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\begin{document}

\title{Intercomparison of measurements of bulk snow density and water
equivalent of snow cover with snow core samplers: instrumental bias and
variability induced by observers}



\author[1]{Ignacio Lopez-Moreno}%
\author[2]{Leena Leppänen}%
\author[3]{Bartłomiej Luks}%
\author[4]{Ladislav Holko}%
\author[5]{Ghislain Picard}%
\author[6]{Alba Sanmiguel-Vallelado}%
\author[7]{Esteban Alonso-González}%
\author[8]{David C. Finger}%
\author[2]{Ali Nadir Arslan}%
\author[9]{Katalin Gillemot}%
\author[10]{Aynur Sensoy}%
\author[10]{Arda Sorman}%
\author[10]{Mustafa Cansaran Ertaş}%
\author[11]{Charles Fierz}%
\author[11]{Christoph Marty}%
\author[12]{Steven Fassnacht}%
\affil[1]{Pyrenean Institute of Ecology}%
\affil[2]{Finnish Meteorological Institute}%
\affil[3]{Polska Akademia Nauk Instytut Geofizyki}%
\affil[4]{Slovak Academy of Sciences}%
\affil[5]{University of Grenoble Graduate School of Environmental and Organisational Systems Science and Engineering}%
\affil[6]{Instituto Pirenaico de Ecologia}%
\affil[7]{Instituto Pirenaico de Ecología}%
\affil[8]{Sustainability Institute and Forum (SIF), School of Science and Engineering, Reykjavik University, Iceland}%
\affil[9]{University of Vienna}%
\affil[10]{Eskişehir Technical University}%
\affil[11]{Federal Institute for Snow and Avalanche Research}%
\affil[12]{Colorado State University}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\selectlanguage{english}
\begin{abstract}
Manually collected snow data are often considered as ground truth for
many applications such as climatological or hydrological studies.
However, there are many sources of uncertainty that are not quantified
in detail. For the determination of water equivalent of snow cover
(SWE), different snow core samplers and scales are used, but they are
all based on the same measurement principle. We conducted two field
campaigns with 9 samplers commonly used in observational measurements
and research in Europe and northern America to better quantify
uncertainties when measuring depth, density and SWE with core samplers.
During the first campaign, as a first approach to distinguish snow
variability measured at the plot and at the point scale, repeated
measurements were taken along two 20 m long snow pits. The results
revealed a much higher variability of SWE at the plot scale (resulting
from both natural variability and instrumental bias) compared to
repeated measurements at the same spot (resulting mostly from error
induced by observers or very small scale variability of snow depth). The
exceptionally homogeneous snowpack found in the second campaign
permitted to almost neglect the natural variability of the snowpack
properties and focus on the separation between instrumental bias and
error induced by observers. Under such measurement conditions, the
uncertainty in bulk snow density estimation is about 5\% for an
individual instrument and is close to 10\% among different instruments.
Results confirmed that instrumental bias exceeded both the natural
variability and the error induced by observers, even in the case when
observers were not familiar with a given snow core sampler.%
\end{abstract}%



\sloppy


\textbf{}

\par\null

1 INTRODUCTION

Water equivalent of snow cover (SWE) is one of the most commonly
measured snowpack properties (Pirazzini et al., 2018). Hydrological
studies need to quantify this variable since it is mass of snow that can
be released as water during the melt season. Moreover, SWE is commonly
used in long-term climatological or hydrological studies (Marty, 2017;
Helmert et al., 2018), and as data for calibration, evaluation, or
assimilation of remote sensing and numerical models (Dong, 2018).
Furthermore, long-term measurements are used for developing statistical
models (e.g. Jonas et al., 2009) that can be used in combination with
LiDAR measurements and other depth measurement over space (Sch\selectlanguage{ngerman}öber et
al., 2014) or in the framework of snow data assimilation (Magnusson et
al., 2014).

SWE can either be measured automatically by pressure sensors (Johnson,
2004), or retrieved by various emerging techniques like Global
Navigation Satellite System antennas (Guttmann et al., 2012; Koch et
al., 2014), radio frequency transmission lines (Stähli et al., 2004),
passive gamma ray sensors (Choquette et al., 2013), cosmic-ray neutron
sensors (Schattan et al., 2017) or ground penetrating radar (Schmid et
al., 2015). Moreover, microwave remote instruments, both active and
passive, proved their capability to estimate information on SWE (Takala
et al., 2011), although there are clear limitations in mountain regions.

Despite the existence of a wide array of geophysical and remote sensing
methods to measure bulk snow density and SWE at different spatial scales
(Kinar \& Pomeroy, 2015), it is still very important to perform
classical manual measurements, which indeed are generally used to
validate automatic sensors. Bulk snow density and SWE in a snow column
can be retrieved in two ways, either by weighting snow cores extracted
with a snow core sampler or by sampling snow density along the wall of a
snow pit with dedicated density cutter at either regular depth intervals
or layer by layer. According to a recent survey by Pirazzini et al.
(2018) snow core samplers are still the most widely used devices, due to
the simplicity and speed of the snow data acquisition (at least for
shallow snowpacks), both in research and operational networks.

