Plain Language Summary
Delta restoration projects may take the form of building new land
through diverting water and sediment from a river or channel to a chosen
location. The presence or absence of vegetation changes how deltas
respond to different volumes of water (water discharge) and different
amounts of sediment in the water (sediment discharge). We study the
effect that the water and sediment discharge have on the behavior of
channels on river deltas using a simple model. We find that deltas
without vegetation and with lower water discharge have few channels and
experience occasional large changes in channel location. However, with
higher water discharge, deltas have many channels and experience
frequent but small changes in channel location. On deltas with
vegetation, we find that increasing the water discharge creates deltas
with more stable channel networks, as vegetation makes creation of a new
channel unlikely by confining water in channels and making the land
outside of channels difficult to erode. Increasing the sediment
discharge also increased channel stability deltas by burying young
plants and preventing vegetation from growing in channels. This study
will help us better understand how water and sediment discharge
influences delta shape and channel behavior.
Introduction
The evolution of deltas and their distributary channel networks can be
controlled by a number of factors, including the balance between river,
wave, and tidal influences (e.g. Galloway, 1975; Syvitski et al., 2009;
Nienhuis et al., 2015; Geleynse et al., 2011; Leonardi et al., 2015;
Nienhuis et al., 2018), water and sediment discharge (Powell et al.,
2012; Hoyal and Sheets, 2009; Orton and Reading, 1993; Edmonds et al.,
2010), fraction of cohesive sediment (Caldwell and Edmonds, 2014; Hoyal
and Sheets, 2009; Straub et al., 2015; Edmonds and Slingerland, 2009;
Liang et al., 2015a; Tejedor et al., 2016) or cohesion from vegetation
(Lauzon and Murray, 2018), base level rise (Chadwick et al., 2020;
Jerolmack, 2009; Liang et al., 2016a; Martin et al., 2009; Ratliff et
al., 2018), and many others. Recent research has focused on the role
these factors play in shaping delta morphology and influencing autogenic
timescales: the timescales at which deltas undergo cycles of
channelization, channel extension and aggradation, avulsion and incision
of a new channel (e.g. Hoyal and Sheets, 2009; van Dijk et al., 2009;
Kim et al., 2006). Cohesion is thought to alter these timescales,
decreasing channel mobility and avulsion frequency (Straub et al., 2015;
Edmonds and Slingerland, 2009; Hoyal and Sheets, 2009; Caldwell and
Edmonds, 2014; Liang et al., 2015a; Lauzon and Murray, 2018), favoring
progradation even with high cross-levee slopes (Edmonds and Slingerland,
2009) and resulting in rugose shorelines.
Vegetation has many of the same cohesive-like effects as fine-grained
sediment – elongating, deepening, and stabilizing channels and
increasing shoreline rugosity – and may be even more effective at
stabilizing channel networks, resulting in well-sorted sandy channel
beds and potentially decreasing deltaic fine-grained sediment retention
(Lauzon and Murray, 2018; Nardin and Edmonds, 2014). However, while
recent research has begun to assess the cohesive effects of fine
sediment under varied environmental conditions (e.g. Martin et al.,
2009, Liang et al., 2016a,b), vegetation may be sensitive to
environmental conditions in ways that cohesive sediment may not be. The
influences of water and sediment discharge are particularly important to
understand, as humans are increasingly modifying the distribution of
water and sediment to the coast (e.g. Syvitski and Saito, 2007) which
could have important implications for the evolution of natural deltas
(e.g. Ericson et al., 2006; Anthony et al., 2014) and the success of
engineered and restored deltas (e.g. Kim, 2012; Kim et al., 2009; Paola
et al., 2011; Allison and Meselhe, 2010).
Increasing water discharge can increase the number of bifurcations in
delta channel networks (Syvitski and Saito, 2007; Edmonds et al., 2010).
Delta slope is also (inversely) correlated with discharge and plays an
important role in autogenic cycles (Powell et al., 2012). Increasing
water discharge leads to a more organized channel system; channel
mobility decreases and sediment transport capacity increases (Powell et
al., 2012).
Increased sediment discharge increases deposition rates and can increase
avulsion frequency and channel mobility as a result (e.g. Orton and
Reading, 1993; Hoyal and Sheets, 2009; Bryant et al., 1995). Autogenic
timescales generally decrease as sediment discharge increases relative
to water discharge (Powell et al., 2012).
