Where is your evidence that it exactly matches the globe radius?
I did not say "exactly matches the globe radius" and in fact it probably does not "exactly match the globe radius"! Whatever you say or fuss about quite variable refraction is a fact of life in microwave link design, celestial navigation, surveying and astronomical observations near the horizon.
You could take a look at
Basic Principles for understanding atmospheric refraction phenomena.
atmospheric refraction
Introduction
Green flashes, mirages, astronomical refraction, dip of the horizon: these are all related phenomena. But there are some basic ideas that are helpful in understanding all of them. The purpose of this page is to point these out. (A more technical page is also available.)
Overview
One principle is to realize how all these pieces fit together:
Astronomical refraction is all the atmospheric refraction between the observer and some point outside the atmosphere.
Green Flashes are caused by the dispersion of astronomical refraction.
Terrestrial refraction is just the part between the observer and some object inside the atmosphere.
Mirages are extreme examples of terrestrial refraction that sometimes occur for objects that are (usually) beyond the horizon.
Dip involves just the refraction between the observer and the apparent horizon (usually, the sea horizon).
Designers of these links commonly make a rough allowance for "typical" refraction by using an effective earth's radius of (
4/
3) x raduis, but the actual refraction very near the horizon if rarely near its "typical value".
I said that the do their designs of the basis of the globe radius, and
basically the links work and they also find that if the beam width is too wide the main lobe will get too close the the waves (for a sea crossing) and cause multipath transmission problems.
I have, I believe, given copious references to these designs in the past and don't intend wasting my time with your nit-picking now!