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A new automatic shoreline detection method by using a bidirectional Long Short-Term Memory (bi-LSTM) Network that processes images column by column is presented. The model is trained on manually extracted shorelines from time-exposure video-images and is very robust against the selection of images for training. Thanks to the novelty of working with image columns, instead of with the whole image, the amount of labelled images for training is limited to a few tens or even less if the conditions are good. Moreover, this column approach makes the model to be robust to variable illuminated images and more easily interpretable, light and fast. There is a wide range of configuration parameters for the bi-LSTM layer by which the system works correctly, which facilitate to use the same network in different video stations. The highest accuracy is obtained by using CIELAB colour space. Without pre-processing the raw colour channels or defining a region of interest and without post-processing the obtained shorelines, the model demonstrates impressive accuracy with mean errors of 2.8 pixels (1.4 m) in Castelldefels and 1.7 pixels (0.85 m) in Barcelona. The method could also be effective for satellite shoreline detection by using as input channel the water index of the satellite detection techniques.

The quantification of sediment exchanges between the beach and the lower shoreface, although being still poorly understood, is required to adequately forecast long-term coastal evolution. The effect of extreme storms on the morphodynamics of the nearshore and the sediment budget of the coastal zone seems to be strongly conditioned by local parameters, which should be incorporated into studies of medium- and long-term coastal evolution. In the upper shoreface, the dynamics of shore-parallel bars in sandy coasts have been extensively studied, but their implications for the sediment budget remain controversial as it is unclear whether their evolution simply represents a morphological change or denotes an escape of sediment from the upper shoreface. In order to provide new knowledge to address these questions, fifteen topo-bathymetric surveys that extend from the emerged beach to 15 m water depth were carried out along 1 km of Castelldefels beach (Llobregat Delta, Barcelona, western Mediterranean Sea) during the period 2011–2022. Morphological variations on the shoreface are studied, volumetric changes are estimated and implications on sedimentary exchanges in the littoral profile are inferred. The largest morphological (volumetric) changes are caused by cross-shore displacements of the nearshore bars, usually onshore during fair-weather conditions and offshore during storms. Volumetric changes suggest that shoreline retreat and the erosion of the shallow section of the profile during the last decade provides sediment to both the distal upper shoreface and the lower shoreface. The resulting sediment budget in the profile is almost zero in absence of extreme storms, but becomes highly negative when including extreme storms events that cause a net offshore transfer of sediment from the upper to the lower shoreface and, probably, the inner shelf. The characteristics of the study area (morphology, sediments, waves, tides) and in-situ hydrodynamic measurements at the lower s

In this Supplementary Information document, two extra figures with their captions are included, as well as an extra text describing model limitations.

Mean sea-level rise (MSLR) will induce shoreline recession, increasing the stress on coastal systems of high socio-economic and environmental values. Localized mega-nourishments are meant to alleviate erosion problems by diffusing alongshore over decades and thus feeding adjacent beaches. The 21-st century morphological evolution of the Delfland coast, where the Sand Engine mega-nourishment was built in 2011, was simulated with the Q2Dmorfo model to assess the Sand Engine capacity to protect the area against the effects of MSLR. The calibrated and validated model was forced with historical wave and sea-level data and MSLR projections until 2100 corresponding to different Representative Concentration Pathways (RCP2.6, RCP4.5 and RCP8.5). Results show that the Sand Engine diffusive trend will continue in forthcoming decades, with the feeding effect to adjacent beaches being less noticeable from 2050 onward. Superimposed to this alongshore diffusion, MSLR causes the shoreline to recede because of both passive-flooding and a net offshore sediment transport produced by wave reshaping and gravity. The existing feeding asymmetry enforces more sediment transport to the NE than to the SW, causing the former to remain stable whilst the SW shoreline retreats significantly, especially from 2050 onward. Sediment from the Sand Engine does not reach the beaches located more than 6 km to the SW, with a strong shoreline and profile recession in that area, as well as dune erosion. The uncertainties in the results are dominated by those related to the free model parameters up to 2050 whilst uncertainties in MSLR projections prevail from 2050 to 2100.

