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Streambed mobility in gravel-bed rivers is largely controlled by the rate at which particles with different grain sizes are recruited from the riverbed into the bed load. In this paper, we present a study case in which we explored this question, based on combining field observations using painted plots and the grain size analysis of a large flood sediment deposit in the River Esva, northwest Spain, and the generalized threshold model (GTM) competence model developed by Recking. The main aim was to accomplish a complete characterization of streambed mobility in this river. The obtained results suggest the large potential of the GTM model compared to previous competence models when searching for the quantitative description of particle entrainment and streambed mobility in the River Esva. We observed how the grain size of the bed load in the River Esva tended to be closer to that of the sub-armour bed material during large floods, while moderate magnitude flows tended to carry a relatively fine bed load. Additionally, we compared our results with previously published field observations on flow competence. This comparison outlined the large degree of site specificity in the links between grain size of the bed load and that of the bed material.
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Article
Quantifying the Variability in Flow Competence and
Streambed Mobility with Water Discharge in a
Gravel-Bed Channel: River Esva, NW Spain
Daniel Vázquez-Tarrío1, 2, * , Elena Fernández-Iglesias 1, María Fernández García1and
Jorge Marquínez 1,2
1INDUROT, University of Oviedo, Campus de Mieres, s/n 33600 Mieres, Spain;
elena.indurot@uniovi.es (E.F.-I.); fernandezgarmaria@uniovi.es (M.F.G.); marquinez@uniovi.es (J.M.)
2Department of Geology, University of Oviedo, c\Jesús Arias de Velasco, s/n 33005 Oviedo, Spain
*Correspondence: danielvazqueztarrio@gmail.com or vazquezdaniel@uniovi.es
Received: 16 November 2019; Accepted: 13 December 2019; Published: 17 December 2019


Abstract:
Streambed mobility in gravel-bed rivers is largely controlled by the rate at which particles
with dierent grain sizes are recruited from the riverbed into the bed load. In this paper, we present a
study case in which we explored this question, based on combining field observations using painted
plots and the grain size analysis of a large flood sediment deposit in the River Esva, northwest Spain,
and the generalized threshold model (GTM) competence model developed by Recking. The main
aim was to accomplish a complete characterization of streambed mobility in this river. The obtained
results suggest the large potential of the GTM model compared to previous competence models when
searching for the quantitative description of particle entrainment and streambed mobility in the River
Esva. We observed how the grain size of the bed load in the River Esva tended to be closer to that of
the sub-armour bed material during large floods, while moderate magnitude flows tended to carry
a relatively fine bed load. Additionally, we compared our results with previously published field
observations on flow competence. This comparison outlined the large degree of site specificity in the
links between grain size of the bed load and that of the bed material.
Keywords:
flow competence; critical shear stress; streambed mobility; bed load; bed surface texture
1. Introduction
Unravelling the complex interplays between flow strength, grain-size distribution (GSD) of the
bed load, and that of the bed material is a central issue in river morphodynamics [
1
,
2
]. This topic has
been classically approached in fluvial geomorphology and sediment transport studies through the
analysis of the thresholds for bed particle entrainment as long as the ability of the stream to displace
riverbed particles controls the GSD of the bed load in alluvial channels [
2
5
]. In this regard, the
inception of motion for streambed particles also exerts significant control over the area of bed surface
that is actively involved in bed load motion and the vertical extent of scour and fill processes. Thus,
particle entrainment is closely related to the overall streambed stability and the spatial extent of bed
disturbance caused by sediment erosion and deposition during floods [
6
], which ultimately represent
important drivers of aquatic habitat quality in river ecosystems [710].
Additionally, particle entrainment is closely related to the “flow competence” concept, introduced
first by Gilbert and Murphy (1914) [
11
] and defined based on the size of the largest clast moved by a
given flow. The idea of river competence relies on assuming that the coarsest clast transported by a
streamflow provides a measure of the stream’s ability to entrain the bed sediment. Consequently, the
measure of the largest clast size of fluvial deposits has been a common and important tool for most
Water 2019,11, 2662; doi:10.3390/w11122662 www.mdpi.com/journal/water
Water 2019,11, 2662 2 of 26
geologists. This procedure was frequently used as an instrument to infer velocities, discharges, mean
stresses, and depths of flows that transported the particles found in fluvial conglomerates [
12
19
], or
in the evaluation of extreme flood hydraulics [
20
]. However, the use of the largest moved clasts in this
way, i.e., as a technique to infer dierences in flow strength and stream’s ability to convey sediment
between dierent sites, involves the implicit assumption that finer grains are always entrained at lower
flows than coarser grains and over a relatively broad range of flow discharges [
21
,
22
]. This implies
ignoring important physical aspects of sediment entrainment that nuance the (in principle) expectable
“weight selective” assumption for particle entrainment [2,23,24].
Consequently, there is a clear interest in better understanding the links between the GSD of the
bed material, the streambed surface, the bed load, and the spatial–temporal patterns of streambed
mobility in coarse bed rivers. Previous works have already explored the relationship between the
grain size of the bed load, sampled using sediment traps and/or dierent samplers, and the grain size
of the bed material [
1
,
13
,
18
,
25
]. However, in many cases, these observations were made before some
of the more modern bed load transport and flow competence models were developed (i.e., Parker
(1990) [
26
]; Wilcock and Crowe (2003) [
27
]; Recking, (2016) [
2
]), so the former could still benefit from
new field testing. Additionally, available field measures of the GSD of the bed load were carried out in
many cases during moderate and regular bed load transport episodes (when sampling bed load with
Helley-Smith and other kinds of samplers is easier), whereas information about relatively strong events
is still scarce. In summary, more field studies are needed in order to better grasp several questions
related to streambed mobility, such as understanding whether the GSD of the bed material proxies that
of the bed load or not, or how the bed state modulates the relationship between particle entrainment
and flow strength.
In this regard, the current paper presents a case study accomplished in a gravel bed stream from
northwest Spain, where an extreme flood episode occurred in January 2019. It left important sediment
deposits, and its GSD was sampled in the field. Additionally, painted plots were employed in order to
monitor streambed mobility during regular, low-magnitude floods occurring before this major flood
episode. Both sources of data were used in order to calibrate a streambed mobility model, based on
Recking (2016) [
2
], which, in turn, was used for modelling the GSD of the average annual bed load
and the temporal patterns of streambed mobility. The obtained results highlight how the grain size
of the bed load in the River Esva tends to be closer to that of the sub-armour bed sediment during
large floods, while moderate magnitude flows carry a relatively finer bed load. These results show
the potential of coupling a competence model (such as the GTM model [
2
]) with field observations in
order to predict streambed mobility. We also compared our measures and estimates with the bed load
information available in Milhous (1973) [
28
], Andrews (1994) [
29
], Lisle (1995) [
25
] and Whittaker and
Potts (2007) [
1
]. This comparison outlined how the relations between grain size of the bed load and
that of the bed material can be largely variable with flow strength and among dierent sites.
2. Rationale
2.1. Physical Basis for Flow Competence Models
Flow competence and streambed mobility are closely related to particle entrainment and the
hydraulic thresholds for incipient sediment motion. In this regard, classical research tried to relate
shear stress and/or flow velocity to the size of the largest particles set in motion [
30
33
]. Initially,
threshold stresses for sediment entrainment were related to particle size [30]:
τc=τ
c×(ρsρ)×g×D(1)
where
ρ
is the density of water,
ρs
that of sediment, gis the gravity acceleration, Dthe grain size of the
bed sediment,
τc
is the critical bed shear stress for incipient motion (dimensional), and
τc
* is the critical
dimensionless Shields stress, for which a large range of values have been proposed, normally between
Water 2019,11, 2662 3 of 26
0.03 and 0.06 [
23
,
34
]. Once known the value of this parameter, the grain size of the particles that are
mobilized with increasing flow discharges (Dmax) are easy to estimate:
Dmax =τ
τ
c×(ρsρ)×g(2)
The previous model Equation (2) holds well in the ideal case of uniform sized particles. In the
case of a graded mixture, some works revealed how the eective stress acting on a given grain is
strongly influenced by the relative size of the grain within the mixture [
35
,
36
]. Sand content seems to
influence gravel mobility by reducing the flow resistance and intergranular friction [
11
,
27
,
37
]. Clast
arrangements and imbrications may also have a large impact on streambed mobility [
38
]. As a result, a
large variability of situations has been documented regarding the relative mobility of each size class of
a sediment mixture in gravel-bed rivers with several studies reporting size selective mobility over a
significant range of flow [
13
,
15
,
28
,
39
41
], while others suggested that all sizes in a sediment mixture
may begin moving over a range of narrow flow conditions [
42
46
]. So-called hiding functions were
proposed in order to mathematically describe this range of situations:
τ
ci =τ
cRe f × Di
Dre f !α
(3)
where
τci
is the critical Shields parameter for incipient motion of a given diameter D
i
and
τcref
the
critical Shields parameter for incipient motion of a reference particle diameter D
ref
;
α
is a coecient
whose value varies from 0 in the case of a total size selective behaviour (threshold conditions only
depend on particle size) to
1 in case of perfect equal mobility conditions (all sizes are entrained at the
same threshold stress, independent of their size). Rearranging Equation (3), we can estimate again the
size of the largest clast moved during floods:
Dmax =Dre f ×
τ
ci
τ
cRe f
1
1+α
(4)
In spite of the great improvement hiding functions (such as Equations (3) and (4)) provide for
modelling flow competence and streambed mobility, there are still some open issues. For instance,
some researchers have found that a simple power law (Equations (3) and (4)) is not enough to represent
the complete relation for any particle size critical stresses in gravel mixtures [
34
,
47
]. In addition,
gravel-bed rivers are systematically armored [
48
52
], i.e., the streambed surface is commonly coarser
than the underlying sub-armor deposit. The potential changes in the shape of the hiding parameter
α
with armor break-up are not considered when using a single hiding function. Additionally, the
entire bed load GSD cannot be computed directly from Equation (4) (which only supplies the coarsest
mobile size) but must be deduced from the bed load rates computed for each size class [
26
,
27
,
34
,
49
].
This commonly requires the use of an indirect scaling approach [
3
], implying that the same bed load
function can capture (on average) the transport of each individual size class for a given shear stress, an
idea that still needs field validation [2].
