Here is all the data on the office buildings in downtown Chicago. Willis tower is 1482' high. Aon tower is 1136' high, the second highest building. You should not be able to see any of this Aon Center tower.1136 - 1398 = -262. This means Aon tower should be 262' under water by RE reckoning. However you see it, and many other smaller buildings. This could not be possible on a round earth.
I did a quick Google search of photographs of Chicago from New Buffalo and these two were the only ones I found:
The problem with these is that they're impossible to tell how high off the water they are. It's certainly not at the water's edge, which makes calculating drop distances a bit more difficult. For my calculations, a camera at height
h will have the same view as a camera
x kilometers closer, with
x being the horizon of the camera at height
h.
First, let's calculate the base drop of a camera at water level of the upper picture (all references will be to that upper picture, by the way). That pier gives a good indication that the picture was taken near 41 48 03.30 N, 86 44 51.43 W. From there to the base of the Willis Tower is 74.29 kilometers. That gives us a drop of 434 meters[nb]The equation I'm using is h = R
earth - R
earth * cos[(d/C
earth)*360] with d being the distance form the camera to the object[/nb].
The road near the beach at which this photo was taken is 10 meters above the surface of the lake. Assuming the photograph was taken there, that gives it an effective view of a camera 11.3 kilometers closer to Chicago (that is, a camera floating on the lake 11.3 kilometers from New Buffalo would be able to see both Chicago and the camera at New Buffalo).
This new data gives us a drop of only 312 meters. Now, let's calculate for each of the other identifiable buildings in the picture.
Right of Willis Tower are a trio of buildings, two tall and the middle one short.
The left building is Aon Center (346 m, drop of 301 m for 45 m visible)
The right building is Trump Tower (357 m (roof), drop of 305 m for 52 m visible)
The far right is the John Hancock Center (344 m (roof), drop of 304 m for 40 m visible).
In general, the drop for the skyline of Chicago is around 306 meters, the closest buildings experiencing only 284 meters. There are seven buildings taller than 290 meters. While there are a few more visible in the picture, keep in mind the second photograph.
In that one, only the Aon Center is visible in the middle, with the Trump Tower, both physically and apparently taller, completely missing. This shows that refraction can account for at least 50 meters either way, which puts both pictures easily within the realm of RE possibility.