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A snow-profile-based forecasting model for skier-triggered avalanches on surface hoar layers in the Columbia Mountains of Canada
Cold Regions Science and Technology 37 (2003) 373 – 383 www.elsevier.com/locate/coldregions
A snow-profile-based forecasting model for skier-triggered avalanches on surface hoar layers in the Columbia Mountains of Canada Thomas S. Chalmers a, J. Bruce Jamieson b,c,* a Mt. Revelstoke and Glacier National Parks, Revelstoke, Canada Department of Civil Engineering, University of Calgary, Calgary, Canada c Department of Geology and Geophysics, University of Calgary, Calgary, Canada b
Received 1 September 2002; accepted 2 July 2003
Abstract Surface hoar crystals grow on the snow surface and can form a persistent weak layer in the snowpack when buried. Skiers may trigger slab avalanches on such layers. These events can be difficult to forecast. During the winters 1995 – 2002, measurements of snowpack properties including surface hoar layers were collected at study sites in the Columbia Mountains of western Canada. These data were used to develop an empirical model to forecast the shear strength of buried surface hoar layers. The model, which is based on a snow profile and does not require shear strength measurements, accounts for 72% of the variability in the data. For five independent time series, the model estimates shear strength, on average, to within 22% of measured values within 8 days of the snow profile measurements. The profile-based shear strength model was used to forecast a stability index, which shows promise for forecasting skiertriggered slab avalanches on surface hoar layers in the Columbia Mountains. To further verify the suitability of the stability index, skier-triggered avalanche activity on buried surface hoar layers was correlated with the stability index based on shear frame tests, rather than snow profiles. D 2003 Elsevier B.V. All rights reserved. Keywords: Avalanche forecasting; Snowpack stratigraphy; Surface hoar; Snow strength; Snow stability
1. Introduction When buried by snowfall, layers of surface hoar or hoarfrost may form a weak layer in the snowpack. These weak layers may remain reactive as a failure * Corresponding author. Department of Civil Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4. E-mail address: [email protected] (J.B. Jamieson). 0165-232X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0165-232X(03)00077-6
plane for slab avalanches for several weeks or more (e.g. Fo¨hn, 1992). Skier-triggered slab avalanches on such layers can be common, yet are often difficult to predict, even for professional avalanche decisionmakers (e.g. Jamieson and Johnston, 1992). Over the winters 1992– 2002, 84 time series of buried surface hoar were collected in the Columbia Mountains of western Canada through snow profiles, strength measurements, snowpack tests, and records of skier-triggered avalanches.
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The goal of this study was to develop a model that relates the strength of a buried weak layer of surface hoar to snowpack factors commonly observed by avalanche workers at snow study sites. Thus, practical near-standard observation techniques may be used about once per week to estimate the strength of a buried surface hoar layer in the Columbia Mountains. The strength estimates can be used to calculate daily values of a stability index for skier-triggered avalanches in the Columbia Mountains.
2. Literature review Surface hoar grows by vapour deposition on the snow surface during relatively calm and clear nights with high relative humidity in the near-surface air (Lang et al., 1984; Breyfogle, 1986; Hachikubo and Akitaya, 1998). When buried by snowfall, surface hoar may become a persistent weak layer in the snowpack (e.g. Fo¨hn, 1992; Jamieson, 1995, pp. 141 –155). Skier-triggered slab avalanches on layers of buried surface hoar occur mostly within the first 15 to 20 days after a layer is buried, and the transition of such layers from unstable to stable conditions is difficult for avalanche professionals to forecast (Jamieson and Johnston, 1992). Stability indices based on shear frame measurements can indicate the stability—susceptibility to slab avalanching—of buried weak layers in the snowpack in the Columbia Mountains (Jamieson and Johnston, 1993). Schleiss and Schleiss (1970) introduced a snow ‘‘stability factor’’ or Stability Ratio, SF (Canadian Avalanche Association, 2002) based on shear frame tests of the weak layer, which has been used since ca. 1960 at the Mount Fidelity study plot to extrapolate snowpack stability for natural avalanches in the Rogers Pass highway corridor, but not for skier-triggered avalanche activity. Roch (1966) introduced a stability index S, the ratio of shear strength to shear stress on the weak layer, and Fo¨hn (1987) produced a stability index incorporating skier loading, SV. Fo¨hn and Camponovo (1996) showed that the shear strength of weak layers strongly correlated with this ‘‘skier’’ stability index. Jamieson and Johnston (1998) summarize stability indices for skier triggering, including Sk, which relates measurements on avalanche slopes to the
frequency of skier triggering on the same slopes. When the index is based on shear frame tests in a study plot and extrapolated to surrounding avalanche slopes (average slope angle of 38j), the index is denoted Sk38 (Jamieson, 1995). This extrapolated index is used in the present study.
3. Methods Data for this study were collected at two helicopter skiing operations and a national park in the Columbia Mountains of western Canada during the years 1992– 2002. The changes in snowpack properties, including buried surface hoar layers were observed at fixed study locations. These locations were selected, in consultation with the appropriate co-operating organisation, to be representative of the snowpack in surrounding avalanche starting zones. These sites included two ‘‘air boxes’’, each with a surface area of 3 16 m, which were shovelled clear in early winter and subsequently developed a relatively shallow snowpack (Jamieson and Johnston, 1999). Study sites were visited on a fixed schedule, usually with no more than 8 days between visits. Two sites, Mt. Fidelity and Mt. St. Anne, are located in or adjacent to areas for which skier-triggered avalanches in the surrounding region (up to approximately 100 km away) were reported (Fig. 1). Considering the size of these areas, many slopes with buried surface hoar layers lay untouched by skiers during the period in which each layer was monitored. On each measurement day, buried surface hoar layers were identified in a snow pit wall with a profile of snowpack layers, compression test, rutschblock test, or shovel test (Canadian Avalanche Association, 2002). A snow profile was observed, including properties of the surface hoar layers (minimum and maximum grain size, layer thickness, temperature, temperature gradient, shear strength) and of the overlying slab (load, slab thickness), and the height of the snowpack. The shear strength of each layer is the average obtained from a set of approximately 12 shear frame tests. The snow overlying the buried surface hoar layer was removed, leaving 40– 45 mm of undisturbed snow above the weak layer. A shear frame was carefully inserted into the snow such that the frame bottom was 2 –5 mm above the weak layer (Perla and
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Fig. 1. Study areas in the Columbia Mountains: (1) Mike Wiegele Helicopter Skiing, (2) Canadian Mountain Holidays Adamants, Gothics, Monashees, and Revelstoke, (3) Glacier National Park, (4) Canadian Mountain Holidays Bobbie Burns. Mt. St. Anne and Mt. Fidelity study plots shown. Other study sites located within areas 1, 3 and 4. Skier-triggered avalanche activity data for Mt. Fidelity region gathered from areas 2 and 3. Skier-triggered avalanche activity data for Mt. St. Anne region gathered from area 1.
Beck, 1983). Details of the shear frame test method can be found in Jamieson and Johnston (2001). Shear strength is the maximum reading on the force gauge divided by the area of the frame, and adjusted for size effects (Sommerfeld, 1980; Fo¨hn, 1987). The maximum and minimum extent of the characteristic surface hoar crystals in a buried layer were observed according to international and Canadian guidelines (Colbeck et al., 1990; Canadian Avalanche Association, 2002), manually separating the crystals from the snowpack and observing them with a low magnification (8 ) hand lens on a crystal screen with 1-, 2-, 3-, and 10-mm grids. The thickness of a buried surface hoar layer was measured by placing a millimetre scale against the
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vertical snow pit wall and recording an average layer thickness, obtained from three locations on the snow pit wall. The load (vertical weight per unit area) due to the snow slab overlying a buried surface hoar layer (r) was the average of the value calculated from a vertical series of layer-by-layer snow density measurements, and an average value from vertical core samples, from the snow surface to the weak layer (Jamieson and Johnston, 1999). Manual measurements of snowpack temperatures and temperature gradients across the buried surface hoar layers were taken on each observation day with digital display thermometers having a resolution of 0.1 jC. The temperature gradient across a buried surface hoar layer was calculated from the temperatures 50 mm above and below the suspected failure plane. For layers at least 30 cm below the surface, these manual measurements, taken once or twice per week, agree well with the average of hourly measurements from thermisters with an accuracy of 0.1 jC (Jamieson and Johnston, 1999). The snowpack and avalanche observations of this study are consistent with observation guidelines (Canadian Avalanche Association, 2002), except for measuring the thickness of a buried surface hoar layer to the nearest millimetre.