Since Church (1933) popularized the use of a snow core sampler, many
surveyors have developed a variety of models that mainly differ in
length and diameter, material (basically metal or plastic), weighting
system (snow and sampler combined, or only the snow in a separate bag or
container), and the type of the tooth-cutter applied. The specificities
of each snow core sampler aim to adapt to the most common
characteristics of the snowpack in a given area (mostly in terms of snow
depth, hardness and presence of ice layers) or aim to facilitate its
portability in the field, when relevant.

It is well known that measurements of SWE and density from snow core
samplers present a number of problems that affect the accuracy of the
collected data (Stuefer et al., 2013). The most common problem is the
loss of part of the sample due to snowpack collapse, when the sampler
encounters hard layers. Snow can also be lost when the sampler is
extracted from the snowpack for weighting (Dixon \& Boon, 2012). This is
the reason why many surveyors only consider the samples that collect at
a significant percentage of the measured snow depth to be valid. Another
problem is accumulation of compacted snow at the mouth of the sampler
impeding the penetration further to sample more snow. The presence of
ice layers may lead to the false perception that the ground is reached,
also leading to snowpack undersampling. Indeed, when density and SWE
measurements from snow core samplers are compared to those from density
cutters in snow pits, an underestimation of the former is generally
found (Fassnacht et al., 2010; Proksch et al., 2016). Other authors have
highlighted other sources of errors, including the human factor (Stuefer
et al., 2013) and errors in the weighting process due to a lack in
accuracy of the scales used, or the effect of wind on hanging scales
(Goodison et al., 1987, Doesken \& Judson, 1996). Several previous
studies have attempted to quantify the error of different models of snow
core samplers, considering data from snow pits or the mass of a volume
of snow as ground truth, or by directly analyzing the variation between
different samplers (Work et al., 1965; Peterson \& Brown, 1975; Farnes
et al., 1982; Dixon \& Boon, 2012). Most of the results have identified
a different behavior between snow core samplers under different snow
conditions, and most of the reported errors ranged between 3 \% and 13\%
(Beaumont, 1967; Work et al., 1965; Farnes et al., 1982; Berezovskaya \&
Kane 2007; Dixon \& Boon, 2012). These analyses are important
as\emph{in-situ} SWE measurements are often used as ground truth for the
evaluation of both hydrological models (Pirazzini et al., 2018) and
remote sensing products. While analyzing SWE or density data sets it is
important to remember that different institutions and observers may use
different snow core samplers (even changing them over time), which may
introduce significant spatial and temporal inhomogeneities in the data
(Beaumont \& Work, 1963; Haberkorn et al., 2019).

In the framework of the COST Action ES1404 HarmoSnow (A European network
for a harmonized monitoring of snow for the benefit of climate change
scenarios, hydrology and numerical weather prediction,
http://www.HarmoSnow.eu/), field campaigns were conducted to compare
widely used snow core samplers under different snow conditions (depth,
density). The objectives were to 1) estimate the range of differences in
measurements obtained from various samplers, and 2) possibly separate
the effect of the natural variability of bulk snow density and SWE from
the instrumental error, and the error introduced by the different
observers.

2 FIELD CAMPAIGNS, INSTRUMENTS AND METHODS

A preliminary campaign to demonstrate instruments and error sources took
place in March 2016 on two plots located midway between Güzelyayla and
Senyurt villages (40.195°N, 41.48ºE, 2071 and 2210 m a.s.l.,
respectively), close to the city of Erzurum (39.9ºN, 41.3ºE) in Eastern
Turkey. It was primarily intended to increase the awareness of local
water managers and the Action participants about possible sources of
errors and questions of spatial variability when performing in-situ snow
measurements. The campaign thereby provided a first, qualitative
comparison of seven snow core samplers (the results are not shown in
this study) and allowed for the identification of key points for the
design of the subsequent quantitative comparison campaigns.

Two such field campaigns were then carried out: the first one in March
2017 in the Bláfjöll area near Reykjavik (F1, Iceland,) and the second
one in February 2018 in Sodankylä (F2, Finland). The sampling strategies
followed during each campaign are presented in Figure 1. All the
measurement sites had a seemingly homogeneous snowpack in terms of depth
and density, small sized sampling plots with very smooth topography
(slope \textless{} 5º and low roughness) and a shallow to moderate snow
depth (\textless{}80 cm).

