Introduction
Snow depth is one of the most important and basic
characteristics of snow on the ground. Measurements and modelling of this
variable is crucial for numerous applications, such as in hydrology
, avalanche forecasting ,
meteorology and for sea ice
or permafrost research .
Snow depth is commonly reported on in operational databases and measured at
research monitoring stations or occasionally in the field. Many techniques
are available to measure or monitor snow depth, the most common being manual
measurements with a stick (e.g. )
and ultrasonic ranging probes . Their inherent accuracy is of
the order of 1 cm which is largely sufficient for most applications.
Nevertheless, the vast majority of these measurements are representative of a
small area, typically less than 1 m2, corresponding to the footprint
of the sensor or the “homogeneous” area around the stick, whereas the
spatial scale of interest is usually much larger than this, ranging from the
area of meteorological monitoring stations (hundreds of square metres) to
that of catchments (from a few square kilometres).
Since the snow cover is in general heterogeneous at any scales from the small
scale to the application scale, the actual uncertainty of the snow depth in a
given area is much larger than the inherent accuracy of individual
measurements and is primarily governed by the spatial variability in this
area . This variability stems
from a variety of processes. Snowfall repartition is not uniform
because of the ground topography at metre-to-kilometre
scales, vegetation and other obstacles. Wind transport tends to amplify
heterogeneity because erosion and redeposition are sensitive to small initial
differences in the snow properties. Sastrugi, dunes and other wind-formed
features are frequent and their formations are still not well understood
. Metamorphic and melt processes can also contribute to the
decrease or increase of the spatial variations . All these
processes are complex and interact with each other so that the spatial
variability can only be explicitly predicted using high-resolution
atmospheric–snowpack coupled models . Simpler
approximate approaches have been devised to implicitly represent and predict
the variability . As a consequence, from the
perspective of snow depth estimation with ground-based measurements, the
spatial variability has to be considered random noise with largely unknown
characteristics . In some
extreme cases such as on the Antarctic Plateau, the mean annual accumulation
(which is the snow depth change during a year) can even be smaller than the
spatial standard variations of the distribution .
It means that in one point, net ablation or accumulation
higher than twice the spatial average occurs frequently
. In general, accurate snow depth estimate
requires averaging many independent point measurements to reduce the impact
of this noise. As minimizing the number of measurements is often of practical
importance, a good knowledge of the spatial variability (i.e, the statistical
properties of the noise) is required .
Terrestrial laser scanning TLS, is a
fast-developing tool for characterizing the spatial variability of snow
depth. Recent advances have allowed improved range and increased density of
measurements (number of points per square metre), thus allowing all the
relevant scales from the metre scale to the application scale to be covered
. Most studies have explored the rich spatial information
content provided by TLS e.g. but only used a few scans
acquired at two or a few different dates . While this may be
enough to estimate the seasonal peak accumulation or study snow
redistribution processes and geomorphology of the surface
, it is insufficient to capture the individual events
that affect snow depth over a season. The cost of these devices – about
100 times the price of a single-ranging probe – and the constraints on the
operating conditions make their deployment in the field for continuous
monitoring relatively challenging. Nevertheless, this application is rapidly
emerging and it is expected that a few catchments will
be instrumented in the coming years. A cheaper emerging alternative uses an
unmanned autonomous vehicle with on-board camera and an image processing
technique known as Surface from Motion SfM,
e.g. to construct digital elevation models from
multiple images. A snow depth map is then derived by differentiating a
no-snow acquisition taken before or after the snow season like with the TLS.
While the technique can not reach vertical accuracy of 1 cm yet, the
density of measurements and range are of the same order as those of modern
TLS. Operating conditions also constrain, which limits the frequency as with
TLS. The same approach can also be applied at a higher resolution
and seems promising for continuous monitoring.
The purpose of this paper is to introduce and evaluate the performances of a
new instrument which, in terms of spatial range, acquisition frequency and
cost, lies between the spatial-oriented techniques (TLS, SfM) and
temporal-oriented techniques (ultrasonic and laser ranging probes). The
initial aim of this development was to measure mean snow depth with accuracy
approaching 1 cm at a temporal resolution adequate to capture
precipitation and wind transport events, snow densification and melt. The
instrument is able to scan areas of over a hundred square metres every day,
for a cost less than 10 single ranging probes or at a tenth of the cost of a
common TLS. The robustness is another important factor since our goal was to
cover full snow seasons up to a year without attending the instrument in the
harsh Antarctic conditions. As this factor was a strong constraint and drove
many of our technical choices, the instrument is called the Rugged Laser
Scan (RLS). Two instruments have been built: the first one has been
deployed at the Col de Porte alpine site in the French Alps (45∘ N
and 6∘ E, 1325 m altitude) during one of the
winter campaigns of the World Meteorological Organization-Snow Precipitation
InterComparison Experiment (WMO-SPICE) project (winter season 2014–2015)
with the specific aim of investigating the accuracy and value of the device
compared to traditional ranging probes. The second has been set up at Dome C
in Antarctica (75∘ S and 123∘ E) in December 2014 and has
been operating most of the time for over 1 year until it was dismantled for
maintenance and improvements. The specific objective was to observe the snow
accumulation processes at daily-to-weekly temporal scales which are
unaccessible with other glaciological methods, such as readings of stake
emergence .
The paper is organized as follows: Sect. introduces the instrument
along with the calibration and data processing developed to produce gridded
surface elevation maps and snow depth. Section presents an
evaluation of the stability and accuracy of the system as well as the spatial
resolution. Based on this knowledge of the performance, it then analyses the
snow depth time series in terms of physical processes at both sites.
Section evaluates the benefit of this instrument compared to
single ranging probes in the context of the estimation of the mean snow
depth. The present paper focuses on this estimation and does not cover the
wide scope of spatial information content of the data set which will be
addressed in future work.
