Contiguous US 1000 Steepest: Map/List

[-wren-]

Map: https://listsofjohn.com/PeakStats/Conte ... p?lid=2350

List: https://listsofjohn.com/steepness/angle ... =&state=CO

For those unaware, Tim Worth has put a painstaking amount of effort into calculating the average slope angle of all the ranked Contiguous US peaks on Lists of John, and there are lists of the Cont. US 1000 steepest as well as each Western state's 100 steepest on the site. More so than elevation and prominence, I have always loved this metric as a way to explore interesting/impressive peaks in states other than CO. One thing that always bothered me was there wasn't a way to view these all laid out on a map, so with some free time over a few days I duplicated the list so it would be viewable as one. I think it's quite interesting to see the density of steep geography laid out on a map like this. CA, WA, MT, UT, AZ and WY sure do put us to shame! Anyhow hopefully this is of interest to some of you, I certainly find it entertaining to browse through.

P.S. there are 2 peaks missing from the map, I must have glazed over them, and have no desire to figure out which ones they are, so I apologize!

[Jorts]

Nice compilation. Thanks for sharing.

[seano]

Thanks for sharing a very interesting list! I'm a bit surprised about some familiar things that don't make the list, like Organ Needle, Pedernal, and Cabezon down here in NM, but it also points to some really obscure goodies, like Cerro Alesna, which I've only looked at from the super-remote dirt road nearby.

EDIT: Whoa, looks like I'm somehow the LoJ leader on this one... Kinda surprising, since I only just now became aware of it.

[justiner]

Huh, that's an interesting idea, with some curious results. I was surprised to see Chief's Head, since the western flank of it is fairly tame all the way down to the col between it and Mt. Alice, as well its SE ridge to Mt. Orton. The Glacier Gorge sided faces are indeed quite steep.

[-wren-]

Huh, that's an interesting idea, with some curious results. I was surprised to see Chief's Head, since the western flank of it is fairly tame all the way down to the col between it and Mt. Alice, as well its SE ridge to Mt. Orton. The Glacier Gorge sided faces are indeed quite steep.

There are many, many peaks on the list with either one very steep feature or a steep summit block and otherwise tame terrain (like sheep peak in AZ). Not a perfect metric but definitely showcases some of the finer obscure peaks in the nation. Particularly I love how it highlights just how gnarly the North Cascades are, only the Winds, Sierra and Glacier really come close as far as alpine terrain is concerned.

[Scott P]

Nice! That's a great map!

CA, WA, MT, UT, AZ and WY sure do put us to shame!

For sure. With the exception of Nevada, Colorado's mountains are overall the least rugged of the Western states. It's mostly due to most of the ranges being old and folded mountains. For better or worse, they are the easiest (on average) to climb. That means you can really bag a lot of peaks quickly here.

[twhalm]

How is steepness defined here? I feel like the changes to the definition could substantially change a list like this.

[seano]

How is steepness defined here? I feel like the changes to the definition could substantially change a list like this.

I'm not sure. It's different from, and seems more primitive than, Spire Measure (gory details).

[mike offerman]

How is steepness defined here? I feel like the changes to the definition could substantially change a list like this.

per the LOJ page

https://listsofjohn.com/steepness/?State=CO

Steepest Average Angle at 100m lists originally
created/conceptualized by Tim Worth using
National Elevation Dataset and LoJ peak data

[twhalm]

per the LOJ page

https://listsofjohn.com/steepness/?State=CO

Steepest Average Angle at 100m lists originally
created/conceptualized by Tim Worth using
National Elevation Dataset and LoJ peak data

Thanks. That is pretty arbitrary. I wonder how much the list would change if something like 300m was chosen or if it was an average of averages at different slices of elevation.

[bdloftin77]

per the LOJ page

https://listsofjohn.com/steepness/?State=CO

Steepest Average Angle at 100m lists originally
created/conceptualized by Tim Worth using
National Elevation Dataset and LoJ peak data

Thanks. That is pretty arbitrary. I wonder how much the list would change if something like 300m was chosen or if it was an average of averages at different slices of elevation.

He also has 800m on his current website: http://summitsteepness.com/
And 1600m on an older version: https://web.archive.org/web/20180817011 ... es/co.html

[martinleroux]

per the LOJ page

https://listsofjohn.com/steepness/?State=CO

Steepest Average Angle at 100m lists originally created/conceptualized by Tim Worth using National Elevation Dataset and LoJ peak data

Thanks. That is pretty arbitrary. I wonder how much the list would change if something like 300m was chosen or if it was an average of averages at different slices of elevation.

That's basically the idea behind the Spire Measure mentioned in seano's post above (a.k.a. "Omnidirectional Relief and Steepness" or ORS) . If I'm reading the description correctly, here's how ORS works:

1. For any given direction and base distance (B) from a given summit, measure the "point-to-point relief and steepness" (PPRS), defined as the drop-off in height (H) multiplied by the slope angle, i.e. H * arctan(H/B).
2. Calculate the average PPRS for all base distances in that direction. More precisely, calculate the root-mean-square, i.e. the square root of the average of (PPRS squared) for all values of B.
3. Finally, calculate the average of the average PPRS in all directions. This is the ORS.

ORS has the advantage that it doesn't depend on an arbitrary choice of base distance. The peaks with the highest ORS are generally quite prominent, although a very prominent peak such as Denali doesn't have as high an ORS as Mt St Elias, say, which isn't quite as prominent but is generally steeper. A formation such as The Titan would have quite a modest ORS because it's not very prominent, even though the top part is very steep in all directions, at least for a few hundred feet.

One issue with both ORS and average steepness is that a peak with an easy approach can still have a high score if it has a very steep drop-off in most directions. I'd be more interested in peaks that don't have an easy approach in any direction. In other words, instead of calculating the average steepness (or relief-and-steepness) in all directions, calculate a peak's lowest steepness in any direction. (In practice one would have to take the 99th percentile, or something like that). But I don't have access to the computer resources that would be needed to do this.