Substantial uncertainties in bedload transport predictions in
steep streams have encouraged intensive efforts towards the development of
surrogate monitoring technologies. One such system, the Swiss plate geophone
(SPG), has been deployed and calibrated in numerous steep channels, mainly
in the Alps. Calibration relationships linking the signal recorded by the
SPG system to the intensity and characteristics of transported bedload can
vary substantially between different monitoring stations, likely due to
site-specific factors such as flow velocity and bed roughness. Furthermore,
recent flume experiments on the SPG system have shown that site-specific
calibration relationships can be biased by elastic waves resulting from
impacts occurring outside the plate boundaries. Motivated by these
findings, we present a hybrid calibration procedure derived from flume
experiments and an extensive dataset of 308 direct field measurements at
four different SPG monitoring stations. Our main goal is to investigate the
feasibility of a general, site-independent calibration procedure for
inferring fractional bedload transport from the SPG signal. First, we use
flume experiments to show that sediment size classes can be distinguished
more accurately using a combination of vibrational frequency and amplitude
information than by using amplitude information alone. Second, we apply this
amplitude–frequency method to field measurements to derive general
calibration coefficients for 10 different grain-size fractions. The
amplitude–frequency method results in more homogeneous signal responses
across all sites and significantly improves the accuracy of fractional
sediment flux and grain-size estimates. We attribute the remaining
site-to-site discrepancies to large differences in flow velocity and discuss
further factors that may influence the accuracy of these bedload estimates.
Introduction
Flood events across Europe in the summer of 2021 have illustrated the threat
of bedload-transport-related hazards to human life and infrastructure,
especially in small and steep mountainous catchments (Badoux et al., 2014;
Blöschl et al., 2020). Understanding sediment transport processes is
also essential for efforts to return rivers to their nearly natural state by
restoring their continuity and re-establishing balanced sediment budgets
(e.g., Brouwer and Sheremet, 2017; Pauli et al., 2018; Logar et al., 2019;
Rachelly et al., 2021). However, monitoring and predicting bedload transport
still represent a considerable challenge because of large
spatiotemporal variability (e.g., Mühlhofer, 1933; Einstein, 1937; Reid
et al., 1985; Rickenmann, 2017; Ancey, 2020). This is especially true for
steep streams because they are poorly described by traditional bedload
transport equations, which have mainly been developed for lower-gradient
channels (e.g., Schneider et al., 2016). Predicting sediment transport in
steep channels is challenging, notably due to the presence of
macro-roughness elements affecting the flow energy (e.g., Manga and Kirchner,
2000; Yager et al., 2007, 2012; Bathurst, 2007; Nitsche et al., 2011;
Rickenmann and Recking, 2011; Prancevic and Lamb, 2015). It is further
complicated by a sediment supply that varies in both space and time due in
part to cycles of building and breaking of an armoring layer at the riverbed
(e.g., Church et al., 1998; Dhont and Ancey, 2018; Rickenmann, 2020; Piantini
et al., 2021).
Bedload transport equations established for lower-gradient streams typically
result in errors spanning multiple orders of magnitude when applied to steep
streams, motivating the development of new indirect monitoring techniques
for steep mountain channels (e.g., Gray et al., 2010; Rickenmann, 2017).
Indirect monitoring techniques provide complete coverage of selected river
transects at high temporal resolution, reduce personal risk related to
in-stream sampling, and enable consistent data collection at widely varying
flow conditions, including during flooding events (e.g., Gray et al., 2010;
Rickenmann, 2017; Geay et al., 2020; Bakker et al., 2020; Choi et al., 2020;
Le Guern et al., 2021). The drawback of these monitoring technologies with
regards to absolute bedload transport estimates lies in their need for
intensive calibration through direct bedload sampling with retention basins
(Rickenmann and McArdell, 2008), slot samplers (e.g., Habersack et al., 2017;
Halfi et al., 2020), or mobile bag samplers (e.g., Bunte et al., 2004;
Dell'Agnese et al., 2014; Hilldale et al., 2015; Mao et al., 2016; Kreisler
et al., 2017; Nicollier et al., 2021).
Among indirect monitoring techniques, the Swiss plate geophone (SPG) system
has been deployed and tested in more than 20 steep gravel-bed streams and
rivers, mostly in the European Alps (Rickenmann, 2017). Typically, linear or
power-law calibration relationships have been developed between measured
signal properties and bedload transport characteristics (Rickenmann et al.,
2014; Wyss et al., 2016a; Kreisler et al., 2017; Kuhnle et al., 2017). Such
calibration equations permit absolute quantification of bedload fluxes (e.g.,
Dell'Agnese et al., 2014; Rickenmann et al., 2014; Hilldale et al., 2015;
Halfi et al., 2020; Nicollier et al., 2021) as well as their variability in time and
space (i.e., across a river section; e.g., Habersack et al., 2017; Rickenmann,
2020; Antoniazza et al., 2022), estimates of bedload grain-size distribution
(e.g., Mao et al., 2016; Barrière et al., 2015; Rickenmann et al., 2018),
and the detection of the start and end of bedload transport (e.g., Turowski
et al., 2011; Rickenmann, 2020). However, these equations require a
calibration procedure against independent bedload transport measurements at
each individual field site because until now we have lacked generally
applicable signal-to-bedload calibration equations that are valid across
field settings. Although similarities between calibration relationships at
various field sites are encouraging, it is not well understood why the
linear calibration coefficients for total mass flux can vary by about a
factor of 20 among individual samples from different sites or by about a
factor of 6 among the mean values from different sites (Rickenmann et al.,
2014; Rickenmann and Fritschi, 2017). Given the substantial field effort
required for calibration campaigns, a generally applicable calibration
equation would represent a significant advance.
Numerous studies have reported successful calibration of impact plate
systems in laboratory flumes (e.g., Bogen and Møen, 2003; Krein et al.,
2008; Tsakiris et al., 2014; Mao et al., 2016; Wyss et al., 2016b, c; Kuhnle
et al., 2017; Chen et al., 2022), although transferring these flume-based
calibrations to the field remains challenging. Nonetheless, flume
experiments are valuable because they allow systematically exploring
relationships between the recorded signal, the transport rates of different
sediment size fractions, and the hydraulic conditions. For example, the
experiments of Wyss et al. (2016b) showed that higher flow velocities induce
a weaker SPG signal response per unit of transported sediment. More recent
flume experiments have highlighted another important site-dependent factor
influencing the SPG signal response, namely the grain-size distribution
(GSD) of the transported bedload (Nicollier et al., 2021), with coarser
grain mixtures shown to yield a stronger signal response per unit
bedload weight.
Subsequent impact tests and flume experiments showed that this grain-size
dependence arises because the impact plates are insufficiently isolated
from their surroundings (Antoniazza et al., 2020; Nicollier et al., 2022).
The elastic wave generated by an impact on or near a plate was found to
propagate over several plate lengths, contaminating the signals recorded by
neighboring sensors within a multiple-plate array. Nicollier et al. (2022)
introduced the notion of “apparent packets” (in opposition to “real”
packets) to define the portions of the recorded signal that were generated
by such extraneous particle impacts.
The main goal of this contribution is to examine the feasibility of a
general, site-independent signal conversion procedure for fractional bedload
flux estimates. We follow a comprehensive hybrid signal conversion approach
that encompasses a set of full-scale flume experiments conducted at an
outdoor facility, as well as 308 field calibration measurements performed
with direct sampling methods at four different bedload monitoring stations
in Switzerland between 2009 and 2020. We present the amplitude–frequency
(AF) method, aiming to reduce the bias introduced by apparent packets in the
relationship between the signal characteristics and the particle size.
Finally, we compare the performance of this novel AF method against the
amplitude histogram (AH) method developed by Wyss et al. (2016a) for both
fractional and total bedload flux estimates.
