Geophysical Research Letters

Start and end of bedload transport in gravel-bed streams

Authors


Abstract

[1] The threshold of incipient bedload motion, expressed either as a critical force or as a critical water discharge, is a key parameter in bedload transport prediction. Measuring the threshold of motion is difficult, and reliable data from natural streams are rare. By recording the vibrations triggered by bedload particles when moving over a steel plate mounted in the channel bed, we determined the time at start and end of bedload transport in four streams, where discharge is continuously monitored. The threshold discharge scatters over approximately one order of magnitude for each stream, reinforcing previous observations that critical discharge is characterized by a distribution of values. We interpret a strong correlation between the discharge at the start of transport and the discharge at the end of transport of the previous event to reflect temporal changes in bed structure and consequent effects on the driving and resisting forces acting on the bed.

1. Introduction

[2] During flood events, coarse sediment can be transported by the flow as bedload, that is, by rolling or sliding on the stream bed, or by short hops. Bedload transport not only constitutes a major natural hazard, especially in mountain regions [Marston, 2008], but also drives fluvial bedrock erosion [Sklar and Dietrich, 2004; Turowski et al., 2008], and is an important mechanism of sediment transfer from production to deposition areas [Schlunegger and Hinderer, 2003]. In addition, bedload transport influences the spatial distribution of aquatic habitats [Jensen and Johnsen, 1999] and its accurate prediction is important in river engineering and stream restoration [Chin et al., 2009; Dietrich et al., 1989].

[3] The threshold of motion of sediment, expressed either as a critical discharge or a critical shear stress, is a key parameter in predicting transport rates, being one of only two free parameters in many commonly used bedload equations [Fernandez Luque and van Beek, 1976; Meyer-Peter and Müller, 1948; Rickenmann, 2001]. Consequently, the hydraulic conditions at incipient motion have been studied for decades, both in the laboratory and in the field [Buffington and Montgomery, 1997]. To initiate motion of an individual sediment grain, a threshold force needs to be overcome; this threshold is determined by the local environment of the grain, which determines for example its friction angle and its protrusion into the flow, and its size, shape and weight [Lamb et al., 2008; Wiberg and Smith, 1987]. All of these parameters are highly variable, and the range of threshold values for individual grains within a single bed often exceeds the differences of means of different beds [Buffington et al., 1992; Kirchner et al., 1990]. In the field, the threshold of motion is commonly determined in one of two ways. In the first method, a trend in measured transport rates is extrapolated to zero or a small reference value [Parker, 1990]. However, the method is indirect, and the quality of the extrapolation depends on the chosen approach, and on the number of available datapoints to constrain the bedload function [Buffington and Montgomery, 1997]. Furthermore, it is unclear which reference value should be used and how it depends on site-specific conditions. In the second method, known as the flow competence method, the largest grain that moved in a flood gives an indication of the ability of the stream to transport [Komar, 1987; Lenzi et al., 2006]. Here, statistical outliers can strongly affect the results and the underlying assumptions necessary to analyse the data cannot be validated [Wilcock, 1992]. As a consequence, reliable field data on start and end of bedload transport is scarce. Conventionally, for streams where no direct determination is possible, the discharge at start of motion is calculated from semi-empirical deterministic equations dependent on channel properties, such as the bed slope and a representative grain size [Bathurst, 1987; Ferguson, 1994]. This approach assumes that a single critical discharge value is adequate to characterize the transport behaviour at all times under the given conditions.

[4] Here, we have determined the time at start and end of bedload transport with impact sensors in four mountain streams, where discharge is continuously measured [Reid et al., 2007; Richardson et al., 2003; Rickenmann and McArdell, 2007, 2008]. Data have been recorded continuously at 15 minute resolution over two years in three of the streams, and at one minute resolution over more than 20 years in the fourth stream. In all four streams the discharge at start and end of motion varies over approximately one order of magnitude. The data shows a strong correlation between the discharge at start of transport and the discharge at the end of transport of the previous event, which we interpret to imply that the local topography around a grain, affecting friction angle, grain protrusion and the local flow field, significantly affects its threshold of motion.

