FECore does not explain how they did their refraction calculations. The correct refraction calculation is the most essential part of the experiment. I figured out, how they did their refraction calculation. And I found fatal errors in FECore's document concerning refraction.
So their results and conclusions are all wrong.
Link to FECore's final results of the LASER Level Experiments
I will use the values of the 4th measurement on the lake Ijssel as an example as published, but all their refraction calculations are wrong in the same way!
Distance  28.68 km 
Laser height  2.85 m 
Laser visible height at target  0.85 m 
Temperature at 2.85 m height  11.8°C 
Temperature at 0.85 m height  7.6°C 
Refraction index n1 at 11.8°C  1.000283508 
Refraction index n2 at 7.6°C  1.000287811 
This is an excerpt from the FECore document:
Angle of incidence (theta1): 0.0040°
Refractive index calculation
(based on Edlén Equation)
n1 = 1.000283508 (445 nm, 11.8°C, 74%)
n2 = 1.000287811 (445 nm, 7.6°C, 85%)
Angle of refraction is calculated with Snell's law:
sin theta2 = (n1 * sin theta1)/n2 = 0.003999983 degrees
Angle of deviation = 0.000000017°
We concluded the ambient conditions refracted the laser beam downward by maximum of 0.494 mm (0.0194 inches)
Here is what I figured out about the refraction calculation of FECore:
According to the refraction math that FECore applied, they assumed a flat earth and that the air consists of 2 flat layers with constant refractive indices each, derived from 2 atmospheric measurements at the LASER site and the target site respectively.
Wrong: Inappropriate Refraction Model
The FECore refraction model is not an appropriate model for the atmosphere at all.
Refraction in the atmosphere is continuously, even if the earth is flat. It depends mainly on the temperature gradient (continuous change of the temperature with altitude), which results in a corresponding density gradient. In a density gradient a light ray is never straight but bent the whole way. If you have a density gradient, you cannot apply Snell's law like FECore did.
Wikipedia explains in simple terms how terrestrial refraction can be derived and used in practice:
Terrestrial Refraction; Wikipedia
FECore states they calculated the refraction indexes n_{1} and n_{2} based on Modified Edlén Equation.
To compute the refraction indexes n_{1} and n_{2}, depending on pressure (standard 101,300 Pa used), temperature, humidity and LASER wavelength 445 nm, they seem to have used the calculator from the following website (I checked it for 3 measurements and got exactly the values they used):
Refractive Index of Air Calculator
Based on Modified Edlén Equation
https://emtoolbox.nist.gov/
Edlén published 1966 empirical equation for n of standard dry air and corrections for water vapour, based on experimental data. To get an impression of the Edlén formula see here:
https://pdfs.semanticscholar.org/
To compute the angle of refraction θ_{2} by Applying Snell's law you need the angle of incidence θ_{1}:
Wrong: angle of incidence not measured
FECore did not measure the angle of incidence but calculated it by making the following assumptions:
They assumed a flat earth and calculated the dip angle = angle of incidence θ_{1} measured down from eye level at h_{1} = 2.85 m LASER height to h_{2} = 0.85 m target height in d = 28.68 km distance, which yields:
(1) 
 
where^{'} 

Even if we grant the 2 layer model, where Snell's law can be applied, FECore did it wrong. Snell's law says:
(2) 

Snell's law  
where^{'} 

Note: Both angles must be measured with respect to the perpendicular to the boundary layer.
FECore calculated the angle of refraction as follows:
(3) 
\theta_2 = \arcsin\left( { n_1 \cdot \sin( \theta_1 ) \over n_2 } \right) = 0{.}00399998279°
 
where^{'} 

Fatal Error: wrong angles used in applying Snell's law
FECore did not use the correct angle of incidence measured from the perpendicular to the boundary layer, but the angle measured up from the boundary layer. So they should have used \theta_1^{\,\prime} = 90°  0{.}00400° instead, which yields a much bigger angle of refraction \theta_2 = 90°  \theta_2^{\,\prime}:
(4) 

