Recently in In from the cold Category

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.

Rupert's adventure with Jack and Jenny Frost, 1974.

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.

In glaciology we like to distinguish between maritime glaciers and continental glaciers, because the climates that sustain these two kinds of glacier are quite different. The two adjectives make it sound as though the maritime ones ought to be near the sea and the continental ones oughtn't, but the reality is more complicated and more subtle.

Most glaciers consist of an accumulation zone at high altitude, where they gain mass, and an ablation zone at low altitude, where they lose mass. Roughly in the middle is the equilibrium line, at an altitude (the equilibrium line altitude or ELA) where loss and gain just balance.

From year to year the ELA varies through hundreds of metres, but on average over the decades it changes much more slowly, as the changing climate alters the balance. But what pins the equilibrium line to a particular average altitude? Why 1000 m, say, and not 2000 m, or 0 m?

A short but inaccurate answer is "Temperature". The hotter it is, the more ice you can melt. A slightly longer but much more accurate answer is "Temperature and snowfall". The more snow falls, the more heat you need to melt it. So the climate at the slowly-changing ELA is a measure not just of how hot it is, or of how snowy it is, but of how hot and snowy it is.

By definition, you need just the right amount of heat at the ELA to melt just the amount of snow that falls. Observations show that, although the ratio varies quite a bit, you get about 5 mm of melted snow for every positive degree-day, that is, for every degree Celsius sustained above the melting point for 24 hours. The snowier it is, the lower the ELA has to be, because it is warmer at lower altitude.

If the winter snowfall is equivalent to 10,000 mm of meltwater, you need about 2,000 positive degree-days in summer to melt it all. A snowfall of 1,000 mm of meltwater-equivalent requires only 200 positive degree-days, and 100 mm means only 20 positive degree-days. These numbers span very roughly the range of actual snowfall on real glaciers, from coastal Norway and Patagonia near the snowy end to the highest glaciers in Bolivia and Tibet near the dry end.

If your glacier has to keep flowing downhill to find an ELA that is hot enough, it eventually reaches sea level. It becomes a tidewater glacier, and icebergs start falling off. The ocean is doing some of the work (of adjusting the size of the glacier to the climate) that the atmosphere can't manage by itself.

Mountain ranges are traps for moisture, and potentially for snow, because they force the air to rise, cooling it and condensing out the moisture. What is more, once the wind has negotiated the mountain range it will be a lot drier, so we invariably find that across our glacierized mountain ranges the ELA rises to leeward.

This is the essence of what "maritime" and "continental" mean to glaciologists. We stretch the words so that maritime means "warm and snowy ELA" and continental means "cold and dry ELA". Some of the most "continental" glaciers are close to shorelines. There are not many maritime glaciers far inland, but the ones in the eastern Himalaya probably qualify, because the monsoon still packs a punch even after blowing over peninsular India.

Like all scientists, I get a lot of scientific papers to review. Between a fifth and a third of the ones I get start with "Glaciers are sensitive indicators of climate change", and I always cross it out, commenting that it is a boring cliché. The thing about glaciers is that they are insensitive indicators of climate change, because they integrate over temperature, precipitation, winter, summer, altitude, and possibly a significant horizontal extent. In the process they tell us things that no thermometer or rain gauge can.

They tell us, for example, that there is more to climatic change than rising temperatures. Because it had got snowier, the maritime glaciers of coastal Norway, but not the continental ones further inland, were gaining mass until about a decade ago. But more recent measurements show that rising temperature has now overcome this effect. And in the big picture, careful comparisons make it clear that less snowfall is definitely not why nearly all glaciers are losing mass. The message from the glaciers is that ELAs are rising, and rising because it is getting warmer. The reduction of snowfall that would be required to explain rising ELAs is enormous, and far beyond what we observe.

Rupert the Bear, a staple of my early literary diet, was regularly very impressed by the window art of his visitors Jack Frost and his sister Jenny Frost. We can explain much of this art rationally, but that enhances rather than diminishes its strange beauty.

