Geopotential height

Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level (assumed zero potential) that represents the work done by lifting one unit mass one unit distance through a region in which the acceleration of gravity is uniformly 9.80665 m/s2. Geopotential height (altitude) differs from geometric (tapeline) height but remains a historical convention in aeronautics as the altitude used for calibration of aircraft barometric altimeters. Geopotential is the gravitational potential energy per unit mass at elevation : where is the acceleration due to gravity, is latitude, and is the geometric elevation. Geopotential height may be obtained from normalizing geopotential by the acceleration of gravity: where = 9.80665 m/s2, the standard gravity at mean sea level. Expressed in differential form, may be substituted into the hydrostatic equation and ideal gas law in order to relate pressure to ambient temperature and geopotential height for measurement by barometric altimeters regardless of latitude or geometric elevation: where and are ambient pressure and temperature, respectively, as functions of geopotential height, and is the specific gas constant. For the subsequent definite integral, the simplification obtained by assuming a constant value of gravitational acceleration is the sole reason for defining the geopotential altitude. 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 that 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.