Posts by: Graham Cogley

New-laid drumlins

By Graham Cogley

You can find some surprising things at the bed of the glacier. Normally it is inaccessible to direct observation, but these days most glaciers are retreating. If you don’t mind waiting a bit — and glacial geomorphologists don’t really have the option — then keeping a close eye on what is emerging can be very informative.

In a paper published recently in Geology, Mark Johnson and co-authors present another surprise: nice fresh drumlins. Múlajökull is an outlet glacier, draining one of the ice caps in Iceland. Like almost every other glacier, it has been retreating. Like only a small proportion of other glaciers, it is a surging glacier — which is going to set the cat among the pigeons when we have had time to think it over and decide whether the surging is relevant. For the retreat of Múlajökull has exposed a field of drumlins.

Johnson and his co-authors were able to show that the drumlins consist of multiple layers of till, sediment carried by the glacier and deposited by a mixture of lodgement — expulsion from the moving ice — and deformation of the sediment over which the ice was flowing. The evidence suggests that each of the till layers represents a surge of the glacier. What is more, at least one of the boundaries between till layers is an erosion surface. That is, the lower layer has been truncated before the upper layer was draped over it.

This is yet another confirmation that the old question about drumlins, “Are they formed by erosion or by deposition?”, was the wrong question to ask. The answer is “Sometimes one and sometimes the other, and often (as at Múlajökull) a bit of both, with some deformation of what was there already mixed in”.

The resemblance of drumlin fields to baskets of eggs has been remarked on before. Lowland Britain is covered with them — tens of thousands of eggs. What is most interesting about the Múlajökull drumlins is that they are new-laid eggs, and the hens are still busy in the coop.

Nobody believes that the drumlins we see today in places like Great Britain and central North America have changed much since the retreating ice margins exposed them to view thousands of years ago. All the same, drumlins that are henhouse-fresh exert a powerful pull on the geomorphological and geological imagination. This is because of actualism, the ingrained principle that the present is the key to understanding the past. The likelihood is that there are lots more drumlins still forming behind the present-day retreating margin of Múlajökull, and as the authors point out we know as yet of no other drumlins that are in process of formation.

One thing that bothers me about the Múlajökull drumlins is that I have trouble seeing the multiple till layers in the photograph that is supposed to illustrate them. But among the reasons why I am not a sedimentologist is that dirt is not very photogenic, and I am prepared to go along with the authors’ interpretation of what they saw in the field. Let us take it that these drumlins are indeed layered, and let us go one step further and accept their evidence that the layers have probably formed during the successive surges of the glacier. (They come along every 15 to 20 years, short-lived advances of a couple of hundred metres, punctuating a retreat that has been going on for about 200 years.)

Does this mean that there is something special about drumlins that are shaped by surging glaciers? Surging glaciers are sufficiently uncommon, and drumlins sufficiently widespread, that it is not likely that surging behaviour is a necessity for drumlinization. It is, however, interesting, and maybe significant, that the deposition probably accompanies the surges and not the longer intervals of retreat, during which there was either erosion or at least non-deposition.

Is there, instead, significance in one or both of two observations made in the Johnson paper: that the drumlins appear to have formed very close to the ice margin, within a kilometre; and that they appear to have formed beneath crevasses that run parallel to the flow direction of the ice? The authors offer only a sketch of an argument for why these associations might be a source of insight. But drumlins have been a puzzle for more than a hundred years. More facts can only help, even if all they do is to make us confused in a deeper and richer way — but especially if they are new-laid facts.

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The future of Pine Island Glacier

By Graham Cogley

Pine Island Glacier is a giant, an outlet glacier draining about 160,000 km2 of the West Antarctic Ice Sheet. It is the focus of intense current concern because the area near its grounding line, where it feeds a floating ice shelf, has exhibited rapidly increasing rates of thinning and concurrent retreat of the grounding line. With its neighbours along the coast of the Amundsen Sea, it is now contributing something like 0.15 to 0.30 mm per year to a total rate of sea-level rise of about 2.5 to 3.2 mm/yr.

