COORDINATE SYSTEMS

1
CO-ORDINATE SYSTEMS DATUMS IN AFRICA
CHARLES L MERRY SCHOOL OF ARCHITECTURE,
PLANNING GEOMATICS UNIVERSITY OF CAPE TOWN
2

• OUTLINE

• Definitions
• Classical Datums
• Datums and Projections in Africa
• Problems
• The Future

3

• REFERENCE SYSTEM

• A three-dimensional cartesian co-ordinate
  system, where the origin and scale are
  defined, as are the directions of the
  three axes.

• An example is the ITRS
• geocentric - centre of mass of the Earth,
  including oceans and atmosphere
• orientation given by the BIH orientation (mean
  pole, mean Greenwich meridian)

4

• REFERENCE FRAME

• Practical realisation of a reference system,
  using co-ordinates (and velocities) of a
  number of sites

An example is the ITRF2000, where the
co-ordinates and velocities are given for some
200 tracking stations distributed around the
world.
5

• CO-ORDINATE SYSTEM

• Type of co-ordinate used to describe the
  position of a point

Examples are Cartesian (3D) -
X, Y, Z
(2D) - y, x or E, N
Ellipsoidal (geographical) - f, l,
h Polar -
r, a, q
6

• REFERENCE ELLIPSOID

• Solid body formed by rotating an ellipse
  around its minor axis

There are many geodetic reference ellipsoids,
defined by either a, b or by a, f.
Examples Clarke 1866Clarke 1880
(modified)Bessel 1841International 1924WGS84
7

• ELLIPSOID / SPHEROID

• Spheroid is a sphere-like body
• In Europe and elsewhere, Spheroid generally
  means a more complex body than an
  Ellipsoid.
• In England, Spheroid is identical to
  Ellipsoid.

8

• GEODETIC DATUM

• A specific ellipsoid in a specific position
  and orientation with respect to the Earth.
  Generally NOT geocentric, but with axes
  nearly parallel to those of the ITRS.

There are many examples, to be discussed
later.Normally, the co-ordinate system
associated with this datum is the ellipsoidal (f,
l, h).
9

• ELLIPSOID / DATUM

• There are many ellipsoids and many (more)
  datums. There is not a one-to-one
  correspondence between them. One
  ellipsoid can be used for several datums.

Datum 1
Datum 2
Ellipsoid A
Datum 3
10
(No Transcript)
11

• PROJECTION

• A geometrical or mathematical projection of
  the surface of the ellipsoid onto a plane.

2D cartesian co-ordinates (y, x or E, N) on the
surface of the plane are used for mapping and
surveying tasks.
12

• PROJECTION / DATUM

• There are many projections and many datums.
• Applying the same projection to two different
  datums will result in two different sets
  of plane co-ordinates for the same
  points.
• Applying two different projections to the
  same datum will result in two different
  sets of plane co-ordinates for the same
  points.

13

• DATUM DEFINITION

• Choose a specific ellipsoid
• Choose it's orientation three translations,
  three rotations

14

• CLASSICAL DATUM DEFINITION

• Choose a specific ellipsoid
• Define an initial point, and the orientation
  of the ellipsoid wrt the geoid

Position f, l, N Orientation x, h, a
15

• CLASSICAL DATUM DEFINITION - 2

• Generally, deflections of the vertical (x, h)
  and geoidal height (N) are chosen to be
  zero at initial point
• This implies that ellipsoidal position is set
  equal to astronomic position at initial
  point, and ellipsoidal height is set equal
  to orthometric height (above (MSL)
• This leads to a datum which is non-geocentric

16

• DATUMS IN AFRICA

• A legacy of the Colonial era - datums based
  upon ellipsoids determined by European
  geodesists
• Classical approach used astronomically-define
  d origin ellipsoid from Europe classical
  triangulation
• Many so-called "datums" are just
  re-computations of all or part of existing
  networks, using the same initial point
  e.g. the Arc 1950, Arc 1960, Circuit datums

17

• ELLIPSOIDS IN AFRICA

• Bessel 1841 Eritrea, Namibia
• Clarke 1866 Angola, Mozambique
• Clarke 1880 Algeria, Botswana, Burkina
  Faso, Burundi, Cameroon, Chad, Congo,
  DRC, Ethiopia, Gabon, Ghana, Guinea,
  Kenya, Lesotho, Liberia, Malawi, Mali, Morocco,
  Niger, Nigeria, Senegal, Tanzania, Tunisia,
  Zambia, Zimbabwe
• International 1924 Bissau, Egypt,
  Guinea-Bissau, Libya, Madagascar, Tunisia
• Krassovsky 1940 Somalia

18

• AFRICAN DATUMS

Sources NIMA TR8350.2 C Mugnier
(PERS) EPSG Database
19

• PROJECTIONS IN AFRICA

• Mapping of ellipsoidal co-ordinates (f, l) to
  a plane
• Common Projections

• Universal Transverse Mercator (UTM)
• Transverse Mercator / Gauss Conform / Gauss
  Krüger
• Lamberts Conformal Conic
• Labordes

20

• PROJECTIONS IN AFRICA - 2

• Remember that the same projection applied to
  two different ellipsoids will yield two
  different sets of plane co-ordinates
• The same projection applied to the same
  ellipsoid, on different datums, will
  yield two different sets of plane
  co-ordinates

21

• PROJECTIONS IN AFRICA - 3

• Example Gauss Conform projection on Cape datum
  yields co-ordinates for the same point that
  differ by up to 300m from Gauss Conform
  projection on the Hart94 datum

Acknowledgements Chief Directorate of Surveying
Mapping
22

• PROBLEMS

A multitude of different datums, different
ellipsoids and different projections
? Variations on the same datum Point 58
/ Adindan / Blue Nile Cape / Arc 1950 / Arc
1960 / Circuit ? Variations on the same
ellipsoid Clarke 1880 (modified) - Arc /
IGN / RGS ? Variations on the same projection
Transverse Mercator different origins and
false origins, different scale factors
23

• PROBLEMS - CONSEQUENCES

• Confusion within countries as to appropriate
  datums, projections and transformations to
  use
• Confusion and conflict regarding
  international borders
• Confusion and delays in cross-border projects
  - boundary definition, transport
  corridors, mapping, exploitation of
  mineral resources

24

• THE FUTURE

• AFREF - a single consistent co-ordinate
  frame
• Establishment of a network of permanent GNSS
  stations is only the FIRST step
• The next step is to tie the existing networks
  into this frame, establishing the
  necessary transformations between the
  local datum at the ITRF
• Ideally, also converting all co-ordinated
  points and maps to the ITRF