Topographic prominence
Encyclopedia
In topography
, prominence, also known as autonomous height, relative height, shoulder drop (in North America
), or prime factor (in Europe
), categorizes the height of the mountain
's or hill
's summit by the elevation between it and the lowest contour line
encircling it and no higher summit. It is a measure of the independence of a summit.
, the Earth's highest mountain, is taken to equal the elevation of its summit above sea level
. Apart from this special case, there are several equivalent definitions:
because it is an objective measurement that is strongly correlated with the subjective significance of a summit. Peaks with low prominences are either subsidiary tops of some higher summit or relatively insignificant independent summits. Peaks with high prominences tend to be the highest points around and are likely to have extraordinary views.
For example, the world's second highest mountain is K2
(height 8,611 m, prominence 4,017 m). While Mount Everest
's South Summit (height 8,749 m, prominence about 10 m) is taller, it is a subsummit of the main summit. Only summits with a sufficient degree of prominence are regarded as independent mountains.
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), and Alan Dawson's list of Marilyn
s 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 "fourteener
s" (14,000 foot / 4268 m peaks) uses a cutoff of 300 ft / 91 m (with some exceptions). Also in the U.S., 2000 feet (610 m) of prominence has become an informal threshold that signifies that a peak has major stature.
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 that may be viewed by some as insignificant.
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 are qualitatively different from lists ranked by elevation. Such lists tend to emphasize isolated high peaks, such as range or island high points and stratovolcano
es. One advantage of a prominence-ranked list is that it needs no cutoff, since a peak with high prominence is automatically an independent peak.
In that example, there is no controversy over the hierarchy; in practice, there are different definitions of parent. These different definitions follow.
A special case occurs for the highest point on an oceanic island or continent. Some sources define no parent in this case; others treat Mount Everest as the parent of every such peak with the ocean as the "key col".
For example, the encirclement parent of Mont Blanc
, the highest peak in the Alps
, is Mount Everest
. Mont Blanc's key col is a 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 Sea
s. This is the meeting place of two 113 m contours, one of them encircling Mont Blanc; the other contour 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 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, a "closer" peak than the encirclement parent (if there is one), which is still "better" than the peak in question. The differences lie in what criteria are used to define "closer" and "better."
For hills with low prominence in Britain
, a definition of 'parent Marilyn
' is sometimes used to classify low hills. This is found by dividing the region of Britain in question into territories, one for each Marilyn. Once again, the parent Marilyn is the Marilyn whose territory the peak is in. Obviously, if a peak is the highest point of its island, it has no parent. Likewise, if a hill is on an island (in Britain) whose highest point is less than 150m, it has no parent Marilyn.
Prominence parentage is the only definition used in the British Isles
because 'encirclement' parents break down when the key col approaches sea level. Using this definition, the parent of any low-lying bump next to the sea would be Ben Nevis - which could be said to be irrelevant and confusing. Similarly 'height' parentage is not used because there is no obvious standard for what the cutoff used should be.
This might seem arbitrary, but it gives a clear and unambiguous definition for the 'parent' of a mountain that is more significant than, connected to and reasonably close to it. It also enables one to make a 'hierarchy' of peaks going back to the highest point on the island. One such chain in the British Isles would read;
Billinge Hill
→ Winter Hill → Hail Storm Hill
→ Boulsworth Hill
→ Kinder Scout
→ Cross Fell
→ Helvellyn
→ Scafell Pike
→ Snowdon
→ Ben Nevis
.
At each stage in the chain both the height and prominence are increasing.
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.
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.
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.
. However, when the key col is far away, or when one wants 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
.
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. Optimistic prominence assumes that the saddle is as low as possible, yielding an upper bound value for the prominence. Midrange or mean prominence uses the mean of these two values.
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).
Dry prominence, on the other hand, ignores water, snow, and ice features and assumes that the surface of the earth is defined by the solid bottom of those features. The dry prominence of a summit is equal to the wet prominence of that summit unless the summit is the highest point of a landmass or island, or a summit surrounded by snow or ice. If a summit is completely surrounded by a water, snow, or ice feature, the dry prominence of that summit is equal to the wet prominence plus the depth of the highest col.