It is natural to be rattled by these observations. There is no immediately obvious reason why the rate of ice loss should not continue to increase. Indeed, the recent observations might presage even faster acceleration, perhaps involving the discharge of a substantial fraction of the 1500 mm of sea-level equivalent still stored in Pine Island Glacier and its neighbours. And we have a serious enough problem even if Pine Island Glacier simply maintains its present rate of loss.

Knowing what they know and what they don’t know, “alarmist” is therefore not a label about which glaciologists need to be embarrassed. But they also know that alarmist projections have a way of turning out to be exaggerated.

Consider the energy-balance models, that describe how the climate responds to changes in radiative forcing. The two first such models, published independently by Mikhail Budyko and William Sellers in 1969, projected that the Earth’s surface temperature would drop to tens of degrees below freezing if the output of the Sun were to decrease by only two percent. That made people sit up, and yielded a flurry of publications showing that there are plenty of ways in which the climate system moderates the severity of the negative feedback which was the basis for the original findings.

Even though they are based on measurement rather than on modelling, might our concerns about the recent behaviour of outlet glaciers in Antarctica and Greenland be similarly exaggerated? In a recent modelling study, Ian Joughin and co-authors suggest that the answer is “Probably, but not necessarily”.

The model is not quite state-of-the-art, in that it does not solve the full Stokes equation but a simpler form of the dynamical system that is appropriate for ice shelves and ice streams. The authors were obliged to handle the grounding line, where the grounded ice stream feeds into the floating ice shelf, somewhat roughly. Nevertheless the calculations allow for careful treatment of the rapid sliding at the base of the ice stream, and the implied very large rates of basal melting. And the model does a good job of reproducing the documented behaviour of Pine Island Glacier up to 2009.

Most of the ice in the Pine Island Glacier catchment is flowing very slowly indeed, at a few metres per year at most. But as it converges on the outlet of the catchment it accelerates spectacularly, and is moving at thousands of metres per year by the time it starts to float at the grounding line. Most of the speed is the result of basal sliding, so the ice stream is not unlike a rigid plug, punching its way through the much slower ice on its flanks. This peculiar setup is the core of the problem.

Joughin and his co-authors simulated responses of the glacier to a variety of scenarios that might or might not represent the next hundred years. Even the more extreme scenarios, featuring basal melting at four times the present rate, did not lead to flotation of the entire 200-kilometre length of the ice stream, as one earlier study had suggested. Nor did the model come anywhere close to an even simpler extrapolation of current behaviour, based on kinematics rather than dynamics.

Don’t breathe out yet, however. The results considered by the authors to be the most probable have Pine Island Glacier continuing to lose mass at rates comparable to the recent rates. It doesn’t continue to accelerate, but it doesn’t slow down either. The grounding line doesn’t continue to migrate inland, but the inland thinning implied by the fast flow does continue.

It would be wrong to write off this heroic but tentative modelling effort, which is an important step towards the goal of understanding Pine Island Glacier. Models like this one, and like the energy-balance models that followed up on Budyko and Sellers, are part of the learning process. They suggest that doomsday isn’t going to happen just yet. But, in short, doomsday scenarios are educational.

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A new take on water at the beds of glaciers

By Graham Cogley

Plenty of evidence has emerged recently to show that the beds of glaciers can be complicated places, especially when we consider the liquid water down there and the fact that much of that water must have come from the surface.

In a paper just published in Nature, Christian Schoof explores this complexity and explains at least some of it.

One of Schoof’s insights is that cavities and channels are two very different ways to store subglacial water. The size of a bed cavity, in the lee of a bump for example, is governed by the respective rates at which the basal ice continues to flow horizontally down-glacier, opening the cavity, and creeps downwards, lowering the cavity roof. The size of a channel is governed by the rate at which its wall expands by melting and the rate at which the wall shrinks by inward creep of the ice. Cavity or channel, the creep rate depends on the difference between the pressure of the ice on the void and the pressure of whatever is in the void, water or air, on the ice.

For a given thickness of ice overburden, this pressure difference depends on the fluid pressure. Air is useless at opposing the weight of the ice, so we are only interested in the water pressure, which requires that we acknowledge the importance of meltwater from the surface. Water melted at the bed, by geothermal heating and by friction between the ice and the bed, is insignificant, and the pressure of the void-filling water on the overlying ice is likely to depend entirely on how fast water is arriving at the bed from above.