Coastal environments are dynamic ecosystems, constantly subject to erosion/accretion processes. Erosional trends have unfortunately been intensifying for decades due to anthropic factors and an accelerated sea level rise might exacerbate the problem. It is crucial to preserve these areas for safeguarding not only coastal ecosystems and cultural heritage, but also the population living there. In this context, monitoring coastal areas is essential and geomatics techniques, especially satellite remote sensing imagery, might prove very advantageous. In this paper, a semi-automatic methodology to extract shorelines from SAR (Synthetic Aperture Radar) Sentinel-1 and optical Sentinel-2 satellite images was developed. An experimental algorithm, called J-Net Dynamic, was tested in two pilot sites. The semi-automatic methodology was validated with GNSS (Global Navigation Satellite System) reference shorelines and demonstrated to be a powerful tool for a robust extraction of the shoreline both from optical and SAR images. The experimental algorithm was able to extract the shoreline closer to the reference with SAR images on the natural beach of Castelldefels and it was demonstrated to be less sensitive to speckle effects than the commonly used Canny Edge Detector. Using the SAR images of the urban beach of Somorrostro, the Canny detector was not able to extract the shoreline, while the new algorithm could do it but with low accuracy because of the noise induced by man-made structures. For further investigation, the Sentinel-2-extracted shorelines were also compared to the ones extracted by a state-of-the-art tool, CoastSat, in the two beaches using both automatic and manual thresholds. The mean errors obtained with J-Net Dynamic were generally higher than the ones from CoastSat using the manual threshold but lower if using the automatic one. The proposed methodology including the J-Net Dynamic algorithm proves to extract the shorelines closer to the reference in most of the ca

Shoreline position is a key parameter of a beach state, often used as a descriptor of the response of the system to changes in external forcing, such as sea-level rise. Changes in shoreline position are the result of coupled hydrodynamic and morphodynamic processes happening in the nearshore and acting at different temporal scales. Due to this complexity, methodologies aimed at reproducing shoreline evolution at decadal time scale require many simplifications. Simpler methods usually consider an equilibrium beach profile whose shape depends only on beach morphology, and whose location varies depending on incoming forcing. Here, we derive a general equation for shoreline evolution using equilibrium beach profiles. We particularize it based on several common assumptions, and evaluate changes on shoreline position caused by sea-level rise, combined with simultaneous wave and high-frequency sea-level forcing. We compare our model against other analytical equilibrium beach profile-based models and with a dynamic model explicitly computing sediment transport. Results indicate that: (i) it is necessary to consider the area of the emerged beach subject to marine forcing rather than focusing only on the submerged part, (ii) the rates of shoreline recession may change for narrow beaches, defined as those for which marine forcings act onto all of their aerial surface, and (iii) Bruun's Rule can describe beach shoreline evolution, but the uncertainty in selecting the landward boundary of the active profile entails a huge uncertainty in the magnitude of shoreline evolution. This problematic uncertainty can be drastically reduced if instantaneous forcing conditions are used instead of the arbitrary emerged/submerged active profile boundaries typically defined by only one statistic parameter of extreme conditions.

Alongshore changes in shorelines along sandy beaches are a result of variations in wave conditions and nearshore morphology, which can cause straight shorelines to develop large-scale (100–1000 m wavelength) undulations, called megacusps, which cause local shoreline accretion and erosion. Megacusps are often morphologically coupled to alongshore variability in the nearshore sandbar (crescentic bars). Sandbar rhythmicity has been studied extensively, whilst megacusp dynamics and their coupling with crescentic bars have received less attention. This study uses a long-term dataset of hourly time-exposure video images and detailed propagated wave conditions to investigate megacusp dynamics and the corresponding sandbar–shoreline coupling at the low-energetic, tideless beach of Castelldefels (northwestern Mediterranean Sea, Spain). Megacusps were observed during 24% of the study period. Crescentic bars were present during 91% of the days with megacusps, whilst megacusps were not observed during 50% of the days with crescentic bars. Megacusp wavelengths (100–700 m) were comparable to those of crescentic bars, whilst cross-shore amplitudes (3–8 m) and alongshore migration speeds (0–15 m/day) were smaller than those of crescentic bars. No clear relation was observed between wave conditions and megacusp formation, migration and disappearance. However, megacusp presence was strongly linked to crescentic bar presence, as megacusps mostly developed some days after the formation of a crescentic bar. Coupling between shoreline and inner sandbar was significant during 74% of the time with simultaneous presence of megacusps and crescentic bars. No dominance of one particular coupling pattern was observed, although the pattern depended on the wave height and the wave angle. It is hypothesised that the wave height and angle determine the type of flow pattern over the inner crescentic bar (single or double rip cell circulations versus meandering currents) and thus control the type of

