Introduction
Ice structures form in snowpacks during melt or rain-on-snow events
. Rain either freezes on contact with the surface of the
snowpack, or water refreezes within the snowpack to form ice layers, lenses,
crusts, columns, or basal ice layers . Strong
intercrystalline bonds created from refreezing of liquid water lead to the
formation of cohesive ice structures . Permeability of ice
layers to liquid water and gas is vastly reduced compared to snow
. Impermeable layers are identifiable because
pores do not connect within the ice formation, and the granular snowpack
structure is missing . Ice layers differ from melt–freeze
crusts (often referred to as “ice crusts”) and ice lenses; melt–freeze
crusts are always permeable and have a coarse-grained granular snow-like
structure . Ice lenses can be impermeable, do not have
a granular structure and are spatially discontinuous. Similarly to ice
lenses, ice layers can be impermeable and do not have a granular structure;
however, ice layers are continuous .
Flow chart describing the methodology to measure densities
of ice layers from a snowpack. Photographs show an example pair of photos used in the calculation of ice sample
volume. “A” taken before the sample was added and
“B” taken after. “V” is equal to the volume of the ice
sample. Black lines are guides added to help assess the quality of
the photos.
Ice layers introduce uncertainty into the performance of snow microwave
emission models , which are an important component of
satellite-derived snow water equivalent (SWE) retrieval algorithms
. The radiometric influence of even thin ice layers poses
a significant challenge for physical and semi-empirical snow emission models,
which can treat ice layers either as coarse-grained snow or
as planar (flat and smooth) ice layers . Uncertainties
attributed to not knowing the density of ice layers are greater than any
other parameter in snow emission models . Consequently,
development and evaluation of snow emission models are hindered by poorly
quantified field measurements of microstructure and properties of ice layers
.
Pure ice density ranges from 916 kgm-3 at 0 ∘C
to 922 kgm-3 at -40 ∘C . Only limited field measurements of ice layer
densities have previously been attempted. Ice layer density
measurements taken in the Canadian Arctic by submerging pieces of melt–freeze
crust into oil resulted in a range of densities from 630 to
950 kgm-3 . Ice layer densities of 400
to 800 kgm-3 were measured using a snow fork, which
measures the dielectric properties of snow around
1 GHz in seasonal snow on the Greenland ice
sheet . The results from these studies vary
drastically, and a quantitative assessment of the error in measurement
techniques is absent. Consequently, the aim of this paper is to
describe a newly developed field measurement technique for measuring
ice layer density and to present density measurements made in Arctic and
mid-latitude snowpacks.
Method
Development of ice density measurement method
A new laboratory and field-based method (Fig. ) was developed to
measure the density of ice layers found in seasonal snow, based on volumetric
displacement. The basic principle is that when an ice layer sample is
submerged in a vessel of liquid, calculating the volume displacement and
sample mass will yield an estimate of density. The mass of a sealed
50 mL centrifuge tube with 2.5 mL graduations containing
white spirit (sometimes termed “mineral spirits”) was measured with
a precision of ±0.001 g under laboratory conditions before
entering the field. White spirit is immiscible with water and has a low
freezing point (-70 ∘C), eliminating potential sample melt. White
spirit also has a low density (650 kgm-3), making it likely that
the ice sample would sink and be completely submerged. In the field the
centrifuge tube was held by a fixed, levelled, mounting system within the
macro setting range of a compact camera. Each camera image was centred on
a visible datum on the mounting system to ensure the camera was correctly
focused. Images were captured before and after each ice sample was submerged
as shown in Fig. .
Measurements of ice layer density bubble size and thickness (all
sizes in millimetres, all densities in kgm-3). n is number of samples,
n<0.1 is the number of samples with a bubble diameter of less than 0.1 mm.
All ice layer density values have been
corrected to account for the measured -0.19cm3 bias in
volume.
Bubble diameter
Layer thickness
Density
Type
n
n<0.1
Mean
SD
n
Mean
SD
n
Mean
SD
Care
Natural
–
–
–
–
29
8
0.6
29
906
17
North Bay
Natural
14
4
0.16
0.12
15
3
0.6
15
890
21
Artificial
12
6
0.08
0.03
15
5
0.9
15
921
18
Inuvik
Artificial
–
–
–
–
28
2
0.5
28
915
26
Overall
–
26
10
0.12
0.1
87
5
2.7
87
909
23
In each image three positions were identified during post-processing:
the liquid level, the graduation above the liquid level and the
graduation below the liquid level. Pixel co-ordinates of these
positions were recorded and the proportional height of the liquid
level between the upper and lower graduation was translated to
a volume at a higher resolution than the centrifuge tube graduations
alone would allow. After images were taken, the centrifuge
tube containing the sample was sealed and the change in mass was
measured on return to the laboratory.
