Topographic prominence

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In topography, prominence, also known as autonomous height (in America), relative height (in America), shoulder drop (in America) or prime factor (in Europe), is a concept used in the categorization of hills and mountains. It describes the height of a peak relative to surrounding ground, and in a way that makes precise the intuition that the world's second-tallest mountain is in fact K2 (height 8,611 m, prominence 4017 m), and not, say, Everest's South Summit (height 8749 m, prominence about 10 m). 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.

Only topographic summits with a sufficient degree of prominence are regarded as "mountains" rather than subsidiary peaks.

1 Definition of prominence
2 Parent peak
3 Prominence in mountaineering
4 Interesting prominence situations
5 More detailed explanation
6 See also
7 References
8 External links

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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 (the base contour of the peak).

For a peak with prominence P metres, to get from the summit to any higher terrain, one must descend at least P metres, whatever route is taken.

For all peaks except the highest on a landmass, prominence is the vertical difference between the peak’s summit and the highest "col" connecting it to an area of higher terrain. The usual meaning of col is any low point on a ridge. However, in this definition a specialised, non-standard meaning is given to "col", namely, the lowest point on a ridge connecting a summit to a higher area of land. To determine the "highest" requires investigating all possible ridge routes.

Readers who are confused by the above definitions might like to imagine the sea level rising to the exact level at which the peak in question becomes the highest point on an island. The prominence of that peak is the height of that island.

The highest connecting "col" is called the key col, linking col or just link.

A more detailed explanation is given below.

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Parent peak

Image:Relative-height.png

The parent of the peak is on this higher terrain but 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 the diagram on the right, 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. The key col and prominence are marked for each subpeak.

Types of parentage follow.

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Prominence parentage

Prominence parentage is defined in the following way. Call a peak 'peak A'. The parent peak of A is the nearest peak that is connected by a ridge to A that has a higher topographic prominence than A. Where there is more than one possible parent that meets these criteria, the one closest to the key col of A - and therefore A is connected to it more closely - wins.

Another way of explaining it is this; From peak A, descend along a ridge until you reach the key col of A (the lowest point on the ridge). Now continue in roughly the same direction and always keep to the height of land. Making sure you remain on a watershed, head towards the nearest higher neighbour of A. Stop as soon as you reach a peak that has a higher prominence than peak A.

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Height parentage

Height parentage is a less widely used term, and it requires some sort of topographic prominence cutoff criterion. The height parent is the closest peak to peak A (connected by a ridge) that has a greater height than A, and is above the prominence cutoff. As before, where there is more than one possible parent, the one closest to the key col of A wins. For example, Mont Blanc's height-parent would be a minor peak in the north-west Caucasus, if your prominence cutoff is low, or Elbrus, if your cutoff is high.

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Encirclement parentage

Also called Island parentage, this is defined as follows. The key col of peak A is at the meeting place of two contours, one encircling A and the other (invariably) containing A's parent. The encirclement parent of A is the highest peak that is inside the contour that A meets at its key col. For example, Mont Blanc's parent here would be Everest; Mont Blanc's key col is low ground in Russia at 127 m. The 127 m contour met at that point encircles completely Mount Everest.

A website explaining the advantages and disadvantages of the three parentage situations can be found * here.

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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 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. John and Anne Nuttall's The Mountains of England and Wales uses 15 m (about 50 ft), whereas Alan Dawson's list of Marilyns uses 150 m (about 500 ft). Lists with a high topographic prominence inclusion criterion 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.

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Interesting prominence situations

The key col and parent peak are often close to the subpeak but this is not always the case, especially for major peaks. 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 (6194 m) is a 56 m col near Lake Nicaragua (or was before the Panama Canal was cut!). McKinley’s parent peak is Aconcagua, Argentina (6960 m) and its prominence is 6138 m. Put another way – if sea level rose 56 m North and South America would be separate continents and McKinley would be 6138 m above sea level.

Mount Whitney (4421 m) has its key col 1022 km (635 miles) away in New Mexico at 1347 m. Its parent peak is Pico de Orizaba (5636 m), the highest mountain in Mexico. Orizaba’s key col is in British Columbia.

The key col for Mount Mitchell, the highest peak of the Appalachians, is in Chicago.

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More detailed explanation

The definition of prominence "the vertical difference between the peak’s summit and the highest col connecting it to a higher area of land" deserves more explanation.

"summit". The highest point on a peak or subpeak. The word "peak" is here being used generally to mean any mountain or hill.

"col". A col is a low point on a ridge. There may be several cols on a particular ridge between two peaks – one of the cols will be the lowest. This lowest col will often be the one a mountain pass crosses as it goes over the ridge. Just in the particular context of this definition of prominence, the word "col" is being used to mean "lowest col on a ridge".

"higher terrain". Which higher terrain is meant? In fact to begin with it could be any higher area of land: the actual area is still unknown. It is likely to be nearby but could be very remote. One needs to consider all higher areas in order to determine which one, in retrospect, turns out to be the one in question (which is also the one containing the parent peak).

"the highest col". In the diagram above, the key col of the right hand peak is shown as the lower of the two cols. What has gone wrong? One must consider every possible ridge route from the peak to every higher land area. Each ridge will have a lowest col. There may be several ridge routes between a peak and a single area of higher terrain. All these lowest cols are listed, one for each ridge. Finally, the highest of all these lowest cols is identified. This, then, is the key col. However, for any peak, analysis only extends over the continent or island the peak is on.

To calculate the key col and parent peak seems like a good job for a computer and fortunately Edward Earl thought so too. His program WinProm can be used to make the very involved calculations required, based on the USGS Digital Elevation Model database. The underlying mathematical theory is called "Surface Network Modelling".

Sometimes a definition is given such as "the lowest col connecting the peak to a higher summit". This is very misleading. It is true that the key col is the lowest col on the ridge. However, the ridge has been selected such that its lowest col is the highest one possible considering all ridge routes.

In the light of this complication, to visualise the situation it may be easier to use the first definition in this article "the height of the summit above the lowest contour line encircling it and no higher summit" Call the summit "Home Peak" and imagine sea level raised so that the top of Home Peak is a tiny island. There are other islands around, all with higher summits, the "Original Isles". Imagine the sea level dropping. The islands all get bigger and new ones (with lower summits) appear. Islands start merging together. They may take on contorted outlines of winding ridges if the topography is complex. A map of Sulawesi is a nice example. As sea level drops further a critical, unique event occurs. The island of Home Peak just becomes connected with one of the Original Isles. The point of connection (isthmus) is the key col. Take the extreme example of Mt. McKinley, whose distance from its key saddle is the farthest in the world. North America and South America are of course connected by a land bridge in Central America. Cerro Aconcagua in Argentina is the highest summit in the Americas, and therefore its prominence is equal to its elevation. Mt. McKinley in Alaska is the highest summit in North America. Its key saddle is therefore the lowest point on the ridge connecting North America to South America. This turns out to be a fairly low saddle of 183 feet (56 m) near Lago de Nicaragua. Otherwise put, if the sea were to rise 183 feet, North America would be cut off from South America and Mt. McKinley would become the highpoint of the new North American "prominence island."

Since mountain altitudes are measured above sea level, the analysis above only extends over the geographical island or continent being studied.

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