Macro-roughness model of bedrock-alluvial river morphodynamics

Abstract

Abstract. The 1-D saltation-abrasion model of channel bedrock incision of Sklar and Dietrich, in which the erosion rate is buffered by the surface area fraction of bedrock covered by alluvium, was a major advance over models that treat river erosion as a function of bed slope and drainage area. Their model is, however, limited because it calculates bed cover in terms of bedload sediment supply rather than local bedload transport. It implicitly assumes that as sediment supply from upstream changes, the transport rate adjusts instantaneously everywhere downstream to match. This assumption is not valid in general, and thus can give rise unphysical consequences. Here we present a unified morphodynamic formulation of both channel incision and alluviation which specifically tracks the spatiotemporal variation of both bedload transport and alluvial thickness. It does so by relating the cover fraction not to a ratio of bedload supply rate to capacity bedload transport, but rather to the ratio of alluvium thickness to a macro-roughness characterizing the bedrock surface. The new formulation predicts waves of alluviation and rarification, in addition to bedrock erosion. Embedded in it are three physical processes: alluvial diffusion, fast downstream advection of alluvial disturbances and slow upstream migration of incisional disturbances. Solutions of this formulation over a fixed bed are used to demonstrate the stripping of an initial alluvial cover, the emplacement of alluvial cover over an initially bare bed and the advection–diffusion of a sediment pulse over an alluvial bed. A solution for alluvial-incisional interaction in a channel with a basement undergoing net rock uplift shows how an impulsive increase in sediment supply can quickly and completely bury the bedrock under thick alluvium, so blocking bedrock erosion. As the river responds to rock uplift or base level fall, the transition point separating an alluvial reach upstream from an alluvial-bedrock reach downstream migrates upstream in the form of a "hidden knickpoint". A solution for the case of a zone of rock subsidence (graben) bounded upstream and downstream by zones of rock uplift (horsts) yields a steady-state solution that is unattainable with the original saltation-abrasion model. A solution for the case of bedrock-alluvial coevolution upstream of an alluviated river mouth illustrates how the bedrock surface can be progressive buried not far below the alluvium. Because the model tracks the spatiotemporal variation of both bedload transport and alluvial thickness, it is applicable to the study of the incisional response of a river subject to temporally varying sediment supply. It thus has the potential to capture the response of an alluvial-bedrock river to massive impulsive sediment inputs associated with landslides or debris flows.

Landscape evolution models using the stream power incision model show unrealistic behavior when <i>m</i> ∕ <i>n</i> equals 0.5

“…While scientific questions remain that can be answered with the stream power incision model, there are many more questions that require a more advanced formulation (e.g., Gasparini et al, 2007;Crosby et al, 2007;Egholm et al, 2013). The development of alternative, more physically based models for incision (e.g., Sklar and Dietrich, 2004;Lague, 2014;Zhang et al, 2015) and their application to landscape evolution (e.g., Davy and Lague, 2009;Gasparini et al, 2006Gasparini et al, , 2007 offer exciting prospects for the future.…”

“…Gilbert (1877) theorized two roles that sediment moving as bed load could play in bedrock incision: the first as an abrasive agent that incises the bed via collisions and the second as a protector that inhibits collisions of bed load on the bed. These observations have been implemented quantitatively by many modelers (e.g., Sklar and Dietrich, 2001Lamb et al, 2008;Zhang et al, 2015), some of whom have implemented them in LEMs (e.g., Gasparini et al, 2006Gasparini et al, , 2007. Egholm et al (2013) have directly compared landscape models using SPIM on the one hand and models using a saltation-abrasion model on the other hand.…”

A probabilistic framework for the cover effect in bedrock erosion

“…Inoue et al, 2014), with theoretical approaches also providing some direction (cf. Johnson, 2014;Zhang et al, 2015). Currently available experimental results (Chatanantavet and Parker, 2008;Finnegan et al, 2007;Hodge and Hoey, 2016;Inoue et al, 2014;Johnson and Whipple, 2007) cover only a small range of the possible parameter space, and, in general, not all necessary parameters to constrain P were reported.…”

“…Nelson and Seminara, 2011;Zhang et al, 2015). To achieve this, the dependency of P on various control parameters needs to be specified.…”

“…Seminara (2011, 2012) were one of the first to model the impact that the differing roughness of bedrock and alluvial areas has on sediment patch stability. Zhang et al (2015) formulated a macro-roughness cover model, in which sediment cover is related to the ratio of sediment thickness to bedrock macro-roughness. Aubert et al (2016) directly simulated the dynamics of particles in a turbulent flow and obtained both linear and exponential cover functions.…”