Wednesday, August 3, 2011

Behind the curve

Savants have sought to explain the secret of Mt Fuji's subtly concave slopes for more than a century. Now they're getting close

It was the curve that captivated him – the line that falls, steeply at first, from Mt Fuji’s shoulders, then at an ever-shallower angle until, at Omiya, it blends softly into the horizontal. So elegant was this line, he speculated, that it might have inspired the elegant cusping of Japan’s house roofs and castle walls. Merely to admire this mysterious curve wouldn't do, though. As a Victorian scientist, he had to explain it.

John Milne had joined the staff of the Imperial College of Engineering in Tokyo in 1876. He’d already packed several geological expeditions into his 26 years, including forays to Sinai and Newfoundland. Even his journey to Japan was an adventure; to avoid a long sea voyage, he travelled from England via Russia, riding part of the way on a dog-sled across the Siberian snows.

As one of 3,000 or so ‘o-yatoi’ or foreign technical experts hired by the Meiji government, the young professor’s duties were to teach mining, architecture, metallurgy and chemistry. Today, Milne is remembered as a founder of seismology. During his two decades in Japan, he invented an improved seismograph and later helped set up the first global network for monitoring earthquakes.

He also toured the archipelago, inspecting its volcanoes. Their regular forms contrasted with the “very rough” volcanoes he’d seen in Iceland. Just two years after landing in Japan, he’d acquainted himself with “Fusiyama, 12,365 feet near Yokohama; Ganjosan, 7,000 feet near Morioka, Chokaisan, 6,000 feet, between Niigata and Akita, Iwakisan, 5,000 feet, near Awomori; and Kumagatake, 2,700 feet, near Hakodate”.

Now Milne was ready to start his analysis, which he published in the 1878 edition of the Geological Magazine. All the above mountains, he wrote, appear conical at first sight. Looking closer, though, “we see this upper cone expanding and sweeping outward, forming a graceful curve”.

This curve, he reasoned, could arise in two ways. Either it formed at the start of the volcano's life, from the way its ash and lava were thrown out. Or it developed later, through "denudation" by wind and rain. But which of these factors created the elegant profiles of Japanese volcanoes?

Milne doesn’t waste many pages of the Geological Magazine before delivering a crisp judgment: “This being the case, I think we are justified in regarding mountains, similar to those about which I am now writing, as having a form mainly due to the simple piling up of material and not as cones which have been subsequently modified by a number of secondary causes, such as are advocated in treatises on Physical Geology and Volcanos.”

Two pieces of evidence lead him to this conclusion. First, his volcanic profiles – they form logarithmic curves, he believes – are so similar that they must have a common cause. Secondly, the slope angles are close to what theory would predict “for the stability of a self-supporting mass of loose materials”.

A lesser scientist might have regarded the case as proven. But Milne continued to think about the curve. And he went to look at more volcanoes, in Yezo and the Kuriles. More data, however, led to less certainty. A year later, he sent the Geological Magazine some “Further notes upon the Form of Volcanos”. The tone is now circumspect: the slopes Milne saw on his recent tour, while “generally logarithmic”, are not absolutely so.

Then he puts his theories about slope stability to the test. This he does by pouring onto the floor first sand, next gravel, and finally a mixture of the two. Sadly, the resulting heaps remain resolutely cone-shaped, betraying scarcely a hint of Fuji-like curvaciousness. "Taking these experiments as a whole," Milne admits, "it will be observed that I did not obtain much evidence in favour of my views."

He revisits the ways in which a volcano might get its curve. A self-supporting heap tends to spread out at its base; large particles roll further down the slope than small ones, creating a shallower slope angle lower on the hill; and there’s always "denudation" to fall back on. Incidentally, he's tried sprinkling water on his piles of experimental sand and gravel, but that too fails to produce the elusive line.

Has he missed something? Another savant, a Mr Mallet, has proposed that a volcano's weight might crush the strata under it, causing the mountain to settle into the ground. That might result in curved slopes. Or – and surely a note of desperation creeps in here – the volcano's core might shrink as it cools, pulling its slopes inwards like a child sucking in its cheeks.

This time, Milne’s conclusion is not even tentative; it is an abdication. “Taken as a whole, these causes are very varied ..,” he writes. “If we examine them singly, we can but barely form an idea as to the nature of their actions, and when we remember that … they act irregularly in their relations to each other, we see that the task of unravelling their complications becomes quite hopeless.”