2.2. Recking’s (2016) GTM Model
Because of some of the issues stated above, Recking (2016) [
2
] proposed a new flow competence
model (named “generalized threshold model”, GTM), as an alternative approach for characterizing
streambed mobility and computing the GSD of the bed load. The GTM model computes the GSD of
the bed load after modelling which fraction of sediment in each size range is entrained from and which
fraction remains static on the riverbed. It does so without assuming a particular shape for the bed
load function, in contrast to common approaches based on the hiding function (i.e., Parker (1990) [
26
];
Water 2019,11, 2662 4 of 26
Wilcock and Crowe (2003) [
27
]). The GTM workflow operates in two steps. First, it computes the
maximum competent size from the following expression (see more details in Recking [2]):
M=84 × τ
84
τ
c84 !β
(5)
where Mis the Mth percentile of the surface GSD corresponding to the largest mobile class,
τ84
* is the
dimensionless Shields stress estimated based on the 84th percentile of the surface GSD (D
84
),
τc84
* is
the critical Shields stress for entraining the surface D
84
. The use of the 84-th percentile as reference
parameter in this model is meaningful, insofar as the inception of motion of the coarser particles
defines the moment when the armour layer starts to become disorganized [
53
,
54
]. Then, a transport
stage (
τ84
*/
τc84
*) close to 1 defines the threshold conditions when the armour layer destabilizes. In
this regard, the
β
exponent establishes the rate at which progressively coarser grains are set in motion
with increasing flow strengths. It may take a dierent value depending on whether or not the armour
layer destabilizes. A value of ~0.25 is suggested by Recking [
2
] when the armour layer is broken
(
τ84
*/
τc84
*>1) which implies assuming full mobility conditions at
τ84
*/
τc84
>2 as Wilcock and McArdell
(1997) [
46
] reported in the flume. In cases where the armour layer is not broken (
τ84
*/
τc84
<1), there
is more uncertainty in choosing the right value for
β
as it probably depends on the degree of bed
armoring/pavement. High
β
simulates an abrupt increase in competent size when armour breaks (i.e.,
a well-paved stream), whereas a low value models the case of a bed with a more progressive transition
from partial to full mobility conditions.
The second step of the GTM model is calculating the fraction (
ϕ
) of bed particles mobilized in
individual size ranges (i) of the bed surface:
ϕi=0.01 + 1i
Mγ!(6)
where γcan be estimated from:
γ=0.1 +0.5 × τ
84
τ
c84 !γ2
(7)
where
γ2
is a parameter that needs to be calibrated. The combination of Equations (6) and (7) is very
flexible and allows to model a broad range of streambed behaviors, such as progressive mobilizations
of surface particles or more abrupt transitions from stability to mobility. Thus, a right
γ2
parameter,
based on previous empirical information about riverbed behavior, allows the proper modelling of a
given study reach. This is one of the strongest points of the GTM model: the fact of identifying the
key parameters (
β
and
γ2
) driving streambed behavior and constraining the competence model. The
definition of these parameters from field observations permits to estimate the GSD of the bed load
with the following expression:
Fi=ϕi
PM
j=iϕj
(8)
In summary, there are three main advantages of the GTM model compared to previous approaches
to flow competence: (1) its flexibility, which allows to model a large range of particle entrainment and
streambed stability conditions; (2) the model is well-rooted into our current knowledge on sediment
transport mechanics and considers some situations that were not adequately grasped by previous flow
competence models; i.e., the change in entrainment conditions with armour break up; and (3) while most
of the previous flow competence models focused mainly on computing the mobilized grain sizes, the GTM
model also allows the estimation of the mobile fraction in each size range which is at least as important as
predicting the maximum transported grain in terms of evaluating streambed disturbance (interesting, for
example in many ecological applications). In spite of all these advantages, there have been no previous
Water 2019,11, 2662 5 of 26
attempts to take advantage of the GTM model for the characterization of streambed mobility in specific
field cases (Vázquez-Tarrío et al. (2019) [55] being the only exception to the best of our knowledge).
2.3. Proposed Workflow
The GTM model provides a well-suited practical framework for streambed mobility studies.
Hence, we propose a field workflow adapted to the characterization of streambed mobility in gravel-bed
rivers, which combines the flexibility of the GTM model with field observations (Figure 1). It combines
two dierent sources of field data. Painted tracers, which can be employed in order to characterize
streambed mobility at low transport conditions, and, as consequence, to obtain the best value for the
β
exponent in Equation (5) when
τ84
*/
τc84
*<1. The second source of data comes from collecting in
the field the GSD information of sediment deposited during large floods. This kind of data helps
to calibrate Equation (6) by forward modelling: by changing the
γ
parameter in Equation (6) until
obtaining an adequate value to fit the field measures. Finally, the
γ
parameter obtained from flood
deposits could be combined with the field identification of incipient motion conditions in order to
calibrate the
γ2
parameter in Equation (7). This paper illustrates the implementation, potential and
capabilities of this workflow, using the River Esva (NW Spain) as study case.
Water 2019, 11, x FOR PEER REVIEW 5 of 26
collecting in the field the GSD information of sediment deposited during large floods. This kind of
data helps to calibrate Equation (6) by forward modelling: by changing the γ parameter in Equation
(6) until obtaining an adequate value to fit the field measures. Finally, the γ parameter obtained from
flood deposits could be combined with the field identification of incipient motion conditions in order
to calibrate the γ2 parameter in Equation (7). This paper illustrates the implementation, potential and
capabilities of this workflow, using the River Esva (NW Spain) as study case.
Figure 1. Workflow followed in the present research with the aim of quantitatively characterizing
streambed mobility in the River Esva.
3. Study Site
The River Esva is located in the northern watershed of the Cantabrian Mountains, in NW Spain
(Figure 2). The climate is temperate-oceanic, with average monthly rainfalls ranging between 52 and
146 mm. The River Esva drains a surface of 464 km2. The flood regime is perennial and rainfall
dominated, with larger discharges in winter. Average annual discharge is 10.5 m3/s, with average
maximum and minimum annual discharges of 19.2 and 4.5 m3/s, respectively.
Figure 2. Location of the study river in NW Spain.
We selected a ~1 km study reach located close to the village of Trevias (Figure 3). It is a single
and straight river reach with an average ~0.003 channel slope and 25 m width. This reach was
embanked in 1993 along its entire length in order to protect Trevias from overbank flows.
A lateral gravel bar develops on the left bank in the downstream part of the study reach.
Streambed sediment is mainly composed of sub-angular and rod shaped sandstone gravels and
cobbles. One square plot of blue-painted stones was deployed on this gravel bar in November 2016
Figure 1.
Workflow followed in the present research with the aim of quantitatively characterizing
streambed mobility in the River Esva.
3. Study Site
The River Esva is located in the northern watershed of the Cantabrian Mountains, in NW Spain
(Figure 2). The climate is temperate-oceanic, with average monthly rainfalls ranging between 52 and
146 mm. The River Esva drains a surface of 464 km
2
. The flood regime is perennial and rainfall
dominated, with larger discharges in winter. Average annual discharge is 10.5 m
3
/s, with average
maximum and minimum annual discharges of 19.2 and 4.5 m3/s, respectively.
Water 2019, 11, x FOR PEER REVIEW 5 of 26
collecting in the field the GSD information of sediment deposited during large floods. This kind of
data helps to calibrate Equation (6) by forward modelling: by changing the γ parameter in Equation
(6) until obtaining an adequate value to fit the field measures. Finally, the γ parameter obtained from
flood deposits could be combined with the field identification of incipient motion conditions in order
to calibrate the γ2 parameter in Equation (7). This paper illustrates the implementation, potential and
capabilities of this workflow, using the River Esva (NW Spain) as study case.
Figure 1. Workflow followed in the present research with the aim of quantitatively characterizing
streambed mobility in the River Esva.
3. Study Site
The River Esva is located in the northern watershed of the Cantabrian Mountains, in NW Spain
(Figure 2). The climate is temperate-oceanic, with average monthly rainfalls ranging between 52 and
146 mm. The River Esva drains a surface of 464 km2. The flood regime is perennial and rainfall
dominated, with larger discharges in winter. Average annual discharge is 10.5 m3/s, with average
maximum and minimum annual discharges of 19.2 and 4.5 m3/s, respectively.
Figure 2. Location of the study river in NW Spain.
We selected a ~1 km study reach located close to the village of Trevias (Figure 3). It is a single
and straight river reach with an average ~0.003 channel slope and 25 m width. This reach was
embanked in 1993 along its entire length in order to protect Trevias from overbank flows.
A lateral gravel bar develops on the left bank in the downstream part of the study reach.
Streambed sediment is mainly composed of sub-angular and rod shaped sandstone gravels and
cobbles. One square plot of blue-painted stones was deployed on this gravel bar in November 2016
Figure 2. Location of the study river in NW Spain.
Water 2019,11, 2662 6 of 26
We selected a ~1 km study reach located close to the village of Trevias (Figure 3). It is a single and
straight river reach with an average ~0.003 channel slope and 25 m width. This reach was embanked
in 1993 along its entire length in order to protect Trevias from overbank flows.
Water 2019, 11, x FOR PEER REVIEW 6 of 26
(hereinafter called PP1 painted plot, for more details see Section 4). A second forced bar deposit is
located on the left bank in the upstream part of the study reach, where a second plot of yellow-painted
stones was deployed in May 2017 (hereinafter named PP2 painted plot, more details in Section 2)
(Figure 3).
Figure 3. Aerial image of the study reach and location of the two monitored painted plots.
Figure 3. Aerial image of the study reach and location of the two monitored painted plots.
Water 2019,11, 2662 7 of 26
A lateral gravel bar develops on the left bank in the downstream part of the study reach. Streambed
sediment is mainly composed of sub-angular and rod shaped sandstone gravels and cobbles. One
square plot of blue-painted stones was deployed on this gravel bar in November 2016 (hereinafter
called PP1 painted plot, for more details see Section 4). A second forced bar deposit is located on the
left bank in the upstream part of the study reach, where a second plot of yellow-painted stones was
deployed in May 2017 (hereinafter named PP2 painted plot, more details in Section 2) (Figure 3).
Additionally, a gauging station located at the downstream part of the study reach (Figure 3)
provided water level and flow-discharge records during the whole study period (November 2016 to
May 2019) (Figure 4).
Water 2019, 11, x FOR PEER REVIEW 7 of 26
Figure 4. Flow hydrograph of the River Esva during the study period. Vertical dashed lines represent
dates of field surveys.
4. Materials and Methods
4.1. Painted Plots
As outlined above, two plots of painted stones were deployed in the study site (Figure 3). The
painted plots were deployed on the main body of two lateral gravel-bars. As far as our main aim with
the plots was monitoring incipient motion conditions for coarse sediment particles, doing so with
painted stones is easier in those areas of the channel that are not permanently under water, such as
bars.
The first plot of tagged stones (PP1) covers a surface of 1 m × 1 m square on the riverbed. The
stones were painted blue in situ, without moving or disturbing in any moment their position. Each
grain was labelled and measured with a ruler. Additionally, we took several photographs to record
the initial state of the painted stones. In May 2017, 100 stones were collected from the riverbed and
taken to the lab, painted yellow, measured, and labelled. We seeded them on the riverbed. Several
deployment options were considered for this second generation of tagged stones such as a square
plot, a transverse line on the channel bed, or the random distribution of the stones on the streambed.
