TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-11-891-2017Determination of snowmaking efficiency on a ski slope from observations
and modelling of snowmaking events and seasonal snow accumulationSpandrePierrepierre.spandre@irstea.frFrançoisHuguesThibertEmmanuelhttps://orcid.org/0000-0003-2843-5367MorinSamuelhttps://orcid.org/0000-0002-1781-687XGeorge-MarcelpoilEmmanuelleUniversité Grenoble Alpes, Irstea, GrenobleMétéo-France–CNRS, CNRM UMR 3589, Centre d'Etudes de la Neige, GrenoblePierre Spandre (pierre.spandre@irstea.fr)7April201711289190912August20165September201614February20176March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/11/891/2017/tc-11-891-2017.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/11/891/2017/tc-11-891-2017.pdf
The production of Machine Made (MM) snow is now generalized in ski resorts
and represents the most common method of adaptation for mitigating the impact
of a lack of snow on skiing. Most investigations of correlations between snow
conditions and the ski industry's economy focus on the production of MM snow
though not one of these has taken into account the efficiency of the
snowmaking process. The present study consists of observations of snow
conditions (depth and mass) using a Differential GPS method and snow density
coring, following snowmaking events and seasonal snow accumulation in Les
Deux Alpes ski resort (French Alps). A detailed physically based snowpack
model accounting for grooming and snowmaking was used to compute the seasonal
evolution of the snowpack and compared to the observations. Our results show
that approximately 30 % of the water mass can be recovered as MM snow
within 10 m from the center of a MM snow pile after production and
50 % within 20 m. Observations and simulations on the ski slope
were relatively consistent with 60 % (±10 %) of the water mass
used for snowmaking within the limits of the ski slope. Losses due to
thermodynamic effects were estimated in the current case example to be less
than 10 % of the total water mass. These results suggest that even in
ideal conditions for production a significant fraction of the water used for
snowmaking can not be found as MM snow within the limits of the ski slope
with most of the missing fraction of water. This is due to site dependent
characteristics (e.g. meteorological conditions, topography).
Introduction
Snow is essential for the ski industry . It
encourages ski lift operators to increase the amount of grooming and
snowmaking methods so as to lessen their dependency on the variability of
snow conditions. . Snowmaking has been the main
concern of recent investigations concerning the impact of climate change on
the ski industry
. To the best of
our knowledge however, none of these results accounted for the efficiency of
the snowmaking process i.e. the actual conversion of water volumes used for
the production of Machine Made (MM, ) snow on ski slopes.
Related water losses may be significant .
Dates of the field campaign carried out during the 2015–2016 winter
season. “MM snow Obs.” and “Ski slope Obs.” correspond respectively to
dates when observations were performed on MM snow piles and ski
slope.
Water losses during snowmaking were addressed in a few studies with different
approaches and investigated factors. estimated consumptive
water loss through evaporation and sublimation during the snowmaking process
through a combination of nine field experiments (mass balance) and a
theoretical approach (energy balance). They found an average of 6 % water
loss and a negative linear relationship between the atmospheric temperature
and water loss. implemented the relationship derived by
in a detailed snowpack model and found that for typical
snowmaking conditions, water losses due to evaporation and sublimation ranged
between 2 and 13 %. later showed that water loss during
snowmaking could not be limited to evaporation and sublimation alone. This
was done though the comparison of runoffs simulated by a hydrological model
with observations in six test sites in Colorado ski areas. An additional 7 to
33 % loss was deduced after the initial loss (related to evaporation and
sublimation), resulting in a total consumptive loss of 13 to 37 %.
Recently, reported from interviews with professionals that
water losses due to evaporation, sublimation and wind erosion were estimated
as being between 15 to 40 % for air-water guns and 5 to 15 % for
fan guns. performed observations on four ski slopes and
found a minimum water loss of over 25 % with significant differences
between observation sites (some exceeding 50 %). He concluded that
external factors (wind, topography, vegetation) probably had a significant
impact on the efficiency of MM snow production.
The present study aims to provide a detailed description of the seasonal
evolution of a ski slope snowpack in operational conditions with a high
spatial resolution (0.5 m grid), including the additional MM snow from
snowmaking methods. Equivalent water masses of MM snow piles were measured
prior to any action by the grooming machines, and both snow depth (SD) and
snow water equivalent (SWE) of the prepared ski slope were observed on
several occasions. These observations were crossed with all available data on
snow production (water flow, temperature, wind) and with the results of
simulations using a detailed physically based snowpack model
. This was done so as to compute the ratio of MM snow mass
on the ski slope through snowmaking with respect to the water mass used for
the production of MM snow (ratio defined as the Water Recovery Rate, WRR).
The method is described in the first section, and includes all measurements
and tests set up to characterize uncertainties related to our measurements.
The retained uncertainties and the results of observations as a result of
these tests are detailed in a second section and discussed.
Material and methodsDescription of observations: study area
The “Coolidge” ski slope is a beginner's trail near Les 2 Alpes ski resort,
a village (Oisans range, French Alps) at an elevation of
1680 m a.s.l. The area is mainly a west-facing and almost flat slope
(≈ 5∘). It is an important slope in the resort used for
skiing lessons and as a route back down to the village on skis, obliging
technical services to keep it under operational condition for skiing from the
opening of the resort (early December) to its closure (late April). Two
distinct series of observations were carried out on this site during the
2015–2016 winter season (Table ):
Volume measurements of single snowmaking events and the related mass.
Five production sessions were observed (Table ).
Seasonal snow accumulation measurements of snow depth (SD) and snow water
equivalent (SWE) on the prepared ski slope i.e. in the skiing conditions as
offered to skiers. Three observations were carried out
(Table ).
A single air/water gun was used for our observations. The professional
snowmakers of Les 2 Alpes kindly provided all available data regarding the
production of MM snow on the study site. This covers 15 min time step
records of the water flow of the snowgun (m3h-1), the wet-bulb
temperature (∘C), the wind speed (ms-1) and
direction (∘ from North) measured in the vicinity of the study
area. These data were used both as inputs to force the snowpack model (water
flow, amount of MM snow) and as references for the analysis of the outputs of
the model (same variables, wet-bulb temperature). The data also helped the
characterization of the production conditions (wet-bulb temperature and wind
conditions). Based on communications with the snowgun manufacturer, the
uncertainty of water volumes used for snowmaking was neglected (below 1 %
according to the manufacturer).
The Coolidge ski slope conditions on 4 December 2015, the day before
the resort opened. Edges with unprepared areas and obstacles (trees, lift
infrastructures, snowgun) of the ski slope can clearly be
seen.
