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In from the cold: September 2010 Archives

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.

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.

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.

If the climate were to change, you would expect the snowline altitude to change. It does, and we can show that it has in recent centuries, but we can also turn the proposition around. The snowline makes a very good tool with which to think about the climate. Here, again, is a graph of the global snowline.

A global approximation of the climatic snowlineA global approximation of the climatic snowline. South Pole on the left, North Pole on the right. Each little square is at an altitude which is the average of many "mid-altitudes", each of which is the average of one glacier's minimum and maximum altitude.

It isn't just that the snowline makes sense of the glaciologist's definition of "maritime" and "continental". The temperature at the snowline varies in the graph from purple (very cold and continental, on the ice cap covering Illimani and on other peaks above 6 km in the Bolivian Andes) to dark red (very warm and maritime, in the northern mid-latitudes).

Why is the "line" fat in the northern mid-latitudes? Obviously there are a good many glaciers to sample there, but it is not obvious until we colour the little squares that the fatness is because regional climates vary in continentality. In southern Alaska, for example, the shoreline runs crudely east-west, continentality increases inland, and the snowline actually rises towards the pole.

Putting aside regional variations, why doesn't the global snowline define a neat triangle, highest at the equator and lowest at the poles? The answer lies in the so-called general circulation of the atmosphere. The snowline dips in the tropics, between 30°S and 30°N, because that is the region through which the Inter-Tropical Convergence Zone travels as it follows the Sun. Here the airflow derived from subsidence over the desert belts of each hemisphere converges on the ITCZ. The subsidence implies warming of the air and therefore reduction of its relative humidity, which is why the desert belts are desert belts. Glaciologically, the subsidence means that you don't need much heat to melt what little snow accumulates, so the snowline (strictly, the equilibrium line) is very cold and therefore very high. Between the desert belts, convergence at the ITCZ forces the air to rise and cool, provoking snowfall. The extra snow requires more heat, and a lower and therefore warmer equilibrium line, than in the desert belts.

I wonder if I can convince you that in the mid-latitudes of each hemisphere the snowline is concave up? It is a subtle but physically genuine depression of the equilibrium line, and as at the ITCZ it is due to convergence and thus to lifting and cooling of air. Again, the cooling provokes more snowfall and in turn a lowering of the equilibrium line. This time the converging airmasses are flowing poleward from the desert belts and equatorward from the poles.

Did you notice the asymmetry of the hemispheres? Anywhere poleward of the tropics, the snowline is hundreds of metres or more lower in the southern hemisphere than at the equivalent latitude in the northern hemisphere. It reaches sea level at about 60—65°S, but where we run out of land at 84°N it is still a few hundred metres above sea level.

The temperature at the surface of the Antarctic Ice Sheet is about 25°C colder than at the surface of the Arctic Ocean. Something like 18°C worth of the difference is simply because the ice sheet is about 3 km above sea level. The remainder, and the depression of the snowline throughout the southern extra-tropics relative to the north, are due to the chilling effect of the ice sheet on the general circulation.

Finally, a question that always makes my head spin. What would the altitude of the snowline be if there were no mountain range? There would be no orographic moisture trap, and no glaciers of course. If we knew the temperature of the snowline, we could go to the atmospheric temperature records and find where the snowline would be if there were land. But, first, by supposition there isn't any land. Second, we know that if there were it would draw the snowline down to meet it, that being why glaciers start out maritime at the coast and become more continental the further inland you go. Third, that means that if there were land the temperature would be different from what it is in the free atmosphere, which returns us to where we started from but with the realization that we ought not to have started from there.

So I can't produce an answer to the question. But I can see that the snowline teaches us a lot about the climate, including the proposition that the general circulation, the temperature and the topography are all mixed up in it together.

Hoar, the medium in which Jack and Jenny Frost work on our windowpanes and other canvases, is formed by the condensation of water vapour as ice. But there is also depth hoar, a product of Jack Frost's ingenuity underground, or rather under the surface because it forms in snow, not in the soil.

Glaciologists take a dim view of depth hoar. So do snow scientists, and so should you.

Snow is an excellent insulator, especially when it is not very dense and most of its volume is air. That is why igloos work: partly because air flows only inefficiently through the tortuous void spaces in the snow, and still or sluggish air is an even better insulator — not much use either at conducting heat or at carrying it around — than ice; and partly because, although they are better conductors of heat than the air, the snow grains are in limited contact with each other — so the contacts are thermal bottlenecks.

Good insulation means that the snow can be much warmer below the surface than at the surface. Or colder, but that doesn't favour depth hoar. In Jenny Frost's favourite subsurface setup, the snow at depth is near to the freezing point but the surface is very cold indeed. Because it is in close contact with lots of (frozen) water, the air at depth saturates with water vapour — no, wait, the air throughout the snowpack is saturated. The point is that the warm air below has a much higher capacity to hold water vapour than the very cold air above.

Air flow being inefficient, this gradient in concentration (saturation specific humidity, to get technical) is why water vapour diffuses upwards through the pores to a depth where, because of the cold, it condenses as the crystalline substance we know as hoar.

Crystals like to begin to grow at solid nucleation sites, and the surfaces of the snow grains are perfect for the purpose. Beyond this point, things are explained well in a classic paper by Sam Colbeck. When the temperature gradient is very steep, the crystals like to grow as plates or facets that often join to form upside-down cup-like shapes. What is more, they begin to consume the grains on which they nucleated.

A vertically elongated facet is a better conductor than the mixture of air and grains at the same depth, so its base is slightly colder than average for its depth, while the top of the grain it is consuming is slightly warmer. This means that, at the scale of single facets and their grains, vapour tends to sublimate from the grain top and diffuse downwards to the tip of the facet.

Relying on this physics, Jack Frost can make lots of depth hoar in a single cold snap, say a few days. Sometimes a half or more of the snow gets turned into depth hoar. The resulting facets and cups are commonly a few millimetres across, and single crystals the size of your fingernail are not unknown. These are giants compared to the original snow grains, whose typical sizes might well have been much less than a millimetre.

That is why we are not keen on depth hoar. The cups look cool, but they have replaced not just countless small grains of snow but countless bonds between grains. Depth hoar is weaker than the granular snow it replaces because the giant crystals haven't had time to bond to each other, a phenomenon called "sintering".

What are the consequences? First of all, depth hoar is so friable that it makes retrieving shallow ice cores very difficult. Second, depth hoar complicates the interpretation of microwave emissions from snow and ice which we could otherwise use to estimate the accumulation rate. And finally, layers of depth hoar are among the prime reasons for avalanches. When they collapse, they make excellent slip surfaces for the snow above.

The glaciological attitude to depth hoar is not uniformly disapproving, though. A good place to grow depth hoar is near the bottom of autumnal snowfalls that rest on the so-called summer surface — the glacier surface as it was at the end of summer. When we come along at the end of the winter, we want to measure the mass balance, that is, the mass between the summer surface and the surface at the time of measurement. The depth hoar can be very useful as a marker.

But, all things considered, life would be simpler, and safer, if Jack and Jenny Frost were to concentrate on window art.