2. Field Sites and Methods

[5] We determined start and end of sediment motion in four streams in the European Alps (Table 1 and auxiliary material). Three of the streams, the Pitzbach [Rickenmann and McArdell, 2008; Turowski and Rickenmann, 2009], Ruetz and Fischbach, drain pro-glacial catchments in the Austrian high Alps. There, sediment is abundant and mobile and, during the summer months, the streams show diurnal discharge variation due to glacial meltwater, causing almost daily sediment transport events. Data are available for two years at 15 minute resolution for all three streams. The fourth stream, the Erlenbach, drains an unglaciated, partially forested catchment in the Swiss Prealps [Hegg et al., 2006; Rickenmann and McArdell, 2007; Molnar et al., 2010]. There, hillslopes are highly active and sediment transport is mainly driven by intermittent summer thunderstorms, sometimes leading to periods without bedload motion lasting several weeks [Schuerch et al., 2006; Turowski et al., 2009]. Coarse woody debris, logs and large boulders are abundant in the channel, causing a step-pool morphology. For more than 20 years, data were recorded at one minute resolution during sediment transport events.

Table 1. Catchment Characteristics
 ErlenbachFischbachPitzbachRuetz
 Schwyz, SwitzerlandTyrolia, AustriaTyrolia, AustriaTyrolia, Austria
Measurement period1986–1999, 2002–2009May 2008–Oct. 2009Jun. 1994–Sep. 1995Jun. 2008–Oct. 2009
Site elevation/masl1110154018111684
Maximum elevation/masl1655349734723474
Drainage area/km20.7712728
% glaciation0175322
Channel bed slope0.100.020.090.06
Channel bed width/m4.09.5 (confined)11.08.5 (confined)
D30/cm3111.5
D50/cm8436
D90/cm30203440
Number of events (observed/used)460/454124/95170/120626/429

[6] We characterized basic geomorphic properties of the streams with standard methods (Table 1). The surface grain size distribution was surveyed with the transect-by-number method [Church et al., 1987]. For each stream at least 600 and up to 1300 pebbles were measured. Channel bed slope upstream of the measuring site was determined with a hand-held clinometer over a distance of ∼100 m. Drainage area was obtained from digital terrain models with a flow-routing algorithm. The extent of the glaciated area is based on surveys from 1986 [Hasslacher and Lanegger, 1988]. Although the glaciers probably have shrunk since that time, the numbers give a good impression of the differences between the catchments.

[7] Instead of applying conventional methods of flow competence or back-extrapolation of transport rates, the energy transferred by the moving particles to the stream bed was measured with piezo-electric crystals (up to 1999) and geophones (after 1999) mounted under steel plates (dimensions 36 × 50 cm) in the stream bed [Rickenmann and McArdell, 2007, 2008; Turowski and Rickenmann, 2009]. Sediment particles moving across the plate cause vibrations, which are amplified and recorded. The number of peaks (impulses) above a pre-defined threshold value (used to filter out noise due to flowing water) is stored. The sensors pick up the motion of particles larger than about 1 cm in diameter [Rickenmann and McArdell, 2007]. However, there is some site-to-site variability in this value. In effect, the onset of motion is defined by a threshold of energy delivered to the bed by moving particles, and this energy depends to some extent on the size and shape of the grain, and its mode of transport [Turowski and Rickenmann, 2009]. The method is objective in the sense that there is a clearly defined criterion for the onset of motion (non-zero number of impulses), which is independent of an observer. It is reproducible in the sense that the same input leads to the same sensor output, and it detects the start of motion at a cross section, as is required for modelling purposes [Richardson et al., 2003]. Sensor design and measuring method are described in detail elsewhere [Rickenmann and McArdell, 2007, 2008; Turowski and Rickenmann, 2009, 2011; Turowski et al., 2009]. In the Erlenbach, the upgrade of sensors in the years 1999–2002 induced slightly different threshold values in sensor response [Turowski et al., 2009]. The data from before 1999 and after 2002 are therefore not directly comparable with each other and are treated separately in the following.

[8] In the Erlenbach, hydrographs are flashy, with a strong response to rainfall. Individual sediment transport events can easily be recognized from the hydrograph and the records of the sediment sensors. For the pro-glacial streams, we specified an event to end if bedload transport had ceased for at least two measurement periods (30 min.), while discharge was required to decrease at the end of the event. Events during which periods with no bedload transport occurred for more than 25% of the event duration were excluded from the analysis.