So in fact three variables determine how the meltwater at the bed organizes itself: the melting rate at void walls, the opening rate due to down-glacier flow, and the closure rate due to the pressure difference at void walls, the latter depending in turn on the rate of delivery of surface meltwater. These variables are entangled with each other, but Schoof combines them ingeniously, and consistently, in a model that shows that this is a one-thing-or-the-other problem. A collection of linked cavities can be a stable way to organize the meltwater, and so can a tree-like network of channels, but any other arrangement of the voids will evolve into one of these two.

Linked cavities can be kept full, and can transfer meltwater not too inefficiently, if, or rather because, the water pressure is high. At high water pressure, the ice will flow faster because less of it is in contact with its solid bed, meaning that cavity opening will proceed faster. More of the ice will reach lower, warmer elevations sooner, increasing the production of surface meltwater.

But channels are different. The more meltwater in them, the faster their walls melt and the bigger they get, lowering the water pressure and so tending to drive pressurized cavity water towards and into them. In Schoof’s simulations a few big channels end up discharging the meltwater. But because more of the water is in big channels, less is spread over the bed. More of the ice is in contact with the bed and not with water, and the ice will slow down.

But now comes an intriguing twist in the plot. Surface meltwater tends to reach the bed in pulses, once a day. Closure of the channels by creep is a slower process, requiring days or longer. So the daily pulses raise the water pressure in the channel network, driving water out of the channels, weakening the contact of the ice with the solid bed, and thus speeding the ice up. This speedup is not fully integrated into Schoof’s analysis, but is clearly a way for the subglacial drainage network to have its cake and eat it. More meltwater implies channelization, reduced water pressure, and deceleration of the glacier. But more meltwater arriving in pulses means that a glacier can still slide rapidly over its bed even though the drainage network at its bed has become channelized.

If, over the next century or two, we lose a large fraction of the ice now in the Greenland Ice Sheet — or, perish the thought, the Antarctic Ice Sheet — then greenhouse gases will have a lot to answer for. But Christian Schoof’s analysis shows that so will the Sun. Or, to be more accurate, so will the Earth, because it turns to meet the Sun once a day.

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A new take on water inside glaciers

By Graham Cogley

A recent study by Thomas Phillips and co-authors in Geophysical Research Letters, described here, offers us a new idea: cryohydrologic warming.

When the weather is warm enough, meltwater is produced at the surface of the glacier. Some runs off directly. Some finds its way into the glacier interior and, although much of this englacial meltwater flows out again, some of it is left over at the end of summer.

The Phillips paper focusses on the thermodynamics of the leftover englacial meltwater. If the ice is at the melting point, or is temperate in glaciological jargon, it can’t get any hotter without melting. But what if the ice is cold, which in the glaciological jargon means “below its melting point”? The meltwater can be no colder than the melting point, so we have a difference of temperature and therefore a flow of heat from the water to the cold ice.

If, or rather once, the meltwater is at the melting point, it freezes as the winter advances. The freezing releases about 335,000 Joules of heat for each kilogram of water that turns to ice, roughly equivalent to one 60-watt light bulb burning for an hour and a half (but of course we are talking about lots and lots of kilograms, not just one). This latent heat of fusion adds to the thermal contrast between the cold ice and the gradually freezing meltwater.

Phillips and his co-authors show that, far from being just an interesting curiosity, the whole phenomenon of cryohydrologic warming, heat transfer from meltwater to cold ice, might be highly significant.

Internal accumulation, by refreezing of meltwater, implies warming of the glacier interior. It explains why, in glaciers that are mostly cold, the ice at high altitude in the accumulation zone is usually warmer than the ice at lower altitude in the ablation zone. But Phillips and his co-authors are more interested in cryohydrologic warming of the ablation zone. In particular, they point out that when the equilibrium line rises in a warmer climate, the part of the glacier that was formerly above the equilibrium line switches from net gain of mass (more snowfall than melting) to net loss (more melting than snowfall). The warming climate produces more meltwater, and any of the meltwater that fails to get out of the glacier drainage system will add fast cryohydrologic warming to the slow climatic warming.