Materials and method
Rugged Laser Scan (RLS)
We developed a rugged low-cost laser scan able to operate in harsh conditions
like those encountered at Dome C where temperature regularly falls under
-70 ∘C in winter. Despite milder temperature at Col de Porte (a
midaltitude French alpine site), rain and occasional storms represent another
specific challenge. To minimize the risk, we based this development on an
industrial laser meter (DIMETIX FLS-CH 10) which had been used at both sites
for several years to carry out point measurements. The performance,
robustness and cost were found to be satisfactory. To convert this device
designed to take point measurements into a 2-D scanner, we mounted it on a
2-axis stage which performs the rotations in zenith and azimuth as depicted
in Fig. .
The laser meter has several operating modes to choose from depending on the
expected measurement rate and precision. We selected the fast mode, which
offers a range accuracy of ±2 mm (statistical confidence level of
95.4 %) at a rate of up to 20 Hz according to the user manual of
the device. This rate shall not be confused with the pulse repetition
frequency PRF, , which refers to the number of laser
pulses fired in a second. In fact, the PRF is likely much higher than
20 Hz, but is not specified by the constructor in our case. The
on-board software is in charge of accumulating and averaging all individual
measurements until the estimated accuracy reaches the specifications of the
selected mode. For this reason, the effective rate at which the measurements
are returned to the user is not fixed and can decrease to under 20 Hz
in unfavourable conditions. Among them, it was found during our early tests
that the brightness of the environment was an important factor, probably because
the photoreceiver becomes saturated or the laser return is weak relative to
the background in outdoor conditions. By adding a band-pass optical filter at
the laser-operating wavelength (650 nm) on the optical window, we
greatly improved the outdoor performances. In addition, collecting the scan
at night (or when the sun is at the lowest in Antarctica) also tended to
improve the effective measurement rate. The distance and reflectivity of the
target are two other important factors controlling the measurement rate. The
specifications indicate a maximum range of 65 m when the device is
still. However, for moving targets – or equivalently when the laser spot
moves with respect to the ground as in our application – this range is in
practice largely reduced.
Principle of the scan mode and spot mode of the Rugged Laser Scan
(RLS). The zenith angle θ and azimuth angle ϕ determine the
orientation of the laser meter which measures the range r.
In our set-up, the spatial resolution and the time to cover a given surface
area depend on both the speed of the spot on the ground and the rate of
measurements. With an optimal rate of 20 Hz and a target spatial
resolution of 2 cm, it takes nearly 4 h to cover a surface
area of 100 m2. In this case, the spot on the ground moves at
2cm×20Hz=0.4 ms-1. Higher speeds
have been tried in order to reduce the scan duration but the measurement rate
tends to degrade and even abruptly drop for speeds of 0.8 ms-1
and higher, which completely cancels out any gain.
The scan accuracy (the accuracy of x, y and z) depends on several
factors . The along-range accuracy of the laser meter is
2 mm in ideal conditions, which, projected in terrain coordinates,
can be doubled at the maximum zenith angle of 62∘ used here. In
addition, the accuracy depends on the spot size which is about 8 mm
in diameter (in the cross range direction) at 10 m and 15 mm
at 30 m, according to the manufacturer specifications. Altogether we
estimate that the accuracy in z, considering only the laser meter errors
and the value given by the manufacturer, could reach 5 mm.
Actual performances are presented in Sect. .
The 2-axis stage is composed of two identical reduced motors controlled by a
feedback on the position. This feedback loop is implemented with an analog
proportional–integral–derivative (PID) controller. The accuracy in position
is mainly determined by the quality of the potentiometer, which converts the
angular position in a resistance, and the electronics, which convert the
resistance into a numerical value. The chosen potentiometer model has a linearity of
0.2 % which over a rotation range of 45∘ corresponds to an
accuracy of about 0.1∘. A laser scan set up at z=4 m above ground and
considering a zenith angle of 62∘, this angular error would translate
in 3 cm error on z. It is a significant error for our application, but it is noteworthy that this error is constant in
time and should have a limited impact on the snow depth measurements which
are obtained by difference. The precision (i.e. the reproducibility in
position between different acquisitions) depends on other factors. It is
mainly determined by the noise level of the feedback loop and according to
our measurements is of the order of 0.03∘ corresponding to 0.4 cm for
a zenith angle of 45∘ and 1 cm for the maximum angle of 62∘.
This is 3-fold smaller than the accuracy but is not compensated by
differencing. It remains within our target. Note that the analog–digital and
digital–analog converters used to measure and command the position have a
16-bit dynamic range and autocalibration, which is largely sufficient given
the other above-mentioned sources of error.
Modes of acquisition
An embedded computer controls the stages and the laser meter. Two different
operating configurations have been implemented, called “scan mode” and
”spot mode”.
In scan mode, the sequence starts by setting the zenith angle θ at its
minimum (19.0∘). The range is continuously measured by the laser
meter while the azimuth stage rotates from ϕ= -90.0∘ to
+90.0∘ at a speed of vϕ(θ). The zenith angle is then
increased by a small increment Δθ(θ) and the next arc is
completed from +90.0∘ to -90.0∘. This process is repeated
until the zenith angle reaches the upper limit set to 62∘. The speed
vϕ(θ) and the increment Δθ(θ) vary as a
function of θ in order to ensure a uniform resolution on the surface.
Hence, the speed typically ranges from 8 ∘s-1 at
20∘ to 4.2 ∘s-1 at 62∘. The increment
ranges from 0.4 to 0.1∘. With such parameters, a scan is completed in
4 h and comprises around 200 000 points. One scan is acquired every
day, a balance between scientific relevance and lifetime of the laser meter
and mount (the laser itself has a lifetime of 50 000 h at
20 ∘C according to the manufacturer).
