NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-869-2018Modeling the influence of snow cover temperature and water content on wet-snow avalanche runoutVera ValeroCesarcesar.vera@slf.chWeverNanderChristenMarcBarteltPerryWSL Institute for Snow and Avalanche Research SLF, Flüelastrasse 11, 7260 Davos Dorf, SwitzerlandÉcole Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering, Lausanne, SwitzerlandCesar Vera Valero (cesar.vera@slf.ch)19March201818386988725January20177March20173February20188February2018This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/18/869/2018/nhess-18-869-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/869/2018/nhess-18-869-2018.pdf
Snow avalanche motion is strongly dependent on the temperature and water
content of the snow cover. In this paper we use a snow cover model, driven by
measured meteorological data, to set the initial and boundary conditions for
wet-snow avalanche calculations. The snow cover model provides estimates of
snow height, density, temperature and liquid water content. This information
is used to prescribe fracture heights and erosion heights for an avalanche
dynamics model. We compare simulated runout distances with observed avalanche
deposition fields using a contingency table analysis. Our analysis of the
simulations reveals a large variability in predicted runout for tracks with
flat terraces and gradual slope transitions to the runout zone. Reliable
estimates of avalanche mass (height and density) in the release and erosion
zones are identified to be more important than an exact specification of
temperature and water content. For wet-snow avalanches, this implies that the
layers where meltwater accumulates in the release zone must be identified
accurately as this defines the height of the fracture slab and therefore the
release mass. Advanced thermomechanical models appear to be better suited to
simulate wet-snow avalanche inundation areas than existing
guideline procedures if and only if accurate snow cover information is
available.
Introduction
Avalanche hazard mitigation has historically concentrated on catastrophic
avalanches releasing from dry, high alpine snow covers. There are many regions
in the world, however, where wet-snow avalanche problems are dominant.
Increasingly, avalanche engineers require methods to consider the avalanche
hazard arising from frequent wet-snow slides .
The runout of wet-snow avalanches is especially difficult to calculate
because temperature and liquid water content (LWC) have a strong influence on
the mechanical properties of snow . When warm
snow contains liquid water, the deformation mechanics are controlled by the
liquid film at the grain-to-grain contact . Wet snow can be
plastically deformed until it reaches “packed density”. Granules in wet-snow avalanches are therefore large, heavy and poorly sorted in comparison to
granules in dry avalanches . The bulk flow
viscosity and cohesion of wet-snow avalanches is larger than in dry flows
. The formation of levees with steep vertical shear planes
in wet-snow avalanche deposits is another indication of the viscous and
cohesive character of wet-snow avalanches .
An increased bulk flow viscosity, however, is not the only mechanical change
induced by warm, moist snow. The presence of liquid water on interacting snow
surfaces decreases the magnitude of the bulk sliding
friction coefficient. This decrease has been observed and quantified in many
experiments, particularly those involving ski friction . The decrease in sliding friction results in long-runout
avalanches , making wet-snow flows particularly dangerous.
To model the lower flow velocities associated with wet-snow flows, the Swiss
guidelines on avalanche calculation recommend increasing the velocity-squared
turbulent friction . Wet-snow avalanches are therefore treated
as dense granular flows in the frictional flow regime . Because measured velocity profiles of wet-snow avalanches
exhibit pronounced viscoplastic, plug-like character, they are often modeled
with a Bingham-type flow rheology . uses cohesion to reduce the random
kinetic energy of the avalanche core which effectively hinders avalanche
fluidization and prevents the formation of mixed flowing/powder avalanches
.
The sensitivity of wet-snow avalanche flow on temperature and moisture
content makes predictions of avalanche runout difficult. For example, wet-snow
avalanches often occur after extreme precipitation events followed by
intense warming. Because of differences in snow cover temperature and water
content between the release and runout zones, wet-snow avalanches can start
in sub-zero temperatures and run into moist, isothermal snow covers. That is,
sub-zero release areas can lead to the formation of dry mixed flowing/powder
type avalanches that transition at lower elevations to moist, wet flows.
Clearly, a wet-snow avalanche model must account for the initial temperature
and water content of the snow cover.
In this paper we use snow cover models to establish the initial and boundary
conditions for wet-snow avalanche dynamics calculations. We specify snow cover
information that is derived from detailed physics-based snow cover model
simulations using SNOWPACK . Unlike
existing approaches e.g.,, avalanche dynamics
parameters will not be tuned but are fixed within the framework of empirical
functions parameterized by snow density, temperature and moisture content
. Our goal is to obtain accurate runout and deposition
predictions without ad hoc modifications to avalanche model parameters.
Instead of parameter optimization, we specify snow height, density,
temperature and moisture content in both release (initial conditions) and
entrainment zones (boundary conditions) as input data for the model.
The approach consists of three basic steps (see Fig. ):
simulation of snow cover conditions using measured weather data as
input,
simulation of avalanches using initial conditions defined by snow cover
conditions,
contingency table analysis to define the statistical score of avalanche runout calculation.
The procedure is applied to simulate 12 documented avalanche events, for
which extensive field measurements are available, including measurements from
airborne laser scans, drones and photography, and hand-held GPS devices. To
determine how the procedure performs, we compare the area covered in the
simulations with the deposit area measured in the field. Simulated runout
patterns are compared to field observations. The correspondence of observed
deposits and calculated deposits is checked using a dichotomous contingency
table, splitting the terrain into four different classes: hits, misses, false
alarms and correct negatives.
Flow diagram depicting the three-step model chain. The
procedure begins by simulating snow cover conditions using measured weather
data as input. Next, avalanche runout is simulated using initial and boundary
conditions defined by snowpack modeling. Finally, a statistical score of the
avalanche runout modeling is calculated.
Additionally, a sensitivity study is performed by interchanging the initial
and boundary conditions of the 12 case studies and by varying the
calculation grid cell size. The same contingency analysis and runout
comparison are performed with the results obtained from the sensitivity
analysis. This establishes to what extent the initial and boundary conditions
indeed control the model performance.
Wet-snow avalanche modeling
Wet-snow avalanche modeling necessitates the simulation of four physical
processes :
the rise in avalanche temperature by frictional dissipation,
phase changes and the production of meltwater,
entrainment of snow mass and the associated internal
(thermal) energy change of the avalanche,
constitutive models describing how the avalanche flow rheology changes as a function of temperature and moisture content.
One model that fulfils these requirements was developed by
and.
Avalanche core
The flow of the dense avalanche core (subscript Φ) is described by nine
independent state variables:
UΦ=(MΦ,MΦuΦ,MΦvΦ,RΦhΦ,EΦhΦ,hΦ,MΦwΦ,NK,Mw)T.