At the Earth's surface, water ice crystallizes in the hexagonal system and snowflakes tend to have six arms or to grow as six-sided plates — which begins to account for their beauty. You can find beautiful snowflakes by the million in cyberspace. And of course when the weather is right you can just go outside, or even look at your window. But crystallography isn't the whole story.

What got me thinking about the beauty and strangeness of frozen water was a recent article by Toshiyuki Kawamura and co-authors. They describe spray ice, derived from the freezing of spray onto trees and shoreline structures. In bulk, the spray ice resembles "very large monster-like forms", as they put it.

They also describe ice balls, spheres (roughly) of ice, up to tens of centimetres across. The ice balls seem to form from lumps of slush on the surface of the lake. The lumps get rolled about by the waves and swell, frozen hard after a drop in temperature, then washed ashore by the waves and the wind.

The Kawamura photographs are technical rather than dramatic, but the freezing of liquid water onto solid objects can offer more drama than you need. Around where I live, we still remember the ice storm of 1998. Across eastern Ontario and Québec there are still trees, bent over in 1998, that haven't yet got back to something like vertical.

That ice was technically glaze, with a density near that of pure ice. The Kawamura spray ice is technically rime, less dense because it forms in irregular masses. Hoar is the equivalent, usually of still lower density, that forms by the deposition of water vapour as ice.

Rime or hoar often forms on our glaciological instruments when they are left out over the winter. If the instrument is a simple mass-balance stake, you just end up with an interesting photograph, like the one taken by my co-author Marco Möller on Austfonna in Svalbard. We like this one so much that we are hoping to persuade the publisher of our forthcoming Glossary of Glacier Mass Balance and Related Terms to put it on the front cover.

A mass-balance stake photographed by Marco Möller on the ice cap Austfonna in Svalbard. The sun has done just enough work to loosen the rime (or hoar?) with which the stake had been coated, and the rime has fallen to the surface as an intact body. (I also like the waves in the middle troposphere, picked out at the thinning edge of the cirrostratus veil by ice crystals condensing at the wave crests and sublimating in the troughs.)

But rime can be a glaciological nuisance. If your instrument is an automatic weather station or AWS, it will have been built for ruggedness and is likely to be still chugging away, recording the temperature, wind speed and other variables, even while more or less buried in the rime. How do you know how to interpret these records, or indeed whether you should?

For me, the weirdest frozen phenomenon of all has to be ice spikes. These protuberances grow out of confined bodies of water that are freezing from the top down. Their base-to-tip length can exceed 10 cm, and can be 10 or more times the base breadth. They taper towards the tip and grow upwards at seemingly random angles. According to Kenneth Libbrecht, the best way to study them is in ice-cube trays filled with distilled water and placed in an ordinary freezer with an air temperature near to —7° C. About half of the ice cubes will produce spikes in these conditions. A fan to promote air circulation also promotes spike formation. Although tap water doesn't yield as many spikes, plenty of spikes have been reported from out of doors, including the very first in 1921.

Water in a tray freezes at its free surface, starting at the confining walls and growing inwards. When the ice cover is all but complete, the water, under gentle pressure, has nowhere to go but up and into the little hole. If the liquid travels to the edge of the hole before entering the solid phase, you have a hollow tube that is evidently a working funnel for liquid water, which doesn't freeze until it reaches the propagating tip.

But why? Evidently there is an exquisite balance at the tip between the arrival of liquid, the removal of heat, the release of heat due to the freezing, and probably other factors. Nobody has yet managed to write down the algebra describing this balance.

Upside-down and inside-out icicles are somewhere beyond the borderline of relevance, but a lot of science is like that. The fact that the irrelevant is also the unexplained has a lot to do with why people get excited about ice spikes. And although they can't compete with Jack and Jenny Frost for beauty, they do show that strangeness can sometimes be strangely close to beauty.

By Graham Cogley

If you burrow in the literature of palaeoclimatology, climatic dynamics and glacial geomorphology, you can find all kinds of snowline: the transient snowline, the annual snowline, the climatic snowline, the regional snowline, the orographic snowline, and for all I know some others. Most of them are misnomers.

