GIS Data and the Coastline Paradox

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By: Joe Akintola

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.

What is the Coastline Paradox?

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 ruler, right?

However, the result you get will now be based on the length and size of the rule you use. The smaller the ruler 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.

A large scale map (L) and a small scale map (R) of Point Sur, California from the USGS.
The length of a coastline will vary depending on how precisely the individual nooks and crannies are measured. The 1:100000 scale USGS map on the left shows far less detail than the 1:24000 scale map of Point Sur in California. If you were to measure the length of the coastline at Point Sur using the larger scale map, you will end up with a smaller length than if you measured the more detailed and smaller scale map on the right. Maps; USGS Topo maps.

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:


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.

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