3. Results and Interpretation

[9] Both at the start and end of transport, the threshold discharge scatters over about one order of magnitude in all four streams (Figure 1). Thus, as has been reported previously [e.g., Buffington et al., 1992; Einstein, 1950; Kirchner et al., 1990], a single critical discharge, as commonly used, is inconsistent with the data. For the pro-glacial streams, the distribution of discharge at the end of transport matches the distribution at the start (Figures 1a1f). For the Ruetz and the Fischbach, these distributions are bimodal, while they are unimodal for the Pitzbach. We interpret the two modes and their relative size to reflect the different role of bed armoring in the streams' dynamics. The first mode at a low discharge is probably due to the start of motion of an unarmored bed, while the second mode at a higher discharge may represent an armored bed. For the Erlenbach, the distribution of discharge at the start of transport is unimodal, while at the end of transport it is bimodal, with the dominant peak at a similar value as for the start of transport, and a secondary peak at a higher value (Figures 1g and 1h). This causes a slightly larger average discharge at the end of transport than at the start.

Figure 1.

Histogram of the discharge at the (left) start and (right) end of transport for the four study streams. (a–f) The distribution for the discharges at the start and end of transport is similar for the three pro-glacial streams. For the Erlenbach data from 1986–1999, (g) the distribution at the start of transport is unimodal, (h) while it is bimodal for the end of transport. The second Erlenbach data set (2002–2009) gives similar results.

[10] So what causes the observed variations in critical discharge? There are three possible answers to this question. First, small discharge fluctuations and turbulent sweeps can affect the magnitude of the forces acting on sediment grains on the bed [Grass, 1970]. Second, if the grain size distribution in the channel reach above the monitoring site stays the same from event to event, the spatial arrangement of the grains and their relative position, their friction angle and protrusion may change, which can affect the threshold of motion [Buffington et al., 1992; Kirchner et al., 1990; Wiberg and Smith, 1987]. In addition, a change in the bed topography will affect the local flow field, which could alter the forces acting on individual grains. Third, to the same effect, the grain size distribution on the bed surface in the area of interest may change.

[11] If turbulent sweeps and discharge fluctuations are the dominant cause of the observed variability, this will lead to an essentially random distribution of the threshold parameters, that is, a temporal correlation of the values cannot be expected. Conversely, if changing grain sizes or bed topography are responsible for the variability, a temporal structure can be expected, as can be seen from the following argument. Transport ceases if the forces exerted by the water fall below the critical value. This critical value is determined by the current conditions on the bed, which are a combination of the local grain size distribution and the relative arrangement of the grains. During transport, the bed continuously evolves, either by replacing individual grains with other grains of a different size, by rearranging the grains on the bed, or both. Thus, the threshold of motion changes. When transport stops, the current bed configuration is locked until transport begins again. Assuming (i) that the physical processes of entrainment and deposition at the start and end of transport are symmetrical, and (ii) that the bed is not disturbed between fluvial transport events, the discharge at the start of transport should equal the discharge at the end of transport of the previous event.

[12] The second of these two assumptions is fulfilled in the pro-glacial streams. There, due to the cyclic nature of the hydrograph in the summer, bedload transport stops during cold weather spells, and/or for a few hours during the night. It is unlikely that the bed is disturbed during this time (for example, by lateral sediment input due to landslides or debris flows). As expected, when the discharge at the start of transport is plotted against the discharge at the end of transport in the preceding event, all data points fall close to the one-to-one line (Figures 2a2c). This rules out a dominant control of random fluctuations of the forces at the bed due to turbulent sweeps, and the first assumption made above – that the physics of the entrainment and deposition processes are symmetrical – is justified a posteriori. In addition, it suggests that the configuration of the grains, and thus friction angles and grain protrusion, is a dominant factor in setting the threshold value for initiation of transport. These insights can be used to interpret the more complicated situation pertaining in the Erlenbach.

Figure 2.

