The ability to model morphological changes on complex, multi-landform coasts over decadal to centennial timescales is essential for sustainable coastal management worldwide. One approach involves coupling of landform-specific simulation models (e.g. cliffs, beaches, dunes and estuaries) that have been independently developed. An alternative, novel approach explored in this paper is to capture the essential characteristics of the landform-specific models using a common spatial representation within an appropriate software framework. This avoid the problems that result from the model-coupling approach due to between-model differences in the conceptualizations of geometries, volumes and locations of sediment. In the proposed framework, the Coastal Modelling Environment (CoastalME), change in coastal morphology is represented by means of dynamically linked raster and geometrical objects. A grid of raster cells provides the data structure for representing quasi-3-D spatial heterogeneity and sediment conservation. Other geometrical objects (lines, areas and volumes) that are consistent with, and derived from, the raster structure represent a library of coastal elements (e.g. shoreline, beach profiles and estuary volumes) as required by different landform-specific models. As a proof-of-concept, we illustrate the capabilities of an initial version of CoastalME by integrating a cliff–beach model and two wave propagation approaches. We verify that CoastalME can reproduce behaviours of the component landform-specific models. Additionally, the integration of these component models within the CoastalME framework reveals behaviours that emerge from the interaction of landforms, which have not previously been captured, such as the influence of the regional bathymetry on the local alongshore sediment-transport gradient and the effect on coastal change on an undefended coastal segment and on sediment bypassing of coastal structures.
Coastal managers worldwide must plan for decadal to centennial time horizons (e.g. Nicholls et al., 2012) and may well need to also assess longer-term adaptation measures (Brown et al., 2014; Hall et al., 2012). However, quantitative prediction of morphological coastal changes at meso-scales (decades to centuries and tens to hundreds of kilometres) is scientifically challenging. Physics-based, reductionist models that represent small-scale processes have proven to be of limited use in this task, both because of the accumulation of small errors over long timescales (de Vriend et al., 1993) because of the omission of processes that govern long-term change (Murray, 2007; Werner, 2003) and computational limitations (Daly et al., 2015). Faced with this impasse, coastal geomorphologists have begun to adopt simpler behaviourally based approaches or large-scale coastal behavioural (LSCB) models (Terwindt and Battjes, 1990). LSCB models seek to represent the main physical governing processes on appropriate time and space scales (Cowell et al., 1995; French et al., 2016b; Murray, 2013). Central to these approaches has been selective characterization of the coastline: thus, we have seen the development of models that simulate the temporal evolution of a range of individual elements of coastal morphology, such as coastal profiles, shorelines or estuary volumes. However, modelling of complex coastlines involving multiple landforms (for example, beaches and tidal inlets) requires consideration of interactions between the component landforms, subject to the principles of mass conservation. This is difficult: modelling these interactions is still not commonplace.
One possible way forward is the development and use of model-to-model interfaces: software wrappers that allow coupling of independently developed component models (Moore and Hughes, 2016; Sutherland et al., 2014). Significant effort has been oriented in this direction during the last decade, in particular by the Open Modelling Interface (OpenMI) and Community Surface Dynamics Modelling System (CSDMS). OpenMI emerged from the water sector as a way to link existing stand-alone models that were not originally designed to work together (Gregersen et al., 2005), while CSDMS draws on a large pool of well-understood open-access models (Hutton et al., 2014). The promise of OpenMI and CSDMS is to provide a unified system to link various models in order to explore broader system behaviour. However, a range of challenges becomes apparent when linking component models in this way. These include difficulties associated with fully accounting for the cumulative effect of various assumptions made by, and uncertainties in, the constituent models, and non-trivial technical issues concerning variable names and units (Peckham et al., 2013). Such software-coupling frameworks are themselves agnostic with regard to the spatial structures of component models. This creates a further significant challenge when coupling existing LSCB models due to fundamental between-model differences in the conceptualizations of geometries, volumes and locations of sediment. For example, the Soft Cliff and Platform Evolution (SCAPE; Walkden and Hall, 2011) model assumes a beach of finite thickness perched at the top of the bedrock shore profile, while “one-line” approaches assume infinite beach thickness (Payo et al., 2015). Similarly, a 2-D estuary model uses the bathymetry to define the form as a continuum, whereas an aggregated model, such as ASMITA (Stive et al., 1997; Townend et al., 2016), uses only the volume of user-defined constituent elements. In this context, coastal modellers need an alternative approach to model integration.
We suggest that integrated modelling must go beyond the software coupling issues that have been the focus of OpenMI and CSDMS. Instead, as argued by Raper and Livingstone (1995), integrated modelling should deal more directly with the semantics of the various entities modelled. We propose a way to address this: by means of a modular, object-oriented framework in which these entities are the primary constructs. In other words, the objects that interact within the model framework should correspond to the main real-world constructs considered by coastal scientists and managers. Figure 1 illustrates the modelling approach underpinning the proposed modelling framework; representation of space, and of the changes occurring within its spatial domain, involves both raster (i.e. grid) and vector (i.e. coastline, profile and sediment-sharing polygons) representations of spatial objects. This is commonplace in modern GIS (geographic information system) packages. What is relatively unusual, however, is that in the proposed framework, data are routinely and regularly transformed between these two representations during each time step of a simulation.
Schematic diagram of the proposed modelling approach. Coastal
morphology change is simulated as dynamically linked line and raster
objects. The hierarchy of panels illustrate how a real coastal
morphology
In this paper, we provide a detailed description of the proposed Coastal Modelling Environment (CoastalME). We also provide a proof-of-concept illustration of its integrative capacity by unifying independently developed cliff, beach and wave propagation models. Validation of the geomorphological outcomes of model runs against real-world data will be the subject of a future study. This paper is organized in six sections. In Sect. 2, we have outlined the background and rationale for the proposed coastal modelling environment. In Sect. 3, we explain in detail the proposed framework, including the representation of space and time, inputs and outputs, main operations within time steps, treatment of the domain boundary conditions, implementation and CoastalME modular design. In Sect. 4, we present some simulation results to illustrate how the different model components integrated in this first composition interact to produce realistic coastal morphological changes and we discuss its advantages and limitations. In Sect. 5, we discuss and in Sect. 6 summarize the main conclusions. In the Code Availability section, we outline the main websites and weblinks from which the code, the input files used for the test cases and a dedicated wiki site are available.
