Coastal Dynamics Analysis Based on Orbital Remote Sensing Big Data and Multivariate Statistical Models

: As the interface between land and water, coastlines are highly dynamic and intricately tied to the sediment budget. These regions have a high functional diversity and require enlightened management to preserve their value for the future. In this study we assess changes to the S ã o Paulo State (SE Brazil) coastline over the last 36 years. The study innovatively employs big data remote sensing techniques and multivariate statistical models to evaluate and generate erosion/accretion rates (1985–2021) relative to beach orientation and slope. Shoreline change rates have been obtained for sandy beaches at 485 one-kilometer-spaced transects. Our ﬁndings capture the complexity and heterogeneity of the analyzed coastline, at a regional and local scale. No association was found between shoreline changes and beach face orientation. Nonetheless, a dependency relationship was found between dissipative beaches with moderate to high accretion. Beaches facing south, with relative stability, were prone to sediment accumulation. Locations with slow accretion, like sandy spits and tombolo-protected beaches, were associated with dissipative beaches with moderate to high accretion. The southeast-oriented beaches are more prone to erosion due to storm waves from the south. Results provide a broad, fast, and relatively low-cost methodology that can be used in any sandy beach context, bringing essential information for coastal management and decision-making related to the use and occupation of the coastal zones.


Introduction
Climate change refers to the alteration (cooling or heating) of Earth's atmospheric temperature and its ensuing implications (i.e., extreme events).These shifts can occur due to natural forcings such as variations in solar activity, alterations in the Earth's orbital characteristics (Milankovitch Cycles), and volcanic eruptions (which cause a reflection of solar radiation followed by subsequent cooling).Anthropogenic, or human-caused changes, can excessively introduce greenhouse gases (GHGs) into the atmosphere.These gases contribute to global warming by blocking the escape of radiated heat and causing, among other issues, polar ice melt, changes in atmospheric circulation, oceanic circulation, and the hydrological cycle [1][2][3][4].
In coastal zones, these changes increase the Mean Sea Level (MSL), currently at 3.55 mm/year [5][6][7].According to projections from the International Panel on Climate Change (IPCC), this could reach up to 1.2 m by 2100 under the most pessimistic scenario The ~600 km long coast of São Paulo State (SE Brazil) is divided into six compartments, which are: (1) Ilha do Cardoso-Serra do Itatins; (2) Peruíbe-Praia Grande; (3) Santos-Bertioga; (4) Bertioga-Toque-Toque; (5) Toque-Toque-Tabatinga; and (6) Tabatinga-Picinguaba (Figure 1), according to Tessler et al. [29].Its physiography presents a variety of geomorphological features, such as beaches, rocky shores, sandbars, and mangroves.It is marked by a complex interaction between geological, geomorphological, climatic, and anthropogenic processes.Some of these features (i.e., vegetated areas, mangroves, sandy beaches, and rocky shores) are common on the southern part of the coastline.The flatter topography includes ecologically essential areas, such as the Juréia-Itatins and Itinguçu State Park [29,30].In this portion of the coastline, the Serra do Mar escarpment appears farther from the coast (10 km-70 km), creating room for a broad coastal plain with long, straight beaches and some islands [29,31].
From the central portion to the northernmost part, the Serra do Mar Mountain chain range gradually approaches the coast, generating a narrow coastal plain and smaller hydrographic basins, when compared to those in the southern portion of the São Paulo coast.This part of the coast is geomorphologically more irregular, with smaller and more sheltered beaches in the form of coves, separated by pre-Cambrian rocky promontories such as those observed at Itaguaré, Massaguaçu, and Praia Vermelha do Norte [29,31].This region is home to important cities such as Santos, which has the largest port in Latin America [32].While the northern coast has sandy beaches in pockets between rocky outcrops and presents a more rugged topography, with the presence of the Serra do Mar and dozens of islands near the coast [33].
The circulation of the Brazilian continental margin is dominated by the Brazil Current (BC), which flows southwards in deep waters.Meanwhile, the Brazil Coastal Current (BCC) moves from the south-southeast to the northeast on the continental shelf during spring and winter [34][35][36] (Figure 1).The prevailing winds are from the east-northeast, generating currents parallel to the northeast-southwest coastline.However, under the influence of cold fronts, frequent during winter, winds from the south-southeast generate more intense currents and waves coming mainly from the southern quadrant [22,[37][38][39][40] (Figure 1).Urban occupation and the construction of coastal infrastructure also significantly impacts the coastal physiography and dynamics, which can result in erosion and progradation processes [41,42].
Coasts 2023, 3, FOR PEER REVIEW 3 spring and winter [34-36] (Figure 1).The prevailing winds are from the east-northeast, generating currents parallel to the northeast-southwest coastline.However, under the influence of cold fronts, frequent during winter, winds from the south-southeast generate more intense currents and waves coming mainly from the southern quadrant [22,[37][38][39][40] (Figure 1).Urban occupation and the construction of coastal infrastructure also significantly impacts the coastal physiography and dynamics, which can result in erosion and progradation processes [41,42].

