What we mean by a mountain hierarchy is a hierarchial arrangement of mountains, showing ancestors and descendants of any given mountain. There are several ways such a hierarchy can be defined, but all methods are based on prominence (the highest connecting ridges between the mountains). Below is one possible mountain hierarchy for North America:

Thus a mountain hierarchy has a single peak at the top level, and then a list of peaks at the second level, and so on. In reverse, every peak has a single "parent" peak.

We have three different systems for defining a mountain hierarchy: Line Hierarchy, Source Hierarchy and Island Hierarchy (Contour Hierarchy). In every case, Mount McKinley is the top of the hierarchy, but which peaks are below depends on what system you are using. Each system has a different definiton of "parent" peak.

The diagram to the left shows three peaks that are all higher than Peak A. Each of the other peaks is the parent of Peak A, depending on what definition you use. I call the three definitions "line parent", "island parent" and "source parent".

 - the Line Parent is the first higher significant peak you come to on the prominence line. In this case Peak B is the line parent. The line parent is all that is required to establish the prominence of a given peak, you don't need to know the source parent. Example: Gannett peak is the line parent of Mount Robson.

 - the Island Parent is the first peak you come to on the prominence line that has a base contour that also surrounds the peak in question. In other words, its key saddle must be lower than the key saddle of the peak in question. The word "island" refers to the idea of the island that would be formed if you raised the water level to the key saddle of the parent. You would then have an island containing the given peak, with the "parent" being the highest peak. In our diagram, the island parent of Peak A is Peak D, because only it has a base contour low enough to surround peak A. Neither Peak B or C have a low enough contour to form an island containing A. Eg: Only Orizaba is the "Island Parent" of Mount Robson, neither Gannett, Elbert or Whitney have a contour which surrounds Robson.

 - the Source Parent is the first higher prominence peak you come to. In this case, it is peak C. Peak B is not superior to A, even though it is higher, because it has less prominence. As far as A is concerned, Peak B is just a bump on the ridge going towards C. Another way to think about it: if you started at the top and subdivided the island of D in prominence order, peak A would be chopped off Peak C. It would not be chopped off peak D directly, because the pass between D and C is deeper, and thus that cut would have to be made first.

The break sequence is below:

          Prom     Source
---------------------------------
  Peak D  2500m     -
  Peak C  1500m     D
  Peak A   500m     C
  Peak B   300m     C

Now that you know the basic idea, we can discuss the usefulness of each definition in detail.

Line Parent (Higher Peak)(Next Highest Neighbour) The "line parent" is the first higher peak that you come to on the prominence walk. It is what we used to call the "Higher Peak" when we started figuring out the Canadian prominences. Our first step was always to find the higher peak, and then find the lowest saddle on the way to that peak. You can start anywhere, and figure out any prominence, key saddle and "Higher peak".

In order to ensure that there is only one unique "line parent", we need to make a rule about minimum prominence. Otherwise, any unnamed bump on a ridge that was high enough could be designated as the line parent. Therefore we say that any peak worthy of being called the line parent must itself have more than 300m prominence. With this definition, the lineage for Robson is below:

  McKinley.Logan.Orizaba.Whitney.Elbert.Gannett.Robson

The word "subpeak" could be used as the opposite to "parent". However, we avoid using the word in that way because it has a strong connotation of "nearby". Most climbers would reject the notion that Robson is a subpeak of Gannett (or even Whitney or Mckinley). However, they would probably accept that Gannett is the parent peak of Robson.

In some cases, a ridge might fork on the far side of the lowest col. In this case, the Line Parent is the closest of the two peaks.

The "isolation" of a given peak is the distance between it and its Line Parent.

Island Parent (Topographic Parent) The Island Parent is the highest peak on the "prominence island" that completely surrounds the peak in question. The topographic parent is the same thing. The "topographic parent" of any given peak is some higher peak whose base contour completely surrounds the peak, and contains no higher peak. The term "Island Parent" is the name originally used by the prominence pioneers in the USA such as Edward Earl and David Metzler and Aaron Maizlish. It now seems better to me than my original term "Topographic Parent".

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).

Here's another way to explain it: For any given peak, there is a pair of contour circles which just barely touch at the prominence col for that peak. The topo parent is the highest peak in the contour island on the far side of that col. Just slightly below the level of the key saddle will be a contour that surrounds both peaks.

Usefulness: Although the idea of island parent is very clean and non-arbitrary, it turns out to be very difficult to figure out. If you start with some peak in the middle of an unknown area, you can usually easily figure out its line parent just by looking at the map. But the island parent requires an extended search well beyond the line parent. For example, to determine the island parent of Mount Robson, you can't just trace as far as Gannett peak, you have to keep going up the prominence tree. In fact, the only practical way I know to determine topographic parents is to already have a database with the line parents, such that it is practical to examine the key saddle of each peak you come to as you go up the line. Gannett goes to Elbert, but Gannett's key saddle is not as low as Robson's, so you have to keep going. Elbert's key saddle is also not low enough, and so you arrive at Whitney. And its key saddle is 1345m which is still too high compared to Robson's key saddle of 1130m. The next step up from Whitney is Orizaba, whose key saddle is 710m. Therefore Orizaba is the island parent for Robson! With this definition, the lineage of Robson is:

  Mckinley.Orizaba.Robson

Note that Whitney is not an ancestor of Robson in the "island parent" lineage. Whitney's connection to Orizaba is not lower than Yellowhead pass, and we need a lower pass.

To search for the island parent, you have to keep going up the chain until you find a deeper pass than the key pass of the peak in question. To find Robson's island parent, here is the "line sequence" (in m):

           Height  Key Pass
  Robson   3954     1130
  Gannett  4207     2050
  Elbert   4399     1630
  Whitney  4418     1345  
  Logan    5959      709

Source Parent (Superior Peak) The superior peak is the first peak on the promline that is both higher and more prominent. The chain of superiors (command chain) is most easily figured out from the top down. This top down approach leads to the idea of "source parent". The source parent is a higher prominence peak from which a given peak has been subdivided. The advantage of this definition over the "line parent" is that in a top down list of peaks sorted by prominence, the source peak has already been introduced higher on the list. See the list below:

                   (Superior) 
Prominence          Source
----------------------------------------
 6149 Mckinley     
 5250 Logan         McKinley
 4930 Orizaba       Logan
 4027 Rainier       Logan
 3956 Fairweather   Logan
 3546 Blackburn     Logan       
 3429 Saint Elias   Logan
 3289 Waddington    Fairweather
 3266 Marcus Baker  McKinley
 3073 Whitney       Orizaba
 3051 Lucania       Logan
 2977 Shasta        Whitney
 2930 Monarch       Waddington
 2857 Shishaldin    -
 2824 Robson        Whitney

  McKinley.Logan.Orizaba.Whitney.Robson

Determining source parents is inherently a top down process, because you need to know the prominence of any higher peak in order to decide if it has more prominence.

Note that in order to get to a peak that has higher prominence, you must pass over several higher peaks. In going from Robson to Whitney, you haev to pass over both Gannett and Elbert.

           Prominence
-----------------------
   Robson    2824
   Gannett   2157
   Elbert    2769
   Whitney   3073

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