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Avalanche forecasting in a heavy snowfall area using the snowpack model
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Cold Regions Science and Technology 51 (2008) 191 – 203 www.elsevier.com/locate/coldregions
Avalanche forecasting in a heavy snowfall area using the snowpack model Hiroyuki Hirashima a,⁎, Kouichi Nishimura a,1 , Satoru Yamaguchi a , Atsushi Sato a , Michael Lehning b a
b
Snow and Ice Research Center, NIED, Suyoshi, Maeyama, Nagaoka 940-0821, Japan WSL, Swiss Federal Institute for Snow and Avalanche Research, SLF, Fluelastrasse 11, CH-7260 Davos Dorf, Switzerland Received 23 October 2006; accepted 28 May 2007
Abstract We describe the use of SNOWPACK, a snow cover model, for areas with heavy snowfall. Record-breaking snowfall was recorded over the Sea of Japan and northwest coast of Honshu in the winter of 2005/2006. Avalanche forecasting was conducted at Tsunan, Niigata Prefecture, where the snow depth exceeded 4 m. Measurements from an Automated Meteorological Data Acquisition System (AMEDAS) operated by the Japan Meteorological Agency were used as the model input data. To verify the model output, snow pit observations were carried out at 10-day intervals. Simulated snow profiles were verified by applying a comparative method developed by Lehning et al. [Lehning, M., Fierz, C., Lundy, C., 2001. An objective snow profile comparison method and its application to SNOWPACK. Cold Reg, Sci. Technol. 33, 253–261.] and were in reasonable agreement with the observed results, with an agreement score of 0.74. However, the equations for the stability index (SI) were unsuitable for the study area considered. Dangerous conditions continued for more than two months in the model, but they were caused by unsuitable parameterisation of the shear strength for Japanese snow. Thus, the parameterisation of shear strength was improved. The empirical equations formulated by Yamanoi and Endo [Yamanoi, K., Endo, Y., 2002. Dependence of shear strength of snow cover on density and water content. Seppyo., 64(4), 443–451, (in Japanese with English Abstract)] were the most suitable for simulating SI for this region; therefore, they were incorporated into the SNOWPACK model. The unstable conditions that occurred during heavy snowfall were reproduced. To expand the forecasting area to include the area along R405, a national road, the distributions of meteorological parameters in the study area were estimated for grid points with 10-m spacing using simple lapse rate and interpolation methods. In an avalanche on 24 December 2005, a car was pushed off the road and into a valley. The snow depth increased by about 70 cm within 24 h; such large and intense snowfall is commonly associated with avalanching and, hence, instability. Thus, the snow stability decreased. This was reproduced by the SNOWPACK model. Furthermore, the stability index maps showed that most slopes were dangerous on that day. The improved SNOWPACK results were compared with other avalanche events on the Sea of Japan side of Japan. Nine of 11 surface avalanches occurred when the simulated stability index was lower than 2. Two shortcomings responsible for the failure to predict avalanches had to do with the reproduction of the graupel layer and the estimation of the shear strength of layer interfaces. © 2007 Elsevier B.V. All rights reserved. Keywords: SNOWPACK model; Avalanche forecasting; Heavy snow; Stability index
⁎ Corresponding author. E-mail address: [email protected] (H. Hirashima). 1 Present affiliation: Faculty of Science, Niigata University, Ikarashi, Niigata 950-2181, Japan. 0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2007.05.013
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1. Introduction In the winter of 2005–06, the northern region of Japan along the Sea of Japan received record-breaking snowfall. One hundred and fifty-two people perished due to snow disasters, such as accidents during the removal of snow, snow falling from the roof of houses, and avalanches. Thus, the Japan Meteorological Agency termed this winter as ‘Heisei 18-nen Gousetsu’ which means ‘Heavy snow in 2006’. The areas most affected due to this extraordinary snowfall are located in Tsunan, Niigata prefecture, Japan. The depth of snow on the ground in this region was greater than 4 m. R405, a national road that passes through the mountainous regions of Niigata and Nagano-prefectures, was exposed to an unusual avalanche risk and was, therefore, closed. Traffic restrictions continued for 3 months. Vehicles were permitted to use the road at scheduled times during the day. For six days, the road was closed. Furthermore, the inhabitants of this mountainous region were isolated. In such situations, the estimation of the probability of avalanche would have value when determining whether the road closure is justified. In order to achieve this, avalanche professionals conducted field surveys and reported their findings to a road administrator. In addition to this, computational forecasting is a useful because it can simulate the snow conditions and the snow stability index (SI), which may change on short time scales. A computational model – SNOWPACK – for avalanche forecasting was developed in Switzerland (Lehning et al., 2002a,b; Bartelt and Lehning, 2002). This model can also simulate the stability indices (Lehning et al., 2004) and has recently been developed into a distributed model of alpine surface process for diverse applications (ALPINE3D, Lehning et al., 2006). The SNOWPACK model was introduced in Japan. At first, some discrepancies were noted in the simulation results regarding the amount of snowmelt and types of snow. Yamaguchi et al. (2004) improved the parameterization of the surface energy balance to make the model suitable for wet Japanese snow. In an earlier study, we (Hirashima et al., 2004a) introduced the rapid growth mechanism of faceted grains (Fukuzawa and Akitaya, 1993) into SNOWPACK to reproduce the faceted grains at the surface layer. The SNOWPACK model was then modified for application to Japanese winters. SNOWPACK simulations for a complex terrain were carried out by Nishimura et al. (2005) by combining the SNOWPACK model and a snow redistribution model (Liston and Sturm, 1998; Hirashima et al., 2004b). The validation of the avalanche forecasting by Nishimura et al. (2005) focused on the example of a slab avalanche.
In this study, the avalanche-forecasting model was applied around R405, which is an area of wet and heavy snow. In this paper, we discuss suitable parameterizations for estimating the stability index, predictable avalanche types, and future issues for accurate avalanche forecasting. 2. Simulation method 2.1. Study site and weather station The study site, Tsunan (36°59.8′N, 138°41′E), Niigata prefecture, Japan, is an area of heavy snowfall. Fig. 1
Fig. 1. Study area (a: Locations of Tsunan; b: Simulated area of Tsunan). The rectangle shows the detailed study area at Tsunan.
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shows the location and maps of the study area. The maximum snow depth this year was 416 cm, whereas it is 215 cm for an average year. Since this area is temperate and snowy, faceted crystals and depth hoar rarely form. Avalanches tend to occur during heavy snowfall and on warm days. The Automated Meteorological Data Acquisition System operated by the Japan Meteorological Agency (AMEDAS) observes the air temperature, wind speed, wind direction, precipitation, duration of sunshine, and snow depth. The AMEDAS data was used as model input data. Since AMEDAS does not measure solar radiation and longwave radiation, the empirical equations suggested by Kondo et al. (1991) were used in order to estimate them. The input solar radiation S↓(Wm− 2) was calculated as follows by using the incident solar radiation at the top of the atmosphere S0↓(Wm− 2) and the duration of sunshine. 8 N N > > < S0A 0:244 þ 0:511 0b V1 N N A 0 0 ð1Þ s ¼ N > > : 0:118S0 ¼ 0A N0 S0A
2 d0 ¼ I00 cosh d
ð2Þ
where, N is the duration of sunshine; N0, the possible duration of sunshine; I00, the solar constant (=1365 Wm− 2); d, the distance between the earth and the sun; d0, the average distance between the earth and the sun; and θ, the zenith angle. Longwave radiation is also estimated from meteorological data as follows: LA ¼ rs T 4 ½1 ð1 vÞC 8 3 2 > N N N > < 0:826 þ 0:298 1:234 þ1:135 N N N 0 0 0 C¼ > > 0:2235 :
ð3Þ N 0b V1 N0 N ¼0 N0
ð4Þ v ¼ 0:74 þ 0:19w þ 0:07w2
ð5Þ
w ¼ 0:0315Td 0:1836
ð6Þ
where σs is the Stefan–Boltzmann constant ( = 5.67× 10− 8 Wm− 2 K− 4), T is the air temperature (K), w is the logarithm of the column effective water vapour, and Td is the dew point temperature (°C).
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2.2. Simulation A workstation, DELL Precision 380 equipped with an Intel Pentium 4 CPU 3.00 GHz was used for the SNOWPACK simulations. The computer was equipped with the Microsoft Windows XP professional x64 software. The computation time to calculate SNOWPACK from 1 December to 31 March is about 60 s. If the SNOWPACK simulation is carried out every day using the calculation results from previous runs as initial input, the computational time for a 24-hour calculation is about 1.1 s when the snow depth is 4 m. Our objective was to achieve a stability index distribution for a 5 km × 10 km area with 10 m mesh. If a simulation is carried out for each grid point, 7.8 km2 is the limitation for real-time simulation. Therefore, we used the following technique to make the SI distribution. Input data was made per 100 m altitude considering a lapse rate of 6.5 × 10− 3 °C m− 1. The altitudes of the simulated area ranged from 400 to 1700 m a.s.l. A snowpack model simulation was conducted for each elevation. The calculation results of the nearest elevation were applied for each 10 m grid point. The stability index was calculated for each grid based on the snowpack results and slope angle. Under this technique, the effect of the slope angle and direction of incoming solar radiation were not considered. However, in this technique, a real-time simulation was accomplished within 30 min of obtaining the meteorological data. SNOWPACK simulations for each 10 m grid were also conducted. The SI distribution results used in this paper were calculated for each 10 m grid. 3. Observations 3.1. Snow pit observations Snow pit observations were carried out from January to March at the AMEDAS point at 10-day intervals. The snow conditions observed are shown in Fig. 2a. The snow profiles showed that the snow comprises new snow, decomposed snow, rounded grains, and wet grains. However, no faceted grains or depth hoar were observed. The wet grains observed at the bottom layer were formed at the beginning of winter. The wet grains in the middle layer were formed on 14 and 15 January, which were warm days with rainfall. Most of the layers became wet grains after 20 February. The snow densities observed are shown in Fig. 2b (solid line). Snow densities below 1 m are more than 400 kg m− 3. After 20 February, snow at the bottom was saturated. The snow density at the saturated layer exceeded 800 kg m− 3.
