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Tag Archives: glaciers

Marco Polo’s brush with the cryosphere

By Graham Cogley

Hannibal is not the only figure from deep in history who is known to have come close to noticing a glacier. One of the better known references to glaciation is from early renaissance times, in the Travels of Marco Polo.

There is a good deal of uncertainty about this book. Marco Polo set off from Venice in 1271, bound for the Orient. On his return to Italy in 1291 he was captured by the Genoese, who were then at war with Venice, and clapped into jail. The usual account is that he told the story of his travels to a cellmate, Rustichello of Pisa, who wrote them up in Old French. There is, however, no authoritative text. The travels were an immediate hit, and manuscript copies proliferated in several languages.

The uncertainty extends to the contents. It is unclear how close Marco Polo ever came to Mount Ararat, of which Rustichello says he said (in the English rendition of Henry Yule and Henri Cordier from 1902):

And you must know that it is in this country of Armenia that the Ark of Noah exists on the top of a certain great mountain on the summit of which snow is so constant that no one can ascend; for the snow never melts, and is constantly added to by new falls. Below, however, the snow does melt, and runs down, producing such rich and abundant herbage that in summer cattle are sent to pasture from a long way round about, and it never fails them. The melting snow also causes a great amount of mud on the mountain.

Except perhaps for some in the Icelandic sagas, this is one of the earliest glaciological remarks ever written down. It is therefore worth a close look. Resist the tempting byways (Noah’s Ark; the pastoral aspect; the mud), and never mind whether it is the account of an eye-witness. This is an avenue for gauging the extent to which late 13th-century observers understood glaciers.

First, it is not true that no one can ascend Mount Ararat, as alpinists have shown repeatedly since the first ascent in 1829. This late date has more to do with lack of time, lack of inclination, and in short with attitude, than with any real difficulty. Of course Ararat is a long way from Italy, and there may have been a religious tint in the attitude of 13th-century Armenians. But the scientific attitude to glaciers, and to mountains generally, was a thing of the future.

Second, it is probably not true that the snow on top of Mount Ararat never melts. Ararat is about 50 km south of Yerevan on what is now the Turkish side of the River Araks. At 5,137 m above sea level in latitude 39.7° north, there should be at least a short season of above-freezing temperatures every year. But here Marco Polo was on the ball at least to the extent of recognizing, or even taking for granted, a basic fact of glaciology and meteorology: it is colder higher up. He was, however, more a traveller than an analytical thinker. Taken literally, his account implies that Mount Ararat should have been getting steadily higher and, probably, pointier.

And so we come to the big gap in 13th-century understanding. How does the snow manage to stay perpetual at the top of the mountain but to stay ephemeral part way down? Apparently Marco Polo and his contemporaries didn’t even notice the contradiction — that you cannot pile snow up indefinitely, as observed at the tops of mountains (including the Alps, only 200 km from Marco Polo’s birthplace), without something having to give.

If this contradiction was difficult to recognize, it was yet harder to explain. What was required was the realization, first, that snow will turn into ice if it keeps on piling up, and then that if the snow keeps coming the ice must flow.

Neither of these discoveries was proposed until the 18th century, and neither was nailed down firmly until the 19th. Making the necessary intellectual progress called not just for more detailed observation, but for a change of attitude. To show that the ice moves you can put a stake in it, and measure its position accurately twice — not all that difficult. Why it was not sensible, or possible, to do this or to think this way in the 13th century, but it became sensible by the 18th century, is another question.

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GRACE and the dance of the kilograms

By Graham Cogley

The GRACE satellites have transformed our understanding of how kilograms dance around on and beneath the Earth’s solid surface, but nobody would claim that analyzing what they are telling us is a simple job. A recent analysis by Riccardo Riva and co-authors exemplifies this point.

The problems start with a list of technical details to do with processing of the raw observables. “Observables” is jargon, short for “observable quantities”, but it is a valuable clue to how to think about the “inferables” that we are concerned about.

The point is that an “inferable”, such as relative sea-level change, may be quite some distance down the chain of reasoning from the observable, which in this case is the rate at which the two satellites are accelerating away from or towards each other. This rate depends directly on all the gravitational attractions they feel at the time of each measurement. We want to remove the technical noise so that we can infer the signal of the fluctuating gravity field experienced by the satellites, and so infer the transfers of mass that explain the gravitational fluctuations.

One of the technical details, for example, has to do with spatial resolution, which for GRACE is about 300 km. But the regions between which mass is being transferred generally have quite sharp boundaries, for example the coastline. The jargon for this part of the problem, “leakage”, is quite expressive. It hints that part of the signal we want has strayed out of our study region and into neighbouring regions.

