Coordinate Systems, Map Projections, and GIS Applications

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Coordinate Systems and Map Projections

There are two types of coordinate systems

-Geographic Coordinate Systems

-Projected Coordinate Systems

Because the shape of the earth is approximately spherical, locations on

the earth's surface are often described in 

an angular coordinate or

geographi­cal system

, with latitude and longitude specified in degrees

(°) , minutes (') , and seconds (") .

Unfortunately, the calculation of distances and areas in an angular

coordinate system is complex. More significantly, it is impossible to

accurately represent the three dimensional surface of the earth on the

two-dimensional planar surface of a map or image without introducing

distortion in one or more of the following elements: shape, size, distance,

and direction. Thus, for many purposes the geo­graphical coordinates are

transformed to a planar, or Cartesian 

(X-Y) 

( 

Projected coordinate

system

 ) . The result of this transformation process is referred to as a

map projection

.

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Types of Map projections

Map projections include

cylindrical

 , 

conic

 , and 

azimuthal or planar 

surfaces.

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Figure 1

Properties of map pro­jection

A 

conformed 

map pro­jection

 preserves angular relationships, or shapes, within

local areas; over large areas, angles and shapes become distorted.

An 

azimuthal 

(or 

zenithal) 

projection

 preserves absolute directions relative to

the central point of projec­tion.

An 

equidistant 

projection

 preserves equal distances, for some but not all points.

scale is constant either for all distances along meridians or for all dis­tances from

one or two points.

An 

equal-area 

(or equivalent) projection

 pre­serves equal areas.

Important Map projections

Universal Transverse Mercator ( UTM )

UTM

 is an international plane (rectangular) coordinate system developed by the

US Army that extends around the world from 84°N to 80°S. The world is divided

into 60 zones each covering six degrees longitude. Each zone extends three

degrees eastward and three degrees westward from its central meridian. Zones are

numbered consecutively west to east from the 180° meridian. Figure 2 shows UTM

Grid Zones of the World.

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Dadum

A 

datum

 is a mathematical definition of the three-dimensional solid (generally a

slightly flattened ellipsoid) used to represent the surface of the earth.

The actual planet itself has an irregular shape that does not correspond

perfectly to any ellipsoid. As a result, a variety of different datums have been

described, some designed to fit the surface well in one particular region and

others designed to best ap­proximate the planet as a whole.

Most of the world has adopted the 

World Geodetic System of 1984

( WGS 1984 )

The 

geoid

 is defined as the surface of the earth's gravity field , which is

approximately the same as mean sea level. It is perpendicular to the direction of

gravity pull. Since the mass of the earth is not uniform at all points, and the

direction of gravity changes, the shape of the geoid is irregular.

To simplify the model, various spheroids or ellipsoids have been devised. A

spheroid or ellipsoids

 is a three-dimensional shape created from a two-

dimensional ellipse. The ellipse is an oval , with a major axis (the longer axis) and

a minor axis (the shorter axis). If you rotate the ellipse, the shape of the rotated

figure is the spheroid.

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Example

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Figure 2  UTM Grid Zones of the World

Geographic and Map Coordinate Systems in Iraq

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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a  = Semi major axis

b = Semi minor axis

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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X = (  N +  ) cos φ cos λ

Y = (  N + H ) cos φ sin λ

Z = [ N ( 1 – e

2

 ) + h ] sin φ

Where

φ , λ , h = geodetic latitude , geodetic longitude  , and height above

ellipsoid .

X , Y , Z = Geocentric Coordinates of any point

N = radius in the prime vertical of the ellipsoid at a point

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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1

Given the following major axis and minor axis of the WGS84 datum, Major axis=

12,756,274 m , Minor axis= 12,713,504.628 m . Find the flattening, inverse

flattening, first eccentricity, and second eccentricity.

Solution

,

e

=

0

.

0

8

1

8

1

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     ,      

eʹ = 0.082094438

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

Example 2

Compute the Cartesian coordinates (X, Y, Z) of point A whose geodetic latitude equals 22° ,

geodetic longitude equals 30° , and geodetic height equals 10 m. Use the WGS84 ellipsoid

whose parameters are: Semi-major axis 6378137 m , and  Semi-minor axis 6356752 m.

Solution

X = (  N + H ) cos φ cos λ = 5123834.673 m

Y = (  N + H ) cos φ sin λ =2958247.328 m

Z = [ N ( 1 – e ) + h ] sin φ = 2374416.423 m

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Remote Sensing and GIS Application                                                    Lecturer

Remote Sensing and GIS Application                                                    Lecturer

                   Third Year                                                                   Ruba Yousif Hussain

                   Third Year                                                                   Ruba Yousif Hussain

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1.

Search for an address or the place you want to locate Google Maps. This will

open a Google map.

2. Drop a pin. Click on the exact location you'd like coordinates for.

3. Right-click on the pin and select "What's here?".

4. Get your location's latitude and longitude.

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The geodetic latitude , longitude , and height of a point  A  are  41° 15ʹ 18.2106ʺ N  ,

 75° 00ʹ 58.6127ʺ W ,  and  312.391m  , respectively . Using WGS84 values , what

are the geocentric coordinates of the point ?

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the earth or other round body on a 2-dimensional plane in cartography  (mapmaking).

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