Accelerating Glacier Shrinkage

In the last post I mentioned two important results from the study by Zemp et al.: first, that glaciers worldwide are shrinking (which we already knew); and second, that shrinkage has accelerated. They certainly know what they’re doing and got it right, and WGMS (the World Glacier Monitoring Service) collected and organized that data that enables me to see it with my own eyes. So I decided to see with my own eyes.

One of the measures of glacier wasting is its mass loss, usually expressed as mmwe for “millimeters of water equivalent.” The annual mass balance measures how much the glacier has changed, which is the “velocity” (to misuse the term only slightly) of its mass (actually mass per unit area). If the mass balance changes, then its velocity has changed so we can describe it as “acceleration.” We can even get fussy and call it acceleration only if it’s increasing, while if it’s decreasing call it “deceleration,” but I usually won’t bother to be so fussy.

Their main result in this regard is that glacier loss was greater (more negative) since 2000 than it was during the 1990s. So I decided to examine mass balance since 1990, to discover whether or not I could find a downward trend. Again I reiterate that a trend in mass balance signals changing velocity, hence accelerating mass, and that’s what I’m looking for. My approach supplements theirs, because I’m not directly comparing the 1990s to the 2000s+, I’m looking for any real change since 1990.

I took the data, which extends through 2012, and isolated glaciers with at least 10 mass balance measurements since 1990, leaving 81 glaciers in the sample. I fit a straight line (by least squares) to the mass balance measurements. For each, I recorded the rate of change as well as its significance (the “p-value” for those into that sort of thing). As is customary, I’ll use a standard of 95% confidence, so only p-values 0.05 or less are indicators of significance.

By that standard, 23 out of 81 glaciers showed significant deceleration. That’s quite a lot — if the whole sample were random we’d only expect about 2 (and 2 accelerating). So, surely there’s a change underway in how glacier mass is changing. All the rates of change were negative; all 23 showed a faster rate of wasting away since 1990, none showed a statistically significant increase in their mass balance.

The two most rapidly decelerating turned out to be in France, Sarennes and Saint Sorlin:



The name of the glacier is above the left-hand graph, above the right is the country code (FR for France) and the WGMS ID number. The plots show only data since 1970; some glaciers have mass balance data prior to that but I just wanted to show some context leading up to the post-1990 period.

The left-hand graphs show the annual mass balance. Most of the values are negative because for most years the glacier lost rather than gained mass. There is a good bit of fluctuation, so even these rapidly decelerating glaciers show several years with mass gain. But there are far more years with mass loss, and since 2002 no years show gains, only losses.

The right-hand graphs show cumulative mass balance, which represents the mass of the glacier over time. It shows that since 1970 these two glaciers have shed a lot of ice. Note that the right-hand graphs plot mwe for meters rather than millimeters of water equivalent.

More to the point is that the mass balance has been decreasing. It’s visually evident, and it shows up in the numbers as statistically significant. Yes, Zemp et al. got it right — glacier loss has accelerated (i.e., glacier mass has decelerated). For this sample, 23 of 81 show it clearly — and that’s a lot — while none show clearly the opposite effect.

The closest to statistically significant decrease in mass loss is Lemon Creek glacier in the good old USA:


Its p-value is 0.057, not quite significant. One should bear in mind that if the sample were random, we’d expect about 2 of them to show statistically significant decrease in mass loss, just by random fluctuation, because the sample is big enough. Of course it’s entirely plausible that none of them would either, which is what we observed. The point is that having one glacier in a sample of 81 skirt the edge of statistical significance, is not a sign of significance, it’s just the kind of random fluctuation that we expect from such a sample.

And of course it’s worth noting that just in terms of its changing mass, this glacier too is wasting away.

One of the glaciers in the sample showed statistically significant deceleration, but happens to be growing — just not as fast as before. It’s the Engabreen glacier in Norway:


But this is the only glacier in the sample of 81 for which the average mass balance since 1990 is positive with statistical significance, i.e. it’s the only one which can be claimed to be growing with statistical significance. Meanwhile, 61 of 81 (75%) of the glaciers can be claimed to be shrinking with statistical significance. Not all of them show a statistically significant change in their rate of shrinkage, but they can confidently be said to be shrinking. The fact that we’re able to establish consistent shrinkage, with statistical significance, for three fourths of glaciers over a sample period of barely 20 years, is remarkable — it shows just how strongly, and how unambiguously, the world’s glaciers are wasting away.

In fact since 2000 Engabreen doesn’t seem to be growing any more than it’s shrinking. As short as it is already, even the list of the growing glaciers (the only ones deniers talk about) is shrinking!

If we don’t require statistical significance, but just count how many glaciers have an average positive mass balance whether significant or not, we find 5 of 81 glaciers. That’s a whopping 6%, while 76 of 81 (94%) seem to be shrinking. Norway is of course part of Scandinavia, and Zemp et al. noted in their paper that in that region coastal glaciers are more likely to gain mass while inland glaciers lose mass.

