Inverse computational morphology of debris and alluvial fans

Yuan-Hung Damiel Chiu , Tzu-Yin Kasha Chen, Hervé Capart

In mountain areas, debris flows and fluvial transport often build up conical deposits at the confluence between steep tributaries and trunk rivers. The resulting debris and alluvial fans typically exhibit a well-defined relationship between slope or elevation and the distance from the fan apex. This relationship, however, becomes more difficult to characterize when fans are constrained by the topography of the valley, causing the paths of steepest slope to bend around obstacles. In previous work, a forward modeling approach was developed to reconstruct these more complex fan surfaces from an assumed elevation-distance profile. In this paper, we complement this forward algorithm with its inverse: a systematic, fast method to deduce the elevation-distance profile from either the observed fan topography or just its perimeter curve. Using the visibility polygon, the method maps the shortest path distance from the apex to all observation points, taking obstacles into account. We then fit a quadratic function to the resulting elevation-distance data pairs, processed using a median filter. For synthetic fan surfaces produced by the forward algorithm, we check that the inverse method precisely recovers the assumed elevation-distance curve, to within numerical error. We then extract empirical relations between elevation and shortest path distance from actual fan surfaces in Italy and Taiwan, and show that they provide a better approximation of fan topography than the relations between elevation and direct distance assumed in previous works.