These variables include the core mass MΦ (which contains both the ice
mass and the water mass Mw); the flow height hΦ;
depth-averaged velocities parallel to the slope uΦ=(uΦ,vΦ)T, and, in the slope-perpendicular
direction wΦ, the sum of the kinetic and potential
energies associated with the configuration and random movement of snow
particles RΦ and the internal heat energy (temperature) EΦ.
The formulation includes the dispersive pressure NK.
The model equations can be written as a single vector equation:
∂UΦ∂t+∂Φx∂x+∂Φy∂y=GΦ,
where the components (Φx, Φy,
GΦ) are
Φx=MΦuΦMΦuΦ2+12MΦg′hΦMΦuΦvΦRΦhΦuΦEΦhΦuΦhΦuΦMΦwΦuΦNKuΦMwuΦ,Φy=MΦvΦMΦuΦvΦMΦvΦ2+12MΦg′hΦRΦhΦvΦEΦhΦvΦhΦvΦMΦwΦvΦNKvΦMwvΦ,GΦ=M˙Σ→ΦGx-SΦxGy-SΦyP˙ΦQ˙Φ+Q˙Σ→Φ+Q˙wwΦNK2P˙ΦV-2NwΦ/hΦM˙Σ→w+M˙w.
The flowing avalanche is driven by the gravitational acceleration in the
tangential directions G=(Gx,Gy)=(MΦgx,MΦgy). The model equations are solved using the same numerical schemes as
outlined in .
The model assumes nonzero slope-perpendicular accelerations and therefore
calculates the slope-perpendicular velocity of the core wΦ. The center of mass of the granular ensemble moves
with the slope-perpendicular velocity wΦ. When wΦ> 0, the
granular ensemble is expanding; conversely when wΦ< 0, the volume
is contracting. The densest packing of granules defines the co-volume height
0hΦs and density 0ρΦs.
The co-volume has the property that hΦs≥0hΦs and
ρΦs≤0ρΦs. The normal pressure at the base of the
column N is therefore no longer hydrostatic but includes the impulsive
reaction NK associated with the slope-perpendicular accelerations
:
NK=MΦw˙Φ.
The total acceleration in the slope-perpendicular direction is denoted
g′; it is composed of the slope-perpendicular component of gravity
gz, dispersive acceleration w˙Φ and centripetal accelerations
fz, . The total normal force at the base of the avalanche
is given by N:
N=MΦg′=MΦgz+NK+MΦfz.
Changes in density are induced by shearing: the shearing stress in the
avalanche core SΦ induces particle trajectories that are no
longer in line with the mean downslope velocities uΦ. The kinetic energy associated with the velocity
fluctuations is denoted RΦK. The potential energy associated with
the dilation of the core is denoted RΦV.
The production of free mechanical energy P˙Φ is given by an
equation containing two model parameters: the production parameter α
and the decay parameter βsee:
P˙Φ=αSΦ⋅uΦ-βRΦKhΦ.
The production parameter α defines the generation of the total free
mechanical energy from the shear work rate SΦ⋅uΦ; the parameter β defines the decrease of
the kinetic part RΦK by inelastic particle interactions. The energy
flux associated with the configurational changes is denoted P˙ΦV
and given by
P˙ΦV=γP˙Φ.
The parameter γ therefore determines the magnitude of the dilatation
of the flow volume under a shearing action. When γ=0, there is no
volume expansion by shearing. For wet-snow flows the value of γ is
small, γ< 0.2. The basal boundary plays a prominent role because
particle motions in the slope-perpendicular direction are inhibited by the
boundary and reflected back into the flow. The basal boundary converts the
production of random kinetic energy P˙Φ in the bulk into an
energy flux that changes the z location of particles and therefore the
potential energy and particle configuration of the core. The potential energy
of the configuration of the particle ensemble is denoted PΦV.
Avalanche temperature
We model-temperature dependent effects by tracking the depth-averaged
avalanche temperature TΦ within the flow . The
temperature TΦ is related to the internal heat energy EΦ by
the specific heat capacity of snow cΦ:
EΦ=ρΦcΦTΦ.
The avalanche temperature is governed by (1) the initial temperature of the
snow T0, (2) dissipation of kinetic energy by shearing Q˙Φ,
(3) thermal energy input from entrained snow Q˙Σ→Φ and (4) latent heat effects from phase changes Q˙w
(meltwater production); see . Dissipation is the part of the
shear work not being converted into free mechanical energy in addition to the
inelastic interactions between particles that is the decay of random kinetic
energy, RΦK.
Q˙Φ=(1-α)SΦ⋅uΦ+βRΦKhΦ
A fundamental assumption of this model is that liquid water mass is bonded to
the ice matrix of the snow particles and therefore is transported with the
flowing snow. Mathematically, the governing equations treat moisture content
as a passive scalar. Meltwater production is considered as a constraint on
the flow temperature of the avalanche: the mean flow temperature TΦ
can never exceed the melting temperature of ice Tm=273.15 K.
The energy for the phase change is given by the latent heat L,
Q˙w=LM˙w,
under the thermal constraint such that within a time increment Δt∫0ΔtQ˙wdt=MΦcΦ(TΦ-Tm)forT>Tm.
Obviously, when the flow temperature of the avalanche does not exceed the
melting temperature, no latent heat is produced; Q˙w=0.
Snow entrainment
Another source of thermal energy is snow entrainment. The total mass that is
entrained from the snow cover (Σ) is given by
M˙Σ→Φ=ρΣκuΦ,
where ρΣ is the density of snow and κ the dimensionless
erodibility coefficient. The value of the erodibility coefficient depends on
snow quality. Values for warm, wet snow are reported in and
. The liquid water mass entrained by the avalanche is therefore
M˙Σ→w=θΣwM˙Σ→Φ,
where θw is the LWC of the entrained snow. The thermal energy
entrained during the mass intake is
Q˙Σ→Φ=θΣici+θΣwcw+θΣaca+12uΦ2TΣM˙Σ→ΦTΣ,
where ci, cw and ca are the specific heat
capacity of ice, water and air, respectively. When the snow layer contains
water θΣw>0, then the temperature of the entire layer is
set to TΣ= 0 ∘C. Equation () takes into
account the thermal energy contained in the entrained snow.
Flow friction
To model frictional resistance SΦ=(SΦx,SΦy) in wet-snow avalanche flow, we apply a modified Voellmy model
,
SΦ=uΦuΦSμ+Sξ,
consisting of both a Coulomb friction Sμ (coefficient μ) and a
velocity dependent stress Sξ (coefficient ξ). The friction terms
Sμ and Sξ are given by
Sμ=μN-(1-μ)N0expNN0+(1-μ)N0
and
Sξ=ρΦguΦ2ξ.
