SNOW AVALANCHE FORMATION
Swiss Federal Institute for Snow
and Avalanche Research SLF,
J. Bruce Jamieson
Department of Civil Engineering
and Department of Geology and
Geophysics, University of Calgary,
Calgary, Alberta, Canada
Swiss Federal Institute for Snow and
Avalanche Research SLF,
Received 11 November 2002; revised 23 June 2003; accepted 14 July 2003; published 15 November 2003.
 Snow avalanches are a major natural hazard, endan-
gering human life and infrastructure in mountainous
areas throughout the world. In many countries with
seasonally snow-covered mountains, avalanche-forecast-
ing services reliably warn the public by issuing occur-
rence probabilities for a certain region. However, at
present, a single avalanche event cannot be predicted in
time and space. Much about the release process remains
unknown, mainly because of the highly variable, layered
character of the snowpack, a highly porous material that
exists close to its melting point. The complex interaction
between terrain, snowpack, and meteorological condi-
tions leading to avalanche release is commonly de-
scribed as avalanche formation. It is relevant to hazard
mapping and essential to short-term forecasting, which
involves weighting many contributory factors. Alterna-
tively, the release process can be studied and modeled.
This approach relies heavily on snow mechanics and
snow properties, including texture. While the effect of
meteorological conditions or changes on the deforma-
tional behavior of snow is known in qualitative or semi-
quantitative manner, the knowledge of the quantitative
relation between snow texture and mechanical proper-
ties is limited, but promising developments are under
way. Fracture mechanical models have been applied to
explain the fracture propagation, and micromechanical
models including the two competing processes (damage
and sintering) have been applied to explain snow failure.
There are knowledge gaps between the sequence of
processes that lead to the release of the snow slab: snow
deformation and failure, damage accumulation, fracture
initiation, and fracture propagation. Simultaneously, the
spatial variability that affects damage, fracture initiation,
and fracture propagation has to be considered. This
review focuses on dry snow slab avalanches and shows
that dealing with a highly porous media close to its
melting point and processes covering several orders of
scale, from the size of a bond between snow grains to the
size of a mountain slope, will continue to be very chal-
lenging. INDEX TERMS:1863 Hydrology: Snow and ice (1827); 1827
Hydrology: Glaciology (1863); 1899 Hydrology: General or miscella-
neous; KEYWORDS:snow, avalanche
Citation: Schweizer, J., J. B. Jamieson, and M. Schneebeli, Snow
avalanche formation, Rev. Geophys., 41(4), 1016, doi:10.1029/
 Snow avalanches are snow masses that rapidly
descend steep slopes. They can contain rocks, soil, veg-
etation, or ice. There are two types of release: loose
snow avalanches and slab avalanches. Loose snow ava-
lanches start from a point in a relatively cohesionless
surface layer of either dry or wet snow. Initial failure is
analogous to the rotational slip of cohesionless sands or
soil but occurs within a small volume (⬍1m
) in com-
parison to much larger initiation volumes in soil slides.
Snow slab avalanches involve the release of a cohesive
slab over an extended plane of weakness, analogous to
the planar failure of rock slopes rather than to the
rotational failure of soil slopes [Perla, 1980] (Figures
1–3). The observed ratio between width and thickness of
the slab varies between 10 and 10
. Slab thickness is
usually ⬍1m[Perla, 1977; Schweizer and Jamieson,
2001]. As shear fracture below the slab spreads along the
plane of weakness, high tensile stress and tensile fracture
develops upslope. Accordingly, slab failure appears to
begin with the propagation of tensile crown fracture
across the slope. The triggering of a snow slab avalanche
can occur by (1) localized rapid near-surface loading by,
for example, people or explosives (called artiﬁcial trig-
gering), (2) gradual uniform loading due to, for example,
precipitation, or (3) a no-loading situation that changes
snowpack properties, for example, surface warming (called
natural triggering or spontaneous release). The main dif-
ference in triggering modes is the rate of loading, which
is important since snow is highly rate-dependent.
 Slab avalanche release can be subclassiﬁed by the
type of instability [McClung, 2002]. New snow instabili-
ties are commonly the result of overloading due to rapid
precipitation during storms. They lead to direct-action
avalanches. Climax avalanches follow from old snow
Copyright 2003 by the American Geophysical Union. Reviews of Geophysics, 41, 4 / 1016 2003
instabilities due to the failure of a buried layer of kinetic
growth crystals. These crystal types include surface hoar,
(near-surface) faceted crystals, and depth hoar, and they
compose persistent weak layers [Jamieson and Johnston,
 Natural avalanches threaten residents and infra-
structure, whereas human-triggered avalanches are the
main threat to recreationists [Jamieson and Geldsetzer,
1996; Tschirky et al., 2001]. The average number of snow
avalanche fatalities worldwide is estimated at 250 per
year [Meister, 2002]. In the United States, snow ava-
lanches cause on an average annual basis more fatalities
than earthquakes or landslides [Voight et al., 1990].
 Avalanche formation is the complex interaction
between terrain, snowpack, and meteorological condi-
tions leading to avalanching. Avalanche formation can
be broken down to the following questions: Where and
when does what kind of avalanche occur? These are key
questions for the backcountry traveler, the avalanche
forecaster, and the snow safety manager alike. “How”
and “why”are additional questions for the researcher.
There is usually no clear answer to the questions of
occurrence, and current science is not able to give def-
inite answers on the processes involved. In fact, because
of the stochastic nature of some of the meteorological
processes acting on the snow cover, a purely determin-
istic approach to the questions of “where”and “when”
will have limited success.
 The dynamics of avalanche motion and mitigation
by planning and structures are not dealt with in this
review. Barbolini et al.  provide a recent overview
on avalanche dynamics models.
 Avalanche formation can be approached in two
ways: (1) The complex interaction between terrain,
snowpack, and meteorological conditions can be ex-
plored by association or statistics, or (2) the physical and
mechanical processes of avalanche formation can be
studied and modeled. Whereas the latter approach is
physical, the former is applied by most avalanche-fore-
casting services. By empirically weighting the inﬂuence
of the contributory factors in a speciﬁc situation, the
avalanche probability and characteristics are estimated,
and a forecast is made. The contributory factors are
known [Atwater, 1954; de Quervain, 1966; Perla; 1970]
and have physical meanings that are related to the ava-
lanche formation process.
Figure 1. Crown fracture of a huge snow slab avalanche.
Figure 2. Snowpack conﬁguration at the crown of a slab
avalanche: cohesive slab on top of a thin weak layer (buried
surface hoar crystals).
Figure 3. Slab avalanche nomenclature and coordinate sys-
tem (adapted from Perla  with permission of the Na-
tional Research Council of Canada).
2-2 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
 Snow slope failure has been studied with a
strength-of-material approach. Snow stability Sis calcu-
lated for a given time, depth within the snowpack, and
location on the slope. Hence the avalanche problem is
reduced to the question of balance between snow
and stress (normal stress and shear stress )
at time tand location x:
Theoretically, unstable conditions will occur when the
stability index Sapproaches 1. Since strength and load
vary spatially and temporally within the snowpack, the
application of this critical stress concept for snow slope
failure is not straightforward, and snow stability depends
on scale. Important parameters (strain and strain rate)
and processes (fracture propagation) are not considered.
While crack initiation will depend on stresses, the for-
mation and propagation of cracks requires deformation
energy [Bazant and Planas, 1998]. Therefore the failure
of a snow slope needs to be considered from a fracture
mechanical view focusing on three critical variables:
stress, ﬂaw size, and toughness [Anderson, 1995].
 The snow slope failure process involves a wide
range of scales. Avalanche formation starts at the mi-
croscale, where single bonds break (10
m), and ﬁn-
ishes with fracture propagation leading to the release of
the slab (macroscale 10
m). The mesoscale is pri-
marily the scale of the snowpack thickness (10
Variability of the mechanical parameters due to varying
meteorological conditions is inherent on all scales and is
fundamental to both fracture initiation and fracture ar-
 In the following we assess the state of knowledge
on avalanche formation considering both the contribu-
tory factors and the failure mechanics at different scales.
We focus on dry snow slab avalanches because they
represent the major type of avalanche hazard.
Mellors  monograph on avalanches is a
landmark, and McClung and Schaerer  have com-
prehensively summarized the subject for a broader pub-
lic. Our aim is a synthesis that steers the interested
reader to the references that either represents recent
developments or starting points for more detailed stud-
2. CONTRIBUTORY FACTORS
 Most contributory factors are related to either
strength or load and their variation. Atwater  pro-
posed 10 weather and snow factors that contribute most
to avalanche danger but did not consider terrain. We
describe ﬁve essential factors: terrain, precipitation (es-
pecially new snow), wind, temperature (including radia-
tion effects), and snowpack stratigraphy. If consistent
avalanche occurrence data are available, the contribu-
tion of weather and snow variables can be determined
quantitatively [e.g., McClung and Tweedy, 1993]. Assess-
ing the avalanche release probability by estimating and
weighting of each of the contributory factors in a given
situation has been successfully applied because all rele-
vant meteorological factors can be measured by auto-
matic weather stations [Gubler, 1993].
 Terrain is an essential factor and the only factor
that is constant over time. A slope angle of ⬎30⬚is
usually required for dry snow slab avalanches. However,
there are different scales/ways to measure slope angle
that affect the critical angle and hinder the comparison
of data from different sources. For avalanche forecasting
the critical slope is the steepest angle from the horizon-
tal averaged over about 20 m in the starting zone.
