1.
Introduction
Mud (grain diameter,
D
< 62.5 μm) dominates the sediment load carried by rivers globally (e.g., Baronas
et al.,
2020
; Lupker et al.,
2011
) and its fate is important for our understanding of fluvial geomorphology and
biogeochemical cycling. For example, mud-rich fluvial deposits are a major component of the rock record
(Aller,
1998
; McMahon & Davies,
2018
; Zeichner et al.,
2021
). Mud cohesion increases bank strength in allu
-
vial rivers, affecting river morphodynamics (e.g., Dunne & Jerolmack,
2020
; Kleinhans et al.,
2018
; Lapôtre
et al.,
2019
; Millar & Quick,
1998
). Mud is also a primary carrier of organic carbon and pollutants because of its
high specific surface area (e.g., France-Lanord & Derry,
1997
; Galy et al.,
2015
; Pizzuto et al.,
2014
). Despite its
importance, we lack well-tested mechanistic models for mud transport in rivers.
Mud in rivers has traditionally been treated as washload, or sediment that is too fine to regularly settle to and
interact with the riverbed (Church,
2006
; Garcia,
2008
). In contrast, recent work suggests that flocculation—
the aggregation of particles into composite structures called flocs—can enhance mud settling velocities and
Abstract
The transport and deposition of mud in rivers are key processes in fluvial geomorphology
and biogeochemical cycles. Recent work indicates that flocculation might regulate fluvial mud transport by
increasing mud settling velocities, but we lack a calibrated mechanistic model for flocculation in freshwater
rivers. Here, we developed and calibrated a semi-empirical model for floc diameter and settling velocity in
rivers. We compiled a global data set of river suspended sediment concentration-depth profiles and inverted
them for in situ settling velocity using the Rouse-Vanoni equation. On average, clay and silt (diameters <39 μm)
are flocculated with settling velocity of 1.8 mm s
−1
and floc diameter of 130 μm. Among model variables,
Kolmogorov microscale has the strongest positive correlation with floc diameter, supporting the idea that
turbulent shear limits floc size. Sediment Al/Si (a mineralogy proxy) has the strongest negative correlation
with floc diameter and settling velocity, indicating the importance of clay abundance and composition for
flocculation. Floc settling velocity increases with greater mud and organic matter concentrations, consistent
with flocculation driven by particle collisions and binding by organic matter which is often concentrated in
mud. Relative charge density (a salinity proxy) correlates with smaller floc settling velocities, a finding that
might reflect the primary particle size distribution and physical hosting of organic matter. The calibrated model
explains river floc settling velocity data within a factor of about two. Results highlight that flocculation can
impact the fate of mud and particulate organic carbon, holding implications for global biogeochemical cycles.
Plain Language Summary
The fate of fine sediment in rivers is important for understanding
contaminant dispersal, organic carbon burial, and the construction of river floodplains and deltas. Individual
grains of silt and clay dispersed in water settle under the pull of gravity at extremely slow rates. However,
in natural rivers, these mud particles can aggregate together into larger structures called flocs, resulting in
far faster settling rates. Here, we built on prior work from estuaries to develop a settling velocity model for
flocculated mud in freshwater rivers. Our results demonstrate that mud settling velocity increases in rivers
with less vigorous turbulence because turbulence can break flocs apart. Mud settling velocity also increases
with greater concentrations of mud and particulate organic matter, which promote particle collisions and
binding. Counterintuitively, settling velocity decreases with greater clay abundance and greater river water
salinity, possibly due to how they affect organic matter in binding mud particles into flocs. Our results improve
understanding of floc behavior in rivers and indicate potential links between the routing of mud and organic
matter, river geomorphology, and global climate.
NGHIEM ET AL.
© 2022. American Geophysical Union.
All Rights Reserved.
