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Figure 6. Methodological approach followed to classify the elevation profiles along the Great Britair coastline. The scripts used for the different steps are indicated and included as supplementary information Figure 6. Methodological approach followed to classify the elevation profiles along the Great Britain (in the order of millions of transects) to cover the extent of the whole coastline of GB, including the islands, which is 31,368 km, according to Ordnance Survey (OS). To delineate the orthogonal transects, we chose the same approach used in the CliffMetric algorithm proposed by [9], which was specifically designed to resolve coastlines with very irregular shapes such as the GB coastline. As our goal was to assess the likely response of the different elevation transects to a sea-level rise, based uniquely on backshore topographical data, we selected the OS High Water Line as the preferred coastline for generating the orthogonal transects. The CliffMetric code proposed by [9] automatically delineates the coastline for a given still water level but does not allow the user to define a coastline as an input. Our first step was then to modify the CliffMetric code to add the option of a user-defined coastline. This improved version of CliffMetric was then used to extract the elevation profiles from a DTM provided by BlueSky International Limited (5 m resolution) and the most up-to-date available DTM for GB (BlueSky is a commercial product subject to license). The dimensionality of the transects extracted was then reduced using Principal Component Analysis (PCA) [11]. The reduced dimension set of the elevation transects was then clustered using the K-means-partitional clustering approach in MATLAB [12]. We chose a partitional clustering approach over a hierarchical approach due to the large number of transects on the order of 10° that we needed to cluster: the number of distance calculations for hierarchical approaches increases geometrically with the number of observations. [he partitional approach is an iterative process in which experts have to assess the number of clusters and the algorithm iteratively guesses the centroids or central point in each cluster, and assign points to the cluster of their nearest centroid. The sensitivity of the number of clusters and location was tested by using different number of clusters from 5 to 10. We found that ten clusters were the minimum required to separate all types of environments; in particular, we needed to increase from 9 to 10 to be able to separate the low-lying cliff of East England (Cell 3) from the abundant cluster 8. The sensitivity to the seed centroid was tested by running the clustering ten times for Nc = 10, mapping the clusters over aerial photography as shown in Figure 12 and confirming that the regional statistics remained unchanged (i.e., that the top five dominant clusters per region remained dominant).

Figure 6 Methodological approach followed to classify the elevation profiles along the Great Britair coastline. The scripts used for the different steps are indicated and included as supplementary information Figure 6. Methodological approach followed to classify the elevation profiles along the Great Britain (in the order of millions of transects) to cover the extent of the whole coastline of GB, including the islands, which is 31,368 km, according to Ordnance Survey (OS). To delineate the orthogonal transects, we chose the same approach used in the CliffMetric algorithm proposed by [9], which was specifically designed to resolve coastlines with very irregular shapes such as the GB coastline. As our goal was to assess the likely response of the different elevation transects to a sea-level rise, based uniquely on backshore topographical data, we selected the OS High Water Line as the preferred coastline for generating the orthogonal transects. The CliffMetric code proposed by [9] automatically delineates the coastline for a given still water level but does not allow the user to define a coastline as an input. Our first step was then to modify the CliffMetric code to add the option of a user-defined coastline. This improved version of CliffMetric was then used to extract the elevation profiles from a DTM provided by BlueSky International Limited (5 m resolution) and the most up-to-date available DTM for GB (BlueSky is a commercial product subject to license). The dimensionality of the transects extracted was then reduced using Principal Component Analysis (PCA) [11]. The reduced dimension set of the elevation transects was then clustered using the K-means-partitional clustering approach in MATLAB [12]. We chose a partitional clustering approach over a hierarchical approach due to the large number of transects on the order of 10° that we needed to cluster: the number of distance calculations for hierarchical approaches increases geometrically with the number of observations. [he partitional approach is an iterative process in which experts have to assess the number of clusters and the algorithm iteratively guesses the centroids or central point in each cluster, and assign points to the cluster of their nearest centroid. The sensitivity of the number of clusters and location was tested by using different number of clusters from 5 to 10. We found that ten clusters were the minimum required to separate all types of environments; in particular, we needed to increase from 9 to 10 to be able to separate the low-lying cliff of East England (Cell 3) from the abundant cluster 8. The sensitivity to the seed centroid was tested by running the clustering ten times for Nc = 10, mapping the clusters over aerial photography as shown in Figure 12 and confirming that the regional statistics remained unchanged (i.e., that the top five dominant clusters per region remained dominant).

