## 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
The over-the-horizon propagation effects caused by duct considering the irregular terrain, different surface dielectric parameters at the lower boundary, and non-uniform tropospheric turbulence at the upper boundary of the duct layer were simulated on inter-city links. The simulation results were compared with the results of numerical modeling software, AREPS (advanced refractive effects prediction system). The tropospheric atmosphere uses the refraction index n to describe the refraction characteristics of electromagnetic waves. The propagation of electromagnetic waves on the earth's surface needs to consider the influence of the earth's curvature. The atmospheric refraction index \(n\) is expressed by the modified refraction index \(m\) as  
\[m(h)=n(h)+h/a, \tag{1}\]  
The modified refractive index \(M\) is expressed as  
\[M=(m-1)\times 10^{6}=N+10^{6}\times h/a=N+157h, \tag{2}\]  
Figure 8:0 Schematic diagram of over-the-horizon forward-propagation of intercity links based on multi-source data fusion. \begin{table}
\begin{tabular}{c c} \hline
**IGBP Land Cover Type** & **Dielectric Constant** \\ \hline Savannas (SAV) & 2.85 + i0.33 \\ Grasslands (GRA) & 40 + i0.085 \\ Permanent wetlands (WET) & 26.5 + i1.2 \\ Croplands (CRO) & 4.0 + i0.93 \\ Urban and built-up (URB) & 5 + i0.070 \\ Snow and ice (SNO) & 15.8 \(-\) i1.8 \\ Barren or sparsely vegetated (BSV) & 18.2 + i4.5 \\ Water Bodies (WAT) & 81 + i0.22 \\ \hline \end{tabular}
\end{table} 
Table 3: Dielectric constant used on simulated intercity links. When simulating the tropospheric duct propagation, the refractive index profile used a hybrid four-parameter three-line model to represent a hybrid duct with a base layer:  
\[M(z)=\left\{ \begin{array}{cl}M_{0}+k_{1}z&0\leq z\leq z_{1}\\ M_{1}+k_{2}(z-z_{1})&z_{1}<z\leq z_{1}+z_{2}\\ M_{2}+0.118(z-z_{1}-z_{2})&z>z_{1}+z_{2}\end{array} \right. \tag{3}\]  
where \(z_{1}\) is the height of the duct base layer and \(z_{2}\) is the duct thickness. When tropospheric ducts appear over land due to changes in meteorological conditions, the electromagnetic wave wavelength and emission elevation angle satisfy the following conditions:  
Maximum cut-off wavelength that can trap the wave in the duct  
\[\lambda_{\text{max}}=C\int_{h_{\text{L}}}^{h_{\text{U}}}[M(h)-M_{\text{U}}]^{ \frac{1}{2}}dh \tag{4}\]  
where \(M_{\text{U}}\) is the modified refractive index of the top of the duct trapping layer. When studying the propagation through the duct structure with the base layer, the above formula is simplified as  
\[\lambda_{\text{max}}=\frac{2}{3}Ct\sqrt{\triangle M} \tag{5}\]  
where \(t\) is the duct thickness in \(m\) and is the modified refractive index difference corresponding to the duct layer height and the surface. The critical trapping angle is simplified by derivation using [PERSON]'s law, as:  
\[\theta_{c}\approx\sqrt{2\times 10^{-6}\cdot(M_{s}-M_{\text{U}})} \tag{6}\]  
When the wavelength of the electromagnetic wave was less than the cut-off wavelength, and the emission elevation angle was within the trapping angle, the electromagnetic wave was trapped in the duct and propagated over a long distance beyond the horizon. In the two-dimensional Cartesian coordinate system, it was assumed that the electromagnetic wave propagated along the x-axis, the electromagnetic field component was independent of the y-axis, the refractive index \(n\) of the propagating medium was isotropic, and the field component satisfied the two-dimensional scalar wave equation. \[\frac{\partial^{2}\psi(x,z)}{\partial x^{2}}+\frac{\partial^{2}\psi(x,z)}{ \partial z^{2}}+k_{0}^{2}+n^{2}\psi(x,z)=0 \tag{7}\]  
where \(k_{0}\) is the electromagnetic wavenumber in vacuum, \(\psi\) is the electronic or magnetic field. \(\psi(x,z)=E_{y}(x,z)\) for horizontally polarized, and \(\psi(x,z)=H_{y}(x,z)\) for vertically polarized.