A Mechanistic Model for Mud Flocculation in Freshwater
Rivers
Justin A. Nghiem
1
, Woodward W. Fischer
1
, Gen K. Li
1,2
, and Michael P. Lamb
1
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA,
2
Now at Department
of Earth Science, University of California, Santa Barbara, CA, USA
Key Points:
•
Turbulence, sediment concentration
and mineralogy, water chemistry, and
organics affect river floc size and
settling velocity
•
Controlling variables are incorporated
into a model for mud floc diameter
and settling velocity in rivers
calibrated on a global data set
•
Mud flocs in rivers can respond to
river hydraulics and biogeochemistry
with implications for the carbon cycle
and fluvial morphodynamics
Supporting Information:
Supporting Information may be found in
the online version of this article.
Correspondence to:
Justin A. Nghiem,
jnghiem@caltech.edu
Citation:
Nghiem, J. A., Fischer, W. W., Li, G. K.,
& Lamb, M. P. (2022). A mechanistic
model for mud flocculation in freshwater
rivers.
Journal of Geophysical Research:
Earth Surface
,
127
, e2021JF006392.
https://doi.org/10.1029/2021JF006392
Received 15 AUG 2021
Accepted 2 APR 2022
Corrected 12 SEP 2023
This article was corrected on 12 SEP
2023. See the end of the full text for
details.
10.1029/2021JF006392
RESEARCH ARTICLE
1 of 24
Journal of Geophysical Research: Earth Surface
NGHIEM ET AL.
10.1029/2021JF006392
2 of 24
drastically affect mud transport dynamics in rivers (Bouchez, Métivier,
et al.,
2011
; Lamb et al.,
2020
; Zeichner et al.,
2021
). Similar to sand, floc
-
culated mud might be in a dynamic interchange between the flow and bed
material (Lamb et al.,
2020
). Mud flocculation has been well-studied in estu
-
arine and marine systems where flocs form in part because salinity promotes
van der Waals attraction between particles (e.g., Hill et al.,
2000
; Mehta &
Partheniades,
1975
; Winterwerp,
2002
, Figure
1
). In addition, flow turbu
-
lence, sediment concentration, organic matter concentration, and clay miner
-
alogy are important for estuarine and marine flocculation (e.g., Kranck &
Milligan,
1980
; Meade,
1972
; Verney et al.,
2009
). In contrast to the wealth
of studies on flocculation in saline environments, knowledge on floccula
-
tion in freshwater rivers is relatively limited (e.g., Bungartz & Wanner,
2004
;
Droppo et al.,
1997
; Droppo & Ongley,
1994
).
Studies in rivers identified flow characteristics, organic matter concentra
-
tion, and suspended sediment concentration as potential controls on floc size,
settling velocity, and strength (Figure
1
). Through microscopy of samples
from Canadian rivers, Droppo and Ongley (
1994
) observed organic matri
-
ces binding together mineral sediment into flocs. They observed correlations
between floc size and suspended sediment concentration, attached bacteria
count, and particulate organic carbon concentration. Bungartz et al. (
2006
)
characterized floc setting velocities at three transects along a lake outlet
and found faster-settling flocs at higher discharge, a result they attributed to
faster floc growth at higher flow turbulence. They also showed that settling
patterns of suspended sediment and particulate organic carbon were simi
-
lar, supporting the idea that flocculation controlled transport of both mineral
sediment and organic carbon. Gerbersdorf et al. (
2008
) examined bed mate
-
rial composition in the Neckar River, Germany, and identified rich networks
of microbe-derived extracellular polymeric substances (EPS). They found
positive correlations between concentrations of EPS moieties and the critical
shear stress for erosion, indicating that EPS can help stabilize bed sediment.
Lamb et al. (
2020
) used a field data compilation to infer the presence of wide
-
spread mud flocculation in rivers. They showed that in situ particle settling velocity can be inferred by fitting the
Rouse-Vanoni equation to grain size-specific suspended sediment concentration-depth profiles. However, they
did not explain the order-of-magnitude variation in the inferred floc settling velocities.