It is easy to see how the word "snowline" became popular. If you look at a mountain the line separating snow-covered from snow-free terrain is often the most striking feature of the view. This transient snowline is often straight and, as far as the eye can judge, horizontal. But it doesn't have to be. It can be messy, because of outlying disconnected patches of snow and patches above the snowline that are free of snow. What is more, it can and does wander up and down over the contours, which leads to uncertainty because we often say "snowline" when we mean "snowline altitude". On a single mountain or even a single glacier the snowline can range in altitude through hundreds of metres, so we really mean "average altitude of the snowline".

In glaciology, we have two further complications: we don't really want to know about the transient snowline but about the annual snowline, and we don't even want to know that so much as the annual equilibrium line.

The annual snowline is the transient snowline just before the first snowfall of winter, or whenever the mass of the glacier reaches its minimum in the annual cycle. Year upon year, comparing annual snowlines is much safer than comparing transient snowlines from random points in the cycle of the seasons. On the other hand, observing these annual snowlines is much trickier because of the likelihood that you won't get there in time or won't see anything if you do (because of the weather).

The annual snowline sometimes separates the glacier into an upper part that has gained mass over the year from a lower part that has lost mass, which makes it the same as the annual equilibrium line. But not always. If meltwater from the surface refreezes when it reaches the contact of the snow with the underlying glacier ice, we distinguish it as "superimposed ice", which represents mass gained by the glacier during the current mass-balance year. This is important for accurate book-keeping, but it also means that the snowline altitude can be tens of metres or more above the equilibrium-line altitude, with exposed superimposed ice in between.

In climatology, especially at regional and broader scales, these complications are usually set aside. This is where the word "misnomer" comes into its own, because except when they plot the snowline altitude on a graph against latitude the climatologists' snowline (regional, climatic, orographic, whatever — let's agree to call it the climatic snowline) is not a line at all. It is a two-dimensional surface. But we all know what the climatologists mean, and misuse of words is sometimes curiously unimportant as a barrier to the advancement of understanding.

The climatic snowline is a generalization, but a very valuable generalization, summarizing the state of the atmosphere near the Earth's surface in a very distinctive way.

Look at the climatic snowline in the graph. Set aside the complications and inaccuracies of usage, and ignore for a moment the colour scheme and the fact that the "line" is discontinuous — pretty fat at some latitudes, missing altogether at others. What we see is the altitude at which, if there were some land, there would probably be glaciers, or glacier equilibrium lines to be precise.

A 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.

One curious thing about the climatic snowline is that it is nearly always assumed to be an isotherm, often the one representing a mean annual temperature of 0° C. The colour scheme shows that this is only a good assumption if you are willing to do a lot of ignoring. For example at latitudes between 55° N and 65° N the mean temperature of the snowline during the warmest month can be as high as +8° C (the lowest snowlines) or as low as —4° C (the highest snowlines).

The graph has been lying around on my hard drive for two decades. I only dug it out because I wanted to put Snezhnika, at 44.8° N and an altitude of 2450 m, into context. You can find small but stable glaciers like Snezhnika in mountain ranges where the climatic snowline is well above the highest peaks, but they are not a reliable reflection of the big picture. There is a lot more to be said about the big picture, but it will have to wait for another occasion.

What a bad idea it was for some layout person at New Scientist to label the photo of a Himalayan glacier with the caption "Himalayan glaciers will vanish by 2035". Putting "Some" before "Himalayan" would have made the story true, as opposed to false. Of course it would also have made the story boring, as opposed to attention-grabbing. That glaciers are vanishing is a commonplace of the journalists, and up to a point it is a truism.

But truisms need to be seen in true perspective. Some Himalayan glaciers have undoubtedly vanished already. When any regional inventory of glaciers is repeated, typically after a few decades, the count usually goes down slightly. Sometimes it goes up, if larger glaciers have fragmented into smaller ones. More often a few percent, or even just a fraction of a percent, of the glaciers have indeed vanished.

The true perspective on this is that the glaciers that have vanished were never very big in the first place. The last large-scale episode of glacier growth, the Little Ice Age, culminated 100—300 years ago depending on where you look. But wherever we look, the evidence is that nearly all glaciers have been shrinking since that time. It is likely that the ones that have vanished already are mostly the ones that came into existence during the few centuries leading up to the date of peak ice.

