It's not fair to say we globers do not take measurements of refraction when we observe. It's not our problem that flat earther ignore our measurements. The whole purpose of geodesy is to measure the shape of the earth. It's done since centuries and we have reached mm accuracy. Now we even have to take plate tectonics into account. Each GPS navigation device and smartphone containes a database of this so called Geoid to calculate the mean sea level elevation.
Some of us Globers have done rigorous measurements in experiments and observations. Look up
Where are such experiments from flat earther? Where is their data? Where did flat earthers ever measure Refraction? Do they even know how refraction works? Where did they ever use devices developed to measure the geometrical shape of the earth, e.g. Differential GPS/GNSS?
Yes, we can measure and correct for refraction since centuries. The methods are well established in geodesy. Yes we can and have measured the pure geometry of the earth using different methods, which all agree with each other.
We know the surface features, including the oceans, and the radius of the earth at each position up to mm accuracy. We even know how the tectonic plates are moving and have to take that into account in high precision measurements, e.g. measuring the locations of the GPS satellites.
The Rainy Lake Experiment is well documented in minute detail, all data and tools are provided:
The Causeway was not only observed hundreds of times at very different conditions and altitudes, it also was modeled with a globe model and a flat earth model taking refraction into account and it was messured to 5 cm accuracy using Differential GPS. It is curving over curved water without any doubt. All data and footage is available:
Differential GPS measurements of the Bonneville Salt Flats and measuring the radius of the earth:
I studied atmospheric refraction and from the gained knowledge I programmed a Refraction Simulator that can not only produce all real observations, but it can simulate globe and flat earth with refraction.
Refraction can be calculated from known atmospheric conditions.
Because we have ways to measure refraction, e.g. by making simultaneous reciprocal zenith angle measurements, and because we know how atmospheric parameters bend light, we can make measurements that clearly show that it is physically impossible that the earth is flat. We can prove that curvature is the reason for hiding objects and that normal standard refraction conditions make the earth appear 7/6 flatter than it is:
My Earth Curvature Calculator takes altitude AND refraction into account since I have programmed it. So it can calculate the unrefracted (called geometric) and the refracted horizon: