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Ice sheets and baskets of eggs

The term “basket-of-eggs topography” in glacial geomorphology is a metaphor for the appearance of drumlin fields. Drumlin is Gaelic for a rounded but elongate hill or ridge. Where you find one drumlin you usually find a whole field. They tend to be quite tightly packed, and a basket of eggs is a rather apt analogy.

More apt than you might think. Laying an egg is a practical problem in hydrodynamics, solved long ago by our amphibian and reptilian ancestors. Forcing glacier ice over a resistant bed is an analogous problem, at least to the extent that both the bird and the glacier – usually an ice sheet – have to balance force against resistance. One of the most distinctive attributes of drumlins is that they are smooth.

This does not get us very far, though. Drumlins might look like eggs because they represent roughening of an originally smooth (flattish) glacier bed or, equally likely, smoothing of a rough bed. But why did the ice sheet and its bed find it mutually convenient to generate the particular amount of smoothness that we can see today? Why don’t we see drumlin fields everywhere? Are there drumlin fields beneath the modern Antarctic and Greenland Ice Sheets? And if so, can we learn about the behaviour of ice sheets, and in particular their behaviour in the worrisome near future, by working out how the ancient ice sheets drumlinized their beds?

The answer to the last question is Yes. Progress, however, has been frustratingly slow. Several intriguing papers demonstrate, either analytically or by numerical modelling, how drumlins could possibly form, but as yet there is no sign of a compelling universal explanation.

Now, Chris Clark and co-authors have fallen back on an old strategy, that of compiling a large sample of simple measurements in the hope that insight will emerge from the sheer weight of the evidence. It is easy to criticize this approach as mindless, and it is true that they have not tackled the big questions, but in my view they have indeed produced food for thought.

The first thing to note about the Clark sample is its impressive scale. They counted all of the drumlins in the British Isles – all 58,983 – and assembled aggregate statistics for half as many more from other glaciated regions. Inadequate sampling is not likely to be one of the major concerns about their results.

They measured the length and, when possible, the width of each drumlin. The average elongation (length divided by width) is 2.9, and the most common elongations are between 2.0 and 2.3, so drumlins are typically two or three times as long as they are wide.

Several non-obvious facts emerge immediately. First, drumlin lengths and widths have unimodal frequency distributions (well-defined single peaks). I buy the argument that this means that “drumlin” is a meaningful single concept and not, for example, a jumble of other concepts. Second, drumlins are no shorter than 100 m. This suggests that, whatever dynamical phenomena are represented by the word “drumlinization”, they have a physical lower limit. (To me it smells like a fraction of the ice thickness, but that is as far as my intuition takes me.) Third, the frequency distributions are skewed, meaning that increasingly small proportions of the total sample are very long (or wide, or elongate). There does not seem to be any particular upper limit to the dimensions of drumlins. Perhaps they grade into the very elongate features that geomorphologists call megaflutes.

What Clark and colleagues find most surprising about their sample is that it exhibits a clear scaling law: for any given drumlin length, the greatest observed elongation is equal to the cube root of the length. I agree that this is both clear and surprising, and that it must mean something, although I have no idea what. But for me the most striking thing about their paper is Figure 7, a map that shows that drumlins are essentially lowland landforms. (For some reason, they left the ice-sheet margin off this map, but you can find it in many textbooks. Right now I am looking at Figure 12.1 of Glaciers and Glaciation by Benn and Evans.) Drumlin-free lowlands are not uncommon in the glaciated parts of the British Isles, but all of the uplands, especially the most rugged parts, seem to be entirely free of drumlins. Were they already too rugged, so that drumlinization was unnecessary? Was the ice too thin? Too slow? Too cold? As I said, food for thought.

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