Jens M. Turowski

Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology

The sediment load of a bedrock river plays an important role in the fluvial incision process by providing tools for abrasion (the tools effect) and by covering and thereby protecting the bed (the cover effect). We derive a new formulation for the cover effect, in which the fraction of exposed bed area falls exponentially with increasing sediment flux or decreasing transport capacity, and explore its consequences for the model of bedrock abrasion by saltating bed load. Erosion rates predicted by the model are higher than those predicted by earlier models. In a closed system, the maximum erosion rate is predicted to occur when sediment supply is equal to transport capacity for a flat bed. By optimizing the channel geometry to minimize the potential energy of the stream and using representative values for both discharge and grain size, we derive equations for the geometry of a bedrock river and explore how predictions for width, slope, and bed cover vary as functions of drainage area, rock uplift rate, and rock strength. The equations predict a dependence of channel width on drainage area similar to the relations using a simple shear stress incision law. The slope-area relationship is predicted to be concave up in a log-log regime, with a curvature dependent on uplift rate. However, this curvature does not deviate sufficiently from a straight line to allow discrimination between models using empirical data. Dependence of channel width and slope on rock uplift rate can be separated into two domains: for low uplift rates, channel geometry is largely insensitive to uplift rate due to a threshold effect. At high uplift rates, there is a power law dependence. Bed cover is predicted to increase progressively downstream and to increase with increasing uplift rate. In our model, the width-to-depth ratio is a function of both tectonic and climatic forcing. This indicates that the scaling between channel width and bed slope is neither a unique indicator of tectonic forcing at steady state nor a signature of transience or steady state. We conclude that sediment effects need to be taken into account when modeling bedrock channel morphology.

Response of bedrock channel width to tectonic forcing: Insights from a numerical model, theoretical considerations, and comparison with field data

The morphology of bedrock river channels is controlled by climatic and tectonic conditions and substrate properties. Knowledge of tectonic controls remains scarce. This is partly due to slow tectonic rates and long response times of natural channels and partly due to the difficulty in isolating and constraining tectonic forcing conditions in the field. To study the effect of tectonic forcing on channel geometry, we have developed a numerical model of the cross-sectional evolution of a detachment-limited channel. Its predictions are matched by an analytical model based on the assumption of the minimization of potential energy expenditure. Using these models, we illustrate how local tectonics can alter the observed width-discharge scaling and discuss published field data in light of our findings. Except for one case, the models fail to correctly describe field observations of well-constrained cases. This implies that the shear stress/stream-power family of models is too simple to describe the behavior of natural channels. Additional complexities such as sediment effects and discharge variability exert a strong control on channel morphology and need to be taken into account in the modeling of channel dynamics and steady state.

Bedload transport measurements with impact plate geophones: comparison of sensor calibration in different gravel-bed streams

Indirect bedload transport measurements have been made with the Swiss plate geophone system in five gravel-bed mountain streams. These geophone sensors record the motion of bedload particles transported over a steel plate mounted flush with the channel bed. To calibrate the geophone system, direct bedload transport measurements were undertaken simultaneously. At the Erlenbach in Switzerland, a moving-basket sampler was used. At the Fischbach and Ruetz streams in Austria, a Helley–Smith type bedload sampler provided the calibration measurements. A Bunte-type bedload trap was used at the Rofenache stream in Austria. At the Nahal Eshtemoa in Israel, Reid-type slot bedload samplers were used. To characterize the response of the geophone signal to bedload particles impacting on the plate, geophone summary values were calculated from the raw signal and stored at one second intervals. The number of impulses, i.e. the number of peaks above a pre-defined threshold value of the geophone output signal, correlated well with field measured gravel transport loads and was found to be a robust parameter. The relations of impulses to gravel transport loads were generally near-linear, but the steepness of the calibration relations differed from site to site. By comparing the calibration measurements from the different field sites and utilizing insights gained during preliminary flume experiments, it has been possible to identify the main factors that are responsible for site specific differences in the calibration coefficient. The analysis of these calibration measurements indicates that the geophone signal also contains some information about the grain size distribution of bedload.