Changes in environmental conditions leading to increased deposition
rates may have a significant effect on vegetation influence. Enhanced
deposition may increase vegetation mortality, as plants are buried or
uprooted (Pasquale et al., 2014; Perona et al., 2012), or make parts of
the delta less suitable for vegetation colonization. If sediment
transport processes act on timescales faster than those for vegetation
growth, vegetation will likely not be able to influence delta morphology
or dynamics (e.g. Murray and Paola, 2003; Pasquale et al., 2014; Perona
et al., 2012).
We use the delta-building model DeltaRCM (adapted to include key
vegetation effects by Lauzon and Murray, 2018) to investigate the
effects of different environmental conditions (and therefore different
climates) on vegetation’s role in shaping delta evolution. We explore
the effects of varying water and sediment discharges and test the
hypothesis that high rates of sediment discharge will result in sediment
transport processes that outpace the timescales of vegetation growth and
establishment, therefore reducing the effects of vegetation on delta
morphology and channel dynamics.
Methods
2.1 Model Description
DeltaRCM consists of a rule-based flow routing scheme and a set of
sediment transport rules governing the behavior of water and sediment
‘parcels’ which build a small, river-dominated delta. In a previous
study (Lauzon and Murray, 2018), we modified DeltaRCM to include the
effects of vegetation to 1) reduce lateral transport of sediment and 2)
increase flow resistance. A brief description of the model and our
modifications are below, and a more detailed description of the
vegetation rules can be found in Lauzon and Murray (2018). A more
detailed description and an assessment of the hydrodynamic component of
DeltaRCM can be found in Liang et al. (2015a,b). Model deltas have also
been extensively compared to several observational, experimental, and
numerical-model (Delft3D) datasets (Liang et al., 2015b; 2016a).
Each model run begins with a 5 m deep basin with an inlet channel of
fixed width and depth on one side. In each time step, water and sediment
“parcels” enter the domain through the inlet channel and are routed by
a weighted random walk. Weights are determined by the average downstream
direction (representing inertia), the water surface gradient
(representing gravity), and a depth dependent resistance to flow. The
proportion of sediment parcels which are sand
(fsand ) can be specified; remaining parcels are
mud, and each has a different set of erosion and deposition rules. After
the water parcels are routed, the depth-averaged flow field and then the
water surface profile are updated, the sediment parcels are routed, and
finally the bed elevations are updated. The model timestep, dt ,
is set so that a characteristic sediment volume, related to the volume
of the inlet channel, enters the domain in each time step. Optimizing
computational efficiency and model stability, this volume was determined
by Liang et al. (2015a) to be:
\(dt=\frac{0.1N_{0}^{2}V_{o}}{Q_{s}}\) (1)
where V0 is the volume of one cell of the inlet
channel, N0 is the number of cells in the inlet,
and Qs is the input sediment discharge.
We incorporate two main effects of vegetation (represented as a
fractional cover of each cell and representing emergent vegetation such
as marsh grasses) into the model: 1) stabilizing channel banks, thereby
reducing lateral transport, and 2) introducing friction, which increases
resistance to flow. Lateral transport, previously dependent only on
local slope and sand flux, now also decreases as vegetation cover
increases. Flow resistance, previously only depth dependent, now
increases with vegetation density representing friction and drag
introduced by the plants.
Vegetation can establish in any cell near sea level (elevation
> -0.5 m) with bed elevation change over the previous
timestep less than 1% of the rooting depth of the vegetation.
Fractional cover increases logistically between “flood” periods. We
set the flood length equal to 3 days and the time between floods equal
to 100 days, assuming about 10 days of bankfull flood per year. As the
model represents bankfull flow, we increase fractional cover everyn th timestep where n is the number of
timesteps in each flood. Mortality occurs during floods (that is, during
each timestep) and is proportional to the magnitude of erosion and
deposition events relative to the rooting depth of the vegetation.
2.2 Experimental set-up
We use a model grid of 120 by 240 50 m2 cells, and a
sediment composition of 50% sand, as Lauzon and Murray (2018)
demonstrated that vegetation has a less significant effect on the delta
morphology and channel dynamics of deltas with higher proportions of
mud, which are therefore already cohesive. We run a set of experiments
to explore the effects of varying sediment (Qs )
and water (Qw ) discharge. For both sets of
experiments, parameters were selected to be in line with those
previously used for DeltaRCM (Liang et al., 2015a; 2016a,b), to be
varied enough to be expected to influence delta evolution (e.g. an
increase in discharge of at least 60%; Edmonds et al., 2010), and to be
reasonable enough for inferences to be made to experimental and natural
deltas (Syvitski and Saito, 2007). Details of experimental set-ups can
be found in Table 1.
