A spectral clustering search algorithm for predicting shallow landslide size and location

The potential hazard and geomorphic significance of shallow landslides depend on their location and size. Commonly applied one-dimensional stability models do not include lateral resistances and cannot predict landslide size. Multidimensional models must be applied to specific geometries, which are not known a priori, and testing all possible geometries is computationally prohibitive. We present an efficient deterministic search algorithm based on spectral graph theory and couple it with a multidimensional stability model to predict discrete landslides in applications at scales broader than a single hillslope using gridded spatial data. The algorithm is general, assuming only that instability results when driving forces acting on a cluster of cells exceed the resisting forces on its margins and that clusters behave as rigid blocks with a failure plane at the soil-bedrock interface. This algorithm recovers predefined clusters of unstable cells of varying shape and size on a synthetic landscape, predicts the size, location, and shape of an observed shallow landslide using field-measured physical parameters, and is robust to modest changes in input parameters. The search algorithm identifies patches of potential instability within large areas of stable landscape. Within these patches will be many different combinations of cells with a Factor of Safety less than one, suggesting that subtle variations in local conditions (e.g., pore pressure and root strength) may determine the ultimate form and exact location at a specific site. Nonetheless, the tests presented here suggest that the search algorithm enables the prediction of shallow landslide size as well as location across landscapes.