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avalanches were detected in an area of 40.2 km2. For the avalanches that released, the total area of the avalanche paths was 2.38 km2 (5.9% of observed area). The slope angles at fracture line (ψ) and sighting angles from the maximum runout position to the top of the starting point (α) were estimated for each avalanche. The frequency distributions of ψ and α for surface avalanches are shown in Fig. 3. The average value of ψ was 41.2°. Two-thirds of avalanches (about 69%) occurred on slopes with inclinations between 35° to 45° (Fig. 3a). These results demonstrate that Japanese avalanches occur on steeper slopes more often than as noted by McClung and Schaerer (2006, p. 91). The average value of α was 37.9°. Furthermore, 88.6% of α of avalanches ranged between 30–45° (Fig. 3b). 4. Results and discussion 4.1. SNOWPACK-simulated profiles Simulated snow profiles are shown in Fig. 4. Snow accumulation begins in early December. The snow depth approached 4 m in early January. Since snow metamorphosed under small temperature-gradient conditions, faceted grains and depth hoar rarely formed. On 14 and 15 January, the upper layer snow metamorphosed into wet grains during warm days with rainfall.
Fig. 2. Observed and simulated snow cover a: snow structures for each observed day. The left profiles are the observed results, and those on the right are the simulated ones, b: snow densities.
3.2. Remote sensing Aerial photographs were taken on 5 March to develop the avalanche distribution map. One hundred and sixty-four surface avalanches and five full-depth
Fig. 3. Frequency distribution for a surface avalanche. a: slope angles at fracture line, ψ; b: sighting angles from the maximum runout position to the top of the starting point, α.
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tween the observed and modelled profiles. The overall score calculated was 0.74. The highest score was the temperature (0.93 in average). In most layers, the snow temperature is 0 °C in this region (the average snow temperature from the snow pit observation was − 0.06 °C.). As a result, the large agreement score, small mean bias error (0.02 °C) and small root mean square error (0.33 °C) were obtained. However, the correlation coefficient was low (r = 2.0 × 10− 3). In this region, discrepancy in the energy transport, rather than the snow temperature, affects the water content. Lehning et al. (2001) used five classifications for estimating water content. In this study, since the water content was measured using a dielectric probe (Denoth, 1994), the liquid water content was obtained as the weight water content. The agreement score for the water content was calculated using the same method as for the temperature and density. The agreement score for the water content was averaged 0.65. The agreement score of the water content was the lowest in this region, whereas the one at the site in Switzerland was the highest (Lehning et al., 2001). On 20 February, most of the snow in the simulation consisted of wet grains, whereas 39% of snow in the observations consisted of rounded grains (Fig. 2a). At this time, the agreement scores for the liquid water and grain types were low (0.37 and 0.56, respectively). The discrepancies in liquid water were attributed to errors in the amount of liquid precipitation and solar and long wave radiation, the parameterisation of surface energy balance, the heat conduction in the snow, and the water transport in the snow. Snowpack parameters could be improved by the use of more accurate input data. In this case, the effect of the errors in the input parameters on the simulated snow stratification was assessed. According to Kondo et al. (1991), the standard estimated error of S/S0 in Eq. (1) is 0.0434, that
Fig. 4. Simulated snow profile at the Tsunan AMEDAS point in 2005/ 06 winter. a: snow type; b: SI calculated using the original SNOWPACK; c: SI calculated using the equations of Yamanoi and Endo (2002) and Abe et al. (2006).
All of the snow layers were transformed into wet grains on 15 February. The comparisons of the observed and simulated snow types are shown in Fig. 2a. The comparisons of the observed and simulated snow densities are also shown in Fig. 2b. The simulated snow profiles were evaluated using a comparison method developed by Lehning et al. (2001). Fig. 5 is a time series of individual and overall agreement scores be-
Fig. 5. Time series of individual and overall agreement scores between the observed and modeled profiles at the AMEDAS station in Tunan for the winter season in 2005/2006.
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of Ldf /σsT 4 in Eq. (3) is 0.0158, and that of C in Eq. (4) is 0.1066. We conducted a sensitivity experiment varying the parameters by ±1 standard deviation. However, the error leading to the discrepancies of snow stratification could not be explained exclusively by the estimation error on the solar and long wave radiation. An error in the input of liquid precipitation could also have caused a discrepancy. In the simulation, the precipitation amount was multiplied by 1.6 to fit with the observed snow depth and snow water equivalent. However, the capture rate for rain is larger than that for snow. Therefore, when the air temperature exceeded 0 °C, 1 was used as the multiplied value. As a result, the percentage of the wet layer decreased, but it was still larger than the observed result. Even for a combined sensitivity experiment with decreased solar and longwave radiation and unchanged rain condition, the percentage of wet grains was greater than that in the observed results. However, the simulation results were more similar to the observed results. In this case, the average agreement score for the snow type changed from 0.73 to 0.80. The agreement scores for the grain size and water content were also higher, whereas those for the snow temperature and density were slightly lower. The average overall score changed from 0.74 to 0.79. There are still problems associated with the snowpack parameters and method used for the estimation of input data. One possibility to improve the snowpack representation would be to directly assemble observed snow cover data. However, it needs to be noted that manual snow observations are also subjective and vary from observer to observer.
where ρdry is the dry density; θ (%) , the volumetric water content; K (Nm− 1(kg m− 3)− a), a coefficient that is determined experimentally by the snow type, a is 2.91, and b is − 0.235 (%− 1). K is 9.40 × 10− 4 for new snow, decomposed snow and rounded grains and 4.97 × 10− 4 for wet grains. This formulation was derived from snow where densities range from 50 kg m− 3 to 500 kg m− 3. The shear strength of faceted grains and depth hoar is formulated by Abe et al. (2006) as follows: r ¼ kexp 1:51 102 qdry
ð8Þ
where k is 3.24 × 10− 2 Nm− 2. This formulation was derived from snow densities ranging from 150 kg m− 3 to 350 kg m− 3.
4.2. Estimation of snow stability index 4.2.1. (a) Previous studies on parameterizations A simple stability index (SI) is the shear strength divided by the shear stress, which is usually called the natural stability index (Lehning et al., 2004). The original SNOWPACK model estimates shear strength using the empirical equation suggested by Jamieson and Johnston (2001), who formulated the relationship between the shear strength and the snow density for each snow type. Formulations were derived from snow densities ranging from 50 kg m− 3 to 330 kg m− 3. The relationships between snow density and shear strength have also been studied in Japan. Yamanoi and Endo (2002) formulated the shear strength σ (Nm− 2) from the density and water content as: r ¼ Kqadry ebh
ð7Þ
Fig. 6. Comparisons of each estimation technique for SI. The value estimated from the hardness is used as a true value. a: profiles of shear strength at Yuzawa, where snow was dry; b: profiles at Tsunan, where snow was wet.
H. Hirashima et al. / Cold Regions Science and Technology 51 (2008) 191–203 Table 1 MBE, RMSE, and r2 for each calculated results compared with the value estimated value from the hardness
MBE RMSE 12
Yamanoi and Endo (2002)
Jamieson and Johnston (2001)
Perla et al. (1982)
−0.06 0.17 0.97
− 0.87 0.96 0.94
−0.50 0.53 0.96
In addition to this, Yamanoi et al. (2004) formulated a shear strength depending on the hardness measured by a digital push gauge. This equation is expressed as: r ¼ KH H c
ð9Þ −2
where H is the measured hardness (Nm ). KH (= 0.018 (Nm− 2)1 − c) and c (= 1.18) were determined experimen-
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tally. Hardness is highly correlated with shear strength (r2 = 0.80). These models were used for the improvement of the simulation for shear strength. 4.2.2. (b) Estimation The calculated profiles of a SI simulated by original SNOWPACK are shown in Fig. 4b. According to the simulated profiles including the parameterizations of strength in SI, the snowpack was unstable for longer than two months and the rounded grains appeared to be a weak layer. This is inconsistent with the observed decrease in avalanche activity days after the storm, even if we assume that part of the decrease in avalanche danger was due to the fact all dangerous slopes had already released as discussed above. The original SNOWPACK uses the
Fig. 7. Maps of SI as simulated by SNOWPACK over a 10 m grid. This area is rectangle area in Fig. 1(b). a: 23 December; b: 24 December; and c: 25 December. White circles on a black background indicate the site of the avalanche.
