“Α contemporary
perspective of GEODESY in
positioning spatial geodata”
M.G.Doufexopoulou
Associate professor “Physical Geodesy” NTUA, Athens
Review for Master-courses
Spring 2010
M.G.Doufexopoulou - Lectures
about Geodesy 2010
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What is Geodesy Why needed?
How it applies & who needs it?
 A “system” (=model) is a reasonable configuration
about reality
 Systems „react” to internal ( physical ) and external
changes (= knowledge, manmade, professional needs,
social conditions ).
 There is need for standards of reference ( = a model of the
Earth’s system ) Goal is = the comparison of the Earth’s
system ( to same system or another system) in spatial
or temporal coordinates
 The “Earth’s system” is a platform used to describe all
information about geo-spatial data. In particular it “says”
“WHERE” are the geo-data?
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Positions of geo-data
 Need to represent all “information” related to the Earth’s
system by a position with respect to an Earth’s standard (=
an Earth’s prototype!)
 Less accurate positions are provided by “images” of the
Earth ( general maps, satellite imagery, photos, Earth
Google ).
 A uniform and accurate positioning is given by GEODESY.
Geodesy aims to determine an Earth’s prototype in its geometry
& gravity field and to use it for positioning.
 Users of Geodesy need to know positions with respect
to a coordinate system
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1.What is Geodesy? - many perspectives
2.Why needed ?- too many applications
3.How it applies?- many methods ( ONE principle )
4.Who needs Geodesy? - many professions
4000 years existence of GEODESY as Earth discipline
Many perspectives: LEARN about - USE GEODESY.
Many types of measurements
BUT
ONE PRINCIPAL OBJECTIVE!!
( find POSITIONS in geo- environment with respect to the
Earth or to an Earth related coordinate system)
Objective: find Coordinates of positions with respect to an
adopted model about the EARTH & its gravity field
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Foundations of Geodesy
 A GEOMETRY perspective of 3D space
 A configuration about the “geometry” of Earth ( shape and
size )
 Description of the 3D space by surface coordinates ( 2D )
& height ( 1D ) using two different Earth’s models!
 Relativity theory introduces also time as coordinate (4D! )
 The Earth’s general shape depends on laws of Newton’s
Physics applied to Earth. Consequence: PHYSICS has to
involve in Geodesy!!!!
 GEODESY IS FOUNDED ON COORDINATE GEOMETRY
AND LAWS OF PHYSICS
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Definition of the goals of Geodesy
 Geodesy aims goals to determine the shape and size
of Earth, its gravity field and the time / space variations
at different size of regions (local, regional, entire Earth)
 The goals “serve” to answer all 4 questions at the start, if
needed measurements are available!
 Geodesy provides an answer “where” is “something” IF the
measurements to compute “where” ( set of 3D coordinates
( local coordinates, global coordinates ) are used
 Measurements, coordinate systems, a “model” of the
Earth are the basic entries to apply Geodesy to provide
3D positions.
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Models of the shape of the Earth (I)
 The models of the Earth’s shape
depend on the size of a region
at which we need the “where”
 “Where” is given within a part of
Earth or for entire Earth (relative
- absolute coordinates)
 More than one models of Earth’s
shape are used - many
coordinate systems ( local &
global ) - Geodetic frames
 An Earth’s model expresses a
Mathematical or a Physical
model of its own topography!
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Models of the shape of the Earth (II)
A Mathematical model of the
Earth represents at “best” the
topography in a region ( criteria )
The extend of the region defines
which is the “better” model!
A plane, a sphere or ellipsoid
express with respect to their
geometry, relations among the
coordinates, used to compute
(distances, volumes, areas,
orientations )
A geodetic Coordinate system is
planar, spherical, ellipsoidal
We choose its origin and axes
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Models of the Earth’s geometry (III)
Two reasons why Geodesy is
based in parallel Mathematical
and Physical model of Earth.
1.ALL measuring devices are
aligned to the local horizon &
thus the perpendicular is the
direction of local gravity force
2.Most used heights H are the
elevations above the Mean
Sea Level ( the zero height ).
These reasons are the cause
to use an Earth’s physical
model, based on its gravity
field. This model is computed
by measures of the gravity
field
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Conclusions about foundations
Geodesy provides coordinates of positions with respect to Earth
models using a Geometry configuration of the space. This Geometry is
affected by the impact of gravity field ( only locally space is Euclidean)
The particular geometry in use depends on the extend of a region ( =
how much the Earth’s curved shape affects the “parallelism” of local
verticals)
Except geometry to use with a coordinate system for the full description
of a position, two models of the Earth’s shape are used in parallel: A
Mathematical model used as reference surface for horizontal
coordinates
Physical model used as reference surface for elevations above Mean
Sea Level, along the local vertical.