Observed water volumes used for production (red) and the equivalent
mass on the ski slope surface (blue). Bars stand for the daily production
(bottom). Production sessions when observations were performed on MM snow
piles (cyan bars) and dates when ski slope observations were carried out
(light brown) are outlined.
The study area was defined as being based on the local topography and the
initial surface of the ski slope. The Coolidge ski slope is wide (up to
75 m from January to March). It is a relatively flat grass covered
area. In such a case defining limits to the ski slope can be tricky and quite
subjective. In order to be as objective as possible and consistent throughout
the season we defined the following rules which were systematically applied:
All MM snow piles were measured on the total surface where MM snow was
observed, unless a major obstacle (a tree, a building) stood in the area,
bypassed by us.
The surface of the operational ski slope defined by the ski patrollers
changed during the ski season by a factor of up to 1.75, depending on snow
conditions. The ski slope was wider in January (6632 m2) and April
(7067 m2) than on 4 December (4063 m2) since there was very
little natural snow at this time. This also made the edge easier to identify
(Fig. ). On 20 January and 6 April we collected data
across the total of the marked out ski slopes even though the study area for
SD and SWE calculations was consistently limited to the area defined by the
edge on 4 December 2015 in order to provide comparable data. A sensitivity
test of the SD and SWE concerning the study surface was conducted by
considering an offset of ±2 m from the edge. The impact on SD and
SWE was computed and discussed.
The surface considered to calculate the MM snow production rate in the
model was defined as the total marked out ski slope area: the “useful” area
(Fig. ). Beyond the initial MM snow production (late
November) natural snowfall occurred and the ski slope was enlarged. The
enlarged area was thereafter defined as the spreading area for MM snow.
The relationship between the average snow depth (Sect. ) and the
study surface (defined by the 4 December 2015 edge) was explored through the comparison of the calculated snow depth
within the study area (4063 m2) and buffered surfaces of
±2 m from the edge of the study area (3425 and 4749 m2
respectively). Differences between a buffered snow depth and a snow depth
calculated for the study area are consistent over the three observation
sessions (data not shown). The larger the surface i.e. the further the edge
from the snowgun, the smaller the average snow depth. The average difference
is +0.03 and -0.03 m for the smaller (-2 m) and larger
(+2 m) areas respectively, showing little variation from one
observation session to another (5 % relative difference maximum). This
suggests that the surroundings of the study area undergo consistent
evolutions throughout the season and that to address the evolution of the
snowpack from initial observation the most important thing to do is to follow
the exact same area. This tends to confirm that the MM snow produced after
4 December 2015 was in fact spread over the total usable surface after the
slope was enlarged.
Snow depth measurement method and related uncertaintiesSnow surface elevation point measurements
Snow surface elevation was measured on several occasions
(Table ) thanks to a geodetic double frequency Differential
GNSS (GPS + GLONASS) Leica GS10 high precision receiver. A permanent
frame was set up close to the study area on 17 November 2015 in order to
provide a positioning antenna carrier at the reference station. The position
of the GPS antenna once mounted on this frame was post processed to obtain
the absolute position of the reference station within a few centimeters. To
measure points coordinates in the investigated area, we used a rover receiver
operating in real time kinematics (RTK) from the reference station. Specific
points were defined (painted dots on concrete ground) and systematically
re-measured during each GPS session as a control. The baseline
(reference-to-rover) was less than 500 m for every single session
which ensures a relative position from the reference station with a spatial
(3-D) accuracy below 0.02 m. The intrinsic uncertainty on the Z
(altitudinal) position of the Differential GPS was 0.012 m for all of
the observation sessions. The average density of points concerning the
measurement of the elevation of the MM snow piles surface was
11.1 m2 per point (±3.3 m2 per point) i.e. each point
covered a surface equivalent to a 1.88 m radius disk (±0.3 m).
The average density for the measurement of the elevation of the ski slope
surface was 16.4 m2 per point (±4.4 m2 per point) i.e.
each point covered a surface equivalent to a 2.29 m radius disk
(±0.31 m). The point density was adapted to the local conditions
(terrain complexity), for each session i.e. the larger the changes in the
snow surface, the more points were taken. This explains why the average
surface per point concerning the measurement of the elevation of the ski
slope surface (when snow surface is equalized by grooming machines) is larger
than that of MM snow piles.
The bare ground surface elevation was also measured on 17 November 2015 in
order to be compared with the snow-free helicopter-borne laser scan Digital
Elevation Model (DEM) of the area acquired in November 2015. Before checking
the elevation consistency between our GPS survey and this snow-free DEM, we
adjusted (-0.0032 m) the elevation of our reference station on a
local common levelling control point (800 m apart) provided by
Institut Géographique National (IGN).
Average difference and RMS of the differences between interpolated
snow surface elevation and Terrestrial Laser Scan measurements on a snow pile
(1 December 2015), between the elevation of bare ground with the GPS method
and the existing Digital Elevation Model (DEM) and between interpolated snow
depths and probe measurements on ski slopes
(Appendix ).
Comparison methodType/sessionNumber of pointsAverageRMS ofdifference (m)differences (m)Terrestrial Laser ScanGPS points156-0.00460.055Interpolated points8072 pixels (2018 m2)-0.0120.048Digital Elevation ModelGPS points1450.0320.047Interpolated points16 179 pixels (4044 m2)0.0030.064Probe manual measurements4 December 201513-0.0020.04120 January 20168-0.0190.0466 April 20168-0.0060.073All29-0.0080.053Interpolation on a regular grid
In order to compare snow surface elevations with each other or with the DEM
on the bare ground, data need to be interpolated on a regular grid. The
existing snow-free DEM had a spatial resolution of 0.5 m
(0.25 m2 pixels) which we nominated as the working grid. All data
were interpolated on this grid thanks to a preliminary Triangular Irregular
Network (TIN) method with a Delaunay natural neighbour triangulation
. The same method was used to treat all observation
sessions. Once interpolated on the working grid, all observation sessions
could be compared to each other or with the bare ground, providing a spatial
observation of the snow depth across the study area.
Such a method implies several sources of uncertainty (instrument,
interpolation) which we intended to assess through three distinct tests:
a high-resolution Terrestrial Laser Scan (TLS, ) was
used on 1 December 2015 on a MM snow pile which we also measured with the GPS
method. We were then able to compare the differences on both the GPS points
alone and the interpolated GPS points with the TLS points in order to obtain
the error that arises when interpolation is executed (effect of point
density).
Differences with the DEM of the bare ground of both the GPS points alone
and the interpolated points of the bare ground by the GPS method (17 November
2015) were calculated.
Hand made snow depth measurements were made on three occasions
(observations of the ski slope) with a probe and compared with the
interpolated snow depth by the GPS method.
