Snow avalanche penetration into mature forest from timber-harvested terrain

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1 477 Snow avalanche penetration into mature forest from timber-harvested terrain G. Anderson and D. McClung Abstract: Clear-cut logging in British Columbia, Canada, is creating new avalanche start zones from which snow avalanches sufficient in size to penetrate and destroy mature forest cover can initiate. In addition to creating new start zones, the presence of these logging cut blocks can augment the destructive potential of previously existing avalanche paths. Forest-penetrating avalanches can pose a significant risk to down-slope structures and resources. This study is the first to develop and utilize a database containing information on penetration distances and lateral spread from avalanches that have penetrated forest cover. The study area for this research spans the Southern Coast and Columbia Mountains of British Columbia, Canada. Analysis focuses on terrain characteristics related to forest penetration and the resultant destruction of mature standing forest. Physical terrain and vegetation characteristics in the avalanche starting zone, track, and runout zone of 45 forest-penetrating avalanches are described, measured, and parameterized. The results provide tools to assess and evaluate potential forest-penetrating avalanche terrain, and runout models for avalanches in forested terrain. Key words: snow avalanche, maximum runout, timber harvest, forest damage, clear-cut. Résumé : La récolte du bois par coupes à blanc, en Colombie-Britannique, Canada, crée des nouvelles zones de départ d avalanches qui peuvent initier des avalanches de neige de dimension suffisante pour pénétrer et détruire le couvert forestier mature. En plus de créer des nouvelles zones de départ, la présence de ces blocs coupés peut augmenter le potentiel de destruction des trajets d avalanches existants. Les avalanches qui pénètrent dans la forêt peuvent poser un risque significatif aux structures et ressources en aval. Cette étude est la première à développer et à utiliser une base de données contenant des informations sur les distances de pénétration et l épanchement latéral d avalanches ayant pénétré le couvert forestier. La zone d étude couvre la Côte du Sud et les Montagnes Columbia en Colombie-Britannique, Canada. L analyse se concentre sur les caractéristiques de terrain liées à la pénétration dans la forêt et la destruction de la forêt mature encore debout. Les caractéristiques physiques et de végétation du terrain dans la zone de départ de l avalanche, son trajet et parcours, sont décrites, mesurées et paramétrées, et ce, pour 45 avalanches ayant pénétré la forêt. Les résultats offre des outils pour étudier et évaluer les terrains susceptibles d initier des avalanches pénétrant la forêt, et des modèles de parcours pour les avalanches en terrain forestier. Mots clés : avalanche de neige, parcours maximal, récolte de bois, dommage à la forêt, coupe à blanc. [Traduit par la Rédaction] Introduction Old-growth timber in British Columbia, Canada, is becoming less readily available as it has been extensively logged in valleys across the province. The diminishing lower valley supply and other external factors have resulted in logging being conducted on steep slopes, some existing above transportation corridors, human settlement, and other development. Logging clear-cuts in high alpine areas of B.C. receive sufficient snow and contain slope gradients steep enough to lead to the creation of new avalanche terrain (Stitzinger 2001). This new avalanche terrain can lead to longitudinal and lateral expansion of existing paths as well as creating entirely new avalanche paths (Stitzinger et al. 2001). The study presented here is the continuation of a research initiative started in 1996 by the Avalanche Research Group (ARG) at The University of British Columbia (UBC). The ultimate goal is to gain a thorough understanding of the processes characterizing the behaviour of snow avalanches caused by clear-cut logging and their destructive potential. Our study is the first to contain characteristics and analysis on avalanche paths that have penetrated into mature forest cover. Avalanches occurring in timber-harvested terrain have been classified by the UBC ARG into three types Type I: Initiate within a logging cut block and terminate within or below the cut block. Type II: Initiate above cut blocks and terminate within or below the cut block. Received 20 July Accepted 21 February Published at on 29 March G. Anderson* and D. McClung.** Department of Geography, UBC Avalanche Research Group, The University of British Columbia, Vancouver, BC, Canada. Corresponding author: G. Anderson ( geoff.anderson@tc.gc.ca). *Present address: Transport Canada, Surface, Agnes Street, New Westminster, BC V3M 5Y4, Canada. **Present address: The University of British Columbia, 1984 West Mall, Vancouver, BC V6T 1Z2, Canada. Can. Geotech. J. 49: (2012) doi: /t

