Normal heights (symbol

H^*

H^N

;

SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

, m) is a type of height

above sea level Height above mean sea level is a measure of a location's vertical distance (height, elevation or altitude) in reference to a vertical datum based on a historic mean sea level. In geodesy, it is formalized as orthometric height. The zero level ...

introduced by the Soviet scientist Mikhail Molodenskii. The normal height of a point is defined as the quotient of a point's

geopotential number Geopotential (symbol ''W'') is the potential of the Earth's gravity field. It has SI units of square metre per square seconds (m2/s2). For convenience it is often defined as the of the potential energy per unit mass, so that the gravity vector i ...

''C'' (i.e. its geopotential difference with that of sea level), by the vertically averaged normal gravity: :

H^N=C/\bar\gamma

The average is evaluated along the normal potential's

plumb line A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical direction as a reference line, or plumb-line. It is a precursor to the spirit level and used to est ...

(a curve, approximated by the ellipsoidal normal, a straight line). The evaluation ranges from the

Earth ellipsoid An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximation ...

up to the point of interest; the procedure is thus recursive. Normal heights are slightly dependent upon the

reference ellipsoid An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximation ...

chosen. 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 height The orthometric height (symbol ''H'') is the vertical distance along the plumb line from a point of interest to a reference surface known as the ''geoid'', the vertical datum that approximates mean sea level. Orthometric height is one of the sci ...

s. The reference surface where normal heights are zero is called the quasi-geoid (or quasigeoid), a representation of

mean sea level A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...

similar to the ''

geoid The geoid ( ) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exte ...

'' and close to it, but lacking the physical interpretation of an

equipotential surface In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can als ...

. The '' geoid undulation''

N

with respect to the reference ellipsoid,

N=h-H

, finds an analogue in the so-called height anomaly,

\zeta

: :

\zeta=h-H^N

The geoid–quasigeoid separation (GQS),

N-\zeta

, is zero over the oceans and maximum in the

Himalayas The Himalayas, or Himalaya ( ), is a mountain range in Asia, separating the plains of the Indian subcontinent from the Tibetan Plateau. The range has some of the Earth's highest peaks, including the highest, Mount Everest. More than list of h ...

, where it attains approximately 5 meters. Russia and many other Eastern European countries have adopted a height system based on normal heights. In practice, it is determined starting with geodetic levelling and applying correction terms. Alternatives to normal heights include orthometric heights (geoid-based) and

dynamic height Dynamic height (symbol H^\text or H^\text) 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 loca ...

References

Vertical position Geodesy {{Geodesy-stub

See also

References