# Analysis of Coastal Zone Data of Northern Yantai Collected by Remote Sensing from 1990 to 2018
## 2 Materials and Methods
### Calculation of Coastline Change  
In this study, the end point change rate (EPR) and linear regression rate (LRR) of the digital coastline analysis system module developed by the U.S. Geological Survey are used to analyze the coastline change rate in northern Yantai [25]. The main steps are as follows. First, based on the coastline data of the past years, a baseline is extracted from the land or seaside by establishing a buffer zone, factor transfer line, and adjustment. Then, all of the annual coastline data is integrated into one factor class, that is, all coastlines. Second, equidistant tangents perpendicular to the above baselines and intersecting with all coastlines are made along the baselines. Then, the DSA system is used to calculate all sections, and the coastline transition rate can be obtained by calculation. The terminal change rate is used to analyze the change rate of two coastlines and several coastlines in different periods [26]. The formulas are as follows:  
\[\mathrm{E}_{(\mathrm{i}j)}=\frac{\mathrm{d}_{j}-\mathrm{d}_{i}}{\Delta Y_{( \mathrm{j}j)}} \tag{1}\]  
where \(\mathrm{E}_{(\mathrm{i}j)}\) is the rate of change of coastline endpoint from the beginning to the end of the study, namely EPR. i is the coastline time at the beginning of the study, j is the coastline time at the end of the study, \(\Delta Y_{(\mathrm{j}j)}\) is the time interval between the beginning of the study and the end of the study, \(\mathrm{d}_{j}\) and \(\mathrm{d}_{i}\) are the distance from the vertical direction of the coastline to the baseline when the time is i and j, respectively.  
The linear regression rate (LRR) is better than the terminal change rate in studying the changes in multiple coastlines [27]. In this study, LRR analyses the proportional relationship and changes of multiple coastlines at different times, and its mathematical expression are as follows:  
\[\mathrm{y}=\mathrm{a}+\mathrm{b}\mathrm{x}, \tag{2}\]  
\[\mathrm{a}=\sum_{i=1}^{n}(\mathrm{x}_{i}-\overline{\mathrm{x}})\big{(}y_{i}- \overline{\mathrm{y}}\big{)}, \tag{3}\]  
Figure 2: The main coastline types of Yantai. (**a**) Silty boundary line, (**b**) Gravelly boundary line, (**c**) Bedrock boundary line, (**d**) Estuary boundary line, (**e**) Construction of coastline near sea. Protective engineering coastline, (**f**) Breeding boundary line, (**g**) Port and wharf boundary line.  
\[\mathrm{b}=\overline{\mathrm{y}}-\mathrm{a}\overline{\mathrm{x}}, \tag{4}\]  
where \(\mathrm{y}\) is a dependent variable, which is the spatial position of the coastline, \(\mathrm{x}\) is the independent variable of the year, \(\mathrm{a}\) is the constant intercept of the fitting, \(\mathrm{b}\) is the regression slope, which represents the \(\mathrm{y}\) change corresponding to each unit \(\mathrm{x}\) change, namely LRR.  
In order to clearly see the variation degree of coastline length for different time periods, the following formula is used to express the annual variation information of coastline length, that is, the coastline variation intensity [28]:  
\[\mathrm{LCI_{ij}}=\frac{\mathrm{L_{j}-L_{i}}}{\mathrm{L_{i}(j-i)}}\ \times 100\%, \tag{5}\]  
where \(\mathrm{LCI_{ij}}\) is the variation intensity of coastline length in the study area from year \(\mathrm{i}\) to year \(\mathrm{j}\), and \(\mathrm{L_{i}}\) and \(\mathrm{L_{j}}\) are the coastline lengths in the study area in year \(\mathrm{i}\) and year \(\mathrm{j}\), respectively.