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.
Data Sources
The peaks in the Peakbagger.com database all have four primary and essential peices of information: Name, elevation, latitude, and longitude. Most everything else about the peak--it's location in various jurisdictions or areas, various links to other info, and who climbed it--are all secondary or derived from the lat/long. So on each individual peak page, the source of the primary information is given so users can judge the accuracy of the peak's listed name, elevation, and geographic coordinates.
Among map sources, Peakbagger.com places implicit trust in large scale (1:25,000 or better) national survey topographic maps--this is the "gold standard". These are available from governmental mapping agencies, such as the USGS in the USA, the OS in the UK, the IGN in France, and others. For some nations, the best topographic survey maps are at 1:50,000, or at even less detailed scales. Old Soviet military maps can often be good sources, too, as can special maps made for certain famous peaks. In general, the site strives to locate the most accurate topographic maps available for a given peak, and then records the scale of the map used.
When government survey maps are not available, other sources are used, and are noted as such on peak pages. The Shuttle Radar Topography Mission (SRTM) data is often used in places where no good maps are available, as are various databases or other personal projects on the internet, as attributed. Often the map source listed was used only to determine the peak's latitude and longitude, with the elevation listed as the value most often quoted in other reference materials. User added peaks that have only undergone cursory validation are also noted.
In some cases, a lat/long is listed from a GPS reading at the summit--the horizontal locations recorded are usually quite satisfactory. Elevation readings from consumer-grade GPS units (and SRTM data) are usually only accurate to about 5-10 meters, but there are cases where a quality topographic map may have small contour errors and a GPS reading can help accurately determine the location of a high point.
Elevation Lists
An elevation 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 elevation list with a very
specific, non-round number elevation threshold.
All elevation 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 elevation could be a peak on the list, so these lists often use
prominence or isolation as a qualifying factor. On
this site, all elevation 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.
E-Index
The E-Index (Elevation Index) for a climber is the number N, such that the climber has climbed N peaks with N meters of elevation--and over 100 meters of prominence. For example, a climber with an E-Index of 500 has climbed 500 peaks over 500 meters high, excluding "bumps" with less than 100m of prominence. It is a rough measure of the number of high-elevation peaks a climber has summitted.
For many peakbaggers, their E-Index will closely track their total summit count, since climbing peaks over 1000m/3281' is quite common in most places, and not many people have climbed 1000 summits. Also, note that the prominence exclusion (100m/328') is necessary to exclude minor bumps, in much the same way every elevation-based list has a prominence cutoff, too. Once a climber has a large number of summits, there is an advantage in living in a relatively high-elevation area when it comes to increasing E-Index.
The E-Index is a natural extention of the P-Index for prominent peaks and the I-Index for isolated peaks. It has been added to this site at the suggestion of Andrew Kirmse.
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 above 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.
In 2017 researcher Andrew Kirmse created software that calculated the isolation distance for virtually
every summit on earth, based on digital terrain models. With his help, the vast majority if peaks in
the Peakbagger.com database now have a reasonably accurate true isolation value. Click here for more information on this project.
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 can be very difficult to mnaully determine precise ILP coordinates for a peak. Fortunately, in 2017 programmer Andrew Kirmsie used an algorithm to automatically calculate ILPs for tens of thousands of peaks, based on digital terrain model (DEM) data from Jonathan de Ferranti. On
this web site, most peaks know have an accurate ILP, either hand placed, from Andrew's code, or a combination (using the automated point to help in manual placement). A big thank you to Andrew and Jonathan for this invauluable research, which has, for the first time ever, shown the true distribution of isolation values for the majority of the world's significant peaks.
In the cases where an ILP is not present for a peak, the isolation value reported is based on the distance to the nearest higher peak in the Peakbagger.com database. This value is approximate and almost always overstated.
I-Index
The I-Index (Isolation Index) for a climber is the number N, such that the climber has climbed N peaks with N kilometers of isolation or more. For example, a climber with a I-Index of 50 has climbed 50 peaks with over 50 kilometers of Isolation. It is a rough measure of the number and quality of isolated peaks a climber has summitted.
