A baseless claim?

It’s true that no agreed upon or precise definition of a mountain base exists. In fact, there’s not even a universally accepted definition for “mountain” itself. Nonetheless, I’m certain that one of my geology-related homework readings from the previous millenium claimed that Mauna Kea — the volcano that forms most of the Island of Hawai’i — is taller than Mount Everest if you compare them from base to summit, since Mauna Kea’s base extends below sea level to the ocean floor. Assuming this decades-old elementary school assignment was justified in its claim, what threshold or criteria was used to constitute Mauna Kea’s and Everest’s respective bases?

In the case of Mauna Kea, its base turns out to be fairly apparent. As a shield volcano born of the Hawai’ian hotspot , its lava pillowed out to form an upward slope relative to the sea floor. Furthermore, the combined weight of Mauna Kea and its fellow volcanoes depress the oceanic crust below them by an estimated 8 kilometers (4.9 miles), which results in an underwater moat ringing the chain of islands, known as the Hawai’ian Trough. The bowing of the sea floor causes the surface outside the weight-bearing region to rise up even higher, forming an arch where the crust buckles upwards. This all makes it simple — though still somewhat subjective — to tell where Mauna Kea begins, so to speak. From the bottom of the Hawai’ian trough to its top, Mauna Kea comes in at about 9.7 kilometers (6.0 miles) tall.

Mount Everest and other Himalayan peaks are fold mountains , resulting from the collision of the Australian-Indian tectonic plate into the Eurasion plate. The materials these mountains are made from more or less match those of the surrounding land, the way a wrinkle in a rug is made of the rug itself, although the crumpled nature of the Himalayan range does reveal older (and therefore normally buried) layers of the crust. This — and the fact that the “rug” from which it arises is itself not necessarily on a horizontal or flat “floor” — make Everest’s base a much more arbitrary call. Proposed base elevations for Everest range from 4.2 kilometers (2.6 miles) on its south to 5.2 kilometers (3.2 miles) on its north in the Tibetan Plateau, which — when averaged and subtracted from the peak’s 8,848-meter (29,029-foot) elevation — result in a summit-to-average-base height of 4,148 meters (13,579 feet).

Leaving home base

Despite its uncomfortably abstract squishiness, this base-to-summit measurement method seems to work in some cases, at least conceptually. Given that many of the extraplanetary promontories that us Earthlings have come to be aware of are volcanic in origin (and as we’ve seen in the case of Mauna Kea and Everest, a volcanically created peak generally lends itself to a much more apparent base than mountains and ranges caused by tectonic forces), perhaps this approach can be applied to extraterrestrial mountains, too?

Mars is the perfect planet to start with, as it’s propagated a number of truly massive shield volcanoes, many plenty heavy enough to crush the crust beneath and around them into indentations — just like the Hawai’ian islands do. Several are also sharply defined by sheer escarpments — 8 kilometers (5 miles) high in some places — that aid in creating distinctive thresholds with which to delineate the volcanoes’ boundaries. These cliffs are likely the result of erosion at the outer edges of past lava flows. However, the bases of these pedestal-like scarps surrounding the peaks’ perimeters are at different heights relative to each other, so it’s still tricky to determine where to set the starting point of each mountain. Nonetheless, Olympus Mons is easily Mars’ tallest mountain, coming in at nearly 22 kilometers (13.7 miles) from the foot of its northwestern cliffs to its peak. Despite its height, it has an average slope of just 5 degrees, spreading over a footprint of 300,000 square kilometers (120,000 square miles), roughly the area of New Mexico. It’s so large that, according to astrophysicist Neil deGrasse Tyson, “you could be on its slopes and you would not know [it] … the base is so huge before you get to its summit.” ¹

The mountain that came from outer space

Volcanoes aren’t the only way that interplanetary peaks come to be, though. With an average width of just under 530 kilometers (or 330 miles), 4 Vesta is the second-largest known asteroid within our Solar System. It hosts a crater called Rheasilvia that takes up most of its southern hemisphere, the bottom of which lies about 13 kilometers (8.1 miles) below the surrounding surface. Rheasilvia likely formed from a collision so colossal that the impacting body made its way through several layers of crust and possibly even into 4 Vesta’s mantle , as evidenced by spectral signatures of olivine — the primary mineral composing Earth’s own mantle — captured by the Hubble Telescope. Beneath layers of post-pummel debris, the remnant of the impacting body itself forms the foundation of a soaring summit at the center of the crater. This peak is essentially deadlocked with Olympus Mons for tallest known mountain in the Solar System: ² both behemoths’ undulating surroundings — and therefore the large margins of error surrounding their extremely approximated baselines — make it impossible to objectively discern which deserves the honor.

