of 11
Origin of a Preferential Avulsion Node on Lowland
River Deltas
A. J. Chadwick
1
, M. P. Lamb
1
, A. J. Moodie
2
, G. Parker
3
, and J. A. Nittrouer
2
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA,
2
Department of
Earth, Environmental and Planetary Sciences, Rice University, Houston, TX, USA,
3
Department of Civil and
Environmental Engineering and Department of Geology, University of Illinois at Urbana
Champaign, Urbana, IL, USA
Abstract
River deltas are built by cycles of lobe growth and abrupt channel shifts, or avulsions, that
occur within the backwater zone of coastal rivers. Previous numerical models differ on the origin of
backwater
scaled avulsion nodes and their consistency with experimental data. To unify previous work, we
developed a numerical model of delta growth that includes backwater hydrodynamics, river mouth
progradation, relative sea level rise, variable
fl
ow regimes, and cycles of lobe growth, abandonment, and
reoccupation. For parameter space applicable to lowland deltas, we found that
fl
ow variability is the primary
mechanism to cause persistent avulsion nodes by focusing aggradation within the backwater zone.
Backwater
scaled avulsion nodes also occur under less likely scenarios of initially uniform bed slopes or
during rapid relative sea level rise and marine transgression. Our
fi
ndings suggest that
fl
ow variability is a
fundamental control on long
term delta morphodynamics.
Plain Language Summary
River deltas are important for farming and drinking water,
human populations, and diverse wildlife. Rivers on deltas are unstable and abruptly change course every
10
1,000 years. These channel shifts are necessary for sustaining coastal landscapes and also pose signi
fi
cant
hazards. Here we present a mathematical model that shows how rivers require occasional
fl
oods,
similar to what is observed on natural rivers, to give rise to a predictable location where rivers shift their
course. Model simulations without
fl
oods produce rivers that change course at random locations, unlike
natural rivers. Our
fi
ndings resolve differences in previous studies about the importance of
fl
oods and
illustrate that occasional
fl
oods are necessary for natural delta growth.
1. Introduction
Many deltas are built through the deposition of discrete lobes punctuated by lobe
switching events called
river avulsions (Jerolmack, 2009; Slingerland & Smith, 2004). River avulsions pose a hazard to human life
and property (Kidder & Liu, 2017; Soong & Zhao, 1994) and are fundamental for building new land and
nourishing wetland ecosystems (Edmonds et al., 2009; Richards et al., 2002). We need to understand where
avulsions occur on lowland deltas to improve predictions of
fl
ooding hazards and sustainability.
Deltaic avulsions tend to occur repeatedly at a similar location, termed the avulsion node, which sets the
delta apex location and determines delta size (Ganti, Chadwick, Hassenruck
Gudipati, Fuller, & Lamb,
2016; Jerolmack, 2009). The avulsion node on some landforms, typically steeper fan deltas and alluvial
fans, is controlled by valley width and slope variations (Blair & McPherson, 1994; Ganti et al., 2014;
Hartley et al., 2017), but on lowland deltas avulsion nodes persist on uncon
fi
ned alluvial plains. The distance
from the shoreline to the avulsion node, termed the avulsion length (
L
A
), typically scales with the backwater
length scale of the river (
L
b
), that is, the ratio of channel depth (
H
c
) to bed slope (
S
; i.e.,
L
A
L
b
¼
H
c
S
; Figure 1a;
Chatanantavet et al., 2012; Jerolmack & Swenson, 2007; Paola & Mohrig, 1996). The backwater length
approximates the distance that sea level in
fl
uences river
fl
ow upstream and can extend for hundreds of
kilometers for low
sloping rivers (Lamb et al., 2012).
The Huanghe, China, provides an example where seven consecutive backwater
scaled avulsions occurred
before major engineering (Ganti et al., 2014). In addition, abandoned lobes record six Holocene avulsions
on the Mississippi that occurred within the backwater zone (Chatanantavet et al., 2012; Coleman et al.,
1998), while two avulsions occurred farther upstream (Chamberlain et al., 2018; Saucier, 1994). Because
river avulsions occur infrequently and are dif
fi
cult to observe directly,
fl
ume experiments and numerical
©2019. American Geophysical Union.
All Rights Reserved.