It is a matter of simple physics to work out what “slow” and “fast” mean. The warming proceeds by conduction, so divide the heat content per unit volume by the thermal conductivity, both of which can be looked up in a book. The resulting number is about 212,000 seconds per square metre. Then imagine that the ice is divided into a grid of square columns, every one of which has a meltwater conduit in the middle. Now multiply 212,000 by the cross-sectional area of each column. If the conduits are 20 m apart, the cross-sectional area is 400 square metres and the cryohydrologic warming happens on a time scale of 2.7 years. (There are 31,536,000 seconds in a year.)

The same kind of back-of-the-envelope calculation works for the slow climatic warming, but now all of the heat has to be conducted downwards from the surface. An appropriate number to substitute for the conduit spacing is the ice thickness, say 100 to 1000 m. The resulting time scale for the climatic warming is about 70 to 7,000 years.

Bringing cold ice to its melting point in a few years, instead of a few centuries, implies that the ice suddenly becomes able to move a lot faster. Temperate ice is ten times less viscous (less stiff; runnier) than ice at —10°C.

Cryohydrologic warming has further implications for the response of cold glaciers to climatic change, but for the present there are loads of questions to be answered, starting with geometrical ones. What about the varying size and spacing of the meltwater conduits? Is 20 m a good representative number for the spacing? How thoroughly does the system of conduits permeate the bulk of the cold ice? What if no englacial meltwater remains at the end of summer? What if there is some, but not all of it freezes in the winter? Does the ice really speed up as expected, and if so does that mean more cracks for the meltwater to penetrate, and thus still faster cryohydrologic warming?

All this reminds me of the undergraduate essay I had to write on the subject ‘Clever ideas, whether right or wrong, stimulate research.’ Discuss.

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The first stake in a glacier

By Graham Cogley

I was wondering about when the first measurement was made on a glacier. This is probably a diffuse thing to wonder about, because you can measure properties of the atmosphere and even of the solid Earth as a whole while standing on a glacier. You could, for example, measure the air temperature or the air pressure, the latter giving you a decent chance of estimating the surface altitude.

So I sharpened my focus slightly, to the first measurement of a glacier, but still on the glacier. A measurement of retreat or advance of the terminus might be very interesting, but it would not count because it would be made from in front of the terminus. But a measurement of the glacier’s velocity would count.

The idea is fundamentally simple, and is conveyed well by one of the terms we use for it: feature tracking. Identify some feature on the glacier surface that is easy to see, such as a boulder, a particular crevasse, whatever. Measure its position accurately once, relative to an immobile reference point or baseline on land rather than on the ice. Measure it again at some later time. The distance between the two positions divided by the time between the measurements is the glacier speed. The velocity (that is, the speed and the direction, both together) requires only the simple trigonometry that you needed anyway to work out the distance.

The only problem might be lack of features that are easy to see. So make your own feature. As long as it is immobile relative to the ice, and you have a fixed point from which to observe it, any artificial object will do. For 240 years the object of choice has been a stake, jammed into the glacier by brute force or, much better, lowered into a hole drilled for the purpose.

Simple as it is, the idea had yet to occur to anyone at the time — the late 13th century — of the description in Marco Polo’s Travels of the glacier on Mount Ararat.

Apparently the idea that the motion of glaciers presents a problem did not arise until the 18th century. One intellectual roadblock was the need to get clear on the two motions in question. First, the glacier can get longer or shorter. That is, its terminus can move forward or backward, but this is an intellectual trap. The motion of the terminus depends on the mass balance. If more ice arrives than melts or falls off, the terminus advances; if less ice arrives, the terminus retreats.

I smuggled the second kind of motion into that description of the first: the ice can only “arrive” if it is itself in motion. The velocity of the ice and velocity of the terminus are two different things.

Once in a while I come across someone who is surprised to learn that No, the ice itself does not go backwards up the valley. The ice is obeying the forces that are driving it — gravity, pressure and the frictional resistance of its bed. There is no force that can make it flow backwards. But I am not surprised at this surprise in someone who has never had to think about the problem before. It is a tough nut, and it seems to have taken some decades to crack it.