The dynamic behaviour observed in coastal geomorphology is the result
of complex feedback relationships linking hydrology, sediment
transport and resulting bed evolution, driven by time-variant or
stationary boundary conditions and modulated by the underlying geology
(Cowell et al., 2003). While coastal scientists do not have a full
understanding of the key processes that control the dynamics of
coastal morphology as observed at meso-scales, there are a number of
processes that have been consistently identified as important:
Gradients in wave-driven alongshore transport, related to coastline
shape and wave-incidence, provide the alongshore connectivity between
different landform complexes (Murray et al., 2013; Werner, 2003). Sediment sources and sinks in the nearshore system generate an
alongshore-propagating curvature and a shoreline change
signal. Sources and sinks include human manipulations (localized
sources or sinks), river mouths (sources), eroding cliffs (sources),
spits that grow into bay or estuary mouths (sinks), and sediment
fluxes to or from the continental shelf (Woodroffe, 2002). Wave-shadowing effects from protruding coastline features such as
headlands tend to create a down-drift zone of diverging
alongshore flux and associated shoreline response (Ells and Murray,
2012). These effects give rise to emergent coastline features such as
cuspate capes and spits (Ashton et al., 2001; Ashton and Murray,
2006), which themselves contribute autogenic wave-shadowing effects
and result in shoreline undulations. Underlying lithology and coastline topography exert significant
influence on shoreline change rates, in combination with both
alongshore transport gradients and sea-level rise (Carpenter et al.,
2015; Valvo et al., 2006; Walkden and Hall, 2011). Beach–cliff interactions influence the local cliff and shore platform
erosion rate (Payo et al., 2014) and provide a significant sediment
source (Walkden and Dickson, 2008). Estuaries and tidal inlets are net sediment importers and/or exporters
from or to the open coast (de Swart and Zimmerman, 2009) and are
controlled by a number of ecological processes (Friedrichs and
Perry, 2001).
Any model framework which is capable of realistically simulating changes in the morphology of complex coasts during decadal to centennial time periods must (at least) include representations of all the above.
Common amongst most LSCB models is the use of simple geometries to
represent complex real-world 3-D coastal geomorphology. Profile
models, coastline models and volumetric models are the three most-used
conceptualizations employed to represent meso-scale coastal
morphodynamics (e.g. de Vriend et al., 1993; Fagherazzi and
Overeem, 2007; Hanson et al., 2003). These three
conceptualizations are, between them, capable of representing a great
number of different coastal landforms:
Coastal profile models simplify the coastal system to a 2-D system
(with elevation and cross-shore distance being the two dimensions)
that assumes alongshore uniformity (e.g. Kobayashi, 2016). In coastline models, the sand beach morphology is represented by
a single contour, and such models are therefore often referred to as
one-line models (e.g. Hanson and Kraus, 2011) Volumetric models represent the different landforms as sediment-sharing entities (e.g. Stive et al., 1997).
The Coastal One-line Vector Evolution (COVE) model is a special case
of a one-line model designed to handle complex coastline
geometries, with high-planform-curvature shorelines (Hurst et al.,
2015). COVE was inspired by the coastal evolution model of Ashton
et al. (2001) but also includes wave refraction around
headlands. In COVE (as in other one-line models), the shoreline is
represented by a single line (or contour) that advances or retreats
depending on the gradient of alongshore sediment flux. This approach
necessarily makes a number of simplifying assumptions to conceptualize
the coastline in a way that is consistent with a single-line
representation:
The cross-shore beach profile is assumed to maintain a constant
time-averaged form. This implies that depth contours are
shore-parallel, and allows the coast to be represented by a single
contour line. Short-term cross-shore variations due to storms or rip currents are
considered temporary perturbations of the long-term trajectory of
coastal change (i.e. the shore face recovers rapidly from storm-driven
and tidal-driven cross-shore transport). Wave action is considered to be the main driver of alongshore sediment
transport within the surf zone characterized by the height and angle
of incidence of breaking waves. Gradients in alongshore transport
therefore dictate whether the shoreline advances or retreats, and
whether depositional landforms diffuse, migrate or grow.
A key innovation of COVE is that it uses a local, rather than global, coordinate scheme, enabling coastal cells to take on a variety of polygonal shapes such as triangles and trapezoids (see also Kaergaard and Fredsoe, 2013). The coastline is represented as a series of nodes, each of which is associated with a single polygonal cell; between-cell boundaries are created by the projection of cell boundaries perpendicular to the linking-line between nodes, i.e. approximately normal to the local shoreline orientation. Bulk alongshore sediment flux is driven by the height and incidence angle of breaking waves in each polygon.
The SCAPE model is a time-stepping model of soft-shore recession and morphological change on a profile that is assumed normal to the coastline. It comprises both process descriptions and behaviour-oriented representations. Beach sediment volumes are quantified and conserved, although fine-grained sediments are assumed to be lost from the system (i.e. transported offshore). Sediment is released to the beach through rock erosion and is then moved across- and alongshore. The beach form is assumed to be in a morphological steady state, which is consistent with a one-line model, since its profile is unchanging in time, whilst being translated landward or seaward during the simulation. Alongshore variations in beach volume are captured by the representation of a series of shore-normal profiles. Beach volumes at each shore-normal profile are increased or decreased at each time step by the amount released from the rock to the beach system, and by gradients in alongshore sediment flux, including transport across the littoral boundaries.
Offshore waves in SCAPE and COVE are transformed according to linear wave theory and assuming shore-parallel depth contours with no refraction or loss of energy due to bottom friction. These simplifications are appropriate for gently sloping bathymetries and low planform curvature, open coasts but additional modifications are required to account for diffraction and refraction in shadowed regions where these assumptions may not be appropriate. COVE includes simple rules for the diffraction and refraction of waves when the coast is shadowed from incoming waves. An alternative model that includes energy dissipation due to wave breaking and bottom friction (while assuming alongshore uniformity) is the Cross-Shore Model (CSHORE, Kobayashi, 2016). CSHORE solves a combined wave and current model based on time-averaged continuity, cross-shore and alongshore momentum, wave energy or action, and roller energy equations to estimate wave-induced hydrodynamics.
