Land–sea interaction and morphogenesis of coastal foredunes — A modeling case study from the southern Baltic Sea coast

Coastal Engineering 99 (2015) 148–166

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Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng

Land–sea interaction and morphogenesis of coastal foredunes — A modeling case study from the southern Baltic Sea coast Wenyan Zhang a,⁎, Ralf Schneider b, Jakob Kolb b, Tim Teichmann b, Joanna Dudzinska-Nowak c, Jan Harff c, Till J.J. Hanebuth a a b c

MARUM — Center for Marine Environmental Sciences, University of Bremen, Leobener Str. 1, 28359 Bremen, Germany Institute of Physics, Ernst-Moritz-Arndt-University of Greifswald, Felix-Hausdorff-Str. 6, 17489 Greifswald, Germany Institute of Marine and Coastal Sciences, University of Szczecin, Mickiewicza 18, 70-383 Szczecin, Poland

a r t i c l e

i n f o

Article history: Received 8 November 2014 Received in revised form 13 March 2015 Accepted 16 March 2015 Available online 28 March 2015 Keywords: Coastal dunes Aeolian transport Cellular automata Extreme wind event Vegetation

a b s t r a c t Coastal foredunes are developed as a result of the interplay of multi-scale land–sea processes. Basic driving mechanisms of coastal foredune morphogenesis as well as natural processes and factors involved in shaping the foredune geometry are quantitatively studied in this paper by a numerical model. Aeolian sediment transport and vegetation growth on the subaerial part of a beach is simulated by a cellular automata (CA) approach, while the sediment budget in the subaqueous zone, serving as a sediment source/sink for the foredune ridges, is estimated in a process-based model. The coupled model is applied to a 1 km-long section of a barrier coast (Swina Gate) in the southern Baltic Sea for a 61-year (1951–2012) hindcast of its foredune development. General consistency is shown between the observational data and simulation results, indicating that the formation of an established coastal foredune results from a balance between wind-wave impacts and vegetation growth. Driven by an effective onshore wind and a boundary sediment supply, small-scale dunes develop on the backshore and migrate landward. They are then trapped in a narrow strip characterized by a large density gradient of vegetation cover which separates the hydrodynamically-active zone and the vegetated zone. Continuous accumulation of sediment in this strip induces the development of a foredune ridge. According to the simulations, the formation of an established coastal foredune has to meet three preconditions: 1. an effective onshore aeolian transport; 2. a net onshore or lateral sediment supply; and 3. a climate favoring vegetation growth. The formation of a new foredune ridge in front of an already existing foredune is determined by a combination of the sediment supply rate, the extreme wind-wave event frequency and the vegetation growth rate. Simulation results demonstrate a remarkable variability in foredune development even along a small (1 km) coast section, implying that the medium-to-long term land–sea interaction and foredune morphogenesis is quite sensitive to boundary conditions and various processes acting on multi-temporal and spatial scales. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Dunes are a common morphological feature in many coastal and arid environments. The basic factors involved in the formation of a dune are a certain amount of movable sediment on the surface, a flow (of e.g., water or air) acting on the bed surface which is strong enough to transport the sediment and an obstacle or perturbation which triggers a settling of the moving sediment. However, although the mechanism for the formation of a dune is clear, combinations of different flow strength and directions, sediment properties (e.g., grain size and composition), constraints of local topography and boundary conditions (e.g., source supply) can lead to quite different and complex dune patterns (Werner, 1999; Kocurek and Ewing, 2005). The interplay among aeolian transport, vegetation cover and hydrodynamic forces ⁎ Corresponding author. Tel.: +49 421 218 65642. E-mail address: [email protected] (W. Zhang).

http://dx.doi.org/10.1016/j.coastaleng.2015.03.005 0378-3839/© 2015 Elsevier B.V. All rights reserved.

(e.g., storms) makes the morphological development of coastal dunes even more variable compared to dunes in an arid environment (e.g., desert) and imposes challenges to researchers for a comprehensive study of the dune morphogenesis (Hesp, 2002). Among various dune patterns developed at the backshore, foredunes are most vulnerable as they stand at the foremost seaward line on the edge of the backshore, persistently reshaped by hydrodynamic and aerodynamic forces. Foredunes are able to develop where winds are effective in moving sediment onshore and a trapping of the moving sediment by a line of shore-parallel obstacles exists. This trapping of sediment is usually caused by vegetation (e.g., pioneer grasses and shrubs). Foredunes can range from relatively flat terraces to markedly convex ridges (Hesp, 2002) due to a variation of the driving wind spectrum, the sediment supply, the vegetation coverage and the growth rate. On a longer time scale their morphology is affected by climate change such like sea level oscillations (Tamura, 2012). Morphological development of a coastal foredune can be generally divided into three phases: incipient (or

W. Zhang et al. / Coastal Engineering 99 (2015) 148–166

embryo) period, established period, and relict period (Hesp, 2002). However, as there are many environmental factors (e.g., wind strength and direction, storm frequency, beach width and migration, vegetation growth, sea level change) involved in the evolution of foredunes, some natural coastal foredunes may not go through all these three phases. For example, the foredune plains developed on a barrier coast (Swina Gate) at the southern Baltic Sea (as shown in Fig. 1) are characterized by well-preserved established sequences with a relatively stable accretion rate during the last several millenniums (Reimann et al., 2011). Foredune dynamics is investigated usually within a framework of beach–dune interaction (e.g., Psuty, 1988; Hesp, 2002; Saye et al., 2005; Ollerhead et al., 2012). Cycles of sediment exchange between the foredune system and the beach, and between the beach and the nearshore submarine zone are recognized in this framework, within which processes involved in the beach–dune interaction and foredune evolution are studied at a range of spatial and temporal scales. On a short-term scale characterized by a temporal scale of seconds to days and a spatial scale of tens of meters, considerable efforts and progress have been made by field experiment (e.g., Hesp, 1983; Arens, 1994; Davidson-Arnott et al., 2005; Bauer et al., 2009) and modeling (e.g., Kriebel and Dean, 1985; Arens et al., 1995; Bauer and Davidson-Arnott, 2003; Jackson et al., 2011) to improve the knowledge about mechanisms that control the morphological development of coastal dunes. For the medium-term (temporal scale of months to decades and spatial scale of hundreds to thousands of meters)

149

and long-term (temporal scale of centuries to millennia and spatial scale of kilometers to tens of kilometers) morphological evolution of coastal dune fields most of the existing studies are conceptual and descriptive (e.g., Hesp, 1988, 2002; Sherman and Bauer, 1993; Orford et al., 2000; Aagaard et al., 2007; Anthony et al., 2010; Reimann et al., 2011; Ollerhead et al., 2012; Tamura, 2012; de Vries et al., 2012). Only recently numerical modeling became a tool for investigation of medium-to-long term coastal dune morphogenesis (e.g., Baas, 2002; Nield and Baas, 2008; Luna et al., 2011). Morphogenesis of some coastal dune types such as parabolic, nebkha and transgressive dunes has been studied numerically. However, there seems to be still a lack of a numerical model which is able to simulate a complete morphogenesis and evolution of coastal foredunes and foredune sequences on a medium-to-long term, probably due to the multi-scale characteristics of the physical and biological processes acting on a beach system and technical challenges in accurately describing the morphological response of the system to these processes. In fact, although a coastal system is composed of two parts, i.e., subaqueous and subaerial, little effort has been done to combine these two parts into one integrated numerical model. Existing modeling studies on medium-to-long term coastal morphological evolution may underestimate the contribution of the subaerial coastal part to the whole system, especially the role of fordunes played in the transition between land and sea (Zhang et al., 2012). Thus, the main target of this

Fig. 1. The Swina Gate barrier (southern Baltic Sea) with its well-preserved foredune sequences (modified from Łabuz, 2005). The foredune ridges developed since 1951 in a 1 km-long section of this system are marked by white lines in the upper panel.

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study is to develop an integral model that is able to resolve the morphogenesis of coastal dune fields (especially the foredunes) on a medium-tolong term scale and on the other hand provide a reasonable estimate of the sediment budget for the subaqueous zone of the beach system. The rest of the paper is organized as follows. After a brief explanation of the modeling principles on medium-to-long term coastal dune morphogenesis, details of a cellular automata approach for resolving subaerial processes, a process-based model for calculating alongshore and cross-shore subaqueous sediment budget and the coupling of these two models are described in Section 2. Application of this integrated model to a 1 km-long coastal section in the southern Baltic Sea is presented in Section 3. Discussion of the model with respect to its potentials as well as its shortcomings is given in Section 4, followed by conclusions in Section 5. 2. The model Numerical models for aeolian sediment transport fall into two categories: (1) conventional models based on the approximation of Navier– Stokes equations to solve the aerodynamics and the resulting sediment transport on the dune surface (e.g., Jackson and Hunt, 1975; Weng et al., 1991; Van Boxel et al., 1999; Van Dijk et al., 1999; Herrmann et al., 2005; Luna et al., 2011); and (2) probabilistic models such as cellular automata (e.g., Werner, 1995; Baas, 2002; Zhang et al., 2010). Although the first category of models is able to resolve the detailed flow structure over a dune surface, their application to medium-to-long term coastal dune morphogenesis is severely hindered not only because they are computationally too expensive, but also due to the fact that the processes involved in a medium-to-long term coastal dune development and their synergistic behaviors remain less well understood. Improving the mathematical description of individual processes does not guarantee to improve the overall simulation result (Delgado-Fernandez, 2011). Cellular automata (CA) models have shown their capabilities in reproducing almost all types of dune patterns with a high computational efficiency (e.g., Werner, 1995; Baas, 2002; Bishop et al., 2002; Nield and Baas, 2008; Zhang et al., 2010; Fonstad, 2013). They are especially suitable to model self-organization in a natural system. Therefore, a cellular automata approach is chosen in our study to develop the subaerial model. Morphogenesis of a natural coastal foredune is influenced by many processes and environmental factors (Hesp, 2002). It is a major challenge to modelers to identify the hierarchy of different processes needed for a realistic description. Thus, instead of incorporating all relevant factors which may vary considerably due to environmental changes, only some elements which are regarded to be critical for coastal dune morphogenesis are considered in the model construction. The following principles are followed in the development of the integral model in this work: (1) The model should be computationally efficient for a medium-tolong term simulation, and on the other hand able to produce high-resolution (both temporally and spatially) details on the morphological development of coastal foredunes; (2) Winds, wave swash/backwash, storms, sediment supply and vegetation are assumed as the key factors controlling the medium-to-long term morphogenesis of coastal foredunes; (3) The aeolian transport module should be able to apply a variable wind spectrum (i.e., with time-varying speeds and directions) as the driving force; (4) The effect of vegetation on the dune morphogenesis is described by representative growth functions, which reflect the growth status and corresponding impact on local aeolian transport.

