Thank you, this link is much better.
How is it strange that I have doubts over a theory and want to see properly documented evidence for its existence in the real world? I always thought that this is what science should be about - not believing anything, unless it can be objectively proven in the real life.
So *on paper* this theory applies to all electromagnetic waves. However, in the link you provided the author claims that “the measurement of positions in space using Differential GPS enables us to measure the radius of the earth and earth's curvature without optical detours”. So does refraction affect all electromagnetic waves including radio waves used by GPS, or does it not? Seems like you and the author of the linked study are of different opinions on this subject. Anyway, I am interested in the supposed optical phenomena which is why I am only considering evidence regarding light waves.
For some reason, I do believe that light traveling through air is different from light traveling though water and glass (and especially through all of the above media combined at the same time)… Indeed, why would I believe that (if you exclude the fact that it is completely logical)?
I have looked through all of the equations that you mentioned and beyond, almost none of them have anything to do directly with the supposed terrestrial refraction. In many of them earth’s curvature is simplified away and calculations are made either with earth considered being flat or light rays considered being straight. And most of these equations are admittedly just approximations of a purely theoretical phenomena.
Regarding the study you linked, the author created a straw man of how refraction supposedly should act on a flat earth, and then disproved it using his purely theoretical simulations like it actually means something. Moreover, this study lacks all the necessary data points to objectively prove the existence of terrestrial refraction. Namely the temperature, pressure and humidity of air layers captured on video (and their relative placement) are completely absent. If you manage to find another study that does include them, please do share. I genuinely try my best to look into things, and am always open to changing my opinion on any given subject, but only if proper evidence presents itself. So far there is no properly documented evidence for me to believe light bends many kilometres up from below the earth’s supposed physical horizon.