Coordinate Systems

1. Coordinate System
&
Geo-Referencing

2.  Geographic (GCS)
◦ Degrees……
 Projected (PCS)
◦ Meters, feet….

3.  A GCS is a three dimensional
“spherical” surface used to
define a location on the
earth by:
◦ Equator
◦ Prime meridian

4.  A point on the earth is
referenced by
longitude and latitude
values, angles
expressed in degrees
 LONGitude: angle
measured on the
sphere from the prime
meridian
 LATitude: angle
measured from the
equator
equator
Prime meridian

5.  Parallels: horizontal lines of equal latitude
 The line of latitude midway between the
poles of the sphere is the equator (latitude
=0)
 The equator (latitude =0) divides the
sphere in north (top) and south (bottom)
latitude sides
 Meridians: vertical lines of equal longitude
 The conventional line of 0 longitude is the
prime meridian
 The prime meridian divides the meridians
in a west (left) and east (right) sides of
longitude
 Parallels and Meridians form the
geographical grid with the origin (0,0) at
the intersection of the equator and the
prime meridian

6. For most of the GCSs, the
prime meridian is the line of
longitude passing through
Greenwich (UK)

7.  Latitude and longitude are
measured in degrees, minutes
and seconds (DMS) or decimal
degrees (DD)
 Longitude ranges between -180°
(or 180 west) and +180° (or 180
east)
 Latitude ranges between -90° (or
90° south) and +90° (or 90°
north)
 Above and below the equator the
latitude lines (circles) gradually
become smaller
 Only along the equator one
degree of latitude represents the
111.12 Kilometers)

8.  The GCS surface is:
◦ Ellipse defined by two radii, the
longer radius is the semi major
axis (a), the shorter is the semi
minor axis (b)
◦ The rotation of an ellipse around
its semiminor axis creates an
ellipsoid
◦ An ellipsoid is defined by the two
axes, a and b or by an axis and the
flattening, f
f= (a-b)/a
a
b

9.  The earth has been surveyed many times,
by many topographers
 we have many ground measured ellipsoids
representing the shape of the earth
(International 1909, Clarke 1866, Bessel)
 Each of them has been chosen to better fit
and cartographically represent one limited
region in the world
 Because of gravitational and surface feature
variations, the earth can not be a perfect
ellipsoid; satellite technnology allowed the
creation of new and more accurate
ellipsoids for worldwide use
 the most recent and the most widely used
is the one defined in the World Geodetic
System of 1984 (WGS 1984 or WGS84)

10.  A geographic position on the
earth is defined by:
◦ Latitude from the equator
◦ Longitude from a prime meridian
◦ A specific GCS
 A position on the earth could
have different longitude and
latitude if the GCS is different
 The difference is always around
seconds or fractions of a second
 The error of setting a wrong
GCS in a GPS system could
affect the coordinates on a map
even of hundred meters
equator
Prime meridian

11.  An ellipsoid approximates the shape of the earth.
It is the mathematical or geometrical reference surface of
the earth.
 A Datum
◦ defines the ellipsoid and the position of the ellipsoid relative
to the center of the earth
◦ The center of the earth is defined as its center of mass as
calculated by satellite measurements
◦ Provides a frame of reference for combining data from
different GCS
◦ The most widely used datum is the WGS84
◦ WGS84 it is the framework for locational measurements
worldwide

12.  A geographic position on
the earth is defined by:
◦ Latitude from the equator
◦ Longitude from a prime
meridian
◦ A specific DATUM or GCS
 Ellipsoid
 Relative position according to
WGS84

13.  To preserve or measure some
properties (distance, area, shape,..)
on maps we need a PCS
 A PCS is defined on a flat two
dimensional surface
 Locations based on x,y(,z)
coordinates on a grid/cartesian
plane
 The grid is made by a network of
equally spaced lines (same
distances between horizontal and
vertical)
 Based on a GCS

14.  The ellipsoid is transformed from
a three dimensional surface to
create a flat map sheet
 This mathematical transformation
is commonly referred to as a map
projection
 Like shining a light through the
earth surface casting its shadow
onto a map sheet wrapped around
the earth itself
 Unwrapping the paper and laying
it flat produces the map
 A map projection uses
mathematical formulas to relate
spherical coordinates on the globe
to flat, planar coordinates.
 Representing the earth’s surface in
two dimensions causes distortion
in the shape, area,distance, or
direction of the data.

15.  Different projections cause different
distortions
 Projections could be:
◦ Conformal
 Preserve local shapes, mantaining angles
 Meridians and parallels intersect at 90° angles
◦ Equal area
 Preserve the area
 Meridians and parallels may not intersect at right angles
◦ Equidistant
 Preserve distances betweeen certain points
 No projection is equidistant for all points in the map

16.  Some of the
simplest
projections are
made onto
developable
shapes as cones,
cylinders, and
planes, tangent or
secant to the earth
ellipsoid

17.  Samples of
projections

18.  Universal Transverse Mercator:
 Central meridian as the tangent
contact
 Developing the cylinder creates
distortion:
◦ used for an area spanning 3° east
and 3° west from the central
meridian
◦ Used for representing lands below
80° of latitude
 The earth is divided into 60
zones each covering 6° of
longitude

19.  a

20. x,y x,y

21.  Why considering coordinate systems, projections
and transformations?
◦ Locating correctly a GPS point onto a map
◦ Overlaying different map data sources (a vegetation map, a
soil map, etc. )
◦ Performing spatial analysis
◦ Deriving coordinates using a topographic map in the field
◦ Specifying coordinates without errors

22.  equipotential surface of the Earth
gravitational field that most closely
approximates the mean sea surface
 The geoid surface is described by geoid
heights that refer to a suitable Earth
reference ellipsoid
 Geoid heights are relative small, the
minimum of some -106 meters is located at
the Indian Ocean, the maximum geoid
height is about 85 meters.
 Elevation/altitude is measured above mean
sea level (AMSL)

25. global map with geoid heights of the EGM96 gravity field model,
computed relative to the GRS80 ellipsoid