In the Coulomb friction term, N0 is the cohesion; see for
values of N0 for wet snow. The form of Eq. () ensures that the
shear stress Sμ=0 when N=0, in accordance with shear and normal
force measurements in snow chute experiments (). To model the decrease in
friction from meltwater lubrication, we make the Coulomb stress dependent on
the meltwater water content hw. We use the following lubrication
function to replace the standard Coulomb friction coefficient μ:
μ(hw)=μw+(μd-μw)exp-hwhs,
where μd is the dry Voellmy friction coefficient, μw is
the limit value of lubricated friction (Voellmy assumed this value to be
μw=0 in the limiting case) and hs is a scaling factor
describing the height of the shear layer where meltwater is concentrated. The
dry friction μd depends on the avalanche configuration:
μd=μ0exp-RΦVR0+N0,
where μ0 is the dry Coulomb friction associated with the flow of the
co-volume, which we take to be μ0=0.55; see . The
parameter R0 defines the activation energy for fluidization. Cohesion
enhances the activation energy and therefore hinders the fluidization of the
avalanche core .
Selected wet-snow avalanche events and modeling procedure
We apply the numerical model to simulate documented wet-snow avalanches. The
data set includes 12 wet-snow avalanches that occurred in the Swiss Alps
and in the Chilean Central Andes between 2008 and 2015. The avalanches were
selected for three reasons: (1) the avalanche was located in the vicinity of
an automatic weather station (henceforth AWS); (2) the release area and the
area inundated by the avalanche were measured by hand-held GPS, drone
or terrestrial laser scanning; and (3) a high-resolution digital elevation
model (DEM; i.e., 2 m or higher) is available to simulate the terrain. This
information is summarized in Table . The avalanche release volumes
varied between 7000 and 330 000 m3. Most avalanches released from a wet
snow cover and entrained additional wet snow. However, in three events
(Grengiols, Braemabuhl Verbauung and Gatschiefer) the avalanche released as a
dry slab at subzero temperatures but entrained warm, moist snow at lower
elevations. The release, transit and deposit zone of 10 of the 12 case
studies were additional photographed from a helicopter. The two remaining
avalanches (Drusatscha and Braemabuhl, 2013) were photographed by the authors
from the deposition zone. The measurements from the release areas and
deposit outlines for every avalanche path are shown in Supplement A in the
online supplement.
List of case studies with date and estimated time of occurrence. The designation
for the automatic weather station (AWS) in the release zone contains the nearest
weather station followed by the exposition and altitude. The AWS at the bottom of the valley
was used to characterize the deposit area. The column “Fracture” contains the
method used to determine the location and height of the released snow mass.
For the more accurate laser scan and drone measurements,
the measured mean fracture heights are additionally provided.
The data provided by the automatic weather stations allow us to run
detailed, physics-based snow cover simulations. We apply the SNOWPACK
model in a similar setup to that of the
snow-height-driven simulations in . Because
SNOWPACK is a one-dimensional model, we must transfer point
simulation results to the slope in order to apply a two-dimensional avalanche
dynamics model operating in three-dimensional terrain. The horizontal
distance between release zone or deposits zone and the meteorological station
varied between 200 m (the nearest) and 2200 m (the farthest). More important
than the linear distance is the difference in altitude. The elevation
differences between the release zones or deposits zones and the weather
stations (see Table ) are typically less than 200 m, which we
consider sufficiently small, given typical lapse rates in the atmosphere, to
provide representative snow cover simulations to estimate the initial and
boundary conditions of the case studies .
To determine the initial temperature and moisture content of the snow cover
requires an accurate modeling of the surface energy fluxes (sensible and
latent heat exchanges, incoming short- and longwave radiation), which are
influenced by the slope exposition. We account for exposition effects on
surface energy fluxes in the release zones using the virtual slope concept
proposed by , which was found to provide accurate slope
simulations that correspond with wet-snow avalanche activity
. We obtain snow cover layering, temperature, density
and LWC in the release zones using virtual slope angles of 35∘ (see
Table ). The real slope angles of the release zones varied between
32 and 45∘. Shortwave radiation measured at the AWS as well as
snowfall amounts are re-projected onto these slopes, taking into account the
exposition of the slope .
For a few cases, field measurements using drones or laser scanning allowed
for an estimate of the fracture height. For the Gruenbodeli case, a fracture
height of 0.70 m has been determined from the field measurements. Given a
slope angle of 35∘, this translates to a perpendicular fracture
height of 0.57. SNOWPACK provides a slope-perpendicular fracture height of
0.56 m here, based on the position of the highest water accumulation.
Similarly, for the Salezer and Gatschiefer case, an observed fracture height
of 1.1 m (0.90 m slope perpendicular) and 2.0 m (1.64 m slope perpendicular)
is found, respectively, which was estimated by SNOWPACK to be 0.95 and
1.72 m slope perpendicular, respectively. All these cases occurred on the
same day, and the SNOWPACK simulations clearly correctly identify fracture
heights for these cases. Similarly, for the Braemabuhl Wildi and CV-1 case, a
fracture depth of 1.1 m (0.90 m slope perpendicular) was determined from
drone measurements. The SNOWPACK simulations provide a slope-perpendicular
fracture height of 1.10 and 0.95 m, respectively.
To describe the snow cover at lower elevations in the transit and runout
zones, we used the simulated snow cover based on meteorological data measured
at a station at the bottom of the valley. In this case, flat-field simulations were
analyzed, as deposits zones of large avalanches are often in relatively flat
terrain, compared to the release zones. The simulated snow cover information
provides us with the snow temperature, snow height, density and LWC at lower
elevations. In 8 of the 12 case studies, the snow cover in the
avalanche model can be considered as a single homogeneous layer, while for the
remaining case studies the snow cover was best modeled as a two-layer system
consisting of old wet snow covered by dry new snow; see Table . The
elevation-dependent properties of the snow cover along the avalanche path were
determined by constructing a linear gradient between the upper and lower
meteorological stations. This procedure could be applied for the case studies
that occurred near Davos (seven case studies) and the cases in Chile (two
cases).
For the remaining case studies (Verbier Mont Rogneux, Verbier Ba Combe and
Grengiols) we estimated snow cover conditions along the avalanche track by
applying a negative linear gradient of one-third of the snow cover height per
1000 m of altitude. This rule provides gradients of snow cover height of 2 to
6 cm per 100 m of elevation (see Table ). This method is in
agreement with the Hydrological Atlas of Switzerland. In these special cases, the snow
temperature, density and LWC were kept constant to the values estimated by
the SNOWPACK model at the release altitude. In the case of avalanches
with new snow on top of the wet old snow cover, we consider the new snow
amount measured at the AWS and estimate a decreasing linear gradient of new
snow height with altitude.