Finally, we decided to seed the stones defining a square of tracers (1 m × 1 m) on the streambed (PP2)
(Figure 3). Three were the main reasons: (1) to assure that all the stones were submitted to similar
hydraulic conditions; (2) to keep coherence with the strategy previously followed with PP1; and (3)
the identification in the field of incipient displacements and stone disturbance is easier with a painted
plot
We made regular visits to the field (once every month, on average, and after each major peak of
flow), in order to monitor the changes experienced by the painted plots. Each time the painted stones
were displaced, we measured the grain size of the largest moved clast. To help this task, we compared
photographs of the painted plots taken before and after the transport episode. We also measured the
downstream transport distance travelled by the recovered clasts and registered the amount of
painted stones recovered and lost after each flood.
Figure 4.
Flow hydrograph of the River Esva during the study period. Vertical dashed lines represent
dates of field surveys.
4. Materials and Methods
4.1. Painted Plots
As outlined above, two plots of painted stones were deployed in the study site (Figure 3). The
painted plots were deployed on the main body of two lateral gravel-bars. As far as our main aim
with the plots was monitoring incipient motion conditions for coarse sediment particles, doing so
with painted stones is easier in those areas of the channel that are not permanently under water, such
as bars.
The first plot of tagged stones (PP1) covers a surface of 1 m
×
1 m square on the riverbed. The
stones were painted blue in situ, without moving or disturbing in any moment their position. Each
grain was labelled and measured with a ruler. Additionally, we took several photographs to record
the initial state of the painted stones. In May 2017, 100 stones were collected from the riverbed and
taken to the lab, painted yellow, measured, and labelled. We seeded them on the riverbed. Several
deployment options were considered for this second generation of tagged stones such as a square
plot, a transverse line on the channel bed, or the random distribution of the stones on the streambed.
Finally, we decided to seed the stones defining a square of tracers (1 m
×
1 m) on the streambed (PP2)
(Figure 3). Three were the main reasons: (1) to assure that all the stones were submitted to similar
Water 2019,11, 2662 8 of 26
hydraulic conditions; (2) to keep coherence with the strategy previously followed with PP1; and (3) the
identification in the field of incipient displacements and stone disturbance is easier with a painted plot
We made regular visits to the field (once every month, on average, and after each major peak of
flow), in order to monitor the changes experienced by the painted plots. Each time the painted stones
were displaced, we measured the grain size of the largest moved clast. To help this task, we compared
photographs of the painted plots taken before and after the transport episode. We also measured the
downstream transport distance travelled by the recovered clasts and registered the amount of painted
stones recovered and lost after each flood.
4.2. Grain Size Analysis of Flood Deposits
In January 2019, a high-magnitude flow event occurred in the study river. Aerial photographs
were available before and after the flood episode, thanks to a monitoring program with an unmanned
aerial vehicle (UAV-drone platform). This helped the identification of a conspicuous gravel body
deposited on the top of a gravel bar located in the study reach, undoubtedly related to the large flood.
This sediment accumulation consists in an elongated gravel-sheet body overlapping a lateral bank
deposit along the left margin of the river (Figure 5). Field visits were carried out to identify this deposit
and to sample its GSD. We also sampled the GSD of the streambed surface and subsurface.
Water 2019, 11, x FOR PEER REVIEW 8 of 26
4.2. Grain Size Analysis of Flood Deposits
In January 2019, a high-magnitude flow event occurred in the study river. Aerial photographs
were available before and after the flood episode, thanks to a monitoring program with an unmanned
aerial vehicle (UAV-drone platform). This helped the identification of a conspicuous gravel body
deposited on the top of a gravel bar located in the study reach, undoubtedly related to the large flood.
This sediment accumulation consists in an elongated gravel-sheet body overlapping a lateral bank
deposit along the left margin of the river (Figure 5). Field visits were carried out to identify this
deposit and to sample its GSD. We also sampled the GSD of the streambed surface and subsurface.
Figure 5. (A) and (B) UAV-aerial image of the River Esva before (A) and after (B) January 2019 flood.
(C) and (D) gravel sheet body studied and sampled in the field, days after the flood. Blue arrows
indicates flow direction
In the case of the streambed surface and the flood deposit, we used the Wolman (1954) [56]
pebble count method. Each pebble count consisted of 200 grains collected along two ~50 m sampling
lines spaced ~15 m apart. The sampling of grains was done systematically, extracting them at every
1 m intersection along a tape (around twice the largest grain size visually estimated in the field). To
minimize the operator’s bias, all the grains were selected and measured by the same person. Metallic
templates were used to measure the b-axis of grains > 8 mm and to classify them into half-Ψ size
classes. Smaller grains were classified into two groups: grains between 4 and 8 mm and grains < 4
mm.
To sample the GSD of the subarmoured bed material, we used a variant of the pebble count
method [56] adapted for the subsurface sediment [57,58]. A surface of 1.5 × 1.5 m was selected on the
streambed, and the most superficial and coarse sediment layer was retired. We then mixed the
underlying sediment using a shovel. Afterwards, a purpose-designed 10 × 10 cm wide sampling grid
was deployed over the 1.5 × 1.5 m square surface. We measured the grain size of each pebble falling
in each node of the grid. We repeated this operation at three different emplacements, measuring the
size of the b-axis on ~100 subsurface particles per site. Finally, we integrated the three measures into
a single GSD for the subarmour bed material. The sampled surface was 100 times larger than the
largest clast, so we satisfied the Diplas and Fripp’s (1992) [59] criterion for a representative sample.
Figure 5.
(
A
,
B
) UAV-aerial image of the River Esva before (
A
) and after (
B
) January 2019 flood.
(
C
,
D
) gravel sheet body studied and sampled in the field, days after the flood. Blue arrows indicates
flow direction
In the case of the streambed surface and the flood deposit, we used the Wolman (1954) [
56
]
pebble count method. Each pebble count consisted of 200 grains collected along two ~50 m sampling
lines spaced ~1–5 m apart. The sampling of grains was done systematically, extracting them at every
1 m intersection along a tape (around twice the largest grain size visually estimated in the field). To
minimize the operator’s bias, all the grains were selected and measured by the same person. Metallic
templates were used to measure the b-axis of grains >8 mm and to classify them into half-
Ψ
size classes.
Smaller grains were classified into two groups: grains between 4 and 8 mm and grains <4 mm.
Water 2019,11, 2662 9 of 26
To sample the GSD of the subarmoured bed material, we used a variant of the pebble count
method [
56
] adapted for the subsurface sediment [
57
,
58
]. A surface of 1.5
×
1.5 m was selected on
the streambed, and the most superficial and coarse sediment layer was retired. We then mixed the
underlying sediment using a shovel. Afterwards, a purpose-designed 10
×
10 cm wide sampling grid
was deployed over the 1.5
×
1.5 m square surface. We measured the grain size of each pebble falling in
each node of the grid. We repeated this operation at three dierent emplacements, measuring the size
of the b-axis on ~100 subsurface particles per site. Finally, we integrated the three measures into a
single GSD for the subarmour bed material. The sampled surface was 100 times larger than the largest
clast, so we satisfied the Diplas and Fripp’s (1992) [59] criterion for a representative sample.
4.3. Modelling Streambed Mobility in the River Esva
Data from the painted plots were used with the purpose of defining the maximum mobile grain size
at dierent discharges and to calibrate Equation (5) at low magnitude flows (size-selective conditions).
Similarly, the GSD of the January 2019 flood deposit was used for the calibration of Equation (6)
at high-magnitude flows (equal mobility conditions). The parameters
β
(in Equation (5)) and
γ
(in
Equation (6)) were iteratively modified until obtaining those values that minimize the root square
mean of dierences between the observed (in the field) and the modelled competent sizes (Equation
(5)) and GSD of the January 2019 flood deposit (in Equation (6)), respectively. Finally, Equation (7) was
calibrated based on the value of
γ
computed for the January 2019 flood and the
γ
=0 assigned to the
May 2017 transport episode (close to the incipient motion conditions, see Section 5.3).
The resulting GTM model was applied to characterize streambed mobility in the River Esva.
More specifically, we used the calibrated model to answer three questions: i. how the maximum and
median competent sizes evolve with flow strength in the Esva river; ii. how the mobile fraction of fine
particles (<8 mm) changes with flow stage; and iii. how the number of mobile particles grows with
flow discharges. The maximum and median competent sizes were estimated using Equations (5)–(8).
The fraction of bed load finer than 8 mm was estimated with Equation (6). The increase in the number
of mobile particles was computed based on the mobile fraction of particles in each i-size range:
fs=Pϕi×pi
Ppi
(9)
where f
s
is the portion of the streambed particles that are entrained and p
i
the relative fraction of each
i-size class in the surface GSD.
Applying the GTM model requires the computation of shear stresses from flow discharge. To
achieve this, we used the Rickenmann and Recking (2011) [
60
] fit to the Ferguson (2007) [
61
] flow
resistance equation and estimated flow depths (d) from flow discharge using:
d=0.015 ×D84 ×Q2p
p2.5 (10)
where:
Q=Q/w×qgSD3
84 (11)
where Qis the water discharge, Q* the dimensionless water discharge, wthe channel width, Sthe
channel slope, and p=0.24 if Q*<100 and 0.31 otherwise. Then, assuming a rectangular cross-section,
we estimated the hydraulic radius (R) from:
R=d×w
(2d+w)(12)
and, finally, shear stresses were directly computed from the hydraulic radius–slope product:
τ=ρ×g×S×R(13)
Water 2019,11, 2662 10 of 26
The GTM model also needs a value for the critical threshold of motion of the D
84
(
τc84
*). We based
it on the slope dependent relation proposed by Recking (2009) [62]:
τ
c84 =(1.32 ×S+0.037)× D84
D50 !0.93
(14)
Finally, we computed the average GSD of the bed load mobilized during the entire study period
(November 2016–July 2019). We used the 15 min discharge record available from the gauging station
for the study period. Then, we applied the calibrated GTM model and Equation (8) to estimate the
evolution of the GSD of the bed load at each 15 min time step of the flood hydrograph.
Then, the time integrated bed load volumes (V
i
) in each size class, during the entire study period,
can be estimated from:
Vi=
T=Tf
X
T=T0
qsT·ppiT×T(15)
where T
0
and T
f
are the departure and final times of the study period (respectively), qs
T
is the bed load
rate at each time step T, and pp
iT
is the proportion of the i-size class in the bed load. Bed load rates
were estimated using Recking’s (2013) [63] sediment transport equation, which appears to work well
in coarse-bed rivers with the same range of slope and bed conditions as the River Esva [
63
,
64
]. Once
we computed V
i
for the dierent size classes, we calculated the percentage of each size class in the
total bed load volumes (VT) mobilized during the study period:
%i=Vi/VT(16)
4.4. Comparison to Previous Studies
We compared the GSD of the flood deposit sampled in the field to both the surface and subsurface
GSD, in order to see how the grain size of the carried load relates to the grain size of the bed material.
