GIS Data and the Coastline Paradox

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Imagine that you’re taking a GIS class and your instructor tasks everyone with coming up with the answer to, “what is the length of the coastline of Maine?”  Everyone downloads a different GIS data set to calculate the length and everyone comes back with a completely different answer to that question.

The phenomenon is known as the Coastline Paradox. This phenomenon has raised interesting questions in the world of Geography and how differing resolutions of data covering the same geographic area can yield remarkably different measurements of length. Questions such as: “How long is the coastline of Australia?” or “did you know that the coast of the U.S. state of Maine is longer than the coast of California?” become harder to answer consistently and depend greatly on the resolution of the GIS data used to measure the coastlines in question.

So what is the Coastline Paradox?  It is a paradox that occurs when measuring a coastline that causes the total length of the coastline to increase each time you measure it with a smaller unit of measurement, due to the extra features that can be measured.

What does that mean? Just imagine you were told to manually measure the length of a jagged feature maybe a map and you have got no ‘thread’ to measure with. What do you do? You get a meter rule, right? However, the result you get will now be based on the length and size of the rule you use. The smaller the meter rule the more precise your measurement will be and vice versa. Using a few straight lines to approximate the length of a curve will produce a low estimate. That is why you use a thread to get the most precise measurement possible.


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The coastline is the most obvious example of this situation due to its fractal-like (jagged recurring pattern) properties. This phenomenon was first observed by Lewis Fry Richardson (1881 – 1953) and is sometimes referred to as the Richardson effect.

The advancements in technology and computing and its consequent adoption in the field of geography especially the visualization and management of geographically referenced information which includes GPS (global positioning systems) data and remotely sensed imagery with the use of software specifically geographic information systems (GIS) and remote sensing (RS) has really increased our ability to create maps of the world’s coastline in a more precise way and in some way deal with the paradox to a large extent.

So the next time you are tasked with measuring the length of a coastline, river, or other lengthy feature, consider the resolution of the GIS data you need to use.  As discussed in an earlier article, larger scale GIS data sets tend to show more detail than smaller scale data.

Coastline paradox

An example of the coastline paradox. If the coastline of Great Britain is measured using units 100 km (62 mi) long, then the length of the coastline is approximately 2,800 km (1,700 mi). With 50 km (31 mi) units, the total length is approximately 3,400 km (2,100 mi), approximately 600 km (370 mi) longer. Source: Wikipedia

References

Coastline paradox: http://en.wikipedia.org/wiki/Coastline_paradox

Fractal: http://en.wikipedia.org/wiki/Fractal

Mandelbrot, B. B. “How Long Is the Coast of Britain.” Ch. 5 in The Fractal Geometry of Nature.  New York: W. H. Freeman, pp. 25-33, 1983.

Mapping Monday: The Coastline Paradox: http://blog.education.nationalgeographic.com/2013/01/28/mapping-monday-the-coastline-paradox

Coastline paradox: http://mathworld.wolfram.com/CoastlineParadox.html

The Coastline Paradox: How can one coastline be two different lengths?: http://www.richannel.org/the-coastline-paradox

What Is The Coastline Paradox?: http://www.youtube.com/watch?v=I_rw-AJqpCM


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