2.1. The cellular automata model Conceptually the construction of our CA model follows the framework of Werner (1995), who successfully predicted aeolian dune

morphologies in a bare-sand environment based on simple rules governing the motion of sediment. In order to fulfill the modeling principles, an extension of the ‘rules’ which govern the transition of the cell states are introduced in our model. Besides an application of more complex rules described in the following sections, a major difference between our model and a conventional CA model is that both the temporal and spatial scales (e.g., time step, cell size and number of movable slabs) are pre-defined in a physical manner in order to resolve a complete morphogenesis of coastal foredunes. The iteration time step is determined by the corresponding transport processes and refers to field measurements (details are given in the following sections). In a conventional CA model (e.g., Werner, 1995) these scales are usually set arbitrarily. A general flowchart of the complete model is described in Fig. 2. In the initialization phase the model requires the specification of initial conditions: morphology (i.e., digital elevation), vegetation cover (types & distribution) and bed properties (sediment grain size & erodible thickness). These spatial distributions are then mapped onto a grid of square cells, which represent the model domain. The model domain comprises two parts, i.e., the subaerial and subaqueous zone. At the beginning of each time-step iteration the operation of the CA and the subaqueous model are separated by a land–sea boundary that is determined by the wave run-up height. With a predefined uniform cell size of 0.5 m × 0.5 m, the rules governing the transition of the subaerial cell states are described in the following sections. 2.1.1. Aeolian erosion Due to the wind shear stress a certain volume of sediment above every erodible cell is dragged into the air at every time step. In the simulation, a base erosion height E0, which represents the eroded height on a bare-sand cell of a flat surface, is introduced at every time step. E0 cannot be specified directly as it is related to the time step and sediment properties (grain size, porosity and moisture). By definition of a characteristic transport length L0 (L0 ≥ a cell width) which indicates the travel distance of E0 on a flat bare-sand surface during one time step, a relationship between these quantities holds: q¼

E 0 L0 I

ð1Þ

where q is the transport flux (in a unit of m3m−1 day−1) and I is the time step (in a unit of day) implemented in the CA model. The choice of one day as the time step unit is due to two considerations: firstly, the time span of a storm or wind event (i.e., within a narrow band of spectrum regarding the distribution of speed and direction) is usually characterized by days; and secondly, the transport of E0 is conceptually linked to the migration of ripples which can be resolved on the grid cells, rather than an analogy with saltation trajectories. By an analysis of the ripple celerity and associated volumetric transport flux over a realistic range of shear velocities, Nield and Baas (2008) suggests a minimum value of 0.077 l (l represents the cell width) and a maximum value of 0.13 l for the height of transport slabs per iteration. In our model these values correspond to 0.038 m and 0.065 m, respectively. In a prograding coastal foredune environment dominated by moderate wind-wave climate with a typical onshore sediment transport rate ranging between 5 and 10 m3m−1 a−1 (e.g., Arens, 1997; Christiansen and Davidson-Arnott, 2004; Delgado-Fernandez, 2011; Ollerhead et al., 2012; Keijsers et al., 2012), the corresponding daily-average transport flux (q) is between 0.014 and 0.028 m3m−1. As the minimum transport length L0 is a cell width (0.5 m in the model) during an iteration, a combination of L0 = 0.5 m, E0 = 0.038 m and q = 0.014 m3m−1 day−1 yields a value of 1.4 days for I in Eq. (1). This defines the minimum effective transport parameters in our model. However, during an extreme event like storm, the transport rate can be several orders of magnitude higher than normal conditions. Therefore, a time step of 0.25 day is used for storm conditions. With a pre-defined time step of 1.4 and 0.25 day for

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151

Fig. 2. Flowchart of the integrated model.

calm and stormy weather conditions respectively and constraints of E0, our next step is to obtain a possible range of q and L0 based on an estimation of natural wind conditions. The Bagnold equation (Bagnold, 1954) is used to estimate the critical shear velocity of sand motion U⁎,t: U ;t

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ρs −ρa ¼A gD ρa

ð2Þ

where ρs = 2650 kg/m3 is the density of sands and ρa = 1.225 kg/m3 is the air density. D is the medium grain size of the sand particles and A is an empirical coefficient of about 0.1 to 0.118 for D larger than 0.1 mm. Substituting D = 0.2 mm and A = 0.118 in Eq. (2) yields a value of ~0.24 m/s for U⁎,t. This critical shear velocity corresponds to a wind velocity of ~7 m/s at 10 m above the sand surface (U10) according to the well known logarithmic profile described by: U 10 ¼

U 10 ln z0 κ

ð3Þ

where U⁎ is the wind shear velocity at the bed surface, κ = 0.41 is the von Karman's constant and z0 is the aerodynamic roughness height which is typically between 10−5 and 10−2 m. A widely-used parameterization z0 = D/30 is assumed in the calculation.

A value of 0.014 m3m−1 day−1 for q corresponds to the transport rate induced by a wind velocity U10 = ~ 7.14 m/s persistently blowing on a flat bare-sand surface according to the formula given by Kawamura (1964): q ¼ Ck

 2 ρa  U  −U ;t U  þ U ;t ρs g

ð4Þ

where Ck is called the Kawamura constant with a reference value of 2.78. However, due to the influence of limited onshore wind fetch, moisture, vegetation and bed geometry, the onshore sediment transport rate at a natural beach is normally below the equilibrium saturated level calculated from the widely-used equations above. The effect of bed geometry and vegetation on the aeolian transport is explicitly included in the model and will be described later in this section and Section 2.1.4, respectively. The influence of wind fetch is estimated by a saturation length ls, which is the characteristic length-scale over which the sediment transport flux adapts to the wind forcing and reaches to the saturated level. An accurate quantification of ls is still missing. Laboratory experiments show that the fetch distances are only a few meters for dry sands (e.g., Dong et al., 2004), while some field studies indicate that such fetch distances are usually some tens of meters and can be particularly large on beaches with surface moisture contents above 4% (e.g., Gillette et al., 1996; Davidson-Arnott et al., 2005). Hersen (2005) found that ls varies with the inertia length ldrag (~ 0.5 m for D = 0.2 mm), which represents a typical length needed

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for a sand grain to reach the velocity of a turbulent flow. Dunes can develop only when a sand pile is longer than a few times ldrag. Based on Hersen's study we use ls = 20ldrag in the model to define the fetch limit. A linear increasing trend on the erosion height from 0 m at the waterline to a saturated value defined by E0 is used on the downwind dry cells within a distance of ls from the waterline to reflect the wind fetch effect. In order to simplify the wind driving force due to a temporal constraint imposed by the predefined computational time steps (i.e., 1.4 and 0.25 day) and incorporate a moisture effect the wind inputs are categorized by six transport modes (Table 1). The latter four (i.e., mild1,2, medium and strong) in Table 1 are described as effective transport modes. Simulation results by these transport modes are illustrated in Fig. 3. Well ordered transverse dunes are formed by the mild transport (note that the two mild transport modes produce the same results), while barchan dunes are developed by the medium transport. The strong transport erodes completely the sand layer and does not allow development of any dune patterns. Real weather time series are classified into the six transport modes in our CA model. On a bed surface with irregular geometry, wind shear stress is strengthened upslope and weakened downslope. In order to implement this impact on the aeolian erosion a formulation suggested by Nishimori and Ouchi (1993) is adopted: E ¼ E0 f1 þ b tanh½∇u hði; jÞg