Scaling relationships between bed load volumes, transport distances, and stream power in steep mountain channels

Bed load transport during storm events is both an agent of geomorphic change and a significant natural hazard in mountain regions. Thus, predicting bed load transport is a central challenge in fluvial geomorphology and natural hazard risk assessment. Bed load transport during storm events depends on the width and depth of bed scour, as well as the transport distances of individual sediment grains. We traced individual gravels in two steep mountain streams, the Erlenbach (Switzerland) and Rio Cordon (Italy), using magnetic and radio frequency identification tags, and measured their bed load transport rates using calibrated geophone bed load sensors in the Erlenbach and a bed load trap in the Rio Cordon. Tracer transport distances and bed load volumes exhibited approximate power law scaling with both the peak stream power and the cumulative stream energy of individual hydrologic events. Bed load volumes scaled much more steeply with peak stream power and cumulative stream energy than tracer transport distances did, and bed load volumes scaled as roughly the third power of transport distances. These observations imply that large bed load transport events become large primarily by scouring the bed deeper and wider, and only secondarily by transporting the mobilized sediment farther. Using the sediment continuity equation, we can estimate the mean effective thickness of the actively transported layer, averaged over the entire channel width and the duration of individual flow events. This active layer thickness also followed approximate power law scaling with peak streampower and cumulative stream energy and ranged up to 0.57min the Erlenbach, broadly consistent with independent measurements.

Applicability of bed load transport models for mixed‐size sediments in steep streams considering macro‐roughness

In steep mountain streams, macro-roughness elements typically increase both flow energy dissipation and the threshold of motion compared to lower-gradient channels, reducing the part of the flow energy available for bed load transport. Bed load transport models typically take account of these effects either by reducing the acting bed shear stress or by increasing the critical parameters for particle entrainment. Here we evaluate bed load transport models for mixed-size sediments and models based on a median grain size using a large field data set of fractional bed load transport rates. We derive reference shear stresses and bed load transport relations based on both the total boundary shear stress and a reduced (or “effective”) shear stress that accounts for flow resistance due to macro-roughness. When reference shear stresses are derived from the total boundary shear stress, they are closely related to channel slope, but when they are derived from the effective shear stress, they are almost invariant with channel slope. The performance of bed load transport models is generally comparable when using the total shear stress and a channel slope-related reference shear stress, or when using the effective shear stress and a constant reference shear stress. However, dimensionless bed load transport relations are significantly steeper for the total stress approach, whereas they are similar to the commonly used fractional Wilcock and Crowe (WC) transport model for the effective stress approach. This similarity in the relations allows the WC model, developed for lower-gradient streams, to be used in combination with an effective shear stress approach, in steep mountain streams.

Measuring the Statistics of Bed-Load Transport Using Indirect Sensors

Several indirect methods have been proposed to measure bed-load transport rates. We analyze the relationships between bed-load transport rates, water discharge, and sensor response and determine what can and what cannot be measured with such sensors. We argue that indirect sensors are in most cases unsuitable to develop a rating curve of bed-load transport rates. Instead, they can be used to estimate sediment yields of individual events as proposed previously. We develop a method to estimate the standard deviations of transport rates and apply it to the field data from the Pitzbach in Austria, where direct high-resolution bed-load transport measurements are available. The method gives good results, depending on the choice of bed-load function used for the calculation. The standard deviations are overestimated by about 30%. DOI: 10.1061/ASCEHY.1943-7900.0000277 CE Database subject headings: Bed loads; Measurement; Statistics; Probe instruments. Author keywords: Bed-load transport measurement; Statistics; Indirect sensor; PBIS; Standard deviation; Pitzbach.

Bed load sediment transport inferred from seismic signals near a river: BED LOAD TRANSPORT FROM SEISMIC SIGNALS