2 478 Can. Geotech. J. Vol. 49, 2012 Type III: Type I, type II or other avalanches that have penetrated and destroyed mature forest. This study is based on type III avalanches. The results of analyses on lateral spread, forest penetration distances, and runout distances are presented. The basis for runout prediction tools are developed with the objective of assessing the potential for new avalanche paths to penetrate through mature forest cover and pose a risk to down-slope resources. Study area The study area spans the Coast and Columbia Mountains of Southern British Columbia, Canada. Individual study sites are characterized by avalanches that have penetrated into and destroyed mature forest cover. Figure 1 is a map depicting the location of the avalanche paths used in the analysis. Methods Site selection and data collection Avalanche path locations were initially identified by personal communication and consultants reports. Avalanche paths were also identified through extensive 1: scale airphoto searches. Confirmation of path location and measurement of the necessary variables were completed during field visits or using a geographic information system (GIS). Where possible, measurement of new variables was done on site. For cases where site visits had been conducted for previous research, site photos, airphotos, field notes, terrain resource information maps, and forest cover survey sheets were used in combination with a GIS to calculate variables not collected during the initial visit. Data collection methods expanded upon those in McClung (2001) and were focused on physical terrain variables. The type I (within block) and type II (above block) analyses were conducted using 40 physical terrain shape and vegetation variables. Further descriptions of the type I and II datasets can be found in Stitzinger (2001) and Weisinger (2004). Here, we focus on type III (forest-penetrating) data for which a number of additional variables were measured or calculated as described in the section titled Type III (forest-penetrating) variable description. The hypothesis of the study is that mature forest cover retards avalanche motion and therefore shortens runout distances. Very young, weak forest is excluded as its influence on a moving snowpack is minimal. In this study, forest cover refers to living forest that is at least 5 m in height. This definition is important as re-growth in existing paths is destroyed annually by avalanches and is not substantial enough to have a retarding effect on sliding snow. The 5 m height cut-off ensures that there was sufficient trunk length protruding above the snow surface in winter to interact with avalanche activity given that a typical snowpack depth is on the order of 2 m deep. Also, indicated in the ARG data, there appears to be a difference in the manner in which trees shorter than 5 m react to the impact forces of avalanches compared to those taller than 5 m. Data collected for this research suggest avalanches tend to bend trees shorter than 5 m and break or overturn trees larger than 5 m. This assumption is drawn from data collected by the UBC ARG, but has not been verified by any analysis, nor is it explored any further in this work. Type III (forest-penetrating) variable description Over 60 variables were collected, calculated or measured for the type III analysis. In addition to the 40 type I and type II variables described in McClung (2001), selected type III variables were collected and are described in Table 1 and Fig. 2. Analysis Distributions of the various parameters were plotted to evaluate the physical terrain differences between characteristics of type III (forest-penetrating) avalanche paths and type I (within block) and II (above block) avalanche paths. Descriptive statistics of the physical terrain characteristics in the start zone, track, and runout zone were produced for all the variables collected. Tests of significance were applied to variables that could potentially be used to distinguish between terrain that leads to forest penetration and terrain that does not. For standard 10 b point runout ratio analyses (see section titled Runout ratio probability analysis ), ratios of distance to the runout zone tip from the b point to the distance from the b point to the top of the start zone were calculated. The b point itself is assigned a value of zero so that Dx measured down-slope from the b point has a positive value and if Dx is measured up-slope it has a negative value. A resulting negative runout ratio indicates a runout termination point upslope of the b point, a positive value indicates the avalanche travelled to a position below the b point. Probabilistic predictions of avalanche runout for forest cover penetration Normally in applications one is concerned with risk-based methods of avalanche runout, which imply estimates of the probability that avalanches reach or exceed a given location on the ground. The two common methods of calculating avalanche runout are the use of avalanche dynamics models and empirical, statistical estimates. Of these two methods, only the latter can be used at the present time when forest cover is penetrated because no avalanche dynamics model exists that has the capability to handle the complex interaction of flowing snow involved in penetration and destruction of forest cover. Accordingly, we pursue here the probabilistic approach. For applications, we have completed the analysis for two simple measures of extreme runout position for the dense part of flowing avalanches. In