The compared snow core samplers (Figure 2) are used for operational
monitoring and research in several European countries that participated
in HarmoSnow (Finland, Estonia, Lithuania, Poland, Czech Republic,
Slovakia, Switzerland, Italy, Turkey, Spain, Russia and other countries
of former Soviet Union; Haberkorn, 2019) as well as in North America
(USA and Canada). Each instrument was always operated by a person, who
has a long of experience with the device. The only exception was the
experiment on the potential observer bias during F2, when each
instrument was operated by a so-called untrained person. These persons
were the same as for the other experiments, but just switched their
instrument with one from another country, which they were not familiar
with. Table 1 provides a summary of the nine different instruments used
in the campaigns and their main characteristics. Links to manufacturers
and more detailed descriptions are provided in Table S2 in the
supporting material. There is a wide variety of snow core samplers
covering different diameters, lengths, materials and weighting systems
(Figure 2 and Table 1). During the field campaigns a common protocol was
applied by all observers. It was based on recommendations currently
listed in the preliminary 2018 edition of the WMO nº8 CIMO guide
(\emph{https://www.wmo.int/pages/prog/www/IMOP/CIMO-Guide.html}). Snow
core samplers are inserted vertically from the top surface to the
snowpack. Samplers with teeth need to be twisted, the ones with
sharpened rims only need to be twisted in really dense snow. Depending
on the design, samples can be excavated with (cylinder samplers) or
without digging a snow pit (tube samplers). When the snowpack is deeper
than the height of the cylinder, measurements need to be repeated until
the soil surface is reached. To clearly separate one measurement level
from the next, the application of a thin plate is favorable. However,
such a plate was neither used with all cylinders nor for all
measurements in the campaigns. In both cases, depending on the weighing
system, either weight is measured or a direct reading of SWE is
conducted. If the depth of the core in the tube was less than 80 \% of
the depth of the undisturbed snow, the core had likely spilled from the
tube or was not captured by the tooth-cutter. In this case, the observer
had to repeat the measurement. However, snow conditions during the field
campaigns were rather favorable and almost no need of repeating
measurements was necessary. Snow sample weight and volume data, combined
with the snow depth, result in bulk snow density and SWE values for
specific measurements.

In the case of Sodankylä, the Mann-Whitney-Wilcoxon test (Wilcoxon,
1945) was used to determine if the differences in the density
measurements performed by the different instruments are statistically
significant (p\textless{}0.05).

2.1 Field campaign in Blájföll, Iceland (March 2017, F1 in Fig. 1)

The first field campaign was conducted on March 1st 2017 on two plots
located approximately 25 km south-east from Reykjavik in the foothills
of the Hengill volcano. The two plots were in close proximity to one
another but they differed in the nature of the ground surface. Plot 1
was located in an open area, approximately 200 m north of the
Hellisheiði Geothermal power plant (64.04ºN, 21.40ºW, 260 m a.s.l.).
Measurements on Plot 1 were taken at a paved parking lot of the power
plant. The ground was almost completely level and covered with a mix of
grass and asphalt. Plot 2 was located approximately 190 m to north of
Plot 1, at a lava plateau, with an irregular ground surface covered by
soft moss. With such setting, uncertainty related to sampling on uneven
terrain was largely reduced on Plot 1, while Plot 2 was considered as a
test polygon with challenging, very high ground surface irregularity. On
both plots the snowpack was cold and dry, with an average snow depth of
48 cm and 53 cm for Plot 1 and 2, respectively. Windblown surface
features and ice layers resulting from rain-on-snow events were
identified within the snowpack structure.

Bulk snow density or SWE measurements, depending on the type of
instrument, were made with the nine different core samplers listed in
Table 1. At the same time, snow depth measurements were taken at each
sampling point with the snow tubes or probes (in the case of EV2 and
Custom EV2). The sampling strategy was to measure along a 20 m long snow
trench. Depending on the duration of a single measurement, three to six
measurements were taken at each spot with one instrument, with each
instrument sampling at two to three spots along the trench (Figure 1).
Repeated measurements at each spot were made as close as possible to
each other (\selectlanguage{english}[?]5-10 cm) to minimize errors resulting from natural
variability in snowpack properties. Thus it was possible to associate
the differences among repetitions to measurement uncertainty. This was
especially true at Plot 1 where the ground surface was smooth and level.
On the other hand, differences between the measurement spots (Figure 1)
were due to a combination of the instrumental bias, observer errors and
natural differences in snowpack characteristics along the 20 m long
trench. The overall aim of the campaign was to compare the variability
among repeated measurements at the same spot using one instrument to the
variability observed along the trench as an attempt to separate the
natural variability of the snowpack from the variability amongst the
measurements.

