Satellite-derived sandy shoreline trends and interannual variability along the Atlantic coast of Europe

Monitoring sandy shoreline evolution from years to decades is critical to understand the past and predict the future of our coasts. Optical satellite imagery can now infer such datasets globally, but sometimes with large uncertainties, poor spatial resolution


Introduction
Sandy shorelines, which cover approximately one third of the Earth's ice-free coastline [1], provide important natural [2] and socio-economical [3] resources.They are also amongst the world's most energetic and dynamic environments [4] and in the long term they are threatened by climate change and declining sediment supply [5].It is thus critical to improve our understanding and predictive capacity of shoreline evolution over a broad range of timescales spanning days-to-century, to support the development and sustainability of sandy coastal environments [6].Past multidecadal shoreline trends can be extrapolated to provide insight into future shoreline positions at the 2100 horizon [e.g. 7, 8], while interannual shoreline variability will typically dominate the shoreline signal and its uncertainties during the next few decades before sea level rise takes over [e.g.9].Such interannual shoreline variability is often primarily enforced by large-scale climate patterns of atmospheric or coupled ocean-atmospheric variability [e.g.El Niño-Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO) 10,11].The seasonal to decadal predictability of these climate patterns recently showed increasing skill [12,13], which may allow a reduction in shoreline evolution uncertainties in the next decades.Understanding shoreline evolution on inter-annual to decadal timescales, and at local to regional spatial scales is therefore critical to understand the past and predict the future of our coasts.
Until recently, observation of coastal change on decadal/multi-decadal timescales at a sufficient temporal resolution (e.g.days, month) was only available at a small number of well-monitored sites using GNSS surveys and/or video monitoring techniques [14][15][16][17][18][19][20].Within only a few years satellite remote sensing has transformed decadal timescale coastal science from a data-poor into a data-rich field [see literature review in 21].In particular, free-of-charge publicly-available optical satellite imagery can now be used to derive shoreline positions on large spatial (O(1,000) m to global) and temporal (O(10) years) scales at relatively high frequency (O(1-10) days) using a wealth of techniques [e.g.[22][23][24].[1] first provided a high spatial (transect spacing ranging approximately 200-500 m) and temporal (yearly) resolution Satellite-Derived Shoreline (SDS) dataset at global scale, focusing on long-term shoreline trends, offering fresh perspectives of increased understanding of shoreline change globally [25].However, although SDS uncertainties are typically around 10-15 m on many beaches [e.g.22], SDS accuracy dramatically worsens on high-energy and/or low-gradient and/or mesomacrotidal beaches [26,27].Water-level (including wave action) correction [26,27] can be applied to reduce uncertainties.However, it cannot be applied globally because the type of water-level correction depends on the beach state [27] and breaking wave conditions, which are not available along the global coastline.Spatial and temporal averaging of uncertain SDS datasets can be performed to filter out some of the SDS noise and to further provide fair insight into the spatial and temporal modes of shoreline variability [28,29].Although such an approach can work on relatively straight stretches of coast, it is challenging in other environments such as embayed beaches, sandspits or estuary mouths where the time and space patterns of shoreline change can strongly vary alongshore.Because of some of these limitations, there has been a growing number of concerns raised by the coastal science community [e.g. 5, [30][31][32] on global applications where satellite-derived data, including SDS, are used to provide debatable conclusions on the past or future of our coasts globally.Another limitation of previous SDS studies at regional to global scales is that shoreline change characteristics are typically averaged geographically [i.e.latitude, longitude, country, continent 1,33,34] or at too-coarse a spatial resolution [34], which cannot capture the variability of shoreline response at the scale of the coastal environments.A large body of literature based on field data shows that coastal settings, such as coastline orientation with respect to the dominant wave climate [e.g.35] and/or wave sheltering from major headlands or offshore islands [36,37] is crucial to the spatial and temporal modes of shoreline response.
It is unclear if, and to what extent, a global SDS dataset can be used to provide a robust estimation of long-term trends, to identify the primary climate modes of atmospheric variability affecting interannual shoreline change, and to provide new insights into the spatial variability of these controls depending on some basic coastal settings.Here we focus along the Atlantic coast of Europe because: (1) the large waves [38] and tides [39] challenge SDS accuracy [26,27] and thus provide a conservative assessment for global SDS applications; (2) it comprises a large variability of coastal settings with long sandy barriers, embayed beaches, estuary mouths and tidal inlets, with also a large variability in terms of exposure and coastline orientation; (3) it contains some of the most monitored and studied stretches of coast in the world [18][19][20]35].The Atlantic coast of Europe is exposed to high-energy ocean waves generated in the North Atlantic Ocean with trends and climate controls which have been identified locally already [e.g.28,32,35,[40][41][42], and with such previous work providing critical information to interpret and validate our findings.
In this contribution, we validate and consult an improved state-of-the-art global SDS dataset to address the spatial distribution of long-term trends and interannual variability of sandy shores along the Atlantic coast of Europe, and to further identify the primary drivers and coastal settings affecting this spatial variability.By applying a moving-average approach based on distance and coastline orientation, we show that west-facing fully-exposed coasts are more affected by long-term erosion, with interannual shoreline variability controlled by the North Atlantic Oscillation [NAO, 10] at the most northern ≳ 50 • N and southern ≲ 40 • N extents, and by the West Europe Pressure Anomaly [WEPA,40] in between.In contrast, sheltered sandy beaches tend to be more prone to long-term accretion on average, and coastlines not fully exposed to the dominant ocean waves show complex and variable correlations with the dominant climate indices, providing a spatial continuum between previous local-scale studies.
While recognizing the uncertainties associated with satellite-derived shoreline analysis, we advocate that geographically-averaged SDS analyses, especially based on coarse transect spacing (O(1-10) km), can miss crucial information on the drivers and coastal settings affecting shoreline variability and trend, and that future global SDS analysis will benefit from including such information at high spatial resolution to robustly cluster forcing-response shoreline modes.

