Projections

 

Cartographers are challenged to represent 3-dimensional information (the earth’s surface) in two dimensions (a piece of paper). One solution to this problem is to use a globe rather than a plane. Globes provide the smallest distortion of features, however globes are expensive, difficult to mass produce, bulky, difficult to use to measure distances and features, and the user is unable to see objects on both sides of a globe at the same time. However, the earth is not flat. Therefore, in order to depict a three-dimensional object on a flat plane like a piece of paper, you must project it. Projections need to accurately portray the surface of the earth in terms of:

  1. Shape
  2. Area
  3. Distance
  4. Direction

Why are there so many projections?

When three dimensions are reduced to two, one or more of these characteristics will be sacrificed. Therefore, projections are created and used to accurately portray characteristics that are most important. For example…

Conformal Projections

  1. Preserve local shapes
  2. To preserve individual angles describing the spatial relationships, a conformal projection must show graticule lines intersecting at 90-degree angles on the map
  3. The drawback is that the area enclosed by a series of arcs may be greatly distorted in the process

Equal-Area Projections

  1. Retain all areas at the same scale – all other properties are distorted
  2. In some instances, especially maps of smaller regions, shapes are not obviously distorted, and distinguishing an equal area projection from a conformal projection may prove difficult unless documented or measured

Equidistant Projections

  1. Preserve distance between certain points – scale is not correct except along specific lines which are based upon which projection is used
  2. No projection is equidistant between all points on a map

True-Direction Projections

  1. The shortest route between two points on a curved surface such as the earth is along the spherical equivalent of a straight line on a flat surface – called the great circle
  2. True direction – or azimuthal – projections maintain some of the great circle arcs

How can I choose a map projection?

The purpose of the map, its scale, and the geographic extent of the mapped area dictate the selection of a map projection.

Purpose Key Feature Projection
Navigation True direction Mercator
Road Maps Equidistant Azimuthal
Thematic Map Conformal (preserves shape) Lambert, Mercator
Thematic Map Equal-area Cylindrical, Albers

 

What happens if I mix projections?

The simple answer is that the data will not overlay, as shown in the following figure.

 

 

 

I have heard of Universal Transverse Mercator (UTM). What is that about?

UTM is a specialized application of the Transverse Mercator projection. The globe is divided into 60 north and south zones with each having its own central meridian. The origin for each zone is its Central Meridian and the Equator. To eliminate negative coordinates, the coordinate system alters the coordinate values at the origin. The value given to the central meridian is the false easting, and the value assigned to the equator is the false northing. A false easting of 500,000 meters is applied. A north zone has a false northing of zero, while a south zone has a false northing of 10,000,000 meters.

Properties

  1. Shape – UTM is conformal – shapes are preserved in small areas
  2. Area – minimal distortion of larger shapes occurs within the same zone
  3. Distance – local angles are true
  4. Direction – Scale is constant along the central meridian, but at a scale factor of 0.9996 to reduce lateral distortion within each zone

Limitations

  1. Designed for a scale error not exceeding 0.1 percent within each zone
  2. Error and distortion increase for regions that span more than one UTM zone – UTM is not designed for areas that span more than a few zones