The Aggregated Scale Morphological Interaction between Inlets and Adjacent Coast (ASMITA) model is a behaviour-oriented model that describes the evolution of a tidal inlet towards an equilibrium which is forced by external conditions and geometrically constrained by human interventions (Stive et al., 1997; Townend et al., 2016). The ASMITA concept has been applied to simulate the effects of the closure of tidal basins, dredging and dumping of sediment, and sea-level rise, on both hypothetical and real tidal basins (Rossington et al., 2011; Van Goor et al., 2003). ASMITA conceptualizes the estuary as a highly schematized representation of geomorphic elements, for example the ebb-tidal delta, sub-tidal channel and intertidal flats (as found on barrier island coasts such as the Wadden Sea). The most important assumption underpinning the ASMITA conceptualization is that a morphological equilibrium for each estuary element is a function of the controlling hydrodynamic (e.g. tidal prism, tidal range) and morphometric (e.g. basin area) conditions. The tidal system can thus be schematized as one, two or three sediment-sharing elements involving the ebb-tidal delta, channel and tidal flat. Ebb-tidal deltas are important sediment reservoirs that may supply the tidal system with sediment, unless the delta is sediment-starved, in which case the system may demand sediments from the adjacent coast. The volume of an ebb-tidal delta can be defined assuming the coast is undisturbed by a coastal inlet, and therefore its bathymetry is assumed equal to that of the adjacent barrier coast. Thus, in ASMITA, the volume of the ebb-tidal delta is equal to the volume above this virtual no-inlet coast.
The three LSCB models outlined above each have different sediment
conservation and morphological updating principles, each operates on
a different abstraction of coastal geometry, and each uses different
sediment accounting structures. However, they also possess some
salient attributes, which potentially provide a basis for a shared,
generic, geometric and sediment budget-modelling
framework. Considering these three models, and LSCB models in general,
we observe the following:
All meso-scale models conserve sediment volume and mass. Sediment is stored as deposited material (gravel, sand, fine) or held in
suspension. LSCB models typically employ some characterization of hydrodynamic forcing
(e.g. breaking wave height and direction, 1-D-estuary water levels and tidal
flows, fetch-limited estuary wave's heights). Sediment accounting is on a two-dimensional horizontal grid (2-DH; e.g. triangular irregular network
(TIN),
regular, curvilinear, quad-tree, raster); 1-D geometries (e.g. shore profiles
or a one-line model) may be represented with a 2-DH. Behavioural models operate on some abstraction of a full 3-D
topography or bathymetry (e.g. shorelines, shore profiles, sandbank or delta
volumes, estuary volumes or cross sections, estuary channel networks, mudflat
areas), and appropriately make some classification of the modelled landforms
(e.g. one-line models apply to curving sandy-rich coastlines, SCAPE models
apply to shore profiles).
Thus, we suggest that these three LSCB models can, in common with other LSCB models, be integrated within a modelling framework that respects and emphasizes the above-listed attributes. In the next section, we describe the initial implementation of such a framework.
We next present a detailed description of the CoastalME framework objectives and methods and how they operate together to capture a generic morphodynamic feedback loop. To demonstrate the integration capacity of the proposed framework, we also describe how two landform-specific models (COVE for sediment-rich open beaches and SCAPE for soft-cliffed open coast) can be integrated, combining the simple diffraction and refraction rules used in COVE's wave propagation module and the less restrictive CSHORE wave propagation module. In choosing component models, our aim was to demonstrate how the CoastalME framework permits distinct but morphologically linked processes to be represented in a consistent manner.
CoastalME is not a simulation model but a framework to integrate
different model components, and therefore most of the classes and
methods that are likely to be modified by a coastal modeller using
CoastalME can be simply replaced by an overloading method or
class. Some concepts of the model components described above are
hard-coded into CoastalME (i.e. are unlikely to be changed by the
modeller). We provide more details about the modularity of CoastalME
at the end of this section, but the most salient example of
a hard-coded concept is the use of simple polygons, like in COVE, to
calculate the alongshore sediment transport. Gradients in wave-driven
alongshore transport, related to coastline shape, provide the
alongshore connectivity between different landform complexes. The use
of simple triangular and trapezoidal shapes can accommodate a very
straight coast as well as highly irregular coastlines, ensuring that
alongshore connectivity is well captured. Figure 2 illustrates how
these polygons looks like on a real coastal stretch (Benacre Ness on the
east coast of the UK). The length of the coastline-normal used to
define the polygon boundaries for this example are 4
In CoastalME, the shore face is conceptualized as a set of
sediment-sharing cells interconnected by the alongshore sediment
transport:
Input parameters for CoastalME are supplied via a set of raster files, and a text-format configuration file. CoastalME's output consists of GIS layer snapshots, a text file, and a number of time-series files. The GIS files include both raster layers such as digital elevation models (DEMs) and sediment thickness, and vector layers such as the coastline. Optionally, there is also the ability to output snapshots of individual geometrical objects such as the shore profile.
Figure 3 illustrates the model's block-data structure used to
represent the topography and stratigraphy. The smallest spatial scale
within CoastalME is a block; blocks are square in plan view and of
variable thickness. A coastal stretch is characterized by a minimum of
two raster input files. These are (i) a basement file giving the
elevation of non-erodible rock that underlies (ii) a single sediment
layer giving the thickness of a single sediment size fraction, either
consolidated or unconsolidated. More sediment layers, representing
other sediment size fractions (both consolidated and unconsolidated)
may be specified if desired. Whilst the basement is a non-erodible
layer, consolidated and unconsolidated sediment layers may increase or
decrease their thickness during a simulation. Each sediment layer
potentially comprises three size fractions: fine (mud and/or silt), sand
(0.063
Ground elevation is characterized as a set of regular square
blocks. Each block has a global coordinate
Two files are required to represent structural human interventions such as groynes and breakwaters. One raster file represents the thickness of the intervention above the ground while a second raster file represents the class of human intervention (null if no intervention is present and 1 if a structural intervention is present on a given cell of the raster grid).
