Peak List Column Descriptions

The following descriptions of the columns appearing in the peak lists provide a little more detail than the text found in the floating Help Tips:

• Climbed - If the user is currently logged into the VRMC site as a registered climber (or a climber is explicitly specified in the request) and a climb of this peak has been recorded by that climber in the VRMC database, then a green checkmark () appears in this column. The entire column is omitted if no climber is logged in or specified.
• Rank - Each peak is ranked among all peaks with at least 300 feet of prominence (given the user’s passing criteria). Note that the (official VRMC) rank displayed near the top of the peak detail page may be differerent from the rank displayed for that peak in a peak list using non-VRMC passing criteria.
• Peak Name - I list either the official name or a widely accepted unofficial name (with unofficial names surrounded by quotation marks). If no such name exists, I refer to peaks using their approximate Universal Transverse Mercator location relative to the North American Datum of 1927 (NAD27) in “summary format” (i.e., providing three digits of easting followed by three digits of northing, which locates the peak to the nearest 100 meters of each). Clicking a peak name brings up a peak detail page including all of the gory details for that peak. The peak detail page also provides a way for registered climbers to record climbs for a given peak.
• Elevation - The summit elevation displayed is determined via the passing criteria selected by the user. For ‘Best available data’ (the VRMC criteria), this means the first available source from the list below:
  1. Published Elevation - from the most recent USGS quadrangle
  2. Previously Published Elevation - where this is consistent with the contour information from the most recent USGS quadrangle
  3. DEM Elevation (see below) - where this is at least as high as the contour information shown on the most recent USGS quadrangle
  4. Contour Data - elevation of the highest closed contour surrounding the summit on the most recent USGS quadrangle [a plus sign (+) appears after the elevation in this case], where this was higher than the DEM Elevation
  Clicking the elevation value displays the peak detail page (see above), but automatically opens a (2-D) Google Map of the summit vicinity. An Info tip giving the margin of possible values (determined via the marginality criteria selected by the user) appears whenever the mouse hovers over a marginal summit elevation.
• Prominence - The difference in elevation between the peak itself and the low point in the highest ridge connecting it to some higher summit, all determined given the passing criteria selected by the user. For ‘Best available data’ (the VRMC criteria), this means the first available source from the list below:
  1. Difference Between Published Elevations - where both summit and saddle spot elevations are published on a (perhaps outdated) USGS quadrangle
  2. Field Altimeter Measurement - of the difference between the summit and saddle elevations, where the estimate is plausible and the conditions were favorable
  3. DEM Elevation Difference - where this is at least as great as the Map-DEM Elevation Difference (see below)
  4. Map-DEM Elevation Difference - between the (minimum) summit height from a (perhaps outdated) USGS quadrangle and the DEM Elevation of the saddle
  If the prominence is greater than 300 meters then “300m+” appears here instead. An Info tip giving the margin of possible values (determined via the marginality criteria selected by the user) appears whenever the mouse hovers over a marginal prominence.

Why I Favor Using Digital Elevation Model (DEM) Data

Other list developers use simple interpolation of USGS contour data to calculate summit and saddle elevations which have not been surveyed. This is a perfectly reasonable approach (and registered climbers can now select ‘Interpolated betwen contours’ on the My Peaks page to generate peak lists via this approach). Using the USGS Digital Elevation Models certainly adds more precision to my results. The open question is whether doing so also increases their accuracy. A few clarifying points:

1. As I understand it, nearly all of the DEM data originated from raw contour data. Thus, one could argue that any additional “precision” in the DEM data is really just noise. However, I believe the algorithms used to construct the DEM data from the contour data may actually do a better job of modeling the surface than is possible through simple “jagged model” interpolation. For example, in the DEM data the partial derivatives of height with respect to northing and easting can be made more continuous functions.

