Bed load transport is a highly stochastic, multiscale process, where particle advection and diffusion regimes are governed by the dynamics of each sediment grain during its motion and resting states. Having a quantitative understanding of the macroscale behavior emerging from the microscale interactions is important for proper model selection in the absence of individual grain-scale observations. Here we develop a semimechanistic sediment transport model based on individual particle dynamics, which incorporates the episodic movement (steps separated by rests) of sediment particles and study their macroscale behavior. By incorporating different types of probability distribution functions (PDFs) of particle resting times Tr, under the assumption of thin-tailed PDF of particle velocities, we study the emergent behavior of particle advection and diffusion regimes across a wide range of spatial and temporal scales. For exponential PDFs of resting times Tr, we observe normal advection and diffusion at long time scales. For a power-law PDF of resting times (i.e., f(Tr)Tr-ν), the tail thickness parameter ν is observed to affect the advection regimes (both sub and normal advective), and the diffusion regimes (both subdiffusive and superdiffusive). By comparing our semimechanistic model with two random walk models in the literature, we further suggest that in order to reproduce accurately the emerging diffusive regimes, the resting time model has to be coupled with a particle motion model able to produce finite particle velocities during steps, as the episodic model discussed here.
Bibliographical noteFunding Information:
Financial support from National Natural Science Foundation of China (51509172, 51539007), Science Project of China (2012BAB05B02), Sichuan University (2015SCU11046), and support from the U.S. National Science Foundation (NSF) under a Water Sustainability and Climate project (grant CBET 1209402), as well as an International Research project (LIFE: NSF grant EAR 1242458) are gratefully acknowledged. The first author received a fellowship from the China Scholarship Council. All the simulated data in this paper can be requested from the authors
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- episodic Langevin equation
- resting time