## 4 Experiment and Analysis
### Results and Analysis
#### 4.2.3 Validation of Calculation Accuracy in Simulated and Real Grid DEMs
(**a**-l) correspond one-to-one with Figure 7a-l.  
(1) Elevation Terrain Entropy  
The elevation terrain entropy values of plain [(a-d)], hilly [(e-h)], and mountainous regions [(i-l)] are all around 9.8, indicating that elevation terrain entropy fails to effectively reflect the terrain complexity of various grid DEMs. (2) Relative Elevation Terrain Entropy  
Compared to absolute elevation terrain entropy, relative elevation terrain entropy can more clearly reveal subtle terrain variations after eliminating the influence of elevation values themselves. It avoids the impact of large-scale elevation values. However, the relative elevation terrain entropy values of twelve real grid DEMs (a-l) extracted from different regions do not exhibit significant differences. It suggests that relative elevation terrain entropy fail to fully capture the terrain complexity of various grid DEMs. (3) Elevation Probability Terrain Entropy  
The elevation probability terrain entropy values of twelve real grid DEMs extracted from three different regions show clear distinctions. The elevation probability terrain entropy values of (a-d) from the plain region are generally low. The elevation probability terrain entropy value of (a) is 1.0416, slightly higher than that of (b) (0.9892) and (c) (0.9253). The reason may be less elevation value categories and more concentrated distributions of elevation value categories in (a). Among (e-h) from the hilly region, the entropy value of (e) (3.0215) is significantly higher than that of (f-h) (all being around 2.5). Despite the presence of large areas with identical elevation values in the lower right corner and continuous terrain in the middle of (e), its entropy value should not be significantly higher than that of (f-h). It suggests that the algorithm may not have fully captured spatial distribution differences in elevation values. With the increase in the number of elevation value categories in (i-l) from the mountainous region, terrain complexity also increases, and the entropy values are generally higher, which is consistent with the increase in terrain complexity. (4) Slope Terrain Entropy  
The slope terrain entropy values of (a-d) from the plain region are significantly lower than those of other eight DEMs, just as expected. As terrain complexity increases, the slope terrain entropy values exhibit a marked increase. However, the variation in slope terrain entropy of (e-h) from the hilly region is relatively large. For example, the entropy value of (e) is 4.0716, which even exceeds that of some DEMs from the mountainous region. The slope terrain entropy values of (i-l) from the mountainous region further increase, reflecting greater changes in slope. (5) Euclidean Distance Terrain Entropy  
The Euclidean distance terrain entropy values of (a-d) from the plains are concentrated between 1 and 2. For (e-h) from the hilly areas, the Euclidean distance terrain entropy values are concentrated between 2 and 3, showing a significant increase compared to the plains. The Euclidean distance terrain entropy values of (e-h) from the mountainous areas range from 3.097 to 4.478, showing a significant difference from the other two regions. Compared with other four terrain entropy values, Euclidean distance terrain entropy values show a significant increase across all twelve DEMs, especially in hilly and mountainous regions [(e-l)]. This result indicates that Euclidean distance terrain entropy is highly sensitive to changes in terrain complexity, capable of effectively capturing differences in elevation distributions. Particularly, in hilly and mountainous regions, the increase in terrain complexity leads to a marked rise in entropy values.