Evaluation of uncertainties on snow depth
First of all we compared the interpolated snow surface elevations with data
from a Terrestrial Laser Scan (see Appendix for more
details). An average elevation difference of -0.012 m was measured
between the interpolated GPS and the TLS snow surfaces (2018 m2).
The Root Mean Square of the differences (RMSD) was 0.055 m
(Table ). A significant variability (standard deviation) was
measured within each 0.5×0.5m2 pixel thanks to the TLS
measurements: 0.031 m on average across the 8072 pixels. Secondly, we
compared the interpolated snow-free surface elevations with the existing
Digital Elevation Model of the ground. An average 0.003 m average elevation
difference was measured between the GPS interpolated ground surface and the
DEM data (4044 m2). The standard deviation of differences was
0.064 m (Table ). Lastly, the GPS interpolated snow
depth was compared with hand made measurements on several occasions
(Table and Appendix ). An average -0.008 m
average difference was measured between the GPS interpolated snow depth and
the manual observations. The standard deviation of differences was
0.053 m (Table ).
To sum up uncertainty analyses, the average difference in the snow surface
elevation interpolated from the Differential GPS points with respect to
either TLS measurements or DEM data, ranged between -0.012 and
0.003 m (Table ) whilst the RMS of the differences
ranged between 0.048 and 0.064 m. The distribution should
statistically not be considered as being normally distributed, though
distributions are close in both cases to normality
(Appendix ). Beyond these results we compared the interpolated
snow depth with hand made measurements. The agreement was excellent (average
error of -0.008 m, RMSD = 0.053 m) and a statistically
significant test for normality (Table ,
Appendix ). Regarding the internal variability of the snow
surface elevation within a pixel (0.031 m) and the sensitivity of the
snow depth to the study area, we therefore considered σSA=0.03m as the uncertainty concerning the elevation of the snow
surface. We also considered the error on the snow surface elevation to be
normally distributed, which was a reasonable approximation. Consequently the
combined uncertainties on the elevations of snow surfaces
(σSA) to obtain the snow depth uncertainty
σSD can be deduced assuming errors to
be uncorrelated and providing a consistent value to the calculated RMS of the
differences with the comparison methods (Table ):
σSD=2⋅σSA=0.042m.
Conversion of snow volumes into snow masses
The snow density was measured in several distinct locations on MM snow piles
using a dedicated snow sampler (1/2L) and by weighing the snow
samples. We used the average density and standard deviation of all
observations for the sessions when we could not perform density measurements
(23 November and 1 December 2015). The uncertainty on MM snow density
σρ for single snowmaking events was defined as the standard
deviation of all density measurements (Table ). The density
showed a weak variation of 4 % on MM snow density (Table )
from one production session to another. This supported the assumption that
one use the average and standard deviation of density across all observations
regardless of the dates when measurements were missing.
We also performed measurements of the average density of the snowpack on the
ski slope using a PICO coring auger for each session of
observations. The snowpack average density on the ski slope showed a
significant increase during the season. The uncertainty on the snowpack
density was defined as the variability (standard deviation) of all density
measurements for each single session (Table ).
Average MM snow density for each session of observations (top) and
average snowpack density observed on the ski slope for all three sessions
(bottom).
Date ofNumber ofAverageStandardobservationmeasurementsdensitydeviation(ρav, kgm-3)(σρ, kgm-3)Average density on MM snow piles (prior to any action by grooming machines) All sessions2143718Average density on the ski slope (as opened to skiers) 4 December 2015135453120 January 20168528376 April 2016961826
Whether on MM snow piles or on the ski slope, the Snow Water Equivalent (SWE,
kgm-2) was computed for each point of the grid by the
Eq. () between snow depth and density:
SWEpt=SDpt⋅ρav.
The uncertainty on the SWE is computed assuming that the uncertainties on the
snow depth (σSD) and density (σρ) are
independent and normally distributed . The uncertainty
on snow depth and density are considered to be ±σ therefore with a
standard confidence interval of 68 % .
σSWESWEav2=σSDSDav2+σρρav2
The uncertainty σSWE is obtained for each session thanks to
the the averages SWEav and SDav of the session by the
Eq. (). The resulting uncertainties σSWE
ranged between 20 kgm-2 for MM snow observations and up to
35 kgm-2 on ski slopes.
Modelling of snowpack conditions on ski slope
Crocus Resort is an adapted version of the multilayer physically based
snowpack model SURFEX/ISBA-Crocus . It explicitly takes
into account the impact of grooming and snowmaking .
Crocus Resort solves equations governing the energy and mass balance of the
snowpack on the ski slope. The model time step is 900 s
(15 min). All simulations in this paper with MM snow production
include the impact of grooming on the snow. The snow management component
Crocus-Resort of Crocus model requires the setting of a
series of grooming and snowmaking rules and thresholds. For grooming, we used
the standard approach described in . For snowmaking,
Crocus-Resort can be driven either with a target production framework, or by
using observed production time series as an input. In both cases, production
is only possible below wet bulb temperature and wind speed thresholds, and
the snowmaking efficiency, i.e. the mass of snow corresponding to the mass of
liquid water used (formally equivalent to the WRR), can be specified. The
default value is 1 (no water loss accounted for, see ).
In French mountain regions, Crocus Resort is usually run using outputs of the
meteorological downscaling and surface analysis tool SAFRAN
.
SAFRAN operates on a geographical scale on meteorologically homogeneous
mountain ranges (referred to as “massifs”) within which meteorological
conditions are assumed to depend only on elevation and slope aspects. All
simulations in this paper are based on meteorological forcing data from
SAFRAN corresponding to Les 2 Alpes site (elevation, slope angle and aspect).
We specifically analysed the natural snow conditions provided by
SAFRAN-Crocus Resort with in situ observations on a local scale from ski
patrollers and Automatic Weather Stations (wind, snow/rain elevation limit,
precipitation amount). If relevant we adjusted the SAFRAN meteorological
forcing data (amount and snow/rain phase of precipitations) to local
conditions for this site. The deposition rate of dry impurities on the
snowpack surface was also adapted to match the natural melting rate at the
end of the season . We also took into account the
surrounding slopes of each site and the consequent shading effects
. Lastly, the wet-bulb temperature was computed
from SAFRAN dry-air temperature and specific humidity using the formulation
from as described by .
efinition and computation of the water recovery rate
The Water Recovery Rate (WRR) is defined as the mass balance between the
initial mass of water used for production and the resulting mass of MM snow
(Eq. ). The WRR therefore ranges between 0 and 1, and can be
expressed in % and computed either for a MM snow pile prior to any action
by grooming machines or for a ski slope snowpack such as that offered to
skiers.
