As a wanna be photographer I love blue skies. A few happy little white clouds add a lot, but I love the deep cobalt blue.
First it is true the skies in the desert are blue–really blue. Not puny blue like back home. This is real blue.
There is a reason that the skies are so blue in the desert. In all skies the sky appears to be blue. It is not really blue. The sky appears to be blue because of the way that sunlight interacts with air. Most ordinary visible light passes through the atmosphere with relatively little disturbance. However once in a while, a tiny particle of light–a photon— collides with an air molecule and bounces off it. This process is called scattering. The light we see in the sky is sunlight that has been scattered off air molecules. Yet the question remains why is blue instead of white?
Since the time of Isaac Newton that great British scientist, we have realized that ordinary white light is a mixture of all of the colours of the rainbow from red all the way through violet. Two other scientists Tyndall and Rayleigh showed that how strongly light is scattered by air molecules depends on the wavelength of the light. Light from the blue/violet end of the spectrum is much more likely to bounce off the air molecules than is light from the red/orange end of the spectrum. As a result of that most reddish light travels through the atmosphere more or less unimpeded by air molecules. However, enough of the light from the blue/violet end of the spectrum is scattered into our eyes to make the sky appear blue to us. So the sky appears to be blue, because we see more of that light than from the other end of the spectrum.
Of course ultra violet light, which is even farther beyond the blue/violet end of the spectrum, is scattered even more than the blue or violet light but that light is invisible to us. Some animals like hummingbirds and bees can see it but we can’t.
As David Wentworth Lazaroff said,
Sonoran Desert skies are such a deep blue (to human eyes) because desert air is unusually pure, that is, compared to the air above many other places on the planet; its relatively free of the tiny floating particles and droplets called aerosols. Aerosols come in a wide range of sizes, and the larger ones reduce the blueness of he sky. Unlike air molecules, they scatter light of all colors about equally. As a result, they seem to fill the sky with white light, diluting the blue.
Desert air has so few of these large aerosols partly because it’s so dry. In more humid climates water vapor condenses on microscopic airborne particles, forming tiny droplets that we see as hazes and fogs. This is especially true in coastal areas, where tiny salt crystals from evaporating ocean spray are especially good at capturing water vapor and creating water droplets. In fact morning fog is a routine occurrence in parts of the Sonoran Desert along the western coast of Baja, California. 
 David Wentworth Lazaroff, “Desert Air and Light,” in A Natural History of the Sonoran Desert, edited by Steven J. Phillips & Patricia Wentworth Comus (2000) p.55-56