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.



Geomorphology
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:



January 25, 2011, 4:07 am
Filed under: Mountain | Tags:

I recently discovered that airborne lidar data is freely available for a handful of US locations. And one of those locations: Yosemite Valley. That’s right, as a climber, I couldn’t have been happier. Visualizing the data is not a simple task. Airborne lidar data is produced by flying a plane low over the region of interest with a laser scanning over the surface of the earth. At each spot that the laser reflects off the ground, the elevation and position of the ground is recorded. The result is huge collection of x,y,z points blanketing the earth. It takes special software to manage the lidar data, primarily because a laser scan can easily produce millions of points. One piece of the Yosemite Valley lidar data covers the area around El Capitan with about 8.6 million points.

Thankfully there is academic work being done on lidar data and analysis and the software that has been developed is also freely available. Coincidently, the Institute for Data Analysis and Visualization here at UC Davis, is one of the organizations working on this topic and I used their LidarViewer and VRUI to visualize the El Cap lidar data. In addition, LASTools, developed at the University of North Carolina, provide a number of useful software tools to inspect and manipulate the lidar data (which has the file ending .las, hence the name LASTools).

The result of all of this is a cool 3D model of El Capitan.

There are holes in the data which I think were caused by overhanging sections of rock where the airplane mounted laser was not able to reach. I should also point out, that although the surface looks continuous in some places, it is actually composed of discrete points (about 8.6 million of them). You can zoom in quite close and see that the points reveal the fine detail in the cliff.

This is a close up view of the Alcove and Footstool

This one shows Mammoth Terraces and the Half Dollar