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WHAT AVALANCHE OBSERVATIONS TELL US ABOUT THE PERFORMANCE OF
NUMERICAL MODELS
Peter Gauer1,∗, Nellie Sofie Body1, Anniken Helene Aalerud1
1Norwegian Geotechnical Institute, Norway
ABSTRACT: Avalanche velocity is an important parameter to characterize the avalanche dynamic behavior.
Observations imply that the maximum velocity of major avalanches scales with the total drop height. Com-
bining this information with observations of runout and volume of major avalanches can provide hints on the
choice of the empirical parameters of numerical avalanche models. To this end, a simple track geometry is
used to test the performance of present-days avalanche models. The model tracks varied in drop height and
mean steepness. The model results are compared with expected values of the maximum velocity and runout
based on avalanche observations.
Keywords: avalanche observations, avalanche models, performance test
1. INTRODUCTION
Runout observations provide limited only con-
straints for the validation of the empirical parameters
used in common present-day numerical avalanche
models. This is demonstrated in Fig.1, which shows
five simulations with a simple mass block model
governed by the equation of motion:
dU
dt =gsin ϕ−aret , (1)
where
aret =a0gcos ϕ+a2U2or aret =a3. (2)
Here, Uis the velocity, dU/dt the acceleration, g
the gravitational acceleration, and ϕis the slope
angle of the track. The model parameters for the
retarding acceleration are the Coulomb-friction pa-
rameter a0and the turbulent frictional parameter a2.
Both parameters can be related to the parameters
commonly used in the Voellmy-fluid type friction law:
a0≡µand a2≡g/(ξhf), with the flow depth hf, or
a2≡D/Min the case of the PCM-model (Voellmy,
1955; Perla et al., 1980). The simple mass block
model is ideal for illustration purposes as it is easy
to follow, and yet, the model is an admissible first-
order approximation. For comparison also the case
with a constant retarding acceleration, a3, is consid-
ered.
In this example, all the simulations are forced
to reach the expected αm-point according to the
statistical α-β-model (Lied and Bakkehøi, 1980),
but depending on the choice of the empirical pa-
rameters they show very different velocity distri-
butions along the track. Assuming a flow depth
∗Corresponding author address:
Peter Gauer, Norwegian Geotechnical Institute,
P.O. Box 3930 Ullevl Stadion, NO–0806 Oslo, Norway
Tel: ++47 45 27 47 43; Fax: ++47 22 23 04 48; E-mail:
pg@ngi.no
Figure 1: Velocity of a mass block moving with various parameter
combinations of {a0; a2HSC }along a cycloidal track (black line;
steepness in release area is ϕ0= 45◦) and reaching the αm-
point. Velocity and length are scaled with the total drop height
HSC . The gray dotted lines mark the probability of exceedance of
the scaled velocity based on observations (c.f. Fig. 2 a)
hfof 2 m and a drop height HSC = 1000 m,
the corresponding Voellmy parameters {µ,ξ}are
{0.43, ∞},n0.155, 3500 m s-2o,n0.13, 2450 m s-2 o,
and n0.09, 1000 m s-2o. This choice of the param-
eters is inspired by values like µ= 0.155 or ξ≈
1000 m s-2, or a2HSC = 2, which can be found in the
literature (e.g., Buser and Frutiger, 1980; Bakkehøi
et al., 1983; Perla et al., 1980). However, those au-
thors only focused on runout observations as con-
straint. For comparison, a simulation with a constant
retarding acceleration is included too.
In all cases with a pronounced velocity depen-
dency of the friction low, the parameter choice
should depend on the drop height.
The differences in the predicted velocities can be
crucial for the delimitation of endangered areas or
the design of mitigation measures. The latter case
is considered in the following example. Simple di-
mensioning criteria for avalanche catching dams re-
Proceedings, International Snow Science Workshop, Bend, Oregon, 2023
120
late the required height of the free board Hfb to the
avalanche velocity (see for example Chapter 8.4 in
Rudolf-Miklau et al., 2014).
Hfb =U2
2gλ+hf(3)
where λis an empirical constant typically set to a
value between 1 and 3, depending on the avalanche
type (dry or wet). In the case of the example in
Fig. 1, the avalanches, stopping at the αm-point,
still have a scaled velocity U/pgHSC/2 of approxi-
mately 0.75, 0.70, 0.41, 0.35, or 0.22 at the β-point.
