ESurfEarth Surface DynamicsESurfEarth Surf. Dynam.2196-632XCopernicus PublicationsGöttingen, Germany10.5194/esurf-5-417-2017Lateral vegetation growth rates exert control on coastal foredune
“hummockiness” and coalescing timeGoldsteinEvan B.evan.goldstein@unc.eduhttps://orcid.org/0000-0001-9358-1016MooreLaura J.Durán VinentOrenciohttps://orcid.org/0000-0001-8459-582XDepartment of Geological Sciences, University of North Carolina at
Chapel Hill, 104 South Rd, Mitchell Hall, Chapel Hill, NC 27599, USADepartment of Physical Sciences, Virginia Institute of Marine
Science, College of William and Mary, P.O. Box 1346, Gloucester
Point, Virginia 23062, USAEvan B. Goldstein (evan.goldstein@unc.edu)8August2017534174279January201719January201712June201719June2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://esurf.copernicus.org/articles/5/417/2017/esurf-5-417-2017.htmlThe full text article is available as a PDF file from https://esurf.copernicus.org/articles/5/417/2017/esurf-5-417-2017.pdf
Coastal foredunes form along sandy, low-sloped coastlines and range
in shape from continuous dune ridges to hummocky features, which are
characterized by alongshore-variable dune crest elevations. Initially
scattered dune-building plants and species that grow slowly in the lateral
direction have been implicated as a cause of foredune “hummockiness”. Our goal
in this work is to explore how the initial configuration of vegetation and
vegetation growth characteristics control the development of hummocky coastal
dunes including the maximum hummockiness of a given dune field. We find
that given sufficient time and absent external forcing, hummocky foredunes
coalesce to form continuous dune ridges. Model results yield a predictive
rule for the timescale of coalescing and the height of the coalesced dune
that depends on initial plant dispersal and two parameters that control the
lateral and vertical growth of vegetation, respectively. Our findings agree
with previous observational and conceptual work – whether or not
hummockiness will be maintained depends on the timescale of coalescing
relative to the recurrence interval of high-water events that reset dune
building in low areas between hummocks. Additionally, our model reproduces
the observed tendency for foredunes to be hummocky along the southeast coast
of the US where lateral vegetation growth rates are slower and thus
coalescing times are likely longer.
Introduction
Vegetated coastal foredunes display various morphologies in the alongshore
direction, ranging on a spectrum from continuous to hummocky (i.e., varying
in dune crest elevation). Examples of hummocky foredunes from Fort Fisher
State Recreation Area, NC, US, are shown in Fig. 1. As described below, three
explanations have been used (separately and in conjunction) to explain the
existence of hummocky vegetated foredunes at a given site – initial
configuration (i.e., spatial distribution) of plants, the rate of plant
lateral expansion, and forcing or boundary conditions that control the pace
and style of the biophysical feedback that gives rise to coastal dune growth.
Ground-based photo of 1–2 m hummocky foredunes covered with
Uniola paniculata at Fort Fisher State Recreation Area, NC, USA.
(Note the person in the center left wearing black with a 2 m fixed height
survey pole for scale). The hummocky foredunes are seaward of an older
continuous dune ridge.
New coastal dunes can be initiated when there is sufficient cross-shore width
seaward of the existing foredune for plants to colonize (e.g., Hesp, 2002) or when elevated water levels destroy existing dunes. The presence of plants
causes the deposition of sand (e.g., Hesp, 1989; Arens 1996; Kuriyama et al.,
2005), leading to the formation of small dunes (Hesp, 1981; Pye, 1983). These
incipient dunes have a typology that depends on the mechanism (plant, seed,
rhizome, flotsam, etc.) and alongshore continuity of plant establishment
(Hesp, 1989, 2002; Hesp and Walker, 2013), and variability in the location
where plants initially grow can cause the formation of hummocky dunes. For
example, Godfrey (1977) noted that in some settings vegetation initializes
from drift lines (wrack), so discontinuous drift lines would cause an
initially discontinuous or patchy development of dune plants (and therefore
discontinuous dunes). Therefore, continuous or discontinuous plant
initialization (in the alongshore direction) can control the initial alongshore
continuity of the foredune (continuous or hummocky).