The first person to assert that glacier ice moves was Peter Martel, writing in 1742. His assertion did not go unchallenged. At least one critic thought that ice flow was impossible. On the other hand, at least one interested person thought that a good approach to the question was to look into it. In November 1772, at the instigation of Pierre-Michel Hennin, three stakes were placed in the Mer de Glace on the northeast flank of Mont Blanc. The next spring, it seems, they had advanced about 4.5 metres with respect to a fir tree on the valley side.

So that is our first serious record of a measurement of a glacier. It is a bit of a pity that it was probably flawed. In 1842 James Forbes, one of the giants of 19th-century glaciology, measured velocities more than ten times as great at nearly the same place.

But that Hennin got it wrong isn’t really the point. The point, grasped by Hennin and made repeatedly, and forcibly, by Forbes, is that if you want the truth about a matter of fact, the best bet is a measurement.

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Ice, apatite and the Gamburtsev Mountains

By Graham Cogley

How long have the Gamburtsev Mountains been there, deep in the interior of Antarctica? In a paper just published in Geophysical Research letters, S E Cox and co-authors explain how they think have the answer, which is a bit surprising.

Apatite is an interesting mineral. It contains most of the phosphorus in the Earth’s crust, is familiar to many as the mineral that defines a hardness of 5 on Mohs’ scale of hardness, and is unfamiliar to just about everybody as a basic constituent of tooth enamel. Its name comes from Greek apatao, “I cheat” — allegedly because of the variety of its forms, although all the chunks of apatite I have ever seen are a pleasing shade of light green with a hint of lemon.

One curious attribute of apatite is that uranium quite likes it, snuggling in happily, in trace amounts, into the basic structure of the crystal lattice. Every so often, an atom of uranium-238 splits into two fragments that set off at high speed, crashing through the molecules in their neighbourhood. The collisions slow the fragments down and eventually they stop, but not before having done a good deal of damage. The trail of wreckage is a fission track, and it can be brought to light under the microscope.

Here comes one of the more fascinating twists in the tale: the damaged crystal lattice gets better. It can heal itself by restoring the disordered array of molecules to something like its original tidy state, a process called annealing.

The payoff for the drudgery of counting fission tracks in apatite crystals is that annealing reduces the number of tracks in a way that depends principally on temperature and time. Above about 120°C, the so-called closure temperature, annealing erases the tracks as fast as they form. Below about 90°C, annealing is so slow that the number of tracks depends on the time elapsed since cooling through the closure temperature.

The temperature decreases as the apatite crystal travels upwards through the geothermal gradient, which is about —30°C for every kilometre nearer to the surface. The fission tracks tell us when the crystal was last at a depth greater than 3 to 4 km. (Very roughly. The geothermal gradient had to be guessed in this study.)

In other words, fission-track dating is a way to estimate long-term erosion rates.

How do you estimate the erosion rate of a mountain range buried beneath several kilometres of ice? You go to the sediments deposited offshore as a result of the erosion. Cox and co-authors went to Prydz Bay, offshore from Lambert Glacier, the largest outlet of the Antarctic Ice Sheet. It drains the northern part of the Gamburtsev Mountains. They sampled Eocene sediments, about 35 Ma (million years) old, and found fission-track erosion rates of the order of 10 to 20 m Ma-1 that must have been sustained for at least 250 Ma.

Such rates are extraordinarily low. The Alps are shedding sediment at 400 to 700 m Ma-1, and while the Appalachians are suffering rates of only about 30 m Ma-1 they are much less rugged than the Gamburtsevs. The Gamburtsev rates are more typical of very low-relief terrains like the Canadian Shield. Incidentally, they are upper limits. The crystals sampled in this study are likely to have come from whichever part of the Lambert basin has been shedding sediment fastest.

The geomorphologists, then, have the problem of explaining why the Gamburtsev Mountains have been rugged without yielding significant detritus for several hundred Ma. One possibility is aridity. If the Gamburtsevs and their surroundings were a desert for most of the required time span, that would account for their not evolving very rapidly. It doesn’t seem probable. They have been far from the desert belts for at least 100 Ma.

