Vegetation controls on the maximum size of coastal dunes

Abstract

Coastal dunes, in particular foredunes, support a resilient ecosystem and reduce coastal vulnerability to storms. In contrast to dry desert dunes, coastal dunes arise from interactions between biological and physical processes. Ecologists have traditionally addressed coastal ecosystems by assuming that they adapt to preexisting dune topography, whereas geomorphologists have studied the properties of foredunes primarily in connection to physical, not biological, factors. Here, we study foredune development using an ecomorphodynamic model that resolves the coevolution of topography and vegetation in response to both physical and ecological factors. We find that foredune growth is eventually limited by a negative feedback between wind flow and topography. As a consequence, steady-state foredunes are scale invariant, which allows us to derive scaling relations for maximum foredune height and formation time. These relations suggest that plant zonation (in particular for strand “dune-building” species) is the primary factor controlling the maximum size of foredunes and therefore the amount of sand stored in a coastal dune system. We also find that aeolian sand supply to the dunes determines the timescale of foredune formation. These results offer a potential explanation for the empirical relation between beach type and foredune size, in which large (small) foredunes are found on dissipative (reflective) beaches. Higher waves associated with dissipative beaches increase the disturbance of strand species, which shifts foredune formation landward and thus leads to larger foredunes. In this scenario, plants play a much more active role in modifying their habitat and altering coastal vulnerability than previously thought.

Dune height and dune recovery following storms are critical in determining coastal vulnerability to climate-change–induced shifts in forcing (e.g., sea-level rise and changing storms). Coastal dunes arise from interactions between ecological and physical processes yet the mechanisms involved in dune formation and the impact of climate change on these mechanisms has been poorly understood. Here we argue that plant zonation, rather than sediment supply, controls coastal vulnerability to storms by determining maximum dune size. In addition, plant zonation may also control the resiliency of coastal environments to climate fluctuations by altering the dune mobility threshold, potentially leading to dune destabilization.

Foredunes, the first shore-parallel dune ridge encountered landward of the shoreline, are a crucial part of coastal landscapes. As natural barriers, they increase biodiversity by sheltering more sensitive inland ecosystems from impacts of the sea while also providing protection from storm-induced overwash, which is particularly important on barrier islands. Coastal dune formation and evolution result from complex interactions among coastal plant communities, aeolian and subaqueous sediment transport, fluid dynamics, coastal and beach topography, and storms (1–4). Because so many different factors may contribute to dune morphology, identifying primary controls of foredune development and recovery following storms is particularly challenging.

Foredunes are formed by the continuous accumulation of wind-blown beach sand, which is trapped by burial-tolerant vegetation. Ecologists have studied the response of plant communities (e.g., spatial sorting, zonation, and diversity) to physical and chemical gradients (including sand burial, wind exposure, salt spray, soil moisture, underground water salinity, soil pH, and nutrients) many of which are affected by the topography (5–10). From an ecological perspective, once pioneer salt-tolerant strand species colonize a shore in the presence of active aeolian transport, trapped sand acts as a positive selection mechanism for burial-tolerant “dune-building” grasses (5, 6, 8). The resulting foredune further reduces salinity and landward sand transport, thus creating favorable conditions for new species, ecological competition, and plant succession (5, 6).

Although the relevance of dune-building grasses has been recognized (3, 11), most geomorphological research has focused on the role of sand supply (a combination of sand availability and wind-transport potential) as a function of beach morphology and wind regime in the dune-forming process (1, 2, 4, 12, 13). The empirical finding that foredune size correlates with beach type, with foredunes up to 10 times higher on dissipative beaches than on reflective ones (1, 2), combined with conceptual models that predict enhanced aeolian transport on dissipative beaches (1, 14, 15), has motivated the common assumption that maximum foredune size is primarily controlled by sand supply (1, 4, 15, 16). However, this explanation is problematic based on reports of large foredunes on dissipative beaches with a negligible sand input (17, 18) and findings of very small foredunes formed on a reflective beach under high sand supply (19). In addition, there seems to be no general empirical relation between foredune size and beach morphology, i.e., beach width and slope (15, 20, 21), characteristics traditionally used, along with grain size, as a proxy for potential sand transport (which is notoriously difficult to measure at the beach).