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Figure 1. Applications of the essential Bruun rule to different control volumes produce different instantiations. (a) Application to a shoreface and beach gives the classic Bruun rule. (b) Application to a beach and shoreface backed by a barrier island gives a barrier Bruun rule. (c) Application to a beach and shoreface backed by a cliff gives a cliff Bruun rule. In each case, the implied transgression slope (black dashed line) equals the average profile slope S, but only in the classic Bruun rule is this equal to the nearshore slope S; (gold solid line). (Adapted by authors from [7]). expert elucidation. This approach enabled (1) the classification of the types of coastline morphology that occur around the GB coastline; (2) an estimation of the main contributions to the generalized sediment conservation equation for each coastline type; and (3) the attribution of the entire Great Britain coastline with these coastline types.
Figure 1. Applications of the essential Bruun rule to different control volumes produce different instantiations. (a) Application to a shoreface and beach gives the classic Bruun rule. (b) Application to a beach and shoreface backed by a barrier island gives a barrier Bruun rule. (c) Application to a beach and shoreface backed by a cliff gives a cliff Bruun rule. In each case, the implied transgression slope (black dashed line) equals the average profile slope S, but only in the classic Bruun rule is this equal to the nearshore slope S; (gold solid line). (Adapted by authors from [7]). expert elucidation. This approach enabled (1) the classification of the types of coastline morphology that occur around the GB coastline; (2) an estimation of the main contributions to the generalized sediment conservation equation for each coastline type; and (3) the attribution of the entire Great Britain coastline with these coastline types.
Table 1. Shoreline sediment conservation equation parameters °. Figure 2. The shoreline response to a sea-level rise for both passive inundation and morphodynamic evolution is best understood from a general analysis of the conservation of sediments over a cross-shore profile z = n[x] at a fixed alongshore position y, using a shoreface control volume s < x < u. The sediment conservation Equation (1) assumes the control volume contains a relatively homogeneous deposit with an average sediment concentration c, but allows the possibility of a compositional change at the shoreline s, where the sediment concentration cg may differ from c. In general, c may represent bulk sediment or sediment of a particular size range. Symbols explained in Table 1. (Figure adapted by authors from [7]).
Table 1. Shoreline sediment conservation equation parameters °. Figure 2. The shoreline response to a sea-level rise for both passive inundation and morphodynamic evolution is best understood from a general analysis of the conservation of sediments over a cross-shore profile z = n[x] at a fixed alongshore position y, using a shoreface control volume s < x < u. The sediment conservation Equation (1) assumes the control volume contains a relatively homogeneous deposit with an average sediment concentration c, but allows the possibility of a compositional change at the shoreline s, where the sediment concentration cg may differ from c. In general, c may represent bulk sediment or sediment of a particular size range. Symbols explained in Table 1. (Figure adapted by authors from [7]).