Study site characteristics
The study area covers the west coast of Europe (Figure 1a,b) which is exposed to high-energy waves generated in the North Atlantic ocean.We used the global Shoreline Monitor (SM) yearly SDS dataset made of approximately 250-to 500-m spaced transects [1].This dataset was extended to 2021 (1984-2021 coverage) and used an improved sandy (including gravel) shoreline classification [43,see Methods].In total, the study area covers approximately 11,000 km of coastline, including approximately 2,840 km of sandy shores (≈ 25.8%).Such distribution largely varies latitudinally (Figure 1c) with, overall, a larger proportion of sandy coastlines in the south (< 50 • N, ≈ 46.6% of sandy shores), than in the north (exposed coast of UK at > 50 • N, ≈ 10.7% of sandy shores).Hereafter, only the sandy coast part of the study area is analysed.
West-facing open coastlines are particularly represented in southwest France and western coast of Portugal (Figure 1d).A substantial proportion of sandy shores (≈ 750 km, 26.5%) are relatively sheltered (D < 50 km, see Methods), and are primarily located in northwest Spain, west-northwest France and UK (Figure 1e).Important to the SDS analysis is the amount of satellite images used to generate the yearly composite and further compute shoreline position.Figures 1f and 1g show that both the percentage of available SDS data in a given transect time series N y and the number of individual images used in a yearly composite image N c decrease northwards due mostly to increased cloud cover [44], indicating that the accuracy of SDS time series decreases at the highest latitudes.Long-term shoreline trends  autumn recovery, correlations are expected to be much lower than with post-winter shoreline position as demonstrated by [32] using on in situ shoreline time series.

Interannual shoreline variability and climates modes of atmospheric variability
The Scandinavian pattern (SCAND) shows relatively poor correlation with winter wave activity (Figure 4a).In contrast, the NAO shows larger positive and negative correlation with winter-mean wave height at the most northern and southern lati- In all panels, for clarity only the shoreline points with a statisticallysignificant correlation at a 80% confidence level have been plotted, while the grey dots on the wave field show statistically-significant correlations at the 95% confidence level.
To provide a broader insight into the correlations between the climate indices and shoreline response, Figure 5 shows the average correlation binned at 2.5 • intervals for different coastline orientations.While SCAND does not show any correlation pattern, a clear latitudinal gradient is found with the NAO for the west-facing coasts (Figure 5g), which is more subtle for the other coastline orientations.Also in line with the wave climate, WEPA, and to a lesser extent EA, shows positive correlation in the NAO-transition zone (Figure 5f,h).Similar WEPA patterns are found for the south-facing coastlines (Figure 5d), which are more subtle for the east-and northfacing coastlines.Importantly, except for the west-facing southwest coast of France, bin-averaged correlations are weak (< 0.5), which will be discussed in the next section.

