NavList:

Mark Coady, you wrote:
"OK, I apologize for rambling question the other day."

No, you shouldn't apologize. It was a useful introduction to this more specific question. It gives us an idea where you were headed with this and what got you started on this topic. For anyone who missed that earlier "intro" post, have a look here.

You asked what constant we should use for range of visibility, maybe based on weather conditions. That's a good question, but I fear it has no easy answer. It's closely related to the anomalous dip of the horizon. We can certainly consider the theoretical refraction dynamics and work out how the constant changes under certain constrained conditions. These are useful for putting reasonable ranges on the "constants" and from those ranges developing some idea that the commonly quoted formulas (for dip, range, etc.) are only valid "on average". But there seems to be much more variety in Nature and relatively little correlation between the standard theoretical models and accessible observables. That is, we might hope that we could test the air temperature close to the water and maybe the air temperature at the top of a mast and possible the water temperature, and these things could be compared against real-world cases. As far as I know, despite literally centuries of attempts along these lines, it just hasn't worked out! 

That last paragraph ends on a pessimistic tone, but I'm actually optimistic that this could benefit from more modelling and especially more data. And though I hate to say the letters... this is, in fact, the sort of puzzle that a good A.I. system might explore successfully.

Short answer: I tell people 1.15 or 1.16 ...somewhere in that range. :)

Good to see you, Mark. It's been a while!

Frank Reed