WRR=MasssnowMasswater=MasssnowMasswater=SWEav⋅SurfaceVolumewater⋅ρwater
The SWEav was computed as defined in Sect. .
The surface is determined by the study area. Since we neglected the
uncertainty on the volume of water used for snowmaking
(Sect. ), the uncertainty on the WRR is related to the
uncertainty on the SWE (Eq. ). σSWE was
computed as defined in Sect. .
σWRR=σSWE⋅SurfaceVolumewater⋅ρwater
We performed simulations of the ski slope conditions which took into account
recorded production (100 % water mass, Table ) and
where there was no production (0 % i.e. groomed only snow). We ran
additional simulations using water recovery rates values prescribed to Crocus
Resort below 1 and computed the RMS of the differences between the
simulations and the observations. We used distinct water recovery rates for
the first (20 November–5 December 2015) and the two later periods, regarding
the differences in production conditions (Table ).
We simulated snow conditions using water recovery rates from 100 to 30 %
with a step of 5 % and compared the snow conditions (SWE, SD) with the
observation on 4 December 2015. The simulations which provided conditions
within the range of uncertainty of the observations were selected.
From this initial step providing distinct potential snowpack conditions on
5 December 2015 we performed additional simulations over the second period of
the season (after 5 December 2015) using various water recovery rates
prescribed to Crocus Resort to determine the overall water recovery rate
based on the minimum RMS of differences between simulations and observations.
ResultsSingle snowmaking eventsObservations
Snow piles were usually not that far ahead of the snowgun with a significant
MM snow depth at the bottom or even at the back of it
(Fig. ) in consistency with the low wind speed
conditions observed in all sessions (Table ), mainly originating
from the East or South-East on average (wind direction not shown). All
observed snow piles showed similar geometric patterns
(Figs. and ) resulting in consistent
distributions of the snow around the center of the MM snow piles
(Fig. ). The uncertainty on the snow volume within a
distance from the snowgun was computed as the product of the surface within
the circle and the uncertainty on the snow depth (error bars in
Fig. ).
The snow depth raster for 23 November 2015 production session along
with the positions of the snowgun, the center of the MM snow pile and the
concentric circles of radius R=5, 10, 20 and 30 m. The edge of
the ski slope on 4 December 2015 is also shown.
Average snow depth (x) and cumulative snow volume (•) within
concentric circles around the center of the MM snow pile of radius R from
2.5 to 30 m. The larger the circle the lower the average snow depth
and thus the larger the uncertainty on the snow volume.
The water recovery rate (%) within concentric circles around the
center of the MM snow pile. The larger the circle the larger the uncertainty
on the snow volume and therefore the larger the uncertainty on the water
recovery rate.
The average snow depth and the resulting snow volume were calculated for each
session of MM snow production within concentric circles around a common fixed
point. This point was defined from observations and named “center of MM snow
pile” (identical for all sessions, Fig. ). The
equivalent water mass was calculated as the product of the average SWE within
the considered circle (Eq. ) and the surface of the disk inside
the circle, providing the mass of water (kg).
Detailed production conditions for every session, with the average
value in bold (±σ).
Session23 November 201524 November 201528 November 20151 December 201521 January 2016Water flow (m3h-1)18.4 (±1.7)18.2 (±1.7)17.1 (±1.7)13.1 (±1.7)12.4 (±1.7)Production duration (h)19.619.215.817.312.0Wet-bulb temperature (∘C)-8.1 (±1.5)-8.7 (± 1.1)-8.5 (±1.4)-7.5 (±1.1)-7.8 (±1.7)Wind speed (ms-1)1.82 (±0.8)1.06 (±0.48)0.53 (±0.53)0.56 (±0.47)0.53 (±0.58)Recorded water volumeused for snowmaking361351275227152(m3)
The water recovery rate within 10 m/ 20 m
(average value in bold ±σ) around the center of the MM snow
pile.
Performance of the snowpack model in simulating the natural snow
conditions before and after the adjusting of the meteorological forcing data
and impurities rate (Sect. ) quantified by the RMS of
differences between model and observations.
Natural snowRMS differences Melt-out dateSWESDDensity(kgm-2)(m)(kgm-3)ObservationsN=6 observations 1 April 2016SAFRAN – Crocus510.21826 April 2016Adjusted SAFRAN – Crocus140.14222 April 2016Water recovery rate from observations of single snowmaking events
The MM snow mass (kg) was calculated for single sessions of production
from the snow volumes (m3) within concentric circles around the
“center” point (Fig. ) and the MM snow density
(kgm-3, Table ). The MM snow mass was further
divided by the mass of water used for MM snow production for the given
session (Fig. , Table ), providing the water
recovery rate (WRR, %, Fig. ). The uncertainty on the
snow mass within a distance from the snowgun was computed as defined in
Sect. and divided by the mass of water used for MM snow
production for the given session to provide an uncertainty on the WRR
(σ in %, error bars in Fig. ).
Beyond a distance of 20 to 25 m from the center of the snow pile, the
MM snow volume no longer increases whereas the uncertainty is considerable
(over 10 %, Fig. ). This prevents any conclusion in
relation to the recovery rate including those areas. All sessions before the
resort opened showed an approximate 20 to 30 % water recovery rate within
10 m and 40 to 50 % within 20 m (Table ).
The 21 January 2016 session showed similar behavior with significantly higher
WRR (57 and 89 % within respectively 10 and 20 m distances). Such
differences are discussed further in Sect. .
Seasonal snow accumulationPerformance of the model in simulating natural snow conditions and wet-bulb temperatures
The computation of the uncertainty on the natural snow water equivalent was
based on the simulation results with and without correction of the forcing
data and impurities rate (Sect. ). The RMS of the differences
between the simulations and the in situ observations are highly reduced
(improved simulations) when fitting the meteorological forcing data to the
specificities of the site (Table ). The final RMS of the
differences on SWE (after corrections) is 14 kgm-2 and final
errors on the snow depth, SWE and density are similar to ,
confirming that SAFRAN-Crocus provides realistic simulations of the natural
snowpack evolution once adjustments are made in albedo (impurities) and
forcing data. We therefore assumed that the SAFRAN-Crocus Resort model would
also provide realistic simulations of the groomed snowpack. We accounted for
a larger uncertainty on the snow water equivalent of the groomed snowpack
(σSWE=30kgm-2 i.e. 0.06 m uncertainty on
snow depth for a 500 kgm-3 density, ).
Apart from the natural snow conditions, the cumulated time-span over which
wet-bulb temperature fell within specific ranges was calculated for the MM
snow production period i.e. from 20 November 2015 until 15 March 2016, both
from the in situ data recorded by the snowgun sensor and the data from SAFRAN
(Fig. ). The distribution of the wet-bulb temperature from
SAFRAN meteorological data is very consistent with the Tw
distribution from the snowgun sensor.