2.2 Field campaign in Sodankyla, Finland (February 2018, F2 in Fig. 1)

The second field campaign was conducted from the
20\textsuperscript{th}to 22\textsuperscript{nd} of February 2018 at
Sodankyla (67.37degN, 26.63degE, 175 m a.s.l.) in Lapland, Finland making
use of the installation operated by the Finnish Meteorological Institute
(INTERACT, 2015; Leppanen et al., 2018). The measurements were conducted
during three consecutive days in a Bog plot (Bog site; Leppanen et al.,
2016) and a Forest opening (Intensive Observation Area; Leppanen et al.,
2016) following scheme F2A, as well as in a wide open plot (hereinafter
called the Antenna plot; Sodankyla SPICE site; Nitu et al., 2018)
following scheme F2 (Figure 1). As a consequence of persistent cold
conditions during the whole winter, the snowpack was dry (wetness index
1; Fierz et al., 2009) and rather soft (hardness index mostly 1-3)
consisting mostly of faceted crystals and depth hoar with grain size
larger than 1 mm, showing very homogeneous characteristics on all three
plots. All three plots are flat and the snow depth measured with probes
or SWE samplers did not vary by more than 11 \% (CV\textless{}0.11) at
any of the three plots. Average snow depths were 53.2, 71.1 and 62.7 cm
at bog, forest and antenna plots respectively. The ground was frozen,
facilitating the identification of the contact point between snow and
soil. Low vegetation (lichen, moss, heather), height of approximately
5-15 cm on average, was present at the Forest and Antenna plots, whereas
there was only isolated grass on a mostly icy ground at the Bog plot.
The aim of this campaign was to systematically distinguish the
instrument based error from both the observer induced error and the
natural variability of the snowpack. The sampling strategy was to divide
a plot (ca. 10x20 m) into four subplots, where each of the nine snow
core samplers collected five replicates. In one of the subplots at the
Antenna plot, each instrument was used to measure snow density or SWE
and snow depth along a transect of 10 m with a spacing of approximately
0.5-1 m between measurements where the transects were 0.5-1.5 m apart
(Figure 1). In addition, at both sides of the Bog and Forest plots three
measurements were taken with each instrument by observers who were not
familiar with its use (Figure 1). We attempted to assess the effect of
the expertise with using a specific instrument to the reliability of the
measured data. Finally, stratigraphic records of the snowpack were taken
in one to two snow pits at each plot (see Figures S1 to S3 and Table S1
in the supporting material). The local procedure is presented in
Leppanen et al. (2016).

A major advantage of this campaign was the availability of the
SnowMicroPen (SMP), which measures the penetration resistance of snow.
The relative uncertainty among repeated, objective penetration
resistance measurements is low and thus a good measure for the spatial
variability of the snowpack is obtained (see e.g. Kronholm et al.,
2004). This is further discussed in the supporting material and shown in
Figures S1 to S3. Thorough analysis of such measurements can also be
used to obtain snow density at the millimeter scale (see Equation 9 in
Proksch et al., 2015). However, this calibration does not hold for the
version of our SMP (see also Proksch et al., 2016), yielding bulk snow
densities biased towards higher values. A total of 99 SMP measurements,
more than 26 on each plot, were taken in undisturbed snow after all SWE
measurements were completed on each subplot.

Finally, the potential role of the weighing process in the error
estimation of snow density and SWE measurements was tested in two ways.
Nine different weight scales were compared to check how the low air
temperature may affect the accuracy of weighing. We used reference
weights of 50, 200, 500, 1000 and 2000 g, performing measurements
indoors (at approximately +20 oC) as well as outdoors at -26 oC after
waiting for 20 minutes for the scales to cool.

3 RESULTS

3.1 Field campaign in Blafjoll

The depth, bulk density and SWE measured with six different snow core
samplers (SH, VS-43, Dolfi, K-M, IG PAS and Federal) along two 20 m long
snow trenches (Figure 1, scheme F1) are shown in Figure 3. In this field
campaign the relative position of each instrument was annotated and the
figure reproduces the order in which different devices were used.
Important variability can be seen in the measurements when the different
samplers are compared, but also a non-negligible variability between
repetitions with each instrument at some specific spots.

For Plot 1, characterized by a very homogeneous ground surface, the
coefficient of variations (CV, the ratio of the standard deviation to
the mean) for snow depth and density between different spots were 0.08
and 0.11, respectively. The combination of both lead to a CV for SWE
among the 14 measured spots equal to 0.22. The repeated depth
measurements at each spot were almost identical (with maximum
differences of 3\% in some spots). In general, bulk snow density at each
spot measured with the same device showed a variability of less than
5\%, which was exceeded on only four out of 14 spots: twice with the
Federal sampler, once with the K-M and once with the VS-43. Variability
in repeated measurements of SWE was very similar to the reported
variability of the bulk snow density.

Plot 2 exhibited a larger spatial variability for snow depth between
spots at the plot scale, with a CV of 0.12, and also a high variability
between replications at each spot (CV exceeding 0.05 in eight out of 12
spots). On this plot, however, the variability of bulk snow density
between the spots was smaller compared to snow depth with a CV close to
0.1, as well as the differences among several repeated measurements at
the same spot (CV never exceeded 0.1). The combination of depth and
density variability leads to a CV for SWE of 0.14 among the 12 spots.

In this campaign the SH sampler provided systematically lower values for
bulk snow density than most other devices. Nevertheless, the CV for bulk
snow density obtained by SH at individual spots was comparable to the
values obtained for the other devices. The Federal sampler provided high
variability among repeated measurements in the same spot when used in
Plot 1. There was no clear systematic bias induced by the instrument or
the observers for the remaining samplers.

3.2 Results from the field campaign in Sodankyla

The variability of bulk snow density estimated from SMP measurements
(27, 28 and 44 measurements for bog, forest and antenna, respectively)
using the Proksch et al. (2015) parametrization for the three plots is
shown in Figure 4. While the mean and median values are too high
compared to the measurements (see Figure 5 and Section 2.2), these
estimates reveal an almost negligible variability in snow density (CV
not exceeding 0.01 on any of the three plots). The homogeneity of the
snowpack on each plot is further supported by data of the median
penetration force with a resolution of 1 mm, and in the snow pits that
were dug at each of the analyzed plots (Figures S1 to S3 in the
supporting material). This implies that the differences between
estimates from each SWE sampler or the variability between replicates
for each device are primarily due to either instrumental errors or
errors induced by the observer.