RESEARCH LETTER
10.1029/2019GL082491
Key Points:
Rivers on lowland deltas have
repeated avulsions at a preferential
location at the delta apex that scales
with the backwater length
A preferential avulsion node occurs
due to
fl
ow variability that focuses
bed aggradation in the backwater
zone
A preferential node under constant
discharge simulations in previous
work resulted from assumed initial
conditions of uniform bed slope
Supporting Information:
Supporting Information S1
Correspondence to:
A. J. Chadwick,
achadwick@caltech.edu
Citation:
Chadwick, A. J., Lamb, M. P., Moodie,
A. J., Parker, G., & Nittrouer, J. A.
(2019). Origin of a preferential avulsion
node on lowland river deltas.
Geophysical Research Letters
,
46
,
4267
4277. https://doi.org/10.1029/
2019GL082491
Received 17 FEB 2019
Accepted 31 MAR 2019
Accepted article online 4 APR 2019
Published online 25 APR 2019
CHADWICK ET AL.
4267
modeling have contributed substantially to our understanding. These modeling studies, however, differ in
their explanation for the origin of persistent, backwater
scaled avulsion nodes.
Chatanantavet et al. (2012) hypothesized that avulsion nodes on lowland deltas originate from heightened in
channel
bed aggradation in the backwater zone that emerges due to
fl
ows of variable discharge. Using quasi
2
D morphodynamic simulations, they showed that low
fl
ows deposit sediment in the upstream part of the
backwater zone and high
fl
ows focus erosion and bypass farther downstream, resulting in a persistent peak
in net aggradation in the middle of the backwater zone. Constant discharge simulations, in contrast, yielded
quasi
uniform
fl
ow and uniform bed aggradation rates. Chatanantavet et al. (2012) did not simulate avul-
sions and lobe switching, and the river mouth in their study was unrealistically
fi
xed, which prevented riv-
erbed aggradation due to progradation. Nonetheless, subsequent
fl
ume experiments that included
progradation and natural lobe switching and reactivation supported their hypothesis by showing persistent
avulsions about a preferential node at
L
A
0.5
L
b
, coinciding with a peak in channel bed aggradation for an
experiment with variable
fl
ows (Ganti, Chadwick, Hassenruck
Gudipati, Fuller, & Lamb, 2016; Ganti,
Chadwick, Hassenruck
Gudipati, & Lamb, 2016). In contrast, a comparable constant discharge experiment
did not produce a persistent node, indicating that
fl
ow variability is the dominant mechanism to produce
backwater
scaled avulsions.
Later numerical modeling studies by Moran et al. (2017) and Ratliff (2017), however, simulated delta growth
with river mouth progradation under a range of relative sea level rise rates and constant discharge conditions
and found backwater
scaled avulsion nodes despite the lack of
fl
ow variability. In their models, a wedge of
sediment migrated downstream on a riverbed with an initially uniform slope, and eventually aggradation
exceeded an imposed avulsion threshold. Thus, in contrast to experiments (Ganti, Chadwick, Hassenruck
Gudipati, Fuller, & Lamb, 2016; Ganti, Chadwick, Hassenruck
Gudipati, & Lamb, 2016) and earlier models
(Chatanantavet et al., 2012), these studies suggest that backwater
scaled avulsions can be produced in mod-
els with constant water discharge. However, these models invoked a potentially unrealistic riverbed of uni-
form slope as an initial condition and measured the potential for avulsion in terms of sediment accumulation
thickness relative to the initial topography. In contrast, in natural environments, deltas tend to reoccupy
lobes and build over previous
fl
uvio
deltaic deposits. Thus, the assumed initial conditions in these numerical
models might affect the emergence of an avulsion node.
Here we aim to elucidate the origin of a preferential avulsion node and unify the contradictory results of
previous work. In particular, the model of Chatanantavet et al. (2012) requires
fl
ow variability to produce
a persistent avulsion node, consistent with available experimental data, but the elimination of river mouth
progradation in their model might have biased their results. In contrast, more recent models (Moran et al.,
2017; Ratliff, 2017) can produce persistent avulsion nodes with constant discharge, but they impose an
unrealistic initial condition. To address these potentially problematic assumptions, we constructed a
Figure 1.
