GIS211

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GIS211

• COORDINATE SYSTEMS
• Week 2
• Wilma Britz

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• Coordinate System
• A fixed reference framework superimposed onto
  the surface of an area to designate the position
  of a point within (McDonnell, 1995)
• Coordinate Systems can be Projected e.g. UTM and
  Lo or Geographical, not projected
• Map Projection
• A method by which the curved surface if the
  earth is portrayed on a flat surface. This
  generally requires a systematic mathematical
  transformation of the Earths graticule of lines
  of longitude and latitude onto a plane
  (McDonnell, 1995)
• Datum
• A model of the Earth used for geodetic
  calculations (McDonnell, 1995)

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Coordinate System
Two map layers are not going to register
spatially unless they are based on the same
coordinate system.
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Figure 2.1 The top map shows the road networks in
Idaho and Montana based on different coordinate
systems. The bottom map shows the road networks
based on the same coordinate system.
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Geographic Coordinate System

• The geographic coordinate system is the location
  reference system for spatial features on the
  Earths surface.
• The geographic coordinate system is defined by
  longitude and latitude.

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Figure 2.2 The geographic coordinate system.
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Figure 2.3 A longitude reading is represented by
a on the left, and a latitude reading is
represented by b on the right. Both longitude and
latitude readings are angular measures.
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Figure 2.4 The flattening is based on the
difference between the semimajor axis a and the
semiminor axis b.
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Datum

• A datum is a mathematical model of the Earth,
  which serves as the reference or base for
  calculating the geographic coordinates of a
  location.
• A shift of the datum will result in the shift of
  positions of points.

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Geographical co-ordinates differences in South
Africa Within South African latitudes, The
Hartebeesthoek94 Datum(WGS84) latitude is always
numerically greater than its Cape Datum(modified
Clarke 1880) counterpart at a point of interest.
The magnitude of this difference ranges from
approximately 9" at the equator to approximately
0" at latitude 37 South. The Hartebeesthoek94
Datum(WGS84) longitude is always numerically less
than its Cape Datum(modified Clarke 1880)
counterpart at a point of interest. The magnitude
of this difference ranges from approximately 2"
at 15 east of Greenwich to 0" at approximately
39 east of Greenwich. To translate the above
differences from seconds () of arc to distances
in metres on the ground, the following rules of
thumb comes in handy (only valid in South
Africa)            1 of latitude     
30m            1 of longitude    27m
                                                  
                                                  
                          
http//w3sli.wcape.gov.za/SURVEYS/MAPPING/wgs84.ht
m
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Gauss conform co-ordinates (Lo system) in South
Africa The Hartebeesthoek94 Datum(WGS84) XLo co-
ordinate is between 290 and 300 metres greater
than its Cape Datum(modified Clarke 1880)
counterpart at a point of interest. This
difference is directly related to the
displacement in the equatorial planes of two
ellipsoids. The Hartebeesthoek94 Datum(WGS84) YLo
co-ordinate will always be algebraically greater
than its Cape Datum(modified Clarke 1880)
counterpart, at a point of interest. The
magnitude of this difference ranges from
approximately 70 metres at 15 east of Greenwich
to 0 metres at approximately 39 east. The
relationship between the longitude differences
and Gauss conform YLo co-ordinate differences are
opposite in sign. The reason for this is that
longitude, by convention, increases eastward and
the projection YLo co-ordinate, by definition,
increases westwards. Effectively the relationship
is the same.                                    
                                                  
                                                  
    
http//w3sli.wcape.gov.za/SURVEYS/MAPPING/wgs84.ht
m
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• Def Cartesian coordinates
• Coordinates locating points in space expressed
  by reference to two or three perpendicular axes
  (x,y,z)
• Def Latitude
• The angular distance north or south between a
  point on the Earths surface and the Equator.
  This distance is measured with reference to an
  idealized, spheroid-shape of the earth
• Def Longitude
• The angular distance of a point east or west
  of an arbitrarily defined meridian, usually taken
  to be the Greenwich meridian. The distance is
  measured with reference to an idealized, spheroid
  shape of the Earth

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Projected Coordinates

• Plane coordinates are the simplest type of
  coordinates to use for everyday practical
  applications
• Coordinates must be projected onto a plane
  surface
• This is not possible without some distortion
• Projections which have the properties of
  preserving angles and shapes are called Conformal
  or Orthomorphic projections

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Approximation of the Earth

• The simplest model is a sphere, which is
  typically used in discussing map projections.
• But the Earth is not a perfect sphere the Earth
  is wider along the equator than between the
  poles. Therefore a better approximation to the
  shape of the Earth is a spheroid, also called
  ellipsoid, an ellipse rotated about its minor
  axis.