Properly registering the time evolution of the shoreline—the coastal land-water interface—is a crucial issue in coastal management, among other disciplines. Video stations have shown to be powerful low-cost tools for continuous monitoring of the coast in the last 30 years. Despite the efforts of the scientific community to get algorithms able to properly track the shoreline position from video images without human supervision, there is not yet an algorithm that can be recognized as fully satisfactory. The present work introduces a methodology to combine the results from different shoreline detection algorithms so as to obtain a smooth and very much improved result when compared to the actual shoreline. The output of the introduced methodology, which is fully automatic, includes not only the shorelines at all available times but also a measure of the quality of the obtained shoreline at each point (called self-computed error). The results from the studied beaches—located in the region of Barcelona city (Spanish Mediterranean coast)—show that such self-computed errors are in general good proxies of the actual errors. Using a certain threshold for the self-computed errors, the final computed shorelines have RMSE (Root Mean Squared Errors) that are in general smaller than 2.5 m in the great majority of analysed images, when compared to the manually digitized shorelines by three expert users. The global RMSE for all dates and beaches is of 1.8 m, with a mean bias <1 m and percentage of retrieval success >95% of the points

Accurate directional wave conditions at shallow water are crucial for nearshore field studies and necessary as boundary conditions for morphodynamic models. However, obtaining reliable results for all wave parameters can be challenging, particularly regarding wave direction. Here, the accuracy of two global hindcast models and propagation of measured wave conditions using linear wave theory or the SWAN wave model (forced by integrated wave parameters or 2D spectra) is assessed to obtain directional wave conditions at shallow water for Castelldefels beach, northwestern Mediterranean Sea. Results are analyzed using different statistical error parameters and for different wave climates (shore-normal, shore-oblique and bimodal). The analysis shows that global hindcast models correctly predict the trends in wave height and mean wave period but predictions for mean wave direction are only accurate for shore-normal waves. Linear wave theory provides good results for wave height but underestimates refraction, resulting in significant errors in mean wave direction for shore-oblique waves. Finally, SWAN forced with 2D spectra results in the most accurate predictions for all wave parameters. When using integrated wave parameters as boundary conditions, the results for wave height and mean period stay the same whilst the errors in peak period and mean direction worsen for shore-oblique and bimodal wave climates. The reason is that for these wave conditions the directional spectrum constructed out of integrated wave parameters does not resemble the actual directional spectrum.

Crescentic sand bars have attracted significant attention from coastal scientists during the last decades, which has lead to comparatively good understanding of their formation mechanism, as well as their characteristics and dynamics (e.g. Van Enckevort et al., 2004; Price and Ruessink, 2011). However, the effect of wave obliquity on crescentic bar formation is not yet clear, and processes like coupling of crescentic bars with megacusps deserve further attention. Furthermore, the mechanisms leading to crescentic bar straightening are not well understood. Previously, this was mainly linked to high-energetic wave conditions, but more recent studies (e.g. Price and Ruessink, 2011; Garnier et al., 2013) indicate that this is not always the case. Instead, those studies have found that bar straightening predominantly occurs when the waves are obliquely incident. Finally, there are not many studies of crescentic bars in fetch-limited environments with insignificant tides (such as Mediterranean beaches). Therefore, the objective of the present work is to increase our knowledge on the dynamics of crescentic bars (including bar straightening) using data from an open, Mediterranean beach (Castelldefels beach, 20 km southwest of Barcelona) with hardly any tides and limited fetch. Crescentic bar dynamics have been analysed using a nearly 8-year dataset of time-exposure video images (October 2010 to August 2018). The crescentic bar events, including formation and destruction moments, have been detected using visual analysis. Wave conditions in front of the study site have been collected by propagating 2D spectra (measured by a permanent wave buoy in front of Barcelona harbour) using the SWAN spectral wave model. The first results indicate that there is a lot of morphodynamic variability at the study site, even for low-energetic wave conditions (Hm0 < 0.5 m). Tens of crescentic bar events, including formation, evolution and destruction, can be observed. The bars show a large varia