Features of avalanches based on aerial photograph interpretation in Japan

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1 International Snow Science Workshop Grenoble Chamonix Mont-Blanc Features of avalanches based on aerial photograph interpretation in Japan Kazuya AKIYAMA and Shinji IKEDA Snow Avalanche and Landslide Research Center, Pubic Works Research Institute, Myoko, Japan ABSTRACT: Avalanche geometry including factors, such as horizontal run-out distance (HL) and vertical height of avalanche drop (h), were investigated by interpreting three sets of aerial photographs taken in Japan. The aerial photographs were taken during the snow-cover season in 1) 1997, 21, and 22 around Mt. Naeba and Mt. Torikabuto near the border between Niigata and Nagano Prefectures; 2) 2, 26, and 28 around Mt. Kasagatake in Takayama City, Gifu Prefecture; and 3) in 21 in the northern Japanese Alps. Approximately 23 avalanches were identified in the aerial photographs. The release zones of avalanches were mostly at inclinations of The frequency histograms of the direct angle of elevation from the outer end of the avalanche deposit zone to the highest point of the release zone had a normal distribution with the highest frequency in the range of The horizontal run-out distances of surface-layer avalanches and full-depth avalanches averaged approximately 1.7 to 1.8 and 1.3 to 1.4 times larger than the vertical avalanche drop in regression analysis, respectively. Some surface-layer avalanches showed the mobility of large-scale avalanches because the excessive travel distances (Le=HL h/tan32 ) reached up to approximately 19 m. However, most full-depth avalanches did not share the characteristics of the mobility of largescale avalanches, showing excessive travel distance of approximately m or less than m. The relationship between avalanche frequency and scale (area of the release zone or horizontal run-out distance) exhibited a power-law relationship when excluding large-scale avalanches with more than 1 5 m 2 of release area or more than 2 m of horizontal run-out distance. KEYWORDS: aerial photograph interpretation, surface-layer avalanche, full-depth avalanche, avalanche geometry, avalanche scale and frequency 1 INTRODUCTION In addition to basic surveys of the slope inclinations on which avalanches occur and of the horizontal run-out distance of avalanches, recent studies have reported the relationships between various elements of the crown surface in the release zone and the frequency of avalanche occurrence (Louchet et al., 22; Rosenthal and Elder, 23; McClung, 23; Faillettaz et al., 24, 26; Bair et al., 28). The relationship between the U.S classification of avalanche size (5 classes from 1 to 5; McClung and Schaerer, 1993) and the frequency of avalanche occurrences has also been investigated (Birkeland and Landry, 22; Naisbitt et al., 28). However, for Japan, data are severely lacking concerning the characteristics of avalanche release zones and avalanche size. Furthermore, few surveys of numerical specifications of avalanches have been conducted in Japan, and no surveys exist of the relationship between the scale and frequency of avalanches. Corresponding and Presenting author address: 2-6-8, Nishiki-cho, Myoko, Niigata, Japan tel: ; fax: ; akiya486@pwri.go.jp; s-ikeda55@pwri. go.jp The purpose of the present study was to clarify the characteristics the geometry of avalanches and the avalanche scale in Japan by analyzing aerial photographs of three regions. The photographs were taken during three winters near the border between Niigata and Nagano Prefectures, in Gifu Prefecture, and in the northern Japanese Alps. 2 SURVEY REGION AND METHODOLOGY 2.1 The survey region Aerial photographs (aerophoto) were obtained of the following three regions (Figure 1 and Table1): Region a): An approximately 1 km 2 area surrounding Mt. Naeba (2145 m a.s.l.) and Mt. Torikabuto (237 m a.s.l.) near the boundary of Niigata and Nagano Prefectures. Aerial photographs of this region were taken three times: April 2, 1997, May 13, 21, and April 29, 22 (Akiyama and Sekiguchi, 213). Region b): An approximately 9 km 2 area around Mt. Kasagatake (2897 m a.s.l.) in Takayama City, Gifu Prefecture. The largest avalanche ever recorded in Japan occurred along Anage Valley on March 27, 2 in this area. This avalanche was a dry-slab surfacelayer avalanche that released at an elevation of approximately 27 m. The released snow volume was approximately m 3, and its 77