MethodsThe SPG system
The Swiss plate geophone (SPG) consists of a geophone sensor fixed under a
steel plate of standard dimensions 492 mm × 358 mm × 15 mm (Fig. 1a;
Rickenmann, 2017). The geophone (GS-20DX by Geospace Technologies;
https://www.geospace.com/, last access: 10 January 2022) uses a magnet moving inside an inertial coil (floating on
springs) as an inductive element. The voltage induced by the moving magnet
is directly proportional to its vertical velocity resulting from particle
impacts on the plate. The SPG system can detect bedload particles with a
minimum diameter of 10 mm (Rickenmann et al., 2014; Rickenmann, 2020; Wyss et al.,
2016a). Typically, an SPG array includes several plates mounted side by side,
acoustically isolated by elastomer elements and covering the river
cross-section. The array is either embedded in a concrete sill or fixed at
the downstream face of a check dam. A detailed description of the SPG system
can be found in Rickenmann et al. (2014). For all the calibration
measurements and flume experiments analyzed in this study ranging in
duration from a few seconds to 1 h, the raw 10 kHz geophone signal was
recorded (Fig. 1b).
(a) Swiss plate geophone (SPG) system before installation. Each
plate is equipped with a uniaxial geophone sensor fixed in a watertight
aluminum box (1) attached to the underside of the plate. The plates are
acoustically isolated from each other by elastomer elements (2). (b) Example
of a packet (grey area) detected by the SPG system. A packet begins 20 time
steps (i.e., 2 ms) before the signal envelope crosses the lowest amplitude
threshold of 0.0216 V and ends 20 time steps after the last crossing of the
lowest amplitude threshold (see Sect. 2.4).
Field calibration measurements
To test the AF and AH methods, this study uses 308 field measurements from
four Swiss bedload monitoring stations equipped with the SPG system (Fig. 2;
Table 1). Field calibration samples were collected at the Albula, Navisence,
and Avançon de Nant stations, and extensive calibration efforts have
been undertaken at the fourth field station in the Erlenbach since 2009
(Rickenmann et al., 2012). The Erlenbach offers an interesting comparison
with the other sites due to different channel morphology and flow
characteristics upstream of the SPG plates. Field calibrations at the four
sites consisted of the following steps: (i) direct bedload sampling
downstream of an impact plate using either crane-mounted net samplers
adapted from Bunte traps (Bunte et al., 2004; Dell'Agnese et al., 2014;
Nicollier et al., 2019; Fig. 2a, b), automated basket samplers (Rickenmann
et al., 2012; Fig. 2d), or manual basket samplers (Fig. 2c; Antoniazza et
al., 2022); (ii) synchronous recording of the raw geophone signal; (iii)
sieving and weighing of bedload samples using 10 sieve classes (see Sect. 2.4); and (iv) comparing the fractional bedload mass of each sample to the
geophone signal to derive the corresponding calibration coefficients. A more
detailed description of the sampling procedure is reported in Sect. S1 in the Supplement, including the mesh sizes used for bedload sampling. For the
analysis, only particles larger than 9.5 mm were considered as they are close to
the SPG detection threshold. Streamflow information was derived from various
stage sensors (Table 1). Flow velocity Vw was introduced by Wyss et al. (2016c) as a possible governing parameter affecting the number of particles
detected by the SPG system. Unfortunately, due to the lack of continuous
streamflow measurements at the Albula and Navisence sites, we were not able
to account for the effect of the flow velocity in the signal conversion
procedure described in the present study.
Channel and flow characteristics based on in situ measurements during the
calibration campaigns at the four field sites. The year of the field
calibration campaigns, the sampling technique, and the number of collected
samples are also indicated.
Oblique view of the Obernach flume test reach with a total length of
24 m and width of 1 m. The bed surface is paved with particles with
diameters equaling the characteristic D67 and
D84 sizes of the natural beds of the reconstructed sites.
Grains were fed into the channel 8 m upstream from the SPG system location
(G1 and G2) using either a vertical feed pipe or a tiltable basket (1). The
sensor plate G1 (in red) was shielded from direct particle impacts by the 4 m long partition wall (2). The partition wall and the impact plates were
decoupled from each other by a 2 mm vertical gap to prevent disturbances of
the recorded signal. Plexiglas walls (3) on each side of the flume
facilitated video recordings of the experiments.
Flume and hydraulic characteristics for the reconstruction of the
Albula and Avançon de Nant field sites.
Reconstructed field site setup ParameterUnitsAlbulaAvançon de Nant(without partition wall)(with partition wall)Flume widthm1.021.02Flume gradient of the natural bed%0.74.0Bed surface D67amm120200Bed surface D84amm190320Number of D67 particles m-2m-215.05.0Number of D84 particles m-2m-25.02.5Min. water depth above SPGm0.790.35Max. water depth above SPGm0.910.35Min. flow velocity 10 cm above SPGbm s-11.63.0Max. flow velocity 10 cm above SPGbm s-12.43.0Min. unit dischargem2 s-11.60.8Max. unit dischargem2 s-12.40.8Number of different flow velocity settings–21Total number of single-grain-size experiments–35551Total number of tested particles–10 7052485
a On the basis of line-by-number pebble counts at the natural site and
a photo-sieving-based granulometric analysis with BASEGRAIN software (Detert
and Weitbrecht, 2013).
b Flow velocities measured with the OTT MF Pro magnetic-inductive
flowmeter.
Flume experiments
The first part of the signal conversion procedure described in this study is
based on flume experiments conducted at the outdoor flume facility of the
Oskar von Miller Institute of TU Munich in Obernach, Germany. There, we
reconstructed the bed slope and bed roughness of the Albula, Navisence, and
Avançon de Nant field sites one after another in a flume test reach
with dimensions of 24 m × 1 m equipped with two impact plates at the
downstream end of a paved section (Fig. 3). For each site reconstruction, we
tested bedload material collected during field calibration measurements, and
we adjusted the flow velocity, flow depth, and bed roughness (D67 and
D84) to match the respective field observations. A detailed description
of the original flume setup and the performed experiments can be found in
Nicollier et al. (2020). In the present study, we primarily use a set of
experiments conducted in 2018 with the flume configured to match conditions
at the Albula field site (Table 2). These experiments were single-grain-size
experiments and consisted of feeding the flume with a fixed number of grains
for each of the 10 particle size classes described in Sect. 2.4 below. Two
different feeding systems were used, namely a vertical pipe and a tiltable
basket (for particles larger than 31.4 mm). While these particles were
transported over the SPG system, the full raw geophone signal was recorded.
The experiment duration ranged from 15 s for the smallest particles to
around 1 min for the largest particles. Up to 33 repetitions were conducted
until a representative range of amplitude and frequency values for each
grain-size class was obtained (Nicollier et al., 2021). The same procedure
was repeated for two different flow velocities (Vf=1.6 and 2.4 m s-1). The obtained information was then used to
derive empirical relationships between the mean particle size
Dm,j for a given grain-size class j and properties of the SPG
signal, as described in Sect. 2.5.2 below.
To illustrate the AF and AH methods and their respective performance, we use
a second set of flume experiments, which mimics the Avançon de Nant
field site. The main difference to other experimental setups is the presence
of a 4 m wooden partition wall along the center of the flume (Fig. 3) that
shields one geophone plate from impacting particles (Nicollier et al.,
2022). This special setup facilitates the characterization of the signal
propagated from an impacted plate to the neighboring non-impacted plate.
With this modified setup, single-grain-size experiments were run (n=51;
Table 2) using grains from each of the 10 particle size classes and bedload
material sampled at the Avançon de Nant field site. The flow velocity
was set to 3 m s-1 to facilitate particle transport through the
narrower flume section and is therefore not representative of the
Avançon de Nant site, where typical flow velocities were roughly 1.3 m s-1.