Figure 3. Idealized geometry and mass balance on a steep coast. Nearshore geometry is fixed but cliff height H- can vary in time. Shoreline s located at cliff toe. Beach top elevation 1s rises with sea level Zseq, maintaining a fixed beach relief. Cliff erosion produces sediment flux q;, which fuels nearshore aggradation. Sand fraction cg of cliff deposits may differ from nearshore sand fraction cs. (Figure adapted by authors from [7]). where S is the average slope of the combined cliff and nearshore profile (Figure 3). This simplified model assumes cliff erosion (4 < 0) produces a seaward flux of sediment (q, > 0) in concert with shoreline retreat and produces sediment that is instantly available to feed nearshore aggradation. For a rocky coast, cliff retreat occurs only after shoreline retreat undercuts the cliff, and produces rock fragments, which must be weathered before sand becomes available to the nearshore. In the special case where cliff and nearshore deposits are homogeneous, cp = cs, Equation (5) reduces to the cliff Bruun rule of Equation (1) and Figure 1c. However, the slope S will vary as the cliff relief H.[t] changes through time. sea level Zseq, maintaining a fixed beach relief. Cliff erosion produces sediment flux q;, which fuels
Figure 3. Idealized geometry and mass balance on a steep coast. Nearshore geometry is fixed but cliff height H- can vary in time. Shoreline s located at cliff toe. Beach top elevation 1s rises with sea level Zseq, maintaining a fixed beach relief. Cliff erosion produces sediment flux q;, which fuels nearshore aggradation. Sand fraction cg of cliff deposits may differ from nearshore sand fraction cs. (Figure adapted by authors from [7]). where S is the average slope of the combined cliff and nearshore profile (Figure 3). This simplified model assumes cliff erosion (4 < 0) produces a seaward flux of sediment (q, > 0) in concert with shoreline retreat and produces sediment that is instantly available to feed nearshore aggradation. For a rocky coast, cliff retreat occurs only after shoreline retreat undercuts the cliff, and produces rock fragments, which must be weathered before sand becomes available to the nearshore. In the special case where cliff and nearshore deposits are homogeneous, cp = cs, Equation (5) reduces to the cliff Bruun rule of Equation (1) and Figure 1c. However, the slope S will vary as the cliff relief H.[t] changes through time. sea level Zseq, maintaining a fixed beach relief. Cliff erosion produces sediment flux q;, which fuels
Figure 4. Idealized geometry and mass balance on a gentle coast. Barrier island consists of subaqueous shoreface, subaerial island (overwash zone) and subaqueous back-barrier. Island bounded seaward by shoreline s and landward by backshore b, both at sea level Zseq. Shoreface and island have fixed geometry. Back-barrier slope S, and shape ay are fixed, but back-barrier length L, and relief Hy can vary in time. Island maintained by overwash flux qs across the shoreline. Back-barrier growth fuelled by overwash flux qp across the backshore. Sand fraction cs of barrier island deposits may differ from sand fraction cy of backshore deposits. (Figure adapted by authors from [7]).
Figure 4. Idealized geometry and mass balance on a gentle coast. Barrier island consists of subaqueous shoreface, subaerial island (overwash zone) and subaqueous back-barrier. Island bounded seaward by shoreline s and landward by backshore b, both at sea level Zseq. Shoreface and island have fixed geometry. Back-barrier slope S, and shape ay are fixed, but back-barrier length L, and relief Hy can vary in time. Island maintained by overwash flux qs across the shoreline. Back-barrier growth fuelled by overwash flux qp across the backshore. Sand fraction cs of barrier island deposits may differ from sand fraction cy of backshore deposits. (Figure adapted by authors from [7]).
Figure 5. Graph of the two real branches of Lambert W,=9 function and geometrical interpretation based on our simple cliff-shoreface model assuming (co /cs) = 1 or that cliff and shoreface sediment composition are the same. The black arrows indicate the direction towards which an initial state will evolve over time. Points I, II and III are all on the principal branch W;—9, and all tend toward equilibrium (x = 0), while Point IV is the only one over W;,_ and represents an unstable point that will evolve towards -oo over time. based on our simple cliff-shoreface model assuming (cg/cs) = 1 or that cliff and shoreface sediment where z, and Zy, are the initial values of z in x = ze* for the cliff and back-barrier models of Equations (9) and (15), respectively, and are functions of both the geometry of the coast and the sediment fraction composition. Equations (20) and (21) provide a simple geometrical relationship between the topography and the sediment fraction ratio for z, and zp to be equal to —1, 0 and > 0 which corresponds with the x values x = —1/e, x = 0 and x >> 0, with the maximum, median and minimum characteristic rates of change of W with x. From the expected rates of change of H,[t] and H,[t] and Equations (7) and (12), we can also infer if the shoreline position will retreat (4 < 0) or advance (4 > 0) as | sea-level rises. We first notice that the condition for the shoreline to advance requires ac <0 and 4 sat > 0 for our cliff and back-barrier models, respectively. Hereinafter, we will only consider the main branch W,<p solution, which will continuously evolve towards equilibrium and therefore, the condition for shoreline advance under a sea-level rise can be expressed as composition are the same. The black arrows indicate the direction towards which an initial state