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parameterisation of Jamieson and Johnston (2001) to calculate the shear strength. This relationship was derived for relatively light snow (less than 270 kg m− 3 for rounded grains). However, in our heavy snow area, the snow density at the lower snowpack exceeds 400 kg m− 3 even if the snow is dry. Thus, the equations of Jamieson and Johnston (2001) are not suitable for estimating shear strength in such a heavy snow area. This formula underestimated the shear strength of heavy snow. Therefore, an alternate formula is needed for measuring shear strength for heavy snow. The models of Jamieson and Johnston (2001), Perla et al. (1982), and Yamanoi and Endo (2002) were compared. The shear strength calculated from the hardness based on Yamanoi et al. (2004) was used for validation. The hardness profiles were measured on 27 February. On that day, all the snow layers were wet, and, unfortunately, no hardness data for dry snow could be measured in the snow pit observations at Tsunan. However, the hardness profiles for dry snow were observed at Yuzawa, which is located about 13 km southeast of Tsunan, on 4 January. The shear strength profiles were estimated using these hardness profiles and Eq. (9). Furthermore, shear strengths were calculated from snow types and snow densities by using the equations by Yamanoi and Endo (2002) (Eq. (7)), Jamieson and Johnston (2001), and Perla et al. (1982). The comparisons between these estimations are shown in Fig. 6. The mean bias error (MBE), the root mean square error (RMSE), and the correlation coefficient (r2) for each equation compared with the value estimated from hardness are shown in Table 1. Obviously, the shear strengths estimated by Yamanoi and Endo (2002) have the smallest error for the dry snow conditions. Thus, their estimation is most suitable for this region. On the other hand, the errors for wet snow are comparable with the equation of Perla et al. (1982). Eqs. (7) and (8) were incorporated into SNOWPACK. The simulated result using new parameterization is shown in Fig. 4c. The stability index of rounded grains was then corrected to be extremely strong. As a result, the SI decreased during heavy snowfall when avalanching was likely, and wet grains sometimes appeared as a weak layer as is common in this snow climate (e.g. Izumi and Akitaya, 1982).
using techniques similar to those of Nishimura et al. (2005). As an example, the SI maps between 23 and 25 December are shown in Fig. 7. The SI maps show that most of the steep slopes were subject to avalanche danger on 24 December despite having been relatively safe prior to and following that date. In fact, on 24 December, an avalanches occurred, and a car was pushed off from the road and into the valley. The profiles for snow type and SI around the day of the avalanche are shown in Fig. 8. The SNOWPACK result shows that the SI decreases in a new snow layer. The snow depth increased by about 70 cm within 24 h. This led to an unstable snow condition, since the snow was strongly loaded with newer snow before densification. The weak layer was not detected in the snow pit observation of 25 December. However, the depth of new snow layer exceeded 40 cm. Therefore, it was considered that the avalanche was released on storm snow instability in the upper snow. The instability of storm snow was reproduced in the SNOWPACK model. Traffic restrictions were implemented on 24 December. First, R405 was closed during the nighttime. The
4.3. Simulations for the R405 area SI distribution maps were charted using a 10-m mesh around R405. GISMAP Terrain, a 10-m-mesh DEM obtained from 1:25,000 maps of Geographical Survey Institute (GSI), was used as topographic data. The local variation of meteorological conditions, such as air temperature, solar radiation, and wind speed, was calculated
Fig. 8. The profiles for the snow type and SI around the day of the avalanche, 24 December. a: simulated snow cover structure for 23–27 December; b: simulated stability index for the same period.
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section, the predictability for other avalanche events, including those that lead to fatal accidents, is discussed. Several large avalanches were recorded on the Sea of Japan side in 2005 and 2006. Field surveys were conducted after each of the 16 avalanche events. Eleven of them were surface avalanches. Table 2 summarizes information on the avalanches. Stability indices were calculated for each avalanche using the following techniques. Fig. 9. Simulated SI and traffic restrictions in 2005/06 winter. (1) closed during the nighttime, (2) completely closed, (3) permitted only vehicles belonging to residents and those carrying supply shipments, (4) allowed on the road for 4 h period (5) closed during the nighttime.
road was completely closed from 8 to 13 January. Only vehicles of belonging to residents and those carrying supply shipments were permitted from 13 to 16 January. After 16 January, all vehicles were allowed on the road for a 4 h period. From 14 February, the road was closed during the nighttime. On 21 March, R405 was opened again. A comparison between the simulated SI at the AMEDAS station and traffic restrictions is shown in Fig. 9. Overall, the simulated SIs were small during the traffic restrictions. Small SIs were caused by a wet-grain layer (Fig. 4). The SI sometimes declined rapidly due to instability of the storm snow. Although this model was not used to make decisions regarding traffic restrictions, the simulated SI was recognized as an important source of information by road administrators. 4.4. Predictability of an avalanche An avalanche during heavy snowfall around R405 could be predicted by introducing a new parameterization of shear strength of snow to SNOWPACK. In this
1. Search the AMEDAS station closest to avalanche point. 2. Download the meteorological data input. 3. Correct the air temperature on the basis of the difference in altitude between the AMEDAS station and avalanche location and an assumed lapse rate of 6.5 × 10− 3 °C m− 1. 4. Correct the solar radiation based on the slope angle and aspect of avalanche starting zone and solar altitude and aspect on the basis of the parameterisation of Funk and Hoelzle (1992). 5. Simulate the snow cover and calculate of SI for the avalanche accident. The calculated stability indices are shown in Fig. 10. Nine of the avalanche accidents (82%) occurred when the calculated stability index was below 2.0. The total time with the simulated SI being below 2 was 31% of the snow season of selected AMEDAS points on average. Now, this period is defined as an avalanche warning period. This implies that if the situation is judged to be dangerous for SIs smaller than 2 (31% of the winter), 82% of avalanches would be predicted. Although the accuracy rate increases with raising the threshold value for avalanche warning, this would lead to a smaller overall performance of the warning since extended
Table 2 Information of each avalanche event in which field surveys were conducted after the avalanche Number
Place
Avalanche date
Latitude and longitude
Weak layer
1 2 3 4 5 6 7 8 9 10 11
Ebisusawa Tubame onsen Ooakasawa Tutitaru Ludens Naeba Sizukuishi Hakkatouge Yunotani Nyutou onsen Bentousawa
23 Jan 2005 26 Feb 2005 24 Dec 2005 28 Dec 2005 03 Jan 2006 03 Jan 2006 04 Jan 2006 12 Jan 2006 12 Jan 2006 10 Feb 2006 14 Feb 2006
39°56′54″N, 140°55′0″E 36°54′9″N, 138°8′42″E 36°52′57″N, 138°38′11″E 36°53′16″N, 138°52′12″E 36°52′9″N, 138°51′46″E 36°47′29″N, 138°46′23″E 39°42′26″N, 140°48′34″E 37°5′6″N, 138°49′30″E 37°12′18″N, 139°4′29″E 39°48′15″N, 140°46′47″E 38°2′56″N, 139°51′2″E
Interface between melt-freeze grains and rounded grains New snow New snow New snow Faceted grains Faceted grains Graupel – New snow Unknown Wet snow
Avalanches 1, 2 and 10 resulted in fatal accidents.
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Fig. 10. Simulated stability indices at the avalanche sites when the avalanche occurred. Information for each avalanches are shown in Table 2.
warning times would cover even completely safe conditions. Fig. 11 shows the accuracy rate with the length of avalanche warning period as a function of an assumed SI value. Jamieson et al. (2007) mentioned that stability index cannot be extrapolated from one site to another, and that the correlation between stability index at the study site and avalanche activity will decrease as the loading rate varies spatially in windy range or during windy storms. In our study cases, many of avalanches occurred under the gentle wind conditions, which seem fairly adequate for the regional avalanche forecasting. Surface avalanches mainly occur during heavy snowfall in this region of Japan. The SI of new snow or weak layers decreases significantly during snowfall. However, avalanches did occur when the calculated SI was larger than 2. They occurred when no snow or small amounts of snow fell. The field survey shows that the first of these avalanches was caused by the failure of the layer interface between melt-freeze grains and rounded grains. This avalanche was triggered by a skier. Therefore, we recalculated the SI considering the weight of the skier on the basis of a study conducted Jamieson and Johnston (1998). The recalculated SI was 4.2. This case is isolated from other avalanches because it was triggered by a skier and the fracture occurred from layer interface. The estimation of SI for this type is one of the shortcomings of the natural stability index as has already been pointed out by Schweizer et al. (2006). The new stability estimators proposed there, which include skier triggering and interface snow characteristics, have not been the focus of the study presented here. The field survey also showed that the avalanche number 7 was caused by the collapse of a graupel layer (see Table 2.). The shear strength of graupel was formulated by Abe (2004). However, it is difficult to reproduce a graupel layer using meteorological input data on the ground because the formation process of
graupel depends on the processes in the cloud high in the atmosphere. Although this study uses meteorological data on the ground, the snow disaster forecasting system (Sato et al., 2004) developed by National Research Institute for Earth Science and Disaster Prevention (NIED) uses predicted meteorological input data calculated using the non-hydrostatic model (NHM). NHM can simulate the formulation of graupel. However, at the present stage, the NHM cannot accurately reproduce regional snowfall amounts. Therefore, observed meteorological data were used as input data in this study. The accuracy of NHM will need to be improved before avalanches caused by the collapse of a graupel layers can be predicted. 5. Model uncertainties The uncertainty of the simulated stability index was estimated on the basis of a similar method by Conway and Wilbour (1999). They suggested there are three contributions to the uncertainty: inexactness of the strengthdensity relationship, error of measurement of density, and measurement of precipitation. They estimated the uncertainty from the strength-density relationship using the root mean square (rms). However, Yamanoi and Endo (2002) did not estimate the rms. They used their original snow data and that of Endo (1992), who formulated a similar equation and estimated the minimum and maximum value for the proportionality coefficient. Therefore, we substituted the range of his estimation to calculate the uncertainty and estimated the uncertainty at ±0.84σ. With the equation of Yamanoi and Endo (2002) or that of Endo (1992), if the measurements of the density have an error ±10%, the contribution of the measurement to the uncertainty in strength is 3 × 0.1σ. The total uncertainty is q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:84Þ2 þð0:3Þ2 r ¼ 0:89r. Estimating the uncertainty for precipitation is difficult because the avalanche release points described in Section 4.4 are, on an average, about
Fig. 11. Accuracy rate and percentage of avalanche warning period relative to the threshold SI values.