4. Observations The dataset for this model consisted of 84 time series of measurements of buried surface hoar layers in the Columbia Mountains from the years 1992 to 2002. Each time series is a sequence of three or more measurements of a particular layer at a particular study site over time (10 – 100 days). In an effort to better model the strength changes of these layers over realistic intervals between operational study plot observations, measurements spanning intervals longer than 8 days were rejected. Furthermore, in order to model strength changes over the time frame in which buried surface hoar layers are prone to release skier-triggered slab avalanches, only measurements within the first 30 days of burial were included. This created a dataset of 361 strength measurements, or 278 measurement intervals (Table 1). For purposes of model testing and application, five
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Table 1 Surface hoar layers used in shear strength model
Table 1 (continued )
Location
Burial date
No. of intervals
Mt. St. Anne Study Plot Mt. St. Anne Study Plot Sam’s Study Plot Mt. St. Anne Study Plot Sam’s Study Plot Sam’s Study Plot Mt. St. Anne Study Plot Sam’s Run Sam’s Study Plot Mt. St. Anne Study Plot Tower Study Slope Vermont Study Plot Elk Study Plot Vermont Study Plot Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Landing Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Airbox Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Study Plot Vermont Study Plot Vermont Airbox Pygmy Run North Moose Log Cut Mt. St. Anne Study Plot MSA RP Airbox Elk Study Plot Elk Study Slope Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Cutblock Vermont Study Plot Vermont Airbox Pygmy Run North Moose Log Cut North Moose Log Cut Pygmy Run Vermont Airbox Vermont Study Plot Middle Moose Study Plot Vermont Study Plot Middle Moose Study Plot Pygmy Run Mt. St. Anne Study Plot Mt. St. Anne Airbox Middle Moose Study Plot Vermont Study Plot
15-Nov-93 04-Dec-93 18-Dec-93 29-Dec-93 29-Dec-93 29-Dec-93 21-Jan-94 05-Feb-94 05-Feb-94 05-Feb-94 05-Feb-94 15-Dec-94 15-Dec-94 07-Jan-95 07-Jan-95 07-Jan-95 07-Jan-95 14-Feb-95 14-Feb-95 28-Dec-95 28-Dec-95 01-Jan-96 01-Jan-96 04-Feb-96 17-Feb-96 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 10-Feb-97 10-Feb-97 10-Feb-97 11-Feb-97 11-Feb-97 11-Feb-97 11-Feb-97 01-Mar-97 01-Mar-97 01-Mar-97 01-Mar-97 26-Dec-97 26-Dec-97 03-Feb-98 03-Feb-98 13-Feb-98 13-Feb-98 17-Feb-98 17-Feb-98
3 4 2 4 2 2 2 2 2 4 2 3 5 7 7 7 2 2 3 3 3 2 3 2 4 8 8 5 5 7 5 3 4 6 6 5 7 7 6 7 2 2 2 2 5 6 2 2 6 7 3 2
Location
Burial date
No. of intervals
Mt. St. Anne Cutblock Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Cutblock Middle Moose Study Plot Vermont Airbox Vermont Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Cheops Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Mt. St. Anne Airbox Cheops Study Plot Cheops Study Plot Fidelity Study Slope Mt. St. Anne Cutblock Fidelity Study Slope Fidelity Study Slope Fidelity Study Slope Mt. St. Anne Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Fidelity Study Slope Fidelity Study Slope Fidelity Study Slope Mt. St. Anne Study Plot
25-Feb-98 25-Feb-98 25-Feb-98 25-Feb-98 28-Feb-98 28-Feb-98 28-Feb-98 03-Jan-99 03-Jan-99 24-Jan-99 24-Jan-99 16-Feb-99 16-Feb-99 12-Mar-99 30-Dec-99 30-Dec-99 30-Dec-99 31-Jan-00 31-Jan-00 31-Jan-00 31-Jan-00 05-Feb-00 21-Feb-00 21-Feb-00 21-Feb-00 17-Nov-00 24-Nov-00 13-Jan-01 20-Jan-01 28-Jan-01 23-Feb-01 23-Feb-01 02-Jan-02 16-Feb-02 16-Feb-02
2 5 5 2 3 3 3 3 4 2 4 6 7 2 3 5 5 5 6 8 8 3 5 4 6 3 5 6 7 8 4 7 5 5 6
Highlighted layers excluded from model construction.
time series were removed from the dataset prior to developing the model, and are highlighted in Table 1. The time series of strength measurements of a buried surface hoar layer is shown in Fig. 2. As is typical of buried layers of surface hoar in the Columbia Mountains, this layer showed rapid strength gain during the first 20 to 30 days after burial. Most skiertriggered slab avalanches on these layers typically occurred over this same time period (e.g. Chalmers and Jamieson, 2001). Subsequent strength gain was typically more gradual. Apparent decreases in shear strength of a surface hoar layer were sometimes measured (Fig. 2). Since
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Fig. 2. Shear strength of the surface hoar layer buried 20 January 2001 in the Mt. St. Anne study plot.
each set of shear frame measurements was observed approximately 2 m from the previous measurements, apparent decreases in shear strength may be due to natural spatial variability of layer properties in the study site. In the Columbia Mountains, surface hoar layers are often too deep in the snowpack for strength decreases within 8-day intervals to be due to external (meteorological) conditions. Shear strength decreases are often observed later in the winter months as snowpack temperatures warm to around 1 jC, but are not associated with increased avalanche activity on the surface hoar layer.
