## 5 Discussion
### Comparison of the Result of EMR-SF between Different Interval Distances of the Grid Point by LRBF  
In this section, the applicability of the grid point interval distance acquisition method provided in this paper will be discussed. The maximum impact distance is compared with other grid interval distances, the layered interval distance of the LRBF is 25 m, and their error statistics are shown (Table 3).  
The accuracy of LRBF increases gradually as the distance between the grid points decreases. The accuracy of LRBF is improved substantially when the grid point interval distance reaches a certain level, but it does not improve the interpolation accuracy by decreasing the interval distance of the grid point all the time. Compared with the interval distance of 7 m, the accuracy of the interval distance of 6 m in LRBF does not improve significantly. At the same time, the time cost increases significantly as the interval distance of the grid points decreases.  
The EMR-RF constructed by the LRBF at different interval distances of grid points is shown (Figure 18). When the interval distances of grid points are 6 m, 8 m, 9 m, and 10 m, the EMR-SF construction is not sufficiently smooth, and the EMR-SF constructed by them in the central region shows obvious discontinuities. The EMR-SF constructed by  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Interval Distance of Grid Point (m)** & **RBFGP** & **LRBF** \\ \hline
17 & 0.0741 & 0.0713 \\
12 & 0.0697 & 0.0645 \\
7 & 0.0425 & 0.0378 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Error of different methods for different interval densities (\(\upsilon/m\)).  
Figure 17: Different interval distances of grid points.  
using LRBF with the maximum influence distance (grid point interval distance is 7 m) is smoother compared with others, and the space field grading is more obvious.  
Figure 18: Comparison of LRBF with different interval distances of grid points. (**a**) The interval distance is 6. (**b**) The interval distance is 7. (**c**) The interval distance is 8. (**d**) The interval distance is 9. (**e**) The interval distance is 10.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Interval Distance of Grid Points (m)** & **RMSE** & **MAE** & **MAXE** & **MINE** \\ \hline
10 & 0.0618 & 0.0322 & 0.508 & \(0.2\times 10^{-5}\) \\
9 & 0.0568 & 0.0292 & 0.512 & \(0.1\times 10^{-7}\) \\
8 & 0.0568 & 0.0289 & 0.524 & \(0.1\times 10^{-4}\) \\
7 (maximum influence distance) & 0.0378 & 0.0179 & 0.45 & \(0.3\times 10^{-4}\) \\
6 & 0.0356 & 0.0211 & 0.32 & \(0.8\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Error of different interval distances of grid points (\(v/m\)).  
In the LRBF interpolation method, each added grid point is derived from the value of the sampling point, and the distance between the grid points will also affect the degree of influence of the sampling point on the grid point. When the distance between grid points is too large, such as 10 m or 9 m, the influence of sampling points on grid points is weakened, and the interpolation accuracy of LRBF is very low. It is important to choose the optimal grid point interval distance for LRBF. The Gaussian function is used to obtain the maximum influence distance of the sampling data, and the interaction between point pairs is considered. Half of the maximum influence distance is used as the grid point interval distance, and the influence of the sampling point on the grid point is considered. This can quickly obtain the grid point interval distance, and the comparison of the results shows that setting the grid point spacing distance according to the maximum influence distance can improve the construction accuracy of the EMR-SF by LRBF.