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Form of the Earth orThe figure of the earth

• Earth is an oblate ellipsoid also called the
  ellipsoid of revolution.
• Since the earth is in fact flattened slightly at
  the poles and bulges somewhat at the equator, the
  geometrical figure used in geodesy to most nearly
  approximate the shape of the earth is an
  ellipsoid of revolution. The ellipsoid of
  revolution is the figure which would be obtained
  by rotating an ellipse about its shorter axis.
• The Ellipsoid is assigned dimensions based upon
  the best geodetic information for the lengths of
  meridian arcs in various parts of the earth
• Unfortunately these measurements do not agree
  from one region to another for the earths
  curvature at any given latitude

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• An ellipsoid (of revolution) is uniquely defined
  by specifying two dimensions. Geodesists, by
  convention, use the semimajor axis and
  flattening. The size is represented by the radius
  at the equator-the semimajor axis-and designated
  by the letter, a. The shape of the ellipsoid is
  given by the flattening, f, which indicates how
  closely an ellipsoid approaches a spherical
  shape. The difference between the ellipsoid
  representing the earth and a sphere is very
  small.

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Spheres and Spheroids

• Why is the earth not a perfect sphere?
• The earth rotates rapidly around its own axis,
  causing the globe to expand at the equator and
  flatten at the poles.
• For small-scale maps the earth can be treated as
  a sphere
• For larger scale maps the squashed beach ball
  effect has to be taken into account

In order to take these factors into
consideration, cartographers use ellipsoids
called spheroids to model the surface of the
globe. In South Africa The Clarke 1880 spheroid
was used before 1999 and the World Geodetic
System 1984 is used since then.
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Geoid It was stated earlier that measurements
are made on the apparent or topographic surface
of the earth and it has just been explained that
computations are performed on an ellipsoid. One
other surface is involved in geodetic
measurement-the geoid. In geodetic surveying, the
computation of the geodetic coordinates of points
is performed on an ellipsoid which closely
approximates the size and shape of the earth in
the area of the survey. The ellipsoid is a
mathematically defined regular surface with
specific dimensions. The geoid, on the other
hand, coincides with that surface to which the
oceans would conform over the entire earth if
free to adjust to the combined effect of the
earth's mass attraction and the centrifugal force
of the earth's rotation. As a result of the
uneven distribution of the earth's mass, the
geoidal surface is irregular and, since the
ellipsoid is a regular surface, the two will not
coincide.
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World Geodetic System 1984(WGS 84)

• Before 1 January 1999
• The coordinate reference system, used in SA as
  the foundation for all surveying, engineering and
  geo-referenced projects and programmes, was the
  Cape Datum
• This Datum is based on the Clarke 1880 ellipsoid
  and has its origin point at Buffelsfontein near
  Port Elizabeth
• Flaws and distortions became easily detected
  using modern positioning techniques (GPS)
• The upgrading, recomputation and repositioning of
  the SA coordinate system was driven by the
  advancement of modern positioning technologies
  and the globalization of these techniques for
  navigation and surveying.

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• Since 1 January 1999
• The official coordinate system for SA is based on
  the World Geodetic System 1984 ellipsoid,
  commonly known as WGS84
• The Hartebeesthoek Radio Astronomy Telescope is
  the origin of the system
• This new system is known as the Hartebeesthoek 94
  Datum
• NB At this stage all heights will remain
  referenced to mean sea level, as determined in
  Cape Town and verified at tide gauges in Port
  Elizabeth, East London and Durban

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Geoids Ellipsoids

• The earths physical surface is irregular
• A more smoothed representation of the earth is
  the Geoid
• Def The Geoid is that surface that would be
  assumed by the undisturbed surface of the sea,
  continued underneath the continents by means of
  small frictionless channels
• Def The Ellipsoid is a smooth mathematical
  surface that best fits the shape of the geoid and
  is the next level of approximation of the actual
  shape of the earth

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Elements of an ellipse a Semi Major Axis b
Semi Minor Axis f Flattening (a-b)/a
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Datums/ Spheroids

• A National geodetic coordinate system is defined
  by a Geodetic Datum
• This Datum consists of two parts
• A defined geodetic reference ellipsoid, in terms
  of the a,b or a,f parameters
• A defined orientation, position and scale of the
  Geodetic system in space
• From this, it can be deduced that a specific
  ellipsoid can be used to define an infinite
  amount of datums.