The dry prominence of Mount Everest
is, by convention, equal to its wet prominence (8848 m) plus the depth of the deepest hydrologic feature (the Challenger Deep
at 10,911 m), or 19,761 m. The dry prominence of Mauna Kea
is equal to its wet prominence (4205 m) plus the depth of its highest col (about 5125 m), or about 9330 m; this is the world's second greatest dry prominence after Mount Everest. The dry prominence of Aconcagua
is equal to its wet prominence (6962 m) plus the depth of the highest col of the Bering Strait
(about 50 m), or about 7012 m.
Dry prominence is also useful for measuring submerged seamount
s. Submerged summits have both a dry topographic prominence and a topographic isolation
.
The following mental exercise may illustrate the meaning of topographic prominence. Imagine you are standing at the top of a mountain peak. Let an imaginary sea level slowly rise to the top of your peak. As the imaginary sea level rises, the mountain will shrink into an ever smaller island until the island disappears at your feet. Now let the imaginary sea level slowly drop. The island will reappear with your peak as its highest point. As the sea level continues to drop, the island will grow and merge with adjacent islands. At some point, unless you are atop Mount Everest, your island will touch another island with a higher summit. This point is called your peak’s key col, and the elevation rise from its key col to your summit is called its topographic prominence.
Topography
Topography is the study of Earth's surface shape and features or those ofplanets, moons, and asteroids...
, prominence, also known as autonomous height, relative height, shoulder drop (in North America
North America
North America is a continent wholly within the Northern Hemisphere and almost wholly within the Western Hemisphere. It is also considered a northern subcontinent of the Americas...
), or prime factor (in Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
), categorizes the height of the mountain
Mountain
Image:Himalaya_annotated.jpg|thumb|right|The Himalayan mountain range with Mount Everestrect 58 14 160 49 Chomo Lonzorect 200 28 335 52 Makalurect 378 24 566 45 Mount Everestrect 188 581 920 656 Tibetan Plateaurect 250 406 340 427 Rong River...
's or hill
Hill
A hill is a landform that extends above the surrounding terrain. Hills often have a distinct summit, although in areas with scarp/dip topography a hill may refer to a particular section of flat terrain without a massive summit A hill is a landform that extends above the surrounding terrain. Hills...
's summit by the elevation between it and the lowest contour line
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...
encircling it and no higher summit. It is a measure of the independence of a summit.
Definitions
By convention, the prominence of Mount EverestMount Everest
Mount Everest is the world's highest mountain, with a peak at above sea level. It is located in the Mahalangur section of the Himalayas. The international boundary runs across the precise summit point...
, the Earth's highest mountain, is taken to equal the elevation of its summit above sea level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
. Apart from this special case, there are several equivalent definitions:
- The prominence of a peak is the height of the peak’s summit above the lowest contour lineContour lineA contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...
encircling it and no higher summit. - If the peak's prominence is P metreMetreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
s, to get from the summit to any higher terrain one must descend at least P metres. Together with the convention for Mount Everest, this implies that the prominence of any islandIslandAn island or isle is any piece of sub-continental land that is surrounded by water. Very small islands such as emergent land features on atolls can be called islets, cays or keys. An island in a river or lake may be called an eyot , or holm...
or continentContinentA continent is one of several very large landmasses on Earth. They are generally identified by convention rather than any strict criteria, with seven regions commonly regarded as continents—they are : Asia, Africa, North America, South America, Antarctica, Europe, and Australia.Plate tectonics is...
al highpoint is equal to its elevation above sea levelSea levelMean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
. - For every ridge (or path of any kind) connecting the peak to higher terrain, find the lowest point on the ridge. This will be at a colMountain passA mountain pass is a route through a mountain range or over a ridge. If following the lowest possible route, a pass is locally the highest point on that route...
(also called a saddle pointSaddle pointIn mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives from the fact that in two dimensions the surface resembles a saddle that curves up in one direction, and curves down in a different direction...
or passMountain passA mountain pass is a route through a mountain range or over a ridge. If following the lowest possible route, a pass is locally the highest point on that route...
