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A 'curved-earth' reference model of the world is referred to as a geodetic

datum. The summary of the characteristics of a geodetic are:

* A geodetic datum is a simplified mathematical representation of the size

and shape of the earth.

** It usually takes the form of a spheroid, this being an ellipse rotated about

its minor (shorter) axis.

*** A geodetic datum is vital to all activities involving spatial data. The

spheroid provides a mathematically simple surface for performing surveying

and navigation computations over a wide area. It also provides a reference

surface on which to base mapping and Geographic Information Systems

(GIS).

****The surface of the spheroid is positioned such that it is a best-fit to the

Earth's sea level surface (ie to the geoid). An exact fit to sea level is not

possible due to anomalies in the Earth's gravity field. Gravity anomalies

(caused by variations in the density and distribution of the earth's mass)

cause irregularities in the sea level surface. This renders sea level

unsuitable as a horizontal reference surface for mapping activities.

*****Sea level is widely used as the reference surface for the measurement

of height. The contours on a map will usually show height above sea level.

However their position will be mapped on the spheroid.

A Local Geodetic Datum is a datum which best

approximates the size and shape of a particular part of the

earth's sea-level surface

A Geocentric Datum is one which best approximates the size and

shape of the Earth as a whole. The centre of its spheroid coincides

with the Earth's centre of mass

The Global Positioning System (GPS), which is operated by the United States

Department of Defence, utilises a geocentric datum to express its positions because of

its global extent. The Russian GLONASS satellite navigation system also uses a

geocentric datum. However it is a different datum to that used by GPS

Reference Ellipsoids

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

Datum Shifts

Datum Conversions

Seven Parameter Transformation Formulae

(Bursa-Wolf Model)

= + SC where

X1, Y1, Z1 = Cartesian Coordinates of Datum 1

X2, Y2, Z2 = Cartesian Coordinates of Datum 2

DX, DY, DZ = The difference between the centres of the two spheroids

RX, RY, RZ = The rotations around the three coordinate axes

SC

= The scale difference between the coordinate systems

Rotations are positive anticlockwise about the axes of Datum 2 coordinate system when viewing the origin from the

positive axes.

Three-Parameter Transformation Formulae X1 = X2 + DX Y1 = Y2 + DY Z1 = Z2 + DZ

where

X1, Y1, Z1 = Cartesian Coordinates of Datum 1

X2, Y2, Z2 = Cartesian Coordinates of Datum 2

DX, DY, DZ = The difference between the centres of the two spheroids

The Standard Molodensky formulas can be used to convert latitude, longitude, and ellipsoid height in one datum to

another datum if the Delta XYZ constants for that conversion are available and ECEF XYZ coordinates are not required.

Coordinate systems

Latitude, Longitude, and Height

The most commonly used

coordinate system today is the

latitude, longitude, and height

system.

The Prime Meridian and the

Equator are the reference planes

used to define latitude and

longitude.

The geodetic latitude (there are

many other defined latitudes) of a

point is the angle from the

equatorial plane to the vertical

direction of a line normal to the

reference ellipsoid.

The geodetic longitude of a point

is the angle between a reference

plane and a plane passing

through the point, both planes

being perpendicular to the

equatorial plane.

The geodetic height at a point is

the distance from the reference

ellipsoid to the point in a direction

normal to the ellipsoid

Geographic Coordinates

Many GIS systems store locations as numbers using latitude and longitude or

geographic coordinates. Latitude and longitude are almost always geocoded, or

captured from the map into computer, in one of two ways.

First format record geographic coordinates in degrees. Precision below degree is

geocoded as minutes and seconds, and decimals of seconds, in one of two

formats: either plus or minus DD.MMSS.XX, where DD are degrees, MM are

minutes, and SS.XX are decimal seconds; or alternatively, as DD.XXXX, or decimal

degrees

Universal Transverse Mercator (UTM)

Universal Transverse Mercator (UTM) coordinates

define two dimensional, horizontal, positions.

UTM zone numbers designate 6 degree longitudinal

strips extending from 80 degrees South latitude to 84

degrees North latitude.

UTM zone characters designate 8 degree zones

extending north and south from the equator.

There are special UTM zones between 0 degrees and

36 degrees longitude above 72 degrees latitude and a

special zone 32 between 56 degrees and 64 degrees

north latitude.

World Geographic Reference System (GEOREF

The World Geographic Reference System is used for aircraft navigation

These 15 degree areas are further divided into one degree units identified by 15 characters.