Sediment disentrainment and the concept of local versus nonlocal transport on hillslopes

A local formulation of the sediment flux on a hillslope describes the flux as a unique function of local hillslope conditions at any contour position x, whereas a nonlocal formulation must take into account nonlocal (upslope or downslope) conditions that influence the flux at x. Local formulations are reasonable when particle motions involve small length scales associated with localized bioturbation of the soil column or with proximal surface transport such as rain splash. Nonlocal formulations may be more appropriate in steeplands where patchy, intermittent motions involve large travel distances, mostly over the surface. Once sediment motions are initiated, the disentrainment process determines the distribution of particle travel distances, which, in turn, forms the basis of nonlocal formulations that involve a convolution of hillslope surface conditions, for example, the land-surface slope. The kernel in the convolution integral, which weights the effect of land-surface conditions (e.g., slope) at all positions upslope or downslope of x, derives from the formulation of the disentrainment rate and characterizes whether particle travel distances depend on conditions at the position where motions originate or vary as particles experience changing surface conditions during their downslope motions. If hillslope properties controlling transport (e.g., surface slope) are defined or measured at a specified resolution, then motions smaller than this resolution cannot be attributed to these properties resolved at a smaller scale. In essence, the relative importance of local and nonlocal transport depends on the scale of particle motions compared to the relevant scale of hillslope properties that drive transport.