Potential density
Potential density is a dynamically important property: for static stability potential density must decrease upward. If it doesn't, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward; similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions (potential density decreasing upward) motion along surfaces of constant potential density (isopycnals) is energetically favored over flow across these surfaces (diapycnal flow), so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.
Köhler theory
where formula_2 is the droplet water vapor pressure, formula_3 is the corresponding saturation vapor pressure over a flat surface, formula_4 is the droplet surface tension, formula_5 is the density of pure water, formula_6 is the moles of solute, formula_7 is the molecular weight of water, and formula_8 is the cloud drop diameter.