As if taking this warning to heart, few scholars since Milne’s day have troubled themselves about volcanic curves. Current textbooks, if they raise the question at all, often take the opposite line to Milne’s: "Initially, a pristine volcano will form a pure conical form,” intone Jon Davidson and Shan de Silva in the Encyclopaedia of Volcanoes, “[until] Mass wasting results in a transfer of mass from the upper parts of the edifice to the lower flanks, building out a talus apron. The edifice evolves to a steady-state profile with concave-upward slopes..."

Yet denudation doesn’t do it for everybody. A trio of highly numerate geologists from Oxford and Cornell proposed – this was in 1981 – that "hydraulic resistance to the flow of magma determines the geometrical form of volcanoes". Feeding their equations for the stickiness of lava into a model, they came up with a slope profile that nicely mimics that of Mt Fuji. However, they note, “the theory is not expected to be valid near the summit, where the solution is singular”.

And there the matter rested – an unresolved tussle, if you like, between the Lords of Lava Dynamics and the Maharajahs of Mass Wasting – until the Space Shuttle blew onto the scene. On one of its flights, the vehicle carried a radar that produced accurate three-dimensional profiles of all the landforms a scientist could possibly want to ogle.

Using this data, a group of researchers led by a Hungarian volcanologist named Dávid Karátson took another look at volcanic slope profiles. They started by picking out 19 highly symmetrical stratovolcanoes from around the Pacific rim. All these mountains turned out to have lower slopes that curve in a logarithmic manner, just as Milne had surmised. This the researchers ascribe to “a combination of different volcano-related mass transport processes on the lower flanks”. In other words, denudation and stuff.

But the upper slopes told a different story. Eight of the mountains looked like true cones, with ruler-straight upper skylines – the researchers called these C-type, for conical – while the rest had concave upper slopes. These were termed P-type, for parabolic. Yotei-zan in Hokkaido is a classic C-type volcano, while Mayon in the Philippines is a P-type.

Erosion cannot explain the upper-slope profiles, Karátson & Co believe. Instead, they suspect that the differing "eruption styles" of P- and C-type volcanoes may be responsible. Parabolic slopes form when volcanoes put out more lava than ash. (By what exact mechanism is left unexplained.) Conversely, straight-sided cones result when eruptions are explosive and ash-rich. Just in time for Milne's centenary, it looks as if the mystery of Mt Fuji's curve may be on the way to being solved.

But what happened to Mt Fuji in all this? Regrettably, the top Hyakumeizan didn't make it into Karátson's elite group of 11 "parabolic" volcanoes. Marred by an eighteenth-century flank eruption, its form was deemed too irregular for study. To its admirers, of course, it may be this very irregularity that transforms Mt Fuji into an image of perfection. But that raises a different kind of question altogether…


Milne, J (1878): On the Form of Volcanos, Geological Magazine (Decade II), 5: 337-345

Milne, J (1879): Further Notes upon the Form of Volcanos, Geological Magazine (Decade II) (1879), 6: 506-514

Lacey, A, Ockendon, J and Turcotte, D (1981): On the geometrical form of volcanoes, Earth and Planetary Science Letters, Volume 54, Issue 1, June

Davidson, J and De Silva, S (1999): Composite Volcanoes: Chapter 43 in The Encyclopedia of Volcanoes, Elsevier

Karátson, D, Favalli, M, Tarquini, S, Fornaciai, A, and Wörner, G (2010): The regular shape of stratovolcanoes: a DEM-based morphometrical approach, Journal of Volcanology and Geothermal Research, 193, 171–181. (And many thanks to Dávid Karátson for explaining some key points about this paper to Project Hyakumeizan.)

Photos: Portrait of John Milne from Wikipedia; photos of Fuji from The Volcanoes of Japan, Part 1, Fujisan by John Milne & W.K. Burton; Collotype Plates by K. Ogawa, ca 1892


Iainhw said...

Interesting post. The first time that Fuji's captivating curves caught my eye was staring at a Hokusai Red Fuji print. Nearer home a similar sweeping curve on Ben Dorrain in the western highlands always reminds of Fuji.
I guess that Ben Dorain is also volcanic but unfortunately the rest of it isn't conical.

