## 2 Canyon/Valley Composite Rough Surface Modeling  
As shown in Figure 1, the canyon/valley environment has a natural semi-enclosed cavity structure. The sides are often terrestrial settings with varying slope degrees, while the bottom surface may be an aquatic or terrestrial environment. We designate the composite rough surface with a terrestrial bottom as a canyon and a water environment as a valley to make descriptions more convenient. When modeling the canyon/valley composite rough surface, the terrestrial parts of the environment can be simulated using Gaussian rough surfaces with the expression of the Gaussian spectral function as [32]  
\[W_{\text{Gauss}}(k_{x},k_{y})=\frac{l_{x}l_{y}h_{\text{rms}}^{2}}{4\pi}\exp \left(-\frac{k_{x}^{2}l_{x}^{2}}{4}-\frac{k_{y}^{2}l_{y}^{2}}{4}\right) \tag{1}\]  
where \(h_{\text{rms}}\) denotes the root mean square (RMS) height of the rough surface, which is used to quantify the fluctuation range of the rough surface, and \(l_{x}\) and \(l_{y}\) are the correlation lengths of the rough surface in \(x\)- and \(y\)- dimensions, respectively. By using Pierson-Moskowitz (PM) sea surface [33], the water component environment may be reproduced, and the expression for the PM spectrum function is  
\[W_{\text{PM}}(k)=\frac{\alpha_{p}}{2k^{3}}\exp(-\frac{\beta g^{2}}{v_{19.5}^{4 }k^{2}}) \tag{2}\]  
where \(k^{2}=k_{x}^{2}+k_{y}^{2}\), \(\alpha_{p}=8.10\times 10^{-3}\), \(\beta=0.74\), \(g\) is the acceleration of gravity \(g=9.81\) m/s\({}^{2}\), and the \(v_{19.5}\) is the wind velocity 19.5 m above the sea surface. It should be pointed out that when the wind velocity is small, the water surface is calm enough, and the waves on the water surface are slight. So the approximation of the water component environment is reasonable. In this paper, the wind velocities are set 1 m/s, 0.6 m/s and 0.2 m/s. Figure 1: Natural canyon and valley environment: (**a**) canyon with terrestrial bottom; (**b**) valley with water bottom. By adjusting parameter values and combining the aforementioned spectral functions, rough surfaces with various statistical properties can be simulated using the Monte Carlo approach. The rough surface contour function can be represented by using the fast Fourier transform as follows. \[f(x,y)=\frac{1}{L_{x}L_{y}}\sum_{m=-\infty}^{\infty}\sum_{n=-\infty}^{\infty}b_{ mn}\exp\left(\frac{\mathrm{i}2\pi mx}{L_{x}}\right)\exp\left(\frac{\mathrm{i}2 \pi ny}{L_{y}}\right) \tag{3}\]  
\[b_{mn}=2\pi\sqrt{L_{x}L_{y}W(k)}\times\left\{ \begin{array}{ll}\frac{N(0,1)+ \mathrm{i}N(0,1)}{\sqrt{2}}&m\
eq 0,N_{x}/2,n\
eq 0,N_{y}/2\\ N(0,1)&m=0,N_{x}/2\ or\ n=0,N_{y}/2\end{array} \right. \tag{4}\]  
where \(N(0,1)\) denotes random points following standard normal distribution, \(L_{x}\) and \(L_{y}\) represent the simulated rough surface lengths in \(x\)- and \(y\)-dimensions, respectively; and \(N_{x}\) and \(N_{y}\) are the number of sampling points in \(x\)- and \(y\)-dimensions. The canyon/valley composited rough surface can be regarded as the composite of three parts of the rough regional surface. We present three sets of weighting functions to weigh the connection of various areas of the rough surfaces, ensuring that the rough surfaces of different regions may preserve their distinct statistical properties and the transition regions are smoothly connected while compounding. The following are the fundamental formulae for the weighted composite rough surface contour function:  
\[\left\{ \begin{array}{ll}f_{\mathrm{com}}(x,y)=f_{\mathrm{sur1}}(x,y)\cdot w _{1}+f_{\mathrm{sur2}}(x,y)\cdot w_{2}+f_{\mathrm{sur3}}(x,y)\cdot w_{3}\\ w_{1}=\frac{[\pi/2+\arctan(y-y_{1})]}{\pi}\\ w_{2}=\frac{[\pi/2-\arctan(y-y_{1})]}{\pi}\\ w_{3}=\frac{[\pi/2-\arctan(y-y_{2})]}{\pi}\end{array}