There is more to the true perspective, though. For a start, given the climatological evidence for warming, we need to know whether the rate of loss of ice is greater now than, say, a few decades ago. Here the glaciological evidence is unequivocal: it is. But there is still more to be said.

Plenty of small glaciers have failed to make it. South Africa lost its only glacier during the 1990s. Chacaltaya Glacier in Bolivia was highlighted as a disappearing glacier in volume II of the IPCC's Fourth Assessment, where you can see it dwindling from 0.22 km² in 1940 to 0.01 km² in 2005. It disappeared in 2009.

On the other hand, some tiny glaciers have survived. Recently Grunewald and Scheithauer reported on those of southern Europe (excluding the Caucasus). It might be a challenge to identify in some of them the flow that is required by most definitions of the difference between a glacier and a snowpatch, but all are the genuine article in the sense that they are still there at the end of every summer.

I bet you didn't know that there are two glacierets in Bulgaria. (I am betting on whether you knew, not whether you care.) The authors managed to retrieve ice cores from one of them, Snezhnika. It was 12 m thick at its thickest, and on average 3 m thick over an area of 0.01 km², or 10,000 m². Since the early-20th-century disappearance of Corral del Veleta in the Sierra Nevada of southern Spain, Snezhnika has been western Europe's southernmost glacier, at 41.77° N. Working their way northwards, Grunewald and Scheithauer document glaciers in Albania, Montenegro (this one a monster, five times the size of Snezhnika) and Slovenia.

These shrimps seem to be doing OK, although the picture is mixed elsewhere. For example in the Cantabrian mountains of northwest Spain all that is now left of the Little Ice Age glacierets is four buried lumps of ice, while Calderone Glacier, in the Apennines of Italy, split in two during 2009.

All this might provoke subdued mirth among more macho glaciologists, but glaciers that refuse to go away should elicit admiration for their pluck and stubbornness. They also remind us that gains by snowfall and losses due to sunshine are not the whole story of glacier mass balance.

Chris de Beer and Martin Sharp studied 86 glaciers smaller than 0.4 km² in southern British Columbia and showed that between 1951 and 2004 a few disappeared and a few shrank, but most didn't change much. By careful analysis, they found that these objects have found sizes that are in equilibrium with their prevailing microclimates. Nearly all were in shadow for much of the time and were nourished significantly by snow avalanches from the surrounding terrain.

So the survivors offer a twist in the plot of the mass-balance story, but they do not point to flaws in our understanding of climatic change, and nor do the less fortunate ones. We should expect more and more disappearances as time passes, but should not panic when the journalists tell us that "Glaciers are vanishing".

The Dutch Environmental Assessment Agency, PBL, has released the results of a minutely detailed search for errors in part of the second volume of the Fourth Assessment of the Intergovernmental Panel on Climate Change. The search focussed on the eight chapters that assessed regional impacts.

It turned up quite a number of errors, mostly too trivial to waste time over, but two of them glaring. One was about how much of the Netherlands is below sea level. The IPCC gave a wrong figure, 55%. A quarter is much closer to the truth. But in the words of the PBL, "the error was made by a contributing author from the PBL[!], and the [IPCC Coordinating Lead Authors and Lead Authors] are not to blame for relying on Dutch information provided by a Dutch agency." Really? My atlas shows land below sea level in a tasteful strawberry shade, so I would have thought that a glance at the atlas would make it seem unlikely that more than half of the Netherlands is below sea level. On the other hand, the Dutch have had their finger in the dyke for centuries, and so are unlikely to be misled for long by anything the IPCC, or for that matter their own government, says on this point.

The other error was about the water tower of Asia, but I don't want to revisit that one just now other than to repeat that blunders happen.

This is all so predictable, and in a cosmic sense so trivial. There is, however, a way to view these blunders in proper perspective, even though I know I shouldn't use the word "paradigm" in an article for popular consumption.