In comparison with plant zonation and sand supply, the role of plant communities in foredune development has yet to be well studied. For example, there is evidence that plant physiology can alter foredune aspect ratio (22) or connectivity, i.e., either forming a continuous shore-parallel ridge or discontinuous “hummocky” dunes (3). However, there is no clear understanding of the individual role of the different physical and biological factors on foredune size. Fundamental questions remain unanswered: what limits foredune size, do coastal dunes reach a steady state, and what controls foredune formation time?

The inherent complexity of the experimental/field study of aeolian bedforms with or without vegetation (ripples, dunes, megadunes, foredunes, etc.), has led to the use of modeling as a viable alternative to empirical approaches (23–31). Following van Dijk et al. (24), the process-based model developed by Kroy et al. (25) was the first to quantitatively reproduce the steady state of crescent dunes (32). Further iterations of the model successfully addressed dune collisions (33), Martian dunes (34), and dune formation under bimodal winds (35) (see ref. 36 for a recent review). Durán and Herrmann (27) added another layer of complexity to this model by incorporating vegetation dynamics and were able to successfully predict the stabilization of mobile dunes as a result of vegetation growth (37).

Here, we extend the model of Durán and Herrmann (27, 38) to include the ecological and physical effects of a coastal environment, and we quantify the influence on foredune development of key interactions between wind flow, sand transport, topography, the shoreline, and vegetation. We then demonstrate that the inherent complexity of coastal ecomorphodynamic processes can be greatly reduced by focusing on a few fundamental quantities.

Formation and Stabilization of Foredunes

The coastal dune model consists of differential equations for the physical and biological processes describing aeolian sand transport on a vegetated surface at the shore during low tide. It resolves the coevolution of the sand-surface elevation h relative to the water table at low tide, and the vegetation-cover fraction under a constant onshore wind, characterized by the surface shear stress on a flat bed (see Appendix for the model description).

For a typical simulation, aeolian transport begins at the foreshore (during low tide), slightly above the water table, at the first location where the wind shear stress is above the transport threshold . Sand flux then steadily increases up to the maximum, saturated value that the wind can sustain (Fig. 1A). Under a constant onshore wind, sand blows continuously across the beach into the backshore where it is trapped by dune-building vegetation and a foredune begins to form (Fig. 1 A and B). We assume that the spatial distribution (zonation) of the vegetation is characterized by the minimum distance from the shoreline (called vegetation limit ) needed by the plants to survive long enough to build a mature foredune. (We are not aware of any field measurements to quantify this distance.) Closer to the shoreline, plant growth is hampered by wave runup, soil salinity, storms, etc., and any incipient foredune will be short lived.

Fig. 1.

Mechanisms behind foredune formation and stabilization. (A) Simplified coast used as initial condition for the model. For visual reference, the foreshore is shown in blue. (B) Stationary foredune for and undisturbed wind shear stress , where is the threshold shear stress for dry sand (vegetation cover fraction is green). (C) Evolution of the central cross-shore slice of the foredune elevation, (D) wind shear stress, and (E) sand flux. (F) Evolution of the foredune height H rescaled by the maximum height , the computed wind shear stress at the shoreline rescaled by the undisturbed shear stress over a flat bed and the computed sand flux into the foredune rescaled by the saturated (maximum) flux over a flat bed . Solid lines correspond to exponential fits with constant relaxation time. (G) Proportionality between the rescaled wind shear stress at the shoreline and the rescaled foredune height . The dashed line is the rescaled transport threshold for dry sand . For a realistic timescale it is assumed transport only takes place 20% of the time.