Schweizer and Jamieson  analyzed a large data set
of skier-triggered avalanches from Switzerland and Can-
ada including data on aspect (compass direction that the
slope faces) and slope angle (Figure 4). The results do
not differ substantially from previous studies on natural
avalanches or data sets of avalanches with different types
of triggering [Perla, 1977]. Analysis of the catastrophic
avalanches in the Alps during winter 1999 has shown
that few avalanches released on terrain of ⬍30⬚[Am-
 On some Swiss ski touring maps the terrain
steeper than 30⬚is specially colored. Munter  has
proposed rules of terrain selection for recreationists by
coupling slope angle to danger level (ﬁve-degree Euro-
pean avalanche danger scale: low, moderate, consider-
able, high, very high [Meister, 1995]). If, for example, the
Figure 4. Slope angle in starting zone of human-triggered
avalanches (N⫽809, ﬁrst quartile, 37⬚, with median of 39⬚;
third quartile, 41⬚, with mean of 38.8⬚⫾3.8⬚). The mean
thickness of the sampled slabs was 0.49 ⫾0.22 m (reprinted
from Schweizer and Jamieson  with permission from
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-3
public avalanche bulletin rates the danger level as mod-
erate, it is recommended not to ski slopes steeper than
40⬚. As there are no data on the frequency of skiing by
slope angle, no real risk analysis can be done, and the
true relation between slope angle and probability of
triggering has not been established.
 There are no well-established rules on the effect
of the microtopography of starting zones [e.g., Bozhin-
skiy and Losyev, 1998]. However, avalanches are more
frequent in starting zones with concave cross-slope pro-
ﬁles [Gleason, 1995; McClung, 2001]. Slope angle varia-
tions (convex downslope curvature, e.g., a bump) pro-
voke stress concentrations that favor avalanche
formation [e.g., Fo¨hnetal., 2002].
 With digital terrain models (DTM) and geo-
graphical information systems (GIS) [Lied et al., 1989],
potential starting zones can be identiﬁed and their char-
acteristics compared to avalanche occurrence [Stoffel et
al., 1998] (Figure 5) or used as input for avalanche
dynamics calculations [Gruber et al., 1998]. However, this
approach is only reliable if the DTM resolution and
accuracy are not larger than 20–30 m, and even then
they do not indicate small-scale variations in slope angle
that are of interest for avalanche forecasting. One of the
ﬁrst approaches along this line was the French expert
system for avalanche starting zone path analysis [Buisson
and Charlier, 1989]. So far, the systematic identiﬁcation
of starting zones has been restricted to slope angle
(terrain between 30⬚and 50⬚, occasionally 60⬚) and veg-
etation (no forest). However, in order to improve hazard
mapping the frequency of avalanching in a given poten-
tial starting zone needs to be known. The combined
effect of topographic parameters (cross-slope curvature,
slope, distance to the next ridge, and aspect) on the
frequency of large avalanches has been analyzed using
GIS and the extensive avalanche occurrence data from
the region of Davos, Switzerland [Maggioni and Gruber,
2002]. It conﬁrmed that highly concave cross-slope cur-
vature in combination with a high mean slope angle
(⬎36⬚) leads to high avalanche frequency but small
release area compared to the potential starting zone
 Terrain roughness inﬂuences avalanche forma-
tion by hindering the formation of continuous weak
snowpack layers. A minimal snow depth of 0.3–1mis
necessary to smooth out most terrain roughness. There-
fore, when analyzing the effect of new snow loading, the
snow depth prior to the snowfall is relevant, reducing the
threshold value of the 3-day sum of new snow depth for
a given avalanche probability [Stoffel et al., 1998]. Highly
variable terrain roughness can inﬂuence the internal
evolution of thin snowpacks. Rocky outcrops or slightly
covered rocks may promote instability through growth of
faceted crystals due to the higher temperature gradients
where the snowpack is thinner [Arons et al., 1998; Logan,
 Forests inhibit avalanche formation. In dense for-
ests (⬎200 trees of diameter ⬎16 cm ha
) the snow
cover is too irregular to produce avalanches [Frey et al.,
1987; Gubler and Rychetnik, 1991; Schneebeli and Meyer-
Grass, 1993]. In particular, snow interception modiﬁes
the old snow surface and hinders weak layer formation;
Figure 5. Spatial distribution of frequency of avalanche occurrence during the 14-year period of avalanche
observations for the area of Zuoz, Engadine Valley, Switzerland (adapted from Stoffel et al. , reprinted
from the Annals of Glaciology with permission of the International Glaciological Society).
2-4 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
it also changes the distribution and accumulation rate of
new snow during the storm. Extreme slab avalanches
with fracture depth ⬎1 m should only develop where a
continuous weakness with no signiﬁcant interruption
exists within an open area of about 10 m width and
10–20 m length. Avalanches starting from clear-cut log-
ging have destroyed timber and caused substantial losses
in western Canada [McClung, 2001].
2.2. New Snow
 For large (catastrophic), new snow avalanches,
precipitation is the strongest forecasting parameter
[Fo¨hn et al., 2002] and is closely related to avalanche
danger (Figure 6). Accumulation of a new snow depth of
about 1 m within a storm is considered critical for the
initiation of extreme avalanches; about 30–50 cm is
critical for naturally released avalanches in general.
However, even with large amounts of new snow, the
combined release probability of a group of avalanche
paths is frequently ⬍50% [Schaer, 1995]. This shows that
the new snow depth alone is not sufﬁcient to explain
 For natural releases during or shortly after
storms the precipitation rate or loading rate can strongly
inﬂuence the critical balance between stress and
strength. If the new snow loading is rapid (ⱖ2.5 cm h
the weak layer below the storm snow layer might not
gain strength sufﬁciently quickly. The strength gain fol-
lows from the load of the overlaying slab. Hence there is
a competition between the rate of loading from snowfall
and the rate of strengthening of buried weaknesses.
Forecasting models were developed based on this simple
stress criterion (stability) [Conway and Wilbour, 1999;
Endo, 1991]. Considering a planar snowpack inclined at
angle and neglecting longitudinal stresses, the stability
(t) for a weak layer at given depth zand time tis
where Ais a constant, gis the gravitational acceleration,
˙wis the rate of loading [Conway and Wilbour, 1999].
The basal shear strength
(t) is estimated by ﬁtting a
power law relationship to measurements of shear
strength and density [Jamieson, 1995]. In a maritime
climate the model to predict direct-action avalanches
during storms showed promising results, despite the fact
it used an average strength value, which depends only on
 For skier-triggered avalanches, even lower criti-
cal values of new snow thickness were proposed, de-
pending qualitatively on wind, temperature, surface con-
ditions prior to the snowfall, and prior skiing activity on
the slope [Munter, 1997]. The critical new snow values
vary between 10–20 cm under unfavorable and 30–50
cm under favorable conditions, based on the above men-
 If new snow depth is not measured, it can be
estimated from the increase in snow depth by taking into
account settling of underlying layers [Kominami et al.,
1998]. This same approach is used operationally for the
Swiss avalanche warning service based on continuous
snow depth measurements from automatic weather sta-
tions [Lehning et al., 1999].
 The density of new snow also affects avalanche
formation. Mueller  showed that decreasing den-
sity with depth (denser snow above less dense snow) is
associated with increased avalanche activity.
 Wind contributes to loading and is often consid-
ered the most active contributing factor after new snow.
Loading by wind-transported snow can be fast and pro-
duces irregular deposits with locally increased loading
rates. Variations in wind speed and snow drift form
layers of different density or hardness, creating stress
concentrations within the layered snowpack. de Quervain
 proposed that the wind transforms the snow into
a more brittle material and that wind-deposited snow
layers are more prone to avalanching. Meister 
studied the relation between new snow density, air tem-
perature, and wind speed and suggested that wind-hard-
ened slabs have high viscosities. However, neither de
Figure 6. New snow depth during 3-day storm periods in
relation to the veriﬁed degree of avalanche danger (ﬁve-degree
uniﬁed European danger scale) for the region of Davos, Swit-
zerland (N⫽1512). Spearman rank-order correlation coefﬁ-
cient between 3-day sum of new snow depth and danger degree
was 0.58 (p⬍0.001). Boxes span the interquartile range from
ﬁrst to third quartile with a vertical line showing the median.
Whiskers show the range of observed values that fall within 1.5
times the interquartile range above and below the interquartile
range. Asterisks show outliers; circles show far outside values
(adapted from Schweizer and Fo¨hn , reprinted from the
Journal of Glaciology with permission of the International
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-5
Quervain nor Meister determined brittleness that is a
fracture mechanical property. In addition, the character-
istics of the weak layer below the wind-deposited layer
are at least as important.
Gauer  measured the snow deposition (and
erosion) pattern on both sides of a mountain ridge. The
patterns were highly irregular, in particular on the lee
slope, probably because of turbulent eddies. The eddies
can be stationary for a certain wind speed and direction
(dunes are formed), but they will change as wind speed
or direction change. Averaged over the whole slope,
20–30% more snow was deposited compared to a level
study plot, but locally much larger differences existed.
