Orthometric height

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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. [1] [2] Orthometric height is one of the scientific formalizations of a layman's "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 h above the reference ellipsoid. It can be related to orthometric height H above the geoid by subtraction of the geoid height N:

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

Related Research Articles

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Geodesy or geodetics 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. Geodesy is an earth science as well as a discipline of applied mathematics, and many consider the study of Earth's shape and gravity to be central to the science.

<span class="mw-page-title-main">Geoid</span> Ocean shape without winds and tides

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 through the continents. According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.

<span class="mw-page-title-main">Physical geodesy</span> Study of the physical properties of the Earths gravity field

Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.

<span class="mw-page-title-main">World Geodetic System</span> Geodetic reference system

The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.

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

The National Geodetic Survey (NGS) is a United States federal agency based in Washington, D.C. that defines and manages a national coordinate system, providing the foundation for transportation and communication, mapping and charting, and a large number of science and engineering applications. Since its founding in 1970, it has been part of the National Oceanic and Atmospheric Administration (NOAA), a division within the United States Department of Commerce.

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<span class="mw-page-title-main">Geodetic datum</span> Reference frame for measuring location

A geodetic datum or geodetic system is a global datum reference or reference frame for precisely representing the position of locations on Earth or other planetary bodies by means of geodetic coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a location across the Earth's surface, in latitude and longitude or another coordinate system; a vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums.

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

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<span class="mw-page-title-main">Benchmark (surveying)</span> Point with known height used in surveying when levelling

The term benchmark, bench mark, or survey benchmark originates from the chiseled horizontal marks that surveyors made in stone structures, into which an angle iron could be placed to form a "bench" for a leveling rod, thus ensuring that a leveling rod could be accurately repositioned in the same place in the future. These marks were usually indicated with a chiseled arrow – specifically a broad arrow – below the horizontal line. A benchmark is a type of survey marker.

Normal heights 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, by the average, normal gravity computed along the plumb line of the point.

Mikhail Sergeyevich Molodenskii was a Russian physical geodesist. He was once said to be "probably the only geodesist who would have deserved a Nobel Prize".

<span class="mw-page-title-main">North American Datum</span> Reference frame for geodesy on the continent

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 United States Coast and 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> Geometric figure which approximates the Earths shape

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. The system is based on the datums NAD 83 and NAVD 88.

<span class="mw-page-title-main">Geodetic coordinates</span> Geographic coordinate system

Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal heighth. The triad is also known as Earth ellipsoidal coordinates.

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 by dividing the location's geopotential number by the normal gravity at 45 degree latitude and zero height, a constant value . Dynamic heights are usually chosen so that zero corresponds to the geoid.

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. 77 (5–6). Springer Science and Business Media LLC: 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".