Valley incision by debris flows: Evidence of a topographic signature

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Abstract
The sculpture of valleys by flowing water is widely recognized, and simplified models of incision by this process (e.g., the stream power law) are the basis for most recent landscape evolution models. Under steady state conditions a stream power law predicts that channel slope varies as an inverse power law of drainage area. Using both contour maps and laser altimetry, we find that this inverse power law rarely extends to slopes greater than ∼0.03 to 0.10, values below which debris flows rarely travel. Instead, with decreasing drainage area the rate of increase in slope declines, leading to a curved relationship on a log‐log plot of slope against drainage area. Fieldwork in the western United States and Taiwan indicates that debris flow incision of bedrock valley floors tends to terminate upstream of where strath terraces begin and where area‐slope data follow fluvial power laws. These observations lead us to propose that the steeper portions of unglaciated valley networks of landscapes steep enough to produce mass failures are predominately cut by debris flows, whose topographic signature is an area‐slope plot that curves in log‐log space. This matters greatly as valleys with curved area‐slope plots are both extensive by length (>80% of large steepland basins) and comprise large fractions of main stem valley relief (25–100%). As a consequence, valleys carved by debris flows, not rivers, bound most hillslopes in unglaciated steeplands. Debris flow scour of these valleys appears to limit the height of some mountains to substantially lower elevations than river incision laws would predict, an effect absent in current landscape evolution models. We anticipate that an understanding of debris flow incision, for which we currently lack even an empirical expression, would substantially change model results and inferences drawn about linkages between landscape morphology and tectonics, climate, and geology.