Geopotential height
Geopotential height or geopotential altitude is a
Geopotential height differs from geometric height (as given by a
Definition
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.[1]
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.[4] Expressed in differential form,
Role in planetary fluids
Geopotential height plays an important role in atmospheric and oceanographic studies. The differential form above 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
Usage
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.[citation needed]
The National Weather Service defines geopotential height as:
"...roughly the height above sea level of a pressure level. For example, if a station reports that the 500 mb [i.e.
millibar] height at its location is 5600 m, it means that the level of the atmosphere over that station at which the atmospheric pressure is 500 mb is 5600 meters above sea level. This is an estimated height based on temperature and pressure data."[6]
See also
- Atmospheric model
- Above mean sea level
- Dynamic height, a similar quantity used in geodesy, based on a slightly different gravity value
References
- ^ a b Minzner, R. A.; Reber, C. A.; Jacchia, L. G.; Huang, F. T.; Cole, A. E.; Kantor, A. J.; Keneshea, T. J.; Zimmerman, S. P.; Forbes, J. M. (May 1976). "NASA Technical Report R-459: Defining Constants, Equations, and Abbreviated Tables of the 1976 Standard Atmosphere" (PDF). Archived from the original (PDF) on 2017-03-07.
- Bjerknes, V. (1910). Dynamic Meteorology and Hydrography: Part [1]-2, [and atlas of plates]. Carnegie Institution of Washington publication. Carnegie Institution of Washington. p. 13. Retrieved 2023-10-05.
- ^ Anderson, John (2007). Introduction to Flight. McGraw-Hill Science/Engineering/Math. p. 109.
- ^ Minzner, R. A.; Reber, C. A.; Jacchia, L. G.; Huang, F. T.; Cole, A. E.; Kantor, A. J.; Keneshea, T. J.; Zimmerman, S. P.; Forbes, J. M. (May 1976). "NASA Technical Report R-459: Defining Constants, Equations, and Abbreviated Tables of the 1976 Standard Atmosphere" (PDF). Archived from the original (PDF) on 2017-03-07.
- ^ Anderson, John (2007). Introduction to Flight. McGraw-Hill Science/Engineering/Math. p. 116.
- ^ "Height". NOAA's National Weather Service Glossary. NOAA National Weather Service. Retrieved 2012-03-15.
Further reading
- Hofmann-Wellenhof, B. and Moritz, H. "Physical Geodesy", 2005. ISBN 3-211-23584-1.
- Eskinazi, S. "Fluid Mechanics and Thermodynamics of our Environment", 1975. ISBN 0-12-242540-5.
External links
- Media related to Geopotential height at Wikimedia Commons