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In from the cold: June 2010 Archives

When I was doing field work in Arctic Canada, for my master's thesis, we were under orders always to travel from A to B along the coast at 22 metres above sea level, with our eyes on the ground. There was method in this madness.

The orders originated with Wes Blake Jr, a friend of my thesis supervisor. Through us, Wes was hunting for drift pumice. Pumice forms when gas-rich, frothy lava is cooled very rapidly. Because of the gas bubbles, pumice floats. If it gets into the sea, it drifts, for a few years or decades and perhaps a few hundred to a few thousand kilometres, and eventually some of it drifts ashore. Our pumice erupted, possibly from Hekla in Iceland, in about 3,000 BC.

The pumice drifts ashore at sea level. We were following a raised-beach strandline at the elevation at which Wes Blake reckoned the shoreline of 3,000 BC ought to be today. The whole region has rebounded from the weight of the ice that was there up to about 7,000 BC.

Sadly, we never found any drift pumice, but Wes Blake and others did, all around the Canadian Arctic. Its altitude today varies, lower than 10 m in the marginal parts of the archipelago but reaching 25 m and more along a broad axis trending north-eastwards from Bathurst Island to Ellesmere Island. The higher the 5,000-year-old strandline, the thicker the ice used to be. This evidence helped to settle a then-current debate in favour of the idea that the Queen Elizabeth Islands were once covered by an Innuitian Ice Sheet, as opposed to each island having had a smaller ice cap of its own.

Other things wash up on beaches all the time, including whalebone and driftwood that are datable by radiocarbon dating. Sometimes you find datable fossils of shelly organisms that used to live in the beach (or at any rate the nearshore) sediment.

My crowning achievement in this way was to find a bivalve in the "position of death". Its two shells were still joined and the shell aperture was facing upwards. I forget its age, except that it was older than 22 m, but my bivalve was a small contribution to the relative sea-level curve for the locality.

RSL curves tell you lots of things besides the age and altitude of the marine limit (the highest sea level, reached just after the disappearance of the ice) and the history of emergence. With enough curves, you can reconstruct the former dimensions, including the thickness, of the ice sheet. But you are not limited to where the ice used to be. The land around the ice sheet also emerges when the ice load is taken away. During the ice age, it formed a depressed moat around the ice margin. Go somewhat further and you reach the peripheral bulge.

The peripheral bulge is where most of the toothpaste in the Earth's mantle went when it got squeezed away by the growing ice sheet. Upon deglaciation, the toothpaste flows back slowly. All right, I know the analogy is breaking down (ever tried getting the toothpaste back in the tube?), but the peripheral bulge subsides, and here you observe not emergence but submergence of old shorelines.

If you go far enough from the ice sheet, you enter what the geophysicists call the "far field", where relative sea-level change can be complicated, and in any case subtle. But taken together the available RSL curves are an incomparable tool for probing the Earth's inaccessible deep interior. The subtleties in the curves are best explained by variations in the flexural rigidity of the lithosphere and by subtleties in the depth profile of viscosity, or stiffness, in the deeper mantle. Indeed, the information flows both ways (just like the toothpaste).

Another way in which RSL curves help is by showing that toothpaste takes its time. So drift pumice and dead bivalves help us with the complications of interpreting things like the changing gravity field as monitored by the GRACE satellites. Any redistribution of mass, be it due to modern exchanges between glaciers and the ocean or to the slow flow of toothpaste, shows up in the signal from GRACE. Which just goes to show that it's an interconnected world.

The grounding line is where, in its forward path, the glacier switches from being grounded to being afloat. Glaciers that reach the sea have to have a calving front somewhere, because the ice can't keep going forever, but there need not be a grounding line.

But suppose there is one. What is the problem? At one level, it is trivial. The glacier remains aground until it satisfies the condition for flotation: there must be just enough water to support the weight of the ice. Multiply ice thickness by ice density (about 900 kg m-3), and water depth by seawater density (about 1028 kg m-3). Unless other forces are at work, the ice ungrounds when the two products are just equal. Seven eighths (900 over 1028) of a column of floating ice is below the water level — which of course explains the phrase "the tip of the iceberg".

Assume that the water depth doesn't change. (It might, but we have enough to worry about without changes of sea level.) The position of the grounding line, then, depends on the thickness of the ice at the grounding line.