Initial conditions derived from SNOWPACK simulations at the release
for each avalanche.
Erosion conditions derived from the snow cover simulations for each
avalanche case study. Upper and lower denotes two different erosion layers.
The two-layer system was used when new snow was lying over old snow cover and
both layers were part of the studied avalanche. In the case of only one layer, all
the fields at the second, lower layer are set to zero.
LWC Erosion height Erosion height gradient Density Vol water Temperature Temperature gradient Erodibility (%) (m) (m per 100 m) (kg m-3) (mm m-1) (∘C) (∘C per 100 m) (–) AvalancheUpperLowerUpperLowerUpperLowerUpperLowerUpperLowerUpperLowerUpperLowerUpperLowerGruenbodeli1.45–0.560.000.02–197–8.1––0.2–0.0–0.8–Salezer1.89–0.950.000.03–317–18.0–0.0–0.0–0.7–Gatschiefer0.001.470.550.950.030.041853600.014.0–1.00.00.00.00.60.7Braemabuhl 20132.97–1.110.000.04–353–33.0–0.0–0.0–0.6–Drusatscha3.41–0.540.000.02–291–18.4–0.0–0.0–0.6–MO-4 Andina Chile2.44–0.900.000.03–296–22.0–0.0–0.0–0.6–Grengiols0.004.670.430.600.030.001752700.028.0–7.40.01.50.00.70.8Verbier Mont Rogneux3.00–0.600.000.02–317–18.0–0.0–0.0–0.6–Verbier Ba Combe2.59–0.580.000.02–349–15.0–0.0–0.0–0.6–Braemabuhl verbauung0.001.410.250.850.000.041583350.012.0–2.00.00.00.00.80.8Braemabuhl Wildi0.001.250.300.800.000.031643350.010.0–2.00.00.00.00.60.6CV-1 Andina Chile1.51–0.370.000.00–359–5.6–-0.1–0.0–0.6–Avalanche dynamics calculations: initial and boundary conditions
We apply two different models to simulate the 12 case studies. The first
is based on the thermomechanical avalanche dynamics equations presented in
Sect. 2 see; the second avalanche model follows the
Swiss guidelines on avalanche calculation . The
numerical model is outlined in . Both models are implemented
in the RAMMS (RApid Mass MovementS) software. Models and model parameters are compared in
Table .
In the calculations, we are primarily concerned with the initial and boundary
conditions, which are given by the snow cover model simulations; the release
area is given by the field measurements. The fracture height is defined by
the location of the highest water accumulation within the snow cover
as was previously suggested by . Once the
fracture height is known, we set the snow density, snow temperature and liquid
water values as the mean values over the slab which extends from the location
of the maximum liquid water to the snow surface. We take the values at the
estimated time of avalanche release. These values are shown in
Tables and . The amount of erodible snow is also
calculated using the location of the ponding layer. However, we calculate a
gradient between the snow cover conditions at the release and the conditions
at the bottom of the valley. This means that the depth of the fracture height and
erodible layer decreases with elevation. The erosion model used is described
by and .
Once the initial and boundary conditions were found, the first set of
simulations using the extended model was performed. As input parameters, the
model uses the release area (measured), the snow cover initial conditions
(calculated), and a set of friction and avalanche parameters. The avalanche
parameters were found by , and . These parameters
were kept constant for all 12 case studies as in . The
fluidization parameters α and γsee
are fixed to pre-determined values based on the terrain characteristics for
each avalanche path. Once these parameters are fixed, they are not tuned for
the remaining set of simulations. All simulations were carried out using a
grid resolution of 3 m except for the CV-1 case, where the confined and
gullied terrain was found to require a higher grid resolution of 1 m.
To perform standard Voellmy-Salm snow avalanche simulations following the
Swiss guidelines , it is necessary to include the entire
avalanche mass within the release volume. The guidelines do not consider
entrainment along the avalanche path, and therefore erosion was not considered
in the Voellmy-Salm simulations. This procedure was adopted to follow as
closely as possible the Swiss guideline procedures for avalanche calculations
and allows a comparison between models which consider entrainment conditions
(extended model) and models which employ calibrated parameters
(Voellmy-Salm). The avalanche mass of the release area was estimated from the
final mass (released plus eroded) calculated using the extended model. The
total mass calculated in the extended model is concentrated in the measured
release area. With this approach, a higher fracture height is obtained than
in model calculations with entrainment. This method ensures that
the total mass in both simulations is similar. The Swiss guidelines provide
the user a set of friction parameters to use depending on the avalanche size
and avalanche return period. Those friction parameters correspond to extreme,
fast-moving, dry-flowing avalanches, which have longer runouts than wet ones.
For the 12 case studies, the friction parameters used are the ones
corresponding to the class “small” avalanches and a return period of 10 to 30
years. This parameter combination led to the overall best fit to
observations. The calculations were performed with the same terrain and grid
resolution.
Overview of model and model parameters used to simulate the 12 case studies.
Guidelines-VSThermomechanicalCommentsReference;Both models in RAMMS;μ0 (–)Calibrated/guidelines0.55Reduced by lubricationμw (–)None0.12Constant in all simulationsξ0 (m s-2)Calibrated/guidelines1300Reduced by fluidizationN0 (Pa)200200Measured; see α (–)0.000.05–0.07Depends on roughnessβ (1 s-1)None1.0Depends on temperatureR0 (kJ m-3)None2Constant in all simulationshm (m)None0.1Size of lubricated layerκ (–)None0.6–0.8VS guidelines no entrainment
Method to construct the contingency table, based on measured
deposits outline (a), which is then combined with the simulated
deposit area (b) to identify hits (blue), false alarm (red),
misses (yellow) and correct negatives (no color, map only)
(c).
Mathematical definition of the statistics scores: probability of
detection (POD), false-alarm rate (FAR), equitable threat score (ETS) and
Hanssen–Kuipers score or true skill statistic (HKS).
FAR =falsealarmshits+falsealarmsPOD =hitshits+missesHKS =hitshits+misses-falsealarmsfalsealarms+correctnegativesETS =hits-hitsrandomhits+misses+falsealarms-hitsrandom*
* where
hitsrandom=(hits+misses)(hits+falsealarms)total.
Contingency table analysis for deposition area
The results obtained with the two models are compared through a statistical
contingency table analysis. We compare the area covered by the avalanche
deposits calculated with both models with the deposit area measured for each
case study. The terrain is divided into squared cells which correspond with the
calculation cells used in the avalanche simulations (see Fig. a and b).