Figure 5 shows the variability of all replicates for snow depth, bulk
snow density and SWE measurements (Figure 1b) obtained from the nine
different instruments (Table 1) at each plot. The 20 measurements (15
measurements at the Antenna plot) are made up of five close replicates
on each of the subplots. In this campaign the snow-ground interface was
very easy to identify during sampling, and thus the CV for snow depth
measurements was very low (\textless{}0.06), being almost negligible for
all observers. More significant were the observed differences between
the bulk snow densities measured by the different snow core samplers.
Variability between the repeated measurements was much higher than that
observed for the SMP but still relatively low (CV of 0.07 to 0.10),
especially compared to the field campaign in Iceland (CV ranging from
0.04 to 0.12; see section 3.1). The instruments that yield the highest
variability between replicates were EV2 (in particular the customized
model EV2-C), Federal, and IG PAS. The entire snowpack is sampled at
once with EV2 and Federal, i.e. no digging is needed; SWE may have been
underestimated due to the loss of snow from the bottom of the tube after
its removal from the snowpack, due typically lacking soil plug
originating from frozen soil and ice on top of the ground. This may have
negatively influenced the consistency of their measurements.
Measurements with SH were made after digging because its larger diameter
impeded the retrieval of the snow sample directly from the top of the
snow surface. On the other hand, the resolution of the scale used with
IG PAS was low (50 g), which contributed substantially to the relatively
high variability for the bulk snow density observations. The length of
the IG PAS, which is only 50 cm, also caused problems with snow depth
exceeding it. In such a case, two measurements were taken. The behavior
of each sampler with regards to the plot average of all instruments is
very similar on all three plots, except for the EV2-C (Figure 5). The
median value for ETH, SH, and K-M lie consistently close to the plot
median on all plots. In addition, SH and K-M as well as VS-43 and Dolfi
provided pairwise very close values for bulk snow density on all three
plots. Table 2 shows the statistically significant differences in
measured bulk snow density between pairs of samplers based on the
Wilcoxon rank test. Results show that K-M, SH and ETH tend to provide
similar data, as do VS-43 and Dolfi, while bulk snow density
measurements with the Federal were significantly different than all
other samplers on all three plots. Because the CV for bulk snow density
was generally low, the variability in SWE among the replicates made by
the same device at the same subplot is similar to that of snow depth.
Accordingly, the differences between SWE values measured with different
snow core samplers were very similar to those for the bulk snow density
(Figure 5).

The variability of bulk snow density obtained from close replicates by
individual devices at each subplot is presented in Figure 6. Most
devices show similar results for the three plots, except for EV2, EV2-C,
Federal sampler and IG PAS. The patterns in the graphs are very similar
for each plot, which suggests that each device has an intrinsic
systematic bias. This bias was within +-10\% except for EV2 and EV2-C in
a few cases.

The snow density measurements for each snow core sampler when used by
the experienced and untrained observers are shown in Figure 7. Except
for a few cases (i.e., EV2), the variability between replications was
lower when the device was used by the experienced users. However, the
differences were statistically significant (from the
Mann-Whitney-Wilcoxon test) for only a few devices, i.e. for the SH in
bog, and the Federal sampler in the forest. Inconsistency in the
differences in measured average densities between the Bog and Forest
plots was observed for two snow samplers. For example, the ETH snow core
sampler used by untrained users provided lower average snow density at
the Bog plot, but higher density at the Forest plot. This is probably
due to the fact that the untrained users for each instrument were not
the same at both plots. Clear differences in snow density between the
two plots were also found for the IG PAS and Federal sampler.

The measured snow depth and bulk snow density at the Antenna plot
following a 10 m transect sampled at 0.5-1 m intervals (Fig. 1) for each
instrument are presented in Figure 8. In general, snow depth varies
little along the lines with almost identical values for the 10
replicates by each observer (Figure 8b). An analysis of bulk snow
density revealed that the 10 measurements performed with any instrument
have a low, very similar variability, with a mean CV of 0.04 per
instrument (SMP 0.02). However, notable differences were observed among
the different instruments, with the mean for each instrument varying
from 192 kg m\textsuperscript{-3} to 233 kg m\textsuperscript{-3} with a
CV of 0.08 (Figure 8a).

4 DISCUSSION

Two field campaigns conducted in the framework of the COST Action
HarmoSnow (ES1404) provided a unique opportunity to compare the snow
samplers widely used in operational networks and research across Europe
and North America. The results have been used to illustrate the spatial
variability of snow depth, bulk snow density and SWE at small spatial
scales, and to assess the extent that the use of different snow core
samplers and the error involved in the measurement procedure may affect
density and SWE measurements. Collected data have enabled the
distinction of the three main sources of uncertainty when measuring snow
density and SWE at the local scale: i) natural variability of snowpack
at small spatial scales; ii) error induced in the measurement process;
and iii) instrumental bias when different types of snow core samplers
are used at the same time and place.