Riva and co-authors have two study regions, the land and the ocean. Signal could be leaking either way across the coastline, but they argue that the oceanic signal of mass gain, expressed as relative sea-level change, is probably much smoother than the terrestrial signal of mass loss. So they simply define a 250-km wide buffer in the offshore waters and “unleak” all of its supposed signal back onto the landmasses.

There then follow a number of other corrections, including a correction for movements of mass within the solid Earth and a trial-and-error phase that seeks to undo the addition of some oceanic signal to the land signal during the unleaking phase.

Now the geophysical part of the problem can be addressed. Riva and co-authors reckon that +1.0 mm/yr of equivalent sea-level rise moved from the continental surfaces to the oceans between 2003 and 2009, give or take 0.4 mm/yr. This surprises me.

My estimate for the transfer from small glaciers (those other than the ice sheets) is about +1.2 mm/yr for the same period. Several recent estimates for the transfer from the Greenland Ice Sheet lie between about +0.5 and +0.7 mm/yr, and for the Antarctic Ice Sheet at about +0.5 mm/yr. (All of these abouts are partly because of the uncertainty of the measurements, or rather of the inferables, but also because of the difficulty of matching the different time spans of the analyses.) The glaciers, then, seem to be adding more than twice the mass to the ocean that is estimated by the Riva analysis.

It gets worse. Yoshihide Wada and co-authors, in a paper to appear shortly, argue that the mining of groundwater is running at present at a rate equivalent to +0.8 mm/yr. This addition is partly offset by the filling of reservoirs, estimated at —0.5 mm/yr over the past 50-60 years. The rate during the past decade is probably lower, because the frenzy of dam-building has abated somewhat recently. But it is not possible to get all of the continental surface contributions to add up to less than, say, +2.6 to +2.8 mm/yr, give or take perhaps 0.4 mm/yr.

What we have here is stark discord, well outside the error bars, between several “inferables”, and we haven’t even got to the sea-level rise due to thermal expansion and the estimated sea-level rise itself. This is a classic example of unsettled science in a context of settled science. We can draw a diagram to depict the water balance of the ocean, or write down a little equation. A balance is, after all, simple arithmetic. The boundary between the settled and unsettled parts of the problem lies somewhere beyond the diagram, and indeed beyond the signs, + or —, attached to the various terms in the equation. But at the moment it is definitely before we get to the first decimal digits of the numbers, at least one of which must be wrong.

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Reservoirs and the dance of the kilograms

By Graham Cogley

Suppose you have a kilogram of something, and you know where it is, somewhere near the surface of the Earth. And suppose it has been there for quite a long time.

It will have been obeying Newton’s laws of gravitation, like all the other six trillion trillion kilograms. They will all have got used to each other, and will be relatively at rest, because all of the gravitational accelerations will have decreased to zero (pretend).

Now suppose you take your kilogram and put it somewhere else. It will attract all the other kilograms towards its new location, more strongly the nearer they are. Remember, Newton says that the acceleration drawing any two bodies together is inversely proportional to the square of the distance between them.

As kilograms move around, they induce other kilograms to move around as well. Recently Julia Fiedler and Clinton Conrad identified the steps in one part of this dance of the kilograms: the removal of about 10,000 trillion kilograms from the ocean into reservoirs since 1950. These kilograms represent a hypothetically uniform lowering of sea level by 28 mm, and a nearly equivalent displacement of fresh air by reservoir water. (Only nearly, because almost a quarter of the sea water has seeped into the aquifers beneath the new reservoirs.)

The surface of the sea is an equipotential, a surface on which the gravitational potential is a constant. The value of the constant is of no interest, except that it is just right for accommodating all the sea water there is. Take some water out of the sea and the new sea surface is still an equipotential, but a different, lower one (the new constant is smaller).

Sea level, though, has been rising steadily. As the ocean warms, it expands — each of its kilograms takes up more space. And as the glaciers melt — which is where I come in — they add kilograms to the ocean. Since the early 1990s we have been able to track this rise with satellite altimeters, but for times before then we have to rely on tide gauges. A tide gauge measures RSL or relative sea-level, the distance between the sea-surface equipotential and the part of the solid Earth to which it is attached.

In the present context the solid Earth is more like toothpaste than rock. It moves because the reservoirs squeeze the toothpaste, which flows away towards where the kilograms came from. The solid surface falls beneath the reservoirs, so relative sea level rises there. There is a compensating relative fall, spread over the oceanic source of the kilograms.

