## 5 Conclusions  
In this study, we developed an improved model to calculate the depolarization ratio of reflection and transmission for polarization lidar propagating through a rough sea surface based on the Cox-Munk  
Figure 12: Depolarization of reflection and transmission of sea surface: (**a**) depolarization ratio of reflected light for air-incident case; (**b**) depolarization ratio of transmission light for air-incident case; (**c**) depolarization ratio of reflected light for water-incident case; (**d**) depolarization ratio of transmission light for water-incident case. surface model and Gaussian quadrature method. The comparison of different simulations indicated that our method is effective for simulating the propagation of lidar interacting with a wind-blown rough sea-air interface. The shadowing effects were also considered in this model. In particular, we analyzed the polarized properties in different azimuth and zenith angles and found that rough sea surfaces have a non-negligible influence on polarization of incident light. For unpolarized light, the reflectance tends to polarize the source light; however, for lidar light, it depolarizes the source light. The depolarization of the sea surface is not negligible at small zenith angles. Our model will be applied to simulate the echo signal of oceanographic lidar in future work, and the simulation results will also be used to retrieve the depolarization within water. In addition, a comparison between measurements and simulations will be carried out to improve our method. Methodology, Z.Z. ; Supervision, P.C. ; Funding Acquisition, D.P. ; Project Administration, Z.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China (Grant No. 2016 YFC1400902), the Scientific Research Fund of the Second Institute of Oceanography (SIO), the Ministry of Natural Resources (Grant No. QNYC1803), the National Natural Science Foundation (Grant No. 41901305), and the Zhejiang Natural Science Foundation (Grant No. LQ19D060003). It was also supported by the Fund of the Key Laboratory of Space Active Opto-electronics Technology. We thank the anonymous reviewers for their suggestions, which significantly improved the presentation of the paper. The authors declare no conflicts of interest. Appendix A The detailed calculation of _raa_ (\(\mu^{\prime}\), \(\varphi^{\prime}\),\(\mu\),\(\varphi\)), _rvw_ (\(\mu^{\prime}\), \(\varphi^{\prime}\),\(\mu\),\(\varphi\)), _taw_ (\(\mu^{\prime}\), \(\varphi^{\prime}\),\(\mu\),\(\varphi\)), and _twa_ (\(\mu^{\prime}\), \(\varphi^{\prime}\),\(\mu\),\(\varphi\))  
For convenience, \(\overset{\rightarrow}{s}\), \(\overset{\rightarrow}{v}\), and \(\overset{\rightarrow}{n}\) are the unit vectors of incidence, reflection, and wave normal, respectively. \[\overset{\rightarrow}{s}=(\sin\theta^{\prime}\cos\varphi^{\prime},\sin \theta^{\prime}\sin\varphi^{\prime},\cos\theta^{\prime}). \tag{1}\]  
\[\overset{\rightarrow}{v}=(\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos \theta). \tag{2}\]  
\[\overset{\rightarrow}{n}=(\sin\theta_{n}\cos\varphi_{n},\sin\theta_{n}\sin \varphi_{n},\cos\theta_{n}). \tag{3}\]  
For the air-incident case (see Figure 2a), the relationship among these three vectors is  
\[\overset{\rightarrow}{n}=\frac{\overset{\rightarrow}{v}-\overset{ \rightarrow}{s}}{\left|\overset{\rightarrow}{v}-\overset{\rightarrow}{s} \right|}, \tag{4}\]  
where \(\left|\overset{\rightarrow}{v}-\overset{\rightarrow}{s}\right|=\sqrt{2-2 cos\Theta}\), and \(\cos\Theta=\overset{\rightarrow}{s}\cdot\overset{\rightarrow}{v}=\cos\theta \cos\theta^{\prime}+\sin\theta\sin\theta^{\prime}\cos(\varphi^{\prime}-\varphi)\) is the cosine of the scattering angle.