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In topography, prominence (also referred to as autonomous height, and shoulder drop in US English, and drop in British English) is the relative height of a mountain or hill's summit relative to the lowest contour line encircling it but containing no higher summit within it. It is a measure of the independence of a summit. The key col ("saddle") around the peak is a unique point on this contour line and the parent peak (if any) is some higher mountain, selected according to various criteria.
A way to visualize prominence is to imagine raising sea level so the parent peak and subject peak are two separate islands. Then lower it until a tiny land bridge forms between the two islands. This land bridge is the key col of the subject peak, and the peak's prominence is its elevation from that key col.
One can also refer to it as the tallest possible path between the two peaks, where the key col is the lowest point on that path.
Only summits with a sufficient degree of prominence are regarded as independent mountains. 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 11 m) is taller than K2, it is not considered an independent mountain because it is a sub-summit of the main summit (which has a height and prominence of 8,849 m).
Many lists of mountains use topographic prominence as a criterion for inclusion in the list, 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 Marilyns uses 150 m (about 500 ft). (Dawson's list and the term "Marilyn" are limited to Britain and Ireland). In the contiguous United States, the famous list of "" (14,000 foot / 4268 m peaks) uses a cutoff of 300 ft / 91 m (with some exceptions). Also in the U.S., 2000 ft (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 favor 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 . One advantage of a prominence-ranked list is that it needs no cutoff since a peak with high prominence is automatically an independent peak.
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 elevation), on the Water divide between lands draining into the Baltic Sea and . This is the meeting place of two 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.
Figure 3 shows a schematic range of peaks with the color underlying the minor peaks indicating the encirclement parent. In this case the encirclement parent of M is H whereas an intuitive view might be that L was the parent. Indeed, if col "k" were slightly lower, L would be the true encirclement parent.
The encirclement parent is the highest possible parent for a peak; all other definitions indicate 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 ("Marilyn" being a British term for a hill with a prominence of at least 150 m).Alan Dawson (1997). 9780952268079, TACit Press. There are several related booklets covering Britain and Ireland.. ISBN 9780952268079 This is found by dividing the region of Britain in question into territories, one for each Marilyn. The parent Marilyn is the Marilyn whose territory the hill's summit is in. If the hill is on an island (in Britain) whose highest point is less than 150 m, it has no parent Marilyn.
Prominence parentage is the only definition used in the British Isles because encirclement parentage breaks down when the key col approaches sea level. Using the encirclement definition, the parent of almost any small hill in a low-lying coastal area would be Ben Nevis, an unhelpful and confusing outcome. Meanwhile, "height" parentage (see below) is not used because there is no obvious choice of cutoff.
This choice of method might at first seem arbitrary, but it provides every hill with a clear and unambiguous parent peak that is taller and more prominent than the hill itself, while also being connected to it (via ridge lines). The parent of a low hill will also usually be nearby; this becomes less likely as the hill's height and prominence increase. Using prominence parentage, one may produce a "hierarchy" of peaks going back to the highest point on the island. One such chain in Britain 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 height and prominence increase.
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 Water divide.
For example, the key col of Denali in Alaska (6,194 m) is a 56 m col near Lake Nicaragua. Denali's encirclement parent is Aconcagua (6,960 m), in Argentina, 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 Denali would be 6138 m, its current prominence, 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 Denali, since Denali 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, Denali). This illustrates the disadvantage in using the encirclement parent.
A hill in a low-lying area like the Netherlands will often be a direct child of Mount Everest, with its prominence about the same as its height and its key col placed at or near the foot of the hill, well below, for instance, the 113-meter-high key col of Mont Blanc.
Since typically show elevation using contour lines, the exact elevation is typically bounded by an upper and lower contour, and not specified exactly. Prominence calculations may use the high contour (giving in a pessimistic estimate), the low contour (giving an optimistic estimate), their mean (giving a "midrange" or "rise" prominence) or an interpolated value (customary in Britain).
