5. Coordinate System

Coordinate System

coordinate system

coordinate system

Global 3D coordinates are ok, but ... Have you ever seen them? Usually 3D location is split up into • 2D horizontal • 1D height

The shape of the earth

Geodetic Horizontal Datum How to fix a coordinate surface to the Earth? approximate the real shape of the earth by an ellipsoid: •fix the dimensions of the ellipsoid define its location with respect to the shape of the earth

Approximations of the Earth

Transformation of Scale Factor

local ellipsoid:

It defines the origin and orientation of latitude and longitude lines. A local datum aligns its spheroid to closely fit the Earth’s surface in a particular area and its 'origin point' is located on the surface of the Earth. The coordinates of the 'origin point' are fixed and all other points are calculated from this control point. The coordinate system origin of a local datum is not at the center of the Earth. NAD27 and the European Datum of 1950 are local datums.

global best-fitted ellipsoid:

In the last fifteen years, satellite data has provided geodesists with new measurements to define the best Earth-fitting ellipsoid, which relates coordinates to the Earth’s center of mass. An Earth-centered, or geocentric, datum does not have an initial point of origin like a local datum. The Earth’s center of mass is, in a sense, the origin. The most recently developed and widely used datum is the World Geodetic System of 1984 (WGS84). It serves as the framework for supporting locational measurement worldwide. GPS measurements are based upon the WGS84 datum.

Relation Between Earth’s irregular surface Ellipsoid and Geoid

Datum shifts

Accuracy ~10 m

Datum

Ellipsoid

dX

dY

dZ

Region of use

Adindian

Clarke 1880

-118

-14

218

Mean for Ethopia, Sudan

Arc 1950

Clarke 1880

-143

-90

-294

Mean for Botswana, Lesotho, Malawi, Swaziland, Zaire, Zambia, Zimbabwe

Djarkarta (Batavia)

Bessel 1841

-377

682

-50

Indonesia

European 1950

International 1924

-87

-98

-121

Mean for Western Europe

Indian

Everest (India 1830)

282

726

254

Bangladesh, India and Nepal

Minna

Clarke 1880

-81

-84

115

Cameroon

North American 1927 (NAD 27)

Clarke 1866

-8

160

176

Mean for USA

South 1969

South American 1969

-57

1

-41

Mean for Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Trinidad&Tobago, Venezuela

Datum

American

Concept of Map Projection and Coordinate System

Map Projections conical

cylindrical

azimuthal

map projections

normal

transversal

Coordinate System • Locating points relative to one another requires use of concepts of direction an distance. Basically there are two types of coordinate systems. – Geographical Coordinate system – Plane rectangular coordinates (Cartesian Coordinate system) For larger areas geographical coordinate system is used and for small areas rectangular coordinate system is used

Geographic coordinates

Geographic coordinates • • • •

•

North south distance called latitude East west distance called longitude The one dividing the earth in half, equidistant between the poles was named, the equator The series north of equator is called north-latitude and the series south of equator is called south latitude. Since the earth is an oblate (flattened at the top), the north-south line (meridian) has less curvature at poles and more curvature at equator. 1º difference in latitude near the equator is about 110.6 km and 1º difference in latitude near the poles about 111.7 km near the poles. Longitude is defined by infinite set of great circles called meridians arranged perpendicular to the parallels. Since all parallels are concentric circles, they all rotate at the same angular speed 360º per day or 15º per hour. In 1884 it was agreed in an international conference that a meridian passing through Royal Observatory Greenwich, near London will be accepted as reference meridian and 0º longitude.

geographic coordinates

•advantages of geographic coordinates: •one system for the entire earth •more or less conform to the shape of the earth, so no systematic distortions •easy to map in different map projections

•disadvantages of geographic coordinates: •spherical, not planimetric coordinates •must use spherical trigonometry to measure areas and distances •must project onto flat maps where the grid lines are curved

Plane rectangular coordinates (Cartesian Coordinate system) •

A point of origin at the intersection of two conveniently located perpendicular “axes”.

Y- axis

(0,0) X-axis Origin

The UTM system •

It is very common

•

The area of the earth between 84º N and 80º S latitude is divided into north-south columns 6º of longitude wide called zones. There are numbered 1 to 60 east ward, beginning at the 180 º meridian.

•

Each column is divided into quadrilaterals 8 º of latitude high.

•

The rows of quadrilaterals are assigned letters c to x consecutively (with 1 and 0 omitted) beginning at 80 º S latitude. Row x is beginning 12 º latitude extending from 72 º N to 84 º N. Each quadrilateral is assigned a number letter combination.

UTM Zone

Georeferencing Georeferencing refers to the location of a layer in space as defined by co-ordinate referencing system. The geo-relational approach involves abstracting geographic information into a series of independently layers or coverage’s each representing a selected set of closely associated geographic features (e.g. roads, landuse, river, etc.). Each layer is a theme of geographic feature and the database is organised in the thematic layers. That way users can combine simple feature sets representing complex relationship in the real world. This approach borrows heavily the concepts of relational DBMS, and is typically closely integrated with such systems.

Georeferencing real world

object

map

control point

rotation

2 translations, scale