## 3 Results  
### Model Evaluation Based on RMSE  
Based on the model extraction coordinates and measured checkpoint coordinates, the vertical and horizontal _RMSE_ for each project were calculated using Equations (1)-(4). The GCP density was calculated from the number of GCPs used divided by the area investigated; the relationship between GCP density and _RMSE_ was obtained, as shown in Figure 5. The results show that when the GCP density was highest, the vertical and horizontal _RMSE_ were 0.032 and 0.015 m, respectively, representing approximately 1.88 and 0.88 GSD. When GCPs were not used, the vertical and horizontal _RMSE_ increased to 0.087 and 0.041 m, respectively, representing a GSD of approximately 5.12 and 2.41. \(RMSE_{XY}\) was less than \(RMSE_{Z}\) in all projects. The mean ratio of \(RMSE_{Z}\):\(RMSE_{XY}\) is approximately 2.3. As the density of the GCP increased, the vertical and horizontal _RMSE_ gradually decreased; this trend is fitted by the nonlinear curve in Figure 5. As shown in Figure 5a, when \(d>12\) GCP/km\({}^{2}\), the vertical _RMSE_ did not significantly decrease (the change from the maximum was less than 20%). In Figure 5b, the same is true for \(d>10\) GCP/km\({}^{2}\) when considering the horizontal _RMSE_ (the error does not show significant change).  
There are some cases when the GCP density increased and the _RMSE_ increased, which may be due to the error introduced by the ground measurement of the newly added GCPs. Our results for the horizontal error evaluation are influenced by manually setting the coordinates in the center of the GCPs. A similar uncertainty is expected when determining the coordinates of the GCP centers on the DOM.  
Statistical analysis of the vertical differences of the three projects is shown in Figure 6. In Figure 6a-c, the histograms of the differences between RTK checkpoint elevations and DSM extraction elevations correspond to 0, 1, and 2 GCPs, respectively; all of the curves exhibit a Gaussian distribution. The mean value depicted in Figure 6a is \(-0.08\) m, indicating a systematically biased distribution. The mean value in Figure 6b is \(-0.025\) m, indicating that the addition of a single GCP is conducive to reducing the vertical error. When two GCPs are considered (Figure 6c), the mean value is 0.003 m, and the distribution is significantly improved. A single sample t-test was conducted, as shown in Table 2. The null hypothesis is that there is no significant difference between the mean and the test value 0. The significance of one GCP is less than 0.05, rejecting the original hypothesis, that is, there is a significant difference between the mean of one GCP and zero at a 95% confidence interval. The significance of two GCPs was 0.449, greater than 0.05, and the original hypothesis was accepted--that is, there was no significant difference between  
Figure 5: Effect of GCP density on the _RMSE_ of (**a**) DSM vertical and (**b**) DOM horizontal. GCP density was calculated by dividing the quantity of GCPs used by the measurement area of 0.5 km\({}^{2}\). d represents the density of point clouds on the horizontal axis. Add error bars at \(\pm 1\) standard error at GCP density of 2, 4 and 8, respectively.  
the mean of two GCPs and zero at a 95% confidence interval. Therefore, the DSM has systematic dome error in the vertical direction when zero or one GCP was used, and it is important to use at least two GCPs to improve DSM elevation accuracy. The standard deviation did not show a significant difference, with one GCP having the lowest standard deviation, at 0.033. Figure 6d shows the linear fit of the height difference between the DSM obtained by checkpoints and zero GCPs used; the coefficient of determination (R2) is 0.99.