If one were to plan a catching dam at the β-point,
one could directly relate the required free board Hfb
to the drop height HSC
Hfb ≈fv
HSC
4λ+hf(4)
where the factor fvin our examples is 0.56, 0.49,
0.17, 0.12, or 0.05, respectively. That is, the design
dam height may differ by a factor up to 10 or more,
depending on the choice of the model parameters.
Furthermore, the predicted avalanche runtime,
which is an important design parameter for some
temporal mitigation measures such as automated
road closures, may differ considerably with the
choice of the friction parameters. In our example,
the non-dimensional runtime, tav /pHSC /g, varies
between approximately 6 and 13. This factor may
determine wether an automated road closure is fea-
sible or not. These are only two examples to show
that not only the prediction of the runout is important
but also the correct prediction of the velocity along
whole track.
2. OBSERVATION
Therefore, velocity observations that could constrain
model calibrations are desirable. Fig. 2 a shows the
exceedance probabilities (i.e. the probability to ob-
serve a value larger than a given one) for a series
of observed Umax /pgHSC /2 (McClung and Gauer,
2018) and expected αvalues according to the α-β-
model (Lied and Bakkehøi, 1980). The assumption
of the empirical α-β-model is that the data behind
it reflect rare avalanches, that is events with return
periods of the order of 100 years. With this in mind,
one might be tempted to multiply the exceedance
probability in Figure 2 b by a factor of the order of
10−2to obtain annual probabilities. However, this is
a crude approximation. The complementary cumu-
lative distribution function (CCDF) of Umax can be
approximated reasonably well by a Generalized Ex-
treme Value (GEV) distribution. Here and in the fol-
lowing, the term “major avalanche” is used in the
sense that these avalanches have return periods of
at least several years and can be considered large
relative to the path, but not necessary the most ex-
treme.
a)
b)
Figure 2: Complementary Cumulative Distribution Function
(CCDF, survivor function) of observed values of Umax /pgHSC /2
at Ryggfonn and for major avalanches at various locations. The
gray rectangle indicates a region that covers typical rare events
(cf. Fig. 3 b; and b) estimated exceedance probability of αver-
sus βaccording to the α-β-model (αm= 0.96β−1.4◦; gray
shaded area indicates αm±σ-range; for explanation see Lied
and Bakkehøi, 1980).
Fig. 3 a shows the calculated (dimensionless) ve-
locity of a mass block moving with a constant retard-
ing acceleration along a cycloidal track. The retard-
ing acceleration is chosen in such a way that the
mass block stops at the β-point (which is close to
the αm+σ-point), the αm-point, or the (αm−σ)-point
respectively. The light gray polygon indicates ex-
pected ranges for major avalanches according to the
observations in Fig. 2. Fig. 3 b shows correspond-
ing avalanche observations from major events with
drop heights between 100 m and 1200m. These ob-
servations have implication for the choice of model
parameters as further discussed in the next section.
Fig. 4 shows a collection of observed deposition
volumes. They show an increasing trend with drop
height.
3. MODEL TESTS
3.1. Method
As mentioned, avalanche velocity is an important
parameter to characterize the dynamic behavior.
Observations imply that the velocity and especially
the maximum velocity of major avalanches scale
with the total drop height HSC , that is Umax ∼
pgHsc /2 (McClung and Gauer, 2018; Gauer, 2018,
2014). Combined with estimates on the expected
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121
a)
b)
Figure 3: Scaling behavior of the front velocity of major
avalanches combined with runout estimates. a) based on analyt-
ical calculations (cycloidal track and constant retarding acceler-
ations; ϕ0= 48◦) and b) corresponding avalanche observations
from major events. The blue line shows the mean, the shaded
area the ±σ-range and the red dashed line the observed maxi-
mum derived from observations along the track. The black line
represents a “mean path” geometry and the dark gray shaded
area the envelope of all path geometries. The light grey polygon
provides a reference from Fig. 2.
Figure 4: Observed avalanche deposits of “major events” versus
total drop height HSC (for references to the data see Gauer et al.,
2010). ♦indicate the volumes used in the model simulations
in the next section. The lines show the estimated exceedance
probabilities derived from the observations.
runout of major avalanches, e.g., by using statisti-
cal models, these observations provide implications
for the choice of the empirical parameters used in
numerical avalanche models. Like for the Voellmy-
type friction models that find application in most of
the present-day avalanche models.