In 2017 ILPs for most of the peaks in the database were calculated, so the I-Index is now reasonably accurate, but there are still peaks where the isolation value is a "pseudo-isolation" value based on nearest higher peak, not nearest higher ground. It does appear as if a climber's maximum possible value is about 360, since there are likely around 360 peaks in the world with 360 km of isolation. This is a somewhat nice number, corresponsing to the number of longitude degrees on earth. Anyone with a value over 100 can be considered an exceptional globe-trotting peakbagger.
The I-Index was proposed by David Sanger and based on the "P-Index" for prominence.
Jut
Jut is an objective measurement of a mountain’s impressiveness. To calculate jut, one first finds the point at the base of the mountain where the slope rises most steeply to the summit, and then measures the elevation difference—that is the jut number. Peaks with steep cliffs will have higher numbers, since the angle is steeper when looking up at those peaks than for low hills.
This article explains the concept in greater detail. Mathematician Kai Xu derived this concept, building on the work of David Metzler and Edward Earl and their ORS and RORS ideas..
Every peak will have a jut base point, the spot at or near the mountain’s base where the angle of relief to the summit is at a maximum. From the jut base point, the horizontal distance to the summit and the angle to the summit can also be calculated, in addition to the jut height.
With the help code supplied by Mr. Xu, jut is being calculated for many peaks in the Peakbagger database.
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.
While this 1:1 ratio is true in a theoretical sense when ultra-precise elevation surveys are used, in practice there is often ambiguity as to which key col is for which summit due to poor data.
The Peakbagger.com database, however, enforces the 1:1 mapping of peak to key col, based on best available information, and, failing that, arbitrary assignment. As new survey data
becomes available, the mapping will be updated as the database moves towards greater accuracy. Do note that any current arbitrary assignments of key col to peak rarely impact the prominence value of a peak significantly.
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, three, 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 highest 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 is 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 Veritical
Datum of 1929 (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 48 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 50,000 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.
Climbers use of optimistic prominence mainly when trying to insure that they have completed all possible peaks above a certain prominence threshold.
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 sometimes
"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 50,000 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 on the highest ridge 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 elevation 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 elevation list, and a
lively debate about the right value to use surrounds many of the more famous
elevation 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 elevation
lists, but intangibles such as ruggedness, beauty, and personable
inspiration are still not factored in.
Prominence Calculation
In 2016-2017, computer scientist Andrew Kirmse was able to create an algorithm that theoretically calculated the topographic prominence of every peak
on earth. Working with DEM data created by Jonathan de Ferranti (from SRTM and other sources), Andrew built upon the pioneering WinProm
program written by the late Edward Earl. The results of this analysis were used to add prominence information (key saddle elevation and location) for many thousands
of peaks in the Peakbagger.com database, and to add many new high-prominence peaks (including over a dozen new "Ultras") as well. Click here for more information on this project.
A big thank you to Andrew and Jonathan for undertaking this project--the "peak geeks" of the world are forever in your debt.
Like WinProm, the accuracy of the output from Andrew's analysis is limited by the quality of the worldwide DEM used for input. Digital Elevation Models will sometimes not capture
exact summit elevations, and this will frequently lead to an incorrect peak being assigned the high prominence that truly belongs to another summit. So this output does
need to be checked by hand before it can be imported wholesale. This will be an ongoing project that will take years--the results are a huge help and certainly save tremendous amounts of time,
but more work will be needed before a 100% accurate picture of the world's prominence hierarchy is complete. Indeed, given the survey and mapping limitations in many
parts of the world, it is likely that until some new worldwide remote-sensed terrain database is available (maybe ground-corrected LIDAR), there will always be some uncertainty.
A goal for the medium-term future is to get a reasonably accurate listing of all the approximately 32,000 summits worldwide with over 600 meters of prominence.
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.
P-Index
The P-Index for a climber is the number N, such that the climber has climbed N peaks with N meters of prominence or more. For example, a climber with a P-Index of 300 has climbed 300 peaks with over 300 meters of prominence. It is a rough measure of the number and quality of prominent peaks a climber has summitted.