Experiments have also supported organic matter, dissolved species, and sediment concentration as important
controls on freshwater flocculation (Figure
1
). Chase (
1979
) showed that the presence of organics increased floc
settling velocity, a result attributed to the interaction of sediment surface coatings, organic chemistry, and dissolved
solutes. Subsequent experiments showed that sediment concentration positively correlated with floc size while
fluid shear rate affected floc size and settling velocity differently (e.g., Burban et al.,
1990
; Tsai et al.,
1987
).
More recent experiments examining the role of organics on flocculation in freshwater highlighted the importance
of nutrients, biomass, and organic matter composition on floc size and settling velocity (Furukawa et al.,
2014
;
Lee et al.,
2017
,
2019
; Tang & Maggi,
2016
; Zeichner et al.,
2021
). For instance, Zeichner et al. (
2021
) showed in
experiments modeled after rivers that organic matter increased clay floc settling velocities by up to three orders
of magnitude, depending on organic matter type and clay mineralogy.
Process-based flocculation theory is required to link field studies and experiments into a coherent framework.
Floc population balance models use particle aggregation and breakage kernels, and have been successful at repro
-
ducing floc size distributions (e.g., Lick & Lick,
1988
; Spicer & Pratsinis,
1996
; Xu et al.,
2008
). These studies
showed that sediment concentration and fluid shear enhance floc aggregation by increasing particle collision
frequency, but greater shear causes floc breakage (Figure
1
). Winterwerp (
1998
) introduced a simplified model
(hereafter, the Winterwerp model) tracking a characteristic floc diameter (e.g., the median), making it more easily
coupled to hydrodynamic models (e.g., Maggi,
2008
; Son & Hsu,
2011
; Winterwerp,
2002
). The Winterwerp
model includes the effects of fluid shear and sediment concentration, but subsumes other factors into coefficients
Figure 1.
Schematic of a cross-section through a river water column
illustrating physicochemical processes operating at different scales that could
be important for mud flocculation in rivers. Key variables are turbulence
(Kolmogorov microscale,
η
), volumetric mud concentration (
C
m
), sediment
mineralogy (molar Al/Si of river suspended sediment), organic matter
concentration (fraction of sediment surface covered by organic matter,
θ
), and
dissolved species concentrations (relative charge density of river water, Φ).
These variables affect the diameter,
D
f
, and settling velocity,
w
s
,floc
, of flocs
composed of primary particles with diameter
D
p
.
21699011, 2022, 5, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JF006392 by California Inst of Technology, Wiley Online Library on [06/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Journal of Geophysical Research: Earth Surface
NGHIEM ET AL.
10.1029/2021JF006392
3 of 24
of the aggregation and breakage rates. The model describes well the equilibrium size of flocculated estuarine mud
(Winterwerp,
1998
) and flocs in saline laboratory experiments (e.g., Kuprenas et al.,
2018
; Maggi,
2009
; Son
& Hsu,
2008
). However, these models have yet to be compared or adapted to flocculation in freshwater rivers.
Here, we built on the Winterwerp approach to develop a semi-empirical process-based model for mud floccu
-
lation in freshwater rivers. First, we proposed new forms for flocculation efficiency coefficients to explicitly
cast floc diameter and settling velocity as functions of physicochemical variables that prior work has shown
are important for flocculation in freshwater: turbulence, sediment concentration, sediment mineralogy, organic
matter concentration, and dissolved ion concentration (Figure
1
). Next, we calibrated the new model against field
data. We compiled a global data set of river grain size-specific suspended sediment concentration-depth profiles
and inverted them for in situ settling velocity using the Rouse-Vanoni equation (Lamb et al.,
2020
). Together with
a river geochemistry data compilation, we fitted the model to help explain the variance in floc settling velocities.
Finally, the results are discussed in the context of fluvial geomorphology, organic carbon, tectonics, and climate.
2.
Model Development
2.1.
