How Much Length Do You Really Need? Ahhh, Shoreline Length That Is!

One of the questions that we often get here at Digital Coast  is, “How long is the U.S. shoreline?” My joking answer back is, “How long do you need it to be?”

All joking aside, giving a one number answer for that question is clearly impossible. The shoreline length paradox is quite interesting for geospatial geeks. It’s obvious when you really think about it, but it often perplexes lay people. Can you imagine us telling Congress that we don't know the length of the U.S shoreline? So the number is…drum roll please…95,471 statue miles of shoreline (The Coastline of the United States NOAA/PA 71046, 1975).

The Legend Around Shoreline Length Measurement

Legend has it is that this was collected back in the 1960s at NOAA by the premier nautical cartographer, Aaron Shalowitz, using the state of the art technology to hand roll a mechanical measurement wheel around the largest scale nautical chart. In my imagination, I can see the the large paper charts laid out on beautiful wooden map tables, the cartographers sitting side by side, the scratching of the paper, creaking of the instruments, and maybe an occasional grunt as an error was made and the measurement was forced to start over. Nostalgia aside, I can imagine because it was just like my own cartography classes long before the digital revolution.

The Shoreline Length Paradox

To explain the shoreline length paradox, you have to examine what happens with shoreline length at different map scales. Look at a coastal map for any given area for which you know the map scale. A common source might be a NOAA nautical chart or a USGS quad. The shoreline data for a large scale map (for example, 1:10,000) shows lots of details. You see the nooks and crannies of the shoreline with small inlets, islands, and maybe even rocks that have significance for navigation. Now look at that same area on a map used for world views (1:100,000,000). The shoreline is smoother with less details. Lots of details are eliminated for clarity's sake.  

In case you thought this was really straightforward and analytical, let's throw another curve ball. What is the definition of shoreline? How far inland does it go? You often hear “Head of Tide” as an inland extent of shoreline. You need a salinity measurement to calculate it and it doesn’t exist for every coastal river or stream.

Wait, there’s more. What happens to the shoreline data measurement when the tide goes in or out? There is a whole other body of science around tidal measurements that impacts shoreline measurement. Imagine measuring the shoreline at the Bay of Fundy during low tide vs. high tide.

Say It Ain’t So. Maps Aren’t Real?

Maps are just “models” of reality and are inherently inaccurate. That last sentence is important enough to read a second time. The lay person often thinks that once it's on a map, it's “gospel.” It's not practical to make a map at the scale of reality (1:1) and trace every intricate shoreline detail. Or, if you want to really think deeply, the mathematician Mandelbrot used shoreline in explaining infinite fractal curves. When you start tracing the line through the grains of sand or into the molecular structure, what happens to the length?

So all this talk of fractals and sand is hurting my head. Anyone working in the geospatial field knows that with better data and modern technology, we can improve our measurements. But the answers could be highly politically charged as boundaries, ownership, money, and natural resources might be tied to the measurements. What would the ripple effects be if new data were introduced? Would it really matter, since it's all relative?  

This paradox is just one reason that I love the field of cartography. It's both an art and a science, and working in the coastal zone is especially interesting. Here at Digital Coast, we're in the business of helping people use maps for decision making. Sometimes that means not always giving them the most detailed data, information, or tool. It’s hard to back away from the most accurate, highest resolution, but often that is the most useful position to take.

I'm still trying to contemplate the impacts of digital data. Is that helping mask the paradox or making it more complex? Let me know what you think my answer should be next time I get the question on shoreline length!

Want to Learn More?

• Coastlines by Mark Monmonier – An enjoyable read and very timely considering all the climate-induced shoreline changes.
• NOAA Shoreline Website – The One NOAA shoreline site has info on different shoreline data products and intended use.
• Shore and Sea Boundaries by Aaron Shalowitz – Out of print, but available online for a fascinating read into the technical and legal issues surrounding coastal mapping.