For each cell we check whether the cell
was covered by the observed avalanche deposits or not and whether the cell
was covered by the avalanche simulation once the simulation stops or not. A
cell will be considered as covered by the avalanche simulations only if the
calculated flow height with the mass at rest is more than 20 cm, corresponding
approximately to two granules in diameter . Variations in
modeled and observed deposition heights are not captured with this
procedure. The calculated flow height at the last calculation step provides
us with the inundation area. These flow heights might not represent the
observed deposition depth, which is governed by different deposition
mechanisms. The correspondence of observed and calculated inundation area is
checked using a dichotomous contingency table (see Fig. )
that splits the terrain into four different classes:
hits, misses, false alarm and correct negatives (see Fig. c). Computing the amount of cells for each class
allows us to calculate different metrics to judge how both models perform. In
this study the probability of detection (POD), false-alarm rate (FAR),
equitable threat score (ETS) and Hanssen–Kuipers skill score or true
skill statistic (HKS) (see Table ) are calculated
. For POD, ETS and HKS a score of 1 would mean a perfect
score; in the case of FAR a score of 0 would indicate a perfect score.
These two-dimensional procedures avoid the problem of defining a
one-dimensional measure of avalanche runout.
Avalanche runout
In addition to the contingency analysis study for the inundated area, runout
distance in analyzed. The runout distance was calculated from the difference
in meters between the maximum distance reached by the avalanche in the
measurements and the avalanche simulation calculated over the line of
steepest descent for each avalanche path in a DEM smoothed to a resolution of
20 m (see Fig. ). The line of steepest
descent was chosen as the longest line of steepest descent among all the
possible ones departing from the depicted release area for each avalanche
path. All simulations stopped when the avalanche simulation contained less
than 5 % of the maximum calculated momentum .
Runout distance calculation procedure. From each calculation cell
at the release area the line of steepest descent is calculated. The
intersection of the lowest part of the avalanche deposits with the longest
calculated flow line (red dot) define the avalanche runout. The same procedure
is repeated with the simulation results. The distance measured on the
steepest line between the two intersection points is defined as the runout
calculation error.
Influence of initial conditions on avalanche runout: sensitivity study
In addition to using an avalanche dynamics model where snow temperature and
wetness directly influence the flow rheology, we use a novel approach here to
use simulated snow cover conditions to directly drive the avalanche dynamics
model. We constructed a sensitivity study (i) to investigate the influence of
initial snow cover conditions on the simulated avalanches and (ii) to
investigate if the snow cover simulations by the SNOWPACK model for a specific
case add information. We consider the 12 case studies to represent 12
individual cases of wet-snow avalanches. We construct the members of the
sensitivity study by interchanging the initial conditions from the 12 case
studies. This way, we ensure realistic and self-consistent simulated
snow cover results which represent real wet-snow avalanche cases, in contrast
with when individual variables would be varied one by one. Furthermore, we
consider that, for the avalanche dynamics simulations, the snow cover
conditions can be separated meaningfully in mass of the slab on the one hand
(given by slab height and snow density), and temperature and LWC on the other
hand.
For the study, three sets of simulations were constructed as follows:
Twelve simulations for each avalanche path interchanging the initial and boundary conditions (fracture
and erosion height, snow temperature, density and LWC at the erosion and at the release) for the 12 different
avalanches, thereby obtaining a set of 144 simulations.
A second set of simulations were performed by using the snow temperature and LWC that was simulated by the
snow cover model for that track. However, we varied the release and erosion heights and the snow density of the
12 different case studies. This set contains another 144 simulations and is used to verify the model sensibility
to changes in avalanche mass at the release and at the erosion.
A third set of simulations is constructed by keeping the snow heights and snow densities constant. The remaining
conditions (i.e., temperature and LWC) were taken from the 12 case studies, leading to another set of 144 simulations,
to investigate the importance of snow cover properties in relation to snowpack mass.
Consequently, for each of the 12 case studies we performed three
different sets of simulations, resulting in a total of 432 simulations
(3 × 12 × 12) where we interchanged the initial and boundary conditions from the
12 different initial and boundary conditions. For each simulation, we
determined the difference between the observed and simulated runout as well
as the contingency scores for the inundated area.
Results
The contingency table analysis is used to explore the following questions:
Is it possible to drive avalanche dynamics calculations with initial and boundary conditions
derived from snow cover modeling? Does the application of thermomechanical models improve the area covered by avalanche deposits and runout distances?
How sensitive are the simulated deposit areas and runout distances to released mass and snow cover properties?
What role does the calculation grid resolution play in the simulated areas covered by the deposits and runout distances?
The results of the model runs are presented extensively in the paper's
supplement. The graphs in Supplement A facilitate a direct comparison
between the thermomechanical approach, the standard Voellmy-Salm procedure
and the actual avalanche measurements, including the location of the deposits
with respect to the observed release zone. Supplement B contains the results
of the model permutations. This graphical output enables a quick assessment
of the model sensitivity. In the following we statistically analyze model
performance.
Comparison between the guideline-VS and the thermomechanical model
The 12 avalanche events were simulated using the guideline-VS model
and the thermomechanical wet-snow avalanche model presented in
Sect. 2. Recall that the guideline friction parameters were used for wet-snow
avalanches and that best overall fit to the observed inundation areas was
found using the classification small and frequent return period of 10–30 years.
The thermomechanical model used the fracture and entrainment heights
derived from the snow cover modeling. Bulk snow temperature and moisture
contents were determined by layer averaging of the fracture height. The
contingency table analysis for deposition areas and runout distances is
shown in Fig. .
A comparison between the guideline-VS and the wet-snow avalanche model
reveals that the thermomechanical model obtains significantly better results
than the guideline-VS model. The POD in conjunction with FAR scores achieved by the
thermomechanical model improves the results by more than 0.15 points (see
Fig. ). The ETS achieved by
the thermomechanical model improves the guideline procedure by 0.13 points
(see Fig. ). Additionally, the HKS reached by the thermomechanical model improves by 0.17
points in comparison to the HKS reached by the guideline model. Therefore,
the thermomechanical model statistically outperforms the guideline procedure
in all four contingency metrics.
The difference in performance between guideline-VS and thermomechanical wet-snow
avalanche model simulations differs per avalanche path (see Fig. ).
The guideline-VS procedure has particular
difficulties with tracks containing a smooth transition between the
acceleration and deposition zones. These avalanche paths have a long distance
where the steepness gets progressively flatter (i.e., Braemabuhl, Mont
Rogneux, Ba Combe and Drusatcha; see the online supplement). In contrast,
the guideline-VS model does much better on avalanche paths with a sharp
transition between the acceleration and runout zones (Gruenbodeli, Salezer
and Gatschiefer). In the examples where the slope angle changes smoothly the
guideline calculations systematically overran the measured deposits
(Braemabuhl, Wildi, Mont Rogneux, Ba Combe). Thus, the guideline-VS does
achieve good scores on detection (POD) but at the same time exhibits a
high FAR.
