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Encyclopedia > Topographic prominence

In topography, prominence, also known as autonomous height, relative height or shoulder drop (in America) or prime factor (in Europe), is a concept used in the categorization of hills and mountains, also known as peaks. It is a measure of the independent stature of a summit. By definition, it is the elevation difference between the summit and the lowest contour that encircles it and no higher summit. It is also the smallest descent which one would have to make from a summit in order to re-ascend to a higher peak. It has been suggested that Geomorphometry be merged into this article or section. ... A hill in Hungary with a hillside vintage garden For the landform that extends less than 600 metres above the surrounding terrain and that is smaller than a mountain, see the mountain article. ... A mountain is a landform that extends above the surrounding terrain in a limited area. ... A topographical summit is a point on a surface which is higher in elevation than all points immediately adjacent to it. ... Basic Definition In geography, the elevation of a geographic location is its height above mean sea level (or some other fixed point). ... It has been suggested that Isohypse be merged into this article or section. ...


For example, it is standard that the world's second highest mountain is K2 (height 8,611 m, prominence 4,017 m) and not Mount Everest's South Summit (height 8,749 m, prominence about 10 m), a subsummit of the Main Summit. This is because only summits with a sufficient degree of prominence are regarded as independent mountains rather than subsidiary peaks. K2 is the second highest mountain on Earth. ... Everest redirects here. ...

Contents

Definition of prominence

There are several equivalent definitions:

  • The prominence of a peak is the height of the peak’s summit above the lowest contour line encircling it and no higher summit.
  • For all peaks except Mount Everest, if the peak's prominence is P metres, to get from the summit to any higher terrain, one must descend at least P metres, whatever route is taken. Note that this implies that the prominence of any island or continental highpoint is equal to its elevation above sea level. In this definition, Mount Everest is a special case: its prominence is considered to be equal to its elevation, in order to agree with the previous definition.
  • For all peaks except Mount Everest, the prominence can be calculated as follows. For every ridge (or path of any kind) connecting the peak to higher terrain, find the lowest point on the ridge. This will occur at a col (also called a saddle point or pass). The key col (or key saddle, or linking col, or link) is defined to be the highest among all of these cols, among all connecting ridges. (If the peak is the highest point on a landmass, the key col will be the ocean, and the prominence of the peak is equal to its height.) The prominence is the difference between the elevation of the peak and the elevation of the key col. See Figure 1 below.
  • Suppose that the sea level rises to the lowest level at which the peak becomes the highest point on an island. The prominence of that peak is the height of that island. The key col represents the last isthmus connecting the island to a higher island, just before they become disconnected.
Figure 1. Vertical arrows show the topographic prominence of three peaks on an island. A dotted horizontal line links each peak (except the highest) to its key col.
Enlarge
Figure 1. Vertical arrows show the topographic prominence of three peaks on an island. A dotted horizontal line links each peak (except the highest) to its key col.

It has been suggested that Isohypse be merged into this article or section. ... Col may refer to: the French word for mountain pass a common abbreviation for the military rank colonel This is a disambiguation page, a list of pages that otherwise might share the same title. ... Plot of y = x3 with a saddle-point at (0,0). ... In a range of hills, or especially of mountains, a pass (also gap, notch, col, saddle, bwlch or bealach) is a lower point that allows easier access through the range. ... Image File history File links Relative-height. ... Image File history File links Relative-height. ...

Prominence in mountaineering

Prominence is interesting to mountaineers because it is an objective measurement that is strongly correlated with the subjective significance of a summit. Peaks with low prominences are really just subsidiary tops of some higher summit. Peaks with high prominences tend to be the highest points around and are likely to have extraordinary views. In the U.S., 2000 feet (610 m) of prominence has become an informal threshold that signifies that a peak has major stature. This article or section is not written in the formal tone expected of an encyclopedia article. ...


Many lists of mountains take topographic prominence as a criterion for inclusion, or cutoff. John and Anne Nuttall's The Mountains of England and Wales uses a cutoff of 15 m (about 50 ft), whereas Alan Dawson's list of Marilyns uses 150 m (about 500 ft). (Dawson's list and the term "Marilyn" are limited to the British Isles.) In the contiguous United States, the famous list of "fourteeners" (14,000 foot / 4268 m peaks) uses a prominence cutoff of 300 ft / 91 m (often with some exceptions). Lists with a high topographic prominence cutoff tend to favour isolated peaks or those that are the highest point of their massif; a low value, such as the Nuttalls', results in a list with many summits which may be viewed by some as insignificant. This is a list of peaks by prominence; that is, a list of mountains on Earth ordered by their topographic prominence. ... A Marilyn is a hill with a relative height of at least 150 metres, regardless of absolute height or other merit. ... In mountaineering in the United States, a fourteener is a mountain that exceeds 14,000 feet (4,267. ... In geology, a massif is a section of a planets crust that is demarcated by faults or flexures. ...


