Table 1.

Definitions of the parameters used in this paper.

symbol of parameter	meaning
p	degree (%) of linear polarization of skylight
α	angle of polarization of skylight measured from the local meridian
ψ	zenith angle (angular distance from the zenith)
φ	azimuth angle from an arbitrary reference azimuth direction
<x>	mean of parameter x
≪x≫	average of the mean of parameter x
σ‖,σ⊥	standard deviations (along two orthogonal great circles crossing each other at the average Sun position) of the positions of the invisible Sun behind clouds located with the naked eye
σφ	standard deviation of the azimuth angle φ of the Sun
δmax	maximum angular distance between the estimated Sun positions
γmax	maximum angular distance between the estimated solar azimuth directions
max(δmax), max(γmax)	maximum values of δmax and γmax
θS	elevation angle of the Sun above the horizon
Δα = |αmeasured − αRayleigh|	difference between the measured (αmeasured) and the theoretical (αRayleigh) angles of polarization of skylight
NRayleigh	number of celestial points for which Δα < αthreshold = 5°
Nnon-Rayleigh	number of celestial points for which Δα > αthreshold = 5°
Noverexposed	number of celestial points for which the detector was overexposed
r = NRayleigh/N	proportion of the N examined points of the sky for which the direction of polarization differs from that of Rayleigh's theory by less than αthreshold = 5°
n = Nnon-Rayleigh/N	proportion of the N examined points of the sky for which the direction of polarization differs from that of Rayleigh's theory by more than αthreshold = 5°
o = Noverexposed/N	proportion of the overexposed celestial points
rred, rgreen, rblue	values of r in the red, green and blue parts of the spectrum
ɛ	the noisiness n of the celestial α-pattern
s	similarity of the celestial α-pattern to the theoretical (Rayleigh) α-pattern
d	dissimilarity of the celestial α-pattern in comparison with Rayleigh's theory