## 4 Experiment and Analysis
### Results and Analysis
#### 4.2.3 Validation of Calculation Accuracy in Simulated and Real Grid DEMs
The number of elevation value categories increases significantly, and the entropy value rises rapidly. As the terrain complexity increases further, the rate of increase in information content gradually decreases, showing a trend in becoming saturated. Generally, the Euclidean distance terrain entropy effectively reflects the increase in terrain complexity of the simulated DEMs. This method shows a significant positive correlation between terrain complexity and entropy values, and more complex terrains contain more information and thus have higher entropy values. 2. Terrain entropy values of twelve real DEMs were calculated using the four existing terrain entropy methods and the Euclidean-distance-based method proposed in the present study. The results are presented in Table 4.  
To facilitate the analysis of entropy values, elevation value frequency histograms were used to analyze twelve real grid DEMs extracted from different regions shown in Figure 7. The histograms are presented in Figure 9.  
The number of elevation value categories and their distribution in grid DEMs significantly influence terrain complexity. The number of elevation value categories and the proportions of each category in the grid DEM can be visualized by elevation value frequency histograms. Based on the analysis of grid DEMs in Figures 6 and 8, the number of elevation value categories in the four grid DEMs extracted from the plain region does not exceed 5, and there is usually only one or two most frequent categories. These elevation value categories are often represented by large, continuous areas, indicating that the terrain in this type of DEM is relatively simple, and thus its entropy value is low. In the four grid DEMs extracted from the hilly region, as terrain complexity increases, the number of elevation value categories also increases, and the distribution of different elevation values tends to become more uniform. This change partitions the continuous space into a number of smaller regions, thus reducing spatial redundancy. As a result, the terrain entropy values of these DEMs are high. The number of elevation value categories in the four grid DEMs extracted from the mountainous region increases significantly, and spatial redundancy decreases notably. However, due to the presence of numerous slope features in local areas, the terrain entropy is not significantly increased, compared with that of other terrain types. Nonetheless, the terrain entropy values of these DEMs are still high, but the difference in terrain entropy value between these DEMs and other terrain types is not significant. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Simulated**} & \multirow{2}{*}{\begin{tabular}{c} **Elevation** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Relative** \\ **Elevation** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Elevation** \\ **Topability** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Slope** \\ **Distance** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Euclidean** \\ **Distance** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} } \\  & & & & & \\ \hline (a) & 9.812 & 9.698 & 1.042 & 1.604 & 1.457 \\ (b) & 9.812 & 8.626 & 0.989 & 1.918 & 1.483 \\ (c) & 9.813 & 9.655 & 0.925 & 1.522 & 1.498 \\ (d) & 9.812 & 9.612 & 1.748 & 2.120 & 1.849 \\ (e) & 9.805 & 9.251 & 3.022 & 4.072 & 2.631 \\ (f) & 9.812 & 9.736 & 2.478 & 3.205 & 2.765 \\ (g) & 9.763 & 9.625 & 2.599 & 3.740 & 2.798 \\ (h) & 9.809 & 9.690 & 2.695 & 3.177 & 3.016 \\ (i) & 9.807 & 9.563 & 3.254 & 3.592 & 3.097 \\ (j) & 9.801 & 9.592 & 3.872 & 4.047 & 3.268 \\ (k) & 9.759 & 9.552 & 4.174 & 5.347 & 4.054 \\ (l) & 9.807 & 9.652 & 4.661 & 5.205 & 4.478 \\ \hline \end{tabular}
\end{table} 
Table 4: Euclidean distance terrain entropy values of twelve real DEMs. Figure 9: Elevation value frequency histogram.