Chapter 2. Position on the Earth

Chapter 2. Position on the EarthChapter 2. Position on the Earth

ContentsContents

The Importance of position Basic coordinate systems Reference systems Geodetic datums

Accurate referencing of geographic location is fundamental to all geo-information

Many different coordinate systems are used to record location

– global systems, latitude and longitude

– regional or local

– postal codes Combining data referred to different systems requires

that positions be carefully converted, transformed, or projected from one system to another

The Importance of position The Importance of position

Geographic position is related to the shape of the Earth

– Sphere => ellipsoid

– the Earth shape, geodetic datums Phenomena whose positions are recorded by street

address or postal code can also referenced using geographic coordinates

The process of matching street addresses and postal codes to geographic coordinate systems is called discrete georeferencing

represent points in two-dimensional or three-dimensional space

Cartesian systems polar systems

Basic Coordinate Systems Basic Coordinate Systems

Reference systems and map projections extend the ideas of coordinate systems over the Earth

are based on various models for the size and shape of the Earth (sphere; ellipsoidal + gravity models )

Ellipsoidal earth models are required for precise distance and direction measurement over long distances.

semi-major (equatorial radius) and semi-minor (polar radius) axes

Reference Systems Reference Systems

Global systemsGlobal systems

Latitude, Longitude, Height The Prime Meridian and the Equator are the

reference planes used to define latitude and longitude

Earth Centered, Earth Fixed (ECEF) Cartesian coordinates

with respect to the center of mass of the reference ellipsoid

Universal Transverse Mercator (UTM) coordinates

define two dimensional, horizontal, positions Each UTM zone is identified by a number - 6

degrees wide longitudinal strips extending from 80 South latitude to 84 North latitude

central meridian given a false easting of 500 km (so that only positive eastings are measured anywhere in the zone)

Northings increase northward from the equator for Southern Hemisphere locations, the Equator

is given a false northing of 10,000 km

Regional systemsRegional systems

different systems are used regionally to identify geographic location

Some of these are true coordinate systems, such as those based on UTM

Others, such as the metes and bounds and Public Land Survey systems describe below, simply partition space

Transverse Mercator Grid Systems – the British National Grid (BNG), administered

by the British Ordnance Survey (http://www.ordsvy.gov.uk/)

– the Ordnance Survey of Great Britain Datum 1936

– The true origin of the system is at 49? north latitude and 2 degrees west longitude

– Scale factor at the central meridian is 0.9996012717

Universal Polar Stereographic (UPS) – defined above 84° north latitude and south of

80° south latitude– eastings and northings are computed using a

polar aspect stereographic projection

Metes and Bounds – lengths and directions of a sequence of lines

forming the property boundary – Line lengths are measured along a horizontal

level plane – Directions are bearing angles measured with

respect to the previous line in the survey

Geodetic DatumsGeodetic Datums

Hundreds of geodetic datums are in use around the world

North American Datum of 1983 is used for United States marine, aviation, and topographic maps (based in the past on NAD 1927)

The Global Positioning system is based on the World Geodetic System 1984 (WGS-84)

Horizontal (NAD27), Vertical (NAVD88 ), complete (World Geodetic System 1984 )

account for irregularities in the earth's surface due to factors in addition to polar flattening

Topographic and sea-level models (the average surface of the oceans) attempt to model the physical variations of the surface

gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface

levelling

Gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface

Local variations in gravity: caused by variations in the earth's core and surface materials

Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone

In the United States, this work is the responsibility of the National Geodetic Survey (http://www.ngs.noaa.gov/)

The WGS-84 Geoid defines geoid heights for the entire earth

National Geodetic Survey Geoid-96

Datum conversionsDatum conversions

seven parameter transformations:– 3 for translation, 3 rotation, and 1 scale

Simple three parameter conversion between latitude, longitude, and height in different datums– conversion through Earth-Centered, Earth

Fixed XYZ Cartesian coordinates in one reference datum and three origin offsets that approximate differences in rotation, translation and scale.

ReferencesReferences

Bomford, G. 1980. Geodesy. Oxford: Clarendon Press.

Maling, D.H. 1992. Coordinate systems and map projections.  2nd ed. New York: Pergamon Press.

Schwarz, Charles R. 1989. North American Datum of 1983. Rockville, MD: National Geodetic Survey.

Torge, Wolfgang. 1991 Geodesy, 2nd Edition, New York: deGruyter

QuestionsQuestions

1. In what ways does the existence of hundreds of local and regional geodeitc datums limit the possibility of for international cooperation in GIS projects?

2. To what extent is the problem of georeferencing a major obstacle to the creation of global GIS?