Using a simple parabolic track, model perfor-
mance can be tested. To this end, simulations were
performed on slightly channelized parabolic tracks
Figure 5: Model grid; the (•) mark the β-, αm-, (αm−σ)-, and
(αm−2σ)-point.
where the thalweg is given by
z1/HSC =a(x/HSC )2+b(x/HSC ) + c(5)
and
z(x,y) = z1(1 + f(y)) . (6)
Here, f(y) defines the degree of canalization. Using
a slight canalization should reduce lateral spread-
ing, which is caused by numerical diffusion and
therefore is an artifact. The parameter a,b,care
determined by the initial slope angle ϕ0, which is
also a proxy of the mean slope angle β≈0.72ϕ0−
1.4◦(for explanations see Gauer, 2018). Fig. 5
shows an example grid.
At the low point, the track is horizontally extended.
The initial volume is adjusted according to expected
deposition volumes (see Fig. 4). The corresponding
release areas are located above the actual track (i.e.
zSC >1) with an assumed fracture depths Dfrac ≈
[1 m, 1.5 m, 2 m] ·cos ϕ0and a constant slope angle
ϕ0given by the initial tangent of the track.
The simulations were done with the commer-
cial version of RAMMS:avalanche (version 1.7.20;
(Christen et al., 2010)) and the MoT-Voellmy model
(Version 2020-05-12, (Issler et al., 2023)).
The RAMMS friction parameters are chosen ac-
cording to standard values (Bartelt et al., 2017) cor-
responding to the respective volume class. How-
ever, only the highest elevation class is used, which
gives the lowest friction values—that is, they should
favor longer runouts and higher velocities. The pa-
rameter for the MoT-Voellmy model are chosen sim-
ilarly.
In addition, simulations were done with the
SAMOS-solver for dense flow (Sampl and Granig,
2009) including entrainment, however, with a modi-
fied friction law that favors Coulomb-type behavior:
τb=µ ρfg hfcos ϕ+CDρaU2
+τcmax exp −u2/25, exp −10h2
f , (7)
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122
where hfis the flow depth, the avalanche density
ρf= [100, 200] kg m-3, the Coulomb friction factor
µ= 0.3, CDρa= 0.05 kg m-3 and τc= 100 Pa. The
second term on the right accounts for some air drag
and the last term on the right introduces some co-
hesion, which should mainly suppress spreading of
very shallow flows. This friction law is inspired by
the simple model tests in Gauer (2020). The en-
trainment is set to ≤300 kg m−2.
3.2. Results
Using the simple parabolic track, model perfor-
mance can be tested as shown in Fig. 6 and Fig. 8.
Here, we focus mainly on the RAMMS (Christen
et al., 2010) as it is probably one of the (if not the)
most used model by practitioners at present. Fig. 6
shows an example of the kind of simulations and
show the overall maximum values of the simulation
at a given grid point.
a)
b)
Figure 6: Simulation with RAMMS on a parabolic track: a) maxi-
mum velocity and b) maximum flow depth. The velocity is scaled
as USC =Umax /pgHsc /2 and the flow depth as h=hf/Dfrac,
where Dfrac is the initial fracture depth.
Fig. 7 shows a comparison of avalanche simula-
tions with RAMMS for different drop heights HSC =
[100, 300, 500, 750, 1000, 1500, 2000] m. The vol-
umes were adjusted according to expected depo-
sition volumes (see Fig. 4). The corresponding re-
lease areas are located above the actual track with
an assumed a fracture depth Dfrac = 2 cos ϕ0m and
a constant slope angle (in this case ϕ0= 35◦) given
by the initial tangent of the track; the mean slope
a)
b)
Figure 7: a) Simulated velocities with RAMMS along the thal-
weg for seven different drop heights. The maxima are marked
with (♦). The release volumes are adjusted to the drop height,
the fracture depth is set to 1.64 m and ϕ0= 35◦. As a ref-
erence, the β-, αm-, (α−1σ)- and (αm−2σ)-point are shown
(for explanation see Lied and Bakkehøi, 1980). b) Simulated
maximum velocity, Umax , versus square root of the drop height,
√Hsc , marked by (♦); the color illustrates the scaled velocity
USC =Umax /pgHsc /2 and the marker size corresponds to the
EAWS avalanche size classes. The lines show the estimated ex-
ceedance probabilities derived from observations shown in gray.
angle is β≈23.6◦.