). The key col (or key saddle, or linking col, or link) is defined as the highest of these cols, along 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 elevation.) The prominence is the difference between the elevation of the peak and the elevation of the key col. See Figure 1. - 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 isthmusIsthmusAn isthmus is a narrow strip of land connecting two larger land areas usually with waterforms on either side.Canals are often built through isthmuses where they may be particularly advantageous to create a shortcut for marine transportation...
connecting the island to a higher island, just before they become disconnected.
In mountaineering
Prominence is interesting to some mountaineersMountaineering
Mountaineering or mountain climbing is the sport, hobby or profession of hiking, skiing, and climbing mountains. While mountaineering began as attempts to reach the highest point of unclimbed mountains it has branched into specialisations that address different aspects of the mountain and consists...
because it is an objective measurement that is strongly correlated with the subjective significance of a summit. Peaks with low prominences are either subsidiary tops of some higher summit or relatively insignificant independent summits. Peaks with high prominences tend to be the highest points around and are likely to have extraordinary views.
For example, the world's second highest mountain is K2
K2
K2 is the second-highest mountain on Earth, after Mount Everest...
(height 8,611 m, prominence 4,017 m). While Mount Everest
Mount Everest
Mount Everest is the world's highest mountain, with a peak at above sea level. It is located in the Mahalangur section of the Himalayas. The international boundary runs across the precise summit point...
's South Summit (height 8,749 m, prominence about 10 m) is taller, it is a subsummit of the main summit. Only summits with a sufficient degree of prominence are regarded as independent mountains.
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), and Alan Dawson's list of Marilyn
Marilyn (hill)
A Marilyn is a mountain or hill in the United Kingdom, Republic of Ireland or Isle of Man with a relative height of at least 150 metres , regardless of absolute height or other merit...
s 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 "fourteener
Fourteener
In mountaineering terminology in the United States, a fourteener is a mountain that exceeds 14,000 feet above mean sea level. There are 547 fourteeners in the world. The importance of fourteeners is greatest in Colorado, which has the majority of such peaks in North America...
s" (14,000 foot / 4268 m peaks) uses a cutoff of 300 ft / 91 m (with some exceptions). Also in the U.S., 2000 feet (610 m) of prominence has become an informal threshold that signifies that a peak has major stature.
Lists with a high topographic prominence cutoff tend to favour isolated peaks or those that are the highest point of their massif
Massif
In geology, a massif is a section of a planet's crust that is demarcated by faults or flexures. In the movement of the crust, a massif tends to retain its internal structure while being displaced as a whole...
; a low value, such as the Nuttalls', results in a list with many summits that may be viewed by some as insignificant.
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 are qualitatively different from lists ranked by elevation. Such lists tend to emphasize isolated high peaks, such as range or island high points and stratovolcano
Stratovolcano
A stratovolcano, also known as a composite volcano, is a tall, conical volcano built up by many layers of hardened lava, tephra, pumice, and volcanic ash. Unlike shield volcanoes, stratovolcanoes are characterized by a steep profile and periodic, explosive eruptions...
es. One advantage of a prominence-ranked list is that it needs no cutoff, since a peak with high prominence is automatically an independent peak.
Parent peak
It is common to define a peak's parent as a particular 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.
A special case occurs for the highest point on an oceanic island or continent. Some sources define no parent in this case; others treat Mount Everest as the parent of every such peak with the ocean as the "key col".
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 no higher peaks) 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
Mont Blanc
Mont Blanc or Monte Bianco , meaning "White Mountain", is the highest mountain in the Alps, Western Europe and the European Union. It rises above sea level and is ranked 11th in the world in topographic prominence...
, the highest peak in the Alps
Alps
The Alps is one of the great mountain range systems of Europe, stretching from Austria and Slovenia in the east through Italy, Switzerland, Liechtenstein and Germany to France in the west....
, is Mount Everest
Mount Everest
Mount Everest is the world's highest mountain, with a peak at above sea level. It is located in the Mahalangur section of the Himalayas. The international boundary runs across the precise summit point...
