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.
Pressure
Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height "h" and density "ρ" is given by the hydrostatic pressure equation , where "g" is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury or inches of mercury are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These "manometric units" are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.