Discussion
Our results show that, on average, sandy SDS have been accreting (+0.21 m/yr) over the last nearly 40 years along the exposed Atlantic coast of Europe (Figure 2).This finding goes against the many local observations showing eroding sandy shorelines along the Atlantic coast of Europe.However, many of these works investigated the 173 Portuguese sandy coast [e.g.45,46] or the southwest Coast of France [47,48], which 174 were also found to mostly erode in our dataset (Figure 4).There is also evidence 175 that many embayed beaches in e.g.France and the UK, are dominated by shoreline 176 rotation and/or show no significant long-term eroding trend [19,20].Some accreting 177 sectors found here have also been identified in the field [e.g.49].In addition, the SM SDS long-term trends were validated here with both high-frequency SDS derived from other approaches [22] and field data (see Figures 8 and 10 in Methods), which can give some confidence in the averaged long-term shoreline trends computed herein.
However, additional work needs to be done to verify these findings and to provide more detailed and validated insights the spatial distribution of eroding and accreting sandy coasts.For instance the SDS dataset used herein approximately corresponds to the MSL shoreline proxy which behaviour can contrast with the dune foot shoreline proxy, a relevant shoreline proxy along sandy coasts, due sediment exchanges and redistribution between the dune and the intertidal beach.This is particularly true on meso-macrotidal beaches, which are ubiquitous along the Atlantic coast of Europe, as evidenced by [50]  advocate that such averaging approach through e.g.coastline orientation and degree of sheltering [51], but also potentially other shoreline characteristics, should help to better understand shoreline response at regional to global scale.We also anticipate that the, yet weak, average accretion trend (+0.21 m/yr) of the Atlantic sandy coast of Europe is because west-facing open (D > 50 km) sandy coasts occupy less than half (39.5%, with a long-term trend of +0.03 m/yr) of the total coastline and because of the absence of deltaic coastlines, many of which erode globally [52,53], and which may contribute disproportionally to global averages.Finally, it must be acknowledged that the extension and revision of the SM SDS dataset used herein (see Methods) largely reduced the proportion of classified sandy shores [1,7], and also reduced the average accretion trends along the Atlantic coast of Europe compared to [1].A detailed inspection of the transects classified as sandy using the new classification [43] still show a few stretches of rocky, embayed, and/or fixed coastline, some of which include transects with large shoreline trend values.Future global shoreline trend analyses will need to be updated with improved shoreline classification.
Contrary to some previous work [e.g.34], we addressed the correlation between different climate indices against the yearly change in shoreline position dS [28,54], not against the yearly-mean shoreline position S. Indeed, addressing correlation between shoreline position S and a climate index assumes a linear response of the shoreline position to incident wave conditions, which is against fundamental understanding of beach and shoreline response [4,55], and against field evidence on many coasts [32,56].
Another relevant approach could have been to compute the anomalies in shoreline position during the prolonged positive and negative phases of the different climate indices, similar to [33] from prolonged positive and negative ENSO phase for the Pacific Ocean coast.However, given the complex interplay between the different dominant climate indices for the Atlantic coast and their lack of multi-annual periodicity and persistence, a systematic comparison between the yearly shoreline change dS and the winter climate indices was preferred.Finally, only winter (December to March) climate indices were used here, which is based on field evidence that winter wave conditions control interannual shoreline variability at many sandy coast environments along the Atlantic coast of Europe [41].
The latitudinal distribution of correlations between shoreline and the climate indices (Figure 5) are in line with the spatial correlation maps of the winter-mean wave height (Figure 4).Correlation maps with winter-mean wave height are essentially in line with previous work [40,56].However, the details around some sheltered and protected areas, which are typically characterised by multi-directional wave climates, are not reproduced as they require high-resolution wave modelling [57].We found that, particularly along west-facing coastlines, shoreline response is positively (negatively) correlated against NAO at the highest (lowest) latitudes, meaning that positive (negative) NAO results in increased (decreased) winter erosion.This is in line with local observation in Northern Ireland [38] and south Spain [58].In between, WEPA and to a lesser extent EA, is positively correlated with shoreline response, which is also in line with a wealth of observations [e.g.28,35,41,42,47,59,60].The impact of the outstanding winter of 2013/14 [38] is also relatively well captured in the time series of the mean shoreline position (Figure 2), with sediment redistribution between the dune and the intertidal beach [50] assumed to smooth the signature of this winter on the MSL shoreline.
Latitudinally-binned average correlations are mostly weak (Figure 5), but show clear latitudinal distribution for WEPA and NAO.Correlation were also computed for different time periods, showing similar patterns and thus providing confidence in the overall patterns.Only open coast beaches show a consistently statistically significant correlation.This is illustrated in Figure 6a for the period 2008-2021 for the southwest coast of France, with a positive correlation against WEPA except close to the tidal inlet of Arcachon, and in Figure 6b for the south coast of Spain with a negative correlation against NAO, except once again to inlets and structures.Such weak correlation is also observed with field data, primarily because of the influence of the antecedent morphology (memory effects) on winter erosion [32].In contrast, along a substantial amount of small coastal embayments, correlations are weak (Figure 6c,d) and sometimes not fully in line with previous work based on high-resolution data [60].Along such embayed coastlines, shoreline response can result from the complex response of multiple atmospheric indices [32,42], which can explain the weaker correlation.Future

