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Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level (assumed zero geopotential) that represents the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. [1] In SI units, a geopotential height ...
Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the negative of the potential energy per unit mass , so that the gravity vector is obtained as the gradient of the geopotential, without the negation.
GeographicLib provides a utility GeoidEval (with source code) to evaluate the geoid height for the EGM84, EGM96, and EGM2008 Earth gravity models. Here is an online version of GeoidEval . The Tracker Component Library from the United States Naval Research Laboratory is a free Matlab library with a number of gravitational synthesis routines.
Certain vertical coordinates are not based on length, for example, geopotential numbers have units of m 2 /s 2. Normalization by a constant nominal gravity value (units of m/s 2) yields units of metre, as in geopotential height (based on standard gravity) or dynamic height (based on normal gravity at 45 degrees latitude).
The increase in altitude necessary for P or ρ to drop to 1/e of its initial value is called the scale height: H = R T M g 0 {\displaystyle H={\frac {RT}{Mg_{0}}}} where R is the ideal gas constant, T is temperature, M is average molecular weight, and g 0 is the gravitational acceleration at the planet's surface.
The main assumption made by the thermotropic model is that while the magnitude of the thermal wind may change, its direction does not change with respect to height, and thus the baroclinicity in the atmosphere can be simulated using the 500 mb (15 inHg) and 1,000 mb (30 inHg) geopotential height surfaces and the average thermal wind between them.
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The zonal and tesseral terms for n = 1 are left out in . The coefficients for the n=1 with both m=0 and m=1 term correspond to an arbitrarily oriented dipole term in the multi-pole expansion. Gravity does not physically exhibit any dipole character and so the integral characterizing n = 1 must be zero.