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Erosion of steepland valleys by debris flows

Jonathan D. Stock^,1 and William E. Dietrich²

¹ U.S. Geological Survey, Menlo Park, California, USA
² Earth and Planetary Science, University of California, Berkeley, California, USA

Episodic debris flows scour the rock beds of many steepland valleys. Along recent debris-flow runout paths in the western United States, we have observed evidence for bedrock lowering, primarily by the impact of large particles entrained in debris flows. This evidence may persist to the point at which debris-flow deposition occurs, commonly at slopes of less than 0.03–0.10. We find that debris-flow–scoured valleys have a topographic signature that is fundamentally different from that predicted by bedrock river-incision models. Much of this difference results from the fact that local valley slope shows a tendency to decrease abruptly downstream of tributaries that contribute throughgoing debris flows. The degree of weathering of valley floor bedrock may also decrease abruptly downstream of such junctions. On the basis of these observations, we hypothesize that valley slope is adjusted to the long-term frequency of debris flows, and that valleys scoured by debris flows should not be modeled using conventional bedrock river-incision laws. We use field observations to justify one possible debris-flow incision model, whose lowering rate is proportional to the integral of solid inertial normal stresses from particle impacts along the flow and the number of upvalley debris-flow sources. The model predicts that increases in incision rate caused by increases in flow event frequency and length (as flows gain material) downvalley are balanced by rate reductions from reduced inertial normal stress at lower slopes, and stronger, less weathered bedrock. These adjustments lead to a spatially uniform lowering rate. Although the proposed expression leads to equilibrium long-profiles with the correct topographic signature, the crudeness with which the debris-flow dynamics are parameterized reveals that we are far from a validated debris-flow incision law. However, the vast extent of steepland valley networks above slopes of 0.03–0.10 illustrates the need to understand debris-flow incision if we hope to understand the evolution of steep topography around the world.

Key Words: geomorphology • erosion • debris flows • river incision • landscape evolution

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