But here comes a new arabesque of the dance. The dammed kilograms are busily attracting all the others — including the ones still in the ocean — towards the reservoirs. They have changed the shape of the sea-surface equipotential, which is higher (further from the Earth’s centre of mass) near the reservoirs than it used to be, and lower over the oceanic source. For practical reasons we can only install tide gauges on coastlines, so they give us a biased view: no sampling at all of the open ocean, and an index of coastal RSL that deviates from the global average, gauge by gauge, depending on the number of kilograms we have moved into reservoirs nearby.

Fiedler and Conrad estimate that some gauges, in southern locations far from reservoirs, have been recording less than the global-average change of RSL that is due to the reservoirs. Others have been recording more, and at some the sea level has actually gone up simply because they are close to big reservoirs. Gauges in Ghana, not far from the 148 trillion kilograms that we moved into Lake Volta beginning in 1965, are good examples. But, based on a sample of 200 gauges, Fiedler and Conrad reckon that the tide gauges have been seeing only about —0.3 mm/yr instead of the true average reservoir signal, —28 mm over 58 years or about —0.5 mm/yr.

So the tide-gauge estimates of global-average sea-level rise are too high by +0.2 mm/yr. There are reasons for thinking that the necessary correction might be smaller, but the total rate (over the past few years) is in the neighbourhood of +2.5 to +3.0 mm/yr. Looking on the bright side, we have reached the stage of worrying about tenths of a millimetre. All the same, people like me, who try to estimate contributions to the water balance of the ocean, now have to learn new dance steps because the band is playing a subtly different tune.

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Dirt on glaciers

Dirt is more or less ubiquitous on glaciers. Even when there isn’t much, it makes the ice darker, a climatically important fact that can also be put to intriguing uses. Sometimes the dirt gives us striking visual effects in the form of multiple medial moraines. When there is enough dirt to cover the surface nearly completely, we call the glacier a debris-covered glacier.

The glacier isn’t necessarily buried entirely. In the accumulation zone, fresh snow will mask older debris, and usually not all of the ablation zone, where all of the snow melts, is debris-covered. Indeed the debris typically covers only a few to perhaps 20 percent of the surface, at the lowest elevations. But this part is critical, because it is where we expect to observe most of the mass loss that is supposed to balance the mass gain in the accumulation zone.

Debris-covered glaciers are a nuisance from a number of standpoints. Probably the biggest nuisance is that we don’t know how to judge the effect of the debris on the mass balance. Conventional wisdom has it that thin debris increases, and thick debris reduces, the melting rate of the underlying ice. The debris, being darker than the ice, absorbs more of the incoming radiation, but the more debris there is the less radiative heat reaches the ice.

In a recent laboratory study Natalya Reznichenko and co-authors reinforced the conventional wisdom. In an interesting twist, they showed that the daily cycle of radiation makes a big difference. If you irradiate a sample of debris-covered ice continuously, then after a delay of some hours, increasing with the thickness of the debris, you get the same rate of meltwater production as if there were no debris at all. But if you cycle your lamps with a 12-hour period, to mimic day and night, the underlying ice never gets a steady input of heat. The night undoes much of the work accomplished during the day.

The melt rate is slower beneath debris more than 50 mm thick, about half a handsbreadth, and faster beneath thinner debris. This is the “critical thickness”, at which the debris has no net impact on the melting rate. In an elegant graph summarizing the field measurements, the Reznichenko study shows that the critical thickness varies with altitude or equivalent latitude. On higher-latitude glaciers, or equivalently at lower altitude, the critical thickness can be as low as 20 mm, but it can exceed 100 mm at low latitudes or high altitudes.

So the real world is a bit more complicated than the laboratory when it comes to the effect of real debris on real glaciers. What about real-world melting rates? There are distinct signs that real debris-covered glaciers are even harder to understand than ideal ones.

For example, Akiko Sakai and co-authors pointed out that on debris-covered glaciers in Nepal there are lots of small meltwater ponds. One such pond absorbed seven times more heat than the debris cover as a whole, accelerating the melt rate and producing a knock-on effect because the departing warm meltwater enlarged its own conduit, a phenomenon known as “internal ablation”. And on a debris-covered glacier in the Tien Shan of central Asia, Han Haidong and co-authors showed that exposed ice cliffs, accounting for only 1% of the debris-covered area, produced about 7% of all the meltwater generated across the debris-covered area.