2 International Snow Science Workshop Grenoble Chamonix Mont-Blanc b) Survey Area (Mt. Kasagatake) Three aerial photograph sets taken in snow cover season a) Survey Area (Mt. Naeba and Mt. Torikabuto) Three aerial photograph sets taken in snow cover season Toyama Gifu Nagano Figure 1. Map of the study areas. Niigata Prefecture Gunma c) Survey Area (Northern Japanese Alps) Aerial photographs provided by Google Earth horizontal run-out distance was about 4.6 km (Japanese Society of Snow and Ice, 21). Aerial photographs of this region were taken three times: April 13, 2, April 17, 26, and April 15, 28 (Akiyama et al., 28). Region c): Google Earth has been providing satellite and aerial photographs since June 25. The resolution of the photographs varies, but some are high-resolution orthophotos that can show the state of snow cover. Google Earth images showed this region on May 5, 21. Interpretation of these images revealed that avalanches occurred at elevations from 1 to 3 in and around the northern Japanese Alps. Table 1. Information of aerial photographs. a) photographing flying height aerial coverage photo scale number of shots camera/ tone April 2, m 8 km 2 1/125 2 film camera/ monochrome May 13, m 8 km 2 1/1 23 film camera/ color April 29, m 1 km 2 1/15 29 film camera/ color b) photographing flying height aerial coverage photo scale number of shots camera/ tone April 13, m 5 km 2 1/15 18 film camera/ color April 17, m 5 km 2 1/1 22 film camera/ color 38~ April 15, m 9 digital camera(16 km2 1/1 841 milion pixcels)/ color c) photographing flying aerial color aerophoto (orthophoto) provided by Google height coverage Earth ( 213 ZENRIN, Data Japan Hydrographic May 5, km 2 Association, Image 213 DigitalGlobe, 213 Cnes/Spot Image) 2.2 Interpretation and digitalization of avalanches The avalanche geometry and scale (magnitude) for release, path, and deposit were obtained as shown in Figure 2 (Akiyama et al., 212). The parameters relating to avalanche release and deposit are the slope inclination of the release or deposit zone (θ R, θ D ), elevation of the release or deposit zone (h R, h D ), and the surface area of the release zone (S R ). Parameters relating to the avalanche pass (avalanche movement) are the horizontal runout distance (HL), excessive travel distance (Le), vertical height of avalanche drop (h), and direct angle of elevation from the outer end of the deposit zone to the highest point of the release zone (α ). The avalanche excessive travel distance (Le) denotes the difference between the horizontal run-out distance of an actual avalanche flow and the horizontal run-out distance in the case of the avalanche flowing with the angle of kinetic friction of snow (32 ). Denoting the excessive travel distance of the avalanche by Le, the horizontal run-out distance of the avalanche by HL, and the vertical height of the avalanche drop by h, then Le can be calculated as follows: Le = HL-h/tan32. (1) Excessive travel distance (Le) is an index representing the mobility of the avalanche (Izumi, 1986). The volume and mass of an avalanche are important in determining its scale (magnitude). However, it is difficult to obtain these factors by aerial photograph interpretation. Therefore, the area of the release zone, which is related to quantity, and the horizontal run-out distance, which is related to scale, were used to determine the avalanche scale. h = h R h D tanα= h/hl tanα = h/hl Le: excessive travel distance Le = HL h/tan32 α HL α h D Figure 2. Geometry of the avalanche release zone, avalanche pass, and avalanche deposit zone. 3 RESULTS OF PHOTOGRAPH INTERPRETATION L Avalanche deposit zone h D: elevation (height of the outer end) θ D: slope inclination α Avalanche release zone hr: elevation (height of