Discharge at the start of transport plotted against discharge at the end of transport in the previous event for all four streams. (a–c) For the pro-glacial streams (Pitzbach, Fischbach, Ruetz), the data scatter closely around the 1:1 line (dashed). (d) For the Erlenbach, discharge at the start of transport is, on average, lower than at the end of transport in the previous event.

[13] For the Erlenbach, data points deviate more frequently from the one-to-one line and scatter is larger (Figure 2d). Part of the observed scatter could be due to turbulent sweeps, which arguably play a larger role in step-pool channels than in plane-bed or pool-riffle channels such as the pro-glacial streams. In addition, note that, on average, the discharge at the end of transport is higher than at the start, indicating that, in general, the bed material becomes more mobile between events. At the Erlenbach, hillslopes are highly active [Schuerch et al., 2006], and sediment delivery to the stream occurs regularly between sediment transport events due to landsliding, earth flow and soil creep. Landslide material is typically loose, in contrast to fluvially deposited bed material, which often forms chains of jammed and interlocked rocks [Church and Zimmermann, 2007]. Substantial sediment input due to hillslope processes is more likely to occur between two transport events if the intermittent time is longer. The mean time between transport events for all Erlenbach events in the period 1986–1999 was 324 hrs. If the ratio of discharges at end of transport and start of transport in the following event was in the range 0.8–1.25 (i.e., close to one), the mean time between events was 246 hrs, and 478 hrs if it was outside this range. Thus, large deviations of these two discharges appear to be more likely when the time separating them was longer.

[14] Individual deviations may, however, be due to other effects than lateral sediment input. For example, the largest deviation observed so far in the Erlenbach, from 0.47 m3/s at the end of transport on the 7th Dec. 2007 to 1.97 m3/s at the start of transport on the 7th Jan. 2008, was due to the freezing of soils and water in sub-zero temperatures between the events. In addition, local bed topography can be altered by grains that rotate and re-orient in their position in low-flow conditions without being substantially moved or entrained, or by transport of sediment with grains too small to trigger a sensor response.

4. Conclusions

[15] In many frequently used models the bedload transport rate is a power function of the excess shear stress or discharge over a critical value [Fernandez Luque and van Beek, 1976; Meyer-Peter and Müller, 1948; Rickenmann, 2001]. Frequently, these models fail to give adequate predictions, especially in gravel-bed rivers with broad grain size distributions [Gomez and Church, 1989; Rickenmann, 2001]. It has been shown previously that sediment transport behaviour displays a strong dependence on the recent history of the stream [Gintz et al., 1996; Lenzi et al., 2004; Turowski et al., 2009]. The large variability in critical discharge in the four streams described herein points to the need to reconsider how the onset of motion, and thus bedload transport rates, are calculated. As has been concluded from laboratory investigations [Buffington et al., 1992; Kirchner et al., 1990], our data suggest that the threshold of motion is strongly affected by the relative arrangement of the sediment grains, which affects parameters such as the friction angle and grain protrusion, and the local flow field. However, a direct demonstration of this interpretation is still needed. In addition, critical values may change considerably throughout a transport event, and conventional concepts of a single, constant excess discharge or shear stress need to be reconsidered. However, the forecast of the initiation of motion from detailed surveys of the bed topography between transport events is currently out of reach. As an alternative, the discharge at the end of transport in the most recent event can be used to predict the threshold discharge for the next event. For many sites it will be difficult to obtain such observation and traditional approaches assuming a single threshold value are currently the only option. However, it may be possible to determine the end of motion in a transport event from acoustic recordings using simple underwater microphones (hydrophones), which can be installed at low cost without major site requirements [e.g., Barton et al., 2010].

Acknowledgments

[16] We would like to thank B.W. McArdell for suggesting studying initiation of motion with the Erlenbach data, and J.W. Kirchner for insightful discussions. Our work would not have been possible without the continuing commitment of B. Fritschi, who designed, built and maintained the indirect sensors, and the many other people who helped running the observatories over the years. The Tyrolean hydropower company TIWAG supported the campaigns in Austria and shared data. K. Thatcher and E. Casale proof-read the manuscript. We thank J. Buffington and an anonymous reviewer for their valuable comments. This study was supported by SNF grant 200021_124634/1.

[17] Paolo D'Odorico thanks J. Buffington and an anonymous reviewer.

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