5. Results 5.1. Model construction The model is broken into two components: (1) estimating shear strength of the buried surface hoar layer (r) on the day when the snowpack observations are made and, (2) estimating the strength change between the measurement day and an arbitrarily selected day up to 8 days in the future. In an operational situation, the next measurement day would be the day on which a new set of snowpack observations is made (and the model is re-initialised). This model thus consists of the sum of two empirical parameters: Rj * ¼ Ri * þ Dtij ðDR=DtÞij *;
ð1Þ
where Ri* and (DR/Dt)ij* are functions of snowpack observations on day i. In Eq. (1), Ri* is the estimated shear strength on day i (kPa), Dtij is the time interval between day i and day j (tj ti), where 1 V i < j V i + 8,
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(DR/Dt)ij* is the model estimated rate of change in shear strength (kPa day 1) between day i and day j, and Rj* is the forecast shear strength on day j. Considering operational usefulness, only snowpack variables measurable at the start of the prediction interval, at time ti, were used as input variables. In the interests of optimising model construction, predictor variables that did not have a significant correlation with the response variables, (DR/Dt)ij and Ri, were eliminated from the list of input variables, via Spearman rank correlations (Chalmers, 2001). The snowpack variables used in the development of the model are shown in Table 2. In order to examine which measurable snowpack factors correlated with shear strength, a stepwise, multiple least-squares regression technique was used. Stepwise regression was deemed suitable for this analysis because it selects important predictor variables from a long list of input variables (Mendenhall and Sincich, 1996, p. 242). The use of this technique was validated by testing the residuals of regression (Mendenhall and Sincich, 1996, pp. 115, 175). The regression was first performed on the response variable (DR/Dt)ij, rate of strength change over measurement interval. The shear strength at the start of the interval Ri was included in the list of input variables. The regression was then performed on Ri. The results of this regression are shown in Tables 3 and 4 for (DR/ Dt)ij and Ri, respectively. Deriving empirical formulae for (DR/Dt)ij* and Ri* in Eq. (1) was completed using the regression results. Table 2 Snowpack variables and units at time ti (age of weak layer, in days, at start of prediction interval) Variable
Description (units)
Ri ri
Shear strength of weak layer (kPa) Vertical load (force per unit area) due to snow overlying weak layer (kPa) Thickness of snow slab overlying weak layer, measured vertically (m) Total height of snowpack (m) Thickness of weak layer (m) Temperature of weak layer (jC) Magnitude of temperature gradient across weak layer (jC m 1) Minimum grain size in weak layer (mm) Average temperature gradient across weak layer divided by average weak layer temperature (m 1)
Hi HSi Thicki Twli TGi Emini (TG/Twl)i
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Table 3 Results of multiple stepwise regression on (DR/Dt)ij Adjusted R2 = 0.317, p < 0.00001
Coefficient B
Standard error of B
Intercept ti Ri ri Hi HSi Thicki TGi (TG/Twl)i
0.119 0.000547 0.124 0.107 0.0131 0.0176 4.73 0.00378 0.00827
0.022 0.00087 0.016 0.031 0.048 0.0067 1.1 0.0011 0.0045
These formulae are linear functions of the variables of regression and their coefficients of regression, B (Mendenhall and Sincich, 1996, p. 353), which are shown in Tables 3 and 4. Thus, the formulae are: Ri * ¼ 0:336 kPa þ ð0:0139 kPa day1 ti Þ þ ð1:18ri Þ ð0:625 kPa m1 Hi Þ þ ð0:0804 kPa m1 HSi Þ ð28:7 kPa m1 Thicki Þ þ ð0:0187 kPajC1 Twli Þ þ ð0:0204 kPa mm1 Emini Þ
ð2Þ
ðDR=DtÞij * ¼ 0:119 kPa day1 ð5:47 104 kPa day2 ti Þ ð0:124 day1 Ri Þ þ ð0:107 day1 ri Þ
the significant independent predictor variables and the response variables of the shear strength model and physical snowpack processes may be addressed. This evaluation is largely based on the sign of the coefficients of each predictor variable (Tables 3 and 4); a ‘‘ + ’’ sign indicates an increasing relationship, a ‘‘ ’’ sign indicates a decreasing relationship. 5.2.1. Age of the weak layer (t) Older layers are stronger but slower to gain strength, as illustrated in Fig. 2. 5.2.2. Load on the weak layer (r) More load is associated with surface hoar layers that are stronger and gain strength faster. This strength increase is probably due to increased thinning of the weak layer, which implies more bonding and greater strength (e.g. Davis et al., 1996; Jamieson and Schweizer, 2000). 5.2.3. Thickness of slab overlying the weak layer (H) Surprisingly, thinner slabs are associated with higher weak layer strength. Since slab load and slab thickness are positively correlated, the inclusion of the thickness variable by the step-wise algorithm may be an adjustment for denser (older) slabs, which have had more time to respond to the slab load. More intuitively, greater slab thickness is associated with faster strength gain. 5.2.4. Layer thickness (Thick) Thicker layers of buried surface hoar are associated with lower strength and are slower to gain strength. This strength lag is likely due to larger crystals having
þ ð0:0131 kPa day1 m1 Hi Þ þ ð0:0176 kPa day1 m1 HSi Þ ð4:73 kPa day1 m1 Thicki Þ ð3:78 103 kPa day1 m jC1 TGi Þ ½8:27 103 kPa day1 m ðTG=Twli Þ :
ð3Þ
Finally, estimating the strength of a buried surface hoar layer on day j after a layer is buried is possible from a set of snowpack observations on day i (1 V i < j V i + 8). 5.2. Proposed interpretation of predictor variables Closely following the example of Jamieson and Johnston (1999), the possible associations between
Table 4 Results of multiple stepwise regression on Ri Adjusted R2 = 0.742, p < 0.0001
Coefficient B
Standard error of B
Intercept ti ri Hi HSi Thicki Twli Emini
0.336 0.0139 1.18 0.625 0.0804 28.7 0.0187 0.0204
0.098 0.0037 0.12 0.22 0.029 4.8 0.011 0.010
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more spacing between crystals and between bonds with the underlying layer. Also, larger crystals may provide an ‘‘umbrella effect’’ in which few precipitation particles from the storm that buries the surface hoar fall between surface hoar crystals, to form additional bonds (Davis et al., 1996). 5.2.5. Weak layer temperature (Twl) Warmer (sub-zero) temperatures are associated with stronger layers of buried surface hoar. Since the magnitude of the temperature gradients across the buried surface hoar layers were in the range associated with equi-temperature metamorphism (e.g. Colbeck, 1987), warmer temperatures will be associated with increased bonding between crystals. 5.2.6. Magnitude of temperature gradient across the buried surface hoar layer (TG) Larger magnitude temperature gradients are associated with lower strength and slower rates of strength gain. This correlation may be due to slower bonding associated with a high-TG regime of metamorphism (Colbeck, 1987). Or this may also be due to reduced load on the surface hoar layer since larger TG occurs when layers are near the snow surface and/or in an area of shallow snowpack. 5.2.7. Snowpack depth (HS) Greater snowpack depth is associated with stronger surface hoar layers and larger rates of strength gain. Deeper snowpacks are also associated with larger loads (r), thicker slabs (H), and likely smaller magnitude temperature gradients (TG) across buried weak layers. 5.2.8. Characteristic minimum grain size of the surface hoar layer (Emin) Layers of larger crystals are associated with lower shear strength. Larger grains are also associated with thicker layers (Thick) of buried surface hoar (see above) and usually with greater spacing between surface hoar crystals and the bonds to the underlying layer. 5.2.9. Weak layer temperature gradient (TG) divided by weak layer temperature (Twl) Higher values are associated with slower rates of strength gain, and also with thinner snowpacks (HS),
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thinner slabs (H), and larger magnitude of temperature gradient (TG). 5.3. Model testing The model was tested for fit to the data used to construct it, using surface hoar time series at the Mt. St. Anne and Mt. Fidelity study sites from the winters 1995– 2002. Predicted shear strength values at the end of each measurement interval were computed and compared to the measured shear strengths. The adjusted R2 statistic gives the fraction of variability in the data that is explained by the model. The model test of fit yields an adjusted R2 of 0.72, and thus explains 72% of the variability in the data. Five time series of buried surface hoar were withheld from the dataset used in model construction. The model was applied to these time series, and forecast shear strength at the end of an interval (22 Table 5 Surface hoar time series used in forecasting application Location
Burial date
Skiertriggered activity records
Sk38
Used to build or test model
Mt. Mt. Mt. Mt. Mt.
29-Dec-93 05-Feb-94 07-Jan-95 28-Dec-95 10-Feb-97
yes yes yes yes yes
build build build build test
Mt. Fidelity
30-Dec-99
yes
Mt. St. Anne
30-Dec-99
yes
Mt. Fidelity
21-Feb-00
yes
Mt. St. Anne
20-Jan-01
yes
Mt. Fidelity
28-Jan-01
yes
Mt. St. Anne
23-Feb-01
yes
Mt. Fidelity
23-Feb-01
yes
Mt. Fidelity
02-Jan-02
yes
Mt. Fidelity
16-Feb-02
yes
Mt. St. Anne
16-Feb-02
yes
measured measured measured measured measured, forecast measured, fitted measured, forecast measured, fitted measured, fitted measured, fitted measured, fitted measured, fitted measured, forecast measured, forecast measured, forecast
St. St. St. St. St.
Anne Anne Anne Anne Anne
build test build build build build build test test test
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Fig. 3. Measured and estimated time series of skier stability index Sk38 and associated skier-triggered avalanche activity.
