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Clean Prominence

Prominence is the vertical distance a given summit rises above the lowest col connecting it to a higher summit. To calculate it, you must know the elevation of a summit and the elevation of its key col. A problem arises when one or both of these elevations are not known precisely. Most commonly, col elevations are not given on topographic maps, so all that is known is a range based on a contour interval. Many summits also are represented by just a closed contour and no exact elevation.

There are three ways to deal with this uncertainly when calculating prominence:

  • Optimistic (or Dirty) Prominence: Use the lowest contour line at a col, and the highest possible elevation for peaks, yielding the maximum possible prominence value.
  • Interpolated (or Average) Prominence: Use the middle elevation between contours for cols and peak closed contours.
  • Clean (or Pessimistic) Prominence: Use the highest contour line at a col, and the lowest contour line for peak closed contours, yielding a minimum possible value.

So, as an example, imagine a topographic map with a 40-foor contour interval, a summit with no exact elevation and a highest closed contour of 8000 feet, and a key col in the range of 6960 feet to 7000 feet.  The Clean Prominence is 1000 feet (8000 - 7000), the Interpolated Prominence is 1040 feet (8020 - 6980), and the Optimistic Prominence is 1080 feet (8040 - 6960).

This site uses clean prominence for ranking peaks and setting cut-off values, mainly because it is impossible to overstate a peak elevation or prominence value using that method. Values may be higher, but no peak will ever get extra undeserved elevation. This seems like the safest method, and is commonly used by current prominence researchers.


Col

Col is the standard term used on this site to refer to the lowest point on the ridge between two summits. There are many synonyms: Pass, Gap, Saddle, Notch, or Cut; Joch in German, Colle in Italian, etc. See Key Col for the specialized meaning of that term.


County High Points by Andy Martin

In compiling the lists for this site, an extremely valuable reference work was a book called, simply, County High Points. This spiral-bound "bible" lists the highest points of all 3,141 counties in the United States, plus the most prominent peaks in virtually all mountainous areas of the country. It also contains unexpected goodies such as a list of Mexican State high points and U.S. National Park high points, plus a nice explanation of the prominence concept.

Ordering Summary Information for the County High Points book by Andy Martin:

To order send check or money order for $13 (2011 price) to Andy Martin, 3030 N. Sarsaparilla Pl., Tucson AZ 85749-9237

Details:

This 128 page soft cover comb bound 8.5" x 11" book lists the 3140+ county high points for all 50 states. Lists are also given for high prominence peaks, National Park HPs, and Mexican state HPs. The introduction goes into some detail on how the lists were prepared.

The information in the lists can be used to look up high point area maps on www.topozone.com. For example, the Pima county Arizona high point is listed:
    COUNTY HIGH POINT ELEV. LOCATION USGS 7.5' MAP
    Pima Mount Lemmon 9,157 26-11S-15E Mount Lemmon

Lists are also available for the 50 "finest" peaks in 14 western states - AZ, CA, NM, NV, CO, UT, TX, OR, WA, ID, MT, WY, HI and AK. Finest lists for the NE and SE sections of the US are also included.

To order send a check or money order for $13.00 to:
Andy Martin (520) 760-0337
3030 N. Sarsaparilla Pl.
Tucson AZ 85749-9237

Price is current for 2011 and includes shipping and handling.

Shipping will be by USPS book rate, which will take a week or more. If not satisfied for any reason, book can be returned for a full refund.

Credits for Lists on Peakbagger.com that also appear in County High Points

Some of the county high point and prominence lists on the Peakbagger.com site were largely developed by myself over a long period of years, but Andy Martin's County High Points book was used as an indispensible reference as I compiled my lists. Here is a summary of some of the differences between the lists on this site and in the book:

  • Every summit that is added to the PBC Database was verified independently by myself and given a latitude-longitude. From this lat-long, it is possible to derive the state, county, national forest or park, mountain range, topographic map, drainage basin, etc. for any peak. The County High Points book does not list latitude-longitudes.
  • Instead of lat-long, the County High Points book geo-references peaks with their USGS topographic map, and with the Public Land Survey System (PLSS) township, range and section location. Peakbagger.com does list the topographic maps for peaks, derived from its lat-long, but not on the main list pages. Instead, the main extra reference column on all Peakbagger.com lists is a mountain range or sub-range, derived from the PEMRACS taxonomy. PLSS information is not stored on Peakbaggger.com in any way.
  • County High Points lists topographic map information for key cols with its prominence lists. Most of the key col location information on this site has been assigned latitude-longitudes as a way of independent verification.

