## detailed analysis of prominence definitions

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• Hello folks, Many of you will be merely intrigued by this work - http://www.cohp.org/prominence/definitions/prominence_definitions.html - while some will
Message 1 of 3 , Apr 29, 2012
Hello folks,

Many of you will be merely intrigued by this work -

http://www.cohp.org/prominence/definitions/prominence_definitions.html

- while some will actually read it all because it features much new
material
addressing the various "flavors" of prominence: mean ("interpolated"),
clean and optimistic from a purely theoretical view.

How well they fare, and WHY, in selecting "gray zone" peaks at the
bottom of a prominence list is a major topic.

I recommend reading all BUT the Appendix. It contains some serious
mathematics required to evaluate certain error properties for these
measures.

Still, if you want to see how Jacobians, orthogonal transformations
and double integrals actually work in the "real world" then, by all means,

****************************************

There is a new measure related to prominence just as intimately as
peaks and saddles are related to one another. I denote it "q" in the
derivations,
having failed to conjure a decent English name for it.
"Continentality" comes to mind but that's too long and has too many
syllables.
Your recommendations are welcome for naming this measure which seems to
select-out peaks that are high and yet NOT prominent.

It would make a terrible list-builder except for those "heightists" who
love
bashing prominence. In fact, "q" could very well be their poster-child.

This work consumed the better part of one week.
So I hope that somebody takes note of its contents and concludes
it might be of value.

Sincerely,
• OK, Dave, I will make it simple for you: 1. Interpolated prominence has overwhelmingly superior mathematical properties compared against clean and optimistic
Message 2 of 3 , Apr 30, 2012
OK, Dave, I will make it simple for you:

1. Interpolated prominence has overwhelmingly superior mathematical properties compared against clean and optimistic prominence.

a. It more frequently correctly assigns and expels peaks from appearing at the bottom of a prominence-based peak list.
EVERY combination of {prominence type, list cutoff value, map contour spacing} is exhaustively considered.

b. It is an unbiased estimator for the unknowable true prominence when the latter is only available as a range of values,
i.e. the average error (calculated - true prominence) is 0 for interpolated ("mean") prominence. The other prominence definitions
are biased, but can also recover the same 0 mean error by simple linear transformations:

clean prominence -> clean prominence - half contour interval
and
optimistic prom -> optimistic prom + half contour interval

2. The q-value, defined as (peak elevation + saddle elevation) (although more properly as (peak elevation + saddle elevation) / sqrt (2) ).
From a purely theoretical perspective it is the equal of prominence. However from a practical aspect it suffers....

a. Living in Colorado you should note that every tiny bump just under the top of all 14ers are climbworthy: for they, along with
Point Success on Mount Rainier, will lead the list of CONUS peaks ordered by their "continentality" q - the antithesis of prominence.

b. When you climb Denali this Spring be certain to also do Archdeacons Tower at 19,500 feet.
In theory it leads North America in q-value unless there's a minor bump higher-still between it and the top.

I'll add a "Summary" expounding on these critical points.

****************************************************************************************************************************

Non-USA residents should note that a P610 meter list will have a larger fraction of correct gray zone peak assignments than a P600 meter list.

Sincerely,

PS Good luck at Denali. WHEN do you fly?
----- Original Message -----
From: Dave_Covill@...
Cc: davidwmolson@... ; dmg@... ; esquared@... ; gregslayden@... ; jkirk_14@... ; john.hamann@... ; mark Adrian ; oldadit@... ; Petter.Bjorstad@... ; prominence@yahoogroups.com ; rfbolton@... ; rhwxyz@... ; robert.packard@... ; Roy Schweiker ; surgent@...
Sent: Monday, April 30, 2012 9:17 AM
Subject: Re: detailed analysis of prominence definitions

Yikes !!!!!!!!!! I have a headache.....

;)

[Non-text portions of this message have been removed]
• Reverse the signs to obtain these (corrected) prescriptions - clean prominence - clean prominence + half contour interval and optimistic prom - optimistic
Message 3 of 3 , Apr 30, 2012
Reverse the signs to obtain these (corrected) prescriptions -

clean prominence -> clean prominence + half contour interval
and
optimistic prom -> optimistic prom - half contour interval

> b. It is an unbiased estimator for the unknowable true prominence when the latter is only available as a range of values,
> i.e. the average error (calculated - true prominence) is 0 for interpolated ("mean") prominence. The other prominence definitions
> are biased, but can also recover the same 0 mean error by simple linear transformations:

> clean prominence -> clean prominence - half contour interval
> and
> optimistic prom -> optimistic prom + half contour interval

*******************************************************************

Fortunately the online article already had the correct versions as Equations (4a,b).