(a) Correlation between avulsion length (
L
A
) and backwater length (
L
b
) from lowland river deltas and back-
water
in
fl
uenced experiments. (b) Planview schematic. Black solid lines are active channel of width
B
within a
fl
ood-
plain/lobe of width
B
f
(lobe 3). Broken lines are abandoned channels. After an avulsion, abandoned lobe 4 is reoccupied
and its pro
fi
le is joined with trunk channel at avulsion node (yellow star). (c) Cross
section schematic, showing channel
aggradation and
fl
oodplain superelevation of the active lobe (lobe 3) relative to the lowest abandoned lobe (lobe 4).
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CHADWICK ET AL.
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quasi
2
D numerical model that allows for repeated lobe construction and avulsion such that lobes build on
top of one another, thereby minimizing the role of initial topography as the delta evolves. The model also
allows for river mouth progradation. We explored the model behavior over parameter space relevant to
natural lowland deltas, including variable
fl
ow regimes and relative sea level rise, to identify the conditions
that cause a preferential backwater
scaled avulsion node.
2. Methods
We aimed to isolate the cause of preferential avulsion nodes using a simpli
fi
ed model that captures delta lobe
construction, avulsion and reoccupation, and river mouth progradation on lowland river deltas. The model
does not represent a speci
fi
c delta. Instead, the framework is generic and includes a deltaic plain with an
imposed number of lobes (Figure 1b).
Following previous work, we modeled each lobe as a coupled river and
fl
oodplain of uniform
fl
oodplain
width (
B
f
), channel sinuosity (
Ω
), wash load ratio (
Λ
), and bed porosity (
λ
p
), which is well described by a
quasi
two
dimensional mass balance framework (Chatanantavet et al., 2012; Parker, 2004; Parker et al.,
2008a, 2008b). Sediment mass balance also incorporates a
fl
oodplain representing the active delta lobe
extent:
η
b
t
þ
σ
¼
1
þ
Λ
ðÞ
Ω
1
λ
p

B
f
Bq
t
x
(1)
where
η
b
is channel bed elevation relative to sea level,
t
is time,
σ
is relative sea level rise rate,
x
is down-
stream distance, and
q
t
is width
averaged
fl
ux of total bed material load. Sediment is transported in a river
of width
B
and deposited uniformly over the
fl
oodplain width
B
f
(Parker, 2004). We routed water using a
quasi
2
D backwater equation for water mass and momentum conservation under quasi
steady
fl
ow condi-
tions (Chatanantavet et al., 2012),
d
H
d
x
¼
S
S
f
1
Fr
2
þ
Fr
2
1
Fr
2
H
B
d
B
d
x
(2)
where
H
represents the channel depth,
S
is channel bed slope, and
S
f
=
C
f
Fr
2
is friction slope with friction
coef
fi
cient
C
f
and Froude number
Fr
. We assumed uniform channel width and a plume with constant
spreading angle offshore (Chatanantavet et al., 2012; Lamb et al., 2012), but unlike previous formulations
the plume in our model advances and retreats in concert with the river mouth (Text S1 in the supporting
information). We routed sediment according to Engelund and Hansen (1967) for total bed material load:
q
t
¼
ffiffiffiffiffiffiffiffiffiffiffi
RgD
3
q
α
C
f
τ
*

n
(3)
where
R
is submerged speci
fi
c density of sediment,
g
is gravity,
D
is the median grain size of bed material,
τ
*
is Shields number, and
α
= 0.05 and
n
= 2.5 (Engelund & Hansen, 1967). Equations (2) and (3) adequately
describe backwater hydrodynamics and sediment transport of sand
bedded rivers (Lamb et al., 2012;
Nittrouer et al., 2012; Chatanantavet & Lamb, 2014).
We approximated deltaic evolution over multiple cycles of lobe switching using four one
dimensional pro-
fi
les of prede
fi
ned width, representing four distinct lobes (Figures 1b and 1c). Our choice of four lobes is arbi-
trary but reasonable based on
fi
eld observations (Chu et al., 2006; Roberts, 1997) and
fl
ume experiments
(Carlson et al., 2018; Reitz et al., 2010). One delta lobe was active at a given time (Hajek & Edmonds,
2014; Slingerland & Smith, 2004), and the active lobe evolution was governed by equations (1)
(3) and solved
using
fi
nite differences (Text S2). We varied sediment supply at the upstream end with water discharge such
that the normal
fl
ow bed slope was held constant, and therefore, erosion and deposition were not driven by
changes in sediment supply and water discharge ratios (Paola, 2000). For the delta front, we used a moving
boundary formulation following Swenson et al. (2000) and others (Text S1). Inactive lobe shapes were
unchanged when abandoned, approximating a river
dominated delta where reworking is minimal
(Galloway, 1975); however, abandoned lobes were partially drowned in cases due to relative sea level rise.
