# How thick is this (Himalayan) glacier?

by Graham Cogley, environmentalresearchweb, September 20, 2010

If you drill a hole right through your glacier, one of the things you get is a measurement of its thickness. But if you want the mean thickness of the entire glacier, an expensive and time-consuming borehole doesn’t get you very far. The only realistic way to measure the mean thickness of a glacier is ground-penetrating radar (GPR).

You drag your radar across the glacier surface. It emits pulses of radiation and keeps track of the echoes, in particular those reflected from the bed. With one or two additional items of information you can convert the travel time of the echo to a thickness. This is still expensive, especially if you try to improve coverage by flying your radar in an airplane instead of dragging it over the surface.

But with reasonably dense coverage, you do end up with a reasonable estimate of the mean thickness. With a measurement of the area, and some reasonable assumption about the bulk density, you can estimate the total mass.

One problem with all this is that we only have measurements of mean thickness for a few hundred glaciers at most. What do we do about the mean thickness of the remaining several hundred thousand?

The most common answer is “Volume-area scaling”. The term, which is a firm fixture in glaciological jargon, is misleading because it is really

*thickness*-area scaling. When we plot the measured mean thicknesses against the areas of their glaciers, we get a nice array of dots that fall on a curved line — or a straight line on logarithmic graph paper. The thickness appears to be proportional to the three-eighths power of the area. There is an equally nice theoretical scaling argument that predicts this power and makes us suspect that we are working on the right lines.Unfortunately the so-called coefficient of proportionality, the factor by which we multiply the three-eighths power of the area to turn it into an estimated thickness, is much harder to pin down. It varies substantially from one collection of measurements to another.

Recently I have been using volume-area scaling to try to say something useful about the size of the water resource represented by Himalayan glaciers. As you may have noticed, the fate of Himalayan glaciers has been in the news lately. Will they still be there in 2035? Yes. Will they be smaller in 2035? Yes. How much smaller? Don’t know.

Among the reasons why we can’t say anything useful about Himalayan glaciers as they will be in 2035, one is that we can’t say much about how they are in 2010. So I have been trying to work out some basic facts, by completing the inventory of Himalayan glaciers and using the glacier areas to estimate their thicknesses and masses. The inventory data were obtained over a 35-year span centred roughly on 1985. So forget the challenge of getting to 2010. What can we say about Himalayan glaciers in 1985 or thereabouts?

It turns out that, including the Karakoram as well as the Himalaya proper, there were about 21,000 of them. To estimate total mass by volume-area scaling, we have to treat each glacier individually. The result depends dismayingly on which set of scaling parameters you choose. Five different — but on the face of it equally plausible — sets give total masses between 4,000 and 8,000 gigatonnes. (Difficult to picture, I agree, but these numbers translate to region-wide average thicknesses between 85 and 175 metres.)

In short, we only know how much ice there used to be in the Himalaya to within about a factor of two. Let me try, like a football manager whose team has just been given a hammering on the pitch, to take some positives from this result. For example, it pertains to a definite time span and to a region that is defined quite precisely. Earlier estimates have been hard to compare for lack of agreement on, or definition of, the boundaries. It is also a better estimate than the 12,000 gigatonnes suggested casually by the Intergovernmental Panel on Climate Change in 2007.

But what does “better” mean in this context? Apart from being wrong about the longevity of Himalayan glaciers, it looks as though the IPCC was also wrong about the size of the resource, which is a good deal smaller than suggested. Where does that leave us as far as water-resources planning is concerned? With a lot of work still to do, that’s where.

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