the highest point) θ R: slope inclination S R: surface area HL L: actual flow distance HL: horizontal run-out distance HL : shortest horizontal run-out distance h: vertical height of avalanche drop α: direct angle of elevation from the outer end of the deposit zone to the highest point of the release zone The interpretation of the aerial photographs revealed the following for survey regions a) to c). a): Figure 3 shows the interpretation results for the aerial photographs taken on April 29, 22. The majority of avalanches were fulldepth avalanches. In total, 1139 avalanche traces from the release zone to deposit zone L Avalanche pass HL hr h h D 78

3 International Snow Science Workshop Grenoble Chamonix Mont-Blanc could be clearly tracked, including 3 surfacelayer avalanches and 119 full-depth avalanches (Table 2). Mt.Nunoiwa (1495m a.s.l.) Nakatsu River Mt.Kurokura (1778m a.s.l.) Mt.Nukidodake (2813m a.s.l.) Mt.Torikabuto (237m a.s.l.) Legend Range of aerial photographs Surface-layer avalanche Full-depth avalanche Mt.Naeba (2145m a.s.l.) Mt.Kaguragamine (23m a.s.l.) Figure 3. Results of aerial photograph interpretation for the area surrounding Mt. Naeba and Mt. Torikabuto (April 29, 22). Mt.Kasagatake (2897m a.s.l.) Mt.Syakujyoudake (2168m a.s.l.) Anage Valley Hidarimata Valley Migimata Valley b): Figure 4 shows the interpretation results for the aerial photographs taken on April 15, 28. Most were surface-layer avalanches. However, many deposit zones for surface-layer avalanches were not clear because more than two avalanches converged. In total, 589 avalanche traces from the release zone to deposit zones could be clearly tracked, including 546 surface-layer avalanches and 43 full-depth avalanches (Table 2). c): Figure 5 shows the interpretation results for the Google Earth images. Among the identified avalanches, 13 were surface-layer avalanches and 1111 were full-depth avalanches. However, for many avalanches, the Kamata River Kamata River Legend Range of aerial photographs Surface-layer avalanche Full-depth avalanche Figure 4. Results of aerial photograph interpretation for the area around Mt. Kasagatake (April 15, 28). deposit zone was clear but the release zone was unclear owing to the color tone or resolution of the photographs. In the images, 84 surfacelayer avalanches and 498 full-depth avalanches could be clearly tracked with traces from the Legend Range of aerial photographs Surface-layer avalanche Surface-layer av. (release zone unclear) Full-depth avalanche Full-depth av. (release zone unclear) Figure 5. Results of orthophoto interpretation for the northern Japanese Alps region (May 5, 21). 79

4 International Snow Science Workshop Grenoble Chamonix Mont-Blanc Table 2. Results of photograph interpretation in the three regions. a) number of avalanches* b) c) photographing surface- full-depth layer av. av. April 2, May 13, April 29, sum photographing number of avalanches* surface- full-depth sum layer av. av. April 13, April 17, April 15, sum photographing sum number of avalanches* surface- full-depth sum layer av. av. 5 May * clearly tracked with traces from the release zone to deposit zone release zone to deposit zone. More detailed analyses of this region are planned, and thus the remainder of this paper focuses on regions a) and b). 4 GEOMETRY OF AVALANCHES This section presents the results of the aerial photograph analyses of avalanches in survey regions a) and b). 4.1 Characteristics of slope inclination at the release and deposit zones a): Of the 1139 avalanches identified in the aerial photographs, 719 inclinations of avalanche release zones (θ R ) and 785 inclinations of avalanche deposit zones (θ D ) were obtained. In Figure 6, the inclinations of the release and deposit zones are categorized in 5 classes according to avalanche type. Release zone inclinations ranged from 25 to 65, with many surface-layer avalanches released on slopes of 3 to 45. Many full-depth avalanches were released from slopes of 35 to 45. Both surface-layer and full-depth avalanches were mostly released from slopes of 4 to 45, and only a few avalanches were released