Geophysical Research Letters

Modelling vegetated dune landscapes

Authors


Abstract

[1] This letter presents a self-organising cellular automaton model capable of simulating the evolution of vegetated dunes with multiple types of plant response in the environment. It can successfully replicate hairpin, or long-walled, parabolic dunes with trailing ridges as well as nebkha dunes with distinctive deposition tails. Quantification of simulated landscapes with eco-geomorphic state variables and subsequent cluster analysis and PCA yields a phase diagram of different types of coastal dunes developing from blow-outs as a function of vegetation vitality. This diagram indicates the potential sensitivity of dormant dune fields to reactivation under declining vegetation vitality, e.g. due to climatic changes. Nebkha simulations with different grid resolutions demonstrate that the interaction between the (abiotic) geomorphic processes and the biological vegetation component (life) introduces a characteristic length scale on the resultant landforms that breaks the typical self-similar scaling of (un-vegetated) bare-sand dunes.

1. Introduction

[2] Aeolian dune landscapes developing in vegetated coastal and semi-arid environments are controlled by interactions between physical (abiotic) sediment transport processes and ecological response and regulation. Quantitative conceptual and simulation models exist for the development of various types of desert (bare-sand) dunes–such as barchans, transverse, linear and star dunes – as a function of wind directional regime and sediment availability [Wasson and Hyde, 1983; Werner, 1995]. For dune development influenced by vegetation, however, understanding has been limited to qualitative descriptions and case-studies, and the dynamic behavior of ecogeomorphic interactions and their impact on the resulting landforms have not been adequately quantified.

[3] In this letter we present a self-organising cellular automaton model capable of simulating the evolution of vegetated aeolian dunes, such as nebkha fields and parabolic dunes, with multiple types of vegetative response in the model environment. It shows how the biotic component imposes a characteristic length scale on developing morphology and it reveals the sensitivity of the evolving landscape to parameters of the vegetation response to local sedimentation conditions. We present a phase diagram for vegetated dunes, analogous to that for bare-sand dune types, that classifies different types of coastal dune landscapes, evolving from initial blow-outs, as a function of vegetation vitality. The sensitivity analysis of ecogeomorphic behavior helps quantify potential reactivation of dormant dune fields in response to climate change and anthropogenic impacts, while the emergent length scales have implications for scalability of landscapes and topographic signatures of life.

[4] Eco-or bio-geomorphology is deservedly gaining more attention [Viles and Naylor, 2002] as most Earth surface systems are affected to a greater or lesser extent by flora and fauna, and this letter may provide a template for quantifying such systems using landscape state variables and advanced statistical analysis.

2. Model Algorithm

[5] The model is based on a cellular automaton (CA) developed for bare sand dune simulations by Werner [1995], extended with vegetation components and interactions along the principles of Baas [2002]. The original Werner model simulates a sedimentary topography composed of stacks of discrete sand slabs on a Von Neumann-neighbourhood cellular grid with periodic boundaries. Slabs are picked up and moved downwind to the adjacent cell – mimicking transport by wind – and erosion and deposition of slabs are governed by probabilities (pe and pd, respectively). Two additional rules enforce the angle of repose (30°) via avalanching and a ‘shadow zone’ in the lee of topography where slabs are not susceptible to erosion (defined as an angle of 15° from horizontal). Without modelling complex airflow and sand transport dynamics, this simple model is capable of generating fairly realistic barchans, transverse dunes and linear dunes through self-organization of accumulating and migrating heaps of sand. The Werner model matches the phase diagram for these dune types as a function of wind regime and sediment supply [Bishop et al., 2002].

