Coordinate Systems in Geodesy
By
K.V.Ramana Murty, O. S.
Contents:

What is Geodesy?

Coordinate system in Geodesy
• Geocentric Cartesian Coordinate System
• Geodetic Coordinate System
• Topocentric Cartesian or local Geodetic Cartesian
Coordinate System
• Planimetric Cartesian Coordinates System

UTM

LCC
What is Geodesy ?


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.
N
N
INDIA
CG
Geoid Best Fitting Local ellipsoid and Geocentric
Ellipsoid
Geocentric & Locally Best Fitting Ellipsoids
Zw
P(X,Y,Z)
(,,h)
Geoid
Globally Fitting
Ellipsoid
CG
Yw
Locally Best
Fitting Ellipsoid
Xw
Xe
Translations - x, y, z
Rotations - x, y, z
Scale
- s
BENCH MARK
HEIGHT OF BENCH
MARK ABOVE
MEAN SEA LEVEL
WAVEHIGH WATER
MEAN SEA LEVEL
LOW WATER
HEIGHT
OF
BENCH
MARK ABOVE TIDEPOLE
ZERO
TIDE POLE ZERO
NEW GENERATION WATER LEVEL MEASUREMENT SYSTEM
FLOAT TYPE
TIDE GAUGE
PRESSURE SENSOR
TIDE GAUGE
BEDPLATE
BENCH MARK
HEIGHT
OF
BENCH
MARK
ABOVE
TIDE
GAUGE ZERO
HEIGHT OF BENCH
MARK ABOVE
MEAN SEA LEVEL
WAVEHIGH WATER
HEIGHT OF
BED PLATE
ABOVE
ZERO OF
TIDE
GAUGE
MEAN SEA LEVEL
LOW WATER
ZERO OF PRESSURE SENSOR
STILLING WELL
NEW GENERATION WATER LEVEL MEASUREMENT SYSTEM
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:
Y
P (x, y)
y
O
x
X
Three dimensional coordinate System:
Z
P
(X, Y, Z)
Z
O
Y
X
Y
X
Coordinate System in Geodesy

There are four coordinate
generally used in geodesy.
systems
• Geocentric Cartesian Coordinate System
• Geodetic Coordinate System
• Topocentric
Cartesian
or
local
Geodetic
Cartesian Coordinate System
• Planimetric Cartesian Coordinates System
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.)
Z
(X, Y, Z)
Earth Surface
Z
Y
X
Y
Equator
X
Greenwich Meridian
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 433m
Geodetic Coordinate System

Geodetic Coordinate are:
• Geodetic Latitude
• Geodetic Longitude
• Ellipsoidal Height.

Geodetic latitude () of a point on the surface
of the earth is
normal
passing
the angle between ellipsoidal
through
the
equatorial plane, positive to north.
point
and
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
Z
Earth Surface
(, , h)
h
P


Equator
X
Greenwich Meridian
Y
Latitude, Longitude, Ellipsoidal Height and X, Y, Z:
Z
(X, Y, Z)
Earth Surface
(, , h)
h
.


Equator
X
Greenwich Meridian
P
Y
GPS Computed Coordinates:
(X2, Y2, Z2)
(X3, Y3, Z3)
Satellite in Space
(X1, Y1, Z1)
(X4, Y4, Z4)
(, , h)
(X0, Y0, Z0)
P
Z
Earth’s Surface
Gr
e
Me e n w i
rid ch
ian
h
Q
O
X

Y
X

Z
Y
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
X 0  (  h)CosCos
Y0  (  h)CosSin
b2
Z 0  ( 2  h) Sin
a
Where  is given by
a

(1  e 2 Sin2 )1/ 2
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
x, y, z 
P
Coordinates of
P w. r. t. ECEF
 x ' , y ' , z '
Coordinates of
P w. r. t. ENU
Ellipsoidal Normal
of origin
xo , yo , zo  Coordinates
w. r. t. ECEF
o , o 
Geographic Coordinates
of origin
Relation Between ECEF and ENU
(ECEF
 x    m11
  
 y    m21
 z    m31
 
(ENU
ENU)
m12
m22
m32
m13 
m23 
m33 
 x  xo 
y  y 
o

 z  z o 
ECEF)
 x
 x   xo 
 y   M 1  y   y 
 
   o
 z 
 z   zo 
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
Northwards 4 degrees.
Norway,
it
was
extended
Universal Transverse Mercator (UTM)
0
84 N
0
80 S
How UTM Looks?:
UTM ZONE:
840 N
UTM ZONE:
X
720 N
W
640 N
V
560 N
U
480 N
T
400 N
S
320 N
R
240 N
44
Q
P
1
2
30
N
080 N
32
44
00 0
M
080 S
L
160 S
K
240 S
J
320 S
H
400 S
G
480 S
F
560 S
E
640 S
D
720 S
C
180W
174W 0
160 N
06E 12E
78E 84E
800 S
UTM ZONE:
44N
24 0 N
16 0 N
False Easting : 5, 00, 000
At Central Meridian
08 0 N
False Northing : 0 for N
00 0
0 and
10, 000, 000 for S
78E
81E
84E
Lambert Grid:
Lambert Grid:

In Lambert Grids
cone.
the meridian and parallels are projected on

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