It's even simpler than that, too: https://en.wikipedia.org/wiki/Refractive_index
There are whole communities of photographers trying to get the longest shots possible, and they use this to their advantage, picking optimal locations, climates, time of day etc to maximize the refraction of light. This is where you find these 'record length' shots. They didn't just climb a mountain, they prepared hard for it.
And their observations always matches the models! I mean people should stop and ask themselves why, by chance, everything works when we use nautic miles and when photographers, like you say, use this model to find places to take photos.
Anyhow, my reply was just as much just trying to explain calmly why it is that we don't see the same rate of curvature that you get when you plug it into the calculators you find online.