What happens to air when it sinks?

Due to the fact that pressure and temperature are proportionate—that is, as pressure increases, so does temperature—the surrounding air pressure increases as an air parcel descends. This relationship is established by Gay-Lussac's law.

The relative humidity will decrease because there won't be any water added to a sinking parcel of air, meaning the dew point will stay constant. For instance, if the air temperature is 10 degrees and the dew point is 10 degrees, you will have 100% humidity and clouds will form. As the air sinks, the temperature may warm to 20 degrees, but since there won't be any water added, the dew point will remain at 10 degrees, the relative humidity will be roughly 75%, and no clouds will form.

When air sinks, it compresses and becomes warmer. This compression increases the air pressure and decreases its volume. As the air descends, it also becomes drier due to compression, which inhibits cloud formation and precipitation.