We examine broadband (5–480Hz) seismic data from the Erlenbach stream in the Swiss Prealps, where discharge, precipitation, and bed load transport are independently constrained. A linear inversion of seismic spectra, exploiting isolated discharge or rain events, identifies the signals generated by water turbulence and rainfall. This allows us to remove the contributions of turbulence and rainfall from the seismic spectra, isolating the signal of bed load transport. We calibrate the regression for bed load transport during one storm and then use this regression with precipitation and discharge data to calculate bed load transport rates from 2months of seismic spectra. Our predicted bed load transport rates correlate reasonably well with transport rates from calibrated geophones embedded in the channel (r ~ 0.6, p< 10 ). We find that the seismic response to rainfall is broadband (~16–480Hz), while water turbulence and sediment transport exhibit seismic power primarily in lower frequencies (<100Hz), likely due to longer attenuation path lengths. We use the varying attenuation at each seismometer to infer that a downstream waterfall is the primary source of the water turbulence signal. Our results indicate that deconstruction of seismic spectra from rivers can provide insight into the component signals generated by water turbulence, rainfall, and sediment transport. Further, the regression of seismic spectra with precipitation, discharge, and bed load transport data for a single calibration period enables the estimation of transport for subsequent periods with only precipitation, discharge, and seismic data. Hence, in combination with precipitation and discharge data, seismic data can be used to monitor bed load sediment transport.

Laboratory flume experiments with the Swiss plate geophone bed load monitoring system: 1. Impulse counts and particle size identification

We performed systematic flume experiments using natural bed load particles to quantify the effect of different parameters on the signal registered by the Swiss plate geophone, a bed load surrogate monitoring system. It was observed that the number of impulses computed from the raw signal clearly depends on bed particle size, mean flow velocity, bed roughness, and to a minor extent on particle shape. The centroid frequency of the signal resulting from the collision of a bed load particle against the geophone plate was found to be inversely related to particle size but to be less sensitive to variations in mean flow velocity and bed roughness than the signal amplitude, which is also related to particle size. Combining frequency and amplitude information resulted in a more robust identification of the transported particles size over a wide range of sizes than using amplitude information alone.

Self-adjustment of stream bed roughness and flow velocity in a steep mountain channel

Understanding how channel bed morphology affects flow conditions (and vice versa) is important for a wide range of fluvial processes and practical applications. We investigated interactions between bed roughness and flow velocity in a steep, glacier-fed mountain stream (Riedbach, Ct. Valais, Switzerland) with almost flume-like boundary conditions. Bed gradient increases along the 1 km study reach by roughly 1 order of magnitude (S = 3–41%), with a corresponding increase in streambed roughness, while flow discharge and width remain approximately constant due to the glacial runoff regime. Streambed roughness was characterized by semivariograms and standard deviations of point clouds derived from terrestrial laser scanning. Reach-averaged flow velocity was derived from dye tracer breakthrough curves measured by 10 fluorometers installed along the channel. Commonly used flow resistance approaches (Darcy-Weisbach equation and dimensionless hydraulic geometry) were used to relate the measured bulk velocity to bed characteristics. As a roughness measure, D84 yielded comparable results to more laborious measures derived from point clouds. Flow resistance behavior across this large range of steep slopes agreed with patterns established in previous studies for both lower-gradient and steep reaches, regardless of which roughness measures were used. We linked empirical critical shear stress approaches to the variable power equation for flow resistance to investigate the change of bed roughness with channel slope. The predicted increase in D84 with increasing channel slope was in good agreement with field observations.

A probabilistic formulation of bed load transport to include spatial variability of flow and surface grain size distributions

Bed load fluxes are typically calculated as a function of the reach averaged boundary shear stress and a representative bed grain size distribution. In steep, rough channels, heterogeneous bed surface texture and macro-roughness elements cause significant local deviations from the mean shear stress but this variability is often omitted in bed load calculations. Here we present a probabilistic bed load transport formulation that explicitly includes local variations in the flow field and grain size distribution. The model is then tested in a 10% gradient stream, to evaluate its predictive capability and to explore relations between surface grain size sorting and boundary shear stress. The boundary shear stress field, calculated using a quasi-3D hydraulic model, displayed substantial variability between patch classes, but the patch mean dimensionless shear stress varied inversely with patch median grain size. We developed an empirical relation between the applied shear stress on each patch class and the reach averaged shear stress and median grain size. Predicted sediment volumes using this relation in our bed load equation were as accurate as those using complete shear stress distributions and more accurate than current bed load transport equations. Our results suggest that when spatially variable grain size distributions (e.g., patches of sediment) are present they must be explicitly included in bed load transport calculations. Spatial variability in shear stress was relatively more important than grain size variations for sediment transport predictions.