on slopes less than 3 or greater than 6. The inclinations of deposit zones varied widely from 1 to 6. Many surface-layer avalanches were deposited from 2 to 3 and many full-depth avalanches were deposited from 25 to 45, with most ranging from 25 to 3 and from 3 to 35, respectively. b): Figure 7 shows the results for the 589 avalanches identified in region b), organized in the same way as for region a). Many surfacelayer avalanches were released on slopes from 35 to 5, and many full-depth avalanches were released from 4 to 55. Only rarely were Surface-layer av. (N=27) full-depth av. (N=692) Surface-layer av. (N=29) Full-depth av. (N=756) Figure 6. Inclination of the avalanche release and deposit zones (survey region: a). avalanches released from slopes less than 25 and greater than 6. Most surface-layer avalanches were released from slopes of 4 to 5 and most full-depth avalanches were released from slopes of 4 to 45. The inclination of the deposit zone was widely distributed from 15 to 65. Both surfacelayer and full-depth avalanches were often deposited from 2 to 4, ranging mostly between 3 and 35. According to surveys conducted by various organizations in Japan (Japanese Society of Erosion Control Engineering, 1993), avalanche release was most frequent on slopes between 3 and 45. A survey conducted in America, Swiss and Japan found that 1 large-scale slab avalanches were released at inclinations from 35 to 45, with most between 35 and 4 (Perla and Martinelli, 1977). The same results were found for approximately 2 dry slab avalanches (McClung and Schaerer, 1993). For the deposit zone, the typical slope angles of the run-out zone were 15 or less, and in some avalanches, the run-out zone was as far as it would be in flat (-15)- Full-depth av. (N=43) Inclination of release zone θ R Inclination of deposit zone θ D 3-35 Full-depth av. (N=43) Figure 7. Inclination of the avalanche release and deposit zones (survey region: b) Inclination of release zone θ R Inclination of deposit zone θ D

5 International Snow Science Workshop Grenoble Chamonix Mont-Blanc terrain (McClung and Schaerer, 1993). The aerial photographs of regions a) and b) included avalanches of various scales. In contrast, most previous surveys outside Japan have focused on large-scale slab avalanches. The difference in avalanche scale may be why the most frequent inclinations of release and deposit zones of avalanches in regions a) and b) are larger than the previous results. 4.2 Characteristics of the direct angle of elevation from the outer end of the deposit zone to the highest point of the release zone a): Figure 8 (upper figure) shows the frequencies in 2 classes of the direct angle of elevation from the outer end of the deposit zone to the highest point of the release zone for 1139 avalanches according to avalanche type. Frequency histograms of surface-layer avalanches produced a peak in the range of 32 to 34, with low frequency for steep slopes. Fulldepth avalanches produced a normal distribution with peaks in the range of 38 to 4. b): Figure 8 (lower figure) shows the 589 avalanches organized in the same way as for region a). Frequency histograms of surfacelayer avalanches showed a normal distribution peaking at 36 to 38 and full-depth avalanches peaked in the range of 34 to 36 with none in the 32 class or lower class. The cumulative frequency for surface-layer avalanches is larger for most classes than for full-depth avalanches in regions a) and b). The above results suggest that, in cases where sufficient avalanche data are available, the frequency distribution of the direct angle of elevation from the outer end of deposit zone to the highest point of release zone produces a a) Direct angle of elevation from the outer end of deposit zone to the highest point of release zone α b) Surface-layer av. (N=3) Full-depth av. (N=119) Full-depth av. (N=43) Direct angle of elevation from the outer end of deposit zone to the highest point of release zone α Figure 8. Inclination of the direct angle of elevation from the outer end of deposit zone to the highest point of release zone (survey regions: a and b) normal distribution, and the cumulative frequency is larger and more frequently distributed on gentle slopes for surface-layer avalanches than for full-depth avalanches. 