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data points) to within an average of 22% of the measured values, where %error ¼ 100%jRmeasured Rforecast j=Rmeasured :
ð4Þ
5.4. Forecasting regional slab stability for skiers The stability index Sk38 was calculated from snow profiles and/or shear frame tests of 15 surface hoar time series (Table 5) from the Mt. St. Anne and Mt. Fidelity study sites. Sk38 was then correlated with skier-triggered avalanche activity on these layers reported by helicopter skiing operations in the surrounding regions. All but five of these series were used to construct the model; measured (based on shear frame tests) values of shear strength were used to generate the skier stability index Sk38, and modelfitted Sk38 values were calculated for six of these series. The others had insufficiently detailed snow profiles and were used to produce measured Sk38 only. The five series not used to construct the model were used to assess model-predicted Sk38 with avalanche activity. The values of the skier stability index and skier-triggered avalanche activity for the five model-testing series are plotted in Fig. 3. From these data, the number of days with and without skier-triggered avalanches for these time series are tabulated for the days when Sk38 indicated unstable (Sk38 < 1) and stable (Sk38>1.5) conditions. Four of these contingency tables were constructed (Table 6): (a) model-building layers with measured Sk38, (b) model-building layers with model-fitted Sk38, (c) model-testing layers with measured Sk38,
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and (d) and model-testing layers with model-forecast Sk38. The Chi-square test of independence was performed on each of these tables (Stephens, 1998, pp. 253– 256). Chi-square values with significant p-levels ( p < 0.1) indicate that days with/without avalanche activity were significantly associated with Sk38. Table 6a shows that measured Sk38 was a highly significant predictor of regional skier-triggered avalanche activity ( p < 10 4) (89% of avalanche days outside of the transitional period occurred while Sk38 < 1). Table 6b shows that the model-fitted Sk38 is also a highly significant predictor of skier-triggered avalanche activity ( p < 10 4) (93% of avalanche days outside of the transitional period occurred while Sk38 < 1). For the surface hoar layers not used to formulate the model, Table 6c shows that measured Sk38 was a highly significant predictor of regional skier-triggered avalanche activity on these layers ( p = 3 10 4), and Table 6d shows that the model forecast Sk38 was also such a predictor ( p < 10 4). The results of Table 6c and d may be influenced by the small number of avalanche days where Sk38>1.5. The test statistic adjusted for small sample size (Statistica, 1999) showed that the results of Table 6c and d are significant ( p = 7 10 4, p < 10 4, respectively). The skier stability index Sk38, when generated from shear frame tests in a representative study plot, is a predictor of regional skier-triggered avalanche activity in the Columbia Mountains. Furthermore, the snow profile based model developed in this study may be used to estimate Sk38 up to 8 days in the future, with similar predictive merit.
Table 6 Contingency tables for assessing Sk38 Model building layers
Measured (a) p < 10 4 Sk38 < 1 Sk38 >1.5 Modelled (b) p < 10 4 Sk38 < 1 Sk38 >1.5
Model testing layers # Avalanche days
# Non-avalanche days
64 8
62 108
36 53
40 3
# Avalanche days
# Non-avalanche days
(c) p = 3 10 4 Sk38 < 1 Sk38 >1.5
19 7
29 58
(d) p < 10 4 Sk38 < 1 Sk38 >1.5
28 5
29 59
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6. Conclusions Surface hoar layers buried in the Columbia Mountains of western Canada present a serious hazard to both recreational and professional backcountry users. During the first 30 days in which these layers are buried in the snowpack, they show substantial increases in shear strength, and most skier-triggered slab avalanches occur. The model developed in this study establishes a number of variables as predictors for the shear strength of a buried surface hoar layer. These include age of the layer, load, slab thickness, height of snowpack, layer thickness, weak layer temperature, minimum constituent grain size, and temperature gradient across the layer. The model explains 72% of the variability in the data. Testing the model on five test series shows that it is accurate to within an average of 22% of measured shear strength. The skier stability index Sk38, based on a snow profile in a well-located study plot, is a significant predictor of regional skier-triggered avalanche activity, up to 8 days in advance for layers of buried surface hoar in the Columbia Mountains. The shear strength predictive model developed in this study shows potential as an regional avalanche forecasting tool in the Columbia Mountains. It was developed using data from the first 30 days after burial and for layers of surface hoar with sector plate crystals between 5 and 30 mm in size. This model requires standard snowpack observation techniques, and additional measurements of surface hoar layer thickness to the nearest millimetre. This model is limited to regional forecasting only, as extrapolating study plot stability indices over a large region will not indicate stability specific to avalanche start zones where terrain or weather yield snowpack conditions atypical of the forecast area. In order to determine if the shear strength prediction model may be applied to snowpack climates outside of the Columbia Mountains, time series observations of surface hoar layers in other regions are required. Such data would also serve to better isolate the influence of specific snowpack properties on the shear strength of buried surface hoar layers. This study provides important associations between snowpack properties, buried surface hoar
layers, and skier-triggered avalanches on these layers, but these associations are empirical and statistical only. Much more research is required in order to examine the physical mechanisms that link micromechanical and textural properties of surface hoar layers to the shear strength of these layers.
Acknowledgements The authors are grateful to Jill Hughes, Leanne Allison, Ken Black, James Blench, Joe Filippone, Michelle Gagnon, Ryan Gallagher, Torsten Geldsetzer, Sue Gould, Brian Gould, Phil Hein, Alec van Herwijnen, Nick Irving, Crane Johnson, Greg Johnson, Alan Jones, Kalle Kronholm, Paul Langevin,Steve Lovenuik, Greg McAuley, Rodden McGowan, Jennifer Olson, Mark Shubin, Kyle Stewart, Adrian Wilson and Antonia Zeidler for their careful field work. Our thanks to Canadian Mountain Holidays and Mike Wiegele Helicopter Skiing for providing the avalanche occurrence reports from their ski guides. For their assistance with field studies, we thank the avalanche control section of Glacier National Park including Dave Skjo¨nsberg and Bruce McMahon, Mike Wiegele Helicopter Skiing, and the BC Ministry of Transportation. This study was funded by the Natural Sciences and Engineering Research Council of Canada, Canada West Ski Areas Association, Intrawest, the Canadian Avalanche Association and the BC Helicopter and Snowcat Skiing Operators Association.
References Breyfogle, S.R., 1986. Growth characteristics of hoarfrost with respect to avalanche occurrence. Proceedings of the International Snow Science Workshop, 1986. ISSW Workshop Committee, Homewood, CA, USA, pp. 216 – 222. Canadian Avalanche Association, 2002. Observation Guidelines and Recording Standards for Weather, Snowpack and Avalanches. Canadian Avalanche Association, Revelstoke, British Columbia, Canada. Chalmers, T.S., 2001. Forecasting shear strength and skier-triggered avalanches for buried surface hoar layers. MSc Thesis, Dept. of Civil Engineering, University of Calgary, Calgary, Alberta, Canada. Chalmers, T.S., Jamieson, J.B., 2001. Extrapolating the skier stabil-
T.S. Chalmers, J.B. Jamieson / Cold Regions Science and Technology 37 (2003) 373–383 ity of buried surface hoar layers from study plot measurements. Cold Regions Science and Technology 33, 163 – 177. Colbeck, S.C., 1987. A review of the metamorphism and classification of the seasonal snow cover. In: Salm, B., Gubler, H. (Eds.), Avalanche Formation, Movement and Effects. International Association of Hydrological Sciences, Wallingford, Oxfordshire, UK, pp. 3 – 33. Publication No. 162. Colbeck, S., Akitaya, E., Armstrong, R., Gubler, H., Lafeuille, J., Lied, K., McClung, D.M., Morris, E., 1990. International classification for seasonal snow on the ground. International Commission for Snow and Ice (IAHS). World Data Center A for Glaciology U. of Colorado, Boulder, CO, USA. Davis, R.E., Jamieson, J.B., Hughes, J., Johnston, C.D., 1996. Observations on buried surface hoar—persistent failure planes for slab avalanches in British Columbia, Canada. Proceedings of the International Snow Science Workshop, 1996. Canadian Avalanche Association, Revelstoke, British Columbia, Canada, pp. 81 – 85. Fo¨hn, P., 1987. The stability index and various triggering mechanisms. In: Salm, B., Gubler, H. (Eds.), Avalanche Formation, Movement and Effects. International Association of Hydrological Sciences, Wallingford, Oxfordshire, UK, pp. 195 – 207. Publication No. 162. Fo¨hn, P., 1992. Characteristics of weak snow layers or interfaces. Proceedings of the International Snow Science Workshop, 1992. Colorado Avalanche Information Centre, Denver, CO, USA, pp. 160 – 170. Fo¨hn, P., Camponovo, C., 1996. Improvements by measuring shear strength of weak layers. Proceedings of the International Snow Science Workshop, 1996. Canadian Avalanche Association, Revelstoke, British Columbia, Canada, pp. 158 – 162. Hachikubo, A., Akitaya, E., 1998. Daytime preservation of surface hoar crystals. Annals of Glaciology 26, 22 – 26. Jamieson, J.B., 1995. Avalanche prediction for persistent snow slabs. PhD Thesis, Dept. of Civil Engineering, University of Calgary, Calgary, Alberta, Canada. Jamieson, J.B., Johnston, C.D., 1992. Snowpack characteristics associated with avalanche accidents. Canadian Geotechnical Journal 29, 862 – 866.
