## 5 Numerical Results and Discussion  
### Simulation Parameters  
The system parameters set in our simulation are shown in Table 1, and we employed observed ocean data, including the pressure, temperature, and salinity of seawater, from the Global Ocean Argo gridded dataset [35]. In order to identify the reliability of the simulation results, we selected four Argo nodes from ocean areas with different longitudes and latitudes in our simulation, as shown in Table 2. All the results presented in Sections 5.2 and 5.3 were verified via Monte-Carlo simulations. First, we present the numerical results for the scintillation indexes, effective received spot size, and the Malaga parameters (\(\alpha\), \(\beta\)) for the four Argo nodes in Table 2. It can be seen from Figure 2 that the received spot size \(W_{\text{LT}}\) and the scintillation index \(\sigma_{\text{T}}^{2}\) synchronously increased with increasing \(z\) and \(\chi_{T}\). In Figure 3, the change trend for the parameters \(\alpha\) and \(\beta\) with increases in \(z\) and \(\chi_{T}\) is shown. It can be clearly seen that the value of \(\alpha\) was always larger than that of \(\beta\) under a wide variety of turbulence conditions, and \(\beta\) could move closer to 1 for strong ocean turbulence. Based on Equations (5)-(8), the scintillation indexes and Malaga model parameters (\(\alpha\), \(\beta\)) were calculated when the link lengths were 26 m and 30 m, respectively, as shown in Table 3. They were used in the following simulation. Based on Equation (15) and the ocean turbulence parameters from Argo node 4, the effects of the long-term beam spreading coefficient \(W_{\text{z}}/a\), and the received aperture diameter \(D_{\text{rx}}\) on the received optical power with the pointing error displacements are shown in Figure 4. It can be seen that the received optical power gradually increased with the decrease in \(W_{\text{z}}/a\) and the increase in \(D_{\text{rx}}\). According to Figure 4, \(W_{\text{z}}/a\) is larger in strong turbulence than in weak turbulence when \(D_{\text{rx}}\) is fixed. The received optical power at the finite receiving aperture is smaller in strong turbulence than in weak turbulence. Therefore, when determining the optimal received power for the optical signal, increasing \(D_{\text{rx}}\) can mitigate the effects of pointing errors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Symbol** & **Value** \\ \hline Optical transmitter divergence angle & \(\theta\) & 1.5 mrad \\ Number of transceivers & \(M\times N\) & \(2\times 3\) \\ Optical wavelength & \(\lambda\) & 532 nm \\ QAM order & m & 8, 16, 32 \\ Normalized pointing error deviation & \(\sigma_{\text{p}}/a\) & \(1\leq\sigma_{\text{p}}/a\leq 10\) \\ Initial beam waist & \(W_{0}\) & 10 mm \\ Outage SNR threshold & \(\gamma_{\text{th}}\) & 20 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters in the simulation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Argo Node** & **Location** & **Average** & **Average** & \\  & **(Longitude, Latitude)** & **Temperature** & **Salinity** & **Pressure** \\ \hline
1 & 2,902,718 & (126.6860, 21.051001) & 23.351 \({}^{\circ}\)C & 34.828 ppt & 150.02 P \\
2 & 1,901,811 & (113.4048, \(-\)59.34197) & 2.165 \({}^{\circ}\)C & 34.469 ppt & 256 P \\
3 & 6,904,085 & (8.6100, 77.9200) & 4.513 \({}^{\circ}\)C & 35.001 ppt & 183.10 P \\
4 & 5,902,507 & (161.52393, \(-\)41.63458) & 10.103 \({}^{\circ}\)C & 34.812 ppt & 386 P \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected Argo Node information.