Initial foredune growth is then driven by the abrupt sand-flux decrease induced by the vegetation at the vegetation limit (Fig. 1 C–E). Plants act as roughness elements that absorb part of the momentum transferred to the sand surface by the wind, effectively reducing the surface shear stress and thus the sand-transport rate. Once a proto-dune emerges, its evolution is determined by its interaction with the wind flow, with the vegetation playing a secondary role as a passive roughness element anchoring the dune crest and thus preventing dune motion. Growth of the foredune produces a deceleration of the flow upwind thereby reducing the surface shear stress—which is roughly proportional to the wind velocity—(Fig. 1D) and the sand flux (Fig. 1E), until the shear stress at the shoreline is below the threshold for transport and sand flux ceases. At this point, there is no net sand supply to the backshore feeding dune growth and the foredune reaches a steady state of maximum height (Fig. 1F).

Foredune development can be captured by a simplified analytical morphodynamic model based on the linear relation for the topographic forcing on the wind flow, as shown in Fig. 1G, where the wind shear stress at the shoreline decreases with foredune height H. The topographic forcing is a function of the foredune windward slope, which can be approximated as , where the vegetation limit approximates the position of the crest relative to the shoreline. The topographically induced reduction of the undisturbed wind shear stress at the shoreline can then be approximated as , where β and are constants obtained from the numerical simulations (for simplicity we will consider in what follows).

The wind shear stress at the shoreline determines the ratio of the actual sand flux crossing the shoreline to reach the foredune and the potential sand supply , defined as the maximum sand flux on a beach without foredunes: .

The foredune height H for a given cross-shore profile results from mass conservation at the dune crest: , which can be rewritten as after assuming the flux gradient is essentially given by the total influx to the backshore decaying to zero over a length with a proportionality constant α. After substituting into , the equation for the foredune height can be rearranged into the form

with a maximum size and formation time defined as

Here and are obtained from the numerical simulations and is the transport threshold for dry sand. We assume that during most transport events the threshold is close to that of dry sand .

Eq. 1 integrates as the exponential relaxation in agreement with simulation results (Fig. 1F). Therefore, as Fig. 2 shows, foredune evolution can be solely characterized by the maximum size and the formation time .

Fig. 2.

(A) Foredune profiles from the numerical model for different winds, characterized by the ratio of the undisturbed to threshold shear stress , and vegetation limits . (Inset) Rescaled profiles. (B) Evolution of foredune height for different vegetation limits and . (Inset) Rescaled evolution curves; and are given by Eqs. 2 and 3.

From the sand-transport model (Appendix) the potential sand supply can be derived from the wind regime as:

where Q is a dimensional constant and is the fraction of the time the undisturbed wind is above the transport threshold. In the numerical simulations we use a constant wind regime and thus by definition (for the figures we use ). However, under real conditions, this is not the case and we define as the shear stress corresponding to the “formative wind,” i.e., the wind that contributes most to sand transport and dune formation, and the fraction of the time this wind is present.

Discussion and Implications

The negative feedback between the topography and the wind flow that eventually limits foredune growth has two important consequences. The first one is the scale invariance of the steady-state foredune profile (as evidenced by Fig. 2A). Analogous to mobile crescent dunes (25), scale-invariant fordunes result from the scale invariance of the flow field within the turbulent boundary layer, by which both small and large dunes deflect the wind in a similar way. The scale invariance, as confirmed by measured foredunes (Fig. 3A), suggests a characterization of foredune development based on the windward slope. For typical winds , simulated foredunes reach the steady state for windward slopes in the range 18–25°, in agreement with measurements (Fig. 3C). Indeed, Arens et al. (17) and Bauer et al. (18) reported no transport activity during favorable wind conditions on the windward side of steep dunes (∼27° and ∼22° respectively; Fig. 3C). In contrast, flatter foredunes have room to grow, as those in Fig. 3B where sand accretion has been reported (2, 42).