The amplitude histogram method
Wyss et al. (2016a) introduced the packet-based amplitude histogram (AH)
method to derive grain-size information from geophone signals. A packet is
defined as a brief interval, typically lasting 5 to 30 ms,
reflecting a single particle impact on a plate (Fig. 1b); it begins and ends
20 time steps before and after the signal envelope crosses a threshold
amplitude of 0.0216 V. The signal envelope is computed in Python with the
Hilbert transform (Jones et al., 2002), yielding the magnitude of the
analytic signal, i.e., the total energy. Each packet's maximum amplitude is
then used to assign it to a predefined amplitude class j delimited by
amplitude histogram thresholds thah,j (Table 3), yielding a
packet-based amplitude histogram (e.g., Fig. 4 in Wyss et al., 2016a). Each
amplitude class j is related to a corresponding grain-size class through
the following relationship between the mean amplitude
Am,j [V] and the mean particle size
Dm,j [mm]:
Am,j=4.6×10-4×Dm,j1.71.
The coefficients in Eq. (1) were determined using 31 basket samples
collected at the Erlenbach for which the maximum geophone amplitude was
analyzed as a function of the b axis of the largest particle found in the
sample (Wyss et al., 2016a). The grain-size classes are delimited by the
size of the meshes Dsieve,j used to sieve the bedload samples
from field calibration measurements. For a given bedload sample, it is
assumed that the number of packets between two amplitude histogram
thresholds thah,j is a good proxy for the fractional bedload
mass between the respective sieve sizes (Wyss et al., 2016a). In the present
study, we have extended the 7 size classes used by Wyss et al. (2016a)
to 10 classes in order to also assess the performance of the AH and AF
methods for larger particles.
Characteristics of the size classes j according to Wyss et al. (2016a) with the sieve mesh sizes Dsieve,j, the mean particle
diameter Dm,j, and the amplitude histogram thresholds
thah,j derived from Eq. (1). Additionally, the lower and
upper amplitude–frequency thresholds thaf,low,j and
thaf,up,j respectively derived from Eqs. (4) and (5) are
provided (see Sect. 2.5.2). The value of Dm,j for the largest
class (10) in brackets is an estimate because this size class is open-ended,
and as such the mean varied somewhat from site to site.
Class jDsieve,jDm,jthah,jthaf,low,jthaf,up,j[–][mm][mm][V][V][V Hz-1]19.512.30.02160.01321.55×10-5216.017.40.05270.03642.33×10-5319.021.80.07070.05094.45×10-5425.028.10.11300.08687.67×10-5531.437.60.16700.13621.78×10-4645.053.20.30880.27253.93×10-4763.071.30.54890.52447.05×10-4880.795.50.83780.84891.56×10-39113.0127.91.49191.63422.79×10-310144.7(171.5)2.27602.6438–The amplitude–frequency method
In a recent study, Nicollier et al. (2022) showed that the SPG system is
sensitive to extraneous particle impacts despite the isolating effect of the
elastomer. Extraneous signals at individual geophone plates can arise from
impacts occurring on neighboring plates or from impacts on the concrete
sill surrounding the SPG array. While attenuated to some extent, the elastic
waves generated by such impacts can reach multiple geophone sensors with
enough energy to be recorded as apparent packets. Thus, packet histograms
(i.e., counts of the number of packets per class j) are subject to a
certain bias, especially in the lower size classes. The degree of bias was
found to depend mainly on two factors. First, coarser grain sizes of
transported bedload were shown to generate more apparent packets. Second,
more apparent packets were recorded for a given bedload mass at transects
containing more SPG plates. Nicollier et al. (2022) showed that packet
characteristics such as the start time, amplitude, and frequency help
in identifying apparent packets and filtering them out from the final packet
histograms. This filtering method was subsequently applied to all four field
calibration datasets (Albula, Navisence, Avançon de Nant, and Erlenbach)
and helped to reduce the differences between the site-specific mean
calibration relationships for the total bedload flux by about 30 %
(Nicollier et al., 2022). Based on these observations, the present study
proposes an amplitude–frequency (AF) method as an adaptation of the
amplitude histogram (AH) method presented by Wyss et al. (2016a). By
introducing two-dimensional (amplitude and centroid frequency) size class
thresholds, the new method aims to reduce the effect of apparent packets and
improve the accuracy of fractional bedload flux estimates. Note that the
procedure does not allow for the differentiation of multiple particles
impacting one plate simultaneously, but the high recording frequency (10 kHz) of the SPG system minimizes its probability of occurrence.
Power-law least-squares regression relationships between the mean
particle diameter Dm,j and the 75th percentile of the
packets' amplitude MaxAmpenv,75th,j(a) and
amplitude–frequency
(MaxAmpenv/fcentroid)75th,j(b) values obtained from the single-grain-size experiments after filtering
out apparent packets using the filtering criterion in Eq. (3).
Centroid frequency
According to the Hertz contact theory, the frequency at which a geophone
plate vibrates is controlled by the size of the colliding particle (Johnson,
1985; Thorne, 1986; Bogen and Møen, 2003; Barrière et al., 2015;
Rickenmann, 2017). In the present study, the frequency spectrum of a packet
is characterized by the spectral centroid fcentroid. It
represents the center of mass of the spectrum and is computed as
fcentroid=∑fn⋅AFFT,n∑AFFT,n,
where AFFT,n [V ⋅ s] is the Fourier amplitude
(computed with the fast Fourier transform – FFT) corresponding to the
frequency fn [Hz]. Following Wyss et al. (2016b), before applying the
FFT, each packet is preprocessed in two steps. First, a cosine taper is
applied at the edges of a max. 8 ms time window around the peak amplitude of
each packet. Second, the signal contained in this time window is zero-padded
on either side to reach an optimal number of sample points nFFT. The taper is
used to smooth the transition between the packet and the concatenated zeros
and to suppress spectral leakage, which results in a more accurate amplitude
spectrum. The value of nFFT was set to 27 in order to adequately resolve
the amplitude spectrum of the raw signal contained in the max. 8 ms time
window. This time window focuses on the first-arrival waveform to obtain a
more accurate evaluation of the high-frequency content of the packet
(Nicollier et al., 2022). The single-sided Fourier transform of the
processed packet is then computed in order to extract AFFT and
derive fcentroid (Eq. 2). A decrease in fcentroid with increasing particle size was observed for different bedload
surrogate monitoring techniques (Belleudy et al., 2010; Uher and Benes,
2012; Barrière et al., 2015). Furthermore, fcentroid
has the advantage of showing weaker dependency on the flow velocity and
transport mode than the maximum registered packet amplitude (Wyss et al.
2016b; Chen et al., 2022). As shown by Nicollier et al. (2022),
fcentroid also contains information about the impact
location of a packet-triggering particle. Because high frequencies are more
rapidly attenuated than low frequencies along the travel path of a seismic
wave (apparent), packets triggered by impacts on a given plate typically
have higher fcentroid values than packets triggered by
impacts occurring beyond that plate's boundaries.
Flume-based amplitude–frequency thresholds
The particle mass associated with an individual signal packet is strongly
dependent on the size of the impacting particle. Inferring sediment
transport rates from SPG signals thus requires assigning each packet to a
corresponding sediment size class using threshold values of packet
characteristics (Table 3). Wyss et al. (2016a) derived size class thresholds
(or AH thresholds) of packet peak amplitude from field measurements (Eq. 1).
