The San Gabriel Mountains geographical centroid

[Nate U]

Proposed Expedition: The San Gabriel Mountains geographical centroid.


A little more than 3 weeks ago, minds delirious and euphoric after indulging in wildly grotesque and delicious variations of JeffH’s smorgasborg of trail-grilled-cheese magnificence, I forget who asked the question, may have been Uncle Rico or maybe even myself, of what the center of the San Gabriel Mountains was.

This question has since remained with me, torturing and teasing at the fringes of consciousness.

And this morning, my work being rather slow right now amid the striking, I took it upon myself to answer this question with the degree of accuracy it deserves.

My method:

I carefully have traced, as a polygon in Google Earth, the outline of the San Gabriel Mt range. My criteria for the outline is not scientific. It is not spanning comprehensive watersheds like the Peak Bagger PEMRAC system, or following anything strictly geological. It is a primarily topographical approach, tracing around the edges of the San Gabriel, San Fernando, Santa Clarita and Antelope valleys where there is an, initial, discreet, definitive shifting in slope angle when approaching the range. When in doubt I would ask myself, “Whats *feels* like you are in the mountains or foothills?” And would defer to that intangible concept. Subjective judgements abound in the details of each canyon or alluvial fan, but I think most would agree on my general perimeter.

The resultant polygon was a total of 1,754 sides. I then fed that .kml file into this useful tool:

https://www.earthpoint.us/shapes.aspx

And after a spell of complex calculation, these were the results:

The center point of the wild and ragged Mtn Range we make our collective backyard playground is no less and no more than 34.5261665°, -117.3856633°
I have attached the .kml files of the point and the perimeter I made it is calculated from.

So this is it:

We find ourselves in the middle of the Northeast face of East Twin, at an elevation of 6,490ft, above a canyon (not sure the name?) of a upper tributary of Bear Creek.

This point is pretty darn representative of all the things that make the San Gabriels what they are, I have to say. It is extremely steep, full of crumbling intrusive igneous rock, with our point specifically lying in the middle of a big shoot of scree next to a couple ancient conifers holding on for dear life. It is a point worthy of its title, I believe.

Closeup:

The idea of a centroid is, If the San Gabriel Mountains perimeter shape was precision cut into a piece of plywood, you could balance that piece of plywood on the head of a pin placed in this exact spot.

Now of course the next thought that comes to mind…. CAN IT BE REACHED?

I believe it would make for an appropriate Eis Piraten expedition to attempt this point, to reach the very Heart of the SGs Darkness.

Looking through the archives, I see a few on the board have bagged East Twin. Those that have will know this area best, and it sounds like gnarly, pretty unforgiving country. As I suspected before starting this project, the Angeles Crest Highway would be vital for making this hike reasonable, (I wouldn't even know where to begin without it?) so we probably need to wait until it gets re-opened. It looks like the easiest route would be something like this:

Out and back, we’re looking at 8.3 miles and 2,700 ft of gain. The numbers are perfectly reasonable for a day hike. But that last 3/4 of a mile traversing across the NE face of East Twin is going to be very interesting…..

You folks who know this area better, do you think this point can be reached? Who’s interested in making an attempt? A forum hike once the ACH reopens? Has this ever been calculated or done before by anyone you know of?

[dima]

I'll just leave this here: the-pole-has-been-accessed-t7040.html

[Nate U]

I'll just leave this here: the-pole-has-been-accessed-t7040.html

Super cool, Sean had mentioned something about this. Your math is rad. Its neat other people a followed your lead and have since accessed it as well.

We should leave a register at the centroid, but the only issue is the perimeter polygon its calculated from I made myself, its not publicly accessible (beyond this forum) like open street map.
You could calculate the centroid based on the PeakBagger San Gabe PEMRAC, but that tracing is not nearly precise enough for my tastes, and following watercourses the way the PEMRACS do gives you so much San Gabriel and Antelope Valley I think it doesn't feel focused enough on the mountains themselves.

[JeffH]

Way cool, Nate. It was the conversation about birthday hikes and such, I mentioned we had pinpointed the east and west ends of the gabes.
Centroid Point sounds like an adventure!

[Nate U]

Just realized the centroid and the entire proposed approach hike is within the realm of the Bobcat fire.... ?

[Tom Kenney]

If you manufactured several Centroid Detection Templates from different materials with a range of density and mass distribution, perhaps a better center point could be determined. You could thereby increase the chance of access, and decrease the chance of excess tiredness.

Sounds like you're doing this with proper science, so I thought I'd point this out. ?

[Nate U]

If you manufactured several Centroid Detection Templates from different materials with a range of density and mass distribution, perhaps a better center point could be determined. You could thereby increase the chance of access, and decrease the chance of excess tiredness.

Sounds like you're doing this with proper science, so I thought I'd point this out. ?

