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Payo et al., (2016) described in detail the rationale behind CoastalME and demonstrated how it can be used to integrate; the Soft Cliff and Platform Erosion model SCAPE, the Coastal Vector Evolution Model COVE and the Cross Shore model CSHORE.
Coastal morphology change is simulated as dynamically linked line and raster objects. The hierarchy of panels illustrate how a real coastal morphology (upper panel) is conceptualized as shoreline, shoreface profiles and estuary elements (middle panel). All elements can share sediment among them (double-headed arrow). The shoreface comprises both consolidated and non-consolidated material that forms the cliff, shore platform and beach respectively (bottom panel). At every time step the shoreline is delineated at the intersection of the Sea Level and the ground elevation. Shore face profiles are delineated perpendicular to the shoreline. The Sea Level and wave energy constrains the proportion of shoreface profiles that are morphologically active at each time step. Eroded sediment from the consolidated profile is added to the drift material to advance the shoreline or loss as suspended sediment. Gradients of the littoral drift further controls the advance and retreat of the beach profile and the amount of sediment shared with nearby sections of the shoreline.
Ground elevation is characterized as a set of regular square blocks. Each block has a global coordinate x, y, z. Left panel illustrates the DEM of Gorsleston-on-Sea (East coast of UK) provided by © Environment Agency copyright and/or database right 2015 with a raster resolution of 2m (DEM detail). Each block might be composed of six different sediment fractions (Blocks detail) made of coarse, sand and fine sediment sizes. Each sediment size fraction can be in a consolidated (capitalised) or unconsolidated state (lower case). Block types a, b, c and d illustrate blocks of same total elevation but with different sediment composition.
CoastalMe landform classification mapping, and how raster and vector coastline are used to creat sediment sharing polygons. (a) Detail of raster coastal points and the smoothed vector coastline used to draw the coastline normal. Each cell of the grid is mapped as a landform type that will be later used to apply different behavioural rules (i.e. eroding coastal cliff). (b) Coastline normal are projected seaward and merged if the intersect before the end of the user defined normal is reached. © Triangular and trapezoidal sediment sharing polygons are created using the merged coastline normal as polygon edges. Polygons at the boundary of the grid are created differently to ensure that all cells are within the grid.
Two wave propagation modules are integrated in CoastalME. Deep water waves are propagated along each coastline normal (a) and then the results interpolated to all grid cells. The wave height distribution for incoming waves at 315, 270 and 225 degrees (using the CSHORE module) are shown in panels b, c, d respectively. A comparison of the wave height distribution along the same transect using CSHORE and COVE approaches is shown in panel (e).
Schematic diagram of a groin to illustrate shadowing and wave adjustment in the shadowed region. (a) The shadow zone is generated with respect to the offshore wave direction (black arrow). The angle within the shadow zone is defined by 𝜔. (b) The length of coast affected by rules for diffraction is twice the length of the shadow zone as shown by the sea cells marked as either within the shadow zone (dark grey) or on the area of influence of the shadow zone (light grey). © Adjustment of wave approach angle (arrows) by factor 1.5 times the angle within the shadow zone 𝜔 (equation (2)). The adjustment only proceeds up to 𝜔 = 90 since wave heights are zero beyond this value. Reduction in wave height due to wave crest spreading, which is defined by a sinusoidal function (equation (3)) with the wave height at the edge of the shadow zone assumed to be reduced by a factor of 0.5 with that factor increasing to 1 at 𝜔 = 90. Wave heights outside the shadow zone are also reduced to conserve wave energy following equation (4). Properties of wave at breaking are stored for into a vector coastline. Coloured dots in panel b shows wave height at breaking.
Schematic diagram illustrating how the SCAPE concept of down-wearing of the consolidated shore platform is integrated in CoastalME. (a) CoastalME represent the profile as a set of vertical blocks of consolidated and unconsolidated material. The profile of the consolidated shore platform (brown line) is obtained by querying the top elevation of the consolidated material. Beach thickness on each block is represented as the thickness of any unconsolidated material on top of the shore platform. (b) The shape function used in SCAPE is queried as a look up table along each cell of a profile to estimate the erosion potential for a given wave height at breaking and water depth (f1 in equation 5). © The beach thickness protection factor is also calculated for each cell. Shore platform is fully protected if thickness is larger than 0.23 times the wave height at breaking (Hb) and protection factor linearly increases to 1 as beach thickness decreases to zero (f2 in equation 5). (d) The SCAPE’s horizontal shore platform erosion component is converted to its vertical component using a trigonometric conversion (equation 6). The sum of all f1 values along a coastline profile are equal to 1. (e) Shore platform erosion for each cell between coastline normal is calculated as explained above and by traversing the coastline cells (in both directions) using temporary profile parallel to the right and left boundaries. CoastalME checks that shore platform erosion is calculated for all cells within the surf zone.
Illustration how notch evolution (from SCAPE) is simulated in CoastalME. (a) Notch initiation represented as vertical blocks. Eroded sediment from the cliff is transferred to a talus/beach (coarse and sand fractions) and total suspended sediment (fine-sized sediment fraction). (b) Cliff collapses if the threshold cliff notch length is reached. © Notching continues on a partially collapsed block until the block is fully eroded (d) and notching may continue in the next-landward block.
Simulation results showing how sediment fraction composition affects the shoreline responses. (a) Both simulated cases start with the same cuspate shoreline and gently sloping DEMs but shoreline after one year (coloured lines) shows opposite responses (retreat/advance). (b) DEM containing only fine sediment is eroded creating a cliff fronted with a horizontal platform, like the chalk cliff of East Sussex (UK). Eroded sediment from the Sandy DEM forms a protective beach and no cliff. © Elevation profiles at a cross section reveals how the eroded sediment from the submerged platform has formed a protective beach and how a horizontal platform has been created.
Simulated embayment creation on an initially rectilinear coastline. (a) At the start of the simulation, all the coastline of a gently sloping topography is protected by a breakwater but a short segment in the centre that is un-protected. (b) Location of the vector coastline at different time steps and final topography after three years of simulation. © The resulting embayment is bounded by a cliff similar to the Lulworth Cove bay in the south of the UK.
Simulation results showing how a groin interrupt the alongshore sediment transport. (a) Simulation starts with a rectilinear and gently sloping DEM interrupted by a groin and waves coming at 225deg (arrow). (b) After one year of simulation an eroding cliff and a beach of different widths is created. Sediment is accumulated at the up-drift side of the groin and eroded on the down drift side where the shadow zone intercepts the coastline. © Shows a groin with accumulated sand on the up-drift side and less sand on the downdrift side.