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10 km away from the meteorological point. We compared newly fallen snow depths between AMEDAS data and snow data at Maekura about 11 km south-southwest from the AMEDAS point of Tsunan. The comparison was done using the total precipitation of 8 h when the total new fallen snow depths in 8 h were more than 16 cm. This was done because Endo (1992) suggested that an avalanche occurs after 8 h under 2 kg m− 2 h− 1 snowfall. The root mean square error between precipitations obtained using AMEDAS and Maekura station was ±47%. Therefore, at this time, the value of 0.47 is used as the q uncertainty for ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi precipitation. The total uncertainty is then ð0:89Þ2 þð0:47Þ2 r ¼ 1:00r. The uncertainty of precipitation should be analysed using the data for various meteorological points. The study of the difference in precipitation at a point distant from the meteorological station remains as issue to be investigated. 5.1. Future issues Destabilization during heavy snowfall was predicted by the SNOWPACK model. However, there are still a number of issues to be resolved. First, the SI shows consistently low values on most of steep slopes during heavy snowfall (Fig. 7b). The specification of a dangerous location of an avalanche is difficult at present. One useful method to specify a dangerous place is to predict the location of a snow cornice. A snow cornice can be predicted by simulating snow redistribution. It has to be validated by using the observed snow depth distribution. Since topographic surveys using laser measurements in a snowy season have already been carried out, the snow depth distribution can be obtained by laser measurements during the non-snow season. If laser measurements were obtained, the accuracy of avalanche predictions would be increased. Second, surface avalanches due to the failure of wet grains and full-depth avalanches as well as avalanches caused by the collapse of new snow often occur in temperate snowy areas. The shear strength of wet grains declines exponentially with the volumetric water content (Yamanoi and Endo, 2002). Full-depth avalanches tend to occur when liquid water (snowmelt water or rain) reaches the ground. An accurate simulation of the moisture movement in the snowpack is necessary for the prediction of these avalanches. The moisture movement scheme in the SNOWPACK model is that the liquid water moves downward when it exceeds a certain value. However, the two types of avalanches discussed above are affected by more complex water movement. Thus, we plan to develop a numerical snowpack model that
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considers the existence regime of liquid water (capillary regime, pendular regime, and funicular regime (Colbeck, 1973)), the formation of a water percolation channel, and the water movement through the percolation channel (Colbeck, 1978). The model will be expanded into a two-dimensional model in order to model the water transport. 6. Conclusions The snow cover model SNOWPACK was applied to avalanche forecasting for a heavy snow area. The input data for the SNOWPACK model was meteorological data obtained from the Japan Meteorological Agency. Solar and long wave radiation were estimated using the estimation equation developed by Kondo et al. (1991). The lapse rate of 6.5 × 10− 3 °C m− 1 and the estimation method for the influence of the slope angle on incoming solar radiation by Funk and Hoelzle (1992) were used to allow distributed calculations of the SI on a grid. Snow pit observations were also carried out at 10-day intervals. During the 2005/2006 winter, snow depth exceeded 4 m in the study region, Tsunan. The pit observations revealed that the snowpack comprised new snow, decomposed snow, rounded grains, and wet grains without faceted grains or depth hoar. The profiles simulated by the SNOWPACK model were verified on the basis of a comparison method developed by Lehning et al. (2001) and roughly agreed with the observed profiles with an average agreement score of 0.74. Refining the estimated input data with the results from the manual observation would be desirable for achieving a better agreement score. The equations for the natural stability index (SI) were unsuitable for this study area. The empirical equations formulated by Yamanoi and Endo (2002) and Abe et al. (2006) were incorporated to calculate the SI. The calculated SI then agreed better with the SI estimated from the hardness, and the unstable snow conditions during heavy snowfall were more accurately reproduced. To expand the forecasting area to include R405, a national road, we used data from an AMEDAS and a DEM with a grid size of 10 m. The distribution of the meteorological parameters was estimated and used for the SNOWPACK simulation in order to obtain the distribution of SI. The SI maps showed a considerable decline during the heavy snowfall; they stabilised after the snow stopped. Avalanches occurred when the SI maps depicted an unstable condition. The simulation techniques used in this study were applied to other surface avalanches that had occurred over the past two years. Nine of 11 avalanches occurred when
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the calculated SI was below 2. The total time with a simulated SI below 2 amounted to 31% of the snow season calculated from an average of selected AMEDAS points. These results suggest that, if a situation is determined to be dangerous for SIs smaller than 2 (31% of the winter), 82% of avalanches would be predicted. Although more accurate models are needed, the simulation of a variety of types of avalanches provides information regarding the types of improvements that are needed to obtain more accurate predictions. In the cases reviewed in this study, the effects of skiers, the shear strength of layer interface, and the reproduction of graupel would be necessary to predict avalanches that were not detected. In addition, we are considering a number of improvements in order to make the model more practical. One improvement calls for more accurate descriptions of distributions of snow depth. This could be improved by laser measurements. Another possibility involves the modelling of liquid water movement to the prediction of surface avalanches caused by the collapse of a wet-grain layer and full-depth avalanches in temperate heavy snow regions, such as the one in this study. Future studies will involve the modeling of liquid water movement in a snowpack with the use of a two-dimensional model. Acknowledgements This study was supported with a Special Coordination Fund for the Promotion of Science and Technology and a grant from the Ministry of Education, Science, Sports and Culture, Japan (No. 17800006: principal investigator A. Sato). We give special thanks to T. Sato, O. Abe and M. Nemoto of the NIED, and K. Izumi and K. Kawashima of the Niigata University for their assistance with the snow pit observations. Helpful comments and suggestions from anonymous reviewers, and Scientific Editor Garry W. Timco are greatly acknowledged. We are also grateful to the Highland Agricultural Technology Center for providing us with a place for carrying out the observations. References Abe, O., 2004. Shear strength and angle of repose of snow layers including graupel. Proceedings of cold region technology conference. Ann. Glaciol. 38, 305–308. Abe, O., Xu, J., Liu, J., Hirashima, H., Mochizuki, S., Yamaguchi, S., Sato, T., Sato, A., 2006. Shear strength of natural and artificial depth hoar layers. ISSW 2006 proceedings, Marmot, CO, pp. 7–14. Bartelt, P., Lehning, M., 2002. A physical SNOWPACK model for the Swiss avalanche warning. Part I. Numerical model. Cold Reg. Sci. Technol. 35 (3), 123–145. Colbeck, S.C., 1973. Theory of metamorphism of wet snow. CREEL Res. Rep. 313.
Colbeck, S.C., 1978. The physical aspects of water flow through snow. Adv. Hydrosci. 11, 165–206. Conway, H., Wilbour, C., 1999. Evolution of snow slope stability during storms. Cold Reg. Sci. Technol. 30, 67–77. Denoth, A., 1994. An electronic device for long-term snow wetness recording. Ann. Glaciol. 19, 104–106. Endo, Y., 1992. Time variation of stability index in new snow. Proc. The Japan-U.S. Workshop on Snow Avalanche, Landslide, Debris Flow Prediction and Control, Science and Technology Agency of Japanese Government, pp. 85–94. Fukuzawa, T., Akitaya, E., 1993. Depth-hoar crystal growth in the surface layer under high temperature gradient. Ann. Glaciol. 18, 39–45. Funk, M., Hoelzle, M., 1992. A model of potential direct solar radiation for investigating occurrences of mountain permafrost. Permafrost and Periglacial Processes 3, 139–142. Izumi, K., Akitaya, K., 1982. Hardness of wet snow. Low Temperature Science Ser. A 41, 89–97 (In Japanese with English summary). Jamieson, J.B., Johnston, C.D., 1998. Refinements to stability index for skier-triggered dry-slab avalanches. Ann. Glaciol. 26, 296–302. Jamieson, J.B., Johnson, C.D., 2001. Evaluation of the shear frame test for weak snowpack layers. Ann. Glaciol. 32, 59–68. Jamieson, J.B., Zeidler, A., Brown, C., 2007. Explanation and limitations of study plot stability indices for forecasting dry snow slab avalanches in surrounding terrain. Cold Reg. Sci. Technol. doi:10.1016/j.coldregions.2007.02.010. Hirashima, H., Nishimura, K., Baba, E., Hachikubo, A., Lehning, M., 2004a. SNOWPACK model simulations for snow in Hokkaido, Japan. Ann. Glaciol. 38, 123–129. Hirashima, H., Ohata, T., Kodama, Y., Yabuki, H., Sato, N., Georgiadi, A., 2004b. Non-uniform distribution of tundra snow cover in eastern Siberia, J. Hydromet. 5 (3), 373–389. Kondo, J., Nakamura, T., Yamazaki, T., 1991. Estimation of the solar and downward atmospheric radiation. Tenki 38, 41–48 (in Japanese). Lehning, M., Fierz, C., Lundy, C., 2001. An objective snow profile comparison method and its application to SNOWPACK. Cold Reg, Sci. Technol. 33, 253–261. Lehning, M., Bartelt, P., Brown, B., Fierz, C., Satyawali, P., 2002a. A physical SNOWPACK model for the Swiss avalanche warning. Part II. Snow microstructure. Cold Reg. Sci. Technol. 35 (3), 147–167. Lehning, M., Bartelt, P., Brown, B., Fierz, C., 2002b. A physical SNOWPACK model for the Swiss avalanche warning. Part III. meteorological forcing, thin layer formation and evaluation. Cold Reg, Sci. Technol. 35 (3), 169–184. Lehning, M., Fierz, C., Brown, B., Jamieson, B., 2004. Modelling instability for the snow cover model SNOWPACK. Ann. Glaciol. 38, 331–338. Lehning, M., Völksch, I., Gustafsson, D., Nguyen, T.A., Stähli, M., Zappa, M., 2006. ALPINE3D: A detailed model of mountain surface processes and its application to snow hydrology, Hydrol. Processes 20, 2111–2128. Liston, G.E., Sturm, M., 1998. A snow-transport model for complex terrain. J. Glaciol. 44, 498–516. McClung, D., Schaerer, P., 2006. The Avalanche Handbook. The Mountaineers, Seattle. 342 pp. Nishimura, K., Baba, E., Hirashima, H., Lehning, M., 2005. Application of the snow cover model SNOWPACK to snow avalanche warning in Niseko, Japan. Cold Reg. Sci. Technol. 43, 62–70. Perla, R., Beck, T.M.H., Chang, T.T., 1982. The shear strength index of alpine snow. Cold Reg. Sci. Technol. 6, 11–20. Sato, A., Ishizaka, M., Shimizu, M., Kobayashi, T., Nishimura, K., Nakai, S., Sato, T., Abe, O., Kosugi, K., Yamaguchi, S., Iwamoto, K.,
H. Hirashima et al. / Cold Regions Science and Technology 51 (2008) 191–203 2004. Construction of snow disaster forecasting system in Japan. Snow Engineering. V.A.A. Balkema Publishers, Switzerland, pp. 235–238. Schweizer, J., Bellaire, S., Fierz, C., Lehning, M., Pielmeier, C., 2006. Evaluating and improving the stability predictions of the snow cover model SNOWPACK, Cold Reg. Sci. Technol. 46, 52–59. Yamaguchi, S., Sato, A., Lehning, M., 2004. Application of the numerical snowpack model (SNOWPACK) to the wet snow region in Japan. Ann. Glaciol. 38, 266–272.