If you see something a bit peculiar in that assertion, you are getting a grip on the problem. Next, assume that we know where the grounding line is. What determines the ice thickness there? We can probably ignore the snow that falls on the grounding line itself, so it must be the imbalance, if any, between the delivery of ice from the thicker grounded ice sheet and the discharge of ice into the thinner floating ice shelf.

Suppose less ice arrives than leaves. The ice must get thinner. Now, instead of just meeting the condition for flotation, it more than meets it. So it starts to float. The grounding line retreats. This argument works the other way around: the grounding line advances if more ice arrives than leaves.

This is an excellent example of a nonlinear problem: the position of the grounding line depends on the position of the grounding line. It will stay put only if just as much ice arrives as leaves. That means that we have to consider the forces driving the ice towards the grounding line from the landward side and away from it on the seaward side.

This balance of forces was first stated accurately, but in an order-of-magnitude way, by Johannes Weertman in 1974. His equation has the grounding-line thickness on both sides of the equals sign: on one side, an expression appropriate for grounded ice, where the dominant force is shearing of the basal ice over the bed; and on the other an expression for flow due predominantly to along-flow stretching — acceleration of the now-floating ice towards the calving front.

Weertman graphed these two expressions. The rate of shearing in the grounded ice depends on the surface slope and the rate of change of the ice thickness, which means that it also depends on the slope of the bed. He found that, if the bed slopes upwards towards the grounding line, his two curves either fail to meet — the equation has no right answer at all — or they meet once. If the bed slopes the other way, the curves can meet twice — there can be two right answers.

It is not uncommon for nonlinear problems to have unexpected numbers of right answers. But there is a twist. The answers can be of two kinds, stable and unstable. In the two-right-answer case, the "small" answer is unstable in a reassuring way. If you decrease the snowfall, the ice sheet will go away. Increase the snowfall, and the ice sheet will grow until it reaches the "large" answer, which is stable.

The one-right-answer case is unstable. Knock it off its perch, for example by reducing the supply of snow below that with which it was in equilibrium, and the equation pushes the grounding line forward until it reaches the edge of the continental shelf, while if you increase the snowfall the equation makes the ice sheet dwindle and disappear.

It takes some getting used to, but all the evidence and analysis now point to the one-right-answer case being the "right" right answer. It seems that the West Antarctic Ice Sheet — an ice body grounded below sea level with its bed sloping upwards down-flow — can coexist peacefully with the rest of an unchanging universe only if its margin is at the edge of the continental shelf — or nowhere.

In a newly-published paper, Matthias Huss and colleagues squeeze a bit more information out of the well-studied records of mass balance from the Swiss Alps. We know more about alpine glaciers than those of any other region, except perhaps Scandinavia, so it is surprising and interesting to learn that there is yet more to be said.

Huss and his co-authors compile a surprising amount of quantitative information. As well as conventional mass-balance measurements made over the past 60-odd years, they have found scattered records, and made geodetic measurements of surface elevation changes from maps, back to 1910, and have also brought measurements of meltwater discharge to bear on the problem.

They do an impressive job of tying these diverse kinds of information together with a model of glacier responses to climatic forcing. They simulate the climate, day by day, with precipitation and temperature data from weather stations extrapolated to the elevations at which the glacier ice is found. Their model of the response to temperature, for example, is a so-called temperature-index model. There is abundant evidence that, when it gets hotter, the glaciers yield more meltwater, and we can use temperature to predict meltwater in a reproducible way.

Their main contribution, however, is the light thrown on the evolution of glacier mass balance in the Alps over recent, and maybe near-future, decades. The authors show that there is a clear signal of the Atlantic Multidecadal Oscillation embedded in the 20th-century history of alpine mass balance.

I have trouble keeping up with the acronyms in this field. ENSO (El Niño-Southern Oscillation) and NAO (North Atlantic Oscillation) are easy because they have become familiar, but the AMO was new to me. This oscillation of sea surface temperature in the North Atlantic has a period, or quasi-period, of 60-70 years, and like all of the others (except perhaps for ENSO) it is an empirical fact rather than an understood physical phenomenon. That is, we can see it in the climatic records, but we have no explanation of why it is there. Is it real? Good question.

I don't think there is any question, though, that we can now see the AMO in the response of the glaciers of the Swiss Alps. As the authors point out, this signal may have predictive value. Large as the year-to-year variability is, we know that the glaciers of the Alps have been suffering particularly badly in recent years. The link to the AMO suggests that things may not be quite so bad in the next couple of decades. Of course we have to assume that the AMO is a phenomenon that is "real" enough that it will evolve as its past course suggests, but the fact is that we don't know enough about it yet.

