## 3 Materials and Methods
### Remote Sensing Indices and Analytical Tools for Shoreline Monitoring
#### 3.2.2 Digital Shoreline Analysis System (DSAS) Overview
The Net Shoreline Movement (NSM) is the total distance between the oldest and most recent shorelines, without considering the time interval. It is calculated using the formula: \[\text{NSM}=\text{\text{\text@underline{1}}}\text{D\_ new}-\text{D\_ old}\text{\text{\text@underline{1}}}\] (5) where D_new = distance of the most recent shoreline and D_old = distance of the oldest shoreline. 5. The Weighted Linear Regression Rate (WLRR) uses linear regression with weights to account for differences in data accuracy or time intervals. It is calculated using the formula: \[\text{NSM}=\text{\text{\text@underline{1}}}\text{D\_ new}-\text{D\_ old}\text{\text{\text@underline{1}}}\] (6) where D_new = distance of the most recent shoreline and D_old = distance of the oldest shoreline. 5. The Weighted Linear Regression Rate (WLRR) uses linear regression with weights to account for differences in  
\[WLRR=\frac{\sum(w_{i}\cdot(y_{i}-\overline{y}))}{\sum(w_{i}\cdot(x_{i}-\overline{x} ))} \tag{6}\]  
where w_i = weight for each data point, y_i = individual shoreline positions, x_i = corresponding times, \(\overline{y}\) = mean of all shoreline positions, and \(\overline{x}\) = mean of all times. Figure 4 illustrates the Weighted Linear Regression (WLR) method for analyzing shoreline change over time, incorporating the concept of shoreline uncertainty. [PERSON] et al. (2022) [10] revealed on the Pacific coast (Panama) that EPR values indicated the rate of shoreline change over specific periods, with maximum erosion values recorded as \(-\)11.29 m/year (1998-2004) and maximum accretion values as 4.14 m/year (1998-2004), offering ease of use in only two shorelines for analysis. However, it neglects intermediate information when more than two shorelines are used. The LRR provided a mean shoreline change rate of 0.45 m/year across the zones, with a maximum rate of 1.75 m/year and a minimum of \(-\)0.98 m/year. The NSM provides the distance between the oldest and most recent shoreline, with maximum negative distances recorded as \(-\)80.51 m in Zone III, offering a clear measure of shoreline change over time, where it may not account for short-term fluctuations in shoreline position. In Joao Pessoa city (Brazil), [PERSON] et al. (2021) [31] used EPR for short-term analysis and indicated significant erosion in all zones from 1985 to 1990, with a mean rate of \(-\)3.15 m/year. The highest erosion was recorded in Zone I (\(-\)4.51 m/year) and Zone II (\(-\)3.55 m/year) where LRR provided a mean shoreline change rate of 0.45 m/year across the zones, with a maximum rate of 1.75 m/year and a minimum of \(-\)0.98 m/year. These findings highlight the importance of long-term analysis and providing a more stable estimate of shoreline change, maintaining the drawback that occurs from data point  
Figure 4: A shoreline dataset (baseline (black), transect (gray), and shorelines and intersects (multicolor), with shoreline position uncertainty) presented on a map and as a graph of distance from the baseline versus the shoreline date in relation to the weighted linear regression (WLR) line. The WLR rate is determined by plotting the shoreline positions with respect to time. Smaller positional uncertainty values (shown as vertical bars around each data point in the graph) have more influence than other values in the regression calculation because of the weighting component in the algorithm. The slope of the regression line is the rate (1.14 m per year). WR2, R-squared of weighted regression. Note. Adapted from [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON], 2021, Digital Shoreline Analysis System (DSAS) version 5.1 user guide: U.S. Geological Survey Open-File Report 2021-1091, 104 p., [[https://doi.org/10.3133/off20211091](https://doi.org/10.3133/off20211091)]([https://doi.org/10.3133/off20211091](https://doi.org/10.3133/off20211091)) [79]. selection and missing short-term fluctuations of importance.