Fig. 3.

Scale invariance. (A) Mature foredunes: simulation (solid line) and measurements from Australia (39) (1), Canada (×) (40), Florida (41), and Netherlands (17). (B) Incipient foredunes: simulation (dashed line) and measurements from Australia (2) and Netherlands (17, 42). A simulated mature foredune is shown for comparison (solid line). Notice that the model underestimates the downwind dune profile as it simulates sand transport via saltation and neglects suspended sand transport, which can be significant (and occur above the vegetation canopy) during storms (42). (C) Evolution of the characteristic slope of a simulated dune, defined as (solid line). Superimposed symbols: slopes of measured mature (steady) and incipient (unsteady) foredunes, from A and B, respectively. Sand repose (avalanche) angle is shown for comparison (dotted line). All simulations were performed for . For simplicity the origin of the x coordinate is set at the foredune crest.

The second consequence is that some of the details of how vegetation grows are irrelevant to the resulting foredune morphology as long as the typical vegetation growth rate, defined by the ratio of the maximum plant height and typical growth time , is much higher than the maximum erosion/deposition rate, which is a necessary condition for dune stabilization (27).

Measurements of wind deflection and sand accretion upwind of foredunes provide additional support for foredune stabilization driven by the flow–form interaction. Arens et al. (17) and Hesp et al. (40) reported wind deflections at a distance about (H is dune height) upwind of the foredune crest, a value comparable to found on crescent dunes and reproduced by simulations (32). Furthermore, Arens (42) and Nordstrom (43) have reported sand deposition as far as upwind of the crest of low foredunes attributed to topographic effects, also in agreement with simulations (Fig. 4).

Fig. 4.

Measurements on a cross-shore slice of a growing foredune (17): rescaled profile (dashed line), vegetation cover (gray areas), and sand flux q rescaled by its maximum value at the beach (the scattering is due to different wind velocities). Solid lines: simulation for and . Flux reduction in nonvegetated areas is due to flow–form interaction; closer to the crest is due to vegetation.

Plant Zonation and Foredune Size.

The scalings in Eqs. 2 and 3 explicitly relate the morphological and dynamical properties of foredunes to wind and transport regimes, characterized by the undisturbed shear stress and the potential sand supply , respectively, and the interaction of the vegetation with the shoreline, which defines the plant zonation described by . From Eq. 2, the maximum foredune height is primarily controlled not by the sand supply, as traditionally assumed (1, 2, 4), but by the zonation of dune-building plants, i.e., the vegetation limit , with a secondary contribution from the average wind intensity during transport events. Because the steady state of a foredune is determined by its slope, the farther from the shoreline a foredune forms, the higher it can be. Therefore, by determining where an incipient foredune can develop relative to the shoreline, pioneer strand species play a critical role in controlling dune size. This coupling has important consequences beyond morphology because foredunes strongly modify the abiotic gradients that ultimately determine how the associated coastal ecosystem develops (9, 10).

The causal relationship between plant zonation and foredune size provides a simple explanation for the empirical correlation between beach type and foredune size (1). We know that dissipative beaches have larger average wave heights than reflective beaches (1), and that several limiting factors for vegetation growth are related to average wave height, e.g., wave runup during extreme tides and storms, soil salinity, and salt spray (2). As a consequence, plant zonation is wider on dissipative beaches than it is on reflective beaches (2, 15, 44). Therefore, foredunes tend to be larger on dissipative beaches than on reflective beaches. This conclusion is quantitatively supported by field data, which suggests a linear correlation between average wave height and vegetation limit, and hence between wave height and foredune height (Fig. 5), and it is consistent with measurements of foredune size and beach characteristics by Saye et al. (20).

Fig. 5.

Foredune height versus characteristic wave height for beaches in Australia (, modified from ref. 2), Oregon (, ref. 21), and Brazil (, ref. 45). The solid line corresponds to the model prediction for a wind and assuming plant zonation increases linearly with wave height as , with a fit parameter .