Methods Shoreline Monitor (SM) dataset
The Shoreline Monitor (SM; http://shorelinemonitor.deltares.nl/)SDS dataset [1984-2016 in 1] is based on Landsat (5 to 8) and Sentinel-2 (only 2016) yearly composite images and comprises over 2.2 million transects distributed globally (see Figure 7 for a schematic visualization).It is derived by leveraging the petabyte image catalogue and parallel computing facilities of the Google Earth Engine (GEE) [61].A thresholding method [62] was used on yearly Top-Of-Atmosphere (TOA) reflectance composites to remove the effects of noise (clouds and shadows).For each composite image the Normalised Difference Water Index (NDWI) was computed which, combined with the Otsu thresholding method [63] and a region growing algorithm [64], provided the most probable threshold to classify water and land on the image.The water line was then smoothed using a 1D Gaussian smoothing operation to obtain shoreline vectors at sub-pixel resolution without the need of supplementing field data [65].The resulting shoreline approximately matches the MSL contour as the composite image analysis decreases the influence of the tidal stage on the detected shoreline positions.
An updated version of the SM SDS dataset is used in this study.The updated version only contains Landsat (5 to 8) images.Furthermore, the dataset is extended up to December 2021 and hence adds another five years of data.The total length of the dataset now equals 38 years.Previously, the years 1990-2000 contained a very low number of usable composite images.Recent updates to the image catalogs of Landsat (and therefore also the updated SDS dataset) increased the available composite images in this period significantly.Besides, the cloud cover threshold is adjusted.This increased the number of available composite images even more.Finally, a new classification of sandy, muddy, and cliff coasts [43] is added to allow for a better distinction between sandy and other environments.This decreased by approximately 38% the amount of muddy and rocky coastline previously classified as sandy in our study area.
Noteworthy, such correction was critical in the UK where 58% of the coasts previously classified as sandy are now correctly identified as rocky using the new classification [43].
In the present work, only the SM SDS dataset along the western part of Europe was used, from Gibraltar in the South to the northern tip of the Scottish coast.In order to focus on regions which are primarily affected by ocean waves generated in the North Atlantic ocean [57], we also disregarded the Irish Sea coastline, the French and UK coastline east of the Cotentin peninsula in the English Channel, and some sheltered and/or east-facing Scottish coastline (see Figure 1b).This resulted in a total of 34,874 transects, comprising 8,281 sandy transects (≈ 24%), which were analysed in the present work.The SM SDS dataset was further processed to compute some other shoreline characteristics (Figure 7).First, shoreline orientation θ was computed using the start and end points of each transect.Secondly, for each transect we computed the orthogonal distance D to the closest coast to quantify the degree of coastal sheltering.
It must be acknowledged that such approach does not consider the degree of embaymentization or orientation in relation to dominant storm wave incidence.Because spatial averaging can help to smooth out uncertain, noisy, SDS datasets [28,29] we also defined a moving average distance L considering neighbouring transects with a coastline orientation θ within ±δθ (Figure 7).Such moving averaging was performed accounting for the varying transect spacing which ranged in the study area from approximately 250 m to 400 m, increasing northward, with a mean of 315 m.
Validation [1] already provided a validation of the SM SDS dataset at multiple sites in the world where ground-truth field data are available.However, validation was restricted to sandy coasts with large shoreline variability (amplitude of O(100 m)) and/or a small tidal range.In addition, validation was only performed on long-term trends and interannual variability, which is typically O(1-10 m) on most of sandy coasts, was not addressed.Below, validation is performed along the southwest coast of France, which is a high-energy meso-macrotidal environment.This coast is characterised by alongshore-variable trends [28]

