Adam Helman Prominence Parent Hierarchy and Distance Ladder

NAD27 Center (32°56'37.3" N, 117°14'14.7" W)

Prominence Parent Hierarchy

peak
name		 prominence
(feet)		 elevation
(feet)		 coordinates
(NAD27 datum)
unnamed () 140±20 410±10 (32°57'17" N, 117°13'11" W)
Black Mountain () 902±10 1,552 (32°58'53" N, 117°07'00" W)
Woodson Mountain ()1 1,464±10 2,894 (33°00'31" N, 116°58'11" W)
Volcan Mountain () 1,579±20 5,719 (33°09'52" N, 116°37'10" W)
Mount Laguna ()2 1,598±20 6,378 (32°50'21" N, 116°23'59" W)
Cuyamaca Peak () 2,852±20 6,512 (32°56'48" N, 116°36'21" W)
San Jacinto Peak () 8,339±20 10,839 (33°48'53" N, 116°40'43" W)
Mount Whitney () 10,080±5 14,495 (36°34'43" N, 118°17'29" W)
Pico de Orizaba () 16,148 18,491 (19°01'48" N, 97°16'15" W)
Mount Logan () 17,224 19,550 (60°34'00" N, 140°24'14" W)
Mount McKinley () 20,156 20,320 (63°04'11" N, 151°00'16" W)
Aconcagua () 22,841 22,841 (32°39'12" S, 70°00'39" W)
Mount Everest () 29,028 29,028 (27°59'18" N, 86°55'27" E)

1 The parent of Woodson Mountain is either Volcan Mountain or Mount Laguna since the walks to both go
coincidentally as low as a pair of 4,120-4,160 foot saddles. Either peak can serve as the Woodson Mountain
parent even though Mount Laguna might (cf footnote [2]) be the parent of Volcan Mountain.

Thus the true hierarchy can be any of three possibilities:

Woodson Mountain -> Volcan Mountain -> Mount Laguna -> Cuyamaca Peak .
A uniform distribution for the various saddle elevations yields a 43.1% probability of this lineage.

Woodson Mountain -> Volcan Mountain -> Cuyamaca Peak.
A uniform distribution for the various saddle elevations yields a 6.9% probability of this lineage.

Woodson Mountain -> Mount Laguna -> Cuyamaca Peak.
A uniform distribution for the various saddle elevations yields a 50% probability of this lineage.

Summing over these three outcomes, Volcan Mountain has a 50% probability of being in the true lineage;
and Mount Laguna has a 93.1% probability of being in the true lineage.

2 The Volcan Mountain and Mount Laguna prominence ranges overlap. Assuming a uniform distribution for their true saddle elevations, there is a 86.2% probability that Mount Laguna's prominence exceeds that of Volcan Mountain. In that case Volcan Mountain's parent is Mount Laguna, and Mount Laguna's parent is Cuyamaca Peak. Otherwise Volcan Mountain's parent is Cuyamaca Peak with Mount Laguna absent from the hierarchy.

Prominence Distance Ladder

peak
name		 prominence
(feet)		 distance
(statute miles)		 elevation
(feet)		 coordinates
(NAD27 datum)
BM Town () 200±10 0.78 430±10 (32°57'01" N, 117°14'54" W)
BM Miramar () 254±10 7.14 844 (32°56'06" N, 117°06'57" W)
Soledad Mountain () 512±10 7.20 822 (32°50'23" N, 117°15'06" W)
Black Mountain () 902±10 7.56 1,552 (32°58'53" N, 117°07'00" W)
Mount Whitney () 1,046±10 12.36 1,736 (33°06'32" N, 117°09'16" W)
Woodson Mountain () 1,464±10 16.17 2,894 (33°00'31" N, 116°58'11" W)
El Cajon Mountain () 1,985±10 24.38 3,675 (32°54'53" N, 116°49'09" W)
Otay Mountain () 2,106±20 33.23 3,566 (32°35'40" N, 116°50'38" W)
Cuyamaca Peak () 2,852±20 36.70 6,512 (32°56'48" N, 116°36'21" W)
Palomar Mountain ()1 2,840±20 37.14 6,140 (33°21'48" N, 116°50'07" W)
Santiago Peak () 4,397±10 55.55 5,687 (33°42'38" N, 117°32'00" W)
San Jacinto Peak () 8,339±20 68.17 10,839 (33°48'53" N, 116°40'43" W)
Mount Whitney () 10,080±5 257.6 14,495 (36°34'43" N, 118°17'29" W)
Mount Rainier () 13,197±33 988.8 14,411 (46°51'11" N, 121°45'33" W)
Pico de Orizaba () 16,148 1,564 18,491 (19°01'48" N, 97°16'15" W)
Mount Logan () 17,224 2,177 19,550 (60°34'00" N, 140°24'14" W)
Mount McKinley () 20,156 2,544 20,320 (63°04'11" N, 151°00'16" W)
Aconcagua () 22,841 5,462 22,841 (32°39'12" S, 70°00'39" W)
Mount Everest () 29,028 7,951 29,028 (27°59'18" N, 86°55'27" E)

1 The Cuyamaca Peak and Palomar Mountain prominence ranges overlap. Assuming a uniform distribution for their true saddle elevations, there is only a 24.5% probability that Palomar Mountain's prominence exceeds that of Cuyamaca Peak. As Palomar Mountain is farther, there is thus a roughly one-in-four chance that it belongs to the true distance-based prominence hierarchy.

Edward Earl and Richard Carey professionally surveyed their respective key saddles. Unfortunately their relative prominences remain uncertain.

back to individual prominence hierarchies index