It would be nice if we knew the fractional debris cover of every glacier, and even nicer if we could say by how much the mass balance of each glacier is altered by its debris cover. This is a pipe dream for the moment, but the careful small-scale measurements on debris-covered ice seem to suggest that ignoring the debris, as we have to do now when estimating mass balance on regional and larger scales, could overestimate the mass loss quite seriously.

The trouble is that although we have very few measurements of the whole-glacier mass balance of debris-covered glaciers, they seem not to be consistent with the detailed laboratory and field studies. One of the most careful regional-scale measurements, by Etienne Berthier and co-authors, found that Bara Shigri Glacier, in the Lahul region of the western Himalaya, thinned by —1.3 m/yr over five years, a rate significantly faster than the —0.8 m/yr determined by photogrammetry for all the glaciers in the region.

“Bara Shigri” means “great debris-covered glacier” in Hindi. Clearly we don’t know enough about the behaviour of debris-covered glaciers, great or small, and as there are lots of them, and lots of people depend on them, they need continued study.


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Diamonds in glaciers

You can find all sorts of things in glaciers if you look hard enough. Among the oddities that come to mind are volcanic sulphur, soot, and bacteria and fungi.

But now Andrei Kurbatov and co-authors, writing in the Journal of Glaciology about fieldwork on the western margin of the Greenland Ice Sheet, have found something really surprising: diamonds. Don’t get too excited. If you look in just the right place you can expect to find trillions of them per litre of melted ice, but these are nanodiamonds, the biggest only a few hundred billionths of a metre across. There is no danger of prices collapsing in the international diamond market.

However there is definitely a likelihood of a diamond rush spearheaded by scientists. The stimulus for this work was the discovery of nanodiamonds in ordinary sediments from several sites across North America. At all of the sites, much of the diamond is actually lonsdaleite, and there are other indications that point to the material being non-terrestrial. Lonsdaleite is elemental carbon that has crystallized in the hexagonal system, so it is a polymorph of the more familiar diamond belonging to the cubic system. Cubic diamond forms at temperatures and pressures appropriate to depths greater than about 150 km beneath the Earth’s surface. To make lonsdaleite it appears that you need much greater temperatures and pressures even than that. At any rate, it is known only from meteorites and impact craters. We conclude that either it arrived with the meteorite or it formed during the impact.

The next exciting thing about these non-terrestrial diamonds is their age. They are found exactly at the base of the Younger Dryas cold snap, dating to about 11,000 BC. You could not ask for a sharper spike in abundance than the one shown in the Kurbatov paper, and it matches the evidence from elsewhere perfectly.

The first synthesis of this evidence showed that there are non-terrestrial “event markers” all across North America at the base of the Younger Dryas. It was a bold, if partly conjectural, synthesis, linking the impact not just to the cold snap but to the extinction of the mammoths, the disappearance of the palaeoamerican Clovis culture and the formation of the Carolina Bays.

The Carolina Bays can be seen in the atlas as the multiple arcs that form the coastline of the two Carolinas, but inland from the coast there are also numerous lakes of elliptical outline. They might be just quirks of Nature, but they would also be consistent with the putative Younger-Dryas impact having been in fact an airburst, followed by the impact of multiple smaller fragments.

We are now unambiguously in the realm of conjecture, but the Carolina Bays have been a geographical puzzle for centuries. Perhaps they are about to turn out to be not just a puzzle, as happened with the jigsaw fit of western Africa and eastern South America. Whatever their status, we can expect an energetic search over the next few years for the locality of the impact or airburst at the base of the Younger Dryas. We can also expect energetic discussions about its efficiency as a trigger for cooling.

The Greenland nanodiamonds are thus a small part of what is beginning to look like a much bigger picture, but they also represent a glaciological tour de force. I said that the Kurbatov spike was found “exactly” at the base of the Younger Dryas. So it was, but not in an ice core, as you might have guessed. The authors went to the ice exposed in the ablation zone about 1 km in from the margin of the ice sheet. All of it must have travelled some hundreds of kilometres from where it fell as snow in the ice-sheet interior. The text is rather coy here: “One of the authors (Jorgen Steffensen) … identified a candidate for the Younger-Dryas-age section based on visual inspection of dust stratigraphy.”

The atmosphere is slightly dustier when it is colder, and the dust makes ice that accumulated during cold episodes greyer. The nanodiamonds were found at the base of a band of greyish ice bounded above and below by whiter ice. There is therefore a sense in which the “exact” location of the base of the Younger Dryas has only been pinpointed circumstantially. But I doubt that there will be much questioning of the identification, and the success of the search is not less astonishing and gratifying for being due to use of the human eyeball as a search tool.