some cases, it is possible for the powder component of avalanches to penetrate and destroy forest cover, but this case is ignored here. The two parameters for which we provide probabilistic estimates of extreme avalanche runout are the a angles and the runout ratios designated here as RR = Dx/X b. The procedure is to fit the data to a probability density function (pdf) that is chosen on the basis of three goodnessof-fit statistics: the Kolmogorov Smirnov (K S) statistic, the Anderson Darling (A D) statistic, and the chi-squared (c 2 ) statistic. For all the analyses in this paper we fit the datasets to at least 38 pdfs, with one selected from ranked values of the three goodness-of-fit statistics. In addition, we constructed a probability plot to confirm the fit for the chosen pdf, which may be considered a fourth goodness-of-fit criterion. All four goodness-of-fit criteria apply to the cumulative distribution function, which is directly expressed in terms of

3 Anderson and McClung 479 Fig. 1. Forty-five type III (forest-penetrating) avalanche path locations in Southern British Columbia. Table 1. Selected type III variables. Variable Description Slope and horizontal distance to forest cover Horizontal and slope distance measured from the top of the start zone to the point of forest penetration (m). Accuracy: ±20 m. Vertical fall to forest penetration point Difference in elevation between the top of the start zone to the point of forest penetration (metres above sea level (m.a.s.l.)). Accuracy: ±20 m (vertical). Slope and horizontal distance of forest penetration Horizontal and slope distance from the point of forest penetration to the bottom of mature forest destroyed (m). Accuracy: ±20 m. Slope and horizontal distance below forest penetration Horizontal and slope distance from the point of forest penetration to the bottom of the runout zone (m). Accuracy: ±20 m. Vertical fall of forest penetration Difference in elevation between the point of forest entry to the bottom of the forest cover destroyed (m.a.s.l.). Accuracy: ±20 m (vertical). Maximum damage width Maximum width of mature forest damage measured along an elevation contour (m). Accuracy: ±5 m. Slope angle at forest penetration point Slope angle at the point of forest penetration (degrees). Accuracy: ±1. Crown closure class at penetration point Percentage of forest canopy closure, proportion of the ground visible from above (%). Forest damage area Area of destroyed forest on the ground surface (ha). Error is approximately 0.04 ha. Damage area Total area damaged by the slide (ha). Error is 0.04 ha. (10% of the area if damage area is smaller than the summed distance error.) Alpha (a) angles Angle at the bottom of the runout zone to the top of the start zone ( ). Accuracy: ±1. Beta (b) angles Angle from the point at which the slope first becomes 10 to the top of the start zone ( ). Accuracy ±1. probability as opposed to the pdf that must be integrated to yield any estimate of probability. Selected results As penetration of forest occurs in the track and runout zone, the focus of the study was on these segments of the avalanche paths. No single variable could be correlated with the extent of damage, lateral spread or distance of penetration. Lateral spread Lateral spread is the horizontal spread of an avalanche as it decelerates in the runout zone. Absolute spread and spread ratios were calculated by subtracting the average width of the runout zone from the average width of the track for each path, and by dividing the same values. Extensive testing was conducted on cross slope shape (CSS) as an indicator of potential lateral spread. The CSS is a five-part categorical sys-

4 480 Can. Geotech. J. Vol. 49, 2012 Fig. 2. Variables of interest in forest-penetration analysis. Fig. 3. Normal probability plot of lateral spread values for forestpenetrating avalanches. tem ranging from 2 to +2, reflecting the degree of confinement in the avalanche path. Negative values represent horizontally convex terrain and positive values represent concave (gullied) terrain (McClung 2001). No significant relationship could be found between any one variable and lateral spread. The main reason for the lack of a significant relationship is that the runout zone crossslope shape is skewed to concave with only two cases exhibiting negative (convex) values. This indicates that there would be little opportunity for avalanches to spread in the runout zone because generally they remain confined in gullies. The spreading that is evident can be attributed to spreading of the mass as the snow decelerates and terrain shape rather than a forest effect. Figure 3 is a normal probability plot of the range of spread values. Negative values indicate a narrowing and positive values indicate a lateral expansion of the path in the runout Fig. 4. Approximately linear relationship between damage area and slope penetration distance. zone. The largest spread measurement was 55 m wider in the runout zone than in the track, representing a lateral expansion of approximately 27.5 m on either side of the avalanche as it decelerated in the runout zone. This case was different from its neighbours in that the runout zone was less steep and the avalanche stopped within forest cover rather than travelling into the nonforested cutblock below. Damage areas Damage areas (DA) are roughly rectangular in geometry as shown by the relationship between path length of penetration and damage area. Figure 4 shows an approximately linear least-squares relationship between damage areas and path length of forest penetration (PLFP). The relationship indicates that forest penetration is a rectangular phenomenon: the damage area is directly proportional to the length of penetration. The probable damage widths of an avalanche runout