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Jamieson, J.B., Johnston, C.D., 1993. Shear frame stability parameters for large-scale avalanche forecasting. Annals of Glaciology 18, 268 – 273. Jamieson, J.B., Johnston, C.D., 1998. Refinements to the stability index for skier-triggered dry-slab avalanches. Annals of Glaciology 26, 296 – 302. Jamieson, J.B., Johnston, C.D., 1999. Snowpack factors associated with strength change of buried surface hoar layers. Cold Regions Science and Technology 30, 19 – 34. Jamieson, J.B., Johnston, C.D., 2001. Evaluation of the shear frame test for weak snowpack layers. Annals of Glaciology 32, 59 – 69. Jamieson, J.B., Schweizer, J., 2000. Texture and strength changes of buried surface hoar layers with implications for dry snow-slab avalanche release. Journal of Glaciology 46 (152), 151 – 160. Lang, R.M., Leo, B.R., Brown, R.L., 1984. Observations on the growth process and strength characteristics for surface hoar. Proceedings of the International Snow Science Workshop, 1984. Mountain Rescue-Aspen, Aspen, CO, USA, pp. 188 – 195. Mendenhall, W., Sincich, T., 1996. A Second Course in Statistics: Regression Analysis, 5th ed. Prentice-Hall, Upper Saddle River, NJ, USA. Perla, R.I., Beck, T.M.H., 1983. Experience with shear frames. Journal of Glaciology 29 (103), 485 – 491. Roch, A., 1966. Les variations de la resistance de la neige. Proceedings of the International Symposium on Scientific Aspects of Snow and Ice Avalanches. IAHS Publication, Gentbrugge, Belgium, pp. 182 – 195. Schleiss, V.G., Schleiss, W.E., 1970. Avalanche hazard evaluation and forecast Rogers Pass, Glacier National Park. National Research Council of Canada, Technical Memorandum 98, 115 – 121. Sommerfeld, R.A., 1980. Statistical models of snow strength. Journal of Glaciology 26 (94), 217 – 223. Statistica, 1999. Electronic Manual. Statsoft, Tulsa, OK, USA. Stephens, L., 1998. Beginning Statistics McGraw-Hill, New York, NY, USA.
A snow-profile-based forecasting model for skier-triggered avalanches on surface hoar layers in the Columbia Mountains of Canada Thomas S. Chalmers a, J. Bruce Jamieson b,c,* a Mt. Revelstoke and Glacier National Parks, Revelstoke, Canada Department of Civil Engineering, University of Calgary, Calgary, Canada c Department of Geology and Geophysics, University of Calgary, Calgary, Canada b
Received 1 September 2002; accepted 2 July 2003
Abstract Surface hoar crystals grow on the snow surface and can form a persistent weak layer in the snowpack when buried. Skiers may trigger slab avalanches on such layers. These events can be difficult to forecast. During the winters 1995 – 2002, measurements of snowpack properties including surface hoar layers were collected at study sites in the Columbia Mountains of western Canada. These data were used to develop an empirical model to forecast the shear strength of buried surface hoar layers. The model, which is based on a snow profile and does not require shear strength measurements, accounts for 72% of the variability in the data. For five independent time series, the model estimates shear strength, on average, to within 22% of measured values within 8 days of the snow profile measurements. The profile-based shear strength model was used to forecast a stability index, which shows promise for forecasting skiertriggered slab avalanches on surface hoar layers in the Columbia Mountains. To further verify the suitability of the stability index, skier-triggered avalanche activity on buried surface hoar layers was correlated with the stability index based on shear frame tests, rather than snow profiles. D 2003 Elsevier B.V. All rights reserved. Keywords: Avalanche forecasting; Snowpack stratigraphy; Surface hoar; Snow strength; Snow stability
1. Introduction When buried by snowfall, layers of surface hoar or hoarfrost may form a weak layer in the snowpack. These weak layers may remain reactive as a failure * Corresponding author. Department of Civil Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4. E-mail address: [email protected] (J.B. Jamieson). 0165-232X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0165-232X(03)00077-6
plane for slab avalanches for several weeks or more (e.g. Fo¨hn, 1992). Skier-triggered slab avalanches on such layers can be common, yet are often difficult to predict, even for professional avalanche decisionmakers (e.g. Jamieson and Johnston, 1992). Over the winters 1992– 2002, 84 time series of buried surface hoar were collected in the Columbia Mountains of western Canada through snow profiles, strength measurements, snowpack tests, and records of skier-triggered avalanches.
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The goal of this study was to develop a model that relates the strength of a buried weak layer of surface hoar to snowpack factors commonly observed by avalanche workers at snow study sites. Thus, practical near-standard observation techniques may be used about once per week to estimate the strength of a buried surface hoar layer in the Columbia Mountains. The strength estimates can be used to calculate daily values of a stability index for skier-triggered avalanches in the Columbia Mountains.
2. Literature review Surface hoar grows by vapour deposition on the snow surface during relatively calm and clear nights with high relative humidity in the near-surface air (Lang et al., 1984; Breyfogle, 1986; Hachikubo and Akitaya, 1998). When buried by snowfall, surface hoar may become a persistent weak layer in the snowpack (e.g. Fo¨hn, 1992; Jamieson, 1995, pp. 141 –155). Skier-triggered slab avalanches on layers of buried surface hoar occur mostly within the first 15 to 20 days after a layer is buried, and the transition of such layers from unstable to stable conditions is difficult for avalanche professionals to forecast (Jamieson and Johnston, 1992). Stability indices based on shear frame measurements can indicate the stability—susceptibility to slab avalanching—of buried weak layers in the snowpack in the Columbia Mountains (Jamieson and Johnston, 1993). Schleiss and Schleiss (1970) introduced a snow ‘‘stability factor’’ or Stability Ratio, SF (Canadian Avalanche Association, 2002) based on shear frame tests of the weak layer, which has been used since ca. 1960 at the Mount Fidelity study plot to extrapolate snowpack stability for natural avalanches in the Rogers Pass highway corridor, but not for skier-triggered avalanche activity. Roch (1966) introduced a stability index S, the ratio of shear strength to shear stress on the weak layer, and Fo¨hn (1987) produced a stability index incorporating skier loading, SV. Fo¨hn and Camponovo (1996) showed that the shear strength of weak layers strongly correlated with this ‘‘skier’’ stability index. Jamieson and Johnston (1998) summarize stability indices for skier triggering, including Sk, which relates measurements on avalanche slopes to the
frequency of skier triggering on the same slopes. When the index is based on shear frame tests in a study plot and extrapolated to surrounding avalanche slopes (average slope angle of 38j), the index is denoted Sk38 (Jamieson, 1995). This extrapolated index is used in the present study.
