Dynamic height: Difference between revisions

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'''Dynamic height''' is a way of specifying the [[Vertical position|vertical position]] of a point above a [[Vertical datum|vertical datum]]; it is an alternative for [[Orthometric height|orthometric height]] or [[Normal height|normal height]]. It can be computed by dividing the location's geopotential number by the normal gravity at 45 degree latitude and zero height (a constant equal to 9.806199203 m/s<sup>2</sup>).<ref name=Jekeli/>
'''Dynamic height''' (symbol <math>H^\text{d}</math> or <math>H^\text{dyn}</math>) is a way of specifying the [[Vertical position|vertical position]] of a point above a [[Vertical datum|vertical datum]]; it is an alternative for [[Orthometric height|orthometric height]] or [[Normal height|normal height]]. It can be computed (in SI units of [[Metre|metre]]) by dividing the location's geopotential number (symbol ''C'', in square metre per square second) by the normal gravity (symbol {{math|''g''<sub>c</sub>}}, in metres per square second) at 45 degree latitude and zero height, a constant value (9.806199203 m/s<sup>2</sup>):<ref name=Jekeli/>
Dynamic height is constant if one remains at the same [[Physics:Geopotential|geopotential]] (equigeopotential) as one moves from place to place. Because of variations in Earth's gravity, surfaces having a constant difference in dynamic height may be closer or further apart in various places. Dynamic heights are usually chosen so that zero corresponds to the [[Geoid|geoid]].
:<math>H^\text{d}=C/g_c</math>
Dynamic heights are usually chosen so that zero corresponds to the [[Geoid|geoid]].


Dynamic height is the most appropriate height measure when working with the level of water (as in [[Earth:Hydrology|hydrology]] or [[Physics:Oceanography|oceanography]]) over a large geographic area;<ref name=Jekeli>{{cite journal | last=Jekeli | first=Christopher | title=Heights, the Geopotential, and Vertical Datums | website=KB Home | url=https://kb.osu.edu/handle/1811/78667 | date=November 2000 | hdl=1811/78667 | access-date=2022-09-21}}</ref> it is used by the Great Lakes Datum in the US and Canada.<ref>{{cite web|url= http://www.ngs.noaa.gov/web/about_ngs/history/Zilkoski4.pdf|title=Zilkoski, National Geodetic Survey}}</ref>  
As dynamic height is proportional to the [[Physics:Geopotential|geopotential]], it remains constant over a given equigeopotential surface.
Therefore, dynamic height is the most appropriate height measure when working with the level of water (as in [[Earth:Hydrology|hydrology]] or [[Physics:Oceanography|oceanography]]) over a large geographic area.<ref name=Jekeli>{{cite journal | last=Jekeli | first=Christopher | title=Heights, the Geopotential, and Vertical Datums | website=KB Home | url=https://kb.osu.edu/handle/1811/78667 | date=November 2000 | hdl=1811/78667 | access-date=2022-09-21}}</ref> For example, it is used by the [[Engineering:International Great Lakes Datum|International Great Lakes Datum]], across the US and Canada.<ref>{{cite web|url= http://www.ngs.noaa.gov/web/about_ngs/history/Zilkoski4.pdf|title=Zilkoski, National Geodetic Survey}}</ref><ref name="m481">{{cite web | title=IGLD - International Great Lakes Datum | website=NOAA Tides & Currents | url=https://tidesandcurrents.noaa.gov/datum-updates/igld/ | access-date=2024-08-09}}</ref>  


However, because of variations in Earth's gravity, two surfaces having a constant difference in dynamic height or in geopotential do not have a constant geometric distance; for example, they are closer and further apart at the poles and at the equator, respectively.<ref name="e578">{{cite web | last=Ghilani | first=Charles D. | title=Where Theory Meets Practice: The Geiod and Leveling | website=xyHt | date=2015-03-21 | url=https://www.xyht.com/professional-surveyor-archives/geoid-and-leveling/ | access-date=2024-08-09}}</ref>
When differential leveling is done, the path corresponds closely to following a value of dynamic height horizontally, but not to orthometric height for vertical changes measured on the leveling rod. Thus small corrections must be applied to field measurements to obtain either the dynamic height or the [[Orthometric height|orthometric height]] usually used in engineering. US  National Geodetic Survey data sheets<ref>{{cite web|url= http://www.ngs.noaa.gov|title= The National Geodetic Survey}}</ref> give both dynamic and orthometric values.
When differential leveling is done, the path corresponds closely to following a value of dynamic height horizontally, but not to orthometric height for vertical changes measured on the leveling rod. Thus small corrections must be applied to field measurements to obtain either the dynamic height or the [[Orthometric height|orthometric height]] usually used in engineering. US  National Geodetic Survey data sheets<ref>{{cite web|url= http://www.ngs.noaa.gov|title= The National Geodetic Survey}}</ref> give both dynamic and orthometric values.


Latest revision as of 00:55, 24 May 2026

Dynamic height (symbol Hd or Hdyn) is a way of specifying the vertical position of a point above a vertical datum; it is an alternative for orthometric height or normal height. It can be computed (in SI units of metre) by dividing the location's geopotential number (symbol C, in square metre per square second) by the normal gravity (symbol gc, in metres per square second) at 45 degree latitude and zero height, a constant value (9.806199203 m/s2):[1]

Hd=C/gc

Dynamic heights are usually chosen so that zero corresponds to the geoid.

As dynamic height is proportional to the geopotential, it remains constant over a given equigeopotential surface. Therefore, dynamic height is the most appropriate height measure when working with the level of water (as in hydrology or oceanography) over a large geographic area.[1] For example, it is used by the International Great Lakes Datum, across the US and Canada.[2][3]

However, because of variations in Earth's gravity, two surfaces having a constant difference in dynamic height or in geopotential do not have a constant geometric distance; for example, they are closer and further apart at the poles and at the equator, respectively.[4] When differential leveling is done, the path corresponds closely to following a value of dynamic height horizontally, but not to orthometric height for vertical changes measured on the leveling rod. Thus small corrections must be applied to field measurements to obtain either the dynamic height or the orthometric height usually used in engineering. US National Geodetic Survey data sheets[5] give both dynamic and orthometric values.

See also

  • Geopotential height, a similar quantity used in meteorology, based on a slightly different gravity value

References

  1. ↑ 1.0 1.1 Jekeli, Christopher (November 2000). Heights, the Geopotential, and Vertical Datums. https://kb.osu.edu/handle/1811/78667. Retrieved 2022-09-21. 
  2. ↑ "Zilkoski, National Geodetic Survey". http://www.ngs.noaa.gov/web/about_ngs/history/Zilkoski4.pdf. 
  3. ↑ "IGLD - International Great Lakes Datum". https://tidesandcurrents.noaa.gov/datum-updates/igld/. 
  4. ↑ Ghilani, Charles D. (2015-03-21). "Where Theory Meets Practice: The Geiod and Leveling". https://www.xyht.com/professional-surveyor-archives/geoid-and-leveling/. 
  5. ↑ "The National Geodetic Survey". http://www.ngs.noaa.gov. 




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