[NOTE: way back during the mists of my MSc whilst research the runout of high frequency avalanches in British Columbia, Canada, I asked a fellow student (Matthias Jacob) to translate a paper written in German from the Swiss Federal Institute for Snow and Avalanche Research. He very kindly did so and I was recently reminded that this was sitting in one of my files. So I thought the world might (slightly!) benefit from this translation. PDF of original below as well]

Determination of the mean scarp thickness d0 to compute flow avalanches

1. Introduction

The degree of avalanche hazard is determined by the pressure impact (300 kN/m2) and return interval (RI; up to 300 years) in populated areas. In some avalanche chutes, avalanches with large volumes are more rare than small volumes. Using a known RI the major can then be estimated. Avalanche technical calculations lead from the magnitude to avalanche pressure. The pressure of a certain point is therefore correlate with the RI. Considering the rare and thus important precipitation events - which were usually not observed - pressures and frequencies (F) have to be calculated. In the institute the deterministically statistically Voelling-Sahn model is applied for these calculations. In this model runout distances and pressure results are approximately proportional to the mean d0. On the other hand d0 is correlated to the RI which was the runout distance on a statistical variable with a certain probability.

De Quervain (1974) [1] wrote relating to the problem of the determination of XXX possibilities “the entire study area was built on XXX correlations and the question is posed how one can get to a concrete understanding. In the long term the statistics of snowfall data and d0 will contribute data to the desired functions. In addition, snow mechanical experiments can yield more information. Presently one has to rely on experience data of d0 in areas of catastrophes or one has to back calculate them from extreme runout distances. It is important to XXX between snow rich (abundant) and snow poor areas in terms of d0 of avalanches within the same RI class. Or one considers such a variation within one climatic region with avalanches with varying RI as being treated.

Today it is possible to differentiate quantitatively between snow rich and snow poor climate regions. The base assumption which contributes to the determination of d0 are shown in this report.

By appropriately choosing d0 in different climatic regions in the Swiss Alps, the same hazard scales (classes) can be obtained in all hazard maps and constructive avalanche mitigation measures. This is a manifested in the manual for calculation flow avalanches for practicioners.

2. Assumptions and assessment of d0

The main influencing factors of d0 are arroding to [3]:

a. New Snow: the climatically possible precipitation in 3 subsequent days is considered (fig1). Consideration longer precipitation periods has been found to be not significant. it is also assumed that large avalanches - in comparison to sl called skier avalanches - are always triggered by precipitation events and that basically it is only new snow that glides off. Investigations have confirmed this, although scarring in old snow are possible. In addition RIs of new snow increases are set equal to those of the particular avalanches (conservative assumption)

b. Slope: the shear strength limites the amount of new snow deposited on a slope. Before the climatically possible preipitation is reached the snow glides off. The strength is assumed according to Coulomb-Mohr (3.3), The strength should be greater for larger precipitation events. Otherwise, considering a constant strength - d0 would be constant at constant slope, independent from RI and climate.

c. Drift snow: On less slopes the new snow measured XXX d0 are locally increased due to wind transport (consider the predominant wind direction during precipitation events). The mean d0 (take the mean over the whole scarp area, does usually not correspond to a mean d0 along an onserved scarp line) which is determined perpendicular to the slope by:

(Eq 1)

In summary d0 is a factor consisting of climate, snow mechanics and topography.

3. Base Data

The most important basis are snow data from comparative stations and measurement stations which as been obtained and analysed in the Swiss Alps. The snow data is collected over periods between 20-60 years. The base data are obtained from horizontal measurement fields (altitude 1100-2000 m asl). How does one obtain d0 with varying RI and climatic region by using the basic data?

3.1 3-day delta HS - increase - values (climatically possible snow height increase)

The data of the various comparative stations and measurement stations were analysed by the Institute of Geography, University of Bern [4] under the guidance of the Institute SLF until 1982. From this year on they are reported and uopdated by the SLF - Section I (section Fohn).

