Normal heights is a type of height

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

introduced by

Mikhail Molodenskii Mikhail Sergeevich Molodenskii (russian: Михаил Серге́евич Молоденский, – November 12, 1991) was a Soviet physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel prize". ...

. The normal height

H^*

(or

H^N

) of a point is computed as the ratio of a point's

geopotential number Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the ''negative'' of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the nega ...

(i.e. its geopotential difference with that of sea level), by the average,

normal gravity In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing Earth. The most common model of a smoothed Earth is a rotating Earth ellipsoi ...

computed along the

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 reference line, or plumb-line. It is a precursor to the spirit level and used to establish a vertic ...

of the point. (More precisely, along the

ellipsoidal normal The ''n''-vector representation (also called geodetic normal or ellipsoid normal vector) is a three-parameter non-singular representation well-suited for replacing geodetic coordinates (latitude and longitude) for horizontal position representa ...

, averaging over the height range from 0 — on the reference ellipsoid — to

H^*

; 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 geodetic precise levelling. Normal gravity values are easy to compute and "hypothesis-free", i.e., one does not have to know, as one would for computing

orthometric height The orthometric height is the vertical distance ''H'' 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 scientific fo ...

s, the density of the Earth's crust around the plumb line. The reference surface that normal heights are measured from is called the quasi-geoid (or quasigeoid), a representation of

mean sea level There are several kinds of mean in mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. ...

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 extended ...

'' 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 ...

. The ''

geoid undulation 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 exten ...

N

with respect to the reference ellipsoid: :

N=h-H

finds an analogue in the so-called height anomaly,

\zeta

: :

\zeta=h-H^*

The maximum geoid–quasigeoid separation (GQS),

N-\zeta

, is on the order of 5 meters 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 planet's highest peaks, including the very highest, Mount Everest. Over 100 ...

. Alternatives include orthometric heights (geoid-based) and

dynamic height Dynamic height 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 dividing the location's geopotential number by the normal gravity at 4 ...

References

Vertical position Geodesy {{Geodesy-stub

See also

References