1 Territories, Environment, Remote Sensing & Spatial Information Joint Research Unit Cemagref - CIRAD - ENGREF GIS: concepts, methods & tools GIS: concepts, methods & tools Georeferencing and projections Georeferencing and projections METIER METIER Graduate Graduate Training Course no. 2 Training Course no. 2 – – Montpellier Montpellier - - February February 2007 2007 Information Management in Information Management in Environmental Environmental Sciences Sciences
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Territories, Environment, Remote Sensing & Spatial Information Joint Research Unit Cemagref - CIRAD - ENGREF
Georeferencing and projectionsGeoreferencing and projections
METIER METIER GraduateGraduate Training Course no. 2 Training Course no. 2 –– Montpellier Montpellier -- FebruaryFebruary 20072007
Information Management in Information Management in EnvironmentalEnvironmental SciencesSciences
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
The problemThe problem
surface ≅ sphere ���� plane surface (map)
M(λ,ϕ) → m(x,y)
m
x
y
– modelling the surface to be projecteddetermining the shape and dimensions of the surface
– projection of the surface on a planeestablishing a projection algorithm
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
System of geographic coordinatesSystem of geographic coordinates
• Given that:the Earth presents heterogeneities due to:
• the non-sphericity of the terrestrial volume
• heterogeneity of its density
• the variable altitude of its surface
• Modelling of the terrestrial surface:– geodetic reference base (position/centre of the Earth)
• Cartesian coordinates
–ellipsoid (longitude, latitude):
• mathematically defined envelope
• geographic coordinates (polar)
– geoid (Z):
• gravitational equipotential surface
• mean sea level
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
Geoid and Geoid and
ellipsoidsellipsoids
•• Mean sea level:
This is the reference level for altitude measurements. It corresponds to the mean height of
the sea surface calculated for all tidal stages.
• Altitude:
Difference of gravitational potential between a point (or an object) on the Earth’s surface
and a reference surface (normally the mean sea level).
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
Definition: Equipotential surface of the Earth’s gravity field that best coincides with the
mean sea level.
This corresponds to the topography that a terrestrial surface would have if it was covered by oceans at rest, only subject to terrestrial gravity, i.e., a surface on which
water does not flow.
The geoid The geoid -- 11
Exaggerated altitudes
×××× 15,000
(ref. Geiger, 1987
in U. Frei et al., 1993)
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
The ellipsoid The ellipsoid –– geographic geographic
coordinatescoordinates
X
Y
Z
λ
φO
a
b
X,Y,Z: geocentric coordinates
λ,φ, OM: geographic coordinates
M
m
ellipsoid: a,b
a=equatorial radius
b=semi axis at the poles
The ellipsoid is often defined by:
- flattening: f = (a-b)/a
- square of the eccentricity: e²=(a²-b²)/a²
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
Some ellipsoids & their parametersSome ellipsoids & their parameters
Geodesic
system
Associated
ellipsoid
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS
JRU TETIS
Changing the ellipsoidChanging the ellipsoid
X
Y
Z
O
X’
Y’
Z’
O’
OO’: ∆X, ∆Y, ∆Z
Rotations: δX, δY, δZ
Scale: ∆e
Normal reference: WGS 84
Use of parameters which geometrically
define the ellipsoid:
the DATUM
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GEOREFERENSING AND PROJECTIONSGEOREFERENSING AND PROJECTIONS