Measurements in Geodesy depend on the direction of the vertical and
on much more physical and instrumental factors.
GEODESY IS FOUNDED
ON A COORDINATE GEOMETRY AND
M.G.Doufexopoulou - Lectures
NEWTONEAN PHYSICS- APPLIED
about GeodesyWITH
2010 2 EARTH’S MODELS
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Geodesy applies to determine
coordinates
GEODESY IS FOUNDED ON A COORDINATE
GEOMETRY ( 2D+1D or 3D ) AND NEWTONEAN
PHYSICS
APPLIED WITH 2 EARTH’S MODELS
Mathematical model = surface coordinates
Physical model= elevations above “Mean Sea”
The size of region defines the coordinates
M.G.Doufexopoulou
- Lectures or “other” )
( planar, spherical,
ellipsoidal
about Geodesy 2010
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MEASUREMENTS IN GEODESY
TYPES OF MEASUREMENTS
PRINCIPLES OF USE
At present (2010) many and
different types of
measurements can be used for
the goals of Geodesy.
Classified under perspectives
( terrestrial / spatial, mechanical
/ automated, direct/indirect)
All types have to be processed
for two goals: to be converted as
geometry quantities ( distances
or coordinates ), to evaluate
their accuracy
Use of geodetic measurements
is pretty simple in concept!!!!
After processing they
represent geometry quantities
( distances, coordinates, elevation
difference, or orientation angles )
We use coordinate Algebra to solve
for the coordinates of points, which
are line intersections of few or many
simple geometric configurations and
connect known with unknown positions
through geometry or mathematical rules!
A particularity is that figures should be
over-determined for UNIQUE solution
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Types of measurements used in
Geodesy(I)
Classification ( direct or indirect )
A direct measurement aims to measure a geometric
quantity ( distance, angle of orientation, elevation difference )
An indirect measurement provides measures of variables
which relate to a geometric quantity by a formula. By an
analytic computation we can estimate a measure of the
optimal value of the needed geometric quantity.
Obviously, we consider measurement & computational
errors and we need to know values about parameters
which can have impact on the result of a measurement
We need to estimate the ACCURACY of any measurement
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Types of measurements used in
Geodesy(II)
Classification according to spatial and terrestrial character
Until 1960 Geodesy was based on using terrestrial measurements
only { angles mainly, elevation differences & very few small distances
to scale the geometry of simple figures on a reference surface.
Instruments operated mechanically ( Classic Geodesy - geometry )
Instrumentation progressed greatly after 1950. Presently (2010 ) the
“market” provides fully automated electronic measuring systems, a built
in computational software and can be connected to a computer
network ( Automated Geodesy ) - measurements go to a computer .
Users of all measurements need training about how to use them for
his/her needs and how to estimate the accuracy of the result.
This knowledge is widely extended, with experience and skills to use
instruments ( for professionals in Geodesy ).
The start of Space exploration ( 1957 ) initiated an abundance of
new types of space-based
measurements
M.G.Doufexopoulou
- Lectures ( direct and indirect )
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Types of measurements used in
Geodesy(III)
Space-based data
Satellite altimeters
Gravity field models
Global Positioning
( GPS )
Radar on satellites
Processing methods, impact of
many factors, large numbers of data
“Black-box” operation, software to
use ( geometry & physics )
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Use of measurements as “geometric” data
Processing ends to data
After the elimination of all not
wished impacts ( from various
causes ) most data represent a
“distance in space” with respect
to a model “geometry”
(Euclidean, spherical, ellipsoidal,
differential)
Inputs distances = to solve for
the coordinates at the common
points of many intersections
Over-abundant data need to
optimize for unique positions
Need for ERROR models!
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Example: GPS coordinates
GPS coordinates = a common
point at which 4 imaginary
spheres with radii ri intersect
The radii represent distances
from the radar on satellite to the
GPS receiver.
distances are estimated after
the arrival time of a pulse from
the radar to the receiver
Parametric space, abundance of
observations, not Euclidean
geometry, statistical model
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From a Reference coordinate system to U.T.M
coordinates
Basic stages between theory and practical use
Notice: ALWAYS the space to represent by its coordinates, has LESS
parameters (X) than the number of impacts(Y) for processing
measurements into input data
( Y>>X )
Earth's system geometry
Mathematical Earth
Physical Earth
Reference coordinate system
origin and axes
Coordinates of a "skeleton" of reference points
A GEODETIC DATUM
M.G.Doufexopoulou - Lectures
about Geodesy 2010
Cartographic Projection of Datum on plane
UTM Planar coordinates
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The Cartographic Projection PLANAR
coordinates (UTM )
UTM coordinates are planar X, Y coordinates after the projection of
meridians and parallels of Earth’s datum onto an enveloping surface
of a cylinder and then the “stressing” of the surface into planar!