On the other hand, there are some ideas out there. The A for "Atlantic" might be an important clue, for example, suggesting a link with the oceanic meridional overturning circulation, in which the shallow northward flow in the North Atlantic sinks at high latitude and returns southward at depth — taking dissolved atmospheric gases with it.

Wang and Dong offer an intriguing new twist on this angle. They show that the AMO pattern can be seen in the atmospheric concentration of carbon dioxide, measured at Hawaii and the South Pole since 1958. You have to subtract both a noticeable seasonal cycle (the vegetated landmasses take up CO2 in northern summer and release it in northern winter) and a long-term trend (the more affluent and numerous we get, the more gas we emit). What remains is a definite low in CO2, reaching about 2 parts per million below the 1958-2008 average, between the late 1960s and the mid-1990s. This matches in time persuasively with a cool phase of the AMO.

We are still far from a physical explanation of why the North Atlantic climate oscillates. Nobody knows why the oscillation takes about 60-70 years. We can't even be sure which way the arrow of causality is pointing. Is the CO2 low because the ocean surface is cooler and better able to take it up? Or is the ocean cooler because there is less CO2? In fact, the arrow of causality could well be chasing its own tail. But these links between ocean temperature, greenhouse gas and the behaviour of glaciers are worth exploring because of the prospect that we might be able to turn guesswork about the future into predictability.

We all know something about icebergs, even if only that one of them sank the Titanic. Working back from what you know about that, you will probably recall that icebergs come from glaciers that reach the sea, and that they are produced in calving events. But that is as far as most people's knowledge goes.

It may come as a surprise that until recently glaciologists didn't know much more than this either. Even now we cannot predict the rate of production, still less single calvings. But our ideas have taken some steps forward lately.

The calving rate is the velocity at which bits drop off the glacier at the calving front. One complication is that the calving front need not be immobile. The calving rate is actually the rate at which ice arrives at the front — the ice velocity — minus the rate at which the front advances or retreats — the rate at which the glacier's length changes.

Why doesn't the ice just keep going? One answer, only partial, is that sometimes it does. Instead of a calving front we have a grounding line. But this is turning one question into two (or more).

The first question, Why do some glaciers end in floating tongues?, is rather easy to answer, although much harder to model. The glacier stays in contact with the solid bed until it satisfies the condition for flotation, which is that there must be just enough water to support the weight of the ice.

The second question, What makes the iceberg finally decide to calve?, has been harder to answer. Early observers noted an apparent relationship between calving rate and water depth: the deeper the water, the faster the rate. But this fails to account for variations of the calving rate with time. Kees van der Veen found that during its rapid retreat the calving front of Columbia Glacier was where the glacier was 50 metres thicker than required for flotation. This was an advance, but still did not relate the calving rate to what we know about glacier dynamics. The same can be said of the argument of Andreas Vieli and co-authors that the glacier-specific 50 m should be replaced by some constant fraction of the water depth.

That missing link between observed behaviour and understanding of dynamics may finally have been forged by Doug Benn, Nick Hulton and Ruth Mottram. They argue that calving happens when a transverse (across-flow) surface crevasse deepens to a state in which its base reaches water level. It is a very fruitful idea.

The tip of the crevasse is at that depth at which the weight of overlying ice is just able to keep the crevasse walls together against the longitudinal tensile stress that is pulling them apart. So there is our link to dynamics, because the longitudinal stress is just the rate at which the ice is accelerating towards the terminus, and is something we can have a shot at predicting.

But there is more. A crevasse that propagates down as far as water level is likely to fill with water, the weight of which will help to resist closure and make it much more likely that the crevasse will propagate all the way to the bottom of the glacier, or in other words to produce an iceberg.

There may be yet more. No ice shelves are known to exist where the mean annual temperature is warmer than about —5°C. Perhaps that is because ice colder than that keeps going when it reaches the sea, and perhaps in turn that is because its crevasses fail to make contact with water when they propagate downwards. But that is an idea awaiting exploration.

The Benn work is certainly not the last word on this subject. For example in the latest issue of Journal of Glaciology Jaime Otero and co-authors make the new idea more numerically versatile by improving the calculation of the crevasse depth and of the stress field. Relying on measured ice velocities, they reproduce numerically the stable position of the calving front of a small tidewater glacier in the South Shetlands.

We still can't stop icebergs hitting ocean liners, but there are plenty of other reasons for wanting to understand calving rates, and the dynamicists are starting to make progress.