### Conceptual Description of Transport Processes by Hopping  
Laboratory experiments have not only been essential in developing empirical bed load equations, but they have also been used to clarify some of the more detailed processes and mechanics in sediment transport from near above-threshold to higher solids transport flow conditions [16; 17; 18]. As mentioned before, the dominant mode of bed load transport is saltation, characterized by particle hops or bounces along the bed surface. This is due to the action of hydrodynamic forces exceeding the resisting component of its submerged weight. A typical demonstration for particles laying in a bed surface of slope \(\alpha\), transported by saltation a range of particle packings and local arrangements and hinderance from surrounding particles, is given in Figure 2. Sediment motion is initially driven by almost impulsive turbulent flow events (\(\mathrm{I_{i}}\)), making the particle ascend for a certain distance (from a fraction of its diameter to a lengthscale comparable to its diameter), and then descend towards the bed surface, under the action of gravity, eventually ceasing its motion after one or more collisions with the particles comprising the bed surface [12]. Sediment movement (number of hops and individual hop characteristics) is controlled by the particle's collisions with the bed surface and driven by the resultant force, which comprises the component of the submerged particle's weight (\(\mathrm{W_{sub}}\)), and hydrodynamic drag (\(\mathrm{F_{D}}\)) and lift (\(\mathrm{F_{L}}\)) force components, orthogonal to the particle's local coordinate system centered at its center of mass [20; 21]. The almost impulsive [22] kick offered by the turbulent flow event towards pushing a particle out of its pocket by saltation is the temporal integral of the total force acting on the particle, for the duration where the driving hydrodynamic (combination of drag and lift) forces exceed the resisting forces (component of the submerged particle's weight), as shown in Figure 2. For the case of a fully exposed particle, the hydrodynamic drag has a greater potential of resulting in an incipient entrainment (for a coarse particle, see green colored particle in Figure 2). The applied drag force, \(\mathrm{F_{D}}\), can be estimated by the classical quadratic local flow velocity parameterization or as a function of the pressure differential between the upstream and downstream face of the particle, \(\mathrm{F_{D}}=(\Delta\mathrm{P_{h}})\). Aparticle, where Aparticle is the particle area projected on a plane perpendicular to the streamwise flow direction and \(\Delta\mathrm{P_{h}}\) is the pressure difference between the particle's upstream and downstream face [23]. For the fully exposed particle arrangement, Aparticle is about 87% of the area of the particle's cross-section, because of limited partial blockage by the upstream base particles. For greater ranges of partial hinderance (e.g., orange colored particle), this percentage will reduce all the way to zero for the case of fully buried particles (red colored particle, Figure 2). For the latter case, the impulsively applied lift force (\(\mathrm{F_{L}}\)) is the driving force to lift the particle above its pocket, whenever it exceeds the submerged component of its weight. Hydrodynamic lift can be estimated as the pressure difference between the bottom and the top of the particle (\(\Delta\mathrm{P_{v}}\)) because of the velocity gradient near the bed surface, as \(\mathrm{F_{L}}=(\Delta\mathrm{P_{v}}-\varrho\mathrm{gD}\cos\alpha)\) Aparticle, in which Aparticle \(=\pi\mathrm{D^{2}}/4\) is the particle area projected on a plane along the bed surface, and \(\varrho\mathrm{gD}\) is the difference in hydrostatic pressure between the top and bottom of the particle [24; 25; 26; 27]. In the case of a partially buried particle, which is the common case for loosely packed sediment particles (e.g., shown in orange color, Figure 2), a combination of drag and lift forces may contribute to the particle's saltation.