Topographic prominence
In topography, prominence 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 around the peak is a unique point on this contour line and the parent peak is some higher mountain, selected according to various criteria.
Definitions
The prominence of a peak is the least drop in height necessary in order to get from the summit to any higher terrain. This can be calculated for a given peak in the following manner: for every path connecting the peak to higher terrain, find the lowest point on the path; the key col is defined as the highest of these points, along all connecting paths; the prominence is the difference between the elevation of the peak and the elevation of its key col. On a given landmass, the highest peak's prominence will be identical to its elevation. An alternative equivalent definition is that the prominence is the height of the peak's summit above the lowest contour line encircling it, but containing no higher summit within it; see Figure 1.Illustration
The parent peak may be either close or far from the subject peak. The summit of Mount Everest is the parent peak of Aconcagua in Argentina at a distance of 17,755 km, as well as the parent of the South Summit of Mount Everest at a distance of 360 m. The key col may also be close to the subject peak or far from it. The key col for Aconcagua, if sea level is disregarded, is the Bering Strait at a distance of 13,655 km. The key col for the South Summit of Mount Everest is about 100 m distant.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.
In mountaineering
Prominence is interesting to many mountaineers because it is an objective measurement that is strongly correlated with the subjective significance of a summit. Peaks with low prominence are either subsidiary tops of some higher summit or relatively insignificant independent summits. Peaks with high prominence tend to be the highest points around and are likely to have extraordinary views.Only summits with a sufficient degree of prominence are regarded as independent mountains. For example, the world's second-highest mountain is K2. While Mount Everest's South Summit is taller than K2, it is not considered an independent mountain because it is a sub-summit of the main summit.
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, and Alan Dawson's list of Marilyns uses 150 m.. In the contiguous United States, the famous list of "fourteeners" uses a cutoff of 300 ft / 91 m. Also in the U.S., 2000 ft 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 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.
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 many higher peaks there are various ways of defining which one is the parent, not necessarily based on geological or geomorphological factors. The "parent" relationship defines a hierarchy which defines some peaks as subpeaks of others. For example, in Figure 1, the middle peak is a subpeak of the right peak, which is a subpeak of the left peak, which is the highest point on its landmass. In that example, there is no controversy about the hierarchy; in practice, there are different definitions of parent. These different definitions follow.Encirclement or island parentage
Also known as prominence island parentage, this is defined as follows. In Figure 2 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 falling-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 piece of low ground near Lake Onega in northwestern Russia, on the divide between lands draining into the Baltic and Caspian Seas. 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 peak on the combined island, a "closer" peak than the encirclement parent, 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 parent peak of peak A can be found by dividing the island or region in question into territories, by tracing the two hydrographic runoffs, one in each direction, downwards 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, 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. The parent Marilyn is the Marilyn whose territory the hill's summit is in. If the hill is on an island 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 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. 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.
Line parentage
Line parentage, also called height parentage, is similar to prominence parentage, but it requires a prominence cutoff criterion. The height parent is the closest peak to peak 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.
In general, the analysis of parents and lineages is intimately linked to studying the topology of watersheds.