The spot mode was developed to follow the evolution of snow depth with a
higher temporal resolution and potentially better accuracy than with the scan
mode. This mode monitors a limited set of points which are specified at the
beginning of the season by their (x, y) horizontal position. The
measurement in spot mode consists of determining the angles (θ,
ϕ) so that the laser spot hits the surface of the snow at the vertical
of the point (x, y). Figure shows the principle in the
vertical plane. The azimuth is constant regardless of the actual snow depth
and is easily calculated from x and y. In contrast, the zenith angle
depends on the snow surface elevation z, which is unknown and is actually
the value we want to measure. An optimization algorithm was implemented to
iteratively minimize the horizontal distance between the target point (x,
y) and the actual projection of the laser spot in the horizontal plane.
This distance is given by rsin(θ)-x2+y2,
where r is the range measured by the laser meter and θ the actual
zenith angle. Once this distance is minimized to within a specified tolerance
(e.g. 2 cm), 100 measurements of the laser meter and angles are
accumulated and averaged with the aim of reducing the reproducibility error.
The snow surface elevation z is then calculated with the same formulas as
the scan mode. To speed up the optimization process, the optimal angle
θ is stored for every point and used as first guess for the next
acquisition. In practice, this mode allows us to sample one point in about
30 s, depending on the convergence time of the optimization. We have
used this mode at Col de Porte to monitor the snow depth of 64 points in the
scanned area over the season every 2 h, except during the 4 h
when RLS operates in scan mode (20–24 UTC).
Pictures of RLS during the installation at Col de Porte (October
2014) and at Dome C (December 2014). Zoomed image of RLS (2-axis mount, laser
meter and protection) and calibration spheres at Dome C.
Deployment
Pictures of the set up are shown in Fig. . At Col de Porte (left),
the laser scan was installed on the meteorological tower of the site at
5.4 m above ground. At Dome C (right), such a big structure would
perturb the wind flow and cause artificial accumulation in the
scanned area. To limit these effects, we use a very thin structure (38 mm
diameter vertical steel rod) and try to avoid wind drag by limiting the
installation height to 3.0 m above the surface. The stability of the
structure is indeed an important factor for the accuracy
and can be challenging over a long period. Any movement of the device, either
a translation or a rotation, directly results in position errors in the
scans. The most likely movement is a tilting of the structure with
consequences for both the orientation of the device and its horizontal
position. We estimate that stability as small as 0.1∘ is required, as
it corresponds to about 2 cm bias for an installation height of 5 m.
In addition, vertical movements can occur at Dome C because the structure is
anchored in the snow. We connected the rod holding the device to a
square wood board of 0.3 m2 buried horizontally at a depth of about
1.5 m. The structure thus sinks as the snow beneath the board
densifies. However, this movement is considered negligible compared to the
surface elevation variations occurring at the surface due to accumulation,
surface snow densification etc. The same approach is used to measure
accumulation with stakes e.g..
To record any movement during the season, we employed two strategies: at
Dome C where the snow accumulation is only a few centimetres a year, it was
possible to install polystyrene spheres (14.7 cm in diameter) in the
field of view of the RLS about 20 cm above the surface. The spheres were
mounted on a stick which was anchored into the snow at about 30 cm depth
using a small plastic board following the same principle as for the
structure. The spherical shape was chosen because the estimation of the
centre position from scans can be very robust even with an irregular number
of points. Following the (x, y, z) position of the sphere centres
allows monitoring of the overall stability of the scanner including the
structure, stages and laser meter. Sinking of all the spheres and structure
at the same rate would be undetectable but is unlikely. At Col de Porte,
spheres were installed at the beginning of the season to check the horizontal
levelling of the RLS but they were removed before the first snow because they
would be buried during the season and may disturb the accumulation pattern.
Instead, we installed a 2-axis inclinometer on the RLS, to record the changes
of inclination.
Data processing
The procedure for computing the position of the points in the (x, y, z)
coordinates system from range measurements and stage angles is similar to any
TLS and is briefly recalled here with emphasis on some RLS-specific details.
It consists of the following steps:
The laser meter returns measurements only when a satisfying quality is
estimated by the on-board proprietary software, which ensures that the number
of unrealistic or inaccurate measurements is limited. Nevertheless,
additional checks are needed. A first filter is applied to remove ranges that
are too short (< 3 m) and ranges that are too long
(> 17 m). A second filter further tracks outliers once the data
are projected in (x, y, z) (see below).
The position of the spot in the (x, y, z) coordinate system is
calculated as follows:z=-rcosθ+Δrsinθrxy=rsinθ+Δccosθx=rxycosϕy=rxysinϕ,where θ is the zenith angle (laser beam relative to the vertical),
ϕ is the azimuth angle and r is the range measured by the laser.
Δr is the distance between the point r=0
(close to the window of the laser)
and the centre of rotation of the laser projected along the beam direction.
Δc is the same but projected perpendicularly to the beam direction. rxy is the range in the (x,y) plane.
Based on an estimate of the levelling of the laser scan (see below),
a rotation R is applied to ensure that the (x, y) plane is
perfectly horizontal. In addition, the z coordinate is shifted for
convenience so that the origin z=0 is at the mean ground level (for Col de
Porte) and on a reference plane (for Dome C) instead of at the centre of
rotation of the laser, which is meaningless.
The second filter is then applied. It considers that any point higher
or lower by 5 cm from the mean height of its neighbours is removed.
The neighbourhood is taken as the disk in the horizontal plane of 5 cm
in diameter centred at the tested point. This filter is efficient to remove
outliers and thin objects like blowing flakes or the cables used to hang the
structure. However, it can also erroneously remove areas with a summit or
hollow if the local slope is abrupt (over 45∘). At last, permanent
artefacts in the scanned area (stacks, spheres, etc.) are removed with
specific ad hoc criteria.
The surface formed by the points (x, y, z) is resampled on a regular
grid using the bilinear interpolation implemented in matplotlib.mlab.griddata
Python library (version 1.5.1). The same grid is used throughout the season
allowing easy calculation of the snow depth and other statistics with
weighting. This approach is simple but may degrade the resolution compared to
mesh-based approaches . The chosen spacing was 2 and
3 cm at Col de Porte and Dome C respectively, reflecting the
difference of installation height.