   If you graph elevation on the Y-axis, and longitude along the X-axis for any east-west path through a USGS quadrangle, the straight interpolation model assumes that the graph will be a sequence of straight lines connecting points where the path intersects contour lines. In contrast, the DEM construction algorithm would ideally try to smooth out the data so that the DEM points (several between each pair of contour lines) all fell along a curve that was a continuous function intersecting the contour lines. There may be even better models that might statistically give closer approximations based on typical surface feature characters, even region-specific ones (though it’s probably unlikely that the USGS approach was that sophisticated).

   I have sent numerous emails to the USGS attempting to get more details on the methods used to construct the DEM data, some metadata that would give location-specific error bars, etc. Unfortunately, my requests have not yet reached anyone who both knows the answers and is willing to take the time to respond.

2. In some instances I have found gross errors in the DEM data (e.g., a couple of ridiculous data points that I had to remove by hand from the DEM data). The Colorado DEMs had more such problems than did the California DEMs, by the way. In my view, these do not necessarily indicate more serious problems (e.g., local elevation bias, at least when compared to the contour data).

   I have also reported these problems to the USGS, and I hope that they resolve the errors, though it seems unlikely that my feedback has made its way to anyone who could do so.

3. Others have apparently compared the DEM elevations of U.S. summits to their spot elevations as reported on USGS maps, and they claim statistics suggesting both a large negative bias and a large standard deviation. I conducted an analysis of all 144 peaks on my Thirteeners and non-Thirteeners lists that had spot elevations on the USGS 7.5' quadrangles. I threw out Mt. Humphreys, because that DEM has obvious problems (which I’ve reported previously to the USGS). The difference between the DEM elevation and the spot elevation for the remaining 143 peaks had an arithmetic mean of -1.535 meters and a standard deviation of only 5.024 meters.

   It would seem that either the California DEMs are of higher quality, or there was a problem in the analysis conducted by these other investigators. In particular, I think it’s imperative that outliers not be allowed to skew the results for the overwhelming majority of peaks. (I also wonder how the DEM elevations for the peaks were extracted - I hope software like RidgeWalker or WinProm was used to locate the high point in the DEM for each peak, rather than just pulling a single elevation at the assumed summit location.)

   I would certainly be much happier if the DEMs were in complete agreement with the spot elevations (and I don’t see why the USGS couldn’t make it so). However, the DEM data still seem to be within an acceptable error margin, at least for the highest California summit spot elevations.

4. I do expect the DEM data to improve in the future. As soon as DEM updates are available, I intend to run RidgeWalker over the new data to provide revisions to my list (as I did when the 10m DEMs replaced the 30m DEMs). This is consistent with my desire to use the best available data for my list (e.g., field altimeter measurements) and to continue updating the list as more data become available.

5. Most importantly, I do not believe that I have reported any summit or saddle data originating from DEM data that is in significant conflict with the contour data, though it will nearly always be in conflict with a simple interpolation of the elevation as the value halfway between the contours. Again, I also have (slightly) more confidence in reasonable field altimeter checks than I do in contour data, as long as they are in near agreement.

In summary, I favor spot elevations, then contour data, then field altimeter measurements, then DEM data (in that order).

RidgeWalker Analysis of Digital Elevation Models

The list incorporates the results from my RidgeWalker software, which I used to determine unknown summit and critical saddle elevations. A few notes (not for the faint of heart):

