That glaciers are shrinking is a commonplace observation in the media. The journalists are right, but defining "shrinkage", pinning down its rate, and deciding how unsure we ought to be about that rate, are not as straightforward as you’d think.

There are four main ways of describing glacier change. Here I will leave changes of length to one side and focus on changes of area, volume and mass. I will also focus on the global scale and on "small glaciers". The others, the two ice sheets of Antarctica and Greenland, are so big that they call for completely different approaches to measurement.

Measuring glacier shrinkage

A measurement of shrinkage, defined as reduction of the glacier’s area, requires two measurements of the area at known dates. In the dataset described here, nine-tenths of the measurements record shrinkage and the rest show expansion. In fact, most glaciers have been shrinking for the last 100-200 years, since the culmination of the so-called Little Ice Age when many deposited prominent terminal moraines. These enable the estimation of maximum extents with fair accuracy. Accuracy improves as we enter the era of good maps and of photography, especially from the air or space.

Both the quantity and quality of such information have increased greatly in recent decades. Glaciers are remote from most inhabited regions, and visiting them is expensive. But satellites with cameras fly over regularly, and we only have to wait for a cloudless overflight to get valuable observations. It is a little surprising that nobody has yet tried to put the accumulating evidence of shrinkage together. Recently I began an attempt to do just this; it has meant trawling the scientific literature, including some of its darkest depths.

For some glacierized regions there are still no quantitative estimates of shrinkage, for others we have partial coverage, and for some coverage is complete. In the latter category, the glaciers of the Austrian Alps shrank at -0.58%/year from 1969 to 1998, while those of Franz Josef Land in the Russian Arctic shrank at -0.04%/year from 1952 to 2002. This comparison illustrates two of the difficulties glacier scientists face: the measured rates vary by tenfold or more, and the dates of surveys do not match.

Nevertheless, we can begin to think about a global average estimate. For example the average rate for 270 regions since 1970 is -0.22%/year. If we weight each region by the amount of ice it had to start with, the average is only -0.12%/year. That is, more extensively glacierized regions appear to be losing ice extent more slowly.

Faster change

Has the shrinkage rate increased recently? It is too early for a confident answer. A “yes” would of course fit with how we think the Earth responds to greenhouse forcing, and some of the glaciological evidence does seem to point that way. For example when we look at regions with at least two measurements of shrinkage rate, the more recent rates are faster than the earlier in 35, or 60%, of the cases.

So how reliable are these rates? Not very, unfortunately. Setting aside the errors in the measurements themselves, they sample only about one fifth of the total extent of glaciers worldwide. But we also stumble on a serious barrier in the shape of what I will call "size dependence". When the shrinkage rate is tabulated in terms of initial size (glacier area at the first survey date), some regions do show strong variation while others do not. The smallest glaciers in the Alps and the Canadian High Arctic are shrinking much faster than their larger neighbours. Elsewhere, as in western North America and parts of Tibet, glaciers of all sizes are shrinking at about the same rate. So far there is no convincing explanation for this variable size dependence.

Much of the total worldwide glacier extent is accounted for by smaller glaciers, and until we learn more about size dependence we cannot rule out any estimate between the two extremes. The best way to think of the global average rate of glacier shrinkage is that it is probably within a factor of two of -0.2%/year. This may not sound like much, but it translates to -1400 km2/yr and of course, as suggested by the map below, it adds up over time.

As shown in "glacier map", 14 states of the northeastern US happen to have a similar area to the world’s glacierized area 50 years ago. The map suggests lower ("at least") and upper ("at most") bounds for the loss over the past half-century, which lies somewhere between 5 and 20% depending on whether size dependence is or is not important. The corresponding annual rates are about -500 to -700 km2/year for no size dependence, and -2,600 to -3,000 km2/year if data from the Alps and Arctic Canada are globally typical.

Measuring mass balance

For many purposes we need to know not just the rate of shrinkage, but the mass balance: the rate of change in the mass of the glacier. Measuring this accurately is a challenge, but we can idealize the process by thinking of it as measuring the change in volume and multiplying by the density, which is mass per unit volume. The slow conversion of newly-added snow to ice is a complication, because its density changes from about 50-200 kg/m3 to about 900  kg/m3.

Measuring the mass change itself, using data from the GRACE satellite mission, is an important innovation which I will not pursue in this article as GRACE does not yet provide routine information.

