Tail Risk vs. Alarmism

March 31, 2014 7:46 pm6 comments

The American Association for the Advancement of Science just published a statement on climate risk (link) on which I am a co-author. This statement has several aims, one of which is to highlight the importance of societal risk in the low-probability tail of the climate change probability distribution. I would like to take this opportunity to explain why we think it necessary to talk about tail risk, and the road blocks we scientists face in doing so.

Tail risk is a concept that everyone is familiar with at some level. To take a rather obvious example, suppose an 8-year-old girl comes to a busy street which she must cross to catch her school bus. Unsure what to do, she asks an adult bystander for advice.  The adult replies that, most probably, she will make it across the street unharmed.


Image by Will Mego via Flickr (link).

Any other reasonable adult listening to such advice would regard it as radically incomplete. Surely, no one would encourage the girl to cross the street if there were a 1% chance that she would be run over. The most probably outcome is, in this example, largely irrelevant. But here there is very little downside to walking the girl up the street to where there is a traffic light.

In assessing risk, one has to estimate the probability distribution of the event (car colliding with girl), convolve that with an outcome function (girl likely dies if hit), and account for the cost of mitigation (take 5 minutes to walk to a traffic light). In the realm of climate change, climate scientists are the ones charged with estimating the event risk, while other disciplines (e.g. economics, engineering) must be brought to bear on estimating outcome, and the costs of mitigating the risk or adapting to it.

In assessing the event risk component of climate change, we have, I would argue, a strong professional obligation to estimate and portray the entire probability distribution to the best of our ability. This means talking not just about the most probable middle of the distribution, but also the lower probability high-end risk tail, because the outcome function is very high there. For example, here is an estimate of the probability distribution of global mean temperature resulting from a doubling of CO2 relative to its pre-industrial value, made from 100,000 simulations using an integrated assessment model. (We use this here as an illustration; it should not be regarded as the most up-to-date estimate of global temperature increase probabilities.)

Temperature rise probability distribution for a doubling of CO2. Figure from Chris Hope, University of Cambridge

Figure from Chris Hope, University of Cambridge.

More or less in agreement with the most recent IPCC report, the most probable “middle” of the distribution runs from about 1.5 oC to about 4.5oC , while there is a roughly 5% probability of temperature increases being less than about 1.8 oC and more than about 4.6 oC. But, given the corresponding distributions of rainfall, storms, sea level rise, etc., the 5% high-end may be so consequential, in terms of outcome, as to be justifiably called catastrophic. It is vitally important that we convey this tail risk as well as the most probable outcomes.

But there are strong cultural biases running against any discussion of this kind of tail risk, at least in the realm of climate science. The legitimate fear that the public will interpret any discussion whatsoever of tail risk as a deliberate attempt to scare people into action, or to achieve some other ulterior or nefarious goal, is enough to make almost all scientists shy away from any talk of tail risk and stick to the safe high ground of the middle of the probability distribution. The accusation of “alarmism” is quite effective in making scientists skittish in conveying tail risk, and talking about the tail of the distribution is a sure recipe to be so labelled.

Predictably, the AAAS statement evoked just such responses. For example, in her climate blog (link), Judith Curry states that “ …..these particular experts seem more alarmed than the expert authors of the IPCC report (well, the WG1 anyways), citing many very low probability events as something to be alarmed about……When scientists become alarmists, I don’t think it helps public opinion.” And this, from Roger Pielke (Sr): “This AAAS report is an embarrassment to the scientific community”.

Judy Curry is right that the IPCC working group 1 (WG1) almost entirely avoids the issue of tail risk (which is one reason that the AAAS felt compelled to do so), and Drs. Pielke and Curry speak for most scientists in expressing the fear of embarrassment in any discussion of low probability events. After all, by their very definition, such risks are unlikely to be the outcome. If we want to be admired by our descendants, the best strategy is to stick with the peak of the probability distribution, and with high probability, we can then ridicule those “alarmists” who warned of the tail risks, just as the adult who advises the girl to cross the street will, in all likelihood, be able after the fact to chastise the one who counseled against it.

And yet. Does the dictum to tell “the truth, the whole truth, and nothing but the truth” not apply to climate scientists? If we omit discussion of tail risk, are we really telling the whole truth?