Winterwerp Model
Winterwerp (
1998
) proposed a flocculation model in which fluid shear drives particle collisions and floc aggre
-
gation and breakage. The model casts the time rate of change of floc diameter,
D
f
(or median
D
f
for a floc size
distribution) as the difference of floc aggregation and breakage rates:
d
μ
d
푡푡
=
푘푘
퐴퐴
푛푛
푓푓
휂휂
2
휈휈휈휈
퐷퐷
푓푓
(
퐷퐷
푓푓
퐷퐷
푝푝
)
3−
푛푛
푓푓
−
푘푘
퐵퐵
푛푛
푓푓
휂휂
2
휈휈퐷퐷
푓푓
(
퐷퐷
푓푓
−
퐷퐷
푝푝
퐷퐷
푝푝
)
3−
푛푛
푓푓
(
휏휏
푡푡
휏휏
푦푦
)
푗푗
(1)
On the right-hand side of Equation (
1
), the first term is the floc aggregation rate, scaled by the aggregation
efficiency,
k
A
(dimensionless), and the second term is the floc breakage rate, scaled by the breakage efficiency,
k
B
(dimensionless). The shear rate,
G
(s
−1
), quantifies fluid mixing and relates to the smallest turbulence length
scale— the Kolmogorov microscale,
퐴퐴퐴퐴
=
√
휈휈
∕
퐺퐺
(m), where
ν
is the fluid kinematic viscosity (m
2
s
−1
) (Tennekes
& Lumley,
1972
). Greater fluid mixing and volumetric sediment concentration,
C
(volume sediment/total volume;
dimensionless), drive more frequent collisions of primary particles with diameter
D
p
(m) and thereby increase
aggregation rate (Figure
1
).
Flocs break up if fluid shear is too high relative to floc strength, an effect that Winterwerp (
1998
) expressed
in Equation (
1
) using the ratio of fluid stress on the floc,
τ
t
=
ρ
(
ν
/
η
)
2
(Pa), and floc strength,
퐴퐴퐴퐴
푦푦
=
퐹퐹
푦푦
∕
퐷퐷
2
푓푓
(Pa),
where
ρ
is fluid density (kg m
−3
).
F
y
is floc yield strength (in terms of force) and has been estimated to be of
order 10
−10
N (Matsuo & Unno,
1981
). Floc fractal dimension,
n
f
∈ [1,
3] (dimensionless), describes floc struc
-
ture assuming it is approximately self-similar (Kranenburg,
1994
). Floc structure can vary from a linear string of
particles (
n
f
= 1) to a solid, compact particle (
n
f
= 3). An average
n
f
= 2 is typical for natural flocs (e.g., Tambo
& Watanabe,
1979
; Winterwerp,
1998
). In practice,
n
f
describes the relationship between floc diameter and floc
density by
퐴퐴퐴퐴
푓푓
퐴퐴
푠푠
=
(
퐷퐷
푓푓
∕
퐷퐷
푝푝
)
푛푛
푓푓
−3
where
R
f
is the floc submerged specific gravity (dimensionless) and
R
s
is the
submerged specific gravity of the primary particle sediment (dimensionless) (Kranenburg,
1994
). Although the
parameter
j
in Equation (
1
) is an empirical constant, Winterwerp (
1998
) used
j
= 0.5 to ensure that floc settling
velocity, floc diameter, and sediment concentration are linearly related to each other based on estuarine floc data.
We retained
j
as a fit parameter to maintain generality.
2.2.
Modifications to the Winterwerp Model for River Flocs
We proposed changes to floc strength, and floc aggregation and breakage efficiencies to adapt the Winterwerp
model to rivers.
2.2.1.
Floc Strength
Experiments in freshwater have shown that, for constant
D
f
, floc settling velocity,
w
s
,floc,
increases with larger
mixing rate due to an increase in floc density (Burban et al.,
1990
). This behavior suggests that flow conditions
during floc formation can affect floc strength, where more porous and lighter flocs are weaker because they have
fewer interparticle contacts and vice versa. Bache (
2004
) proposed that floc strength,
τ
y
, is a balance of local
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Journal of Geophysical Research: Earth Surface
NGHIEM ET AL.
