Modeling the celestial distribution of skylight polarization patterns by incorporating the influence of both the sun and the moon through an analytical model.

The orientation of many polarization-sensitive animals and the hypothetical sky-polarimetric Viking navigation both rely on the polarization pattern of skylight. For 40 years, scientists have attempted to construct various models to simulate this pattern. However, existing theoretical models have only analyzed the polarization pattern of skylight that is influenced separately by the sun or the moon and have built their modeling frameworks based on the position of one light source. This approach fails to account for the combined influence of the sun and the moon on the distribution of skylight polarization patterns at certain times. In fact, ignoring the influence of the moon during the dawn and dusk periods in clear weather conditions may lead to significant errors in the simulation results compared to the measured data. In this paper, we present an analytical model that considers various factors, including skylight intensity, horizon correction factor, atmospheric turbidity condition, and combined influence of both the sun and moon on the distribution of polarized skylight. We believe our model demonstrates enhanced agreement with measured data and will further our understanding of how animals use the celestial polarization pattern for navigation, particularly when both the sun and the moon appear in the sky. Moreover, the findings of this study may facilitate the advancement of bio-inspired navigation systems.