Given a discontinuous initial plant configuration, the spaces between plant
sites infill through the establishment of new plants and/or the lateral
expansion of existing plants via rhizomes (e.g., Keijsers et al., 2015). In
this way, plant dynamics can also control the existence of hummocky dunes.
Some plants grow laterally faster than others – Godfrey and coworkers
(Godfrey, 1977; Godfrey and Godfrey, 1973; Godfrey et al., 1979) found that
dunes of the northeastern US had more continuous ridges than the hummocky
isolated dunes of the southeastern US, which they attributed to differences
in plant lateral growth rates for the dominant species in each region.
Geologic and geomorphic templates have also been used to explain
variability in dune height. Low areas without dunes can remain low because of
shell or coarse-grained lags, a high water table that causes plant stress,
and/or climatic conditions such as cold temperatures prohibiting plant growth
(e.g., Mountney and Russell, 2006, 2009; Wolner et al., 2013;
Ruz and Hesp, 2014; Ruz et al., 2017a). Godfrey (1977) hypothesized that
barrier island orientation relative to the prevailing winds exerts a control
on foredune morphology, with taller dunes occurring when winds blow directly
onshore, perpendicular to the shoreline. Sediment supply has also been
implicated in causing alongshore dune height variability – specifically that
a geomorphic and geologic framework influences the morphology of bars, beaches and sediment supply, therefore controlling the height of coastal dunes
(Houser et al., 2008; Houser and Mathew, 2011).
These proposed mechanisms may explain the formation of hummocky dunes, though
foredunes, once formed, are dynamic features, evolving and growing through
time. Both mature hummocky dunes as well as continuous dune ridges may evolve
from initially hummocky dunes. Ritchie and Penland (1988, 1990)
developed a conceptual model of coastal foredune development following
flattening of foredune topography by a storm, stating that a mature,
continuous foredune can develop from a washover terrace given sufficient
time. The transition from washover terrace (a low surface) to a continuous
dune requires individual incipient dunes to grow and merge, eventually
developing into a single continuous ridge. (Ritchie and Penland, 1988, 1990;
Pye, 1983; Carter and Wilson, 1990; Davidson-Arnott and Fisher, 1992; Mathew
et al., 2010; Montreuil et al., 2013). Such a conceptual model, consistent
with widely observed field conditions, does not address why some initially
hummocky foredunes coalesce to a linear foredune ridge, while others remain
hummocky, having variable dune height in the alongshore direction, though
Godfrey (1977) discussed the potential for recurring storm events to prevent
the coalescing of hummocky dunes, even in locations where vegetation grows
rapidly in the lateral direction.
In this contribution we develop and explore a model of coastal foredune
growth and hummocky dune evolution –that is consistent with this previous
work – to better understand the mechanisms behind the development of
hummocky foredunes in the alongshore direction. Previous work by Moore et
al. (2016) has investigated the cross-shore dynamics. Our work here is a
quantitative investigation of several of the hypotheses of Godfrey (1977),
notably that vegetation exerts a fundamental control on alongshore dune
morphology. Our findings suggest that, given no preexisting template and
sufficient time prior to the occurrence of a storm event, alongshore hummocky
dunes eventually coalesce to form a continuous coastal foredune ridge. Model
results are well explained by a predictive rule for both the coalescing
timescale and the height of the coalesced dune that depend on the initial
spatial distribution of dune vegetation (which controls the location of
incipient dunes) and the lateral and vertical growth rate of vegetation.
Eco-morphodynamic model
We use a recently developed model of coastal dunes that includes the lateral
propagation of vegetation (Moore et al., 2016). This model is based on the
coastal dune model of Durán and Moore (2013), itself based on previous
models used to study a variety of dunes (e.g., Parteli et al., 2009;
Durán and Herrmann,
2006; Durán et al., 2010). We briefly summarize the model and the
vegetation formulation below.
