Terrain Influences on Total Length of Snow-Avalanche Paths in Southern Glacier National Park, Montana

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1 Terrain Influences on Total Length of Snow-Avalanche Paths in Southern Glacier National Park, Montana Jay K. Gao Graduate Student David R. Butler Professor Department of Geography University of Georgia Athens, Ga ABSTRACT This research was designed to determine the impact of topographic variables on the total length of avalanche chutes in southern Glacier National Park, Montana. Seventy-eight snow avalanche paths were manually interpreted from aerial photographs within the study area, and their outlines were delineated on U.S. Geological Survey topographic maps with a scale of 1 :24,000. Terrain variables were either measured directly from the maps or derived from the original ones. Terrain parameters were first analyzed by using the descriptive statistical method. Total path length was then regressed against the independent variables elevation, orientation, and slope gradient. We found that: (a) the majority of the avalanche chutes are oriented north, south, and southwest; (b) total path length is highly correlated with source area as well as with top elevation but negatively with slope gradient; (c) longitudinal slope gradient is a significant determinant of path length only for north-facing slopes. Sou rce zone area, to a large extent, determines the length of the avalanche path. However, top el evation is of greatest importance in explaining the total length is the specific contribution made by each individual factor is considered. KEY WORDS: snow avalanche path, terrain analysis, Montana, geomorphology, mass wasting. INTRODUCTION Snow avalanches are a common and widespread geomorphic process in the Rocky Mountains. Most of the recent studies on avalanching within the area concentrated on description of avalanches (Luckman, 1978; Malanson and Butler, 1984). The description ranged from geomorphic features of avalanche sites or paths to vegetational impact on avalanche paths. For instance, Gardner (1970) studied the geomorphic significance of avalanches and avalanche frequency in the late-spring through summer in the Lake Louise area of the Canad ian Rocky Mountains. The geo- 91

2 morphic features of snow avalanches in the same area were described by Luckman (1978). In addition to terrain features, Butler (1979) also examined vegetative cover on snow avalanche chutes. Vegetational and geomorphic changes on snow avalanche paths were further determined through repeated field visits (Butler, 1985). Quantitative analysis of the impact of terrain on avalanches has also been undertaken. Mears (1980) identified the pa rameters of greatest importance in determining the total length of avalanche chutes. No correlation was found between runout distance (the low angle portion below the source zone) and the runout zone slope. Based on their study of 67 avalanche paths, Bovis and Mears (1976) predicted snow avalanche runout distance by means of regression analysis. Results showed that starting zone area alone accounted for 65 percent of the variance in runout distance. Bakkeh <j)i et al. (1983) used four topographic parameters to predict maximum runout distance for 206 avalanche paths. Regression analysis was also conducted for the same data set. The goodness of fit was found to vary w ith grouping criterion, with the maximum R value being All these quantitative analyses focused on predicting avalanche runout distance from terrain-related factors. The specific amount of variation in the total length of avalanche chutes explained by each of the contributing variable has not been examined. Thus, the significance of each factor in determining avalanche path length remains unknown. The objective of this research is to determine morphometric characteristics of snow avalanches in southern Glacier National Park, Montana, and to determine the influences of such terrain pa rameters as elevation, gradient, and slope orientation on the total length of avalanche paths, a measure of natural hazard potential resulting from distance travelled by past avalanches. This paper first introduces the geographic settings of the study area. The methods used in this research are outlined next. Finally, the findings of this research are discussed. STUDY AREA Glacier National Park is located in the northwestern corner of Montana (Fig. 1). partitioned into two approximately equal sections by the Continental Divide. This park has spectacular alpine scenery resulting from extensive glaciation during the Pleistocene and Holocene Epochs. A large portion of the area has a continental climate except the western slope whose climate may be broadly categorized as Pacific maritime. Predominant winds from the west are conducive to the development of snow cornices (Fig. 2) on southeasterly oriented slopes. These cornices are significant factors in avalanche development (Schaerer, 1977). Winter precipitation in the park is moderately high, and heavy snow may continue well into June. Snow can accumulate up to 280 cmjyear at terrains with high elevation (Dightman, 1976). Such a precipitation pattern, coupled with warm, mild spells created conditions conducive to avalanche development in many parts of the park during the spring months. Most avalanches in the study area are of the wet-snow type. Evidence suggests that windblasts are associated with powder clouds and dry-snow avalanches in some avalanche paths below treeline. METHODOLOGY Black-and-white aerial photographs (Fig. 3) of the study area taken in 1981 at 1 :34,400 were visually interpreted under a stereoscope. Seventy-eight avalanche paths were interpreted and their outlines delineated on the photographs. The corresponding locations of these avalanches were also drawn on 1 :24,000 U.S. Geological Survey 7.5-minute quadrangles. Measurements were made for 24 initial variables from the maps. A few variables were transformed to ground dimension by multiplying by the map scale factor. These data were computer-formatted using Quattro and derivative variables such as slope gradient were calculated from the original ones. Because previous studies suggest only a limited number of variables affect total avalanche-path length (Bakkeh <lji et al., 92

