## 3 Experiment and Analysis
### Comparison with Other Methods  
Common coastline extraction methods based on LiDAR data include the coastal profile and isoline tracking methods. In the coastal profile method, a DEM is first constructed using LiDAR data; it is then divided into many profiles with different elevations, and finally a profile in which the coast is located is identified. In the isoline tracking method, a DEM is first built using the LiDAR data and then the isoline at which the average high-tide surface elevation is located is identified; this isoline is known as the coastline. However, the coastline extracted by the coastal profile method has large errors and discontinuities; therefore, the isoline tracking method is considered superior to the coastal profile method. In this context, the present study selected and compared the performance of our proposed method with that of the isoline tracking method. Since the present study mainly focused on the extraction of the coastline at the cliff, the object of comparison was the coastline of the cliff section. The contour tracing method identifies the contour corresponding to the elevation of the average high-tide surface of the spring tide in DEM; however, according to the elevation characteristics of points in the cliff section, all points close to the elevation of the average high-tide surface of the spring tide are in the lower part of the cliff toward the land; thus, the extracted points will be far away from the outermost edge of the cliff. The isoline point cloud obtained using the extraction principle of the isoline tracking method is shown in Figure 15. The superimposed display of the coastline point cloud extracted using the proposed method and that generated using the isoline tracking method is also presented in Figure 15. As shown in Figure 15, the elevation of several blue points, that is, points generated by the isoline tracking method, abruptly increases, indicating a large jitter here, which is an anomaly. And there are large gaps in some areas behind, indicating that the points here are discontinuous. Compared with the red points, that is, points generated in the present study using the proposed method, the height change is relatively gentle and the points are not evenly divided, indicating excellent continuity. The superimposed display of the coastline point clouds calculated using the proposed method and the isoline tracking method and the point cloud of the cliff segment are presented in Figure 16a. Points in the red box, that is, green points, were calculated with the isoline-tracking method. In the figure, the green points will be projected into the water surface, so the red and green points are approximately in the same plane, and their elevations are close. Figure 16b shows the superposed display of coastlines generated based on the two types of points and point clouds of the cliff section. The green coastline shows a large error and a large deviation from the actual trend, whereas the red coastline is smoother, continuous, and closer to reality. Figure 15: The superposition of this method and isoline tracking method. According to error theory, when the true value is unknown and there are multiple groups of observations, the average value of each group of observations can be regarded as its approximate true value. Therefore, assuming that the coastlines generated by the proposed method and the isoline tracking method are correct, the position of the average coastline can be calculated from these two groups of observations. Specifically, the two coastlines are converted to the same elevation plane; that is, they are in the same plane, and only the accuracy of their x- and y-coordinates is assessed. For the adjacent straight lines perpendicular to the x-axis, the difference in x values was fixed and small, which was set to 0.05 m in this case. These lines perpendicular to the x-axis intersect both shorelines, and the y-coordinate of the intersection can be inversely calculated according to the straight line composed of two points before and after the intersection.