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Coordinate SystemsCoordinate Systems

1.1. Spheroids and spheres.Spheroids and spheres.2.2. Datums.Datums.3.3. Coordinate systemsCoordinate systems..

1.1. geographic coordinate system.geographic coordinate system.2.2. projected coordinate system.projected coordinate system.3.3. Universal Transfer Mercator System.Universal Transfer Mercator System.

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Definition of a spheroidDefinition of a spheroid

A sphere is based on a circle, while a A sphere is based on a circle, while a spheroid (or ellipsoid) is based on an spheroid (or ellipsoid) is based on an ellipse. ellipse.

SphereSphere SpheroidSpheroid

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Definition of a spheroidDefinition of a spheroid

The shape of an ellipse is defined by two radii. The The shape of an ellipse is defined by two radii. The longer radius is called the semi-major axis, and the longer radius is called the semi-major axis, and the shorter radius is called the semi-minor axis. shorter radius is called the semi-minor axis.

A spheroid is defined by either the semi-major axis, a, A spheroid is defined by either the semi-major axis, a, and the semi-minor axis, b, or by a and the flattening. and the semi-minor axis, b, or by a and the flattening. The flattening is the difference in length between the two The flattening is the difference in length between the two axes expressed as a fraction or a decimal. The axes expressed as a fraction or a decimal. The flattening, f, is: flattening, f, is:

f = (a - b) / a f = (a - b) / a

Major Min

or

Semi-minor, b

Semi-major, a

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DatumsDatums

While a spheroid approximates the shape of the While a spheroid approximates the shape of the earth, a datum defines the position of the earth, a datum defines the position of the spheroid relative to the center of the earth.spheroid relative to the center of the earth.

Earth’s surfaceEarth-centered (WGS84) datumLocal (NAD27) datum

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0º

20º

40º

60º

0º 20º 40º 60º 80º-20º-40º

(80ºE 55ºN)

80º Long.

55º Lat.

Equator(Latitude/ Parallel)

Prime Meridian(Longitude)

North

EastWest

South

Coordinate SystemCoordinate System

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Coordinate systemsCoordinate systemsThere are two types of coordinate systems: There are two types of coordinate systems:

geographic and projected.geographic and projected.ZZ

(80ºE 55ºN)

80º Long.

55º Lat.SpheroidSpheroid

YY XX

++ ==

80º Long.

55º Lat.

0º +20º +40º -20º -40º +180º -180º … …

0º

+20º

+40º

+90º

-90º

projected coordinate system

geographic coordinate system

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Geographic Coordinate SystemsGeographic Coordinate Systems

A GCS uses a three-dimensional spherical A GCS uses a three-dimensional spherical surface to define locations on the earth. A GCS surface to define locations on the earth. A GCS is often incorrectly called a datum, but a datum is often incorrectly called a datum, but a datum is only one part of a GCS. A GCS includes an is only one part of a GCS. A GCS includes an angular unit of measure, a prime meridian, and a angular unit of measure, a prime meridian, and a datum datum (based on a spheroid)(based on a spheroid)..

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Geographic Coordinate SystemsGeographic Coordinate Systems

DescriptionDescription The earth is modeled as a sphere or spheroid. The The earth is modeled as a sphere or spheroid. The

sphere is divided into equal parts usually called degrees; sphere is divided into equal parts usually called degrees; some countries use grads. A circle is 360° or 400 grads. some countries use grads. A circle is 360° or 400 grads. Each degree is subdivided into 60 minutes, with each Each degree is subdivided into 60 minutes, with each minute composed of 60 seconds. minute composed of 60 seconds.

The geographic coordinate system consists of latitude The geographic coordinate system consists of latitude and longitude lines. and longitude lines. Each line of longitude runs north-south and measures the Each line of longitude runs north-south and measures the

number of degrees east or west of the prime meridian. Values number of degrees east or west of the prime meridian. Values range from -180 to +180°.range from -180 to +180°.

Lines of latitude run east-west and measure the number of Lines of latitude run east-west and measure the number of degrees north or south of the equator. Values range from +90° degrees north or south of the equator. Values range from +90° at the North Pole to -90° at the South Pole.at the North Pole to -90° at the South Pole.