The thermomechanical model performs equally well on both types of slope and
is able to reproduce runout distances on slopes with gradual transition to
the runout zone. In the case of Grengiols, the runout distance is somewhat
underestimated; however, this was found to be caused by the uncertainty of
the elevation of the snowfall limit. This is an important result since it
indicates that the snow cover modeling must be able to accurately predict the
snow line elevation.
Comparison of the statistical results from the thermomechanical
model RAMMS (black) and the guideline-VS model (blue), for POD (a),
FAR (b), ETS (c) and HKS (d).
Sensitivity analysis
The scores of the contingency table analysis reveal that the thermomechanical
model, which utilizes the modeled initial and boundary conditions, can
outperform a model based on calibrated guideline friction parameters. The
primary result of the preceding section is that guideline-based avalanche
dynamics models with calibrated friction parameters (avalanches with return
periods greater than 10 years) will have difficulty reconstructing individual
case studies and that they are not easily linked to snow cover conditions. The
next step is to check how sensitive the thermomechanical model is to changes
in the simulated initial and boundary conditions.
Role of initial conditions
To demonstrate the role of initial conditions, we simulated the 12 case
studies using the initial conditions of all the other case studies, creating
a total of 144 permutations. The initial conditions consist of fracture
height, snow density, temperature and LWC. For example, we simulated the Ba
Combe case study with the initial conditions from the other 11 case
studies. The simulation results of every one of the permutations for each
avalanche path are shown in Supplement B in the online supplement.
Figure depicts the results of the 144 simulations. In
these plots, the red dots indicate the simulations performed with the
SNOWPACK-modeled initial conditions belonging to the specific
avalanche path; the small black dots represent the remaining combinations of
11 simulations. The large open circle represents the average of the
11 permutations.
The first result of this sensitivity analysis is that the score difference
varies by more than 0.2 statistical points for every avalanche path and
indicator (POD, FAR, ETS and HKS scores). This result indicates a large
variability of the model with different initial conditions. The POD scores
using the “right” initial conditions are higher than using those from the
other case studies. Furthermore, the FAR is lower. The
average of the four statistical indicators calculated with the real initial
and boundary conditions (red line in Fig. )
outperformed the calculations with the interchanged initial and boundary
conditions for every case study. However, for particular cases, simulations
with initial conditions from another avalanche path outperformed the one
calculated with the real initial conditions. A last important observation is
that the spread of scores provided by the permutations of the initial
conditions exceeds the spread of scores for all 12 simulations with the
real initial conditions.
Again, for the longer avalanche paths with a smooth transition to the runout
zone (Gatschiefer, Drusatcha, Grengiols, Verbier Mont Rogneux and
Braemabuhl), the scores varied up to 0.5 points in comparison to avalanche
paths where the transition is marked by an abrupt change in slope angle
(MO-4, CV-1 and Gruenbodeli). Thus, long avalanche tracks with a smooth
transition to the runout zone benefit the most from a correct initialization
using SNOWPACK simulations.
Sensitivity study simulating every avalanche path with the 12
different initial and boundary conditions using the thermomechanical model
RAMMS. The red dot denotes the simulation performed with the initial and
boundary conditions calculated for the corresponding avalanche path. The open
black circle denotes the average of the 11 permutations (filled black
dots). In this plot for every avalanche path fracture and erosion height,
temperature, density and LWC at the release and along the avalanche path
(erosion) are varied.
Role of snow cover mass and density
The initial conditions include both mass/density and temperature/water
content. To quantify the relative importance of initial mass versus initial
snowpack properties, we performed another set of 144 simulations where only
the mass (both the fracture mass and entrainment heights) varied. The results
of the contingency table analysis are depicted in
Fig. . The results are similar to the first
sensitivity analysis, where the entire set of initial and boundary conditions
were varied. This suggests that the selection of the initial and boundary
conditions for mass is more important than for temperature/LWC. For
wet-snow avalanches, this implies that the layers where meltwater accumulates
in the release zone must be identified accurately as this defines the height
of the fracture slab and therefore the release mass. A change in the fracture
height of 10 cm can lead to a large variability in the predicted avalanche
runout. This is a problematic result because it indicates the critical role
of fracture height as an input parameter in avalanche simulations.
Sensitivity of the thermomechanical model RAMMS to permutations of
avalanche mass (fracture height and density). For every avalanche path 12
different fracture heights, released densities, erosion heights and eroded
densities are permuted, keeping the LWC and snow temperature constant.
Markers and colors as in Fig. .
Role of snow cover temperature and water content
Figure displays the results of the other set of 144
thermomechanical model simulations where the temperature and LWC in the
release and entrainment zones were permuted. The mass (release and eroded)
was defined by the snow cover simulations driven by the meteorological data
for each case study. The statistical results are less sensitive to changes in
temperature and LWC than to mass. This is due to the fact that only wet-snow
avalanches were considered, and the temperature range did not vary outside the
wet-snow regime. This too is a reasonable result because moisture contents
in the 12 case studies varied only between 0 and 5 %; see
Table . Although the variations are less pronounced than those
caused by mass changes, Fig. illustrates that
correctly specifying initial snow temperature and LWC also contributes
positively to the model performance. The strong variation on long avalanche
tracks with a smooth transition to runout zone demonstrates, once again, that
path geometry dominates over changes in snow cover boundary conditions.
Sensitivity of the thermomechanical model to different snow
temperature and LWC. For every avalanche path 12 different snow
temperatures and LWCs in the release and erosion zones are varied, keeping the
release and eroded height and density constant. Markers and colors as in
Fig. .
Sensitivity to calculation grid size
Contingency table scores for the thermomechanical model can also depend on
the selected grid resolution. This would imply that the constant set of
friction parameters of the wet-snow model is bounded to a particular cell
size. We subsequently repeated the simulations using three different grid
sizes: 3 × 3, 5 × 5 and 10 × 10 m. The influence
on the contingency scores is depicted in Figs. and
for 10 and 5 m, respectively.
Sensitivity study simulating every avalanche path with the 12
different initial and boundary conditions, but with a simulation resolution
(grid size) of 10 m for the 144 simulations (compare to
Fig. for 3 m resolution). Markers and colors as in
Fig. .
