What is the role of cooling air in producing precipitation from clouds?

Clouds are condensed droplets or ice crystals from atmospheric water vapor. Clouds form by the rising and cooling of air caused by convection, topography, convergence, and frontal lifting. Convection occurs when the Sun's radiation heats the ground surface, and warm air rises, cooling as it goes. Air also is cooled if an air mass is forced to move upward as a result of higher topography (e. g., a mountain range) in a process known as orographic lifting. Interestingly, when the air mass descends on the other side of the mountain, it warms and the clouds may disappear as the droplets transfer back to vapor. *

The counterclockwise motion of a low-pressure center draws air inward, and the convergence forces the air upward. Air also is lifted and cooled along either a cold front or a warm front. A cold front is the leading edge of an air mass that is colder than the air it is replacing. The front forms a wedge that pushes under the warmer air ahead, lifting it. A warm front is the leading edge of an air mass warmer than the air it is replacing. As the air mass pushes forward, the warm air slides up over the wedge of cold air ahead of it, as shown in the following figure.