In the present study, we take advantage of the single-grain-size experiments
conducted at the flume facility (without the partition wall) (Nicollier et
al., 2021) to derive size class thresholds combining packet amplitude and
frequency (or AF thresholds). Each packet is assigned to a given class j
delimited by a lower threshold thaf,low,j based on the
maximum amplitude of the packet's envelope MaxAmpenv [V]
and an upper threshold thaf,up,j based on the ratio
MaxAmpenv/fcentroid [V Hz-1]. Compared to
the raw signal, the envelope has the advantage of returning the magnitude of
the analytical signal and thus better outlines the waveform by omitting the
harmonic structure of the signal (Fig. 2b). Similar combinations of
amplitude and frequency have been used to infer particle sizes and improve
the detectability of bedload particles in previous studies involving impact
plates (Tsakiris et al., 2014; Barrière et al., 2015; Wyss et al.,
2016b; Koshiba and Sumi, 2018) and pipe hydrophones (Choi et al., 2020).
The lower and upper amplitude–frequency thresholds are obtained as follows.
First, all packets recorded during the single-grain-size experiments are
filtered with respect to the following criterion adapted from Nicollier et
al. (2022):
criterion:fcentroid>ac⋅e(bc⋅MaxAmpenv),
with ac=1980 Hz and bc=-1.58 V-1. The values of the linear coefficient ac and the exponent
bc were obtained through an optimization process discussed below
(Sect. 4.1) and were found to best separate apparent packets from real
packets. Packets identified as apparent packets using this criterion are
ignored in the further analysis in order to obtain more accurate threshold
values. Note that in the present study, the criterion in Eq. (3) has not been
applied to the data when implementing the AH method developed by Wyss et al. (2016a).
The next step consists of fitting a power-law least-squares regression line
through the 75th percentile amplitude MaxAmpenv,75th,j
and amplitude–frequency
(MaxAmpenv/fcentroid)75th,j
values of the packets detected for a given grain-size class j fed into
the flume that met the filtering criterion (Fig. 4), resulting in the
following two equations:
4MaxAmpenv,75th,j=1.66×10-4⋅Dm,j1.95,5MaxAmpenvfcentroid75th,j=2.26×10-8⋅Dm,j2.36.
Finally, the lower threshold values thaf,low,j are obtained
by replacing Dm,j in Eq. (4) with the lower sieve sizes
Dsieve,j, while the upper threshold values
thaf,up,j are obtained by replacing
Dm,j in Eq. (5) with the upper sieve sizes
Dsieve,j+1 (Table 3 and triangles in Fig. 5). Fitting
functions such as Eqs. (4) and (5) allows for the computation of thresholds
for any classification of particle (sieve) sizes.
When considering all the packets detected for a given grain-size class, it
was found that apparent packets can greatly outnumber real packets. This is
particularly pronounced for the largest grain sizes because the energy
released by their impact, especially outside the plate boundaries, is
more likely to be detectable by the geophone sensors. Due to signal
attenuation, however, these numerous apparent packets have relatively small
amplitudes, which substantially dilutes the average signal response
associated with the largest grain sizes (Fig. 5). However, filtering out
apparent packets reveals a rather clear relationship, which would otherwise
be obscured, between the mean particle size Dm,j and both the
amplitude MaxAmpenv and the ratio MaxAmpenv/fcentroid (Fig. 5). Overall, the
filtering with criterion (Eq. 3) at the Obernach flume site eliminated about
61 % of all the packets.
Range of signal responses obtained for each individual grain-size
class fed into the flume before (red boxes) and after (blue boxes) filtering
out apparent packets using the filtering criterion in Eq. (3), with (a) the
maximum amplitude of the envelope MaxAmpenv and (b) the
ratio MaxAmpenv/fcentroid as functions of
the mean particle diameter Dm,j. In (a), the lower threshold
values thaf,low,j are obtained by replacing
Dm,j with the lower sieve sizes (Dsieve,j) in
the equation of the dashed power-law regression line (Eq. 4). In (b), the
upper threshold values thaf,up,j are obtained by replacing
Dm,j with the upper sieve sizes
(Dsieve,j+1) in the equation of the dotted power-law
regression line (Eq. 5).
Application to field calibration measurements
The lower and upper thresholds thaf,low,j and
thaf,up,j obtained from the filtered flume
experiments can be transferred to the field datasets if the SPG apparatus
and the geophone data recording and preprocessing routines are identical in
both cases. The following steps allow us to derive the final general
calibration coefficients kb,j,gen (Fig. 6).
First, for each field measurement i, the thresholds thaf,low,j and thaf,up,j are used for
counting the number of packets per class from the recorded
geophone signal. Second, a sample- and class-specific calibration
coefficient kb,i,j (units: kg-1)
is obtained by dividing the number of recorded packets
PACKi,j by the sampled fractional mass
Mmeas,i,j as follows:
kb,i,j=PACKi,jMmeas,i,j.
Finally, the general calibration coefficient
kb,j,gen is computed for each class j
using
kb,j,gen=1Nstations∑stationskb,j,med,station,
where kb,j,med,station is the site-specific median
calibration coefficient computed over all samples i, and
Nstations is the number of stations. Even though the number of
calibration measurements differs from site to site, each coefficient
kb,j,med,station in Eq. (7) is equally weighted in
order to give the same importance to site-specific factors possibly
affecting the signal response at each site.
Workflow leading from the single-grain-size flume
experiments with particles from 10 size classes j (top right) to
the final array of general calibration coefficients
kb,j,gen. Central
elements are the lower and upper threshold values
thaf,low,j and
thaf,up,j, the number of
recorded packets PACKi,j per
sample i and class j, the sampled fractional mass
Mmeas,i,j, the
sample- and class-specific calibration coefficient
kb,i,j, and
finally the site-specific median calibration coefficient
kb,j,med,station.
To enable a comparison with the AH method developed by Wyss et al. (2016a),
the “field calibration” part of the workflow was also carried out with the
AH thresholds thah,j (see Table 3).
Characteristics of the packets recorded during single-grain-size
experiments conducted with the Avançon de Nant flume setup using the
partition wall, with the maximum amplitude of the envelope
MaxAmpenv and the centroid frequency
fcentroid. The red and blue dots correspond to packets
recorded by the shielded plate G1 and the unshielded plate G2, respectively.
The grey rectangles are the class boundaries delimited by the thresholds
obtained for the AH method (a) and the AF method (b). The number of packets
PACKj located within the class boundaries delimited by the AH
thresholds and the AF thresholds are indicated in (c) and (d), respectively.
In (a), fcentroid is shown as a function of
MaxAmpenv for information purposes only.
At this point, the single array of calibration coefficients
kb,j,gen is applied as follows to each field
calibration measurement i in order to obtain fractional bedload mass estimates
Mest,i,j:
Mest,i,j=kb,j,gen⋅PACKi,j.
Rickenmann and Fritschi (2017) showed that bedload mass estimates derived
from SPG measurements are more accurate at higher transport rates. The
estimated fractional bedload mass Mest,i,j can be
converted to a unit fractional transport rate
qb,est,i,j [kg m-1 s-1] using
qb,est,i,j=1wp⋅np⋅Mest,i,jΔti,
where wp is the standard width of an impact
plate (0.5 m), np is the number of plates (which may include
the whole transect or a section of particular interest), and Δti is the sampling duration in seconds. Finally, the estimated unit
total bedload flux qb,tot,est,i can be computed as follows:
qb,tot,est,i=∑j=110qb,est,i,j.
Note that the exact same procedure was followed using the AH thresholds
thah,j derived from Wyss et al. (2016a) (Eq. 1; Table 3) to
compare the performance between the AH method and the new AF method.
General calibration coefficients kb,j,gen
obtained for each grain-size class j with the AH method and the AF
method using Eq. (7). Dm,j indicates the mean particle
diameter of each grain-size class j.
