Geopotential height
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thus, it can be considered a "gravity-adjusted height". Definition. At an elevation of "h", the geopotential is defined as: where formula_2 is the acceleration due to gravity, formula_3 is latitude, and "z" is the geometric elevation. Thus geopotential is the gravitational potential energy per unit mass at that elevation "h".<ref name="https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19760017709.pdf"></ref> The geopotential height is: which  normalizes the geopotential to formula_5 = 9.80665 m/s, the standard gravity at mean sea level. Usage. Geophysical sciences such as meteorology often prefer to express the horizontal pressure gradient force as the gradient of geopotential along a constant-pressure surface, because then it has the properties of a conservative force. For example, the primitive equations which weather forecast models solve use hydrostatic pressure as a vertical coordinate, and express the slopes of those pressure surfaces in terms of geopotential height. A plot of geopotential height for a single pressure level in the atmosphere shows the troughs and ridges (highs  and lows) which are typically seen on upper air charts. The geopotential thickness between pressure levels – difference of the 850 hPa and 1000 hPa geopotential heights for example – is proportional to mean virtual temperature in that layer. Geopotential height contours can be used to calculate the geostrophic wind, which is faster where the contours are more closely spaced and tangential to the geopotential height contours. The National Weather Service defines geopotential height as: