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Topographic prominence

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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.

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.

Contents

Definition of prominence

There are several equivalent definitions:

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.
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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.

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.

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 feet/91m (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.

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.

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 A's parent. 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, Mont Blanc's encirclement parent is Mount Everest. For, Mont Blanc's key col is a certain piece of low ground in Russia (at 113 m elevation). 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 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 (among 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.

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].

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.

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 100m and key col 50m. 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.

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 Modelling," and is closely related to Morse Theory. 

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