The discharge experiments are run with Qw values
of 1000 and 2000 m3/s and Qsvalues of 0.5, 1, and 2 m3/s, both with and without
vegetation, resulting in 12 unique model inputs. As the timestep depends
on Qs and the inlet size
(N0 ; Equation 1), which varies withQw , the discharge experiments are run until the
same total amount of sediment has entered the model domain, which occurs
after fewer timesteps for higher Qw (Table 1).
All experiments are run in triplicate, resulting in 36 total model
simulations. We present averaged data wherever possible, and values for
individual model simulations can be found in Table 2.
2.3 Data Analysis
To capture the dynamics of the channel network over time we measure the
decay in channel planform overlap (Wickert et al., 2013). Using channel
maps (determined using a velocity threshold equal to the minimum
velocity for sediment transport) for the second half of each run, we
measure the overlap in the channel network using a varying time lag. To
eliminate differences in the channel network due to delta growth, we
consider only the channels within the delta area at the initial time
(halfway through the run). We fit an exponential decay function to the
channel planform overlap data to obtain a decay constant M .M is a measure of how quickly the spatial configuration of the
channel network changes. A high value suggests little similarity in the
configuration of the channel network through time and would be a
signature of frequent avulsions to new channels or frequent switching
between existing channels. Using the same channel maps, we measure the
decay in the fraction of the delta surface unreworked by the channel
network to obtain a decay constant R , which approximates the rate
dry cells are converted to wet cells. A high value suggests highly
mobile channels, reflecting channel migration and/or avulsions to new
(rather than previously occupied) channels.
By summing the channel maps analyzed above, we measure the fraction of
time that each cell which is ever part of the channel network remains
part of the channel network (Liang et al., 2016a). Again, we consider
only those cells that were within the delta area at the halfway point
and consider the second half of the run. These channel maps also allow
us to qualitatively assess the spatial distribution of the channel
network across the delta. We also calculate the average number of
channels on the delta by counting the number of channels along the arc
of a semicircle that has an area equal to 2/3 of the delta area at each
time step. We average this over the second half of the model run to
obtain an average number of channels for the delta.
We complement these measures of channel dynamics with an analysis of
sediment distribution across the delta. Shoreline roughness (equal to
the shoreline length divided by the square root of the delta area;\(L_{\text{shore}}/\sqrt{A}\); Wolinsky et al., 2010) provides a measure
of the evenness of the distribution of sediment across the delta by the
channel network, with more stable channel networks tending to build more
lobed deltas. To understand patterns in aggradation on the delta
surface, we consider the cumulative distribution function of subaerial
delta elevations. We use detrended elevations for this, which we obtain
by subtracting the trend in delta slope imposed by the model (a function
of sediment composition). We also examine maps of these detrended
elevations to assess spatial patterns in aggradation. Finally, we
measure the distribution of mud and sand across the delta by vertically
averaging the stratigraphy to obtain a sand fraction for each cell of
the model domain (Liang et al., 2016a).
Results and Discussion
The results we present below, taken together, suggest the following
insights about how changing water and sediment discharge affect channel
dynamics and how channels and vegetation interact. 1) Without
vegetation, increasing Qw results in a regime
shift from a few active channels undergoing infrequent large avulsions
to many channels undergoing frequent but small-scale avulsions. However,
2) with vegetation, both high Qs or highQw lead to increased channel network stability
through consistent channel reoccupation because 3) vegetation is both
unable to fill in partially abandoned channels under those conditions
and offers greater resistance to the creation of new channels.
3.1 Dynamics on unvegetated
deltas
For unvegetated runs, channel mobility (as measured by R , the
decay rate for remaining unreworked fluvial surface) increases with
increasing Qw (Figure 1a), suggesting that
increased Qw enhances channel migration and
increases avulsion frequency (converting dry cells on the delta surface
to channels more quickly). Increased Qw tends to
increase channelization (Powell et al., 2012), and we find that at highQw the number of channels is the same for all
values of Qs and is higher than that for lowQw (Figure 1b), as flow is distributed more
evenly across the delta and increasingly through channels instead of
overbank flow. The increased number of channels results in a lower value
of M , corresponding to slower decay in channel planform overlap
(Figure 1c), suggesting more similarity in the configuration of the
channel network through time with higher Qw .
