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The article is likely referring to the estimated dry prominence of Mauna Kea. Topographic prominence [1] measures the height of a peak relative to its lowest su

The article is likely referring to the estimated dry prominence of Mauna Kea. Topographic prominence [1] measures the height of a peak relative to its lowest surrounding contour line (that doesn't also contain another, taller peak). Usually the ocean's surface is considered "flat ground" when computing this measure (called a "wet prominence"), but one can alternatively imagine the Earth to have no water, and compute a "dry prominence" that permits the lowest surrounding contour line to be below sea level. [1]: https://en.wikipedia.org/wiki/Topographic_prominence https://en.wikipedia.org/wiki/Topographic_prominence The above Wikipedia article specifically mentions the dry prominence of Mauna Kea, estimating it to be 9330m which is taller than Everest's conventional height of 8848m. However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans.

wallace_f 8y ago
>However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans What? This does not make sense, if I am not mistaken? Topographic prominence would place Mauna Kea as the tallest (highest peak from base contour line), but it would certainly not be the second highest above the Challenger Deep... And the Challenger Deep is not the base contour line of any mountain..?
- jake-low 8y ago
  Think about it this way: imagine standing at the bottom of the Challenger Deep. Draw a small circle around yourself on the ocean floor. Now step outside the circle. Because you're standing on a spherical object (Earth), the area outside your circle isn't infinite like it would be on a plane. It's another finite region, which covers almost the entire Earth, and contains both yourself (standing just beside the lowest point of the Challenger Deep) and also the peak of Mount Everest. Therefore the circle is a base contour line for Everest, and Everest's wet prominence can be measured from the circle. However, this same contour line cannot be used for the wet prominence measure of Mauna Kea, since it contains every mountain on Earth, many of which are taller. Mauna Kea's lowest contour line that doesn't contain another taller mountain would probably enclose a sizeable portion of the floor of the Pacific Ocean, but wouldn't include the Andes, Japan, or the Sierra Nevada, since those peaks are taller. The contour line would therefore be deep below the ocean surface, but not as deep as the Challenger Deep.
  - desdiv 8y ago
    >Draw a small circle around yourself on the ocean floor. That circle encloses two areas. One roughly a square metre, and the other one roughly 5e8 km². In geology only the smaller area is used, and the smaller area does not contain the peak of the Everest and thus is not considered a valid base contour line of the Everest.
    - dasil003 8y ago
      Why not? You are looking for the lowest contour that can surround everest, at what would would you stop going lower because the countour is getting too big? 50% of the planet's surface? This seems like an arbitrary bound.
  - PhasmaFelis 8y ago
    Is this measurement conceptually useful, or is it completely arbitrary? I thought it was an attempt to rigorously define "surrounding terrain" for purposes of measuring a mountain's height above the surrounding terrain, but if it defines the Challenger Deep as "surrounding" Everest, that's topologically interesting but doesn't seem like a useful way of thinking about geology.
SilasX 8y ago
Thank you, that's the kind of concept I was looking for.
vesinisa 8y ago
Yes, that is correct. At almost 20,000 km, the dry prominence of Everest is by definition the maximum possible on Earth. You only get to claim Kea more prominent if you use a different standard to measure it!
- thefifthsetpin 8y ago
  I'm not seeing why that is true. If one were to imagine a deep moat around Kea, wouldn't that increase its prominence w/out impacting that of Everest? Or are you suggesting that Everest's dry prominence would be measured from whatever the deepest point on Earth is? Or something else?
  - vesinisa 8y ago
    Everest dominates Mauna Kea in prominence. In fact, Everest dominates any peak on Earth in prominence, since it's the tallest peak. By the mathematical definition of prominence, the dry prominence of Everest is always measured from the deepest point on Earth, the Challenger Deep. If you dug a moat around Mauna Kea, it would indeed increase its prominence, but would not affect the prominence of Everest. Until you dug the moat deeper than the Challenger Deep (about -11,000 m), at which point the dry prominence of Everest would start to be measured from the bottom of your moat and not Challenger Deep. At this point, digging the moat any deeper would increase the prominence of both Everest and Kea by equal amount, but Everest as the higher mountain would nevertheless always dominate Kea.
njarboe 8y ago
From your link, the lower elevation of a dry prominence of Everest would be the lowest contour that encircles Everest. That won't be nearly as deep as Challenger Deep but a quick google search does not find the correct dry prominence for me.
- vesinisa 8y ago
  The lowest bottom of the Challenger Deep encircles the Everest. Think of the "outside" of the circle being the deepest point, and the "inside" of the circle being all rest of the Earth.
  - njarboe 8y ago
    Got me on that one. Seems to me "topographic prominence" is useful for people talking about peaks in a mountain range. Not so much when the spherical shape of the Earth starts to be significant.
  - SilasX 8y ago
    Reminds me of the joke where the mathematician is told to use a fixed length of fencing to enclose the biggest area possible and builds a tiny corral and stands inside and says "I define myself as outside the corral". (Legit point on your part, though.)
    - starbeast 8y ago
      In Douglas Adams''So Long And Thanks For All The Fish', Wonko the Sane resided either outside or inside, depending on your point of view, an inside-out house that he had built as an asylum for the world, after reading the instructions on a packet of toothpicks.
- hannasanarion 8y ago
  The correct dry prominence of everest is the same as the regular prominence of everest, because there are no bodies of water between it and the nearest peaks.
Steko 8y ago
> The article is likely referring to the estimated dry prominence of Mauna Kea. It's talking around a mountain's "surrounding base" which is a related concept but doesn't take you in the absurd direction of 'drawing a circle around yourself in the challenger deep and claiming everything else is part of Everest'. There is no precise definition of surrounding base, but Denali, Mount Kilimanjaro and Nanga Parbat are possible candidates for the tallest mountain on land by this measure. The bases of mountain islands are below sea level, and given this consideration Mauna Kea (4,207 m (13,802 ft) above sea level) is the world's tallest mountain and volcano, rising about 10,203 m (33,474 ft) from the Pacific Ocean floor. Ojos del Salado has the greatest rise on Earth—13,420 m (44,029 ft) from the summit[citation needed] to the bottom of the Atacama Trench about 560 km (350 mi) away, though most of this rise is not part of the mountain. https://en.wikipedia.org/wiki/List_of_highest_mountains_on_Earth https://en.wikipedia.org/wiki/List_of_highest_mountains_on_E...