All of us in the sciences know what a paradigm is, because we have either read or been told about Thomas Kuhn's 1962 book The Structure of Scientific Revolutions. A paradigm is a big, governing idea, one that makes sense of a lot of other ideas that would be disparate without it. Kuhn argued that when a scientific discipline undergoes a revolution, it is actually undergoing a paradigm shift, in which an old paradigm is replaced by a new one.

I am not sure about the old paradigm. Kuhn says that a paradigm is a set of one or more past achievements that some scientific community acknowledges for a time as supplying the foundation for its further practice. The achievements have to be unprecedented enough to attract adherents, and open-ended enough to leave all sorts of unsolved problems for them to work on. I detest the relativistic sociology of "acknowledges for a time", but this paraphrase is important as a key to understanding the recent fusses about climatic change and IPCC mistakes.

I don't think there ever was an old paradigm in the atmospheric and neighbouring sciences. First of all, there has been no revolution. Climatologists have been doing what Kuhn calls "normal science" for centuries. The foundations in dynamics and thermodynamics are as they have been since the 17th century, and in radiation as they have been since the late 19th century. But atmospheric and oceanic dynamics, and radiative physics, describe systems that, though they change continually, always stay the same unless you mess with them.

In fact, the big unifying idea didn't burst onto the scene. It evolved. Fifty years ago and more, there weren't many "adherents" in the study of global environmental change because there was little to adhere to other than a vague idea that another Ice Age ought to begin any millennium now. But there is certainly something to adhere to today. These days, the big unifying idea is the greenhouse effect, and in particular the anthropogenic greenhouse effect. It unifies because it is triumphant at explaining the facts while generating more questions than it answers.

Denialists are fond of criticizing climatological claims that "The science is settled", or equivalently that "The debate is over". If any climatologists have ever used those particular words, then what they meant to say was that the paradigm is doing fine. It did not originate in a revolution, but it has adherents who see it as unprecedentedly successful and find it so open-ended that the science of climatic change is still growing explosively.

If you can find a big enough concept, like Kuhn's paradigm, even mistakes about Asian water towers and Dutch polders fall into intellectual place. They are storms in a teacup. Debate about Himalayan glaciers and the risk of flooding in the Netherlands will go on indefinitely, enlivened by the occasional howler. If and when something more intellectually powerful comes along, we will replace the paradigm, but for now it is firmly in place and there is no sign of a replacement.

The Zwally effect is an acceleration of the flow of marginal ice in the ice sheets due to lubrication of the bed by meltwater percolating from the surface. Up to a point, this phenomenon is not surprising. It is well documented on smaller, thinner valley glaciers. The surprise, first documented by Zwally and co-authors in 2002, is seeing the same phenomenon in ice as thick as 1,200 m.

The Zwally paper has stimulated a growing literature with two main threads. One thread tries to explain how meltwater can find its way through more than a kilometre of ice. The other tends to show that the Zwally effect is not the reason for dramatic increases in the speed of tidewater outlet glaciers, where the evidence favours, quite strongly, warm ocean water as the culprit. But that doesn't mean that seasonal acceleration is uninteresting.

Ian Bartholomew and co-authors report on more dramatic seasonal acceleration than has been measured hitherto. It still doesn't rival the speed-ups observed on some tidewater outlets, but the observations highlight the potential of GPS from a different angle, and suggest fascinating insights into how the surface meltwater does its subglacial work.

This new report relies on time series of positions obtained with four Global Positioning System receivers deployed along 35 km of a land-terminating flowline at 67.1° N in southwest Greenland. The data include not just horizontal but also vertical velocities, as well as near-surface air temperature. Averaged over the summer, the speed-up from winter background values was rather modest. But the fascinating bits are the details.

The further up-glacier, the later the onset of speed-up, by more than a month. The natural explanation is a later onset of melting at higher elevations. The highest site was at 1,063 m and the lowest at only 390 m above sea level.

More interesting is that the horizontal velocity correlates very nicely with the vertical acceleration, or in other words with the rate of uplift of the surface. The ice goes faster when the surface is uplifting rapidly. Or rather, rapid uplift seems to provoke speed-up. This is a subtle observation in more ways than one. For one thing, the amounts of uplift are a few decimetres at most. That we can detect such subtle vertical motions is a payoff for all the trouble it took to loft a couple of dozen GPS satellites into orbit.