Observed production conditions for the main periods of production
before and after the resort opened.
The production period was divided in the model into three distinct periods:
before and after the resort opened (5 December 2015) and after 1 February
2016, the reasons being that the average conditions significantly differ
(Table ) and the ski slope surface opened to skiers was
significantly enlarged as the season progressed, modifying the usable surface
of the ski slope.
As a result, we used the water flow recorded by snowmakers and the observed
ski slope surface area (Table ) to force the MM snow
precipitation rate in the model which is constant for each period (expressed
in kgm-2s-1). The daily production time was set in the model
to match the observed daily production (expressed in kgm-2,
Fig. ). A wet-bulb temperature threshold of
-3.5 ∘C was found to be the minimum temperature for the triggering
of snowmaking which afforded the production of the observed amount of MM snow
during the first period (21 November–5 December). Afterwards, the observed
MM snow production could be simulated using a triggering temperature of
-5 ∘C.
Cumulated time-span over which wet-bulb temperature fell within
specific ranges, from the in situ data (snowgun sensor) and SAFRAN
(20 November 2015–15 March 2016).
The average SWE observed on the ski slope (SWEav) along
with the standard deviation of the raster values within the study area
(Fig. ) and the uncertainty (σSWE)
resulting from the computation in
Sect. .
Date ofSnow water equivalent observation(kgm-2) AverageSpatial variabilityUncertaintySWEav(standard deviation)σSWE4 December 2015278872820 January 2016393111356 April 201650112033Observations and modelling of the seasonal snow accumulation
The variability of the snow depth (Fig. ) and thus of
the associated snow water equivalent (SWE) on the ski slope was significant.
The variability (standard deviation) of the SWE values in the study area
showed a factor from 3 to 4 with the uncertainty σSWE
(Sect. , Table ). Two major observations
can be made from the distribution of the snow depth on the ski slope
(Fig. ):
the shape of the MM snow piles was not completely erased by the grooming
machines. The maximum values of snow depth surrounded the center of the MM
snow piles in December and January and was slightly further in April. This
may be due to the slow erosion of the snow towards the bottom of the slope by
skiers, despite the work made by the grooming machines;
the initial distribution of the MM snow on the “useful area” defined
on 4 December 2015 could still be noticed on the two latest dates (e.g. the
northern and southern edge).
Snow depth mapping for the three observation dates 4 December 2015
(top), 20 January 2016 (center) and 6 April 2016 (bottom). See
Appendix for details on the location of the observation
site.
The average SWE difference between the simulation accounting for MM snow and
the observations was 172 kgm-2
(RMSD = 204 kgm-2) whilst between the simulation of groomed
snow (no production) and the observations the average difference was
-239 kgm-2 (RMSD = 282 kgm-2). On the three
observation dates, neither of the two simulations provided conditions (SD,
SWE) within the range of uncertainty of observations. Even though accounting
for MM snow production significantly improved the simulation, the differences
with observations remained high and suggested the actual amount of MM snow
stood between these two simulations.
Based on the observations and the simulations of the natural and groomed
snowpacks, we calculated the number of days when the snowpack equivalent
water mass exceeded thresholds of 1 and 80 kgm-2 i.e.
respectively the number of days with snow on the ground
and with suitable conditions for skiing (a minimum of 20 cm of snow
with a density of 400 kgm-3, ). The following
number of days were calculated:
Concerning the natural snow, the ground was covered by snow for 107 days
and the SWE exceeded 80 kgm-2 for 48 days of the season.
Concerning the groomed snowpack (no production), the ground was covered
by snow for 133 days and the SWE exceeded 80 kgm-2 for 82 days
of the season.
Concerning the ski slope (grooming plus snowmaking), the ground was covered
by snow for 165 days and the SWE exceeded 80 kgm-2 for 159 days
of the season (estimated from the observed melt-out date and the melting rate
between 6 April and 3 May 2016).
In Les 2 Alpes ski resort, the ski season lasted from 5 December 2015 until
30 April 2016 i.e. 148 days. The days when the ground was covered by either
natural or groomed snow were not consecutive: the snow melted entirely in
late December and there was no snow during the Christmas holidays in both
cases. Even though grooming significantly lengthened the snow cover period,
the length of the season with suitable skiing conditions was far shorter than
the period open to skiers (82 instead of 148 days). The production of MM snow
therefore achieved the objective for the provision of consecutive days with
snow on the ground, ensuring suitable conditions for skiing during the
Christmas holidays and a sufficiently long skiing season.
Water recovery rate from observations and simulations of the seasonal snow accumulation
The MM snow mass was calculated as the difference between the observed total
mass of snow within the edge of the ski slope and the mass of natural snow
from the simulated groomed snowpack (Sect. ). The MM snow mass
was further divided by the cumulated mass of water used for MM snow
production up until the date of observations (Fig. ,
Table ), providing the water recovery rate
(Table ). Note that this calculation is based on each date
on the total surface of the marked ski slope. This means that a significant
part of the early production (before 5 December 2015) may have fallen beyond
the edge of the ski slope when opened to skiers on 4 December 2015 but
within the edge of the ski slope when opened to skiers on 20 January 2016
(or 6 April 2016). This may partially explain the higher recovery rate on
20 January and 6 April 2016 compared to 4 December 2015
(Table ).
Water recovery rate (Average value in bold ±σ) from
observations of the snow mass difference between ski slope snow conditions
and simulated groomed snowpack conditions (i.e. without
snowmaking).
DateSki slope surfaceCumulated water massObserved mass differenceWater recovery rate(m2)for production (kg)(kg)(%)4 December 201540631629×103974×103 (±167 ×103)59.8 (±10.2)20 January 201666322286×1031551×103 (±306 ×103)67.9 (±13.4)6 April 201670672947×1031896×103 (±315 ×103)64.3 (±10.7)
Considering the first period of production (20 November–5 December 2015),
the simulations provided conditions within the range of uncertainty of the
observation for water recovery rates of 65, 60 (minimum RMS of differences)
and 55 % (Table ). From this initial step providing three
potential snowpack conditions on 5 December 2015 (Fig. ),
we performed twelve simulations across the second period of the season (after
5 December 2015) using four distinct water recovery rates of 100, 65, 55 and
45 %. Of these twelve simulations, three provided results within the
range of uncertainty for all three dates of observations (n=3,
Table ) along with the minimum RMS of differences on the SWE
(10–20 kgm-2). Detailed results can be found in
Table .