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4 of 24
turbulent kinetic energy per unit volume acting on the floc and the energy per unit volume required to rupture
the floc:
휏휏
푦푦
=
휌휌
30
(
휈휈
휂휂
)
2
(
퐷퐷
푓푓
휂휂
)
2
(2)
The power-law form of Equation (
2
) holds in general but the numerical constants apply for small
D
f
/
η
(Bache,
2004
).
2.2.2.
Floc Aggregation and Breakage Efficiencies
In the Winterwerp model, all contributions to flocculation outside of fluid shear and sediment concentration are
captured in the constant floc aggregation and breakage efficiency terms,
k
A
and
k
B
, respectively. We investigated
whether
k
A
and
k
B
in rivers depend on organic matter concentration, sediment mineralogy, and dissolved ion
concentration, as functions rather than fit constants.
Organic matter can adsorb onto sediment surfaces and form connective “bridges” between grains (Ruehrwein &
Ward,
1952
; Smellie & La Mer,
1958
; Molski,
1989
, Figure
1
). In rivers, biogenic molecules like EPS can act as
sticky media for bridging flocculation (Droppo & Ongley,
1994
; Gerbersdorf et al.,
2008
; Larsen et al.,
2009
; Lee
et al.,
2019
). Smellie and La Mer (
1958
) proposed a functional form of bridging flocculation efficiency,
푘푘
퐴퐴
,푘푘
−1
퐵퐵
∝
휃휃
(1−
휃휃
)
(3)
in which
θ
is the fraction of the sediment surface covered by a polymeric substance. We used Equation (
3
) and
calculated
θ
for organic matter (Section
3.3
).
We accounted for sediment mineralogy using the molar elemental ratio Al/Si as a proxy variable (Figure
1
). More
intensely weathered rocks typically generate sediment with larger Al/Si because chemical weathering produces
Al-rich clay minerals (e.g., Ito & Wagai,
2017
; Jackson et al.,
1948
; Lupker et al.,
2012
). Mineralogy can affect
flocculation because it determines the range of potential chemical interactions between particles through cation
exchange capacity (CEC) and therefore the ability to attract cations in solution (Mehta & McAnally,
2008
). Further
-
more,
cations can affect the ability of organic matter to adsorb to particle surfaces and the physical orientation of
adsorbed organic matter (Galy et al.,
2008
; Mehta & McAnally,
2008
). We used a simple power law model as a
starting point,
푘푘
퐴퐴
∝(
Al
∕
Si
)
퐴퐴
1
(4)
푘푘
퐵퐵
∝(
Al
∕
Si
)
퐵퐵
1
(5)
where
A
1
and
B
1
are dimensionless fit constants.
Dissolved ions in river water might promote flocculation through the same mechanism as salinity by boosting
the effectiveness of van der Waals attraction between particles (e.g., Seiphoori et al.,
2021
, Figure
1
). To express
ionic effects, we used a dimensionless parameter, Φ, to quantify the relative densities of charges in solution and
on the sediment (Rommelfanger et al.,
2020
):
Φ=
휆휆휆휆
CEC
휌휌
푠푠
퐿퐿
∕2
(6)
in which the Debye length,
λ
(
m
), is the average length from the particle in which an electrostatic effect from
the charged surface is sustained,
I
is the solution ionic strength ((number ions) m
−3
), CEC is the sediment CEC
((number ions) kg
−1
),
ρ
s
is sediment density (kg m
−3
), and
L
(
m
) is a grain length scale that is nominally the face
length of a plate-shaped clay particle, which we set to
D
p
. Physically, Φ quantifies the ionic strength of river water
relative to the ionic strength in a volume surrounding primary particles. As Φ increases, the positive charge in
the water within the Debye length overcomes the negative charge on the sediment surface and causes attraction
between nearby sediment grains (Rommelfanger et al.,
2020
). We proposed power-law relations as starting points
to relate Φ and the flocculation efficiencies:
푘푘
퐴퐴
μ
퐴퐴
2
(7)
푘푘
퐵퐵
μ
퐵퐵
2
(8)
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Journal of Geophysical Research: Earth Surface
NGHIEM ET AL.
