Inspired Stone


Geomorphometry

As I continue to think and learn about terrain analysis and geomorphology (see these posts), I find that the issues are complicated. My first project was to develop an algorithm to extract ridge lines from a digital elevation model (DEM). The first ingredient for such an algorithm is a clear definition of what a ridge is and I came to realize that the way I identify a ridge is rather ambiguous. At first I thought that a ridge would be any place with a certain convexity, but as you can see in the image below, two terrain features with the same convexity might be classified as different things.

The iconographic ridge is long, straight and sharp at its apex, like many ridges of the High Sierra. As the ridge becomes more broad and rounded, at some point the landform will be identified as a hill rather than a ridge. But what is that point? This issue has been considered by others. I recently found a book, “Geographic Information Science and Mountain Germorphology”, in which a chapter was co-authored by a philosopher and dealt with the ontology of topography and how we as humans identify objects such as mountains or canyons that don’t have a clear boundary.

Despite all that, I still did my best to write some code that would isolate what I would identify as a ridge in some mountain terrain. Here’s the best I’ve come up with so far with the “ridges” being the white lines or points:

On the left is the raw elevation data. On the right is roughly how I would identify the ridges by hand and in the middle is the result from the computer identification. You can see that the main features are there, but there seem to be many extraneous points and some of the main ridges are fragmented.

One landform that is not ambiguous is peak. Mathematically, a peak is a local maximum, it’s the point with the highest elevation within some neighboring area. Below is an image of all the local maxima from the elevation data shown above. Now you can start to ask questions about why the peaks are organized the way they are, why are there as many as there are and so on. I found that this type of analysis is done in the field of geomorphometry and a new book, “Geomorphometry: Concepts, Software, Applications”, has been my introduction. There is much more to learn.

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