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Steepness/Ruggedness

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  • David Metzler
    Hi prominence folks. Prompted by a discussion I had a little while ago with Edward, I decided to do some ruggedness calculations for various parts of the US.
    Message 1 of 5 , Oct 16, 2000
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      Hi prominence folks. Prompted by a discussion I had a little while ago
      with Edward, I decided to do some "ruggedness" calculations for various
      parts of the US. You can define ruggedness in various ways (Edward
      has one way involving prominence) but a straightforward way is simply
      to measure the average slope throughout a region. So I downloaded some
      of the USGS digital data and calculated the average slope over various
      regions.

      The answer should be very pleasing news to Bob Bolton: the North Cascades
      come out as the most rugged mountain range in the United States. Not
      just the lower 48, mind you--this is including Alaska! That fact was
      a bit surprising to me. In terms of the numbers, here's one: over the
      region between 48N and 49N and between 120 12W and 121 42W (which is
      approximately square, and is very roughly "the North Cascades")
      the average slope is 46%. That might not sound like much, but remember
      that it includes all of the valleys, lakes, everything. For
      comparison, the best similar-size square region around Denali
      has an average slope of only 28%.

      It is true that on a small scale Denali is steeper than the North Cascades,
      but still not by much. If you average over squares that are about 12 miles
      on a side, Denali gets an average slope of 63%, and the winner in the North
      Cascades is none other than Johannesburg Peak (and environs) with 61%.

      And on a range-wide scale, the fact that the North
      Cascades have so much up and down over such a large area make them the winner.
      In fact the ranges that come out best by this measure are the coastal
      ranges which get a lot of rain but are not cold enough to have the large
      glaciers (i.e. big flat areas!) that the Alaska and St. Elias Ranges have.

      If you want to know the average steepness of any other mountainous
      area in the US, it's pretty easy for me to calculate it, on any scale
      above 6 minutes. (I'm using 1:250K data so anything below that might be
      a bit suspect). Let me know.

      Dave Metzler
    • Adam Helman
      David - I d be interested in the formula you used to actually compute slope over a region. The simple prescription (rise / run) requires a delta_x ( run ) in
      Message 2 of 5 , Oct 16, 2000
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        David -

        I'd be interested in the formula you used to actually compute slope
        over a region. The simple prescription (rise / run) requires a delta_x
        ("run") in order to get the delta_y ("rise"). Furthermore, how did you
        average over angles for a given point?

        I'm certain you've taken all of that into account. I just want to see
        the formulas so I can make an informed interpretation of the results.

        Finally, the computed slope will be a function of the delta_x, such
        that it really should be specified. In the extreme limit, setting delta_x
        to perhaps 1000 miles will yield no slope at all since mountain ranges
        seldom get that big. Setting delta_x to perhaps a few feet captures
        silly detail like invididual rocks and boulders.

        Thanks, Adam

        David Metzler wrote:

        > Hi prominence folks. Prompted by a discussion I had a little while ago
        > with Edward, I decided to do some "ruggedness" calculations for various
        > parts of the US. You can define ruggedness in various ways (Edward
        > has one way involving prominence) but a straightforward way is simply
        > to measure the average slope throughout a region. So I downloaded some
        > of the USGS digital data and calculated the average slope over various
        > regions.
        >
        > The answer should be very pleasing news to Bob Bolton: the North Cascades
        > come out as the most rugged mountain range in the United States. Not
        > just the lower 48, mind you--this is including Alaska! That fact was
        > a bit surprising to me. In terms of the numbers, here's one: over the
        > region between 48N and 49N and between 120 12W and 121 42W (which is
        > approximately square, and is very roughly "the North Cascades")
        > the average slope is 46%. That might not sound like much, but remember
        > that it includes all of the valleys, lakes, everything. For
        > comparison, the best similar-size square region around Denali
        > has an average slope of only 28%.
        >
        > It is true that on a small scale Denali is steeper than the North Cascades,
        > but still not by much. If you average over squares that are about 12 miles
        > on a side, Denali gets an average slope of 63%, and the winner in the North
        > Cascades is none other than Johannesburg Peak (and environs) with 61%.
        >
        > And on a range-wide scale, the fact that the North
        > Cascades have so much up and down over such a large area make them the winner.
        > In fact the ranges that come out best by this measure are the coastal
        > ranges which get a lot of rain but are not cold enough to have the large
        > glaciers (i.e. big flat areas!) that the Alaska and St. Elias Ranges have.
        >
        > If you want to know the average steepness of any other mountainous
        > area in the US, it's pretty easy for me to calculate it, on any scale
        > above 6 minutes. (I'm using 1:250K data so anything below that might be
        > a bit suspect). Let me know.
        >
        > Dave Metzler
        >
      • Bob Bolton
        Pleased? Yes! Surprised? Not on your life! I m no mathematician, but I ve seen most of the rugged areas that you must have calculated (Sierra Nevada, Wind
        Message 3 of 5 , Oct 17, 2000
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          Pleased? Yes! Surprised? Not on your life! I'm no mathematician, but I've seen most of the rugged areas that you must have calculated (Sierra Nevada, Wind Rivers, Glacier National Park, Rocky Mountain National Park, etc.), plus the Canadian Rockies, and nothing compares or even comes close to the North Cascades on a measure such as this. My buddies and I now go to other areas just to take a break from the NCs. They're just too vertical, with too much relief, and we're getting OLD! Fascinating stuff! I'll be looking for the numbers!

