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Marcel, you wrote:
"My suggestion would be that one measures the temperature of the water
and of the air. If this temperature difference is "considerable",
extreme refractions may be likely. Unfortunately I'm not in a position
to quantify the "considerable". From my own experience at my present
location these effects are more likely during spring and autumn. In
spring the water is still cold from winter and the air may already be
warm; this leads at the surface to inversions with ducting. In autumn
the sea is still warm from summer and the air already cold; this leads
to "Omega" sunsets or inferior mirages."

This was tried out in the late 19th/early 20th centuries, primarily for
reducing dip anomalies. It seems that in practice it wasn't sufficiently
predictive. I would imagine there are formal papers on the results of these
experiments from a century ago, but I haven't seen any. Here's a brief
extract from Chauvenet who discussed this possibility:
"For an altitude of a few feet, the difference of pressure will not sensibly
affect the value of D', and may be disregarded, especially since a very
precise determination of the dip is not possible unless we know the density
of the air at the visible horizon, which cannot usually be observed. We may,
however, assume the temperature of the water to be that of the lowest
stratum of the air"

 -FER



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