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.

Understanding landscape denudation and its relation to climate requires an
understanding of how a flood hydrograph drives the sediment mass flux leaving
the system through rivers. While suspended sediment represents the largest
fraction of mass exiting the landscape

Passive tracer particles, in particular passive integrated transponder radio-frequency identification (PIT RFID) tagged particles, are becoming an
attractive low-cost and low-maintenance method of measuring bed load particle
dynamics. The application of passive tracer particles has taken various
forms, such as exotic lithologies

In this paper we present the results of a 2-year deployment of several
populations of RFID tracer cobbles within alluvial and bedrock sections of a
river, for single-flood and yearly timescales. Throughout this manuscript, we
define bedrock channels following the definition of

In the following sections we present the relevant theoretical background that guides the analysis and interpretations of our tracer particle results. The theoretical background is intended as a brief introduction to the topics of sediment transport mechanics and dynamics, quantifying hydrologic forcing, and the downstream sorting of sediment by particle size.

Under a wide range of bed load transport conditions, coarse sediment
particles undergo short steps separated by longer periods of rest, which
leads to probabilistic descriptions of particle motion

Treating the particle behavior probabilistically, we focus on the
distributions of particle steps and rests. In the laboratory, the
distribution of particle step lengths for a given stress and grain size have
been observed to follow exponential or gamma-like distributions

Upon deposition, the rest duration before subsequent entrainment is
constrained by two criteria: first the stress must exceed the threshold of
motion locally, and second the particle must be exposed to the flow

Flows in natural coarse-grained rivers are inherently unsteady: from the
microscopic scale of variations in turbulence, to macroscopic fluctuations in
discharge within a flood, to the rise and fall of the hydrograph throughout
a series of floods. At the smallest relevant scales of turbulence, the
threshold of motion is determined by the impulse, the product of shear stress
magnitude, and duration

The spatial pattern of diminishing grain size with increasing distance from
the headwaters is near universal among gravel rivers, and results from
a combination of size-selective sorting and particle abrasion

Field deployment of tracer particles took place in the Mameyes River basin,
located within the Luquillo Critical Zone Observatory in northeastern Puerto
Rico. Coarse-grained tracers equipped with PIT RFID tags were deployed in the
main stem of the Mameyes River, and in a steep tributary
(Fig.

To characterize the spatial sorting of the stream bed, we performed pebble
counts at 200 m intervals from the start of the Mameyes RFID tracers
to the perceived gravel–sand transition. When analyzing the stream sorting we
restrict the analysis to the depositional part of the river, and thus we only
use measurements downstream of the start of the alluvial plain (approximately
200 m downstream of tracer installation location). The

Two populations of 150 tracers were installed in the summers of 2010 and 2011
in the Mameyes as it exits the mountains near the start of the alluvial
plain. A smaller population of 51 tracers was installed in the Bisley 3
stream in the summer of 2010. All three tracer particle populations are
composed of cobbles from the stream bed and have narrow grain size
distributions centered on the bed

For the study reaches,

The value of

Calculation of the dimensionless impulse (

River discharge is the most commonly reported variable in relating long-term
sediment dynamics to hydrologic forcing. However, the momentum framework
presented in Sect.

Fraction of mobile tracers (

The magnitude–frequency distribution for

We analyze the magnitude–frequency distribution of

The distribution of particle displacements resulting from several floods was
determined from surveys of both populations of tracers at the Mameyes site,
in the summers of 2010 and 2011. We normalize each tracer's transport
distance (

Mean displacement data for the first (red

At the multi-flood scale we analyze the long-term behavior of the tracer
particles' displacement. We normalize the CDFs of cumulative travel distance
by each survey's mean value, which results in a collapse of the data. This
collapse suggests that the mean value is a reasonable descriptor of the
dynamics of each tracer population. We note here that the CDFs in
Fig.

Due to time limitations in the field we were unable to survey more than three
individual floods for the Bisley 3 stream, and thus are unable to determine
the threshold of motion from the fraction of mobile tracers. In order to
compare the Mameyes data with the Bisley 3 tracer data, values for

Mean displacement data for the first (red

At longer timescales, tracer particle sorting by size is readily apparent in
the Mameyes, as observed in other studies

The cumulative effects of minor grain size sorting at the flood scale
(Fig.

Turning to the tracers emplaced in the Mameyes, sorting of both populations
by size is readily apparent (Fig.

At the single-flood scale, tracer particle displacements have been shown to
be well described by exponential, gamma, and power-law distributions

The agreement of observed tracer displacement distributions from the Mameyes
with models and laboratory data

Collapse of the tracer data for the first (red

We now turn to data from the Bisley 3 tracer deployment, which can serve as
a critical test of the generality of the impulse framework and tracer
displacement results. Because it is currently unknown how
many tracer particles are required to produce accurate statistics, we note here that we only
analyze the limited number of Bisley 3 tracers alongside the larger set of
Mameyes tracers. Until such a number is known we caution that researchers
should not solely rely on a limited set of tracers to inform their results.
Given the small number of tracers deployed and the particularly variable
stream profile (Fig.

A pitfall of the dimensionless impulse is its sensitivity to the
determination of

The pattern of smaller particles having larger displacements
(Fig.

The cumulative sorting results over annual timescales appear to substantiate
aspects of the self-similar sorting theory of

The full model predicting the mean concentration of the sediment plume
downstream consistently underpredicts the data further downstream
(Fig.

In this paper we have presented field results on bed load tracer displacement
data at the event to annual timescales, and used simple theory to
rationalize the displacement scaling of tracer particles, show how
a heterogeneous population of particles sorts downstream, and explore the
implications of these findings on the statistical scaling of the hydrograph.
At the scale of single floods, the distribution of particle displacements is
well described by an exponential distribution. Close agreement with
laboratory data and theory

We thank J. Singh, K. Litwin Miller, D. Miller, R. Glade, J. Evaristo, and
G. Salter for outstanding field assistance. We thank D. N. Bradley for
assistance concerning tracer tracking equipment. We thank A. E. J. Turowski,
M. Schmeeckle, M. Chapuis, and the two anonymous reviewers for thoughtful comments
that enhanced the clarity of this manuscript. Data for the Mameyes tracers
are available at