National UTM coordinates carry Cartographic deformations
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National UTM coordinates ( continued )
The entire Earth is divided into 60 zones between meridians apart at
6o degrees (= keeps small scale deformations at edges)
Along the CENTRAL meridian of each country NO scale deformation
Beware: Different geodetic datum give different UTM coordinates
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Height reference systems & height datum
Two DIFFERENT systems are
in use:
1. Mean Sea Level (geoid)
H=0 H, along the vertical
2. Surface of horizontal datum
h=0 h, along perpendicular
small angle ε of different
orientation= deflection of the
vertical
H is not the same with h!!!!
“Surface” 1 with respect to
“surface” 2 gives geoid height ,
N= geoid height / undulation
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More useful the NATURAL heights only δΗ show the real
direction of mass flow - δh do NOT
GPS heights are h heights- need conversion to H ( h=N+H )
Leveling with vertical rods from
point to point and “add” the sum
gives a δΗ
Imagine an orthogonal triangle,
measure necessary quantities,
solve to find the δΗ
( Trigonometric method )
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Need to determine accurate height datums for
many reasons & applications
Many methods and perspectives to determine a height
datum ( “a” geoid ) for a region ( relative datum ) or for the
entire Earth ( absolute datum)
Problem to set up:
Find: measures N(φ,λ) and ε(φ,λ) accurate to +/- 0.01m
and at least +/- 0.1’’ for ε
Given: gravity field data ( various types )
Hints:
Use good theory, accurate and dense data, do accurate
computations. Use optimally many types of observations
and data types! - A HIGHT REFERERENCE
- Lectures of Geodesy )
( a particularM.G.Doufexopoulou
extended subject
about Geodesy 2010
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Principles of all Methods in Geodesy
1.The common approach is the GEOMETRY as defined by
the used Reference datum ( =used to compare the results)
2.Use as many observations as possible among known
and not known positions ( over- determined geometric
figures )
3.Process the observations for the objective to eliminate
all known impacts ( instrumental, environmental, e. t. c ).
4. Use then the processed observations to compare with
their expected value as it can be expressed with the
geometry induced by the Reference datum
5. Apply to residuals r=x( is ) - x( should be ) a
statistical error model ( stochastic ) - optimize extra
observations for UNIQUE coordinates
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Applications of positioning & heights
POSITIONS
Accurate surface coordinates ( maps, survey plans for engineering
projects and for scaling satellite imagery, Earth’s dynamics )
Less accurate surface coordinates ( positioning geo-data - Geography
and environmental issues)
HEIGHTS ( DEPTHS )
Height differences δΗ can be used to find exact slopes ( engineering &
environment - roads, highways, floods, water basins, lod)
Changes of heights per time are used for Earth’s kinematics(stability)
Accurate topography and ocean depths used to predict the evolution of
dynamical Earth’s phenomena ( weather, streams, wind, pollution,
- Lectures
tsunamis, e. t. c) - long M.G.Doufexopoulou
term / short term
about Geodesy 2010
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The near future for Earth’s models
By year 2015 all Earth disciplines will be suggested to use ONE Earth’s
model common for use ( = to avoid inconsistency among datum )
Global Geodetic Observation System ( = GGOS ) through the data of
many dedicated satellite missions
WGS84 - ITRF - EUTRF - National Datum ( coordinate transformation)
Geodetic coordinates ( φ,λ,Η(h) or X,Y, H(h) ) project onto the National
UTM system. Heights H or h form either a contour map or DTM or DEM
( there are small linear scale deformations 0.4% - to be corrected )
3D position coordinates + any other geo-data “information”
USERS restrict to possess and use these data bases
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Visit please the site to learn how Geodesy is useful for
you:
http://www.iag-ggos.org/You_and_GGOS/
These slides will be available soon at:
http://www.doufexopoulou.com
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Examples of geo-applications




Simply positions of geo-data of any sort
Monitor changes in land use
Monitor changes of land form ( from many causes)
Find optimal locations for “services” or engineering
constructions
 Confirm that a region ( soil, geology ) is stable
 Delineate the contour of basins, volume of
excavations, estimate lengths of transport
 Many others depending on the profession…..
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Did you learn about Coordinates?
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