In his thesis "Real Time Rendering of Atmospheric Scattering Effects for Flight Simulators" Ralf Stokholm Nielsen states that the color of haze/distant objects gets darker and more blue the further they are away from the viewer (page 33, areal perspective. I was wondering if this can be deduced from the scattering formulas and is correct or if the author is mistaken.
So here we have the first counterexample - the sky was rather clear, but with a haze layer quite high up with lots of Rayleigh scattering - as a result, objects at the horizon were fading to orange-red rather than blue despite of the high sun angle.
Why? Sun illuminates white object pretty directly, object is effectively emitting white light - but on the way up to my view position again the white light crosses a lot of Rayleigh-scattering medium and hence objects appear red since the blue light is scattered out.
At one point, I saw three distinct horizon line phenomena - against the sun, there was a very high line sharp below which everything was radiant milky-white. At about 50 degrees with the sun, this changed to the true horizon line becoming visible as a dark line in front of a bright sky. At about 110 degrees, this changed to a higher haze-top line as my shader generates it. I couldn't see the other side unfortunately.
There were directly lit faint clouds appearing really dark (almost black) - almost pure Mie scattering in action. There was a haze layer showing blue top, fading to green and then to orange-brown below - wavelength dependent light diffusion in a primarily Rayleigh scattering medium. It was like nature's demonstration of all phenomena you can do with light scattering at the same time.
This whole stuff is so fascinating that I would like to spend half a year to just code something that solves the general scattering problem for any distribution of Rayleigh, Mie and diffuse scatterer density. Unfortunately it's never going to run in real time on the present or next generation of GPUs...