Seasonal evolution of the ski slope snowpack. Simulations of natural
snow and groomed natural snow conditions are shown along with simulations of
the ski slope conditions including MM snow production, accounting for water
recovery rates (WRR) of 100 %, 65 % and the three combinations
(Table ) which provided the best agreement with the
observations (dots with error bars).
These results suggest that 55 to 65 % of the total water mass used for
production can be recovered as MM snow within the edge of the ski slope
during the first period. This is consistent with the water recovery rates
calculated in Sect. . The sensitivity test on the water recovery
rate did not show any significant difference between the first period of
production compared to later in the season. The water recovery rate may even
be slightly lower with 45 to 55 % of the SWE observed on the ski slope.
The season duration was computed from simulations similar to
Sect. for the three combinations of water recovery rates
providing the best agreement with observations (Table ). The
ground was covered by snow for 170 to 171 days and the SWE exceeded
80 kgm-2 for 164 to 166 days during the season, which is
consistent with the observed lengths (Sect. ). The bias on the
ski season duration and total melt-out date is attributed to a lower melting
rate in the snow model compared to observations: an average -15.8 to
-16.2 kgm-2day-1 for the simulations using the three
combinations of water recovery rates (Table ) with respect to
-17.8 kgm-2day-1 for the observations from 1 April 2016
to the total melt-out date.
Performance of the snowpack model in simulating ski slope snow
conditions. n is defined as the number of simulations found within the
range of uncertainty for the observation dates. The RMS of the differences
between the simulations and the observations are detailed for the 100 and
65 % water recovery rate (WRR) simulations, for the three combinations of
WRR which provided the best agreement with the observations
(Fig. ) and for the simulation of the groomed snowpack (no
production, WRR = 0 %). Period 1 extends from 20 November until
5 December 2015. Periods 2 and 3 extend from 5 December 2015 until the
melt-out date.
Water recovery rate nRMS difference Melt-out datePeriod SWESDDensity12 and 3(kgm-2)(m)(kgm-3)Observations N=3 observations 3 May 20160 %0 %02820.518910 April 2016100 %100 %02040.285015 May 201665 %65 %1510.035110 May 201660 %45 %390.05639 May 201655 %55 %3150.04549 May 201655 %45 %3110.07628 May 2016
The interest in both the professional (technical issues, investments) and
research (climate change investigations) approaches of the production of snow
lies in the consideration of the amount of “useful” additional MM snow that
can be used on the ski slope. Any difference between the mass of water used
for production and the additional snow mass on the ski slope can be
considered as water loss in the mass balance. Such losses may be due either
to the evaporation and sublimation of water droplets or snow particles
(thermodynamic effects). They may also be due to the produced snow falling
beyond the edge of the ski slope (mechanical effects). We intend in the
following sections to address the impacts of such effects.
DiscussionsWater losses due to thermodynamic effects (evaporation and sublimation)
Losses related to evaporation and sublimation can be calculated for the sake
of the present study thanks to the linear relationship proposed by
. Although significant changes in snowguns technology have
occurred in the last 30 years, this work remains at present the most detailed
on this topic to the best of our knowledge. We might also consider this
approach as a “worst case” scenario since the technological evolution has
presumably evolved positively since, for better efficiency. The observed
average temperatures of production were respectively -9.5, -6.7, and
-6.9 ∘C for the first, second and third periods of production
(Table ), resulting in respectively 5.84, 7.9, and
7.7 % water losses due to water vapor evaporation from droplets and
sublimation of ice particles, both during and after their deposition on the
ground . The overall water loss over the total
2947 m3 used for snowmaking would be 6.7±3 %
, i.e. well below the observed differences in the present
study. Evaporation and sublimation processes may explain to some extent the
differences reported by either , ,
or those observed in the present study. An overall water
loss of 40 % (±10 %) was observed and simulated, in which less
than 10 % may be due to thermodynamic effects according to
. This results in an additional mechanical water loss of
approximately 30 % of the total water mass used for MM snow production.
The influence of external factors (topography, wind) proves a major concern
for water loss.
Water losses due to mechanical effects
Although the wind conditions were ideal, a significant amount of snow was
found at the toe or even at the back of the snowgun (Sect. ).
Wind drift of already deposited MM snow was very unlikely due to both the
density and the cohesion of snow grains (capillarity/refrozen water). Since
snowguns are usually installed on one side of the ski slope, a part of the
production may fall outside the slope, behind the snowgun. The MM snow may
also fall beyond the edge of the slope on the opposite side of the snowgun.
performed a detailed study of technical snow in an
Austrian ski area with 37 km of ski slopes for a total surface of
92 ha i.e. average ski slopes of 25 m in width.
reported similar data from a survey of French ski
resorts with average ski slope widths of 20 m. The width of a ski
slope may have a significant impact on the amount of MM snow falling within
the edge of the ski slope in terms of the equivalent water masses of MM snow
piles within 10 to 20 m from the center point (Table ).
These results also suggest that the best position of a snowgun is, if
possible, in the middle of the ski slope (as is already the case in certain
situations).
The surroundings of the ski slope are very important for the computing of the
amount of “useful” MM snow. If the slope can be enlarged (as is the case
for Les 2 Alpes Coolidge slope), the MM snow falling outside the initial edge
of the ski slope can either be displaced by grooming machines or used for the
extension of the slope. In the opposite case where the surroundings have
complex topography (e.g. rough surfaces, with rocks) or are covered by
vegetation (trees), the amount of snow falling beyond the edge of the ski
slope is definitively lost. Consequently the potential for the extension of a
ski slope is a significant factor for differences in MM snow efficiency
between slopes (or even resorts). As a focus for this point, the study site
may not be representative of the majority of ski slopes. The Coolidge slope
is wider (it has a minimum width of 45 m, and a maximum of 75 m) than
the ski slopes with average dimensions that have been referred to
. This makes it a favourable site for the
efficiency of MM snow: a maximum amount of the produced snow can be found
within the edge of the slope. The total mass of water used for MM snow
production also exceeds usual amounts: found that the
usual capacity of water reservoirs was 150–190 kg of water per
m2 for an equipped ski slope with snowmaking facilities with a
maximum of 390 kgm-2. In the present case, 2947 m3 of
water were used for snowmaking (Table ) across a maximum
ski slope surface of 7067 m2 (Sect. ) i.e.
417 kgm-2.
The influence of meteorological conditions on the efficiency of MM snow
remains unknown to a great extent and requires further observation in order
to be analysed, in light of the findings from .
Meteorological conditions observed in this study appeared ideal for the
production of MM snow: low wind speed and temperatures (Table ).
Such investigations may prove useful for operational purposes in providing
objective data on the impact of producing snow in extreme conditions of wind
or temperature.