Processing Steps
The methodology of this research is divided into three steps: (1) acquisition of orbital remote sensing images for the generation of the modified normalized difference water index (MNDWI), binary mask (BM), and slope parameter (tanβ) derived from horizontal (HD) and vertical (VD) distances; (2) generation of maps of the annual erosion and accretion rate (CLr), beach face direction (FaceDir), and morphodynamic stage trend (Mstg); (3) analysis of associations, dependency relationships, and clusters by correspondence analysis (CA), chi-square test (X²), standardized residual analysis (SRA), and cluster (K-means) (Figure 2).

Processing Steps
The methodology of this research is divided into three steps: (1) acquisition of orbital remote sensing images for the generation of the modified normalized difference water index (MNDWI), binary mask (BM), and slope parameter (tanβ) derived from horizontal (HD) and vertical (VD) distances; (2) generation of maps of the annual erosion and accretion rate (CLr), beach face direction (FaceDir), and morphodynamic stage trend (Mstg); (3) analysis of associations, dependency relationships, and clusters by correspondence analysis (CA), chi-square test (X 2 ), standardized residual analysis (SRA), and cluster (K-means) (Figure 2).

Orbital Remote Sensing Images
This study uses annual medians of Landsat 5/TM and Landsat 8/OLI multispectral satellite/sensor images for 1985 and 2021.These images have a spatial and temporal resolution of 30 m and 16 days respectively, with calibrated top-of-atmosphere (TOA) reflectance acquired by the Google Earth Engine (GEE) platform [43][44][45][46][47][48] (Figure 3a).The water/non-water (or land) interface was mapped using the Modified Normalized Difference Water Index (MNDWI) [49] (Figure 3b), calculated for each year using a binary mask (water "1" and non-water "0" classes) with a spatial mode filter to eliminate noise [50] (Figure 3c).The assessment of the accuracy of the "water" and "non-water" area map classification was carried out using the analytical technique of global accuracy (GA) and global error (GE) indices, represented respectively by Equations 1 and 2. This was implemented The assessment of the accuracy of the "water" and "non-water" area map classification was carried out using the analytical technique of global accuracy (GA) and global error (GE) indices, represented respectively by Equations 1 and 2. This was implemented based on the percentage of correctly classified samples from the total available samples, as well as the overall percentage error of the matrix [51].
V represents the correctly classified values, and T represents available samples.

