1. GIS Coordinate Systems Instructor: G. Parodi
Implementation of the Training Strategy of the Monitoring for Environment and Security in Africa (MESA) Programme
GIS Coordinate Systems Instructor: G. Parodi
Date: 03/03/2017
Training Reference: 2017 RSGIS_01
Document Reference: 2017RSGIS_01/PPT/L2
Issue: 2017/L2/1/V2
Addis Ababa, Ethiopia

2. Lecturer ITC, University of Twente
Name
Responsibility
Contribution from
Gabriel Parodi
Lecturer ITC, University of Twente
Edited by
Tesfaye Korme 
Team Leader and Training Manager, Particip GmbH 
Reviewed by
Martin Gayer 
Project Manager, Particip GmbH 
Approved by
Robert Brown
Technical Development Specialist (TDS), TAT

3. Short Introduction GIS Trainer: Mr. Gabriel Parodi
Department of Water Resources, Geo-Information Science and Earth Observation (ITC) at the University of Twente, Enschede, The Netherlands.
MESA Training Contractor: Particip-ITC-VITO Consortium
Consortium partners Particip GmbH Martin Gayer: ITC – Faculty of Geo-Information Science and Earth Observation Chris Mannaerts:
VITO – Remote Sensing Unit Applications Team Sven Gilliams:
Particip is the main Contractor

4. Spatial referencing
(a) International Terrestrial Reference System: ITRS
(b) International Terrestrial Reference Frame: ITRF

5. Two spatial referencing systems
Geographical coordinates Cartesian coordinates

6. Reference surfaces: Geoid & Ellipsoid
The surface of the Earth is far from uniform. Its oceans can be treated as reasonably uniform, but the surface or topography of its land masses exhibits large vertical
variations between mountains and valleys. These variations make it impossible to approximate the shape of the Earth with any reasonably simple mathematical model.
Consequently, two main reference surfaces have been established to approximate the shape of the Earth : one is called the Geoid, the other the Ellipsoid

7. The Vertical datum : The Geoid
To describe height we need a imaginary zero surface.
A surface where water doesn’t flow is a good candidate.
Geoid: Level surface that most closely approximates all Earth’s oceans.
Main ocean level was recorded locally, so there are many parallel “vertical datums”.
Owing to the irregularities in mass distribution caused by the direction of gravity, the surface of the global ocean would be undulating. The
resulting surface is called the Geoid. A plumb line through any surface point would always be perpendicular to the surface.
Exaggerated illustration
of the geoid

8. Vertical datums
Altitudes (heights) are measured from the vertical datums
Mean sea level (geoid)
Different countries, different vertical datums. E.g.:
MSLBelgium m = MSLNetherlands
The Geoid is used to describe heights.
In order to establish the Geoid as a reference for heights, the ocean’s water level is registered at coastal locations over several years using tide gauges (mareographs). Averaging the registrations largely eliminates variations in sea level over time. The resultant water level represents an approximation to the Geoid and is termed mean sea level (m.s.l)
Several definitions of local mean sea levels (also called local vertical datums) appear throughout the world. They are parallel to the Geoid but offset by up to a couple
of metres to allow for local phenomena such as ocean currents, tides, coastal winds, water temperature and salinity at the location of the tide gauge. Care must be taken
when using heights from another local vertical datum . This might be the case, for example, in areas along the border of adjacent nations.
As a result of satellite gravity missions, it is currently possible to determine height (H) above the Geoid to centimetre levels of accuracy. It is foreseeable that a global
vertical datum may become ubiquitous in the next 10–15 years. If all geodata, for example maps, were to use such a global vertical datum, heights would become globally
comparable, effectively making local vertical datums redundant for users of geoinformation.

9. Ellipsoids and horizontal datums
To describe the horizontal coordinates we also need a reference.
To “project” coordinates in the plane we need a mathematical representation. The geoid is only a physical model.
The oblate ellipsoid is the simplest model that fits the Earth (also oblate spheroid)
The ellipsoid is selected to fit the best mean local sea level.
Then the ellipsoid is positioned and oriented with respect to the local mean sea level by adopting a latitude, a longitude and a height of a fundamental point and an azimuth to an additional point.
We have defined a physical surface, the Geoid, as a reference surface for heights. We also need, however, a reference surface for the description of the horizontal coordinates of points of interest.
Since we will later want to project these horizontal coordinates onto a mapping plane, the reference surface for horizontal coordinates requires a mathematical definition and description
The most convenient geometric reference is the oblate ellipsoid (An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it)
Many different sorts of ellipsoids have been defined. Local ellipsoids have been established to fit the Geoid (mean sea level) well over an area of local interest, which in
the past was never larger than a continent. This meant that the differences between
the Geoid and the reference ellipsoid could effectively be ignored, allowing accurate
maps to be drawn in the vicinity of the datum (Figure 3.5).

10. Horizontal datums
Datum: ellipsoid with its location. The ellipsoid positions are modified by the datums.
One datum is built for one ellipsoid, but one ellipsoid can be used by several datums!

11. Datum shifts (1)

12. Datum shifts (2)
Care: A wrong datum and you miss the point!!

13. Ellipsoid semi-major axis semi-minor axis equatorial plane Pole
Mathematically describable rotational surface

14. Commonly used ellipsoids
GPS uses the World Geodetic System 1984 (WGS84) as its reference system

15. Datum transformations
It is mathematically straightforward.
It is a 3D transformation
3 origin shifts
3 rotation angles
1 scale factor Δα Δy Δx

16. Translations (3 Parameters)
Movement of points along an Axis X Y Z

17. Rotations (3 Parameters)
Movement of points around an Axis   

18. Changing the distance between points
Scale (1 Parameter)
Changing the distance between points S

19. 7 Parameters X’ Y’ Z’ X Y Z X Y Z =
S Rxyz +

20. 3 Parameters X’ Y’ Z’ X Y Z X Y Z = +

21. Classes of map projections
A map projection is a mathematical described technique of how to represent curved planet’s surface on a flat map.
There’s no way to flatten out a pseudo-spherical surface without stretching more some areas than others: compromising errors.

22. Secant projections

23. A transverse and an oblique projection

24. Azimuthal projection

25. Cylindrical projection

26. Conic projection

27. Properties of projections
Conformality
Shapes/angles are correctly represented (locally)
Equivalence ( or equal-area )
Areas are correctly represented
Equidistance
Distances from 1 or 2 points or along certain lines are correctly represented

28. Conformal projection
Shapes and angles are correctly presented (locally). This example is a cylindrical projection.

29. Equivalent map projection
Areas are correctly represented. This example is a cylindrical projection.

30. Equidistant map projection
Distances starting one or two points, or along selected lines are correctly represented. This example is a cylindrical projection.

31. Compromise projection (Robinson)

32. Principle of changing from one into another projection

33. Comparison of projections (an example)

34. Universal Transverse Mercator: The UTM coordinate system
Transverse cylindrical projection: the cylinder is tangent along meridians
60 zones of 6 degrees
Zone 1 starts at longitude 180° (in the Pacific Ocean)
Polar zones are not mapped
X coordinates – six digits (usually)
Y coordinates – seven digits (usually)

35. UTM-Zones …. 29 30 31 32 ….. 0o 0o 6o Equator Central Meridian
… …..
Central Meridian
Greenwich
Equator 0o

36. Two adjacent UTM zones

37. Classification of map projections
Azimuthal
Cylindrical
Conical
Aspect
Normal
Oblique
Transverse
Property
Equivalent (or equal-area)
Equidistant
Conformal
Compromise
Secant or Tangent projection plane
( Inventor )

38. Lecture End