While the use of prominence as a cutoff, to form a list of peaks ranked by elevation, is standard, and is the most common use of the concept, it is also possible to use prominence as a mountain measure in itself. This generates lists of peaks ranked by prominence, which have different features than lists ranked by elevation. Such lists tend to emphasize isolated high peaks, such as range or island high points and stratovolcanoes. One advantage of a prominence-ranked list is that it needs no cutoff, since a peak with high prominence is automatically an independent peak. Stratovolcano Mount St. ...


Parent peak

Given a peak, it is common to define a parent for this peak as a certain peak in the higher terrain connected to the peak by the key col. If there are several higher peaks there are various ways of defining which one is the parent. These concepts give ways of putting all peaks on a landmass into a hierarchy showing which peaks are subpeaks of which others. For example, in Figure 1, the middle peak is a subpeak of the right peak, which is in turn a subpeak of the left peak, which is the highest point on its landmass. In that example, there is no controversy over the hierarchy; in practice, there are different definitions of parent. These different definitions follow.


Encirclement or island parentage

Also called prominence island parentage, this is the most mathematically natural definition, and is defined as follows. The key col of peak A is at the meeting place of two closed contours, one encircling A and the other containing at least one higher peak. The encirclement parent of A is the highest peak that is inside this other contour. In terms of the rising sea model, the two contours together bound an island, with two pieces connected by an isthmus at the key col. The encirclement parent is the highest point on this entire island.


For example, the encirclement parent of Mont Blanc, the highest peak in the Alps, is Mount Everest. Mont Blanc's key col is a certain piece of low ground near Lake Onega in northwestern Russia (at 113 m elevation), on the divide between lands draining into the Baltic and Caspian Seas. The 113 m contour met at that point encircles Mount Everest. This example demonstrates that the encirclement parent can be very far away from the peak in question when the key col is low. This article is about the Alpine mountain. ... The West face of the Petit Dru above the Chamonix valley near the Mer de Glace. ... Everest redirects here. ... Lake Onega (also known as Onego, Onezhskoe ozero (from Russian, Онежское озеро), and Onezhskoe lake) is a lake in the Russian Federation. ... A water divide, or watershed, is relatively high ground between water basins. ... The Baltic Sea is located in Northern Europe, from 53°N to 66°N latitude and from 20°E to 26°E longitude. ... The Caspian Sea is the largest lake on Earth by both area and volume,[1] with a surface area of 371,000 square kilometres (143,244 mi²) and a volume of 78,200 cubic kilometres (18,761 mi³).[2] It is a landlocked endorheic body of water and lies between...


This means that, while simple to define, the encirclement parent often does not satisfy the intuitive requirement that the parent peak should be close to the child peak. For example, one common use of the concept of parent is to make clear the location of a peak. If we say that Peak A has Mont Blanc for a parent, we would expect to find Peak A somewhere close to Mont Blanc. This is not always the case for the various concepts of parent, and is least likely to be the case for encirclement parentage.


The encirclement parent is the highest possible parent for a peak; all other definitions pick out a (possibly different) peak on the combined island, by picking a "closer" peak than the encirclement parent, which is still "better" than the peak in question, if there is one. The differences lie in what criteria are used to define "closer" and "better."


Prominence parentage

Prominence parentage is defined in the following way. The parent peak of peak A is found by continuing along a ridgeline from the key col; the nearest peak to A found in such a manner that has a higher topographic prominence than A is the prominence parent.


Height parentage

Height parentage is a less widely used term. It is similar to prominence parentage, but it requires some sort of prominence cutoff criterion. The height parent is the closest peak to peak A (along all ridges connected to A) that has a greater height than A, and is above the prominence cutoff. For example, Mont Blanc's height-parent would be a minor peak in the north-west Caucasus, if the prominence cutoff is low, or Mount Elbrus, if the cutoff is high. This article is about the Alpine mountain. ... The Ethnolinguistic patchwork of the modern Caucasus - CIA map Russia Georgia Azerbaijan (Azer. ... Mount Elbrus (Russian: Эльбрус) is a peak located in the western Caucasus mountains, in Russia, near the border of Georgia. ...


The disadvantage of this concept is that it goes against the intuition that a parent peak should always be more significant than its child. However it can be used to build an entire lineage for a peak which contains a great deal of information about the peak's position.


Other criteria

To choose among possible parents, instead of choosing the closest possible parent, it is possible to chose the one which requires the least descent along the ridge.


