, wind speed is a crucial parameter for the inter-station
variability of ρHN.
Seven existing parameterizations for estimating new snow densities were
tested, and most calculations overestimate ρHN in comparison to
the results from the hourly automated measurements. Two of the tested
parameterizations were capable of simulating low ρHN at sheltered
inner-alpine stations. This reveals that it has to be carefully considered
which parameterization should be used for which application and environment.
Nevertheless, the natural variability of ρHN is masked using the
combination of ultrasonic ranging and snow pillow data for ρHN
calculation because of the limited accuracy of the sensors and snow depth
changes due to settling of the snowpack and wind drift. We conclude that the
value of the analysed data is given by the mean and median ρHN
and its variation between different stations and time periods, and the
considerably lower ρHN values in contrast to ρHN
calculated on daily or event-based measurements.
The study shows the potential of collocated measurements of HS and SWE for
determining ρHN automatically. However, recent
developments in optical distance sensors and weighing devices increase the
accuracy of such snow measurements and hence decrease the uncertainty of
subsequent calculations. We therefore recommend the use of high-accuracy
sensors for the determination of ρHN at sub-daily intervals.
Data availability
A processed set of SNOWPACK input data from Weissfluhjoch
station is available in WSL Institute for Snow and Avalanche Research
SLF (2015) (WFJ_MOD: Meteorological and snowpack measurements from
Weissfluhjoch, Davos, Switzerland) at 10.16904/1.
Detailed information about the Weissfluhjoch data set can be found in WSL
Institute for Snow and Avalanche Research SLF (2015) and in Marty and
Meister (2012). Data of Kühtai station are published by Krajči et
al. (2017) and are available from the Zenodo repository at
10.5281/zenodo.556110 (Parajka, 2017).
Data of Kühroint station are available on request from the Bavarian
Avalanche Warning Service
(https://www.lawinenwarndienst-bayern.de/organisation/lawinenwarnzentrale/kontakt.php,
last access: 2 May 2018).
Data of Wattener Lizum station are available on request from the Austrian
Federal Research and Training Centre for Forests, Natural Hazards and
Landscape (BFW; https://bfw.ac.at/rz/bfwcms.web?dok=6057, last access:
2 May 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/hess-22-2655-2018-supplement.
Author contributions
KH is the main investigator of this study. LH performed
snow density analysis within the pluSnow project. RK performed
initial quality control, provision and set-up of the project database for all
station and meta-data. CM prepared the data of Weissfluhjoch
station, contributed fruitful discussions and helped to hone the focus of the analysis
and the manuscript. MO contributed significantly to analysis and
discussions as the main project partner within the framework of the pluSnow
project.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The pluSnow project is financed by the Gottfried and Vera Weiss Science
Foundation (WWW). The project funding is managed in trust by the Austrian
Science Fund (FWF): P 28099-N34. The project duration was October 2015–September 2018. The
authors want to thank the colleagues of the Tiroler Wasserkraft AG (TIWAG),
of the Federal Research and Training Centre for Forests (BFW) and of the
Bavarian Avalanche Warning Service for data provision. In particular we are grateful
for the close collaboration with Johannes Schöber (TIWAG) and Reinhard
Fromm (BFW). We also want to thank Michael Lehning, Charles Fierz and the
two reviewers for their helpful comments and fruitful discussion of the
results.
Edited by: Thom Bogaard
Reviewed by: two anonymous referees
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