Later, in order to nourish the discussion on how the grain size of the carried load may or may not
correlate to flow strength and the GSD of the streambed material, we re-analyzed previously published
information on the grain size of the bed load available in Milhous (1973) [
28
], Andrews (1994) [
29
], Lisle
(1995) [
25
] and Whittaker and Potts (2007) [
1
] (Table 1) and we compared them to our field observations.
Table 1.
Data of grain size of the bed load, compiled from previous studies and compared to our own
data for the River Esva. S: Slope. W: Channel width (in m). D
50s
and D
50ss
: Median size of the surface
and subsurface grain-size distribution (in mm), respectively. D
50bl
: Median size of the bed load. D
max
:
Largest mobile grain (in mm). Q
bkf
: Water discharge at bankfull (m
3
/s). Q: Water discharge (m
3
/s)
during the sampled sediment transport episodes. Sample: Bed load sediment transport method.
River Source S W D50sD50ss D50bl Dmax Qbkf QSample
Oak creek [28] 0.0094 3.7 54 20 3–27 8–98 3.4 0.2–3.4 Vortex sampler
Sagehen creek [29] 0.0102 2.6 58 30 12–65 31–126 0.3 0.2–0.6 HS
Bambi creek [25] 0.0082 3.6 - 9 3 22 1.7 2.5 HS
Goodwin creek [25] 0.0033 12.9 12 8 8 24 90.0 81 HS
Jacoby creek [25] 0.0063 17.2 27 8 4 25 9.0 34.2 HS
NF Caspar creek [25] 0.0130 4.4 15 9 4 80 3.1 6.2 Pit
Redwood creek 1 [25] 0.0140 44.6 5 4 1 30 430.0 374.1 HS
Tanana river [25] 0.0008 315.0 13 1 17 22 - 2040 HS
Tom Mac Donald
Creek [25] 0.0060 6.1 19.8 11 8 22 3.6 12.6 HS
Turkey brook [25] 0.0086 3.0 22 16 11 100 13.0 16.9 Pit
Dupuyer creek [1] 0.0100 8.0 54 - 47–60 88–155 6.5 4.6–10.3 Basket sampler
River Esva This study 0.0030 25.2 59 22 - 16–208 -
31.3–183.9
Painted stones
Water 2019,11, 2662 11 of 26
5. Results
5.1. Painted Plots
Four floods were monitored with the painted stones from November 2016 to March 2019 (Table 2).
Table 2. Summary of results of the field surveys in the River Esva accomplished here.
Date Painted Plot Q(m3/s) τ*/τc*Dmax % Recovery L(m)
17/01/2017 PP1 41.93 0.73 54.5 86 ~0.2
02/03/2017 PP1 74.63 0.98 90 82 4.0
29/05/2017 PP1 31.34 0.63 0 82 0.0
12/11/2017 PP1 183.95 1.55 208 82 35.2
29/05/2017 PP2 31.34 0.63 16 96 <0.1
12/11/2017 PP2 183.95 1.55 158 3 19
Q: Peak flow discharge.
τ
*/
τc
*: Transport stage ratio (at peak discharge). D
max
: Maximum mobile size (mm). L:
Maximum distance travelled by the retrieved painted stones.
The first of the studied flood episodes occurred on 17 January 2017. It had a 41.93 m
3
/s peak
discharge which corresponds to a frequent, regular peak of flow (<1 year return period discharge).
This episode was able to move 23% of the seeded painted stones, but displacements were not very
important, i.e., the maximum measured transport distances were relatively low (~0.2 m). The b-axis
of the largest moved clast was 55 mm. These field observations can be considered as reliable, as
approximately 85% of the tracers initially painted were retrieved. They reflect a partial mobility regime
and close to the threshold of motion for the median-sized particles in the streambed.
The second transport episode, which occurred on 2 March 2017, was also monitored with the PP1
painted plot. It corresponded to a 74.63 m
3
/s discharge (<1 year return period flow). During this peak
of discharge, a larger amount of painted tracers was disturbed (55%), but the displacements were again
not very important; the maximum measured downstream transport distance was around 4 m. The size
of the largest moved clast was 90 mm, coarser than in the previous episode. All these observations
suggest partial mobility conditions and bed shear stresses close to the threshold of motion for the
coarser particles in the riverbed. We recovered a large number of the initially painted stones (~82%), so
all our observations were reliable.
The third transport episode took place on 29 May 2017. It was a 31.34 m
3
/s peak of discharge that
was monitored with both the PP1 and PP2 painted plots. The PP1 painted stones did not experience
any apparent movement. Conversely, the stones from the PP2 painted plot experienced some kind
of reorganization, consisting in rolling and pivoting of some clasts and a very short downstream
dispersion (<0.1 m). The PP2 was painted only six days before this event happened, while the PP1
painted stones had already experienced two previous peaks of flow. Consequently, dierences in clast
structuration may explain why the positions of PP2 stones were reorganized while those of PP1 clasts
remained undisturbed.
The fourth and relative high-magnitude transport episode occurred on 12 November 2017 and
was surveyed with both PP1 and PP2 painted stones. It had a peak discharge of 183.95 m
3
/s, which
corresponds to a ~2 year return period flow. This episode displaced 86% of the painted stones from PP1,
with some of the retrieved tracers experiencing downstream displacements as far as 35 m. The b-axis
of the largest moved clast was 210 mm. We were able to recover 82% of the initially PP1 painted stones,
so again the observations made with PP1 tracers could be considered as trustworthy. In contrast, we
could only recover three of the initially painted stones from PP2; the rest were lost. The largest clast of
the three PP2 retrieved stones measured 158 mm.
5.2. GSD of a Large Flood Deposit
An exceptionally large flood episode occurred in the River Esva between the 19th and 29th of
January 2019. Peak discharge during this event reached 545 m
3
/s, which according to the available
Water 2019,11, 2662 12 of 26
gauging records corresponds to a ~50 year return period flow discharge. A large sediment deposit was
accumulated during this flood over a gravel bar in our study site (Figure 5). This deposit was first
identified with the help of a UAV drone. Later, we recognized it in the field and we measured its GSD
using the Wolman (1954) [56] method (Figure 6).
Water 2019, 11, x FOR PEER REVIEW 12 of 26
gauging records corresponds to a ~50 year return period flow discharge. A large sediment deposit
was accumulated during this flood over a gravel bar in our study site (Figure 5). This deposit was
first identified with the help of a UAV drone. Later, we recognized it in the field and we measured
its GSD using the Wolman (1954) [56] method (Figure 6).
Figure 6. The grain-size distribution (GSD) curves for the River Esva: (A) non-truncated and (B)
truncated at 8 mm.
Figure 6.
The grain-size distribution (GSD) curves for the River Esva: (
A
) non-truncated and (
B
)
truncated at 8 mm.
Water 2019,11, 2662 13 of 26
We also compared the GSD of the flood deposit to those of the surface and subsurface streambed
material (Figure 6and Table 3). The GSD of the flood deposit was very similar to that of the subsurface
GSD, and both were considerably finer than the surface GSD. The similarity between the GSD of the
January 2019 flood and the subsurface GSD suggests that the GSD of the bed material was mainly
sculpted by large floods along the River Esva. Nevertheless, the flood deposit showed a larger
percentage of sediment finer than 16 mm than the subsurface GSD. This dierence might be related to
winnowing of fine sediment during low floods, coarsening the topmost layer of the streambed and
washing relatively fine particles out of the riverbed. However, potential bias when sampling GSD of
the subsurface bed material cannot be discarded. Actually, when the three GSD are truncated at 8 mm,
the GSD of the January 2019 flood deposit and the subsurface bed material seem to collapse into a
very similar curve. This reinforces the idea that the subsurface sediment is depleted in fine sediment
compared to the bed load carried during large floods.
Table 3.
Comparison between the grain-size distribution (GSD) of the surface sediment, the subarmour
bed material, and the January 2019 flood deposit in the River Esva. Values between brackets correspond
to the grain size metrics estimated for the truncated (<8 mm) GSD.
GSD % Particles <8 mm D16 (mm) D50 (mm) D84 (mm)
Surface 0 34 (34) 59 (59) 107 (107)
Subsurface 8 11 (20) 22 (30) 47 (58)
January 2019
(flood deposit) 22 3 (20) 22 (30) 42 (49)
5.3. Calibrating the GTM Model
The results from our field observations were used to calibrate the GTM competence model [
2
]
for the River Esva. Painted plots allowed the calibration of Equation (5) which describes how the
maximum mobile percentiles evolve with flow stage. We obtained an optimum ~3
β
parameter for
transport stages below 1. In the case of transport stages larger than 1, we noticed how the painted
plot data were in accordance with the 0.25
β
parameter initially suggested by Recking (2016) [
2
] that
involves full mobility conditions when transport stages are larger than 2 (Figure 7A).
To calibrate Equation (6) (quantifying how mobile fraction in each size evolves with flow strength)
at high flows (equal mobility conditions) we based on the GSD of the January 2019 flood deposit.
We searched for the value of the
γ
parameter (in Equation (6)) that best minimizes the root mean
square of dierences between observed and modelled GSD (Figure 7B). We obtained a 2.58
γ
value.
Nevertheless, according to Reference [
2
], the value of the
γ
parameter may vary with flow strength
(Equation (7)). In order to better constrain our calibrated model, based on the data of 29 May peak
of flow (when painted tracers practically did not move), we considered that the fraction of mobile
particles in all size classes decreased to almost 0 at transport stages close to 0.6; this involves a
γ
parameter ~0. According to this and the ~2.6
γ
value for transport stages close to 3.3, the best fit for
Equation (7) was obtained with a 1.60 γ2parameter (Figure 7C).
5.4. Characterizing Streambed Mobility in the River Esva
Using the GTM model calibrated for our study site, we accomplished an analysis on how streambed
mobility evolves in the River Esva with flow stage. We estimated four parameters: (1) the median size
of the entrained particles; (2) the size of the coarsest mobile clast; (3) the fraction of fine sediment (<8
mm) in the bed load at every flow stage; and (4) the number of bed surface particles that are entrained
and actively incorporated into bed load motion with increasing discharges.
The modelled values clearly show how all these four parameters changed with flow strength
(Figure 8). There was a remarkable change around ~75 m
3
/s where both the grain size and the number of
entrained particles experienced a sudden jump. This discharge corresponded to a transport stage close
Water 2019,11, 2662 14 of 26
to 1; that is to say, close to the moment when the coarser clasts in the riverbed started to incorporate
into motion and the armour layer destabilized and broke up.
Water 2019, 11, x FOR PEER REVIEW 14 of 26
of entrained particles experienced a sudden jump. This discharge corresponded to a transport stage
close to 1; that is to say, close to the moment when the coarser clasts in the riverbed started to
incorporate into motion and the armour layer destabilized and broke up.
Figure 7. Results of the GTM model calibration for the River Esva. (A). Calibrating Equation (5) using
data from painted plots. (B): Calibrating Equation (6) using the GSD of the January 2019 flood deposit.
(C): Calibrating Equation (7) using data derived from painted plots and the GSD of the January 2019
flood deposit.