(There is no relationship between M andQs. )
An increase in similarity in the channel network through time may seem
to be at odds with an increase in channel mobility, but we suggest both
can be explained by separating spatial and temporal variability in the
channel network. We propose a regime shift from a few active channels
that distribute sediment regionally via overbank flow and periodically
undergo large-scale (global) avulsions at low Qwto many channels distributed across the delta with limited overbank flow
and frequent small-scale (local) avulsions at highQw . Such as shift would increase R (as
channel migration and/or more frequent, but local, avulsions would be
required to distribute flow across the delta in the place of overbank
flow) while also decreasing M (as smaller-scale avulsions would
result in smaller changes in the configuration of the channel network
than abandoning and carving out an entire new channel). Considering the
maps of the fraction of time that each channel cell remains a channel,
we do see that deltas with low Qw have fewer and
shorter-lived channels which are not evenly distributed over the delta
(Figure 2b,f,j), while deltas with high Qw have
relatively long-lived channels which are distributed over most of the
delta area (Figure 2a,e,i).
The distribution of detrended elevations on the subaerial delta supports
this proposed regime shift. The cumulative distribution function (CDF)
of detrended elevations has a steeper slope for deltas with highQw ; in other words, elevations across a delta
with high Qw are more similar than on deltas with
low Qw (Figure 3). For deltas with lowQw , higher elevations are focused on certain
areas of the delta along and near channel banks, suggesting regional
distribution of sediment as described above (Figure 4a,c,e). For deltas
with high Qw , elevations are relatively constant
across the delta as a more well-organized and extensive channel network
distributes sediment more evenly across the delta (Figure 4b,d,f).
3.2 Dynamics on vegetated
deltas
We find that both Qw andQs influence channel dynamics on vegetated
deltas. For low values of Qw , channel mobility
(R ) on vegetated deltas is lower than mobility on unvegetated
deltas for low and medium values of Qs (Figure
1a). However, channel mobility on vegetated deltas for the highestQs we tested is comparable to that on an
unvegetated delta, suggesting that vegetation’s ability to decrease
channel mobility is, as expected, reduced with highQs (e.g. Murray and Paola, 2003). However, for
high values of Qw , channel mobility is not
strongly influenced by Qs . For vegetated deltas,
at high Qs , R values remain comparable at highQw to those at low Qw . In
other words, the tendency for vegetation to stabilize channels by
introducing roughness on channel banks is not inhibited by highQw . Reworking of the delta surface likely occurs
at similar rates for low and high Qw because the
increased resistance to flow in vegetated areas likely makes avulsions
to previously abandoned channels—in which increased sedimentation
rates prevent vegetation from becoming established—more likely than
the incision of new channels through vegetated areas. This is further
supported by the average number of channels (Figure 1b). With highQw , vegetated deltas have fewer channels (4.46 ±
0.99) than unvegetated deltas (5.9 ± 0.39).
When vegetation is present, the number of channels decreases with
increasing Qs at low Qw(Figure 1b). At high Qw , the number of channels
does not depend on Qs . The number of channels
remains constant for vegetated deltas with highQs for both values of Qw .
This suggests that at high Qw , increased water
flow results in increased erosion and deposition events in channels,
preventing the establishment of vegetation and favoring reoccupation of
a few channels regardless of Qs , whereas at lowQw , vegetation’s ability to establish in channels
depends on Qs .
M is not determined by Qs at lowQw but decreases with increasingQs at high Qw (Figure 1c).
This suggests that with vegetation, there is more similarity in the
configuration of the channel network through time with increasingQs at high Qw . While we
might expect M to increase with Qs as
rapid avulsions spread sediment across an aggrading delta, the decrease
in M may be due to consistent channel reoccupation during
avulsions. Aggradation and increased channel switching frequency that
prevents vegetation from establishing in less active channels, combined
with the fact that vegetation offers resistance to incising new flow
paths, results in frequent channel reoccupation.
If the channel network is distributed evenly across the delta surface,
as channel frequency maps suggests is true for vegetated deltas with
high Qw (Figure 2), consistent channel
reoccupation would still facilitate the even distribution of sediment
across the delta necessary for the high aggradation rates typical of
high Qs . Channels do appear to be less long-lived
for vegetated deltas with high Qw than for
unvegetated ones (Figure 2). This also explains why we do not see the
same trend at low Qw , as the increased
organization of the channel network that comes with highQw is necessary to facilitate even distribution
of sediment across the delta.
Detrended delta elevations tend to be lower on vegetated deltas than
unvegetated ones (between 15-30% of elevations are below 0.25 m on
vegetated deltas, compared to only 5% on unvegetated ones), though
deltas with high Qw still tend to have steeper
slopes or more similar elevations than those with lowQw (Figures 3 and 4). The distribution of
elevations shifts to the left with decreasing Qs ,
representing lower elevations. Differences in elevation distributions
with different Qw and Qsconditions are larger on vegetated deltas than unvegetated ones.
With increasing Qw , more even distribution of
channels across the delta surface results in a decreased tendency for
vegetation to increase shoreline roughness. Shoreline roughness is
typically higher for vegetated than unvegetated runs (Figure 1d);
however, the magnitude of the difference decreases with increasedQw .
This consistent reoccupation hypothesis is qualitatively supported by
the delta stratigraphy. The effect of high Qs to
increase channel aggradation and avulsion (by increasing cross-levee
slopes through aggradation), encouraging even distribution of sediment
across the delta, appears to result in less strong channelization of
flow (less evidence of levee formation; Figure 4), especially when
vegetation is present. This is supported by the decrease in the
prevalence of sandy channel deposits with increasingQs (Figure 5c, g, k). The detrended elevation
maps show evidence of pronounced levees suggesting long-lived channels
for deltas with low Qw but not for highQw (Figure 3).
Potential for Future Work
Our results raise some interesting questions that could be answered by
future work.
In natural delta systems, multiple species and types of vegetation (e.g.
aquatic plants or trees in addition to marsh grasses) exist in close
proximity. In addition to each type of vegetation having different
properties and levels of cohesive influence, both competition and
facilitation effects could occur which would introduce more spatial and
temporal variability in vegetation influence and may enhance or inhibit
vegetation’s overall level of influence. We have purposefully chosen to
include only a simple representation of vegetation dynamics, with one
type of vegetation, as a first examination of the basic question of how
the effects of vegetation vary with water and sediment discharge
conditions. With this question in mind, we incorporated only the
cohesive effects of vegetation, though other dynamics such as organic
sediment production may be important to consider in other contexts.
Similarly, we provide a starting point for future research by
considering ranges in water and sediment discharge, but our model deltas
develop under constant discharge conditions (i.e., they could be
considered at equilibrium). Natural deltas are subject to changes in
discharge over time due to changing environmental conditions or human
alteration of water or sediment fluxes to the coast (Syvitski and Saito,
2007), and so may be expected to experience transient effects as they
respond to changing conditions which would not be captured by our
equilibrium deltas. In addition to long-term trends in discharge,
natural deltas experience stochastic variations in flow, which would
likely have a different effect on vegetation than the constant flood
height represented in our model. However, we have provided a foundation
by identifying different behaviors in the delta channel networks across
different experimental set-ups, which are consistent with experimental
studies with changing discharge trends (but no vegetation; e.g. an
increase in water discharge increasing the number of channels; Edmonds
et al., 2010).
Summary and Implications
In agreement with previous research, we find that increasingQw increases the number of channels on
unvegetated deltas (Edmonds et al., 2010), and (at lowQw ) channel mobility increases withQs (Powell et al., 2012; Orton and Reading, 1993;
Hoyal and Sheets, 2009) and vegetation’s ability to decrease channel
mobility is decreased (e.g. Murray and Paola, 2003). We also propose two
new insights into the evolution of delta channel networks under
different discharge conditions: 1) a regime shift in avulsion dynamics,
without vegetation, from a few active channels supplemented by overbank
flow and undergoing episodic global avulsions at lowQw to many active channels experiencing limited
overbank flow and frequent local avulsions at highQw ; and 2) that while vegetation’s ability to
establish in less active channels is decreased by more frequent channel
switching and aggradation under high Qsconditions, vegetation is still able to stabilize the channel network by
favoring reoccupation of abandoned channels over incising new channels
through vegetated areas.
The proposed insights into channel dynamics under highQw and Qs conditions have
important implications for deltaic channel-island exchange. As
vegetation may reduce fluxes between channels and islands (e.g. Nardin
and Edmonds, 2014), vegetation’s effectiveness at channelizing flow
under different sediment and water discharge conditions, and
vegetation’s tendency to remain established outside of channels even
under high Qw and Qsconditions, will affect sediment and nutrient fluxes to islands (Hiatt
and Passalacqua, 2015). On a larger scale, a shift from more lobate
delta growth with low Qw to more fan-like growth
with high Qw has implications for the delivery of
sediment and nutrients across the entire delta through potential changes
in network connectivity (e.g. Tejedor et al., 2016; Passalacqua, 2017).
These implications will be particularly important for restored or
engineered deltas, which are subject to natural delta processes after
initial construction (Paola et al., 2011), or for diversions with
controlled water and sediment discharges. If restoration efforts aim to
build new deltaic land, they will need to consider the implications of
discharge and sediment load on channel network configuration and
dynamics, including the influence of vegetation.