Doorschot et al.  reported up to fourfold increase
in snow deposition in the lee area close to the ridge
compared to the ﬂat ﬁeld (Figure 7). This indicates that
fracture depth taken at the fracture line of large cata-
strophic avalanches might substantially overestimate the
average slab thickness in the starting zone. In contrast to
gentle terrain, in alpine terrain the transport by suspen-
sion is more important than transport by saltation. This
is due to the higher turbulence in the mountains in
general and particularly to the larger upward component
of the ﬂow velocity [Gauer, 1999].
 Numerical modeling of snow erosion and depo-
sition has become increasingly sophisticated with in-
creasing computing power [e.g., Doorschot et al., 2001;
Gauer, 1999, 2001; Greene et al., 1999; Guyomarch and
Me´rindol, 1998; Lehning et al., 2000a, 2000b; Naaim et al.,
1998]. When discussing the role of snow drift in ava-
lanche formation, Lehning et al. [2000b] took four con-
nected processes into account: (1) the wind ﬁeld over
steep topography, (2) the preferential deposition of
snow during snowfall, (3) the possible redistribution of
already deposited snow, and (4) the different snowpack
conditions and development at the sites of erosion and
deposition. Their model parameterized preferential dep-
osition and redistribution by coupling the numerical
model for drifting and blowing snow with the snow cover
model called SNOWPACK [Lehning et al., 1999]. Fo¨hn
 and Meister  previously proposed an empir-
ical formulation relating the additional snow depth H
deposited in lee slopes per day to the third power of the
daily average wind speed u(uⱕ20ms
Hwind ⫽ku3, (3)
where the coefﬁcient k⫽8⫻10
determined empirically based on 3 years of mass balance
measurements over a mountain ridge.
Gauer  showed that the initially rapid in-
crease in mass ﬂux with increasing wind speed decreased
with further increase in wind speed. The power de-
creased from approximately 4 to 2. When only saltation
was modeled, the power was about 3, corresponding to
the empirical formulations. So far, it has been assumed
that snow drift peaks at a wind speed of about 20–25 m
and decreases with even higher wind speeds. Con-
sidering saltation and suspension, the calculations by
Doorschot et al.  suggest that snow drift might level
off at lower wind speeds because of saturation. The
saturation effect is particularly pronounced during snow-
fall where the amount of redistributed snow is limited
and preferential deposition of the falling snow domi-
nates snow loading. The numerical simulations repro-
Figure 7. Snow distribution on windward and lee slopes of a mountain ridge with 5-m contour lines
(Gaudergrat, near Davos, Switzerland) after a snowdrift period (26–31 January 1999). Main wind direction
was northwest. The difference in snow depth dH compared to the snow depth prior to the snowdrift episode
is shown. Negative values of dH indicate erosion [from Doorschot et al., 2001] (reprinted from the Annals of
Glaciology with permission of the International Glaciological Society).
2-6 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
duce the general snow deposition patterns across a
mountain ridge (Figure 8) but are limited to a single
slope. In order to achieve useful results at the scale
relevant for avalanche formation a high resolution (⬍20
m) of the wind ﬁeld is needed, requiring extensive com-
puting time. Application to whole mountain ranges for
avalanche forecasting is presently not feasible.
 Alternatively, a more empirical approach can be
followed using GIS [e.g., Purves et al., 1998; Mases et al.,
1998], comparable to the approach by Buisson and Char-
lier . However, forecasters and hazard mapping
engineers who assess the run out from extreme ava-
lanches use judgment to assess the additional loading in
starting zones. As a step toward applicability, Lehning et
al. [2000a] developed the drift index for the additional
amount of snow in a typical lee slope based on wind
speed measured on a mountain crest and on modeled
surface conditions (snow mobility) at the site of an
automatic snow station. Snow mobility depended on
grain size and bond size, parameters that were available
from the numerical snow cover model.
 A new device to assess snow drift, FlowCapt, is
used for local avalanche forecasting. This acoustic sen-
sor determines wind velocity and particle ﬂux based on
the particle impacts on the sensor pipe [Chritin et al.,
 Temperature is a decisive factor contributing to
avalanche formation, particularly in situations without
loading. Its effect on snow stability is complex since
changes in air temperature affect snow stability in vari-
ous ways. Again, the rate of change is important. Rising
temperature during a storm and rapid temperature in-
crease shortly after a storm contribute to instability.
Changes in air temperature primarily affect surface lay-
ers, i.e., the slab, whereas the weak layer is relatively
unaffected because of the generally low thermal conduc-
tivity of snow [Sturm et al., 1997]. Although snow
strength decreases with increasing snow temperature,
instability after rapid warming does not develop from a
weakening of the weak layer below the slab but from
increased deformation of the surface layers of the slab,
leading to increased strain and strain rates at the slab/
weak layer interface.
 The mechanical properties of snow are highly
temperature-dependent [McClung, 1996]. McClung and
Schweizer  reviewed temperature effects on snow
hardness, failure toughness and shear strength. In gen-
eral, there are two important groups of competing ef-
fects: (1) metamorphism (depending on temperature,
temperature gradient, and other snow properties) and
creep and (2) mechanical properties (excluding meta-
morphism effects) including snow hardness, fracture
propagation potential (toughness), and strength (Table
1). Group 1 effects need more time, whereas group 2
effects change snow stability rapidly.
Schweizer  studied the shear strength of
natural samples taken in a study plot at different tem-
peratures in a cold laboratory. The stiffness (initial tan-
gent modulus) was the most temperature-sensitive me-
chanical property of snow. Camponovo and Schweizer
Figure 8. Comparison of modeled to measured snow distri-
bution across a mountain ridge (Gaudergrat, near Davos,
Switzerland) [from Lehning et al., 2000b] (䉷Swets and
Table 1. Snow Temperature Effects According to Time Required and Stability
Snowpack Property or Process Change due to Warming Response Time Effect on Stability
Stiffness or hardness of slab signiﬁcant decrease immediate decrease
Toughness increase immediate decrease
Strength of weak layer/interface slight decrease immediate decrease
Bond formation (metamorphism) increase of bond formation rate and strength delayed increase
Creep increase of creep rate causing settlement and
densiﬁcation hand hence increasing strength
Snow temperature (temperature
gradient) usually decrease of temperature gradient
causing change of crystal form and increasing
For warming, immediate effects promote instability; delayed effects promote stability. Under warming, instability is likely to come from
immediate not delayed effects. Strength effects may be immediate (decrease) or delayed (time-dependent with increase) under warming, with
the greatest strength changes being delayed [after McClung and Schweizer, 1997].
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-7
 recently measured the viscoelastic properties of
snow by using a rheometer. By applying small deforma-
tions with a linear and recoverable response, continuous
measurements, while changing the ambient tempera-
ture, yield the temperature dependence of the modulus
[Schweizer and Camponovo, 2002]. The temperature de-
pendence of the dynamic shear modulus G⬘follows an
Arrhenius relation up to about ⫺6⬚C, with a much
accelerated decrease toward 0⬚C (Figure 9). The varia-
tion of the modulus is important for the penetration of
load from the surface to the weak layer and also for
fracture processes. Even if the strength in the weak layer
decreases with increasing temperature, which is delayed
and attenuated with respect to the surface perturbation,
the fracture toughness increases. Because of that in-
crease, fracture initiation and fracture propagation be-
come less probable with increasing snow temperature.
The high fracture toughness at temperatures close to the
melting point also explains why triggering of moist or
wet slab avalanches by localized rapid loading, e.g.,
explosives, is rare. On the other hand, rain on fresh snow
triggers wet slabs by loading, by contraction-related
stresses, and by changes in the properties of the surface
layers [Conway, 1998].
 Radiation can reduce snow stability similarly to
rapid warming but can be more effective. Snow cover
modeling [Bader and Weilenmann, 1992; Brun et al.,
1989] as well as the high-quality input data that drive the
models has substantially increased our understanding of
the effects of radiation on the snowpack and has ex-
plained some of the processes leading to weak layer
formation at the snow surface (see section 2.5). The
energy balance for any aspect, slope angle, elevation,
and time of the year can be calculated [Durand et al.,
1999]. However, there is little veriﬁcation, and the effect
of the surrounding terrain (e.g., shading effects, reﬂec-
tions, and emission from terrain) is not included or is
only considered for the ablation period [Fierz et al.,
1997]. The energy balance can be dominated by the
outgoing long-wavelength radiation during the winter
months of December and January, particularly on shady
slopes and in clear-sky conditions. This effect prevents
an increase in air temperature (warming) from affecting
the temperature of the snow and thereby its stability.
However, this knowledge has not been applied system-
atically to stability evaluation or avalanche forecasting.
 Whereas there are many comprehensive mea-
surements on snow albedo [Sergent, 1998], measure-
ments of the radiation absorption in the snow cover
suggest that this process in the uppermost 5–10 cm is not
fully understood [Gaia, 1993]. Detailed temperature
measurements in the snow cover have shown that daily
variations affect the upper 10–20 cm. High-frequency
radiation (blue and UV) might cause very minor effects
on the snow temperature up to 50 cm depth but without
substantial effect on snow stability.
