The Relation of Variability in Sand Bed Topography to Sediment Transport

The estimation of bed material flux by comparing successive bathymetric surveys was developed under a deterministic light. However, an analogous stochastic treatment can be straightforwardly cast as an extension to the original bedload equation. Instead of an analysis that presumes a regular, geometrically defined bed topography, this accepts the natural noisiness of sandy systems and uses it to explicitly calculate sediment flux. Further, the sediment flux can be treated as the sum of 2 components, a translative flux and a deformative flux. The terminology for these two parts is explicitly related to their relative impacts on the bed. Because the translational part is exactly the same as the original, deterministic model, it estimates only the flux that advects the bed topography. In contrast, the deformational part encompasses all of the remaining bed material flux, the component that serves to change the shape or arrangement of the bed topography. Also, the deformative flux is constant of integration obtained a from manipulation of Exner's equation into average flux; this has been assumed null since the inception of the bedload equation. Analysis of data from the N. Loup River, Nebraska, show that the ratio of deformative to translative fluxes is constant over relevant timescales. The consequences of this are twofold. First, the amount of deformation can be directly calculated and the associated estimates of moved sediment volume are valid as the bed translates many characteristic lengths. In this case the Qtotal=1.8*Qtranslative. Second, it suggests that the fraction of deformation can be explicitly related to the characteristic length of beds. If true, it would greatly improve estimates of flux for all sandy systems and not just those for which extensive amounts of data have been collected.