The “Quality” parameter of MM snow chosen by professional snowmakers may
also have a significant impact on the water recovery rate
(Tables and , Figure ). The
sessions concerning 21 January 2016 and 1 December 2015 differ mainly due to
the parameterization of the “Quality” with significant differences in the
WRR. To the best of our knowledge this parameter acts on the volume of
compressed air versus water volumes within the cloud expelled by the snowgun.
There are objective reasons why this parameter has a significant impact on
the water recovery rate. Higher air/water ratio leads to a lower specific
humidity in the cloud of droplets and thus a lower gradient with the
surrounding ambient air. This likely leads to decreasing latent heat
exchanges (evaporation and sublimation) and increasing sensible heat transfer
i.e. further freezing due to a higher surface for heat transfer between
liquid water and air. Lastly, a lower water flow means a lower speed for
droplets when they are expelled by the snowgun. There is then a higher
probability that they fall within the edge of the ski slope. To provide an
example, on 28 November 2015 the water mass used for production was
275×103kg, leading to 159×103kg of snow
(WRR = 53 %, Tables and ). On 21 January
2016, the water mass was 152×103kg whilst the snow mass was
135×103kg (WRR = 89 %). The water mass used on
28 November 2015 was 1.8 times higher than that of 21 January 2016 which had
only 1.08 times more in terms of snow mass. Further investigations are
required to improve our understanding of the impact of this parameter and to
confirm its influence.
Limitations of this work: assessment of water recovery rates and current modelling of ski slope snowpacks
The MM snow mass within the edge of the ski slope was computed from
observations (Sects. and ) or simulations
(Sect. ) and compared with the recorded mass of water used for
production. These computations provided consistent values of the water
recovery rate for the first period of production (before 5 December 2015)
with 60 % of the total water mass used for production within the edge of
the ski slope open to skiers. Afterwards, the observations of the total mass
of snow showed a higher WRR when accounting for the total surface of the ski
slope (Sect. ) compared with calculations with the surface limited
to the edge of the ski slope on 4 December 2015 (Sect. ). This
suggests that a part of the initial production may have fallen beyond the
initial edge of the ski slope. This higher WRR could also be due to an
improved recovery of individual productions after 5 December 2015 as
suggested by the observations on the MM snow pile on 21 January 2016.
Simulations performed from the initial conditions of the snowpack on
4 December 2015 suggest however that the WRR is lower for the subsequent
period than for the first. Several factors may explain these differences in
the WRR. They could either be related both to objective factors not accounted
for and to some weaknesses of the method. We intend hereafter to address such
factors:
The representativity of observations may be questioned. The observations
of MM snow piles (Sect. ) covered 75 % of the total mass of
water used for production during the first period (1214 out of
1629 m3) while they covered only 11 % of the production after
5 December 2015 (152 out of 1318 m3). The observation on 21 January
2016 may not be representative of the whole period of production after
4 December 2015.
The difficulty in monitoring human action on the ski slope (e.g. snow
displacement by grooming machines) is a potential source of error. The
distribution of snow on 6 April 2016 (Fig. ) suggests
that there was a significant volume of snow displaced from the study area
(within the 4 December 2015 edge) to the North-West corner of the ski slope
(6 April 2016). Such displacements of snow may explain why the observed snow
mass within the initial edge (4 December 2015) did not increase in the second
period of production as we expected from initial snow conditions and further
MM snow productions (after 4 December 2015).
Thirdly, the snowpack evolution highlights strong non-linear thermal
behavior the effect of which might be significant for
this study. In one case the natural and groomed snowpacks in December
completely melted, in the other the simulations accounting for the production
of MM snow did not show a significant loss of equivalent water mass within
the same period (Fig. ). Consequently, the SWE of the
groomed snowpack on 4 December 2015 might not be lost on the ski slope and
should be subtracted when calculating the mass of MM snow
(Sect. ). If accounting for an additional 20 kgm-2
equivalent water mass on the 4 December 2015 snowpack, we obtain adjusted
water recovery rates of respectively 62.1 and 59.5 % for 20 January and
6 April 2016. These corrected WRR are closer to those computed for the first
period (59.8 %, Sect. ) and would tend to confirm that there is
no significant difference in the WRR between the first and the two latest
periods of production.
Lastly, complementary observations might have reduced the uncertainty
across estimations of the equivalent water recovery rate (an observation was
performed on 2 March 2016 but could not be treated due to a GPS failure
lasting until early April). Since the calculation of the mass of MM snow
(Sect. ) depends on the snow water equivalent of the groomed
snowpack, observations on ski slopes without production would have been of
great help. Every slope in study site surroundings is, however, equipped with
MM snow facilities or is under the influence of these facilities. Extra
observations on MM snow piles after 5 December 2015 could have clarified
whether or not the higher WRR observed on 21 January 2016 was representative
of the period or not. Additional observations with different types of
snowguns would also have been of interest, although the snowgun used at the
observations site is the most sold air/water gun of a brand which
manufactures approximately 80 % of the snowmaking facilities in French
ski resorts (communication from the manufacturer). It may therefore be
considered as representative of the current technology.
One dimensional (z-vertical) models feature several limitations for the
simulation of ski slope conditions. These are highlighted in the present
study through the bias on the total melt-out date related to lower melting
rates of the simulations with respect to the observations.
Firstly, the model can not account for snow/ground partitioning. The
variability of the snow depth on the ski slope (Fig. ,
Sect. ) showed there were horizontal heterogeneities of snow
properties, either due to the mass transport by skiers or the partial
spreading of MM snow piles by grooming engines. This is particularly obvious
when the total melting of the natural (and even groomed) snowpack in December
and April made the ski slope an isolated snow patch in a mostly snow-free
area with strong edge-effects. In such a situation the energy balance of the
snowpack can be significantly affected by the modification of turbulent
fluxes and horizontal ground fluxes from snow-free areas
in the vicinity . Since snow free areas have lower albedo
values than the snow and are not limited to a 0 ∘C maximum
temperature, they can become significantly warmer than the surrounding snow
and advect heat to the snow through the air (and respectively the ground),
providing additional sensible heat energy to the snowpack. These two effects
of the snow ground partitioning would enhance the melting rate in the model
if they were accounted for, which is not the case.
Secondly, the initial content of impurities in MM snow may also differ
from natural snow. The amount of impurities in a snow layer is based on
Crocus in both an initial value of impurities (i.e. initial albedo) and a
deposition rate of dry impurities on the snowpack . There is
no reason for the dry deposition to show a difference between natural snow
and the snow on ski slopes (at the same location). The initial amount of
impurities in MM snow could differ however from that in natural snow: the
water used for production is stored in open reservoirs and probably contains
more impurities than snow can capture in the air during growth and
precipitation. This could be a reason for a lower albedo of MM snow which
would also enhance the melting rate on ski slopes.