You mean take into consideration elevation as contributing to how the mass is distributed throughout the mt range? I thought about that, but I'm not sure how one would go about the calculation...the elevations (as we all well know) are wildly variable throughout the mountains....hence them being mountains!

Taking into consideration elevation as contributing to mass *could* make the centroid easier to reach, as I know that would put it further east more in the vicinity of Crystal Lake. But I wouldn't be so sure... as steep and rugged as my centroid is currently on the side of East Twin, it could be a whole lot worse in terms of accessibility then that ?

[Sean]

That would be awesome if the volume centroid were under Crystal Lake and we had to dig a tunnel to it. We might finally solve the mystery of how the lake drains through the bedrock.

[Tom Kenney]

You mean take into consideration elevation as contributing to how the mass is distributed throughout the mt range? I thought about that, but I'm not sure how one would go about the calculation...the elevations (as we all well know) are wildly variable throughout the mountains....hence them being mountains!

Doing that might yield something closer to the Surface Area Centroid, no? There are different kinds of Centroids.

[Sean]

"It is a primarily topographical approach"

While we're being nerds, the type of centroid you've calculated seems more geometric than geological or topographical. Essentially you subjectively drew a geometric shape resembling the 2D outline of the Gabes. With objective, logical boundaries you could refine the shape and argue for a precise geometric centroid. That seems like a lot more work though.

[Nate U]

"It is a primarily topographical approach"

While we're being nerds, the type of centroid you've calculated seems more geometric than geological or topographical. Essentially you subjectively drew a geometric shape resembling the 2D outline of the Gabes. With objective, logical boundaries you could refine the shape and argue for a precise geometric centroid. That seems like a lot more work though.

It was a topographical approach I took in deciding where the perimeter of the range exists. Then I used the resulting shape that created (a 1,754-sided polygon) to calculate its centroid, which is inherently geometric, because the definition of a centroid is: "the center of mass of a geometric object of uniform density."
How would one generate "objective, logical boundaries" of the San Gabes?

[Nate U]

You mean take into consideration elevation as contributing to how the mass is distributed throughout the mt range? I thought about that, but I'm not sure how one would go about the calculation...the elevations (as we all well know) are wildly variable throughout the mountains....hence them being mountains!

Doing that might yield something closer to the Surface Area Centroid, no? There are different kinds of Centroids.

Yes, a "surface area" centroid would be yet another unique location. The steeper, deeper canyons and peaks will inherently contain more surface area then more gentle topography. The "surface area" centroid would also exist further east I would think because of the higher peaks and deeper canyons in the eastern portions of the range, but it wouldn't make as big a difference as actual mass above sea level.
As a professional musician, I lack the math skills to create my own calculations for this sort of thing, but I do find it fascinating.

[Sean]

How would one generate "objective, logical boundaries" of the San Gabes?

The Gabes were created from activity along certain faults that form the borders of the uplifted block of earth. I'd start by identifying and tracing these faults. I quickly found the below map, but you'd have to find more detailed faultline maps to generate an accurate border.

(Map source)

[Nate U]

How would one generate "objective, logical boundaries" of the San Gabes?

The Gabes were created from activity along certain faults that form the borders of the uplifted block of earth. I'd start by identifying and tracing these faults. I quickly found the below map, but you'd have to find more detailed faultline maps to generate an accurate border.

The geologic approach! I like it.

So this means we have a 2 different ways to create a perimeter of the San Gabriel Mts, (topographic, geologic) and then 3 different criteria for creating a centroid from that (geographic, mass, surface area) which means currently we could calculate 6 different San Gabriel Mts centroids.

So you know what this means we have to do... once we've figured out those six centroids, we have a create a hexagon connecting each of them, and THEN CALCULATE THE CENTROID OF THAT HEXAGON TO DETERMINE THE CENTROID OF THE GABES' CENTROID!!!!

[dima]

I would do it from topography. You can get a surface mesh from USGS (the SRTM data), or a higher-res thing from the county. The "mountains" can be defined as the region with a non-constant-ish gradient high-ish gradient (i.e. anything not flat). Then you start in the middle, and find the largest contiguous region that meets the definition of "mountains". Would be relatively straightforward to do. But then you'd have another estimate of the centroid. Do we really WANT a second one?

[Nate U]

I would do it from topography. You can get a surface mesh from USGS (the SRTM data), or a higher-res thing from the county. The "mountains" can be defined as the region with a non-constant-ish gradient high-ish gradient (i.e. anything not flat). Then you start in the middle, and find the largest contiguous region that meets the definition of "mountains". Would be relatively straightforward to do. But then you'd have another estimate of the centroid. Do we really WANT a second one?

This is all super neat! I *think* I follow you but I have questions.
I want to pick your brain on this the next time we are out there ... ?
IMHO, the San Gabriel centroid is not the real deal unless it gets Dima's endorsement!!