A snowpack may exhibit differences in density at very small spatial
scales (Komarovet al., 2019). This fact partially explains the high
variability of density (CV of 0.10 and 0.11 for plots 1 and 2
respectively) and SWE (CV of 0.14 and 0.22 for plots 1 and 2
respectively) among measurement points found in Iceland. This
variability far exceeds the differences among repeated measurements at
each spot that was roughly half of that between the measured spots. The
CV for density still ranged between 0.03 and 0.15 for the majority of
the measurements due to irregular wind crusts and ice layers. When snow
is measured on a homogeneous surface like at Plot 1 (smooth parking lot
and lawn) the snow depth measurement has minimal impact on uncertainty
of SWE estimation. The opposite occurred at Plot 2, where snow depth was
largest source of uncertainty in SWE estimation. This can be explained
by uneven rocky and moss covered ground, and does confirm previous
studies highlighting that snow depth measurement may be an important
source of uncertainty in SWE estimation for various environments, namely
when ground is covered by shrubs or unfrozen bog areas and snowpack is
shallow (Sturm et al., 2010; Lopez-Moreno et al., 2013; Stuefer et al.,
2013).

Homogeneous ground (frozen grass or bog) and snowpack found in Finland,
provided an excellent opportunity to separate the effect of natural
variability of the snow properties from the instrumental and observer
induced errors. Homogeneity of snow was confirmed by 99 SMP measurements
with a very low spatial variability in snow penetration resistance and
density (CV of variation lower than 1\% at each study plot). The low
cohesion of snow during this campaign was challenging for some snow core
samplers due to partially losing snow during their removal from the
snowpack, preventing direct retrievals of core samples from the snowpack
surface. This was the case for the SnowHydro, IG PAS, and VS-43 samplers
(Table 1). This problem was avoided by digging a pit and inserting a
spatula below the sampler at base of the snow-soil surface. Density
measurements taken by different snow core samplers exhibited a CV
between 0.02 and 0.06, while SMP revealed a CV of only 0.01. This
confirms the existence of instrumental bias and error induced by an
observer that cannot be attributed to the natural variability of the
snowpack. Indeed paired comparison of density data collected with
different samplers exhibited a statistically significant difference
according to the Mann-Whitney-Wilcoxon test (Table 2). Measurements
along a 10 m transect (Figure 8) demonstrated that in a snowpack with a
homogeneous density, the instrumental bias was the main source of
variability while observers introduced only very low variability. It has
also been detected that in most of the cases the snow densities measured
by an experienced user and by the new user of the sampler did not
significantly differ (Figure 7).

In Iceland the natural variability of snow along a 20 m long snow pit
hindered the identification of instrumental bias, except for the SH that
systematically measured a lower density compared to the average of all
samplers. This is similar to the results found by Dixon \& Boon (2012)
who compared to the Federal sampler and the MSC (Meteorological Service
of Canada) tubes. In Finland, the data also showed that the Federal
sampler, EV2 and EV2-C provided the least consistent measurements
(Figure 7). In general K-M, SH, Dolfi and ETH provided the most similar
values and a low variability between the replicates. Three of them (K-M,
Dolfi and ETH) have a relatively high diameter compared to the others,
which could be beneficial for the very soft and low density snowpack we
experienced over the Sodankyla campaign. The shorter snow core samplers
(ETH, IG-PAS, VS-43) were in general not long enough to sample the whole
snow column at once and measurements needed to be split into two steps,
which increases the probability of errors. This process required more
time and had a higher measurement uncertainty. Finally, it is logical
that the EV2, EV2-C and Federal samplers have a higher uncertainty in
Sodankyla (as was also shown for the Federal sampler in Iceland). The
aforementioned difficulty to retrieve snow samples all the way to the
ground under very soft and dry snow condition may explain the higher
uncertainty for both devices. Indeed, the EV2 (and EV2-C) was designed
to be used on glaciers and the Federal sampler was designed to sample
deep and very dense, even icy snow (Marr, 1940). The reduced diameter
and ``no-digging'' retrieval procedure may cause problems for sampling
very soft snow. Dixon and Boon (2012) indicated for the Federal sampler
that it performed much better when the snowpack was highly consolidated.

Even if this was not the main objective of the study, in Finland we
could also confirm that scales may introduce some error, especially when
they measure very light loads, with a maximum absolute error of 10\% in
the weighing process (see Supplementary Material, Text S2 and Table S3).
Both spring scales and electronic scales yielded errors when measuring
light weights, but electronic scales generally showed an increase of the
error under very cold outdoor conditions. Although not analyzed in this
study, it is necessary to consider that errors in electronic scales may
be higher when batteries start to drain, when hanging samples are
weighed in windy conditions, or if a scale is not properly leveled. In
any case frequent checking and calibration of the scales is highly
recommended.

