On a completely flat Earth with no visual interference (such as trees, hills, or atmospheric haze) the ground itself would never obscure distant objects; one would be able to see all the way to the edge of the surface. A spherical surface has a horizon which is closer when viewed from a lower altitude.
In theory, a person standing on the surface with eyes 1.8 metres (5 ft 11 in) above the ground can see the ground up to about 4.79 kilometres (2.98 mi) away, but a person at the top of the Eiffel Tower at 273 metres (896 ft) can see the ground up to about 58.98 kilometres (36.65 mi) away.
This phenomenon would seem to present a method to verify that the Earth's surface is locally convex. If the degree of curvature was determined to be the same everywhere on the Earth's surface, and that surface was determined to be large enough, it would show that the Earth is spherical.
In practice, this turns out to be an unreliable method of measurement, due to variations in atmospheric refraction. This additional effect can give the impression that the earth's surface is flat, curved more convexly than it is, or even that it is concave, by bending light travelling near the surface of the earth (as happened in various trials of the famous Bedford Level experiment).
The phenomenon of variable atmospheric bending can be empirically confirmed by noting that sometimes the refractive layers of air can cause the image of a distant object to be broken into pieces or even turned upside down. This is commonly seen at sunset, when the sun's shape is distorted, but has also been photographed happening for ships, and has caused the city of Chicago to appear normally, upside down, and broken into pieces from across Lake Michigan (from where it is normally below the horizon).
Because of their longer wavelengths, radio waves are even more susceptible to atmospheric refraction and reflection, which can cause radio and television signals to be received from towers thousands of miles away which cannot be seen with visible light.
When the atmosphere is relatively well-mixed, the visual effects generally expected of a spherical Earth can be observed. For example, ships travelling on large bodies of water (such as the ocean) disappear over the horizon progressively, such that the highest part of the ship can still be seen even when lower parts cannot, proportional to distance from the observer. The same is true of the coastline or mountain when viewed from a ship or from across a large lake or flat terrain.