So, if you are serious about county high pointing, especially in non-mountainous areas, you should definitely purchase the book and not rely on the information on Peakbagger.com. On this site you can pull up lists for selected states, and link to a topo map of the general area, but there may be other areas not listed that are higher. See also County Highpointer Site.

This web site gives credit to the County High Points book on all peak list pages where it was used as a reference. The specific credit information from the book is listed at the bottom of each of these lists.


High Point Lists

Every peak on a high point list is the highest point of something. Every piece of geography on earth (natural or human-defined) theoretically has a high point; continents, countries, states, counties, parks, islands, mountain ranges, and even backyards all have area extent and some kind of topography. The lists in this section can be thought of as having two parameters: the kind of geography giving us the high points (e.g. countries, states); and the universe that holds these geographies (e.g. the world, the U.S.A.). Note that it is very common for two or three geographies to share the same exact summit as a high point, and in these cases the summit is listed two or three times, once for each geography.


Island Parent

The island parent for a peak is the other summit that would be the highpoint of a hypothetical island if the ocean rose to a point just below the key col elevation.

For many peaks, the island parent is the same as the Line Parent and/or the Prominence Parent. It is the strongest parent, mathematically, and will always be higher and more prominent than the source peak.

However, many coastal summits with low key cols will have an island parent that is the landmass high point, often very far away.


Isolation

Isolation for any given summit is defined as the distance from that summit to the nearest higher land. This distance is usually given in miles or kilometers, and represents the radius of the area where the peak is the highest point. The concept is easy to grasp with some examples. The isolation for Mt. Everest is undefined or infinite, since there is no nearest higher land. But every other summit can be assigned an isolation value. After Mt. Everest, the peak with the highest isolation is Aconcagua, with a value of 10,257 miles to the nearest higher land in Afghanistan. For K2, the isolation is 818 miles, the distance to a point near Mt. Everest.

There are a few quirks to using this method as a measuring tool for mountains. Low hills that are highpoints of isolated mid-oceanic islands will often have abnormally high isolation values, since there is no land at all (higher or not) nearby. The highest peak on Tristan da Cunha in the mid-Atlantic is not on many lists of the world’s most significant summits, but it ranks about #16 in the world in isolation. For this reason, in some isolation lists on this site small island high points are excluded from rankings.

Compared to prominence, isolation rewards summits that may be very low but that dominate a large area. For example, Eagle Mountain in Minnesota and Magazine Mountain in Arkansas both have isolation values that make them seem much more impressive than prominence ever would.

The nearest higher point of land to a peak is called the Isolation Limit Point (see below).  To calculate the isolation for a peak, the ILP must be determined and the distance to it measured (using ellipsoidal "great circle" distance).  However, it can be difficult to find an ILP for a peak, so an approximation of isolation can be calculated by finding the distance to a Nearest Higher Neighbor (NHN) peak.  This value will always be an overstatement of the true isolation number, but if the set of peaks used to find the NHN is large and comprehensive, then the value will often be very close to the true number.


Isolation Limit Point

The Isolation Limit Point (ILP) for a peak is the closest point of land to a peak that is higher than the summit of that peak. An ILP is always an undistinguished spot on a ridge or slope, perhaps a boulder or clump of dirt in a seemingly random location. It will often be on the slopes of the Nearest Higher Neighbor.

The isolation for a peak is formally defined as the distance from the summit of a peak to its ILP. Even if there is a nearby summit 1 millimeter higher than a given peak, the ILP is theoretically a millimeter below that higher peak.  If two nearby peaks have the exact same elevation, then neither one can be each other's ILP, since neither one is higher than the other.  The definition of Isolation is distance to a higher point of land, not higher or equal.

It is very difficult to determine precise coordinates for the ILP for a peak. On this web site, some peaks have ILP latitude-longitudes located as closely as topographic maps allow. These peaks therefore have very accurate isolation values. In practice, though, most isolation values on this site are calculated as the distance to the Nearest Higher Neighbor peak, using peaks in the PBC database. This is a much easier calculation.


Key Col

The key col (saddle, pass, gap) is an important concept related to Prominence. Every peak that is not a landmass/island high point is connected to a higher peak by ridges and has exactly one key col, which is the lowest pass on the highest ridgewalk leading to a higher peak. The mathematical correspondence between (non island/landmass high point) peaks and key cols is 1:1, so any given pass is the key col for just one peak.