In CoastalME, we use the International System of Units and the
convention for wave direction is the “true north-based azimuthal
system”. This is the oceanographic convention in which zero indicates
that the waves are propagating towards the north, and 90
Convention used in CoastalME for a global coordinate system and
wave direction. All layers (consolidated and unconsolidated) and sea
elevations are referenced to a basement level
CoastalME uses an implicit method (i.e. find a solution by solving an equation involving both the current state of the system and the later one) to iteratively erode and deposit the different sediment fractions over the entire model grid. There is a fixed time step that could be, in principle, of any duration (i.e. hours, days, months, years). In practice, however, there are constraints on time step duration due to the amount of sediment that can be eroded or deposited on a single time step without unrealistically de-coupling the morphology change and assumed hydrodynamic forcing during a given time step (Ranasinghe et al., 2011). Table 1 summarizes the raster-to-vector transformations that take place during a single CoastalME time step: we describe each one in detail below.
Pseudo-code of CoastalME workflow.
At the beginning of each time step a set of non-landform-specific operations are executed to update the external forcing, trace the coastline and map all landform types.
External forcing values modify the SWL and the deep-water properties of incoming waves (significant wave height, peak period and direction). In the present version of the framework, SWL may be fixed or it can change linearly every time step, so at the end of the simulated period the user-defined sea-level change is achieved (i.e. SWL curve is defined by the initial SWL, duration of the simulation and the SWL at the end of the simulation).
Next, the CoastalME framework traces the coastline on the raster grid
by finding the intersection of the ground elevation and the current
SWL. For this, we use the well-known wall-follower algorithm
(Sedgewick, 2002). Unlike other LSCB models, such as one-contour
models, CoastalME does not require the user to define the shoreline
location at the initial time step: the framework determines
this. Raster cells “on” the shoreline are marked; the coastline is
also stored as a vector object made up of a set of consecutive points,
where each coastline point has an associated location (
The framework classifies each grid cell as a member of a given coastal landform. Of course, such an approach requires a consistent ontology. Here, we have adopted the ontology suggested by French et al. (2016a), which includes both human interventions (structural and non-structural) and natural landform components (Table 2). For this first version of CoastalME, we have selected a subset of these landforms to illustrate how they can be incorporated into the framework. First, all grid cells associated with a human intervention (user-defined) are marked and stored as an intervention vector object. Structural interventions are assumed non-erodible. At the first time step, the framework traverses the coastline cells and marks them as cliff or drift type if the sediment-top-elevation material is consolidated or unconsolidated, respectively. If a cliff cell is identified along the coastline, it creates a cliff object with the default cliff properties (i.e. notch overhang, notch base level, accumulated wave energy, remaining cliff to be eroded). On successive time steps these cliff properties will be modified accordingly to the user-specified cliff erosion rules. A cliff cell that is transformed into a drift cell at the next time step is classified as an eroding coastal cliff. Other cells are marked as hinterland, non-coastal cliff or sea cells, but no landform object has been associated with them yet. Figure 5a illustrates the concepts of raster and vector coastlines as well as landform type classification. In COVE, the coastline is made of a relatively small number of discrete nodes, while in CoastalME the coastline is made of a considerably greater number of coastline cells. Therefore, in CoastalME there are many more coastal points between two polygon boundaries than in COVE. CoastalME uses a smoothed vector coastline to trace the coastline-normal. This smoothed coastline is conceptually equivalent to the use of adjacent nodes in COVE.
Schematic diagram of CoastalMe landform classification
mapping and how raster and vector coastline are used to create
sediment-sharing polygons.
CoastalME adopted ontology of coastal landforms and human interventions (French et al., 2016a). The terms in bold are those already included in version 1.0 of CoastalME.
Once a coastal stretch has been classified as open coast, a set of
sediment-sharing polygons are traced using a combination of raster and
vector geometries. First, coastline-normal profile objects are created
(Fig. 5a). Each coastline-normal profile object is equivalent to
a shore-normal elevation profile, being a vector line made up of a set
of consecutive points where each point has an associated location in
the global geographic reference system. The elevation of each point of
the coastline normal is then determined using the elevation of the
centroid of the closest raster cell. Figure 5a shows the relationship
between the coastline normal in vector and raster format. Elevation
values derived directly from rasters can be unrealistically jagged, so
(as with the grid-traced coastline) some smoothing of the
raster-derived elevation profiles is necessary to give realistic
point-to-point gradients along the profile. Each profile point also
holds other local attributes such as landward-marching gradient (i.e.
the slope of the profile as we move from the seaward limit towards the
landward limit). The landward limit of each coastline normal is the
centroid location of the cell that has been marked as a coastline cell
(i.e. where the profile elevation intersects the SWL). The seaward
limit of the profile is, in the present version of the CoastalME
framework, a user-defined elevation value: it must, however, be deeper
than the depth of closure (i.e. the sea depth beyond which no
significant erosional change to unconsolidated sediments is
expected). The depth of closure (
All pairs of coastline-normal profiles are then checked for intersection. If any two profiles intersect then they are merged seaward of the point of intersection, with a planform orientation which is the mean of the two profile orientations. This is necessary because the coastline-normal profiles also serve as boundaries between coastal polygons (see below). The process is repeated until no two coastline-normal profiles cross, prioritizing merging of interceptions nearest to the coastline. Figure 5b shows the coastline normals traced along a coastline stretch with a vertical groyne interrupting the alongshore sediment transport. Coastline normals far from the intervention do not intersect, while those close to the intervention intersect and are merged as described above. Coastal polygons are thus created using the coastline normals as inter-polygon boundaries. Coastal polygons in CoastalME are broadly similar to their equivalents in COVE. However, in COVE the inter-polygon boundaries are determined using a linking line which connects up-coast and down-coast nodes, whereas in CoastalME the coastal normals (and hence the inter-polygon boundaries) are constructed as from a larger number of coastal grid cells.