Database
The coastal erosion and/or accretion rate (CLr) was derived from the difference between the reference year (1985) and the current analyzed year (2021) positions.This was achieved using binary masks and the intersection of equidistant transects (1 km × 1 km), with Landsat 5 and 8 satellites as the base reference [52].Quantitative variables were transformed into qualitative ones and standardized according to the nature of the data.
Thus, according to Thieler and Hammar-Klose [53], the CLr values were transformed into the following intervals: high erosion-HEr (<−2.0 m); moderate erosion-MEr (−1.0 m-−2.0 m); stable-Stb (−1.0 m-1.0 m); average accretion-MAc (1.0 m-2.0 m); and high accretion-HAc (>2.0 m).The beach face direction (FaceDir) was determined by the transect direction relative to geographic north as follows: north-N (0 The slope model (tangβ in Equation ( 3)) was derived from the horizontal (HD) and vertical (VD) distances, respectively, between the differences between high and low tide coastlines (CL) (Figure 4a) and from the spring tide range.For example, near the Port of Santos (the central point of the study area), the average spring tide range is 1.58 m (Figure 4b), according to the Mean Sea Level (MSL) of the Imbituba/SC datum of the Brazilian Geodetic System (BGS) [22,55].
HD was obtained from multispectral remote sensing (RS) harmonized between Landsat 8 and Sentinel-2 (HLS) images, resampled to 30 m spatial resolution (Figure 4a) for the years 2019 and 2021.This technique can improve temporal resolution by up to 7 scenes per month at the exact location [56].The median HSL images were acquired synchronously between satellite pass time (~10:30 A.M.) and high and low spring tide stages, obtained through the WXTIDE32 software [57].This resulted in two High Tide (HT) and Low Tide (LT) images from the median of 26 HT images and another of 27 LT images covering the entire study area.The satellite-derived slope information (Figure 4c) provides a rapid empirical assessment of the morphodynamic beach stage (Mstg) trend, which can be divided into: steeper-ST (0.12 < tanβ); intermediate-IN (0.05 < tanβ < 0.12), and sloping-SL (tanβ < 0.05) [28,58].

Multivariate Statistical Models
The satellite-derived slopes were statistically calibrated using 24 topographic profiles collected in situ through the positioning of the Global Navigation Satellite System (GNSS) and a Box-Cox transformation regression model, which maximizes the adherence of the new variableʹs distribution to normality [22,28,[59][60][61][62]. Correspondence analysis (CA) examined dependency relationships due to associations between categories of the variables of interest using the chi-square (X 2 ) test.Meanwhile, standardized residual analysis (SRA) assessed the existence of interdependence relationships between these categories based on the reference critical value (+1.96≤) of the standard normal curve, with a significance level of 5%.Thus, if the adjusted standardized residual value in a cell is greater than 1.96, it is interpreted that there is a significant association between these categories [61,63,64].
Cluster analysis using the non-hierarchical K-means method employs the coordinates of the rows and columns of the contingency table, grouping their observations based on centroid proximity in a perceptual map.The advantage of this method is that it can be

Multivariate Statistical Models
The satellite-derived slopes were statistically calibrated using 24 topographic profiles collected in situ through the positioning of the Global Navigation Satellite System (GNSS) and a Box-Cox transformation regression model, which maximizes the adherence of the new variable's distribution to normality [22,28,[59][60][61][62]. Correspondence analysis (CA) examined dependency relationships due to associations between categories of the variables of interest using the chi-square (X 2 ) test.Meanwhile, standardized residual analysis (SRA) assessed the existence of interdependence relationships between these categories based on the reference critical value (+1.96≤) of the standard normal curve, with a significance level of 5%.Thus, if the adjusted standardized residual value in a cell is greater than 1.96, it is interpreted that there is a significant association between these categories [61,63,64].
Cluster analysis using the non-hierarchical K-means method employs the coordinates of the rows and columns of the contingency table, grouping their observations based on centroid proximity in a perceptual map.The advantage of this method is that it can be applied to samples with large amounts of data [61,62].To this end, the Elbow method was employed to select the number of clusters [61,62,[64][65][66].