ð5Þ

where E is the modified erosion height and b is an empirical constant representing the change of the shear stress according to the slope of the surface. ∇uh(i, j) is the bed surface slope in wind direction on the considered cell. It is determined by measuring the height difference between the two adjacent cells in wind direction and dividing it by twice the cell size. From parameter studies by Teichmann (2010) the most realistic results were derived by b = 0.9. Furthermore it is assumed that in a certain zone (characterized by a back-flow eddy) on the leeward side of the dune with an angle of 15° from the dune crest the shear stress decreases drastically (Frank and Kocurek, 1996), so that no erosion occurs and the deposition probability is unity at any site within this shadow zone. 2.1.2. Aeolian transport After the sediment is eroded from the cell it is blown downwind. The transport process starts with an initial characteristic length L0 that is gradually decreased as the sediment travels on the grid. Analogous to the base erosion height E0, L0 represents the aeolian transport strength in an ideal setting. This does not mean that the eroded sediment will travel exactly the length of L0 on the grid during each time step as several factors (vegetation, bed geometry and wind direction) can impose significant impacts on the aeolian transport path. In the model, the cell to which the sediment will move next is determined probabilistically. Taking the polled cell (i, j) and a wind direction with an angle α (0° ≤ α ≤ 45°) relative to the x axis for example, the probabilities for the two downwind adjacent cells that the eroded sediment will move to are given by pi; j→i; jþ1 ¼ tanðα Þ=2 pi; j→iþ1; j ¼ 1− tanðα Þ=2:

ð6Þ

Here the sediment is allowed to travel only along the x and y axes. The probability that the sediment travels to the corner cell (i + 1,

j + 1) thus equals to pi, j → i,j + 1. pi, j + 1 → i + 1, j + 1 + pi, j → i + 1, j. pi + 1, j → i + 1, j + 1 = tan α(1 − 0.5 tan α). However, the travel distance in this case is larger than in reality as the sediment has to pass through either cell (i, j + 1) or cell (i + 1, j) to reach cell (i + 1, j + 1), rather than a direct transport from cell (i, j) to cell (i + 1, j + 1). To compensate this extra cost in travel distance in the case of an oblique wind direction, the characteristic transport length is modified by: 0

L0 ¼

L0 cosα

ð7Þ

where L'0 is the modified transport length for an oblique wind direction. pffiffiffi 0 A maximum increase of L0 (L0 ¼ 2L0 ) is achieved when α = 45°. Note that 0° ≤ α ≤ 45° is assumed for this example. For other ranges of wind incoming angle the transport is treated in a similar way. When the sediment moves to the next cell, L0 is decreased by a certain length L−. The value of L− depends on a combination of the traveled ! distance (i.e., a cell width l) and the slope of the traveled path ∇ hði; jÞ: n h! io 0 L− ¼ l 1−b tanh ∇ hði; jÞ L1 ¼ L0 −L−

ð8Þ

b′ is an empirical constant representing the change of the shear stress according to the slope of the surface. Eq. (8) implies that an increase of shear stress on the stoss side of a dune results in an increased transport length and a decrease of shear stress on the lee side results in a decreased transport length. b′ = 1 is found to best fit the model based on parameter studies (Teichmann, 2010). If L1 ≤ 0 the amount of sediment is dropped on the current cell, otherwise a probability of deposition pd is calculated based on the vegetation cover of the current cell (see Section 2.1.4 for details). A random number Rn (0 ≤ Rn ≤ 1) is then generated and compared with pd. In case of Rn ≤ pd the sediment is deposited on the cell mimicking a hindering effect on aeolian transport by vegetation, otherwise it is moved again to the next cell according to Eqs. (6) and (8). This process is repeated until either Li drops below zero or Rn ≤ pd is met. This transport scheme has been proven by our tests to be effective and efficient in capturing the dune patterns driven by different wind directions. 2.1.3. Avalanche In each polling of a cell, the avalanche threshold is checked twice: after the erosion of the polled cell and after the deposition on the destination cell. The avalanche threshold is reached whenever the local slope exceeds a critical angle of repose of the sands, i.e., 34°. Once an avalanche occurs, the sediment starts to move in the direction of the steepest slope. The amount of sands (Δh) moving from the top to the bottom cell is given by: Δh ¼

ht −hb −d tan β 2

ð9Þ

where ht and hb are the elevations of the top and the bottom cell, respectively. d is the distance between the two cell centers. β = 30∘ is the angle that the dune becomes stable after the avalanche. After the movement of the sands the model checks whether there will be more avalanches

Table 1 Model settings of the environmental conditions (i.e., modes) and corresponding aeolian transport parameters. Mode

Iteration-average onshore wind velocity (U10)

Moisture condition (precipitation: mm/day)

q (m3m−1 day−1)

E0 (m/iteration)

L0 (m/iteration)

Non-transport1 Non-transport2 Mild transport1 Mild transport2 Medium transport Strong transport

b7 m/s 7–35 m/s 7–35 m/s 7–10 m/s 10–14 m/s N14 m/s

0–100 N10 N2 & b10 b2 b2 b2

0 0 0.014 0.014 0.055 0.78

0 0 0.038 0.038 0.05 0.065

0 0 0.5 0.5 1.5 3

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Fig. 3. Dune patterns simulated by different transport modes after 1000 iterations on a grid of 600 × 600 cells. Transport is unidirectional, from left to right with a constant boundary sediment supply of 0.8E0. A: initial morphology: an erodible sand layer (0.35 m thick) with small random perturbations on the surface; B: result of the mild transport; C: result of the medium transport; and D: result of the strong transport.

triggered by the changes of elevation of these two cells. In our case study the critical angle of sand repose for triggering an avalanche is assumed to be constant in the subaerial area (i.e., not affected by vegetation). 2.1.4. Vegetation In reality vegetation plays a critical role in the development of dune patterns (Hesp, 2002) at a coast. In our model the effect of vegetation on aeolian transport is introduced in two quantities: the erosion height E and the depositional probability pd for each vegetated cell. A parameter named ‘vegetation effectiveness’, ρ, is introduced following Nield and Baas (2008). This parameter stands for a measure of the ability of vegetation to affect the local aeolian transport. On each dry cell the exact erosion height and the probability of deposition are given by: 8 if ρ≤0; < E; 0 E ¼ Eð1−ρÞ; if 0 b ρ≤1; : 0; if ρ N 1; 8 < 0; if ρ≤0; pd ¼ ρ; if 0 b ρ≤1; : 1; if ρ N 1:

ð10Þ

where E is the erosion height defined in Eq. (5). The value of ρ is determined by the status of vegetation cover of the cell. In a mathematical scheme the change of ρ is described by the sum of the so-called ‘growth functions’ of the dominant vegetation types at the coast (Nield and Baas, 2008). An example of a detailed parameterization of ρ will be shown in our test case presented in Section 3.2.

2.2. The subaqueous model The subaqueous model is used to define the time-varying boundary between land (i.e., the CA domain) and sea (i.e., the subaqueous domain) and provide an updated morphology of the foreshore at each computational time step. Considering that the model aims at mediumto-long term coastal morphogenesis with relatively large computational time steps (i.e., 1.4 and 0.25 days), it seems appropriate to adopt a subaqueous sediment transport model working on corresponding temporal scales. This triggers our motivation to adopt an energy-dissipation type model formulation which is proven suitable for medium- to long-term beach profile development (Larson and Kraus, 1995).

2.2.1. Land–sea boundary and alongshore sediment transport A self-developed 1-dimensional vertical (1DV) model (Zhang et al., 2013) is used to derive the land–sea boundary (i.e., the maximum wave run-up point) and alongshore sediment transport rate at each time step. Based on the offshore water level, wave parameters and a high-resolution cross-shore beach profile the 1DV model provides an estimate of the first wave breaking height and corresponding water depth. Starting from the first wave breaking point and assuming alongshore uniformity (i.e., the nearshore bathymetric isobaths are parallel to the shoreline) the 1DV model approximates the shoreward water level variation and wave propagation processes by resolving a momentum balance equation (Eq. (2.2.3) in Zhang et al. (2013)) and a wave surfaceroller energy dissipation equation (Eq. (2.2.10) in Zhang et al. (2013)) along the profile. The alongshore sediment transport rate for each profile results from multiplying the vertically- and time-averaged values of the alongshore current velocity and the sediment concentration. It should be

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noted that the original 1DV model does not include a calculation of the wave run-up zone and the offshore pre-breaking zone. For an estimation of the wave run-up limit Ru2 % (above the offshore water level driven by tides and regional winds) an empirical relation from Battjes (1974) is used: m Ru2% ¼ CH 1=3 ξ where ξ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H 1=3 =L1=3

ð11Þ

where H1/3 and L1/3 are offshore deepwater significant wave height and length, respectively, m is the slope of the foreshore and C is an empirical coefficient with a reference value of 0.9 proposed by Ruggiero et al. (2001). In the wave run-up zone the alongshore sediment transport rate is assumed to be zero, while in the pre-breaking zone an external alongshore current velocity (see Eq. (2.2.8) in Zhang et al. (2013)) is used to estimate the alongshore sediment transport rate. 2.2.2. Cross-shore sediment transport and beach profile change With the predicted wave propagation parameters provided by the 1DV model, the cross-shore net sediment transport rate along the coastal profile is calculated based on the formulas given by Larson and Kraus (1989). The reason for adopting Larson and Kraus's formulation is that their model (SBEACH) has proven to be robust for mesoto macro-scale beach profile development through applications to both large wave tank and field cases (e.g., Schoonees and Theron, 1995; Zheng and Dean, 1997; Carley, 2001; Donnelly et al., 2006). Among assumptions and empirical relationships derived from large wave tank experiments, two are fundamental in the cross-shore sediment transport according to Larson and Kraus (1989) as explained below: (1) There exists an equilibrium shape which a beach profile in the surf zone will evolve towards if exposed to constant wave conditions for a sufficiently long period. This equilibrium status corresponds to an effective dissipation of incident wave energy without causing net sediment transport at any location of the profile: 3=2

x ¼ ðh=AÞ

þ

h m

ð12Þ

where h is still water depth, x is distance from the shoreline (i.e., the still waterline), A is an empirical shape coefficient related to the sand grain size and wave properties. The latter term on the right hand side of Eq. (12) indicates a planar zone (i.e., the foreshore) close to the shoreline that is characterized by a constant slope m. Seaward of this zone the water depth is gradually dominated by the 2/3 power law proposed by Dean (1977). Corresponding to the equilibrium profile shape is an equilibrium wave energy dissipation term Deq suggested by Dean (1977): Deq ¼