Figure 7.
Results of the GTM model calibration for the River Esva. (
A
). Calibrating Equation (5) using
data from painted plots. (
B
): Calibrating Equation (6) using the GSD of the January 2019 flood deposit.
(
C
): Calibrating Equation (7) using data derived from painted plots and the GSD of the January 2019
flood deposit.
Water 2019,11, 2662 15 of 26
Water 2019, 11, x FOR PEER REVIEW 15 of 26
Figure 8. Streambed mobility model for the River Esva, derived from the calibrated GTM model.
5.5. Modelling the Long-Term Averaged GSD of the Bed Load
Using the flow discharge records available for the study site, we estimated the GSD of the bed
load integrated for the whole study period. This covers almost three entire hydrological years (2016
2017, 20172018, and 20182019), so we could consider it somewhat a proxy of the annual average
GSD of the bed load. The obtained GSD is considerably finer than the GSD of the January 2019 flood
deposit and the subsurface bed material (Figure 6). Indeed, this difference persists even when the
GSDs are truncated at 8 mm (Figure 6B), so this is not just a consequence of a larger amount of fine
sediment: the time integrated GSD of the bed load is still finer than the subsurface bed material, even
when the fine sediment bed material load is not considered.
5.6. Comparison to Previous Studies
In Figures 9 and 10 we plotted the River Esva data together with data from previous studies
[1,25,28,29]. This comparison shows a statistically significant (p-value < 0.05) correlation between the
largest clast size of the bed load and the transport stage ratio. The grain size of the largest transported
clast approximates the diameter of the D84 when transport stages were close to 1 (Figures 9A and
Figure 8. Streambed mobility model for the River Esva, derived from the calibrated GTM model.
5.5. Modelling the Long-Term Averaged GSD of the Bed Load
Using the flow discharge records available for the study site, we estimated the GSD of the bed load
integrated for the whole study period. This covers almost three entire hydrological years (2016–2017,
2017–2018, and 2018–2019), so we could consider it somewhat a proxy of the annual average GSD of
the bed load. The obtained GSD is considerably finer than the GSD of the January 2019 flood deposit
and the subsurface bed material (Figure 6). Indeed, this dierence persists even when the GSDs are
truncated at 8 mm (Figure 6B), so this is not just a consequence of a larger amount of fine sediment: the
time integrated GSD of the bed load is still finer than the subsurface bed material, even when the fine
sediment bed material load is not considered.
5.6. Comparison to Previous Studies
In Figures 9and 10 we plotted the River Esva data together with data from previous
studies [1,25,28,29]
. This comparison shows a statistically significant (p-value <0.05) correlation
between the largest clast size of the bed load and the transport stage ratio. The grain size of the
largest transported clast approximates the diameter of the D
84
when transport stages were close to
Water 2019,11, 2662 16 of 26
1 (
Figures 9A and 10A
). This confirms how once the thresholds of motion of the coarser grains are
reached, these coarse particles become incorporated into the bed load mass.
Water 2019, 11, x FOR PEER REVIEW 16 of 26
10A). This confirms how once the thresholds of motion of the coarser grains are reached, these coarse
particles become incorporated into the bed load mass.
Figure 9. Comparison of the results obtained for the River Esva with those of previous studies focused
on flow competence. In this figure, we compare the grain size of the bed load to that of the streambed
surface, accounting for flow strength. (A) Maximum mobile size compared to surface D84. (B) Median
mobile size compared to surface D50. References: Oak creek [28]; Sagehen creek [29]; Dupuyer creek
[1]; Other [25].
Figure 9.
Comparison of the results obtained for the River Esva with those of previous studies focused
on flow competence. In this figure, we compare the grain size of the bed load to that of the streambed
surface, accounting for flow strength. (
A
) Maximum mobile size compared to surface D
84
. (
B
) Median
mobile size compared to surface D
50
. References: Oak creek [
28
]; Sagehen creek [
29
]; Dupuyer creek [
1
];
Other [25].
Water 2019,11, 2662 17 of 26
Water 2019, 11, x FOR PEER REVIEW 17 of 26
Figure 10. Comparison of the results obtained for the River Esva with those of previous studies
focused on flow competence. In this figure, we compare the grain size of the bed load to that of the
streambed subsurface, accounting for flow strength. (A) Maximum mobile size compared to
subsurface D84. (B) Median mobile size compared to subsurface D50. References: Oak creek [28];
Sagehen creek [29]; Dupuyer creek [1]; Other [25].
Conversely, in the case of the median sizes of the bed load, we did not observe any connection
with the flow strength (Figures 9B and 10B). Data from the different study sites appear well
segregated which outlines the high degree of site specificity in the relations between GSD of the bed
load and flow strength. This highlights the importance of site-specific controls on streambed mobility.
Additionally, data plots corresponding to transport stages higher than 1 show an important amount
Figure 10.
Comparison of the results obtained for the River Esva with those of previous studies focused
on flow competence. In this figure, we compare the grain size of the bed load to that of the streambed
subsurface, accounting for flow strength. (
A
) Maximum mobile size compared to subsurface D
84
.
(
B
) Median mobile size compared to subsurface D
50
. References: Oak creek [
28
]; Sagehen creek [
29
];
Dupuyer creek [1]; Other [25].
Conversely, in the case of the median sizes of the bed load, we did not observe any connection
with the flow strength (Figures 9B and 10B). Data from the dierent study sites appear well segregated
which outlines the high degree of site specificity in the relations between GSD of the bed load and flow
strength. This highlights the importance of site-specific controls on streambed mobility. Additionally,
data plots corresponding to transport stages higher than 1 show an important amount of scatter. This
Water 2019,11, 2662 18 of 26
brings into question the idea of a simple relation between the GSD of the subarmour material and that
of the bed load during large floods.
Moreover, correlation between the size of the largest clast and flow strength is stronger when
the largest moved clast sizes are normalized by the D
84
of the surface sediment than when they are
normalized using the D
84
of the subsurface bed material. This may suggest how the remobilization of
the coarser grains from the riverbed surface may largely control the size of the largest clast in motion.
6. Discussion
6.1. General Discussion
Our work illustrates the great potential and interest of combining a simple and open model such
as the GTM [
2
] with relatively easy-to-take field measures in order to characterize the largest mobile
size, fine sediment mobility or overall streambed mobility/stability behavior (Figure 8). Indeed, our
field observations were in good accordance with the general shape of the GTM model [
2
] which is
partially due to the large flexibility of the GTM model compared to previous competence models
(Figure 11).
Water 2019, 11, x FOR PEER REVIEW 18 of 26
of scatter. This brings into question the idea of a simple relation between the GSD of the subarmour
material and that of the bed load during large floods.
Moreover, correlation between the size of the largest clast and flow strength is stronger when
the largest moved clast sizes are normalized by the D84 of the surface sediment than when they are
normalized using the D84 of the subsurface bed material. This may suggest how the remobilization of
the coarser grains from the riverbed surface may largely control the size of the largest clast in motion.
6. Discussion
6.1. General Discussion
Our work illustrates the great potential and interest of combining a simple and open model such
as the GTM [2] with relatively easy-to-take field measures in order to characterize the largest mobile
size, fine sediment mobility or overall streambed mobility/stability behavior (Figure 8). Indeed, our
field observations were in good accordance with the general shape of the GTM model [2] which is
partially due to the large flexibility of the GTM model compared to previous competence models
(Figure 11).
Figure 11. Comparison between the GTM model (calibrated for the River Esva) and several other flow
competence models applied to the River Esva. In general, previous competence models simulated
either a progressive increase in the size of the mobile clast with flow discharge (size-selective
behavior, e.g., Komar [13], Andrews [42], Shields [30]) or a sudden incorporation of all the particle
sizes at a narrow range of discharges (equal mobility, e.g., Parker et al. [41] and Recking [62]).
However, the GTM model was able to simulate a combination of size-selective behaviors at low flows
and equal mobility once the armour layer destabilized entirely which seems to agree better with our
field observations in the River Esva.
One main advantage of the GTM model relies is in its ability to model armour break-up and its
adaptability to a broad range of armour destabilization conditions. The Esva calibrated GTM model
0
100
200
300
400
500
0100 200 300 400 500
Largest moved clast (mm)
Discharge (m3/s)
Figure 11.
Comparison between the GTM model (calibrated for the River Esva) and several other flow
competence models applied to the River Esva. In general, previous competence models simulated
either a progressive increase in the size of the mobile clast with flow discharge (size-selective behavior,
e.g., Komar [
13
], Andrews [
42
], Shields [
30
]) or a sudden incorporation of all the particle sizes at a
narrow range of discharges (equal mobility, e.g., Parker et al. [
41
] and Recking [
62
]). However, the GTM
model was able to simulate a combination of size-selective behaviors at low flows and equal mobility
once the armour layer destabilized entirely which seems to agree better with our field observations in
the River Esva.
Water 2019,11, 2662 19 of 26
One main advantage of the GTM model relies is in its ability to model armour break-up and its
adaptability to a broad range of armour destabilization conditions. The Esva calibrated GTM model
shows two break points at ~75 and ~275 m
3
/s (Figure 11), corresponding to the flow discharges when
the coarser grains started to be entrained and when full mobility conditions were reached, respectively.
According to Figure 11, the GTM was able to model a situation where we have size-selective entrainment
at low flows, a progressive armour destabilization at moderate flows and a sudden final breakup of the
armour layer at very large flows. In fact, this involves some complex combination of size-selective and
equal mobility conditions, very suitable for the River Esva (Figure 11). Previous competence models
based on power-law hiding functions (Equation (3)) seem unable to grasp such behavior (Figure 11),
as they are only able to model a progressive mobilization of the dierent grain sizes or a sudden
mobilization of all the grain sizes at a narrow range of flows. The Komar (1987) [
13
] fit to Carling
(1983) [15] data (involving a α-parameter ~0.85) was the one closest to the calibrated GTM model.
In this work, we did not consider the possibility of temporal changes in surface GSD when
calibrating of the GTM model. However, changes in surface GSD could be expected in gravel-bed
rivers, driven by variable flow discharges and temporal fluctuations in sediment supply [
51
,
65
].
Nevertheless, we accomplished several pebble counts (~100 counts per sample) in the study reach
all along the time period of study (Figure 12). Between 2016 and the January 2019 flood, we did not
observe significant grain size changes: we observed a ~15% variability around the mean value for
the D
50
which is comparable to the precision expected for pebble counts based on 100–200 clast-size
measures [
58
,
66
]. Thus, we could consider that surface GSD remained quite stable between 2016
and 2019. However, after the January 2019 flood, we reported significant streambed fining. This
was probably related to the liberation of fines after widespread armour disorganization during this
high-magnitude flow.