Description and Geographic Distribution
The calibration between the slope estimated by satellite and that measured in situ exhibited a coefficient of determination of 0.94 (R 2 ) and a root-mean-square error of 0.18 (RMSE).This indicates that the slope values collected in the field explain approximately 94% of the variance in the satellite-derived data [67].Furthermore, orbital imagery acquired between 1985 and 2021 demonstrated a global accuracy and global error in mapping the land/sea boundary of 99% and 1%, respectively.These results underscore that the classification is suitable for this type of study.
The 485 transects perpendicular to each kilometer of the unconsolidated coastline exhibited an average CLr of −0.17 Table 1 shows the statistical summary for each compartment of the São Paulo coast.The first, Ilha do Cardoso-Serra de Itatins (C1), has a moderate and positive CLr, with more erosive areas in its central-southern portion and accretion in its northernmost portion (Figure 5a).In this compartment, as well as in the others, the direction of the beach face is predominantly SE.However, the average slope of C1 is less than 0.05, indicating a tendency towards a dissipative morphodynamic state.From the Peruíbe-Praia Grande compartment (C2) onwards, the scenario of the average CLr becomes negative and worsens in the Tabatinga-Picinguaba compartment (C6).While the average slope values remained below 0.05 until compartment C2, they gradually increased, becoming intermediate in compartments C3 and C4 (0.05 < tanβ < 0.12), as well as reflective in compartments C5 and C6 (tanβ > 0.12).Transects with moderate and high erosion (MEr and HEr) were observed in greater proportion in compartments C1, C4, and C5.In contrast, they were observed in a smaller proportion in compartments C2 and C6.Compartment C3 did not exhibit erosive processes.In these compartments, southeast-facing (SE) beach faces predominate (Figure 5a).Beaches with faces oriented southward appear primarily in the northern portion of compartments C2 and C4 and throughout compartment C3 (Figure 5b).Beaches with a shore trend (ST) and indeterminate (IN) orientation predominate in compartments C1 through C4, with sloping profiles primarily occurring in compartments C5 and C6 (Figure 5c).

Associations, Dependency Relations, and Clusters
Through Correspondence Analysis (CA), the Chi-square (X 2 ) test found a p-value of 0.4153, suggesting the hypothesis that there is no statistical significance (H0, p-value > 0.05) or association between the variables of the annual erosion and/or accretion rate (CLr) with the direction of the beach face (FaceDir).However, the adjusted standardized residuals (ASR) observed a dependency relationship between relatively stable beaches (Stb) with beach faces facing the S quadrant (1.96≤; red dashed cell in Figure 6a).The remaining Coasts 2023, 3 167 cells in Figure 6a indicated random or statistically non-significant processes between CLr and FaceDir (values < 1.96).For the same variables (CLr and FaceDir), Figure 6b of the K-means Cluster analysis identified three different groupings.The first (cluster 1) observed SE-facing transects with beaches with moderate and high erosion (CLr_MEr and CLr_HEr).The second (cluster 2) indicated E-facing beach faces grouped with those having moderate accretion rates (CLr_MAc).Cluster 3 grouped stable transects (CLr_Stb) with beach faces facing S, W, and NE (Figure 6b).Transects with moderate and high erosion (MEr and HEr) were observed in greater proportion in compartments C1, C4, and C5.In contrast, they were observed in a smaller proportion in compartments C2 and C6.Compartment C3 did not exhibit erosive processes.In these compartments, southeast-facing (SE) beach faces predominate (Figure 5a).Beaches with faces oriented southward appear primarily in the northern portion of compartments C2 and C4 and throughout compartment C3 (Figure 5b).Beaches with a shore trend (ST) and indeterminate (IN) orientation predominate in compartments C1 through C4, with sloping profiles primarily occurring in compartments C5 and C6 (Figure 5c).