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We used an avulsion criterion given by a critical thickness of aggradation, which we refer to as supereleva-
tion (
Δ
η
):
Δ
η
x
ðÞ
H
*
H
c
(4)
in which
H
c
is the bankfull channel depth and
H
*
is the avulsion threshold, a dimensionless number that is
of order unity (Ganti et al., 2014; Jerolmack & Mohrig, 2007), which we set to
H
*
= 0.5 consistent with
fi
eld
and experimental observations (Ganti et al., 2014; Ganti, Chadwick, Hassenruck
Gudipati, & Lamb, 2016;
Mohrig et al., 2000). The critical superelevation
Δ
η
may represent the local
fl
oodplain (or levee) elevation
relative to the distant
fl
oodplain or inactive lobes, or the bed aggradation thickness since the last avulsion
(Figure 1c; Ganti et al., 2014; Hajek & Wolinsky, 2012; Mohrig et al., 2000). In our model the
fl
oodplain
(
η
f
) aggrades in concert with the channel bed (
η
f
=
η
b
+
H
c
; Text S1 and Figure 1c) and inactive lobes remain
unchanged once abandoned, so both explanations hold. We triggered an avulsion when and where the
fl
ood-
plain elevation of the active lobe exceeded the
fl
oodplain elevation of the lowest
elevation abandoned lobe
(
η
f
,abandoned
), evaluated at the same distance downstream from the trunk channel:
Δ
η
x
ðÞ¼
η
f
x
ðÞ
η
f
;
abandoned
x
ðÞ
for
x
x
m
;
abandoned
η
f
x
ðÞ
ξ
sea
for
x
>
x
m
;
abandoned
(
(5)
where x
m,abandoned
is the streamwise coordinate of the abandoned lobe shoreline (Figure 1c). Seaward of the
abandoned lobe, superelevation is measured relative to sea level (
ξ
sea
), consistent with assumptions in pre-
vious work (Ratliff, 2017). The occurrence of extreme
fl
oods and hydraulic connectivity with abandoned
channels may also affect the location and timing of any one avulsion (Ganti et al., 2014; Nicholas et al.,
2018), but following previous work, these effects were neglected in our treatment of multiple avulsion cycles
(Hajek & Wolinsky, 2012; Jerolmack & Paola, 2007).
After an avulsion, the river was routed to the lowest abandoned lobe by joining the bed pro
fi
le of the active
channel upstream of the avulsion site (the trunk channel) with the bed pro
fi
le of the new
fl
ow path down-
stream (the daughter channel; Text S2). This process mimics the tendency of rivers to select steeper paths,
fi
ll
in topographic lows (Slingerland & Smith, 2004; Straub et al., 2009), and reoccupy previously abandoned
channels (Reitz & Jerolmack, 2012). After establishing the new
fl
ow path, lobe construction (equations (1)
(3)) and avulsion setup (equation (4)) began anew.
At the start of each model run, the initial state of the riverbed was assumed planar with a uniform down-
stream slope set to the transport slope for normal
fl
ow, similar to previous studies (Chatanantavet et al.,
2012; Moran et al., 2017; Ratliff, 2017). However, due to the imposed number of lobes, after four avulsion
cycles the river was forced to reoccupy lobes that were previously active. Thus, unlike previous work, the
effect of the initial conditions were minimized after the fourth avulsion cycle.
For variable discharge simulations, we implemented
fl
ow variability using a log
normal distribution of nor-
mal
fl
ow depths (Text S3). The distribution is de
fi
ned by the bankfull exceedance probability
F
bf
, which
describes the frequency of overbank
fl
ows relative to all possible
fl
ows, and the coef
fi
cient of variation
CV, which describes the magnitude of low
fl
ows and high
fl
ows relative to the average
fl
ow. We randomly
sampled the distribution with a characteristic
fl
ow event duration (
T
e
;Figure S1). Gauge data of monthly
mean stage height (
T
e
= 1 month) from several lowland rivers show
F
bf
~5
20% and
CV
~ 0.2
0.9
(Table S1; Ganti et al., 2014).