10.1029/2021JF006392
5 of 24
where
A
2
and
B
2
are dimensionless fit constants.
2.3.
River Floc Model
We substituted Equations
(2)
–
(8)
into Equation (
1
) to derive a modified semi-empirical model for floc diameter,
D
f
:
d
μ
d
−
=
푘푘
′
퐴퐴
휃휃
(1−
휃휃
)(
Al
∕
Si
)
퐴퐴
1
Φ
퐴퐴
2
푛푛
푓푓
휂휂
2
휈휈휈휈
퐷퐷
푓푓
(
퐷퐷
푓푓
퐷퐷
푝푝
)
3−
푛푛
푓푓
−
푘푘
′
퐵퐵
(
Al
∕
Si
)
퐵퐵
1
Φ
퐵퐵
2
휃휃
(1−
휃휃
)
푛푛
푓푓
휂휂
2
휈휈퐷퐷
푓푓
(
퐷퐷
푓푓
−
퐷퐷
푝푝
퐷퐷
푝푝
)
3−
푛푛
푓푓
(
휂휂
퐷퐷
푓푓
)
2
푗푗
(9)
in which
퐴퐴퐴퐴
′
퐴퐴
and
퐴퐴퐴퐴
′
퐵퐵
are new dimensionless constants that absorb all constant dimensionless parameters related
to floc aggregation and breakage, respectively. At dynamic equilibrium, the time derivative of
D
f
vanishes,
resulting
in
퐷퐷
푓푓
=
푘푘푘푘
(
퐶퐶퐶퐶
2
(1−
퐶퐶
)
2
)
푞푞
(
Al
∕
Si
)
푟푟
Φ
푠푠
(
1−
퐷퐷
푝푝
퐷퐷
푓푓
)
−
푞푞
(
3−
푛푛
푓푓
)
(10)
in which
퐴퐴퐴퐴
(
퐴퐴
′
퐵퐵
∕
퐴퐴
′
퐴퐴
)
1∕(2
푗푗
)
,
q
= −1/(2
j
),
r
= (
B
1
−
A
1
)/(2
j
), and
s
= (
B
2
−
A
2
)/(2
j
). We consolidated the unknown
dimensionless coefficients and variables into the coefficient
k
and exponents
q
,
r
, and
s
.
D
f
appears on both sides
of Equation (
10
), so we simplified the equation by assuming that
D
f
≫
D
p
:
퐷퐷
푓푓
=
푘푘푘푘
(
퐶퐶퐶퐶
2
(1−
퐶퐶
)
2
)
푞푞
(
Al
∕
Si
)
푟푟
Φ
푠푠
(11)
The assumption
D
f
≫
D
p
makes
D
f
independent of
D
p
in Equation (
11
) and implies a model domain of validity
of intermediate fluid shear such that
D
f
does not converge to
D
p
. We validated the assumption through analysis
of our field data compilation (Section
4.1
). The equilibrium
D
f
model is plausible in rivers because experiments
and field studies have shown the time scale for unsteady floc behavior to reach equilibrium in river conditions
is typically on the order of tens of minutes to hours, and most dynamic river processes (e.g., floods) have longer
time scales (e.g., Bungartz et al.,
2006
; Garcia-Aragon et al.,
2011
).
