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Line Parent Definition And Database Stability
    Date first written: 2004.10.07

Table of Contents
1. Line Parent and Database Rules
2. Examples and Test Cases
3. When to Add Peaks

1. Line Parent and Database Rules
I assume you have already been introduced to Mountain Prominence - Definition, and know that every mountain has exactly one "key saddle" joining it to higher terrain. The line parent is just the first peak you come to on that "higher terrain". A loose definition of a "line parent" is that it is the first higher peak you come to after the key saddle. In other words, you go down to the "key saddle" of the peak, and then follow the ridge upwards till you come to a higher peak.

But the above definition obviously depends on what bumps a given database designates as "peaks". You might start out with one peak being the line parent, but if you add an intermediate peak later, then you might want to update the line parent. For example, suppose you've got two peaks, Peak A is 3000m and its parent is Peak C which is 3200m. But later on, you also decide to insert Peak B which is 3100m into the database, and lies on the same ridge between A and C. Is your original line parent for A now "wrong", just because your database now includes the bump "B"? We say no. Your database is not wrong because it still designates C as the parent of A. You could revise it, but the original is not wrong, because there could be other databases that don't contain B.

The only way a bunch of databases could completely agree on a certain line parent for every peak is if they all agreed on a prominence threshold. Eg: You only consider peaks with 300m prominence as potential line parents. But having a single prominence threshold is not appropriate for all of North America, so this is not typically done in any database. What to do? This is the discussion of this document.

CONCLUSION: As of March 2012, it is now clear that when trying to reconcile two databases, there is no point in trying to make the line parents agree, unless both databases also define a prominence threshold. "Line Parent" is just a convenient method to prove the prominence. It is generally the nearest higher peak at the time the prominence was determined. For peaks with distant parents, it is usually a significant named peak, not a lesser unnamed peak.

The only thing that is definitive about a peak is its height and its prominence, and its key saddle. But not its line parent.

For example, suppose that at the time the prominence was figured out, a given database had Peak C as the parent of A. If at a later time, an intermediate peak B is inserted into the database, and it is also higher than A. It is still acceptable to have that C is the line parent of A. It is not regarded as a database mistake.

When reconciling two databases, there is no point in trying to make the line parent info agree.

Another case where the "line parent" on file can vary is when a peak has a distant parent, we typically "skip over" a less significant peak as you approach a better known peak. For example, in the Canadian Rockies, the parent of Mount Joffre can be said to be Assiniboine. Assiniboine is about 50 km from Joffre. If you start traversing the ridge from Joffre toward Assiniboine, you don't come to higher ground until you start going up the final south ridge of Assiniboine. But less than 1 km before the summit of Assiniboine, you encounter a bump called Lunette Peak, which itself has only 28 m of prominence. Should Lunette be the "line parent" of Assiniboine? No, because it is a low prominence subpeak of Assiniboine.

The reason Lunette is skipped is because it is "almost" to Assniboine. If had been only half way to Assiniboine then it would be the proper "line parent" of Joffre.

2. Examples and Test Cases

  1. Assiniboine and Lunette Peak
     The distance from Mount Joffre to Assiniboine is 49 km. Lunette Peak is 48 km. Since 48/49 is more than 90%, we skip Lunette.

  2. Mount Seymour
     Near Vancouver is a popular area around Mount Seymour, where every little bump is named. Brockton Point -> Pump Peak -> Second Peak -> Mount Seymour. In this case, we put Pump Peak as the parent of Brockton despite its low prominence of only 45m, because it is not 90% of the distance to Seymour. And then from Pump to second, the same rule applies. The result is that all the low prominence subpeaks are linked to their "technical" line parent, and no peaks are skipped. This example works perfectly with our rule.

  3. Ulysses and Fairweather Example
     This is the case of several unnamed peaks between a given peak and a distant well known peak. Ulysses is about 800km away from Fairweather, and between them is Mount Root and also three nnamed subpeaks, all higher than Ulysses:

      Ulysses 3024 2289
      Root N7 3049 414
      Root N6 3237 452
      Root N2 3770 465
      Root 3928 918
      Fairweather 4671 3956

    So one temptation is to just put Fairweather as the parent of Ulysses. Or at least Root. The way it is on the database as of 5.102 is that the line parent chain shows every peak above P300, regardless of distance. (the rule is never to ignore P300 peaks).

    If this proves to be REALLY undesirable, then I suppose we could raise the threshold from P300 to P500 if the distance is more than 100 km. (Or a ratio, like if distance is 800 km, then threshold is 800m, if distance is 600 km, then threshold is 600m. (With this rule, Ulysses could be "wired" directly to Root (P918), and we could jump over the obscure Root N7, Root N6, etc. But of course once someone has done the more detailed work, no-one should "undo" that work unless there was some other bug or confusion and you were redoing the whole thing.

  4. Murray Peak, Mull Peak

      Mull Peak 2153 463
      Murray Peak 2147 80
      Murray S2 1933 110 Murray
    Initially the database had Murray S2 linked directly to Mull. By the ratio rules, this is clearly a mistake, because Murray is too close. Therefore the line parent was changed to Murray Peak.

