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ESTIMATES ON THE REACH OF THE POWDER PART OF AVALANCHES

Peter Gauer1,∗

1Norwegian Geotechnical Institute, Norway

ABSTRACT: Avalanche observations from Norway, Austria and Switzerland, which distinguish between

dense (ﬂuidized) ﬂow and powder part, are analyzed to obtain probability information about the reach of

the powder part. The analysis suggests that the relative run-out distance of the powder part increases with

increasing mean slope angle of the track. The data provide useful hints for avalanche practitioners about the

reach and the corresponding probabilities of the powder part of avalanches.

Keywords: avalanche observations, powder part, hazard mapping

1. INTRODUCTION

Snow avalanches pose a deadly peril to human and

a danger to their belongings. Avoidance of areas

that can be impacted by avalanches is the most efﬁ-

cient mitigation measure. Thereby, hazard mapping

is an important tool and practitioners are often con-

fronted to assess the run-out distance and return

period of dry-mixed avalanches; avalanches that

are partially ﬂuidized and accompanied by a pow-

der cloud or air blast. The destructive effect of the

suspension cloud or air blast can often be observed

a considerable distance ahead of the more obvi-

ous deposits of the dense part of those avalanches.

Fig. 1 shows examples of the impact signs of the

powder cloud.

There is a long lasting interest in the destructive

pressure wave from the powder cloud or air blast,

respectively, and various explanations exist (e.g.

Coaz, 1889; Sprecher, 1911; B¨

utler, 1937; Hein-

rich, 1956; Moskalev, 1975; Mellor, 1978). Also sev-

eral expressions are linked to the phenomenon, for

example, powder snow avalanche, air blast, wind

blast, and in Norway ’skredvind’.

However, little is published about observations or

measurements on the actual reach of the powder

cloud. This paper presents some observations.

2. OBSERVATIONS FROM AVALANCHE

The analysis involves a series observations from

major events (i.e. avalanches of the relative size

R4 and R5 (Greene et al., 2016)) in which also the

run-out distance of the a powder part was observed.

The return period of those events is assumed to be

in the order of 100 years.

∗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: Signs of “air blast” impacts: top) snow deposits and

damage caused by the ’skredvind’ of the powder snow avalanche

from Stortuva, Mosjøen, Norway, on 29.02.1996 (photo NGI);

bottom) building damage caused by the Meira powder snow

avalanche, Arvigio, Switzerland, on 12.01.1977 (photo Canton

police, Grisons)

2.1. Data

The data mainly consist of the avalanche path pro-

ﬁle, the estimated position of the crown in the

avalanche release zone, and the (estimated) posi-

tion of the “maximum run-out”. For the dense part

this is typically marked by the tip of the obvious de-

position. For the powder part the limit is somewhat

scattered, but probably somewhere between the 1

Proceedings, International Snow Science Workshop, Innsbruck, Austria, 2018

815

Table 1: Analyzed avalanche data.

Group number mean(Δzb)∗std(Δzb) mean(β) std(β) estimated

return period

source

(m) (m) (◦)(

◦) (years)

Norway 47 1031 270 36.4 7.1 30 – 300 (Haug, 1974) and others

Austria 59 999 328 28.5 5.7 100 (Klenkhart and Weiler, 1994)

Switzerland 6 844 185 30.9 2.1 – (F¨

orster, 1999; Issler et al.,

1996)

total 112 988 294 31.9 7.3 –

∗Δzbis the drop height from the top of the release area down to the β-point.

kPa and 3 kPa pressure limit; a pressure that still

could cause noticeable damage at houses or vege-

tation.

For 59 data sets from Austria the run-out was

clearly distinguished between dense (ﬂuidized) ﬂow

and powder part. Most of the Norwegian data orig-

inate from Sunndal (Haug, 1974) or Møre & Roms-

dal area. For those data the so-called ’skredvind’

was especially marked. In addition several data

from Switzerland are included. Table 1 gives a brief

overview of the data included in the analysis.

The mean drop height of the analyzed avalanches

is around 988 m with a standard deviation of

294 m. Fig. 2 shows the α-angle of the dense

part and the one for the reach of the powder

part of the avalanches versus the β-angle. For

comparison, the Norwegian relation of the well-

known α-β(Lied and Bakkehøi, 1980) for mean the

“Fahrb¨

oschungswinkel” ,

αm= 0.96β−1.4◦, (1)

is also included. The standard deviation of this re-

lation, σ, is 2.3◦. Gauer et al. (2010) derived a cor-

responding relation for the mean retarding acceler-

ation,

ar

g≈0.82 sin β+ 0.05 , (2)

Figure 2: α-angle of the dense part (ﬁlled marker) and for the

reach of powder part of the avalanches (open marker) versus

the β-angle. The dashed line shows the ﬁt Eq. (1) according to

(Lied and Bakkehøi, 1980) and the gray-shaded area marks the

corresponding-range.

with ±σ/g= 0.04 and gis the gravitational acceler-

ation.

2.2. Mean retarding acceleration

For the our analysis, we focus on the mean retarding

acceleration of the dense and of the powder part.

The effective retarding acceleration is a measure for

the energy dissipation along the track and is given

as

ari=gΔzi

Si

. (3)

Here, Δziis the drop height from the top of the re-

lease area to the end of run-out area and Siis dis-

tance along the track (arc-length). The subscript i

marks either the dense part (DF ) or the powder part

(PSA).

Fig. 3 shows an example of an avalanche pro-

ﬁle from the area around Hellesylt, Norway, and the

mean retarding acceleration.