The flume experiments performed in the modified Avançon de Nant setup
with the partition wall help to illustrate the performance of the two
calibration methods. Figure 7a and b show the amplitude and frequency
characteristics of all packets detected by the SPG system during these
experiments. Packets detected by the shielded sensor G1 all originate from
impacts that occurred either on the concrete bed or on plate G2 (Fig. 3;
Nicollier et al., 2022). Packets detected by the unshielded sensor G2 are
considered apparent if they are located in the area of the
amplitude–frequency graph (Fig. 7a) where G1 and G2 packets overlap. Such
packets are presumed to have been triggered by impacts on the concrete bed.
This overlapping area arises from the fact that a seismic wave generated by
an impact on the concrete bed follows a similar path towards both sensors,
resulting in the recording of two apparent packets with comparable
characteristics. The remaining packets, detected by G2 and located in the
non-overlapping area of the amplitude–frequency graph, are considered real.
The difference in fcentroid between real and apparent packets
(Fig. 7a) reflects the faster attenuation of higher frequencies during wave
propagation. Size class boundaries derived by the AH method of Wyss et al. (2016a) encompass all of the packets, both apparent and real (Fig. 7a). This
is because the boundaries are defined solely by AH thresholds
(thah,j). By contrast, in the AF method proposed here, the
two-dimensional class boundaries given by thaf,low,j and
thaf,up,j cover only a fraction of all detected packets
(Fig. 7b). Applying the step-like AF thresholds leads to a strong reduction
of the number of packets PACKj within each size class j for plate
G1 (shielded), particularly for the smaller classes. Meanwhile, the AF
thresholds had little effect on the number of detected packets for G2
(unshielded), except for a strong decrease for classes j=1 and 2
and a slight increase for classes j=6 to 10 (Fig. 7c and d). The AH
thresholds encompass in total 1945 packets for the shielded geophone G1 and
4823 packets for the unshielded geophone plate G2. In comparison, the AF
thresholds encompass in total 159 packets for the shielded geophone G1 and
2202 packets for the unshielded geophone plate G2 (counting the packets in
the overlapping class boundaries only once). Considering apparent packets to be
noise and real packets to be signal, applying the new AF method results in an
increased signal-to-noise ratio, as shown by the larger vertical separation
between the blue (signal) and red (noise) lines in Fig. 7d compared to 7c.
The kb,i,j calibration coefficients obtained with
the AH method (a) and the AF method (b) for each field site. The colored
areas indicate the range between the 5th and 95th percentile
kb,i,j values, the full lines indicate the site-specific
median coefficients kb,j,med, and the black dashed
lines indicate the final general calibration coefficients
kb,j,gen as a function of the mean particle diameter
Dm,j of each grain-size class j.
Field calibration coefficients
As discussed in the previous section, the number of packets
PACKi,jdetected for a given class j varies together with
the thresholds thah,j, thaf,low,j, and
thaf,up,j. Because the measured fractional bedload mass
Mmeas,i,j remains constant, the calibration
coefficients kb,i,j will depend on the number
of packets detected and thus on the thresholds that are used to classify
them. We can make the following observations regarding the calibration
coefficients kb,i,j obtained using the AF
method compared to the AH method (Fig. 8). First, the
kb,i,j coefficients of the smaller size
classes are substantially lower, meaning that fewer packets per unit mass
are detected. Second, for the larger size classes, slightly more packets are
detected per unit mass. Third, the overall scatter of the
kb,i,j coefficients across all sites is
smaller, in particular for the six smallest classes j. This is reflected in
the decrease in the mean coefficient of variation (CV) across all classes j and all sites from CV = 1.17 (in the AH method) to CV = 0.93 (in the
AF method). Fourth, the scatter of the site-specific
kb,i,j coefficients is usually smaller. This
is supported by the change in the mean CV across all classes from 0.89 to
0.54 for Albula, from 0.83 to 0.75 for Avançon de Nant, and from
1.31 to 1.00 for the Erlenbach between the AH and AF methods. The mean CV
for the Navisence site, however, remains unchanged at 0.85. The general
coefficients kb,j,gen obtained from the
site-specific median coefficients kb,j,med using Eq. (7) are listed in Table 4.
Performance of the AH method and the AF method regarding
fractional flux estimates for each class j with the
following parameters: the linear coefficient a, the
exponent b and the correlation coefficient
r of the power-law regression lines visible in Fig. 9,
the coefficient of determination
R2, the root mean square error
RMSE, and the percentage of all detected samples
for which the estimated value differs from the measured value by less than a
factor of 2 and 5 pfactor_2 and pfactor_5, respectively. These values were first computed for each site
separately and then averaged over all four sites. The number of measured
Nsamples,meas and the number of
estimated samples Nsamples,est showing a positive unit fractional rate were summed over all four sites.
Unit fractional transport rate estimates obtained with the AF
method for each size class j and each station. The light grey dots in the
background indicate the estimates obtained with the AH method and are
represented in more detail in the Supplement (Fig. S1). Each
panel is annotated with the mean particle size Dm,j of
the represented class. The solid black lines correspond to the reference 1:1
line, while the dotted lines delimit factors of 5 above and below it (from
0.2 to 5). The dashed colored lines are power-law regression lines; the mean
coefficients over all four sites are listed in Table 5. The dots along the
axes indicate samples for which either the measured or estimated unit
fractional flux equals 0. These samples are not considered for the
computation of the trend lines.
Bedload flux estimates
We can now apply the general calibration coefficients
kb,j,gen in Eq. (8) to compute fractional
bedload mass estimates Mest,i,j and subsequently
estimates of the fractional flux per unit width
qb,est,i,j (Eq. 9) for every sample collected
at the four field sites (Fig. 9). The results obtained with the AH method
can be found in Sect. S3 in the Supplement, and Table 5 provides further
information on the performance of the two methods.
When applied to the field calibration data, the AF method generally yields
more accurate flux estimates than the AH method does, particularly for the
five smallest grain-size classes. This improvement is most notably reflected
by the coefficient of determination R2 values, describing the accuracy
of the estimates relative to the 1:1 line (Table 5). R2 increased from
0.4 to 0.71 for class j=1 and from 0.51 to 0.72 for class j=2, but by
contrast, R2 decreased slightly from 0.57 to 0.55 for class j=8. The
root mean square error (RMSE), which quantifies the expected error of the
estimates, leads to similar observations (Table 5). The RMSE decreased
from 0.094 to 0.068 kg m-1 s-1 for class
j=1 and from 0.031 to 0.021 kg m-1 s-1
for class j=2, but increased slightly from 0.037 to 0.039 for class j=8.
A further interesting result is the increase for the first eight classes of
the percentage pfactor_5 of all detected
samples, whose estimated bedload fluxes differ by less than a factor of 5
from the measured values (Fig. 9; Table 5).
Ratio rqb,tot between the estimated and
measured unit total mass flux as a function of the total sampled mass
Mtot,meas for each collected sample i and each station with
the AH method (a) and the AF method (b). The box plots on the right (c)
indicate the range of rqb,tot values obtained for each
station. The boxes in solid colors show the results obtained with the AH
method, and the hatched boxes show the results obtained with the AF method.
Aside from these comparative observations, it is also worth mentioning the
following more general findings that are valid for both methods. (i) For most
size fractions, the relative scatter of the estimates (on the log–log plots)
decreases with increasing transport rates. (ii) At low transport rates, mass
fluxes are generally overestimated, while at high transport rates they are
generally underestimated. This is shown by the dashed colored power-law
regression lines shown in Fig. 9, described by the corresponding linear
coefficient a and exponent b in Table 5. (iii) As indicated by the yellow dots
and regression lines in Fig. 9, mass fluxes for the Erlenbach closely follow
the 1:1 line but tend to be slightly underestimated. (iv) The numbers of
measured (Nsamples,meas) and estimated
(Nsamples,est) samples both decrease with increasing particle
size. While more than 300 samples were measured and estimated for each of
the five smallest grain-size classes, these numbers gradually decrease to
around 100 for the largest class j=10. Furthermore, samples for which
either the measured or estimated flux equals 0 are indicated as dots
along the axes in Fig. 9. If the measured flux is zero but the estimated
flux is positive, the sample can be regarded as a false positive (Fawcett,
2006). The difference between Nsamples,meas and
Nsamples,est in Table 5 indicates that the occurrence of such
false positive samples increases with increasing particle size. Further
performance metrics derived from the confusion matrix can be found in the
Supplement (Table S2).