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Yamanoi, K., Endo, Y., 2002. Dependence of shear strength of snow cover on density and water content. Seppyo. 64 (4), 443–451 (in Japanese with English Abstr.). Yamanoi, K., Takeuchi, Y., Murakami, S., 2004. Evaluation of snow stability index by using a digital push-gauge. Seppyo. 66 (6), 669–676 (in Japanese).
Cold Regions Science and Technology 51 (2008) 191 – 203 www.elsevier.com/locate/coldregions
Avalanche forecasting in a heavy snowfall area using the snowpack model Hiroyuki Hirashima a,⁎, Kouichi Nishimura a,1 , Satoru Yamaguchi a , Atsushi Sato a , Michael Lehning b a
b
Snow and Ice Research Center, NIED, Suyoshi, Maeyama, Nagaoka 940-0821, Japan WSL, Swiss Federal Institute for Snow and Avalanche Research, SLF, Fluelastrasse 11, CH-7260 Davos Dorf, Switzerland Received 23 October 2006; accepted 28 May 2007
Abstract We describe the use of SNOWPACK, a snow cover model, for areas with heavy snowfall. Record-breaking snowfall was recorded over the Sea of Japan and northwest coast of Honshu in the winter of 2005/2006. Avalanche forecasting was conducted at Tsunan, Niigata Prefecture, where the snow depth exceeded 4 m. Measurements from an Automated Meteorological Data Acquisition System (AMEDAS) operated by the Japan Meteorological Agency were used as the model input data. To verify the model output, snow pit observations were carried out at 10-day intervals. Simulated snow profiles were verified by applying a comparative method developed by Lehning et al. [Lehning, M., Fierz, C., Lundy, C., 2001. An objective snow profile comparison method and its application to SNOWPACK. Cold Reg, Sci. Technol. 33, 253–261.] and were in reasonable agreement with the observed results, with an agreement score of 0.74. However, the equations for the stability index (SI) were unsuitable for the study area considered. Dangerous conditions continued for more than two months in the model, but they were caused by unsuitable parameterisation of the shear strength for Japanese snow. Thus, the parameterisation of shear strength was improved. The empirical equations formulated by Yamanoi and Endo [Yamanoi, K., Endo, Y., 2002. Dependence of shear strength of snow cover on density and water content. Seppyo., 64(4), 443–451, (in Japanese with English Abstract)] were the most suitable for simulating SI for this region; therefore, they were incorporated into the SNOWPACK model. The unstable conditions that occurred during heavy snowfall were reproduced. To expand the forecasting area to include the area along R405, a national road, the distributions of meteorological parameters in the study area were estimated for grid points with 10-m spacing using simple lapse rate and interpolation methods. In an avalanche on 24 December 2005, a car was pushed off the road and into a valley. The snow depth increased by about 70 cm within 24 h; such large and intense snowfall is commonly associated with avalanching and, hence, instability. Thus, the snow stability decreased. This was reproduced by the SNOWPACK model. Furthermore, the stability index maps showed that most slopes were dangerous on that day. The improved SNOWPACK results were compared with other avalanche events on the Sea of Japan side of Japan. Nine of 11 surface avalanches occurred when the simulated stability index was lower than 2. Two shortcomings responsible for the failure to predict avalanches had to do with the reproduction of the graupel layer and the estimation of the shear strength of layer interfaces. © 2007 Elsevier B.V. All rights reserved. Keywords: SNOWPACK model; Avalanche forecasting; Heavy snow; Stability index
⁎ Corresponding author. E-mail address: [email protected] (H. Hirashima). 1 Present affiliation: Faculty of Science, Niigata University, Ikarashi, Niigata 950-2181, Japan. 0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2007.05.013
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1. Introduction In the winter of 2005–06, the northern region of Japan along the Sea of Japan received record-breaking snowfall. One hundred and fifty-two people perished due to snow disasters, such as accidents during the removal of snow, snow falling from the roof of houses, and avalanches. Thus, the Japan Meteorological Agency termed this winter as ‘Heisei 18-nen Gousetsu’ which means ‘Heavy snow in 2006’. The areas most affected due to this extraordinary snowfall are located in Tsunan, Niigata prefecture, Japan. The depth of snow on the ground in this region was greater than 4 m. R405, a national road that passes through the mountainous regions of Niigata and Nagano-prefectures, was exposed to an unusual avalanche risk and was, therefore, closed. Traffic restrictions continued for 3 months. Vehicles were permitted to use the road at scheduled times during the day. For six days, the road was closed. Furthermore, the inhabitants of this mountainous region were isolated. In such situations, the estimation of the probability of avalanche would have value when determining whether the road closure is justified. In order to achieve this, avalanche professionals conducted field surveys and reported their findings to a road administrator. In addition to this, computational forecasting is a useful because it can simulate the snow conditions and the snow stability index (SI), which may change on short time scales. A computational model – SNOWPACK – for avalanche forecasting was developed in Switzerland (Lehning et al., 2002a,b; Bartelt and Lehning, 2002). This model can also simulate the stability indices (Lehning et al., 2004) and has recently been developed into a distributed model of alpine surface process for diverse applications (ALPINE3D, Lehning et al., 2006). The SNOWPACK model was introduced in Japan. At first, some discrepancies were noted in the simulation results regarding the amount of snowmelt and types of snow. Yamaguchi et al. (2004) improved the parameterization of the surface energy balance to make the model suitable for wet Japanese snow. In an earlier study, we (Hirashima et al., 2004a) introduced the rapid growth mechanism of faceted grains (Fukuzawa and Akitaya, 1993) into SNOWPACK to reproduce the faceted grains at the surface layer. The SNOWPACK model was then modified for application to Japanese winters. SNOWPACK simulations for a complex terrain were carried out by Nishimura et al. (2005) by combining the SNOWPACK model and a snow redistribution model (Liston and Sturm, 1998; Hirashima et al., 2004b). The validation of the avalanche forecasting by Nishimura et al. (2005) focused on the example of a slab avalanche.
In this study, the avalanche-forecasting model was applied around R405, which is an area of wet and heavy snow. In this paper, we discuss suitable parameterizations for estimating the stability index, predictable avalanche types, and future issues for accurate avalanche forecasting. 2. Simulation method 2.1. Study site and weather station The study site, Tsunan (36°59.8′N, 138°41′E), Niigata prefecture, Japan, is an area of heavy snowfall. Fig. 1
Fig. 1. Study area (a: Locations of Tsunan; b: Simulated area of Tsunan). The rectangle shows the detailed study area at Tsunan.