Clearly, a mountain’s base-to-summit height is significantly subjective, even if there happen to be cooperative geological features at play like troughs, craters, or cliffs. While this measurement method may result in an interesting — if conceptual — trait of the peak in isolation, it neglects to capture the global context.

Earth as an ellipsoid

Unlike the base-as-a-baseline approach, sea level excels at accurately plotting a peak’s height relative to the rest of the world. This metric has been a reliable reference point throughout the history of height measurement, providing an ostensibly consistent surface from which to determine elevations. According to the National Geodetic Survey — a branch of the National Oceanic and Atmospheric Administration responsible for establishing latitudes, longitudes, elevations, and shorelines in the US — sea level is defined locally, via various tide surveying stations. Each is constantly collecting sea level data for its own region. Mean Sea Level (MSL) is then defined for each locality by averaging those measurements over the course of 19 years, “the period over which the pull of the sun and the moon on the earth completes a full cycle.” ³ In theory, sea level serves as the stalwart starting point from which to map the elevations of disparate global locations. But in practice, it’s not quite so simple. It helps here to first have a bit of context about Earth’s overall shape, to better understand the disparity between theoretical and practical sea level. Our planet is not a perfect sphere: all distances from its center of mass to its surface are not equal, and not just because of the bumps caused by the very mountains we’re seeking to measure. Earth’s diameter from pole to pole is about 42.8 kilometers (26.6 miles) shorter than its equatorial diameter — a difference of about ⅓ of a percentage point — which makes our planet an ellipsoid or an oblate spheroid, geometrically speaking. ⁴

Earth is just shy of spherical because it spins. The further a point is from its axis of rotation (like a location along the equator), the faster that point must travel through space, compared to points that are closer to the axis (like those nearer the poles). This difference in relative speed results in a phenomenon called centrifugal force . Over time, this bit of extra force has flung Earth’s innards outwards, which has led to a slightly deformed spheroid shape.

After averaging away tidal pull, currents, and weather-induced waves, one would expect the oceans to settle into a flat, global plane — the very embodiment of the ellipsoid model. However, even after accounting for 19-years-worth of tides, this appears not to be the behavior of our seas.

To quote spatial analyst Witold Fraczek: “The reference ellipsoid was intended to closely approximate the MSL; it was surprising when the figures differed greatly.” This wasn’t realized until relatively recently, when the TOPEX/POSEIDON satellite — launched in 1992 expressly to capture surface altitudes — revealed that sea level, even after time-averaging, differed from the ellipsoid by as much as 100 meters (330 feet) in some spots. ⁵ In other words, our oceans appear to have hills and valleys of their own.

Sea level doesn’t seem level

What keeps sea level from spreading out evenly over Earth’s ellipsoidally averaged surface? It actually turns out to be gravity that is not evenly dispersed across the earth, and the seas in turn reflect this. Earth’s crust varies invisibly in its density: in some places comprised of hollow caverns, porous layers, or water-logged aquifers, all of which are much less dense than solid rock — but even rock differs in density from type to type significantly. Moreover, to quote the National Geodetic Survey, “Mountains have greater density and, therefore, cause greater gravitational acceleration than valleys that are mostly filled with air. … If it has lower density than its surroundings, it produces less gravity.” ⁶ And it is gravity that supplies the very characterization of a level surface: like the tool of the same name, level is defined as perpendicular to the gravitational field. Therefore, though the oceans may appear to undulate unevenly, given that they do so in response to Earth’s gravity, they are in fact level by definition.

Across the time-averaged, temperature-normalized surface of the sea, the strength of gravity is exactly equal, and this lumpy, oceanic expanse equates to the actual reference used by surveyors to define elevations, known as the geoid. It extends across the continents too, though — oscillating through raised land masses and over empty valleys, forming a lumpy layer defined by a strength of gravity exactly equaling that at sea level. Scientists use an abundance of different technologies to measure micro-variations in gravity across the continents (a fascinating can of worms that I may pry open in a future post all its own). But another — far more analog — way to find the geoid at any land-based location would be to dig a channel from the ocean inland to that exact point, then wait to see where sea level settled.