A similar analysis was performed by , albeit without a
statistical score and only on a limited number of case studies. The
qualitative results of that study indicate that a coarser resolution smooths
the terrain, causing the wet model simulations to overflow the observed
deposit areas. Due to overflowing, the POD score increases by almost 0.1
statistical points on average in comparison with the 3 m resolution
simulations. The coarser simulations are highly penalized in the FAR indicator, showing a drop of 0.2 statistical points on average in
comparison with the finer resolution. The statistical scores (ETS and HKS)
were positively influenced by the increase in hit rate, but this was
compensated by the even larger increase in false alarms. The ETS score is
severely penalized, dropping the statistical score by 0.15 points for the
coarser simulations (10 m) in comparison to finer simulations (3 m). Even
though the HKS score is more weighted to the number of hits, it likewise
decreased, but by a smaller amount. The increase in false alarms was so large
that it mostly compensated the improvement obtained by an increase in the
number of hits.
The same analysis was repeated using 5 m resolution. In this case, the
results do not differ greatly from the results obtained with a 3 m
resolution. The 5 m resolution overall statistics (see
Fig. ) are close or even equal (in the case of the
HKS score; see Fig. ) to the results obtained by the
3 m resolution simulations. Nevertheless, the 5 m resolution
simulations obtained not only a higher POD score than the 3 m resolution but also a
higher FAR score. This pattern was already observed in the comparison between 3
and 10 m; however, in this case the difference is much lower. In the other
two statistical indicators, ETS and HKS, even more similar results are
obtained. The ETS score (see Fig. ) is slightly lower
for the 5 m resolution than for the 3 m resolution. However both obtained the same
score in the HKS indicator. The results obtained in the ETS and HKS
indicators show the same tendency observed in the comparison between 3 and
10 m. Coarser resolutions lead not only to overflowing and obtaining more hits but
also to more false alarms, which penalize the overall score. Nevertheless, in
the case of 3 and 5 m, it is necessary to compare avalanche path by
avalanche path and to check which resolution better suits a particular
avalanche path. Narrow, steep gullies with pronounced topographic features (Ba
Combe, MO-4 and CV-1) require higher resolution than open slopes (Drusatscha,
Mont Rogneux, Wildi and Gatschiefer).
Sensitivity study simulating every avalanche path with the 12
different initial and boundary conditions, but with a simulation resolution
(grid size) of 5 m for the 144 simulations (compare to
Fig. for 3 m resolution). Markers and colors as in
Fig. .
In summary, we found the following results regarding grid resolution:
Changes in grid resolution lead to variations in statistical scores comparable to changes in initial conditions (mass and snow conditions).
There appears to be an optimal grid resolution between 3 and 5 m. Coarser resolutions (10 m) smooth out the terrain too much
and lead to larger inundation areas and longer runouts.
For frequent avalanches (10-year return period) the 3–5 m resolution is adequate, based on the statistical scores. This
implies that the digital smoothing is comparable to the natural smoothing of the snow cover over bare ground.
The 3 m resolution gives better statistical scores for avalanches following narrow gullies; the 5 m resolution gives better
statistical scores for avalanches on open slopes.
Runout analysis study
A commonly used measure for avalanche size is the runout distance.
Figure shows the difference in simulated and measured
runout distance for each studied avalanche for different grid cell sizes
using the thermomechanical model RAMMS as well as the guideline-VS model.
The absolute error in runout distance calculated by the thermomechanical
model is about 3 times smaller than that predicted by the guideline-VS
model. The difference between both models was larger on paths where the
transition to the deposition zone was smoother (Drusatscha, Braemabuhl, Mont
Rogneux, Ba Combe, Gatschiefer). On the paths where this transition is more
pronounced, the calculated runout distances are closer (e.g., Gruenbodeli,
MO-4, CV-1; see Fig. ).
The analysis was repeated using two coarser grid resolutions (10 and 5 m cell
size) for the thermomechanical model (see Fig. ). In the
case of 10 m resolution, the model tends to overrun measured runout
distances. The average error between simulated and measured runout increases
from around 49 with 3 m resolution to 72 with 10 m resolution. The
difference between 3 and 5 m resolution is much smaller, and the 5 m
resolution calculations slightly outperform the 3 m ones in terms of runout
distance. On the other hand, the 3 m resolution simulations show on average
a higher ETS score than and equal HKS score to the 5 m simulations (see
Sect. 4.3).
Runout error plot comparing thermomechanical wet-snow model
calculations (black dots) with guideline-VS runout calculations (blue
triangles), as well as runout calculations with 5 and 10 m model resolution
with the thermomechanical model (red squares and green triangles,
respectively). The legend shows the absolute average simulation error for
each set of simulations. It was necessary to simulate the CV-1 case with a
1 m grid resolution to better account for a vertical wall.
We repeated the sensitivity study for runout distance with three sets of 144
simulations interchanging the initial and boundary conditions as described in
the previous section (see Fig. ). The results obtained
performing the sensitivity analysis confirmed the results achieved in the
previous contingency analysis. The thermomechanical model is sensitive to
changes in the initial and boundary conditions. Those changes are more
important on avalanche paths where the transition to the runout is smooth. On
those paths, changes in the initial and boundary conditions lead to
deviations of hundreds of meters in runout calculations )Gatschiefer,
Drusatscha, Mont Rogneux, Ba Combe; Fig. ). The runout
calculations were more sensitive to changes in mass than to changes in
snow cover conditions (temperature and LWC). Varying the mass in the release
and erosion doubles the absolute error obtained by varying only snow
temperature and LWC.
Difference between simulated and measured runout distance for the
wet-snow model simulations with the corresponding initial conditions (red
dots) and permutations (black dots). The average of the 11 permutations
is depicted as a black open circle. (a) Varying both snow mass
(fracture height and density) and snow properties (temperature and LWC),
(b) varying snow mass only and (c) varying snow properties
only. The red and black lines show the average absolute error in meters of
the whole set of simulations (sensitivity and real simulations) to the runout
distance measured in the field.
Discussion
Our analysis is limited to evaluating deposition areas and runout distances
for the 12 case studies. Other important avalanche variables – such as
speed, dynamic flow heights and impact pressures – are not considered in the
analysis, although they are crucial in many aspects of assessing avalanche
risks. Thus, we are considering only one primary component of the avalanche
flow problem: calculating the area covered by the avalanche deposits. We
circumvent the lack of flow data by considering well-documented
avalanche case studies in a single flow regime (wet) with return periods of
approximately 10 to 30 years. An advantage of this approach is that we
consider more than one track geometry, allowing us to draw conclusions about
the application of snow cover models and avalanche dynamics calculations in
different terrain.
The starting mass was specified by performing snow cover simulations to
determine the fracture height, density, temperature and water content of the
release zone. The snow cover simulations were driven by measured
meteorological data from stations near the release zone. The spatial extent
of the release was known from observations and/or measurements. Having
accurate information on where the avalanche released contributes significantly to the
goodness of the statistical scores. Knowing the location of the release zone
and a DEM of the avalanche track predetermines the flow path of the avalanche
in the simulations, making a contingency table analysis useful. The model has
one parameter α, which depends on the avalanche path
and still has to be chosen by the avalanche expert. Therefore the application
will demand experience in terrain and modeling of avalanches by the avalanche
expert, even though the range of α is well constrained .