Our simulations explore how deltaic avulsion patterns respond to variable river discharge, relative sea level
rise, and initial topography by systematically varying the discharge and sea level parameters for a base case
characteristic of large, low
sloping deltas. We nondimensionalized the model so that it can be applied to a
wide range of river conditions (Text S4). The model is governed by nine input dimensionless parameters:
bankfull Froude number in the normal
fl
ow reach (
Fr
n
,bf
), bankfull Shields number in the normal
fl
ow
reach (
τ
*
n
;
bf
), friction factor (
C
f
), offshore basin
fl
oor depth normalized by bankfull depth
H
*
b

, time normal-
ized by the channel adjustment timescale
t
*
tq
t
L
b
H
c

, a dimensionless rate of relative sea level rise (
σ
*
σ
L
b
q
t
),
and the
fl
ow variability parameters (
F
bf
;
CV
;
T
*
e
; Text S3), where
T
*
e
¼
T
e
q
t
L
b
H
c
is a dimensionless
fl
ow duration.
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In all simulations presented here, we assumed constant values typical of large sand
bedded rivers where
Fr
n
,bf
= 0.17,
τ
*
n
;
bf
¼
1,
C
f
= 0.005,
H
*
b
¼
2 (Table S1) and changed only
fl
ow variability parameters
(
F
bf
,
CV
, and
T
*
e
) and relative sea level rise (
σ
*
). Model sensitivity to the other parameters is discussed in
Text S6. For each set of dimensionless parameters, simulations proceeded until 13 avulsions occurred, which
was suf
fi
cient to capture trends in avulsion location (Text S4).
3. Avulsion Nodes Originating From Initial Conditions and Flow Variability
We
fi
rst considered a scenario of constant river discharge equal to the bankfull condition and constant rela-
tive sea level (
F
bf
=1,
CV
=0,
σ
*
= 0), with other model parameters set to the base case. During the
fi
rst four
avulsion cycles, the delta built lobes on the initial surface, which was a plane with a uniform seaward slope.
The
fi
rst avulsion occurred after 1.8 normalized time (
Δ
t
*
= 1.8), equivalent to 9
720 years for a range of
parameters typical of natural deltas (Table S1 and Text S4), with an avulsion length equal to 0.78
L
b
L
*
A
¼
0
:
78
;

Figure 2a). Avulsion lengths were similar for the second, third, and fourth avulsions
L
*
A
¼
0
:
74
;
0
:
68
;
0
:
98
;
respectively

. In contrast, after avulsion cycle four the constant discharge delta built
upon previously abandoned delta lobes and did not produce a backwater
scaled avulsion node. Normalized
avulsion lengths varied considerably for these later avulsions (
L
*
A
= 0.79
8.3), and when avulsions occurred a
reach of 3
5
L
b
was within 10% of the avulsion threshold, indicating no dominant avulsion location.
The consistent avulsion length during the
fi
rst four avulsion cycles was a consequence of the assumed initial
bed topography, and not due to backwater hydrodynamics. Delta front progradation led to channel aggrada-
tion and a quasi
steady concave
up bed elevation pro
fi
le (Bijkerk et al., 2016; Muto & Swenson, 2005), in
contrast to the uniform slope bed pro
fi
les that were assumed for all lobes as initial conditions.
Differencing the concave
up active lobe pro
fi
le from the uniform slope of the lowest inactive (and yet to
be active) lobe pro
fi
le resulted in a systematic downstream increase in superelevation (Figure 2b).
Therefore, avulsions occurred at the farthest downstream location that was allowed, where superelevation
was greatest, equivalent to the shoreline location on the inactive lobe of lowest elevation. Seaward of the
inactive lobe shoreline, avulsions did not occur because the active lobe elevation approached sea level and
thus superelevation approached zero (equation (5)). Avulsions that occurred at the shoreline of abandoned
lobes necessarily scaled with the backwater length due to geometry; lobes prograded a unit fraction of the
backwater length
scale before avulsing (i.e., the lobe progradation distance
D
scales as
D
H
*
H
c
/
S
H
*
L
b
; Ganti et al., 2014).