Evolution of the mean (black) and standard deviation (green) of the
snow depth at Col de Porte over the winter season 2014–2015 measured by the
RLS.
The procedure requires a few site-specific inputs, i.e. the rotation matrix
and the reference plane. To determine the rotation, we installed four spheres
in the scanned area and used a professional laser level to ensure they were
in the same horizontal plane with an accuracy estimated to be
±5 mm. The position of each sphere was determined by first
selecting only the points of the scan that reasonably lay in the sphere
vicinity based on its expected position (first guess), then minimizing the
norm-1 of the function measuring the distance between the points (x, y,
z) and the sphere surface: (x-xc)2+(y-yc)2+(z-zc)2-R where R=7.3 cm is the known sphere radius
and (xc, yc, zc) is the unknown sphere
centre in the unrotated coordinate system (obtained after step 2). The
minimization uses the random sample consensus algorithm RANSAC,
to automatically detect and remove outliers. A plane is
then fitted onto the four sphere centres by least square fitting and the
rotation R which puts this plane horizontal is deduced using the Cloud
Compare software. The rotation angle was found to be 0.5∘ at both
Dome C and Col de Porte demonstrating that the levelling of the laser scan
mounting was good.
Evolution of the mean (black) and standard deviation (green) of the
surface elevation change at Dome C in 2015 and January 2016 measured by the
RLS. Orange points show the mean accumulation deduced from emergence
measurements of the GLACIOCLIM 50-stack network. The reference is calculated
so that the first GLACIOCLIM measurement (3 January 2015) equals the mean RLS
snow elevation measured the same day.
Once rotated, the z=0 reference was taken at the mean elevation of the
gridded data for the first scan taken at Dome C (1 January 2015) and for the
average of all scans in the snow-free period between 9 and 16 November 2014
at Col de Porte.
WMO-SPICE data at Col de Porte
For the evaluation of the RLS, we use data collected in the framework of the
WMO-SPICE experiment at Col de Porte. Two fixed laser
meters, OTT/Lufft/Jenoptik SHM 30.11 and Dimetrix FLS-CH 10, were used during
the season. They were both set up on the same structure as RLS but shifted by
a 2 m-long horizontal arm. The laser meter were tilted by about 20∘
from the vertical so that the measured footprint was not perturbed by snow
accumulating on the arm and sensors and occasionally falling down or melting.
However, with such an angle, the footprint position in the horizontal plane
moves during the season as a function of the snow depth. It will be shown to
be a limitation for the comparison with RLS data. The two snow depth time
series were calculated using range measurements, the tilt angles precisely
measured for each sensor and the offsets determined using the snow-free
period:
dDimetix=4.2603+0.92666×rDimetixdJenoptik=4.2835+0.93643×rJenoptik.
Measurements were carried out every minute during the entire period of
operation of the RLS at Col de Porte. For the needs of the WMO-SPICE
experiment, the location of these sensors was chosen in an area of the
experimental site known to feature generally very low natural variability of
snow depth, based on visual inspection over the years. The goal was to
concentrate on the possible measurement differences between the instruments
tested, which could be due to the instruments themselves.
Results
The evolution of snow depth at Col de Porte and of surface elevation (i.e.
snow depth with respect to the horizontal reference plane) at Dome C is shown
in Figs. and . In order to provide an unbiased
geophysical interpretation of these variations and distinguish spurious
trends from actual variations, which is the ultimate goal of this section, it
is necessary to assess in detail the performance, accuracy and precision of
the RLS. To this end, we first describe the periods of operation and discuss
the causes of failure (Sect. ), then the stability of the
instrument and the structure supporting it (Sect. ) and the
accuracy in spot and scan mode (Sect. ). The spatial resolution
is estimated in Sect. . Eventually, Sect. provides
the geophysical interpretation with a knowledge of the limitations.
General operating results
The Col de Porte scans were acquired from 7 October 2014 to 3 May 2015
(207 days) with a success rate of 90 %. The snow period started with
first ephemeral snowfall on 4 November 2014 and ended on 22 April 2015 when
snow was completely absent from the scanned area. At Dome C, the time series
ranges between 1 January 2015 and 11 January 2016 when the device was
dismantled. A major interruption occurred from 17 October to 5 December
2015 (49 days). Reports of the laser
internal temperature indicated malfunction of the internal heating. After a
power shutdown from the Concordia station, it started to work again but the
stability of the laser temperature was degraded compared to the first period
(not shown). Considering that the laser meter has a minimum operating
temperature of -40 ∘C according to the manufacturer and that it
was exposed for several months to less than -70 ∘C, it is possible
that the lifetime of the heating element and control electronics were
shortened. We cannot, however, conclude that it is the cause of failure based
on this single incident. Overall, the success rate over the period is
65 % (and 75 % when excluding the internal heating failure period).
At both sites, the main cause of failure (after the heating failure at
Dome C) is the jamming of the stages. This could be caused by snow
accumulation in the housing of the device or possibly ice formation on the
motors. Since Dome C conditions were windier than Col de Porte and RLS is set
up at a lower height than at Col de Porte, the occurrence and impact of
blowing snow may be higher, contributing to the lower success rate. In
addition, the lower temperature lengthens the recovery time after such an
event because of the slower sublimation. The second longest interruption at
Dome C from 5 to 16 July following a large accumulation event is very likely
to have been caused by this problem. Snow or frost on the laser window is
another issue and were the likely cause of a few short interruptions (the
laser meter reports the out-of-range error in this case). They were rapidly
cleared in 1 or 2 days due to the laser meter heating. Erroneous laser
returns due to airborne particles was a minor issue only. The data
accumulation and filtering done by the laser meter internal software as well
as the filter we implemented removed any occasional short-range acquisitions.
Evolution of the four reference spheres coordinates (x, y, z) at
Dome C. δ and δ′ respectively refer to the changes with respect
to the first scan (1 January 2015) and to a scan just after a period of
settling (1 February 2015).
