Quantifying nonlocal bedload transport: A regional-based nonlocal model for bedload transport from local to global scales

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Recent studies have emphasized the importance of nonlocal models in characterizing bedload transport in natural rivers, particularly in mixed-size gravel beds or steep hillslopes. Nonlocality denotes that a quantity (flux) at a specific location x is dependent on the conditions in the surrounding area, as opposed to solely at the location itself. This concept applies in bedload transport even in planar flumes, where particles are entrained at an upstream position and travel a finite distance, ultimately contributing nonlocally to the sediment flux. However, existing bedload transport models, such as the advection–diffusion equation (ADE) or the fractional derivative equation (FDE) models, are inadequate in characterizing the nonlocal transport behavior of bedload at a regional scale. Large errors may arise from the lack of an accurate description of the nonlocal bedload transport processes at regional scales. This study proposes a regional-based nonlocal bedload transport model, which is conceptualized from the probabilistic Exner-based equations and the peridynamic (PD) differential operator. The PD model encapsulates the nonlocal motion of bedload sediments on the basis of the PD differential operator, by utilizing a pre-defined weight function and influence domain. Comparisons demonstrate that the PD model serves as a generalized tool connecting the local and the global models with different PD functions and influence domains. Its variability on kernel function and influence domain, enable it conveniently describe sub-, super-, and normal diffusion behaviors of bedload transport.