Since there are approximately 1500 peaks on Earth with 1500 meters of prominence, a P-Index of 1500 is the maximum value attainable. This symmetry is also why the index is calculated using meters, instead of feet. Additionally, note that this site uses a peak's clean prominence value for calculating a climber's P-Index. Any climber with a P-Index over about 500 can be considered an exceptionally prolific prominence-oriented peakbagger.
The P-Index was proposed by Lee Newton and is based on the H-Index concept that is used to track the number and quality of a scientist's research papers.
Note that on this site the P-index was calculated using average prominence in the past, but has been updated to use clean prominence. Clean is the default prominence used throughout Peakbagger.com and for the sake of consistency the P-Index now does the same.
Omnidirectional Relief and Steepness
See this page at peaklist.org for a detailed discussion of ORS (Omnidirectional Relief and Steepness) and RORS (Reduced ORS). Here are some excerpts from that page:
"Omnidirectional relief and steepness (ORS) is a purely objective mountain measure which takes into account how high the peak rises above local terrain, and how steeply. Since it is a local measure it does not take absolute elevation into account, only the relative height of the peak above its surroundings."
"There is another related measure called reduced ORS (RORS), formerly reduced spire measure (RSM), which combines ORS data (local relief and steepness) with the peak's degree of independence from nearby better peaks. Roughly, it takes the spire measure of the peak in question and subtracts off a piece for each nearby better peak, based on how close together they are."
ORS and RORS are difficult to compute, since they require a detailed digital terrain model in the area of a peak and lots of algorithmic number crunching based on that DEM data. This site hosts a limited number of these values, taken from Peaklist.org
The reduced measure (RORS) seems to be more popular and intuitive measurement.
Mathematicians David Metzler and Edward Earl did most of the work on these concepts and computations.
Jut is a similar concept.
Shore Distance
Shore Distance for a given peak is defined as the distance from that peak to the nearest sea-level ocean water. This can include bays, inlets, estuaries, and other mostly salt-water areas, but not inland lakes and rivers. The point at which a river becomes ocean water is a judgment call, so values may not be super-precise.
This measure helps quantify the high peaks near the ocean that often offer exceptionally scenic views.
Every peak has a Shore Distance Point, the spot on the edge of the ocean water that is closest to the peak.
The Shore Distance Angle for a peak is the angle the peak’s summit rises above the level ocean surface, from the Shore Distance Point. Peaks with steep angles are a sign of impressive sea cliffs. For this calculation, the curvature of the earth is ignored for long distances—the angle is determined using simple Pythagorean geometry.
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 the late mathematician Edward Earl, who wrote a computer program called WinProm that uses 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.
Winter Ascents
Defining a "winter ascent" can be a difficult subject. The precise dates and times for the beginning and end of astronomical winter vary by location and the specific year; the concept of winter is not applicable to the tropics;
and, most importantly, using rigid cutoff dates means that many ascents done under "winter conditions" are technically not in the winter (and vice-versa). Many experienced (northern hemisphere) climbers have done snow-free late-December climbs and April ascents in howling blizzards.
So, for ease of computation, this web site defines a winter ascent as one that occurs between December 21st and March 21st (inclusive) on a peak located north of the Tropic of Cancer. And, of course, an
ascent between June 21st and September 21st (inclusive) on a peak south of the Tropic of Capricorn. "Winter ascents" of peaks in the tropics are not possible. If a climber does not enter a precise-enough
date for a climb, it will also not be credited as a winter ascent. It is best to supply a full month and date, but an ascent logged in January or February, with no specific date, will get credit for
a Northern Hemisphere winter ascent.
Of course, these rules are somewhat arbitrary and perhaps unfair, but so are the weather and route conditions in the mountains. Also note that the locations of the Tropics of
Cancer and Capricorn constantly change by a small amount, too. Perhaps a future update to the site will take into account the true local winter start/end times for all time zones, and the movement of the tropics,
so a more precise astonomical winter definition is applied.
The places on the site where winter ascents can be viewed are as follows:
- All List Pages that show a climber's ascent dates in the last column have an option to only show winter ascent dates.
- All Front Runner's List (FRL) pages for a list have an option to only show peak totals that are winter ascents.
- The Ascent Subset query page has a checkbox at the lower left (in the "Date Range" box) that will only show winter ascents in the query results, in conjunction with the other criteria selected.
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