Type of altitude above mean sea level
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 difference of one
meter
implies the vertical transport of a parcel of one
kilogram
; adopting the
standard gravity
value (9.80665
m/s
2
), it corresponds to a constant work or
potential energy
difference of 9.80665
joules
.
Geopotential height differs from geometric height (as given by a
tape measure
) because
Earth's gravity
is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different
vertical distance
in
physical space
: "the unit-mass must be lifted higher at the equator than at the pole, if the same amount of work is to be performed".
[2]
It is a useful concept in
meteorology
,
climatology
, and
oceanography
; it also remains a historical convention in aeronautics as the altitude used for calibration of aircraft
barometric altimeters
.
[3]
Definition
[
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]
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/s
2
, the
standard gravity
at mean sea level.
[4]
Expressed in differential form,
Role in planetary fluids
[
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]
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
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.
[5]
Usage
[
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]
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. 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
[
edit
]
References
[
edit
]
- ^
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
[
edit
]
- 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
[
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]