Figure 5. Graph of the two real branches of Lambert W,=9 function and geometrical interpretation based on our simple cliff-shoreface model assuming (co /cs) = 1 or that cliff and shoreface sediment composition are the same. The black arrows indicate the direction towards which an initial state will evolve over time. Points I, II and III are all on the principal branch W;—9, and all tend toward equilibrium (x = 0), while Point IV is the only one over W;,_ and represents an unstable point that will evolve towards -oo over time. based on our simple cliff-shoreface model assuming (cg/cs) = 1 or that cliff and shoreface sediment where z, and Zy, are the initial values of z in x = ze* for the cliff and back-barrier models of Equations (9) and (15), respectively, and are functions of both the geometry of the coast and the sediment fraction composition. Equations (20) and (21) provide a simple geometrical relationship between the topography and the sediment fraction ratio for z, and zp to be equal to —1, 0 and > 0 which corresponds with the x values x = —1/e, x = 0 and x >> 0, with the maximum, median and minimum characteristic rates of change of W with x. From the expected rates of change of H,[t] and H,[t] and Equations (7) and (12), we can also infer if the shoreline position will retreat (4 < 0) or advance (4 > 0) as | sea-level rises. We first notice that the condition for the shoreline to advance requires ac <0 and 4 sat > 0 for our cliff and back-barrier models, respectively. Hereinafter, we will only consider the main branch W,<p solution, which will continuously evolve towards equilibrium and therefore, the condition for shoreline advance under a sea-level rise can be expressed as composition are the same. The black arrows indicate the direction towards which an initial state
Figure 7. The Principal Component Analysis (PCA) suggests that we can capture the majority of the variability observed on the de-trended elevation profiles with a reduced number of Principal Components (PCs): (a) percentage of variability explained by the first 20 PCs. The percent of cumulative variance explained is on the y-axis, and the Principal Component (PC) number is on the x-axis; (b) comparison of one of the original elevation profiles, x, versus the reconstructed, x, using the first 10 PCs. Top panel shows the elevation profile, and bottom panel, the absolute difference between the original and reconstructed. dimensions of the observation matrix by a factor of 10, from 100 observations for each transect to just 10 PCs, while explaining 99% of the total variability. Figure 7. The Principal Component Analysis (PCA) suggests that we can capture the majority of Components (PCs): (a) percentage of variability explained by the first 20 PCs. The percent of
Figure 7. The Principal Component Analysis (PCA) suggests that we can capture the majority of the variability observed on the de-trended elevation profiles with a reduced number of Principal Components (PCs): (a) percentage of variability explained by the first 20 PCs. The percent of cumulative variance explained is on the y-axis, and the Principal Component (PC) number is on the x-axis; (b) comparison of one of the original elevation profiles, x, versus the reconstructed, x, using the first 10 PCs. Top panel shows the elevation profile, and bottom panel, the absolute difference between the original and reconstructed. dimensions of the observation matrix by a factor of 10, from 100 observations for each transect to just 10 PCs, while explaining 99% of the total variability. Figure 7. The Principal Component Analysis (PCA) suggests that we can capture the majority of Components (PCs): (a) percentage of variability explained by the first 20 PCs. The percent of
Figure 8. Cross-shore eigenvectors for the first three PCs. The percentage shown in the legend indicates the percentage of variability explained by each PC.
Figure 8. Cross-shore eigenvectors for the first three PCs. The percentage shown in the legend indicates the percentage of variability explained by each PC.
Figure 9. Centroids and spreading of scores for all the six clusters obtained. The coloured circle represents the centroid of the cluster, and the solid vertical and horizontal lines represent twice the standard deviation of each PC. The percentage of profiles belonging to each cluster is shown in parentheses in the legend together with the cluster number. Figure 9. Centroids and spreading of scores for all the six clusters obtained. The coloured circle Figure 9 shows the centroid and variability of each one of the ten different clusters obtained when plotted against the first and second PCs. Cluster #8 is the most abundant type of profile, representing 48% of all the profiles, while the remaining clusters combined represent the remaining 42% of the profiles. The spreading of Cluster #8 is also significantly smaller that the spreading of the other clusters as shown by the horizontal and vertical lines that represent twice the standard deviation for each cluster. The low scores for Cluster #8, for both PCs, suggest that profiles belonging to this cluster are close to elevation profiles with constant slopes and low elevation. The large spreading of both PC scores for the other clusters suggests that there is a significant variability in both the cliff top elevation and horizontal location.