To find the key col for a peak, it is helpful to use the concept of a "ridgewak".  From the peak, you need to trace the lines that lead to higher peaks.  Some summits will have drop-offs to river valleys on three sides and only one ridge leading to higher ground; other peaks might have two, theree, or more ridges that eventually lead to higher ground.  Of all possible ridgewalks leading to higher peaks, find the one with the highest low point.  The low point of this ridgewalk is the key col.

Another method is to imagine a great flood that raises the oceans to the exact level where a given peak becomes the high point of its own island.  At this exact moment, the ocean level is the key col elevation, and the location of the key col for the peak is the saddle that the rising ocean just flooded.

A minor sub-peak's key col is usually very close to the sub-peak, being the low point on the ridge connecting it to the nearby higher peak. Major summits, though, will often have a key col far away. For example, to find the key col for Mount McKinley (Denali), you must follow ridges south all the way to the Andes, the closest higher peaks. The lowest point on this three thousand mile ridge walk is in Nicaragua, and that is where McKinley's key col lies. Another famous example is the key col for Mount Mitchell, highest point in the Appalachians--you must follow ridges across the Midwest to the Rockies to find the nearest higher peaks, and the low point is in Chicago, Mitchell's key col.


Line Parent

Every peak that is not a landmass/island high point has a key col and a prominence value. The Line Parent is defined as the first higher peak encountered from the given summit, following ridgelines past the key col.

For a minor sub-peak, the line parent will generally be the main peak that it is subsidiary to. For example, from the South Peak of Mount Elbert you follow a ridge down to the key col, and then up to Mount Elbert itself, the line parent for the South Peak. For major, prominent summits, the line parent is often far away and is sometimes a minor or surprising peak. For example, for Mount Mitchell, highest of the Appalachians, you must follow ridges across the Midwest, past its key col in Chicago, and the line parent will be the first peak rising above Mitchell's 6684-foot elevation as the divide nears the continental divide in Montana (appropriately named Divide Mountain).

Often the ridge past a peak's key col will split, with each fork leading to a higher peak. In this case, the line parent is the peak whose path has the highest low point. The goal of the prominence ridge walk is to stay as high as possible when searching for higher ground, and avoiding the lower col after a ridge fork will accomplish this.

The line parent is not to be confused with the "Prominence Island Parent", which is the generally defined as the peak that will be the high point of a theoretical island if the ocean were to rise to just below the key col for a given peak. So, for example, for Mount McKinley (Denali), the line parent is Chimborazo, the first higher peak you encounter as you move south along the continental divide. The Prominence Parent would be Aconcagua, since that would be the high point of an island with narrow isthmus at the key col. At present, the Peakbagger.com database does not store Prominence Island Parent information.


North America Vertical Datum of 1988

A vertical datum is a model of the earth's surface that is used as a standard reference for calculating elevations.  A datum will define the precise location of sea-level, and peak elevations are given as vertical distance over the sea-level datum surface.

For the most part, Peakbagger.com makes no effort to track the datum used for peak elevations in its master peak database.  Many vertical datums are in use all over the world, and for the most part the difference in elevation among the different datums is a few feet or less.  Elevations reported in meters are even less subject to datum differences, since a meter over three times bigger than a foot.  Survey accuracy is often a few feet off anyway, and virtually no mountain elevation should be considered accurate to a foot or less.

However, the new standard datum in use for the contiguous United States is the North America Vertical Datum of 1988 (NAVD88), while all the USGS topographic maps show elevations and contour lines using the National Geodetic Veritcal Datum of 1920 (NGVD29).  Since this site hosts thousands of US peaks, and in feet the difference for a given peak can be up to seven feet, Peakbagger.com now shows the NAVD88 elevation as an alternate elevation for peaks in the contiguous U48 United States.

The primary elevation used for these US peaks will remain NGVD29, to match the topographic maps and the long-standing traditional values.  If you do want to know the NAVD88 elevation, go to the peak page for a peak and it will be reported in the "Elevation Info" section in the upper left hand corner of the page. The shift from NGVD29 to NAVD88 will be between -2 feet and +7 feet, and, in general, the higher the peak, the greater the shift.  Peaks in Colorado will gain 5 to 7 feet, while hills is Florida will lose 1 or 2 feet of elevation.

The effect on prominence is almost nil--only six US peaks have a prominence shift of 2 or 3 feet, and for all others it is less, since a peak's key col will almost always rise or fall in concert with the peak itself when doing the datum shift.  So no effort has been made to report the NAVD88 elevations of key cols, or to calculate new prominence or isolation values based on the new datum.