5 Anderson and McClung 481 zone can be estimated if assumptions are made about confining terrain features in the track and runout zones. Once potential spread in the runout zone is estimated, the area susceptible to damage can also be estimated given the equation DA = (PLFP) (coefficient of determination, R 2 = 0.88; sample size, n = 44; standard error, S.E. = 0.20 ha). Slope shape The type III (forest-penetrating) data show significantly higher cross-slope shape categories than type I (within block) and type II (above block) data. This confirms that confined paths (positive values) have a greater tendency to penetrate forest than those in terrain with infinite horizontal curvature (nongullied) or convex terrain. Cross-slope shapes in the track and runout zone are skewed strongly toward the positive. Figure 5 shows a bar chart distribution of the runout zone cross-slope shape, and shows just two cases where forest damage occurred on horizontally convex terrain. All other cases were without curvature (0) to highly gullied (2) in the runout zone. Figure 5 demonstrates a clear propensity for forestpenetrating avalanches to occur in gullied runout zones. This distribution is different from that of the type I dataset. Alpha angle probability analysis The alpha angles (a, in degrees) have a mean of 30.3, a median of 30.3, a standard deviation of 3.2, with a range of The a angles have a negative skewness of 0.43 and the ratio of skewness to standard error of skewness is Thus, the data have negative skewness, but the absolute value of the ratio skewness to standard error of skewness is less than 2, so the skewness is not considered highly significant. We fit the data to 64 different pdfs and made the choice based on ranking the three goodness-of-fit statistics, with a check on the fit by constructing a probability plot. The chosen pdf is the shifted log-logistic pdf. All three goodness-of-fit statistics were significant for values of a crit > 0.2, where a crit is the significance level. The values of the three statistics with the critical values (a crit = 0.2) were: K S: 0.07, 0.16; A D: 0.21, 1.37; c 2 : 1.32, The shifted log-logistic pdf is f1 þ½kðx mþ=sšg ½1=ðkþ1ÞŠ ½1Š f ðx; m; s; kþ ¼ sh1 þf1þ½kðx mþ=sšg 1=k i 2 where m, s, and k are the location, scale, and shape parameters, respectively. The pdf has the important property that for k < 0, it has negative skewness and for k > 0 it has positive skewness. The cumulative distribution function (CDF) is ½2Š Fðx; m; s; kþ ¼ 1 1 þf1 þ½kðx mþ=sšg 1=k For the present application, the values of k in the databases are all such that 1 <k < 0 so that eqs. [1] and [2] are subject to the restriction: x m + s / k. This implies a maximum upper limit on the values of x. In both eqs. [1] and [2], for the analysis here, x a. Using PðxÞ ¼ Rx f ðx 0 Þ dx 0 as the x min Fig. 5. Runout zone cross-slope shape distribution. nonexceedance probability (P) and x min as the minimum value of the distribution (often ), we may express eq. [2] as ½3Š aðpþ ¼ m s þ s P k k k 1 P where k = 0.06, s = 1.78, and m = 30.5, which is the median of the distribution. The probability plot corresponding to eq. [3] showed a least-squares line fit with R 2 = 0.98 and S.E. = 0.016; P, was estimated using Hazen plotting positions. The maximum value of a implied by the data and model is 60, which is a reasonable limit as the angle is slightly greater than slope angles on which slab avalanches normally release. Analysis with eq. [3] shows that the model contains the prediction that 95% of the a angles are predicted to be greater than 25. The British Columbia Ministry of Transportation and Highways uses 25 as a screening tool to decide whether or not further assessment is required to determine if avalanche activity could affect a highway (Weir 2002). Our data and model provide confirmation that this is a good criterion. Equation [3] provides a simple probabilistic criterion for expected runout when forest cover is encountered by snow avalanches in motion. Figure 6 shows the cumulative distribution. Beta angle probability analysis Only one of 45 forest-penetrating avalanches terminated down-slope of the 10 b point. The remaining 44 stopped up-slope of or at the b point. This is shown by negative runout ratios and higher a angles than b angles. Figure 7 is a normal probability plot of the 10 b point angle distribution. The minimum value measured was 20, the maximum 35, with a mean of 29. The one case that terminated down-slope of the b point did not encounter forest cover until the slide was down-slope of the b point. Every other avalanche ran into forest cover up-slope of the b point; this is a strong indication that forest cover is acting as a retardant to potential runout distance.

