Supplementary data for "Detrainment and braking of snow avalanches interacting with forests"

Figure 5. Data of Fig. 5. Evolution of the detrainment mass per unit of area of snow with the velocity (regular staggered forest, e= 8m).

Figure 6. Data of Fig. 6.  Evolution of the detrainment mass observed for the one tree arrangement and the fits with the tree diameter for 3 flow regimes: Case 1, Case 2, and Case 3 with respectively a front velocity of 12.5 m/s,10.9 m/s and 10.75 m/s, ‘maximum’ refer to the maximum mass stored behind the tree and ‘final’ refer to the final mass stored. A slope of 30°, and a top wedge angle of 60° (from measurements Feistl et al. (2014)) are used for the theoretical model (Eq. 8). The removed point denotes a special case not considered in the proposed square relation in Eq. 9, since the entire avalanche in this case is stopped due to the low flow velocity and the high tree diameter. Please note that it is a coincidence that Case 1 maximum and Case 2 final agree well.

Figure 8. Data of Fig. 8. Evolution of the detrainment mass per unit of area with the tree diameter for different types of snow and front velocity (regular staggered forest, e = 8 m)

Figure 9. Data of Fig. 9. (a) Evolution of the detrainment mass per unit of area with the forest density for different front velocities (regular staggered forest, snow properties: Case 2, m). (b) Evolution of the detrainment mass per unit of area with the tree diameter for a constant Stand Density Index, SDI = 925 trees/ha (regular staggered forest,  m/s, snow properties: Case 2).

Figure 10. Data of Fig. 10. Evolution of the detrainment mass predicted with the model (Eq. 11) and with the observation, the coefficient of determination r² for the model prediction on the detrainment mass is 0.9912.

Figure 11. Data of Fig. 11. Temporal evolution of the kinetic and potential energy without forest and with a regular staggered forest (Case 2, v0 = 6 m/s).

Figure 12. Data of Fig. 12. Temporal evolution of the detrainment energy and dissipation due to the forest (Case 2, v0 = 6 m/s).

Figure 13. Data of Fig. 13. Energy detrainment and dissipation for different snow properties (1: Case 1, 2: Case 2, 3: Case 3 with M=1) and for 3 types of forest structure (regular aligned, regular staggered and random).