2.5. Snow Cover Stratigraphy and Selected Snow
 Snow cover stratigraphy is recognized as the key
contributing factor for dry snow slab avalanche forma-
tion. Any loading by new or wind-driven snow or any
temperature increase has no effect on snow stability if no
weakness exists in either the old snow or at the old snow
surface underlying the new snow. Therefore the weak
layer or interface is a necessary prerequisite but not
Figure 9. Effective elastic shear modulus G⬘versus temperature. Results are obtained with continuous
oscillation measurements during 8 hours (torsional shear). Laboratory temperature changed from ⫺7⬚Cto
⫺20⬚C and subsequently to ⫺1⬚C and back to ⫺7⬚C. Hardly any hysteresis is apparent, indicating that the
experiment was performed in the linear viscoelastic range without textural changes happening during the
experiment. (a) Dynamic shear modulus and complex viscosity versus temperature in ⬚C. (b) Dynamic shear
modulus versus inverse of absolute temperature to show linear behavior (Arrhenius relation) above about
⫺6⬚C. Dashed vertical line indicates 0⬚C. Snow type tested consisted of small rounded grains and partly
decomposing and fragmented precipitation particles, of size 0.25–0.5 mm, density 220 kg m
, and hand
hardness index 2 (reprinted from Schweizer and Camponovo  with permission from Elsevier).
2-8 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
sufﬁcient condition for avalanche formation (Figure 10).
The properties of the overlying slab also have to be
considered [McClung and Schweizer, 1999; Schweizer,
1993; Schweizer et al., 1998], particularly for fracture
propagation. There are several studies on weak layer
properties. Fo¨hn  and Hachikubo  measured
and modeled the development of surface hoar. Two
other types of weaknesses are near-surface faceting
[Fierz, 1998; Fukuzawa and Akitaya, 1993] and a poor
bond to Sun-generated crusts [Ozeki et al., 1995]. The
formation of near-surface faceted crystals is due to large
temperature gradients near the snow surface resulting
from the heat loss by outgoing long-wavelength radia-
tion. At measured temperature gradients of 150 K m
growth rates were of the order of 0.1 mm d
 has comprehensively summarized the processes
that lead to near-surface faceted crystals: radiation re-
crystallization, faceting adjacent to a wet layer, and
diurnal recrystallization. Near-surface faceting is the
most active process, besides surface hoar growth, that
leads to weak layer formation. Faceting processes above
crusts and wet layers, and to a lesser degree below, are
the only efﬁcient ways to form weak layers within the
snowpack [Colbeck and Jamieson, 2001]. Although the
large majority of avalanches during storms are probably
released by nonpersistent weak layers, 70% of 186 skier-
triggered avalanches were released by weak layers of
persistent grain types (i.e., surface hoar, faceted crystals,
and depth hoar) [Schweizer and Jamieson, 2001]. Analy-
sis of fracture line proﬁles showed that the weak layer
differs distinctly in grain size and hardness from the
adjacent layers. These snowpack properties together
with snowpack test results are the basis of ﬁve stability
classes of snow proﬁles [Schweizer and Wiesinger, 2001].
When comparing stable with unstable proﬁles, the dif-
ferences in grain size and hardness between the weak
layer and the adjacent layer for the unstable proﬁles
were signiﬁcantly larger than for the stable proﬁles (Fig-
ure 11) [Schweizer and Jamieson, 2003b].
Jamieson and Johnston [1999, 2001] made exten-
sive measurements of weak layer strength and calculated
a stability index, which related to skier-triggered ava-
lanches. They provided shear strength for weak layers by
density and grain type. Together with the data on tensile
strength [Jamieson and Johnston, 1990], these are the
most consistent set of brittle strength data for natural
snow. Jamieson and Schweizer  proposed a concep-
tual model to explain strength changes based on bonding
and texture of buried surface hoar layers. Jamieson and
Johnston  reported that on average buried weak
surface hoar layers gained strength at about 100 Pa d
(Figure 12). Jamieson et al.  showed that in con-
ditions characterized by a deep snowpack, the shear
strength was best correlated with the overlaying load.
They suggested loading was the main factor promoting
increased strength through a pressure-sintering process
[Gubler, 1982] by which the number and/or size of bonds
progressively increases with time under load. Rapid
loading produces instability more often than gradual
loading, indicating that during rapid loading the strength
of weak layers tends to lag behind the load on the order
of days [Chalmers, 2001]. Such effects need to be in-
cluded in models of weak layer strength and slab stability
 The cantilever test of unnotched snow beams can
be used to assess the slab properties in combination with
a stability test of the weak layer [Mears, 1998; Perla,
1969]. Johnson  improved the cantilever beam test
and studied remotely triggered avalanches. Compared to
avalanches triggered in steep starting zones, avalanches
remotely triggered from low-angle terrain tended to
have thicker, denser, and harder slabs.
Figure 10. Snow stratigraphy. Weakness below the slab is required for dry snow slab avalanche formation.
(a) A thin weak layer of buried surface hoar crystals that partly fractured (left) and that is still intact (right)
[from Jamieson and Schweizer, 2000] (reprinted from the Journal of Glaciology with permission of the
International Glaciological Society). Layer thickness of unfractured surface hoar is approximately 19 mm. (b)
Weak interface between (below) a depth hoar layer and (above) the new snow layer. Scale of grid is 3 mm.
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-9
 Brittle fracture and fracture propagation are es-
sential parts of snow slab release (see section 3.1). Kirch-
ner et al.  measured the fracture toughness of snow
under tension. Notched cantilever beams of snow (20 cm
⫻10 cm ⫻50 cm in size) were broken under their own
weight in the ﬁeld at temperatures close to the melting
point. Their data included newly fallen snow and snow
consisting of melt-freeze grains. The critical stress inten-
sity factor K
, characteristic of brittle fracture, varied
with relative density as
with B⫽7.84 kPa m
.Kirchner et al.  suggested
these extraordinarily low values of fracture toughness
indicate snow is one of the most brittle materials known.
Kirchner et al. [2002a, 2002b] assessed the effect of
external loading and friction under shear. Homogeneous
(nonlayered) snow samples under laboratory conditions
were tested. However, before fracture toughness can
become a relevant parameter for assessing snow slope
stability, measurements for more different snow types
are needed, and in particular, layered samples need to
be tested. Furthermore, a ﬁeld test must be designed to
complement standard stability tests (see below).
 In view of the importance of snow cover stratig-
raphy for avalanche formation, numerical modeling of
the snow cover evolution from meteorological measure-
ments is a key research subject. The French model
Crocus [Durand et al., 1999] is part of the operational
forecasting model chain SAFRAN-Crocus-ME
which includes stability evaluation and simplistically
takes into account terrain (aspect and elevation). The
Swiss model SNOWPACK [Lehning et al., 1999] (Figure
13) is primarily microstructure-based and simulates the
snow cover evolution in level study plots. It runs opera-
tionally to calculate parameters such as the new snow
depth and drift index for the Swiss avalanche warning
service (see section 2). A stability evaluation tool is
under development [Lehning et al., 2003]. At present,
stability interpretation from manually observed snow
proﬁles surpasses that from modeled or penetrometer
proﬁles [Schneebeli and Johnson, 1998]. In general,
snowpack evolution is well simulated with regard to
snow depth, bulk density, and snow temperature [Du-
rand et al., 1999; Lehning et al., 2001]. Veriﬁcation of
Figure 11. Comparison between 194 unstable (skier triggered) and 207 stable proﬁles. Statistically signiﬁ-
cant differences in (left) grain size (Utest, p⬍0.001) and hardness (Utest, p⬍0.001) across fracture interface
are shown. Boxes span the interquartile range from ﬁrst to third quartile with a horizontal line showing the
median. Notches at the median indicate the conﬁdence interval (p⬍0.05). Whiskers show the range of
observed values that fall within 1.5 times the interquartile range above and below the interquartile range.
Asterisks show outliers; circles show far outside values (reprinted from Schweizer and Jamieson [2003b] with
permission from Elsevier).
Figure 12. Strength changes of three surface hoar layers.
Dates indicate day of burial at Mount Fidelity (Columbia
Mountains, Canada). Dashed-dotted line indicates average
rate of strength increase: about 100 Pa d
2-10 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
snow stratigraphy is limited by the lack of objective
snowpack data. Comparison with manual proﬁles
showed that most layers were correctly modeled in terms
of grain type and size. However, average stratigraphy
might not be relevant for stability evaluation, since for
avalanche formation, snowpack weaknesses are essen-
tial. Most of these result from the complex mass and
energy balance at the snow surface and are more difﬁcult
 Other than avalanche occurrence data, snowpack
stability tests and tests of weak layer strength provide the
only direct information on snowpack characteristics rel-
evant for avalanche formation. McClung and Schweizer
 brieﬂy described the rutschblock test, the shovel
shear test, and the shear frame test. Other relevant tests
used are the compression test [Jamieson, 1999] and the
stuff block test [Birkeland and Johnson, 1999] (Figure
14). Most tests identify potential weak layers or inter-
faces and give an index of snowpack stability, provided
the effect of the slab properties is considered. In situ
snow slope stability testing usually involves isolating a
snow column and loading the surface of the column at
speciﬁed steps. Therefore slab properties and weak layer
properties are tested in combination. All common tests
try to reproduce, to various degrees, the dynamic loading
by a skier or snowboarder, and they cause brittle fracture
in weak layers. Stability tests are most indicative on
slopes, but some can be done in gentler terrain to avoid
exposure to avalanche danger. Larger stability test areas
provide more reliable results [Fo¨hn, 1987a; Tremper,
2001]. None of the tests provides direct information on
fracture propagation propensity. However, all methods
test a size comparable to that required for self-propa-
gating brittle fractures due to rapid loading (0.1–1m)
[Schweizer, 1999]. The type of failure (e.g., planar, partly
nonplanar, etc.) as observed is essential and may serve as
aﬁrst indicator of the propagation propensity [Johnson
and Birkeland, 2002]. In particular, for the rutschblock
test the type of release (whole block versus partial re-
lease) is also indicative of propagation propensity
[Schweizer, 2002]. Besides mechanical stability informa-
tion from stability tests, snow stratigraphical character-
istics, such as changes in hardness or grain size at layer
boundaries, proved predictive for evaluating snowpack
stability with regard to skier loading [Schweizer and
Jamieson, 2003b; McCammon and Schweizer, 2002].
