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Mountain Hierarchy using Prominence Islands
    Date first written: 2003.09.28     Last Review: 2016.07.20

Table of Contents
1. Preface
2. Topographic Subpeaks and Parent Peaks
3. Hierarchial Names (lineage)
4. Alphabetic Glossary

1. Preface
This document describes one of the three systems of Mountain Hierarchies (Line Parent, Subpeak) or "lineage" of a peak. In this system, the parent of each peak is the higher peak whose base contour surrounds the given peak and no other peak. Such peak is referred to as the topographic parent. The two other systems of defining parent peaks are called "line parent" and "source parent", and both are used more often than the topographic parent. All three systems are explained in

In all three systems we are talking about topographic relationships. When I say "subpeak", I mean "topographic subpeak", and my definition knows no limits of geology or distance.

2. Topographic Subpeaks and Parent Peaks
A topographic "subpeak" is a peak which is completely surrounded by a contour from some other peak. We call the other peak the "topographic parent" of the given subpeak. Note that there are numerous other definitions of "subpeak" that do not necessarily involve a contour line that completely surrounds a peak. In this document, I discuss only pure topographic subpeaks.

Although by this definition, all peaks have a parent peak, the examples we are most concerned about are the ones where the parent peak is in fairly close proximity.

Example: Mount Resplendent is a subpeak of Mount Robson because there exists a contour encircling both Mount Robson and Mount Resplendent, and that contour doesn't include any higher peak than Mount Robson. The diagram below provides some simple examples of the main relationships between peaks.

Subpeak Island

The map shows an island, with 100m contours. Peak A (490m) is the highest peak on the island. The lowest contour on that peak is the coastline. I refer to it as the "base contour" for peak A.

Peak D (250m) is a subpeak of peak B, because the 100m contour of peak B surrounds peak D. The term "parent" can be used to denote the reverse relationship to "subpeak". (Or most specifically, the topographic parent). Every peak has exactly one parent peak. Note that Peak A is not the parent of peak D, even though it has a contour surrounding it, because Peak B has a higher contour that surrounds it. The peak with the highest surrounding contour is the parent peak.

The base contour of peak C is about 100 m. Everything above that contour is considered to be part of the mountain mass that is dominated by Peak C. If you had a giant bulldozer and removed all the rock on C above 100 m, you would have completely removed the mountain from the map. Note that by this definition, the last 100 m of Peak C is not part of its mountain. What I mean by mountain is the mass of rock that is uniquely associated with a given high point or peak". To remove the mountain associated with peak C, you don't need to dig a hole below 100 m, you would only need to do that if you were removing Peak A from the face of the earth.

The exact base contour of a mountain does not depend on the contour interval of the map. In this case, the exact contour could be imagined to be 95 meters. The exact base contour defines the autonomous height of a mountain. (also called prominence).

Another term that is sometimes useful is to talk of the "domain" of Peak A. The domain of a mountain is all the area above its "base contour". The domain of peak "A" is the whole island. Peaks B, C and D fall within its domain. The domain of peak B also includes peak D. The domain of a peak covers all its direct descendants (subpeaks), and also all the descendants of those subpeaks. For example, D falls within the domain of A and also B.

3. Hierarchial Names (lineage)
From the general definition of subpeak, every mountain can be considered part of some higher mountain. This fact can be used to assign "hierarchial names" to every mountain, that quickly show which peaks are parents. I construct the hierarchial name simply by separating the string of alpha names by a dot. For example, Robson.Resplendant, or A.B.

For example, below are the full hierarchial names for the peaks:

  Local Name Hierarchial Name ----------------------------
  Peak A A
  Peak B A.B
  Peak C A.C
  Peak D A.B.D

in the previous diagram, the full hierarchial name of peak "B" in the example was "A.B".

The usefulness of these hierarchial names is that they can be processed automaticallly using a computer. They also tell you a lot about the topography of the peak.

4. Alphabetic Glossary
Below is an alphabetic list of definitions. I have attempted to make each definition self-contained. Note that alphabetic glossaries have an inherent disadvantage because the most basic terms may not be the first ones in the alphabet. As with any group of technical terms, it is often better to find the exact place that the term was first introduced and defined in context.