More interesting still is the authors' subdivision of the summer into three phases. In phase 1, there is no particular surface uplift or speed-up: the meltwater, if any, has yet to reach the bed. In phase 2, the cumulative uplift increases towards a maximum, and so do the horizontal velocities, more or less. (You need the eye of faith to see these phases in the noisy data. But I buy them.) The concluding phase 3 sees repeated episodes of uplift and speed-up, but the course of the surface elevation is downward and so, more or less, is that of the horizontal velocity.

Phases 2 and 3 add up to another picture of an invisible world beneath the authors' feet. The meltwater, once it reaches the bed, pressurizes the ice and forces it upwards, filling and enlarging cavities and promoting basal sliding. But the enlargement proceeds at least in part by melting of roofs and walls, implying the creation of connections and, in short, of a network. The network grows steadily better at discharging the arriving meltwater. Phase 2 becomes phase 3 when the network becomes more than able, on average, to cope with the spate of water. Phase 3 ends when the supply of meltwater gives out, and the ice starts winning again, resuming its regular wintertime job of squeezing the summertime channels shut.

If you want real glaciological drama, visual or acoustic, you should probably go to tidewater terminuses, at which most of the ice leaves the ice sheet. But there is still plenty of land-terminating ice, and the main things about the Zwally effect, granting that it is real, are that it must be real everywhere; and that if the surface of the ice sheet gets warmer then the bed of the ice sheet is bound to get busier.

Last year I had occasion to take a 500-km trip by taxi. The taxi had a GPS unit — a talking GPS. I didn't pay much attention along the way, but I had to be impressed when the taxi pulled up on the main street at our destination and the GPS announced, smugly but correctly, "You have reached your destination."

The Global Positioning System has become part of our lives in the last decade or two, but it is much more than talking taxis. Some recent work illustrates dramatically the ability of accurate positioning devices to tell us things about how the world works.

The toothpaste in the Earth's mantle complicates attempts to measure glacier mass balance by the gravimetric method, and also by the geodetic method. (For the latter, you need two maps of surface elevation. Subtract the earlier map from the later, and divide by the time span. The result is nearly a map of the glacier's mass balance, the only missing ingredient being an estimate of the density of the mass gained or lost.)

But what if the elevation of the glacier bed has changed, in conflict with our assumption that surface elevation change equals thickness change, or equivalently that all of the gravity signal is due to the glacier? It can and does happen, and the glacier itself is often to blame. Loading the underlying bedrock, it forces the soft mantle material, at depths below about 100—200 km, away from where the ice is building up. A glacier that is shedding mass constitutes a "negative load", and the mantle material flows back. (The negative load ends up as a positive load spread more thinly over the ocean.)

The trouble is that the mantle deforms viscoelastically. The elastic deformation is instantaneous and reversible, just like that of an elastic band. Very crudely, it amounts to about a third of the equilibrium response to the load. The remaining viscous part of the deformation is what we think of as flow. To model it, though, we need an accurate model of the variation of viscosity (stiffness) throughout the 2,800 km thickness of the mantle. That is a formidable challenge.

The mantle flows so slowly that it is still responding today to the loss of ice at the end of the Ice Age, roughly 10,000 to 15,000 years ago. The toothpaste is pushing the bed of the glacier upward slowly, and before we can interpret a change in its surface elevation as a change in its mass we have to remove the bed-elevation component of the change.

But now Yan Jiang and co-authors offer an ingenious twist on the monitoring of elevation change with GPS. They have collected five or more years' worth of GPS readings of surface elevation from several fixed sites around the North Atlantic. The sites are all on bedrock, not on glaciers. (They wouldn't bear on this particular problem if they were on the ice.)

The surface's vertical velocity varies from place to place. The ingenious twist is to focus on the vertical acceleration of the surface, which turns out to be systematically greater near to large ice masses (in Greenland, Iceland and Svalbard). The authors argue persuasively that, while the vertical velocity will reflect delayed viscous adjustment, the acceleration is a signal of the Earth's elastic response to recent increases in the rate of glacier mass loss.