Figure 9. Centroids and spreading of scores for all the six clusters obtained. The coloured circle represents the centroid of the cluster, and the solid vertical and horizontal lines represent twice the standard deviation of each PC. The percentage of profiles belonging to each cluster is shown in parentheses in the legend together with the cluster number. Figure 9. Centroids and spreading of scores for all the six clusters obtained. The coloured circle Figure 9 shows the centroid and variability of each one of the ten different clusters obtained when plotted against the first and second PCs. Cluster #8 is the most abundant type of profile, representing 48% of all the profiles, while the remaining clusters combined represent the remaining 42% of the profiles. The spreading of Cluster #8 is also significantly smaller that the spreading of the other clusters as shown by the horizontal and vertical lines that represent twice the standard deviation for each cluster. The low scores for Cluster #8, for both PCs, suggest that profiles belonging to this cluster are close to elevation profiles with constant slopes and low elevation. The large spreading of both PC scores for the other clusters suggests that there is a significant variability in both the cliff top elevation and horizontal location.
Figure 10. Statistical comparison between clusters: (a) violin plot of maximum elevation per cluster; (b,c) elevation profiles for each cluster showing the profile closest to the centroid (b) and most frequent profile (c). The percentage of profiles belonging to each cluster is shown in parentheses in the legend together with the cluster number. Figure 10. Statistical comparison between clusters: (a) violin plot of maximum elevation per cluster; cluster varies from 5% for Cluster #1 to 85% for Cluster #7. cluster shown in the violin plots suggests that the most frequent (mode) and the average (mean and median) profiles are not the same. The most frequent profile elevation is consistently smaller than the median and mean values for all clusters. The differences between the most frequent and averaged elevation profiles is shown in Figure 10b,c, which illustrate the closest-to-centroid and most-frequent elevation profiles for each cluster. The elevation profile for Cluster #8 is the flattest of all the de-trended elevation profiles, irrespectively of if showing the closest-to-centroid (Figure 10b) or most-frequent (Figure 10c) profile. The elevation for the closest-to-centroid profiles for all clusters, but Cluster #8, presents a maximum elevation between the coast point (relative chainage = 0%) and the most landward point of the profile (relative chainage = 100%) (Figure 10b). The elevation profile for Clusters # 1, 2, 3, 4,5, 6, 7,9 and 10 differs by both the location of the maximum and the elevation of the maximum. In chainage relative units, the location of the maximum of the de-trended elevation profiles for each cluster varies from 5% for Cluster #1 to 85% for Cluster #7.
Figure 10. Statistical comparison between clusters: (a) violin plot of maximum elevation per cluster; (b,c) elevation profiles for each cluster showing the profile closest to the centroid (b) and most frequent profile (c). The percentage of profiles belonging to each cluster is shown in parentheses in the legend together with the cluster number. Figure 10. Statistical comparison between clusters: (a) violin plot of maximum elevation per cluster; cluster varies from 5% for Cluster #1 to 85% for Cluster #7. cluster shown in the violin plots suggests that the most frequent (mode) and the average (mean and median) profiles are not the same. The most frequent profile elevation is consistently smaller than the median and mean values for all clusters. The differences between the most frequent and averaged elevation profiles is shown in Figure 10b,c, which illustrate the closest-to-centroid and most-frequent elevation profiles for each cluster. The elevation profile for Cluster #8 is the flattest of all the de-trended elevation profiles, irrespectively of if showing the closest-to-centroid (Figure 10b) or most-frequent (Figure 10c) profile. The elevation for the closest-to-centroid profiles for all clusters, but Cluster #8, presents a maximum elevation between the coast point (relative chainage = 0%) and the most landward point of the profile (relative chainage = 100%) (Figure 10b). The elevation profile for Clusters # 1, 2, 3, 4,5, 6, 7,9 and 10 differs by both the location of the maximum and the elevation of the maximum. In chainage relative units, the location of the maximum of the de-trended elevation profiles for each cluster varies from 5% for Cluster #1 to 85% for Cluster #7.
