GEOGRAPHIC COORDINATE SYSTEM & MAP PROJECTION

By- Vishal KediaM.Tech(Remote Sensing & GIS)Maulana Azad National Institute Of TechnologyBHOPAL

OUR EARTH…(SOME FACTS)

Earth is almost a Geoid (ie. Geophysically an equipotential surface) which is a irregular spheroid like structure.Surface of Geoid matches very much with the MSL.Mathematically earth is represented as spheroid.Spheroid is the three dimensional structure formed by the rotation of an ellipse about the minor axis.For the purpose of obtaining R.L. of any point on earth surface Geoid approximation of earth is assumed.For the purpose of obtaining geographic coordinate of earth pure spheroid or ellipsoid is assumed.

Vertical deflection

Geoid undulation

Geoid Undulation: separation between geoid & spheroid at any point on the surface of the earth.

WHAT IS DATUM?

It is the mathematical model of the earth which serves as a reference for calculating the geographic coordinates and R.L. of any point on to the surface of the earth.(chang)

Datum is a model that describes the position direction and the scale relationship of a reference surface for a given point on to the surface of the earth.(yeung)

A datum can basically be classified as: Geodetic datum or Vertical datum; which can further be classified as global or local datum.

GEODETIC DATUM:Geodetic datum are defined by several elements that include the position of origin (in terms of Lat. & Long. Or some other system) , the orientation of the geodetic network ( ie. Azimuth to other point) , the parameters (ie. Major – minor axes & flattening) of the reference ellipsoid selected for computation and the geoid undulation at the origin.

Global geodetic datum are those that have been developed for the purpose of geo referencing based on a single point on to the surface of the earth.

Local geodetic datum are based on ellipsoid that best fits earth surface in a particular area of interest which is some times also known as area of validity.

VERTICAL DATUM:

A vertical datum is the zero surface from which all elevations or height are measured . Generally mean sea level is used as vertical datum because sea surface is available world wide.

Global sea level observing system (GSLOS) is an international organization which includes more than 300 sea level observation station maintained by 80 countries & makes the definition of Global vertical datum a reality.

Local vertical datum are defined to serve the georeferencing needs of a country or group of adjacent countries.

DIFFERENT ELLIPSOID MODELS

EXAMPLE DATUM:

NAD 27(North American Datum 1927) refers ‘clarke 1866’ with origin at Meades ranch Kansas , longitude origin at greenwich meridian and the azimuth orientation is from south(best fitting north america).

NAD 83 (North American Datum 1983) refers ‘GRS 80’ with origin at center of mass of the earth, longitude origin at greenwich meridian and the azimuth origin is from north (world wide).

WGS 84 (world geodetic system 1984) refers ‘GRS 80’ in terms of primary parameters and local datum for the secondary parameters.

WGS 84 – PARAMETERS:

The coordinate origin of WGS 84 is meant to be located at the Earth's center of mass; the error is believed to be less than 2 cm.

In WGS 84, the meridian of zero longitude is the IERS Reference Meridian. It lies 5.31 arc seconds east of the Greenwich Prime Meridian, which corresponds to 102.5 metres (336.3 feet) at the latitude of the Royal Observatory.

As of the latest revision, the WGS 84 datum surface is a pole-flattened (oblate) spheroid, with major (transverse) radius a = 6,378,137 m at the equator, and minor (conjugate) radius b = 6,356,752.314 245 m at the poles (a flattening of 21.384 685 755 km, or 1/298.257 223 563 ≈ 0.335% in relative terms). The b parameter is often rounded to 6,356,752.3 m in practical applications.

WGS 84 – PARAMETERS(CONT.)

Presently WGS 84 uses the 1996 Earth Gravitational Model (EGM96) geoid, revised in 2004. This geoid defines the nominal sea level surface by means of a spherical harmonics series of degree 360 (which provides about 100 km horizontal resolution). The deviations of the EGM96 geoid from the WGS 84 reference ellipsoid range from about -105 m to about +85 m. EGM96 differs from the original WGS 84 geoid, referred to as EGM84.

Many of the original authors of WGS 84 contributed to a new higher fidelity model, called EGM2008. This new model will have a geoid with a resolution approaching 10 km, requiring over 4.6 million terms in the spherical expansion (versus 130,317 in EGM96 and 32,757 in WGS 84).

GEOGRAPHIC COORDINATE SYSTEM

It’s a coordinate system that fixes the location of any point on to the surface of the earth with reference to a given geodetic datum.

In this system any position is determined by two angles (lattitude & longitude) measured on two orthogonal planes (equator and prime meridian) that intersect at the origin.

