This is a refraction simulation of some real observations as shown in the video 9.41 Mile Earth Curvature, Platforms Habitat / Hillhouse by bmlsb69. You can recall the Simulation of the Oil Platforms here.

Refraction Simulation

The image on the left shows extreme refraction due to a temperature inversion (layer of cold air between warm air), while the image on the right shows standard refraction. The magenta line shows where eye level of the observer is, the cyan line shows the location of the geometric horizon. See Simulation Barometric Parameters for what temperature gradients are responsible for this extreme refraction on the left image.

Real Images

This are two real images of the simulated scene above. As the simulation proves the image on the left was taken under exceptionally refraction conditions. This is confirmed by the fact that the platforms are very distorted, clearly visible at the cranes. What the simulation also shows is that the right image was taken at standard refraction conditions. No distortions are visible and the farther platform is partially below the horizon, exactly as predicted by the globe model and standard refraction.

Note: distortions in images are always an indicator for strong refraction. Clear, undistorted images can only be observed under standard refraction conditions. There is always at least standard refraction going on in the atmosphere. Standard refractions causes small looming. The earth appears flatter than it is (7/6 R). Objects appear about 1/6 of the drop due to curvature too high.

Simulation Barometric Parameters

On the left the blue curve was entered in the refraction simulator to produce the strong refraction image. The red curve shows the refraction coefficient depending on the altitude. This curve is directly calculated from the temperature profile (blue curve) using the accepted formulas to calculate the radius of curvature of light rays from atmospheric conditions as described at Deriving Equations for Atmospheric Refraction. The right image shows a vertically magnified view of the bending of the light rays under this conditions.

The temperture profile above corresponds to a layer of cool air between warmer air. This is called a temperature inversion. It can trap light rays and bounce them up and down over long distances. We can see this in the graph below and in the wave patterns in the right graph above. This is the cause of the different strechings and compressions and the waves in straight structures like the cranes. A positive temperature gradient above the ground (cool ground, warm air above) causes additional looming. This is the reason why no distinct horizon is visible. The water simply fades in the distance into the sky. The reason is that light rays get bent along the surface of the earth for hundreds of miles (see right graph). The earth appears flat or in this case even concave without a distinct horizon.

I don't now the temperture gradients from the real images. There are probably many possible similar gradients that can produce this images depending on the observer height. I had to apply trial and error to find a temperature profile that produced a similar image in the simulation.

Alternative Temperature Profile

Inspired by Mick West's video, I could get a similar image with another temperature profile, one that has a sudden jump to warmer air in a layer between 25 and 30 m. Contrary to the profile shown above it does not show the wavy cranes, because light gets not trapped in this layer and does not bounce up and down like in an inversion layer, which produces the waves in the cranes. So we can conclude that there was an inversion layer present when the black swan image was taken.

Flat Earth Simulation

The simulation of standard refraction on the flat earth model produces a similar scene as shown by the left images, but without any distortions. But for the flat earth model to produce the right images where part of the farther platform is hidden, there must be a temperature gradient of −15°C per 100 m throughout the whole atmosphere. This is physically impossible. Only in small surface layers can such a gradient exist when the ground is much hotter than the air above. But this produces strong convection currents, the air is very instable and the images would appear very blurry and unsteady. Measurements prove standard refraction above the ground layer, see Refraction Coefficient as a Function of Altitude.

This images can only be the result of refraction on the globe.