To describe the difference in run-out of dense part

and the powder part, we focus the normalized differ-

ence between the mean retarding accelerations

Δarn =(arPSA −arDF )

arDF

. (4)

Figure 3: Avalanche proﬁle of Burkebakkfonna, Møre & Romsdal,

Norway. The β-point (Lied and Bakkehøi, 1980) and the run-out

position of the dense part (DF) and the powder part (PSA) are

indicated. In addition the mean retarding acceleration ar, (see

Eq. (3)), corresponding to a given horizontal stopping position is

shown (dashed line). The markers indicate arDF and arPSA for the

given example.

Proceedings, International Snow Science Workshop, Innsbruck, Austria, 2018

816

3. DISCUSSION

Fig. 4 shows the Δarn versus sin β. Negative values

imply longer run-out distance or uphill climbing of

the powder part. Despite a considerable variation,

there is a noticeable trend and the Spearman rank

correlation between Δarn and sin βis −0.51. This

suggests that difference of the run-out between the

dense part and powder part increases with increas-

ing mean slope angle. The trend is given by

Δarf ≈−0.23 sin β+ 0.06 . (5)

Figure 4: Δarn versus sin β. The dashed line indicates the mean

trend.

The boxplots in Fig. 5 show the remaining varia-

tion of the de-trended Δarn, that is

σΔ=Δarn −Δarf . (6)

The ﬁgure shows both the variation of the com-

bined data set and split into the three countries.

Figure 5: Boxplot of the variation σΔ. The median is shown by

the red central mark, the 25th–75th percentile as edges of the

blue box, the whiskers extend to the most extreme data points

not considered outliers and outliers are marked with a red cross

(points larger than q3+1.5(q3−q1) or smaller than q1−1.5(q3−q1),

where q1and q3are the 25th and 75th percentiles). The notched

area signiﬁes a 95% conﬁdence interval for the median and the

width of the box indicates the relative size of the respective data

set.

Figure 6: Probability plot of −σΔ.

There is little difference in the median, which may

suggest that the trend is similar in all data sets.

The variation of the combined data set, −σΔ,may

be approximated by a generalized extreme value

distribution whose cumulative probability distribution

is

CDF(−σΔ;μp,σp,kp)=exp⎛⎜⎜⎜⎜⎜⎝−1+kp−σΔ−μp

σp−1/kp⎞⎟⎟⎟⎟⎟⎠, (7)

with a location parameter, μp≈−0.0137; scale pa-

rameter, σp≈0.036; and shape parameter, kp≈

0.147. Fig. 6 shows the corresponding probability

plot.

Using (5) and (7) it is possible to obtain estimates

on the exceedance probability of the ratio

arDF

arPSA

=1

1+Δarn

, (8)

depending on the mean slope angle β.ForΔzDF ≈

ΔzPSA, this ratio is approximately SPSA/SDF . Fig. 7

shows the calculated ratio arDF /arPSA versus sin βfor

various exceedance probabilities. The ﬁgure also

includes our example from Fig. 3.

Figure 7: Ratio arDF /arPSA versus sin βfor a given exceedance

probability. The crosses show the observations and the bullet

marks the example from Burkebakkfonna in Fig. 3.

Proceedings, International Snow Science Workshop, Innsbruck, Austria, 2018

817

Figure 8: Estimated survival probability of mean retarding accel-

eration arPSA/g(= ΔzPSA /SPSA) versus sin β. The crosses show

the observations and the bullet marks the example from Burke-

bakkfonna in Fig. 3.

A ﬁrst estimate on the probability of the mean re-

tarding acceleration of the powder part depending

on the mean slope angle (and with that an estimate

on its run-out distance) might be obtained by com-

bining Eqs. (2) and (8). Fig. 8 shows the calculated

survival probability of arPSA. For comparison the ob-

servation are included.

In similar manner, one could derive estimates

on the probability of the “Fahrb¨

oschungswinkel” α.

Fig. 9 shows the calculated survival probability of

αPSA. For comparison, relation (1) is included in the

ﬁgure.

Figure 9: Estimated survival probability of αPSA versus β. The

crosses show the observations and the bullet marks the exam-

ple from Burkebakkfonna in Fig. 3. For comparison, the dashed

line shows the relation (1) and the gray-shaded area marks the

corresponding ±σ-range.

4. CONCLUDING REMARKS

Avalanche risk management requires knowledge of

run-out distances and the corresponding return peri-

ods as well as intensity measures. At present, most

avalanche models focus mainly on the prediction

of the run-out distance of the dense- or ﬂuidized-

part, respectively. This holds true for the empiri-

cal models (Lied and Bakkehøi, 1980; McClung and

Mears, 1991) as well as for the numerical models

(Perla et al., 1980; Salm et al., 1990; Christen et al.,

2010). This paper presents estimates of the ra-

tio between the mean retarding acceleration of the

dense part of an avalanche and the powder part

depending on the mean slope angle of the track

and a given exceedance probability. The knowledge

of this ratio combined with an approximation of the

run-out distance of the dense part can provide es-

timates on the reach of the powder part. The pre-

sented estimates are based on a limited set of data

of around 100 avalanche observations from Nor-

way, Austria and Switzerland with drop heights of

around 1000 m. Nonetheless, they can provide use-

ful hints for avalanche practitioners on the reach and

the corresponding probability. In combination with

the avalanche release probability of major events

this gives information on the “return period” of an

avalanche to reach a certain distance. The esti-

mates on the reach may also help to evaluate results

from numerical models.

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

to NGI, administrated by the Norwegian Water Re-

sources and Energy Directorate (NVE).

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