Associations, Dependency Relations, and Clusters
Through Correspondence Analysis (CA), the Chi-square (X²) test found a p-value of 0.4153, suggesting the hypothesis that there is no statistical significance (H0, p-value > 0.05) or association between the variables of the annual erosion and/or accretion rate (CLr) with the direction of the beach face (FaceDir).However, the adjusted standardized residuals (ASR) observed a dependency relationship between relatively stable beaches (Stb) with beach faces facing the S quadrant (1.96≤; red dashed cell in Figure 6a).The remaining cells in Figure 6a indicated random or statistically non-significant processes between CLr and FaceDir (values < 1.96).For the same variables (CLr and FaceDir), Figure 6b of the Kmeans Cluster analysis identified three different groupings.The first (cluster 1) observed SE-facing transects with beaches with moderate and high erosion (CLr_MEr and CLr_HEr).The second (cluster 2) indicated E-facing beach faces grouped with those For the variables of CLr and morphodynamic state (Mstg), the X 2 test observed a statistically significant association with a p-value of 0.0017 (H1, p-value < 0.05).The analysis of the ASR values observed that beach faces with dissipative characteristics (ST) exhibited a dependency relationship (1.96≤) with transects of moderate and high accretion (MAc and HAc) (red dashed cells in Figure 6c).For the same variables (CLr and Mstg), Figure 6d of the K-means Cluster analysis found four different groupings.Transects with moderate and high accretion (CLr_MAc and CLr_HAc) appear grouped in clusters 1 and 2 close to beaches with a dissipative tendency (Mstg_ST).In Figure 6d, beaches with relative stability (CLr_Stb) appear grouped at the center of the perceptual map, orbiting with relative equidistance from the different Mstg categories.In the third cluster, transects with moderate and high erosion (CLr_MEr and CLr_HEr) appeared preferentially grouped with beaches having an intermediate morphodynamic tendency (Mstg_IN).Meanwhile, cluster 4 orbits beaches with a reflective tendency (Mstg_SL) closer to transects with moderate erosion (CLr_Mer), high erosion (CLr_HEr), and stability (CLr_Stb).
close to beaches with a dissipative tendency (Mstg_ST).In Figure 6d, beaches with relative stability (CLr_Stb) appear grouped at the center of the perceptual map, orbiting with relative equidistance from the different Mstg categories.In the third cluster, transects with moderate and high erosion (CLr_MEr and CLr_HEr) appeared preferentially grouped with beaches having an intermediate morphodynamic tendency (Mstg_IN).Meanwhile, cluster 4 orbits beaches with a reflective tendency (Mstg_SL) closer to transects with moderate erosion (CLr_Mer), high erosion (CLr_HEr), and stability (CLr_Stb).

Discussion
Global-scale studies such as those by Luijendijk et al. [26] and Mentaschi et al. [27] can provide an overview of coastal erosion or accretion processes by identifying global trends and patterns.However, such global approaches cannot capture the complexity and heterogeneity of coastal environments at a regional or local scale.
In this context, along the São Paulo coast, beaches with relative stability oriented toward the southern quadrant displayed sectors that are more susceptible to accretion processes.This is due to the ~90° angle between storm waves formed by cold fronts coming from the same quadrant, which results in these beaches having their sediment transport almost nullified (Figure 7a), favoring sediment accumulation and, consequently, the formation of frontal dunes in these areas [22,38,68].In addition, beaches with facies oriented

Discussion
Global-scale studies such as those by Luijendijk et al. [26] and Mentaschi et al. [27] can provide an overview of coastal erosion or accretion processes by identifying global trends and patterns.However, such global approaches cannot capture the complexity and heterogeneity of coastal environments at a regional or local scale.
In this context, along the São Paulo coast, beaches with relative stability oriented toward the southern quadrant displayed sectors that are more susceptible to accretion processes.This is due to the ~90 • angle between storm waves formed by cold fronts coming from the same quadrant, which results in these beaches having their sediment transport almost nullified (Figure 7a), favoring sediment accumulation and, consequently, the formation of frontal dunes in these areas [22,38,68].In addition, beaches with facies oriented towards E, W, and NE, impacted by lower-energy waves from ENE during summer or protected by oceanic islands, also favor sediment accumulation.
However, it is essential to note that along the São Paulo coast, these beaches (oriented towards E, W, and NE) are small and underdeveloped, primarily found in C5 and C6 (Figure 7c), where the proximity of the Serra do Mar Mountain chain provides a heavily indented coast with bays and inlets separated by rocky promontories (Figure 7b) [29,68].This configuration may favor significant negative changes in sediment volume due to climate change-related global warming, which has increased wind speed and wave height [69,70], intensifying cyclonic and anticyclonic events in the Southern Hemisphere as well as their trajectories, intensity, and frequency during winter months [71,72].Furthermore, particularly in C5 and C6, anticyclones may generate high-energy ENE waves, causing erosion on these similarly-oriented beaches [73].