Note that this explanation is very simple and should not be considered a thorough technical treatment of the subject of vertical datums.  Also, note that the vertical datum is not related to a horizontal datum, used for latitude-longitude references.  This site uses WGS84 exculsively as a horizontal datum.


Nearest Higher Neighbor

Isolation is the distance from a given summit to the closest higher land. But this can be difficult to determine, so a common approximation is distance to a peak called the Nearest Higher Neighbor (NHN).  The NHN is a summit from among peaks in a certain defined set, for example, peaks in a database.  The more peaks in the set used, the higher the chance that the NHN-derived isolation value is close to the actual Isolation Limit Point (ILP)-derived value.

A peak's NHN is not fixed or objective.  It will depend on the number of peaks in the set used to find the NHN.  It is possible to limit the set of peaks used to ones with a certain prominence value, or that have official names.  But limiting the number of peaks that can be a NHN decreases the accuracy of the true isolation value--often, the NHN will be a very minor sub-peak or an unnamed crag, if minor peaks like those are in the set used.

On Peakbagger.com, the NHN is always the nearest higher peak in the master PBC Database. Even though this database has over 20,000 peaks in it, many areas of the world are not well represented, and the NHN for many summits is nowhere near the location of the ILP, the nearest higher land from which the actual isolation value is calculated.  Isolation values calculated using a NHN are always overstated.

Every peak on earth except Mount Everest has a NHN. Great circle, as-the-crow-flies distance is always used to find the NHN for a peak.


Optimistic Prominence

Many peaks, and most cols/saddles, do not have exact spot elevations on topographic maps. Therefore, the elevations for these features can only be expressed as a range. When calculating a prominence value for a peak (summit elevation minus key col elevation), the value is called "optimistic" when the highest possible summit elevation and lowest possible key col elevation are used. This number is the maximum possible prominence value for a peak, and will almost always be an overstatement of the true value. This site generally uses Clean Prominence for prominence-based lists, not optimistic prominence


Average Prominence

When a peak does not have a precise peak or key col elevation on topographic maps. one method for determining prominence is to "split the difference" and use values at the mid-point of a countour range. This is called "Average Prominence", or sometime "Interpolated Prominence". If, for example, a peak has an exact elevation of 8734 feet and a key col elevation located between the 8000 and 8040 contours, it's Average Prominence is (8734 - 8020) = 714 feet. 8020 is the average elevation of the col, midway between the contour interval. If a peak has a summit elevation with an interval, a similar operation is done for the that, too.

One objection to the use of average prominence is that an invented number that does not appear on the map is being used. However, this number is more likely to be closer than the true number than when using clean or optimistic prominence.


PBC Database

The Peakbagger.com Database (PBC Database) is a large, complex computer database that stores information on over 20,000 mountain peaks, 2000 mountain ranges, and other associated information. However, it is not by any means complete, since there are theoretically millions of peaks that are simply not in it. This means that many of the automatically-generated web pages on this site contain errors of omission. In particular, isolation distances that are calculated for peaks will be greatly overstated if the true nearest higher peak is not in the database. Also, the simple lists of the ten highest peaks in a given mountain range will often have less than ten peaks, or, very often, list the wrong ten peaks.

Of course, the goal of the PBC Database is to eventually have records for most of the world's high, important, prominent, isolated, or otherwise noteworthy peaks. I will freely admit that right now the database is much more complete in the United States than anywhere else, and more complete in Canada and Europe than in Africa and Asia.

In order to be included in the PBC Database, a peak must have a name, an elevation (feet or meters), and an accurate latitude/longitude (WGS84 decimal degrees). If you have this information for a peak you would like to see added, you can add it using the "Add Peak" page on this site. Click here for more information on adding peaks to the PBC Database..


Peakbagger.Com Mountain Range Classification System

The Peakbagger.Com Mountain Range Classification System (PEMRACS) is a hierarchical taxonomy of the mountain ranges of the world, developed as a subjective and arbitrary system that attempts to consistently organize the huge array of ranges and sub-ranges on the planet. For a more detailled explanation, see the main Range Index Page.


Prominence

Prominence is defined as the vertical distance a given summit rises above the lowest col connecting it to a higher summit. Or, put another way, it is the elevation difference between the summit of a peak and the lowest contour that contains the given peak and no higher peaks. Imagine the ocean rising to the exact point where a certain peak is the highest point on its very own island. At that point, the prominence is the elevation of the peak above the risen ocean.

