## 4 Experiment and Analysis
### Results and Analysis
#### 4.2.3 Validation of Calculation Accuracy in Simulated and Real Grid DEMs
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Simulated** & \begin{tabular}{c} **Elevation** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} & \begin{tabular}{c} **Relative** \\ **Elevation** \\ **Elevation** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} & \begin{tabular}{c} **Elevation** \\ **Probability** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} & \
\begin{tabular}{c} **Slope** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} &
\begin{tabular}{c} **Euclidean** \\ **Distance** \\ **Terrain** \\ **Entropy/Bit** \\ \end{tabular} \\ \hline (a) & 9.814 & 0 & 0 & 0 & 0 \\ (b) & 9.785 & 9.503 & 4.907 & 0.491 & 4.529 \\ (c) & 9.780 & 9.709 & 5.762 & 6.543 & 4.860 \\ (d) & 9.677 & 9.713 & 7.692 & 9.397 & 7.331 \\ (e) & 9.673 & 9.275 & 7.650 & 9.531 & 7.415 \\ (f) & 9.679 & 9.656 & 7.776 & 9.568 & 7.466 \\ (g) & 9.694 & 9.716 & 7.830 & 9.571 & 7.552 \\ (h) & 9.688 & 9.703 & 7.891 & 9.594 & 7.632 \\ (i) & 9.687 & 9.720 & 8.053 & 9.592 & 7.802 \\ (j) & 9.688 & 9.703 & 8.100 & 9.599 & 7.823 \\ (k) & 9.688 & 9.715 & 8.187 & 9.607 & 7.947 \\ (l) & 9.689 & 9.701 & 8.244 & 9.604 & 7.980 \\ \hline \end{tabular}
\end{table} 
Table 3: Euclidean distance terrain entropy values of twelve simulated DEMs. (3) Elevation Probability Terrain Entropy  
The elevation probability terrain entropy of (a) is 0, as expected. The elevation probability terrain entropy of (b) is 4.9069, slightly higher than that of the flat terrain. It indicates that the elevation distribution in the simple slope is more complex. The elevation probability terrain entropy of (c) is 5.7617, which is significantly larger than that of the simple slope. It reflects the larger elevation difference and a more complex elevation distribution in the peak terrain. Anomalous decreases in some of the elevation probability terrain entropy values of (d-g) are observed, but the change trend from 7.692 to 9.6503 is relatively reasonable, which aligns with the expected increase in complexity. The elevation probability terrain entropy values of (h-l) show a gradual increase, reflecting a more diverse elevation distribution. It is also consistent with the expected increase in complexity. To conclude, elevation probability terrain entropy effectively reflects the increasing trend in complexity of the twelve simulated DEMs from (a-l), but some anomalies still occur. (4) Slope Terrain Entropy  
The slope terrain entropy of (a) is 0, as expected. The slope terrain entropy of (b) is 0.4912, which is greater than 0, reflecting the variation in slope. Since the slope variation is relatively simple, the low entropy value meets expectations. The slope terrain entropy of (c) is 6.5433, which is significantly larger than that of (a,b). The great increase in slope terrain entropy reflects more complex slope variations in the peak terrain. The slope variation in (d-g) is more complex, leading to an increase in slope terrain entropy, which ranges from 9.3971 to 9.5678. This change in entropy accords with the expected increase in complexity. The entropy values of (h-l) show a change from 9.5943 to 9.5918 and 9.6071 to 9.6035, with a difference of only 0.0153. It indicates that the method has low sensitivity to extremely complex terrains and fails to adequately reflect the complexity of terrains. In summary, although the slope variation is large, the increase in slope terrain entropy is relatively small. Particularly, the entropy value of high-complexity terrains does not significantly increase. (5) Euclidean Distance Terrain Entropy  
The Euclidean distance terrain entropy of (a) is 0, indicating that the terrain does not have complex features, just as expected. For relatively simple terrain types (b) and (c), although there is a slight increase in the number of elevation value categories, entropy values are generally low. It indicates that the terrain information is still simple, and the increase trend in entropy is in line with expectations. In (d-l), random noise is introduced to simulate more complex terrain structures.