Methodological error
Ice layers found in snowpacks are very difficult to accurately and
consistently re-create under laboratory conditions. Therefore to
assess the accuracy of the ice density measurement technique, ball
bearings of known volume were measured. Stainless steel ball bearings
were used (manufactured to a diameter of 1±2.5×10-5 cm), resulting in a volume of
0.5236±0.0004 cm3. The volume of ball bearings was
calculated from before and after images of 10 ball bearings submerged
in the centrifuge tube. The expected total volume of all ball bearings
of approximately 5.236 cm3 is comparable to the mean volume
of ice samples collected. Of 134 samples, each consisting of 10 ball
bearings, the mean volume was 5.045 cm3. Volume
measurements were normally distributed and an error value based on
±1 standard deviations was calculated, resulting in a systematic
volume measurement error or bias of -0.19 cm3.
Identifying the precise height of the surface of the liquid between the
graduation markings on the cylinder is limited by the quality of the camera
focus and resolution of the camera. Based on carrying out 10 repeat
measurements on 10 centrifuge tube photos the (mean) error was found to be
±0.125 cm3 in each volume measurement photo, equating to a
random root-mean-square error in the measurement of the ice sample volume of
±0.18 cm3 (error =0.1252+0.1252), as each volume
measurement involves reading the volume from two photos.
To estimate the potential impact of the uncertainty in volume measurement on
samples taken in the field, the random (±0.18 cm3) volume
measurement error from the ball bearing experiment was applied to
a theoretical ice sample volume of 4.89 cm3 (chosen as it was the
estimated smallest sample volume taken during field trials) and mass
of 4.53 g (equating to a density of 916 kgm-3). This volume
error from the ball bearing experiment translated into an observed volume of
4.53–4.89 cm3 (i.e. 4.71±0.18 cm3). Assuming no
error in the mass balance (precision of ±0.001 g), the upper
density value (minimum volume) was 951 kgm-3 and the lower
density value (maximum volume) was 881 kgm-3, representing an
uncertainty in density of ±35 kgm-3 or 4 %.
Field measurements
During the winter of 2013, ice layer density measurements were collected at
three sites in Canada: North Bay, Ontario (46.33∘ N,
79.31∘ W), between 8 and 9 February; Canadian Centre for Atmospheric
Research (CARE), Egbert, Ontario (44.23∘ N, 79.78∘ W), on 25
February; and Trail Valley Creek, Inuvik, North West Territories
(68.72∘ N, 133.16∘ W), on 9 April. Ice layers were removed
from the surrounding snow and broken to size using a scraper.
In North Bay (NB), an artificial ice layer was created by spraying water onto
the surface of the snowpack. Artificial ice layers have been created in
previous work , so it is important to know whether their
characteristics differ from naturally occurring ice layers. A natural ice
layer covering the entire clearing was also present lower within the snowpack
(formed by 2 mm of rain on 30 January). Density, bubble diameter, and
thickness measurements of both natural and artificial ice layers were made;
whenever bubbles were visible their diameters were measured using a field
microscope and snow grain card, at a resolution of 0.1 mm. Very small
bubbles, with a diameter of <0.1 mm were recorded as being visible
although a diameter could not be applied to them. Layer thickness was
measured to a resolution of 1 mm for each sample.
At CARE, measurements were conducted in an open, grass-covered field.
A spatially continuous ice layer formed over an area of at least 200×100 m in the 10 cm deep snowpack as a result of
above-freezing daytime temperatures for a period of 4 days prior to
measurement. Ice layer thickness and densities were measured in the same
manner as in North Bay.
In Inuvik, water was sprayed onto a 30 cm tundra snowpack when air
temperatures were approximately -25 ∘C to form an artificial ice
layer on the surface of the snowpack. Water was sprayed over an area of
1 m2, concentrating the spraying towards one edge, which created
ice thicknesses between 1 and 6 mm.
Results
Ice layer density
Mass, volume and density measurements were made of 86 samples of ice layers
and are summarized in Table and Fig. . After
measurements were corrected for bias the mean sample volume was
6.4 cm3. After the random error of ±0.18 cm3 was applied to
the volume measurements, an uncertainty of ±28 kgm-3 was
calculated. Ice layer densities varied between 841 and
980 kgm-3, with an overall mean of 909 kgm-3 and
standard deviation of 23 kgm-3. A Kolmogorov–Smirnov test showed
natural ice layers were significantly less dense than artificial ones,
although the difference was within methodological error. The results from
Inuvik show some physically unreasonable high outlying measured densities
(Fig. ). Mass measurements at Inuvik were made outside, and whilst
care was taken to ensure the balance was level and condensation was cleaned
from the balance as it formed, these cannot be ruled out as sources of error.