. Mont Blanc's key col is a piece of low ground near Lake Onega
Lake Onega
Lake Onega is a lake in the north-west European part of Russia, located on the territory of Republic of Karelia, Leningrad Oblast and Vologda Oblast. It belongs to the basin of Baltic Sea, Atlantic Ocean, and is the second largest lake in Europe after Lake Ladoga...
in northwestern Russia (at 113 m elevation), on the divide
Water divide
A drainage divide, water divide, divide or watershed is the line separating neighbouring drainage basins...
between lands draining into the Baltic
Baltic Sea
The Baltic Sea is a brackish mediterranean sea located in Northern Europe, from 53°N to 66°N latitude and from 20°E to 26°E longitude. It is bounded by the Scandinavian Peninsula, the mainland of Europe, and the Danish islands. It drains into the Kattegat by way of the Øresund, the Great Belt and...
and Caspian Sea
Caspian Sea
The Caspian Sea is the largest enclosed body of water on Earth by area, variously classed as the world's largest lake or a full-fledged sea. The sea has a surface area of and a volume of...
s. This is the meeting place of two 113 m contours, one of them encircling Mont Blanc; the other contour 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 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, a "closer" peak than the encirclement parent (if there is one), which is still "better" than the peak in question. The differences lie in what criteria are used to define "closer" and "better."
Prominence parentage
The (prominence) parent peak of peak A can be found by dividing the island or region in question into territories, by tracing the runoff from the key col of every peak that is more prominent than peak A. The parent is the peak whose territory peak A is in.For hills with low prominence in Britain
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, a definition of 'parent Marilyn
Marilyn (hill)
A Marilyn is a mountain or hill in the United Kingdom, Republic of Ireland or Isle of Man with a relative height of at least 150 metres , regardless of absolute height or other merit...
' is sometimes used to classify low hills. This is found by dividing the region of Britain in question into territories, one for each Marilyn. Once again, the parent Marilyn is the Marilyn whose territory the peak is in. Obviously, if a peak is the highest point of its island, it has no parent. Likewise, if a hill is on an island (in Britain) whose highest point is less than 150m, it has no parent Marilyn.
Prominence parentage is the only definition used in the British Isles
British Isles
The British Isles are a group of islands off the northwest coast of continental Europe that include the islands of Great Britain and Ireland and over six thousand smaller isles. There are two sovereign states located on the islands: the United Kingdom of Great Britain and Northern Ireland and...
because 'encirclement' parents break down when the key col approaches sea level. Using this definition, the parent of any low-lying bump next to the sea would be Ben Nevis - which could be said to be irrelevant and confusing. Similarly 'height' parentage is not used because there is no obvious standard for what the cutoff used should be.
This might seem arbitrary, but it gives a clear and unambiguous definition for the 'parent' of a mountain that is more significant than, connected to and reasonably close to it. It also enables one to make a 'hierarchy' of peaks going back to the highest point on the island. One such chain in the British Isles would read;
Billinge Hill
Billinge Hill
Billinge Hill, also known as Billinge Lump, is the highest point in the Metropolitan Borough of St Helens in North West England. It is also the highest point of Merseyside It lies in Billinge, within the historic county boundaries of Lancashire....
→ Winter Hill → Hail Storm Hill
Hail Storm Hill
Hail Storm Hill, also known as Cowpe Moss, is the highest point of the Forest of Rossendale, an area of moorland and hill country situated between the West Pennine Moors and the South Pennines...
→ Boulsworth Hill
Boulsworth Hill
Boulsworth Hill is a large expanse of moorland, the highest point of the South Pennines of south-eastern Lancashire, England, separating the District of Pendle from Calderdale....
→ Kinder Scout
Kinder Scout
Kinder Scout is a moorland plateau in the Dark Peak of the Derbyshire Peak District in England. Part of the moor, at 636 m above sea level, is the highest point in the Peak District, the highest point in Derbyshire, and the highest point in the East Midlands. It is accessible from the villages of...
→ Cross Fell
Cross Fell
Cross Fell is the highest point in the Pennine Hills of northern England and the highest point in England outside of the Lake District.The summit, at , is a stony plateau, part of a long ridge running North West to South East, which also incorporates Little Dun Fell at and Great Dun Fell at...
→ Helvellyn
Helvellyn
Helvellyn is a mountain in the English Lake District, the apex of the Eastern Fells. At above sea level, it is the third highest peak in both the Lake District and England...