After avulsion cycles 1
4 in the constant discharge model, the delta completely reworked its initial uniform
slope and superelevation therefore was assessed by comparing the active lobe to previously occupied lobes,
rather than to the planar initial surface. River pro
fi
les in these later avulsion cycles prograded with a quasi
steady and self
similar shape, causing nearly uniform deposition and a similar likelihood of avulsions every-
where, including far outside of the backwater zone (Figure 2c). Thus, avulsion locations and their apparent
scaling with the backwater length in cycles 1
4 were a geometric artifact resulting from the assumed initial
bed topography. Four avulsions were required to rework the initial condition because four delta lobes were
imposed (Figure 1a and Text S6). In absence of the uniform slope initial condition, constant discharge con-
ditions did not produce a persistent backwater
scaled avulsion node.
Next, we considered a model run identical to the constant discharge case but with variable discharge, using
CV
¼
0
:
53
;
F
bf
¼
0
:
05
;
and
T
*
e
¼
0
:
001
;
which is typical of lowland rivers (Table S1). In this case, we
observed a preferential avulsion node corresponding to an avulsion length nearly equal to the backwater
length scale,
L
*
A
¼
L
A
=
L
b
1 (Figure 2d), which persisted through many avulsion cycles even after there
was no longer an in
fl
uence from the planar initial surface (Figures 2e and 2f). Consistent with previous stu-
dies (Chatanantavet et al., 2012; Ganti, Chadwick, Hassenruck
Gudipati, Fuller, & Lamb, 2016; Lamb et al.,
2012), periods of low
fl
ow had enhanced deposition due to spatial deceleration through the backwater zone
and high
fl
ows eroded the downstream
most reach, resulting in a spatial peak in deposition rate midway
through the backwater zone when averaged over many
fl
ow events. The avulsion node was coincident with
the location of maximum deposition rate, and only a short reach (<0.4
L
b
) was within 10% of the threshold at
the time of an avulsion. Outliers are due to major avulsions that shifted the avulsion node downstream once
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CHADWICK ET AL.
4271
the four lateral lobes were built, causing trunk channel aggradation and overall shoreline progradation (Text
S5 and Figure S2).
4. Necessary Degree of Flow Variability
Given the importance of variable
fl
ows in controlling avulsion location for deltas that lack uniform bed
slopes as initial conditions, we quanti
fi
ed how much
fl
ow variability is necessary to drive a preferential avul-
sion node. We ran 21 numerical experiments to systematically vary the coef
fi
cient of
fl
ow variation (CV),
bankfull exceedance probability (
F
bf
), and dimensionless
fl
ow duration
T
*
e

within a parameter space that
represents many natural rivers (Table S1). For each model run we changed one of these parameters and held
all other parameters to base case values. We focused our analysis on cycles 5
13 that were not affected by the
initial uniform bed slope.
Isolation of the coef
fi
cient of variation (CV) reveals that there is an intermediate range 0.1 <
CV
< 0.6 where
modeled deltas preferentially avulsed within the upstream half of the backwater zone (Figure 3a). Similarly,
avulsions occurred at a preferential node so long as less than 5% of
fl
ows exceeded bankfull (
F
bf
< 0.05;
Figure 2.
Model results for avulsion length through time over 13 avulsion cycles under constant discharge (a) and variable
discharge (d) with parameters set to base case
Fr
n
;
bf
¼
0
:
17
;
τ
*
n
;
bf
¼
1
;
C
f
¼
0
:
005
;
H
*
b
¼
2

:
Red error bars indicate
portion of reach within 10% of threshold superelevation necessary for avulsion. Outliers in cycles 8 and 11 of the variable
discharge case are due to transient long
pro
fi
le adjustment following major avulsions (cycles 7 and 10) that shift the
avulsion node seaward and aggrade the trunk channel (Text S5). Results for channel long
pro
fi
le under constant discharge
conditions (b and c) and variable
fl
ows (e and f) for two example avulsion cycles affected (cycle 1) and unaffected (cycle 5)
by initial conditions. Black lines are riverbed pro
fi
le at start (dashed) and end (solid) of an avulsion cycle. Floodplain
pro
fi
les of active lobe (gray solid line) and lowest inactive lobe (gray dashed line) are used to calculate superelevation (see
inset). Downstream of inactive lobe shoreline location (red circle),
fl
oodplain superelevation is measured relative to sea
level. Black triangles are river mouth at end of the avulsion cycle. Yellow stars show avulsion location. Delta progradation
extended model domain length by
4
L
b
over 13 cycles, leading to an increase in maximum possible avulsion length.
