# Identifying urban centers using an algorithm based on topological prominenceApril 27, 2012 1:51 PM   Subscribe

Calling geographers: has anyone applied the idea of topological prominence to population density?

One of the most common ways of measuring a mountain is to draw a line from its peak to the next-highest mountain, then calculate the height of the mountain above the lowest point on this line. This method -- topological prominence -- ends up being a better way to identify interesting mountains than by measuring height above sea level.

I am curious if anyone has applied the idea to population density, rather than physical height. I think it would be interesting as a totally fair method for drawing the boundaries of urban areas. For example, a point of 100 people per square mile in an otherwise rural area is probably a major cultural and social center, while a point of 1000 people per square mile in a region of mostly 900 people per square mile is probably not even worth mentioning on the map.

I can't find any references to this idea online. It probably has a different name in human geography than in physical geography.

There's lots of stuff about using Voronoi diagrams to locate population centers, and k-means clustering and such, but none of those give you the equivalent of a "height" of a point above its surroundings.

If anyone has made a map of the "population prominence" of the United States, I'd be very interested.
posted by miyabo to Science & Nature (7 answers total) 11 users marked this as a favorite

I haven't seen a map of this, but all you would be making is a map of relative densities, color coded for percent difference not absolute difference, or a heat map, right? It should be fairly easy to do in GIS; you might want to normalize for some overall average, so as to capture both areas of unusually lower as well as higher densities.
posted by Forktine at 3:33 PM on April 27, 2012

For example, a point of 100 people per square mile in an otherwise rural area is probably a major cultural and social center, while a point of 1000 people per square mile in a region of mostly 900 people per square mile is probably not even worth mentioning on the map.

But according to your system, the second point would have prominence 100 and the first point somewhat lower. Do you want to divide instead of subtract?
posted by escabeche at 6:59 PM on April 27, 2012

Sounds like you might also run afoul of the modifiable area unit problem. What's the geographical basis for your population units?
posted by mollweide at 7:27 PM on April 27, 2012 [1 favorite]

Sounds like you might also run afoul of the modifiable area unit problem. What's the geographical basis for your population units?

This is a really good point. I work with geographical information all the time, and I was translating physical data sets (eg 10m DEMs or LiDAR data sets) to population; if population densities were available for every square mile/kilometer like elevation is, you'd be golden. But all of the population data I have seen are by political unit (eg census tract, zip code, county, state, etc), making it really hard to make a useful map of relative densities.

Even so, mapping the relative densities of the smallest unit available (nationally, that would probably be census tracts, no?) might produce an interesting map, especially at the metropolitan level.
posted by Forktine at 8:19 PM on April 27, 2012

Response by poster: Thanks everyone... I obviously haven't thought about this enough yet, but I think there might be something useful in there.
posted by miyabo at 8:59 PM on April 27, 2012

I haven't heard of anyone doing this before, but what you described reminds me a bit of calculating topographic position using map algebra on a raster elevation model. If you calculate the difference between a pixel's elevation and the average elevation of a given radius around it, you can determine the locations of ridge tops and canyon bottoms. The areas that fall outside of these can then be classified according to slope.

Applying this thinking to population, you could map relative population densities using dasymetric mapping. With this, you take something like population counts in Census blocks and assign it to pixels according to relative weights assigned to land cover classes. So if you have four land cover pixels in a Census block, with three forest pixels and 1 urban pixel, there's a good chance your population is located in the urban pixel.

Once you've done this, for each pixel you can use a moving window analysis to calculate (focal pixel population - avg population in radius surrounding pixel) to determine local population high or low points.

This might not make any sense if you're not a GIS/map algebra nerd. I have population density mapped in 100m pixels for Arizona from 1990 and 2000 Census block data. - if I get some time, I'll play around with this and let you know if any interesting trends pop up.
posted by indeterminacy at 3:20 PM on April 28, 2012

here is a 3d population density map that may be an example of what you're looking for?
posted by figTree at 7:55 PM on May 29, 2012

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