Polygons at the boundaries of the DEM are constructed differently, as described above. Boundary conditions are invariably a problem for simulation models (Favis-Mortlock, 2013a) and CoastalME is no exception. Profiles at the start and end of the coastline vector are assumed to project along the main intersecting global axis rather than being normal to the coastline location. This is needed to avoid profiles at the edges moving out of the raster grid domain when projected seaward. To specify the sediment fluxes coming in and out of the polygons with boundaries intersecting or at the edge of the raster grid domain, the user can select from three types of boundary conditions: Eq. (1), an open boundary condition, which permits export of sediment at all grid edges; Eq. (2), a closed boundary condition, which assumes that no sediment enters or leaves the raster grid; and Eq. (3), a periodic boundary condition for which sediment exported from one end of a coastline is re-imported at the other end of the coastline. The first option permits net loss of sediment from the grid, while the other two options do not. For simulations where wave direction produces a net up-drift or down-drift alongshore movement of unconsolidated sediment, the open boundary option gradually leads to impoverishment of, even total removal of, unconsolidated sediment at the up-drift end of the coast, whereas the closed boundary option eventually leads to an accumulation of sediment at the down-drift end of the coast.
Two wave propagation modules are integrated in
CoastalME. Deep water waves are propagated along each coastline
normal
The next step is to propagate the user input wave conditions from deep water to breaking for each raster grid cell and to store a representative set of wave properties, both at every point along the coastline and for every sea cell.
Wave energy flux – the main driver of cliff and shore platform erosion and alongshore sediment transport – can be characterized by the wave height, period and angle at breaking. The CoastalME framework permits wave propagation to be calculated either using the current DEM (i.e. as in many coastal area models), or by assuming a simplified bathymetry (e.g. bottom contours parallel to the shoreline). The current version of the CoastalME framework assumes alongshore uniformity to calculate wave refraction (i.e. application of Snell's law), simple rules to estimate diffraction as described by Hurst et al. (2015) and two different approaches to calculate wave transformation due to shoaling and energy dissipation. The first approach is based on linear wave theory and assumes no energy losses due to wave breaking or bottom friction, in a manner equivalent to the method used by Hurst et al. (2015) in COVE. The second approach uses the CSHORE wave propagation module which includes energy dissipation due to wave breaking and bottom friction (Kobayashi, 2016). To illustrate the modularity of CoastalME, these two approaches have been integrated into CoastalME as separate methods that can be selected by the user in the input configuration file. The integration approach is also different; the simpler COVE approach has been fully coded as a new method while the more complex CSHORE approach is called as an external library.
Both wave transformation approaches involve the calculation of wave
attributes along each coastline normal: this enables us to identify
the depth of breaking and the extent of the surf zone (i.e. the area
where waves are breaking) for each coastline-normal profile. Both
approaches use a constant ratio of wave height to water depth at breaking (0.78) to assess if waves are breaking. Because CSHORE assumes
irregular waves (i.e. instead of COVE's monochromatic waves), the
breaking depth is further defined as the depth at which 98 % of
the waves are breaking. Values for wave attributes (wave height and
wave direction) for cells between normals are then interpolated (using
GDAL's “linear” Delaunay triangulation-based method: GDAL, 2017) to
all other near-coast cells of the raster grid. Incoming waves are
decomposed into their global
Figure 6 shows the wave height distribution for different incoming
wave directions (315, 270 and 225
Schematic diagram of a groyne to illustrate shadowing and wave
adjustment in the shadowed region.
Schematic diagram illustrating how the SCAPE concept of
down-wearing of the consolidated shore platform is integrated in
CoastalME.
We use the simple rules approach described by Hurst et al. (2015) to
modify the wave height and direction due to diffraction of waves in
the shadow zone. CoastalME traverses all coastline cells searching for
shadow zones. Starting with any capes, shadow zones are traced by
projecting a straight line parallel to the deep-water wave direction
until either another coastal cell or grid edge is hit. Figure 7a shows
an example of a projected straight line that crosses another coastal
cell created by a groyne for a 225
In order to conserve wave energy, the length of the coast in the
shadow zone
The current version of CoastalME integrates a slightly modified
implementation of SCAPE for erosion of the submerged consolidated
profile. First, potential down-wearing erosion (unconstrained by
sediment availability) is calculated at every coastline-normal profile
(Fig. 8a). Potential down-wearing erosion is defined as the maximum
erosion estimated to occur during the time step for a given breaking
wave height and angle. The horizontal recession at a given shore
platform elevation (
All parameters in Eq. (6) are either readily available or can be
derived from existing CoastalME parameters. The profile local slope,
Actual (i.e. supply-limited) values for platform erosion at each
raster cell is constrained in CoastalME by the amount of sediment and
its availability – how much can be mobilized on each time step and on each
active layer. SCAPE assumes two sediment fractions with two different
behaviours: fine sediment that, when eroded, is lost as suspended
sediment and coarse sediment that becomes part of the drift material
(i.e. increases beach volume). CoastalME includes three sediment
fractions (fine, sand and coarse) and the percentage of each fraction
is determined by the thickness of each fraction on each raster cell: this is equivalent to in SCAPE. The concept of availability factor is
included in CoastalME, since erosion rates are managed separately for the different sediment fractions, in order to capture the interaction between the different sediment size fractions (Le Hir et al., 2011). CoastalME uses an availability factor
Illustration of how notch evolution (from SCAPE) is simulated in
CoastalME.
In SCAPE, an initially uniform slope under the attack of breaking waves starts developing a cliff notch somewhere in between the high and low tidal levels. After a user-defined number of erosive events, SCAPE assumes that any overhanging material is removed (i.e. the cliff collapses) which produces a vertical cliff starting from the most landward location of the notch: in other words, the profile shifts in a shoreward direction. In CoastalME a cliff is represented by cells that cannot shift: they can only change elevation. This necessitates a modification of the SCAPE approach, as described below. As in SCAPE, we assume that the cliff and shore platform can only be eroded (i.e. no creation of a new consolidated platform is allowed).
In the CoastalME framework, wave energy is accumulated at every point
on the coastline: for cliff objects, this results in the development
of a cliff notch which is also represented in the raster cell which is
associated with this coastline point. The base of the cliff notch is
at a user-specified depth
Next, the alongshore unconsolidated sediment transport budget between all sediment-sharing polygons along the coast object is calculated. There are three stages to this. First, potential erosion or accretion (i.e. only transport-limited; not considering the availability of sediment) for each polygon is quantified using bulk alongshore sediment flux equations, and the direction of unconsolidated sediment movement (up-coast or down-coast) between adjacent polygons is determined. This results in a net potential unconsolidated sediment budget for each polygon. In the next stage, we consider only those polygons experiencing potential net erosion, according to this sediment budget. For these polygons, the availability of unconsolidated sediment in each of the three sediment size classes is quantified: this enables us to construct a between-polygon budget for actual (i.e. supply-limited) unconsolidated sediment movement, for the coarse- and sand- sized sediment classes only (eroded fine unconsolidated sediment is, in the current version of framework, simply stored globally). Finally, actual erosion or deposition is applied for the cells within each polygon in accordance with this supply-limited budget. These three stages are described in more detail below.
