Geopotential height

Geopotential height is a vertical coordinate referenced to Earth's mean sea level — an adjustment to geometric height (elevation above mean sea level) using the variation of gravity with latitude and elevation. Thus it can be considered a "gravity-adjusted height". One usually speaks of the geopotential height of a certain pressure level, which would correspond to the geopotential height necessary to reach the given pressure.

At an elevation of h, the geopotential is defined as:

where ${\displaystyle g(\phi ,z)}$ is the acceleration due to gravity, ${\displaystyle \phi }$ is latitude, and z is the geometric elevation. Thus geopotential is the gravitational potential energy per unit mass at that elevation h.

The geopotential height is:

which normalizes the geopotential to g₀, the standard gravity at mean sea level.

Geophysical scientists often use geopotential height as a function of pressure rather than pressure as a function of geometric height, because doing so in many cases makes analytical calculations more convenient. For example, the primitive equations which weather forecast models solve are more easily expressed in terms of geopotential than geometric height. Using the former eliminates air density from the equations.

...
Wikipedia