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In from the cold: November 2010 Archives

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.

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.

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.

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.

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.