## 3 Materials and Methods
### Remote Sensing Indices and Analytical Tools for Shoreline Monitoring
#### 3.2.2 Digital Shoreline Analysis System (DSAS) Overview  
The Digital Shoreline Analysis System (DSAS, version 6.0.170) is an application software designed by the United States Geological Survey to compute rate-of-change statistics based on several historical shoreline positions. It automates the determination of measurement sites, calculates rates, and delivers related uncertainties [77]. The DSA accommodates multiple statistical methods, such as the End Point Rate (EPR), which measures the shoreline change rate between the oldest and most up-to-date shoreline positions. The EPR is effective in cases where two shoreline positions exist. LRR constructs all shoreline positions based on a least-squares regression line to obtain a rate of change. LRR is more powerful in the presence of multiple shoreline positions, yielding an overall picture of shoreline development. Other measurements provided by the DSA are the Shoreline Change Envelope (SCE), measuring the distance between the most landward and most seaward shoreline positions as a function of time. NSM estimates the distance between the oldest and most up-to-date shoreline positions, quantifying results. The Weighted Linear Regression Rate (WLR) is similar to LRR but it gives weight to shoreline positions based on their uncertainty, providing an improved rate of change. The use of the DSA for shoreline change analysis has been illustrated in different studies [11; 41; 78]. For instance, the DSA has been applied for shoreline changes on the Odisha coast of India based on historical satellite data [4]. In addition, Figure 2 depicts the metrics of EPR, NSM, and SCE in elaborate detail in each of the metrics. 1. End Point Rate (EPR) is calculated by dividing the distance between the oldest and most recent shorelines by their time elapsed. It is calculated using the formula: \[\text{EPR}=(\text{D\_new}-\text{D\_old})/(\text{T\_new}-\text{T\_old})\] (2) where D\(\_\)new = distance of the most recent shoreline, D\(\_\)old = distance of the oldest shoreline, T\(\_\)new = year of the most recent shoreline, and T\(\_\)old = year of the oldest shoreline. Figure 2: A shoreline dataset including baseline (black), transect (gray), and shoreline and intersect data (multicolor) to illustrate the relationship between shoreline change statistics: Net Shoreline Movement (NSM), End Point Rate (EPR), and Shoreline Change Envelope (SCE). NSM is the distance along the transect in meters (m) between the oldest shoreline (1936, red) and the most recent shoreline (2005, magenta). The EPR is the NSM distance divided by the time between the oldest (1936, red) and most recent (2005, magenta) shorelines (69 years in this example). The SCE is the greatest distance between all the shorelines regardless of date. Note. Adapted from [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON], [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/ofr20211091](https://doi.org/10.3133/ofr20211091)]([https://doi.org/10.3133/ofr20211091](https://doi.org/10.3133/ofr20211091)) [79]. 2. The Linear Regression Rate (LRR) uses linear regression to find the rate of shoreline movement over time. It is calculated using the formula: \[LRR=\frac{\sum(y_{i}-\overline{y})}{\sum(x_{i}-\overline{x})}\] (3) where y_i = individual shoreline positions, x_i = corresponding times for each shoreline position, \(\overline{y}\) = mean of all shoreline positions, and \(\overline{x}\) = mean of all times. Figure 3 illustrates the LRR method for analyzing shoreline change over time. 3. The Shoreline Change Envelope (SCE) is the distance between the farthest landward and farthest seaward shorelines over a given time period. It is calculated using the formula: \[\text{SCE}=\text{\text{\text@underline{1}}}\text{D\_ seaward}-\text{D\_ landward}\text{\text{\text@underline{1}}}\] (4) where D_seaward = farthest seaward shoreline and D_landward = farthest landward shoreline. 4.