Exploring a Two-Dimensional Nonlocal Description of the Hillslope Sediment Flux

Abstract:

Landscape evolution models can be used to highlight signatures of particular sediment transport processes or formulae. In particular, there has been an increasing interest in exploring the merits of using nonlocal descriptions of sediment transport in steeplands. To date, all modeling efforts that make use of a nonlocal description are one-dimensional. Although this is effective at highlighting essential characteristics and behaviors of nonlocal transport, one-dimensional hillslopes (planar in planform) are rare, and thus these models apply to a limited part of the landscape. In an effort to further explore impacts of nonlocal transport, we have developed an algorithm for two-dimensional topography that can make use of nonlocal transport formulae. This algorithm therefore increases the type of topography against which formulae may be evaluated, and brings insight into new metrics such as plan-form curvature. Furthermore, this algorithm offers an opportunity to explore transport variables as a function of contributing area as opposed to just land-surface slope and position.

A nonlocal formulation uses a convolution integral of upslope positions to determine the sediment flux at a particular position. Applying such a description to all positions within even a small watershed is computationally expensive. An efficient way to do this, however, is to calculate the flux along flow tubes. To determine the land-surface evolution we use a mass-conserving entrainment form of the Exner equation which takes the difference between the amount of sediment entrained and deposited within a given element. Significant challenges exist in terms of identifying flow paths, treating flow tube boundaries, identifying the flow lines for all contributing areas, and identifying ridges. We apply this algorithm to a set of idealized topographies in order to observe essential characteristics and to determine metrics which may be used to describe the characteristics of real topography.