In general, the analysis of parents and lineages is intimately linked to studying the topology of watersheds. Further discussion of parents can be found in the Orometry article at peaklist.org. A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology. ... A water divide, or watershed, is relatively high ground between water basins. ...


Interesting prominence situations

The key col and parent peak are often close to the subpeak but this is not always the case, especially when the key col is relatively low. It is only with the advent of computer programs and geographical databases that thorough analysis has become possible.

  • The key col of Mount McKinley in Alaska (6,194 m) is a 56 m col near Lake Nicaragua (unless one accepts the Panama Canal as a key col; this is a matter of contention). McKinley’s encirclement parent is Aconcagua (6,960 m), in Argentina, and its prominence is 6138 m. Put another way, to further illustrate the "rising sea" model of prominence – if sea level rose 56 m North and South America would be separate continents and McKinley would be 6138 m above sea level. At a slightly lower level, the continents would still be connected, and the high point of the combined landmass would be Aconcagua, the encirclement parent.

While it is natural for Aconcagua to be the parent of Mount McKinley, since Mount McKinley is a major peak, consider the following situation: Peak A is a small hill on the coast of Alaska, with elevation 100 m and key col 50 m. Then the encirclement parent of Peak A is also Aconcagua, even though there will be many peaks closer to Peak A which are much higher and more prominent than Peak A (for example, Mount McKinley). This illustrates the disadvantage in using the encirclement parent. Denali redirects here. ... Official language(s) English Capital Juneau Largest city Anchorage Area  Ranked 1st  - Total 663,267 sq mi (1,717,855 km²)  - Width 808 miles (1,300 km)  - Length 1,479 miles (2,380 km)  - % water 13. ... Lake Nicaragua (Spanish: Lago de Nicaragua) or Lake Cocibolca (Lago Cocibolca) is a freshwater lake in Nicaragua and it is of tectonic origin. ... two Panamas running the Miraflores Locks. ... The Cerro Aconcagua is located in Argentina and is the highest mountain in The Americas and the Southern Hemisphere, as well the highest peak outside of Asia and one of the Seven Summits. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...

Mount Whitney is the highest point in the contiguous United States at elevation 14,505 feet (4,421 meters). ... Capital Santa Fe Largest city Albuquerque Area  Ranked 5th  - Total 121,665 sq mi (315,194 km²)  - Width 342 miles (550 km)  - Length 370 miles (595 km)  - % water 0. ... A continental divide is a line of elevated terrain which forms a border between two watersheds such that water falling on one side of the line eventually travels to one ocean or body of water, and water on the other side travels to another, generally on the opposite side of... The Pico de Orizaba or Citlaltépetl (in English: Orizaba Peak) is the highest mountain in Mexico and the third highest volcano in the Western Hemisphere. ... Motto: Splendor Sine Occasu (Latin: Splendour without diminishment) Official languages English de facto (none stated in law) Flower Pacific dogwood Tree Western Redcedar Bird Stellers Jay Capital Victoria Largest city Vancouver Lieutenant-Governor Iona Campagnolo Premier Gordon Campbell (BC Liberal) Parliamentary representation  - House seats  - Senate seats 36 6 Area... For other mountains named Mitchell, see Mount Mitchell. ... The Appalachian Mountains are a system of North American mountains running from Newfoundland and Labrador, Canada to Alabama in the United States, although the northernmost mainland portion ends at the Gaspe Peninsula of Quebec. ... Nickname: The Windy City, The Second City, Chi Town, The City of Big Shoulders The 312 Motto: Urbs In Horto (Latin: City in a Garden), I Will Location in Chicagoland and Illinois Coordinates: Country United States State Illinois County Cook Incorporated March 4, 1837 Mayor Richard M. Daley (D) Area... The Saint Lawrence River (French: fleuve Saint-Laurent) is a large west-to-east flowing river in the middle latitudes of North America, connecting the Great Lakes with the Atlantic Ocean. ... The Mississippi River, derived from the old Ojibwe word misi-ziibi meaning great river (gichi-ziibi big river at its headwaters), is the second-longest river in the United States; the longest is the Missouri River, which flows into the Mississippi. ... A drainage basin is the area within the drainage basin divide (yellow outline), and drains the surface runoff and river discharge (blue lines) of a contiguous area. ...