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Figure 3b) and that the duration of
fl
ow events was less than 10% of the reach
fi
lling timescale (
T
*
e
<0
:
1
;
Figure 3c). The conditions needed for a preferential avulsion node predicted by the model are common
for natural lowland rivers (Table S1) and correspond to a state of continuous riverbed adjustment, where
the scours cut by large
fl
oods are partially
fi
lled during intervening low
fl
ows. Continuous riverbed
adjustment is necessary for persistent backwater effects (Chatanantavet & Lamb, 2014) and in our model
resulted in broad convex
up portions of the long pro
fi
le when averaged over many
fl
ood events
(Figure S3). Under milder
fl
ow regimes (
CV
< 0.1) and longer
fl
ow durations
T
*
e
>0
:
1

the riverbed fully
adjusted to normal
fl
ow conditions, resulting in uniform aggradation rates without a preferential avulsion
location similar to the constant discharge scenario. Flashier
fl
ow regimes (
CV
> 0.6) and high
probabilities of bankfull exceedance (
F
bf
> 0.05) also lacked a preferred avulsion node, as the riverbed
adjusted to normal
fl
ow conditions associated with large
fl
oods.
5. Avulsion Nodes Originating From Relative Sea Level Rise
In previous sections, the dimensionless relative sea level rise rate was set to 0 to isolate the initial conditions
and
fl
ow variability. To relax this assumption, we varied the dimensionless relative sea level rise rate across a
range that encompasses many modern deltas (
σ
*
=10
3
10
0
) under constant discharge (Figure 3d) and
variable discharge (Figure 3e) conditions, with other parameters identical to the base case (Table S1).
Similar to the scenario of
σ
*
= 0, constant discharge deltas with
σ
*
=10
3
10
1
did not have a preferential
node, whereas all variable discharge cases had a preferential avulsion node with
L
A
/
L
b
1. Thus, relative sea
level rise at moderate rates common to modern deltas did not signi
fi
cantly affect avulsion node occurrence
(Figures 3d and 3e). However, at very high rise rates (
σ
*
>10
1
) the river mouth retreated upstream, forcing
a strong downstream increase in deposition. Thus, for
σ
*
>10
1
the downstream increase in aggradation
resulted in avulsion locations that coincided with the shoreline of the lowest
elevation inactive lobe, which
scaled with the backwater length for the same geometric reasons as in the cases with planar initial conditions
(Figure S4).
Figure 3.
Model results for avulsion length with changing
fl
ow variability parameters:
CV
(a),
F
bf
(b), and
T
*
e
(c), as well as
variation of relative sea level rise rate
σ
* under constant discharge (d) and variable discharge (e). Black circles show
avulsion locations averaged over cycles not in
fl
uenced by initial conditions (cycles 5
13), and gray shaded areas denote the
average reach within 10% of avulsion threshold at times of avulsion.
10.1029/2019GL082491
Geophysical Research Letters
CHADWICK ET AL.
4273
6. Discussion and Conclusions
Our results reconcile previous work by showing that variable
fl
ow regimes are necessary to produce
backwater
scaled avulsion nodes on lowland deltas. Our
fi
nding is consistent with experiments that isolated
the role of
fl
ow variability (Ganti, Chadwick, Hassenruck
Gudipati, Fuller, & Lamb, 2016) on deltas that
experienced continuous lobe growth, abandonment, and reoccupation. A certain amount of
fl
ow variability
0
:
1<
CV
<0
:
6
;
F
bf
<0
:
05
;
T
*
e
<0
:
1

is necessary to produce persistent backwater effects so that the riverbed
is in a continual state of morphodynamic adjustment (Chatanantavet & Lamb, 2014). These conditions are
common to natural rivers (Table S1). Continual bed adjustment from
fl
oods in our model produced very
broad, low
relief upward convexities in the riverbed in the backwater zone (Figures 2e, 2f, and S3), consis-
tent with the bed topography of the lower 200
700 km of the Mississippi (Harmar, 2004; Nittrouer et al.,
2012; Figure S5), which may be a topographic signature of backwater
mediated avulsions in other rivers.
