Fog that occurs in polar and continental air is primarily due to saturation from above or large radiational cooling. Warm air has a higher capacity to contain and evaporate water vapor than cold air. Because of this, fog associated with maritime air tends to be thicker than fogs that form at very low temperatures. Light drizzle and precipitation saturating PBL from above Warm moist air overrunning a shallow airmass can saturate the shallow air from above and eventually to the surface. The contact cooling between the two air masses causes clouds and fog since the moisture in the warm air is beyond the carrying capacity of moisture relative to the cooler air.
Precipitation evaporating into the air can saturate the atmosphere.
Since moisture is a key component for fog, advection from a moisture source is much more favorable than advection from a dry source. Widespread fog is more common with warm fronts than cold fronts. Rising air lowers the dewpoint depression.