My next plan of attack is to study front variation of glaciers rather than mass balance. There are far more glaciers for which front variation data is available in good quantity, and the time span over which it’s available extends further back, in some cases much further back. But that must await another day.

This much is evident, is crystal clear, in fact is so obvious you really have to be an idiot or a liar to deny it: the vast majority of the world’s glaciers are shrinking, the number that are growing is very very tiny, and the rate at which the vast majority are shrinking is faster now that it was even as recently as the 1990s. Those who deny, or even dispute, this evidence, just aren’t being honest. The best one can say is that they might be lying to themselves. But they sure aren’t telling the truth.

14 responses to “Accelerating Glacier Shrinkage

  1. “the vast majority of the world’s glaciers are shrinking”
    You seem to have shown that a large majority of those 81 glaciers with sufficient data are shrinking. I’m prepared to believe that this probably applies to glaciers without sufficient data too, but I don’t think you have shown that.

    [Response: That is exactly what Zemp et al. did show.]

  2. “I took the data, which extends through 2012, and isolated glaciers with at least 10 mass balance measurements since 1990, leaving 81 glaciers in the sample.”

    One worry I might have about this is whether there are more observations for glaciers that are shrinking, because they are shrinking and therefore more interesting to observe. This then might mean that there is a bias in your sample.

    [Response: As I said in the previous post, the observation of glaciers began in the 19th century. It has expanded as time progressed, not “because they are shrinking” but because glaciologists are interested. They are, quite specifically, interested in representative samples not biased by whether they are growing or shrinking. This kind of argument is really reaching, quite a bit too far.]

    There are other plausible ways in which a bias might enter into the sample – the more accessible and easier to observe glaciers might be expected to be at a lower altitude, for example.

    While I am nit-picking… I really dislike your use of deceleration to describe an increase in the rate of mass loss. I always felt that if one was talking about velocity then any change in velocity was an acceleration, and that it was only when talking about speed [ie the magnitude of the vector] that one talked about acceleration [higher magnitude] and deceleration [lower magnitude].

    The way you use deceleration here is really quite jarring to me. Interested to hear what others think.

    • On your last point, I agree that the use of the word deceleration seems strange. Deceleration (i.e. a negative acceleration) is not the same thing as the acceleration of a negative. Put it another way, a car can accelerate away from me, and it can accelerate towards me, both indicate that the relevant quantity (how far away the car is) is changing more rapidly over time. So I’d say Tamino is discussing accelerating mass loss, in the same way that I would be experiencing accelerating safety loss in the case of the “car approaching me more rapidly” scenario. :-)

  3. The thing with glaciers is that their dynamics are multifactorial. If a glacier is located in a region where ambient temperature at the base hasn’t increased to the extent that it compensates for precipitation that may have increased at the source, then the result will be extention. It’s somewhat similar to the the Arctic/Antarctic sea ice phenomenon.

    Oh, the Denialati will say that this is an example of having cake and eating it, but it’s entirely within the contraints of physics – global warming increases evaporation at lower latitudes, this water vapour is transported to the poles and to altitude, where it falls as snow/ice. Local coditions may have warmed as well, but if they’re still below freezing point then the result will be (for a time, at least) longer glaciers.

    Of course there are further factors that can and should be considered, but it’s important to point out that glacial extention is not disproof of planetary warming.

  4. David B. Benson

    Zebraphile — “Me thinks thou doest protest too much.”

  5. “It’s p-value” => lose the apostrophe.

  6. A problem with looking at rates for glaciers is that there is a real zero mass, and even beyond that the lapse rate implies that there are real zeros at different altitudes as one moves up a glacier. Rates are not very useful near physical limits

  7. To rephrase Eli’s response, when the glacier has zero mass, its loss is also zero. One way to deal with that problem is to normalize by the mass of the remaining glacier.

  8. In regard to those glaciers whose rate of decline is diminishing, it is possible that the decline is due to the fact that they have reached the point where there is a reducing volume of ice left to melt.

    At some point the decline rate for a glacier will reach zero – not because the net gain/loss has turned up, but because there is no more ice left to melt – the glacier is gone.

    [Response: I’m certainly no expert. But a few possibilities suggest themselves. One is that it kept getttin hotter.

    Another is that as glaciers have shrunk, they’re not as tall, so more of the glacier is exposed to warmer air simply because it’s lower-altitude air. I do have some data for glacier mass balance as a function of altitude, and I’ll probably take a look at that quite soon.]

  9. Let me make sure I’ve got something basic correct here, as it’s not quite explicit in the procedural description. The OLS fits you mention generate annual values which are then graphed in the plots shown, right?

    [Response: No, the plots show actual data from WGMS. The left-hand sides show the annual mass balance measurements, the right-hand sides are their accumulations. The OLS fits are only to test for statistically significant changes in mass loss rate.]

  10. I predict that many of the glaciers on the W Norwegian coast will grow this year. We had a very mild winter with much much more precipitation that usual (and we usually get lots), but the summer has been cool.

  11. Maybe they were just in a pool?