The role of topography in the scaling distribution of landslide areas: A cellular automata modeling approach

Power law scaling has been widely observed in the frequency distribution of landslide sizes. The exponent of the power-law characterizes the probability of landslide magnitudes and it thus represents an important parameter for hazard assessment. The reason for the universal scaling behavior of landslides is still debated and the role of topography has been explored in terms of possible explanation for this type of behavior. We built a simple cellular automata model to investigate this issue, as well as the relationships between the scaling properties of landslide areas and the changes suffered by the topographic surface affected by landslides. The dynamics of the model is controlled by a temporal rate of weakening, which drives the system to instability, and by topography, which defines both the quantity of the displaced mass and the direction of the movement. Results show that the model is capable of reproducing the scaling behavior of real landslide areas and suggest that topography is a good candidate to explain their scale-invariance. In the model, the values of the scaling exponents depend on how fast the system is driven to instability; they are less sensitive to the duration of the driving rate, thus suggesting that the probability of landslide areas could depend on the intensity of the triggering mechanism rather than on its duration, and on the topographic setting of the area. Topography preserves the information concerning the statistical distribution of areas of landslides caused by a driving mechanism of given intensity and duration.