Representing Location
Geographic information held in a computer must be able
to be located. Locating geographic information is achieved via mapping it against
some sort of coordinate
system. Any computer system that is able to work with geographic information
must, therefore, be able to create a coordinate
system space into which the
geographic information can be mapped.
In its simplest form, a map can be thought of as nothing more than a two-dimensional
space, with an x and y axis, into which locations of features can be plotted.
As long as the units of the x and y axes are known and a system exists by which
the values along the x and axes can be translated from the map space to a real
location on ground as a map coordinate system, the map forms a valid representation
of real world location.
There are, however, two significant problems associated with plotting real
world locations using such a simple, two-dimensional map coordinate system:
a. The Earth is not a flat, two-dimensional object – it is a three
dimensional
ellipsoid (a sphere that has
been squashed slightly so that the distance around the equator is slightly
further than the distance around the poles).
b. There is no single, correct, description of the shape of the Earth – instead
there are a large number of slightly different ellipsoid descriptions that can
be used.
If we are going to successfully plot the locations of features on the Earth
using a system of two-dimensional coordinates in a computer, the computer
needs to
have methods for reducing the description of a location on the Earth’s
surface from three dimensions to two, and needs to know the shape of the Earth
that it will be locating information on.
Choosing the Earth’s shape
The Earth is wider at the equator than at the poles as a result of centripetal
forces caused by it spinning. Working out just how much wider at the equator
it is has consumed geodesists for centuries. They have been responsible for
working out the ellipsoid models
(a mathematical description of the shape of the Earth) to be used in mapping.
Historically, the shape of the Earth has
been estimated by observing the movement of stars from many different locations
on the Earth's surface. As the technology for stellar observation has
improved, so the ellipsoid models
have improved. The result has been a large number of slightly different ellipsoid shapes.
Since the advent of satellites, it has been possible to calculate the shape
of the Earth from space. The resulting
ellipsoid model is called
the World Geodetic System 1984 (wgs84)
and this Earth shape is fast becoming the standard used across the world in
mapping.
The good news is that the hard work has been done and deciding on the shape
of the Earth to be used in a map simply involves selecting an ellipsoid model
from one of the many available.
Reducing dimensions via map projection
Once the ellipsoid to be used has been decided all that remains is to find
a way of squashing the 3D ellipsoid shape into 2D map space. The problem is
known as map projection. The process can be grasped by attempting to squash
the skin of half a grapefruit (effectively half of the Earth’s surface)
onto a flat surface. Necessarily, the grapefruit skin must be deformed by a
process of stretching out at the edges and squashing in at the center and the
process can be aided considerably be cutting the skin in places.
Map projections perform a very similar process to squashing and cutting a grapefruit
skin. In map projections the ellipsoid is distorted mathematically to reduce
it to a flat surface. You can perform the most simple map projection yourself
by creating a map space with the units of the x and y axes set as degrees.
The latitude (x axis) and longitude (y axis) locations of features to be mapped
can then be plotted directly onto the axes to produce a map. This sort of map
projection is called a geographic projection. The problem with this simple
projection when plotting at a global scale is that it distorts the size of
the polar regions of the Earth relative to the equatorial regions – making
them much larger than they really are. As a result, more complex projections,
that aim to minimize the relative distortions of feature sizes or shapes have
been produced and a wide range of these are used in map production.
So what has all this got to do with geographic information systems?
Geographic information is information that can be located. It should now be
apparent that locating geographical information can be achieved by plotting
locations within a simple, two-dimensional coordinate
system. However, this
system is a simplification of the true three-dimensional nature of the Earth’s
surface. All maps require an ellipsoid and
a map projection to achieve
the simplified 2D representation.
A geographic information systems uses a known ellipsoid and map projection
system to represent the geographic information.