3. MECHANICAL MODELS
 The dry snow slab avalanche is the result of four
types of failures, leading to ﬁve fracture surfaces: one in
tension at the top of the slab (crown), two lateral breaks
on the sides of the slab (ﬂanks) mostly in shear, one
compressive failure at the lower end (stauchwall), and a
failure between the slab and the supporting substratum
[de Quervain, 1966] (Figure 3). It is clear that the pri-
mary failure is between the slab and the substratum,
commonly in slope-parallel shear, but occasionally, com-
pressive failure leads to the loss of shear support, com-
Figure 13. Simulation of snow cover evolution. Simulated grain type within snow cover during 2 and
one-half months in winter 1999 for the Weissﬂuhjoch study plot 2540 m above sea level (Davos, Switzerland)
are shown. On the right, snow stratigraphy from a manually observed proﬁle from 31 March 1999 is given for
comparison. During the 2- and one-half-month period, three major snowfalls occurred. Before the storm
periods, during fair weather conditions, substantial parts of the snowpack had been unfavorably transformed
to faceted grains because of increased temperature gradients within the shallow snowpack. During the
subsequent storm periods several avalanche cycles caused numerous avalanche fatalities in the French, Swiss,
and Austrian Alps (reprinted from Lehning et al.  with permission from Elsevier).
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-11
parable to adhesive versus cohesive fracture in layered
materials [Weietal., 1996]. The compelling argument by
Perla and LaChapelle  that shear failure at the
base of the slab precedes tensile fracture through the
slab is based on observations that the tensile fracture
surface is perpendicular to the slope.
3.1. Slab Release Models
 The simplest model compares the shear strength
of the weak layer to the shear stress due to the overlay-
ing slab and any artiﬁcial near-surface load (equation
(1)). For release by localized rapid near-surface loading,
measurements on the effect of the skier on snow stability
showed the skiers impact strongly decreases with in-
creasing snow depth and that the decrease depends on
slab properties (stiffness) [Schweizer et al., 1995]. These
results agree with the simpliﬁed model for skier loading
as a line load on an elastic half-space [Fo¨hn, 1987b;
Schweizer, 1993], which was introduced in the stability
index. The concept of the stability index proved to be
successful for the case of skier triggering [Fo¨hn, 1987b;
Jamieson, 1995], in part successful for storm snow ava-
lanches [Conway and Wilbour, 1999] but in general not
successful for most other natural avalanches, i.e., under
gradual or no-loading conditions. This indicates that, in
line with linear fracture mechanics, a simple stress cri-
terion is insufﬁcient or even inappropriate for natural
avalanches. Failure starts at locations of below average
strength (ﬂaws). Macroscopic size effects are associated
with such fracture initiation. There is a critical ﬂaw size
needed for catastrophic failure of the whole structure or
 Snow slab failure models [e.g., Bader and Salm,
1990] consider a two-dimensional inclined snowpack
with an assumed prior weakness existing in the otherwise
homogeneous weak layer (Figure 15). In this deﬁcit zone
the shear stress from the overlaying slab is not supported
Figure 14. In situ snow slope stability testing usually involves isolating a snow block including a weak layer
and loading the block at given steps: (a) rutschblock test, (b) compression test, and (c) stuff block test [from
Schweizer and Jamieson, 2003a].
Figure 15. Snow slab release models with preexisting weak-
ness (deﬁcit zone or imperfection): two-dimensional inclined
snowpack with slope angle , slab thickness H, fracture depth
h, and length of deﬁcit zone or imperfection 2L. Resulting
distribution of slope-parallel shear stress
at weak layer
depth zis shown for two models: McClung  in the middle
and Bader and Salm  at bottom. For other parameters
2-12 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
by the shear strength. Not much is known about the
origin of this (assumed) preexisting deﬁcit zone. There is
no obvious process available for initiation of the stress
concentration in the weak layer, except possibly strain
softening during loading conditions. Conclusive experi-
mental evidence for deﬁcit zones is likewise lacking.
McClung [1979, 1981, 1987] was the ﬁrst to apply
fracture mechanical principles. His work focused on
ductile shear failure of the weak layer, followed by shear
fracture and propagation, based on a model for the
growth of a shear band (or slip surface) in an overcon-
solidated clay mass [Palmer and Rice, 1973]. A shear
band is initiated at a stress concentration in the weak
layer (Figure 15). Strain softening at the tip of the band
follows. When a critical length Lis reached, the band
propagates rapidly. The approach is similar to a Grifﬁth
criterion, which leads to analogous results, with the
difference that the stress at the tip of the band is nons-
ingular. The mode II propagation criterion is given by
where His slab thickness perpendicular to slope, is
Poissons ratio, Gis shear modulus,
⫽gH sin, the
shear stress due to the slab, where is average slab
density, gis acceleration due to gravity, is slope angle,
and ␦is the displacement in the shear band from peak
to residual stress
. The two terms on the left
are equivalent expressions for the driving term; the
rightmost term provides the resistance to shear band
extension. Assuming that the end zone length is small
compared to the band extension L, the critical down-
slope length L
for band extension can be given as
H共1⫺兲 共p⫺r兲␦ . (6)
The model can plausibly describe different slab release
scenarios [McClung, 1979]. As for any slab release model
involving a size effect, no veriﬁcation data are available.
 On the basis of the energy balance approach,
conditions for fracture propagation and hence for slab
release can be calculated. The conditions primarily de-
pend on the dimensions of the area over which the shear
strength deﬁcit exists. Accordingly, a critical size for
fracture propagation can be given. In the model pro-
posed by McClung  (see above), the size of the end
zone (or plastic zone) is considered as the minimal
length to initiate any progressive failure process and is
Using typical values of alpine snow combined with re-
sults from laboratory studies on shear failure [McClung,
1977; Schweizer, 1998] shows that the size of the end
zone can be estimated to 0.2–2.2 m. The critical length of
deﬁcit zone for fracture propagation must be a multiple
of the end zone size and decreases with increasing ratio
of peak to residual stress and increasing loading rate.
The rate dependence is consistent with results for con-
crete [Bazant and Planas, 1998] and is plausible in the
light of skier triggering [McClung and Schweizer, 1999].
 In general, a critical length in the two-dimen-
sional model between 0.1 and 10 m can be calculated,
but this is only an estimate [Schweizer, 1999]. The lower
range (0.1–1 m) is associated with slow growth; the
higher is associated with fast growth (1–10 m). For the
case of rapid loading the critical length for fast growth
reduces to 0.1–1m[McClung and Schweizer, 1999], i.e.,
to the order of the slab thickness. The spatial effect of a
skier is of the same order, supporting the estimate of
0.1–1 m, since skiers frequently induce brittle, rapidly
propagating fractures [Schweizer and Camponovo, 2001].
 Alternatively, critical crack size a
can be esti-
mated from preliminary measurements of the fracture
toughness of snow in shear K
[Kirchner et al., 2002a;
For typical values of K
the critical crack size a
is approximately 0.3–1 m. As these values are deter-
mined with linear fracture mechanics, they represent
lower limits since energy dissipated because of the plas-
ticity of the material is not included.
 The fact that the models assume a preexisting
weakness of unknown origin raises the question of frac-
ture nucleation [Nye, 1975]. de Quervain  pointed
out that to form the nucleus of fracture, stress must
locally exceed strength. Accordingly, Schweizer 
argued that slab release should initially start with dam-
age at the microscale rather than with a deﬁcit zone at
the mesoscale. He further proposed to model the failure
process based on two fundamental processes at the mi-
croscale: bond fracturing and sintering (bond forma-
tion). By introducing variability in microstructure, dam-
age could accumulate, leading to failure localization and
ﬁnally fracture propagation. This leads to the unsolved
question of how microstructure is related to strength (or
the mechanical properties in general) (see section 3.2).
 The fracture mechanical approach has recently
been revisited [Louchet, 2001b]. The stability of a basal
crack was analyzed as a Grifﬁth problem depending on
whether shear crack propagation is quasi-static or unsta-
ble. In the case of quasi-static expansion the slab would
ﬁrst meet the stress instability criterion in tension. This
release mode, called undercritical triggering by Louchet
[2001b], assumed a slowly expanding shear failure up to
the moment when tensile fracture takes place, as previ-
ously proposed by Perla and LaChapelle . The
second scenario required that the basal crack meets
conditions for unstable crack growth before the tensile
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-13
stress at the tip of the basal crack reaches the tensile
strength. In that case the critical crack size can be
estimated (equation (8)). Louchet [2001b] argued that
independent of snow characteristics, the transition be-
tween the two triggering modes would occur at a critical
slope angle of about 35⬚. If residual strength in the basal
failure was considered, this critical slope angle in-
creased. There are no observations or data available to
support the proposed transition in triggering modes. In
fact, assuming realistic values for density, slab thickness,
tensile strength, and toughness, Louchets model sug-
gests triggering would be primarily of the undercritical
type, which contradicts experimental evidence in which
the tensile fracture through the slab thickness is often
ﬁrst observed well above the skier (trigger point).