3 British Columbia Alberta CANADA U.S.A. e Sabb 1 N e East Glacier Park MONTANA o, 10, kil ometers 20, Figure 1. Location of the study area in relation to Glacier National Park. 1983; Bovis and Mears, 1976), only four out of the total of twenty-six measured variables were selected as the focus of this research. They were top elevation of the avalanche path, average path inclination or slope gradient source zone area, and total path length. The total length, a dependent variable used in a regressional analysis, is defined as the distance from head of an avalanche path to its farthest runout point. The source zone area refers to the extent encompassed by the outline of source zone. Top elevation is the altitude at which the head of an avalanche chute starts. Slope gradient, measured in degree, is calculated from the ratio of vertical relief to horizontal distance, and thus is the average longitudinal inclination of an avalanche path. Simple linear regression was used to examine the relationship between the dependent variable, total path length, and the other three variables. Scatter diagrams of the dependent variable versus the independent ones revealed that linear relationships exist between total length and slope gradient, as well as between the dependent variable and top elevation. The relationship between to- 93

4 Figure 2. Photograph showing snow cornices. Arrows point to the wind-formed snow cornices overhanging above a mountain highway. The snow shed beneath the cornices protects the highway. tal length and source area appeared to be a logarithmic function, therefore, a logarithmic transformation was performed for this variable in all the subsequent analyses. The prepared data set was later analyzed by SAS (Statistical Analysis System) programs. The analyses ranged from simple descriptive statistics to multivariate regression. The analyses were carried out first for the entire data set, and then for north- and south-facing path subsets subdivided in terms of slope orientation. RESULTS The results of the descriptive statistical analysis are provided in Table 1, in which linear variables are measured in meters and areal variables in square meters. Total path length varies considerably from 402 m to 2,524 m. The average length of these avalanche paths is 1,235 m. The large skewness value (0.784) suggests that it is not quite normally distributed. Avalanche paths are spread over a wide range of elevations, from 1,628 m to 2,316 m above sea level. The normality of top elevation can be inferred from its small value of skewness (0.024). The average slopes for the avalanche paths range from 17.0 to 38.4 degrees, with a mean of The skewness for this variable is 0.417, indicating a slight deviation from normality. Source area has an enormous variation from 6,728 m 2 to 852,028 m 2. The average size of the source zone is 11,854.7 m 2 This variable has the largest skewness (2.541) among the four studied and hence is far from a normal distribution. Such a skewed variable was not suitable for subsequent statistical analyses and was abandoned. A new variable, the logarithmic transformation of source area, was created and utilized under the same name. After the transformation, source area was almost nor- 94

5 Figure 3. A representative air photograph exhibiting the characteristics of snow avalanche paths in the study area. mally distributed with a skewness of In order to appreciate the impact of orientation, the four variables were analyzed separately for each of the eight slope orientations. The entire data set was divided into eight categories, north, northwest, west, southwest, south, southeast, east, and northeast (Table 2). Variable 4 is the logarithmic transformation of source zone area. In addition to containing a direction indicator, column 1 also includes the number of avalanche paths falling in the orientational category. These figures are graphically represented in Figure 2, which demonstrates a strong directional clustering of the 78 avalanche paths identified. The dominant aspects are south and southwest. There is also a high concentration of north and northeast trending avalanche paths. West and northwest-facing slopes have the smallest number of paths. The greatest average total length (1,335 m) is found in the southeast group, and the smallest (1,176 m) in the northeast category. The general relationship among these 95

6 TABLE 1 General characteristics of the four variables No. Variable Min. Max. Mean std. Dev. kewness 1 Total Length(m) Top Elevation(m) Slope Gradient(O) Source Area (m2) Log of Area four variables is shown by their correlation coefficients (Table 3). A fairly high correlation ( ) exists between total path length and source area, implying that a larger source zone will generate a longer avalanche chute. The strong correlation ( ) between total path length and top elevation reflects that longer avalanche paths develop where paths originate at higher altitudes. Table 3 also illustrates that total length is negatively correlated with slope gradient ( ). Essentially, the larger the source area, the more snow it contains, hence the more momentum the snow has, and the farther the snow can travel along gentler slopes, creating longer avalanche paths. Regression analyses were performed for both the entire data set, and for the sub-data sets of north (12 observations) and south (13 observations). The estimated parameters for the three models and their R-Squares are listed in Table 4. The three models take the following forms : Whole: Total Length = x Top Elevation x Slope x 10g,o(Source Area) R2 = North : Total Length = x Top Elevation x Slope x 10g,o(Source Area) R2 = South : Total Length = x Top Elevation x Slope x 10g,o(Source Area) R2 = The R-Square values range from for the whole data set model to for the north model. The R-square values for the two sub-data sets are larger than that of the whole data set because they have fear observations in their regressional analyses. Among the three models, the best one is for the north data set, and the worst is for the entire data set. In these models, the total path length increases with the increment of both top elevation and source area, but decreases with slope gradient. Therefore, avalanche paths with slope gradient. Therefore, avalanche paths with a larger source zone occur at higher al titudes and have gentler slopes. The significance of each explanatory variable in affecting the total length of an avalanche path is determined by partial correlation coefficients. The specific contributions of each component in the model to the variance in the total length are calculated and provided in Table 5. Among the three independent variables, source zone area is the most important factor. It explains percent of the variance in total length explained by the model. The average slope gradient is the least important one, accounting for only percent of the variance by the model. This results from the fact that 96