5 3=2 2 3=2 ρ g γ A 24 w

ð13Þ

where ρw is the water density and γ is the ratio between wave height and water depth at breaking (calculated by Eq. (2.1.4) in Zhang et al. (2013)). Larson and Kraus (1989) suggested a 75% of the value given by Eq. (13) to be used in Eq. (12) and calculation of the cross-shore sediment transport rate; (2) Accretion and erosion of a beach profile is distinguished by an empirical criteria (i.e., Eq. (2) in Larson and Kraus (1989)):  3 H0 H0 ¼M L0 wT

ð14Þ

where H0, and L0 are offshore deepwater mean wave height and wave length, respectively. T is the mean wave period and w is the sand settling velocity. M (=0.0007 in Larson and Kraus (1989)) is an empirical constant that has been questioned by some other researchers (e.g., Thieler et al., 2000). In our study M serves as a calibration parameter to ensure a calculated sediment budget close to observation. Berms will develop in an accretionary wave event, while bars are a result in the opposite case. Transport is directed onshore everywhere on the profile in an accretionary case, while offshore in an erosional case. For calculating the net cross-shore sediment transport rate at each time step, Larson and Kraus (1989) divided the profile into four transport zones where different formulas are used. The same procedure and parameters are adopted in our model. A slight modification on the

Fig. 4. (a): Location of the repetitively measured profiles in our model domain (indicated by the frame). Shore-parallel bathymetric contour lines are also shown; (b), (c), and (d): repetitively measured profile shapes from 2005 to 2012 and corresponding best-fit curves for these profiles using Eq. (12). The vertical coordinate indicates elevation (m) relative to the still water level and the horizontal coordinate indicates the seaward distance (m) from the anchor point which remained constant during this 7-year period.

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formulation of bathymetry update after each time step as proposed by Larson et al. (1990) is implemented in our model to include the contribution of the alongshore sediment transport: ∂h ∂q ∂q ð1−pÞ ¼ − cr − lst ∂x ∂y ∂t

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affected part to the non-erodible (consolidated) base level pre-defined in the model.

2.3. Model coupling ð15Þ

where p is the porosity of sediment, qcr and qlst are the net volumetric cross-shore and alongshore sediment transport rates, respectively. The same discretization schemes as used by Larson et al. (1990) (i.e., Eq. 37, 38 & 39 in their publication) are used to solve the transport rates and bathymetrical update. To avoid unrealistic slopes generated at a bar/berm, the avalanche routine as described in Section 2.1.3 is used. The slope threshold of a subaqueous avalanche is 28° and the restoring angle is 18° (Larson and Kraus, 1989). Storm scarp on a foredune ridge is implemented in the model by eliminating the stoss part of the dune that is immersed in water during the storm surge. This is done by a reset of the elevation of the storm-

The coupling between the CA model and the subaqueous model is flexible as only the information of the land-sea boundary and the foreshore morphology is communicated between these two models at each time step (Fig. 2). This enables to parallelize these two models to increase the computational efficiency. The computational time step of the integrated model is specified by the CA model, i.e., 1.4 day (~34 h) for normal wind conditions and 0.25 day (6 h) for storms. However, wind-wave periods are much smaller than this time step and significant bathymetrical changes might be induced already within one time step, thus an internal computational loop with a fixed time step of 1 h is used in the subaqueous model. Within a CA model time step, the estimated maximum wave run-up limit based on external input time series of offshore water level defines the land–sea boundary. The accumulative bathymetrical change calculated by the subaqueous model is used

Fig. 5. Top panel: examples of profile reconstruction for 1951 and foredune sequences developed in three periods derived based on a comparison of geo-referenced aerial photographs and orthoimages (Dudzinska-Nowak, 2006); and middle panel: the fixed anchor points used for profile measurements from 2005 to 2012. The foredune ridge on which these points are located indicates the shoreward boundary of our model domain; and bottom panel: estimated sediment volume change per unit meter along the shoreline in the model domain in three periods.

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to update the foreshore morphology for the CA model to carry out the next time step calculation. 3. Model application and result analysis The integrated model is applied to a 1 km-long section of a barrier coast (Swina Gate, see Fig. 1) in the southern Baltic Sea for a 61-year (1951–2012) hindcast of its foredune development. The reason for choosing this particular coastal section for a numerical study is that: (1) this section represents a naturally accretionary coast characterized by well-preserved established foredune ridges (Fig. 1). It is more than 5 km away from an artificial pier (constructed in the 18th century) at the mouth of the Odra River and beyond a direct impact of this engineering structure according to hydrodynamic and sediment transport modeling results (Zhang et al., 2013); (2) sediment in this coastal section is moderately to well-sorted fine sands with D = 0.22 mm (Zhang et al., 2013), avoiding the need to model different-sized sediment; and (3) a slight variation of external boundary conditions has induced a remarkably different response of the foredune morphogenesis on a medium-term temporal scale along even such a small coastal section, with six foredune ridges developed in the western part and only three in the eastern part from 1951 to 2012. This provides us an excellent example for a study of the sensitivity of foredune morphogenesis to boundary driving conditions. 3.1. Model set-up for the study area The subaqueous 1DV model has been successfully applied to this area already (Zhang et al., 2013), thus corresponding modeling parameters and offshore external boundary conditions (time series of water level, current, wave and sediment transport flux) can be directly used for this study. A surface sediment grain size map indicates that the study area is covered by moderately to well-sorted fine sands with D = 0.22 mm. For this grain size values of 0.098 m1/3 and 0.106 m1/3 are suggested for A in Eq. (12) by Moore (1982) and Dean et al. (2001), respectively. However some researchers (e.g., Pilkey et al., 1993) have questioned the use of a constant A in different seasons. In this study we use three annually repetitively (2005–2012) measured beach profiles (Fig. 4) with a spatial interval of 500 m in this section to obtain an estimation of A. Measurements of these profiles were done mostly in summer between June and August (calm weather),

with an exception for the year 2012 which was done in October (start of rough weather). Details of these profiles are illustrated in Fig. 4b, c, and d. The best-fit curves using least squares suggest an eastwarddecreasing value of A along the coastal section, from 0.125 in profile 1 to 0.118 in profile 3. A linear interpolation of A between these values is used to describe the equilibrium profiles in the blank zone between two adjacent measured profiles. To initiate a model hindcast the historical profiles along this coastal section has to be reconstructed. No detailed bathymetric information exists for 1951 except a georeferenced aerial photograph taken in this year (Dudzinska-Nowak, 2006) which clearly shows a bar along the waterline similar to the recent situation. Thus the Digital Elevation Model (DEM) in 2012, which indicates a similar distance from the shoreward-most bar to the foredune ridge according to a comparison between the geo-referenced aerial photograph in 1951 and an orthoimage from 2012 (DudzinskaNowak, 2006), is used to approximate the initial DEM at 1951 by shifting the cross-shore profiles shoreward according to the distance derived from the comparison (e.g., Fig. 5, Top panel). Relative sea level rise in this 61-year period is ~7 cm and affects only a minor portion of the total sediment budget change in our study area (Deng et al., 2014), thus is not considered in our calculation. A rectangular grid (Fig. 4a), created on a base of airborne laser scanning data form 2012, is used for the model with equally-spaced cells having a resolution of 0.5 m × 0.5 m. The offshore limit of the model domain is at the distal points where the best-fit equilibrium profiles intersect with the measured profiles. These points are located 900 m seaward from the anchor points and in a depth of ~8.4 m along the entire section according to the calculation, which is close to the closure depth (8 m) for the area for a 30 year time span (1980–2010) found by Deng et al. (2014). The shoreward limit of the model domain is at the anchor points (Fig. 5, Middle panel) which are assumed invariable during the simulation period. By the use of the invariable anchor points and closure depth as the onshore and offshore model boundary, respectively, the cross-shore sediment transport budget is conserved within the model domain without net exchange at the boundary. The external source/sink term is introduced only by the alongshore sediment transport at the lateral boundary. A comparison among the geo-referenced aerial photographs for the year 1951 and 1973, and orthoimages from 1996 to 2012 provides us quantitative information on the development of the foredune ridges (Fig. 5, Top panel) and an estimation of sediment budget change for these periods can be derived based on the use of equilibrium profile

Fig. 6. Left panel: parameterization of the vegetation effectiveness ρ in response to the local sedimentation balance, normalized by the size of the physiological range of each vegetation type, respectively. The curves are modified from Nield and Baas (2008); and right panel: parameterization of ρ in response to weather condition, normalized by the size of the physiological range of each vegetation type, respectively. A day is tagged dry if its precipitation is less than 2 mm, otherwise it is tagged wet. The critical values for model calibration are marked by capitals from A to G.

