Vertical position

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Vertical position or vertical location is a position along a vertical direction (the plumb line direction) above or below a given vertical datum (a reference level surface, such as mean sea level). 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.

Contents

Definitions

The International Organization for Standardization (ISO), more specifically ISO 19111, offers the following two definitions: [1]

ISO 6709 (2008 version) makes the following additional definition:

The International Civil Aviation Organization (ICAO) offers similar definitions: [2]

ICAO further defines:

I.e., elevation would be the altitude of the ground or a building.

Derived quantities

Several physical quantities may be defined based on the definitions above:

Units

Vertical distance quantities, such as orthometric height, may be expressed in various units: metres, feet, etc.

Certain vertical coordinates are not based on length, for example, geopotential numbers have units of m2/s2. Normalization by a constant nominal gravity value (units of m/s2) yields units of metre, as in geopotential height (based on standard gravity) or dynamic height (based on normal gravity at 45 degrees latitude). Despite the physical dimension and unit of length, the vertical coordinate does not represent distance in physical space, as would be measured with a ruler or tape measure. Sometimes a geopotential metre (symbol gpm or m') or dynamic metre is introduced for emphasis. [3] [4] However, this practice is not acceptable with the International System of Units (SI). [lower-alpha 1]

Another non-SI unit is the vertical metre, introduced when there may be confusion between vertical, horizontal, or slant distances. It is used for distance climbed during sports such as mountaineering, skiing, hiking, running or cycling [6] In German-speaking countries the abbreviation 'Hm' for Höhenmeter ("height metre") is used; if it is preceded by a '±' it refers to the cumulative elevation gain.

Measurement

Various instruments and techniques may be used for measuring vertical position:

Phenomena

Many physical phenomena are related to vertical position, as driven by gravity:

See also

Notes

  1. The Guide for the Use of the International System of Units, section 7.5 (Unacceptability of mixing information with units), states: [5]
    When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit.

Related Research Articles

<span class="mw-page-title-main">Geodesy</span> Science of measuring the shape, orientation, and gravity of the Earth and other astronomical bodies

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.

Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage.

<span class="mw-page-title-main">Sea level</span> Geographical reference point from which various heights are measured

Mean sea level is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum – a standardised geodetic datum – that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels. A common and relatively straightforward mean sea-level standard is instead a long-term average of tide gauge readings at a particular reference location.

Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level that represents the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. In SI units, a geopotential height difference of one meter implies the vertical transport of a parcel of one kilogram; adopting the standard gravity value, it corresponds to a constant work or potential energy difference of 9.80665 joules.

<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.

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 the geopotential, without the negation. In addition to the actual potential, a hypothetical normal potential and their difference, the disturbing potential, can also be defined.

<span class="mw-page-title-main">Height</span> Measure of vertical distance

Height is measure of vertical distance, either vertical extent or vertical position . For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m". For example, "Shaq O’Neal is 7 foot 1 inches in vertical height."

<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.

<span class="mw-page-title-main">Levelling</span> Surveying technique

Levelling or leveling is a branch of surveying, the object of which is to establish or verify or measure the height of specified points relative to a datum. It is widely used in geodesy and cartography to measure vertical position with respect to a vertical datum, and in construction to measure height differences of construction artifacts.

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

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface . The term elevation is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface.

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.

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 formalizations of a laypersons' "height above sea level", along with other types of heights in Geodesy.

<span class="mw-page-title-main">Gravity of Earth</span>

The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation and the centrifugal force . It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm .

<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">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 NAD 83 and NAVD 88.

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.

Height above mean sea level is a measure of a location's vertical distance in reference to a vertical datum based on a historic mean sea level. In geodesy, it is formalized as orthometric height. The zero level varies in different countries due to different reference points and historic measurement periods. Climate change and other forces can cause sea levels and elevations to vary over time.

References

  1. 1 2 3 4 "ISO 6709:2008(en) preview". www.iso.org. ISO. Retrieved 8 June 2016.
  2. 1 2 3 4 United Nations - International Civil Aviation Organization. "Annex 4: Aeronautical Charts - Chapter 1 (Definitions, Applicability and Availability)" (PDF). Archived from the original (PDF) on 2016-09-17. Note: Annex 4 is one of the (currently) 19 annexes to the Chicago Convention on International Civil Aviation (ICAO Doc. 7300).
  3. World Meteorological Organization - Guide to Meteorological Instruments and Methods of Observation - Preliminary seventh edition - WMO-No. 8 - Secretariat of the World Meteorological Organization – Geneva – Switzerland - 2006
  4. Bjerknes, V. (1910). Dynamic Meteorology and Hydrography: Part [1]-2, [and atlas of plates]. Carnegie Institution of Washington publication. Carnegie Institution of Washington. p. 13. Retrieved 2023-10-05.
  5. Thompson, Ambler; Taylor, Barry N. (2018-11-10). "Guide for the Use of the International System of Units (SI)". NIST. Retrieved 2020-12-09.
  6. Nash, Mike, Exploring Prince George: A Guide to North Central B. C. Outdoors, Vancouver: Rocky Mountain Books, 2004, p. 105.

Further reading