# Marching Against a Tail (and All Those Who Don’t Get Risk)

This Saturday 7th March, I will be joining the Time to Act Climate March, which seeks greater government action to prevent climate change. Why? Because of RISK! To remind everyone: Something can be risky even if it has a low probability as long as the impact is high. Imagine a game of Russian roulette. You put a revolver against your head with one loaded chamber–and then you pull the trigger. Feeling lucky? I now offer you \$1 million to play the game once. Remember, an ordinary revolver usually has six chambers, one of which is loaded. Do you take the bet? What about a pistol with 100 chambers? A thousand? With 1,000 chambers, the probability that you blow your brains out is 0.1%. Is that a good bet?

In statistics, that 0.1% likelihood outcome is firmly in the ‘tail’ of the probability distribution. When outcomes cluster around a central estimate, they may not have significant tails; others, have long or fat tails. This is important since generally the tail is where bad stuff happens. In my example above, something really horrible happens in the tail: death. As impacts go, that is pretty bad. So despite the low probability of an adverse outcome and the \$1 million potential pay off, putting a 1,000 chamber pistol against your head with only one bullet is still a very risky bet.

So is frying the planet.

And this is why I think scientists like Judith Curry and Nic Lewis don’t really get risk. They argue that doubling atmospheric CO2 isn’t much to worry about because we may only warm a little. Yes, we may warm only a little; but then again we may not. Here is the climate sensitivity table from a recent paper by the two (click for larger image):

ECS refers to equilibrium climate sensitivity and TCS to transient climate sensitivity. Simplistically, the former has a longer time horizon than the latter.

On the back of this paper, Curry was welcomed with open arms by the Wall Street Journal to do an op-ed (which you can find on Curry’s personal web site here) and feted by climate skeptic blogs across the world. In the op-ed, Curry takes an extract from the table:

Nicholas Lewis and I have just published a study in Climate Dynamics that shows the best estimate for transient climate response is 1.33 degrees Celsius with a likely range of 1.05-1.80 degrees Celsius. Using an observation-based energy-balance approach, our calculations used the same data for the effects on the Earth’s energy balance of changes in greenhouse gases, aerosols and other drivers of climate change given by the IPCC’s latest report.

And then goes on to make a policy recommendation:

This slower rate of warming—relative to climate model projections—means there is less urgency to phase out greenhouse gas emissions now, and more time to find ways to decarbonize the economy affordably. It also allows us the flexibility to revise our policies as further information becomes available.

Now ‘likely’ used in the WSJ op-ed means the 17-83% range. She has 17% of the outcomes in the good tail–warming below 1.05 degrees Celsius–and 17% in the bad tail–above 1.80 degrees Celsius. But from the table we also see that there for a 5-95% range, the outcome of a doubling of CO2 may be above 2 degrees Celsius of warming–2.5 degrees to be exact.

Some rough back of the envelope calculations. The pre-industrial revolution level of atmospheric CO2 was 280 parts per million (ppm). We are now at 400 ppm, so to double from pre-industrial concentrations, we would need to get to 560ppm. Co2 concentrations are also rising at around 2.25-2.50 ppm per annum. So if climate sensitivity to a doubling of CO2 were 3 degrees Celsius, we would get 2 degrees of global warming if CO2 concentrations reached around 450 ppm, which will be in about 20-30 years time. Two degrees of warming is considered (somewhat arbitrarily) to be the borderline for dangerous climate change.

Now Curry and Lewis see a non-negligible risk, that is 5%, that the sensitivity is 2.5 degrees. If right, the current rate of CO2 emissions would lock us into a 2-degree warmer world maybe 10 years later than the consensus, say in 2050. And then we come to the tail.

What is going on further into the tail. I want to know about this low-probability tail risk. It is important. This is the chamber containing the one bullet. If you wouldn’t play Russian roulette at very low odds, how about permanently damaging the planet at such odds?

How deeply do we have to get into the tail before we hit catastrophic climate change of 4 to 6 degrees of warming (remember that this particular risk is a composite of how much carbon we put in the atmosphere and how sensitive climate is to that amount of carbon). Let’s suppose we have a 99% confidence interval that we remain outside of the disastrous outcomes. Now we have 0.5% in the really bad upper tail. That’s odds of one in 200. Are you happy ignoring a disaster movie outcome if it only has odds of one in 200?

Moreover, if we ignore this tail risk of climate sensitivity and feel “there is less urgency to phase out greenhouse gas emissions now”,  isn’t there the possibility that due to fossil fuel infrastructure lock-in, we commit ourselves to a more than doubling of atmospheric CO2?

It gets worse. What if their climate sensitivity numbers are wrong. Curry and Lewis use one particular approach to reach their figures, but there are others. Michael Mann sets out the alternative approaches and the resulting climate sensitivity numbers in a Scientific American article here (click for larger image). In general, they are nearly all higher than those of Curry and Lewis. So Curry and Lewis’ disastrous climate change tail risk, with odds perhaps measured in the hundreds, may actually be a tail risk with odds measured in the tens. We can’t really be sure at this stage.

Finally, going on a march would appear a quixotic act in the face of the wicked problem of climate change. But one can take a risk approach similar to that of extremely unlikely, but very harmful, events here as well. Voting, demonstrating and lobbying may have only a very small chance of changing the probability of the final outcome. But the potential impact of altering an outcome–through in this case encouraging more aggressive Co2 emission mitigation–is monumental. This is reverse Russian roulette, where the chamber with the bullet becomes the benign outcome. And so I march.