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Glaciers and beryllium

Chains of reasoning can be quite long, and quite tortuous, but they can join up the most surprising places. Consider beryllium-ten.

Almost all of the Earth’s beryllium is beryllium-nine, the isotope symbolized as 9Be and defined by having four protons and five neutrons in its nucleus. We also have a small stock of 10Be, which has an additional sixth neutron. Most of the 10Be is created in the atmosphere when incoming cosmic rays collide with gas molecules: it is a cosmogenic nuclide.

Cosmic rays are not rays but particles, mostly protons, that originate outside the solar system. Some are energetic enough to destroy the molecules with which they collide. For example, not only may a molecule of nitrogen be split into its two constituent atoms, but one of those atoms, a 14N (seven protons and seven neutrons), may be split into a helium (4He) and a 10Be.

10Be dissolves in rainwater, which is weakly acidic. When the rainwater falls on land, it becomes more alkaline by reacting with the surface minerals, which induces the 10Be to precipitate out. Unless it is carried away by running water or the wind, it accumulates.

The point of the story so far is simple: the longer a patch of surface has been accumulating the products of cosmic-ray collisions, the greater its stock of 10Be. If it remains in place, as is likely on the surfaces of large boulders, we can count the 10Be atoms, correct for the slow radioactive loss (10Be has a half life of 1.36 million years), and obtain the exposure age of the surface by a relatively straightforward calculation — as long as we know the rate of arrival of the cosmic rays.

But here we come to a tangle in the chain. The cosmic-ray flux is not constant. The list of corrections that have to be made is quite long, allowing for factors such as the varying strengths of the solar wind and the terrestrial magnetic field, the altitude and latitude of the exposed boulder, and the extent to which it is truly “exposed” and not shielded by the surrounding terrain, nearby obstacles, seasonal snow and so on.

The allure of that exposure age, however, has stimulated intense efforts over the past couple of decades. We have developed a good understanding of many of the required corrections, and, like the atoms on the boulders, reliable 10Be exposure ages are now accumulating in the literature.

Writing in Nature, Michael Kaplan and co-authors offer a new collection of 10Be ages from the terminal moraines of a glacier that once occupied a cirque in the Southern Alps of New Zealand. Three of the 37 ages are oddballs, but the remainder all cluster nicely, in groups from different moraines and morainic ridges.

The outermost moraine, about 2 km from the cirque headwall, has boulders that were first exposed to the atmosphere just before 11,000 BC. In sequence, the moraines nearer the headwall have ages of about 10,700 BC, 10,100 BC, 10,200 BC and finally, only a couple of hundred metres from the headwall, 9,500 BC. All of these ages are uncertain by 400-600 years.

The payoff of these observations is in the dates, which span very neatly the cold snap of the Younger Dryas. While abundant evidence for cooling was piling up in various northern palaeoclimatic archives, this little New Zealand glacier was dwindling into nothingness.

Kaplan and co-authors have thus nailed down, much more firmly than before, the conclusion that the hemispheres were out of sync at the end of the last ice age.

The atmospheric concentration of carbon dioxide increased during the Younger Dryas, ruling out a reduced greenhouse effect as an explanation for the northern cooling. The generally agreed explanation is that the north Atlantic received a rapid influx of buoyant fresh water from North America. This reduced the overturning of ocean water, and damped down the meridional circulation. But it also pushed the climate belts southwards, shifting the southern-hemisphere westerlies to higher southern latitudes at which they were better able to provoke oceanic upwelling. The resulting enhanced outgassing of deep-ocean carbon explains the increased atmospheric CO2, and the 10Be atoms on the boulders show that the Younger Dryas was a time of net warming at least as far north as New Zealand.

So beryllium helps us to understand the hemispheric asymmetry of glacial climate. Long and tangled the chain of reasoning may be, but it does illustrate how complexity can be unravelled given doggedness and ingenuity.


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Oetzi the Iceman and Schnidi

Everyone knows something about Ötzi, the Iceman of the Ötztal valley in the Tyrol of Austria. For example, many know that he was found, slightly embarrassingly for Austria, just inside South Tyrol, which is on the Italian side of the frontier. He is now at rest in the South Tyrol Museum of Archaeology in Bolzano.

Schnidi, by contrast, is less well known. There are reasons. First and foremost, he doesn’t exist. He, or quite possibly she, is a collage of human detritus spread over the northern approach to the Schnidejoch, a 2,756 m pass in the Bernese Alps in southwestern Switzerland. More remarkably, Schnidi is spread over 6,500 years of Alpine prehistory. Like Ötzi, though, he has a lot to tell us, and a lot to ask us.