wallace_f 8y ago

>However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans What? This does not make sense, if I am not mistaken? Topographic prominence would place Mauna Kea as the tallest (highest peak from base contour line), but it would certainly not be the second highest above the Challenger Deep... And the Challenger Deep is not the base contour line of any mountain..?

jake-low 8y ago
Think about it this way: imagine standing at the bottom of the Challenger Deep. Draw a small circle around yourself on the ocean floor. Now step outside the circle. Because you're standing on a spherical object (Earth), the area outside your circle isn't infinite like it would be on a plane. It's another finite region, which covers almost the entire Earth, and contains both yourself (standing just beside the lowest point of the Challenger Deep) and also the peak of Mount Everest. Therefore the circle is a base contour line for Everest, and Everest's wet prominence can be measured from the circle. However, this same contour line cannot be used for the wet prominence measure of Mauna Kea, since it contains every mountain on Earth, many of which are taller. Mauna Kea's lowest contour line that doesn't contain another taller mountain would probably enclose a sizeable portion of the floor of the Pacific Ocean, but wouldn't include the Andes, Japan, or the Sierra Nevada, since those peaks are taller. The contour line would therefore be deep below the ocean surface, but not as deep as the Challenger Deep.
- desdiv 8y ago
  >Draw a small circle around yourself on the ocean floor. That circle encloses two areas. One roughly a square metre, and the other one roughly 5e8 km². In geology only the smaller area is used, and the smaller area does not contain the peak of the Everest and thus is not considered a valid base contour line of the Everest.
  - dasil003 8y ago
    Why not? You are looking for the lowest contour that can surround everest, at what would would you stop going lower because the countour is getting too big? 50% of the planet's surface? This seems like an arbitrary bound.
- PhasmaFelis 8y ago
  Is this measurement conceptually useful, or is it completely arbitrary? I thought it was an attempt to rigorously define "surrounding terrain" for purposes of measuring a mountain's height above the surrounding terrain, but if it defines the Challenger Deep as "surrounding" Everest, that's topologically interesting but doesn't seem like a useful way of thinking about geology.