→ Scafell Pike
Scafell Pike
Scafell Pike is the highest mountain in England at . It is located in Lake District National Park sometimes confused with the neighbouring Sca Fell, to which it is connected by the col of Mickledore...
→ Snowdon
Snowdon
Snowdon is the highest mountain in Wales, at an altitude of above sea level, and the highest point in the British Isles outside Scotland. It is located in Snowdonia National Park in Gwynedd, and has been described as "probably the busiest mountain in Britain"...
→ Ben Nevis
Ben Nevis
Ben Nevis is the highest mountain in the British Isles. It is located at the western end of the Grampian Mountains in the Lochaber area of the Scottish Highlands, close to the town of Fort William....
.
At each stage in the chain both the height and prominence are increasing.
Line parentage
Line parentage, also called height parentage, 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 satisfies some prominence criteria.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 choose 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
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
of watersheds
Water divide
A drainage divide, water divide, divide or watershed is the line separating neighbouring drainage basins...
. Further discussion of parents can be found in the Orometry article at peaklist.org.
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 McKinleyMount McKinleyMount McKinley or Denali in Alaska, United States is the highest mountain peak in North America and the United States, with a summit elevation of above sea level. It is the centerpiece of Denali National Park and Preserve.- Geology and features :Mount McKinley is a granitic pluton...
(also called Denali) in AlaskaAlaskaAlaska is the largest state in the United States by area. It is situated in the northwest extremity of the North American continent, with Canada to the east, the Arctic Ocean to the north, and the Pacific Ocean to the west and south, with Russia further west across the Bering Strait...
(6,194 m) is a 56 m col near Lake NicaraguaLake NicaraguaLake Nicaragua or Cocibolca or Granada or is a vast freshwater lake in Nicaragua of tectonic origin. With an area of , it is the largest lake in Central America, the 19th largest lake in the world and the 9th largest in the Americas. It is slightly smaller than Lake Titicaca. With an elevation...
(unless one accepts the Panama CanalPanama CanalThe Panama Canal is a ship canal in Panama that joins the Atlantic Ocean and the Pacific Ocean and is a key conduit for international maritime trade. Built from 1904 to 1914, the canal has seen annual traffic rise from about 1,000 ships early on to 14,702 vessels measuring a total of 309.6...
as a key col; this is a matter of contention). McKinley’s encirclement parent is AconcaguaAconcaguaAconcagua is the highest mountain in the Americas at . It is located in the Andes mountain range, in the Argentine province of Mendoza and it lies west by north of its capital, the city of Mendoza. The summit is also located about 5 kilometres from San Juan Province and 15 kilometres from the...
(6,960 m), in ArgentinaArgentinaArgentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...
, and its prominence is 6,138 m. 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 levelSea levelMean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
. 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. Note that, for the purposes of this article, man made structures such as the Panama CanalPanama CanalThe Panama Canal is a ship canal in Panama that joins the Atlantic Ocean and the Pacific Ocean and is a key conduit for international maritime trade. Built from 1904 to 1914, the canal has seen annual traffic rise from about 1,000 ships early on to 14,702 vessels measuring a total of 309.6...
are not taken into account. If they were, the key col would be along the 26 m Gaillard CutGaillard CutThe Gaillard Cut, or Culebra Cut, is an artificial valley that cuts through the continental divide in Panama. The cut forms part of the Panama Canal, linking Lake Gatún, and thereby the Atlantic Ocean, to the Gulf of Panama and hence the Pacific Ocean...
and McKinley would have a prominence of 6,168 m.
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.
- Mount WhitneyMount WhitneyMount Whitney is the highest summit in the contiguous United States with an elevation of . It is on the boundary between California's Inyo and Tulare counties, west-northwest of the lowest point in North America at Badwater in Death Valley National Park...
(4421 m) has its key col 1022 km (635 mi) away in New MexicoNew MexicoNew Mexico is a state located in the southwest and western regions of the United States. New Mexico is also usually considered one of the Mountain States. With a population density of 16 per square mile, New Mexico is the sixth-most sparsely inhabited U.S...
at 1347 m on the Continental DivideContinental DivideThe Continental Divide of the Americas, or merely the Continental Gulf of Division or Great Divide, is the name given to the principal, and largely mountainous, hydrological divide of the Americas that separates the watersheds that drain into the Pacific Ocean from those river systems that drain...