The conservation equation for beach sediment expressed in terms of
local coordinates states that the change in position of the shoreline
(d
In order to resolve Eq. (9), CoastalME next calculates the alongshore
sediment fluxes in and out of each sediment-sharing polygon. To
calculate potential sediment transport on each polygon, average wave
height and wave angle at breaking along each polygon's coastline
segment and the average beach slope are determined. Wave angle at
breaking (
Transport-limited conditions are assumed in COVE, such that there is always sufficient beach material available for transport. However, in CoastalME the actual alongshore sediment transport can be smaller than the potential bulk alongshore sediment transport (supply-limited conditions). The amount of unconsolidated sediment available on each polygon is defined by the sediment volume between an assumed equilibrium beach profile and the top elevation of the consolidated shore platform. In CoastalME the beach profile is assumed to have a user-defined equilibrium profile. The beach equilibrium profile currently assumed in CoastalME is the Dean profile (Eq. 8; Dean, 1991). By allowing the shore platform to adopt any slope, we do not need to use the analytical expressions used in COVE to calculate the shoreline changes as a function of volume changes, but instead use an iterative numerical scheme.
For each polygon with net potential erosion of unconsolidated
sediment, CoastalME calculates the actual sediment flux by iteratively
fitting Dean profiles in a landward direction until the volume of
change from the start and end of the time step equals the net potential
erosion, or the profile becomes entirely consolidated. This is done by
traversing the polygon's coastline cells and fitting an equilibrium
beach profile that is parallel to one polygon boundary (which is
itself a coastline-normal profile). At each point along the profile,
if the elevation of existing unconsolidated sediment is greater than
the elevation of the assumed equilibrium profile, then some
unconsolidated sediment is removed so that the elevation at that point
becomes that of the assumed equilibrium profile. Sediment which is
removed then becomes available for deposition elsewhere. But if, at
that point, the elevation of the existing unconsolidated sediment is
below that of the assumed equilibrium profile, then sediment is taken
from the available sediment and deposited so that the elevation at
that point becomes that of the assumed equilibrium profile. This is
repeated for every point on the profile. If the available
unconsolidated sediment from the whole profile is smaller than the
target for potential erosion per profile for this polygon, the
equilibrium profile is moved one cell landward iteratively until the
available unconsolidated sediment equals the target for potential
erosion, or all unconsolidated sediment at that coastline point is
removed, or the cell is outside the grid. The target potential erosion
per profile is obtained as the ratio of the polygon's previously
calculated potential erosion sediment flux to the length of the
coastline segment (units are cubic metres (
A budget for actual unconsolidated sediment movement between each polygon may now be drawn up. For those polygons with net loss of unconsolidated sediment, the active layer availability equation (Eq. 7) is applied for each sediment fraction. This gives us the actual (supply-constrained) volumes of sand- and coarse-sized sediment lost from those polygons, and the net gain of unconsolidated sediment in adjacent polygons. At present, CoastalME just tracks the actual volume of eroded fine sediment: this is assumed to go into suspension, but in future developments we can incorporate transport rules for suspended material to make it available in estuarine settings. Actual elevation change (erosion or deposition) for unconsolidated sediment on each raster cell within each polygon is iteratively calculated as described previously, by fitting beach profiles: we search down-coast along the coastline of each polygon and fit beach profiles, iterating inland (for erosion) or seaward (for deposition) until each polygon's target is met; if it is not met then we traverse the coastline in the up-coast direction in case any cells have been omitted.
At the end of each time step, the framework outputs (if desired) spatial patterns as GIS raster or vector layers. It also outputs total sediment gains and losses for this time step. Finally, the updated raster grids (elevation plus stratigraphy) becomes the initial raster grids for the next time step. This loop is repeated until the end of the simulation is reached.
On the previous section, we have shown how different models (CSHORE, COVE and SCAPE) have been integrated within CoastalME. Here we demonstrate the composition for different setup conditions. Validation of the composition will be treated in a separate, dedicated future study. With the current exercise, we aim to illustrate the emergent behaviours that the integrated framework can produce that are beyond the capability of the component models alone. The input files for each run can be downloaded from the project website (see Code Availability).
Simulation results showing how sediment fraction composition
affects the shoreline responses.
The initial conditions and main attributes used for the study cases
presented below have some commonalities. The initial DEM is made of
1
Simulated embayment creation on an initially rectilinear
coastline.
Simulation results showing how a groyne interrupts the
alongshore sediment transport.
We show how the integrated model, starting with the same DEM and forced by the same deep water waves and SWL but with different stratigraphy data, results in a different DEM evolution (Fig. 10).
The initial DEM (Fig. 10a) is made of two different sediment-size
compositions, in Eq. (1) all DEM sediment is consolidated fine material
(i.e. when eroded is lost in suspension), in Eq. (2) 80 % is
consolidated fine and the remaining 20 % is consolidated sand. Wave
forcing is constant with offshore significant wave height of
2
We show how a weak segment of a long continuous line of defence
results in the formation of a bay and cliff on an initially
rectilinear and gently sloping coastal landscape
(Fig. 11). A horizontal breakwater protects all but one segment,
O (
After 3 model years of simulation, results show how an initially straight coastline develops a small cliffed bay at the undefended segment of the coastline (Fig. 11b). The breakwater is not at the coastline at the start of the simulation. After about 90 days of simulation the consolidated platform at the seaward side of the breakwater is eroded and the shoreline retreats. Once the shoreline reaches the breakwater, no more landward erosion occurs on the protected coastline, but erosion continues along the un-protected shoreline where defences are damaged. After a year, a small bay has emerged and evolves asymptotically towards a circular-shaped bay after 3 years of simulation. The resulting bay is bounded by a vertical cliff (Fig. 11c). Similar embayments can be found in nature, for example along the south coastline of the UK (Fig. 11d) and in many other places worldwide.