Evolution of the inclination of the laser over the season at Col de
Porte.
Evaluation of the RLS spot mode against SPICE laser meters at Col de
Porte. Top panel shows the depth, bottom panel shows differences between
sensors.
Stability
Dome C
The stability of the RLS instrument and set-up is evaluated at Dome C using
the four spheres installed in an horizontal plane at the beginning of the
season. Figure shows the three coordinates of the spheres. Until
the event of July 2014, the spheres were detected in nearly every scan. The
time series features a few abrupt variations of the order of 3–4 cm
and slow trends of up to 1 cm. From July 2015 onwards, the series
becomes discontinuous, not only because of the failures of the RLS described
in the previous Section, but also because the spheres were entirely
(sphere 2) or partially buried (the other three). No other abrupt changes are
observed during the second period and the trends seem to remain small, of the
order of 1 cm.
In general, the time series depict complex variations which are difficult to
understand in term of movements of the structure or the spheres. For
instance, the first series of changes in January, visible in z, could be
interpreted as a lateral tilting of the structure (two spheres sink while the
other two rise), but the absence of significant change in δx and
δy at the same time invalidates this hypothesis. Sinking of the
spheres due to the densification (the sphere are “anchored” at only
20–30 cm depth) is another possible hypothesis at this time of the year but
it fails to explain why the sphere 2 is apparently rising. The sudden and
large change experienced by sphere 1 during a wind event in March has the
signature of a lateral movement of the sphere itself. At last, slow
variations of the elevation δ′z of spheres 1, 3 and 4 are visible
from February to July and seem to reverse from July to January. This could be
due to a thermal effect (e.g. dilation of the structure). We also identified
periods with hoar forming on the spheres , which would
result in a positive bias of the z coordinate of the spheres. This
highlights the limit of using the spheres as a calibration system.
Nevertheless, despite these uncertainties, the amplitude of the variations
give a higher bound of the stability and appear to be acceptable. For the
snow depth, the most relevant is the vertical movements of the spheres, which
remain within 1 cm over the year if the period of settling after the
installation is excluded (January 2015). This is small and acceptable but not
negligible compared with the variations depicted in Fig. .
Col de Porte
In the absence of spheres, the stability at Col de Porte is evaluated using
the 2-axis inclinometer fitted on the laser scan. Figure shows the
daily variations along the two axes (calculated by the daily median of the
5 min acquisitions when the scanner is not running). The time series reveals
a shift occurring on 3 November 2014 before the first snowfalls. It is most
probably due to a maintenance operation on the tower and implies to discard
the data before this date, which is not a problem because there are several
available snow-free scans after this date.
From 3 November and until the end of the season, the day-to-day variations
are of the order of 0.6∘ on the two axis (specifications of the
sensors indicate an accuracy of 0.2∘ at -10 ∘C). The long
term trend is of the order of a decrease of 0.02∘ on both axis (too
small to be visible in the figure) which is only slightly larger than the
long term stability of 0.01∘ given by the manufacturer. The impact of
such a trend on the surface is of the order of 8 mm, in the worst
case at 62∘ zenith angle (5.2 × (tan(62∘+0.02∘)-tan(62∘))=0.008). This is acceptable but highlights the need to
take precaution on the laser scan mounting as it could be a significant part
of the uncertainty budget .
Evaluation of the accuracy in spot mode
The comparison between RLS spot mode data and the two fixed laser meters is
presented in Fig. . The overall variations of snow depth are very
similar between the four curves, indicating weak spatial variations between
the Dimetix and Jenoptik points (separated by about 1 m) as well as weak differences
between the laser meters and RLS. The differences are more apparent on the
residual plot in Fig. . They range between ±5 cm and
vary by 1.0 and 1.8 cm RMS over the season for the Jenoptik and Dimetix
points respectively. They show both rapid and slow variations, with an
overall negative bias during the accumulation period for both points and a
positive bias during the melt period for the Dimetix point only.
Different causes explain these two types of variations. The slow variations
seem to be deterministic and could be explained by the slightly different
points measured by the sensors. In fact, because of the constant tilt of the
fixed sensors, the position of measured point on the surface moves toward the
sensors (i.e. to the left in Fig. ) as the snow depth increases
whereas RLS in spot mode measures exactly the same point (x, y)
throughout the season. The distance between the measured points when the snow
depth is maximum reaches about 60 cm. By looking at the scans we
indeed found variations over this distance range of the order of a few
centimetres (Fig. ) with a slope opposite to the sensors which
matches the negative bias. Nevertheless, the precise trajectory of the points
measured by the laser meters is not known, which prevents any further
exploration of this hypothesis.
Two snow depth maps acquired at Col de Porte 26 February 2015 when
the snow depth reaches its maximum and 6 March 2015 after a wind slab
appeared in the northern corner (x=0; y=6 m). North is
approximately in the y-axis direction. The square and round symbols
represent the footprint of the SPICE sensors at the beginning of the
season.
Evaluation of the RLS scan mode against SPICE
laser meters.
Zoomed image of the scans at Dome C and Col de Porte acquired
15 February 2015. Each point shown in the (x, y) plan is an individual
measurement of the laser meter.
The rapid variations, on the other hand, are relatively random. This suggests
they come from reproducibility errors of the sensors. The weekly
standard difference of the 2-hourly data is about 0.4 and 0.7 cm for
Jenoptik and Dimetix points on average over the season. The mean daily
standard difference is about 0.3 cm for both points. These values are
very low and should be compared to the 2σ accuracy of the laser meter
of about 0.3 cm estimated by the manufacturer. The RLS
angle reproducibility error was estimated at 0.03∘ which is
sufficient to explain 0.5 cm RMS (evaluated for a zenith angle of
45∘ and a laser scan height of 5.2 m).