The choice of method depends largely on the preference of the author and historical precedent. Pessimistic prominence, (and sometimes optimistic prominence) were for many years used in USA and international lists, but mean prominence is becoming preferred.
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 its wet prominence unless the summit is the highest point of a landmass or island, or its key col is covered by snow or ice. If its highest surface col is on water, snow, or ice, the dry prominence of that summit is equal to its wet prominence plus the depth of its highest submerged col.
Because Earth has no higher summit than Mount Everest, Everest's prominence is either undefined or its height from the lowest contour line. In a dry Earth, the lowest contour line would be the deepest hydrologic feature, the Challenger Deep, at 10,924 m depth. Everest's dry prominence would be this depth plus Everest's wet prominence of 8848 m, totaling 19,772 m. The dry prominence of Mauna Kea is equal to its wet prominence (4205 m) plus the depth of its highest submerged col (about 5125 m). Totaling 9330 m, this is greater than any mountain apart from Everest. The dry prominence of Aconcagua is equal to its wet prominence (6960 m) plus the depth of the highest submerged col of the Bering Strait (about 40 m), or about 7000 m.
Mauna Kea is relatively close to its submerged key col in the Pacific Ocean, and the corresponding contour line that surrounds Mauna Kea is a relatively compact area of the ocean floor. Whereas a contour line around Everest that is lower than 9330m from Everest's peak would surround most of the major continents of the Earth. Even just surrounding Afro-Eurasia would run a contour line through the Bering Straight, with a highest submerged col of about 40 m, or only 8888 m below the peak of Everest. As a result, Mauna Kea's prominence might be subjectively more impressive than Everest's, and some authorities have called it the tallest mountain from peak to underwater base.
Dry prominence is also useful for measuring submerged . Seamounts have a dry topographic prominence, a topographic isolation, and a negative topographic elevation.
| Mount Everest | Afro-Eurasia | 8848 | Undefined or 19772 | −10924 | (Challenger Deep) | |
| Mauna Kea | Hawaii | 4205 | 9330 | −5125 | (SW of Hawaii) | |
| Vinson Massif | Antarctica | 4892 | 8272 | −3380 | (S of South Georgia) | |
| Piton des Neiges | Réunion | 3069 | 7129 | −4060 | (E of Reunion) | |
| Aconcagua | Americas | 6960 | 7000 | -40 | (Bering Strait) | |
| Mawson Peak | Heard Island, Kerguelen Plateau | 2745 | 6395 | −3650 | (S of Kerguelen Plateau) | |
| Aoraki-Mount Cook | South Island, New Zealand | 3724 | 6354 | −2630 | (W of New Caledonia) | |
| Mont Orohena | Tahiti, French Polynesia | 2241 | 6341 | −4100 | (E of Tahiti) | |
| Silisili | Samoa | 1858 | 6311 | −4453 | (W of Samoa) | |
| Pico do Fogo | Fogo, Cape Verde | 2829 | 6190 | −3361 | (NE of islands) | |
| Queen Mary's Peak | Tristan da Cunha | 2062 | 6179 | −4117 | (W of Namibia) | |
| Puncak Jaya | New Guinea | 4884 | 6178 | −1294 | (E of Timor) | |
| Denali | Americas | 6191 | 6144 | 47 | (Darien Gap) | |
| Mount Paget | South Georgia | 2935 | 5942 | −3007 | (W of South Georgia) | |
| Teide | Tenerife, Canary Islands | 3715 | 5939 | −2224 | (E of Tenerife) | |
| Kilimanjaro | Africa | 5895 | 5885 | 10 | (Suez Canal) | |
| Pico Ruivo | Madeira | 1861 | 5876 | −4015 | (NE of Madeira) | |
| Mount Pico | Pico Island, Azores | 2351 | 5772 | −3421 | (N Atlantic) | |
| Pico de Desejado | Trindade, SE of Brazil | 620 | 5567 | −4947 | (W of Trindade) | |
| Pico Cristóbal Colón | Americas | 5570 | 5509 | 191 | (E of Sierra Nevada) |
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