Given that the mass of a mountain makes its own gravity, how much taller would it be if it weren’t weighed down by this same self-induced gravity? That is, how would a mountain’s height change if we didn’t take into account the relative bulging of the geoid at its exact location?

The original geodesists seeking to measure Mount Everest as a part of British India’s Great Trigonometric Survey claimed that there were “grounds for inferring that sea-level under Mount Everest would be raised by 150 feet on account of the attraction of the mighty mass above it.” ⁷ Subtracting this alleged 150 feet would yield Everest’s ellipsoidal height, and is essentially based on the ellipsoid rather than the geoid. Put another way, we’d ignore the gravitational anomalies that the geoid accounts for, in favor of the visually flat surface provided by the reference ellipsoid — that smooth and mathematically perfect geometric form based solely on the discrepancies between Earth’s polar and equatorial diameters, and which disregards variations in density and landmass. The geoid and the ellipsoid intersect at geoid undulations: direct results of the non-homogeneous nature of Earth.

While the geoid is quite lumpy relative to the ellipsoid, it’s not as rugged as Earth’s actual crest- and canyon-riddled crust, because although gravity does vary in strength due to these landforms, their physical effects on gravity are not equal to their physical volumes. A mountain cannot produce the gravity required for a river to flow all the way uphill to its top; however, it might generate enough that water near it would settle at a relatively higher elevation than if that mountain weren’t there. The fact that the geoid takes these sorts of gravitational variations into account make it a far superior model for floodplain mapping and the like compared to the ellipsoid.

Extraterrestrial elevations

Since scientists have identified a geopotential plane from which to measure height on our planet, it would seem at least theoretically possible that this same concept could be applied to other planetary bodies … and in fact, it has: this extraterrestrial equivalent of the geoid is called an areoid.

Other planets aren’t often enveloped in oceans the way Earth is, though, so how are areoids’ baselines chosen? And if they’re anywhere as arbitrary as the bases of the mountains they aim to quantify, what’s the point?

In the case of Mars’ areoid, its “zero” level had initially been based on atmospheric pressure: the minimum pressure at which water is stable, also known as its triple point . Anything lower than this and ice is capable of skipping its liquid phase and sublimating straight into gaseous form (the way dry ice does even at Earth’s normal surface pressure, since carbon dioxide — the molecule it’s composed of — has a much lower triple point of its own). The thought was that a hypothetical water-based Martian ocean — with a hypothetical sea level from which to measure elevations — could only exist at a pressure below water’s triple point. Otherwise, by definition, there would be no liquid to form imaginary oceans in the first place — just solid ice and water vapor.

The atmospheric pressure at sea level on Earth is just 0.6% of water’s triple point, however, so if we were to base our own geoid on that metric rather than sea level, it’d mean our geoid’s baseline would be high in the sky, no matter your Earth-bound location. Everest’s elevation would recalibrate to (very) approximately -30 kilometers (-18.6 miles) — that’s right, a negative elevation ⁸ — compared to its current elevation of 8,848 meters (29,029 feet). It’s clearly much easier for our surface-dwelling minds to make use of a sea-level-based reference point. All of this means that a triple-point-calculated Martian areoid and the elevations it results in aren’t particularly comparable to those on Earth, thereby rendering them far less relatable.

Sea level, sans seas

Fortunately for those of us in dire need of more fathomable (and accurate) Martian elevations, in 2001 the Mars Orbiter Laser Altimeter provided scientists with enough gravity information to reformulate Mars’ areoid. They now knew where the pull of gravity was relatively stronger and weaker, and could map the concentric gravity gradients that surround the planet like the layers of an onion — each ring its own geopotential surface exhibiting an exactly equal pull of gravity. Earth is circumscribed by its own geopotential surfaces, of which our geoid is one. For convenience and for comprehension, the baseline of the geoid was chosen to match that of the gravity potential at sea level, but it need not have been. It could have been set as a physically higher geopotential surface, but therefore with lower gravity potential.

