# Section 1:  An Introduction to Prominence

### 1.1        Definition of Prominence

Prominence is a term that represents the elevation of a summit relative to the surrounding terrain.  It is defined as the elevation of a summit relative to the highest point to which one must descend before reascending to a higher summit.  There are several ways to describe this both mathematically and conceptually.

Prominence is a non-arbitrary first derivative of elevation that quantifies a summit's height above all surrounding terrain.  Prominence is calculated as the difference in elevation between a summit and the highest saddle that connects that summit to any higher terrain.  A mountain with a prominence (P) value of 2,000 feet could be said to rise at least 2,000 feet above all else.

Put another way, prominence is the elevation difference between the summit and the lowest contour that encircles it and no higher summit.  It is the minimum height by which one would have to descend from a summit along a ridge in order to re-ascend to a higher peak.

### 1.2        Prominence is Relative Elevation

Prominence describes the Relative Elevation value of a mountain summit.

Conceptually, it is easiest to understand prominence if we imagine that we can raise and lower the sea level at will.  At a certain elevation, any mountain range could be made to be its own sea-island.  By extension, at a certain elevation, every summit would become the highest point of its own island.

All islands have a single summit at their highest point. [2]  For example, the summit of Mauna Kea is the highest point on the island of Hawaii at an elevation of 13,796 feet.  In order to ascend to a higher point while staying on the surface of the earth one would first have to descend to sea level, then re-ascend on another island or continent.  Thus the summit of Mauna Kea has 13,796' of prominence, the height by which this summit protrudes above all other points on the earth's surface manifold.  High points of islands and continents [3] have elevations that equal their prominence.

Mauna Loa is the second highest summit on Hawaii.  At 13,679' it is just 117' lower than Mauna Kea.   Let's say that we could raise and lower the sea level at will. As the sea rose, the island of Hawaii would shrink in size until it was essentially dumbbell shaped: a pair of volcanoes.  At 6,600' feet, the rising water would form a channel separating Mauna Loa from Mauna Kea at the low point of the ridge that connects the two volcanoes. At that moment Mauna Loa would be 7,079' above the new sea level; the mountain's prominence value.

The place where two "islands" separate is always a saddle, which is a low point on a ridge.  In the case of Mauna Loa, the separation would occur at a place called Humuula Saddle (elevation 6,600').  We call Humuula the Key Saddle for Mauna Loa.

Every summit that is not the high point of an island or continent has a unique Key Saddle.  Every Key Saddle has a unique summit.  No saddle is a key saddle for more than one summit. [4]  As a rule therefore, a given island or continent will have a quantity of summits equal to the number of Key Saddles plus one. [5]

### 1.3        Prominence as a Qualifying Rule

Prominence turns out to be a convenient way to compare summits.  Mountain climbers can use prominence to rank the importance of mountains.  Prominence is also useful as a qualifying rule to determine inclusion of mountains on lists of summits.

Lists of the highest mountains have been around for at least 100 years.  However, such lists have a classic shortcoming; how does a mountain qualify for inclusion on the list?  In the absence of a qualifying rule, one might say that the earth's ten highest mountains are ten rocky outcrops on the Mt. Everest summit block.  A list of high mountains must either employ a minimum prominence as a criterion or be based on a subjective sensibility as to what constitutes a separate peak (such as limiting entries to named peaks only).

This question of what constitutes a separate peak is a recurring one amongst mountain climbers.  In Colorado, the generally accepted criterion for inclusion on lists is 300' of prominence.  The 300' rule (sometimes referred to as the Colorado rule) is based on a 1950s survey of 14,000' mountains in Colorado published by the U.S.G.S. [6]

Prominence is also used extensively by British hillwalkers, both as a qualifying rule for high elevation summits and as a system of measurement unto itself.  Alan Dawson (1992) published The Relative Hills of Britain, a list of every hill in Great Britain to P>500' [7].  Several hikers have nearly completed this list.

Prominence is sometimes referred to as reascent, drop, shoulder drop, or saddle drop.  The term itself was probably coined by Steve Fry, a Seattle-based mountaineer, in 1981.  Fry published a series of articles proposing various measurements of mountains, such as prominence, steepness, and volume. [8] He also produced many early lists of prominent summits.

### 1.4    The Prominence Theorists

In the United States a group of a few dozen enthusiasts study the subject of prominence.  Slowly the concept is gaining traction amongst the subculture of "peakbaggers".

The creation of prominence lists is significantly aided by a computer program called WinProm that extracts prominence data from digital elevation models. [9]  WinProm's derives key saddles and summits from the terrain.  Map checking must still be done thoroughly by hand.

A comprehensive index of prominence lists worldwide can be found on the website www.peaklist.org.

Over 50 volunteers have worked on various parts of prominence lists.  In the United States, a complete list of U.S. mountains to 2,000' prominence (1,234 peaks) was compiled by a diverse number of authors, most notably Andy Martin, Edward Earl, and Aaron Maizlish.   Others who have contributed significant effort are Jerry Brekhus, Jeff Howbert, Ken Jones, Carl Mills, David Olson, John Roper, Roy Schweiker, and Ron Tagliapietra.  Jeff Howbert is near completion of a massive study of the 4,000+ summits in Washington State with P>400'.[10].  Aaron Maizlish has conducted similar research for California.

