## 3 Results and Discussion  
### Changing Geometry of the Southwestern Gulf  
The baseline method has been widely used in the study of quantitative analysis of coastline changes [34; 35]. This method was first proposed by [PERSON] et al. during their study on the shoreline erosion in southern New Jersey [36]. Subsequently, the Digital Shoreline Analysis System (DSAS) module developed by [PERSON] et al. successfully applied this method to analyze shoreline changes in the U.S. coastal zone [37]. The baseline, which is a line element parallel to the general course of all historic shorelines, should be established in proximity to the series of shoreline positions. This is to facilitate calculations and ensure that all shoreline periods are located on the same side of the baseline. The buffer zone method generates the baseline mainly based on the offset of the existing shoreline and is capable of obtaining a curved shape that is close to the trend of the shoreline. In this study, we select the 2000 coastline as the basis, generate the buffer zone, remove the redundant part (the seaward side), and retain only the landward side to obtain the baseline. Subsequently, perpendicular lines were drawn to the coastline of each period at equal intervals (1.5 km) to obtain 143 analytical profiles for analyzing the changes in shoreline details under different time series. Based on the baseline method, we refer to previous research cases [32] and divide the coastline of Laizhou Bay into three categories according to the end point rate (EPR): dynamic stability zone (\(-\)5-5 m/a), growth zone (\(>\)5 m/a), and erosion zone (\(<\)\(-\)5 m/a). \[EPR_{m(i,j)}=\frac{D_{m(i)}-D_{m(j)}}{T_{(i,j)}} \tag{8}\]  
where \(EPR_{m(i,j)}\) is the terminal change rate of the \(i\)-th and \(j\)-th coastline at the \(m\)-th section, \(D_{m(i)}\) and \(D_{m(j)}\) are the distances from the \(i\)-th and \(j\)-th coastline to the baseline at the \(m\)-th section, respectively, and \(T_{(i,j)}\) is the time interval between the \(i\)-th and \(j\)-th coastlines. Figure 2: (**a**) Fitted curves of fractal dimension (FD). (**b**) Schematic representation of the multi-period shoreline. (**c**) EPR variation of transect profiles. (**d**) Fractal dimension change in the transect profiles. (**e**) Relationship of EPR and fractal dimension changes. In order to quantitatively describe the changes in the length and tortuosity of the coastline and evaluate the evolution of the coastline, we use fractal dimension to describe the degree of evolution of the coastline before and after the two periods. This metric can be defined as the ratio of detail change to scale change. We adopt the box counting method [38; 39]: We set the length of the square to be \(\varepsilon\) and cover the whole study area, and count the number of squares \(N(\varepsilon)\) when all the shoreline elements are covered. By gradually reducing \(\varepsilon\), we obtain multiple sets of \(\varepsilon-N(\varepsilon)\) correlation data, and based on the least squares principle, we obtain the fitted shoreline fractal dimension. \[D=\lim_{\varepsilon\to 0}\frac{\ln N(\varepsilon)}{\ln(1/\varepsilon)} \tag{9}\]  
\[\ln N(\varepsilon)=-D\ln\varepsilon+C \tag{10}\]  
where \(\varepsilon\) is the size of the measurement unit, \(N(\varepsilon)\)is the minimum number of measurement units to achieve shoreline coverage, \(D\) is the fractal dimension of the graph, and \(C\) is the offset. Generally speaking, the larger the fractal dimension, the more complex the coastline and the more severe the tortuosity. After calculation, the fractal dimensions of the Laizhou Bay coastline in 2000 and 2020 were 1.04 and 1.10, respectively. This shows that after long-term coastal development and engineering construction activities, the overall evolution of the Laizhou Bay coastline has become more complex and tortuous.