Condensation of water vapor occurs by cooling, adding moisture, or mixing. Cooling and moisturizing are governed by the Eulerian heat and water budgets, respectively. Turbulent mixing of two nearly-saturated air parcels can yield a saturated mixture. We see the resulting droplet-filled air as clouds or fog.
If clouds are buoyant (i.e., the cloud and subcloud air is statically unstable), thermals of warm air actively rise to form cumuliform clouds. These have a lognormal distribution of sizes, and have fractal shapes. Active clouds are coupled to the underlying surface, allowing thermo diagrams to be used to estimate cloud base and top altitudes.
If the clouds are not buoyant (i.e., the cloud layer is statically stable), the clouds remain on the ground as fog, or they are forced into existence as stratiform clouds by advection along an isotropic surface over colder air, such as at a front.
Clouds can be classified by their altitude, shape, and appearance. Special symbols are used on weather maps to indicate cloud types and coverage.
While almost all clouds are created in rising air and the associated adiabatic cooling, fogs can form other ways. IR radiative cooling creates radiation fogs, while cooling associated with advection of humid air over a cold surface causes advection fogs. Precipitation and steam fog form by adding moisture to the air that touches a liquid water surface (e.g., raindrops, or a lake), followed by mixing with the surrounding cooler air to reach saturation.
Although fog forms in a layer of cold air resting on the ground, that cold-air can be either statically stable or unstable depending on whether continued cooling is being imposed at the bottom or top of the layer, respectively. Heat and moisture budget equations can be used to forecast fog onset, development, and dissipation, but only for some idealized situations.