When exactly is the moment of sunrise?

Sunrise is the moment when the upper edge of the rising sun appears to be right at the horizon assuming an unobstructed view. That includes the effect of refraction of the sunlight by the atmosphere, which averages about 34 arcminutes. Atmospheric conditions in the sunlight's path to the observer can cause sunrise times to vary by over a minute due to the amount of refraction. At higher latitudes the variation can be many minutes due to the smaller angle between the horizon and the sun's apparent path. For the purpose of calculations, scientists define sunrise to be when the center of the sun is 90.83333° below the observer's zenith. The extra 0.83333°, or 50 arcminutes, accounts for the 34-arcminute average refraction and the 16-arcminute apparent radius of the sun.