3. Methods Data for this study were collected at two helicopter skiing operations and a national park in the Columbia Mountains of western Canada during the years 1992– 2002. The changes in snowpack properties, including buried surface hoar layers were observed at fixed study locations. These locations were selected, in consultation with the appropriate co-operating organisation, to be representative of the snowpack in surrounding avalanche starting zones. These sites included two ‘‘air boxes’’, each with a surface area of 3 16 m, which were shovelled clear in early winter and subsequently developed a relatively shallow snowpack (Jamieson and Johnston, 1999). Study sites were visited on a fixed schedule, usually with no more than 8 days between visits. Two sites, Mt. Fidelity and Mt. St. Anne, are located in or adjacent to areas for which skier-triggered avalanches in the surrounding region (up to approximately 100 km away) were reported (Fig. 1). Considering the size of these areas, many slopes with buried surface hoar layers lay untouched by skiers during the period in which each layer was monitored. On each measurement day, buried surface hoar layers were identified in a snow pit wall with a profile of snowpack layers, compression test, rutschblock test, or shovel test (Canadian Avalanche Association, 2002). A snow profile was observed, including properties of the surface hoar layers (minimum and maximum grain size, layer thickness, temperature, temperature gradient, shear strength) and of the overlying slab (load, slab thickness), and the height of the snowpack. The shear strength of each layer is the average obtained from a set of approximately 12 shear frame tests. The snow overlying the buried surface hoar layer was removed, leaving 40– 45 mm of undisturbed snow above the weak layer. A shear frame was carefully inserted into the snow such that the frame bottom was 2 –5 mm above the weak layer (Perla and
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Fig. 1. Study areas in the Columbia Mountains: (1) Mike Wiegele Helicopter Skiing, (2) Canadian Mountain Holidays Adamants, Gothics, Monashees, and Revelstoke, (3) Glacier National Park, (4) Canadian Mountain Holidays Bobbie Burns. Mt. St. Anne and Mt. Fidelity study plots shown. Other study sites located within areas 1, 3 and 4. Skier-triggered avalanche activity data for Mt. Fidelity region gathered from areas 2 and 3. Skier-triggered avalanche activity data for Mt. St. Anne region gathered from area 1.
Beck, 1983). Details of the shear frame test method can be found in Jamieson and Johnston (2001). Shear strength is the maximum reading on the force gauge divided by the area of the frame, and adjusted for size effects (Sommerfeld, 1980; Fo¨hn, 1987). The maximum and minimum extent of the characteristic surface hoar crystals in a buried layer were observed according to international and Canadian guidelines (Colbeck et al., 1990; Canadian Avalanche Association, 2002), manually separating the crystals from the snowpack and observing them with a low magnification (8 ) hand lens on a crystal screen with 1-, 2-, 3-, and 10-mm grids. The thickness of a buried surface hoar layer was measured by placing a millimetre scale against the
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vertical snow pit wall and recording an average layer thickness, obtained from three locations on the snow pit wall. The load (vertical weight per unit area) due to the snow slab overlying a buried surface hoar layer (r) was the average of the value calculated from a vertical series of layer-by-layer snow density measurements, and an average value from vertical core samples, from the snow surface to the weak layer (Jamieson and Johnston, 1999). Manual measurements of snowpack temperatures and temperature gradients across the buried surface hoar layers were taken on each observation day with digital display thermometers having a resolution of 0.1 jC. The temperature gradient across a buried surface hoar layer was calculated from the temperatures 50 mm above and below the suspected failure plane. For layers at least 30 cm below the surface, these manual measurements, taken once or twice per week, agree well with the average of hourly measurements from thermisters with an accuracy of 0.1 jC (Jamieson and Johnston, 1999). The snowpack and avalanche observations of this study are consistent with observation guidelines (Canadian Avalanche Association, 2002), except for measuring the thickness of a buried surface hoar layer to the nearest millimetre.
4. Observations The dataset for this model consisted of 84 time series of measurements of buried surface hoar layers in the Columbia Mountains from the years 1992 to 2002. Each time series is a sequence of three or more measurements of a particular layer at a particular study site over time (10 – 100 days). In an effort to better model the strength changes of these layers over realistic intervals between operational study plot observations, measurements spanning intervals longer than 8 days were rejected. Furthermore, in order to model strength changes over the time frame in which buried surface hoar layers are prone to release skier-triggered slab avalanches, only measurements within the first 30 days of burial were included. This created a dataset of 361 strength measurements, or 278 measurement intervals (Table 1). For purposes of model testing and application, five
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Table 1 Surface hoar layers used in shear strength model
Table 1 (continued )
Location
Burial date
No. of intervals
Mt. St. Anne Study Plot Mt. St. Anne Study Plot Sam’s Study Plot Mt. St. Anne Study Plot Sam’s Study Plot Sam’s Study Plot Mt. St. Anne Study Plot Sam’s Run Sam’s Study Plot Mt. St. Anne Study Plot Tower Study Slope Vermont Study Plot Elk Study Plot Vermont Study Plot Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Landing Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Airbox Mt. St. Anne Study Plot Mt. St. Anne Study Plot Mt. St. Anne Study Plot Vermont Study Plot Vermont Airbox Pygmy Run North Moose Log Cut Mt. St. Anne Study Plot MSA RP Airbox Elk Study Plot Elk Study Slope Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Cutblock Vermont Study Plot Vermont Airbox Pygmy Run North Moose Log Cut North Moose Log Cut Pygmy Run Vermont Airbox Vermont Study Plot Middle Moose Study Plot Vermont Study Plot Middle Moose Study Plot Pygmy Run Mt. St. Anne Study Plot Mt. St. Anne Airbox Middle Moose Study Plot Vermont Study Plot
15-Nov-93 04-Dec-93 18-Dec-93 29-Dec-93 29-Dec-93 29-Dec-93 21-Jan-94 05-Feb-94 05-Feb-94 05-Feb-94 05-Feb-94 15-Dec-94 15-Dec-94 07-Jan-95 07-Jan-95 07-Jan-95 07-Jan-95 14-Feb-95 14-Feb-95 28-Dec-95 28-Dec-95 01-Jan-96 01-Jan-96 04-Feb-96 17-Feb-96 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 17-Jan-97 10-Feb-97 10-Feb-97 10-Feb-97 11-Feb-97 11-Feb-97 11-Feb-97 11-Feb-97 01-Mar-97 01-Mar-97 01-Mar-97 01-Mar-97 26-Dec-97 26-Dec-97 03-Feb-98 03-Feb-98 13-Feb-98 13-Feb-98 17-Feb-98 17-Feb-98
3 4 2 4 2 2 2 2 2 4 2 3 5 7 7 7 2 2 3 3 3 2 3 2 4 8 8 5 5 7 5 3 4 6 6 5 7 7 6 7 2 2 2 2 5 6 2 2 6 7 3 2
Location
Burial date
No. of intervals
Mt. St. Anne Cutblock Mt. St. Anne Study Plot Mt. St. Anne Airbox Mt. St. Anne Cutblock Middle Moose Study Plot Vermont Airbox Vermont Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Cheops Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Cheops Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Mt. St. Anne Airbox Cheops Study Plot Cheops Study Plot Fidelity Study Slope Mt. St. Anne Cutblock Fidelity Study Slope Fidelity Study Slope Fidelity Study Slope Mt. St. Anne Study Plot Fidelity Study Slope Mt. St. Anne Study Plot Fidelity Study Slope Fidelity Study Slope Fidelity Study Slope Mt. St. Anne Study Plot
25-Feb-98 25-Feb-98 25-Feb-98 25-Feb-98 28-Feb-98 28-Feb-98 28-Feb-98 03-Jan-99 03-Jan-99 24-Jan-99 24-Jan-99 16-Feb-99 16-Feb-99 12-Mar-99 30-Dec-99 30-Dec-99 30-Dec-99 31-Jan-00 31-Jan-00 31-Jan-00 31-Jan-00 05-Feb-00 21-Feb-00 21-Feb-00 21-Feb-00 17-Nov-00 24-Nov-00 13-Jan-01 20-Jan-01 28-Jan-01 23-Feb-01 23-Feb-01 02-Jan-02 16-Feb-02 16-Feb-02
2 5 5 2 3 3 3 3 4 2 4 6 7 2 3 5 5 5 6 8 8 3 5 4 6 3 5 6 7 8 4 7 5 5 6
Highlighted layers excluded from model construction.
time series were removed from the dataset prior to developing the model, and are highlighted in Table 1. The time series of strength measurements of a buried surface hoar layer is shown in Fig. 2. As is typical of buried layers of surface hoar in the Columbia Mountains, this layer showed rapid strength gain during the first 20 to 30 days after burial. Most skiertriggered slab avalanches on these layers typically occurred over this same time period (e.g. Chalmers and Jamieson, 2001). Subsequent strength gain was typically more gradual. Apparent decreases in shear strength of a surface hoar layer were sometimes measured (Fig. 2). Since
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Fig. 2. Shear strength of the surface hoar layer buried 20 January 2001 in the Mt. St. Anne study plot.
each set of shear frame measurements was observed approximately 2 m from the previous measurements, apparent decreases in shear strength may be due to natural spatial variability of layer properties in the study site. In the Columbia Mountains, surface hoar layers are often too deep in the snowpack for strength decreases within 8-day intervals to be due to external (meteorological) conditions. Shear strength decreases are often observed later in the winter months as snowpack temperatures warm to around 1 jC, but are not associated with increased avalanche activity on the surface hoar layer.