[6] In our Discrete Ecogeomorphic Aeolian Landscapes model, DECAL, the biotic component is incorporated as a (unitless) ‘vegetation effectiveness’, ρ, at each cell, representing the degree to which the vegetation affects the aeolian sand transport process – conceptually equivalent to a plant coverage density or frontal area index (FAI). Vegetation effectiveness reduces local slab erosion probability and increases local deposition probability (see flow diagram in auxiliary Figure S1). The geomorphically active range of ρ (where it impacts on pe and pd) is [0, 1], but its physiological range can extend beyond this interval to represent resilience and levels of ‘density’ beyond the threshold of blocking sand transport (ρ > 1) and nutrient depletion or vegetation presence below levels of influence (ρ < 0). Each cell can contain multiple types of vegetation and transport probabilities are subject to their combined effectiveness. The development of the vegetation in turn is controlled by growth functions that relate the local erosion/deposition balance at the end of a simulation ‘year’ to an increase or decrease of vegetation effectiveness. The growth functions define the different types of vegetation in the model environment, reflecting levels of tolerance to burial and/or erosion, and peak annual growth rates. We have used three rudimentary functions designed to reflect the qualitative behavior of certain plant species (Figure 1). For coastal dune environments these represent: (1) pioneer grass species such as marram grass (Ammophila) that require fresh input of sediment for optimum growth [Van der Putten et al., 1993], and (2) more conservative woody shrub species (stabilizers) with slower growth rates, such as creeping willow (Salix), while for a semi-arid environment we represent: (3) a fast-growing burial-resistant shrub species such as Tamarix or mesquite [Nickling and Wolfe, 1994].

Figure 1.

Vegetation growth functions relating yearly changes in vegetation effectiveness, ρ, as a function of local sedimentation balance. Growth and decline rates have been normalized by the physiological range of the plant type.

3. Parabolic Dunes

[7] Simulating temperate coastal environments with the first two vegetation types in the model yields realistic-looking parabolic dunes (Figure 2) developing over 50 years starting from 5 m wide blow-outs (bare patches) on an otherwise fully vegetated flat surface (see also auxiliary Animations S1 and S2). The evolving landforms exhibit some of the defining features of classic hairpin or long-walled parabolic dunes [Pye and Tsoar, 1990], such as trailing ridges resulting from the (first) colonization by grass and (then) stabilization by shrubs of the lateral edges of the migrating dune, a deflation plane that exposes the erosion base (analogous to a phreatic level) and which is re-colonized from upwind, and vigorous grass coverage and growth on the lee and sides of the depositional lobe. The animations further confirm that over time the dune reaches a stable width where sediment gained from the plain through migration is balanced against sediment lost to trailing ridges. Furthermore, during the build-up phase the trailing ridges grow higher and larger in volume as the depositional lobe grows to attain its stable migratory size. The model demonstrates how the presence of two different vegetation types is critical to the development of the deflation plane and the trailing ridges, with pioneer species invading up the flanks and slip-face of the migrating lobe to slow it down sufficiently for the stabilizer species to subsequently immobilize the edges into depositional ridges. This development of distinct arms was absent from the precursor model that was limited to one single vegetation response function [Baas, 2002]. The DECAL simulations also show ecological emergent behavior such as local competition between vegetation types in response to changing geomorphic conditions. Indeed, the model requires no rules to constrain the relative proportions of the different types in a cell (i.e. there is no imposed ceiling on their combined effectiveness), because they react differently to sedimentation conditions and occupy separate eco-geomorphic niches.

Figure 2.

(left) Simulated parabolic dunes developed out of flat blow-outs in the upwind region (lower-left side of view) after 50 years. Light-green shading indicates levels of grass effectiveness while density and size of dark-green sticks indicate levels of shrub effectiveness. Sediment transport direction from lower-left to upper-right of view. Grid resolution = 1.0 m, pe = 1.0, pd = 0.6, slab height = 0.1 m. See also animations in the auxiliary material. (right) Photograph of parabolic dune near Dongara, Western Australia, reproduced with kind permission of Patrick Hesp.