In contrast, constant discharge numerical experiments tend toward a graded state without strong backwater
effects or a preferential node location. Our results suggest that previous numerical models that lacked vari-
able discharges and produced backwater
scaled avulsions (Moran et al., 2017; Ratliff, 2017) were likely
affected by initial conditions of uniformly sloped initial surfaces. A backwater
scaled avulsion node under
these conditions is a geometric consequence of assessing superelevation of a prograding channel or lobe rela-
tive to a planar seaward sloping landscape. For similar reasons, relative sea level rise can also cause persis-
tent avulsion nodes under constant discharge conditions, but only under high rise rates that cause marine
transgression. In these cases, avulsions occur at the most downstream location allowed
near the inactive
lobe shoreline, which was
L
b
upstream of the active river mouth at the time of avulsion due to the geometry
of lobe progradation. Although the simulations of Chatanantavet et al. (2012) also had an initial uniform bed
slope and relative sea level rise, they did not produce a persistent avulsion node under constant discharge
conditions because the model lacked river mouth progradation.
In a sensitivity analysis, we found that changing other model parameters does not affect our results on the
origin of preferred avulsion node (Text S6). Larger avulsion thresholds,
H
*
, cause avulsions to occur farther
upstream but do not change the overall results (Figure S6). Likewise, the number of imposed delta lobes
affects the number of avulsion cycles that are affected by the initial conditions, and the frequency of trunk
channel
fi
lling avulsions (Text S5), but does not affect the origin of a preferential avulsion node.
Our variable discharge simulations produced avulsion lengths within a factor of 2 of the backwater length
scale, similar to the distribution of avulsion lengths on the Huanghe (Ganti et al., 2014) and Mississippi
(Chatanantavet et al., 2012; Coleman et al., 1998). Following four lateral avulsions that occupied the avail-
able prograding lobes, the avulsion node in our model shifted downstream in tandem with net shoreline pro-
gradation, as has been documented on the Huanghe (Ganti et al., 2014) and in
fl
ume experiments (Ganti,
Chadwick, Hassenruck
Gudipati, Fuller, & Lamb, 2016). Our model also produced outliers in the avulsion
length distribution, where deltas with a backwater
scaled avulsion node sometimes have avulsions much
farther upstream, similar to the Mississippi (Chamberlain et al., 2018). These larger
scale avulsions occurred
in our model near the time when the avulsion node shifted downstream; once a full set of lateral avulsions
occurred, the trunk channel upstream of the avulsion node must aggrade to allow continued net prograda-
tion (Text S5).
Avulsion node locations could be different when channels reoccupy topographically dissimilar lobes (e.g.,
the Danube; Giosan et al., 2005), cut new channels in the
fl
oodplain (Hajek & Edmonds, 2014), or where
lobes have been modi
fi
ed by marine processes (e.g., the Red River; Mathers & Zalasiewicz, 1999).
However, when channels build upon topographically similar abandoned delta lobe topography, which is a
common scenario, a backwater
scaled avulsion node emerges when
fl
ow variability is suf
fi
cient to cause a
peak in aggradation within the backwater zone. Thus, changing
fl
ow regimes due to climate or built infra-
structure may affect
fl
ood hazards and wetland sustainability by shifting the location of future avulsions.
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10.1029/2019GL082491
Geophysical Research Letters
CHADWICK ET AL.
4274
Acknowledgments
We acknowledge National Science
Foundation grant EAR 1427262 and the
Resnick Sustainability Institute at
Caltech for support. We thank Vamsi
Ganti, Gail Kineke, Ben Hobbs,
Hongbo Ma, Brandee Carlson, Kensuke
Naito, and Lisa Kumpf for insightful
discussions and Elizabeth Hajek and
Wonsuck Kim for constructive reviews.
Data are available at the website
(http://sead
published.ncsa.illinois.
edu/seadrepository/api/researchobjects
/urn:uuid:5c37c889e4b0a8e144f6565f).
Code is available at the GitHub (https://
github.com/achadwick2323/Origin
of
a
preferential
avulsion
node
on
lowland
river
deltas).