My own personal experience with this involves a fire control radar with a pin point beam from an aircraft carrier in the middle of the Indian Ocean during a tracking exercise. Ok sounds interesting
We were doing a tracking exercise against a single aircraft flying extremely low to the water. The point was to see how soon we could pick up the aircraft and at what point we lost the aircraft outbound. The radars were situated well over 100 feet (30meters, approx yeah)off the waterline on the super structure of the ship and though had a featured range of 50 NM we were able to tweak them to about 75 NM. They had audio Doppler conversion as well which was helpful in being able to hear our target as well as see it.
The Indian Ocean, during this time, was glassy... very little waves. It's a surreal view. This is why we did this low flying exercises here, less danger to the aircraft.Whilst it maybe less dangerous to aircraft flying low as in hitting an object sticking up above the ground level , it is very dangerous for the pilot, flying low above any smooth glassy looking body of water
During one of the outbounds I was able to stay on the aircraft until I heard a taletell woosh and lost contact. That woosh was water. He had gone beyond the horizon line which was about 17NM if memory serves me for my radar. This paragraph I have trouble believing, are you sure it was 17NM and not further? 17NM = 27.37Km I can see all along a beach near I live and it's 30Km long, beach curves around a bay, from one end to the other across the bay is 30Km, I took a photo last weekend on my iPhone standing on a break wall at one end, probably not more than 3 to 4 meters off the water line

That's what happened to me. Not a light wave, not line of sight... an electro-magnetic, microwave beam. It's a Bedford Level with a modern twist.
Hi I posted some stuff in red in your above quote.
Safety and glassy oceans: Tell them that. I was just there operating a radar.
Horizon: That was off memory but I did mention the radars were pretty high up, about 150 or so off the waterline on the superstructure of the ship... I'm recounted this from memory so the numbers get fogged. It may have been longer.
I'll throw the disclaimer out there that this is a personal experience, anecdote at best, and should be regarded as proof to any except to explain my own opinions of things. In a real experiment all that shit would be documented and a peer reviewed report would follow.