Georeferencing, Datums & Projections
This module covers three related topics: georeferencing, datums and projections. Georeferencing and datums pertain to “location” and projections are the means by which features from the surface of the earth (or globe) are transferred onto a sheet of paper to make a map.
Georeferencing is a means to provide a reference (name, address or coordinate) for a geographic location. There are several systems, which can be divided into two general categories: metric and non-metric.
· Metric, in this context, can be equated to ‘measure’. Latitude/longitude are measured in degrees (i.e. angles) and UTM coordinates are measured in metres.
· Non-metric systems may be more familiar to us. Examples include place names, addresses, postal codes and landmarks. Many of these non-metric systems can be used in a GIS. There are several GIS applications that utilize non-metric systems; examples include marketing, enumeration/politics, and economic analysis, based on postal codes, addresses or census tracts. Note these examples are cultural in nature. For natural resources, metric georeferencing is dominant. Note that metric georeferencing will still be the underlying base for cultural applications, even if use is made of postal codes or street addresses.
Datum is a reference surface used to generate coordinates (i.e. latitude and longitude). Latitudes and longitude are angular measures, given in degrees. Although latitudes/longitudes are really determined from the surface of the earth, it is easier to imagine yourself in the centre of the world looking out at the earth’s surface.
Imagine looking out at the equator. You would be looking straight out (i.e. flat), therefore your angle would be zero – indeed this is the latitude of the equator. Now imagine looking at VIU (in B.C. Canada). You would be looking up at an angle of about 49 degrees (latitude) from the equator. Looking straight up at Santa’s workshop equates to a right angle, or 90 degrees.
For longitude you start by looking out at Greenwich, England. That is your zero degree mark. As you turn towards the Atlantic Ocean you are turning west. Central America has longitudes around 90 degrees west. Note that 90 degrees East Longitude would run through Asia. So Longitudes go off in both directions from Greenwich and meet in the Pacific at 180 degrees (the international dateline). If the world was perfectly round we could stop here. Unfortunately …
… the world is not a perfect sphere. It’s more of an ellipsoid. This is because the earth is not a hardened rock (centre is molten, also surface is about 75% water). Since the earth spins, centrifugal force pulls out the earth at the equator. But wait, it gets uglier yet. The surface of the earth, and therefore the shape of the earth, is essentially mean sea level (m.s.l.). M.S.L. is determined not only by centrifugal force (pushing out at the equator) but also by earth’s gravity (that force that makes apples fall down instead of up). Here’s the kicker … m.s.l. is not a smooth, perfect ellipsoid. It is essentially a dented ellipsoid (more properly known as a geoid). This is because gravity is not constant. Mass and density of an object determine gravity. The density and mass of the earth’s crust varies,
· therefore, gravity varies,
· therefore, m.s.l. varies,
· therefore, the earth’s surface is an ellipsoid with slight undulations.
It is easy to determine the latitudes and longitudes (a.k.a. the graticule) for a sphere. Figuring out the graticule on an ellipsoid is a manageable task. But determining the graticule on the irregular geoid is very complicated. In the end it was decided that for small-scale maps a sphere would do just fine, but for medium and large-scale maps (1:250,000 to 1:5,000) an ellipse would be more accurate. (The math for the geoid is just too complicated to bother with).
The only complications are:
1. An ellipse that best approximates North America is not the best ellipse for Europe. Thus each part of the world uses its own ellipse. The ellipse used and how it is anchored to the earth is what is known as datum.
2. Our understanding of the earth’s true shape continues to change as technology changes – thus new datums continue to be developed.
For example, the datum (i.e. ellipse) used for North America in 1927 was based on an ellipse developed in 1866. This was known as NAD27 (for North America Datum 1927). After satellites were deployed and better measures of the earth were acquired, a new ellipse was developed in 1980. In 1983 it was decided to use this new ellipse for mapping in North America. The new datum is known as NAD83. Belize City did not move between 1927 and 1983. However, Belize City has different latitude and longitude under NAD83 than it did under NAD27. Indeed, some places in North America had a difference equivalent to 300 metres.
Datums have ‘nothing to do with’ distortions – they have ‘everything to do with’ location … specifically the coordinate (lat/long) of a feature on the earth’s surface. Datum is the choice of ellipsoid to use. As the graticule (latitude/longitude) varies from ellipsoid to ellipsoid, changing datums will change the coordinates of a feature on the earth’s surface. Therefore, when features from different maps are combined onto one map (i.e. for an analysis in GIS) it is essential that the maps be of the same datum.
Projection is the means by which features on the earth’s surface are transferred from the globe onto a flat sheet of paper. It is actually accomplished with mathematical transformations. In your life you will most likely never have to worry about the mathematics of projections. The concepts are better understood by the classic demonstration of wrapping a big piece of ‘photographic’ paper around the globe, turning a light on that is inside the globe, and thus developing an image of the world onto the ‘photographic’ paper. Projection basics are as follows:
·
Four properties that can be distorted include
area, shape, distance and/or direction. Simply put, a map is not a perfect
representation of the features on the surface of the world – the globe is far
more accurate. However, globes are restricted
to relatively small sizes, an accurate globe is very expensive to make and
globes have limited practical use (primarily for display, measurements of
length, area and direction are more challenging).
·
Projections are designed such that one or more
of these properties suffers little (no) distortion. Two important projection types are conformal
and equal-area. Each of these two
projection types is suited to particular uses.
Conformal maintains shape and direction and is well suited to
navigation. Equal-area is obviously well
suited to uses where area calculations (i.e. absolute size of polygons) or
density values (i.e.
number of trees per hectare) are important.
·
Projections can be envisioned as a large piece of
‘photographic’ paper (a.k.a. developable surface) wrapped around a globe. A light inside the globe is turned on and
features on the surface of the globe are projected onto the photographic
paper. The photographic paper generally
takes 3 shapes: cylinder, cone or just left flat. These three shapes are known as developable surfaces because they can be
(unwrapped) laid flat without tearing or distortion – as compared to ‘peeling’
the skin off the globe and trying to lay it flat on a table with tearing. Cylindrical and conic projections are most
common. A cylinder will touch (be
tangent) along the equator and is thus best suited to equatorial regions of the
world. A cone will rest on the globe at
mid-latitude. Thus it is well suited to
countries in the mid latitudes and especially those with a wide east-west
dimension (i.e. Canada, China).
·
Another factor to consider with projections is
where the developable surface touches the globe, i.e. where it is tangent. Along lines of tangency there is no
distortion as the map in this location is a ‘contact print’. The further away from the tangent line(s) the
greater the distortion of the map properties (area, shape, distance and/or
direction). Areas near the equator are
best represented on a map using a cylinder that wraps around this equatorial
region. Areas at mid latitudes are
better represented with a conic map projection as a cone will rest (be tangent)
in this area. And polar
regions are well represented by planar (azimuthal)
projections that utilize a flat developable surface that rests on the pole.
· Deciding which projection is best requires that you consider:
o Which property is to be preserved
o Location (primarily latitiude) of the area of interest
There is much more to projections, but I promised not to emphasize this topic, so I’ll stop here.