Summary of ice layer density measurements. Stacked
histogram showing frequency of each density measurement, colours
show distribution of artificial and natural ice layers across
multiple sites.
Ice layer bubble size and thickness
Table summarizes the measurement of ice layer thickness and
bubble size. In some cases bubbles were visible in the ice layer but
were not large enough to be measured using the field microscope. These
were noted as <0.1 mm in Table . For the purpose
of calculating the mean and standard deviation of the bubble
distribution a value of 0.05 mm was applied to these
bubbles. There was no significant correlation between ice layer
thickness and bubble diameter (p<0.01).
Error analysis
Three sources of error were quantified in the measurement of ice layer
density: (1) systematic error and (2) random error in the volumetric
measurement of the ice samples, which would apply to any object measured
using this method (both discussed in Sect. ), as well
as (3) error from sample porosity, which applies only to the measurement of
ice layer density. The measured ice layers had a closed porosity, where
layers contained bubbles that were not connected in a porous structure. A
greater volume of bubbles in the sample reduces the external dimensions and
volume of the sample. Here we refer to this reduction in volume caused by the
presence of bubbles as effective porosity, represented by a dimensionless
fraction which represents the proportion of sample volume, which is available
for liquid to flow through.
The influence of effective porosity on the ice layer density measurements was
quantitatively evaluated by numerically modelling the bubbles as spheres
within cuboid ice layer samples. This method assumes that the ice layer is
solid ice containing bubbles rather than a granular snow-like structure. For
a theoretical ice sample of size 10mm×10mm×10 mm the sample density was increased in increments of
0.01 kgm-3 from 600 to 916 kgm-3, and effective
porosity was measured through the sample by taking slices at 0.1 cm
intervals.
The relationship between effective porosity and density (ρ) for this
bubble and sample size is linear, and the effective porosity
(ϕeff) is found using
ϕeff=-0.00016ρ+0.14.
Mean bubble diameter and standard deviation
were calculated from all samples. The
root-mean-square error of Eq. () was
0.0007 with an r2 value of 0.998.
The impact of effective porosity on the samples was calculated by assuming
a sample width of 2 cm (the width of the centrifuge tube). As the
density of the sample decreased, volume error from effective porosity in the
sample ranged from 6.5×10-5 to 1×10-3 cm3.
The mean increase using either the maximum or minimum value for density in
the effective porosity calculations was 1.42×10-6 cm3.
The maximum random error (±0.18 cm3), the volume measurement
bias reflecting systematic error (-0.19 cm3), and the effective
porosity correction were applied to each volume measurement. The maximum
range of density was calculated for each sample and the effective porosity
was negligible (less than 0.001 cm3). Overall the measurements
of ice layer density (909±28 kgm-3) were not significantly
different to the actual density of pure ice 916-922±28 kgm-3
between 0 and -40 ∘C .
Discussion and conclusion
New laboratory and field protocols were used to produce direct measurements
of ice layer density including a thorough assessment of measurement
uncertainty. Measurements of natural and artificially made ice layers
produced an average density of 909±28 kgm-3, where
uncertainty is a function of the random error in the method used to measure
the volume of the ice samples. Effective porosity of ice layers was estimated
using observations of bubble size and was deemed to be too low to impact the
accuracy of the method. Our measured density values are higher than those
previously measured by (mean 800 kgm-3) and
(400 to 800 kgm-3). It is unclear whether
previous studies measured the density of ice layers that were permeable,
including thin, non-continuous ice layers. Here only impermeable ice layers
were measured and this may explain the density differences between studies.
In addition, artificially created ice layers had a higher density than
natural ice layers (Table ). A possible reason for this is that the
artificial ice layers were created on the surface of the snowpack, which is
likely to experience lower air temperatures than naturally formed ice layers
within the snowpack.
Densification and ice formation impacts passive microwave brightness
temperatures at the satellite scale . Consequently, the
evolution of ice structures is important in characterization of snowpack
microwave signatures and may play an important role in ice layer detection
algorithms. However, snow microwave emission models are currently unable to
accurately model ice layers . Some snow emission models (e.g.
) include a parameter for ice layer density,
which has previously been very poorly constrained and is a large source of
uncertainty in emission models and remote sensing data
assimilation applications . Consequently, new ice layer
density measurements presented here provide a means to reduce uncertainty in
future snow radiative transfer modelling.