. Its encirclement parent is Pico de OrizabaPico de OrizabaThe Pico de Orizaba, or Citlaltépetl , is a stratovolcano, the highest mountain in Mexico and the third highest in North America. It rises above sea level in the eastern end of the Trans-Mexican Volcanic Belt, on the border between the states of Veracruz and Puebla...
(5,636 m), the highest mountain in MexicoMexicoThe United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...
. Orizaba’s key col is back along the Divide, in British ColumbiaBritish ColumbiaBritish Columbia is the westernmost of Canada's provinces and is known for its natural beauty, as reflected in its Latin motto, Splendor sine occasu . Its name was chosen by Queen Victoria in 1858...
. - The key col for Mount MitchellMount Mitchell (North Carolina)Mount Mitchell is the highest peak of the Appalachian Mountains and the highest peak in the eastern United States. It was the highest point in any state of the United States until Texas joined the union in 1845. The nearest higher point east of the Rocky Mountains is Harney Peak in the Black Hills...
, the highest peak of the Appalachians, is in ChicagoChicagoChicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles...
—the low point on the divide between the St. LawrenceSaint Lawrence RiverThe Saint Lawrence is a large river flowing approximately from southwest to northeast in the middle latitudes of North America, connecting the Great Lakes with the Atlantic Ocean. It is the primary drainage conveyor of the Great Lakes Basin...
and Mississippi RiverMississippi RiverThe Mississippi River is the largest river system in North America. Flowing entirely in the United States, this river rises in western Minnesota and meanders slowly southwards for to the Mississippi River Delta at the Gulf of Mexico. With its many tributaries, the Mississippi's watershed drains...
watershedDrainage basinA drainage basin is an extent or an area of land where surface water from rain and melting snow or ice converges to a single point, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, reservoir, estuary, wetland, sea, or ocean...
s.
Calculations and mathematics
When the key col for a peak is close to the peak itself, prominence is easily computed by hand using a topographic mapTopographic map
A topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and man-made features...
. However, when the key col is far away, or when one wants 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
Digital elevation model
A digital elevation model is a digital model or 3-D representation of a terrain's surface — commonly for a planet , moon, or asteroid — created from terrain elevation data....
. The underlying mathematical theory is called "Surface Network Modeling," and is closely related to Morse Theory
Morse theory
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. According to the basic insights of Marston Morse, a differentiable function on a manifold will, in a typical case, reflect...
.
A note about methodology: when using a topographic map
Topographic map
A topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and man-made features...
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. Optimistic prominence assumes that the saddle is as low as possible, yielding an upper bound value for the prominence. Midrange or mean prominence uses the mean of these two values.
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).
Wet prominence and dry prominence
There are actually two varieties of topographic prominence: wet prominence and dry prominence. Wet prominence is the topographic prominence discussed in this article. Wet prominence assumes that the surface of the earth includes all permanent water, snow, and ice features. Thus, the wet prominence of the highest summit of an ocean island or landmass is always equal to the summit's elevation.Dry prominence, on the other hand, ignores water, snow, and ice features and assumes that the surface of the earth is defined by the solid bottom of those features. The dry prominence of a summit is equal to the wet prominence of that summit unless the summit is the highest point of a landmass or island, or a summit surrounded by snow or ice. If a summit is completely surrounded by a water, snow, or ice feature, the dry prominence of that summit is equal to the wet prominence plus the depth of the highest col.
The dry prominence of Mount Everest
Mount Everest
Mount Everest is the world's highest mountain, with a peak at above sea level. It is located in the Mahalangur section of the Himalayas. The international boundary runs across the precise summit point...
is, by convention, equal to its wet prominence (8848 m) plus the depth of the deepest hydrologic feature (the Challenger Deep
Challenger Deep
The Challenger Deep is the deepest known point in the oceans, with a depth of to by direct measurement from submersibles, and slightly more by sonar bathymetry . It is located at the southern end of the Mariana Trench near the Mariana Islands group...