which was classified mostly as Clusters 8, 1 and, to a lesser degree, 5. The variations of the cluster type observed at the Blakeney area seem to be related with the relief at the end of the shoreline normal. The Wash is a very low-lying area that was also dominantly classified as Clusters 8 and 1. The high cliffs around St. Bees and Flamborough head were mostly classified as Clusters 2, 3 and, mostly, 6. No clear pattern in the spatial distribution was observed for Clusters 4, 7,9 and 10. The spatial distribution of the topographical clusters is best understood by plotting the frequency distribution per region. Figure 11. Cluster types mapped to the coast point along the high water mark line used to delineate the transects. Names of the locations around the GB coastline indicated as text. Source of aerial imagery: Esri, Maxar, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community, v10.6. Figure 11. Cluster types mapped to the coast point along the high water mark line used to delineate the
which was classified mostly as Clusters 8, 1 and, to a lesser degree, 5. The variations of the cluster type observed at the Blakeney area seem to be related with the relief at the end of the shoreline normal. The Wash is a very low-lying area that was also dominantly classified as Clusters 8 and 1. The high cliffs around St. Bees and Flamborough head were mostly classified as Clusters 2, 3 and, mostly, 6. No clear pattern in the spatial distribution was observed for Clusters 4, 7,9 and 10. The spatial distribution of the topographical clusters is best understood by plotting the frequency distribution per region. Figure 11. Cluster types mapped to the coast point along the high water mark line used to delineate the transects. Names of the locations around the GB coastline indicated as text. Source of aerial imagery: Esri, Maxar, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community, v10.6. Figure 11. Cluster types mapped to the coast point along the high water mark line used to delineate the
Figure 12. Example of the regional statistics that we extracted for the 22 regions into which we divided the GB coastline: (a) shows the region coverage; (b—g) show the counts of topographical cluster types for some regions (all other regions are shown in Supplementary Materials). Source of aerial imagery: Esri, Maxar, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community, v10.6. Figure 12. Example of the regional statistics that we extracted for the 22 regions into which we divided
Figure 12. Example of the regional statistics that we extracted for the 22 regions into which we divided the GB coastline: (a) shows the region coverage; (b—g) show the counts of topographical cluster types for some regions (all other regions are shown in Supplementary Materials). Source of aerial imagery: Esri, Maxar, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community, v10.6. Figure 12. Example of the regional statistics that we extracted for the 22 regions into which we divided
Figure 13. Main geometrical attributes extracted from the elevation profiles along the GB coastline. e at e e S there that t We extracted the geometrical attributes of the backshore topographical profile as shown i Figure 13 for all transects and calculated the regional statistics. The backshore shape parameter, a defined for the domain —co < ag < 1 represents how much the area under the backshore elevatio profile from the coast to the end of the transect differs from a rectangle that has the same length and a eva eva similar to a rectangle and smaller if it is not. Negative values of ag can occur for profiles where th eva the backshore slope, So; cliff face slope, S,; and initial cliff relief, H.o. Figure 14 shows the region< atis the end of the profile, z,,,4, because as we saw from the cluster type 7 (Figure 10), Zeng < Zmax, as th tion equal to the maximum profile elevation, Zax. Note that we used Zjay instead of the elevatio tion does not grow continuously backshore. This shape parameter will be close to 1 if the shape : tion is not always larger than or equal to the elevation at the initial point (x = 0). We also extracte tics for the clusters interpreted as cliff-type (i.e., Clusters 2 to 4, 6, 7,9 and 10). We observed thi was a small percentage, of 4%, of the data that produced negative initial cliff relief, suggestin hey did not represent a cliff coast either, and they were omitted for our assessment of the cli coast response to a rising sea level around the GB coastline.