As indicated by Eq. (10), the unit total flux estimates are computed as the
sum of the unit fractional flux estimates over all 10 classes. Figure 10 shows
the ratio rqb,tot between the estimated total flux
qb,tot,est and the measured total flux
qb,tot,meas for all 308 calibration samples as a function of
the sampled total mass Mtot,meas. Here, the estimates for the
Albula, Navisence, and Avançon de Nant sites are slightly more
accurate with the AF method than with the AH method, whereas the estimates
for the Erlenbach improve substantially, with the median
rqb,tot value increasing from 0.31 to 0.64. Note that the
observations (i) to (iii) made earlier regarding the fractional flux
estimates are also valid here. Figure 10 also provides an interesting overview
of the sampled masses at all four stations, reflecting the capacities of the
different devices (automated and manual basket samplers as well as a crane-mounted
net sampler) used to collect the calibration samples.
Grain-size estimates
We can combine the SPG bedload flux estimates for all grain-size fractions
and thus derive grain-size distributions, which can then be compared to the
measured size distributions of each calibration sample. Figure 11 compares the
performance of the AH and the AF methods in estimating the characteristic
grain sizes D30, D50, D67, and
D84 (where Dx is the grain diameter for which x
percent of the sampled bedload mass is finer). The accuracy of the estimates
is indicated by the ratio rDx between the estimated and measured
characteristic grain size Dx. Compared to the AH method, the AF method
mainly improves the estimates of the four characteristic grain sizes for the
Navisence and Erlenbach sites but has little effect at the other two
sites. The largest improvement is achieved for the Erlenbach site, with the
median rD30 changing from 1.37 to 1.02, the median
rD50 changing from 1.48 to 1.01, the median
rD67 changing from 1.46 to 1.05, and the median
rD84 changing from 1.39 to 1.10. In contrast, applying
the AF method to the Avançon de Nant dataset slightly reduced the
accuracy of the characteristic grain-size estimates, with the median
rD30 changing from 0.83 to 0.88, the median
rD50 changing from 0.81 to 0.79, the median
rD67 changing from 0.80 to 0.82, and the median
rD84 changing from 0.85 to 0.83. The overall accuracy of
the estimates decreases with increasing characteristic size Dx for both
methods, and for every characteristic size Dx, the Dx tends to be
overestimated for finer grain mixtures and underestimated for coarser grain
mixtures.
Ratio rDx between the estimated and measured
characteristic grain sizes D30, D50,
D67, and D84 as a function of the measured grain
diameter Dx,meas for each collected sample i and each
station using the AH method (column 1) and the AF method (column 2). Dx
is the grain diameter for which x percent of the sampled bedload is finer.
The box plots in column 3 indicate the range of rDx values obtained
for each station. The boxes in solid colors show the results obtained with
the AH method, and the hatched boxes show the results obtained with the AF
method.
DiscussionThe hybrid calibration procedure
Recent studies have pointed out the difficulty of transferring flume-based
calibrations of impact plate systems to field applications (e.g., Mao et al.,
2016; Wyss et al., 2016c; Kuhnle et al., 2017). In the hybrid calibration
approach presented here, we took advantage of flume experiments to obtain
amplitude and amplitude–frequency thresholds for each particle size class,
which were subsequently applied to field calibration datasets to derive the
general calibration coefficients kb,j,gen.
The entire hybrid calibration procedure was run iteratively until the
optimal linear coefficient and exponent of the criterion (Eq. 3) used to
filter out apparent packets were found (Fig. 6). As an objective function, we
used an equally weighted combination of parameters describing the accuracy
of bedload flux and grain-size estimates, i.e., r, R2,
pfactor_2, pfactor_5, and RMSE as shown in Table 5 and rDx as shown in Fig. 11. The
accuracy is derived from the confusion matrix (Fawcett, 2006) as shown in
Table S2 in the Supplement. We looked for two types of optimal
calibrations. The first type is a general calibration, for which we have
presented the results in Sect. 3. This calibration combines all four
stations in order to investigate the feasibility of a general signal
conversion procedure applicable to multiple sites equipped with the SPG
system. The second type is a site-specific calibration aiming to improve the
accuracy of bedload transport rate estimates at a single monitoring station,
to be used for a more detailed analysis of bedload-related processes at a
given site (details of these site-specific calibrations are available in
Sects. S4 and S5 in the Supplement).
The biases introduced by apparent packets can be removed by site-specific
calibration of the coefficients kb,i,j, so the AF
and AH methods perform about equally well when calibrated separately to each
individual site (see Sects. S4 and S5 in the Supplement). This result
supports the use of the AF method, considering the large proportion of
packets left out by the AF thresholds (up to 91 % in the smallest class
j=1; see Table S4 in the Supplement). However, the abundance of
apparent packets varies considerably from site to site owing to differences
in the channel geometry, the bedload grain-size distribution, and the
construction details of the individual SPG installations. Because the AF
method filters out a substantial fraction of these apparent packets, it
yields substantially better general calibrations than the AH method does
(see Table 5).
We also tested the performance of an adapted version of the AH method
introduced by Rickenmann et al. (2018). This method was originally developed
for the Erlenbach site and aimed to correct for the relationship between the
signal response and the transport rate. In the present study, we applied
this method to each field site. The only notable improvement introduced by
the adapted AH method is the increased number of detected samples at the
Erlenbach station, leading to more accurate estimates of the various
characteristic grain sizes Dx at this site (Tables S8 and S9 in
the Supplement); the results for the other sites were not
substantially improved.
Two-dimensional size class thresholds
To understand the performance of the new AF method it is worth taking a
closer look at the role of the size class thresholds. As shown in Fig. 7,
replacing the upper amplitude thresholds with amplitude–frequency values
results in the following two important changes. First, a dimension is added,
which facilitates focusing on the narrow range of signal responses
characteristic for real packets and filtering out many of the apparent
packets. Second, the areas of the amplitude–frequency domain covered by two
adjacent classes can now overlap. Packets located in overlapping areas are
assigned once to each class and therefore counted twice. This explains why
both the number of detected packets PACKj (Fig. 7c and d) and
subsequently the kb,j values (Fig. 8) are slightly
higher when the AF method (instead of the AH method) is applied to the
larger size classes. Counting such packets twice is not unreasonable, given
that the ranges of signal responses recorded during single-grain-size flume
experiments for two contiguous grain-size classes significantly overlap,
even after apparent packets are filtered out (Fig. 5). Overlapping class
boundaries therefore result in a less strict classification of the few
packets that are on the edges of the grain-size classes. In Fig. 7b, out of
2256 packets recorded by G2 (blue), 144 packets have been counted twice. But
interestingly, this is not true of any of the 153 packets recorded by G1
(red) within the class boundaries. A further result supports the use of the
two-dimensional size class thresholds. When applying the AF method, the
kb,j coefficients obtained for the different sites
(Fig. 8b) reach a maximum value at the third-smallest size class. A similar
yet stronger decrease towards the two smallest classes was described by Wyss
et al. (2016b) and was related to the reduced detectability of the smallest
particle sizes.