          Bob Bolton
          ----- Original Message -----
          From: David Metzler
          To: prominence@egroups.com
          Sent: Monday, October 16, 2000 3:57 PM
          Subject: [prominence] Steepness/Ruggedness


          Hi prominence folks. Prompted by a discussion I had a little while ago
          with Edward, I decided to do some "ruggedness" calculations for various
          parts of the US. You can define ruggedness in various ways (Edward
          has one way involving prominence) but a straightforward way is simply
          to measure the average slope throughout a region. So I downloaded some
          of the USGS digital data and calculated the average slope over various
          regions.

          The answer should be very pleasing news to Bob Bolton: the North Cascades
          come out as the most rugged mountain range in the United States. Not
          just the lower 48, mind you--this is including Alaska! That fact was
          a bit surprising to me. In terms of the numbers, here's one: over the
          region between 48N and 49N and between 120 12W and 121 42W (which is
          approximately square, and is very roughly "the North Cascades")
          the average slope is 46%. That might not sound like much, but remember
          that it includes all of the valleys, lakes, everything. For
          comparison, the best similar-size square region around Denali
          has an average slope of only 28%.

          It is true that on a small scale Denali is steeper than the North Cascades,
          but still not by much. If you average over squares that are about 12 miles
          on a side, Denali gets an average slope of 63%, and the winner in the North
          Cascades is none other than Johannesburg Peak (and environs) with 61%.

          And on a range-wide scale, the fact that the North
          Cascades have so much up and down over such a large area make them the winner.
          In fact the ranges that come out best by this measure are the coastal
          ranges which get a lot of rain but are not cold enough to have the large
          glaciers (i.e. big flat areas!) that the Alaska and St. Elias Ranges have.

          If you want to know the average steepness of any other mountainous
          area in the US, it's pretty easy for me to calculate it, on any scale
          above 6 minutes. (I'm using 1:250K data so anything below that might be
          a bit suspect). Let me know.

          Dave Metzler


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        • Bob and Rhonda Bolton
          (Dave Metzler) The answer should be very pleasing news to Bob Bolton: the North Cascades come out as the most rugged mountain range in the United States...the
          Message 4 of 5 , Nov 15, 2000
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            (Dave Metzler)
            The answer should be very pleasing news to Bob Bolton: the North Cascades
            come out as the most rugged mountain range in the United States...the winner
            in the North Cascades is none other than Johannesburg Peak (and environs)
            with 61%.

            Ever since Dave confirmed my suspicions about the North Cascades, I've
            been trying to put together a photo album of the area. I climbed one of
            Johannesburg's near neighbors, Sahale Peak, last August, and finally the
            photos are ready to view. So if you're interested in how the ruggedest area
            of the country looks, you can find the two albums at my photo sharing
            website by clicking these links: Album 1 Album 2

            My home page there is http://members2.clubphoto.com/robert198786. They're
            mostly mountain pix.


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          • Bob and Rhonda Bolton
            (From earlier message) So if you re interested in how the ruggedest area of the country looks, you can find the two albums at my photo sharing website by
            Message 5 of 5 , Nov 15, 2000
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              (From earlier message)
              So if you're interested in how the ruggedest area of the country looks, you
              can find the two albums at my photo sharing website by clicking these links:
              Album 1 Album 2

              Well, I guess you learn from your mistakes. The two hyperlinks didn't
              survive the massaging at eGroups. So here they are again:


              http://members2.clubphoto.com/robert198786/Climbing_Sahale_Peak_Album_1_Clim
              bing_Sahale_Peak_Album_1/

              http://members2.clubphoto.com/robert198786/Climbing_Sahale_Peak_Album_2_Clim
              bing_Sahale_Peak_Album_2/



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