But how do we know the air was really air? How do we know there wasn't marsh-gas floating on top? How do we know there wasn't a gigantic downward wind blowing a hollow patch in the water?
Well firstly, the experiments were repeated with the same result, so that answers your assertion.
But more importantly it is possible for the water convexity experiment test to be controlled; as it is an experiment which takes place on earth at all points.
Astronomers looking at space phenomena is not controllable. The experimenter can only observe. He cannot experiment with variables of the scenario, make direct samples, or conduct tests elsewhere, to come to the truth of a matter. Astronomy is said to be an "observing science," which is really just an admission that it is not a science at all.
Sure - these are all stupid criticisms - but no worse than you transporting my thought experiment about water temperatures to an alien world so you could pour scorn on it.
Rowbotham did his experiment - and he made one TERRIBLE mistake. He put his eyepoint really close to the water level - which maximised the humidity and temperature gradient and thereby created just enough refractive index change over that LONG distance to bend the light beam.
When the experiment was repeated with the eyepoint high enough above the water to eliminate that mistake - Rowbotham's effect vanished and the result was a clear demonstration of Earth curvature.
In Earth Not a Globe Rowbotham calculates the maximum refractive index and shows that it is not enough to account for what was seen.
Since all of this takes place on earth it is possible for us to know and test the phenomena of refractive indexes. The earth is not alien and refractive tests can show the limits to how light can behave within the atmosphere. Rowbotham references his sources for his determination of maximum refractive index. This is one control that is applied.
Another control is the fact that these water convexity experiments were conducted in several different ways, my multiple observers, over a period of many years.
Your assertion that each of these repeated experiments are affected by a chance phenomena which makes the earth appear to be exactly flat, no more and no less, when it is really a globe, and this despite that known refraction cannot account for what is seen, is absurd.