So with the right application of Snell's law the angle of refraction would be θ_{2} = 0.168°, which results in a angle of deviation of γ = 0.004° − 0.168° = −0.164°, and not only 0.000000017° as published!
Using the correct angle of deviation γ, the refraction correction would be c = −82.1 m, and not c = 0.494 mm. This is 166,000 times more than what they published.
A refraction correction of c = −82.1 m would mean, that the target is 81.3 m under the surface of the flat earth. This result proves that the refraction model FECore uses is wrong.
Sloppy: wrong direction of refraction stated
FECore stated: "We concluded the ambient conditions refracted the laser beam downward by maximum of 0.494 mm."
But if the angle of refraction θ_{2} = 0.00399998279° is smaller than the angle of incidence θ_{1} = 0.00400° then the laser beam is refracted upward.
Sloppy: invalid equation
The publised formula for Snell's law:
looks different than (4). The above published formula is not a valid equation, because sin theta2 (= sin 0.003999983°) is not equal 0.003999983 degrees. What they ment to write is the above formula (4).
Their "angle of deviation" is simply:
(5) 
\gamma = \theta_1  \theta_2 = 0{.}00000001721°
 
where^{'} 

Using the correct angles we get:
(6) 
 
where^{'} 

This would be the correct angle of deviation if the FECore model would be correct, which it is not!
The refraction correction c is simply the deviation of the laser at the target due to refraction compared with the unrefracted beam. An upward bended beam causes a positive refraction correction value. FECore computed the refraction correction using the following equation, which I have reconstructed from the published values. This formula would be correct if the FECore's refraction model would be correct:
(7) 
c = d \cdot \gamma = 0{.}494\ \mathrm{mm}
 
where^{'} 

Error: the angle of deviation γ must be given in radian units in formula (7), not in degrees!
So without this error the refraction correction would be:
(8) 
c = d \cdot \gamma \cdot ( \pi / 180° ) = 0{.}00861\ \mathrm{mm}
 
where^{'} 

So the refraction correction should even be about 57 times smaller. Using the correct angle of deviation, obtained by applying Snell's law with the correct angles, we would get a refraction correction:
(9) 
 
where^{'} 

Note: this refraction is 7.5 times bigger than the refraction correction c = −11.0 m using the mainstream refraction model at standard refraction.
FECore used the difference between the (wrong) angle of incidence θ_{1} and the (hence also wrong) angle of refraction θ_{2} as the angle of deviation γ. In their model refraction takes place only once directly at the laser.
In reality the density gradient of the air acts on the whole way to the target and bends the light to a curve. Such a curve can be approximated by an arc of a certain radius for practical purposes. Over long distances the angle of deviation γ is considerably bigger than what FECore has calculated. In the mainstream refraction model this angle is called refraction angle ρ = −γ. A positive refraction angle means the target appears lifted. The greater the distance, the greater the refraction angle ρ.
In FECore's refraction model the angle of deviation γ does not depend on distance d and the refraction correction c increases linear with distance. In the accepted mainstream refraction model the refraction angle ρ grows linear with distance and the refraction correction c (the negative of the value called Lift absolute in the Advanced Earth Curvature Calculator) grows with the square of the distance d. This is the case for flat earth and globe earth.
Lets recap what we have so far:
Angle of Deviation  

published angle of deviation using FECore's refraction model with errors  γ = 0.00000001721° 
angle of deviation using FECore's refraction model correct  γ = −0.164° 
angle of deviation (refraction angle) using the mainstream refraction model, standard refraction, at 28.68 km  γ = −ρ = −0.022° 
Refraction Correction  

Published refraction correction using FECore's refraction model with errors  c = 0.000494 m 
Refraction correction using FECore's refraction model with using radian units but Snell's law error  c = 0.00000861 m 
Refraction correction using FECore's refraction model without errors  c = −82.1 m (not 0.000494 m) 
Refraction correction using the mainstream refraction model^{1)}, with standard refraction, at 28.68 km  c = −11.0 m 
1) Show refraction calculation in the Advanced Curvature Calculator
Using the wrong refraction angle, a not working refraction model (target would be 81.3 m below the surface) and calculation errors, FECore concluded, refraction can be neglegted. And therefor the WGS84 model is proven wrong.