Scale-invariance of soil moisture variability and its implications for the frequency-size distribution of landslides

Power spectral analyses of soil moisture variability are carried out from scales of 100 m to 10 km on the microwave remotely-sensed data from the Washita experimental watershed during 1992. The power spectrum S(k) has an approximate power-law dependence on wave number k with the exponent −1.8. This behavior is consistent with the behavior of a stochastic differential equation for soil moisture at a point, and it has important consequences for the frequency-size distribution of landslides. We present the cumulative frequency-size distributions of landslides induced by precipitation in Japan and Bolivia as well as landslides triggered by the 1994 Northridge, California earthquake. Large landslides in these regions, despite being triggered by different mechanisms, have a cumulative frequency-size distribution with a power-law dependence on area with an exponent ranging from −1.5 to −2. We use a soil moisture field with the above statistics in conjunction with a slope stability analysis to model the frequency-size distribution of landslides. In our model, landslides occur when a threshold shear stress dependent on cohesion, pore pressure, internal friction and slope angle is exceeded. This implies a threshold dependence on soil moisture and slope angle since cohesion, pore pressure and internal friction are primarily dependent on soil moisture. The cumulative frequency-size distribution of domains of shear stress greater than a threshold value with soil moisture modeled as above and topography modeled as a Brownian walk is a power-law function of area with an exponent of −1.8 for large landslide areas. This distribution is similar to that observed for landslides. The effect of strong ground motion from earthquakes lowers the shear stress necessary for failure, but does not change the frequency-size distribution of failed areas. This is consistent with observations. This work suggests that remote sensing of soil moisture can be of great importance in monitoring landslide hazards and proposes a specific quantitative model for landslide hazard assessment.