## 5 Conclusions  
In this study, we simulate uplink laser transmission through a seawater-sea surface-air channel via ray tracing technology and the Monte Carlo simulation method, with a focus on the impact of the sea surface channel. Owing to the widely used classical statistical sea surface model, a spatial sea surface model with temporal and spatial characteristics can be implemented on the basis of a wave spectrum and FFT technology. We assessed the validity and applicability of six typical wind wave spectra, concentrating on their ability to characterize the optical properties of the sea surface, particularly the MSS. Additionally, we refined the truncation of the Elfouhaily spectrum under low-wind-speed conditions, ensuring that its variance spectrum and slope spectrum remain valid across all wavenumbers and wind speeds. By comparing different MSS models and simulated virtual sea surface states, we find that the Elfouhaily spectrum can most effectively characterize the optical sea surface and align closely with the Hu model, which was derived from actual laser data.  
We applied both sea surface models for an uplink simulation experiment. The classical statistical model lacks information on spatial and temporal variations, whereas the spatial model can capture power fluctuations driven by dynamic changes in the sea surface. The simulation results indicate that the receiving power through both models diminishes with increasing wind speed. Nonetheless, deeper underwater transmission can compensate for the beam distortion and drift caused by the sea surface channel.  
Importantly, deviations between the spatial model and commonly employed statistical models are still considerable. Specifically, at shorter underwater transmission distances, the spatial model may induce considerable drift in the laser output, potentially resulting in lower average power evaluations than those of the statistical model. Furthermore, the azimuth angle of the sea surface follows a W-shaped pattern rather than an isotropic distribution. This behavior results in an elliptical configuration of the energy centroid distribution rather than the expected circular shape.  
Grasping the spatiotemporal correlation within the sea surface channel is essential for analyzing the laser transmission characteristics at the water-air interface. These insights can help optimize cross-media laser links, such as forward transfer modeling, LiDAR simulations and beam tracking, and improve the accuracy and reliability of systems operating in complex marine environments.  
Conceptualization, H.G. and T.Z.; methodology, H.G., T.Z. and R.Y.; software, H.G., T.Z. and R.Y.; formal analysis, H.G.; writing--original draft preparation, H.G.; writing--review and editing, H.G., T.Z., R.Y., L.H. and S.C.; visualization, H.G.; supervision, T.Z. All authors have read and agreed to the published version of the manuscript.  
Funding: This research was funded by the National Natural Science Foundation of China [grant number 41276041] and the NSFC-Shandong Joint Fund for Marine Science Research Centers [grant number U1406405]. Institutional Review Board Statement: Not applicable. Data Availability Statement: The inputs and outputs of model simulation in this study are available upon request to the corresponding author. The method for simulating sea surfaces used in this study is publicly available from Refs [24; 43]. Acknowledgments: The authors truly appreciate the anonymous reviewers who provided constructive suggestions to improve the quality of this article. The work was carried out at the Marine Big Data Center of Institute for Advanced Ocean Study of Ocean University of China. Conflicts of Interest: The authors declare no conflicts of interest.