4. State Variables and Phase Diagram

[8] The evolution of coastal dune landscapes as a function of vegetation vitality was investigated by conducting 1288 simulations with varying permutations of peak annual growth rates (the heights of the maxima in Figure 1) for the two vegetation types, while keeping all other parameters constant, developing from initial blow-outs as shown in Figure 2. The simulations were run to a duration of only 40 years, however, because some dune forms migrate out of the model space if run longer, thereby invalidating statistical comparison. Each outcome was assessed on 114 numerical state variables derived from the resultant topography and vegetation distributions. These state variables were designed to capture a variety of fundamental aspects of morphology, vegetation patterns, and their mutual correlations. They are primarily permutations of averages and standard-deviations over the model grid of (products of), absolute and/or signed, directional gradients and curvatures in elevation and vegetation effectiveness. One state variable, for instance, is defined as the grid-average of the local products of morphology gradient in the ‘downwind’ direction and vegetation effectiveness of the pioneer species, capturing the growth of marram grass on lee slopes. All state variables were standardized with their theoretically attainable minimum and maximum values to range over the interval [0, 1].

[9] In order to reduce the effects of multi-collinearity between the state variables in the classification of resultant landscapes we applied a sequence of cluster analysis and Principal Component Analysis (PCA) following Vaughan and Ormerod [2005]. The 114 state variables were subjected to a cluster analysis adopting their correlation coefficients as an inverse measure (1 − r2) of average Euclidian separation distance. This yielded 11 separate groupings of collinear state variables that reduced remaining correlations between groups to r ≤ 0.78. PCA on the 1288 state variable outcomes within a grouping produced a ‘score’ on the first component axis for each of the simulations. Finally, a cluster analysis was performed on the sets of group-scores (1288 sets of 11 scores each) to arrive at a phase diagram of different dune landscapes as a function of the peak annual growth rates of the two coastal vegetation types, shown in Figure 3. Application of the same methodology on an independent replicate set of 1246 simulations (i.e. involving different random realizations on pe and pd) yielded closely similar results at all stages.

Figure 3.

Phase diagram of vegetated dune landscapes mapping eight classes as a function of normalised peak growth rates (i.e. plant vitality) for the pioneer and stabilizer vegetation types. Examples of each class are presented in auxiliary Figure S2.

[10] The cluster analysis identifies eight classes in the phase diagram that can be compared with qualitative observations of different types of coastal dune morphology [Pye and Tsoar, 1990; Hesp, 1991]. These are: 1&2) bare and vegetated transgressive ridges (TRb & TRb), analogous to a landward migrating erosional foredune; 3) chaotic and broken transverse ridges (CR), comparable to secondary foredunes with woody shrubs recovery and growth in interdune slacks; 4) hummocky topography (H) with broken and chaotic trailing arms; 5&6) parabolic dunes with classic trailing ridges, either continuing parabolics (Pc) that perpetually maintain active migration, or stabilising parabolics (Ps) that slowly develop toward a dormant state; 6) migrating lobes (ML) with no re-colonization of the deflation plane and lacking trailing ridges; and 7) general stabilized or remnant morphology (SM), comparable with dormant and fossilized dunes (examples in auxiliary Figure S2). Even though the cluster analysis operates on simulation outcomes only and is not at any stage informed by the growth parameters, each class occupies a contiguous and logical region of the phase diagram, suggesting that the model yields robust and consistent results that can be plausibly related to real vegetated dune landscapes. The diagram confirms that hairpin parabolic dunes require the active involvement of two types of vegetation: in the absence of a stabilising shrub the blow-outs spawn migrating lobes without trailing arms. In the region where peak effectiveness growth rates vary between 0 and +0.3 the diagram indicates particularly strong gradations of possible landscape outcomes. This parameter range accords well with realistic plant growth and its limiting effect on aeolian sediment transport [Lancaster and Baas, 1998] and it corroborates the notion that vegetated dune landscapes are sensitive to changes in overall plant vitality such that, for instance, dormant dune systems may easily become reactivated under worsening climatological growth conditions [Hugenholtz and Wolfe, 2005; Thomas et al., 2005] or, conversely, once-active coastal dune fields become stabilized under nitrification (fertilization) from atmospheric deposition [Arens et al., 2004; Kooijman and Van der Meulen, 1996].