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Fig. 7. Top panel: annually-averaged (2005–2012) net alongshore sediment transport rate calculated by the subaqueous model. Negative value indicates a westward transport direction. The research area is located between point 50.5 and point 51.5. Results for other coastal areas outside the research section are from a regional model in Zhang et al. (2013) with a coarser spatial resolution; and middle and bottom panels: comparison among the initial profile in 2005, measured profile in 2012 and simulated profile in 2012 at two sites, respectively. Location of these profiles is indicated in the embedded map (top panel) and is consistent with that in Fig. 4.

shapes. Results indicate that the first two periods (1951–1973, 1973–1996) are characterized by comparable sediment budget changes. A slightly eastward-decreasing accretionary rate, from 1.2 m/a at the western boundary to 1.04 m/a at the eastern boundary, is detected for these periods. Since 1996 the gradient became remarkably larger, from 3.25 m/a at the western boundary to 1.31 m/a at the eastern boundary. The drastically increased accretionary rate at the western part of the coastal section induces the formation of three foredune ridges in this 16-year period (1996–2012). This information will be combined with our simulation results for a detailed interpretation of

medium-term foredune development resulting from an interplay of multi-scale land–sea processes. 3.2. Model calibration As a first step the integrated model has to be calibrated. This is done by a hindcast of the seaward-most foredune development from 2005 to 2012. Among numerous parameters that may affect the land–sea interaction, two are most critical in our model formulation: the value of M in Eq. (14) and the vegetation effectiveness ρ in Eq. (10). The first

Fig. 8. Left panel: Wind rose for the period 1951–2012 with the zone of seaward transport directions (i.e., ineffective for foredune development in the area) marked by gray color; and right panel: statistics of transport modes used in the CA model.

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parameter determines the fate of the profile (i.e., whether erosional or accretionary) and the latter one controls the location where a foredune ridge can be formed as well as the maximum size it can reach. Thus these two parameters are used to calibrate the model, while other parameters adopt the recommended values from Larson and Kraus (1989) and Zhang et al. (2013). Large amount of computational runs have been carried out to test the model sensitivity to different settings of these two parameters by a prediction of the morphology 2012 based on the initial condition in 2005. Hourly-updated time series of offshore wind-waves, regional wind-driven currents, water level and alongshore sediment transport flux at the boundary provided by a validated regional study by Zhang et al. (2013) serve as inputs for the subaqueous model. Simplified transport modes based on a classification of the weather conditions (i.e., wind and precipitation) are used to force the aeolian transport in the CA model. The sensitivity study indicates that a value of 0.000647 for M in Eq. (14) and a parameterization of ρ given in Fig. 6 produces a waterline (i.e., the still waterline) change closest to the observation in 2012 (Fig. 7), with a Root-Mean Square Error (RMSE) of 5.53 m along the whole section, which is ~37% of the mean value of observed waterline change. In our model two types of vegetation, pioneer grass and woody shrub, are considered according to a field study of the vegetation types found in this area by Łabuz (2005). The model does not aim to provide a precise

mathematical formulation for each plant species existing in this area. Instead, representative growth functions which reflect the general response of these species to the local sedimentation balance, temperature and moisture conditions, are implemented. The parameterization of ρ is modified based on a study by Nield and Baas (2008) and in consistency with the field condition described by Łabuz (2005). The principle of parameterization follows several basic biological facts: An input of fresh sediment (i.e., a net deposition) is required to maintain a growth of the pioneer grass (psammophilous species), while unchanged surface elevation or erosion leads to a decline of the species. The woody shrub is able to tolerate small changes in sedimentation balance, but prefers a less active landscape and declines rapidly when subjected to a significant erosion or deposition. The woody shrub has a smaller peak growth rate but a longer life cycle compared to pioneer grass. In addition to a sedimentation balance, the weather condition also contributes to the development of vegetation. A year is divided into two seasons regarding the temperature condition, with the warm season from April to September and the cold season from October to March, to parameterize ρ. In general, the growth of vegetation is favored in the warm season, with a maximum growth rate during wet weather (daily precipitation N2 mm). On the contrary, a combination of cold season with dry weather (daily precipitation b2 mm) is detrimental to vegetation growth. Fig. 6 shows a detailed quantification of the change of ρ based on the criterions mentioned above. The physiological range is [0, 1] and [−0.5, 1.5] for pioneer grass

Fig. 9. (a): Comparison between the simulated and measured profiles in 2012; and (b) measured and simulated bed elevation change from 1970 to 2012 for the study area.

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and wood shrub, respectively, which represents the plant's ability to grow or decline beyond the limits that affect sand transport. Several critical values (Fig. 6) are determined by sensitivity studies (see supplementary online material) so that the function of ρ illustrated in Fig. 6 yields a development of foredune ridges closest to the observation (Fig. 7), with a RMSE of 0.45 m on the seaward-most foredune ridge height (calculated above the still waterline) along the whole section, which is ~11% of the mean value. A comparison between the measured and the simulated bedelevation change from 2005 to 2012 shows a good agreement between these two datasets (illustrated in Fig. S4 in the Supplementary material), indicating that the model is able to reproduce a morphological change that is consistent with the observation in both subaerial and subaqueous areas. The RMSE of the simulated bed elevation change for the entire study area is 0.18 m, which is ~45% of the mean bed elevation change measured from 2005 to 2012. Particularly worthy of note is a satisfactory model performance at the land–sea boundary. A new berm developed at ~ 4 m seaward of the pre-existing one, marking a prograded land–sea boundary from which the rate of coastal accretion can be quantified. The pre-existing berm was smoothed mainly by the aeolian transport and served as an important sediment source for the foredune development. A comparison of the initial profile in 2005, the measured profile in 2012 and the simulated profile in 2012 (with examples shown in Fig. 7) indicates that a major part (N 60%) of the sediment budget which supports the coastal accretion in the model domain originates from alongshore sediment transport. The gradient of net alongshore

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sediment transport flux at two lateral boundaries of the model domain shows a net gain of sediment volume of ~28,000 m3 in the model domain per year from 2005 to 2012. It is worth to note that a large annual variability (by one order of magnitude) exists in the change of sediment budget in the area (e.g., Zhang et al., 2013), though a general positive trend in the shoreline accretion is clear. 3.3. Model hindcast from 1951 to 2012 and result analysis Based on the reconstructed coastal morphology in 1951 and boundary conditions taken from time series, the integrated model is used to hindcast the morphological evolution of the research area from 1951 to 2012. A regional alongshore sediment transport model as described in Zhang et al. (2013), is applied based on a fixed coastal bathymetry to estimate boundary inputs for the research area. Existing foredune sequences in 1951 are assumed to be covered initially by a vegetation effectiveness ρ = 1.6, meaning that it is impossible to erode sediment from these areas by aeolian force. This vegetation cover is limited to the base of the seaward-most foredune with an elevation of 2 m above the still water level. A high-resolution historical wind and precipitation time series is used to specify the transport modes defined previously. This hourly time series results from a hindcast in which a regional atmosphere model is driven with the NOAA National Center for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) global re-analysis in combination with spectral nudging. A comparison with the limited number of available observational

Fig. 10. Simulated morphological evolution of the research area between 1970 and 1975. The green dashed line marks the pre-existing foredune ridge which remains unchanged during the simulation.

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data shows the good quality of the model data. For a detailed description of the atmosphere model and its validation the reader is referred to Weisse et al. (2009). The wind climate and transport modes for this period are summarized in Fig. 8. According to the statistics, 53% of the whole wind spectrum is directed onshore favoring a development of foredunes. Among these onshore winds, 69% is effective for aeolian transport with a speed above 7 m/s. The distribution of transport modes shows a notable seasonal difference, with a major part (~63%) of effective transports in cold season. The strong transport modes, which usually reflect extreme wind events, are restricted to the cold season. Excluding a minor influence by foreshore slope on the aeolian transport rate in the estimate, the distribution of transport modes corresponds to a multiyear-averaged onshore transport rate of ~ 3.75 m3m− 1 a− 1 (with a seasonal rate of 6.38 m3m− 1 a− 1 and 1.12 m3m−1 a−1 in cold and warm seasons, respectively). A comparison between measured and simulated coastal profiles in 2012 is shown in Fig. 9a. Four and three established foredune ridges are developed in the western and eastern part of the research area, respectively. The RMSE of simulated subaerial elevation at profiles 1 and 3 is 0.89 m and 0.51 m respectively, which is equivalent to ~ 22% and ~13% of the mean subaerial elevation change from 1951 (reconstructed) to 2012 at these two profiles. For a better comparison of morphological change of the entire study area between the measured data and simulated result the bed-elevation change from 1970 to 2012 from these

two datasets are plotted in Fig. 9b. The RMSE of the simulated bed elevation change for the entire study area is 0.83 m, equivalent to ~ 28% of the mean bed elevation change measured from 1970 to 2012. Simulated evolution of the research area in several different periods is shown from Figs. 10 to 15. The simulated morphology of the entire area until 2012 and measured DEM for the same year are shown in Fig. 14c and d, respectively. Although discrepancies are shown between the simulated and real morphology (Fig. 9; Fig. 14c, d), the model has successfully captured the morphogenesis of three major foredune ridges in the eastern part and an additional foredune ridge in the western part of the research area. The simulated subaqueous change (e.g., seaward migration of the bar) also shows agreement with the observation. This provides us a good argument to believe that the simulation results are reliable enough to analyze them further and derive a reasonable procedure of the coastal foredune morphogenesis in the area. These results will be used in the following to interpret a mediumterm foredune development resulting from an interplay of multi-scale land–sea processes in the southern Baltic Sea. As the upper part of a beach is continuously fed by sediment, a narrow belt (e.g., Figs. 11c and 15a), which is oriented along the shoreline and distinguished by a drastic gradient in the vegetation effectiveness at ρ = ~ 0.7 in the cross-shore direction, appears during a competing process among the aeolian transport, storm wave erosion and vegetation cover. Exact location of this belt is controlled mainly by two

Fig. 11. Simulated total vegetation effectiveness (pioneer grass + woody shrub) of the research area between 1970 and 1975.

