Skip to the content

IOP A community website from IOP Publishing

environmentalresearchweb blog

« The Future of Arctic Sea Ice | Main | Wind, birds and bats »

PDFs, Fat Tails and Collapsing Ice Sheets

Sorry for yet another acronym, and sorrier still that the odds are against your guessing correctly what it stands for. No, it is not a file in Portable Document Format, nor yet a Post-Doctoral Fellow, but a Probability Distribution Function. These PDFs are an essential tool in modern efforts to grapple with environmental risk, uncertainty and just plain ignorance.

Suppose you knocked on a lot of doors, asking to measure the height of the person answering the door. (This is just a thought experiment. Actually doing it would not be a good idea.) At each door you would have a fair chance of getting a measurement equal to the average height of the human population. In fact, averaging your large sample of heights would be the best way to estimate that height, but the sample would also tell you a lot about how often different actual heights crop up. Once in a while the door would be opened by a dwarf or a giant, but the odds are in favour of the person who opens the door being average.

That is the essence of a probability distribution function. The PDF is just the frequency with which anything that varies is spread across the range of its possible values. The idea works just the same for the outcomes of climate model runs as for measured human heights.

We know, from previous large samples, that the PDF of human height is symmetrical. Short people are less likely than average people, and so - with about the same odds - are tall people. This is not true of climate model runs. Their PDFs have fat tails.

All credible climate models predict warming over the next century. The most common outcomes are those in which, by the time the carbon dioxide concentration reaches twice the value it had in about 1850, the temperature will have risen by between 2.0 and 4.5 °C.

The snag is that “most common” is not the same as “average”. A rather small proportion of the model runs predict much greater warming than do the commonest ones, and there is no compensating fatness of frequency on the less-warming side. The average of the predictions is noticeably warmer than the commonest prediction.

How do we respond to this undoubted, unpleasant fact? It is telling us something about the real climate of the future, but in an unsatisfactory way. I think that it is at least a guide to right action. There are actions that will make an improbable catastrophe even more improbable, and if we would not be unhappy with either their costs or their benefits then these actions become more apparently prudent. Policies founded on this reasoning are called “no-regrets policies”. We probably need more of them.

This is supposed to be a blog about glaciology, and I haven’t yet said anything about glaciers. Well, consider the West Antarctic Ice Sheet. Most of it is grounded below sea level, and there is a chance that continued warming will cause it to drain catastrophically into the ocean, starting perhaps in the next hundred years. Our best understanding is that not only is this chance extremely slim but also it would take several hundred years for the catastrophe to play out. But we cannot be certain on either of these points, or on whether the other tail of the PDF (ice-sheet growth because of increased snowfall in a warmer world) is equally probable.

In fact, we glaciologists are so far behind the climatologists that we haven’t even got a PDF yet. One course of right action is therefore obvious: study the problem intensively. The PDF either will or will not turn out to be fat-tailed, and if it is fat it will be either because of physics or because of ignorance. The first exploratory efforts to model the vulnerability of ice sheets are just beginning to appear, and the rush is on to be able to say something quantitative about the likelihood of ice-sheet collapse in time for the next major assessment by the Intergovernmental Panel on Climate Change, due in 2014. At the moment, though, all we can say is “Watch this space”.

Posted by Graham Cogley on July 6, 2009 3:00 PM |

TrackBack

TrackBack URL for this entry:
http://www.iop.org/mt4/mt-tb.cgi/3296

Comments (5)

  • 1 Aaron Lewis July 28, 2009 12:09 AM

    Another point about models the PDF of our climate future is what is and is not in the climate models. While the computer models of climate are complex enough to boggle most minds, there are significant global warming feedback mechanisms that are not included in any of the current models. That means there is some potential for climate change to occur much faster, or to a much greater extent than any of the current climate models predict.

    A good example is loss of Arctic sea ice. Not only did Arctic sea ice retreat faster than expected, but we can expect feedbacks from the loss of sea ice to push other aspects of global warming much faster than would be projected from any the model runs. The effects of loss of sea ice include decreased albedo and increased atmospheric water vapor, which is a powerful greenhouse gas, and which carries latent heat. These are likely to facilitate melting of permafrost. Thus, CO2 and methane will be released from permafrost sooner than expected by the models, creating another feedback not anticipated in past model runs. This strongly suggests much more latent heat available to warm adjacent weather systems than anticipated in any run of any current model.

    As one gram of water vapor condenses on ice, it releases enough heat to melt 7.5 grams of ice resulting in 8.5 grams of runoff. The assumption that this water vapor will be deposited as snow at the top of the ice sheet is purely temperature dependent. The Arctic has warmed since that assumption was made. Now there is less dry air to force the water vapor up, and it can just as easily melt the ice sheet from the bottom up. Can you say, “Basal lubrication!”? So, what do the models say about the ice dynamics of the Greenland Ice Sheet? Nothing! This is a major failure of the climate models.

    I suggest to you that any climate model that does not address ice dynamics is not worth a cup of coffee. We are not yet at a point where we need to start talking about the PDFs of climate models. The models are so bad that the risk is not from the predictions of the models, but the failure of the model to predict.

    Our climate risks are an order of magnitude greater than suggested by our climate models.

  • 2 Graham Cogley Author Profile Page July 28, 2009 5:16 AM

    Dear Aaron – I think you are exaggerating a bit. Climate models have certainly cost more than a cup of coffee, if you reckon forward from the first efforts in the 1960s. They have done more than their share in driving the development of ever bigger and faster computers, for example. In fact, the cost is one of the main difficulties we have in peering into the future. We do not have the number-crunching power to simulate all of the relevant details, even if we understood them.

    And of course another, probably the other, big difficulty is lack of understanding. I don’t see much point in criticizing climate models for leaving out ice dynamics when we don’t know how to include it. We have to learn on the job, taking note that although the models are not perfect they are getting steadily better.

    It is also worth noting that not all feedbacks are runaway feedbacks. If the models do not simulate all of the feedback mechanisms, then there is some potential for the climate to change more slowly than predicted.

    Finally, one of our strengths is that not all of our understanding comes from modelling. For example we can look to the past for possible analogues of possible futures.

    Graham.

  • 3 Graham Cogley Author Profile Page July 28, 2009 5:20 AM

    Dear Aaron – I think you are exaggerating a bit. Climate models have certainly cost more than a cup of coffee, if you reckon forward from the first efforts in the 1960s. They have done more than their share in driving the development of ever bigger and faster computers, for example. In fact, the cost is one of the main difficulties we have in peering into the future. We do not have the number-crunching power to simulate all of the relevant details, even if we understood them.

    And of course another, probably the other, big difficulty is lack of understanding. I don’t see much point in criticizing climate models for leaving out ice dynamics when we don’t know how to include it. We have to learn on the job, taking note that although the models are not perfect they are getting steadily better.

    It is also worth noting that not all feedbacks are runaway feedbacks. If the models do not simulate all of the feedback mechanisms, then there is some potential for the climate to change more slowly than predicted.

    Finally, one of our strengths is that not all of our understanding comes from modelling. For example we can look to the past for possible analogues of possible futures.

    Graham.