4.3 Relationship between avalanche horizontal run-out distance and vertical drop a): Figure 9 shows the relationship between the horizontal run-out distance (HL) and the vertical drop (h) for the 1139 avalanches according to avalanche type. This was a strictly linear relationship, and a regression analysis performed on surface-layer avalanches and fulldepth avalanches yielded the relationships shown in equations (2) and (3), respectively: HL=1.74h. (2) HL=1.31h. (3) When compared for the same avalanche vertical drop, the horizontal run-out distance for surface-layer avalanches tended to be longer than that for full-depth avalanches. Vertical drop h (m) HL =1.31h R 2 =.9 HL =1.74h R 2 =.7 2 Surface-layer av. (N=3) Full-depth av. (N=119) Horizontal run-out distance HL (m) Figure 9. Relationship between the horizontal run-out distance and vertical drop (survey region: a). b): Figure 1 shows the 589 avalanches organized in the same way as for region a). This was also a strictly linear relationship, and regression analysis for the surface-layer avalanches and full-depth avalanches yielded the relationships shown in equations (4) and (5), respectively: HL=1.79h. (4) HL=1.4h. (5) The horizontal run-out distance for surfacelayer avalanches also tended to be longer than that for full-depth avalanches based on the same avalanche vertical drop. If the avalanche vertical drop height was larger than about 5 m, 711

6 International Snow Science Workshop Grenoble Chamonix Mont-Blanc avalanches with horizontal run out distances were longer with increased vertical drop height. The relationship for surface-layer avalanches is shown in equation (6) omitting avalanches with an initial linear relationship: Vertical drop h (m) HL=1.57h (R 2 =.89). (6) Full-depth av. (N=43) HL =1.4h R 2 =.94 HL =1.79h R 2 = Holizontal run-out distance HL (m) Figure 1. Relationship between the horizontal run-out distance and vertical drop (survey region: b). 4.4 Relationship between avalanche release altitude and excessive travel distance a): Figure 11 shows the relationship between the excessive travel distance (Le) and the elevation of the release zone (h R ) for the 1139 avalanches according to avalanche type. Surface-layer avalanches included avalanches with long excessive travel distance as the elevation of the release zone increased. However, the excessive travel distance for fulldepth avalanches was mostly either nearly m or a negative value, regardless of the elevation of avalanche release. b): Figure 12 shows the results for the 589 avalanches organized in the same way as for Elevation of release zone h R (m) Surface-layer av. (N=3) Full-depth av. (N=119) Excessive travel distance Le (m) Figure 11. Relationship between the excessive travel distance and elevation of the release zone (survey region: a). region a). Surface-layer avalanches included avalanches with a long excessive travel distance as the elevation of the release zone increased and the excessive travel distance exceeded 1 m at the elevation of avalanche release, around 25 m or above. The avalanche excessive travel distance on March 27, 2 (Largest avalanche recorded in Japan) extended to a maximum of about 19 m. No full-depth avalanches were observed with excessive travel distance greater than m at any elevation of avalanche release. Elevation of release zone hr (m) Full depth av. (N=43) Excessive travel distance Le (m) Figure 12. Relationship between the excessive travel distance and elevation of the release zone (survey region: b). 5 CHARACTERISITICS OF AVALANCHE SCALE AND FREQUENCY OF AVALANCHE OCCURRENCE This section presents the characteristics of avalanche scale and frequency in survey regions a) and b). a): Figure 13 shows the relationship between the number of avalanches (n) in each class (units of 1 m 2 ) and the median values of each class. The relationship was calculated for 837 avalanches for which the area of the avalanche release zone (S R ) could be measured. The frequency of the smallest class was lower than that of the class directly above it, likely because small avalanches could not be identified in the aerial photographs. With the smallest class excluded, the frequency of avalanche occurrences in Figure 13 decreased with the area of the avalanche release zone. The relationship between the area of the release zone (S R ) and the number of avalanches (n) is shown in equation (7): log 1 n = a log 1 S R +b. (7) where a and b are coefficients. This equation also establishes the powerlaw relationship given in equation (8): 712

