How could air that is saturated with water become oversaturated without adding any water? ?

By cooling the air, which reduces its capacity to hold moisture as water vapor sometimes to the point that the water vapor it holds is sufficient for saturation. This atmospheric cooling can be brought about in a number of ways, as by the arrival of a cooler air mass or by the movement of an air mass up a mountain side. If the cooling continues beyond the point of saturation, and provided there are sufficient condensation nuclei in the air around which tiny cloud or fog droplets can form, the excess moisture will condense out of the air as cloud or fog droplets or various forms of precipitation at the Earth’s surface.

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