3. When to Add Peaks
We sometimes add unnamed peaks to the database in order to make it quicker to check key saddles and line parents. When is it good to add an unnamed peak to the database? To answer that question, we go back to the purpose of the "line Parent" concept. The purpose of designating a "line parent" is to simplify the prominence proof for any given peak. You could have a database that only gave the prominence of each peak, and the lat-long of the key saddle. But to make that data easier to check, it is convenient to be able to name the "higher ground" beyond the saddle. So we pick the first significant higher peak beyond the saddle, and call that the "line parent". This allows somebody to say a statement like: "The Key saddle of Peak 1 is just to the south, and just beyond the saddle is it's parent, Peak 2." You don't want a situation where somebody says: The key saddle of peak 1 is just to the south, but the line parent is 50 km away, with a dozen other higher saddles along the way. The reason the second database is hard to check is because you'd have to re-check those dozen saddles just to make sure the key saddle was indeed the lowest. So in many cases, we add intermediate peaks to the database, which simplify the proofs.

Apart from convenience, there are two absolute "rules" that dictate that an intermediate peak MUST be added:

Rule 1 - Saddle beyond: There cannot be a lower saddle beyond first high ground.
 Rule 2 - High Prom point: There cannot be a higher prominence point between subject and Line Parent

Rule 1 explanation: The database is incomplete if there is a saddle, then higher ground, and then a lower saddle beyond and then the parent. In this case, the first higher ground must be put in as a peak, because it is the only one that can be the Line Parent. We can't use the distant peak beyond the second saddle as the parent because that would imply that the low saddle is the key saddle, which is false. Line Parent is a convenient shorthand for the "higher ground". The key saddle must always be the lowest point between a peak and its parent.

Consider the cases below. The subject peak is Peak 1. Beyond it are peak 2 and Peak 3. For our examples, Peak 2 is an unnamed peak, not yet in the database. The question is: when do we need to add Peak 2 to the database?

  1. Case 1 - Lower Col beyond Peak 2
     (Rule 1 - Saddle Beyond) There is a lower col beyond the first high point you come to after the saddle:

      Peak 1 6000
      Col 1-2 5500 <-- Key saddle of Peak 1
      Peak 2 6500 (is this necessary? - yes
      Col 2-3 5400 (lower saddle, but not key saddle of peak 1
      Peak 3 7500

     In this case, it is essential to put Peak 2 into the database, because there is a lower saddle beyond peak 2. In the above, if we don't put Bump 2 in the database as Peak 2 then we might try to designate Peak 3 as the parent. But it can't be the parent, because the 2-3 col is lower. The key saddle is always the lowest point between a peak and its line parent. So we must insert peak 2 for the database to be self consistent. Col 2-3 is the key saddle of Peak 2, not peak 1.

  2. Case 2 - No higher col, but Peak 2 is higher prom (Rule 2 - High Prom point)

      Peak 1 6000 P500
      Col 1-2 5500 <-- Key saddle of Peak 1, as before
      Peak 2 6500 P800 Higher prom point in center
      Col 2-3 5700 <-- not lower than saddle 1-2
      Peak 3 7500
    In this case, there is no "saddle beyond" the first high point. So Rule 1 is satisfied. However, since the prominence of Peak 2 is 800 which is greater than Peak 1 at 500 I'd put it in to satisfy rule 2. You can draw a diagram of this ridge with peaks 1,2, and 3.

  3. Case 3 - Peak 2 is just bump on Ridge

      Peak 1 5000 P500
      Col 1-2 4500 key saddle of Peak 1
      Peak 2 5500 P200 possible parent of Peak 1
      Col 2-3 5300 //key saddle of Peak 2 saddle higher
      Peak 3 5600

     In this case, Peak 2 is not necessary. It is lower prominence than Peak 1. It can be regarded as a "bump on the ridge" going up to Peak 3. The database below (without Peak 2) is sufficient to satisfy all the rules:
     

      Peak 1 5000 P500
      Col 1-2 4500 key saddle of Peak 1
      Peak 3 5600 parent of Peak 1

ACTUAL EXAMPLES
 Below are examples that you can see on the GMap display:

Conical Peak
Below is a sketch map for the situation around Conical peak, in Alberta. Originally the "convenience" peak SV1 was not in the database and the parent of Conical was put down as Noyes. But adding SV1 makes the parent of Conical much quicker to check because all you need to do is trace to Peak SV1. You don't need to check the ridges beyond which going to Noyes or Quill, whereas without SV1, you'd have to check the low point on both those ridges to verify that Noyes was the line parent.

This case is like case two above - there is no lower saddle that would confuse someone, as long as Noyes was the parent. So it isn't like case 1. However, just to make it simpler I inserted the 9750' peak as "Sv1". This will save future editors the trouble of examining the piece of ridge between it and Noyes. If there was a deeper slot there, then Noyes would not be the parent.

I call this a "case 2" convenience peak, as opposed to a more essential "case 1" peak. In general, in complex areas we often insert peaks every 7 or 8 km along a ridge, just to make things more convenient. That makes it quick to verify line parent information without redoing a detailed prominence sketch map with dozens of saddles to consider.
Quick sketch of ridges leading from Conical to Noyes Peak