Good post - the UV index is related to how short the "column of air" that the sun traverses to get to your skin - noon is the shortest distance. Scattering is a density function (more air, more scattering), so this is why it looks like cos^p when compared to normal irradiance (cos). It also explains why it is hard to get a sunburn in the temperate winter, since the sun always appears at an angle, it doesn't go directly overhead.