Through the reduced area covered by the new amplitude–frequency thresholds
in Fig. 7b, a certain percentage of all the packets recorded during the
field calibration experiments is neglected for general calibration: 55 %
at the Albula site, 63 % at Navisence, 58 % at Avançon de Nant, and
only 9 % at Erlenbach. This suggests that the plates embedded at Erlenbach
pick up less noise from their surroundings. A similar trend was observed by
Nicollier et al. (2022) when comparing the maximum amplitude registered by
two adjacent plates for a given impact at the same location. This difference
in noise detection levels is possibly accentuated by the number of impacted
plates during bedload transport events. The SPG array embedded in the
artificial U-shaped channel of the Erlenbach has the particularity that only
2 of its 12 plates are usually impacted by bedload particles during
floods (and only sediment crossing these two plates is caught by the
automatic basket sampler). At the other sites, in contrast, every 10 to 30
embedded plates are submerged by the flow and can thus potentially be
impacted.
Sampling uncertainties
Even though the AF method improved the overall accuracy of flux estimates
for most classes (Table 5), some trends addressed in Sect. 3 suggest that
factors other than the noise level also control the accuracy of the
estimates. The dataset presented in this study includes 308 calibration
measurements and is to our knowledge the largest dataset gathered for any
impact plate system. Still, it appears that the number of collected samples
is not sufficient to accurately assess the performance of the two methods
for the three largest particle size classes (Fig. 9; Table 5). This mainly
relates to a higher proportion of large particles compared to finer ones
in typical sediment mixtures (Rickenmann et al., 2014; Mao et al., 2016).
Earlier investigations have shown that a larger number of detected bedload
particles reduces the scatter of total mass estimates by averaging over
stochastic factors such as the impact location on a given impact plate, the
particle transport mode (sliding, rolling, saltating, etc.; Chen et al.,
2022), and the impact velocity (Rickenmann and McArdell, 2008; Turowski et
al., 2013). A further uncertainty arises because these larger particles are
transported at higher bed shear stresses (Einstein, 1950; Wilcock and Crowe,
2003), which also mobilize more total material and thus pose a serious
challenge regarding the sampling efficiency of the calibration bedload
samplers. Bunte and Abt (2005) and Bunte et al. (2019) have demonstrated
that reducing the sampling duration with a bedload trap from 60 to 2 min
decreases both the sampled unit total bedload flux qb,tot and the
sampled maximum particle size Dmax by about half. In the present
study, total bedload fluxes up to 4 kg m-1 s-1 were measured
with the net sampler, meaning that the measurement duration had to be
minimized to avoid overloading the sampler. At the Albula stream, for
instance, only four samples contained particles of the largest class, and
all four were sampled over a duration ranging from 1 to 2 min. As a
comparison, the longest sampling duration was reached at the Navisence site
and lasted 25 min. All this suggests that an optimal calibration of the
SPG system requires balancing the sampling duration and the number of
collected particles. Note that uncertainties in the direct measurements do
affect the accuracy of fractional sediment flux and grain-size estimates.
Flume experiments could potentially be used to assess the sampling
efficiency of the various calibration sampling methods, along with the
detection efficiency of the SPG system.
Transport rate
Two further trends are evident in the unit fractional flux estimates
obtained for the seven smallest classes, for which most samples were
detected (Nsamples,est/Nsamples,meas>96 %; Table 5). First, the relative scatter (on the log–log
plots) of the fractional flux estimates around the power-law regression
lines in Fig. 9 is smaller at higher transport rates. Second, both total and
fractional fluxes are generally overestimated at low transport rates and
underestimated at high transport rates (Figs. 9 and 10). These findings agree
with results from previous calibration campaigns with the SPG system
(Rickenmann and Fritschi, 2017; Rickenmann et al., 2018), but a
comprehensive explanation for these trends is still missing. The following
hypotheses can be raised to explain the relationship between the mass flux
estimates and the transport rate qb. (i) The SPG system may suffer from
signal saturation when the transport rate is too high, as has been document
in the Japanese pipe microphone system (Mizuyama et al., 2011; Choi, 2020).
In our SPG data, we have observed long packets containing multiple large
peaks corresponding to several impacts occurring so quickly after one
another that they were not detected as separate packets. One can expect that
the probability of occurrence of such packets increases together with the
transport rate, the transport of large particles (which typically
generate packets of longer durations), and the occurrence of sliding
and rolling particles (Chen et al., 2022). The long packets obscure the
multiple shorter packets that would otherwise be individually counted,
leading to underestimated mass fluxes for a given kb,j value. The development of a procedure to identify such packets and
attribute the peaks contained therein to individual impacts could represent
an interesting aim for future research. (ii) Field observations of bedload
sheets being transported over plates at high transport rates were made at
the Vallon de Nant site. In the presence of bedload sheets, one can expect
that the detection rate of transported particles is hampered by multiple
particle layers (Rickenmann et al., 1997; Turowski and Rickenmann, 2009),
kinetic sieving (e.g., Frey and Church, 2011), or percolation processes (e.g.,
Recking et al., 2009). As such, it would be reasonable to expect a stronger
signal response at lower transport rates (Fig. 10).
We are not able to give a clear explanation for the overestimates of the
characteristic grain size Dx for finer grain mixtures and
underestimates for coarser grain mixtures (as shown in Fig. 11). A similar
trend was also observed by Rickenmann et al. (2018) for calibration
measurements originating from the Erlenbach. We expect that the decrease in
the detection rate along with increasing transport intensity, as mentioned
above, may partly explain this phenomenon.
Ratio rqb,tot between the estimated and
measured unit total mass flux as a function of the mean flow velocity
Vf for each collected sample and each station with the AH
method (a) and the AF method (b). The indicated flow velocity corresponds to
in situ measurements performed during (or close in time to) the
corresponding calibration measurement. Due to the stable flow velocity of 5 m s-1 measured at the Erlenbach site, the range of
rqb,tot values is represented as a box plot. The yellow
circles correspond to outliers.
Effect of the flow velocity
A recurrent feature in the results presented above is an offset between the
estimates obtained for the Erlenbach and those obtained for the three other
stations. A similar offset was observed earlier for linear calibration
relations of total bedload mass between the Erlenbach and other field sites
with more natural approach flow conditions (Rickenmann et al., 2014).
Although applying the new amplitude–frequency method has reduced the offset
in the present study significantly, it remains visible for both fractional
and total bedload flux estimates (Figs. 9, 10, and 12). At the Erlenbach
site, the last 35 m upstream of the SPG system consists of an artificial
bed with a steep channel slope of 16 %, made of large flat embedded
boulders (Roth et al., 2016). This explains the supercritical flow regime
with a Froude number around 5.1 (Wyss et al., 2016c) and a flow velocity
Vf around 5 m s-1 at the check dam with the geophone
sensors (Table S1). Bedload particle velocity Vp was
introduced by Wyss et al. (2016b, c) as a possible governing parameter
affecting the number of particles detected by the SPG system, with fast-moving
particles being less likely to collide against the Swiss plate geophone than
slower moving ones, which are more frequently in contact with the bed. For
the present study, we used Vf as a proxy for Vp,
even though bedload particles generally travel more slowly than the fluid
surrounding them (Ancey et al., 2008; Chatanantavet et al., 2013; Auel et
al., 2017). Past flume experiments (Wyss et al., 2016b; Kuhnle et al., 2017)
have shown that the calibration coefficient kb,j can vary with
the flow velocity Vf such that a 3-fold increase in
Vf can lead to a 2-fold decrease in
kb,j. The better detectability of particles that one could
expect from the higher impact energy (Wyss et al., 2016b) seems to be
insufficient to compensate for the strong reduction of the number of impacts
on a plate as flow velocity increases. This possibly arises from the fact
that larger flow velocities (without increased turbulence) may also lead to
flatter saltation trajectories, thus decreasing the vertical component of
the impact force. Furthermore, bed morphology, bed roughness, and flow
velocity play important roles in determining particle transport mode, i.e.,
sliding, rolling, or saltating (e.g., Bagnold, 1973; Lajeunesse et al.,
2010). Although high flow velocities generally favor the saltating mode
(Ancey et al., 2002; Chen et al., 2022), the shallow flow depths measured at
the Erlenbach (in average 0.1 m; Wyss et al., 2016b) may limit the hop height
of larger particles (Amir et al., 2017). Considering all these aspects, we
hypothesize that the generally underestimated transport rates observed for
the Erlenbach site mainly arise from the exceptionally high flow velocity,
shallow water depths, and related transport mode (Fig. 12). Continuous
streamflow measurements are lacking at the Albula and Navisence sites,
hampering a more detailed analysis of the relationship between flow
velocities and detection rates. Another improvable aspect is the low
variability between the site-specific calibration relationships of the three
natural sites before the implementation the AF method (Fig. 8a). It
would have been interesting to test the method on a larger number (and
variety) of sites. Unfortunately, these four chosen sites are currently the
only ones at which a full geophone signal has been recorded during
calibration measurements.