Edward J. Taylor said...

You've no doubt seen this:

Outdoor Japan Magazine - Issue 39 - Riding an Icon - Skiing Mt. Fuji - Spring Skiing on Mt. Fuji - Yamanashi

Edward J. Taylor said...

I wonder if there is something genetic that draws us to this conical shape, perhaps a metaphor return to the mother's breast. As my newborn gets her 5-star service, I look out the window at the conical shape of Tetilla (teat, Sp.)Peak rising from the desert floor not far to the south. Parallels?

David Mantripp said...

Never mind the science - the photos are wonderful... no credits ?

Project Hyakumeizan said...

Iain: many thanks for the link to Ben Dorain - yep, that looks like a logarithmic-profile lower slope, as identified by Karatson et al - the product of "mass wasting" 'n stuff rather than an eruption. Hokusai's Red Fuji is an interesting reference - the artist seems to have fixed on the curve as Fuji's essential characteristic ("P-type stratovolcano") and accentuated it.

Ted: interesting comment - the gender of Fuji is a surprisingly unstable subject. Evidence suggests that the tutelary deity started off as a male god (sometime in the Heian) but morphed (during or after the Sengoku period) into Konosakuyanohime, who is most definitely female. Perhaps reflecting that duality, "Fuji" is feminine in French and masculine in German (or is it the other way round). Perhaps, when it comes to symbolism, it's just as the Hyakumeizan author said: "Fuji is there for everyone and yet, soaring into eternity, stands for something beyond any man's grasp.”

David: the photos of Fuji are from The Volcanoes of Japan, Part 1, Fujisan by John Milne & W.K. Burton; Collotype Plates by K. Ogawa, ca 1892 - the photos themselves were by W K Burton, an engineer by profession and expert photographer, and printed by the equally expert K Ogawa. So they're an Anglo-Japanese collaboration, as is fitting. If you follow the link (bottom of "References"), you can see some better reproductions than I've been able to post in the article. The original book is rare as hen's teeth, but you can find copies in the Zurich or Basel central libraries to look at. The original photos are stately... Inspect with clean fingers.

Iainhw said...

Last night I discovered another reference to Milne as I was reading through a copy of one of Weston’s talks at the RGS in 1895, recorded in the Geographical Journal (vol vii no 2, p125). Milne was at the talk and spoke after Weston (and Gowland). He had the following to say on the subject of Fuji:

...The next thing I noticed was the beautiful form of Fuji. This so struck me that I photographed it from twenty-six points of view. The analysis of the curves showed that they were mathematically as true as circles and parabolas. The meaning of this curve is that the base is just sufficient to support the material above it, and if you wanted to increase the height of the mountain you would have to increase the size of the base. Given the shape of the mountain, you can tell something of the nature of the material it is composed of, and this is one of the lessons which have been learned from Japanese Mountains.

The material out of which Fuji is built, as determined from its shape, has a strength equal to that of ordinary brickwork. Once I slept on the top for over a week. From observations made with pendulums, it seemed that the mountain heeled over by the wind. This heeling was equal to that which would be produced by a wind pressure of 50lbs. per square foot if a mountain like Fuji was made of brick. We also made observations with barometers, thermometers, and hygrometers, at intervals of two hours, and used this material, together with observations made at the base of the mountain, to determine its height. One result we obtained was that from the same data you will get a different height by different methods of calculation. One man levelled Fuji from the bottom to the top, making the height 12,365ft – an easy number to remember, because there are 12 months and 365 days in a year. One conclusion I came to is, that we are not certain about the exact height of any mountain. Changes in barometrical pressure may cause mountains to vary in height. They may swing from side to side with diurnal waves; they may shiver and tremble in a tremor-storm; while at the time of an earthquake they may wag their heads and dance.

Project Hyakumeizan said...

Iain: many thanks for this - your RGS researches always turn up something fascinating. Appears that, more than a decade after his Geological Magazine articles on Fuji, Milne was still thinking about the problem. What this excerpt dramatises to me is how Milne was thinking about all the forces potentially acting on mountains. He didn't get far with the problem of Fuji's curvature, as we have seen, but this restless analysis of the dynamics involves must have been behind the undoubted progress he made in the nascent science of seismology...

PS: The observation that Fuji is swayed by the wind is particularly interesting - wonder if modern science can confirm that ....?