As s toxic hydrocarbon pollutant, oil spills can become oil slicks on the sea surface, which hinders the material exchange between water and air and poses a serious threat to marine ecological environments as well as the production and life of human beings. Investigation on how to realize early warning and continuous monitoring of pollutants in the early stage of oil spill accidents is of great significance to the protection of marine environments. The marine optical remote sensor is a powerful tool to realize continuous dynamic monitoring of large-area marine environments at different scales and levels. But the solar flare which is the main reason for the saturation and distortion of optical remote sensors brings inherent difficulties in improving information extraction of remote sensing. Some previous studies indicate that the solar flare possesses significant polarization characteristics under specific conditions, and polarization detection is an effective method for oil spill detection. However, under the influence of wind speed and direction, the real sea surface cannot be regarded as a smooth one, and the characteristics and states of oil spills are complex. In the 1950s, Charles Cox and Walter Munk put forward a famous Cox-Munk probabilistic statistical model of rough sea surface after a long-term rigorous investigation, which conforms very well to the real state of the sea surface. In this paper, the Cox-Munk probabilistic statistical model is employed to model the solar flare reflected by rough sea surface affected by wind speed and direction. With the polarization reflection parameter defined by Fresnel's law, this paper quantitatively simulates and studies the spatial distribution and related differences between the degree of linear polarization (DOLP) of solar flare reflected by clean seawater and oil slicks with different refractive indexes under different incident and observation geometries, as well as different wind speed and direction on the sea surface. This paper hopes that the simulation results can facilitate the application of multi-angle polarization remote sensing technology for marine oil spill surveillance.

Firstly, with the polarization reflectance coefficients defined by Fresnel's law, the orthogonal polarization Fresnel reflectance R_p and R_s of the solar flare reflected by calm sea surface are obtained. According to Cox-Munk probabilistic statistical model, the polarization bidirectional reflectance R_glint-p and R_glint-s of the solar flare reflected by rough sea surface are calculated based on R_p and R_s. In the next step, on the basis of R_glint-p and R_glint-s, the spatial distribution of the DOLPof the solar flare reflected by different sea surface media with various refractive indexes on rough sea surface affected by different wind speed and direction is simulated with respect to any incident and observation geometry. Furthermore, the spatial distribution ofDOLP differences between clean seawater and oil slicks is simulated, and the most sensitive polarization observation angle of oil slicks with different refractive indexes is obtained.

The wind speed is set at 5 m/s, with the incident zenith angle set as 15°, 45°, and 56°, and the spatial distribution of theDOLPof the solar flare reflected by clean seawater and oil slicks is simulated (Fig. 2). The contour of theDOLP of the solar flare is approximately a concentric circle, and the minimum of the DOLP is located at the position corresponding to the incident zenith angle within the incident principal plane. As the incident angle gets larger, the distance between theDOLP contour in the direction perpendicular to the incident principal plane is wider than that in the parallel direction, and the contour features an elliptic shape. According to a specific DOLPof the solar flare, within the incident principal plane, the increase in θ_s is equal to the decrease in θ_v. By making the solar incident angle θ_s is 45°, this paper simulates the distribution of theDOLPof the solar flare reflected by oil slicks with three different refractive indexes (Fig. 3). It is shown that the variation rate of the DOLP value with the change in observation geometry is related to the refractive index of sea surface media. When a specific angle is changed in the observation geometry, as the refractive index of sea surface media increases, the variation of theDOLP value becomes slight. In order to improve the oil slick detection sensitivity, the optimum polarization detection area with the largest difference between the DOLP of the solar flare reflected by clean seawater and oil slicks is simulated. When the incident zenith angle θ_s =45°, and the observation azimuth angle φ_v equals 0° and 180° or ranges from 90° to 270°, respectively, the DOLP variation curves with the observation zenith angle φ_v of the solar flare reflected by clean seawater and oil slicks are simulated and compared (Fig. 4). When the incident angle is big enough, as observation zenith angle increases, the DOLPcurves of all media first increase and then decrease. In addition, no matter how θ_s changes, there is a negative linear correlation between θ_s and the observation zenith angle θ_vm corresponding to the most significant DOLP difference between the solar flare reflected by clean seawater and oil slicks. That means the sum of θ_s and θ_vm is a fixed value, which is highly related to the refractive index of oil slicks.

In this paper, the spatial distribution of DOLPof the solar flare reflected by clean seawater and oil slicks are simulated under various incident and observation geometries based on Cox-Munk probabilistic statistical model. The optimum polarization detection angle of oil slicks with different refractive indexes is determined. It is shown that the incident and observation geometry as well as the refractive index of sea surface media are the main factors affecting the spatial distribution of the DOLP of the solar flare. Furthermore, a lower refractive index of the medium is often accompanied by a higher rate of variation of the DOLP of the solar flare with specific changes in the observation geometry. When the incident zenith angle reaches a certain value, it is possible to observe a positive-to-negative reversal of the difference between the DOLP of the solar flare reflected by seawater and oil slicks within a specific range of azimuth angles of the forward reflection area. For oil slicks with specific refractive indexes, the sum of the optimum polarization detection angle and the solar incident zenith angle is constant, which is closely related to the refractive index of the oil slicks. According to the simulation results, under specific incident and observation geometry, polarization detection can significantly improve the sensitivity of oil spill detection. Therefore, this paper is expected to provide support for the protection of marine environments.