Globally the greatest amount of work has been done in Great Britain, where every hill with P>150m has been chronicled and (with a few notable exceptions) climbed.   A team of Canadian researchers have mostly cataloged Canadian summits at www.bivouac.com.   Petter Bjørstad has produced detailed lists of high-prominence summits for Norway and Sweden.  [11]  David Metzler and Eberhard Jurgalski have researched prominence worldwide, and produced a provisional list of the 50 most prominent summits on earth.

Finally, a group of collaborators are in the process of identifying all summits on earth with P>1,500m (4,921 ft.).  There are approximately 1,530 of the so-called ultra-prominences.

### 1.5    Reordering mountains based on Prominence

Prominence correlates very well with the impressiveness and the local importance of major mountains.  As a result it may be a better conceptual tool for visualizing the role of mountains on the Earth's terrain than absolute elevation.  Take for example a side-by-side comparison of the lists of the highest summits and most prominent summits on earth.  The first table lists 14 generally-accepted peaks with elevation >8,000 meters.  This list is confined to High Himalayan peaks.  Table 2 lists the 14 most prominent summits.  This list has a good geographical distribution and includes all of the famous "seven summits" - the highest points of the seven continents. [12]   In short, it is more descriptive of the earth's surface.

TABLE 1:
THE 14 HIGHEST MOUNTAINS ON EARTH COMPARED TO THE 14 MOST PROMINENT MOUNTAINS ON EARTH  [13]

 Name: Location: Elev (ft.) 1 Mt. Everest Nepal/Tibet 29,035 2 K2 Pakistan/China 28,250 3 Kanchenjunga India/Nepal 28,208 4 Lhotse I Nepal/Tibet 27,923 5 Makalu I Nepal/Tibet 27,824 6 Cho Oyu Nepal 26,906 7 Dhaulagiri Nepal 26,795 8 Manaslu I Nepal 26,781 9 Nanga Parbat Pakistan 26,657 10 Annapurna I Nepal 26,545 11 Gasherbrum I Pakistan/China 26,529 12 Broad Peak Pakistan/China 26,401 13 Gasherbrum II Pakistan/China 26,362 14 Shisha Pangma Tibet 26,289 Name: Location: Elev (ft.) Prom (ft.) 1 Mt. Everest High Point (HP) of World 29,035 29,035 2 Aconcagua HP S. America 22,831 22,891 3 Mt. McKinley HP N. America 20,320 20,138 4 Mt. Kilimanjaro HP Africa 19,340 19,308 5 Cristobal Colon (in Colombia) 18,947 18,320 6 Mt. Logan HP Canada 19,550 17,224 7 Pico de Orizaba HP Mexico 18,409 16,079 8 Vinson Massif HP Antarctica 16,066 16,066 9 Puncak Jaya HP New Guinea 16,023 16,023 10 Mt. Elbrus HP Europe (Caucasus) 18,510 15,554 11 Mont Blanc HP Europe (Alps) 15,774 15,403 12 Damavand HP Iran 18,386 15,292 13 Kluchevskaya Volcano HP Kamchatka 15,584 15,252 14 Nanga Parbat (in Pakistan) 26,657 15,118

Prominence, as an independent system of measurement, significantly rewards the highest points of major mountain ranges and freestanding peaks.  Volcanoes and island high points are well represented.  Prominence is a "winner-take-all" measure in that the highest point of a natural feature is ascribed all of the vertical relief for that feature.  Slightly lower peaks may have very low prominence if their relative elevation derives from their nearby higher neighbor.

Prominence is also independent of the specific terrain of the landform.  A round, forested hill might have greater prominence, if it is surrounded on all sides by low-elevation terrain, than a jagged 14,000' alpine peak.  Prominence simply represents the vertical discontinuity of both objects on the surface manifold in a mathematical fashion.

Footnotes:

[2]   The term island in the context of this paper will generally refer to sea-islands whose shores are at zero elevation, as distinct from land and river islands.

[3]   The term continent in the context of this paper will generally refer to natural continents whose shores are at zero elevation. There are five natural continents; Antarctica, Australia, the Americas, Eurasia, and (effectively) Africa.

[4]   There are degenerate cases where this statement appears to be false; generally two saddles that appear close enough together as to be indistinguishable from each other.

[5]   In this example, I consider the ocean surface to be an aspect of the surface.  If you ignore water, then the number of summits on earth equals the number of saddles plus one.

[6]   By a strict interpretation of the 300’ rule, there are 54 14ers in Colorado according to Roach.  Lists have varied over the years from 52 to 55 peaks.  El Diente and North Maroon Peak are found on most lists, even though their prominence is less than 300 feet.

[7]   Throughout this paper this convention will be employed to signify a list of mountains to a given prominence value.  P>500’ signifies a list of all mountains with a prominence greater than or equal to 500 feet.

[8]    Washington’s Steepest Faces, Signpost, April 1984.   Washington’s Highest Mountains and Steepest Faces, The Mountaineer 1983-1990 annual, publ. Aug 1991.   Defining and Sizing-Up Mountains, Summit, Jan. Feb. 1987.

[9]   Winprom is available from the author, Edward Earl.

[10]  Viewable directly on Jeff Howbert's Northwest Peakbagger's Asylum website.

[11]   Viewable directly on Petter Bjorstad's Personal Website.

[12]   The seven summits list generally includes the high point of New Guinea to represent the highest point in Oceania, rather than the high point of Australia.

[13]   Full list is viewable on peaklist.org