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shows the location and maps of the study area. The maximum snow depth this year was 416 cm, whereas it is 215 cm for an average year. Since this area is temperate and snowy, faceted crystals and depth hoar rarely form. Avalanches tend to occur during heavy snowfall and on warm days. The Automated Meteorological Data Acquisition System operated by the Japan Meteorological Agency (AMEDAS) observes the air temperature, wind speed, wind direction, precipitation, duration of sunshine, and snow depth. The AMEDAS data was used as model input data. Since AMEDAS does not measure solar radiation and longwave radiation, the empirical equations suggested by Kondo et al. (1991) were used in order to estimate them. The input solar radiation S↓(Wm− 2) was calculated as follows by using the incident solar radiation at the top of the atmosphere S0↓(Wm− 2) and the duration of sunshine. 8 N N > > < S0A 0:244 þ 0:511 0b V1 N N A 0 0 ð1Þ s ¼ N > > : 0:118S0 ¼ 0A N0 S0A
2 d0 ¼ I00 cosh d
ð2Þ
where, N is the duration of sunshine; N0, the possible duration of sunshine; I00, the solar constant (=1365 Wm− 2); d, the distance between the earth and the sun; d0, the average distance between the earth and the sun; and θ, the zenith angle. Longwave radiation is also estimated from meteorological data as follows: LA ¼ rs T 4 ½1 ð1 vÞC 8 3 2 > N N N > < 0:826 þ 0:298 1:234 þ1:135 N N N 0 0 0 C¼ > > 0:2235 :
ð3Þ N 0b V1 N0 N ¼0 N0
ð4Þ v ¼ 0:74 þ 0:19w þ 0:07w2
ð5Þ
w ¼ 0:0315Td 0:1836
ð6Þ
where σs is the Stefan–Boltzmann constant ( = 5.67× 10− 8 Wm− 2 K− 4), T is the air temperature (K), w is the logarithm of the column effective water vapour, and Td is the dew point temperature (°C).
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2.2. Simulation A workstation, DELL Precision 380 equipped with an Intel Pentium 4 CPU 3.00 GHz was used for the SNOWPACK simulations. The computer was equipped with the Microsoft Windows XP professional x64 software. The computation time to calculate SNOWPACK from 1 December to 31 March is about 60 s. If the SNOWPACK simulation is carried out every day using the calculation results from previous runs as initial input, the computational time for a 24-hour calculation is about 1.1 s when the snow depth is 4 m. Our objective was to achieve a stability index distribution for a 5 km × 10 km area with 10 m mesh. If a simulation is carried out for each grid point, 7.8 km2 is the limitation for real-time simulation. Therefore, we used the following technique to make the SI distribution. Input data was made per 100 m altitude considering a lapse rate of 6.5 × 10− 3 °C m− 1. The altitudes of the simulated area ranged from 400 to 1700 m a.s.l. A snowpack model simulation was conducted for each elevation. The calculation results of the nearest elevation were applied for each 10 m grid point. The stability index was calculated for each grid based on the snowpack results and slope angle. Under this technique, the effect of the slope angle and direction of incoming solar radiation were not considered. However, in this technique, a real-time simulation was accomplished within 30 min of obtaining the meteorological data. SNOWPACK simulations for each 10 m grid were also conducted. The SI distribution results used in this paper were calculated for each 10 m grid. 3. Observations 3.1. Snow pit observations Snow pit observations were carried out from January to March at the AMEDAS point at 10-day intervals. The snow conditions observed are shown in Fig. 2a. The snow profiles showed that the snow comprises new snow, decomposed snow, rounded grains, and wet grains. However, no faceted grains or depth hoar were observed. The wet grains observed at the bottom layer were formed at the beginning of winter. The wet grains in the middle layer were formed on 14 and 15 January, which were warm days with rainfall. Most of the layers became wet grains after 20 February. The snow densities observed are shown in Fig. 2b (solid line). Snow densities below 1 m are more than 400 kg m− 3. After 20 February, snow at the bottom was saturated. The snow density at the saturated layer exceeded 800 kg m− 3.
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avalanches were detected in an area of 40.2 km2. For the avalanches that released, the total area of the avalanche paths was 2.38 km2 (5.9% of observed area). The slope angles at fracture line (ψ) and sighting angles from the maximum runout position to the top of the starting point (α) were estimated for each avalanche. The frequency distributions of ψ and α for surface avalanches are shown in Fig. 3. The average value of ψ was 41.2°. Two-thirds of avalanches (about 69%) occurred on slopes with inclinations between 35° to 45° (Fig. 3a). These results demonstrate that Japanese avalanches occur on steeper slopes more often than as noted by McClung and Schaerer (2006, p. 91). The average value of α was 37.9°. Furthermore, 88.6% of α of avalanches ranged between 30–45° (Fig. 3b). 4. Results and discussion 4.1. SNOWPACK-simulated profiles Simulated snow profiles are shown in Fig. 4. Snow accumulation begins in early December. The snow depth approached 4 m in early January. Since snow metamorphosed under small temperature-gradient conditions, faceted grains and depth hoar rarely formed. On 14 and 15 January, the upper layer snow metamorphosed into wet grains during warm days with rainfall.
Fig. 2. Observed and simulated snow cover a: snow structures for each observed day. The left profiles are the observed results, and those on the right are the simulated ones, b: snow densities.
3.2. Remote sensing Aerial photographs were taken on 5 March to develop the avalanche distribution map. One hundred and sixty-four surface avalanches and five full-depth
Fig. 3. Frequency distribution for a surface avalanche. a: slope angles at fracture line, ψ; b: sighting angles from the maximum runout position to the top of the starting point, α.
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tween the observed and modelled profiles. The overall score calculated was 0.74. The highest score was the temperature (0.93 in average). In most layers, the snow temperature is 0 °C in this region (the average snow temperature from the snow pit observation was − 0.06 °C.). As a result, the large agreement score, small mean bias error (0.02 °C) and small root mean square error (0.33 °C) were obtained. However, the correlation coefficient was low (r = 2.0 × 10− 3). In this region, discrepancy in the energy transport, rather than the snow temperature, affects the water content. Lehning et al. (2001) used five classifications for estimating water content. In this study, since the water content was measured using a dielectric probe (Denoth, 1994), the liquid water content was obtained as the weight water content. The agreement score for the water content was calculated using the same method as for the temperature and density. The agreement score for the water content was averaged 0.65. The agreement score of the water content was the lowest in this region, whereas the one at the site in Switzerland was the highest (Lehning et al., 2001). On 20 February, most of the snow in the simulation consisted of wet grains, whereas 39% of snow in the observations consisted of rounded grains (Fig. 2a). At this time, the agreement scores for the liquid water and grain types were low (0.37 and 0.56, respectively). The discrepancies in liquid water were attributed to errors in the amount of liquid precipitation and solar and long wave radiation, the parameterisation of surface energy balance, the heat conduction in the snow, and the water transport in the snow. Snowpack parameters could be improved by the use of more accurate input data. In this case, the effect of the errors in the input parameters on the simulated snow stratification was assessed. According to Kondo et al. (1991), the standard estimated error of S/S0 in Eq. (1) is 0.0434, that
Fig. 4. Simulated snow profile at the Tsunan AMEDAS point in 2005/ 06 winter. a: snow type; b: SI calculated using the original SNOWPACK; c: SI calculated using the equations of Yamanoi and Endo (2002) and Abe et al. (2006).
All of the snow layers were transformed into wet grains on 15 February. The comparisons of the observed and simulated snow types are shown in Fig. 2a. The comparisons of the observed and simulated snow densities are also shown in Fig. 2b. The simulated snow profiles were evaluated using a comparison method developed by Lehning et al. (2001). Fig. 5 is a time series of individual and overall agreement scores be-
Fig. 5. Time series of individual and overall agreement scores between the observed and modeled profiles at the AMEDAS station in Tunan for the winter season in 2005/2006.
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of Ldf /σsT 4 in Eq. (3) is 0.0158, and that of C in Eq. (4) is 0.1066. We conducted a sensitivity experiment varying the parameters by ±1 standard deviation. However, the error leading to the discrepancies of snow stratification could not be explained exclusively by the estimation error on the solar and long wave radiation. An error in the input of liquid precipitation could also have caused a discrepancy. In the simulation, the precipitation amount was multiplied by 1.6 to fit with the observed snow depth and snow water equivalent. However, the capture rate for rain is larger than that for snow. Therefore, when the air temperature exceeded 0 °C, 1 was used as the multiplied value. As a result, the percentage of the wet layer decreased, but it was still larger than the observed result. Even for a combined sensitivity experiment with decreased solar and longwave radiation and unchanged rain condition, the percentage of wet grains was greater than that in the observed results. However, the simulation results were more similar to the observed results. In this case, the average agreement score for the snow type changed from 0.73 to 0.80. The agreement scores for the grain size and water content were also higher, whereas those for the snow temperature and density were slightly lower. The average overall score changed from 0.74 to 0.79. There are still problems associated with the snowpack parameters and method used for the estimation of input data. One possibility to improve the snowpack representation would be to directly assemble observed snow cover data. However, it needs to be noted that manual snow observations are also subjective and vary from observer to observer.
where ρdry is the dry density; θ (%) , the volumetric water content; K (Nm− 1(kg m− 3)− a), a coefficient that is determined experimentally by the snow type, a is 2.91, and b is − 0.235 (%− 1). K is 9.40 × 10− 4 for new snow, decomposed snow and rounded grains and 4.97 × 10− 4 for wet grains. This formulation was derived from snow where densities range from 50 kg m− 3 to 500 kg m− 3. The shear strength of faceted grains and depth hoar is formulated by Abe et al. (2006) as follows: r ¼ kexp 1:51 102 qdry
ð8Þ
where k is 3.24 × 10− 2 Nm− 2. This formulation was derived from snow densities ranging from 150 kg m− 3 to 350 kg m− 3.