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The Cape Datum The Hartebeesthoek94 Datum
Clarke 1880 ellipsoid WGS84 ellipsoid
Buffelsfontein trig beacon Hartebeesthoek
Defined by astronomic azimuth base line measurements Defined by GPS
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Map Projection

• A map projection is a systematic arrangement of
  parallels and meridians on a plane surface.
• Cartographers group map projections by the
  preserved property into conformal, equal area or
  equivalent, equidistant, and azimuthal or true
  direction.
• Cartographers also use a geometric object (a
  cylinder, cone, or plane) and a globe (i.e., a
  sphere) to illustrate how to construct a map
  projection.

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Types of Projections

• Conic (Albers Equal Area, Lambert Conformal
  Conic) - good for East-West land areas
• Cylindrical (Transverse Mercator) - good for
  North-South land areas
• Azimuthal (Lambert Azimuthal Equal Area) - good
  for global views

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Figure 2.6 Case and projection.
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Figure 2.7 Aspect and projection.
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Conic Projections(Albers, Lambert)
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Cylindrical Projections(Mercator)
Transverse
Oblique
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Azimuthal (Lambert)
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Albers Equal Area Conic Projection
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Data not projected Geographic coordinates
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Projection - Transverse Mercator, Conformal,
Cylindrical Spheroid WGS84 Central Meridian
27º Coordinate System UTM Zone 35
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Projection Lambert Conformal Conic Spheroid
Clarke 1866 Central Meridian 27º
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Projection Albers Equal Area Conic
Projection Spheroid WGS84 Central meridian 27º
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Lambert Azimuthal Equal Area Projection Spheroid
Sphere
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Projections Preserve Some Earth Properties

• Area - correct earth surface area (Albers Equal
  Area) important for mass balances
• Shape - local angles are shown correctly (Lambert
  Conformal Conic)
• Direction - all directions are shown correctly
  relative to the center (Lambert Azimuthal Equal
  Area)
• Distance - preserved along particular lines
• Some projections preserve two properties

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Map Projection Parameters
Map projection parameters include standard lines
(standard parallels and standard meridians),
principal scale, scale factor, central lines,
false easting, and false northing.
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Figure 2.9 The central parallel and the central
meridian divide a map projection into four
quadrants. Points within the NE quadrant have
positive x- and y-coordinates, points within the
NW quadrant have negative x-coordinates and
positive y-coordinates, points within the SE
quadrant have positive x-coordinates and negative
y-coordinates, and points within the SW quadrant
have negative x- and y-coordinates. The purpose
of having a false origin is to place all points
within the NE quadrant.
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Commonly Used Map Projections

• Transverse Mercator
• Lambert conformal conic
• Albers equal-area conic
• Equidistant conic

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Figure 2.10 The Mercator and the transverse
Mercator projection of the United States. For
both projections, the central meridian is 90W
and the latitude of true scale is the equator.
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Figure 2.11 The Lambert conformal conic
projection of the conterminous United States. The
central meridian is 96W, the two standard
parallels are 33N and 45N, and the latitude of
projections origin is 39N.
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Projected Coordinate Systems

• The Universal Transverse Mercator (UTM) grid
  system
• Longitude of Origin (Lo System)
• The Universal Polar Stereographic (UPS) grid
  system
• The Public Land Survey System (PLSS)

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Geographic and Projected Coordinates
(f, l)
(x, y)
Map Projection
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Coordinate Systems

• Universal Transverse Mercator (UTM) - a global
  system developed by the US Military Services
• Longitude of origin (Lo System) a system
  developed and used for South Africa
• The following simple conversion is applicable
  only where the Lo. of the South African system
  and the central meridian of the UTM system
  coincide ie. 15ºE 21ºE 27ºE and 33ºE
• Y(Lo.)(500 000-E(UTM))/0.9996
• X(Lo.)(10 000 000-N(UTM))/0.9996
• The UTM system incorporates a scale distortion
  of 0.9996 at the Lo. to reduce distortion at the
  edges of the belt.

