## 2 Simulation of InSAR Parameters, Power, Coherence and Phase  
[PERSON] et al., in 1996 and 2004, determined InSAR power, phase, and coherence using an extensive derivation process of which quantitative values are also presented with a sequence of simulations [12; 13]. This research employs the parameters of the [PERSON] model, as enumerated in Table 3. In contrast to [PERSON]'s model, this study offers the numerical density of vegetative scatterers (\(\rho_{\text{N}}\)), which is essential for power computation. The estimated parameter values for the simulations are displayed in Table 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Terms in the Treuhaft Model** & **The Corresponding Terms in the Seker Model** \\ \hline \(h_{y}-(z-z_{0})\) & sz \\ \(\rho_{0}\) & \(\rho_{0}\) \\ \(Im<f_{f}>\) & \(Imf\) \\ \(<f^{2}>\) & \(\mid f(0^{+},i^{-})q^{0}\mid^{2}\) \\ \(A^{4}\) & \(\frac{\mid f_{R}(0)\mid^{2}\mid f_{f}(i)\mid^{2}}{4\pi R^{2}R_{1}R_{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The terms used in the models. A simulation evaluating the influence of forest density on InSAR power, concerning tree height, was performed with differing vegetation numerical densities, as illustrated in Figure 5. The power demonstrates clear saturation after around 10 m of tree height, supporting the conclusions of [PERSON]'s model [13]. As forest density increases, the maximum power value correspondingly ascends, exhibiting evident saturation beyond a tree height of 10 m. For a specific numerical density, InSAR power increases with tree height; however, tree height has little effect on power beyond 10 m. The fluctuation in numerical density is assumed to exert no influence on \(\gamma\), given that the extinction coefficient and incidence angle stay constant. When the baseline, polarization, and frequency are specified, the interferometric phase and coherence function as the two InSAR observations employed in parameter estimation. Figure 6 presents the simulation results of InSAR coherence relative to tree height. InSAR coherence decreases with increasing tree height, exhibiting apparent saturation beyond 10 m, thereby corroborating the findings presented in [PERSON]'s model [13]. The vertical wavenumber \(\alpha_{z}\) is influenced by various parameters, including the wavenumber, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\theta\): & \(\sigma_{\mathbf{x}^{\ast}}\) & & \(\mathbf{k}\): & & \\
**Incidence** & **Extinction** & \(\gamma\) & **Wavenumber** & **B/r1** & **\(\alpha_{z}\): Vertical** \\
**Angle** & **Coefficient** & & & & **Wavenumber** \\ \hline
300 & 0.2 db/m & 0.462 & 110.23 & \(10^{-4}\) & 1.909 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Forest density parameters. Figure 5: Power relative to tree height with respect to varying forest density. incidence angle, the angle of the baseline relative to the horizontal, and B/r\({}_{1}\). The known incidence angle and wavenumber from the provided data allow for an investigation into the effects of varying \(\theta_{\rm B}\) and B/r\({}_{1}\) on coherence. Figure 6 illustrates that coherence exhibits periodicity at specific angles due to the characteristics of the cosine function. At \(\theta_{\rm B}\) of 120\({}^{\circ}\), the height of the tree does not influence coherence. At a \(\theta_{\rm B}\) of 30\({}^{\circ}\), InSAR coherence diminishes as tree height increases. As the angle increases, both the maximum value and the rate of decrease in coherence diminish, demonstrating clear saturation beyond 10 m of tree height for all angles. Altering the ratio of B/r\({}_{1}\) influences the computed InSAR coherence. A significant alteration in the ratio, on the order of tens, leads to a rapid increase in coherence, rendering the effects of lower ratios negligible, as illustrated in Figure 7. The maximum ratio of B/r\({}_{1}\) in Figure 7 is 0.1, while the minimum is 10\({}^{-6}\). A change in the order of ten significantly enhances coherence, rendering the previous values negligible.