The delta HS basic data equal a 3-day snow thickness increase on horizontal fields. Extrapolation of 30-60 yr increase data allows gumbel extreme value statistics.

In addition a delta HS-altitude gradient must be recognized: the mean altitude of the measurement fields and compartive stations between 1100 and 2800 m als (mean 1600 m). On the other hand the avalanche scarps are located higher in that a delta HS altitude gradient must be considered. According to [5] page 155 this gradient is between 3-7 XX/100 m altitude, depending on the region. We suggest a value 5 XX/100 m. In addition we suggest a reference height of 2000 m asl because the impact of wind deposition in higher areas and tehrefore drift snow must be considered (d0* is the mean value over the whole scarp area).

3.11 Determintation of factor F (30/300)

The 3-day delta HS increase value with RI of T=30 years is a known measurement value. Extrapolation using extreme value statistics with an RI of 300 years shows icnreasing scatter. It must be asked whether 30-60 years time series can indeed be extrapolated to 300 years and how reliable are these values. In general it can be assumed taht one cannot exceed the period of measurement by a factor of 3. Despite the short period of measurement we are forced to do the extrapolation. XXX (>66 stations) of the 3-day delta HS increase values. T=30 yearse and T=300 years yields a ratio F of the 300 : 30 year value between 1.30 and 1.45 (E_mean ~= 1.37). In addition no regional significant difference are discernible. For further observationswe consider F=1.4. In the following tables A and B the largest and smallest increase values are summarised as well as the consideration per station in a given altitude for T=30. These values are subsequently extrapolated with the factor 1.4 to 300 year values.

3.2 Determination of basic value d0* for slope = 28 degrees. Delta HS increase are perpendicular (to the horizontal field) measured and extrapolated. For avalanches - technical calculations values must be used perpendicular to the slope (fig 1). Determining the potential scar area between 28-50 degrees we determine the base value d0* for mu=28 degrees by assuming that as much snow can accummulate on a flat surface as on a 28 degrees slope. With an increase in slope a slope dependency f (mu) must be considered (section 2).

3.3 Determination of slope dependency

The slope dependency is included by considered the slope factor f (mu). A general criteria for the determination of stability is (yet) unknown. In conjunction with soil mechanics the simple Coloumb-Mohr criteria is used. A scar develops when the stability S <_ 1, with s being the ration between strength of a weak intermediate layer and the shear stress.

According to experience, the values c and f for d0 are assessed:

EQ

For cohesion it is postulated that

EQ

For the angle of internal friction we write

EQ

It is therefore considered independently of d0* since it is probably dependent on the grain form in the glide later (roughness of the scarp area).

in comparison to measured values the data by Roch (1966) [8] are available. He conducted shear box measurements with varying weight. In the important shear from 1-2 kN/m2 the following values were determined:

The assumed value for tg mu = 0.202 is known. The values by Roch seem rather large. Since “snow board” avalanches can break off at 25 degrees, mu must be <25 degrees in some cases. A smooth and fine grained scarp area has been assumed. Roch’s measurements indicate an increasing tendency of mu with increasing grain size.

4.3 Compilation of flow avalanche - a manual for practicitioners with examples.

The valid values are shown in detailed in SLF paper 47 [2] with the title above. They are the topic of this report.

5. Remarks

The table below shows the differences between the valid base values d0* and d0, respectively, and the ones by Salm (1989) and de Quervain (1979/80).

The partly large differences in the determination of d0 could lead to the conclusion that all avalanche hazard maps must be revised. This is in general not true. One has to conisder that avalanche tecchnical calculations are always improved. Besides the reliable determination of mean d0, roughness paramters epsilon (ms-2) and mu [1] were adjusted after field experiments. The factor of turbulent friction epsilon (ms-2) was increased from about 500-1000. this results in an increase avalanche velocity which compensates for the decrease of the 300 year d0 values. In summary we state that today the determination of the 30 year avalanche boundary is stricter. In addition there are no distinct differences in the determination of the 300 year avalanche boundary.