Calculations and mathematics of prominence

When the key col for a peak is close to the peak itself, prominence is easily computed by hand using a topographic map. However, when the key col is far away, or when one want to calculate the prominence of many peaks at once, a computer is quite useful. Edward Earl has written a program called WinProm which can be used to make such calculations, based on a Digital Elevation Model. The underlying mathematical theory is called "Surface Network Modeling," and is closely related to Morse Theory. Example of a topographic map with contour lines Part of the same map in a perspective shaded relief view illustrates how the contour lines of the original follow the terrain Topographic maps, also called contour maps, topo maps or topo quads (for quadrangles), are maps that show topography, or land... A digital elevation model (DEM) is a representation of the topography of the Earth in digital format, that is, by coordinates and numerical descriptions of altitude. ... A Morse function is also an expression for an anharmonic oscillator In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. ...


A note about methodology: when using a topographic map to determine prominence, one often has to estimate the height of the key saddle (and sometimes, the height of the peak as well) based on the contour lines. Assume for simplicity that only the saddle elevation is uncertain. There are three simple choices: the pessimistic, or clean prominence, assumes that the saddle is as high as it can be, i.e. its elevation is that of the higher contour line nearest the saddle. This gives a lower bound on the possible prominence of the peak (assuming that the map is accurate.) Optimistic prominence assumes that the saddle is as low as possible, yielding an upper bound value for the prominence. Midrange prominence uses the mean of these two values. Example of a topographic map with contour lines Part of the same map in a perspective shaded relief view illustrates how the contour lines of the original follow the terrain Topographic maps, also called contour maps, topo maps or topo quads (for quadrangles), are maps that show topography, or land...


Which methodology is used depends on the person doing the calculation and on the use to which the prominence is put. For example, if one is making a list of all peaks with at least 2,000 ft (610 m) of prominence, one would usually use the optimistic prominence, to include all possible candidates (knowing that some of these could be dropped off the list by further, more accurate, measurements).


See also

Peak bagging (also hill bagging, mountain bagging, or among enthusiasts, just bagging) is a popular activity for hillwalkers and mountaineers in which they attempt to reach the summit of each peak in a region above some height, or having a particular feature. ... This is a list of peaks in the British Isles with a relative height of more than 2000 feet (610 m), in descending order of relative height. ... This is a list of peaks by prominence; that is, a list of mountains on Earth ordered by their topographic prominence. ... This is a list of the mountains of the Alps, ordered by their topographic prominence. ... Mount Everest, the worlds highest mountain The following is a list of the worlds 100 highest mountains, all of which are located in Asia. ...

References

  • K2 prominence

External links

  • http://www.peaklist.org a website about mountain prominence, with lists and/or maps covering the entire world down to 1500m of prominence (the "ultras").
  • Prominence at the County Highpointers This page contains links to all relevant on-line prominence resources — including peak lists, climbing records, prominence cell maps, "completion maps", and trip reports. By Adam Helman.
  • Prominence Book By Adam Helman, this is a comprehensive, in-depth study of topographic prominence in all its aspects (Trafford Publishing, 241 pages).
  • Prominence and Orometry a detailed and lucid account by Aaron Maizlish of the theory of prominence.
  • http://groups.yahoo.com/group/prominence/ Yahoo! Groups, Topographic prominence discussion
  • Prominence Front Runners Prominence-oriented climbing records. Lists are maintained by Andy Martin and hosted at cohp.org .
  • Edward Earl’s article on Topographic Prominence
  • Index to definitions in the Canadian Mountain Encyclopedia
  • Mountain Hierarchies a description of the different systems of defining parent peak
  • Mountain Hierarchy using Prominence Islands
  • Surface Network Modelling on the Center for Advanced Surface Analysis website
  • Surface Network Modelling a paper by Sanjay Rana and Jeremy Morley
  • The 100 most prominent peaks in Colorado
  • Alan Dawson's The Relative Hills of Britain

  Results from FactBites:
 
Prominence Theory (1784 words)
Although prominence has been used inadvertently for many years for some purposes, it was used only to support some other concept and not as a primary concept in its own right, and it did not even have a name for most of that time.
To compute the prominence of a peak usually requires a considerable amount of time and a keen eye for detail in examining the contours on a topographic map to find a saddle connecting a given peak to a higher peak and verifying that there is no higher saddle.
In cases where prominence was computed for the purpose of determining whether a given peak should be considered a separate peak for inclusion on an altitude-based list, the peak was usually close to a higher peak, and the area that had to be searched was limited.
Topographic prominence - Wikipedia, the free encyclopedia (2174 words)
The prominence of that peak is the height of that island.
Prominence is interesting to mountaineers because it is an objective measurement that is strongly correlated with the subjective significance of a summit.
Lists with a high topographic prominence cutoff tend to favour isolated peaks or those that are the highest point of their massif; a low value, such as the Nuttalls', results in a list with many summits which may be viewed by some as insignificant.
  More results at FactBites »

 
 

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