But on a Mars unmarred by el mar , how does one choose which onion ring to call “zero”? Scientists settled on the geopotential surface for which the mean radius matches that of Mars’ equator. ⁹ This doesn’t necessarily mean that every point along the Martian equator lies at zero inches in elevation, though: like on earth, a surface defined by equal gravity thereby responds to gravity directly, not to physical features (although it may be indirectly affected by land formations in so far as they in turn affect gravity to a degree), and will therefore vary in its distance from the crust, rising above ground in some places and falling below it in others.

Just like Earth’s geoid, Mars’ areoid also exhibits areas in which gravitational disruptions reflect topographical ones. Olympus Mons and the Tharsis region near it — home to some very voluminous volcanoes — produce the largest gravity anomalies in the entire Solar System. Olympus Mons came in at 22 kilometers (13.7 miles) high when measuring from the base of its bounding cliffs, but its summit is only about 21 kilometers (13 miles) above the Martian areoid. This is the inverse of what we saw with Everest, wherein its elevation is much greater than its base-to-peak height. Olympus Mons’ transposed elevation-to-height ratio actually serves to further emphasize its sheer magnitude: it produces its own gravity (with a lot of help from its neighboring Tharsis Montes and the magma-spawned plateau upon which they perch), thereby raising the areoid’s “onion ring” in its region and leading to elevation measures that are lower due to the areoid’s swell.

It seems sensible to develop areoids for planets and moons exhibiting elevated land formations, but scientists have even developed them for the gas giants, too. Like Mars’ initial areoid, those of Jupiter, Saturn, Uranus, and Neptune are based on pressure. Their baselines fall at the radial distance from their planet’s center of gravity wherein the atmospheric pressure equals 1 bar, which is just under the pressure at sea level on Earth. This threshold actually ends up falling right at the cloud levels that visibly define the “surface” for each of the gas giants.

Lower gravity and lack of tectonics lend a leg up

Although areoids provide a helpful way to compare elevations across planets, they fail to account for the fact that bodies with lower mass exhibit lower gravity: namely, the pull that Martian mountains contend with is just 38% the strength of Earth’s, making it much easier for them to sprout skyward. To literally level the playing field, I normalized for Earth’s gravity (in an overly simplistic, possibly precarious way), and found that beneath its strain, Olympus Mons only makes it to the 8.4 kilometer (5.2 mile) mark when measuring from its base to its summit (compared to 22 kilometers (13.7 miles) under its own planet’s gravity), falling just short of Mauna Kea’s 9.2 kilometers (5.7 miles).

Mars’ relatively low gravity isn’t the only pinnacle-producing trick the planet has up its proverbial sleeve, though: lack of tectonic motion plays a prominent role in the heights that its mountains have managed to reach. Most of the Martian shield volcanoes are significantly more massive than any on Earth, in part because their crustal locations stay statically positioned above the hotspots from which the peaks originate. Meanwhile, the land above Earth’s hotspots are never in the same spot for long (geologically speaking), due to our planet’s plate movements. This explains why the Hawai’ian hotspot led to a chain-like formation of several sea mounts, rather than a single skyscraping summit in the middle of the Pacific.

This made me wonder about the Hawai’ian hotspot’s lava-output potential relative to that of Olympus Mons’: if the Pacific plate had stayed still, how vast a volcano could it have produced? To get a rough idea, I simply used the collective volume of the Hawai’ian chain of islands and seamounts — nearly 750,000 cubic kilometers (180,000 cubic miles) — as a proxy for Mauna Kea’s would-be size on a hypothetical, tectonic-less Earth … I say “simply” on my part, because someone else had already written an article about the hotspot’s total output. And equally fortunate for me and my free time, NASA had already done the legwork to determine Olympus Mons’ volume at 3,862,000 cubic kilometers (just under 2,400,000 cubic miles). From there, it was just a matter of division to discover that over five Hawai’ian-hotspot-outputs-worth of lava would fit inside of Olympus Mons!

Of course, as far as the mountains of the world — that is, the Solar System, if not the universe — are concerned, this is all just semantics. And I think that’s more or less where I’ve landed as well. The behemoths of the land (and sea, and space) are wild things, unbridled by our attempts to bestow metrics and accolades upon them. A mountain’s human-assigned height will always carry with it a whiff of the arbitrary, but from now on when I read an elevation on a map, I’ll understand all that went into it.