Figure 13. Main geometrical attributes extracted from the elevation profiles along the GB coastline. e at e e S there that t We extracted the geometrical attributes of the backshore topographical profile as shown i Figure 13 for all transects and calculated the regional statistics. The backshore shape parameter, a defined for the domain —co < ag < 1 represents how much the area under the backshore elevatio profile from the coast to the end of the transect differs from a rectangle that has the same length and a eva eva similar to a rectangle and smaller if it is not. Negative values of ag can occur for profiles where th eva the backshore slope, So; cliff face slope, S,; and initial cliff relief, H.o. Figure 14 shows the region< atis the end of the profile, z,,,4, because as we saw from the cluster type 7 (Figure 10), Zeng < Zmax, as th tion equal to the maximum profile elevation, Zax. Note that we used Zjay instead of the elevatio tion does not grow continuously backshore. This shape parameter will be close to 1 if the shape : tion is not always larger than or equal to the elevation at the initial point (x = 0). We also extracte tics for the clusters interpreted as cliff-type (i.e., Clusters 2 to 4, 6, 7,9 and 10). We observed thi was a small percentage, of 4%, of the data that produced negative initial cliff relief, suggestin hey did not represent a cliff coast either, and they were omitted for our assessment of the cli coast response to a rising sea level around the GB coastline.
Figure 14. Example of the regional statistics that we extracted for the 22 regions into which we divided the GB coastline. As an example, we show here the stats for region “Cell 3”, and all other regions are in Supplementary Materials; panels show the counts per region of the cliff top elevation (a), slope of cliff face (b), shape of the inland topography (c), inland slope (d) and area per unit length (e). These geometrical attributes were calculated as shown in Figure 14. Region area is shown in Figure 13.
Figure 14. Example of the regional statistics that we extracted for the 22 regions into which we divided the GB coastline. As an example, we show here the stats for region “Cell 3”, and all other regions are in Supplementary Materials; panels show the counts per region of the cliff top elevation (a), slope of cliff face (b), shape of the inland topography (c), inland slope (d) and area per unit length (e). These geometrical attributes were calculated as shown in Figure 14. Region area is shown in Figure 13.
Figure 15. Regional statistics of initial cliff relief H,o along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+” symbol. See Table S1 for correspondence between region number and admin unit used.
Figure 15. Regional statistics of initial cliff relief H,o along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+” symbol. See Table S1 for correspondence between region number and admin unit used.
Figure 16. Regional statistics of initial backshore slope So along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+” symbol. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1, 5 and 8) and 4% of other clusters that had H,9 < 0. See Table S1 for correspondence between region number and admin unit used.
Figure 16. Regional statistics of initial backshore slope So along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+” symbol. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1, 5 and 8) and 4% of other clusters that had H,9 < 0. See Table S1 for correspondence between region number and admin unit used.
Figure 17. Regional statistics of z; along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+2” symbol. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1, 5 and 8) and 4% of other clusters that had H,.9 < 0 and So > 0. We used Equation (20) and assumed a shoreface slope representative of GB’s open coast to be equal to 10-°. See Table S1 for correspondence between region number and admin unit used.
Figure 17. Regional statistics of z; along GB coastline. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+2” symbol. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1, 5 and 8) and 4% of other clusters that had H,.9 < 0 and So > 0. We used Equation (20) and assumed a shoreface slope representative of GB’s open coast to be equal to 10-°. See Table S1 for correspondence between region number and admin unit used.
Figure 18. Cont. percentage of less than 1% being negative.
Figure 18. Cont. percentage of less than 1% being negative.
Figure 18. Regional statistics of Ho — Heo along GB coastline. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1,5 and 8) and 4% of other clusters that had H,9 < 0 and Sp > 0. We used Equation (8b) and assumed a shoreface slope representative of GB’s open coast to be equal to 10~?. Grey bins represent section counts where H.9 — Heo > 0 (i.e., potential sediment sources), and red bins represent section counts for which H,9 — He. < 0 (i.e., potential sediment sinks).
Figure 18. Regional statistics of Ho — Heo along GB coastline. To obtain these stats, we did not include clusters that corresponded with non-cliff coastlines (Clusters 1,5 and 8) and 4% of other clusters that had H,9 < 0 and Sp > 0. We used Equation (8b) and assumed a shoreface slope representative of GB’s open coast to be equal to 10~?. Grey bins represent section counts where H.9 — Heo > 0 (i.e., potential sediment sources), and red bins represent section counts for which H,9 — He. < 0 (i.e., potential sediment sinks).
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