Floc settling velocity,
w
s
,floc
, relates to
D
f
using an adaptation of the Stokes settling law for flocs (Strom &
Keyvani,
2011
; Winterwerp,
1998
) as
푤푤
푠푠푠푠푠푠푠푠푠푠푠
=
푅푅
푠푠
푔푔푔푔
2
푝푝
푠푠
1
휈휈
(
푔푔
푠푠
푔푔
푝푝
)
푛푛
푠푠
−1
(12)
Substituting Equation (
11
) into Equation (
12
) yields a model for
w
s
,floc
푤푤
푠푠푠푠푠푠푠푠푠푠푠
=
푅푅
푠푠
푔푔푔푔
푝푝
푠푠
1
휈휈
[
푘푘
휂휂
푔푔
푝푝
(
퐶퐶퐶퐶
2
(1−
퐶퐶
)
2
)
푞푞
(Al∕Si)
푟푟
Φ
푠푠
]
푛푛
푠푠
−1
(13)
Flocs have irregular shapes and variable porosity which complicate the relationship between floc diameter
and settling velocity (van Leussen,
1988
). In Equation (
13
), the effects of floc shape and porosity on
w
s
,floc
are
captured in the dimensionless parameters
c
1
and
n
f
. We held them constant at
c
1
= 20 (Strom & Keyvani,
2011
;
Winterwerp,
1998
) and
n
f
= 2 (Kranenburg,
1994
; Tambo & Watanabe,
1979
). Combining these assumptions
with Equation (
13
) yields
푤푤
푠푠푠푠푠푠푠푠푠푠푠
=
푅푅
푠푠
푔푔푔푔
푝푝
20
휈휈
푘푘푘푘
(
퐶퐶퐶퐶
2
(1−
퐶퐶
)
2
)
푞푞
(Al∕Si)
푟푟
Φ
푠푠
(14)
Equation (
14
) demonstrates that different
c
1
values do not affect model calibration because model fitting absorbs
multiplicative constants into the prefactor
k
. However, different
n
f
values affect model calibration because Equa
-
tion (
13
) depends nonlinearly on
n
f
, an effect we explored in sensitivity tests (Section
4.2
).
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Journal of Geophysical Research: Earth Surface
NGHIEM ET AL.
10.1029/2021JF006392
6 of 24
3.
Field Data Methods
3.1.
River Suspended Sediment Concentration-Depth Profiles
We compiled a data set of grain size-specific suspended sediment concentration-depth profiles containing 122
profiles from 12 rivers distributed globally (Table S1 in Supporting Information
S1
). We targeted datasets with
suspended sediment concentration for multiple heights in the water column, laser-diffraction grain size analy
-
sis, water depth, and boundary shear velocity data. We used datasets analyzed by de Leeuw et al. (
2020
) and
Lamb et al. (
2020
), and included additional datasets (Abraham et al.,
2017
; Baronas et al.,
2020
; Bouchez,
2022
;
Bouchez, Lupker et al.,
2011
,
2012
; Dingle,
2021
; Dingle et al.,
2020
) (Table S1 in Supporting Infomation
S1
).
Having a detailed grain size distribution for each suspended sediment sample is vital because it permits the
construction of concentration-depth profiles for every grain size class (denoted
i
). We refer to these profiles as
grain size-specific concentration-depth profiles. In other words, a single profile of suspended sediment samples
yields as many grain size-specific concentration-depth profiles as there are measured grain size classes. We took
advantage of grain size data to fit the Rouse-Vanoni equation and invert for in situ settling velocity as a function
of the measured grain size (Figure
1
). The measured grain sizes are those of unflocculated sediment (i.e., the
primary particles) because size distribution measurements were made after dispersing the sediment (e.g., Baronas
et al.,
2020
).