Long-term shoreline trends
The CoastSat [22,66] SDS dataset used here for validation is described in [28] and was averaged yearly for comparison with the SM SDS yearly composites.The period selected was 2000-2020, because prior to 2000 there was a lot of missing years in the CoastSat dataset generated in [28] before recent updates to the image catalogs of Landsat. Figure 8 shows the validation area and the spatial distribution of the percentage (N y ) of available yearly SM (Figure 8a) and CoastSat (Figure 8b) SDS data for 2000-2020.In order to perform a fair comparison only the transects with at least 80% (N y ) of SDS data availability over 2000-2020 were used (blue shoreline in Figure 8c).The shoreline time series were further averaged across four different regions (coloured boxes in Figure 8c) and compared (right-hand panels of Figure 8).
Results show that, using spatially-averaged shoreline transects, the SDS trends of the two datasets are in very good agreement with differences systematically under 0.1 m/year for both eroding (Figure 8d-f) and relatively stable (Figure 8g) zones.
In addition, although performed on a shorter time series (2007-2021), the long-term trends computed here were also compared to shoreline trends computed from in situ measurements at three sites in the UK (Perranporth and two embayment extremities) documented in [32] and with contrasting long-term trends.Using L = 5 km, the SDS  mean for a group of transects.This group of transect was based on e.g.latitude bins and coastline orientation (Figure 3b-e)), coastline exposure D (in Figure 2a), geographic area (see validation in Figure 8) or the moving-averaged approached described above based using L and δθ.The assessment of the statistical significance of the computed long-term trend is a complex issue as it depends on the uncertainties in spatially-averaged SDS data.By assuming the errors in SDS are not significantly biased, the uncertainties are expected to decrease with increasing number of transects averaged, as evidenced by the increased trend accuracy in e.g.[26].Such uncertainty reduction is difficult to estimate and is expected to strongly vary spatially and as a

Fig. 1
Fig. 1 Latitudinal distribution of satellite-derived sandy coastline characteristics.(a) Winter(DJFM)-mean significant wave height Hs and coastline of interest (thick black line) which is zoomed onto in (b).(c-g) Latitudinal distribution (binned at 1 • interval) of (c) length of total (black dots) sandy (blue dots) coastline and its corresponding percentage (grey bars); (d) sandy coastline orientation θ; (e) sandy coastline sheltering distance D; (f) percentage of available SDS data in a given transect time series Ny and (g) number of individual images per yearly composite Nc.In (f,g) the horizontal bars indicate the ± standard deviation σ.

FigureFig. 2
Figure2ashows, averaged over study area sandy coastline, the time series of yearly shoreline deviation around the long-term (1984-2021) mean S, together with the evolution of the yearly-mean SM SDS spatial coverage N y and of the number of images used per yearly composite N c (Figure2b).Accounting for all the sandy shorelines, and despite interannual shoreline variability of O(1 m), a statistically-significant (pvalue < 0.05) accreting trend of +0.21 m/yr is found.This accreting trend is more than doubled if only relatively sheltered transects (D < 10 km) are considered (+ 0.50 m/yr, blue line in Figure2a), and is almost halved, but still statistically significant (p-value < 0.05), considering relatively exposed transects (+0.13 m/yr for D > 50 km, red line in Figure2a).The unexpected and controversial results that satellite-derived shorelines along sandy coasts tend to accrete on average are discussed and tempered later in the Discussion Section.On average, east-facing (dS/dt = +0.33 m/yr), south-facing (dS/dt = +0.29 m/yr) and north-facing (dS/dt = +0.26m/yr) coastal stretches are the most rapidly accreting shorelines on the long term.Although a slight overall accretive trend is found (dS/dt = +0.13m/yr) for west-facing coasts, they tend to be more affected by erosion.Figure3

Figure 4 Fig. 3
Figure 4 shows the spatial correlation of the winter-mean significant wave height H s and yearly shoreline change dS against the primary (December to March) winter-averaged climate indices in the region over the entire time series 1984-2021.Noteworthy, because yearly composites include subsequent spring, summer and early

Fig. 4
Fig. 4 Correlation of winter-mean wave height and shoreline change against dominant winter climate indices.Spatial correlation of the winter-mean Hs and yearly shoreline change dS against (December to March) winter-averaged climate indices over 1984-2021: (a) SCAND; (b) EA; (c) NAO and (d) WEPA.In all panels, for clarity only the shoreline points with a statisticallysignificant correlation at a 80% confidence level have been plotted, while the grey dots on the wave field show statistically-significant correlations at the 95% confidence level.