Åstro¨m and Timonen  proposed a snow slab
failure model based on statistical variation of strength.
The slab was modeled as a two-dimensional square
lattice of beams, connected to the substrate by other
beams. These connecting “friction beams”modeled the
static frictional contact between the substrate and the
slab. Both types of beams failed at a threshold value. The
fracture (slip) thresholds varied according to a statistical
distribution such as the Weibull or modiﬁed Gumbel
[Duxbury, 1990]. Åstro¨m and Timonen  concluded
that the grade of heterogeneity in the local fracture
(slip) threshold and the ratio of the average substrate
slip threshold to the average slab fracture threshold were
decisive for fracture behavior. Although the model is
neither realistic nor supported by data, consideration of
strength variation is important.
 There are few attempts to model snow slab fail-
ure physically or numerically. Physical models using
granular materials such as sand on inclined planes are so
far of little relevance for avalanche formation [Daudon
and Louchet, 2001], but they were successfully applied
for modeling avalanche motion as granular ﬂow [Savage,
1993]. Most numerical modeling has used ﬁnite element
models to calculate stress, strain, and strain rates for
complex geometry, including layering and irregularities
in the snowpack [Bader et al., 1989; Bader and Salm,
1990; Schweizer, 1993; Wilson et al., 1999]. Other numer-
ical models have used the ﬁnite difference method to
solve the stress-strain relations for snow stability condi-
tions using a simple stress failure criterion and a simpli-
ﬁed concave slope [Schillinger et al., 1998]. Implementing
improved material properties and stability criteria will
be the ﬁrst step toward more realistic modeling of slab
release [Stoffel and Bartelt, 2002]. However, numerical
and physical modeling is presently of limited importance
for the advancement of understanding and for practical
 Snow is a porous material consisting of crystalline
ice particles (or grains) welded together. The micro-
structure scale is of the order of 10
m. The microstruc-
ture describes the size, shape, and arrangement of grains
that cannot be seen by the naked eye. Classical snow
characterization [Colbeck et al., 1990] using a 10-power
hand lens focuses on grain type and size. The mechanical
properties are determined by the arrangement of grains
and particularly by the size and number of bonds. These
characteristics, however, usually cannot be seen with a
common hand lens. Whereas the term microstructure is
commonly used in engineering, an alternative term
(snow texture) is more commonly used in the geo-
sciences [Arons and Colbeck, 1995].
 Snow can be considered as cellular solid rather
than as a granular material. It is a sintered material, and
for low densities has foam-like properties [Kirchner et al.,
2001]. However, as the microstructure changes with in-
creasing density, the foam concept is probably not ap-
plicable for the whole density range (50–500 kg m
seasonal snow. The importance of microstructure (tex-
ture) to deformational processes has long been known,
and the large scatter in plots of mechanical properties
versus density [Mellor, 1975] has been attributed to the
inﬂuence of texture. Voitkovsky et al.  showed that
cohesion correlated better with speciﬁc grain contact
surface (total cross-sectional area of the bonds per unit
bulk area) than with density. Kry [1975a, 1975b] and
Gubler [1978b] ﬁrst tried to relate mechanical properties
to microstructure, in particular to bond size. For further
details on microstructural studies the reader is referred
to the work of Shapiro et al. . The bonds, or, more
precisely, the size and number of bonds per unit volume
and their orientation, should be related to strength.
Agrawal and Mittal  suggested that the degree of
bonding between grains and the pore length (or the
mean free distance between grains) should control the
mechanical properties. Classical characterization of
snow does not consider bonding, but size and shape of
crystals/grains have some relation to bonding. Larger
grains, in particular irregular angular (persistent) grains,
usually have fewer bonds per grain (coordination num-
ber) as well as fewer bonds per unit volume. Accord-
ingly, they form layers of low strength. Jamieson and
Schweizer  showed that shear strength of surface
hoar increased with layer thinning, which they argued
was associated with penetration of crystals into adjacent
layers and increased bonding (Figure 16).
 Until recently, producing thin or surface sections
and applying stereological methods to derive structural
parameters has been the standard procedure for char-
acterizing microstructure [Dozier et al., 1987; Good,
1987]. Schneebeli  improved the method by recon-
structing three-dimensional (3-D) representations from
serial sections (Figure 17). Alternatively, snow samples
have been visualized by x-ray microtomography [Cole´ou
et al., 2001; Schneebeli, 2002], scanning electron micro-
scope [Adams et al., 2001], and nuclear magnetic reso-
nance imaging [Ozeki et al., 2002]. Visualizing the snow
microstructure with modern imaging technology is only
the ﬁrst step. Quantitative description and interpreta-
tion of mechanical properties from 3-D images remains
2-14 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
to be done. Local curvature and surface area, two essen-
tial microstructural parameters that inﬂuence metamor-
phism, can now be determined [Brzoska et al., 2001; Flin
et al., 2001]. Microtomography during snow metamor-
phism or deformation experiments should improve our
understanding of microstructural processes [Schneebeli,
2002]. During the deformation process, grains continu-
ously rearrange accompanied by bond fracture and for-
mation. Except for very small strains (about ⱕ10
texture changes [Camponovo and Schweizer, 2001],
greatly complicating the development of constitutive
equations [Bartelt and von Moos, 2000].
Mahajan and Brown  made one of the ﬁrst
attempts to include microstructure in their constitutive
law for snow. After simpliﬁcation it proved applicable
for modeling snow cover evolution [Lehning et al., 1999].
Bartelt and von Moos  have used the same ap-
proach to interpret viscosity values from triaxial tests. To
characterize bulk properties, they used ice properties
and geometric parameters for microstructure, e.g., the
reduced contact area (the total area of bonds per unit
area or volume). Accordingly, the stresses in the bonds
are many times the macroscopic stress, which explains
why snow fails at much lower stress than ice despite the
fact that it consists of the same material.
Shapiro et al.  recommended index proper-
ties since no instrument would be readily available to
determine the required textural information. Recently, a
high-resolution constant speed penetrometer was devel-
oped [Schneebeli and Johnson, 1998; Schneebeli et al.,
1999]. Characterizing snow as a foam [Gibson and Ashby,
1997], Johnson and Schneebeli  developed a micro-
mechanical theory of penetration and used the penetra-
tion force-distance signal to recover microstructural and
micromechanical properties (Figure 18). The coefﬁcient
of variation of the high-resolution signal was related to
the ratio of grain size to density (texture index). Probing
the snowpack reveals highly complex force-distance sig-
nals including more information than from manually
observed hardness proﬁles [Pielmeier and Schneebeli,
2002] (Figure 19). Although identifying layers and snow-
pack weaknesses is not straightforward, the resistance
gradient is suggested to indicate the stiffness gradient
and hence stress concentrations much better than in
3.3. Snow Failure
 Snow deformation and failure are highly rate-
and temperature-dependent. The shear strength de-
creases with increasing strain rate and temperature. The
ductile to brittle transition occurs at a strain rate of
[Fukuzawa and Narita, 1993; Mc-
Clung, 1977; Narita, 1980; Schweizer, 1998] (Figure 20).
The bulk rate and temperature dependence can be ex-
plained based on the properties of ice and an interpre-
tation of deformation and failure at the scale of bonds in
terms of the competing effects of damage (fracturing of
bonds) and formation of bonds (sintering) [Schweizer,
1999]. The effect of sintering in shear deformation must
decrease as deformation rate increases (since some time
is needed for sintering) and as temperature decreases
(since sintering is highly temperature-dependent, unlike
fracturing). Accordingly, Louchet [2001a] developed a
micromechanical model in which the weak layer was
treated as open cell foam made of a network of ice
bonds. These bonds were prone to break under stress,
but broken bonds may reconstruct if in contact with each
Figure 16. In situ photograph of buried surface hoar layer
(layer thickness of 10 mm) sandwiched between two layers with
different snow properties, exemplifying the importance of mi-
crostructure, especially bonding.
Figure 17. Three-dimensional image of snow microstructure
reconstructed from surface sections. Vertical distance between
surface sections is 15 m. The sample taken from the snow-
pack consists of three snow layers: (top) small rounded grains,
(middle) melt-freeze crystals, and (bottom) large faceted crys-
tals. The potential fracture interface is below the melt-freeze
layer at the transition to the large faceted crystals.
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-15
other for some time. Accordingly, Louchet [2001a] de-
scribed creep in relation to the bond-breaking rate
and the bond-welding rate
Figure 18. (bottom) High-resolution, constant speed penetrometer force-distance signals for two different
snow types: (left) small rounded grains and (right) depth hoar. (top) Corresponding surface sections
illustrating the microstructure of the two snow types. The variation in the force signal includes the textural
information: The higher the variation, the larger is the grain size of the sample tested (reprinted from
Schneebeli et al.  with permission from Elsevier).