6 482 Can. Geotech. J. Vol. 49, 2012 Fig. 6. Cumulative a angle distribution. Fig. 8. Comparison of the theoretical models for RR as a function of P. Open points are short-slope data, closed points are forest-penetration data. The plot implies a retarding effect on avalanches encountering forest cover. Fig. 7. Normal probability plot showing the distribution of b angles for 45 forest-penetrating avalanches. Runout ratio probability analysis Horizontal distance runout ratios to the b point were calculated for each path. These ratios are the ratio of horizontal distance from the runout zone tip to the b point divided by the horizontal distance from the top of the start zone to the b point. As only one path ran beyond the b point, forest cover appears to be acting as a retardant to runout distance. The average runout zone angle for forest-penetrating avalanches was 22, significantly higher than a typical 15 reported in McClung and Schaerer (1993). The values of the runout ratio (RR) take both positive and negative values with a median value of 0.16 and mean of The data are highly negatively skewed. The skewness is 1.37 and the ratio of the skewness to the standard error of skewness is 4.04, implying that the negative skewness is highly significant. We fit the data to 38 different pdfs and based on the same criteria as for the analysis of the a angles above, we concluded that the shifted log-logistic pdf was the best choice. The CDF may be obtained from eq. [3] by the replacement RR a. The values of the parameters are k = 0.28, s = 0.09, and m = The least-squares line in the probability plot had R 2 = 0.97 and S.E. = The values of the goodness-of-fit statistics and critical values (a crit = 0.2) were, respectively, K S: 0.075, 0.156; A D: 0.30, 1.37; c 2 : 2.40, Analysis with the CDF of RR(P) shows that 10% of the avalanche events represented by the data are expected to reach or exceed the position on the terrain where the slope angle first reaches 10 denoted by RR = 0. This important result shows the retarding effect of forest cover on runout. It is also of interest that the maximum value of RR is specified to be RR = m + s / k = 0.17, which would correspond to P = 1, or zero probability of exceedance. This is strictly a function of the scale appropriate for the data (mean value of vertical drop = 490 m) and the dataset. However, it suggests that for the available data and the model, such a runout position would be a very safe location. In the next section, we compare the results with another dataset without the retarding effects of forest cover penetration to further illustrate the retarding effect. Comparing forest-penetrating data to nonpenetrating short-slope data using the RR In this section we compare the probability analysis of the last section with data from short slopes (vertical drop mean value = 225 m) as collected by Jones (2002). Our data apply to a mean value of total vertical drop of 490 m, or more than twice that for the short-slope data. In addition, the mean value of a from our data is 30 versus 26.5 for the shortslope data. The median value of RR for our data is 0.16 (mean of 0.20) versus (mean of 0.05) (N = 46 values) for the short-slope data. The skewness of the short-slope data is 0.41 and the ratio of skewness to standard error of skewness is This shows that again the skewness is negative, but the ratio is below the significant value of 2. We applied the same analysis to the short-slope data as above with fits to 38 different pdfs. The analysis again showed that the best choice was the shifted log-logistic pdf. The goodness-of-fit statistics and critical values (a crit = 0.2)

7 Anderson and McClung 483 Table 2. Comparative runout statistics summary. Mean values Location N a ( ) b ( ) d ( ) H 2 Dx/X b Forest-penetrating (type III) * Columbia Mountains Canadian Rockies Coastal Alaska B.C. Coast Range Western Norway Colorado Rockies Sierra Nevada Short slopes *The type III d angles differ from the regular definition of the d angle. As the forest-penetrating avalanches terminate up-slope of the b point, the d angle represents the angle between the b point and the runout position. It is sighted up-slope from the b point to the runout terminus. were, respectively, K S: 0.096, 0.155; A D: 0.34, 1.37; c 2 : 0.74, The probability plot showed R 2 = 0.97; S.E. = The values of the parameters were k = 0.055; s = 0.148; m = These parameters imply an absolute maximum value of RR = 2.75 based on the data and model. Analysis with the CDF showed that 60% of the paths in the short-slope dataset are expected to reach or exceed the 10 slope angle compared to 10% for the penetration data. This