So far it has been difficult to quantify tail risk beyond that implied by figures such as the one above, which resulted from running an integrated assessment model many times with many combinations of parameters varied across plausible ranges. We have also tried to use paleoclimate data and the observed response of climate to large volcanic eruptions to narrow down the probability distribution. A wild card in climate risk assessment is the problem of abrupt, irreversible climate change, which evidence in ice cores and deep sea sediments suggests are general features of past climate variations. We also have to be mindful that the graph above and many risk assessment studies use the canonical doubling of CO2 as a benchmark, whereas we are currently on track to triple CO2 content by the end of this century. (As a rough measure of global temperature change under triple CO2, multiply the values on the horizontal axis of the figure by 1.5.) Unless we find a way to extract carbon from the atmosphere, the climate risks would become alarmingly high (and not just in the tails) in the 22nd Century, even if we stopped emissions by the end of this century.

Do we not have a professional obligation to talk about the whole probability distribution, given the tough consequences at the tail of the distribution? I think we do, in spite of the fact that we open ourselves to the accusation of alarmism and thereby risk reducing our credibility. A case could be made that we should keep quiet about tail risk and preserve our credibility as a hedge against the possibility that someday the ability to speak with credibility will be absolutely critical to avoid disaster. What do you, the reader, think?



  • We do have a professional obligation. Just as an oncologist has a responsibility to review the range of treatment options and the likelihood of various outcomes from each. Emphasis is placed on what we have observed, and given trends what is the likely progression. But we cannot ignore the tails. If we had ignored this potential for example in glaciology we would not have begun intensive work on what appeared to be the weak underbelly of the West Antarctic Ice Sheet-Pine Island Glacier in the 1980′s and hence be able to look at trends that have already developed today. The tail can drive important research directions that have to developed in advance.

  • Great post, Kerry. I came at uncertainty from a different angle in a youtube video I put up not too long ago: https://www.youtube.com/watch?v=iRAL3dWnSNg

  • You make a strong argument to portray and discuss the entirety of the probability distribution, but the AAAS document only discusses the high tail of the probability distribution. What about the low tail, where unmitigated climate change turns out to be below the arbitrary “dangerous” threshold of 2C, and where there’s a large risk that the costs of substantial mitigation of greenhouse gas emissions will easily exceed the benefits for most of the world’s population?

    Scientists have an obligation to talk about the best-case scenario as well as the worst-case scenario.

    People are comfortable with dealing with both scenarios simultaneously. It’s like having car insurance and having, or not having, an accident.

    Car insurance, though, is simple. With car insurance, the cost is well calibrated to the risk. With global warming, neither the costs or risks are known.

    Note to reader: the best-case scenario for climate sensitivity doesn’t help the ocean acidification problem.

    • John: here’s how I would look at the issue. Imagine you’re a citizen year 2100. If it turns out that the climate sensitivity is high and human society does nothing about it, then you would rightfully be pretty angry. If, on the other hand, we switch to renewable energy in the next few decades, I think you are going to be pretty happy. If the climate sensitivity turns out to be high, then you’ll be happy that we addressed the problem. If the climate sensitivity turns out to be low, then you’ll be happy that the air is clean (because we will have reduced air pollution) and because all that carbon is still in the ground and you can happily burn it.

      Put another way, the damage of making the wrong choice is strongly asymmetrical. So while there are tales on both ends, the high tail is much more dangerous than the low tail.

      • That’s true, the folks in 2100 will have things to be happy about either way. So where’d the low-tail risk go? The risk is that the money we spent making the folks in 2100 marginally more happy is money not spent on other worthwhile causes with more immediate benefits.

        Both tails matter.

    • I believe the point of focusing on the high tail of probability is that people ultimately people need to make decisions on risk, not probability, and risk distribution is generally more asymmetrically skewed towards the high tail than probability is. One approach to mitigating the waste of preparing for a high tail event in the face of a low tail possibility is to hedge. For example, a coastal town may be deciding between building an expensive sea wall to deal with expected sea level rise and building an even bigger and more expensive wall to handle a high tail risk. They could feel very silly in the very unlikely event that sea level rise stops and they are too far in debt to operate the schools and fire department. But if they instead invest in beach nourishment, then it will either help protect them from sea level rise on the mid to high tail, or leave them with a big, beautiful beach with higher property values and tourist revenue on the low tail. I’m not claiming that every climate change impact has a hedgeable solution like this, nor even that the costs and risks in this simplified example are sufficiently quantified to be useful, but we should be careful not to frame decision making as a zero sum game between the environment and the economy. It’s absolutely possible to devise win-win scenarios.

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