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Projected coordinate systemsProjected coordinate systems A projected coordinate system is defined on a flat, two-dimensional A projected coordinate system is defined on a flat, two-dimensional

surface.surface. It is always based on a geographic coordinate system that is based It is always based on a geographic coordinate system that is based

on a on a sphere sphere or or spheroidspheroid. . In a projected coordinate system, locations are identified by x, y In a projected coordinate system, locations are identified by x, y

coordinates on a grid, with the origin at the center of the grid. Each coordinates on a grid, with the origin at the center of the grid. Each position has two values that reference it to that central location. One position has two values that reference it to that central location. One specifies its horizontal position and the other its vertical position. specifies its horizontal position and the other its vertical position. The two values are called the x-coordinate and y-coordinate. Using The two values are called the x-coordinate and y-coordinate. Using this notation, the coordinates at the origin are x = 0 and y = 0.this notation, the coordinates at the origin are x = 0 and y = 0.

X<0Y>0

X>0Y>0

X<0Y<0

X>0Y<0

X

Y

(0,0)

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Map ProjectionMap Projection

Projection MethodProjection Method

Cylindrical Projection

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Universal Transfer MercatorUniversal Transfer MercatorFor the Universal Transfer Mercator SystemFor the Universal Transfer Mercator System,, the the globe is divided into globe is divided into 60 zones60 zones; each zone has its own central meridian.; each zone has its own central meridian. each each spanning spanning 6 degrees wide6 degrees wide of longitude of longitude (3 degrees west and 3 degrees east) (3 degrees west and 3 degrees east) X-and Y-coordinates are recorded in X-and Y-coordinates are recorded in metermeters.s. The limits of each zone are The limits of each zone are 84 degree N84 degree Northern, orthern, 80 degree S80 degree Southern.outhern. Regions beyond these limits are accommodated by the Regions beyond these limits are accommodated by the Universal Polar StereographicUniversal Polar Stereographic

projection.projection. The value given to the central meridian is the The value given to the central meridian is the false eastingfalse easting (500, 000m), (500, 000m), and the value assigned to the Equator is the and the value assigned to the Equator is the false northingfalse northing (0m for Northern, 10 000 (0m for Northern, 10 000

000m for Southern).000m for Southern). A scale factor is applied to cylindrical coordinates to average scale error over the A scale factor is applied to cylindrical coordinates to average scale error over the

central area of the map while reducing the error along the east and west boundaries. central area of the map while reducing the error along the east and west boundaries. The scale factor has the effect of recessing the cylinder into the earth so that it has The scale factor has the effect of recessing the cylinder into the earth so that it has two lines of intersection. Scale is true along these lines of intersection. You may see two lines of intersection. Scale is true along these lines of intersection. You may see the scale factor expressed as a ratio, such as 1:2500. In this case it is generally the scale factor expressed as a ratio, such as 1:2500. In this case it is generally called the scale reduction. The relationship between scale factor and scale reduction called the scale reduction. The relationship between scale factor and scale reduction is: is: Scale factor = 1-scale reductionScale factor = 1-scale reduction

In this case the scale factor would be 1-(1/2500) or In this case the scale factor would be 1-(1/2500) or 0.99960.9996

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UTM SpanUTM Span

The Universal Transverse The Universal Transverse Mercator (UTM) systemMercator (UTM) system have 60 north and south have 60 north and south zones, so each spanning zones, so each spanning or zoning 6° of longitude.or zoning 6° of longitude.

EquatorEastWest

North

South

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Coordinate SystemsCoordinate Systems

REFERENCESREFERENCES

1.1. Geographic Information System Geographic Information System and Science, www.gis.com, and Science, www.gis.com, www.wiley.co.uk/gis, www.wiley.co.uk/gis, www.wiley.com/giswww.wiley.com/gis

2.2. Melita Kennedy n Steve Kopp, Melita Kennedy n Steve Kopp, 2000 at USA; Understanding Map 2000 at USA; Understanding Map Projection,. www.esri.comProjection,. www.esri.com

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