## 4 Results and Discussion  
To assess the impact of the sea surface on laser transmission, the beam power distributions through an underwater air channel are first simulated. Figure 6 shows the beam power distributions across a 200 \(\times\) 200 km\({}^{2}\) area of the receiving plane, following the application of the statistical and spatial models. In the statistical model (Figure 6a), the peak power decreases as the underwater transmission depth and the wind speed increase, whereas the shape essentially remains invariable. The performance of a laser beam is influenced primarily by the seawater link rather than by the wind speed. In contrast, the spatial model prominently exhibits variations characterized by fluctuations. Figure 6b first shows that after 20 m of underwater transmission, the high-intensity beam narrows and the maximum power at the center is slightly lower than that predicted by the statistical model. Moreover, the beam shape becomes distorted, deviating from the expected Gaussian profile. This distortion decreases as the underwater transmission depth increases. The sea surface in a real ocean environment is also subject to temporal variations, as illustrated in Figure 5. These changes over time may induce different distortions and drifts of the laser beam. Figure 7 presents the statistical variation in the normalized received power along the \(x\)-axis over a consistent time interval. At a transmission depth of 20 m underwater, different wind speeds influence the distortion and deviation of the laser  
Figure 6: Spatial distribution of beam power in the receiving plane. The sea surface channel is (a) statistical model, (b) spatial model (t = 2 s) based on the Elfouhaily spectrum, for wind speeds of (left to right) 1, 5, 10 and 15 m s\({}^{-1}\) and underwater transmission depths of (top to bottom) 20, 60 and 100 m, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Setting** & **Parameter** & **Value** \\ \hline \multirow{4}{*}{Receiver plane} & Telescope diameter & Optimal \\  & Field of view [rad] & \(\pi\) \\  & Height [km] & 500 \\  & Sawaater & Type \\  & Depth [m] & 20, 60 \& 100 \\ \multirow{4}{*}{Channel} & \multirow{4}{*}{Sea surface} & Model & Statistical model (Hu model) \\  & & Spatial model (Eifouhaily spectrum) \\  & Wind speed [m s\({}^{-1}\)] & 1, 5, 10, 15 \\ \multirow{4}{*}{Channel} & Air & Preliminary cloudless standard atmosphere (see in Table 3) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._beam differently. Concurrently, the average normalized power peak value is reduced by approximately 0.9 dB under the statistical model at similar conditions. With increasing underwater transmission depth (60 m, 100 m), the beam power distributions and shapes predicted by the spatial model align more closely with those of the statistical model, and the spatiotemporal characteristics of the sea surface exert a diminishing influence on the beam. This finding indicates that extending the optical path length in turbid waters may mitigate the scintillation effects attributed to the sea surface, although it necessitates precise adjustment of the beam power and transmission depth to optimize performance [4; 15; 18]. To further elucidate the preliminary results presented in Figure 7a-d, Figure 8a-i depict the dynamics of a high-intensity laser beam transmitted 20 m underwater and interacting with sea surfaces under a wind speed of 1 m s\({}^{-1}\) at different times. The results demonstrate a clear relationship between the spatial distribution of beam power and the temporal and spatial characteristics of the sea surface. Specifically, the beam shapes illustrated in Figure 8a,i exhibit similarities, corresponding closely to the comparable sea surface topographies at 1 s and 50 s in Figure 5. And Figure 8j shows that the average power at the center of the space (\(x=0\), \(y=0\)) gradually decreases as the wind speed increases. The fluctuations in the sea surface primarily influence the variability in link power [2].