7 International Snow Science Workshop Grenoble Chamonix Mont-Blanc n = C S R α. (8) where C is a coefficient and α is an index. When the smallest class is excluded, the value of α is approximately 3.5. Log (avalanche frequency n ) N=837 Log n = 3.54Log S R+13.9 R 2 = Log (area of release zone S R) (m 2 ) Figure 13. Relationship between the area of the release zone and avalanche frequency (survey region: a). Figure 14 shows the relationship between the number of avalanches (n) in each class (units of 1 m) and the median values for each class using 1139 data for the horizontal run-out distance (HL). Similar to the area of the release zone, the frequency of the smallest class was lower than that of the class directly above it. The horizontal run-out distance (HL) and the number of avalanches (n) also showed a power-law relationship in a range excluding the smallest class. The value of α was 3.. Log (avalanche frequency n ) N=1139 Log n = 2.99Log HL R 2 = Log (horizontal run-out distance HL ) (m) Figure 14. Relationship between the horizontal run-out distance and avalanche frequency (survey region: a). b): Figures 15 shows the relationship between the number of avalanches (n) in each class (units of 5 m 2 ) and the median values for each class using 589 data for the avalanche release zone (S R ) organized in the same way as for region a). All avalanches except for five have a release zone area of less than 1 5 m 2. If these five avalanches are excluded as large-scale cases, the frequency of avalanche occurrence decreases as the area of the avalanche release zone increases. The relationship between the area of the avalanche release zone (S R ) and the number of avalanches (n) showed a power-law relationship similar to that observed in region a). The value of α was approximately 2.. Log (avalanche frequency n ) N=589 Log n = 2.3Log S R+9.52 R 2 = Log (area of release zone S R ) (m 2 ) Figure 15. Relationship between the area of the release zone and avalanche frequency (survey region: b). Figure 16 shows the relationship between the number of avalanches (n) in each class (units of 1 m) and the median values for each class using 589 data for the horizontal run-out distance (HL) organized in the same way as for region a). The horizontal run-out distance (HL) and the number of avalanches (n) also showed a power-law relationship similar to that observed in region a). The value of α is approximately 2.3. All avalanches except for five had a horizontal run-out distance of less than 2 m, as shown in Figure 1. When the avalanches with a horizontal run-out distance exceeding 2 m were been excluded as large-scale cases, the value of α became approximately 1.8. The value of the index α in the power-law relationship shows the rate of avalanche Log (avalanche frequency n ) Log n = 2.33Log HL+8.5 R 2 =.95 N= Log (horizontal run-out distance HL ) (m) Figure 16. Relationship between the horizontal run-out distance and avalanche frequency (survey region: b). 713

