What is the full definition of sunrise and sunset?

The point on the celestial sphere directly above an observer is called the zenith. The great circle on this sphere exactly 90 degrees in every direction from the zenith is called the (astronomical) horizon. If the observer is on a flat surface, like the ocean, and has his or her eye on the surface, sunrise or sunset occurs when the upper edge (called upper limb) of the Sun disk intersects with the horizon. Realty is a bit more complex. Light passing through the atmosphere is refracted and bent downward, giving the observer the impression that the object is higher in the sky than it really is. The nearer the object is to the horizon, the larger it appears. When the lower limb of the Sun appears to touch the horizon, the Sun has already gone below it because the refraction “lifts” the Sun by more than the diameter of the Sun disk. Of course, all this means nothing if you happen to live in the shadow of a mountain. Near where I live on the Ohio River is a small town by the name of Shadyside. A high hill on the western edge of town puts it in the shade of the hill hours before true, astronomical sunset.