We examine relations for hydraulic geometry of alluvial, single‐thread gravel bed rivers with definable bankfull geometries. Four baseline data sets determine relations for bankfull geometry, i.e., bankfull depth, bankfull width, and down‐channel slope as functions of bankfull discharge and bed surface median sediment size. These relations show a considerable degree of universality. This universality applies not only within the four sets used to determine the forms but also to three independent data sets as well. We study the physical basis for this universality in terms of four relations, the coefficients and exponents of which can be back calculated from the data: (1) a Manning‐Strickler‐type relation for channel resistance, (2) a channel‐forming relation expressed in terms of the ratio of bankfull Shields number to critical Shields number, (3) a relation for critical Shields number as a function of dimensionless discharge, and (4) a “gravel yield” relation specifying the (estimated) gravel transport rate at bankfull flow as a function of bankfull discharge and gravel size. We use these underlying relations to explore why the dimensionless bankfull relations are only quasi‐universal and to quantify the degree to which deviation from universality can be expected. The analysis presented here represents an alternative to extremal formulations to predict hydraulic geometry.
The Shields and the Isbash equations for predicting the stability of rocks exposed to a turbulent flow were both proposed in 1936, and since then, both equations have been used widely in the analysis of transport thresholds for coarse sediment. These two equations were obtained using two very different approaches, but as demonstrated in this paper, the equation developed by Isbash is consistent with the relation formulated by Shields for predicting the motion of sediments either in the flume or in the field. Comparison of the two equations suggests that standard approaches tend to oversize riprap in mountain streams.
Abstract Analysis of hillslope gradient, landscape relief, and channel steepness in the Daxia River basin provides evidence of a transient geomorphic response to base‐level fall on the northeastern Tibetan Plateau. Low‐gradient channels and gentle hillslopes of the upper watershed are separated from a steeper, high‐relief landscape by a series of convex knickzones along channel longitudinal profiles. Downstream projection of the “relict” portions of the profiles implies ~800–850 m of incision, consistent with geologic and geomorphic records of post ~1.7 Ma incision in the lower watershed. We combine optically stimulated luminescence dating of fluvial terrace deposits to constrain incision rates downstream of knickpoints with catchment‐averaged 10 Be concentrations in modern sediment to estimate erosion rates in tributary basins both above and below knickpoints. Both sources of data imply landscape lowering rates of ~300 m Ma −1 below the knickpoint and ~50–100 m Ma −1 above. Field measurements of channel width ( n = 48) and calculations of bankfull discharge ( n = 9) allow determination of scaling relations among channel hydraulic geometry, discharge, and contributing area that we employ to estimate the patterns of basal shear stress, unit stream power, and bed load transport rate throughout the channel network. Our results imply a clear downstream increase of incision potential; this result would appear to be consistent with a detachment‐limited response to imposed base‐level fall, in which steepening of channels drives an increase in erosion rates. In contrast, however, we do not observe apparent narrowing of channels across the transition from slowly eroding to rapidly eroding portions of the watershed. Rather, the present‐day channel morphology as well as its scaling of hydraulic geometry imply that the river is primarily adjusted to transport its sediment load and suggest that channel morphology may not always reflect the presence of knickpoints and differences in landscape relief.
Abstract This study investigated spatial‐temporal variations of shear stress and bed load transport at three gravel bed river reaches of the Williams Fork River, Colorado. A two‐dimensional flow model was used to compute spatial distributions of shear stress ( τ ) for four discharge levels between one third of bankfull ( Q bf ) and Q bf . Results indicate that mean τ values are highly variable among sites. However, the properties of the mean‐normalized distributions of τ are similar across sites for all flows. The distributions of τ are then used with a transport function to compute bed load transport rates of individual grain size fractions. Probability distributions of the instantaneous unit‐width transport rates, q b , indicate that most of the bed load is transported through small portions of the bed with high τ . The mean‐normalized probability distributions of q b are different among sites for all flows except at Q bf , when the distributions overlap. We also find that the grain size distribution (GSD) of the bed load adjusts with discharge to resemble the grain size distribution of the subsurface at Q bf . We extend these results to 13 locations in the basin, using the mean‐normalized distributions of shear stress and measured subsurface grain sizes to compute bed load transport rates at Q bf . We found a remarkably similar shape of the q b distribution among sites highlighting the basin‐wide balance between flow forces and GSD at Q bf and the potential to predict sediment flux at the watershed scale.
Stream depletion is the reduction in flow rate in a stream due to pumping in an aquifer that is hydraulically connected to the stream. We developed a semianalytical expression for stream depletion for pumping in a homogeneous aquifer, with an infinitely long, straight stream with a streambed conductance, C, that varies cosinusoidally in space and time in the range CL≤C≤CH. The wavelength of the spatial variations is equal to twice the distance between adjacent pools in a pool and riffle sequence, and the period of the temporal fluctuations represents alternating high and low flows. These spatiotemporal variations in streambed conductance produce temporal fluctuations of stream depletion superimposed on a trend that increases at a decreasing rate. Certain combinations of streambed and aquifer hydraulic parameters lead to exaggerated stream depletion, in which the temporally fluctuating stream depletion is not bracketed by the amount that would be obtained with steady, homogeneous streambed conductance of CL and CH. After sufficient time has passed, the same parameter sets produce excessive stream depletion, in which stream depletion exceeds the pumping rate at certain times. The degree of exaggerated stream depletion increases with the distance between pools, and is high if the temporal period of fluctuation matches the times of high rate of change of stream depletion.
Abstract Global compilations of river sediment loads show that mountainous areas produce a high proportion of the sediment transported to the oceans. However, because of the effort involved in measuring sediment fluxes in mountain river systems, the loads of these rivers are generally unknown. Here, we present estimates of contemporary sediment loads of 16 gravel bed rivers draining the Ecrins‐Pelvoux Massif in southeast France. Sediment production in this part of the Alps is relatively high and many river segments are either wandering or braided. We model sediment fluxes and annual sediment yields by coupling hydraulic‐based relations for sediment transport with hydrologic‐based relations for flow frequency. Bed load fluxes are modeled for a range of discharges using a function that relates transport rates to excess shear stress. Fluxes are then weighted by the frequency of individual discharges and summed to get the annual bed load for each site. The suspended load is estimated empirically as a fraction of the bed load. Results suggest that bed load fluxes at channel‐forming flows scale almost linearly with downstream increases in discharge. In addition, it appears that annual sediment loads (bed load + suspended load) scale linearly with drainage area. A complementary relation for specific sediment yield suggests that the load per unit drainage area is constant across the range of basins studied. The modeled sediment yields are comparable to previous field‐based estimates of modern sediment yields, and generally lower than estimates developed from analyses of cosmogenic radionuclides.
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