Given an initial topography h(x,y) and a vegetation field, the model computes
the bed shear stress perturbation due to the presence of a non-flat
topography (Weng et al., 1991), modified by a separation bubble (when there
is flow separation; Kroy et al., 2002) and the subsequent shear stress
reduction due to vegetation (Raupach et al., 1993). From the bed shear stress
field, the local nonuniform sand flux and sand flux divergence is then
computed at every position (Kroy et al., 2002; Durán et al., 2010) –
this determines the temporal change in topography. Sand avalanching occurs
down the steepest descent gradient when topography exceeds the angle of
repose. After the topography has been updated, the change in the vegetation
field is calculated (itself dependent on the local accretion/erosion rate).
We use a simplified version of the vegetation formulation presented in Moore
et al. (2016), which is itself a modification of earlier models (Durán
and Moore, 2013; Duránt Vinent and Moore, 2015; Durán and Herrmann,
2006). We now present the simplified vegetation model and then discuss the
physical interpretation for the two key sensitivity parameters.
Numerical model definition sketch. (a) Initial
conditions. (b) Formation of foredune and the infilling of the
initially unvegetated gap. (c) The final continuous foredune ridge
at the maximum theoretical dune height.
The vegetation is parameterized by the cover fraction ρveg.
The growth and propagation of vegetation is modeled by an advection equation
of the form
dρvegdt=C∇ρveg+G0ρveg1-ρveg,
where the first term is the lateral propagation of vegetation at rate C due
to rhizome growth and the second term is the local growth of biomass to
maximum cover ρveg=1. The intrinsic growth rate (G0) is
assumed to increase with the deposition rate
maxdhdt,0 and to vanish
near the shoreline (x<Lveg, where x is the distance to
the shoreline). This is represented by a Heaviside function Θ that is unity when distance to the shoreline is sufficient for plant
growth x-Lveg>0 and 0 otherwise:
G0=Hv-1maxdhdt,0Θ(x-Lveg).
The lateral vegetation propagation rate C is also assumed to increase with
the deposition rate and to vanish for steep slopes (tanθc<∇h; where θc is
15∘ and is based on field observations from Moore et al. (2016). This
is represented by a Heaviside function Θ that is
unity when the slope of the land surface is not beyond a threshold tanθc-∇h>0
and 0 otherwise:
C=βmaxdhdt,0Θtanθc-∇h.
This formulation of vegetation growth has two parameters that reflect the
sensitivity of plants to changes in surface topography. First, the intrinsic
growth rate G0 of vegetation in the logistic model is
sensitive to plant burial, to simulate the behavior of dune-building plants
that are stimulated by burial (e.g., Maun and Perumal, 1999; Maun, 2004;
Gilbert and Ripley, 2010). This sensitivity term Hv, with
dimensions of [L], encodes the efficiency of vertical plant growth after
burial. Larger Hv results in smaller values of G0 and
therefore slower plant growth, implying that burial is more effective at
reducing plant basal area. Second, the lateral propagation of vegetation is
sensitive to burial rate and the spatial gradient of cover density. Here, the
dimensionless coefficient β can be interpreted as the efficiency of
rhizome propagation after burial. A larger β results in faster plant
propagation from place to place. Note that vertical growth rate relies
exclusively on Hv, but lateral expansion relies on the spatial
gradient of vegetation cover and therefore depends indirectly on
Hv. If Hv is large, the vertical growth rate is
slower and this will cascade to slowness in lateral growth rate (and vice
versa).
Phase plot of two numerical model experiments – the experiment in
black has a larger growth parameter (β) and therefore faster lateral
growth and lower hummockiness than the red experiment. All model iterations
begin at (0.3, 0), reflecting the initial height of the planar sloping
surface (0.3 m) at the location of the dune vegetation plantings. As the
model iterates, the hummocky dunes develop, as vegetated sites grow in height
more than unvegetated sites (which must wait for vegetation to grow before
increasing in height). After vegetation propagates to these sites, a
continuous foredune ridge develops and hummockiness reduces to zero. The
maximum hummockiness and the trajectory through phase space is set by gap
size (w), the vertical vegetation growth parameter (Hveg) and
the lateral vegetation growth parameter (β).