The archaeological finds at the Schnidejoch are documented by Martin Grosjean and co-authors in the Journal of Quaternary Science. They were exposed by the recession of a small ice patch, recently detached from the larger Tungel Glacier, during the record-breaking hot summer of 2003.

This is the second remarkable thing about Schnidi. Among the clothes he discarded were perishable goatskin leggings and shoes, from as long ago as 4,500 BC according to new results announced in 2008. Apart from making the early part of Schnidi a good deal older than Ötzi (about 3,300 BC), this means that 4,500 BC was the last time it was as warm in the Bernese Alps as it is now. The leggings must have been preserved beneath the ice since then.

The Schnidejoch is not a particularly hard climb, but a kilometre or two downvalley a moderate advance of Tungel Glacier from its modern extent would close off the valley, making the route difficult if not positively impassable. This is the simplest explanation for the next remarkable thing about Schnidi. He clusters in time. There is late Neolithic clothing and hunting gear from 2,950 to 2,500 BC; arrows, pins and other material from the early Bronze Age (2,150 to 1,700 BC); shoe nails, coins and a woollen tunic from Roman times (the first century BC to the second century AD); and a few items from mediaeval times.

These intervals coincide rather well with nearby evidence for warm periods, but they are also complementary because Schnidejoch is much higher than the other sources of information, and it is a “binary and non-continuous archive” — the pass was either open or closed.

Ötzi and Schnidi raise all sorts of questions, some sobering and some frivolous. Why do we westerners see Ötzi as someone who can tell us things, while aboriginal Americans see his counterparts on their continent as in need of re-burial, to be left in peace? All I can offer is the reflection that it is a pity we can’t tell things to Ötzi, and the thought that if I were to make an exit like his I would be rather happy than otherwise to have the chance to tell things to my distant descendants.

Why was Schnidi so careless of his belongings? They are strewn over about 100 m of the route just below the the pass. It is easy to see why the discards are preserved just here, in the former accumulation zone of a now-vanished glacier. But I cannot think of a reason why they should have been discarded just here.

Did Schnidi’s religion oblige him, as thanksgiving for a successful crossing of the pass, to take off his trousers? More plausibly, perhaps our ancestors were about as careless as we are, losing stuff at random all along the route, but only the items buried by the ice have been preserved. On this interpretation, the Schnidejoch, when the valley was passable, was a moderately busy thoroughfare. In that case, why didn’t the travellers cross by either of the passes lying a few kilometres to east and west, which are 200 to 500 m lower than Schnidejoch? Perhaps they did. Those passes may never have been in the accumulation zone of a glacier, in which case the Bernese Alps might have been even busier than implied by the Schnidejoch evidence.

Lastly, a question I have asked before, knowing that it won’t be answered. What was Schnidi’s word, or words, for the glacier over which he walked? He or she is concrete evidence for human interaction with glaciers in Roman times, and yet we have no record of a word for glacier in Latin.


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Glaciological mosh pits

Last month I found out what a mosh pit is. Doug MacAyeal told me. I gather that anybody more than about 15 years younger than me already knows this, but for the rest of us a mosh pit is the place in front of the stage at a rock concert, where extreme violence is likely to break out. (But apparently it is good-natured violence.)

Like me, Doug MacAyeal was attending a symposium of the International Glaciological Society to mark the 50th anniversary of the Byrd Polar Research Center in Columbus, Ohio. He is a glaciologist who is unusually gifted in the understanding of forces. In fact, one of the reasons he was at the symposium was to accept the Byrd Polar’s Goldthwait Polar Medal, an award made only intermittently to the most distinguished of glaciologists. Doug’s talk entitled “The glaciological mosh pit” made clear why he is a Goldthwait medallist.

The glaciological mosh pit, just before the violent release of gravitational potential energy that justifies the name, is a collection of icebergs, detached from each other but in close physical contact. They are the descendants of blocks of ice in an ice shelf that were formerly separated along crevasses, but the crevasses have now propagated through the whole thickness of the shelf. The bergs are typically much longer than they are wide, but the crucial point is that they are in a gravitationally unstable state, being several times taller than they are wide.

Although their weight is supported by the water, they would topple over if they were not propping each other up. Do they topple as soon as the crevasses break through to the base of the shelf? If so, why do all the crevasses apparently make the breakthrough at the same time? If not, what keeps them from toppling, and what triggers the eventual catastrophe?

