Content uploaded by Peter Gauer

Author content

All content in this area was uploaded by Peter Gauer on Oct 31, 2023

Content may be subject to copyright.

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

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

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)

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

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

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

123

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.

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

125

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).

REFERENCES

Aaron, J., Conlan, M., Johnston, K., Gauthier, D., and McDougall,

D. (2016). Adapting and calibrating the dan3d dynamic model

for north american snow avalanche runout modelling. In Inter-

national Snow Science Workshop 2016 Proceedings, Breck-

enridge, CO, USA.

Bakkehøi, S., Domaas, U., and Lied, K. (1983). Calculation of

snow avalanche runout distance. Annals of Glaciology, 4:24–

29.

Bartelt, P., B ¨

uhler, Y., Christen, M., Deubelbeiss, Y., Salz,

M., Schneider, M., and Schumacher, L. (2017). RAMMS

User Manual v.1.7.0 Avalanche. WSL Institute for Snow and

Avalanche Research SLF.

Buser, O. and Frutiger, H. (1980). Observed maximum run-out

distance of snow avalanches and the determination of the fric-

tion coefﬁcients µand ξ.Journal of Glaciology, 26(94):121–

130.

Christen, M., Kowalski, J., and Bartelt, P. (2010). RAMMS:

Numerical simulation of dense snow avalanches in three-

dimensional terrain. Cold Regions Science and Technology,

63:1–14.

Conlan, M., Aaron, J., Johnston, K., Gauthier, D., and McDougall,

S. (2018). Dan3D model parameters for snow avalanche case

studies in Western Canada. In Dan3D Model Parameters for

Snow Avalanche Case Studies in Western Canada, pages

783–787.

Gauer, P. (2013). Comparison of avalanche front velocity mea-

surements: supplementary energy considerations. Cold Re-

gions Science and Technology, 96:17–22.

Gauer, P. (2014). Comparison of avalanche front velocity mea-

surements and implications for avalanche models. Cold Re-

gions Science and Technology, 97:132–150.

Gauer, P. (2018). Considerations on scaling behavior in

avalanche ﬂow along cycloidal and parabolic tracks. Cold Re-

gions Science and Technology, 151:34–46.

Gauer, P. (2020). Considerations on scaling behavior in

avalanche ﬂow: Implementation in a simple mass block model.

Cold Regions Science and Technology, 180:103165.

Gauer, P., Kronholm, K., Lied, K., Kristensen, K., and Bakkehøi,

S. (2010). Can we learn more from the data underlying the

statistical α-βmodel with respect to the dynamical behavior of

avalanches? Cold Regions Science and Technology, 62:42–

54.

Issler, D., Gledisch Giss, K., Gauer, P., Glimsdal, S., Domaas, U.,

and Sverdrup-Thygeson, K. (submitted 2023). NAKSIN – a

New Approach to Snow Avalanche Hazard Indication Mapping

in Norway. Cold Regions Science and Technology.

Lied, K. and Bakkehøi, S. (1980). Empirical calculations of snow-

avalanche run-out distance based on topographic parameters.

Journal of Glaciology, 26(94):165–177.

McClung, D. M. and Gauer, P. (2018). Maximum frontal

speeds, alpha angles and deposit volumes of ﬂowing snow

avalanches. Cold Regions Science and Technology, 153:78–

85.

McClung, D. M. and Mears, A. I. (1991). Extreme value predic-

tion of snow avalanche runout. Cold Regions Science and

Technology, 19(2):163–175.

Perla, R., Cheng, T. T., and McClung, D. M. (1980). A two-

parameter model of snow-avalanche motion. Journal of

Glaciology, 26(94):119–207.

Rudolf-Miklau, F., Sauermoser, S., and Mears, A. I., editors

(2014). The Technical Avalanche Protection Handbook. Ernst

& Sohn.

Sampl, P. and Granig, M. (2009). Avalanche simulation with

SAMOS-AT. In Proceedings of the International Snow Sci-

ence Workshop, Davos, pages 519–523.

Voellmy, A. (1955). ¨

Uber die Zerst¨

orungskraft von Law-

inen. Schweizerische Bauzeitung, Sonderdruck aus dem 73.

Jahrgang(12, 15, 17, 19 und 37):1–25.

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

126

Figure 14: Maximum normalized velocity, U/pgHSC/2, along the center line for various drop heights,

HSC = [100, 500,750, 1000, 1500, 2000] m (top to bottom) for the models RAMMS, MoT-Voellmy, and SAMOSCCDTM2

Proceedings, International Snow Science Workshop, Bend, Oregon, 2023

127