Results shown here confirm the need to be cautious when assigning in
situ snow measurements as ground truth, and the necessity to understand
the natural variability of snow characteristics at small spatial scales
and the instrumental and observer induced error. Even under relatively
easy measurement conditions with a lack of ice layers and a moderately
deep homogeneous snowpack, the uncertainty in snow density estimation is
about 5\% for an individual instrument and is close to 10\% among the
different instruments. Thus, for the estimation of SWE this uncertainty
has to be added to the uncertainty of snow depth measurements. The
homogeneous snow conditions found in Sodankyla (Finland) allowed the
direct attribution of the instrumental error. Snow core samplers with
larger diameter performed better than the narrower ones for those snow
conditions, in line with conclusions of Farnes et al. (1982). On the
other hand, snow samplers operated from the surface may miss part of the
loose snow from the base of the snowpack, depending of the snow pack
characteristic and the type of ground. Users should use snow core
samplers best adapted to their prevailing snowpack and ground. Although
careful measurement can partially eliminate some of the above
uncertainties, SWE datasets composed of data from different instruments
are likely to include inhomogeneities. Metadata on snow conditions and
instruments used to measure the SWE together with intercomparison
studies such as ours can help to estimate the accuracy of the data in
such databases. Since this is not always possible to conduct the field
intercomparison of the instruments, one can assume that the uncertainty
of density measurements conducted by various devices in non-ideal snow
conditions is approximately within 10-15\%.

5 CONCLUSIONS

The results of the field campaigns provided a unique opportunity to
analyze the uncertainty of measurements of bulk snow density and water
equivalent of snow cover (SWE) carried out with snow core samplers that
are regularly used in many European countries and beyond. To our
knowledge, such a comparison in terms of number of device and
environments has not been conducted before. The results showed that the
devices provided slightly different uncertainties since they were
designed for different snow conditions. The aim of this article was not
to provide a definitive estimation of uncertainty for manual SWE
measurements, but we think presented results represent a step forward in
illustrating the role of the different uncertainty sources. The main
conclusions can be enumerated as follows:

- In snowpack subjected to natural variability at small scales (e.g.
irregular wind crusts or ice layers), as it was the case in Iceland
campaign, the variability between close measurement points exceeded the
one observed between repetitions at the same spot, although the latter
is still high (often exceeding 5\% and 10\%). In case of uneven ground
surface, snow depth may introduce more variability in SWE estimation
compared to density. Therefore, repeated measurements in an observation
field (at any time scale beyond a day) can reduce the number of SWE
measurements using a fixed installed graduated snow depth stake and
multiply the last measured density with the snow depth at the stake.

- In snowpack subjected to low natural variability at small scales, as
it was the case in the Finland campaign, it was possible to examine
instrumental bias. The largest differences were observed for snow core
samplers introduced directly from the surface to the ground (no
digging).

- Uncertainty induced by instrumental bias was generally less than 10\%
but it can reach 15\%. Such differences suggest that inhomogeneities are
likely to be introduced when there is a change of snow core sampler
along the time, or different snow core samplers are used in a same field
campaign. This is similar to measurements of other components of the
water balance (e.g. precipitation) and it is unlikely that unification
will be reached in near future due to varying snow and ground conditions
in application areas.

- The above mentioned uncertainties refer to a homogeneous tundra-taiga
snowpack (loose, mostly recrystallized snow and no wind impact)
shallower than 1 meter depth. Relative errors will be smaller in deeper
snowpack, with the exception of heavily wind or ice layer impacted
snowpacks.

- The two measurements campaigns were conducted under very different
snowpack conditions. We therefore presume that experiences made during
these two campaigns are applicable to a wider range of snowpacks.

- Weighting process may introduce a considerable uncertainty especially
for shallow snowpacks

ACKNOWLEDGMENTS

We thank H. Lowe and M. Jaggi for the help in analyzing the SMP data.

This research has been taken under the EU-COST Action HarmoSnow (ES1404:
A European network for a harmonized monitoring of snow for the benefit
of climate change scenarios, hydrology and numerical weather
prediction). We also thank to project to HIDROIBERNIEVE
(CGL2017-82216-R) and to the local organizers of the field campaigns who
made possible this work. This work was partially supported within
statutory activities No 3841/E-41/S/2019 of the Ministry of Science and
Higher Education of Poland.

\textbf{DATA AVAILABILITY STATEMENT}

Used data is freely available
in:\emph{https://zenodo.org/record/2549310\#.XErjW5VYZaQ}

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FIGURE CAPTIONS

\textbf{Figure 1.} Schematic representation of the sampling strategy
applied during the two field campaigns. The scheme F1 was applied in
Blafjöll (Iceland) and the scheme F2 in Sodankylä (Finland). In
Sodankylä, the scheme for Bog and Forest plots was applied also in the
Antenna plot, but in one subplot measurements were taken in transects
(10 measurements per transect). In Bog and Forest opening sites (F2) the
four subplots were measured in the same way. Letters N, O and I inform
of the uncertainties contained at each measured spatial scale: Natural,
induced by Observer and Instrumental bias respectively. The letter size
makes reference to H high, M medium and L low relative influence of each
uncertainty source at each site.