That all sounds confusing, yet prominence is actually a fairly intuitive and commonly used concept. It goes by other names ("shoulder drop", "vertical rise", and other terms) and is central to a great deal of mountain peak listing activity. The best way to visualize it is to imagine that you are on a major summit and you start hiking down a ridge. After descending for 1000 feet, you start climbing again and gain 200 vertical feet to gain a sub-peak along the ridge. This sub-peak has a prominence of 200 feet, since that is how far it rises above the col connecting it to the major summit.

See the glossary entries for key col, clean prominence and optimistic prominence for more about prominence.

Also related is the idea of a line parent.

The traditional use of prominence is to use it as a way to determine which peaks belong on a threshold list. If, for example, you wanted to see a list of the peaks above 14,000 feet in Colorado, you could in theory count every large boulder on every ridge as a peak and generate a list with thousands of summits. However, if you say that a peak must rise above 14,000 feet and have a prominence of 200 feet, then you have a much more manageable and appealing list. Prominence provides an essential criteria for any threshold list, and a lively debate about the right value to use surrounds many of the more famous threshold lists.

Calculating prominence for minor summits close to major ones is easy, since the key col is close. Recently, though, dedicated map-readers have started finding the prominence for major summits, where the key col is often very far away. This allows for lists to created that rank peaks by prominence value, not by the traditional elevation. On these lists, a low elevation peak with greater prominence ranks higher than many well-known higher peaks. These lists provide a new and interesting way to look at peaks in an area.

Prominence is not a perfect measure of a mountain. Volcanoes and high points of desert fault-block ranges tend to have very high prominence values, and summits in major mountain ranges outside of the range high point tend to have lower values than one might expect. Many feel that prominence-based lists yield a more impressive line-up of summits than traditional threshold lists, but intangibles such as ruggedness, beauty, and personable inspiration are still not factored in.


Prominence Parent

The prominence parent for a peak is the nearest ridgewalk-connected higher peak with greater prominence than the given peak. It will always be both higher and more prominent than the peak itself.

For any peak that is not a island/landmass high point, you can follow ridges from a source peak to the Key Col and then onward to a higher peak. This higher peak is called the Line Parent, and is not deterministic--the Line Parent might be a very minor bump on a ridge that is just a bit higher than the source peak. If the Line Parent does have greater prominence than the given peak, the Line Parent is also the Prominence Parent. If, however, the Line Parent has less prominence than the given peak, you must continue along ridges, always taking the highest path, until you find a peak that is both higher and more prominent that the given peak.

For example, Mount Lafayette, New Hampshire, has a key col at Crawford Notch, and as you follow the ridges beyond the notch the first higher peak you reach is Mount Monore, slighly higher than Lafayette. However, Monroe has only 254 feet of prominence, far less than Lafayette's 3320 feet. So to get Lafayette's prominence parent, you continue past Monroe to Mount Washington, which has over 6000 feet of prominence and therefore is the true prominence parent.


Threshold Lists

A threshold list shows all peaks above a certain elevation threshold in a certain area. The geographical area is usually a well-defined political unit or mountain range, and the elevation threshold is frequently a round number (e.g. 8000 meters, 14,000 feet). Sometimes these lists have a fixed number of peaks, such as the 100 highest--this is really just a threshold list with a very specific, non-round number elevation threshold.

All threshold lists also require another parameter, which is a way to determine which peaks should get ranked or not. Theoretically, every boulder on a ridge above the threshold could be a peak on the list, so these lists often use prominence or isolation as a qualifying factor. On this site, all threshold lists use an associated prominence value, and peaks with prominence below it are not given a numerical ranking. These sub-peaks are shown in the list for reference, but do not have a rank. To move the unranked sub-peaks to the bottom of the list, click on the rank column to sort the list by the rank number.


WinProm Program

Calculating the prominence of a peak can be very tedious work, since the key col is often very far away from a high-prominence peak, and it can take hours to pore over maps, following obscure divide lines to find the low point of a connecting ridge. A big help was provided by mathematician Edward Earl, who wrote a computer program called WinProm that uses USGS Digital Elevation Model (DEM) databases to automatically calculate peaks, ridges, and key cols. DEMs are large matrices of elevations that cover an area at various resolutions, for example, every 30 seconds (about 0.3 to 0.6 mile). This data is not as accurate as a topographic map, but the program saves time by identifying areas where high peaks are, and areas where the key col is likely to be found. The program is very complex and has many enhancements, such as algorithms that try to match DEM maxima to known peak locations.

Many of the prominence figures on this site for summits with high (greater than 2000 feet) prominence had their genesis in the output from the WinProm program.


 

 

 

 

 

 

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