Orthometric height

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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. [1] [2] Orthometric height is one of the scientific formalizations of a laypersons' "height above sea level", along with other types of heights in Geodesy.

In the US, the current NAVD88 datum is tied to a defined elevation at one point rather than to any location's exact mean sea level. Orthometric heights are usually used in the US for engineering work, although dynamic height may be chosen for large-scale hydrological purposes. Heights for measured points are shown on National Geodetic Survey data sheets, [3] data that was gathered over many decades by precise spirit leveling over thousands of miles.

Alternatives to orthometric height include dynamic height and normal height, and various countries may choose to operate with those definitions instead of orthometric. They may also adopt slightly different but similar definitions for their reference surface.

Since gravity is not constant over large areas the orthometric height of a level surface (equipotential) other than the reference surface is not constant, and orthometric heights need to be corrected for that effect. For example, gravity is 0.1% stronger in the northern United States than in the southern, so a level surface that has an orthometric height of 1000 meters in one place will be 1001 meters high in other places. In fact, dynamic height is the most appropriate height measure when working with the level of water over a large geographic area. [4]

Orthometric heights may be obtained from differential leveling height differences by correcting for gravity variations. [5] Practical applications must use a model rather than measurements to calculate the change in gravitational potential versus depth in the earth, since the geoid is below most of the land surface (e.g., the Helmert orthometric heights of NAVD88). [6]

GPS measurements give earth-centered coordinates, usually displayed as ellipsoidal height above the reference ellipsoid. It can be related to orthometric height above the geoid by subtraction of the geoid height. The geoid determination requires accurate gravity data for that location; in the US, the NGS has undertaken the GRAV-D ten-year program to obtain such data with a goal of releasing a new geoid model as part of the Datum of 2022. [7]

See also

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Geodesy is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.

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<span class="mw-page-title-main">U.S. National Geodetic Survey</span> U.S. federal surveying and mapping agency

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<span class="mw-page-title-main">Elevation</span> Height of a geographic location above a fixed reference point

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Normal heights is a type of height above sea level introduced by Mikhail Molodenskii. The normal height of a point is computed as the ratio of a point's geopotential number, by the average, normal gravity computed along the plumb line of the point.

Mikhail Sergeevich Molodenskii was a Soviet physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel prize".

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The North American Datum (NAD) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, cartography, and land-use planning, two North American Datums are in use for making lateral or "horizontal" measurements: the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). Both are geodetic reference systems based on slightly different assumptions and measurements.

<span class="mw-page-title-main">National Geodetic Vertical Datum of 1929</span> Vertical datum in the United States

The National Geodetic Vertical Datum of 1929 is the official name since 1973 of the vertical datum established for vertical control surveying in the United States of America by the General Adjustment of 1929. Originally known as Sea Level Datum of 1929, NGVD 29 was determined and published by the National Geodetic Survey and used to measure the elevation of a point above and depression below mean sea level (MSL).

<span class="mw-page-title-main">North American Vertical Datum of 1988</span> Vertical datum for orthometric heights

The North American Vertical Datum of 1988 is the vertical datum for orthometric heights established for vertical control surveying in the United States of America based upon the General Adjustment of the North American Datum of 1988.

<span class="mw-page-title-main">Earth ellipsoid</span> Shape of planet Earth

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 approximations.

<span class="mw-page-title-main">Vertical datum</span> Reference surface for vertical positions

In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum, is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.

<span class="mw-page-title-main">National Spatial Reference System</span> NAD 83 & NAVD 88 based National Geodetic Coordinate System

The National Spatial Reference System (NSRS), managed by the National Geodetic Survey (NGS), is a coordinate system that includes latitude, longitude, elevation, and other values. The NSRS consists of a National Shoreline, the NOAA CORS Network, a network of permanently marked points, and a set of models that describe dynamic geophysical processes affecting spatial measurements. Pre-2022, the system is based on NAD 83 and NAVD 88.

<i>Normalhöhennull</i> Vertical datum used in Germany

Normalhöhennull or NHN is a vertical datum used in Germany.

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 45 degree latitude.

Vertical position or vertical location is a position along a vertical direction above or below a given vertical datum . Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc. Points lying on an equigeopotential surface are said to be on the same vertical level, as in a water level.

References

  1. ↑ Paul R. Wolf and Charles D. Ghilani, Elementary Surveying, 11th ed. p. 581
  2. ↑ Hofmann-Wellenhof and Moritz, Physical Geodesy p.47, p. 161
  3. ↑ US Department of Commerce, NOAA; US Department of Commerce, NOAA. "National Geodetic Survey - Home". www.ngs.noaa.gov. Retrieved 2020-09-07.
  4. ↑ Jekeli, Christopher (November 2000). "Heights, the Geopotential, and Vertical Datums". KB Home. hdl:1811/78667 . Retrieved 2022-09-21.
  5. ↑ Hwang, C.; Hsiao, Y.-S. (2003-08-01). "Orthometric corrections from leveling, gravity, density and elevation data: a case study in Taiwan". Journal of Geodesy. Springer Science and Business Media LLC. 77 (5–6): 279–291. Bibcode:2003JGeod..77..279H. doi:10.1007/s00190-003-0325-6. ISSN   0949-7714. S2CID   54939075.
  6. ↑ Hofmann-Wellenhof and Moritz, Physical Geodesy p. 163
  7. ↑ "GRAV-D Project Homepage- National Geodetic Survey".


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