Burial beneath glacier ice seems like a better bet, according to the Cox paper. It also seems harder to swallow. Before, we glaciologists had the problem of the survival of alpine relief in the heart of Antarctica for tens of Ma, and the related problem of the apparent non-glaciation of the polar continent for tens of Ma before that. If Cox and co-authors are on the right track, the problem metamorphoses into trying to explain a protective ice cover on the Gamburtsevs even though they were not near a pole, and even though the rest of the world was warm. They are holding up what Winston Churchill called the flickering lamp of history, and the scene it reveals is decidedly murky at present.

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Salt and the snowline

By Graham Cogley

In parallel with but, for practical purposes, independently of higher temperatures, we expect the environment to respond to an enhanced greenhouse effect with a more intense hydrological cycle. More evaporation where there is enough water (for example over the ocean) and a lot of evaporation already, and more precipitation where there is already a lot of precipitation. There are some pretty good indications that this is happening, but now a group of oceanographers has found more evidence in a surprising place (surprising to non-oceanographers like me, I suppose).

Kieran Helm and co-authors document just the kind of changes in the distribution of salt in the sea that you would expect if the hydrological cycle had intensified. Between 1970 and 2005 the maximum salinity of the water column, found at a depth of about 100 m, increased. In contrast, the minimum salinity, at about 700 m, decreased.

They analyzed the measurements by projecting them on to isopycnals, surfaces of constant density. The density of seawater increases when you add salt and decreases when you add heat. The payoff for the extra complexity is that heat and salt, added to or withdrawn from the ocean at the surface, are carried into or out of the interior of the ocean along these surfaces, and it is reasonable to interpret changes of salinity observed (strictly, inferred) on isopycnals as being due to changes at the surface.

The water balance of the atmosphere is a sort of zero-sum game. There isn’t room up there to store more than the equivalent of a few tens of millimetres of liquid water. In the big picture, more evaporation means more precipitation, but probably in a different place. Added water vapour stays in the air for long enough, on average, to be carried up to several thousand kilometres by the wind before it condenses and falls back out.

The atmospheric water balance is usually studied in terms of the single quantity PE, precipitation minus evaporation, which (because I used to be a hydrologist) I will call Q for brevity. If Q is positive, the surface beneath the air column we are studying is getting wetter. If Q is negative, the surface is getting drier. If the air column is over the ocean, and its Q is positive, the ocean beneath, which is already as wet as it can be, is getting fresher (less salty), while if Q is negative the ocean is getting saltier.

The simplest way to make sense of the Helm results is to interpret the 1970-2005 changes in the distribution of salt as due to increases in oceanic Q of 7% in the higher latitudes of the Northern Hemisphere and 16% in the Southern Ocean, with decreases of 3% in the tropics. Each of these changes is subtle but statistically significant. (Another recent analysis, by Paul Durack and Susan Wijffels, suggests that the numbers might be on the large side.)

What has this got to do with glaciers? For one thing, Q is not the whole story. Glaciers that lose mass, as most do nowadays, are freshening the ocean, and sea ice that melts, as at the surface of the Arctic Ocean, is doing the same. But the thing that really interests me from the glaciological angle is the challenge. The hydrologists and now the oceanographers have produced evidence for a more intense hydrological cycle, and by implication a more intense greenhouse effect. Can we glaciologists rise to the same challenge?

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.

A more intense hydrological cycle should make the shape of the snowline more curvaceous, lowering it by increasing snowfall near the equator and in the middle latitudes, and raising it by increasing evaporation in the desert belts. The snowline, remember, is at the altitude at which accumulation of snow is just balanced by losses due to melting and evaporation (actually, sublimation).

So the challenge is to detect snowline change due to the more intense hydrological cycle, against a background of snowline rise due to general warming. My guess is that, although it would be a big job, we might just be able to manage it. It would also be a race against time, because some of the most important glaciers for the purpose are losing mass so fast that they will not be with us much longer. But it would be worth the attempt, because demonstrating a change in the shape of the snowline is different from demonstrating simply that glaciers are losing mass, which in turn is different from demonstrating that the temperature is rising. The more independent but mutually consistent lines of evidence we have, the more confident can we be that we are on the right lines in interpreting what is happening to our world.

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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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