Figure 19. Comparison of (left) penetrometer hardness signal to (right) hand hardness index. Proﬁles were
taken on 15 January 2002. Hand hardness index (F, ﬁst; 4F, four ﬁnger; 1F, one ﬁnger; K, knife; and P, pencil)
is given on top right horizontal axis. A rutschblock stability test revealed a not very critical weakness at 39 cm
below the snow surface (arrow) [after Pielmeier and Schneebeli, 2002].
2-16 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
where nis the fraction of unbroken bonds, is the local
shear stress, ␣is a factor accounting for the ice strength,
␤is a factor accounting for ice welding kinetics and
including an Arrhenius-type temperature dependence,
and ␥˙is the shear strain rate. Sintering under compres-
sive loading was neglected. The bond-breaking rate was
independent of temperature and proportional to the
number of unbroken bonds and the locally acting shear
stress. The bond-welding rate was proportional to the
square of the broken bond fraction, inversely propor-
tional to the strain rate, and proportional to an Arrhe-
nius factor for temperature dependence. Depending on
the load, the net balance between breaking rate and
welding rate should lead to stable, unstable, or critical
conditions of slope stability. If the weak layer was not
considered homogeneous at a scale larger than the po-
rosity (bond spacing), the creep rate locally increased
because of stress concentrations at the tip of areas of
below average strength.
McClung  proposed a model of progressive
microfracturing based on ice properties only, so the
temperature effect on snow strength becomes plausible.
However, the model did not include sintering. Gubler
and Bader  presented one of the ﬁrst realistic
models of snow failure based on microstructure. Assum-
ing ductile failure and realistic microstructural parame-
ters [Gubler, 1978a, 1978b], Gubler and Bader 
simulated initial stability during precipitation periods
using a micromechanical model (including a statistical
distribution of strength) for weak low-density snow com-
bined with a relation describing the strength increase by
settling and sintering as a function of snow temperature.
 Bond fracturing can be measured by counting the
corresponding acoustic emissions [McClung and Schae-
rer, 1993; Sinha, 1996; Sommerfeld and Gubler, 1983].
Higher acoustic emission rates from natural snowpacks
prior to avalanche release were suggested, but experi-
mental problems and uncertainties hinder conclusions
on the applicability for snow slope stability evaluation
[Sommerfeld, 1982]. The other important bond-scale
process involved in snow failure, sintering, is more dif-
ﬁcult to quantify during a deformation experiment.
However, with simultaneous x-ray microtomography this
might become possible.
 Analyzing snow stratigraphy suggests that differ-
ences in grain size and hardness are indicators of failure
probability [Schweizer and Jamieson, 2003b]. A large
difference in grain size (ⱖ0.75 mm) between adjacent
layers leads to a substantial difference in bond area per
unit area within a short distance across the interface. In
the coarser layer this causes stress concentrations in the
spaced apart bonds near the interface. Hardness differ-
ences further promote this effect that leads to interface
or subinterface failure, consistent with interfacial frac-
ture mechanics [Hutchinson et al., 1987]. The concentra-
tion of deformation in weak layers has been observed
both for artiﬁcially made layered samples tested under
shear [Fukuzawa and Narita, 1993] and on slopes based
on observed downslope tilting of surface hoar crystals
[Jamieson and Schweizer, 2000].
3.4. Fracture Propagation
 Fractures in snow are probably mixed mode frac-
tures. At the scale of the slab thickness, shear is essential
for fracture propagation in a layered sloping snowpack
and is therefore assumed in modeling, consistent with
ﬁeld observation of fracture planes of snow slab ava-
lanches. At the scale of the grains and bonds, fracture
can be any mode.
 Prior to the release of a slab avalanche, condi-
tions for fracture propagation in the weak layer/interface
have to be met. Fracture propagation can be observed
and frequently heard (the characteristic “whumpf”
sound), and fracture speed has been measured [Johnson,
2000]. Remotely triggered avalanches are a special case
in which fracture propagation is obvious. However, even
after fracture propagation in the weak layer, the slab
may not release since slab boundary strength may not be
overcome and/or parts of the slab may not be inclined
steeply enough to overcome bed surface friction. On the
other hand, experience shows that frequently snowpack
weaknesses are found, and stability tests suggest low
stability, but no fracture propagation occurs, or locally
induced fractures do not meet conditions for extensive
fracture propagation. This indicates that traditional sta-
bility tests miss important information on fracture prop-
agation potential and hence on slab release probability.
 Fracture propagation has been measured
through weak layers on horizontal terrain [Johnson et al.,
2003]. A propagation velocity of about 20 m s
measured with geophones. Johnson et al.  con-
cluded that compressive fracture (collapse) of the weak
layer on low-angle terrain provided the energy needed
for fracture propagation and that the velocity of the
Figure 20. Schematic of deformation and failure/fracture for
snow under shear loading. Strain rate increases in order for the
curves labeled a, b, c, and d (based on data of Fukuzawa and
Narita , McClung , Narita , and Schweizer
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-17
resulting bending wave in the overlying slab depended
on the stiffness of the slab. Accordingly, the bending
wave induced a vibration in the air above the snow cover,
thereby causing the “whumpf”sound. Modeling of frac-
ture propagation in collapsing weak layers will require
microstructural models rather than solid mechanics.
Bader and Salm  explored fracture propa-
gation and concluded that once brittle fracture occurs,
the speed of fracture would be of the order 100–1000 m
, which is higher than observed in limited ﬁeld mea-
surements [Johnson et al., 2003]. The extent of fracturing
in their model is entirely controlled by the tensile
of the overlying slab:
 On the basis of interfacial fracture mechanics,
Schweizer and Camponovo,  suggested that frac-
ture propagation would depend on the difference in
stiffness between the weak layer and the slab or, more
precisely, the weak layer and the layer just above it.
Interfacial fracture mechanics has been applied, for ex-
ample, to characterize the failure of ice/substrate inter-
faces. For such bimaterial interface cracks, crack growth
is always mixed mode [Weietal., 1996]. It is likely that
interfacial fracture mechanics can be applied to snow
slab release where fractures between layers of the same
material but with different properties exist. The fracture
resistance of bimaterial interfaces can be determined for
beam specimens. According to Weietal.  the
critical interface fracture energy Gc
int is given by
is the applied bending moment at the initiation
of the crack, Iis the moment of inertia, and subscript c
refers to the composite beam. Further evaluation of
equation (12) reveals that the nondimensional interface
fracture energy Gc
int increases monotonically with in-
crease in relative slab thickness, H
, and de-
creases as the relative modulus of the weak layer, E
, increases. The smaller the interface fracture
energy (because of a large difference in stiffness), the
more likely fracture propagation becomes.
 Accordingly, and based on observation, it is pro-
posed that fracture initiation at the base of a snow slab
is an interface fracture. The fracture is expected to
always be between two snow layers that are poorly con-
nected. For a thin weak layer the fracture should start at
the interface with the layer above or below. However, for
fracture propagation the full thickness of the weak layer
can be involved. Occasionally, cohesive fractures, such as
the collapse of a thick weak layer of depth hoar, are
4. SNOWPACK VARIABILITY
 As described in section 3.1, disorder is fundamen-
tal for the fracture process [Herrmann and Roux, 1990].
The behavior, especially failure, of a material cannot be
based on its average properties. Variations are essential
because they provide the nucleus of fracture and a
necessary stabilizing mechanism to limit damage and
inhibit fracture localization. Spatial variability of snow-
pack properties is believed to be a key issue for under-
standing avalanche formation. However, neither the
scale of variation nor its effect on avalanche formation is
clear. High spatial variability might offer numerous
points of fracture initiation but might also limit fracture
propagation. On the other hand, low variability seems
favorable for fracture propagation, but in this case, fail-
ure initiation will depend on the level of stability. Inter-
mediate snowpack stability with substantial variation at
the scale of a few meters seems to be critical and hence
challenging for the prediction of skier triggering
[Schweizer and Jamieson, 2003a].
 There are several possibilities for variability in
view of avalanche formation. There can be either vari-
ability of the slab properties, e.g., varying thickness, or
variability of the weak layer properties. In particular, the
weak layer may be discontinuous. For any case the scale
of the variability is unknown so far.
 Variability is present at different scales in the
snowpack. The scale depends on the speciﬁc conditions
during formation: micrometeorology during deposition,
wind effects due to small-scale topography (turbulence),
large-scale topography, and climatic differences. Other
sources of variability, particularly in shallow snowpacks,
stem from variable properties of the underlying ground
such as roughness and spatial variations in thermal con-
ductivity. In the case of avalanches released by localized
rapid surface loading, both snow stratigraphy and load-
ing vary spatially. In general, when talking about vari-
ability the scale always needs to be mentioned.
Bloeschl  deﬁned scale as a characteristic
length of a natural process, e.g., the (unknown) correla-
tion length of the spatial variation of the snowpack
stability. Results derived from point measurements are
strongly affected by the scales of sample size, sampling
density, and areal coverage of the domain, which in the
terminology of Bloeschl  is the scale triplet of
support, spacing, and extent.
