Earth's atmosphere as a polarization filter I would like to estimate the effect that Earth's seasonal tilt (with respect to the sun) has on local variations in polarization of sunlight.

If the atmosphere were treated as an interface with index of refraction $n_\text{atm}$ (occuring either discretely at some arbitrary boundary based on density etc, or smoothly increasing over differential layers of atmosphere), then the transition from $\mu_0, \epsilon_0 \rightarrow \mu_\text{atm}, \epsilon_\text{atm}$ at some angle of incidence $\theta_i$ would selectively transmit and reflect different polarizations of sunlight. 
I would think that dipole scattering would then preserve the plane of polarization for light transmitted into the atmosphere, so that a difference in proportion of perpindicular- vs. parallel-polarized light at the upper atmosphere would be preserved as the light propagated/scattered towards the surface of the Earth. From the Figure, this would lead an observer in, say, South Africa ($\theta_i\approx 45^\text{o}$) to measure different amounts of s-pol or p-pol light than an observe in India ($\theta_i\approx 0^\text{o}$)

The two questions, compactly:


*

*Can the atmosphere be treated as an interface that preferentially transmits/reflects different polarizations of sunlight for a given $\theta_i$?

*Would this effect cause observable differences in fractions of polarization types measured by an observer at the surface?

 A: Well, you can model the earth's atmosphere, like you have said, as an interface but the refractive index of the interface will be a time dependent one, since the concentration of gases in the atmosphere is not static; it is dynamic process, continuously changing the refractive index of the atmospheric media. As a result, the so-called preferential treatment dealt by the earth's atmosphere to the transmitted polarisation of the sunlight is not something absolute; rather it changes from time to time. I am not sure but maybe this change has a diurnal variation or even a seasonal variation. As part of the second question, the answer is yes. Strictly speaking, observers on different parts of the earth will see different kind of polarised light. So the sunset in Greenland, India and Africa have different characteristics; they are not unique but distinguishable.
A: That mechanism causes no significant polarization.   The formula for specular
reflection ought not to exclude the refractive index of the medium above
the elevation of the hypothetical reflective sphere.   When the two indices
of refraction are nearly equal (I expect atmospheric density doesn't have
vertical discontinuities below the ionosphere), the resulting reflection
is the sum of squares inversely proportional to small differences in refractive index.   As
the sum is made into a continuous integral, the increase of summed
elements only rises linearly, while the element size decreases quadratically.
The sum tends to zero in a continuous atmosphere gradient.
Skylight, though, IS polarized, by a different effect.   The Rayleigh 
scattering that makes the sky blue, creates scattered  light that propogates
only from the direct sun's ray in a direction perpendicular to the E-field,
and that E-field (in a ray from the sun) has no component oriented toward the
sun.  So if you point at a patch of blue sky, expect that the light
coming from that patch has polarization mainly perpendicular to the
patch-to-sun direction.   This will not be the case for multiply scattered
light (like the dim gray glow under a cloud).
So, while the visible solar disk is not polarized, the blue sky surrounding
it IS.