I have trouble sorting out the ways in which this adds up to an exciting mechanical and glaciological problem. First and foremost, perhaps, the mosh pit is already a horrible mess and is about to get very much messier, but there is the prospect of reducing the chaos to intellectual order.

Then there is the question of how it got that way in the first place. There is a link here to global warming. The crevasses probably would not penetrate to the base of the ice shelf if they were not strengthened by an influx of surface meltwater. The ice shelves have been around for a long time, and that they are disintegrating now suggests that surface meltwater is now more abundant than formerly.

A related question is why some floating slabs of ice disintegrate mosh-pit fashion but some others break up along just a few cracks, or even a single crack, to form ice islands.

And then there is the really big question: what happens to the released energy when the berg finally switches from being a vertically extended slab to being a more civilized, horizontally extended slab? It seems that, apart from a little bit of heat and a little bit of noise (waves in the air), nearly all of the gravitational energy becomes kinetic energy (waves in the water). This wave energy has to go somewhere in turn, and it can do an astonishing amount of damage when the waves break.

Doug MacAyeal and his students are grappling with this question along several lines of attack. Doug’s talk was mainly about the theory of the balance of forces on a collection of gravitationally unstable icebergs, and about how tricky it is to write this balance down algebraically. Justin Burton told us about the research group’s efforts to simulate the mosh pit with fake plastic icebergs in a large tank of water, showing fascinating movies of the collapse and “seaward” advance of the collection and the subsequent sloshing about of the water. Nicholas Guttenberg described early work on computational simulation of the mosh pit, with an equally fascinating movie showing “virtual collapse”.

So far we have a sample of only two observed glaciological mosh pits, the disintegration of most of Larsen B Ice Shelf in 2002 and of part of Wilkins Ice Shelf beginning in March 2008. But two examples are more than twice as interesting as one, as well as being infinitely more interesting than none at all. Two mosh pits suggest a pattern, and the possibility of more to come and perhaps to guard against.


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How thick is this (Himalayan) glacier?

If you drill a hole right through your glacier, one of the things you get is a measurement of its thickness. But if you want the mean thickness of the entire glacier, an expensive and time-consuming borehole doesn’t get you very far. The only realistic way to measure the mean thickness of a glacier is ground-penetrating radar (GPR).

You drag your radar across the glacier surface. It emits pulses of radiation and keeps track of the echoes, in particular those reflected from the bed. With one or two additional items of information you can convert the travel time of the echo to a thickness. This is still expensive, especially if you try to improve coverage by flying your radar in an airplane instead of dragging it over the surface.

But with reasonably dense coverage, you do end up with a reasonable estimate of the mean thickness. With a measurement of the area, and some reasonable assumption about the bulk density, you can estimate the total mass.

One problem with all this is that we only have measurements of mean thickness for a few hundred glaciers at most. What do we do about the mean thickness of the remaining several hundred thousand?

The most common answer is “volume-area scaling”. The term, which is a firm fixture in glaciological jargon, is misleading because it is really thickness-area scaling. When we plot the measured mean thicknesses against the areas of their glaciers, we get a nice array of dots that fall on a curved line — or a straight line on logarithmic graph paper. The thickness appears to be proportional to the three-eighths power of the area. There is an equally nice theoretical scaling argument that predicts this power and makes us suspect that we are working on the right lines.

Unfortunately the so-called coefficient of proportionality, the factor by which we multiply the three-eighths power of the area to turn it into an estimated thickness, is much harder to pin down. It varies substantially from one collection of measurements to another.

Recently I have been using volume-area scaling to try to say something useful about the size of the water resource represented by Himalayan glaciers. As you may have noticed, the fate of Himalayan glaciers has been in the news lately. Will they still be there in 2035? Yes. Will they be smaller in 2035? Yes. How much smaller? Don’t know.

Among the reasons why we can’t say anything useful about Himalayan glaciers as they will be in 2035, one is that we can’t say much about how they are in 2010. So I have been trying to work out some basic facts, by completing the inventory of Himalayan glaciers and using the glacier areas to estimate their thicknesses and masses. The inventory data were obtained over a 35-year span centred roughly on 1985. So forget the challenge of getting to 2010. What can we say about Himalayan glaciers in 1985 or thereabouts?

It turns out that, including the Karakoram as well as the Himalaya proper, there were about 21,000 of them. To estimate total mass by volume-area scaling, we have to treat each glacier individually. The result depends dismayingly on which set of scaling parameters you choose. Five different — but on the face of it equally plausible — sets give total masses between 4,000 and 8,000 gigatonnes. (Difficult to picture, I agree, but these numbers translate to region-wide average thicknesses between 85 and 175 metres.)