So back to volume: there are basically two ways of measuring the change in volume of a glacier. The so-called direct method involves drilling stakes "directly" into the glacier to measure thickness change, usually over a year. One advantage is that the stake is its own benchmark, and there’s no need for elaborate surveying procedures. Another is that since you are already there you might as well measure the density of the added snow. (Mass which has been lost can be assumed to have the density of ice.) Among the disadvantages are expense and danger, the difficulty of getting an adequate sample of variations in thickness change over the extent of the glacier, and the difficulty of measuring the rate of iceberg calving where it is significant. The mean change in thickness times the average area of the glacier is the change in volume; the density measurements allow this change to be converted to a true mass balance.

"Geodetic" methods, on the other hand, do involve elaborate surveying procedures. In essence, they subtract an earlier map from a later one. The difference provides a map of glacier thickness change. Traditional geodetic measurements do indeed involve mapping, usually from aerial photos, but nowadays many rely on laser altimeters and radar interferometers to sample rather than map thickness changes. Geodetic methods require a large up-front investment, but since they can cover much more ice they can be very cost-effective. Their big weakness is that they yield no information about density. To convert a geodetic volume balance to a mass balance you must either visit the glacier to measure the density, or make some plausible assumption about it. The commonest assumption, called Sorge’s Law, is that the right density to use is that of ice. It holds widely but not invariably. It is a pity that we do not yet have a reliable way to estimate density remotely.

Most direct mass balances are measured annually and reported to the World Glacier Monitoring Service in Zürich, Switzerland. They are not without their problems, prominent among which are sparse global coverage and gross under-representation of calving glaciers , but at least they make a fairly tidy whole. Until recently, estimates of global average mass balance have been based entirely on direct measurements.

Most geodetic measurements are multi-annual and are scattered through the scientific literature. Varying in duration and with irregularly-distributed start and end dates, they have been difficult to analyse in the same context as the direct annual measurements. A few months ago, however, I found a simple way around this statistical roadblock, which copes satisfactorily with the extra uncertainty due to the mixture of methods.

The graphs show the impact of including both direct and geodetic measurements. The vertical scale is in sea-level equivalents: the negative of global average glacier mass balance, spread over the ocean surface and expressed as an equivalent depth. On the left the red squares show 5-year averages of direct measurements, the blue circles similar averages of geodetic measurements. (The early error bars are taller because measurements are fewer). The geodetic measurements offer much better spatial coverage as well as the obvious improvement in historical reach; direct measurements began in earnest only in the 1940s. The graph on the right shows a close-up of recent decades, in which we have enough measurements to correct for their uneven geographical distribution – there are too few in remote regions, too many near where glaciologists live. The red squares are corrected global averages of direct measurements, and represent the picture which was conventional until recently. The dark blue circles, with a grey confidence region, are similar averages from the new combined direct and geodetic dataset. Note the importance of spatial correction: in the right panel the average for 2000-2005 is only 1.4 mm/year as against the 1.7 and 2.0 mm/year of the separate, uncorrected averages in the left panel.

The improved spatial coverage of geodetic measurement appears to compensate for its poorer resolution in time, because the net uncertainty does not increase by much. More significantly, the geodetic measurements go far to solving the problem of under-representation of calving glaciers. This is very probably why the new estimates are more negative, showing faster sea-level rise.

Mass lost from glaciers has to go somewhere. It soon ends up in the ocean. To put the current (2000-2005) rate of loss in context, the altimeter-measured rate of sea-level rise over a similar period is about 3.5 mm/year, of which about 1.5 mm/year is due not to additions of water mass but to thermal expansion of the existing seawater. The discrepancy, about 0.6 mm/year, must come from the ice sheets, with perhaps a small contribution from changes in water storage in and on unglacierized land.

Glaciers are often described as "sensitive indicators of climatic change". This cliché misses an important point: glaciers are also independent indicators of climatic change. Mass-balance measurements assume nothing about the temperature at weather stations, so glaciers give us a better-rounded and more secure picture of how the natural world is coping with the changes being forced upon it.

More water in the ocean means trouble not just for New York, Calcutta, the Netherlands, Tuvalu and a long list of other areas with concentrations of people and property near to sea level. The cost of adapting to this change we cannot avoid will fall, sooner or later and in one way or another, on just about everybody.

Negative mass balance is a socioeconomic trap even before the additional meltwater reaches the ocean. We have fallen right into it over the past 200 years, creating thirsty arid-land societies whose local sources of water will run dry before the next 100 years are out.

The least we can do is to get, and keep, a good quantitative grip on the source of these problems.