As a conclusion, we estimate that the spot mode allows a subcentimetre
reproducibility for a measurement rate of about 2–3 min-1. With
our experimental set-up, we are only able to provide an upper bound on the
accuracy of the order of a few centimetres (precise value depends on the
metrics, max or RMS differences). A more precise evaluation would require the depth to be compared at exactly the same points over the season. In addition,
it would be interesting to use complementary measurement techniques because
systematic errors due to the laser meter technique are not taken into account
in our evaluation, most notably the penetration depth of the laser in the
snow. We expect this error to be small and rather constant of the order of
1 cm or lower . As this error
does not concern the ground scans, it would tend to negatively bias all the
snow depth measurements at Col de Porte, while Dome C would not be affected
Evaluation of the accuracy in scan mode
To perform the comparison with the fixed sensors data following a similar
approach to that of the previous section, we estimated for each scan the
z coordinate at constant positions in the horizontal plane (x, y). We
used the same interpolation method as for generating the regularly gridded
product (Sect. ) but interpolated at the points monitored in spot
mode instead of on the regular grid (the difference would not be more than
the grid spacing of 3 cm). In addition, only the fixed sensor data
taken simultaneously with the scans (i.e. 20–24 UTC) were considered to
avoid differences caused by ongoing snowfalls. The results in
Fig. show very similar evolution of the snow depth for the three
types of sensors. The daily residual ranges from -8
to +3 cm and is on average 1.2 and 2.3 cm RMS at Jenoptik
and Dimetix points, similar to that observed in spot mode. The variations of
the residual is also a superposition of rapid variations and a slow component relatively well correlated to the snow depth. The mean weekly standard
difference is 0.5 and 0.8 cm at Jenoptik and Dimetix points
respectively which is nearly as good as in spot mode. This is unexpected
because the latter mode averages a hundred single measurements at the same
place, whereas the former is based on interpolation involving four points at
most. We conclude that the spot mode unnecessarily oversamples the surface
and the number of measurements per point could be reduced, hence allowing for
monitoring either more points or more frequently.
Overall this comparison shows that the RLS in scan mode provides similar
measurement performances to the fixed sensors or the spot mode even when
evaluated at single points. It means that further reduction of the random
errors can be obtained by averaging the points over an area.
Evaluation of the effective spatial resolution
The spatial resolution is an important parameter when not only the mean snow
depth but other characteristics of the surface are of interest, such as the
distribution of snow depth, roughness, slope, etc. The theoretical spatial
resolution can be estimated from scanning parameters (Sect. ). In
the cross-range direction (when the azimuth varies), it is 1.3 cm for
the Col de Porte (RLS at 5.2 m height) and 0.7 cm for Dome C (RLS at
3.0 m height). In the range direction, the Δθ increment
corresponds to 4.1 cm at the Col de Porte and 2.4 cm at
Dome C. Since the increment and azimuth speed are appropriately scaled as a
function of the zenith angle during the scan, the theoretical resolution in
each direction is constant over the scanned area.
The effective resolution should differ because of the angle reading errors,
the laser meter range error and the laser meter measurement rate. It is
interesting to evaluate the resolution directly from the scans rather than
from the theory. However, this is not straightforward because data are not
acquired on a regular grid as highlighted in Fig. , which shows
the scans of 15 February 2015 at both sites.
The number density of points measurements over the scanned area is about 3100
and 5200 m-1 at Col de Porte and Dome C respectively for this date
which corresponds to points every 1.8 and 1.4 cm on average if the
grid were regular. However, because of the cross-range
direction oversampling, these distances are of little interest. The average
distance between successive acquisitions (in azimuth) is easy to compute and
is 0.9 cm on average at both sites, which gives an estimate of the
cross-range resolution. This agrees with the theoretical value considering
that the measurement rate can vary around 20 Hz. Combining theses
values and number density of points gives a first estimate of the resolution
in the other direction. Results are 3.6 cm at Col de Porte and
2.1 m at Dome C which is slightly better than the theoretical value.
However, Fig. highlights the irregularity of the zenith
increments which we believe to come from the mechanics of the zenith stage
and its feedback loop. As a result, the resolution in the zenith direction is
irregular and distance between successive zenith increments ranges from
0 cm (i.e. superposition) up to 5 cm at Dome C and
7 cm at Col de Porte in the area covered in Fig. . These
latter values give an upper limit on the resolution and can be used as
conservative estimates.
Analysis of the evolutions of snow depth and accumulation
To illustrate the capability of the instrument to address geophysical issues
which current monitoring systems cannot adequately observe, we provide
an example of the use of the RLS data to describe time/space variations of
near-surface snow elevation changes at both sites.
Col de Porte
The evolution of the snow depth depicted in Fig. is representative
of an alpine midaltitude site. It features a period of accumulation with
significant snowfall building up a snowpack up to a depth of 1.46 m
(Fig. ). It is followed by an overall decrease due to the
accelerated compaction and melt of the snowpack. With such large accumulation
values compared to the precision estimated in Sect. and the
number of points in the scan (over 150 000), the statistical and
instrumental relative errors are always small. The variations of the mean
snow depth can be attributed with confidence to physical processes. Even the
three ephemeral snowfall events that occurred at the beginning of the season
with maximum snow depth (observed at 20 UTC) of 8 cm (4 November
2014), 8 cm (17 November 2014) and 16 cm (8 December 2014)
