A sub-grid scale closure for nonlinear hillslope sediment transport models

[1] Hillslope sediment transport models express the sediment flux at a point as a function of some topographic attributes of the system, such as slope, curvature, soil thickness, etc., at that point only (referred here as “local” transport models) or at an appropriately defined vicinity of that point (referred here as “nonlocal” transport models). Typically, topographic attributes are computed from digital elevation data (DEMs) and thus their estimates depend on the DEM resolution (1 m, 10 m, 90 m, etc.) rendering any sediment flux computation scale-dependent. Often calibration compensates for this scale-dependence resulting in effective parameterizations with limited physical meaning. In this paper, we demonstrate the scale-dependence of local nonlinear hillslope sediment flux models and derive a subgrid scale closure via upscaling. We parameterize the subgrid scale closure in terms of the low resolution, resolved topographic attributes of the landscape, thus allowing the reliable computation of a scale-independent sediment flux from low resolution digital elevation data. We also show that the accuracy of the derived subgrid scale closure model depends on the dimensionless erosion rate and the dimensionless relief of any given basin. Finally, we present theoretical arguments and demonstrate that the recently proposed nonlocal sediment flux models are scale-independent. These concepts are demonstrated via an application on a small basin (MR1) of the central Oregon Coast Range using high-resolution lidar topographic data.