4.2. Estimation of snow stability index 4.2.1. (a) Previous studies on parameterizations A simple stability index (SI) is the shear strength divided by the shear stress, which is usually called the natural stability index (Lehning et al., 2004). The original SNOWPACK model estimates shear strength using the empirical equation suggested by Jamieson and Johnston (2001), who formulated the relationship between the shear strength and the snow density for each snow type. Formulations were derived from snow densities ranging from 50 kg m− 3 to 330 kg m− 3. The relationships between snow density and shear strength have also been studied in Japan. Yamanoi and Endo (2002) formulated the shear strength σ (Nm− 2) from the density and water content as: r ¼ Kqadry ebh
ð7Þ
Fig. 6. Comparisons of each estimation technique for SI. The value estimated from the hardness is used as a true value. a: profiles of shear strength at Yuzawa, where snow was dry; b: profiles at Tsunan, where snow was wet.
H. Hirashima et al. / Cold Regions Science and Technology 51 (2008) 191–203 Table 1 MBE, RMSE, and r2 for each calculated results compared with the value estimated value from the hardness
MBE RMSE 12
Yamanoi and Endo (2002)
Jamieson and Johnston (2001)
Perla et al. (1982)
−0.06 0.17 0.97
− 0.87 0.96 0.94
−0.50 0.53 0.96
In addition to this, Yamanoi et al. (2004) formulated a shear strength depending on the hardness measured by a digital push gauge. This equation is expressed as: r ¼ KH H c
ð9Þ −2
where H is the measured hardness (Nm ). KH (= 0.018 (Nm− 2)1 − c) and c (= 1.18) were determined experimen-
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tally. Hardness is highly correlated with shear strength (r2 = 0.80). These models were used for the improvement of the simulation for shear strength. 4.2.2. (b) Estimation The calculated profiles of a SI simulated by original SNOWPACK are shown in Fig. 4b. According to the simulated profiles including the parameterizations of strength in SI, the snowpack was unstable for longer than two months and the rounded grains appeared to be a weak layer. This is inconsistent with the observed decrease in avalanche activity days after the storm, even if we assume that part of the decrease in avalanche danger was due to the fact all dangerous slopes had already released as discussed above. The original SNOWPACK uses the
Fig. 7. Maps of SI as simulated by SNOWPACK over a 10 m grid. This area is rectangle area in Fig. 1(b). a: 23 December; b: 24 December; and c: 25 December. White circles on a black background indicate the site of the avalanche.
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parameterisation of Jamieson and Johnston (2001) to calculate the shear strength. This relationship was derived for relatively light snow (less than 270 kg m− 3 for rounded grains). However, in our heavy snow area, the snow density at the lower snowpack exceeds 400 kg m− 3 even if the snow is dry. Thus, the equations of Jamieson and Johnston (2001) are not suitable for estimating shear strength in such a heavy snow area. This formula underestimated the shear strength of heavy snow. Therefore, an alternate formula is needed for measuring shear strength for heavy snow. The models of Jamieson and Johnston (2001), Perla et al. (1982), and Yamanoi and Endo (2002) were compared. The shear strength calculated from the hardness based on Yamanoi et al. (2004) was used for validation. The hardness profiles were measured on 27 February. On that day, all the snow layers were wet, and, unfortunately, no hardness data for dry snow could be measured in the snow pit observations at Tsunan. However, the hardness profiles for dry snow were observed at Yuzawa, which is located about 13 km southeast of Tsunan, on 4 January. The shear strength profiles were estimated using these hardness profiles and Eq. (9). Furthermore, shear strengths were calculated from snow types and snow densities by using the equations by Yamanoi and Endo (2002) (Eq. (7)), Jamieson and Johnston (2001), and Perla et al. (1982). The comparisons between these estimations are shown in Fig. 6. The mean bias error (MBE), the root mean square error (RMSE), and the correlation coefficient (r2) for each equation compared with the value estimated from hardness are shown in Table 1. Obviously, the shear strengths estimated by Yamanoi and Endo (2002) have the smallest error for the dry snow conditions. Thus, their estimation is most suitable for this region. On the other hand, the errors for wet snow are comparable with the equation of Perla et al. (1982). Eqs. (7) and (8) were incorporated into SNOWPACK. The simulated result using new parameterization is shown in Fig. 4c. The stability index of rounded grains was then corrected to be extremely strong. As a result, the SI decreased during heavy snowfall when avalanching was likely, and wet grains sometimes appeared as a weak layer as is common in this snow climate (e.g. Izumi and Akitaya, 1982).
using techniques similar to those of Nishimura et al. (2005). As an example, the SI maps between 23 and 25 December are shown in Fig. 7. The SI maps show that most of the steep slopes were subject to avalanche danger on 24 December despite having been relatively safe prior to and following that date. In fact, on 24 December, an avalanches occurred, and a car was pushed off from the road and into the valley. The profiles for snow type and SI around the day of the avalanche are shown in Fig. 8. The SNOWPACK result shows that the SI decreases in a new snow layer. The snow depth increased by about 70 cm within 24 h. This led to an unstable snow condition, since the snow was strongly loaded with newer snow before densification. The weak layer was not detected in the snow pit observation of 25 December. However, the depth of new snow layer exceeded 40 cm. Therefore, it was considered that the avalanche was released on storm snow instability in the upper snow. The instability of storm snow was reproduced in the SNOWPACK model. Traffic restrictions were implemented on 24 December. First, R405 was closed during the nighttime. The
4.3. Simulations for the R405 area SI distribution maps were charted using a 10-m mesh around R405. GISMAP Terrain, a 10-m-mesh DEM obtained from 1:25,000 maps of Geographical Survey Institute (GSI), was used as topographic data. The local variation of meteorological conditions, such as air temperature, solar radiation, and wind speed, was calculated
Fig. 8. The profiles for the snow type and SI around the day of the avalanche, 24 December. a: simulated snow cover structure for 23–27 December; b: simulated stability index for the same period.
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section, the predictability for other avalanche events, including those that lead to fatal accidents, is discussed. Several large avalanches were recorded on the Sea of Japan side in 2005 and 2006. Field surveys were conducted after each of the 16 avalanche events. Eleven of them were surface avalanches. Table 2 summarizes information on the avalanches. Stability indices were calculated for each avalanche using the following techniques. Fig. 9. Simulated SI and traffic restrictions in 2005/06 winter. (1) closed during the nighttime, (2) completely closed, (3) permitted only vehicles belonging to residents and those carrying supply shipments, (4) allowed on the road for 4 h period (5) closed during the nighttime.
road was completely closed from 8 to 13 January. Only vehicles of belonging to residents and those carrying supply shipments were permitted from 13 to 16 January. After 16 January, all vehicles were allowed on the road for a 4 h period. From 14 February, the road was closed during the nighttime. On 21 March, R405 was opened again. A comparison between the simulated SI at the AMEDAS station and traffic restrictions is shown in Fig. 9. Overall, the simulated SIs were small during the traffic restrictions. Small SIs were caused by a wet-grain layer (Fig. 4). The SI sometimes declined rapidly due to instability of the storm snow. Although this model was not used to make decisions regarding traffic restrictions, the simulated SI was recognized as an important source of information by road administrators. 4.4. Predictability of an avalanche An avalanche during heavy snowfall around R405 could be predicted by introducing a new parameterization of shear strength of snow to SNOWPACK. In this
1. Search the AMEDAS station closest to avalanche point. 2. Download the meteorological data input. 3. Correct the air temperature on the basis of the difference in altitude between the AMEDAS station and avalanche location and an assumed lapse rate of 6.5 × 10− 3 °C m− 1. 4. Correct the solar radiation based on the slope angle and aspect of avalanche starting zone and solar altitude and aspect on the basis of the parameterisation of Funk and Hoelzle (1992). 5. Simulate the snow cover and calculate of SI for the avalanche accident. The calculated stability indices are shown in Fig. 10. Nine of the avalanche accidents (82%) occurred when the calculated stability index was below 2.0. The total time with the simulated SI being below 2 was 31% of the snow season of selected AMEDAS points on average. Now, this period is defined as an avalanche warning period. This implies that if the situation is judged to be dangerous for SIs smaller than 2 (31% of the winter), 82% of avalanches would be predicted. Although the accuracy rate increases with raising the threshold value for avalanche warning, this would lead to a smaller overall performance of the warning since extended
Table 2 Information of each avalanche event in which field surveys were conducted after the avalanche Number
Place
Avalanche date
Latitude and longitude
Weak layer
1 2 3 4 5 6 7 8 9 10 11
Ebisusawa Tubame onsen Ooakasawa Tutitaru Ludens Naeba Sizukuishi Hakkatouge Yunotani Nyutou onsen Bentousawa
23 Jan 2005 26 Feb 2005 24 Dec 2005 28 Dec 2005 03 Jan 2006 03 Jan 2006 04 Jan 2006 12 Jan 2006 12 Jan 2006 10 Feb 2006 14 Feb 2006
39°56′54″N, 140°55′0″E 36°54′9″N, 138°8′42″E 36°52′57″N, 138°38′11″E 36°53′16″N, 138°52′12″E 36°52′9″N, 138°51′46″E 36°47′29″N, 138°46′23″E 39°42′26″N, 140°48′34″E 37°5′6″N, 138°49′30″E 37°12′18″N, 139°4′29″E 39°48′15″N, 140°46′47″E 38°2′56″N, 139°51′2″E
Interface between melt-freeze grains and rounded grains New snow New snow New snow Faceted grains Faceted grains Graupel – New snow Unknown Wet snow
Avalanches 1, 2 and 10 resulted in fatal accidents.