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Fig. 12. Simulated morphological evolution of the research area between 1985 and 1996. The green dashed line marks the pre-existing foredune ridge which remains unchanged during the simulation.

parameters: vegetation growth rate and storm wave impact level. The belt is located above a certain height (~ 1.85 m) from the still water level, which is determined by the maximum storm wave impact level in a certain period around 3 to 5 years. Seaward of the belt is a hydrodynamically-active zone where vegetation struggles to survive. Relatively high sediment transport flux also hinders a growth of vegetation in this zone. Grasses appear sparsely (ρ b 0.4) in this zone with a distance of some meters from the belt, however their growth is quite unstable and may vanish in a short period. Simulation results (Figs. 10, 12, 14) indicate that small-scale embryo dunes exist in this zone, mostly with a SW–NE orientation driven by the dominant W–NW winds. These small-scale transverse-to-barchan shape dunes, with a typical height of ~0.3 m, are mostly bare-sand with only exceptions close to the narrow belt where grasses appear sparsely. These incipient dunes developed in the backshore are very fragile and vulnerable to hydrodynamic impacts during high water level events (e.g., storms). They have a relatively high migrating speed which may exceed 40 m in a cold season characterized by strong westerly winds, and serve as an important sediment source for foredune development. Landward of the narrow belt is a zone where vegetation controls the aeolian sediment transport (e.g., Figs. 11, 15). Vegetation growth is favored in this zone due to rare hydrodynamic impact in combination

with a reduced aeolian sediment transport rate. With a dense vegetation cover at the narrow belt effectively hindering onshore aeolian sediment, it acts as a reservoir for sediment coming from the beach. As sediment continuously accumulates in this belt without significant interruption by storms (e.g., severe scarp), a well-defined established foredune ridge is developed (e.g., Figs. 10, 14). According to the simulation result, the first established foredune ridge in the model domain emerges after ~ 7 years from the initiation of simulation. This foredune ridge keeps on growing in a following period of ~10 years with a gradually decreased rate and reaches a height of ~4.6 m above the still water level and a width of ~19 m in the western part of the research area. In the eastern part this foredune ridge develops to a larger size, with a height of ~ 5.9 m and a width of ~ 21 m. A complete morphogenesis of a new foredune ridge is illustrated in Figs. 10 and 11. Results indicate that only one established foredune ridge is developed in the entire research section after the first 20 years since the initiation of simulation (Fig. 10a), though there is a tendency for development of a new and smaller foredune ridge that is attached to the first foredune ridge in the western part (Fig. 10a). However, this new foredune ridge is erased completely by subsequent storms in 1971 (Fig. 10b). In the following 4 years the growth of vegetation in front of the first foredune ridge is favored (Fig. 11b,c) due to an

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Fig. 13. Simulated total vegetation effectiveness (pioneer grass + woody shrub) of the research area between 1985 and 1996.

increased sediment supply and decreased number of storms (Fig. 16). As soon as the vegetation cover reaches to an effective value (ρ = ~ 0.7), a new narrow belt (Figs. 10c and 11c) forms and sediment accumulates in this belt rather than being transported further onshore, inducing the formation of an independent established foredune ridge (Fig. 10d). In the next 10 years from 1975 to 1985 a continuous growth of this new foredune is favored, until it reaches to a height of ~4.8 m and ~5.2 m in the western and eastern part, respectively (Fig. 12a). It is interesting to note that during the development of the new independent foredune ridge, pioneer grasses in the trough area behind it suffer a decline due to a lack of sediment supply (Fig. 11c). As the major onshore aeolian sediment transport (N90%) is blocked by the newly-formed foredune ridge, a decline of pioneer grass in the trough reduces the vegetation cover effectiveness and a small portion of sediment (with a thickness of 10–20 cm) in the trough is remobilized again, being transported along the trough to feed a further growth of the foredune ridges. Such sediment remobilization process ceases when the loss of ρ is compensated by the growth of woody shrubs (Fig. 11d), thus it only occurs in an early stage (~ 2 years) of the development of the new foredune ridge. The woody shrubs do not contribute directly to the major phase of foredune development due to its low growth rate. However, a calculation of the Pearson correlation coefficient on ρ between the grass and the

shrub over the existing foredune area shows that they are highly correlated with a correlation coefficient of 0.95. This indicates that an increase of the shrub effectiveness is facilitated by an increase of the grass effectiveness, vice versa. Thus the existence and spatial expansion of woody shrubs help to accelerate the process of the foredune development. After 1985 a difference in the foredune development between the western and eastern part of the research area gets pronounced (Fig. 12). A gradually increased sediment supply westwards along the coastal section induces the formation of an additional foredune ridge in the western part (Fig. 12b,c,d). A visible shape of this foredune ridge can be seen already in the result for 1990 (Fig. 12c). Simulation results indicate that the formation of an additional foredune ridge in the western part of the area can be attributed to two major reasons: (1) an increased sediment supply (Fig. 16) results in a rapid lift of the elevation both at the foredune ridge and the backshore area and favors an expansion of vegetation cover in front of the existing foredune ridge (Fig. 13b,c,d); and (2) an increased storm frequency since 1980s (Fig. 16) hinders the development of foredunes in low-land area. A complete destruction of embryo foredune ridges occurs more frequently in low-land areas by storm overwash since the 1980s. Such erosional effect is more significant in the eastern part as there is less sediment supply, thus slowing down the development of new foredune ridges. In the western part, a new foredune ridge is able to reach a higher elevation in its early phase compared to the eastern part.

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Fig. 14. Simulated morphological evolution of the research area between 1999 and 2002. The green dashed line marks the pre-existing foredune ridge which remains unchanged during the simulation.

This provides a larger possibility to resist a storm overwash, leaving only a scarp on the stoss side rather than a complete destruction (e.g., Fig. 12c). The scarp is refilled shortly by abundant sediment supply after the storm. The additional foredune ridge reaches its maximum height of ~ 4.7 m with a width of ~ 12 m around 1996 (Fig. 12d), and then becomes stabilized due to the formation of a new independent foredune in front of it (Fig. 14a,b). Development of the latest foredune (Figs. 14 and 15) is similar to its antecedents (e.g., Figs. 10 and 11) except an accelerated rate. This foredune ridge reaches its maximum height of ~4.7 m in 2005. Its development takes ~10 years (from 1996 to 2005), being ~3 years shorter than the one developed between 1972 and 1985. Both observation and simulation results indicate a positive correlation between storm frequency and number of foredune ridges developed in the western part of the research area, and a negative correlation between storm frequency and ultimate foredune ridge height in the whole area. A regional study by Deng et al. (2014) indicates that a major sediment source supporting coastal accretion in the research area is from the soft cliffs (glacial till) located ~9 km in the east. Collapse of these cliffs occurs during storms and is formulated as avalanche in the regional model (Zhang et al., 2013). The increase of alongshore sediment transport flux (Fig. 16) is directly linked to an increase of cliff erosion by

storms and facilitates the foredune development especially in the western part of the research area. Another interesting fact to note in our case study is that a major onshore aeolian transport is not induced by storms due to an accompanying high hydrodynamic impact level, but by effective westerly winds that do not occur simultaneously with storms. In this case the hydrodynamic impact is limited to a small part of the foreshore and the beach shows its maximum width for a reshaping by aeolian transport (e.g., Figs. 10b and 12d). Wind fetch effect becomes less significant and formation of embryo transverse-to-barchan type dunes at the backshore is facilitated with a maximum size developed. These small-scale dunes can travel a considerably long distance (up to ~100 m) before they are eliminated by hydrodynamic forces or trapped by the narrow belt to feed the foredune development. 4. Discussion Development of a model fulfilling two basic requirements: (1) affordable computational expenses and (2) capture of the external key driving mechanisms and the internal nonlinear responses of the system, is a prerequisite for reliable numerical studies (Zhang et al., 2013). These requirements serve as a base for the principles we follow in constructing

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Fig. 15. Simulated total vegetation effectiveness (pioneer grass + woody shrub) of the research area between 1999 and 2002.

an integrated model for investigation of medium-to-long term coastal foredune morphogenesis. Although the subaerial model is based on a cellular automata approach in which complicated physical and biological processes and their interactions are simplified, the simulated morphogenesis (including temporal and spatial scales) of an established coastal foredune is consistent with observations at the southern Baltic Sea, and the mechanisms involved in developing and reshaping foredunes are reasonably explained by model results. The choice of coupling the CA model with an energy-dissipation type model, in which only a few empirical parameters need to be calibrated, to estimate the cross-shore beach profile change has proven to be robust for our research purpose. A flexible coupling between sub-aqueous and sub-aerial module components (Fig. 2) provides an easy way for other users to couple their own models with the modules presented in this paper. One advantage of the model is that realistic temporal and spatial scales related to coastal foredune morphogenesis are resolved in the model construction. Application of a CA model to a real coast is usually difficult as an appropriate setting of scales requires great efforts due to the variability induced by combinations of many different parameters and the rules involved. Our model performance suggests that a selection of scales motivated directly by the research object is helpful and necessary for a successful model construction. Another advantage of the model is that except for a few parameters (e.g., the criterion for

avalanche), the ‘rules’ (e.g., sediment depositional probability) describing the interactions of the cells are given in a probabilistic manner, which can be easily mapped directly from observational data into the model. However, this does not mean that the simulation results are dominated by large statistical variations. Repetitive model runs using the same input conditions indicate that only minor differences appear among the results, mostly on small-scale morphological structures. This indicates that although uncertainties exist in aeolian transport processes, the morphogenesis of coastal foredunes is mainly controlled by boundary conditions (e.g., sediment supply rate), extreme wind-wave event frequency and vegetation growth. Despite its robustness, several aspects related to an application of the model to a real coast deserve further discussion. First is the specification of transport modes. Real time series of weather conditions (winds, precipitation and seasonal mean temperature) are classified in the model into six transport modes in combination with representative vegetation growth functions in our study and prove to be robust in producing reasonable results close to reality. However, these modes might need to be redefined or further extended in other applications to accommodate different weather conditions, e.g., snow and ice cover. The effect of moisture on aeolian transport seems to be over-simplified in existing modes, especially in the case of mild-to-moderately wet condition when significant aeolian transport might still occur. Only one mode,