result applies even though the penetration events had a mean value of the vertical drop (490 m) that is more than twice that for the short-slope data (225 m) and the slope profiles are steeper for the penetration data (mean a angle, a = 30 ) than for the short-slope data (a = 26.5 ). Figure 8 contains a comparison of the theoretical models for RR as a function of P showing the highly skewed CDF of the penetration data in comparison with the short-slope data. The skewness is due to the choice of the 10 slope angle as the reference point. Negative skewness implies most extreme runouts are above the 10 position on the slope with negative values of RR. Negative runout ratios (Dx/X b ) in Table 2 indicate the average runout zone terminus is up-slope of the b point and positive values indicate a runout tip below the b point. In Jones (2002), a mean b point runout ratio of 0.05 was reported. The mean ratio for the type III dataset was 0.20, indicating the mean runout tip for forest-penetrating avalanches terminates up-slope of the Jones (2002) short-slope (nonforested) avalanche dataset. Conclusions This study contains selected results of the first terrain shape analysis for forest-penetrating avalanches. The varying nature of the individual sites has thus far made it difficult to produce a predictive tool for evaluating the potential for avalanches to reach a given point on a forested slope. However, a number of promising indicators are revealed through the analysis: Slopes with an infinite cross-slope curvature and concave horizontal slope shapes in the track and runout zone prevent significant lateral expansion (spread) of avalanches in the runout zone. Given site-specific assumptions on lateral confinement (down-slope transition of cross-slope shape) and potential distance of penetration, potential damage areas can be estimated by using the regression equation represented in Fig. 4. Higher a angles are contained in the type III database than all regions except for the Columbia Mountains (Table 2). The high mean a angle indicates a runout terminus upslope of the average stopping point for avalanches in nonforested areas. Analysis on 10 b point runout ratios shows that all but one of the 45 forest-penetrating avalanches stop up-slope of the b point. Comparative analyses with short-slope avalanche data show forest cover shortening runout distances by acting as a retardant. Further analysis could be undertaken on a similarly scaled database for avalanches that did not penetrate forest cover to determine whether or not there exists a significant difference in runout zone stopping angles. Classical a and b point analyses and runout ratio analyses are the best indicators of runout distance potential for avalanches penetrating through forest cover. The forest-penetrating avalanches exhibit a smaller (negative) mean b point ratio than the type I and II datasets as well as the eight other regions presented in Table 2. The normal probability plot of a and b angles and runout ratio probability plotting can be used in a field setting to determine the likelihood of an avalanche travelling through forest cover to a given point on a slope. Acknowledgements Funding for this research was provided by Forest Renewal B.C., Canadian Mountain Holidays, and the Natural Sciences and Engineering Research Council of Canada. Their support is greatly appreciated. In kind support was facilitated by Jim Horbay, Transport Canada. References Jones, A Avalanche runout prediction for short slopes. Master s thesis, University of Calgary, Calgary, Alta. McClung, D.M Characteristics of terrain, snow supply and forest cover for avalanche initiation caused by logging. Annals of Glaciology, 32(1): doi: / McClung, D.M., and Schaerer, P The avalanche handbook. The Mountaineers, Seattle, Wash.

8 484 Can. Geotech. J. Vol. 49, 2012 Stitzinger, K Snow avalanche risk and decision support for clear-cut harvested terrain. Master s thesis, The University of British Columbia, Vancouver, B.C. Stitzinger, K., Weisinger, P., and McClung, D Avalanche activity and interaction with harvested terrain: terrain analysis and decision support systems for risk management. In Proceedings of the International Snow Science Workshop 2000, ISSW-meeting, Big Sky, Montana, pp Weir, Peter Snow avalanche management in forested terrain. Land management handbook No. 55. Resources Branch, B.C. Ministry of Forests, Victoria, B.C. Available from bc.ca/hfd/pubs/docs/lmh/lmh55.htm [accessed 14 March 2012]. Weisinger, P Risk management for damage of avalanches descending into clear cuts. M.Sc. thesis, Department of Geography, The University of British Columbia, Vancouver, B.C.