5. Results 5.1. Model construction The model is broken into two components: (1) estimating shear strength of the buried surface hoar layer (r) on the day when the snowpack observations are made and, (2) estimating the strength change between the measurement day and an arbitrarily selected day up to 8 days in the future. In an operational situation, the next measurement day would be the day on which a new set of snowpack observations is made (and the model is re-initialised). This model thus consists of the sum of two empirical parameters: Rj * ¼ Ri * þ Dtij ðDR=DtÞij *;
ð1Þ
where Ri* and (DR/Dt)ij* are functions of snowpack observations on day i. In Eq. (1), Ri* is the estimated shear strength on day i (kPa), Dtij is the time interval between day i and day j (tj ti), where 1 V i < j V i + 8,
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(DR/Dt)ij* is the model estimated rate of change in shear strength (kPa day 1) between day i and day j, and Rj* is the forecast shear strength on day j. Considering operational usefulness, only snowpack variables measurable at the start of the prediction interval, at time ti, were used as input variables. In the interests of optimising model construction, predictor variables that did not have a significant correlation with the response variables, (DR/Dt)ij and Ri, were eliminated from the list of input variables, via Spearman rank correlations (Chalmers, 2001). The snowpack variables used in the development of the model are shown in Table 2. In order to examine which measurable snowpack factors correlated with shear strength, a stepwise, multiple least-squares regression technique was used. Stepwise regression was deemed suitable for this analysis because it selects important predictor variables from a long list of input variables (Mendenhall and Sincich, 1996, p. 242). The use of this technique was validated by testing the residuals of regression (Mendenhall and Sincich, 1996, pp. 115, 175). The regression was first performed on the response variable (DR/Dt)ij, rate of strength change over measurement interval. The shear strength at the start of the interval Ri was included in the list of input variables. The regression was then performed on Ri. The results of this regression are shown in Tables 3 and 4 for (DR/ Dt)ij and Ri, respectively. Deriving empirical formulae for (DR/Dt)ij* and Ri* in Eq. (1) was completed using the regression results. Table 2 Snowpack variables and units at time ti (age of weak layer, in days, at start of prediction interval) Variable
Description (units)
Ri ri
Shear strength of weak layer (kPa) Vertical load (force per unit area) due to snow overlying weak layer (kPa) Thickness of snow slab overlying weak layer, measured vertically (m) Total height of snowpack (m) Thickness of weak layer (m) Temperature of weak layer (jC) Magnitude of temperature gradient across weak layer (jC m 1) Minimum grain size in weak layer (mm) Average temperature gradient across weak layer divided by average weak layer temperature (m 1)
Hi HSi Thicki Twli TGi Emini (TG/Twl)i
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Table 3 Results of multiple stepwise regression on (DR/Dt)ij Adjusted R2 = 0.317, p < 0.00001
Coefficient B
Standard error of B
Intercept ti Ri ri Hi HSi Thicki TGi (TG/Twl)i
0.119 0.000547 0.124 0.107 0.0131 0.0176 4.73 0.00378 0.00827
0.022 0.00087 0.016 0.031 0.048 0.0067 1.1 0.0011 0.0045
These formulae are linear functions of the variables of regression and their coefficients of regression, B (Mendenhall and Sincich, 1996, p. 353), which are shown in Tables 3 and 4. Thus, the formulae are: Ri * ¼ 0:336 kPa þ ð0:0139 kPa day1 ti Þ þ ð1:18ri Þ ð0:625 kPa m1 Hi Þ þ ð0:0804 kPa m1 HSi Þ ð28:7 kPa m1 Thicki Þ þ ð0:0187 kPajC1 Twli Þ þ ð0:0204 kPa mm1 Emini Þ
ð2Þ
ðDR=DtÞij * ¼ 0:119 kPa day1 ð5:47 104 kPa day2 ti Þ ð0:124 day1 Ri Þ þ ð0:107 day1 ri Þ
the significant independent predictor variables and the response variables of the shear strength model and physical snowpack processes may be addressed. This evaluation is largely based on the sign of the coefficients of each predictor variable (Tables 3 and 4); a ‘‘ + ’’ sign indicates an increasing relationship, a ‘‘ ’’ sign indicates a decreasing relationship. 5.2.1. Age of the weak layer (t) Older layers are stronger but slower to gain strength, as illustrated in Fig. 2. 5.2.2. Load on the weak layer (r) More load is associated with surface hoar layers that are stronger and gain strength faster. This strength increase is probably due to increased thinning of the weak layer, which implies more bonding and greater strength (e.g. Davis et al., 1996; Jamieson and Schweizer, 2000). 5.2.3. Thickness of slab overlying the weak layer (H) Surprisingly, thinner slabs are associated with higher weak layer strength. Since slab load and slab thickness are positively correlated, the inclusion of the thickness variable by the step-wise algorithm may be an adjustment for denser (older) slabs, which have had more time to respond to the slab load. More intuitively, greater slab thickness is associated with faster strength gain. 5.2.4. Layer thickness (Thick) Thicker layers of buried surface hoar are associated with lower strength and are slower to gain strength. This strength lag is likely due to larger crystals having
þ ð0:0131 kPa day1 m1 Hi Þ þ ð0:0176 kPa day1 m1 HSi Þ ð4:73 kPa day1 m1 Thicki Þ ð3:78 103 kPa day1 m jC1 TGi Þ ½8:27 103 kPa day1 m ðTG=Twli Þ :
ð3Þ
Finally, estimating the strength of a buried surface hoar layer on day j after a layer is buried is possible from a set of snowpack observations on day i (1 V i < j V i + 8). 5.2. Proposed interpretation of predictor variables Closely following the example of Jamieson and Johnston (1999), the possible associations between
Table 4 Results of multiple stepwise regression on Ri Adjusted R2 = 0.742, p < 0.0001
Coefficient B
Standard error of B
Intercept ti ri Hi HSi Thicki Twli Emini
0.336 0.0139 1.18 0.625 0.0804 28.7 0.0187 0.0204
0.098 0.0037 0.12 0.22 0.029 4.8 0.011 0.010
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more spacing between crystals and between bonds with the underlying layer. Also, larger crystals may provide an ‘‘umbrella effect’’ in which few precipitation particles from the storm that buries the surface hoar fall between surface hoar crystals, to form additional bonds (Davis et al., 1996). 5.2.5. Weak layer temperature (Twl) Warmer (sub-zero) temperatures are associated with stronger layers of buried surface hoar. Since the magnitude of the temperature gradients across the buried surface hoar layers were in the range associated with equi-temperature metamorphism (e.g. Colbeck, 1987), warmer temperatures will be associated with increased bonding between crystals. 5.2.6. Magnitude of temperature gradient across the buried surface hoar layer (TG) Larger magnitude temperature gradients are associated with lower strength and slower rates of strength gain. This correlation may be due to slower bonding associated with a high-TG regime of metamorphism (Colbeck, 1987). Or this may also be due to reduced load on the surface hoar layer since larger TG occurs when layers are near the snow surface and/or in an area of shallow snowpack. 5.2.7. Snowpack depth (HS) Greater snowpack depth is associated with stronger surface hoar layers and larger rates of strength gain. Deeper snowpacks are also associated with larger loads (r), thicker slabs (H), and likely smaller magnitude temperature gradients (TG) across buried weak layers. 5.2.8. Characteristic minimum grain size of the surface hoar layer (Emin) Layers of larger crystals are associated with lower shear strength. Larger grains are also associated with thicker layers (Thick) of buried surface hoar (see above) and usually with greater spacing between surface hoar crystals and the bonds to the underlying layer. 5.2.9. Weak layer temperature gradient (TG) divided by weak layer temperature (Twl) Higher values are associated with slower rates of strength gain, and also with thinner snowpacks (HS),
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thinner slabs (H), and larger magnitude of temperature gradient (TG). 5.3. Model testing The model was tested for fit to the data used to construct it, using surface hoar time series at the Mt. St. Anne and Mt. Fidelity study sites from the winters 1995– 2002. Predicted shear strength values at the end of each measurement interval were computed and compared to the measured shear strengths. The adjusted R2 statistic gives the fraction of variability in the data that is explained by the model. The model test of fit yields an adjusted R2 of 0.72, and thus explains 72% of the variability in the data. Five time series of buried surface hoar were withheld from the dataset used in model construction. The model was applied to these time series, and forecast shear strength at the end of an interval (22 Table 5 Surface hoar time series used in forecasting application Location
Burial date
Skiertriggered activity records
Sk38
Used to build or test model
Mt. Mt. Mt. Mt. Mt.
