Coordinate Systems in GeodesyCoordinate Systems in Geodesy

ByBy

K.V.Ramana Murty, O. S.K.V.Ramana Murty, O. S.

What is Geodesy?What is Geodesy?

Coordinate system in GeodesyCoordinate system in Geodesy

• Geocentric Cartesian Coordinate System

• Geodetic Coordinate System

• Topocentric Cartesian or local Geodetic Cartesian

Coordinate System

• Planimetric Cartesian Coordinates SystemSystem

UTMUTM

LCCLCC

Contents:Contents:

Geodesy is the science concerned with

the exact positioning of points on the

surface of the earth.

It also involves

• The study of variations of the earth’s gravity

• The study of the exact size and shape of the

earth.

What is Geodesy ?What is Geodesy ?

Geoid Best Fitting Local ellipsoid and Geocentric Ellipsoid

INDIA

NN

CG

P(X,Y,Z) (,,h)

CG

Geoid

Geocentric & Locally Best Fitting Ellipsoids

Yw

Xw

Zw

Globally Fitting Ellipsoid

Ye

Ze

Xe

Locally Best Fitting Ellipsoid

Translations - x, y, zRotations - x, y, zScale - s

WAVEWAVE

NEW GENERATION WATER LEVEL MEASUREMENT SYSTEMNEW GENERATION WATER LEVEL MEASUREMENT SYSTEM

BENCH MARKBENCH MARK

TIDE POLE ZEROTIDE POLE ZERO

HEIGHT OF BENCH HEIGHT OF BENCH MARK ABOVE TIDEPOLE MARK ABOVE TIDEPOLE ZEROZERO

LOW WATERLOW WATER

HIGH WATERHIGH WATER

MEAN SEA LEVELMEAN SEA LEVEL

HEIGHT OF BENCH HEIGHT OF BENCH MARK ABOVE MARK ABOVE

MEAN SEA LEVELMEAN SEA LEVEL

HEIGHT OF HEIGHT OF BED PLATE BED PLATE

ABOVE ABOVE ZERO OF ZERO OF

TIDE TIDE GAUGEGAUGEWAVEWAVE

NEW GENERATION WATER LEVEL MEASUREMENT SYSTEMNEW GENERATION WATER LEVEL MEASUREMENT SYSTEM

BENCH MARKBENCH MARK

HEIGHT OF BENCH HEIGHT OF BENCH MARK ABOVE TIDE MARK ABOVE TIDE GAUGE ZEROGAUGE ZERO

LOW WATERLOW WATER

HIGH WATERHIGH WATER

MEAN SEA LEVELMEAN SEA LEVEL

HEIGHT OF BENCH HEIGHT OF BENCH MARK ABOVE MARK ABOVE

MEAN SEA LEVELMEAN SEA LEVEL

BEDPLATEBEDPLATE

ZERO OF PRESSURE SENSORZERO OF PRESSURE SENSOR

PRESSURE SENSOR PRESSURE SENSOR TIDE GAUGETIDE GAUGE

FLOAT TYPE FLOAT TYPE TIDE GAUGETIDE GAUGE

STILLING WELLSTILLING WELL

Coordinate System

The coordinates of the points on the surface of the

earth are required for performing survey operations.

These points are known as control points or stations

The coordinates of these points are determined with

respect to certain coordinate systems.

The coordinate systems are defined by its axes and

origin .

Two dimensional coordinate System:Two dimensional coordinate System:

P (x, y)

X

Y

x

y

O

Three dimensional coordinate System:Three dimensional coordinate System:

(X, Y, Z) P

O

X

Y

Z

YX

Z

There are four coordinate systems

generally used in geodesy.

• Geocentric Cartesian Coordinate System

• Geodetic Coordinate System

• Topocentric Cartesian or local Geodetic

Cartesian Coordinate System

• Planimetric Cartesian Coordinates SystemSystem

Coordinate System in GeodesyCoordinate System in Geodesy

Geocentric Cartesian Coordinate System

The geocentric Cartesian Coordinate system is often called

Earth Centered, Earth fixed (ECEF) or Conventional

Terrestrial Reference System (CTRS).

This system is defined as:

• Origin of coordinate system is placed at the centre of earth

• Z axis aligned to the axis of rotation of earth which has the

direction of the conventional International origin for polar

motion (CIO).

• The X axis passes through the intersection of primary plane

(equatorial plane) and plane containing the Greenwich

meridian

• The systems are right handed.

Geocentric Cartesian Coordinate System (Contd.)

Greenwich Meridian

Equator

Earth Surface

X

Y

Z

(X, Y, Z)

XY

Z

Geocentric Cartesian Coordinate System This system is suitable for mathematical

calculations.

The coordinates do not give any indication that

where the point is on the surface of the earth?

For example the coordinates of STITOP are

X = 1208107.3807m Lat. 17 24 12.28N

Y = 5967336.0758m Long. 78 33 17.87E

Z = 1895612.6425m EHeight m EHeight 433m433m

Geodetic Coordinate System

Geodetic Coordinate are:

• Geodetic Latitude

• Geodetic Longitude

• Ellipsoidal Height.