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Fig. 16. Top panel: annually-averaged net alongshore sediment transport rate in two periods calculated by a regional model in Zhang et al. (2013). Negative value indicates a westward transport direction. The research area is located between point 50.5 and point 51.5; and bottom panel: number of storms occurred during the time span 1951–2012. Criterion for a storm is that the wave impact level reaches to the seaward-most wellestablished foredune base at 2 m above the still water level.

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facilitated and gradually dominates the morphological evolution. Next, a narrow belt which is oriented along the shoreline and distinguished by a drastic gradient in the vegetation effectiveness at ρ = ~ 0.7 in the cross-shore direction appears. Once the belt is formed, a major part of onshore migrating sediment becomes trapped in it, inducing the formation of a foredune ridge. The development of a foredune ridge can be quite complex and goes through several stages due to the impact of extreme wind-wave events. Complete destruction or a scarp may occur during storms depending on the height of the foredune ridge. These erosional processes occur repetitively if the sediment supply is not able to support a growth of the foredune ridge above the storm wave impact level. The second finding is that although being responsible for severe short-term erosions, storms can also be a positive contributor for longterm foredune development. This is the case in the western part of our research area, where the sediment supply in non-storm periods is significantly increased due to more frequent storm erosion on the neighboring glacial-till cliffs that serve as a major sediment source. The third finding is that a remarkable variability in foredune development can be found even along a small (1 km) coastal section, implying that the medium-to-long term land–sea interaction and foredune morphogenesis is quite sensitive to boundary conditions and various processes acting on multi-temporal and spatial scales. Any reliable numerical model for coastal morphological study must be built on a comprehensive understanding of these factors and sensitivity study is necessary to derive a possible range of critical parameters that often come from experience applied elsewhere. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.coastaleng.2015.03.005. Acknowledgments

1

i.e., mild transport , is used to represent these conditions in the current setting, which leaves us a knowledge gap to fill in future work. Another shortcoming of the model is that the storm breaching and overwash on the foredune ridge are not well formulated in our model. The foredune ridge is either completely immersed in water or partly scarped, depending on a comparison between the maximum wave run-up and foredune ridge height. In the first case the foredune ridge is treated like a normal sand bar in the subaqueous model with an unidirectional offshore transport (M b 0.000647 in Eq. (14)), excluding an overwash over the foredune which might induce a remarkable deposit at the trough behind the ridge. In the latter case the stoss part of the foredune below the wave impact level is vertically eliminated, not allowing a further shoreward scour at the foredune which might induce a breaching. These disadvantages are inherent in the formulation of the subaqueous cross-shore transport model, thus seems to be difficult to resolve at the moment unless the transport zones are modified or extended to accommodate the specific processes occurring at the foredune. The problem of a mixture of sediment in the surficial lithology is not dealt with in the current model, inclusion of consolidation and underground water effect also points out a potential improvement of the model in future work, and more tests need to be done for erosional coasts as well as coasts characterized by more complex environmental settings. 5. Conclusions Three major conclusions are drawn from the study. First, a successful application of the integrated model to the southern Baltic coast demonstrates the robustness and potential of a coupling between cellular automata approach and process-based profile-resolving models for a practical study of medium-to-long term coastal foredune morphology. Simulation results indicate that the morphogenesis of coastal foredunes is a result from a competition among wind-wave impacts, external sediment supply and vegetation growth. Driven by an effective onshore wind and a boundary sediment supply, small-scale dunes develop on the backshore and migrate landward. In the elevated coastal area where hydrodynamic impacts seldom reach, vegetation growth is

The historical wind and precipitation data (1951–2012) of the southern Baltic Sea were kindly provided by Dr. R. Weisse from Helmholtz-Zentrum Geesthacht, Germany. The simulations were carried out at MPI-IPP (Max-Plank-Institute for Plasma Physics) in Greifswald and Garching, Germany. We thank the Polish Maritime Office (Szczecin) for providing the valuable source data of high-resolution DEM and annual profile measurement from 2005 to 2012. Constructive comments from two anonymous reviewers and the editor are appreciated for an improvement of the manuscript. W. Zhang is funded through DFG—Research —Research Center/Excellence Cluster “The Ocean in the Earth System” (EXC309). References Aagaard, T., Orford, J., Murray, A.S., 2007. Environmental controls on coastal dune formation: Skallingen Spit, Denmark. Geomorphology 83, 29–47. Anthony, E.J., Mrani-Alaoui, M., Hequette, A., 2010. Shoreface sand supply and mid- to late-Holocene aeolian dune formation on the storm-dominated macrotidal coast of the southern North Sea. Mar. Geol. 276, 100–104. Arens, S.M., 1994. Aeolian Processes in the Dutch Foredunes. PhD dissertation, University of Amsterdam (150 pp.). Arens, S.M., 1997. Transport rates and volume changes in a coastal foredune on a Dutch Wadden island. J. Coast. Conserv. 3, 49–56. Arens, S.M., van Kaam-Peters, H.M.E., van Boxel, J.H., 1995. Air flow over foredunes and implications for sand transport. Earth Surf. Process. Landf. 20, 315–332. Baas, A.C.W., 2002. Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments. Geomorphology 48 (1–3), 309–328. Bagnold, R.A., 1954. The Physics of Blown Sand and Desert Dunes. 2nd edition. (Metheun, London). Battjes, J.A., 1974. Surf similarity. Proceedings of the 14th International Coastal Engineering Conference. American Society of Civil Engineers vol. 1, pp. 466–480. Bauer, B.O., Davidson-Arnott, R.G.D., 2003. A general framework for modelling sediment supply to coastal dunes including wind angle, beach geometry and fetch effects. Geomorphology 49, 89–108. Bauer, B.O., Davidson-Arnott, R.G.D., Hesp, P.A., Namikas, S.L., Ollerhead, J., Walker, I.J., 2009. Aeolian sediment transport on a beach: surface moisture, wind fetch, and mean transport. Geomorphology 105, 106–116. Bishop, S.R., Momiji, H., Carretero-Gonzalez, R., Warren, A., 2002. Modelling desert dune fields based on discrete dynamics. Discret. Dyn. Nat. Soc. 7, 7–17. Carley, J.T., 2001. Validation and application of beach storm erosion models in Australia. Coasts & Ports 2001: Proceedings of the 15th Australasian Coastal and Ocean