are well described. The standard deviation of snow depth over the scanned
area (hereinafter σs) is of the order of 1.2–1.7 cm
for the three events. As it is close to the reproducibility estimated in
Sect. , we can postulate that the true standard deviation of the
snow height is probably smaller than 1.2 cm, that is, the snow depth
is very homogeneous. The three next snowfall events show a similar behaviour,
despite larger accumulation. Over the accumulation period the standard
deviation remains inferior to 4 cm until the maximum is reached on
26 February 2015.
A rain-on-snow event occurred on 1 March 2015, marking the beginning of the
melt season. Four days later, a wind slab was formed in the northern corner
of the scan (y≈ +6 m in Fig. ). This resulted in
a sharp increase of the snow depth standard deviation up to 10 cm,
which remained high (around 8 cm) until 22 April 2015, only a few
days before the scanned area became entirely snow free. Since the wind slab
is only partially viewed by the RLS, the interpretation of the standard
deviation value is delicate. Indeed, from a statistical point of view, the
snow depth field is not stationary over the sampled area, and while
statistical estimators can always be computed, they may be oversensitive to
the choice of the sampled area and eventually become useless. This also
concerns statistical tests and other frameworks that rely on the assumption
of stationarity and may fail more frequently than
predicted by theory. While in practice it is desirable to observe the snow
depth field at a large scale to ensure the stationarity, it is not always
easy to achieve. It was indeed impracticable in our case, not only because of
the limited range of the RLS (limited by the laser meter and by the height of
installation), but also because of the size of the Col de Porte site. The
site is relatively sheltered compared to higher altitude sites and the area
selected for the WMO-SPICE experiment was flat and relatively clear of
obstacles. Our results regarding the homogeneity during the accumulation
period support a posteriori the choice of this particular area to conduct the
WMO-SPICE inter-comparison of snow depth sensors. Nevertheless, a few trees,
the main building of the site and the fence are about only 10 m from
the scanned and WMO-SPICE area, which makes it difficult to reach stationarity of
the snow depth scale. Fortunately, the wind slab – probably formed due to
the presence of the trees and the fence – did not expand up to the WMO-SPICE
sensor footprints.
Dome C
The evolution of the accumulation is radically different at Dome C
(Fig. ) than it is at Col de Porte. The mean accumulation over the
season amounts to only 8 cm which is expected. It corresponds to the
annual mean at this site and is of the same order as the
measurements on the GLACIOCLIM stack network (orange points in
Fig. ) averaging to 6.4 cm over a similar period.
More surprisingly, the time series shows that most of the annual accumulation
comes from a single deposition event happening between 5 and 17 July 2015,
most likely at the beginning of this period, because we believe it to be
responsible for the failure of the instrument. ERA-Interim reanalysis data
confirm this hypothesis.
It is well known that the deposition is mainly driven by wind on the
Antarctic Plateau . Both of these
studies showed that when modelling the time evolution of snow accumulation,
adding new snow to the snowpack at the time of the precipitation event, as
commonly done in alpine environments, was found to be generally inadequate on
the Antarctic Plateau. Instead, better results are obtained by pooling snow
precipitation into a virtual reservoir until some criteria on the wind speed
are met. The reservoir is then emptied on the surface, resulting in a single
large deposition event. This tends to delay and reduce the number of the
deposition events. Our observation is consistent with this approach, showing
that more than six significant snowfalls and a dozen of strong wind events
(here > 8 ms-1) predicted by ERA-Interim reanalysis (lower
panel in Fig. ) could have caused significant accumulation but did
not. Whether this new observation is a rare or common event, or is biased by
the relatively limited scanned area, is an open but important question. Only
a longer time series of observations could provide further insights.
In addition to this particular event, the series shows other remarkable
patterns of variations, particularly visible during the first part of the
series. From February to July, the snow elevation shows two periods of slow
and regular increase separated by an erosion event occurring ca. 20 March.
During each period approximately 2.5 cm accumulated and the erosion
event removed 2 cm in 1 or 2 days. Based on the analysis of the
stability (Sect. ) and accuracy (Sect. ), we are
confident that these values are real. Such periods
of slow accumulation have already been suggested by
based on indirect inferences using microwave remote sensing observations. The
12-year-long time series of satellite data even suggests that most of the
accumulation in winter is due to this slow process, which is not captured by
the ERA reanalysis. This could be explained by clear-sky precipitation
, hoar growth and/or condensation .
The rapid erosion event is associated with a strong wind in the reanalysis;
however it is worth noting that wind speeds over 8 ms-1 are
present throughout the period of observations but did not result in erosion.
The direction of the wind and pre-existing conditions in the near-surface
snowpack are probable factors governing the erosion.
The small temporal evolutions are revealed because many points are averaged.
The spatial variability in the scanned area is indeed significant and changes
over the time series. In absolute values, it is of the same order as in
Col de Porte with σs=3.5 cm RMS in the beginning of the
season and σs=7 cm RMS in the end. However in relative
values, it is about 0.5–1 times the mean annual accumulation whereas at
Col de Porte it never exceeds 0.05 of the maximum accumulation.
Since the surface shape frequently changes due to redistribution, the annual accumulation measured at any point is highly variable around
the mean. It can even be negative at some point, a case called accumulation
hiatus . Figure shows the
distribution of annual accumulation from RLS over the scanned area together
with that calculated from the GLACIOCLIM 50-stakes network near Concordia.
The investigated periods are slightly different due to the availability of
the data but are comparable (3 January 2015 to 18 November 2015 for
GLACIOCLIM and to 5 December 2015 for the RLS). The distributions are similar
except for a general positive offset for RLS which corresponds to the
difference visible on the time series in Fig. between the two
spring acquisitions. This similitude is remarkable considering the much
smaller area covered by the RLS and the distance between the two sites (about
2 km). It highlights the potential to explore new ranges of
spatio-temporal scales using time-lapse laser scanning.
Distribution of the spatial variations of accumulation at Dome C
observed by RLS (measured between 3 January and 5 December 2015) and the
GLACIOCLIM network at 2 km from Concordia station (measured between
3 January and 18 November 2015).
Evolution of the snow surface elevation change at Dome C taken in 6
random points in the scanned area (gray), on average over the 6 points
(green), on average over the scanned area (orange) and measured by a nearby
ultrasonic ranging probe (black).
Discussions
We have demonstrated that the RLS is able to measure snow depth over a very
large number of points with comparable accuracy as with single point sensors.