We show how a groyne interrupts the alongshore sediment transport
and creates accumulation and erosion patterns as typically observed in
nature (Fig. 12). A perpendicular groyne of 84
After 1 year of simulation the initially straight coastline has advanced and prograded at different sections along the coast (Fig. 12b). At the up-drift side of the groyne, sediment is accumulated at the beach but also along the groyne-exposed face and bypasses the groyne tip to be deposited on the down-drift side. No eroding cliff is formed within the shadow zone. As typically observed, erosion occurs at the down-drift side of the groyne where the shadow zone intersects the shoreline, due to limited sediment supply resulting in a negative flux gradient.
Modularity is a fundamental requirement of the design of CoastalME. As discussed previously, the CoastalME framework captures, as software, the “essential characteristics” of component models. Therefore, if a user wishes to replace one component model with another, it must be made relatively easy for one part of the framework to be “exchanged” with an equivalent software component that provides the same functionality. In this work, we have demonstrated the integrative capacity of this novel framework by implementing several component models (Table 3).
Component model, role of component and how it is implemented in CoastalME.
Class diagram showing the three main classes included in CoastalME. Classes with yellow boxes and a CGeom prefix represent geometrical objects (e.g. CGeomLine represents a line with real-valued co-ordinates; CGeomILine is the same but with integer-valued co-ordinates). Pale blue boxes and a CRW prefix denote real-world objects (e.g. CRWCliff). White boxes and a CA prefix (e.g. CA2DShape) represent abstract geometrical or real-world objects which cannot themselves be instantiated (i.e. which can only be used to construct other classes). A full list of classes and methods included in CoastalME can be found in the framework documentation (see Code Availability).
To achieve this kind of plug-in modularity, CoastalME adopts the object-oriented architecture design and programming paradigm (e.g. Rumbaugh et al., 1991). Conceptually, the modelling framework comprises software objects, which are instances of software classes (Fig. 13). The software classes which comprise CoastalME are themselves categorized. They may represent geometrical constructs, such as a point, a line or a raster cell, or real-world objects such as a coastline, a cliff or an intervention (these latter being drawn from the ontology shown in Table 2). The inputs and outputs of each software object are clearly specified (see Code Availability): this in theory enables one software object to be replaced with another, if both offer identical inputs and outputs. Similarly, the framework provides base software elements for the implementation of new model components.
There are, nonetheless, practical limits to this modularity. Whilst the most straightforward modularity would just involve re-implementing an existing software object with an equivalent model that provides slightly different functionality, this replacement might, however, also require additional inputs. This could be the case if, for example, the user wished to try a different equation for alongshore bulk sediment transport. A more ambitious re-implementation of parts of the framework would certainly require extra inputs: this would be the case if replacing the current alongshore uniform wave routing routines with a more physically based approach. Replacing or supplementing other aspects of the CoastalME framework would require considerable redesign. Using an approach other than the current polygon-based scheme for routing unconsolidated sediment would, for example, be challenging, but the basic geometric objects can provide the building blocks for implementation of alternative models.
The model framework (currently about 17 000 lines of C
The CoastalME composition presented in this work has several capabilities than make the integrated model more appealing than using the individual models in isolation (Table 4). The most obvious additional capability relative to COVE as a stand-alone model is the ability to represent cliff and shore platform erosion and beach interaction (i.e. COVE is limited to unconsolidated sediment alone), and the new additional capability relative to SCAPE alone is the ability to reproduce highly irregular coastlines. Less obvious, but equally important, is the added capability, for both SCAPE and COVE, of capturing the effect of the regional bathymetry on the local alongshore sediment transport and the energy dissipation due to wave breaking and bottom friction (i.e. if CSHORE is used as wave propagation module). As with other one-line models (e.g. Hanson and Kraus, 2011), the offshore contour orientation in SCAPE and COVE upon which the incoming waves are refracted is assumed to be parallel to the shoreline orientation. This assumption ensures that the incident waves are realistic while preserving feedback between shoreline change and the wave transformation. However, the assumption has a limitation: an open coast without structures or sources and sinks of sediment will evolve to a straight line if a standard shoreline response model is run for a sufficiently long time. In the integrated CoastalME model, waves are propagated upon the full DEM and therefore the local gradient of the alongshore sediment transport is a combination of the local orientation of the shoreline and the regional orientation of the bathymetry (i.e. regional bathymetry controls wave propagation). Figure 10 illustrates the effect of this regional bathymetry influence on the two simulated cases. For the case of DEM being made of all fine consolidated sediment, the shoreline retreats following the regional bay-shaped bathymetry. The sediment-sharing polygons at the end of the simulation are similar to the ones at the beginning, but translated landward. For the case of mixed consolidated fine and sand DEM, the shoreline also closely follows the regional bay-shaped bathymetry since most of the beach sediment volume is at the shoreline. In this last case, the sediment-sharing polygons at the end of the simulation have not only being translated landward but also have a more intricate sediment-sharing pattern than the former ones.
Capabilities of model components SCAPE and COVE and integrated CoastalME composition.
Y and N: capability included and capability not included, respectively.
CoastalME's representation of space, and of the changes occurring within its spatial domain, involves both raster (i.e. grid) and vector (i.e. line) representations of spatial objects. This is commonplace in modern GIS packages. What is relatively unusual, however, is that in the CoastalME framework data is routinely and regularly transformed between these two representations during each time step of a simulation. This may appear both perverse and computationally inefficient: however, there are advantages which will be discussed below.
A coast is an approximately linear boundary between sea and land: hence (and unsurprisingly) coastal modelling has a strong historical emphasis on linear – i.e. vector – models (see the discussion of LSCB models). It was clear from the outset that CoastalME would build upon this tradition and so would use 2-D vector representations of coastal features.