The Rouse-Vanoni equation is
퐶퐶
푖푖
(
푧푧
)=
퐶퐶
푏푏푖푖
⎛
⎜
⎜
⎝
ℎ
−
푧푧
푧푧
ℎ
−
ℎ
푏푏
ℎ
푏푏
⎞
⎟
⎟
⎠
푝푝
푖푖
(15)
in which the volumetric sediment concentration for the
i
th grain size class,
C
i
, is a function of height from the
bed,
z
, water depth,
h
, and a near-bed concentration,
C
bi
, specified at a near-bed height,
z
=
h
b
(Rouse,
1937
). The
Rouse number (dimensionless) is
p
i
=
w
si
/(
β
i
κu
*
) in which
κ
= 0.41 is the von Kármán constant (dimensionless),
u
*
(m s
−1
) is the boundary shear velocity,
w
s
(m s
−1
) is the sediment settling velocity, and
β
is the ratio of sedi
-
ment and fluid diffusivities (Rouse,
1937
) where
i
indexes the grain size class. Following de Leeuw et al. (
2020
)
and Lamb et al. (
2020
), we fitted Equation (
15
) to the compiled grain size-specific concentration-depth profiles
to estimate
C
b
and
p
for each grain size class. We estimated
p
i
and
C
bi
(at
z
=
h
b
= 0.1
h
) from fitting the
log-transformed Equation (
15
) using ordinary least squares regression. We computed the 68% confidence inter
-
vals on the fitted
p
i
from the regression and discarded profiles in which the lower confidence bound on
p
i
is
negative because these profiles do not follow Rouse-Vanoni theory for unknown reasons (e.g., non-equilibrium
sediment transport, sampling and/or measurement errors).
We needed to specify
u
*
and
β
i
to estimate the grain size-specific in situ settling velocity,
w
si
, from the fitted
value of
p
i
. We used
u
*
reported in the original data sources, which were measured concurrently with suspended
sediment samples and typically calculated by fitting flow velocity profiles measured using an acoustic Doppler
current profiler to the law of the wall (e.g., Wilcock,
1996
).
β
is a major unknown in calculating settling veloci
-
ties from fitted Rouse numbers (e.g., de Leeuw et al.,
2020
). Empirically,
β
is commonly found to increase with
w
s
/
u
*
(de Leeuw et al.,
2020
; Graf & Cellino,
2002
; Santini et al.,
2019
; van Rijn,
1984
).
β
< 1 corresponds
to greater sediment concentration stratification compared to
β
= 1, which could result from turbulence damp
-
ing due to suspended sediment-induced density stratification (Graf & Cellino,
2002
; Wright & Parker,
2004
;
discussion in de Leeuw et al.,
2020
). The reasons for
β
> 1 are less clear, but might be linked to enhanced
mixing from bedform-generated turbulence (Graf & Cellino,
2002
) or the high vertical concentration gradient
of fast-settling particles promoting sediment diffusion relative to eddy diffusion (Smith & McLean,
1977
).
We followed de Leeuw et al. (
2020
) and empirically fitted functions for
β
i
using only suspended sand
because we assumed sand was unflocculated and settled in situ at theoretical settling velocities. To
calculate theoretical sand settling velocities, we used the Ferguson and Church (
2004
) model (that is,
퐴퐴퐴퐴
푠푠
=
(
푅푅
푠푠
푔푔푔푔
2
)
∕
(
푐푐
1
,푠푠푠푠푠푠푠푠
휈휈
+
√
0
.
75
푐푐
2
,푠푠푠푠푠푠푠푠
푅푅
푠푠
푔푔푔푔
3
)
with
c
1,sand
= 20 and
c
2,sand
= 1.1), which follows Stokes law
for small particles and accounts for inertial affects for large particles. We calculated
β
i
using these theoreti
-
cal sand settling velocities,
u
*
, and the fitted
p
i
. We found values of
β
i
and
w
si
/
u
*
that agree with previously
proposed relations for
β
(
w
s
/
u
*
) (Figure
2
). Next, we calibrated the power-law equation
퐴퐴퐴퐴
∝
(
푤푤
푠푠
∕
푢푢
∗
)
푙푙
on the sand
21699011, 2022, 5, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JF006392 by California Inst of Technology, Wiley Online Library on [06/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License