## 2 A Multi-Source Real Data Model for Intercity Link Communication Propagation Computing
### Data Extraction of Land Cover Distribution Types of Intercity Links from MODIS
#### 2.3.1 Land Cover Type Distribution on Intercity Links of East China
We numerically approximate the wave equation to obtain a wide-angle parabolic equation (WAPE) [5] form suitable for computing irregular terrain  
\[\frac{\partial u(x,z)}{\partial x}=ik\Bigg{[}\sqrt{1+\frac{1}{k^{2}}\frac{ \partial^{2}}{\partial z^{2}}-1}\Bigg{]}u(x,z)+ik[n(x,z)-1]u(x,z) \tag{8}\]  
The piecewise linear terrain shift map (PLTSM) algorithm proposed by [PERSON] and [PERSON] was used to model the terrain boundary of the PE propagation model. The D-K algorithm is based on the continuous terrain shift map (CTSM) algorithm of Beilis-Tappert, which improves the difficulty of calculating the terrain curvature data. The core idea of the PLTSM algorithm is to establish a new coordinate system on the irregular terrain section, and translate the PE calculation of each step into a flat ground form for solution. The terrain translation coordinates are expressed as  
\[x=u,z=v-T(u) \tag{9}\]Let the field components expressed in the new coordinate system be equal to the field components expressed in the irregular terrain coordinate system \(\phi(x,z)=\Phi(u,v)\). We introduce simplified functions \(\phi(x,z)=e^{i\theta}\psi(x,z)\). According to the coordinate map formula and wave equation, the forward-propagation PE considering irregular terrain is obtained  
\[\left[\left\{\frac{\partial}{\partial x}+i\frac{\partial\theta}{\partial x}-T^ {\prime}\left(\frac{\partial}{\partial z}+i\frac{\partial\theta}{\partial z} \right)\right\}-i\sqrt{\left(\frac{\partial}{\partial z}+i\frac{\partial \theta}{\partial z}\right)^{2}+k^{2}n^{2}}\right]\psi=0 \tag{10}\]  
In the piecewise linear terrain, the phase function is \(\theta(x,z)=kzT^{\prime}(x)+f(x)\). Let \(f^{\prime}(x)=k(1+T^{\prime})/2\), we obtain the WAPE in the coordinate system expressed in terms of the terrain curvature:  
\[\frac{\partial}{\partial x}=i\sqrt{k^{2}+\frac{\partial^{2}}{\partial z^{2}}} \cdot\psi+ik(n-zT^{\prime\prime})\psi \tag{11}\]  
In this paper, digital elevation model (DEM) data with 90 m resolution were used, which were downloaded from the National Geospatial data cloud. Taking into account the resolution, it was more accurate to use the terrain slope to calculate the long-distance propagation. To avoid dealing with the terrain curvature directly, the PLTSM method was used. The phase factor is expressed in the form of  
\[\theta(x,z)=K_{0}zT^{\prime\prime}(x)+f(x) \tag{12}\]  
Let  
\[f^{\prime}(x)=K_{0}(T^{\prime 2}-1) \tag{13}\]  
where \(K_{0}\) is the undetermined constant. Substituting Equations (11)-(13) into the forward-propagation PE (10) after the coordinate transformation, the simplified approximation of PE can be obtained:  
\[\lambda_{\text{max}}=\frac{2}{3}Ct\sqrt{\triangle M} \tag{5}\]0  
The above equation is the WAPE corresponding to the PLTSM method. We abbreviate this method as TWPE (terrain wide-angle parabolic equation). The atmospheric refraction profile is expressed using the modified refraction index \(m(x,z)=n(x,z)-1+zT^{\prime\prime}\) in Equation (14); Equation (14) is solved by the split-step Fourier transform (SSFT) method. The relationship between the transforming field and the physical field could be expressed as \(\phi=e^{i\theta}\psi\). For the segmented irregular terrain surface, the terrain inflection point changes due to different terrain slopes on adjacent segments, while the phase factor on adjacent segments need to be processed continuously to satisfy the realistic terrain simulation. The required phase correction item when the signal reflects from segment 1 to segment 2 is as follows:  
\[\lambda_{\text{max}}=\frac{2}{3}Ct\sqrt{\triangle M} \tag{5}\]1 \[\lambda_{\text{max}}=\frac{2}{3}Ct\sqrt{\triangle M} \tag{5}\]2  
where \(x_{1,2}\) is the reflection point from segment 1 to segment 2; \(T^{\prime}=\tan\beta\), where \(\beta\) is the angle that the local terrain slop makes with the horizontal. In this modification of the phase factor, this phase item makes the controlling factor of height-dependent sequences of transforming filed expressed by \(\psi(x_{1,2},jdz)\).