However, a raster grid – comprised of multiple cells, usually square or rectangular – is a widely used alternative approach to representing 2-D space. Raster grids have several attractive features when used for the acquisition, storage and manipulation of spatial data (e.g. Densmore et al., 1998). Data such as topography are readily available in grid form and linkage with other environmental models is facilitated, since such models often output their results as raster grids. Also, cellular automaton (CA) models operate upon regular grids and have taught us much regarding the spatial patterns produced by emergent behaviour (e.g. Dearing et al., 2006; Favis-Mortlock, 2013b; Murray et al., 2014). Thus, at an early stage of development it was recognized that using raster grids for data input, storage and output would provide a consistent framework for handling sediment exchange (and hence sediment mass balance), whilst a variety of raster and vector representations could be used to describe morphological change.
A raster grid also has several disadvantages. The first is the creation of axially aligned spatial artefacts: it is not trivial to ensure that cell-to-cell movement is uninfluenced by the alignment of the grid's axes. To achieve this invariably involves some computational expense. There is also the problem of spatial precision and computational needs. The cell is the smallest spatial unit of the grid, so small spatial features can only be adequately captured by using small grid cells. Similar reasoning applies when there is a need to represent cell-to-cell flows that are fast-moving relative to cell size: for explicit formulations, the Courant–Friedrichs–Lewy Condition requires that the time step must be kept small enough for information to have enough time to propagate through the discretized space (Weisstein, 2016), yet this can dramatically increase computation time. A third consideration regarding cell size results from the tendency of the dominant geomorphological process to change with changes in spatio-temporal focus (Schumm and Lichty, 1965). But as raster cells shrink or grid sizes grow, computational requirements increase non-linearly. If the majority of grid cells are involved in computation during most of the simulation, the increase in computational requirements may be roughly the square of the ratio of decrease in cell side, or even worse (Favis-Mortlock, 2013b).
Yet coastal modelling – with its strongly line-oriented focus – does not require an egalitarian treatment of grid cells. The computational focus need only be on the coastal zone, i.e. on a subset of grid cells; with much less happening, computationally-wise, on the remainder of the grid. So we reasoned that despite our need for small cells (since we would be dealing with small features, and sometimes with fast-moving fluxes) and hence a large grid, only relatively few cells within that grid – those on or near the coastline – would require computationally expensive treatment. This was reassuring, but there is of course a computational overhead associated with conversion of spatial features between vector and raster representations. By contrast, the model's treatment of simulated time is conventional. There is a fixed time step that can, in principle as for any implicit method, be of any duration. In practice, however, there are constraints on time step duration due to the amount of sediment that can be eroded or deposited in a single time step without unrealistically de-coupling the morphology change and assumed hydrodynamic forcing during a given time step (Ranasinghe et al., 2011).
In summary, CoastalME's hybrid raster–vector structure involves a trade-off between increased complexity (due to the need to transform between raster and vector representations) and parsimonious spatial structure (because the majority of computation involves only cells on or near the coast).
Numerical modelling of complex coastlines requires consideration of
interactions between multiple coastal landforms. Despite efforts to
couple separate models (e.g. software wrappers such as OpenMI and
CSDMS), there is a need to deal more directly with the semantics of
the various entities being modelled. We have presented here
a description of, and proof of concept results from, a flexible and
innovative modelling framework (CoastalME) for integrated coastal
morphodynamic modelling at decadal to centennial timescales and
spatial scales of 10 to 100
The rationale underpinning CoastalME results from the observation that most of the existing simulation models for coastal morphodynamics on meso-scales conceptualize the real complex 3-D topography of the coastal zone using simplified geometries. Accordingly, we have devised a spatial framework which is consistent with these simple geometries, and which permits the representation of these existing models in terms of behavioural rules which operate within this spatial framework. Thus, the DEM and stratigraphy is represented as a raster grid of regular cells, each of which holds some thickness of consolidated and unconsolidated sediment which is itself comprised from three size fractions (coarse, fine, sand). Vector-based spatial objects are created at each time step that represent features such as the coastline, profiles which are normal to that coastline and polygonal coastal cells that are partially bounded by these normal profiles. Driven by external boundary conditions (waves, currents and sea level), coastal processes which mobilize sediment are simulated using these vector-based objects, and the resulting changes to the spatial distribution of sediment are then stored in the raster grid. Modelled topography therefore changes as each cell's store of sediment changes its thickness during a simulation, with sediment being eroded in some cells and deposited in others, maintained in suspension or lost at the boundaries due to external boundary conditions (waves, currents and sea-level changes). In addition to the set of blocks or raster objects, the authors suggested a minimum set of classes needed to reproduce a generic morphodynamic model. We suggest that a variety of existing coastal models, each of which represents a single landform element or a limited range of elements, contributing to coastal morphodynamics (e.g. estuary, salt marsh, dunes etc.), may be integrated within CoastalME's modelling framework. As a proof-of-concept example, we have integrated a one-line model for very irregular sediment-rich coastlines with a soft cliff and beach erosion model. We then verify that the integrated models behave as expected, for example by Eq. (1) demonstrating that given the same initial topography and forced by the same external drivers, differing stratigraphic inputs produce different coastal morphologies; Eq. (2) showing how a weak segment on a coastline of defence can evolve into an embayment; and Eq. (3) how a groyne can partially block the alongshore sediment transport creating zones of accretion and erosion.
The CoastalME is developed and maintained within the GitHub
web-based repository hosting service. This repository allows users
to download frozen versions of the model (version 1.0 at the time of
writing) to keep their local copy up to date. The version 1 can be
found in
This code is also available from the iCOASST project-mode dedicated
web site at the Coastal Channel Observatory web site
(
CoastalME is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation – either version 3 of the License, or (at your discretion) any later version. This program is distributed in the hope that it will be useful, but without any warranty, without even the implied warranty of merchantability or fitness for a particular purpose. see the GNU General Public License for more details. The user receives a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
The authors declare that they have no conflict of interest.
This work was funded by the Natural Environment Research Council (NERC) as part of the Integrating Coastal Sediment Systems (iCOASST) project (NE/J005541/1), with the Environment Agency as an embedded project stakeholder. Special thanks to Bradley Johnson from the US Army Corp of Engineers for allowing us to include the executable of CSHORE as part of this composition. This paper is published with the permission of the Executive Director, BGS (NERC). The authors would like to thank the two anonymous referees for their constructive and detailed feedback. Edited by: Thomas Poulet Reviewed by: two anonymous referees