Atmospheric polarization patterns have important application value in fields such as biological navigation, remote sensing detection and environmental monitoring [[1], [2], [3]]. Since Wehner revealed the biological mechanism of desert ants navigating using polarized light in the 1960s, scholars progressively uncovered the distribution patterns of clear-sky atmospheric polarization [4]. Cronin et al. found that the angle of polarization (AoP) and degree of polarization (DoP) remained stable during the day-night transition [5]. Kyba et al. discovered that urban skyglow diminished natural moonlight polarization signals [6]. Yan et al. confirmed that DoP attenuated with increasing solar elevation angles [7]. Chen et al. indicated that scattering aerosols generally diminished the sky polarization pattern, while absorbing aerosols exhibited a slight enhancement trend [8]. Cheng et al. also investigated the polarization patterns reflected by undulating water surfaces and established an optical transmission model for polarization over the ocean surface [9]. However, significant limitations persisted in existing research regarding polarization characteristics under multilayered clouds and complex weather conditions. Particularly when considering non-uniform atmospheric layers and varying spectral conditions, changes in the sky polarization pattern remained inadequately explored.

Atmospheric polarization modeling aims to quantitatively simulate the scattering processes in the atmosphere through computational and simulation methods. Existing research primarily relies on the Discrete Ordinates method and the Monte Carlo method. Many researchers have used the Discrete Ordinates method (such as DISORT and VDISORT) to simulate polarized radiative transfer [[10], [11], [12], [13]]. While these methods are effective in handling radiative transfer, they often struggle to accurately account for the complex three-dimensional atmospheric environment and polarization characteristics.

The Monte Carlo method was first applied to the simulation of polarized light scattering in clouds and fog in the 1970s [14], and gradually became the mainstream approach in this field. It was widely adopted in numerous studies: Ballesta-Garcia et al. [[15], [16], [17], [18]] investigated polarized light transmission in foggy conditions. Crnivec et al. [19] analyzed its simulation potential for different cloud layers. Korkin et al. [20] generated spherical atmospheric scattering results using multiple codes—MYSTIC, MCSSA, and VLIDORT. Mao et al. [21] program for precise calculation of vector radiative transfer. Li et al. [22] examined the influence of aerosol scattering on polarization distribution. Although the method could simulate complex multiple-scattering polarization processes, it possessed significant drawbacks: In terms of computational efficiency, the need to track large numbers of low-weight photons led to substantial redundant calculations. At critical regions, its modeling of polarization state transitions relied on simplified Mueller matrices, failing to fully account for cross-polarization interference caused by abrupt refractive index changes.

To address the aforementioned limitations, this study proposed the inverse path integral optimization polarization model (IPIOPM), aimed at achieving high-precision and high-efficiency modeling of atmospheric polarization transmission in complex environments. The model's core objectives included:1.

Enhancing photon convergence speed and precisely capturing local variations in atmospheric parameters by designing an inverse photon tracking mechanism and local correction factors.

2.

Quantifying polarization state transition laws at critical points and providing a unified description of reflection and refraction effects at these points by improving the Mueller matrix.

3.

Breaking through computational efficiency bottlenecks and reducing redundant path tracing by designing a dynamic weight threshold adjustment mechanism (DWT) and a KD-Tree-based low-weight photon energy redistribution strategy.

4.

Through modeling and analysis with IPIOPM combined with full-band observations, the study revealed differences in multi-spectral polarization signal attenuation and resolved the retention mechanism of short-wave polarization information under thick cloud conditions.

The structure of this paper was as follows: Section 2 elucidated the theoretical framework of IPIOPM, including inverse photon transport initialization, polarization state updates, critical point transmission, and the DWT optimization mechanism. Section 3 validated the model's accuracy and efficiency advantages through simulations and comparative measurements in complex environments, and analyzed the evolution patterns of full-sky polarization modes, as well as the influence of cloud optical depth and surface albedo. Section 4 provided a summary and discussion of the paper.