Water 2019, 11, x FOR PEER REVIEW 19 of 26
shows two break points at ~75 and ~275 m3/s (Figure 11), corresponding to the flow discharges when
the coarser grains started to be entrained and when full mobility conditions were reached,
respectively. According to Figure 11, the GTM was able to model a situation where we have size-
selective entrainment at low flows, a progressive armour destabilization at moderate flows and a
sudden final breakup of the armour layer at very large flows. In fact, this involves some complex
combination of size-selective and equal mobility conditions, very suitable for the River Esva (Figure
11). Previous competence models based on power-law hiding functions (Equation (3)) seem unable
to grasp such behavior (Figure 11), as they are only able to model a progressive mobilization of the
different grain sizes or a sudden mobilization of all the grain sizes at a narrow range of flows. The
Komar (1987) [13] fit to Carling (1983) [15] data (involving a α-parameter ~0.85) was the one closest
to the calibrated GTM model.
In this work, we did not consider the possibility of temporal changes in surface GSD when
calibrating of the GTM model. However, changes in surface GSD could be expected in gravel-bed
rivers, driven by variable flow discharges and temporal fluctuations in sediment supply [51,65].
Nevertheless, we accomplished several pebble counts (~100 counts per sample) in the study reach all
along the time period of study (Figure 12). Between 2016 and the January 2019 flood, we did not
observe significant grain size changes: we observed a ~15% variability around the mean value for the
D50 which is comparable to the precision expected for pebble counts based on 100200 clast-size
measures [58,66]. Thus, we could consider that surface GSD remained quite stable between 2016 and
2019. However, after the January 2019 flood, we reported significant streambed fining. This was
probably related to the liberation of fines after widespread armour disorganization during this high-
magnitude flow.
Figure 12. Comparison among the different pebble counts accomplished in the study site during the
time period spanned by the present research (20162019). Calibration of the GTM model was based
in the pebble count accomplished in September 2018.
Consequently, major floods in the River Esva seem to be associated with a temporal
replenishment in fines of the streambed surface. Hence, we could expect differences in the GSD of
the bed load after major floods, which will persist until the streambed exhausts again the fine
sediment. Thus, we repeated the GTM model based on the surface GSD measured after the January
2019 flood and we compared to our previous estimations (Figure 13). In general, we observed how
both the median grain size and the largest mobile clast during moderate flow discharges are finer
after the January 2019 flood than before; conversely, differences tend to disappear for higher water
0
20
40
60
80
100
110 100 1000
November (2016)
January (2017)
May (2017)
February (2017)
December (2017)
March (2018)
September (2018)
February (2019)
Particle size (mm)
Passing fraction (%)
Figure 12.
Comparison among the dierent pebble counts accomplished in the study site during the
time period spanned by the present research (2016–2019). Calibration of the GTM model was based in
the pebble count accomplished in September 2018.
Consequently, major floods in the River Esva seem to be associated with a temporal replenishment
in fines of the streambed surface. Hence, we could expect dierences in the GSD of the bed load
after major floods, which will persist until the streambed exhausts again the fine sediment. Thus, we
Water 2019,11, 2662 20 of 26
repeated the GTM model based on the surface GSD measured after the January 2019 flood and we
compared to our previous estimations (Figure 13). In general, we observed how both the median grain
size and the largest mobile clast during moderate flow discharges are finer after the January 2019
flood than before; conversely, dierences tend to disappear for higher water discharges. On this point,
seasonal and inter-annual changes in bed load rating curves have been documented by several authors
in gravel-bed rivers [
67
,
68
]. We believe that the GTM model has the potential to grasp this kind of
seasonal and annual bed load hysteresis patterns. Changes in in-channel sediment supply conditions
should have an imprint on bed surface texture, grain size and streambed structuration [
38
,
66
]. Hence,
if these changes in surface GSD are adequately monitored in the field, then they could be accounted for
in the workflow here proposed (Figure 1) and the hysteresis behavior in flow competence could be
approached based on the GTM model.
Water 2019, 11, x FOR PEER REVIEW 20 of 26
Figure 13. Comparison of the GTM model estimations for the River Esva before and after the January
2019 flood.
6.2. GSD of the Bed Load and the Streambed Sediment: Implications for Paleo-Hydrological Analysis
According to our results, the GSD of the time-integrated bed load is considerably finer than the
GSD of the subsurface bed material. In addition, the comparison between the GSD of the January
flood deposit and the GSD of the subsurface bed material suggests that the GSD of the subarmour
material proxies that of the bed load carried during large floods in the River Esva. Church and Hassan
(2005) [69] also compared the grain size of the bed load to that of the subsurface bed material in Harris
Creek (Canada), based on bed load volumes collected with a pit trap. They also observed how the
grain size of the bed load approaches that of the subsurface bed material in periods of large floods,
and a time averaged bed load finer than the subsurface sediment.
Low-magnitude peaks of flows and recession limbs of major flows seem able to mobilize a large
amount of fine sediment, which passes over the Esva’s riverbed and is not stocked into the bed
material. Additionally, during large floods, much of the sand fraction of the bed material can escape
as suspension load. Both issues help explain why the GSD of the time integrated bed load is finer
than the GSD of the sub-armour sediment, although some potential methodological bias cannot be
neglected. We defined the GSD of the time integrated bed load based on bed load rates computed
using Recking’s (2013) [63] (updated by Recking et al. (2016) [70]) bed load equation, which is said to
perform well in gravel-bed rivers [64]. However, at low flows, fine sediment exhaustion from the
riverbed surface can give rise to a supply-limited situation, compromising the applicability of bed
load formulae. Thus, the amount of fine sediment in the time integrated bed load may be
overestimated.
In summary, the GSD of the bed load during large floods tends to resemble the GSD of the
subarmour bed material. However, re-analysis of previously published data suggests that this is not
a general trend in gravel-bed rivers, and it could be largely site specific. A wide scatter is present in
the available data (Figures 9 and 10) and the different data sets appear well-segregated, so site-
Figure 13.
Comparison of the GTM model estimations for the River Esva before and after the January
2019 flood.
6.2. GSD of the Bed Load and the Streambed Sediment: Implications for Paleo-Hydrological Analysis
According to our results, the GSD of the time-integrated bed load is considerably finer than the
GSD of the subsurface bed material. In addition, the comparison between the GSD of the January
flood deposit and the GSD of the subsurface bed material suggests that the GSD of the subarmour
material proxies that of the bed load carried during large floods in the River Esva. Church and Hassan
(2005) [
69
] also compared the grain size of the bed load to that of the subsurface bed material in Harris
Creek (Canada), based on bed load volumes collected with a pit trap. They also observed how the
grain size of the bed load approaches that of the subsurface bed material in periods of large floods, and
a time averaged bed load finer than the subsurface sediment.
Low-magnitude peaks of flows and recession limbs of major flows seem able to mobilize a large
amount of fine sediment, which passes over the Esva’s riverbed and is not stocked into the bed
material. Additionally, during large floods, much of the sand fraction of the bed material can escape as
suspension load. Both issues help explain why the GSD of the time integrated bed load is finer than the
GSD of the sub-armour sediment, although some potential methodological bias cannot be neglected.
We defined the GSD of the time integrated bed load based on bed load rates computed using Recking’s
(2013) [
63
] (updated by Recking et al. (2016) [
70
]) bed load equation, which is said to perform well in
gravel-bed rivers [
64
]. However, at low flows, fine sediment exhaustion from the riverbed surface can
Water 2019,11, 2662 21 of 26
give rise to a supply-limited situation, compromising the applicability of bed load formulae. Thus, the
amount of fine sediment in the time integrated bed load may be overestimated.
In summary, the GSD of the bed load during large floods tends to resemble the GSD of the
subarmour bed material. However, re-analysis of previously published data suggests that this is not a
general trend in gravel-bed rivers, and it could be largely site specific. A wide scatter is present in the
available data (Figures 9and 10) and the dierent data sets appear well-segregated, so site-specific
conditions control the existing relations between the GSD of the subsurface bed material and that of
bed load during large floods. Consequently, patterns of armour development and destabilization are
largely site-specific, influencing the links between GSD of the bed load and that of the bed material.
In this regard, the size of the largest clast has been a classical tool in the evaluation of flow
competence by many geologists and sedimentologists interested in the paleohydrological and
paleohydraulical interpretation of old fluvial conglomerate deposits, who used it (for instance)
for paleo-velocity or paleo-slope analysis [
12
20
,
71
75
]. However, translating flow competence
measures, based on the largest clast size, into paleohydraulic conditions is not direct; as we have stated
above, there is no single and general function linking the grain size of the bed load to flow strength. In
addition, particle weight is not the only control on particle mobility, but packing, imbrication, clast
interlocking, fine sediment content and a broad range of exposure and hiding eects distort the links
between particle size and entrainment conditions. On this point, some authors documented equal
mobility conditions for all the grain sizes present in the bed, whilst others have reported a much more
size-selective behavior.
Moreover, gravel-bed rivers are systematically armored [
48
52
], i.e., the streambed surface is
commonly coarser than the underlying subarmour deposit. In this regard, the topmost layer of the
streambed represents the local source of sediment particles during bed load transport and surface
coarsening results from the adjustment of the streambed’s surface to the bed load transfers during
the dominant channel-forming flows. Thus, the dierences between the surface and subsurface
GSDs may potentially provide some interesting clues for evaluating streambed mobility and/or
paleo-hydrological analysis. Unfortunately, the topmost layer of the streambed is rarely preserved in
old fluvial deposits [
75
]. Consequently, the grain size of the subsurface sediment is the only available
information for the stratigraphic application of flow competence. Additionally, grain size of fluvial
deposits is probably driven mainly by hydraulic conditions during deposition [
76
,
77
] rather than by
particle entrainment.
With the above in mind, some doubts arise about the stratigraphic interpretation of flow
competences based on the largest grain measured in subarmour deposits, whether they may be
a good proxy of large magnitude and less frequent transport episodes, or instead they provide an
average picture of the more frequent channel-forming flows. Subsurface grain-size distribution has
been commonly considered a good proxy for the grain size of the average annual bed load [53,78,79],
but our results suggest that there is not a straightforward relation between the GSD of the subsurface
material, the time integrated GSD of the bed load and/or that of the bed load during moderate to large
floods. These relations are largely controlled by the specific streambed conditions (armoring/pavement,
packing, imbrications, etc.) at a given river reach, so the paleo-hydrological interpretation of large clast
measures in fluvial conglomerates could not be straightforward.
6.3. Frequency and Intensity of Streambed Mobility: Implications for Streambed Stability Analysis
The timing and intensity of riverbed mobility are of great interest in river ecology [
6
], since
they determine the evolution of bed surface structure, which is the physical support of habitat for
many aquatic organisms. Therefore, it is not surprising that stream ecologists have also used the
flow competence concept in order to evaluate stream stability during flows [
8
,
22
,
80
,
81
] in relation to
several issues, such as streambed perturbation [
6
] or the response of benthic macroinvertebrates to
floods [8285].