Conclusions
The analysis of orbital images from the coast of São Paulo in 1985 and 2021 allowed the assessment of the annual rate of erosion and accretion along the 485 transects distributed perpendicularly to the coastline at each kilometer of sandy beaches.Therefore, the overall accuracy and global error of the land/sea boundary mapping were deemed suitable for the study.From compartments C1 to C6, a general trend of dissipative morphodynamic state was observed, except for compartment C2, where the intermediate state predominated.Furthermore, beaches oriented towards the southeast were most affected by erosive processes.In contrast, the beaches with dissipative tendencies and moderate to high accretion were associated with locations characterized by slow accretion processes.Furthermore, a dependency relationship was observed between relatively stable beaches facing the southern quadrant and transects with moderate to high accretion.Overall, the results provide essential information for coastal management and decision-making related to the use and occupation of the São Paulo coastline, especially about the accumulation of microplastics.This study contributes to the fulfilment of Sustainable Development Goal 14 (life below water), specifically of target 14.1 with respect to marine debris, scientific knowledge, and investigation.Lastly, it is recommended to include new parameters that may influence the variation of the coastline and aid in better understanding the Beaches with dissipative tendencies and moderate to high accretion are associated with locations characterized by slow accretion processes, such as sandy spits and areas protected by tombolos (Figure 7c,d), respectively, in compartments C1 and C3 [29,[74][75][76].Due to the São Paulo coast's configuration (SW-NE), beach faces oriented toward SE are more susceptible to erosive processes, as the acute angle (~45 • ) of storm wave incidence from the same Southern quadrant can reach up to 4.0 m [20,22,38,40,77] during the austral autumn and winter (April to September), favoring maximum sediment transport capacity (e.g., [78,79]).This process is typical on straight beaches found in the south-central portion of compartment C1 (Figure 7e) and on those with intermediate and steeper tendencies in compartments C4, C5, and C6 of Figure 5c [74,80].Meanwhile, dissipative beaches associated with moderate erosive processes are located near river mouths, estuaries, and tidal channels, naturally dynamic regions in Figure 7f [29].
These sites may undergo drastic changes, such as the disappearance of beaches due to rising sea levels, the intensification of extreme events, and human activities [81,82].Such changes may induce regime shifts and collapse of social-ecological systems, with negative implications for biodiversity and ecosystem services [83][84][85].However, Cooper et al. [86] caution that one should be wary of these projections, given that sandy beaches are highly resilient environments and, if space is available, they can adapt through sediment redistribution, such as those found in the central-northern portion of C1 (Figure 7d).
Nonetheless, not all beaches will be capable of adapting, making coastal conservation and management measures essential [86].This is particularly true in urbanized areas, such as the easternmost portion of the beachfront in Santos near the eponymous canal and port (C3), which experiences frequent flooding due to storm surges [20,77].This highlights the importance of integrated and collaborative approaches among governments, communities, and scientists to address coastal erosion and ensure the safety of coastal communities [87].
Lastly, this work may serve as background information for future studies on the deposition and accumulation of microplastics, given that naturally sediment-prone sites (i.e., accretion) along the São Paulo coast are described as susceptible to this pollutant's accumulation, such as pellets [22].This research contributes to the fulfilment of Sustainable Development Goal 14 (life below water), more specifically of targets 14.1-which aims to prevent and significantly reduce marine pollution of all types, in particular from land-based activities, including marine debris (indicator 14.1.1-density of plastic waste) by 2025and 14.a, which aims, among others, to increase scientific knowledge, develop research capacities, and transfer technology to improve the health of the oceans [88].