7 TABLE 2 Avalanche characteristics by orientation 1 Aspect Variable Min. Max. Mean std. Dev. North (12) N.W (6) West (4) S.W (15) South (13 ) S.E (8) slope gradients vary along the longitu- propagation. Top elevation explains dinal extent of an avalanche path, and percent of the variance. These figures, the mean gradient does not reflect the however, include the shared portions slope gradient critical to avalanche jointly explained by the specified vari- 97

8 TABLE 2 Continued East (10) N.E (10) Variables defined in Table 1. TABLE 3 Correlation coefficients among the variables variable Variables 1, 2, 3, 4 defined in Table 1. able and those present in the model. If the proportion exclusively explained by each variable is considered, top elevation is the most important factor in affecting avalanche-path length. Top elevation alone explains percent of the total variations in the dependent variable, more than the combined amount (13.70) of the other two variables. The second row in Table 5 represents the contributions made by each component in the regression equation for the north model. Here, top elevation is the most important variable in terms of both unique and shared variance explained in the dependent variable. Judged by the common variance, it ranks first. The value is percent or 79.05, higher than the other two values of and The unique variance exclusively explained by 98

9 Figure 4. Star diagram illustrating the relative number of avalanche paths and their corresponding slope aspects within the study area (based on 78 avalanche paths). TABLE 4 Regression parameters and R-squares Intercept Top Elevation Whole North South Slope Source Area R top elevation (12.29) is sl ightly below that by slope gradient (13.10). Source zone area only explains a negligible 0.13 percent of the variance. The large discrepancy between unique and common figures results from the existence of high multi-collinearity. As indicated in Table 6, the dependent variable is closely re- lated to all three explanatory variables. Source zone area is also correlated with the other two components in the model. Consequently, source zone area provides virtually no explanation for the dependent variable. The third row in Table 5 shows the contributions made by each variable in 99

10 TABLE 5 Variance explained by individual terrain components Variable(s) Elevation Slope Source Area Unique Cornman Unique Cornman Unique Cornman Whole Absolute Relative North Absolute Relative South Absolute Relative TABLE 6 Correlation coefficients for north-facing paths variable TABLE 7 Correlation coefficients for south-facing paths Variable the regression for south-facing avalanche paths. In this model the dominant role of top elevation in determining path total length is unequivocal. The amount of variance explained either exclusively or jointly with other components ranks highest for top elevation. The unique figures are consistent with the 100

11 common figures for the other two variables in spite of the high correlation among the four variables (Table 7). Slope alone explains 8.19 percent of the total variance in the dependent va riable. Clearly, the importance of the three explanatory variables descends from top elevation, to slope gradient, and to source area. SUMMARY AND CONCLUSIONS This research attempted to identify the potential impact of three topographic features (top elevation, slope gradient, and source zone area) on avalanche-path total length. The total length was treated as a dependent variable and regressed on the three independent variables. We found that source zone area is of greatest importance in explaining variations in the dependent variable. However, if the specific contribution caused by each variable alone is considered, then top elevation becomes the paramount factor for the whole data set. This conclusion also holds true for avalanche paths on north- and south-facing slopes. Longitudinal slope gradient plays an important part in the separate analyses for north- and south-facing avalanche chutes. Its importance diminishes when the whole data set is indiscriminately treated. REFERENCES Bakkeh<l>i, S., Domaas, U., and Lied, K Calculation of Snow Avalanche Runout Distance. Annals of Glaciology, 4 : Bovis, M. J., and Mears, A. I Statistical Pred iction of Snow Avalanche Runout from Terrain Variables in Colorado. Arctic and Alpine Research, 8(1) : Butler, D. R Snow Avalanche Path Terra in and Vegetation, Glacier National Park, Montana. Arctic and Alpine Research, 11( 1): Vegetational and Geomorphic Change on Snow Avalanche Paths, Glacier National Park, Montana, USA. Great Basin Naturalist, 45(2) : Dightman, R. A Historical and Climatical Study of Grinnell Glacier, Montana. Weather Bureau Tech. Memo., WR-24, 26 pp. Gardner, J Geomorphic Significance of Avalanches in the Lake Louise Area, Alberta, Canada. Arctic and Alpine Research, 2(2) : Luckman, B. H Geomorphic Work of Snow Avalanches in the Canadian Rocky Mountains. Arctic and Alpine Research, 10(2): Malanson, G. P., and Butler, D. R Transverse Pattern of Vegetation on Avalanche Paths in the Northern Rocky Mountains, Montana. Great Basin Naturalist, 44(3) : Mears, A. I A Fragment-Flow Model of Dry-Snow Avalanches. Journal of Glaciology, 26(94) : Schaerer, H Analysis of Snow Avalanche Terrain. Canadian Geotechnical Journal, 14 :