Water 2019,11, 2662 22 of 26
The magnitude and frequency of coarse particle motion contributes to shape habitat for
macroinvertebrates that live on the riverbed surface and defines the bed conditions that render
river gravel more stable through time between large floods. A reductionist view of gravel riverbed
mobility based on the flow competence concept would suggest that the timing and intensity of
streambed disturbance is driven by the ability of the channel to set in motion the coarser clasts.
However, this overlooks the importance of other questions. For instance, the fact that a clast in a given
class size is entrained does not mean that all clasts in that size are actually moving (partial mobility
conditions [
86
]). We believe that the workflow outlined here is well suited for the characterization
of streambed mobility in gravel-bed rivers, always bearing in mind the site-specific character of
each riverbed.
Our results show an abrupt change in the streambed behavior at discharges able to destabilize
the armored surface. The size of the largest moved clast and the median size of the bed load show
a sudden increase. Furthermore, the percentage of fine sediment in the bed load decreases. This
relates to a larger amount of coarser clasts set in motion that decreases the relative proportion of fine
sediment. The percentage of mobile particles in the riverbed also increases, reaching a limiting value
of ~80% during large floods as full mobility conditions are entirely never reached. This implies that
an important number of clasts remain static during floods. This contrasts with observations made
by Lisle et al. (2000) [
87
] and Haschenburger and Wilcock (2003) [
88
] who found that only a small
portion of the bed is inactive during bankfull floods. Nevertheless, other authors have also observed
that a large amount of the riverbed could be immobile during large floods [
6
,
89
,
90
], in agreement with
our observations.
7. Conclusions
In this work, we combined field observations of particle entrainment using painted plots and
grain size analysis of a large flood deposit, with the GTM model, recently developed [
2
], in order to
quantify streambed mobility in the River Esva. The GTM model proved to be a very flexible tool for
the characterization of patterns of particle entrainment and armour destabilization in our study site,
and we illustrated the potential of this workflow to address these complex issues.
Additionally, we compared our results with field observations from previous studies that we
compiled from the literature. We observed how the grain size of the bed load tended to be closer to
that of the sub-armour bed material during large floods, while moderate magnitude flows tended to
carry a relatively fine bed load. However, there was a huge scatter in the data. Hence, inferring the
grain size of the bed load or paleo-flow conditions from the grain size analysis of flood deposits should
be done with care.
Author Contributions:
Conceptualization, D.V.-T.; methodology, D.V.-T., E.F.-I. and M.F.G.; formal analysis,
D.V.-T.; investigation, D.V.-T. and E.F.-I.; resources, E.F.-I., M.F.G. and D.V.-T.; data curation, E.F.-I., M.F.G. and
D.V.-T.; writing—original draft preparation, D.V.-T.; writing—review and editing, D.V.-T.; visualization, D.V.-T.;
supervision, D.V.-T. and J.M.; project administration, J.M. and D.V.-T.; funding acquisition, J.M. and D.V.-T.
Funding:
The present work was possible thanks to the financial support provided by the grant ACB17-44,
co-funded by the post-doctoral “Clar
í
n” program-FICYT (Government of the Principality of Asturias) and the
Marie Curie Co-Fund. The authors acknowledge the support from the project RIVERCHANGES-CGL2015-68824-R
(MINECO/FEDER, UE).
Acknowledgments:
The authors would like to thank Daniel Grace and Hodei Uzkeda Apestegia for their review
of the English of this manuscript. We are also thankful to the three anonymous reviewers that helped improve the
final version of the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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... Palaeo-competence methods rely on the selective sorting of particles transported by floods (Gilbert and Murphy, 1914), usually the largest clasts, to infer flow velocities or discharges for singular events (Carling, 1983;Parker, 1991). Then, site-specific empirical relationships (Costa, 1983;Whitaker and Potts, 2007;Vázquez-Tarrío et al., 2019a) can be defined from computed hydraulic parameters and the largest particles moved by floods (e.g., mean diameter of the largest 10 boulders). Reviews of flow competence methods, including their application and uncertainties, are provided by Williams (1983), Komar (1989Komar ( , 1996, Komar and Carling (1991), Wilcock (1992a,b), O'Connor (1993), Carling et al. (2002), Recking (2016), and Greenbaum et al. (2020). ...
... Reviews of flow competence methods, including their application and uncertainties, are provided by Williams (1983), Komar (1989Komar ( , 1996, Komar and Carling (1991), Wilcock (1992a,b), O'Connor (1993), Carling et al. (2002), Recking (2016), and Greenbaum et al. (2020). Flow competence estimates based on the largest sampled mobile grains have been criticized as being subject to large errors (Wilcock, 1992b(Wilcock, , 2001Vázquez-Tarrío et al., 2019a). The competence method assumes size-selective entrainment, i.e., finer grains are always entrained at lower flows than coarser grains, and increasing large grains are progressively recruited into sediment transport over a broad range of discharges. ...
Chapter
This article reviews concepts and methodological approaches commonly used in fluvial geomorphology to understand and analyze flood hazards, spanning from catchment to reach spatial scales. Modern fluvial geomorphology applied to flood hazard studies has developed close links with hydrology and engineering to provide a holistic approach for flood hazard assessment. Flood geomorphology is being applied to (i) extend the flood record into the past from sediments, (ii) hydro-morphologically map channel and floodplain landforms, (iii) analyze and quantify morphodynamic processes such as channel migration and sediment transport in response to individual or sequential flooding, and (iv) understand natural processes at the landscape scale as a means of reducing flood risk by providing nature-based alternatives to conventional structural solutions. General and specific approaches on the study of flood hazards are considered here for four different fluvial environments: mountain streams, bedrock rivers, alluvial fans, and alluvial rivers. Geomorphologic and stratigraphic signatures of floods are critical to understanding the linkages among climate change, environmental change, flood hydrology, and the geomorphic development of fluvial landscapes.
... Dietrich et al., 1989). However, natural rivers experience very often gradually varied flow hydrographs, and we could expect the amount of entrained bed material and the grain size of the bedload to increase as flow discharge rises (Milhous, 1973;Jones and Seitz, 1980;Kuhnle and Willis, 1992;Andrews, 1994;Lisle, 1995;Wathen et al., 1995;Powell et al., 2001;Ryan and Emmett, 2002;Wilcock andMcArdell, 1993, 1997;Clayton and Pitlick, 2008;Hassan, 2014, 2015;Pitlick et al., 2008;Recking et al., 2016;Vázquez-Tarrío et al., 2019a). In this regard, Hassan et al. (2006) investigated, in a flume, the influence of flow hydrograph on surface armouring, observing varying textural responses to steady vs. gradually varying flows. ...
... The denominator in eq. 5 (q ss ) was estimated based on flow characteristics at the representative channel-forming discharge and the subsurface GSD. We thereby assume a correspondence between the long-term averaged bedload and subsurface GSD distributions, which is often postulated for the GSD of the bedload (Church and Hassan, 2005;Vázquez-Tarrío et al., 2019a). We used Rickenmann and Recking (2011) formula for computing water depth (and shear stresses) from dominant discharges, and Recking's bedload equation (Recking, 2013a(Recking, , 2013bRecking et al., 2016) for bedload computation (the two steps based on subsurface GSD). ...
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The surface of the streambed in gravel-bed rivers is commonly coarser than the underlying bed material. This surface coarsening, or ‘armouring’, is usually described by means of the ratio between surface and subsurface grain-size metrics (the ‘armour ratio’). Such surface coarsening is typical of river reaches that are degrading due to a deficit in sediment supply (e.g. gravel-bed reaches below dams or lakes), but non-degrading gravel-bed streams may also exhibit some degree of armouring in relation to specific hydrological patterns. For instance, selective transport during the recession limbs of long lasting floods may coarsen the bed more significantly than flash floods. Consequently, regional differences in bed coarsening should exist, reflecting in turn the variability in sediment and water regimes. In this paper, we explore the trends linking armour ratios to sediment supply, taking into account the differences in hydrological context. We based our analysis on a large data set of bedload and grain size measurements from 49 natural gravel-bed streams and four flume experiments compiled from the scientific literature. Our main outcome documents how the balances between sediment yields and transport capacities have a quantifiable reflection on the armour ratios measured in the field: we report statistically significant correlations between bedload fluxes and surface grain-size, and an asymptotic rise in armour ratios with the decline of sediment supply. Hydrological controls are also observed. Additionally, the trends observed in the field data are comparable to those previously documented in flume experiments with varying sediment feed. In this regard, different kinds of bedforms and particle arrangements have been commonly described with progressive reductions in sediment inputs and the subsequent coarsening of the streambed. Hence, armour ratios serve as a proxy for the general organization of the streambed of gravel-bed streams, and our results quantify this streambed adjustment to the dominant sediment regime.
... Palaeo-competence methods rely on the selective sorting of particles transported by floods (Gilbert and Murphy, 1914), usually the largest clasts, to infer flow velocities or discharges for singular events (Carling, 1983;Parker, 1991). Then, site-specific empirical relationships (Costa, 1983;Whitaker and Potts, 2007;Vázquez-Tarrío et al., 2019a) can be defined from computed hydraulic parameters and the largest particles moved by floods (e.g., mean diameter of the largest 10 boulders). Reviews of flow competence methods, including their application and uncertainties, are provided by Williams (1983), Komar (1989Komar ( , 1996, Komar and Carling (1991), Wilcock (1992a,b), O'Connor (1993), Carling et al. (2002), Recking (2016), and Greenbaum et al. (2020). ...
... Reviews of flow competence methods, including their application and uncertainties, are provided by Williams (1983), Komar (1989Komar ( , 1996, Komar and Carling (1991), Wilcock (1992a,b), O'Connor (1993), Carling et al. (2002), Recking (2016), and Greenbaum et al. (2020). Flow competence estimates based on the largest sampled mobile grains have been criticized as being subject to large errors (Wilcock, 1992b(Wilcock, , 2001Vázquez-Tarrío et al., 2019a). The competence method assumes size-selective entrainment, i.e., finer grains are always entrained at lower flows than coarser grains, and increasing large grains are progressively recruited into sediment transport over a broad range of discharges. ...
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This chapter demonstrates the value of fluvial geomorphology in flood hazard studies and identifies the links with hydrology and engineering to provide a holistic approach for flood hazard assessment. Applied flood geomorphology deals with the extension of flood records into the past from flood sediments, hydromorphological mapping of channel and floodplain landforms, and analysis and quantification of morphodynamic processes such as channel migration and sediment transport in response to individual or sequential flooding. General and specific approaches on the study of flood hazards are considered for three fluvial environments: mountain streams, alluvial fans, and alluvial rivers. Geomorphologic and stratigraphic signatures of floods are critical to understanding the linkages among climate change, environmental change, flood hydrology, and the geomorphic development of fluvial landscapes.