Conclusions
The analysis of orbital images from the coast of São Paulo in 1985 and 2021 allowed the assessment of the annual rate of erosion and accretion along the 485 transects distributed perpendicularly to the coastline at each kilometer of sandy beaches.Therefore, the overall accuracy and global error of the land/sea boundary mapping were deemed suitable for the study.From compartments C1 to C6, a general trend of dissipative morphodynamic state was observed, except for compartment C2, where the intermediate state predominated.Furthermore, beaches oriented towards the southeast were most affected by erosive processes.In contrast, the beaches with dissipative tendencies and moderate to high accretion were associated with locations characterized by slow accretion processes.Furthermore, a dependency relationship was observed between relatively stable beaches facing the southern quadrant and transects with moderate to high accretion.Overall, the results provide essential information for coastal management and decision-making related to the use and occupation of the São Paulo coastline, especially about the accumulation of microplastics.This study contributes to the fulfilment of Sustainable Development Goal 14 (life below water), specifically of target 14.1 with respect to marine debris, scientific knowledge, and investigation.Lastly, it is recommended to include new parameters that may influence the variation of the coastline and aid in better understanding the coastline its behavior, such as the distance of transects to urbanized areas, rocky promontories, oceanic islands, and channels/estuaries.

Figure 2 .
Figure 2. Flowchart of the steps in the methodology used in this research.RS: orbital remote sensing images; MNDWI: Modified normalized difference water index; BM: binary masks; HD: horizontal distance; VD: vertical distance; tanβ: slope; CLr: annual erosion and accretion rate; FaceDir: beach face direction; Mstg: morphodynamic stage trend; CA: correspondence analysis; X²: chi-square test; SRA: standardized residual analysis; K-means: a cluster analysis.

Figure 3 .
Figure 3. (a) Multispectral image of visible bands; (b) Modified Normalized Difference Water Index (MNDWI); (c) Binary mask with water classes "1" (blue) and land classes "0" (yellow), plus spatial mode filtering.Example from the average year of 2021 for the entire coastline of the State of São Paulo.

Figure 4 .
Figure 4. Shows three parameters: (a) the Horizontal Distance (HD) between the coastlines of Spring High Tide (HT) and Low Tide (LT), which was derived from satellite images; (b) The Vertical Distance (VD) of the tidal range near the port of Santos, São Paulo, Brazil [55,57] and (c) The slope (tanβ) of the right triangle formed by the horizontal and vertical distances.

Figure 4 .
Figure 4. Shows three parameters: (a) the Horizontal Distance (HD) between the coastlines of Spring High Tide (HT) and Low Tide (LT), which was derived from satellite images; (b) The Vertical Distance (VD) of the tidal range near the port of Santos, São Paulo, Brazil [55,57] and (c) The slope (tanβ) of the right triangle formed by the horizontal and vertical distances.
m, with minimum and maximum values of −70.1 m and 103.4 m, respectively.The beach faces displayed an average direction of 148 • (SE), with values ranging from 16 • (N) to 264 • (W).The slope of these faces was predominantly intermediate on average.Coasts 2023, 3

Figure 6 .
Figure 6.(a) Heatmap of adjusted standardized residues (ASR); (b) perceptual map between coastal erosion and accretion rate data (CLr) and beach face direction (FaceDir); (c) Heatmap of adjusted standardized residues (ASR); and (d) perceptual map between the Erosion and accretion rate of the coastline (CLr) and morphodynamic state (Mstg) data.The dashed cells in red are described in the text.

Figure 6 .
Figure 6.(a) Heatmap of adjusted standardized residues (ASR); (b) perceptual map between coastal erosion and accretion rate data (CLr) and beach face direction (FaceDir); (c) Heatmap of adjusted standardized residues (ASR); and (d) perceptual map between the Erosion and accretion rate of the coastline (CLr) and morphodynamic state (Mstg) data.The dashed cells in red are described in the text.

Figure 7 .
Figure 7. (a) Binary mask with water class "1" (blue), land class "0" (yellow), and compartments.(b-g) Google Earth Pro images of the features described in the main text.