SilasX 8y ago

Thank you, that's the kind of concept I was looking for.

vesinisa 8y ago

Yes, that is correct. At almost 20,000 km, the dry prominence of Everest is by definition the maximum possible on Earth. You only get to claim Kea more prominent if you use a different standard to measure it!

thefifthsetpin 8y ago
I'm not seeing why that is true. If one were to imagine a deep moat around Kea, wouldn't that increase its prominence w/out impacting that of Everest? Or are you suggesting that Everest's dry prominence would be measured from whatever the deepest point on Earth is? Or something else?
- vesinisa 8y ago
  Everest dominates Mauna Kea in prominence. In fact, Everest dominates any peak on Earth in prominence, since it's the tallest peak. By the mathematical definition of prominence, the dry prominence of Everest is always measured from the deepest point on Earth, the Challenger Deep. If you dug a moat around Mauna Kea, it would indeed increase its prominence, but would not affect the prominence of Everest. Until you dug the moat deeper than the Challenger Deep (about -11,000 m), at which point the dry prominence of Everest would start to be measured from the bottom of your moat and not Challenger Deep. At this point, digging the moat any deeper would increase the prominence of both Everest and Kea by equal amount, but Everest as the higher mountain would nevertheless always dominate Kea.

njarboe 8y ago

From your link, the lower elevation of a dry prominence of Everest would be the lowest contour that encircles Everest. That won't be nearly as deep as Challenger Deep but a quick google search does not find the correct dry prominence for me.

vesinisa 8y ago
The lowest bottom of the Challenger Deep encircles the Everest. Think of the "outside" of the circle being the deepest point, and the "inside" of the circle being all rest of the Earth.
- njarboe 8y ago
  Got me on that one. Seems to me "topographic prominence" is useful for people talking about peaks in a mountain range. Not so much when the spherical shape of the Earth starts to be significant.
- SilasX 8y ago
  Reminds me of the joke where the mathematician is told to use a fixed length of fencing to enclose the biggest area possible and builds a tiny corral and stands inside and says "I define myself as outside the corral". (Legit point on your part, though.)
  - starbeast 8y ago
    In Douglas Adams''So Long And Thanks For All The Fish', Wonko the Sane resided either outside or inside, depending on your point of view, an inside-out house that he had built as an asylum for the world, after reading the instructions on a packet of toothpicks.
hannasanarion 8y ago
The correct dry prominence of everest is the same as the regular prominence of everest, because there are no bodies of water between it and the nearest peaks.

Steko 8y ago

> The article is likely referring to the estimated dry prominence of Mauna Kea. It's talking around a mountain's "surrounding base" which is a related concept but doesn't take you in the absurd direction of 'drawing a circle around yourself in the challenger deep and claiming everything else is part of Everest'. There is no precise definition of surrounding base, but Denali, Mount Kilimanjaro and Nanga Parbat are possible candidates for the tallest mountain on land by this measure. The bases of mountain islands are below sea level, and given this consideration Mauna Kea (4,207 m (13,802 ft) above sea level) is the world's tallest mountain and volcano, rising about 10,203 m (33,474 ft) from the Pacific Ocean floor. Ojos del Salado has the greatest rise on Earth—13,420 m (44,029 ft) from the summit[citation needed] to the bottom of the Atacama Trench about 560 km (350 mi) away, though most of this rise is not part of the mountain. https://en.wikipedia.org/wiki/List_of_highest_mountains_on_Earth https://en.wikipedia.org/wiki/List_of_highest_mountains_on_E...