coordinate systems in geodesy by k.v.ramana murty, o. s
TRANSCRIPT
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Coordinate Systems in GeodesyCoordinate Systems in Geodesy
ByBy
K.V.Ramana Murty, O. S.K.V.Ramana Murty, O. S.
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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:
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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 ?
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Geoid Best Fitting Local ellipsoid and Geocentric Ellipsoid
INDIA
NN
CG
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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
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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
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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
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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 .
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Two dimensional coordinate System:Two dimensional coordinate System:
P (x, y)
X
Y
x
y
O
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Three dimensional coordinate System:Three dimensional coordinate System:
(X, Y, Z) P
O
X
Y
Z
YX
Z
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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
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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.
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Geocentric Cartesian Coordinate System (Contd.)
Greenwich Meridian
Equator
Earth Surface
X
Y
Z
(X, Y, Z)
XY
Z
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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
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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.
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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.
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Representation of Latitude, Longitude and Ellipsoidal Height
Greenwich Meridian
Equator
Earth Surface
X
Y
Z
P
h
),,( h
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Latitude, Longitude, Ellipsoidal Height and X, Y, Z:
Greenwich Meridian
Equator
Earth Surface
X
Y
Z
(X, Y, Z)
.P
h
),,( h
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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)
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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:
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EGM96: Geoidal Separation Values (N):The 15 x15 global geoid undulations produced by EGM96
The undulations range from -107 m to 85 m.
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Conversion from Geodetic to Geocentric
Sinha
bZ
SinCoshY
CosCoshX
)(
)(
)(
2
2
0
0
0
2/122 )1(
Sine
a
Where is given by
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Conversion from Geocentric to Geodetic
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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.
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Topocentric Cartesian or Local Geodetic Coordinate System
Ellipsoidal Normal
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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
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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)
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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.
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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.
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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.
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Universal Transverse Mercator (UTM)
S080
N084
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How UTM Looks?:
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UTM ZONE:
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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
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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
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Lambert Grid:
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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
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