What is the Clearness Index and how is it determined?   Is it accounting for air mass, or the ratio of direct beam to diffuse radiation, or anthropogenic atmospheric pollution?    

There’s nothing arbitrary about HOMER’s use of the clearness index.  The clearness index has a very simple definition.  It is equal to the global solar radiation on the surface of the earth divided by the extraterrestrial radiation at the top of the atmosphere.  In other words, it is the proportion of the extraterrestrial solar radiation that makes it through to the surface.  It varies from around 0.8 in the clearest conditions to near zero in overcast conditions.  The monthly average clearness index may vary from near 0.8 down to maybe 0.2.

One can calculate precisely the amount of solar radiation that strikes the top of the atmosphere anywhere on earth with just the latitude.  So if you specify the amount of radiation striking the surface, HOMER immediately divides that by the amount of radiation striking the top of the atmosphere to calculate the clearness index.  If you choose to specify the clearness index instead, HOMER immediately multiplies that by the extraterrestrial radiation to calculate the amount of radiation striking the surface.

You can read more by looking up ‘clearness index’ in the Help file.