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Fig. 10. Simulated stability indices at the avalanche sites when the avalanche occurred. Information for each avalanches are shown in Table 2.
warning times would cover even completely safe conditions. Fig. 11 shows the accuracy rate with the length of avalanche warning period as a function of an assumed SI value. Jamieson et al. (2007) mentioned that stability index cannot be extrapolated from one site to another, and that the correlation between stability index at the study site and avalanche activity will decrease as the loading rate varies spatially in windy range or during windy storms. In our study cases, many of avalanches occurred under the gentle wind conditions, which seem fairly adequate for the regional avalanche forecasting. Surface avalanches mainly occur during heavy snowfall in this region of Japan. The SI of new snow or weak layers decreases significantly during snowfall. However, avalanches did occur when the calculated SI was larger than 2. They occurred when no snow or small amounts of snow fell. The field survey shows that the first of these avalanches was caused by the failure of the layer interface between melt-freeze grains and rounded grains. This avalanche was triggered by a skier. Therefore, we recalculated the SI considering the weight of the skier on the basis of a study conducted Jamieson and Johnston (1998). The recalculated SI was 4.2. This case is isolated from other avalanches because it was triggered by a skier and the fracture occurred from layer interface. The estimation of SI for this type is one of the shortcomings of the natural stability index as has already been pointed out by Schweizer et al. (2006). The new stability estimators proposed there, which include skier triggering and interface snow characteristics, have not been the focus of the study presented here. The field survey also showed that the avalanche number 7 was caused by the collapse of a graupel layer (see Table 2.). The shear strength of graupel was formulated by Abe (2004). However, it is difficult to reproduce a graupel layer using meteorological input data on the ground because the formation process of
graupel depends on the processes in the cloud high in the atmosphere. Although this study uses meteorological data on the ground, the snow disaster forecasting system (Sato et al., 2004) developed by National Research Institute for Earth Science and Disaster Prevention (NIED) uses predicted meteorological input data calculated using the non-hydrostatic model (NHM). NHM can simulate the formulation of graupel. However, at the present stage, the NHM cannot accurately reproduce regional snowfall amounts. Therefore, observed meteorological data were used as input data in this study. The accuracy of NHM will need to be improved before avalanches caused by the collapse of a graupel layers can be predicted. 5. Model uncertainties The uncertainty of the simulated stability index was estimated on the basis of a similar method by Conway and Wilbour (1999). They suggested there are three contributions to the uncertainty: inexactness of the strengthdensity relationship, error of measurement of density, and measurement of precipitation. They estimated the uncertainty from the strength-density relationship using the root mean square (rms). However, Yamanoi and Endo (2002) did not estimate the rms. They used their original snow data and that of Endo (1992), who formulated a similar equation and estimated the minimum and maximum value for the proportionality coefficient. Therefore, we substituted the range of his estimation to calculate the uncertainty and estimated the uncertainty at ±0.84σ. With the equation of Yamanoi and Endo (2002) or that of Endo (1992), if the measurements of the density have an error ±10%, the contribution of the measurement to the uncertainty in strength is 3 × 0.1σ. The total uncertainty is q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:84Þ2 þð0:3Þ2 r ¼ 0:89r. Estimating the uncertainty for precipitation is difficult because the avalanche release points described in Section 4.4 are, on an average, about
Fig. 11. Accuracy rate and percentage of avalanche warning period relative to the threshold SI values.
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10 km away from the meteorological point. We compared newly fallen snow depths between AMEDAS data and snow data at Maekura about 11 km south-southwest from the AMEDAS point of Tsunan. The comparison was done using the total precipitation of 8 h when the total new fallen snow depths in 8 h were more than 16 cm. This was done because Endo (1992) suggested that an avalanche occurs after 8 h under 2 kg m− 2 h− 1 snowfall. The root mean square error between precipitations obtained using AMEDAS and Maekura station was ±47%. Therefore, at this time, the value of 0.47 is used as the q uncertainty for ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi precipitation. The total uncertainty is then ð0:89Þ2 þð0:47Þ2 r ¼ 1:00r. The uncertainty of precipitation should be analysed using the data for various meteorological points. The study of the difference in precipitation at a point distant from the meteorological station remains as issue to be investigated. 5.1. Future issues Destabilization during heavy snowfall was predicted by the SNOWPACK model. However, there are still a number of issues to be resolved. First, the SI shows consistently low values on most of steep slopes during heavy snowfall (Fig. 7b). The specification of a dangerous location of an avalanche is difficult at present. One useful method to specify a dangerous place is to predict the location of a snow cornice. A snow cornice can be predicted by simulating snow redistribution. It has to be validated by using the observed snow depth distribution. Since topographic surveys using laser measurements in a snowy season have already been carried out, the snow depth distribution can be obtained by laser measurements during the non-snow season. If laser measurements were obtained, the accuracy of avalanche predictions would be increased. Second, surface avalanches due to the failure of wet grains and full-depth avalanches as well as avalanches caused by the collapse of new snow often occur in temperate snowy areas. The shear strength of wet grains declines exponentially with the volumetric water content (Yamanoi and Endo, 2002). Full-depth avalanches tend to occur when liquid water (snowmelt water or rain) reaches the ground. An accurate simulation of the moisture movement in the snowpack is necessary for the prediction of these avalanches. The moisture movement scheme in the SNOWPACK model is that the liquid water moves downward when it exceeds a certain value. However, the two types of avalanches discussed above are affected by more complex water movement. Thus, we plan to develop a numerical snowpack model that
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considers the existence regime of liquid water (capillary regime, pendular regime, and funicular regime (Colbeck, 1973)), the formation of a water percolation channel, and the water movement through the percolation channel (Colbeck, 1978). The model will be expanded into a two-dimensional model in order to model the water transport. 6. Conclusions The snow cover model SNOWPACK was applied to avalanche forecasting for a heavy snow area. The input data for the SNOWPACK model was meteorological data obtained from the Japan Meteorological Agency. Solar and long wave radiation were estimated using the estimation equation developed by Kondo et al. (1991). The lapse rate of 6.5 × 10− 3 °C m− 1 and the estimation method for the influence of the slope angle on incoming solar radiation by Funk and Hoelzle (1992) were used to allow distributed calculations of the SI on a grid. Snow pit observations were also carried out at 10-day intervals. During the 2005/2006 winter, snow depth exceeded 4 m in the study region, Tsunan. The pit observations revealed that the snowpack comprised new snow, decomposed snow, rounded grains, and wet grains without faceted grains or depth hoar. The profiles simulated by the SNOWPACK model were verified on the basis of a comparison method developed by Lehning et al. (2001) and roughly agreed with the observed profiles with an average agreement score of 0.74. Refining the estimated input data with the results from the manual observation would be desirable for achieving a better agreement score. The equations for the natural stability index (SI) were unsuitable for this study area. The empirical equations formulated by Yamanoi and Endo (2002) and Abe et al. (2006) were incorporated to calculate the SI. The calculated SI then agreed better with the SI estimated from the hardness, and the unstable snow conditions during heavy snowfall were more accurately reproduced. To expand the forecasting area to include R405, a national road, we used data from an AMEDAS and a DEM with a grid size of 10 m. The distribution of the meteorological parameters was estimated and used for the SNOWPACK simulation in order to obtain the distribution of SI. The SI maps showed a considerable decline during the heavy snowfall; they stabilised after the snow stopped. Avalanches occurred when the SI maps depicted an unstable condition. The simulation techniques used in this study were applied to other surface avalanches that had occurred over the past two years. Nine of 11 avalanches occurred when
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the calculated SI was below 2. The total time with a simulated SI below 2 amounted to 31% of the snow season calculated from an average of selected AMEDAS points. These results suggest that, if a situation is determined to be dangerous for SIs smaller than 2 (31% of the winter), 82% of avalanches would be predicted. Although more accurate models are needed, the simulation of a variety of types of avalanches provides information regarding the types of improvements that are needed to obtain more accurate predictions. In the cases reviewed in this study, the effects of skiers, the shear strength of layer interface, and the reproduction of graupel would be necessary to predict avalanches that were not detected. In addition, we are considering a number of improvements in order to make the model more practical. One improvement calls for more accurate descriptions of distributions of snow depth. This could be improved by laser measurements. Another possibility involves the modelling of liquid water movement to the prediction of surface avalanches caused by the collapse of a wet-grain layer and full-depth avalanches in temperate heavy snow regions, such as the one in this study. Future studies will involve the modeling of liquid water movement in a snowpack with the use of a two-dimensional model. Acknowledgements This study was supported with a Special Coordination Fund for the Promotion of Science and Technology and a grant from the Ministry of Education, Science, Sports and Culture, Japan (No. 17800006: principal investigator A. Sato). We give special thanks to T. Sato, O. Abe and M. Nemoto of the NIED, and K. Izumi and K. Kawashima of the Niigata University for their assistance with the snow pit observations. Helpful comments and suggestions from anonymous reviewers, and Scientific Editor Garry W. Timco are greatly acknowledged. We are also grateful to the Highland Agricultural Technology Center for providing us with a place for carrying out the observations. References Abe, O., 2004. Shear strength and angle of repose of snow layers including graupel. Proceedings of cold region technology conference. Ann. Glaciol. 38, 305–308. Abe, O., Xu, J., Liu, J., Hirashima, H., Mochizuki, S., Yamaguchi, S., Sato, T., Sato, A., 2006. Shear strength of natural and artificial depth hoar layers. ISSW 2006 proceedings, Marmot, CO, pp. 7–14. Bartelt, P., Lehning, M., 2002. A physical SNOWPACK model for the Swiss avalanche warning. Part I. Numerical model. Cold Reg. Sci. Technol. 35 (3), 123–145. Colbeck, S.C., 1973. Theory of metamorphism of wet snow. CREEL Res. Rep. 313.
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