## 2 Materials and Methods
### Methods
#### 2.3.4 Coastline Change Quantification  
For the quantification of coastline change along shore-perpendicular transects, only the most seaward intersection point per year was considered for each transect. Information on the distance to the inland transect origin was added to each intersection point. The earliest coastline position was chosen as a baseline to measure the amount of shift [71]. If a transect contained less than five intersection points, it was removed from the analysis. Prior to the quantification of coastline change, outliers on each transect were eliminated to enhance the robustness of the coastline change calculation. Outliers were identified as intersection points deviating more than three times the standard deviation from the median coastline position [72]. The commonly used change metrics Shoreline Change Envelope (SCE) and Linear Regression Rate (LRR) were calculated for each transect [73; 74]. The SCE describes the maximum distance between all coastlines at a given transect and is therefore expressed in metric units without sign [73]. The SCE was used to define the length of the resulting coastline change classification transect. The coastline change rate was calculated by applying linear regressions to all intersection points at the transect. The slope of the linear regression represents the rate of change in meters per year, while the standard error characterizes the average distance of the observed values to the regression line [72].  
Figure 5: Shore-normal transect generation method. (**a**) Transects generated at original GADM land polygon with 200 m spacing and 3 km length, resulting in superimposed and missing areas at hard edges. (**b**) Transects generated at smoothed GADM land polygon. (**c**) Transects clipped to the maximum observed land area through the entire time series from 1986 to 2021 (blue); unclipped transects (grey).  
All transects were then classified on two levels: (1) All transects with a LRR between \(-0.5\) m/year and \(+0.5\) m/year are classified as 'No Change', while all transects with a change rate below \(-0.5\) m/year are classified as 'Erosion' and transects with changes larger than \(+0.5\) m/year as 'Accretion'. (2) The classification on Level 2 differentiates degrees of erosion and accretion and was adopted from the chronic beach erosion classification scheme by [PERSON] et al. (1998) [75]. The scheme was extended with a class for extreme erosion as proposed by [PERSON] et al. (2018) [29]. The accretion class was additionally subdivided equivalent to the erosion class, resulting in the scheme shown in Table 2.  
Based on the coastline change quantification, erosion and accretion hotspot analyses were performed (Figure 6). A clustering approach was chosen, where all adjacent transects of the same class (Level 1) with a tolerance of one transect were combined into one cluster. If the cluster contained more than 20 transects (4 km length) and was either associated with 'Erosion' or 'Accretion', it was defined as a hotspot. To find the most distinct hotspots within this dataset, only hotspots showing extreme erosion or accretion rates (\(>\)+5/\(<\)\(-\)5) on average were filtered.