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The morphodynamics of alluvial rivers is controlled by the mobilization of bed material. However, the details of mobilization of mixed‐texture bed materials at low flows, increasingly common due to climate change, are still unclear. The 161‐km‐long Hungarian alluvial reach of the Drava River, downstream of sections where flow characteristics have been heavily modified by human interference, was investigated in 2019. A monitoring campaign at cross‐sections, on average 5.55 km apart, was launched to study channel morphology, bedload entrainment dynamics with regard to texture. For the survey, a sonar, an ADCP and a Helley–Smith bedload sampler mounted on a double‐hull vessel was used. Our research pointed out an abrupt fining between river kms (hereafter: rkm) 175 and 170 (distance from the mouth), probably due to reduced armouring. The d60 fraction was found to be finer than in 2003 and 2012 for the upstream stations of Botovo and Bélavár, and showed a good correspondence with the records of the Barcs and Drávaszabolcs stations. Temporal fining and higher entrainment rate are due to (a) changing climate of the catchment, that is, diminishing flow between the monitoring dates (2003, 2012 and 2019); (b) reduced armouring, (c) variability of cross‐sectional position of sampling points and (d) the different mesh size of the bedload samplers employed. Calculations of shear velocity, Reynolds and Shields numbers indicate more dynamic sediment motion than observed by previous studies. Our reach‐scale results may be relevant for the alluvial sections of other alpine and subalpine, partially channelized rivers of similar size, flow dynamics and mixed bedload.
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Bedload and river morphology interact in a strong feedback manner. Bedload conditions the development of river morphology along different space and time scales; on the other hand, by concentrating the flow in preferential paths, a given morphology controls bedload for a given discharge. As bedload is a nonlinear response of shear stress, local morphology is likely to have a strong impact on bedload prediction when the shear stress is averaged over the section, as is usually done. This was investigated by comparing bedload measured in different bed morphologies (step-pool, plane bed, riffle-pool, braiding, and sand beds), with bedload measured in narrow flumes in the absence of any bed form, used here as a reference. The initial methodology consisted of fitting a bedload equation to the flume data. Secondly, the morphological signature of each river was studied as the distance to this referent equation. It was concluded that each morphology affects bedload in a different way. For a given average grain shear stress, the larger the river, the larger the deviation from the flume transport. Narrow streams are those morphologies that behave more like flumes; this is particularly true with flat beds, whereas results deviate from flumes to a greater extent in step-pools. The riffle-pool’s morphology impacts bedload at different levels depending on the degree of bar development, considered here through the ratio D84/D50 which is used as a proxy for the local bed patchiness and morphology. In braiding rivers morphological effects are important but difficult to assess because width is dependent on transport rate. Bed morphology was found to have negligible effects in sand bed rivers where the Shields stress is usually sufficiently high to minimize the non-linearity effects when hydraulics is averaged over the section.
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Using particle-scale simulations of non-suspended sediment transport for a large range of Newtonian fluids driving transport, including air and water, we determine the bulk transport cessation threshold $\Theta^r_t$ by extrapolating the transport load as a function of the dimensionless fluid shear stress (\textit{Shields number}) $\Theta$ to the vanishing transport limit. In this limit, the simulated steady states of continuous transport can be described by simple analytical model equations relating the average transport layer properties to the law of the wall flow velocity profile. We use this model to calculate $\Theta^r_t$ for arbitrary environments and derive a general Shields-like threshold diagram in which a Stokes-like number replaces the particle Reynolds number. Despite the simplicity of our hydrodynamic description, the predicted cessation threshold, both from the simulations and analytical model, quantitatively agrees with measurements for transport in air and viscous and turbulent liquids despite not being fitted to these measurements. We interpret the analytical model as a description of a continuous rebound motion of transported particles and thus $\Theta^r_t$ as the minimal fluid shear stress needed to compensate the average energy loss of transported particles during an average rebound at the bed surface. This interpretation, supported by simulations near $\Theta^r_t$, implies that entrainment mechanisms are needed to sustain transport above $\Theta^r_t$. While entrainment by turbulent events sustains intermittent transport, entrainment by particle-bed impacts sustains continuous transport. Combining our interpretations with the critical energy criterion for incipient motion by Valyrakis and coworkers, we put forward a new conceptual picture of sediment transport intermittency.
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The frequency and intensity of riverbed mobility are of paramount importance to the inhabitants of river ecosystems as well as to the evolution of bed surface structure. Because sediment supply varies by orders of magnitude across North America, the intensity of bedload transport varies by over an order of magnitude. Climate also varies widely across the continent, yielding a range of flood timing, duration, and intermittency. Together, the differences in sediment supply and hydroclimate result in diverse regimes of bed surface stability. To quantitatively characterize this regional variation, we calculate multidecadal time series of estimated bed surface mobility for 29 rivers using sediment transport equations. We use these data to compare predicted bed mobility between rivers and regions. There are statistically significant regional differences in the (a) exceedance probability of bed-mobilizing flows (W* > 0.002), (b) maximum bed mobility, and (c) number of discrete bed-mobilizing events in a year.
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A laboratory study was undertaken to investigate how changes in flow regime and hydrograph shape (number of cycled hydrographs and duration of each hydrograph) together impact bedload transport and resulting bed morphology. Three hydrologic conditions (experiments) representing different levels of urbanization, or analogously different flow regimes, were derived from measured hydrometric field data. Each experiment consisted of a series of hydrographs with equal peak discharge and varying frequency, duration and flashiness. Bedload transport was measured throughout each hydrograph and measurements of bed topography and surface texture were recorded after each hydrograph. The results revealed hysteresis loops in both the total and fractional transport, with more pronounced loops for longer duration hydrographs, corresponding to lower rate of unsteadiness until reaching the peak discharge (pre-urbanization conditions). Shorter duration hydrographs (urban conditions), displayed more time above critical shear stress thresholds leading to higher bedload transport rates and ultimately to more variable hysteresis patterns. Surface textures from photographic methods revealed surface armoring in all experiments, with larger armor ratios for longer duration hydrographs, speculated to be due to vertical sorting and more time for bed rearrangements to occur. The direction of bed surface adjustment was linked to bedload hysteresis, more precisely with clockwise hysteresis (longer hydrographs) typically resulting in bed coarsening. More frequent and shorter duration hydrographs result in greater relative channel adjustments in slope, topographic variability and surface texture.
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This study was aimed at untangling the relative impacts of successive phases of human modifications on changes in bedload transport along a 430 km-long river reach: the Rhône River from Motz dam to the sea. We used a 1D hydraulic model to solve for water lines across a range of discharges and all along the reach. Next, using grain sizes measured in the channel, we estimate flow competence and mean annual bedload transport capacities using the Recking (2013) bedload transport equation. In addition, we used the Generalized Threshold Model to estimate the relative fine and coarse fractions of the load. Bedload transport estimates were carried out under present-day hydraulic conditions and compared to estimates based on model runs simulating an unimpeded flow regime and using grain sizes measured in bars as a proxy for conditions prior to armouring. Our results show that present-day bedload transport along the Rhône is significantly fragmented by multiple closely spaced dams. Mean annual bedload capacity varies between 2500 and 16,300 m³/year over all the reaches, with an average of 4700 m³/year. Results of the GTM analysis suggest that this load is composed of 89% fines. We find bed sediment mobility to be very low in most reaches, and that potentially mobile sediments are finer than the median grain size in the riverbed even at high flows. Our results suggest that bedload capacities were 25–35 times higher prior to bed armouring and flow modifications; dams had an impact 2–3 times more important on transport capacities than channel embankments, and bed armouring was foremost a response to channel embankments. Based on an analysis of the ratio of sediment yields to transport capacities, we propose a conceptual scheme illustrating how bedload supply, channel morphology, and surface texture coevolved in the Rhône over the past century and half.
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Field observations in a wide range of environments have shown that sediment availability is a major control on the suspended sediment observations in streams. Here we examine, via laboratory experiments, how the amount of proximal in-channel fine sediment storage relative to the upstream fine sediment distal supply influences the observations of suspended sediment concentrations in streams. Experiments under idealized conditions in a laboratory flume with different ratios of proximal and distal sediment supplies were conducted under a varying flow regime. In addition, the role of the sediment particle size of the supplied sediment on suspended sediment observations was explored. The combinations of proximal and distal sediment supply result in multiple responses of the channel bed and sediment quantity within the channel bed, and the responses adjust through aggradation and degradation. The signature of sediment concentration observed at the upstream section of the channel, given by the distal supply, differs from the downstream observations of the total conveyed sediment (distal and proximal), as shown by an in-phase analysis of sediment concentration-discharge plots. Furthermore, we show that nonuniform sediment mixtures may result in a change in the direction of the hysteresis observed between sediment concentration and discharge (i.e., from a clockwise hysteresis to a counterclockwise hysteresis). We also demonstrate that the ratio between sediment distal supply and proximal sediment availability modulates the magnitude of the aggradation/degradation processes in the channel reach and thus the joint observations of sediment concentration and discharge.
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While the influence of large grains on the morphodynamics of gravel bed rivers has long been recognized, nothing dominates our collective efforts to model such rivers like the bed surface D50, which turns up in virtually all the relevant equations. While researchers interested in flow resistance have recognized the relative importance of large grains and have modified flow resistance equations accordingly, there have been few attempts to quantify the effects of large grains on gravel bed river morphodynamics. However, there is little evidence that the D50 exerts first‐order control over the physics occurring along the channel boundary, and its prevalence seems to be primarily based on the untested, a priori assumption that the best description of a distribution is the mean or median value. This commentary questions the long standing assumption that D50 is the best choice for characteristic grain size, and uses evidence from previous studies to show that mobilization of the largest grains in the bed likely controls morphologic stability, and possibly sediment transport. This article is protected by copyright. All rights reserved.
Article
The performance of seven sediment transport equations for bedload transport is compared using almost 2,600 of more than 8,000 measurements from a recent compilation. Named equations tested include the Meyer-Peter Muller, Barry, Pagosa good condition, Wilcock, Parker (both calibrated and uncalibrated), Recking, and that of Elhakeem and Imran. The purpose of the tests was to evaluate the performance of several empirical and semiempirical formulae using a single calibration point relative to three uncalibrated equations. The seven equations were included because they either have a calibration procedure already developed, are used frequently in practice, are historically foundational in the field, or have recently been proposed. Results are expressed in the root mean square error of the logarithms (RMSEL) and the relative mean error (RME) and show that the Pagosa good and Barry equations best predict bedload sediment transport (RMSEL of 0.02 and 0.02, respectively). The Pagosa good equation requires a data point for bankfull discharge and the corresponding bedload transport. The uncalibrated Recking (2013) equation resulted in lower errors than two of the calibrated formulae (Wilcock 2001 and Parker 1990) and was not far behind the calibrated Elhakeem and Imran (2016) formula. The Meyer-Peter Muller and uncalibrated Parker (1990) equations performed the worst (RMSEL of up to 0.85 and 0.86, respectively). The results herein demonstrate: (1) empirical formulae were more successful at predicting bedload transport than semiempirical alternatives, (2) a single calibration point significantly improves the predictive accuracy of any formula, and (3) calibration cannot compensate for all the shortcomings of a model.