at 10,911 m), or 19,761 m. The dry prominence of Mauna Kea
Mauna Kea
Mauna Kea is a volcano on the island of Hawaii. Standing above sea level, its peak is the highest point in the state of Hawaii. However, much of the mountain is under water; when measured from its oceanic base, Mauna Kea is over tall—significantly taller than Mount Everest...
is equal to its wet prominence (4205 m) plus the depth of its highest col (about 5125 m), or about 9330 m; this is the world's second greatest dry prominence after Mount Everest. The dry prominence of Aconcagua
Aconcagua
Aconcagua is the highest mountain in the Americas at . It is located in the Andes mountain range, in the Argentine province of Mendoza and it lies west by north of its capital, the city of Mendoza. The summit is also located about 5 kilometres from San Juan Province and 15 kilometres from the...
is equal to its wet prominence (6962 m) plus the depth of the highest col of the Bering Strait
Bering Strait
The Bering Strait , known to natives as Imakpik, is a sea strait between Cape Dezhnev, Chukotka Autonomous Okrug, Russia, the easternmost point of the Asian continent and Cape Prince of Wales, Alaska, USA, the westernmost point of the North American continent, with latitude of about 65°40'N,...
(about 50 m), or about 7012 m.
Dry prominence is also useful for measuring submerged seamount
Seamount
A seamount is a mountain rising from the ocean seafloor that does not reach to the water's surface , and thus is not an island. These are typically formed from extinct volcanoes, that rise abruptly and are usually found rising from a seafloor of depth. They are defined by oceanographers as...
s. Submerged summits have both a dry topographic prominence and a topographic isolation
Topographic isolation
The topographic isolation of a summit is the minimum horizontal distance to the nearest point of higher elevation. Topographic isolation represents a radius of dominance in which the summit is the highest point. Topographic isolation can be calculated for small hills and islands as well as for...
.
The following mental exercise may illustrate the meaning of topographic prominence. Imagine you are standing at the top of a mountain peak. Let an imaginary sea level slowly rise to the top of your peak. As the imaginary sea level rises, the mountain will shrink into an ever smaller island until the island disappears at your feet. Now let the imaginary sea level slowly drop. The island will reappear with your peak as its highest point. As the sea level continues to drop, the island will grow and merge with adjacent islands. At some point, unless you are atop Mount Everest, your island will touch another island with a higher summit. This point is called your peak’s key col, and the elevation rise from its key col to your summit is called its topographic prominence.
See also
- Most prominent mountain peaks of the world
- Most prominent mountain peaks of the Alps
- Most prominent mountain peaks of the British Isles
- Table of the most prominent summits of North America
- Table of the ultra-prominent summits of the United States
- Most prominent mountain peaks of Canada
- Most prominent mountain peaks of Mexico
- Most prominent mountain peaks of New EnglandNew England Fifty FinestThe New England Fifty Finest is a list of mountains in New England, used in the mountaineering sport of peak bagging.The list comprises the fifty summits with the highest topographic prominence — a peak's height above the lowest contour which encloses that peak and no higher peak.This list differs...
- List of highest mountains
- Summit (topography)Summit (topography)In topography, a summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. Mathematically, a summit is a local maximum in elevation...
- Topographic elevation
- Topographic isolationTopographic isolationThe topographic isolation of a summit is the minimum horizontal distance to the nearest point of higher elevation. Topographic isolation represents a radius of dominance in which the summit is the highest point. Topographic isolation can be calculated for small hills and islands as well as for...
- Ultra prominent peakUltra prominent peakAn ultra prominent peak, or Ultra for short, is a mountain with a topographic prominence of or more. There are a total of roughly 1,524 such peaks in the world. Some are famous even to non-climbers, such as Mount Everest, Aconcagua, and Mount McKinley , while others are much more obscure...
External links
- K2 prominence
- Peaklist a website about mountain prominence, with lists and/or maps covering the entire world down to 1500m of prominence (the "ultras").
- Europeaklist, 'sister' website to the above, devoted only to European mountains and hills.
- UK Prominent Peaks UK peaks classified by prominence and height
- 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 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 a paper by Sanjay Rana and Jeremy Morley
- The 100 most prominent peaks in Colorado
- Alan Dawson's The Relative Hills of Britain