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Estimates on the Reach of the Powder Part of Avalanches

Abstract and Figures

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.
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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= 0.96β1.4, (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
g0.82 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(q3q1) or smaller than q11.5(q3q1),
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)=exp1+kpσΔμp
σp1/kp, (7)
with a location parameter, μp≈−0.0137; scale pa-
rameter, σp0.036; 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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Snow, Weather, and Avalanches: Observation Guidelines for Avalanche Programs in the United States
  • E Greene
  • D Atkins
  • K Birkeland
  • K Elder
  • C Landry
  • B Lazar
  • I Mccammon
  • M Moore
  • D Sharaf
  • C Sternenz
  • B Tremper
Greene, E., Atkins, D., Birkeland, K., Elder, K., Landry, C., Lazar, B., McCammon, I., Moore, M., Sharaf, D. Sternenz, C., Tremper, B., and Williams, K. (2016). Snow, Weather, and Avalanches: Observation Guidelines for Avalanche Programs in the United States. Technical report, American Avalanche Association.
Snøskred Registrering og Kartlegging innen Sunndal Kommune. Master's thesis
  • J M Haug
Haug, J. M. (1974). Snøskred Registrering og Kartlegging innen Sunndal Kommune. Master's thesis, Universitetet i Oslo.