Inspired Stone


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.

February 18, 2011, 6:19 am
Filed under: cartography, Mountain | Tags: , , ,

My first steps into geographic analysis were to experiment with GIS and get the geographic data into a format I understood and could use. Now the fun starts.

I have a keen interest in the ridge lines of alpine terrain, which I’m sure is influenced by my passion for climbing. So my first idea was to develop an algorithm and computational routine to identify the ridge lines in an elevation map. I started with a small elevation map, shown below, covering the area immediately around Mt. Whitney. Lighter colors correspond with higher elevation (the summit of Mt. Whitney is at the center). Just looking at the image, it’s not difficult to identify the major ridge lines, like the ones I outlined in red. Telling a computer how to do the same thing is not easy.

In my first attempt, I wrote a short octave script that would find the locations where the elevation sloped downward in both east and west, or north and south (if it slopes downward in all four directions, than it’s a peak). The image below displays a white pixel wherever a ridge was identified. The result is mediocre. Of course there are minor ridges identified (like the ones on the west slope of Whitney, which are truly there), but the bigger problem is that even the major ridge lines are discontinuous.

Excitingly, I have found current research being done in this area.:

Taking a hint from the paper above and this group in Zurich, I think I should use some strategy like the Watershed algorithm. Here’s a peak at what I’m working on:

Sierra Crest :: Digitized
January 20, 2011, 4:03 am
Filed under: cartography, Mountain

Cartography is firmly in the digital age and has expanded into the field known as GIS, geographical information systems. Not a very exciting name, but it has revolutionized the way geographic information is presented and analyzed. Anything that can be related to geographic space can be presented on maps and analyzed for statistics or relationships. Want to know how the density of fast food restaurants correlates with political party distribution? I’m sure the answer is just a few mouse clicks away. Or how does highway and road density correlate with topography? Now that sounds interesting. Maybe someday, when I am more skilled with GIS software, I will answer that question.

As an initial foray into GIS, I decided to look at the topography around Mt. Whitney in the Sierra Nevada. In my science work, I manage and analyze spatial data and many of the same concepts apply to topographic data despite the radically different scales (nanometers versus meters). The difficulty was reconciling the different softwares and file formats used in molecular dynamics versus GIS. Once that was worked out, sort of, I started to have fun.

An image of the elevation on the 7.5 minute Mt. Whitney map (higher elevations are lighter), produced with qgis.

The image below shows the slope over the same area. The white regions are very steep and cliffy and the flat lakes are black. For climbers, images like this provide interesting research material. Although you can find cliffs on a topographic map by looking for places where the contours converge, I think it is even clearer in this presentation.

A 3D model of the east face of Mt. Whitney, produced with octave. I’m afraid it’s actually reflected north to south, but the idea is the same.

Lastly, a 3D model rendered in the molecular viewing program vmd. The surface is a sheet of balls because most molecules are represented as a collection of atoms, depicted as spheres.

January 16, 2011, 7:07 am
Filed under: cartography, Mountain

I’m fascinated by the crest of the Sierra Nevada. The Sierra Nevada, especially the southern High Sierra, are mountains of sharply defined ridges, jagged peaks and steep walls. As I alluded to in the post about aesthetics and climbing, there is something pure about the true crest of the Sierra. A rain drop on one side ends up in the Pacific, and a drop on the other winds up in the Great Basin. It’s mathematically well defined as well. Physical chemists talk about chemical reactions using the language of mountains, with it’s troughs and basins and saddles. While scientists are not usually interested in the peaks and ridges of an energy landscape, they are just as well defined.

To satisfy my curiosity, I drew a map of the Sierra crest, from Yosemite to Mt. Whitney. I tried to depict the crest as accurately as possible, with it’s connecting ridge lines, but the ultimate goal is not navigation, it’s inspiration. There is so much more that can be done with this subject: analyze it mathematically, depict it digitally, sketch it differently, traverse it…