Definitions for "Geopotential"
The unit of geopotential difference, equal to the gravity potential of 1 meter squared per second squared, m² / s², or 1 joule per kilogram, J / kg.
Is equivalent to the potential energy of unit mass relative to a standard level (mean sea-level by convention) and is numerically equal to the work which would be done against gravity in raising the unit mass from mean sea-level to the level at which the mass is located. When calculating the thickness of a layer, earth's gravity force plays a role. There where gravity is largest (both poles), the layer is pulled down and becomes slightly smaller.
The projection of the geoid (the acceleration due to gravity) and the height above mean sea-level; it is usefully applied to isobars visualized in the vertical plane.