The model is integrated into a two-dimensional grid (64 m alongshore and
100 m cross-shore with 1 m grid size) with periodic alongshore boundary
conditions. The shoreline is set to a fixed location and vegetation is
“seeded” in one band at an identical cross-shore location (40 m
from the shoreline). There is a gap in this seeding located near the center
of the model domain. The seeded “line” represents the development of
vegetation around a drift line of wrack and is set at the seaward vegetation
limit of plant growth (e.g., Durán and Moore, 2013; Kuriyama et al.,
2005). As a consequence, vegetation does not propagate seaward in model
experiments. We track the evolution of the unplanted gap as a single
representative example of an initially unvegetated gap in an alongshore
foredune. In the absence of observational data that reveal the degree to
which dune-building vegetation establishes via seed versus lateral
propagation, beyond the initial seeding we allow plants to establish in
unvegetated cells only by lateral propagation, which can be thought of as
encompassing establishment via both mechanisms.
Forcing conditions (i.e., undisturbed shear velocity
U*=0.35 m s-1) are kept constant for all model experiments, but
we vary the characteristics of the model vegetation to mimic variability in
vertical and lateral plant growth rates. Experiments are shown for a range of
vegetation lateral growth parameter values spanning over 1 order of
magnitude 10≥β≥0.1, vertical growth parameter
values spanning 1 order of magnitude 0.4m≥Hv≥0.04m and unvegetated gap sizes
(10–20 m).
Results
From the initial condition, the model domain evolves to fill in the
unvegetated gap (Fig. 2). Initially, the vegetation grows from the planted
location in the vertical and lateral direction. Initially planted locations
evolve into developed foredunes. Within the unvegetated gap, only minor
vertical elevation changes occur prior to the establishment of vegetation
(via lateral propagation from the vegetated line). After the establishment of
vegetation, the initially unvegetated sites become vegetated and grow
vertically into a mature foredune. In the final model state, there is no
evidence in the former dune gap to suggest that the site was once
unvegetated. All model results yield a consistent maximum dune height of
between 3.6 and 3.9 m.
We now focus on the lag in height between the unplanted gap and the
surrounding planted dune – we refer to this difference as “hummockiness”,
the difference in elevation between the dune under the initially planted area
compared to the central location at the initially unvegetated gap.
Hummockiness first increases with time as the initially unplanted site lags
behind the planted locations in both vegetation cover and vertical elevation.
Figure 3 is a partial phase plane for model results displaying
hummockiness plotted against the height at the planted dune site. This
partial phase space allows for the inspection of the trajectory of
model results as they evolve from hummocky dunes to coalesced dunes. Initial
trajectories all start at the (0.3, 0) mark (the beach is initially at an
elevation of 0.3 m, with 0 hummockiness), and evolve in a clockwise fashion
as the initially planted sites grow vertically at a faster rate than the
unvegetated gap. After the propagation of vegetation into the initially
unvegetated gap, the dune in the gap grows vertically at a rate faster than
the vegetated sites (which has slowed in vertical growth as it nears the
maximum theoretical dune height). This leads all trajectories toward a
hummockiness of 0. Note that no timescale is shown in this phase space.
Two trajectories are shown in Fig. 3 to illustrate that the maximum
hummockiness (the peak) is a function of Hv and β. As the
lateral vegetation growth parameter (β) decreases from 10 to 0.1, the
lateral growth rate slows down, which increases the variability in alongshore
dune crest heights – hummockiness tends to increase (Fig. 4a). On the other
hand, an increase in the vertical parameter Hv (plants are more
sensitive to burial) slows the growth rate of vegetation, thereby increasing
the maximum hummockiness (Fig. 4a). The unvegetated gap width also plays a
role in controlling hummockiness as smaller initially unvegetated gap widths
result in faster dune coalescing (Fig. 4b).