LATTITUDE & LONGITUDE

The geodetic latitude of a point is the angle between the equatorial plane & the normal line at the point on the surface of the Earth that intersects it on to the plane of meridian.

Geodetic longitude is the angle in the equatorial plane between the line that connects the Earth's centre with the prime meridian and the line that connects the centre with the meridian on which the point lies.

Meridians are the line of equal longitudes(great circles passing through the poles) parallels are the lines of equal lattitude.

LATTITUDE & LONGITUDE(CONT.)

Using prime meridian (at Greenwich – 0 long.) as reference we can measure up to 180 degrees east or west(horizontally). East is taken as positive and west as negative .

Using equator (0 lat.) as reference we can measure up to 90 degrees north and south(vertically). North is taken as positive and south as negative.

PROJECTION ?

It is the mathematical transformation of locations in the three-dimensional space of earth’s surface onto the two dimensional space of a map sheet. Projection

Cylindrical (tangent

across line)

Tangent case

Secant case

Conical (tangent

across line)

Tangent case

Secant case

Planer or azimuthal

(tangent across point)

Tangent case

Secant case

PROJECTION(CONT.)

PROJECTION(CONT.)

CENTRAL LINE IS

EQUATOR

CENTRAL LINE IS

MERIDIANAll the geometric properties tends to preserve along the central line and near by area.

PROJECTION(CONT.)

PROJECTION(CONT.)

PROJECTION(CONT.)

The idea of map projection is about preserving the properties (given below) of real world features when they are depicted on a map.

AREA SHAPE DISTANCE DIRECTION

For the spherical earth all the four properties are applicable but in the case of map projections only few of them can be preserved simultaneously.

RECTANGULAR COORDINATE SYSTEMA coordinate is a set of numerical values that fixes the location of a point in a space of a given dimension. A map is a two dimensional space , in which location of a point is fixed by a set of two numerical values (X,Y).

Rectangular coordinate system is the simplest coordinate system used for fixing the location of any real world feature in two dimensional space. Two dimensional space in this case is defined by two straight lines intersecting each other at right angles (called axes) and they define the direction of two families of lines.

The point of intersection of two line is called ‘origin’. The coordinate of any point is defined by two fixed distances measured perpendicularly from these two lines. Along with rectangular coordinate system there are others also like polar coordinate system

COORDINATE SYSTEM AND MAP PROJECTION

The relationship between coordinate system and map projection is crucial since they are constructed based upon map projection, but they are not map projections themselves.

The function of a map projection is to define how positions on the earth’s curved surface are transformed onto a flat map surface. A coordinate system is then superimposed on the surface to provide the referencing framework by which positions are measured and computed .

There are several projected coordinate system in use for example UNIVERSAL TRANSVERSE MERCATOR COORDINATE SYSTEM, STATE PLANE COORDINATE SYSTEM, WISCONSIN TRANSVERSE MERCATOR COORDINATE SYSTEM, and several others.

UTM COORDINATE SYSTEM

UTM COORDINATE SYSTEM(CONT.)

It is the modified form of Transverse Mercator Projection System in which instead of using one cylinder as developable surface we use multiple cylinders that touch the globe at 6 degree interval meridians resulting in 60 projection zones each of 6 degree longitude width.

To avoid extreme distortions projection zones are limited to 84 N & 80 S.

UTM COORDINATE SYSTEM(CONT.)

UTM coordinate system is formed by superimposing a regular grid on each projection zone such that vertical lines are parallel to the central meridian.

Each UTM zone is divided into horizontal bands spanning 8 degrees of lattitude & these are identified by the letters North to South beginning at 80 S with letter ‘c’ and ending at 84 N with letter ‘X’ , letter ‘I’ & ‘O’ are not used (skipped). Band ‘X’ spans 12 degrees of lattitude.

UTM COORDINATE SYSTEM(CONT.)

UTM COORDINATE SYSTEM(CONT.)

UTM coordinates are expressed as a distance in meters to east – ‘Easting’ & to north – ‘Northing’.

UTM easting of central meridian is 500,000 m east ie. false origin is 500,000 m west of the central meridian.

UTM COORDINATE SYSTEM(CONT.)

Equator is assigned 0 m N (zero northing). To avoid –ve nos for locations south of the equator position fixing in the southern hemisphere is made with equator assigned a value of 10,000,000 m S.

By combining the zone no, the hemisphere, easting and northing values; each point on the earth surface can be uniquely located.

ANY QUESTIONS?

THANKING YOU!