Normal height

Short description: Altitude above quasigeoid or mean sea level

Normal heights (symbol [math]\displaystyle{ H^* }[/math] or [math]\displaystyle{ H^N }[/math]; SI unit metre, m) is a type of height above sea level introduced by Mikhail Molodenskii. The normal height of a point is computed as the quotient of a point's geopotential number (i.e. its geopotential difference with that of sea level), by the average, normal gravity computed along the plumb line of the point. (More precisely, along the ellipsoidal normal, averaging over the height range from 0 — on the reference ellipsoid — to [math]\displaystyle{ H^* }[/math]; the procedure is thus recursive.)

Normal heights are thus dependent upon the reference ellipsoid chosen. The Soviet Union and many other Eastern European countries have chosen a height system based on normal heights, determined by precise geodetic levelling. Normal gravity values are easier to compute compared to actual gravity, as one does not have to know the Earth's crust density. This is an advantage of normal heights compared to orthometric heights.

The reference surface that normal heights are measured from is called the quasi-geoid (or quasigeoid), a representation of mean sea level similar to the geoid and close to it, but lacking the physical interpretation of an equipotential surface. The geoid undulation [math]\displaystyle{ N }[/math] with respect to the reference ellipsoid:

[math]\displaystyle{ N=h-H }[/math]

finds an analogue in the so-called height anomaly, [math]\displaystyle{ \zeta }[/math]:

[math]\displaystyle{ \zeta=h-H^* }[/math]

The maximum geoid–quasigeoid separation (GQS), [math]\displaystyle{ N-\zeta }[/math], is on the order of 5 meters in the Himalayas.

Alternatives to normal heights include orthometric heights (geoid-based) and dynamic heights.

See also

• Physical geodesy