In contrast to foredune height, foredune formation time is limited by potential sand supply and decreases with the transport frequency (Eqs. 4 and 3). Therefore, in places with wider zonation for strand species but low sand-transport frequency (e.g., as a result of wave inundation) dunes have the potential to be large, but they will grow slowly. In this case, recovery following dune erosion/destruction will also be slow and as a consequence, in some cases, even large dunes may be highly vulnerable to changes in the frequency of intense storms.

Plant Zonation and Coastal Dune Fields.

In addition to influencing coastal vulnerability to storms, the relationship between plant zonation and foredune size has important implications for the aeolian sediment budget at the coast (i.e., total amount of sand deposited landward by aeolian transport) and thus the potential development of transgressive dune fields. Following Durán and Herrmann (27), permanent vegetated dunes, such as foredunes, can be destabilized and become mobile once the potential erosion/deposition rate is sufficiently high relative to the vegetation growth rate. Under the condition of a constant sand supply from the shore, destabilization of foredunes can lead to the formation of transgressive dune fields (29).

Simulation results suggest that pioneer species zonation indirectly affects this mobility threshold (Fig. 6). All other factors being equal, an incipient foredune that forms where plant zonation is narrow would result in a reduced sand flux relative to an incipient fordune that forms where zonation is wider. A lower sand flux implies a lower potential erosion/deposition rate, which increases the mobility threshold for vegetation and leads to a more stable foredune (Fig. 6B). In contrast, foredunes forming where zonation is wider can become unstable for strong winds and generate a wide range of mobile and quasimobile dune morphologies (e.g., blowouts, parabolic dunes, and crescent dunes; Fig. 6 C and D). This transition can be enhanced by the physical factors, such as water availability and wind exposure, that further stress dune plants on large foredunes, thereby reducing plant growth rate and further decreasing the mobility threshold.

Fig. 6.

Plant zonation and coastal dune fields. Different model outcomes starting from a flat bed with an undisturbed wind shear stress above the mobility threshold for vegetated dunes such that foredunes can become unstable ( for a vegetation growth rate , down from 0.3 m/d in previous simulations): (A) spontaneous nucleation of a transgressive dune field in the absence of vegetation (46); (B) stable foredune for a narrow plant zonation; (C) unstable foredune, followed by blowouts, parabolic and crescent dunes, for an intermediate plant zonation; and (D) unstable foredunes and formation of a transgressive dune field for a wide zonation. (E) Evolution of the total volume per unit area deposited by aeolian transport for different vegetation limits. (Inset) Rescaled volume per unit area. For a realistic timescale it is assumed transport takes place 20% of the time.

In addition to affecting the onset of coastal dune-field formation, plant zonation also determines the volume of sand transported inland by controlling the storage capacity (size) of foredunes (Fig. 6E). As a consequence, physical factors, such as breaker height, although acting at a local scale, could potentially lead to ecological and morphological changes at a much larger scale. This picture is consistent with field observations and conceptual models (2, 3, 15) in which the degree of mobility and extension of coastal dune fields, from stable foredunes to parabolic to crescent dunes fields, is correlated with beach type. Although most transgressive fields are found on dissipative beaches (high waves, wide zonation), reflective beaches (low waves, narrow zonation) may have just a single foredune ridge (2). Therefore, plant zonation may not only control coastal vulnerability to storms by determining maximum foredune height, it may also control the resiliency of coastal environments to climate fluctuations by altering the mobility threshold, potentially leading to dune destabilization.

Appendix: Coastal Dune Model

Initial Condition.

The sand-surface elevation relative to the mean water-table level during low tide is initially defined by an inclined foreshore, for , and by a flat backshore, for (MHWL: mean high water level). Here, x is the cross-shore distance and the position of the shoreline, defined by the MHWL as . Notice that the origin of the x coordinate is by definition at . In the simulations, is the beach slope and is the relative water-table depth.