\textbf{Figure 2.} Instruments used in the campaigns, snow core samplers
from left to right (see Table 1): Korhonen-Melander, Dolfi, VS-43, U.S.
Federal, IG PAS, SnowHydro, Custom EV2, Enel-Valtecne EV2 and ETH. In
addition, the SnowMicroPen is shown on the far right.

Figure 3. Boxplots showing the distribution of measured snow depth
(upper panels), bulk snow density (middle panels), and SWE (lower
panels) measured with different snow core samplers along two snow
trenches in Iceland. Boxes stand for the 25th and 75th percentiles,
vertical bars indicate the 10th and 90th percentiles and the horizontal
central line is the median. Triangles at the bottom of some boxes inform
about distribution skewness. Numbers above each box is the CV for
repeated measurements. Dashed and dotted lines are the average and
median, respectively, over all measurements on each plot.

Figure 4. Variability of the bulk snow density for the three plots as
obtained from SMP measurements using the Proksch et al. (2015)
parameterization (see text). The number above each box is the CV for all
measurements on that plot. Boxes inform of the 25th and 75th
percentiles, vertical bars indicate the 10th and 90th percentiles and
the horizontal central line is the median. Dashed and dotted lines are
the average and median over all measurements, respectively.

Figure 5. Variability of the 20 measurements (15 in Antenna plot) of
snow depth, bulk snow density and SWE taken at the three plots (composed
of 4 subplots each) conducted with different devices. The number above
each box is the coefficient of variation among repeated measurements.
Boxes inform of the 25th and 75th percentiles, bars indicate the 10th
and 90th percentile and central line is the median. Triangles at the
bottom of some boxes inform about high skewness of distribution. Dots
are outliers. Dashed and dotted lines are the average and median
respectively.

Figure 6. Bulk snow density difference of each sampler with respect to
the total average of all samplers (in percentage) measured at each
subplot for each of the three plots.

Figure 7. Bulk snow density measurements for each sampler when used by
experienced observers and untrained observers on Bog and Forest plot.
Six measurements were conducted with each sampler. Letters indicate the
only pairs with statistically significant differences.

Figure 8. Measurements of snow depth (bottom panel) and bulk snow
density (upper panel) along 10 m long transects at the Antenna plot.

\textbf{Table 1.} Summary of all the snow core samplers used during the
campaigns and their main characteristics.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Name}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Acronym}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Country of origin}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Length} \textbf{(cm)}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Inner diameter} \textbf{(cm)}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Material}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Tooth-} \textbf{cutter}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\textbf{Sharpened} \textbf{cylinder}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Korhonen-Melander sampler\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
K-M\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Finland\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
70\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Plastic\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
ETH sampler\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
ETH\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Switzerland\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
55\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
9.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Aluminium\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
SnowHydro SWE coring tube\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
SH\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
USA\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
165\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6.13\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Lexan\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Dreamly Original Light Fiberglass (Dolfi)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Dolfi\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Czech Republic\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
100\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Glass fiber\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Enel-Valtecne EV2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
EV2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Italy\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6 sections x 50\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Stainless Steel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Custom EV2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
EV2-C\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Italy\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6 sections x 50\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Aluminium\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
IG-PAS snow sampler\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
IG PAS\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Poland\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Stainless Steel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
VS-43\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
VS-43\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Russia\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
60\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Aluminium\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Federal snow sampler\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
U.S. Federal\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
USA\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
7 sections x 76\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3.81\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Stainless steel\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Y\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
N\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 2. Statistically significant differences in measured bulk snow
density (from the Mann-Whitney-Wilcoxon test) between pairs of snow core
samplers in the Bog (B), Forest (F) and Antenna (A) plots during F2. `X'
means that no difference was found.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
& \textbf{VS-43} & \textbf{Dolfi} & \textbf{ETH} & \textbf{EV2} &
\textbf{EV2-C} & \textbf{IG PAS} & \textbf{K-M} & \textbf{SH} &
\textbf{Federal}\tabularnewline
\midrule
\endhead
\textbf{VS-43} & & & & & & & & &\tabularnewline
\textbf{Dolfi} & X & & & & & & & &\tabularnewline
\textbf{ETH} & B,F,A & X & & & & & & &\tabularnewline
\textbf{EV2} & B,F,A & X & F,A & & & & & &\tabularnewline
\textbf{EV2-C} & B,F,A & X & F,A & B,F,A & & & & &\tabularnewline
\textbf{IG PAS} & B,F,A & B,F,A & X & X & X & & & &\tabularnewline
\textbf{K-M} & B,F,A & B,F,A & X & X & B,F,A & X & & &\tabularnewline
\textbf{SH} & B,F,A & B,F,A & B & B,F,A & B,F,A & X & B,F,A &
&\tabularnewline
\textbf{Federal} & B,F,A & B,F,A & B,F,A & B,F,A & B,F,A & B,F,A & B,F,A
& B,F,A &\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-1/Figure-1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-2/Figure-2}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3/Figure-3}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-4/Figure-4}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-5/Figure-5}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-6/Figure-6}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-7/Figure-7}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-8/Figure-8}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