166

W. Zhang et al. / Coastal Engineering 99 (2015) 148–166

Engineering Conference, the 8th Australasian Port and Harbour Conference, pp. 67–72 (Barton, Australia). Christiansen, M.B., Davidson-Arnott, R., 2004. Rates of landward sand transport over the foredune at Skallingen, Denmark and the role of dune ramps. Dan. J. Geogr. 104 (1), 31–43. Davidson-Arnott, R.G.D., MacQuarrie, K., Aagaard, T., 2005. The effect of wind gusts, moisture content and fetch length on sand transport on a beach. Geomorphology 68, 115–129. de Vries, S., Southgate, H.N., Kanning, W., Ranasinghe, R., 2012. Dune behavior and aeolian transport on decadal timescales. Coast. Eng. 67, 41–53. Dean, R.G., 1977. Equilibrium beach profiles: U.S. Atlantic and the Gulf coasts. Dep. Civil Eng., Ocean Eng. Rep. 12. Univ. Delaware, Newark, Del. Dean, R.G., Walton, T.L., Kriebel, D.L., 2001. Cross-shore sediment transport. Coastal Engineering Manual, U.S. Army Coastal and Hydraulics Laboratory. Delgado-Fernandez, I., 2011. Meso-scale modelling of aeolian sediment input to coastal dunes. Geomorphology 130, 230–243. Deng, J., Zhang, W.Y., Schneider, R., Harff, J., Dudzinska-Nowak, J., Terefenko, P., Giza, A., Furmanczyk, K., 2014. A numerical approach for approximating the historical morphology of wave-dominated coasts — a case study of the Pomeranian Bight, southern Baltic Sea. Geomorphology 204, 425–443. Dong, Z., Wang, H., Liu, X., Wang, X., 2004. The blown sand flux over a sandy surface: a wind tunnel investigation on the fetch effect. Geomorphology 57, 117–127. Donnelly, C., Krauss, N., Larson, M., 2006. State of knowledge on measurement and modeling of coastal overwash. J. Coast. Res. 22, 965–991. Dudzinska-Nowak, J., 2006. Coastal morphology changes as an indicator of the coast development tendency. Ph.D. Thesis, Polish: Zmienność morfologii strefy brzegowej, jako wskaźnik tendencji rozwojowych brzegu. Institute of Marine Sciences University of Szczecin Szczecin (226 pp.). Fonstad, M.A., 2013. Cellular automata in geomorphology. In: Shroder, J., Baas, A.C.W. (Eds.), Treatise on Geomorphology. Quantitative Modeling of Geomorphology vol. 2. Academic Press, San Diego, CA, pp. 117–134. Frank, A.J., Kocurek, G., 1996. Toward a model for airflow on the lee side of aeolian dunes. Sedimentology 43, 451–458. Gillette, D.A., Herbert, G., Stockton, P.H., Owen, P.R., 1996. Causes of the fetch effect in wind erosion. Earth Surf. Process. Landf. 21, 641–659. Herrmann, H.J., Andrade Jr., J.S., Schatz, V., Sauermann, G., Parteli, E.J.R., 2005. Calculation of the separation streamlines of barchans and transverse dunes. Phys. A 357, 44–49. Hersen, P., 2005. Flow effects on the morphology and dynamics of aeolian and subaqueous barchan dunes. J. Geophys. Res. 110, F04S07. Hesp, P.A., 1983. Morphodynamics of incipient foredunes in N.S.W., Australia. In: Brookfield, M.E., Ahlbrandt, T.S. (Eds.), Eolian Sediments and Processes. Elsevier, Amsterdam, pp. 325–342. Hesp, P.A., 1988. Morphology, dynamics and internal stratification of some established foredunes in southeast Australia. In: Hesp, P.A., Fryberger, S. (Eds.), Eolian Sediments. Journal of Sedimentary Geology 55, pp. 17–41. Hesp, P.A., 2002. Foredunes and blowouts: initiation, geomorphology and dynamics. Geomorphology 48, 245–268. Jackson, P.S., Hunt, J.C.R., 1975. Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929–955. Jackson, D.W.T., Beyers, J.H.M., Lynch, K., Cooper, J.A.G., Baas, A.C.W., Delgado-Fernandez, I., 2011. Investigation of three-dimensional wind flow behaviour over coastal dune morphology under offshore winds using computational fluid dynamics (CFD) and ultrasonic anemometry. Earth Surf. Process. Landf. 36, 1113–1134. Kawamura, R., 1964. Study of sand movement by wind. Hydraulic Engineering Laboratory Technical Report, HEL-2-8. University of California, Berkely, pp. 99–108. Keijsers, J.G.S., Poortinga, A., Riksen, M.J.P.M., de Groot, A.V., 2012. Connecting Aeolian Sediment Transport with Foredune Development. Jubilee Conference Proceedings, University of Twente, The Netherlands (http://dx.doi.org/10.3990/2.187). Kocurek, G., Ewing, R.C., 2005. Aeolian dune field self-organization — implications for the formation of simple versus complex dune — field patterns. Geomorphology 72, 94–105. Kriebel, D.L., Dean, R.G., 1985. Numerical simulation of time-dependent beach and dune erosion. Coast. Eng. 9 (3), 221–245. Łabuz, T.A., 2005. Present-day dune environment dynamics on the coast of the Swina Gate Sandbar (Polish West coast). Estuar. Coast. Shelf Sci. 62, 507–520. Larson, M., Kraus, N.C., 1989. SBEACH: Numerical Model for Simulating Storm-induced Beach Change, Rep. 1, Empirical Foundation and Model Development. Tech. Rep. CERC-89-9, U.S. Army Eng. Waterways Expt. Stn., Coastal Eng. Res. Center, Vicksburg, Miss. Larson, M., Kraus, N.C., 1995. Prediction of cross-shore sediment transport at different spatial and temporal scales. Mar. Geol. 126, 111–127.

Larson, M., Kraus, N.C., Byrnes, M.B., 1990. SBEACH: Numerical Model for Simulating Storm-induced Beach Change, Rep. 2, Numerical Formulation and Model Tests. Tech. Rep. CERC-89-9, US Army Eng. Waterways Expt. Stn., Coastal Eng. Res. Center, Vicksburg, Miss. Luna, M.C.M.M., Parteli, E.J.R., Durán, O., Herrmann, H.J., 2011. Model for the genesis of coastal dune fields with vegetation. Geomorphology 129, 215–224. Moore, B.D., 1982. Beach Profile Evolution in Response to Changes in Water Level and Wave Height. M.S. Thesis. Department of Civil Engineering, University of Delaware, Newark, DE. Nield, J.M., Baas, A.C.W., 2008. Investigating parabolic and nebkha dune formation using a cellular automaton modelling approach. Earth Surf. Process. Landf. 33 (5), 724–740. Nishimori, H., Ouchi, N., 1993. Formation of ripple patterns and dunes by wind-blown sand. Phys. Rev. Lett. 71 (I), 197–201. Ollerhead, J., Davidson-Arnott, R., Walker, I.J., Mathew, S., 2012. Annual to decadal morphodynamics of the foredune system at Greenwich Dunes, Prince Edward Island, Canada. Earth Surf. Process. Landf. http://dx.doi.org/10.1002/esp.3327. Orford, J.D., Wilson, I.P., Wintle, A.G., Knight, J., Braley, S., 2000. Holocene coastal dune initiation in Northumberland and Norfolk, eastern UK: climate and sea-level changes as possible forcing agents for dune initiation. In: Shennan, I., Andrews, J. (Eds.), Holocene Land–Ocean Interaction and Environmental Change around the western North Sea. 166. The Geological Society, London, UK, pp. 197–217. Pilkey, O.H., Young, R.S., Riggs, S.R., Smith, A.W.S., Wu, H., Pilkey, W.D., 1993. The concept of shoreface profile of equilibrium: a critical review. J. Coast. Res. 9 (1), 255–278. Psuty, N.P., 1988. Sediment budget and dune/beach interaction. J. Coast. Res. SI 3, 1–4. Reimann, T., Tsukamoto, S., Harff, J., Osadczuk, K., Frechen, M., 2011. Reconstruction of Holocene coastal foredune progradation using luminescence dating — an example from the Świna barrier (southern Baltic Sea, NW Poland). Geomorphology 132, 1–16. Ruggiero, P., Komar, P.D., McDougal, W.G., Marra, J.J., Beach, R.A., 2001. Wave runup, extreme water levels and the erosion of properties backing beaches. J. Coast. Res. 17 (2), 407–419. Saye, S., van der Wal, D., Pye, K., Blott, S., 2005. Beach–dune morphological relationships and erosion/accretion: an investigation at five sites in England and Wales using LiDAR data. Geomorphology 72, 128–155. Schoonees, J.S., Theron, A.K., 1995. Evaluation of 10 cross-shore sediment transport/ morphological models. Coast. Eng. 25, 1–41. Sherman, D.J., Bauer, B.O., 1993. Dynamics of beach–dune systems. Prog. Phys. Geogr. 17, 413–447. Tamura, T., 2012. Beach ridges and prograded beach deposits as palaeoenvironment records. Earth Sci. Rev. 114, 279–297. Teichmann, T., 2010. Sand and Snow Dunes With Cellular Automata. Bachelor thesis. University of Greifswald. Thieler, E.R., Pilkey, O.H., Young, J.R.S., Bush, D.M., Chai, F., 2000. The use of mathematical models to predict beach behavior for U.S. coastal engineering: a critical review. J. Coast. Res. 16 (1), 48–70. Van Boxel, J.H., Arens, S.M., Van Dijk, P.M., 1999. Aeolian processes across transverse dunes. I: modeling the air flow. Earth Surf. Process. Landf. 24, 255–270. Van Dijk, P.M., Arens, S.M., Van Boxel, J.H., 1999. Aeolian processes across transverse dunes. II: modeling the sediment transport and profile development. Earth Surf. Process. Landf. 24, 319–333. Weisse, R., Storch, H.v., Callies, U., Chrastansky, A., Feser, F., Grabemann, I., Guenther, H., Pluess, A., Stoye, T., Tellkamp, J., Winterfeldt, J., Woth, K., 2009. Regional meteomarine reanalyses and climate change projections: results for Northern Europe and potentials for coastal and offshore applications. Bull. Am. Meteorol. Soc. 90, 849–860. Weng, W.S., Hunt, J.C.R., Carruthers, D.J., Warren, A., Wiggs, G.F.S., Livingstone, I., Castro, I., 1991. Air flow and sand transport over sand-dunes. Acta Mech. 2, 1–22. Werner, B.T., 1995. Eolian dunes: computer simulation and attractor interpretation. Geology 23, 1107–1110. Werner, B.T., 1999. Complexity in natural landform patterns. Science 284, 102–104. Zhang, D., Narteau, C., Rozier, O., 2010. Morphodynamics of barchan and transverse dunes using a cellular automaton model. J. Geophys. Res. 115, F03041. http://dx.doi.org/10. 1029/2009JF001620. Zhang, W.Y., Schneider, R., Harff, J., 2012. A multi-scale hybrid long-term morphodynamic model for wave-dominated coasts. Geomorphology 149–150, 49–61. Zhang, W.Y., Deng, J., Harff, J., Schneider, R., Dudzinska-nowak, J., 2013. A coupled modeling scheme for longshore sediment transport of wave-dominated coasts — a case study from the southern Baltic Sea. Coast. Eng. 72, 39–55. Zheng, J., Dean, R.G., 1997. Numerical models and intercomparisons of beach profile evolution. Coast. Eng. 30, 169–201.