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Universal Transverse Mercator

• Uses the Transverse Mercator projection
• Each zone has a Central Meridian (lo), zones are
  6 wide, and go from pole to pole
• 60 zones cover the earth from East to West
• Reference Latitude (fo), is the equator
• (Xshift, Yshift) (xo,yo) (500000, 0) in the
  Northern Hemisphere, units are meters

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The Universal Transverce Mercator coordinate
system

• The UTM system divides the earth into 60 zones,
  each 6 degrees of longitude wide.
• These zones define the reference point for UTM
  grid coordinates within the zone.
• UTM zones extend from a latitude of 80 degrees
  South to 84 degrees North.
• UTM zones are numbered 1 to 60, starting at the
  international date line, longitude 180, and
  proceeding east.
• Zone extends from 180W to 174W and is centered
  on 177W.
• Each zone is divided into horizontal bands
  spanning 8 degrees of latitude.

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• These bands are lettered, south to north,
  beginning at 80S with the letter C and ending
  with the letter X at 84N.
• The letters I and O are skipped
• The band lettered X spans 12 of latitude.
• A square grid is superimposed on each zone.
• Its aligned so that vertical grid lines are
  parallel to the center of the zone, called the
  central meridian.
• UTM grid coordinates are expressed as a distance
  in meters to the east, referred to as the
  eastings, and a distance in meters to the
  north, referred to as the northings.

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• Eastings
• UTM easting coordinates are referenced to the
  center line of the zone known as the central
  meridian.
• The central meridian is assigned an easting value
  of 500 000 meters East.
• Since this 500 000m value is arbitrarily
  assigned, eastings are sometimes reffered to as
  false eastings.
• An easting of zero will never occur, since a 6
  wide zone is never more than 674 000 meters wide

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• Northings
• UTM northing coordinates are measured relative to
  the equator.
• For locations north of the equator the equator is
  assigned the northing value of 0 meters North.
• To avoid negative numbers, locations south of the
  equator are made with the equator assigned a
  value of 10 000 000 meters North.
• Some UTM northing values are valid both north and
  south of the equator.
• In order to avoid confusion the full coordinate
  needs to specify if the location is north or
  south of the equator.
• Usually this is done by including the letter for
  the latitude band.
•  
•  

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The South African Coordinate System

• The SA coordinate system is based upon the Gauss
  Conform Projection
• This is an adaptation of the ordinary Mercator
  projection (Transverse Mercator)
• It is turned 90 degrees, so that it may be based
  upon any meridian
• The system consists of belts running north and
  south, 2 degrees of longitude wide, the central
  meridians being every odd meridian example 15
  degree, 17 degree..
• The belt is referred to as Lo15

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20
22
24
26
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0 equator
                     
Central Meridian
Y
-Y
X
Boundary Meridian
Lo21
Lo23
Lo25
Lo27
Coordinates measured in meters from Central
Meridian and the equator
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Mapping South Africa

• All 110 000 Orthophoto maps, 150 000
  Topographical maps, 1250 000 Topo-Cadastral
  maps, and 1250 000 Regional and Aeronautical
  maps prodused in South Africa for South Africa is
  projected using the Gauss Conform projection,
  with the central meridian the nearest odd
  meridian. The ellipsoid used is WGS84, but sheets
  produced prior to 1999 use the Clarke 1880
  (modified) ellipsoid.

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• Other maps such as the 1500 000 Topo-Admin and
  Aeronautical map and 11000 000 International
  Civil Aviation organisation world Aeronautical
  Charts are projected using Lambert Conformal
  Conic projection with 2 Standard parallels.
• The 11000 000 SA Wall map is projected using the
  Albers Equal Area with standard parallels 2410
  South and 3250 South.
• Since 1999 WGS84 is the ellipsoid used, prior to
  that Clarke 1880 ellipsoid was used.

