[1] Recent studies have observed deviation from normal (Fickian) diffusion in sediment tracer dispersion that violates the assumption of statistical convergence to a Gaussian. Nikora et al. (2002) hypothesized that particle motion at short time scales is superdiffusive because of inertia, while long-time subdiffusion results from heavy-tailed rest durations between particle motions. Here we test this hypothesis with laboratory experiments that trace the motion of individual gravels under near-threshold intermittent bed load transport (0.027 < t* < 0.087). Particle behavior consists of two independent states: a mobile phase, in which indeed we find superdiffusive behavior, and an immobile phase, in which gravels distrained from the fluid remain stationary for long durations. Correlated grain motion can account for some but not all of the superdiffusive behavior for the mobile phase; invoking heterogeneity of grain size provides a plausible explanation for the rest. Grains that become immobile appear to stay at rest until the bed scours down to an elevation that exposes them to the flow. The return time distribution for bed scour is similar to the distribution of rest durations, and both have power law tails. Results provide a physical basis for scaling regimes of anomalous dispersion and the time scales that separate these regimes.

Field data show insensitivity of particle trajectories to wind speed and support linear scaling of sand flux with wind stress.

[1] Field and laboratory studies indicate that changes in riverbed morphology often lag changes in water discharge. This lagged response produces hysteresis in the relationship between water discharge and bed form geometry. To understand these phenomena, we performed flume experiments to observe the response of a sand bed to step increases and decreases in water discharge. For an abrupt rise in discharge, we observed that bed forms grew rapidly by collision and merger of bed forms migrating with different celerities. Growth rate slowed as bed forms approached equilibrium with the higher discharge regime. After an abrupt discharge drop, bed form decay occurred through formation of smaller secondary bed forms, in equilibrium with the lower discharge, which cannibalized the original, relict features. We present a simple model framework to quantitatively predict time scales of bed form adjustment to flow changes, based on equilibrium bed form heights, lengths, and celerities at low and high flows. For rising discharge, the model assumes that all bed form collisions result in irreversible merger, due to a dispersion of initial celerities. For falling discharge, we derive a diffusion model for the decay of relict high-stage features. Our models predict the form and time scale of experimental bed form adjustments. Additional experiments applying slow and fast triangular flood waves show that bed form hysteresis occurs only when the time scale of flow change is faster than the modeled (and measured) bed form adjustment time. We show that our predicted adjustment time scales can also be used to predict the occurrence of bed form hysteresis in natural floods.

[1] Hyporheic flow in streams has typically been studied separately from geomorphic processes. We investigated interactions between bed mobility and dynamic hyporheic storage of solutes and fine particles in a sand-bed stream before, during, and after a flood. A conservatively transported solute tracer (bromide) and a fine particles tracer (5 mm latex particles), a surrogate for fine particulate organic matter, were co-injected during base flow. The tracers were differentially stored, with fine particles penetrating more shallowly in hyporheic flow and retained more efficiently due to the high rate of particle filtration in bed sediment compared to solute. Tracer injections lasted 3.5 h after which we released a small flood from an upstream dam one hour later. Due to shallower storage in the bed, fine particles were rapidly entrained during the rising limb of the flood hydrograph. Rather than being flushed by the flood, we observed that solutes were stored longer due to expansion of hyporheic flow paths beneath the temporarily enlarged bedforms. Three important timescales determined the fate of solutes and fine particles: (1) flood duration, (2) relaxation time of flood-enlarged bedforms back to base flow dimensions, and (3) resulting adjustments and lag times of hyporheic flow. Recurrent transitions between these timescales explain why we observed a peak accumulation of natural particulate organic matter between 2 and 4 cm deep in the bed, i.e., below the scour layer of mobile bedforms but above the maximum depth of particle filtration in hyporheic flow paths. Thus, physical interactions between bed mobility and hyporheic transport influence how organic matter is stored in the bed and how long it is retained, which affects decomposition rate and metabolism of this southeastern Coastal Plain stream. In summary we found that dynamic interactions between hyporheic flow, bed mobility, and flow variation had strong but differential influences on base flow retention and flood mobilization of solutes and fine particulates. These hydrogeomorphic relationships have implications for microbial respiration of organic matter, carbon and nutrient cycling, and fate of contaminants in streams.Citation: Harvey, J. W., et al. (2012), Hydrogeomorphology of the hyporheic zone: Stream solute and fine particle interactions with a dynamic streambed,

[1] Sediment transport is an intrinsically stochastic process, and measurement of bed load in the environment is further complicated by the unsteady nature of river flooding. Here we present a methodology for analyzing sediment tracer data with unsteady forcing. We define a dimensionless impulse by integrating the cumulative excess shear velocity for the duration of measurement, normalized by grain size. We analyze the dispersion of a plume of cobble tracers in a very flashy stream over two years. The mean and variance of transport distance collapse onto well-defined linear and power-law relations, respectively, when plotted against cumulative dimensionless impulse. Data suggest that the asymptotic limit of bed load tracer dispersion is superdiffusive, in line with a broad class of geophysical flows exhibiting strong directional asymmetry (advection), thin-tailed step lengths and heavy-tailed waiting times. The impulse framework justifies the use of quasi-steady flow approximations for long-term river evolution modeling.