An advantage of the contingency table analysis is that it can be used to
identify tracks where there will be a large variability in runout depending
on the initial conditions. Our analysis of the simulations revealed a large
variability in predicted runout for tracks with flat terraces and gradual
slope transitions to the runout zone. Here, we showed that the results are
very sensitive to the specification of mass in the release and entrainment
zones. On these tracks, an underestimation of fracture height of only 10 cm
could lead to significant runout shortening and underestimation of the
affected area. However, the initial and boundary conditions estimated from
snow cover modeling have demonstrated a good accuracy in the overall results;
the red dots on Figs. , and
show on average better statistical scores than the
black dots calculated with the variations. This result suggests statistically
that initial conditions derived from snow cover modeling improve randomly
chosen initial conditions derived from a set of wet-snow avalanche days. Once
again, although the coupling between the snow cover modeling and avalanche
dynamics calculations can be automatized, the sensitivity analysis suggests
that a mistake in the mass estimation can lead to entirely wrong results. We
emphasize that we come to this conclusion even though we have restricted our
attention to a single avalanche flow regime. Nonetheless, the coupling of
snow cover models and avalanche simulations could provide avalanche services
with more information to make a risk assessment. Using avalanche dynamics
models in this way differs from traditional avalanche calculations, which are
based on extreme conditions, with no link to particular snow cover or
meteorological conditions.
The general thermomechanical avalanche dynamics model RAMMS performs better
than the guideline-VS model in all statistical scores: HKS, ETS, POD and FAR
(see Fig. ). The guideline procedures are designed to
model extreme dry-flowing avalanches, not particular avalanche events.
However, the guideline model achieved in some cases high contingency table
scores, despite the application on non-extreme wet-snow avalanches. The
guideline-VS model was forced using friction coefficients calibrated by
. It was necessary to use the friction coefficients
corresponding to smaller avalanche sizes in order to achieve a good
correspondence between measurements and simulations. For all case studies,
the friction coefficients chosen correspond to size class “small” and a
return period of 10 to 30 years. The guideline-VS model had to be manipulated
by an expert user to get the best results. For example, the general model was
first applied to determine the mass balance of the event, which was then used
to establish the initial conditions (i.e., released plus eroded mass) of the
guideline-VS model. Another disadvantage of the guideline model is that first
a calibration of the friction parameters is required to obtain reasonable
contingency table scores. Both steps are not required in the general model
applications, because the friction parameters are determined as a known
function of snow cover conditions.
Because we considered only wet-snow avalanches, the range of snow temperature
was rather narrow and close to zero. The water content varied between 1 and
5 %, which is a typical range of bulk LWC for slopes .
The vertical liquid water distribution typically exhibited a thin layer with
high LWC located near layer boundaries (capillary barriers), which supports
the assumption in the avalanche model that the liquid water is concentrated
at the sliding surface. The results of the snow cover simulations were
visually inspected to determine the avalanche fracture height (following
). This height could be verified by the observations of
the actual release zone. The bulk LWC of the slab above the depth of the
maximum local LWC was used to initialize the simulations. In general, the
statistical scores of the contingency table analysis did not change much as a
function of the water content. However, changing water content in some cases
led to a large difference in simulated inundation area and runout distance.
These cases are associated with terrain characteristics and their influence on
the rate of meltwater production as well as the LWC of the eroded snow. For
example, the Grengiols and Mont Rogneux avalanche case studies stopped on a
flat zone when the initial liquid water was reduced below the simulated
SNOWPACK value. This indicates that underestimated LWC can lead to
spurious runout shortening. In general, however, variations of mass (i.e.,
fracture and erosion heights together with snow density) produced larger
variations in the final simulation results (see Fig. ,
and ). The mass variations in
the sensitivity analysis were broad; see Table . Therefore, when using
this set of case studies with only wet-snow avalanche cases, the model is
more sensitive to changes in avalanche mass than in snow cover conditions (LWC
and snow temperature).
The statistical scores of the contingency table analysis are dependent on the
grid resolution of the avalanche dynamics calculations. The 10 m resolution
appears to be far too coarse for the avalanche sizes of the case study
examples. The contingency scores of the 3 and 5 m resolutions are similar.
However, the 3 m runout calculations show a trend towards slightly shorter runout
distances. The statistical scores of the 3 m resolution are overall better
than the 5 m resolution because the 3 m scores were not penalized by excess
runout and therefore obtained fewer false alarms. The 5 m resolution clearly
achieved the best results for open slopes with gradual transition zones. A
3 m resolution might still be necessary when the track contains narrow
gullies, bare ground or shallow snow covers where terrain features, including
the presence of blocky scree, can play an important role. Deposition patterns
of the smaller events can clearly be better represented by the finer 3 m
resolution.
Conclusions
We used the physics-based snow cover model SNOWPACK to set the
initial conditions for avalanche dynamics calculations. We restricted our
attention to avalanches in one flow regime (wet) where the height and spatial
extent of the avalanche release area was known. We used a contingency table
analysis to statistically evaluate how well avalanche dynamics models can
predict deposition area and runout distances. Although we can demonstrate
that physics-based models improve the statistical scores, we note that in
certain track geometries the results of the avalanche dynamics calculations
are extremely sensitive to the specification of the correct starting
conditions, particularly fracture and entrainment heights. These tracks
contain flat track segments below the release zone and gradual transition
zones leading towards the avalanche runout zone. In these cases,
underestimating fracture heights and entrainment heights can lead to
significant underprediction of avalanche runout distances. The problem
appears not to be with the quality of the avalanche dynamics simulations, but
it illustrates that for these cases it is crucial that numerical snow cover
models accurately predict the state of the snowpack from data measured from
automatic weather stations.
The model chain could be applied in regions where considerable experience and
knowledge of local snow cover variability and avalanche history exist. As
these conditions change from year to year, a complete cadaster of documented
events is still invaluable. There are cases where these conditions are
fulfilled; see . In these situations the model chain can
support decisions on a deterministic basis and provide decision makers with a
valuable source of information about current avalanche risks.
Data are available on request.
The Supplement related to this article is available online at https://doi.org/10.5194/nhess-18-869-2018-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
Financial support for this project was provided by Codelco Mining, Andina Division
(Chile). We thank all Codelco avalanche alert center members – Luis Gallardo, Marcel Didier and Patricio Cerda – together with the Mountain Safety crew, not
only for their support but also for their confidence, patience and enormous
help during the last four winters in the Andina mine. Edited by: Sven Fuchs
Reviewed by: Jan-Thomas Fischer and Guillaume Chambon
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