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• The Gridlines/ Grid zones or Coordinate Systems
  used on South African Maps
• Longitudes and Latitudes in degrees, minutes and
  seconds.
• X and Y measured in meters Lo System
• Eastings and Northings measured in meters UTM

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South African Lo System
Y Axis
Lo 25
Longitudes
Equator with a value of 0 meters
0
Every odd degree is a Central Meridian with a
value of 0 meters
Q
Latitudes
The position of Q is calculated by measuring in
meters on the X and Y axis. The longitudinal
value is measure on the Y Axis from the central
meridian which have a value of 0 meters. Thus,
values to the right of the central meridian will
be negative, and values to the left of the
central meridian will be positive. This means
that if you measure a distance of 60 000m from
the central meridian (25) your longitudinal
value will be -60 000Y
25
24
26
27
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X Axis
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South African Lo System
Y Axis
Lo 25
Longitudes
Equator with a value of 0 meters
Every odd degree is a Central Meridian with a
value of 0 meters
Q
Latitudes
The latitudal value is measure on the X Axis from
the Equator which has a value of 0 meters. Thus,
values to the north of the Equator will be
negative, and values to the south of the equator
will be positive. This means that if you measure
a distance of 3 760 000m from the Equator (0)
your latidudal value will be 3 760 000mX The
coordinate for Q will than be -60 000Y 3 760
000X Note When using Lo coordinates in a GIS you
need to swap X and Y around. In a GIS X is always
your longitude and Y is always your latitude. The
signs will also change X is always positive and Y
is always negative.
25
24
26
27
28
X Axis
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UTM in South Africa
X axis
Equator with a false northing value of 10 000 000m
GRID ZONE 35H
Q
Central Meridian with a false easting value of
500 000m
Y axis
Your longitudinal value will be your Easting,
measuring on the X axis from you central
meridian. If you measure 138 000m from the
central meridian (east towards Q) Your Easting
will be 500 000m 138 000m 362 000m. Your
latitudal value will be your Northing, measuring
on the Y axis from the Equator. If you measure 3
769 000m from the equator (south towards Q) Your
Northing will be 10 000 000m 3 769 000m 6 231
000m Your Coordinate will be 362 000E 6 231
000N Note UTM coordinates will never have
negative values for general use, but when used in
a GIS the Latitude (Northing) will take a
negative sign.
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Term definition

• Map units are the units which the spatial data
  is stored in
• Map scale is the relationship between the
  dimensions of a map and the dimensions of the
  Earth
• Distance units are the units used by ArcGIS to
  report the result of operations (e.g. measurement
  (measure tool), dimension of shape (draw tool),
  dimension of selection box (select feature tool))

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http//ebookbrowse.com/an-introduction-to-coordina
te-systems-in-southafrica-pdf-d376434007
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Introduction
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Co-ordinate System 1
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Co-ordinate System 2
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September 2007
Kroonstad
Malmesbury
Stellenbosch
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Applications of TrigNet data

• Post processing applications
• Surveying and GIS
• Atmosperic science
• Monitoring of atmospheric water vapour for
  climate monitoring
• Monitoring of ionosphere for communication and
  positioining
• Geophysics
• Long term monitoring of station positions plate
  techtonics
• Real time applications
• Surveying and GIS
• Navigation
• Weather forecasting ionosphere mapping
• Timing

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Conclusion

• The passive network of Trigonometrical beacons
  has served
• South Africa well for nearly 100 years.
• There is a confidence that TrigNet will serve
  the country just
• as well.
• The services available from TrigNet are easily
  available.
• NTRIP is state of the art in real time
  service provisison.
• The applications of TrigNet are not confined
  to positioning.
• A rebuild is planned to accommodate GPS
  modernization,
• GLONASS and Galileo.

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Co-ordinate System

• Hartebeesthoek 94 will remain the
• official co-ordinate system

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Definitions

• TrigNet network of continuously operating GNSS
  base stations covering SA
• GNSS Global navigation satellite system
• CDSM Chief directorate surveys and mapping
• ITRF international terestrial reference frame

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When adding data that doesnt have a
datum/coordinate system to ArcMap the Following
message appears.
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Go to the toolbox to project/transform your data
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Before transforming your data, you may want to
look at your data/layer properties
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You may want to create a custom geographic or
projected coordinate system/transformation
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These are the parameters for a geographic
coordinate system based on the WGS 1984 ellipsoid
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These are the parameters for a projected
coordinate system (UTM zone 40S) based on the WGS
1984 ellipsoid
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Your input layer may be geographical and your
output layer my be projected
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Sometimes it is better just to define a new
projection for your layer
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It is also possible to import spatial
references/parameters from an existing layer when
transforming your data
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