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EESC 3750 - Geographic Information Systems: Projections

EESC 3750; ANTH 3445: Introduction to GIS: Instructor: Rebecca Boger

Projections Activity

Map Projections

Representing the surface of a sphere on a flat surface of paper requires the mapmaker to make many decisions.  In these decisions, she is creating a simplified 2D model of a 3D reality. Projections are tools that are selected for the "modeling" task at hand.

Map projections that are used today have ancient roots. The simplest projection, and the one that is used frequently to display climate model simulation results is the Equirectangular projection (Equidistant Cylindrical Projection). This map projection was invented about 100 AD by Marnius of Tyre.

Equirectangular projection of the world

(Image Source: Wikipedia By Daniel R. Strebe)

Its called equidistant because the Earth is displayed as a rectangle, and the lengths of degrees of latitude and longitude are the same everywhere.

Bill Hay, a retired Earth Scientist and author of Experimenting on a Small Planet, notes that Claudius Ptolemy (Alexandria, 90-168 AD) who produced an 8 volume geography of the known world, noted that this projection "as the worst representation of Earth he knew of," (2013:31). He points this out because the distortion built into this map creates the false impression that the higher latitudes are much more important than they really are to climate, because the land area poleward of 30 degrees N and S displays 2/3 of the land area, yet 1/2 of the land area actually lies between 30 degrees north and south.

(Image source: Wikipedia By Eric Gaba) 

Equirectangular projection with Tissot's indicatrix of deformation

Why then, is this projection used, if it was deemed so terrible a couple of thousand years ago? It has become an industry standard in thematic mapping, because it is relatively simple using a raster dataset to georeference an image pixel on a map from its location on Earth. (More about georeferencing next week!).

What would this map be terrible for? Its not particularly good for navigation, which is probably what Mr. Ptolemy was referring to in his criticism- GIS had not been developed yet! This example shows pretty clearly that every map has its trade-offs!

Mercator projection of the world between 82°S and 82°N.

 

(Image Source: Wikipedia By Daniel R. Strebe)

The map you might be most familiar with is the Mercator projection, created by Gerardus Mercator in 1569. You'll notice that it is often cut off at 60 or 80 degrees north and south, because of the significant distortion at higher latitudes. This map was created for navigation by sea-as it allows a sailor to keep on a bearing, without changing the direction as measured relative to magnetic north.

 

Mercator 1569 world map (Image Source: Wikipedia Public Domain)

 

 

 

 

 

A third projection we will talk about is the Mollweide equal area projection.  it preserves the correct areas of lands and oceans at the expense of shape distortion. It is particularly useful for maps that display global distributions:

(Image Source: Wikipedia By Daniel R. Strebe)

Equirectangular projection of the world

 

(Image Source: Wikipedia By Eric Gaba, as username Sting)

Mollweide projection with Tissot's indicatrix of deformation

 

 

 

 

 

 

What about those funny orange spots on the maps? Nicholas Tissot (1859 & 1871) developed the indicatrix of deformation- A single indicatrix describes the distortion at a single point. Because distortion varies across a map, generally Tissot’s indicatrices are placed across a map to illustrate the spatial change in distortion. Looking at these projections with the Tissot's indicatrix provides a quick overview of where map projection distortion is most significant.

Map Projections

When we plot 3-D to a 2-D map, we need to make decisions about how to flatten out the Earth’s ellipsoid.

As a result, there are compromises that are made to the geographic integrity, when 3D is flattened out to 2D. The choice is yours to determine which projection is appropriate to your task.

Concept of the datum:

In surveying, the surveyor is able to calculate the location of the feature she is spotting by calculating it’s distance from a known reference, known as a datum. The Datum is the basis for any mathematical model that is used to reference locations and coordinates in a geographic coordinate system.

Fun facts:the Earth is an oblate spheroid- the difference between the equatorial and polar diameters is 43 km; the average diameter of the earth is 12,742 km. If you multiply this by 2 pi you get a circumfrence of 40,000km. An even number? This is because the meter was originally defined as 1/10,000,000 of the distance from the equator to the North Pole as measured on the meridian passing through Paris France.