There are some rough edges: sites with large accelerations and not much glacier ice nearby, and one site not too far from the ice but with relatively low vertical acceleration. But I can't think of a mechanism to explain these observations other than elastic response of the solid earth to recent removal of glacier ice. The viscous response to this unloading has barely begun, and the viscous response to deglaciation cannot possibly change by so much over a period as short as a few years. The authors even have a go with an elastic-response model at estimating the mass balance that would account for the acceleration in west Greenland, and get plausible answers.

The talking GPS on my taxi ride demonstrated the power of positioning accuracy at the few-metre level. For measurements of glacier mass balance we would like millimetre-level (vertical) accuracy, but there are technical and conceptual problems to be ironed out before that becomes reality. For now, Yan Jiang and co-authors have shown that decimetre-level accuracy will do nicely to be going on with.

In a remarkable paper about Pine Island Glacier just published in Nature Geoscience, Adrian Jenkins and co-authors describe the latest step in maturation of an emerging glaciological technology: autonomous underwater vehicles — AUVs — or in other words unmanned submarines, for exploring the undersides of ice shelves.

The United States Navy has been sending manned submarines beneath the ice pack of the Arctic Ocean for more than 60 years. But pack ice, a few metres thick, is small beer by comparison with the ice shelves that fringe much of the Antarctic Ice Sheet. These are typically a few hundred metres thick, and there is no question of surfacing by punching your way through the ice if you run into trouble. Indeed, the cavities beneath ice shelves, between the base of the shelf and the sea floor, must be among the most inaccessible of all the theoretically accessible places near the Earth's surface. Being so hard to reach — until now — the sub-shelf cavity is also one of the least observed, but not necessarily least understood, parts of the climate system.

Climate, you say? Well, the sub-shelf cavity is where the ocean meets the ice sheet. Assuming (safely) that thermodynamic equilibrium prevails, the contact between shelf ice and seawater must be at the freezing point of the seawater, which depends on the pressure of the overlying shelf and the saltiness of the water. But the water and ice at some distance from the contact will not be at the freezing point, so there must be a heat source or sink, and therefore melting or freezing, at the base of the shelf.

If you add warm water to the sub-shelf cavity, you should expect additional melting. In 2002, Rignot and Jacobs inferred, from temperature profiles in the ocean offshore, astonishingly high rates of basal melting near several grounding lines: more than 50 m of ice per year. But this does not mean 50 m/yr of thinning of the shelf. A central part of their analysis was measurement of ice flow across the grounding line by radar interferometry. The inference of rapid melting was required to explain why the floating shelf was "pulling" ice so aggressively out of the grounded ice sheet.

So the contents of the sub-shelf cavity, and what goes on within it, are just as much part of the puzzle of glacier response to climate as are the grounding line itself, the shape of the floor of the cavity, the water at the base of the grounded ice, and of course things that happen in the atmosphere and the wider ocean.

Jenkins and his co-authors have contributed the first large set of in-situ observations from the sub-shelf cavity. What strikes me most forcibly about this dataset is how triumphantly it confirms earlier theoretical analysis of the way things ought to be down there. According to theory, warm water should be flowing inward at depth, melting the shelf base aggressively near the grounding line and — having thus become cooler, fresher and more buoyant — flowing upward and outward along the base. This is exactly what the autonomous underwater vehicle observed, confirming that we did know a thing or two even before measurements became possible on this scale in the sub-shelf cavity.

There are other noteworthy points about this study. For example the AUV found a ridge in the sea floor beneath the floating ice, in just the right place to explain why the grounding line of Pine Island Glacier has been retreating inland since the first observations in the early 1970s, and to confirm that this is something we ought to be worried about.

But perhaps the most noteworthy point of all, looking ahead, is the AUV. Buried in the Methods section of the paper is this, describing an incident part-way through the field campaign: "... the AUV lost track of the rugged ice-shelf basal topography, ascended into a crevasse, collided with the ice and executed avoidance manoeuvres that prompted it to abort its program and take a direct route to the recovery waypoint. After minor repairs, ...". Putting it another way, the world is now a little bit smaller, but not less dramatic, than it used to be.

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.