• While RidgeWalker is searching for saddles, it has its own idea of the summit elevations, which I’ll call the RidgeWalker Summit Elevations. The RidgeWalker Summit Elevation is defined to be the Map Elevation or the DEM Elevation, whichever is higher.
• To determine the Saddle Elevations, I loaded all the level 2 DEMs into RidgeWalker, temporarily substituted RidgeWalker Summit Elevations for all the DEM summit points, and told it to find the highest saddle connecting each summit in my peak list to some location higher than the summit. Note that RidgeWalker bails out of its critical saddle search when it finds a closed contour over 300m below and completely surrounding the summit. I assumed that no one would require a more stringent prominence criterion than 300 meters (984 feet).
• To determine Prominences, I subtracted the Saddle Elevations from the RidgeWalker Summit Elevations (rather than the Official Elevations). I believe this makes the Prominences more accurate where the DEM Elevations exceed the Map Elevations, especially where the Map Elevations had to come from the Contour Data.
• In order to ensure that I didn’t miss any summits, I also loaded all the level 2 DEMs into RidgeWalker, again temporarily substituted RidgeWalker Summit Elevations for all the DEM summit points, and told it to find all summits at least 3950 meters tall with saddles at least 80 meters deep. I then compared the output with that generated from my peak list above, and it agreed.
• The level-2 DEM data sets I used contain integer elevations in meters for locations in a 10 meter by 10 meter grid. The elevations are supposed to be accurate to half a contour, which means something like 6-10 meters (20 to 33 feet).

How Passing and Marginality Criteria Affect Peak Lists

A peak is placed on the passing list if both its summit and prominence (as determined using the passing criteria selected by the user) meet the peak list’s summit elevation requirement and the 300 feet, respectively. If either a passing peak’s summit or prominence (as determined using the passing criteria selected by the user) might possibly fail (as determined using the marginality criteria selected by the user), then the peak passes marginally (otherwise it passes clearly).

A failing peak is placed on the marginal failing list if neither its prominence nor its summit elevation (as determined using the passing criteria selected by the user) clearly fails, but at least one of them does fail.

A peak is placed on the clearly failing list if either its prominence or its summit elevation (as determined using the passing criteria selected by the user) clearly fails. Such peaks are generally not included in peak lists, but they are included on the California non-Thirteeners page.

Marginal Summit Elevations for Rank-Based Peak Lists

Determining the marginality of peaks based on summit height is complex for rank-based peak lists. The marginal passing and marginal failing peaks are treated separately (and somewhat symmetrically):

1. The basic rule determining whether a passing peak has a marginal summit pits the worst-case scenario for this peak against the best-case scenario for the other relevant peaks (i.e., all guaranteed lower passing peaks plus all potentially higher marginal failing peaks). If there are more such relevant failing peaks than relevant (other) passing peaks, then this peak's summit passes marginally (otherwise it clearly passes).
2. The basic rule determining whether a failing peak has a marginal summit pits the best-case scenario for this peak against the worst-case scenario for the other relevant peaks (i.e., all guaranteed higher marginal failing peaks with passing summits plus all potentially lower marginal passing peaks). If there are more such relevant passing peaks than relevant (other) failing peaks, then this peak's summit fails marginally (otherwise it clearly fails).

Note: I ignore the Case #1 possibility that all (or even a significant majority) of the passing peaks with marginal prominences might fail.

In that case, there would be many open slots to be filled, and some of the peaks that would rush in to fill them would themselves have marginal saddles which could fail. On average, you might expect that just as many peaks with marginal saddles would move from failing to passing as vice-versa, and that you'd get the same general mix of rankings (i.e., nearly the same number of peaks in the elevation range for ranks 40-60 would move from failing to passing as would move in the opposite direction.) However, there's a very significant chance that 1 or 2 more currently passing peaks will evnentually fail due to saddle problems than the number of currently failing peaks that will someday pass the saddle criterion. This would open 1 or 2 more spots, which would likely be filled by 1 or 2 peaks already considered marginal. Even if one of their saddles eventually failed, the replacement would likely come from a failing peak already considered marginal.

Although we do not report all of the peaks that would be considered marginal failing peaks if we considered all (remote) possibilities allowed by our marginality criteria, the current algorithm probably gives a more useful report.

Data Submissions Welcome

I welcome information about summit and/or saddle elevations, but please study the above first so you know where my data come from. If you notice a mistake I’ve made (such as an incorrectly listed map elevation) or have accurate survey data for a summit or saddle, please send an email to me at: schmed@transpac.com.