By averaging the spatial variability over these points, the RLS can thus
provide mean snow depth over an area of the order of hundreds of square
metres with a precision approaching the intrinsic precision of the sensor,
i.e. about 1 cm. To evaluate the value of the RLS concept regarding
snow depth estimation in a fair way, other factors need to be taken into
account. The question is in fact whether a network of N point sensors with
an identical overall “cost” could provide the same accuracy or not. The
term “cost” here is open and includes different aspects including device
price, maintenance, logistical constraints, robustness and risks. This
question is closely related to that of designing a snow depth survey from
manual measurements (snow course) or equivalently determining the number (and
location) of measurements needed to reach some accuracy level. This has been
extensively highlighted, e.g. by and investigated in
detail by and using geospatial
statistical frameworks. However, to apply it in our case is not
straightforward because the spatial signal has been shown not to be
stationary at both Col de Porte (wind slab) and Dome C (slope). Nevertheless
it is possible to obtain similar statistical results by picking random
samples from the observed scans which assume ergodicity and negligible
spatial correlation. Practically, we consider that N point sensors are
randomly located in the scanned area and compare their averaged snow depth to
the true snow depth estimated by the average over the whole scanned area. An
example for N=6 at Dome C is shown in Fig. along with the
independent time series acquired by an ultrasonic ranging probe located about
10 m from the RLS. While the individual trajectories are tangled and
each one depicts a particular story about the snow accumulation in 2015, the
trends in the 6-point mean looks similar to the scan mean (i.e. true value).
Nevertheless it quantitatively differs. The difference gives an estimate of
the error ε due to the limited number of observed points. For a
large number of random sampling and for different N, we found that the
rules ε=σs/N precisely apply despite the
non-stationarity and possible correlation. As a result, based on standard
deviation σs given in Sects. and
, we can estimate that a network of N=5 sensors
would have a
1σ error of ≈ 3.5 cm, which is
quite large compared to the centimetre precision of the RLS. With N=10, the error is 2.5 cm. To attain an
error of 1.5 cm, 30 sensors are necessary. An error of 1 cm requires twice as many sensors. We
also should emphasize that these values of error may be over-optimistic as
found large increases of the standard variation as a
function of the size of the covered area, typically 2 to 5-fold between
10 m (the scale of the RLS range) and 100 m because of
long-range correlation.
In any case, this demonstrates that a single sensor or a small network is
unable to approach the centimetre accuracy and that the spatial variability
always dominates the error budget with current sensor technology. While the
centimetre accuracy may be inessential for alpine regions, the detection at
Dome C of the slow accumulation periods and the zero net accumulation observed during
all but one snowfall and strong wind event definitely relies on the ability
to average the spatial variability.
Furthermore, the cost of a N-sensor network generally increases with N
while the gain in accuracy only follows N. The RLS comes with a
higher but fixed cost and provides a large number of points that are
sufficient to reduce the error due to the spatial variability to negligible
levels. Nevertheless, the current design of RLS provides a limited range
which is insufficient to capture some interesting longer spatial scales
and could
become an issue when long-range spatial correlations are important. While the
installation height could be increased by a few metres to improve this –
especially at Dome C where it was only 3 m – some characteristics of
the laser meter (maximal range and measurement rate) and the precision of the
stages are intrinsically limited. In this domain, the recent commercial laser
scans outperform the RLS.
Conclusions
This paper shows that a laser meter designed for snow depth
point measurements can be transformed into an automatic, robust and low-cost
laser scan by adding a 2-axis mechanical stage. About 200 000 points of
measurements can be obtained daily, with a precision of the order of
1 cm, and in an area of 150 m2 when the instrument is set up
5.5 m above the surface. With such a system, the mean snow depth of
an area can be estimated with an accuracy approaching the intrinsic accuracy
of the instrument, i.e. 1 cm. We estimated that this could not be
obtained with a network of point sensors for a similar cost.
The variations of snow depth at Col de Porte over the winter season
2014–2015 is typical of alpine regions, with a few ephemeral snowfalls, then
a period of accumulation comprising about six heavy snowfall events, and at
last a period of melt. At Dome C, the most remarkable result is that most of
the accumulation amount over the year comes from a single event occurring in
July. In addition, the time series features periods of slow and regular
accumulation without apparent snowfall in the meteorological data, which
point to clear-sky precipitation, condensation or hoar formation.
Further work includes improvement of the instrument and further analysis of
the data. The rate of failure (mainly due to snow drift) needs to be
improved, the power consumption could be optimized in order to make the
instrument energy autonomous, and installation at greater heights should be
explored to increase the scanned surface area.
This study was focused on the instrument accuracy and the mean snow depth
estimation for which the RLS is seen as a provider of numerous independent
points of snow depth measurement. However, RLS provides, as any laser scan,
maps, that are continuous field of surface elevation and depth whose spatial
properties – and spatio-temporal properties for the RLS – are very rich and
deserve further exploration. Applications of this new system encompass the
study of accumulation process on a broad range of spatial scales and
timescales, and the evolution of geometrical and aerodynamical roughnesses
for application in remote sensing and surface turbulence.
In the broader context of the WMO-SPICE project, the development of the RLS
demonstrates that escaping the limitations of automated point measurements of
snow depth due to the spatial variability of the snowpack itself becomes
possible only if a significant number (more than 10 typically) of
observations are taken simultaneously at the same measurement point (let
alone longer range variability, which is particularly significant in
mountainous terrain, see e.g. ). This development
paves the way to answer questions and potential operational implementation.
In terms of snow depth data assimilation in meteorological or hydrological
models, while it is well known that snowpack heterogeneity can be found in
virtually all environmental contexts, single snow depth values are generally
considered representative for given monitoring stations in the assimilation
systems, and are most often deducted from a single sensor. Findings by the
RLS make it possible to envision the development of future snow monitoring
devices which could approach the variability of snow depth at the monitoring
station level and, more importantly, determine along with the mean value a
quantitative estimate of the spatial variability, which could be considered
in the assimilation systems as an indication of the representativeness of the
measured mean value. This requires that such measurement campaigns and
analyses are repeated in various environmental contexts to assess to what
extent the findings in this study apply broadly on all terrestrial land
surfaces, and fully assess its implications in terms of the ability to
monitor snow depth using single sensors.