 Whereas previous ﬁeld studies [Conway and
Abrahamson, 1984, 1988; Fo¨hn, 1989; Jamieson, 1995]
have not proven the existence of deﬁcit zones (areas
where the shear stress from the overlaying slab is not
supported by the shear strength), they have clearly doc-
umented snowpack variability. It has been suggested that
the snowpack variability at the scale of a region increases
with increasing avalanche danger based on rutschblock
scores from different aspects [Munter, 1997]. However,
ﬁeld studies on single slopes, as well as on the regional
scale, have shown the opposite [Jamieson, 1995; Kron-
2-18 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
holm and Schweizer, 2003; Schweizer et al., 2003]. Birke-
land  conducted a large-scale study on two single
days in an area of about 90 km
sampling data at over 70
sites. He found correlations between terrain (aspect and
elevation) and stability, but the distance between sam-
pling sites did not affect the correlation. Kozak et al.
 also considered differences at a relatively large
scale, studying the effect of aspect and time on slab
hardness. Measurements of snow stability on small ava-
lanche slopes using a modiﬁed compression test showed
that the relative variation of stability expressed as the
quartile coefﬁcient of variation was of the order of 50%
and dropped to about 20% after removal of slope scale
trends [Kronholm and Schweizer, 2003] (Figure 21). A
similar study in a different snow climate found similar
results [Stewart, 2002]. Areas of relatively low stability
with dimensions from 60 cm up to 9 m were found. Most
slopes with low median stability had low variability.
Landry  found more variation in a ﬁeld study at a
slightly smaller scale.
 Interpreting spatial variability in terms of frac-
ture localization and propagation, Kronholm and
Schweizer  suggested that slope stability is con-
trolled by the mean slope stability, by the spread of the
stability on the slope, and by the scale of spatial patterns
of strong and weak areas on the slope.
 Despite snowpack variability, weak layer forma-
tion is often quite consistent over whole mountain
ranges [Ha¨geli and McClung, 2002]. This is supported by
stability measurements in study plots that can be extrap-
olated and correlated with avalanche activity over con-
siderable distances [Jamieson, 1995; Chalmers and
Jamieson, 2003]. These ﬁndings are from a range with a
deep-snow climate, the Columbia Mountains of western
Canada, and from study sites near tree line. Above tree
line, there is more wind effect and accordingly greater
 The importance of spatial variability is exempli-
ﬁed by the characteristics of avalanche initiation in for-
ests. Beneath a tree the snowpack is highly variable, and
weak layers are often discontinuous. However, in small
clearings the variability is smaller than in the open ﬁeld
because of decreased wind effect, and avalanche initia-
tion is likely, provided the clearing is large enough
[Gubler and Rychetnik, 1991].
 Summing up, quantitative knowledge of the vari-
ability at different scales (simultaneously measured) and
its relation to avalanche formation is still largely lacking.
How large is the variability associated with certain me-
teorological and ground conditions, and what is the
effect of that variability on snow slab stability? Variabil-
ity at the scale of about 1–10 m may be important for
fracture propagation since a weak layer or interface has
to exist over a certain area so that a slab is released.
Variability at the smaller scale (ⱕ10 cm) is probably
related to failure initiation since it promotes local stress
or strain rate concentration. The properties of the slab
and the weak layer and their variation have to be con-
sidered in combination.
5. DISCUSSION AND CONCLUSIONS
 Our understanding of snow avalanche formation
has signiﬁcantly increased in the last 2 decades because
of ﬁeld studies and numerical modeling of the effect of
the contributing factors: terrain, new snow, wind, tem-
perature and radiation, and snow cover stratigraphy.
Modeling the avalanche release mechanism (Figure 22)
has proved to be more challenging. However, progress in
characterizing the complex microstructure of snow, in
particular the number and size of bonds, and ﬁeld stud-
ies on spatial variability of the snowpack and its effects
on avalanche formation will pave the way for detailed
modeling of failure criteria for avalanche forecasting.
 The prerequisite for dry snow slab release is a
snowpack weakness (thin weak layer or weak interface)
below one or more slab layers. A distinctive difference in
hardness and texture favors failure and causes stress and
strain concentrations in the bonds connecting the two
adjacent layers. Whereas failure usually starts at the
interface between two adjacent layers, even when the
weak layer is thin, fracture propagation can involve the
full thickness of layers. If damage becomes localized, the
Figure 21. Results of stability measurements on a small av-
alanche slope. Stability test locations are marked by squares. A
cross through a square marks a fracture at a speciﬁc weakness
present at the date of measurement (14 February 2002). From
the 24 stability tests that have been performed in pairs, 22
showed fractures at this weakness. The drop height (in cm)
that is a measure of stability is shown above the test location.
A linear slope stability trend was found and is indicated by
5-cm contours. The median drop height was 35 cm with a
quartile coefﬁcient of variation of 26% [from Kronholm et al.,
41, 4 / REVIEWS OF GEOPHYSICS Schweizer et al.: AVALANCHE FORMATION ●2-19
initial failure can propagate, and a slab may be released
(Figure 22). The critical size for a self-propagating frac-
ture is estimated to be of the order of 0.1–10 m, with the
shorter lengths being critical for localized rapid surface
loading. Whereas the snowpack conﬁguration prone to
failure is well established, less is known about conditions
for fracture propagation that are strongly affected by,
among other things, the spatial variability of the snow-
pack. Spatial variability of snow mechanical (and tex-
tural) properties is presently being investigated, and
quantitative results are expected in the near future.
Spatial variability provides failure initiation points and
may arrest fractures. Surface warming of the sloping
snowpack leads to increased deformation in the surface
layer, thereby reducing the snow stability, provided the
prerequisites for slab release are fulﬁlled. Although only
mentioned brieﬂy, wet snow avalanche formation is
poorly understood. The textural properties may soon be
characterized based on new means for 3-D imaging, with
x-ray tomography being the most promising method.
Texture can then be related to the mechanical proper-
ties. Present modeling at the microscale considers highly
idealized structures but includes the two fundamental
processes involved in snow failure: bond breaking and
bond formation by sintering. Fracture mechanical mod-
els provide insight into the release condition at the
mesoscale to macroscale. In situ measurements of frac-
ture mechanical properties (such as toughness) should
complete traditional stability evaluation. Modeling will
need to close the gap between the microscale and the
macroscale by linking improved micromechanical mod-
els (including statistical elements) to fracture mechani-
cal models. Physical modeling, as well as numerical
simulations of avalanche formation, lacks adequate pa-
rameterization of the physical processes, but promising
attempts are under way.
 The quantitative understanding of snow ava-
lanche phenomena is hindered by limitations common to
other natural hazards. Avalanches are rare and are not
reproducible events. Access to relevant study areas can
be dangerous; however, safe study plots/slopes are help-
ful for operational forecasting. Field measurements are
often not related closely enough to relevant processes or
limited to a single process instead of covering all rele-
vant parameters simultaneously. No remote device that
directly indicates instability is available. Most ﬁeld mea-
surements include destructive methods thereby compro-
mising studies of temporal evolution. Laboratory exper-
iments with layered natural snow are difﬁcult to perform
because of the fragile nature of snowpack weaknesses
and of low-density snow in general. Because of these
limitations, numerical modeling is essential to advance
our understanding but depends on data that are, as
shown above, difﬁcult to acquire.
 In order to approach a comprehensive under-
standing of snow avalanche formation we propose the
following questions for future research for several areas,
fracture propagation, spatial variability, effect of surface
warming, wet snow avalanches, new snow stabilities,
snow failure, and slab release. These areas are not
ranked in order of importance, and the list is not ex-
1. Which mechanical properties of which slab/weak
layers describe the propensity for fracture propagation?
How can practitioners test for propagation propensity?
2. What are the spatial scales of variability relevant to
slab release as inﬂuenced by topography (aspect, incli-
nation, distance to ridge, and ground cover), snow type,
and meteorological conditions during/after deposition?
In other words, what are the scale and distribution of
areas of low stability and fracture tough areas and their
effect on release probability?
3. How is snow stability affected (quantitatively) by
4. How does failure initiation and fracture propaga-
tion occur for wet slabs?
5. What kind of slab and interface properties favor
new snow avalanches? How can these properties be
predicted by meteorological instruments?
6. How can the damage and sintering process leading
to snow failure be measured and modeled? What should
be measured? Is there a fatigue effect in snow damage/
7. How can the sequence of events and processes
leading to slab release (from the scale of 0.1 mm to
100 m) be measured, modeled, and veriﬁed? In partic-
Figure 22. Conceptual model of dry snow slab avalanche release [from Schweizer and Jamieson, 2003a].
2-20 ●Schweizer et al.: AVALANCHE FORMATION 41, 4 / REVIEWS OF GEOPHYSICS
ular, how can microstructural models be combined with
fracture mechanical models?
 This review shows that dealing with an extraordi-
nary material such as snow and a process that covers
several orders of scale, from the size of a bond to the size
of a mountain slope, will continue to be very challenging.
ACKNOWLEDGMENTS. We would like to thank our
colleagues Paul Fo¨hn, Charles Fierz, and Michael Lehning for
their contributions and comments. J.B. Jamieson is grateful to
the British Columbia Helicopter and Snowcat Skiing Opera-
tors Association, the Natural Sciences and Engineering Re-
search Council of Canada, Canada West Ski Areas Associa-
tion, and the Canadian Avalanche Association for ﬁnancial
support. Suggestions by the Chief Editor Tom Torgersen,
Marcia Phillips, and Paul Langevin and several reviewers im-
proved the manuscript.
 Thomas Torgerson was the Editor responsible for this
paper. He thanks four technical reviewers and one cross-
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