Assessing the probability of volume estimates initial landslide ruptures based on surface area

There exist several relationships between landslide surface areas and volumes. Most of them are based on simple geometric shape such as half ellipsoid or surface prisms. Using a new inventory of 66 small and shallow landslides was created using high resolution digital elevation model in the canton of Vaud (Switzerland). The volume calculation was based on horizontal surface areas (A) and the maximum vertical depth, using both paraboloid-elliptic or half ellipsoid. The relationship between surface area – maximum vertical depth (z_max) is deduced using principal component analysis (PCA) in a log-log space, which leads to a power-law (Jaboyedoff et al., 2020). The distribution of the distances of the 66 couple of values to this line is close to a log-normal distribution. This allows to calculate the probability to overpass a volume using both paraboloid-elliptic and half ellipsoid to calculate volumes based on maximum depth z_max.

The trend of relationship is very similar to the one obtained by Guzzetti et al. (2009), but the confidence level narrower. In our case a volume can be 8 times larger between the two boundaries of the centred 95% confidence level, and for the Guzzetti et al. (2009) it reaches 38 times based on their confidence level.

This approach demonstrates that there are large uncertainties on the volume estimations. But if it is applied to coherent inventories, it can provide good approximations. As the landslide runout distance depends on the volume involved, such approach is promising for improving landslides hazard.

References

Guzzetti F., Ardizzone F., Cardinali M., Rossi M., Valigi, D. 2009. Landslide volumes and landslide mobilization rates in Umbria, central Italy. Earth and Planetary Science Letters, 279(3-4), 222-229.

Meier, C., Jaboyedoff, M., Derron, M.-H., Gerber, C., 2020. A method to assess the probability of thickness and volume estimates of small and shallow initial landslide ruptures based on surface area. Landslides. //doi.org/10.1007/s10346-020-01347-0