Geodetic latitude () of a point on the surface

of the earth is the angle between ellipsoidal

normal passing through the point and

equatorial plane, positive to north.

Geodetic Coordinate System (Contd.)

Geodetic Longitude () is the angle between

the prime meridian (Greenwich meridian) and

the meridian plane passing through the point

(observer’s meridian), positive to the east.

Ellipsoidal height (h) of a point on the surface

of the earth is the distance measured from the

ellipsoid to the point along ellipsoidal normal

passing through the point.

Representation of Latitude, Longitude and Ellipsoidal Height

Greenwich Meridian

Equator

Earth Surface

X

Y

Z

P

h

),,( h

Latitude, Longitude, Ellipsoidal Height and X, Y, Z:

Greenwich Meridian

Equator

Earth Surface

X

Y

Z

(X, Y, Z)

.P

h

),,( h

GPS Computed Coordinates::

(X1, Y1, Z1)

(X2, Y2, Z2)

(X4, Y4, Z4)

(X3, Y3, Z3)

h

P

Q

O

X

Y

Z

Satellite in Space

Gre

enw

ich

Mer

idia

nEarth’s Surface

Y

X

Z

),,( h (X0, Y0, Z0)

h = H + Nh = H + Nh = H + N

• The geoidal undulation may be positive or negative.

EllipsoidEllipsoid

hhPP TopographyTopography

HH

GeoidGeoidNNN = Geoidal Separation

H = Height above Geoid(~Orthometric Height)

h = Ellipsoidal height

Relation between ellipsoidal and MSL Heights:

EGM96: Geoidal Separation Values (N):The 15 x15 global geoid undulations produced by EGM96

The undulations range from -107 m to 85 m.

Conversion from Geodetic to Geocentric

Sinha

bZ

SinCoshY

CosCoshX

)(

)(

)(

2

2

0

0

0

2/122 )1(

Sine

a

Where is given by

Conversion from Geocentric to Geodetic

Topocentric Cartesian or Local Geodetic Coordinate System

The local geodetic coordinate system is defined as under

• The origin is chosen along the ellipsoidal normal passing

through observation station .

• In practice it is at the observation station, on the ellipsoid.

• The Z axis is the ellipsoidal normal.

• The primary plane is the plane containing the origin and

perpendicular to the Z axis.

• Y axis is oriented along the meridian passing through origin

positive to North.

• X axis is oriented along the parallel passing through origin

positive to east.

Topocentric Cartesian or Local Geodetic Coordinate System

Ellipsoidal Normal

Topocentric Cartesian or Local Geodetic Coordinate System

',',' zyxEllipsoidal Normal

oo ,

ooo zyx ,,

P zyx ,,

Coordinates of P w. r. t. ECEF

Coordinates of P w. r. t. ENU

Coordinates of origin w. r. t. ECEF

Geographic Coordinates of origin

Relation Between ECEF and ENU

(ECEF ENU)

o

o

o

zz

yy

xx

mmm

mmm

mmm

z

y

x

333231

232221

131211

o

o

o

z

y

x

z

y

x

M

z

y

x1

(ENU ECEF)

Planimetric Cartesian Coordinates (UTM, Lambert grid)

Planimetric Cartesian Coordinates are often called

easting and northing.

They are the result of a cartographic projection from

three dimensional geodetic coordinate(, ) into a two

dimensional Cartesian space (x, y) on a map.

In this work, projected easting is denoted by x and

northing by y.

Universal Transverse Mercator Projection (UTM)

The need of uniform Grid system was felt during 2nd

World War.

UTM was developed after 2nd World War.

The Meridian and parallel are projected on Cylinder.

Calculation of distances and angles easier than from

Geographical coordinates.

Organization of UTM Grid Zones

Although it is called the Universal Transverse Mercator

Grid System, it does not cover the whole world.

The area covered by the system is the whole extent of

Longitude and 80 degrees South Latitude to 84

degrees North Latitude.

Originally, the coverage of the UTM Grid System was

from 80 degrees S to 80 degrees N.

On the request of Norway, it was extended

Northwards 4 degrees.

Universal Transverse Mercator (UTM)

S080

N084

How UTM Looks?:

UTM ZONE:

UTM ZONE:

S080

S072

S064

S056

S048

S040

S032

S024

S016

S008

000

N008

N016

N024

N032

N040

N048

N056

N064

N072

N084

1 2 30 32 44

0174W180W 06E 12E 78E 84E

C

D

E

F

G

H

J

K

L

M

N

P

Q

R

S

T

U

V

W

44

X

UTM ZONE:

000

N008

N016

N024

0 78E 84E

44N

81E

False Northing : 0 for N

and 10, 000, 000 for S

False Easting : 5, 00, 000At Central Meridian

Lambert Grid:

Lambert Grid:

In Lambert Grids the meridian and parallels are projected on

cone.

The extent is India and adjacent countries.

There are 9 Grid Zones covering India and Adjacent countries.

The North-South extent of each grid zone is limited to 8 and the

E-W extent is limited to 16

Hyderabad falls in Grid IIIA

Origin of Grid III A is Lat. 19 and Long. 80

The coordinates assumed at origin are:

E = 2743196.4m

N = 914398.8m