29-Dec-93 05-Feb-94 07-Jan-95 28-Dec-95 10-Feb-97
yes yes yes yes yes
build build build build test
Mt. Fidelity
30-Dec-99
yes
Mt. St. Anne
30-Dec-99
yes
Mt. Fidelity
21-Feb-00
yes
Mt. St. Anne
20-Jan-01
yes
Mt. Fidelity
28-Jan-01
yes
Mt. St. Anne
23-Feb-01
yes
Mt. Fidelity
23-Feb-01
yes
Mt. Fidelity
02-Jan-02
yes
Mt. Fidelity
16-Feb-02
yes
Mt. St. Anne
16-Feb-02
yes
measured measured measured measured measured, forecast measured, fitted measured, forecast measured, fitted measured, fitted measured, fitted measured, fitted measured, fitted measured, forecast measured, forecast measured, forecast
St. St. St. St. St.
Anne Anne Anne Anne Anne
build test build build build build build test test test
380
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Fig. 3. Measured and estimated time series of skier stability index Sk38 and associated skier-triggered avalanche activity.
T.S. Chalmers, J.B. Jamieson / Cold Regions Science and Technology 37 (2003) 373–383
data points) to within an average of 22% of the measured values, where %error ¼ 100%jRmeasured Rforecast j=Rmeasured :
ð4Þ
5.4. Forecasting regional slab stability for skiers The stability index Sk38 was calculated from snow profiles and/or shear frame tests of 15 surface hoar time series (Table 5) from the Mt. St. Anne and Mt. Fidelity study sites. Sk38 was then correlated with skier-triggered avalanche activity on these layers reported by helicopter skiing operations in the surrounding regions. All but five of these series were used to construct the model; measured (based on shear frame tests) values of shear strength were used to generate the skier stability index Sk38, and modelfitted Sk38 values were calculated for six of these series. The others had insufficiently detailed snow profiles and were used to produce measured Sk38 only. The five series not used to construct the model were used to assess model-predicted Sk38 with avalanche activity. The values of the skier stability index and skier-triggered avalanche activity for the five model-testing series are plotted in Fig. 3. From these data, the number of days with and without skier-triggered avalanches for these time series are tabulated for the days when Sk38 indicated unstable (Sk38 < 1) and stable (Sk38>1.5) conditions. Four of these contingency tables were constructed (Table 6): (a) model-building layers with measured Sk38, (b) model-building layers with model-fitted Sk38, (c) model-testing layers with measured Sk38,
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and (d) and model-testing layers with model-forecast Sk38. The Chi-square test of independence was performed on each of these tables (Stephens, 1998, pp. 253– 256). Chi-square values with significant p-levels ( p < 0.1) indicate that days with/without avalanche activity were significantly associated with Sk38. Table 6a shows that measured Sk38 was a highly significant predictor of regional skier-triggered avalanche activity ( p < 10 4) (89% of avalanche days outside of the transitional period occurred while Sk38 < 1). Table 6b shows that the model-fitted Sk38 is also a highly significant predictor of skier-triggered avalanche activity ( p < 10 4) (93% of avalanche days outside of the transitional period occurred while Sk38 < 1). For the surface hoar layers not used to formulate the model, Table 6c shows that measured Sk38 was a highly significant predictor of regional skier-triggered avalanche activity on these layers ( p = 3 10 4), and Table 6d shows that the model forecast Sk38 was also such a predictor ( p < 10 4). The results of Table 6c and d may be influenced by the small number of avalanche days where Sk38>1.5. The test statistic adjusted for small sample size (Statistica, 1999) showed that the results of Table 6c and d are significant ( p = 7 10 4, p < 10 4, respectively). The skier stability index Sk38, when generated from shear frame tests in a representative study plot, is a predictor of regional skier-triggered avalanche activity in the Columbia Mountains. Furthermore, the snow profile based model developed in this study may be used to estimate Sk38 up to 8 days in the future, with similar predictive merit.
Table 6 Contingency tables for assessing Sk38 Model building layers
Measured (a) p < 10 4 Sk38 < 1 Sk38 >1.5 Modelled (b) p < 10 4 Sk38 < 1 Sk38 >1.5
Model testing layers # Avalanche days
# Non-avalanche days
64 8
62 108
36 53
40 3
# Avalanche days
# Non-avalanche days
(c) p = 3 10 4 Sk38 < 1 Sk38 >1.5
19 7
29 58
(d) p < 10 4 Sk38 < 1 Sk38 >1.5
28 5
29 59
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6. Conclusions Surface hoar layers buried in the Columbia Mountains of western Canada present a serious hazard to both recreational and professional backcountry users. During the first 30 days in which these layers are buried in the snowpack, they show substantial increases in shear strength, and most skier-triggered slab avalanches occur. The model developed in this study establishes a number of variables as predictors for the shear strength of a buried surface hoar layer. These include age of the layer, load, slab thickness, height of snowpack, layer thickness, weak layer temperature, minimum constituent grain size, and temperature gradient across the layer. The model explains 72% of the variability in the data. Testing the model on five test series shows that it is accurate to within an average of 22% of measured shear strength. The skier stability index Sk38, based on a snow profile in a well-located study plot, is a significant predictor of regional skier-triggered avalanche activity, up to 8 days in advance for layers of buried surface hoar in the Columbia Mountains. The shear strength predictive model developed in this study shows potential as an regional avalanche forecasting tool in the Columbia Mountains. It was developed using data from the first 30 days after burial and for layers of surface hoar with sector plate crystals between 5 and 30 mm in size. This model requires standard snowpack observation techniques, and additional measurements of surface hoar layer thickness to the nearest millimetre. This model is limited to regional forecasting only, as extrapolating study plot stability indices over a large region will not indicate stability specific to avalanche start zones where terrain or weather yield snowpack conditions atypical of the forecast area. In order to determine if the shear strength prediction model may be applied to snowpack climates outside of the Columbia Mountains, time series observations of surface hoar layers in other regions are required. Such data would also serve to better isolate the influence of specific snowpack properties on the shear strength of buried surface hoar layers. This study provides important associations between snowpack properties, buried surface hoar
layers, and skier-triggered avalanches on these layers, but these associations are empirical and statistical only. Much more research is required in order to examine the physical mechanisms that link micromechanical and textural properties of surface hoar layers to the shear strength of these layers.
Acknowledgements The authors are grateful to Jill Hughes, Leanne Allison, Ken Black, James Blench, Joe Filippone, Michelle Gagnon, Ryan Gallagher, Torsten Geldsetzer, Sue Gould, Brian Gould, Phil Hein, Alec van Herwijnen, Nick Irving, Crane Johnson, Greg Johnson, Alan Jones, Kalle Kronholm, Paul Langevin,Steve Lovenuik, Greg McAuley, Rodden McGowan, Jennifer Olson, Mark Shubin, Kyle Stewart, Adrian Wilson and Antonia Zeidler for their careful field work. Our thanks to Canadian Mountain Holidays and Mike Wiegele Helicopter Skiing for providing the avalanche occurrence reports from their ski guides. For their assistance with field studies, we thank the avalanche control section of Glacier National Park including Dave Skjo¨nsberg and Bruce McMahon, Mike Wiegele Helicopter Skiing, and the BC Ministry of Transportation. This study was funded by the Natural Sciences and Engineering Research Council of Canada, Canada West Ski Areas Association, Intrawest, the Canadian Avalanche Association and the BC Helicopter and Snowcat Skiing Operators Association.
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