Autonomous Height: The self-contained height of a mountain. The elevation drop to the lowest contour which encircles that mountain and no higher mountain. (See also "base contour"). Autonomous height is the Canadian term for "prominence". The Swedish term is "prime factor". is the minimum drop before you start climbing something higher. The term "prominence" is a problematic term, because many people immediately start to argue with the concept because prominence has a visual connotation. For example, somebody might say that "Atwell Peak is very prominent", even though the drop between Atwell and the summit of Mount Garibaldi is less than 100 m.

(topographic ancestors) The ancestors of a peak are its parent peak, and the parent of its parent, and so on. See also descendant.

Base Contour (topographic base) The lowest contour that surrounds a mountain and no other higher mountain. However, the base contour can surround lower mountains. Example: The base contour for Mount Resplendent is the contour that is 500 m below its summit. Any lower contour would also surround Mount Robson.

A contour is a set of points which all have equal elevation. A "contour line" is an actual line which is drawn on a map. This depends on the "contour interval" for the map. However in topographic discussions, we can talk about any possible contour, not just the ones that are pre-drawn on the map. For example, on a map with a 100m contour interval, we can still discuss the 95 m contour.

Connecting Saddle:
(Connection) (Prominence saddle). The connecting saddle of a subpeak is the saddle that connects it to its parent peak. The connecting saddle for a given peak is the lowest point on the highest route to some higher mountain.

(topographic descendant) This term may be useful for discussing hierarchies of peaks. A peak is the topographic descendant of a given peak if it falls within the domain of the peak. It could be either a direct subpeak, or a subpeak of a subpeak, and so on. The term "subpeak" is reserved for the immediate descendant. (like "child"). For example, the east peak of Logan is a direct subpeak of Logan, but only a topographic descendant of Mount McKinley. It is not a subpeak of McKinley. See also Hierarchial name.

Domain: The domain of a peak is the area surrounded by the lowest contour that encircles the peak and no higher peak. For example, the domain of Mount Columbia is defined by the contour that is exactly the height of Yellowhead pass. Any lower contour would also encircle Mount Robson.

Hierarchial Name
A name for a mountain that specifies the names of its parent peak, and the parent's parent. For example, the full hierarchial name for the east peak of Mount Logan is "McKinley.Logan.EastPeak".

Link is a short, convenient word for "prominence saddle". Mountains can be said to be "linked" to their parent mountains by means of the col between the two of them. For example, Resplendent is linked to its parent Mount Robson by the Resplendent-Robson Col. The saddle itself is the "link" or "connection" between the two. It is useful to have a short word like "link" in order to discuss the methodology for determining prominences. Eg: Mount Robson is more highly linked to peaks in the USA than it is to Mount Waddington."

The land mass above the lowest contour that encircles a peak and no higher peak. By this definition, anything can be considered to be a mountain. See also "Peak". authonomous height.

Any high point. Anything can be considered to be a peak.

Parent peak
(topographic parent). The parent peak of a given peak is the peak with the highest contour that encircles both peaks. For example, Mount Robson has a contour that encircles Mount Columbia. Mount Waddington also has a contour that encircles Columbia, but Waddington is not the parent of Columbia, because its contour is lower than the one on Robson. Mount Waddington has no contour that goes through Yellowhead pass.

(Topographic prominence). See autonomous height. Prominence is a confusing term, but we are stuck with it because it is in common usage.

This term is not essential to discussing mountain hierarchy, but we may as well mention it. A "range" is just a set of mountains, grouped together for some reason. Ranges are often all topographic subpeaks of the highest peak in the range. This is similar to the Rockies concept of "groups", as in "the Joffre Group". Eg: All the peaks in the Cayoosh Range could be considered subpeaks of Cayoosh Mountain. However this naming convention has not always been followed in Ottawa. A more general definition of "Range" is just a group of related peaks. Note also that ranges are usually geologically related, but not necessarily. Eg: People often say that the Cascades includes Mount Baker (a volcano).

The siblings of a given peak have the same topographic parent. It is a useful term for discussing whether or not a higher peak is the parent or merely a sibling. For example, when talking about the prominence of Diamond Head, Atwell Peak is just a sibling, not the parent peak. The parent is Mount Garibaldi, becuase unlike Atwell, it has a contour line that surrounds Diamond Head.

(Topographic Subpeak). A peak which is topographically part of another peak. A peak can only be a subpeak of a single peak (called its parent peak).