As can be seen in Fig. 7 a the runout ends ap-
proximately at the mean expected αm-angle accord-
ing to the α-β-model, even though the large volumes
used could suggest that these simulations represent
more extreme events. For drop heights up-to around
750 m, the simulated maximum velocities are in the
range of rare events (cf. panel b). For drop heights
above, the maximum velocity reaches a terminal ve-
locity, which is not reflected in the observations. For
drop heights larger than 1000 m, the simulations un-
derestimate the velocities significantly compared to
the observations of major events. This is a typical
problem for models based on the Voellmy-fluid rhe-
ology (see also discussions in Gauer, 2014, 2013,
2018). However, also for drop heights smaller than
1000 m a subtle difference seems to exist as the
simulated maximum velocity tends to be obtained
earlier in the path than suggested by observations.
Fig. 8 shows the corresponding simulation as
shown in Fig. 6 for the MoT-Voellmy model. The
results are comparable to those from RAMMS, how-
ever, in this case the simulation suggests also some
spurious numerical artifacts.
As mentioned above, the combination of runout
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a)
b)
Figure 8: Simulation with MoT-Voellmy on a parabolic tracks:
a) maximum velocity and b) maximum flow depth. The veloc-
ity is scaled by USC =Umax /pgHsc/2 and the flow depth by
h=hf/Dfrac, where Dfrac is the initial fracture depth (simulation
to t = 100 s; build version MoT-Voellmy.2020-05-12.exe).
observations and velocity scaling can provide a
more stringent constraint to the choice of the empir-
ical model parameters for the commonly used fric-
tion laws. Choosing a simple track geometry and
the use of expected runout and maximum velocities
along the track can therefore give a fast impression
of model performance versus observations depend-
ing on the model parameters.
The approach is exemplified in (Gauer, 2018,
2020). Fig. 9, Fig. 10, and Fig. 11, show results ob-
tained with a simple mass block model that accounts
for mass entrainment (Gauer, 2020). Although only
a first order approximation, the model captures the
observations for “major” dry-mixed avalanches rea-
sonably well. Therefore, the figures give a reference
for the 2D-simulations shown below in this section.
As the model is basically scale invariant regarding
the drop height HSC , Fig. 11 should be similar for
various drop heights. The colors and isolines in-
dicate the velocity distribution along the horizontal
distance for simulations along tracks with varying
steepness, ϕ0(or β≈0.72ϕ0−1.4◦). For the il-
lustration, the data are interpolated.
Fig. 13 gives now a summary of the simulated
runout angles for the 2D models. As indicated, the
models seem to capture the expected runout ac-
cording to the observations. However, one could
have expected longer runouts considering the sim-
ulation setup that should have favoured higher ve-
locities and longer runout for the Voellmy-type mod-
Figure 9: Simulated runout marked by the α-angle and maximum
velocity (color coded) on a parabolic track with the mean slope
angle, β, as parameter. (•) marks runs with entrainment height
He = 0.25 m and (♦) those with He = 0.5 m. Observations are
shown as gray dots. Estimated exceedance probabilities of α
versus β, according to the α-β-model αm= 0.96β−1.4◦(Lied and
Bakkehøi, 1980); gray shaded area αm±σ.
Figure 10: Simulated maximum velocity, Umax , versus square
root of the drop height, √HSC . The color illustrates the scaled
velocity, USC =Umax /pgHSC /2. The figure shows example
calculations for a cycloidal and parabolic track and two erosion
depths. The initial slope angle ϕ0of the tracks is 40◦. The gray
triangles depict measured maximum front-velocities from ”major
avalanche events” in various tracks (see Fig. 3). The lines depict
the probability of exceedance.
els. Also, it can be noticed that there is a slight in-
Figure 11: MBVM (Mass Block with Variable Mass): Normalized
velocity, U/pgHSC /2 ; iso-lines of scaled avalanche velocities
on some parabolic tracks with different steepness given by the
β-angle. Runout length given to hit the average runout angle αm
corresponding to the α-β-model (Lied and Bakkehøi, 1980). Also
marked are corresponding positions of β,αm, and where zbe-
comes zero. Gray shaded area shows αm±σrange.