K-fold cross-validation
In a last stage, we tested the robustness of the AH and AF methods by
splitting the dataset into calibration and validation subsets. Because the
number of calibration measurements is relatively small and varies between
stations, we applied a 4-fold cross-validation technique (e.g., Khosravi et
al., 2020). The field calibration measurements were distributed over four
folds, each containing an equal number of calibration measurements from each
site (Fig. S4 in the Supplement). One after another, the folds were
used as validation datasets, while the remaining three folds were used for
calibration. General calibration coefficients
kb,j,gen were obtained from the calibration
dataset and subsequently applied to the validation data to derive flux
estimates. Even though each fold contains a total of only 48 samples (12 per
site), the results obtained with the 4-fold cross-validation procedure
support our conclusion that including frequency information in the packet
classification procedure improves the mean accuracy of the estimates over
all sites, in particular for the smaller five to six size classes j (Table S10 in the Supplement). Nicollier et al. (2022) found that the true size of
particles generating apparent packets is mostly underestimated due to the
attenuation of the vibrations as they propagate (see Fig. 7). It is
therefore reasonable that the AF method mainly improves the flux estimates
for these smaller classes.
Conclusions
The Swiss plate geophone (SPG) is a bedload surrogate monitoring system that
has been installed in several gravel-bed streams and was calibrated using
direct sampling techniques. While most site-specific calibration
relationships for total mass flux are robust across multiple orders of
magnitude, the mean calibration coefficients can still vary by about a
factor of 6 between different sites. In this study, we derived a general
procedure to convert SPG signals into fractional bedload fluxes using an
extensive dataset comprising flume experiments as well as 308 field
calibration measurements from four field sites. The proposed hybrid approach
is based on previous findings (Antoniazza et al., 2020; Nicollier et al.,
2022) that the SPG system is biased by elastic waves that propagate through
the apparatus and generate noise in the form of spurious “apparent”
packets. We introduced the amplitude–frequency (AF) method as an alternative
to the amplitude histogram (AH) method developed by Wyss et al. (2016a).
Packets recorded during single-grain-size flume experiments were first
filtered to exclude apparent packets and then used to derive grain-size
class thresholds for packet classification. We found that filtering out
apparent packets results in more consistent relationships between particle
diameter and amplitude–frequency characteristics of the SPG signal.
Furthermore, we showed that including frequency information in size class
thresholds helps in excluding apparent packets and thus improves the
signal-to-noise ratio. In a second stage, we applied these flume-based
thresholds to field calibration measurements and derived general calibration
coefficients applicable at all four sites for 10 different grain-size
fractions. The AH method, by contrast, requires site-specific calibration
because it cannot account for the site-to-site differences in the abundance
of apparent packets. Averaged over the 10 grain-size fractions, the bedload
mass of 69 % and 96 % of the samples was estimated within an offset of a
factor of 2 and 5, respectively, relative to the measured sample mass.
The remaining discrepancies between the site-specific results are mainly
attributed to large differences in flow (and probably particle) velocity.
Finally, the sampled mass, transport rate, and sampling efficiency
were identified as further factors possibly influencing the accuracy of mass
flux and grain-size estimates.
The presented results are highly encouraging regarding future applications
of surrogate monitoring methods to investigate bedload transport processes.
The findings also underline the valuable contribution of flume experiments
to our understanding of the relationship between bedload transport and the
recorded SPG signal. But above all, this study highlights the requirements
for obtaining calibrations that are transferable across sites: accurate and
numerous direct sampling measurements with long sampling durations and large
sampled masses, sensors insulated from surrounding noise sources, and highly
resolved temporal information about the streamflow to identify and account
for variations in the transport conditions.
NotationacLinear coefficient of the criterionAFFTFourier amplitudeAm,jMean amplitude registered for particle size class jbcLinear coefficient of the criterionΔtiSampling durationDm,jMean particle diameter for particle size class jDsieve,jLower sieve size retaining particle class jDxCharacteristic grain sizefcentroidCentroid frequencyiSample indexjParticle size class indexkb,i,jSample- and class-specific calibration coefficientkb,j,med,stationMedian calibration coefficient for particle size class j and a given stationkb,j,genGeneral calibration coefficient for particle size class jMest,i,jEstimated fractional mass per sample and per classMmeas,i,jSampled fractional mass per sample and per classMaxAmpenvMaximum registered amplitude within a packetNsamples,estNumber of detected samplesNstationsNumber of stationsPACKi,jNumber of recorded packets per sample and per classpfactor_xPercentage of all detected samples for which the estimated and the measured values differ from each other by less than a factor of xqb,est,i,jEstimated unit fractional transport rate per sample and per classqb,meas,i,jMeasured unit fractional transport rate per sample and per classqb,tot,est,iEstimated unit total bedload flux per sampleqb,tot,meas,iMeasured unit total bedload flux per sampleR2Coefficient of determinationrCorrelation coefficientrxRatio between estimated and measured values xthah,jAmplitude histogram thresholdsthaf,low,jLower amplitude–frequency thresholdsthaf,up,jUpper amplitude–frequency thresholdsVfMean flow velocitywpStandard width of an impact plateData availability
The dataset presented in this paper is available online on the EnviDat
repository at
https://www.envidat.ch/#/metadata/sediment-transport-observations-in-swiss-mountain-streams (Nicollier et al., 2022).
The supplement related to this article is available online at: https://doi.org/10.5194/esurf-10-929-2022-supplement.
Author contributions
TN designed and carried out the field and flume experiments,
developed the presented workflow, and prepared the paper with
contributions from all co-authors. GA designed and carried
out the field experiments at the Vallon de Nant site. LA helped
develop the methodology and contributed to the formal analysis. DR contributed to the conceptualization and the supervision of the
presented work, contributed to the design of the methodology, and provided
support during the field and flume experiments. JWK
contributed to the development of the methodology and significantly
contributed to the preparation of the initial draft.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
This study was supported by Swiss National Science Foundation (SNSF) grant
200021L_172606 and by Deutsche Forschungsgemeinschaft (DFG)
grant RU 1546/7-1. The authors are grateful to Arnd Hartlieb, the
students of the TU Munich, and the technical staff of the Oskar von
Miller Institute for helping to set up and perform the flume experiments.
They also warmly thank Norina Andres, Mehdi Mattou, Nicolas Steeb, Florian
Schläfli, Konrad Eppel, and Jonas von Wartburg for their efforts and
motivation during the field calibration campaigns. Special thanks go to
Stefan Boss for his support with the measurement systems at all sites and
to Andreas Schmucki, who never gave up repairing the net sampler. Alexandre
Badoux is further thanked for his valuable suggestions regarding an earlier
version of the paper.
Financial support
This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. 200021L_172606) and the Deutsche Forschungsgemeinschaft (grant no. RU 1546/7-1).
Review statement
This paper was edited by Claire Masteller and reviewed by Dan Cadol and two anonymous referees.
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