Conclusions
The present study carried out detailed observations and
simulations of snowmaking events and of the seasonal snow evolution of a ski
slope snowpack in Les Deux Alpes ski resort (French Alps). The production of
MM snow concentrated on the early season with approximately 50 % of the
seasonal production realized within one week in late November
(Fig. ). The production of MM snow significantly improved
the possibility of skiing at the observation site with suitable conditions
from the opening (5 December 2015) to the closing date of the resort
(30 April 2016).
We provided spatial observations of the snow depth and snow water equivalent
of MM snow piles and of the ski slope once it was opened to skiers. A high
spatial resolution of the snow surface elevation was used (0.5 m grid)
thanks to measurements by a Differential GPS method. The related
uncertainties were computed with a final uncertainty of 0.042 m on
snow depth. The density of snow was measured thanks to snow sampling and
weighting, with uncertainties ranging between 4 and 7 %
(Sect. ).
The mass balance between the MM snow mass and the water mass used for
snowmaking was defined as the water recovery rate. The observations of
snowmaking events showed similar distributions around the center of the MM
snow pile with approximately 30 % WRR within 10 m and 50 %
within 20 m for production sessions in the early season
(Sect. ). The water recovery rate within the ski slope edge was
computed on three occasions with approximately 60 % (±10 %) of
the water mass used for snowmaking recovered as MM snow
(Sects. and ). The WRR was found to be
relatively constant between observations and simulations and between the
different periods of the season. The water losses due to thermodynamic
effects were calculated from linear approximation with less
than 10 % of the total water mass either evaporated or sublimated
(Sect. ). Over 30 % of the water used for snowmaking
probably turned to MM snow therefore, but could not be recovered within the
edge of the ski slope, certainly due to mechanical effects (suspension and
erosion by the wind, obstacles, etc) while production conditions can be
considered as ideal (low wind speed and temperatures, large ski slope).
The water recovery rate of the snowmaking process poses therefore a tricky
question regarding its likely dependence to both sites' characteristics
(topography, vegetation) and human decision (attention to marginal
conditions, quality parameter, etc.). Estimating a single value appears to be
impossible even though the best conditions together (as can be considered in
the present study) showed that a significant fraction of the water used for
production was lost for the ski slope. The water recovery rate would have an
optimum value when the most favorable conditions occurred together. An
objective one is definitely the local topography: less than 50 % of the
water mass can be expected within the edge of a typical ski slope width
(approximately 20–30 m, Sect. ) with snowguns on the
side and perpendicular to the slope (a typical installation). The authors
also hypothesize that the wind may have a strong impact on the distances
covered by water droplets and ice particles as well as the quality parameter
chosen by professional snowmakers (although further investigation of such
influences is needed).
Characterizing the actual mass of MM snow that can be recovered on ski slopes
from a given mass of water remains a major issue for ski resorts regarding
the current development of snowmaking facilities and the
related costs of investments and production . Significant
water losses may question the economical interest of snowmaking for resorts
where periods with suitable meteorological conditions are limited in addition
to deteriorating factors for the efficiency of MM snow (obstacles e.g. trees,
wind).
The data used for this publication are available upon request from the authors.
Situation of the observations site
(a) Observations site from above. Temporary structures in
the top left corner were not present during the winter season.
(b) A picture of the production session on 27 November 2015. MM snow
can be seen on the tree and on the cables of the ski lift.
Evaluation of uncertainties on snow depth
Probability density of the elevation differences between the
interpolated snow surface and the TLS snow surface on 1 December
2015.
We used an Optech Ilris-LR laser scanner thewavelength of which
(1064 nm) is adapted to the low reflectance of the snow in the
infra-red spectrum. The laser scan point cloud was adjusted on targets the
coordinates of which were determined thanks to a total station. The internal
consistency of the target network was ±0.0038 m and its relative
positioning with respect to the GPS reference station was 0.008 m in
planimetry and 0.013 m in elevation. We conducted Shapiro–Wilk tests
for normality over samples of 5000 differences between
interpolated elevations and the TLS measurements (see below the average
results). All tests suggest that the differences on snow surface elevation
should not be considered as normally distributed even though the distribution
is coherent with a normal distribution (Fig. ).
Statistical value w=0.979
p value =1.48×10-25 (< 0.05)
Secondly, we compared the interpolated snow-free surface elevations from the
existing Digital Elevation Model of the ground. We conducted once more
Shapiro–Wilk normality tests over samples of 5000
differences between interpolated ground elevations and the Digital Elevation
Model data (see below the average results). All tests suggest that the
differences should not be considered as normally distributed even though the
distribution appears to be very consistent with normality
(Fig. ).
Statistical value w=0.951
p value =1.59×10-34 (< 0.05)
Lastly, the GPS interpolated snow depth was compared with hand made
measurements on several occasions (Table ,
Fig. ). We conducted a Shapiro–Wilk normality
test to ascertain the differences between interpolated
snow depth and the manual measurements (see below). This suggests that the
differences on snow depth are normally distributed:
Statistical value w=0.963
p value = 0.38 (> 0.05)
Probability density of the elevation differences between the
interpolated bare ground surface and the Digital Elevation Model ground
surface.
Interpolated snow depth from GPS method with respect to the hand
made probe measurements for each observations session of ski slope. Average
difference and RMS of the differences are detailed in
Table .
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors thank Fabian Wolsfperger and two additional anonymous reviewers
for their helpful comments and suggestions. The authors also wish to thank
A. Guerrand (Les Deux Alpes Loisirs) for sharing all details about the
management of snow in Les Deux Alpes ski resort, the IGE (Institut des
Géosciences de l'Environnement, Grenoble, France) for provision of the PICO
coring auger (D. Six). We also acknowledge the assistance of F. Ousset
(Irstea), Y. Deliot and G. Guyomarc'h in the set up and analysis of field
observations, M.Dumont in the parameterization of impurities in Crocus as
well as A. Dufour, L. Queno, L. Charrois and J. Revuelto in the fulfillment
of observations (all CNRM/CEN). The Région Rhônes-Alpes funded Pierre
Spandre's PhD through ARC Environment. This work has been supported by a
grant from “Eau, Neige et Glace” foundation, from the LabEx OSUG@2020
(Investissements d'avenir – ANR10LABX56), and fundings from SO/SOERE
GLACIOCLIM, IGE, IRSTEA, and CNRM/CEN.
Edited by: R. Brown
Reviewed by: F. Wolfsperger and two anonymous referees
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