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Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $$\sim$$ 1.5 for the initial regime and $$\sim$$ 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements. 

Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outletlocations. We designed a suite of direction-predicting algorithms (DPAs),each of which exploits a particular morphologic characteristic of thechannel network to provide a prediction of a link's flow direction. DPAswere chained together to create “recipes”, or algorithms that set all theflow directions of a channel network. Separate recipes were built for deltasand braided rivers and applied to seven delta and two braided river channelnetworks. Across all nine channel networks, the recipe-predicted flowdirections agreed with expert judgement for 97 % of all tested links, andmost disagreements were attributed to unusual channel network topologiesthat can easily be accounted for by pre-seeding critical links with knownflow directions. Our results highlight the (non)universality ofprocess–form relationships across deltas and braided rivers.