8 International Snow Science Workshop Grenoble Chamonix Mont-Blanc occurrences from small to large scale. The index α for region b) is smaller than that for region a). This suggests that 119 of the 1139 avalanches (about 97%) identified in region a) were the fulldepth type, whereas 546 of the 589 avalanches (about 93%) identified in region b) were the surface-layer type. 6 CONCLUSION Aerial photographs of three regions were interpreted and approximately 23 avalanches were identified. Two of these regions were further analyzed to determine geometry and scale characteristics of the avalanches. The following results were obtained. 1) Avalanche release zones were most frequently at slopes between 35 and 5, whereas deposit zones most frequently had slopes between 2 and 35. 2) Frequency histograms of the direct angle of elevation from the outer end of the deposit zone to the highest point of the release zone showed an almost normal distribution peaking from 32 to 38 for surface-layer avalanches and from 34 to 4 for full-depth avalanches (i.e., gentler angles for surface-layer avalanches than for full-depth avalanches). 3) The ratio of horizontal run-out distance to vertical drop was 1.7 to 1.8 times larger than that of surface-layer avalanches, and 1.3 to 1.4 times larger than that of full-depth avalanches. Some of the surface-layer avalanches had long excessive travel distance and mobility as seen for large-scale avalanches. However, in fulldepth avalanches, the excessive travel distance was mostly either near m or negative, and no full-depth avalanche displayed the characteristics of the mobility of large-scale avalanches. 4) The relationship between avalanche frequency and scale (area of the release zone or horizontal run-out distance to the scale of avalanche) exhibited a power-law relationship when large-scale avalanches (having a release zone area larger than 1 5 m 2 or horizontal runout distance longer than 2 m) were excluded. REFERENCES Akiyama, K., Osanai, N., Matsuda, H., and Honma, S., 28. Authorization and evaluation of avalanches in wide area using highly precise space information. Cold Region Technology Conference 28, (in Japanese). Akiyama, K., Osanai, N., and Matsuda, H., 212. Characteristics of the path geometry and outbreak scale of avalanches by the difference of avalanche classifications. Journal of Snow Engineering of Japan, 28(1), 3 15 (in Japanese with English abstract). Akiyama, K. and Sekiguchi, T., 213. Features of avalanches and the relationship between avalanche magnitude and frequency based on aerial photograph interpretation. Seppyo (Japanese society of snow and ice). 75 (1), 3 21 (in Japanese with English abstract). Bair, E. H., Dozier, J. and Birkeland, K. W., 28. Avalanche Crown Depth Distributions. Geophysical Research Letters, 35, L2352. Birkeland, K. W. and Landry, C. C., 22. Power-laws and snow avalanches. Geophysical Research Letters, 29(11), Faillettaz, J., Louchet, F. and Grasso J.-R., 24. Two-threshold model for scaling laws of non interacting snow avalanches. Physical Review Letters, 93, 281(1) 281(4). Faillettaz, J., Louchet, F. and Grasso, J.-R., 26. Cellular automaton modeling of slab avalanche triggering mechanisms: from the universal statistical behavior to particular cases. Proceedings of International Snow Science Workshop, ISSW, 26, Izumi, K., Mobility of large-scale avalanche. Annals Report of Saigai-ken, Niigata University, 7, (in Japanese with English abstract). Japan Society of Erosion Control Engineering (Eds.), Sabogaku koza 8, Nadare taisaku (Countermeasure against avalanche, book for erosion control course 8). 28 (in Japanese). Japanese Society of Snow and Ice, Hidarimata-dani nadare saigai tyousa houkokusyo, 68pp (in Japanese). Louchet, F., Faillettaz, J., Daudon, D., Bédouin, N., Collet, E., Lhuissier, J. and Portal, A.-M., 22. Possible deviations from Griffith's criterion in shallow slabs, and consequences on slab avalanche release. Natural Hazards and Earth System Sciences, 2, McClung, D. M., 23. Size scaling for dry snow slab release. Journal of Geophysical Research, 18(B1), McClung, D. M. and Schaerer, P. A., The Avalanche Handbook, Seattle, WA, Mountaineers Books, 271pp. Naisbitt, A., Forster, R., Birkland, K.W. and Harrison, W.L., 28. Avalanche frequency and magnitude: using power-law exponents to investigate snow avalanche size proportions through time and space. Proceedings of International Snow Science Workshop, ISSW(28), Perla, R. and Martinelli, M. Jr., Avalanche Handbook. U.S. Department of Agriculture, Forest Service, 238pp. Rosenthal, W. and Elder, K., 23. Evidence of chaos in slab avalanching. Cold Regions Science and Technology, 37,