In complex environments, unpolarized sunlight undergoes absorption and scattering by atmospheric molecules and fog particles, leading to polarization phenomena that form stable skylight polarization patterns. These patterns change with variations in atmospheric conditions, time, and other factors. The composition, particle size, and properties of aerosols vary significantly over time and across space, making it difficult to quantify their influence on skylight polarization distribution. To accurately simulate the radiative transfer of sunlight through aerosol media, it is essential to consider the aerosols' physical and optical characteristics, as well as their environmental context. Sea fog and land fog differ in their physical and optical properties, which in turn affect the formation of polarization distributions in the sky. However, there has been limited quantitative comparison between theoretical models and field measurements in existing studies. Building on previous research, we simulate the vertical transmission of aerosols by layering the atmospheric medium based on particle size and using the adding-doubling method to solve atmospheric radiation transmission problems. A simulation model for the skylight polarization distribution is developed for both sea and land aerosols. In addition, we design and implement an all-weather, full-period polarization acquisition system to conduct actual measurements and verify the model in both sea and land environments. By quantifying the difference in polarization distribution between sea fog and land fog, we hope to enhance our understanding of sky polarization patterns under different aerosol conditions. It also provides a reference for applying skylight polarization characteristics in polarimetric navigation across sea and land environments.

We use the adding-doubling method to build simulation models for skylight polarization distribution based on the vector radiative transfer equation, applicable to both sea fog and land fog environments. We also develop an all-weather, full-time polarization acquisition system for practical measurements and validation. The study explores the effects of different times of day and aerosol optical depth (AOD) on polarization distribution, comparing the polarization distributions of different fog types under the same weather conditions. A simulation model solves the radiation transfer equation using the adding-doubling method to obtain the degree of polarization (DOP) and angle of polarization (AOP), showing the particle distribution characteristics of both sea fog and land fog. To verify the model’s accuracy, we construct a field experiment setup that captures the actual polarization distribution. We then analyze the simulation and experimental results of sea fog under different conditions and investigate the effects of fog types on the full-sky DOP distributions.

The DOP values across the entire sky decrease as the solar altitude increases, with the smallest values near the sun and larger values farther from it. The AOP distribution shows symmetry around the meridian line (Fig. 6). Simulations and measurements in both sea fog and land fog environments reveal that increasing AOD attenuates DOP; the higher the AOD, the stronger the attenuation (Figs. 9 and 12). The maximum DOP in sea fog is higher compared to land fog (Fig. 15). The consistency between the simulation and experimental DOP distributions in both environments, calculated using the Pearson product-moment correlation coefficient (PPMCC) and root mean square error (RMSE), exceeds 70% (Table 6).

Most research on skylight polarization distribution under different aerosol types remains theoretical, but real foggy environments are dynamic, requiring further field testing to quantitatively assess the differences between theoretical models and practical conditions. We address this challenge by simulating and experimentally studying the effects of different times, AOD levels, and fog types on skylight polarization distribution. The simulation ensures accuracy by solving the vector radiative transfer equation using the adding-doubling method, while the tests employ a fisheye lens and a DoFP polarization camera for rapid image acquisition. The results demonstrate that: 1) the distribution of skylight DOP is more pronounced when the solar elevation angle is low, with smaller DOP values near the sun, and the AOP meridian line shifts counterclockwise over time; 2) as AOD increases, the maximum DOP decreases for both sea and land fog, with sea fog consistently exhibiting higher DOP values; 3) the correlation between simulation and test results, as measured by PPMCC and RMSE, shows good agreement, with a minimum PPMCC of 71.25% and a maximum RMSE of 26.81%. We provide a valuable reference for understanding the influence of different fog environments on sky polarization patterns and their application in polarimetric navigation across both sea and land environments. Further research will focus on minimizing the influence of solar exposure on these measurements.