But WGS-84 is a reference co-ordinate system system , not a globe models. Clearly explained here.

https://gisgeography.com/wgs84-world-geodetic-system/

OP's original post shows how surveyors who believe the earth is a sphere ( he kindly quotes this in his 2nd post) use a set of equations including a constant of refraction k calculated with a value of R = 6370km . This is valid is on a perfect sphere only . We know this is not true whichever model we choose to believe .

WGS-84 is an ellipsoid reference co-ordinate system applied to one of many geoids which in the words of that site leads to Geodesists to " believe the error is less than 2cm which is better than NAD83."

The use of that word " believe " leads me to conclude that we are encouraged to have faith in whatever they tell us. Science now has the appearance of religion in which no one is allowed to question the high priests and the faithful have no need for truth .

Dear somerled,

I find it amazing that you still think about R=6370km used by surveyors when displaying and communicating with each about refraction of light in the presence of thermal and humidity gradients. For a last time : they could have used as well the distance between Glasgow and London as a reference value or any other distance. The choice of a reference variable does NOT ever influence the calculations of the amount of refraction when expressed in terms of lengths and angles .

I realize that it is hard for you to accept that the line-of-sight experiments conducted in the past without taking thermal and humidity ' gradients into account are inconclusive. Therefore, true to the method Zeteticism, we have to strive for more up-to-date experiments, like a laser in a vaccum tube.

And for the record : I did not state that surveyors believe that the earth is a sphere. I used the term "round" which can be a sphere or an ellipsoid or a pear-shaped entity. But, as far as earth is concerned the naked eye is not good enough to discern the difference. The model ellipsoid of GPS is a pretty good approximation to earth with a semi-major and semi-minor axis of 6378137 meter and 6356752 meter, respectively. Choosing 6370 km as a reference length does seem to me a reasonable choice.

An ellipsoid, like the sphere, has no vertices. But you are correct in that the ellipsoid we are talking about is centered on the earth's center of gravity. You might want to study this web site

https://www.state.nj.us/transportation/eng/documents/survey/Chapter4.shtm . I also encourage you to have somebody who has a GPS receiver with the required accuracy for vertical distance, verify the Bedford Level Experiment. Wouldn't it be worthwhile to find the truth ?