(a) Maximum hummockiness (m) as a function of
Hv (vertical vegetation growth parameter) and β (lateral
vegetation growth parameter). (b) Maximum hummockiness (m) as a
function of β and unvegetated dune gap size.
The general behavior of hummockiness and coalescing lends itself to heuristic
analysis. Since the development of coastal dunes relies on the feedback
between vegetation growth and aeolian sediment transport, maximum
hummockiness occurs at the moment just before the center of a given gap
transitions from unvegetated to vegetated (at which point the surrounding
vegetated dunes have grown for some time). Therefore, maximum hummockiness is
related to gap size and lateral propagation of plants – which from
Eqs. (2) and (3) depends on β
and Hv (via the spatial gradient in vegetation cover). For
example, small gap size, high β (fast lateral growth of vegetation)
and low Hv (fast vertical growth of vegetation) lead to low
maximum hummockiness and vice versa. Results from all model simulations
conform to this general behavior (Fig. 4a and b).
Gap size, lateral growth rate of vegetation and vertical plant sensitivity
also impact model timescales for the alongshore coalescing of hummocky dunes.
Maximum hummockiness occurs later (Fig. 5a) and dunes take longer to coalesce
(Fig. 5b) with the decreasing lateral growth rate of vegetation, increasing plant
sensitivity to burial and increasing gap size.
The impact of changes in the vertical vegetation growth parameter
(Hv) and lateral vegetation growth parameter (β) on
(a) the time of maximum hummockiness and (b) the time when
coalescing occurs.
The lateral propagation rate (P) of the dune is defined as the time needed
to propagate the crest a given lateral (alongshore) distance – the lateral
spreading rate of the dune crest. This rate encompasses the spreading rate of
the plant and the biophysical feedbacks that lead to dune growth. The lateral
dune propagation rate is defined as P=(0.5×W)/Ta, where
0.5×W is the half width of the gap (W) and
Tc is the time to coalescing. The half width of the gap is used
since all model experiments include unvegetated gaps that fill in from both
sides. Within the limits of the model experiments, results are well described
by an equation of the form
P=K1β+K2Hv,
where K1 and K2 are dimensional parameters (6.5 m yr-1 and
1.9 m2 yr-1). A high β (fast lateral growth of vegetation) and low Hv (fast vertical
growth of vegetation) lead to fast lateral propagation of the dune crest.
Figure 6 shows the modeled vs. predicted propagation times derived from
Eq. (4).
Rewriting Eq. (4), the coalescing time can be written as
Tc=WK1β+K2HvorTc=WHvK1βHv+K2.
Following Durán and Moore (2013), we assume in the model a constant wind
shear velocity (U*=0.35 m s-1) that represents typical wind
conditions during dune growth. Because in reality conditions sufficient for
transport do not occur all the time, Durán and Moore (2013) suggest that
model time can be converted to real time by multiplying model time by a
factor rt that varies from 0 to 1 and represents the
fraction of time there is no transport. Therefore, reduction in the flux of
sand from beach to dune, because of low wind speeds, large grain sizes or
narrow beaches, can be encapsulated through variation in rt and has an
effect similar to decreasing β and increasing Hv.
The height of the dune crest at the moment of coalescing (Hc) can
be described by
Hc=Hmax1-e-TcTf+Z,
where Hmax is maximum dune size, Tf is the formation time
of the planted sites and Z is the initial beach elevation at the site of
dune nucleation (here 0.3). Both Hmaxand Tf are
functions of the seaward vegetation growth limit as well as other relevant
parameters, defined in Durán and Moore (2013). Figure 7 is the modeled
vs. predicted dune height at coalescing calculated from Eq. (6).
Modeled lateral dune propagation rate vs. predicted propagation rate
from Eq. (4). Black line is 1 : 1.
Discussion and Implications
Godfrey (1977) and Godfrey et al. (1979) observed that foredunes change from
irregular, hummocky dunes in the southeastern US to contiguous long-crested
dunes in the northeastern US. This change in observed dune morphology is
attributed to changes in foredune species dominance (Godfrey and Godfrey,
1973; van der Valk, 1975; Woodhouse et al., 1977; Godfrey, 1977; Godrey et
al., 1979). From Virginia northward, foredunes are dominated by
Ammophila breviligulata (American beachgrass), while south of
Virginia, Uniola paniculata (sea oats) dominates foredunes (Wagner,
1964; Godfrey, 1977; Duncan and Duncan, 1987; Lonard et al., 2011). On the
east coast, A. breviligulata and U. paniculata exhibit
similar rates of vertical growth (including the adapted response of
increasing growth rates when buried by moderate amounts of sand; Disraeli,
1984; Maun, 2004; Ehrenfeld, 1990; Lonard et al., 2011; Wagner, 1964).
However, A. breviligulata and U. paniculata exhibit
differences in rates of lateral growth: 1–3 and 0.6–1 m yr-1
respectively (Woodhouse et al., 1977; Ehrenfeld, 1990; Lonard et al., 2011).
The slower lateral growth rate of U. paniculata provides a potential
explanation for the observation of hummocky dunes along the southeastern US
coast. This species-specific control on dune morphology likely arises from
differences in growth form, similar to observations that explain
species-specific dune morphology along the US west coast (Hacker et al.,
2012; Zarnetske et al., 2012). We can understand these differences in the
context of model findings – though A. breviligulata and U. paniculata may have similar vertical growth characteristics (Hv
is identical), their lateral growth rates (encoded here as β) are
different, resulting in differences in dune hummockiness (Fig. 4a) and
coalescing time (Fig. 5b). The dominant dune-building plant of the
southeastern US has a slower lateral growth rate and therefore a longer
coalescing time, likely leading to the increased prevalence of hummocky
foredunes in this region. Evidence that even U. paniculata can form
continuous dune ridges is present on Sapelo Island, Georgia, US. The lack of
a major hurricane strike in this region (Bossak et al., 2014) is manifest in
the continuous ridge topography even though the foredune is dominated by
U. paniculata (Monge and Stallins, 2016; Stallins, 2005; Stallins
and Parker, 2003).
Modeled dune elevation at coalescing vs. predicted dune elevation at
coalescing from Eq. (6). Black line is 1 : 1.
However, the numerical finding that hummocky dunes always coalesce if given
sufficient time suggests that differences in species-specific lateral growth
rates alone are not sufficient to explain hummockiness that persists through
time. A more complete explanation likely comes from combining our finding
that coalescing time lengthens with decreasing lateral growth rate of the
dominant dune-building grass, with the suggestion by several studies that low
areas (and therefore hummocks) are maintained by overwash during high-water
events (Godfrey, 1977; Hosier and Cleary, 1977; Ritchie and Penland, 1988).
We can understand this using Eq. (7) – if the recurrence time for high-water
events (R) is shorter than the coalescing time Tc, existing
hummockiness will likely be maintained because low areas are more likely to
be overwashed than adjacent higher dunes on either side. When this occurs,
the dune-building process in the low areas is reset, increasing hummockiness
until vegetation again becomes established in the overwashed zone.
Conversely, if R≫Tc, hummockiness will tend to decrease
through time because there will be sufficient time between storms for
coalescing to occur. Along the southeast US coast, it appears that
R<Tc given the previous observations that hummocky dunes are
prevalent there and given the slow lateral growth rate of U. paniculata. Thus, although hummockiness appears to be an intrinsic feature
of foredunes along the southeast coast of the US, model results suggest that
hummockiness is actually a transient characteristic of foredunes that only
becomes persistent when coalescing time is slow relative to the frequency of
storms capable of resetting the dune-building process in the low areas
between hummocks.