In short, we only know how much ice there used to be in the Himalaya to within about a factor of two. Let me try, like a football manager whose team has just been given a hammering on the pitch, to take some positives from this result. For example, it pertains to a definite time span and to a region that is defined quite precisely. Earlier estimates have been hard to compare for lack of agreement on, or definition of, the boundaries. It is also a better estimate than the 12,000 gigatonnes suggested casually by the Intergovernmental Panel on Climate Change in 2007.

But what does “better” mean in this context? Apart from being wrong about the longevity of Himalayan glaciers, it looks as though the IPCC was also wrong about the size of the resource, which is a good deal smaller than suggested. Where does that leave us as far as water-resources planning is concerned? With a lot of work still to do, that’s where.


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Yet another ice island

On or shortly before 5 August 2010, a big chunk of the floating tongue of Petermann Glacier in northwest Greenland broke off. It is now an ice island, about 260 km2 in area, and is destined to do a left turn into Nares Strait, between Greenland and Ellesmere Island, whence it will drift southwards, falling to pieces as it goes. The new ice island joins a quite long list of old ice islands.

The calving event had been expected for at least a couple of years, based on observations of the floating tongue of the glacier. The island itself seems to have been noticed first by Trudy Wohlleben of the Canadian Ice Service, which scrutinizes satellite imagery continuously for the monitoring of hazards to navigation in northern waters.

These days, big environmental events invite speculation that they are “caused” by global warming. Thus a large new iceberg has to be a sign that either its parent glacier is disintegrating or the global-warming alarmists are at it again. The truth, as usual, is that we cannot put any single event down to global warming in this simple-minded fashion. (Which doesn’t mean, by the way, either that the glacier isn’t disintegrating or that we alarmists are not at it again.)

Some ice shelves in the Antarctic have disintegrated spectacularly in the past couple of decades, and there we do suspect a link with global warming. But the calving of icebergs is a normal part of the mass balance of any tidewater glacier, and once in a while we get a berg that, like the new Petermann berg, is big enough to qualify as an ice island. To show that the balance has shifted to faster calving is very difficult because the big events happen so infrequently.

That doesn’t mean that the new ice island isn’t interesting, and especially not that it isn’t dangerous. The Canadian Ice Service will no doubt eventually produce a story about this one at least as interesting as the one about the last big berg from Petermann. It calved in July 2008, and bits of it remained identifiable near the southern tip of Baffin Island a year later.

But as ice islands go, even the much bigger Petermann island of 2010 is not that big a deal. The first ice island to be given a name — of a sort — was T1. The T stands for “target”. T1 was discovered by U.S. Air Force pilots flying out of Barrow, Alaska, in August 1946. By that date it was clear that the tense wartime alliance between the western allies and the Soviet Union had fallen apart. T1 immediately became a military secret, but it took only a few years for the U.S. military to work out that it is a bit silly trying to keep a 700 km2 chunk of ice secret. T1 was followed by T2, of more than 1000 km2; by T3, of about 50 km2; and eventually by several dozen smaller islands, all of them bigger than your typical iceberg.

Most were in the Arctic Ocean. Each of the biggest ones was spotted from time to time, and found to be drifting in about the expected direction, that is, clockwise, around the Beaufort Sea.

Apart from a debatable suggestion that T2 might have been seen at 72°N off east Greenland in 1955, I haven’t managed to find out what happened to either T1 or T2, but T3 became a research station in 1952. It was occupied intermittently until the early 1970s and was last sighted in 1983, after which it is conjectured to have found its way into Fram Strait and thence into the Atlantic.

The odds are heavily in favour of all these objects having broken free from the northern coast of Ellesmere Island, sometime during the 1920s or later. The evidence of the earliest visitors, and the results of more recent field studies, agree that there was once a continuous ice shelf all along that coast. Today, it consists of a dwindling collection of small remnants. According to the Canadian Ice Service, relying on imagery up to 22 August 2010, another 50 km2 fragment has just detached from what is left. This fragmentation over decades is wholly consistent with the emergence of the global climate from the Little Ice Age.

Moira Dunbar, in the paper from which I have distilled this information, presents several accounts from 19th-century explorers which sound persuasively like descriptions of ice islands. So we have a long record of ice islands off the northern coast of North America. What we cannot do, and will probably be unable to do given the small number of calving events, is to establish that the rate of breakoff has increased.


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