5. Nebkhas and Characteristic Length Scale

[11] Simulations employing only the mesquite-type vegetation growth function were successful in reproducing realistic fields of semi-arid shrub-coppice dunes or nebkhas (Figure 4a) that display the typical aerodynamic tail of sand deposits in their lee [Hesp, 1981] with sizes and spatial distribution that closely resembles real nebkha fields [Okin and Gillette, 2001]. The resulting landforms remain of the same physical size regardless of model grid resolution up to a limit where the cell dimensions become smaller than the natural size of an individual effective vegetation element (i.e. a single mesquite shrub). Increasing the cell-dimension from 1.2 m to 2, 5 or 10 m (Figure 4b) does not alter the physical size of the nebkhas so that at the lower resolutions they are represented by single cells (pixels). With smaller cell-dimensions, however, the consistent size breaks down at resolutions ≤0.8 m, where the landscape outcome is radically different. This demonstrates how the presence of vegetation imposes a characteristic physical scale on the resultant morphology, unlike the situation for desert dunes which are found over several orders of magnitudes in size [Wilson, 1972], including on other planets with different gravities and atmospheres. Indeed, the bare-sand CA models are fundamentally scale-less, as the spatial and temporal realms are linked only via the transport rate, and the results can therefore be scaled to any spatial or temporal dimension by re-defining the cell-size and iteration duration. Incorporating the eco-geomorphic interactions, however, introduces a second independent linkage via the growth response, thus fixing the relation between spatial and temporal domain, and a resultant morphology that is fundamentally controlled by the biotic component. Unlike the absence of a ‘topographic signature of life’ in the context of hill slope erosion suggested by Dietrich and Perron [2006] and the typically fractal-like (hence scale-less) nature of other geomorphic features such as coast lines and river networks [Tarboton et al., 1988], we propose that for aeolian landforms the influence of vegetation, i.e. life, may reveal itself in a characteristic size-range that is fundamentally related to the biological limits of physiological and photosynthetic potential. Such characteristic scaling may be confined largely to aeolian environments, where abiotic geomorphic processes and biological dynamics have comparable strengths, but it may also be evident in other Earth surface systems with substantial life components.

Figure 4.

(a) (left) Simulated nebkha field developed out of flat surface under the influence of mesquite-type vegetation, showing classic aerodynamic tails. Density and size of red sticks indicate levels of vegetation effectiveness. Sediment transport direction from upper-left to lower-right of view. Grid resolution = 1.0 m, other parameters as for Figure 2. (bottom right) Photograph of nebkhas on Agate Beach near Luderitz, Namibia, reproduced with kind permission of Heather Viles. (b) Plan views of resulting morphologies after simulating the same physical conditions while changing only the cell-size (indicated in upper left-hand corner of each map). Total size of model space is kept constant at 100 × 100 m2 for all simulations.

6. Conclusion

[12] The DECAL model is capable of simulating realistic dune development under the influence of multiple vegetation species using only simple local rules in a self-organising cellular automaton algorithm. The resulting phase diagram of vegetated dune types as a function of plant vitality can be used to quantify and predict changes in (fossilized) aeolian landscape dynamics as influenced by global warming, anthropogenic disturbance and other impacts on vegetation growth behavior and its response to sedimentation conditions. The model shows how the linkage between abiotic geomorphic processes and biological elements results in a characteristic length-scale that breaks the typical self-similar scaling of bare-sand dunes. The principles of numerical landscape state variables and their use in cluster analysis & PCA in this study may provide a general template for quantifying many other eco-geomorphic systems on the Earth's surface.

Acknowledgments

[13] The research and development of the DECAL model is made possible by the UK Natural Environment Research Council (NE/D521314/1). We thank Patrick Hesp and Heather Viles for their kind permission to use their photographs of parabolic dunes and nebkhas. We are grateful for the constructive comments and suggestions from two anonymous reviewers.

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