How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study

Abstract

We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle ${\theta }_s.$ Our maps display those celestial areas at which the deviation $\mathrm{\Delta }\alpha = |{\alpha }_{\mathrm{meas}}-\hspace{0.5em}{\alpha }_{\mathrm{Rayleigh}}|$ is below the threshold ${\alpha }_{\mathrm{thres}}=5°,$ where ${\alpha }_{\mathrm{meas}}$ is the angle of polarization of skylight measured by full-sky imaging polarimetry, and ${\alpha }_{\mathrm{Rayleigh}}$ is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of $\mathrm{\Delta }\alpha =5°)$ the E-vector alignment of skylight. Depending on ${\theta }_s,$ r is high for clear skies, especially for low solar elevations $(40\%<r<70\%$ for ${\theta }_s\le \hspace{0.5em}13°).$ Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations $(r_{max}=69\%$ for ${\theta }_s=0°).$ The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g., in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial α pattern.