Dynamics and mechanics of bed-load tracer particles

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Abstract

Understanding the mechanics of bed load at the flood scale is necessary to link hydrology to landscape evolution. Here we report on observations of the transport of coarse sediment tracer particles in a cobble-bedded alluvial river and a step-pool bedrock tributary, at the individual flood and multi-annual timescales. Tracer particle data for each survey are composed of measured displacement lengths for individual particles, and the number of tagged particles mobilized. For single floods we find that measured tracer particle displacement lengths are exponentially distributed; the number of mobile particles increases linearly with peak flood Shields stress, indicating partial bed load transport for all observed floods; and modal displacement distances scale linearly with excess shear velocity. These findings provide quantitative field support for a recently proposed modeling framework based on momentum conservation at the grain scale. Tracer displacement is weakly negatively correlated with particle size at the individual flood scale; however cumulative travel distance begins to show a stronger inverse relation to grain size when measured over many transport events. The observed spatial sorting of tracers approaches that of the river bed, and is consistent with size-selective deposition models and laboratory experiments. Tracer displacement data for the bedrock and alluvial channels collapse onto a single curve - despite more than an order of magnitude difference in channel slope - when variations of critical Shields stress and flow resistance between the two are accounted for. Results show how bed load dynamics may be predicted from a record of river stage, providing a direct link between climate and sediment transport.

Figures

  • Figure 1. (a) DEM of northeastern Puerto Rico (inset) with Mameyes watershed outlined in red. The red and green circles represent the approximate starting locations of tracer particles in the main channel and headwaters stream (Bisley 3), respectively. Blue diamonds represent USGS and USFS stream gages. The blue line is the main channel of the Mameyes River; flow is from south to north. The red bounding rectangle represents the area in panel (e). (b) Close-up map of the headwaters stream showing the location of the tracer particles (green circles) at the time of the final survey. (c) Grain size distributions for the main channel site determined by Wolman pebble count for the channel (black line), initial population of tracers (red line), and second population of tracers (blue dashed line). (d) Grain size distributions for the headwaters site determined by Wolman pebble count for the channel (black line), and population of tracers (green line). (e) Close-up map of the main channel field site showing the locations of the first (red circles) and second (blue circles) populations of tracer particles at the time of the final survey. Flow direction is from left to right.
  • Figure 2. (a) Hydrograph for the duration of the study in depth (m) for the main channel of the Mameyes River. The dashed red lines represent two determinations of the critical shear velocity (m s−1). (b) Hydrograph for the duration of the study in depth (m) for the headwaters field site for the duration of the study. The dashed red line represents the critical shear velocity (m s−1). Gray lines represent missing data.
  • Figure 3. (a) Photograph of the main channel of the Mameyes River looking upstream to the location where the tracer particles were installed. The width of the wetted portion of the channel is approximately 20 m. (b) Longitudinal profile extracted from a lidar DEM of the main channel of the Mameyes River. S is the slope. (c) Photograph of the Bisley 3 stream looking upstream, showing the location of the farthest tracer found downstream. The wetted region in the foreground is approximately 2 m wide. (d) Longitudinal profile from field survey; gray crosses represent the location of survey points. S is the slope.
  • Figure 4. Calculation of the dimensionless impulse (I∗) for two estimates of U∗c for a single flood, where the time represents the floods location on the hydrograph in Fig. 2a. The limits of integration for U∗c1 and U∗c2 are t1 to t4 and t2 to t3, respectively. The shaded region represents the region integrated for the calculation of I∗ using U∗c1.
  • Figure 5. Fraction of mobile tracers (f ) for single floods against peak Shields stress (τ∗). The red line represents the best fitting linear relationship, for which the intercept represents the critical Shields stress. See text for discussion of error bars.
  • Figure 6. (a) Frequency magnitude distribution of shear velocity for the main channel of the Mameyes river. The dashed red line represents an exponential function fit to the distribution for U∗>U∗c. (a) Inset: magnitude frequency distribution of discharge. The red line represents a power-law relationship, and the vertical dashed black line is the location of the threshold of motion (U∗c1). (b) Magnitude frequency distribution of the dimensionless impulse (I∗). (b) Inset: PDF of ln (I∗), where 〈U∗〉 is the average value of the distribution of U∗>U∗c1, 〈t〉 is the average duration of a flood above the threshold of motion for the duration of the study, andD50 is the median grain size of the tracer particles.
  • Figure 7. (a) Dimensionless displacement distributions for individual floods normalized by the mean (〈X/D〉) displacement for that flood. The black dashed line is an exponential distribution. Dimensionless mean displacement lengths for each flood are labeled in the legend. (b) Contour density plot of X/D against the excess shear velocity normalized by the settling velocity for each tracer. The contour colors represent the density of tracers within that location. The value of U∗ is for the flood peak, while the value of U∗c is treated as a fitting parameter. The black line represents the expected linear relationship between the dimensionless shear velocity and the modal tracer step length (Eq. 1).
  • Figure 9. Mean displacement data for the first (red +) and second (blue x) populations of tracer particles vs. dimensionless impulse (I∗). The gray line is the linear relationship determined by Phillips et al. (2013). The black lines represent the upper and lower limits of sediment particle transport (see Sect. 2.1 for discussion of limits). The data plotting below limit 1 have unrealistic values for I∗ (see Sect. 3.3 for explanation).

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CITATION STYLE

APA

Phillips, C. B., & Jerolmack, D. J. (2014). Dynamics and mechanics of bed-load tracer particles. Earth Surface Dynamics, 2(2), 513–530. https://doi.org/10.5194/esurf-2-513-2014

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