# Normal height

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{{Short description|Altitude above quasigeoid or mean sea level}}
'''Normal heights''' (symbol <math>H^*</math> or <math>H^N</math>; [SI unit](/source/SI_unit) [metre](/source/metre), m) is a type of height [above sea level](/source/above_sea_level) introduced by the Soviet scientist [Mikhail Molodenskii](/source/Mikhail_Molodenskii).
The normal height of a point is defined as the quotient of a point's [geopotential number](/source/geopotential_number) ''C'' (i.e. its geopotential difference with that of sea level), by the vertically averaged [normal gravity](/source/normal_gravity):
:<math>H^N=C/\bar\gamma</math>
The average is evaluated along the [normal potential](/source/normal_potential)'s [plumb line](/source/plumb_line) (a curve, approximated by the [ellipsoidal normal](/source/ellipsoidal_normal), a straight line). The evaluation ranges from the [Earth ellipsoid](/source/Earth_ellipsoid) up to the point of interest; the procedure is thus recursive.
Normal heights are slightly dependent upon the [reference ellipsoid](/source/reference_ellipsoid) chosen.

Normal gravity values are easier to compute compared to actual gravity, as one does not have to know the [Earth's crust density](/source/Continental_crust). This is an advantage of normal heights compared to [orthometric height](/source/orthometric_height)s.

The reference surface where normal heights are zero is called the '''quasi-geoid''' (or '''quasigeoid'''), a representation of [mean sea level](/source/mean_sea_level) similar to the ''[geoid](/source/geoid)'' and close to it, but lacking the physical interpretation of an [equigeopotential](/source/equigeopotential) surface. 
The ''[geoid undulation](/source/geoid_undulation)'' <math>N</math> with respect to the reference ellipsoid, <math>N=h-H</math>, finds an analogue in the so-called '''height anomaly''', <math>\zeta</math> (lowercase [zeta](/source/zeta)):
:<math>\zeta=h-H^N</math>
The '''geoid–quasigeoid separation''' (GQS), <math>N-\zeta</math>, is zero over the oceans and maximum in the [Himalayas](/source/Himalayas), where it attains approximately 5 meters.<ref>{{cite journal |last1=Sjöberg |first1=Lars E. |title=On the geoid and orthometric height vs. quasigeoid and normal height |journal=Journal of Geodetic Science |date=1 December 2018 |volume=8 |issue=1 |pages=115–120 |doi=10.1515/jogs-2018-0011 |bibcode=2018JGeoS...8..115S |doi-access=free}}</ref><ref name="Foroughi Tenzer pp. 1001–1020">{{cite journal | last1=Foroughi | first1=Ismael | last2=Tenzer | first2=Robert | title=Comparison of different methods for estimating the geoid-to-quasi-geoid separation | journal=Geophysical Journal International | publisher=Oxford University Press (OUP) | volume=210 | issue=2 | date=2017-05-19 | issn=0956-540X | doi=10.1093/gji/ggx221 | pages=1001–1020| doi-access=free }}</ref>

Russia and many other Eastern European countries have adopted a [height system](/source/height_system) based on normal heights. In practice, it is determined starting with [geodetic levelling](/source/geodetic_levelling) and applying correction terms.

Alternatives to normal heights include orthometric heights (geoid-based) and [dynamic height](/source/dynamic_height)s.

==See also==
*[Physical geodesy](/source/Physical_geodesy)

== References == 
{{reflist}}

{{DEFAULTSORT:Normal Height}}
Category:Vertical position
Category:Geodesy

{{Geodesy-stub}}

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Adapted from the Wikipedia article [Normal height](https://en.wikipedia.org/wiki/Normal_height) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Normal_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.