In the case of R>Tc, environmental conditions may be conducive to
bistable dynamics in the alongshore direction–similar to the cross-shore
models of Durán Vinent and Moore (2015) and Goldstein and Moore (2016) –
with alternating stretches of dunes near the maximum height and lower
intervening areas. In addition to storms, other factors such as a high water
table, low sediment supply, grain size variability, development of shell lag
and climatic conditions may also result in the suppression of the coalescing
of coastal foredunes (Mountney and Russell, 2006, 2009; Wolner et al.,
2013; Hoonhout and de Vries, 2016; Ruz and Hesp, 2014; Ruz et
al., 2017a). Feedbacks between the wind, dune vegetation and sediment
transport that are specific to hummocky dunes may also alter the rates of
coalescing (Barrineau and Ellis, 2013; Gillies et al., 2014), such as the development of high wind velocity
regions located adjacent to hummocky dune forms (Hesp and Smyth, 2017). Work
here does not address observations of older foredune ridges that lose their
continuous morphology as a result of plant succession, erosion via rain and
flow in rivulets, or trampling (Levin et al., 2009, 2017). Additionally the
potential for lag between fast cross-shore beach recovery time vs. slower
cross-shore vegetation recovery time (e.g., Castelle et al.,
2017; Keijsers et al., 2016; Ruz et al., 2017b) could
introduce novel dynamics that are not explored in this work.
There exists a potential for climate change to alter the range of the two
dominant species of dune-building grasses along the US east coast. Plantings
of A. breviligulata south of VA tend to die as a result of blight,
pests, drought intolerance and intolerance of high temperature (Seneca, 1972;
Singer et al., 1973; van der Valk, 1975; Woodhouse et al., 1977; Odum et al.,
1987; Seliskar and Huettel, 1993). A warming climate might
lead to further northward expansion of U. paniculata, which is
currently restricted in northward extent by temperature (Seneca, 1972;
Godfrey, 1977) – a northern expansion of the range has already been observed
(Zinnert et al., 2011; Stalter and Lamont, 1990, 2000) and is being sought in
selective breeding trials (USDA, 2013). Additionally, glasshouse experiments
have reported that A. breviligulata is negatively impacted by
competition with U. paniculata (Harris et al. 2017; Brown et al.,
2017). Because changes in β between these two dune-building species
affect variability in alongshore dune height, a change in the dominant
dune-building species from A. breviligulata to U. paniculata has the potential to decrease the protection provided by dunes
during high-water events. Changes in storminess may also impact the
hummockiness of coastal foredunes, with an increase in storm intensity or
frequency leading to a greater tendency for dunes to be hummocky and
therefore to provide less protection to habitats behind them. Here, we have
focused on the development of hummocky dunes from an initially flat
condition, but Lazarus and Armstrong (2015) discuss the
potential for storm events to create regularly spaced overwash throats (via
self-organization) that could also set up hummocky dune topography. Although
beyond the scope of this effort, observational work aimed at assessing the
relationships among storm frequency/magnitude, species composition of
dune-building vegetation and dune development (e.g., van Puijenbroek et al.,
2017a, b) will be useful in addressing the future implications of model
results presented here as climate change is anticipated to alter each of
these factors.
Model code used in this paper is available on the website of EBG and also by request.
Variables
SymbolVariable namehElevationtTimeρvegVegetation cover fractionCLateral vegetation propagation rateG0Intrinsic growth rateLvegSeaward limit of vegetation growthθcCritical topographic angle where vegetation stops expanding laterallyHvVertical vegetation growth sensitivity termβLateral vegetation growth sensitivity termWHalf width of unvegetated gap (i.e., half width of plant spacing)PLateral propagation rate of duneTcTime to coalescingK1Dimensional parameterK2Dimensional parameterHmaxMaximum dune sizeTfDune formation time at planted sites (time to Hmax)ZInitial beach elevation at site of dunesRRecurrence time for high-water events
The authors declare that they have no conflict of interest.
Acknowledgements
Evan B. Goldstein thanks Theo Jass and Elsemarie deVries for valuable
discussions regarding this work. We thank two anonymous reviewers for
comments on the paper. Funding was provided by NSF-GLD (EAR-1324973) and the
Virginia Coast Reserve Long-Term Ecological Research Program (NSF
DEB-123773). Edited by: Andreas
Baas Reviewed by: two anonymous referees
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