Fig. 5
Fig. 5 Latitudinal distribution of correlation of shoreline change against dominant winter climate indices and influence of coastline orientation.Latitudinal distribution (2.5 • bins) of yearly shoreline change dS correlation against the primary winter-mean climate indices (columns) for different coastline orientations (rows) over 1984-2021.In all panels, the bubble size and color indicate the cumulative sandy coastline length, and the horizontal bars indicate the ± standard deviation.
on a beach in French Britany with MSL and dune foot shorelines showing opposite behaviour, i.e. eroding dune versus accreting MSL shoreline.The controversial result that sandy shorelines tend to accrete along the Atlantic coast of Europe on average must be therefore further verified.While previous work essentially geographically averaged shoreline response [1, 33, 34], here we investigated the influence of some coastline characteristics, namely sheltering distance D and coastline orientation θ, on shoreline trend and response.This allowed to demonstrate that west-facing, i.e. fully exposed to the dominant incidence of ocean waves, and relatively open (D > 50 km) sandy coasts are more prone to long-term coastal erosion, and stronger relations between interannual shoreline change and winter climate indices.This is in agreement with local studies showing that enclosed/embayed beaches are less prone to erosion than open beaches [49].Noteworthy, generalising such finding globally is misleading, as some long open coast sectors are known to accrete at substantially large rate [e.g.Northern California 29].Instead, we

Fig. 6
Fig. 6 Influence of coastal settings on correlation of shoreline change against winter climate indices.Zoom onto spatial correlation of yearly shoreline change dS against climate indices on open coast sectors over 2008-2021: (a) WEPA, Landes coast, southwest France and (b) NAO, southwest Spain and embayed coast sectors over 2000-2021: (c) WEPA, Sector of the Cantabria coast, north Spain and (d) WEPA, Cotentin peninsula, northwest France.

Fig. 7 Shoreline
Fig. 7 Shoreline Monitor dataset schematics.Representation of SM SDS dataset and some variables further used in the analysis: coastline orientation θ, transect sheltering distance D, and moving averaged distance L considering neighbouring transects with a coastline orientation θ within ±δθ.

(Fig. 8
Fig. 8 Validation of long-term shoreline trends.Validation of SM SDS trends against Coast-Sat SDS trends in southwest France.Spatial distribution of the percentage N of available yearly composites over 2000-2020 for (a) SM and (b) CoastSat, with (c) the thick blued line indicating transects where CoastSat and SM are both available with Ny > 80% and the coloured polygons showing the areas where the two datasets are compared.(d-g) Comparison of CoastSat (blue) and SM (red) yearly SDS position deviation around the mean and long-term trends (dashed lines).In each panel, the shoreline trend dS/dt and correlation coefficient R between the two datasets are provided.Truc Vert beach location is indicated in (c).

Fig. 9
Fig. 9 Correlation of interannual shoreline variability against field data for different shoreline proxies and alonsghore-averaging windows.Validation of SM SDS interannual variability against in situ surveys over 2003-2022 at Truc Vert beach, southwest France.(a) Mean beach profile, with the horizontal lines indicating the ± standard deviation of shoreline position at 0.5-m elevation intervals; (b) correlation coefficient R (coloured) between SM SDS and yearly-averaged in situ shoreline at Truc Vert, for different in situ shoreline proxy (-1 m < zprox < 6 m) and different SM alongshore-averaging distance L. (c,d) Corresponding zprox-averaged and L-averaged correlation R, respectively.In (c,d) the tick black line shows the maximum correlation, and the grey dots show the mean with the grey lines the ± standard deviations.

Fig. 10
Fig. 10 Validation of long-term shoreline change trends.Time series of SM SDS (blue line/dots) with a moving-averaged window L = 6 km and yearly-averaged shoreline position measured at Truc Vert (black line/dots) from the bimonthly surveys (grey dots) and using shoreline proxy zprox = 1.7 m.(b) Time series of the corresponding number of images used for the SM composites.