## 4 Experiment and Analysis
### Results and Analysis
#### 4.2.3 Validation of Calculation Accuracy in Simulated and Real Grid DEMs  
1. The terrain entropy values of twelve simulated DEMs were calculated using four currently available terrain entropy calculation methods and the Euclidean distance approach proposed in the present study. The results are presented in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Terrain Entropy** & **Validity (V)** & **Reliability (R)** & **Measurement Ability (A)** \\ \hline Euclidean distance terrain entropy & Yes & 44.015 & 0.757 \\ Slope terrain entropy & Yes & 34.111 & 0.941 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Consistency of Euclidean distance and slope terrain entropy with the original meaning of the entropy. Figure 8: Variation in terrain entropy with iterations: (**a**) Euclidean distance terrain entropy. (**b**) Slope terrain entropy. (1) Elevation Terrain Entropy  
The expected terrain entropy of the flat terrain (a) should be 0, as the elevation value is constant. However, the elevation terrain entropy value of (a) attains 9.8138, which is the highest among the twelve simulated DEMs. It indicates a significant calculation error. The elevation terrain entropy values of (b,c) also do not meet expectations as they are higher than those of more complex terrains. (d-g) are four simulated DEMs with added random noise and sine-cosine functions, so they show greater complexity. The elevation terrain entropy values of these four DEMs correctly reflect the increasing trend in complexity. Although (h-l), five high-complexity simulated DEMs, have highly complex terrains, their terrain entropy values are relatively close, around 9.688. It indicates that the elevation terrain entropy method fails to effectively differentiate highly complex terrains. In summary, the elevation terrain entropy of simple terrains is abnormally high, showing the shortcoming of misjudgment. The elevation terrain entropy of highly complex terrains does not significantly increase, indicating poor sensitivity to extremely complex terrains. (2) Relative Elevation Terrain Entropy  
As expected, the relative elevation terrain entropy of (a) is 0, indicating the minimal elevation variation in flat terrains. The relative elevation terrain entropy of (b), a simple slope, is 9.5025, a relatively higher value that is consistent with the larger elevation difference in the slope terrain. However, the relative elevation terrain entropy of (b) is slightly higher than that of complex terrains, presenting an anomaly. Theoretically, the entropy of a simple slope should be lower than that of complex terrains. The reason for this anomaly may be the overemphasis of elevation variations in the slope terrain in this method. The relative elevation terrain entropy of (c), a single peak, is 9.7088, slightly higher than that of the slope terrain. The entropy value is not significantly increased although it reflects the elevation differences in the peak, and it is possibly because this method fails to sufficiently capture larger-scale elevation differences in the peak terrain. (d-g) have moderately complex terrains, and their relative elevation terrain entropy values gradually increase with complexity as expected. Fluctuations in the relative elevation terrain entropy values of (h-l) are observed, but they do not show an increasing trend (with the entropy value fluctuating around 9.71). It suggests that relative elevation terrain entropy has low sensitivity to highly complex terrains and fails to effectively reflect the complexity of terrains.