Upwind Boundary Condition.

We assume, as a first approximation, that the foreshore is stable , i.e., aeolian erosion is balanced by accretion in the swash zone. As a result, the simulated foreshore acts as a sand reservoir supplying an unlimited amount of sediment to the backshore, effectively feeding dune formation.

Fluid dynamics.

The model uses a linear solution of the Reynolds-averaged Navier–Stokes equations for the turbulent boundary layer over smooth terrain (45) to calculate the perturbation of the wind shear stress induced by the topography h. The surface shear stress is (see refs. 35, 46 for details).

For lee slopes steeper than the separation angle ∼20°, nonlinear hydrodynamic effects are simply modeled by a separation streamline below which wind and flux are set to zero. Each streamline is defined by a third-order polynomial connecting the brink with the ground at the reattachment point (46).

Shear Stress Partition.

For randomly distributed plants, and assuming the effective shelter area for one plant is proportional to its basal area, the fraction of the surface shear stress acting on the sand decreases with the local vegetation cover fraction as (47)

where is a dimensionless “roughness factor,” which describes the effectiveness of the vegetation in slowing down the flow and thus in trapping sand. In the model, is calculated from values of plant form drag and geometry reported for creosote communities (see ref. 27 and references therein; it is reasonable to expect a similar value for coastal grasses and desert bushes due to a roughly similar plant geometry).

Effect of Wetting on the Transport Threshold.

We further consider that at the shore, transport is naturally limited by the elevation h relative to the water table, as the transport threshold is much higher for wet grains than for dry ones. This relation is captured by the simple phenomenological expression

where and are the threshold for dry and wet sand, respectively, and characterizes the decrease in water content of the sand as a function of elevation.

Sand Transport.

The sand flux is determined from the shear stress at the sand surface (Eq. 5), the surface gradient , and the transport threshold (Eq. 6). It is well known that the sand flux over an erodible surface increases with the distance downwind as the saltation process spatially adjusts to the wind forcing (25). This effect is modeled as

which describes the spatial relaxation of the sand flux toward an equilibrium “saturated” value over a saturation length (48). The saturated flux and saturation length are defined as: and , where and are slope-dependent dimensional functions (46).

For slopes steeper than the angle of repose 34°, an additional dissipative flux models the surface relaxation due to avalanches (46).

Surface Dynamics.

The sand-surface elevation h is then updated using mass conservation

where the Heaviside function (1 for ; 0 otherwise) distinguishes the dynamics of the nonerodible foreshore from the backshore . For simplicity in the formulation q is defined as a volume, not mass, flux.

Vegetation Dynamics.

To represent vegetation dynamics in a simplified way, we assume a single generic grass species with a cover fraction that is sensitive to erosion and accretion and that can increase up to the maximum cover during a characteristic time . We further assume that growth is also sensitive to the distance from the shoreline such that plants can only growth landward of the vegetation limit :

where γ is plant sensitivity to sand erosion/accretion and is the maximum plant height. Both the growth time and the sensitivity γ are a function of the erosion/accretion rate , which can be varied for different plant species. However, we find that the results presented here are independent of these considerations. Therefore, for simplicity and in agreement with (27), we use a constant growth time , and sensitivity , with .

Integration.

The model is integrated within a 2D domain large enough to include the resulting morphology. The grid spacing and time step are typically ∼ 1/4 m and ∼ 1/2 h, respectively, and are selected to resolve the smallest length and temporal scales involved in the problem, the saturation length and time .

Parameters.

Model outcomes are investigated as function of the vegetation limit and the imposed onshore wind, characterized by the undisturbed shear stress , which is assumed constant throughout each simulation. Time in the model is thus shorter than in more realistic wind conditions, where the wind intensity fluctuates daily and seasonally, with the conversion factor being loosely given by the fraction of the time the wind is above the transport threshold. For the figures we use .