Proceedings, International Snow Science Workshop, Bend, Oregon, 2023
124
crease in runout length with increasing slope steep-
ness. This is especially obvious in the Coulomb fric-
tion dominated SAMOSCCDTM2model. Here, the in-
crease is pronounced for lower drop heights, which
can be observed in Fig. 14.
a)
b)
c)
Figure 12: Simulated runout marked by the α-angle and maxi-
mum velocity (color coded) on a parabolic track with the mean
slope angle, β(varying symbol) as parameter and vertical re-
lease depth HS = 1.5m. Expected runout angle αversus β, ac-
cording to the α-β-model αm= 0.96β−1.4◦(Lied and Bakkehøi,
1980); gray shaded area ±σ. Symbol size gives an impression of
the avalanche size according to EAWS volume classification. a)
RAMMS; b) MoT-Voellmy; c) SAMOSCCDTM2. The additional dot-
ted and dashed lines in c) show the α-β-model for Colorado and
the Sierra Nevada, respectively (c.f. McClung and Mears, 1991).
Fig. 14 shows plots corresponding to Fig. 11.
The values in all cases are taken along the cen-
ter line of the track and then interpolated. On a
first glance, the results suggest that the models are
capable to capture the runout distances reasonably
well, although one could have expected even longer
runouts with respect to the model setting, see also
Fig. 12.
a)
b)
c)
Figure 13: Simulated maximum velocity, Umax , versus square
root of the effective drop height √HSe (i.e., including the height
of the release area) with the mean slope angle, βas parame-
ter (varying symbols; for comparison see Fig. 12) and vertical
release depth HS = 1.5 m. The color illustrates the scaled ve-
locity USC =Umax /pgHSC /2. a) RAMMS; b) MoT-Voellmy; c)
SAMOSCCDTM2.
There are, however, noticeable difference be-
tween the predicted maximum velocities and those
observed, especially for avalanche drops heights
larger 1000 m. This is also very well reflected in
Fig. 13. But also for smaller drop heights it seems
there are differences in the velocity profiles. That
is, the simulations reach its maximum velocity early
on and underestimate the velocity the lower part of
the track as mentioned before. RAMMS and MoT-
Voellmy show quite similar behaviour. Both model
show a pronounced drop height dependency, which
is not reflected in observations of major avalanches.
The drop height dependency is less in the more
Coulomb-type model implemented in the SAMOS-
solver.
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4. CONCLUDING REMARKS
In this paper, a simple track geometry was used
to test the performance of present days avalanche
models. The model tracks varied in drop height and
mean steepness. The model results were compared
with expected values of the maximum velocity and
runout based on avalanche observations.
On a first glance, the results suggest that the
models are capable to capture the runout distances
reasonably well, although one could have expected
even longer runouts with respect to the model set-
ting. There are, however, noticeable difference be-
tween the predicted maximum velocities and those
observed, especially for avalanche drops heights
larger 1000 m. Also for smaller drop heights, it
seems there are differences in the velocity profiles
and that the simulation reaches its maximum veloc-
ity early on and underestimate the velocity the lower
part of the track.
Here, we focused mainly on RAMMS and on
MOT-Voellmy, but similar results are expected and
are known for other models using the Voellmy-
rheology too, like DAN3D (Aaron et al., 2016; Con-
lan et al., 2018) or SAMOS-AT (Sampl and Granig,
2009).
The more Coulomb-type variant of SAMOS pre-
sented here shows less velocity dependency of the
friction term and is better capable to reproduce the
higher observed velocities for larger drop heights.
There is, however, tendency to show longer runouts
than expected by the α-β-model for Norway for
steeper paths, at least for the parameters used here.
On the other hand, these runouts are still in ac-
cordance with observation from Colorado or Sierra
Nevada.
At this point, model developers could argue that
the Voellmy-rheology focuses mainly on the predic-
tion the dense- (or may be the slightly fluidized-) part
of the avalanche, and that the observations are un-
certain and include also events of highly fluidized-
or powder snow events. This refutation might be
justified, but the observations include avalanches
that are highly relevant for practitioners concerned
with hazard mapping and mitigation. Then practi-
tioners need to ask themselves, Are we using the
right tools? Are models that better account for vary-
ing flow-regimes and mass exchange needed?
ACKNOWLEDGMENTS
Parts of this research was financially supported by
the Norwegian Ministry of Oil and Energy through
the project grant “R&D Snow avalanches 2017–
2019 & 2020–2023” to NGI, administrated by the
Norwegian Water Resources and Energy Direc-
torate (NVE).
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Figure 14: Maximum normalized velocity, U/pgHSC/2, along the center line for various drop heights,
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