# Dynamic height

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'''Dynamic height''' (symbol <math>H^\text{d}</math> or <math>H^\text{dyn}</math>) is a way of specifying the [vertical position](/source/vertical_position) of a point above a [vertical datum](/source/vertical_datum); it is an alternative for [orthometric height](/source/orthometric_height) or [normal height](/source/normal_height). It can be computed (in [SI units](/source/SI_units) of [metre](/source/metre)) by dividing the location's [geopotential number](/source/geopotential_number) (symbol ''C'', in [square metre per square second](/source/square_metre_per_square_second)) by the [normal gravity](/source/normal_gravity) (symbol {{math|''g''<sub>c</sub>}}, in [metres per square second](/source/metres_per_square_second)) at 45 degree latitude and zero height, a constant value (9.806199203 m/s<sup>2</sup>):<ref name=Jekeli/>
:<math>H^\text{d}=C/g_c</math>
Dynamic heights are usually chosen so that zero corresponds to the [geoid](/source/geoid).

As dynamic height is proportional to the [geopotential](/source/geopotential), it remains constant over a given [equigeopotential](/source/equigeopotential) surface.
Therefore, dynamic height is the most appropriate height measure when working with the [level of water](/source/level_of_water) (as in [hydrology](/source/hydrology) or [oceanography](/source/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 [International Great Lakes Datum](/source/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](/source/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](/source/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](/source/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.

==See also==
*[Geopotential height](/source/Geopotential_height), a similar quantity used in meteorology, based on a slightly different gravity value

==References==
{{Reflist}}

Category:Geodesy
Category:Vertical position

{{geodesy-stub}}

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Adapted from the Wikipedia article [Dynamic height](https://en.wikipedia.org/wiki/Dynamic_height) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Dynamic_height?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.