Flying in Volcanic Ash, Part 2

The ash cloud over Europe seems to have abated somewhat, and commercial air traffic is returning to the air. The German DLR organisation (equivalent to the US NASA) sent up test flights of a Falcon 20E on Monday and Tuesday 19-20 April, to measure what was up there. The report, in English, makes interesting reading (Here is a local copy, for those having trouble accessing the original URL). There are pictures in which you can see the ash layers below the aircraft.

It has rained, very briefly, say spottily for 5 minutes, on Tuesday and Wednesday here. My windows are now covered with a fine yellowish film of what I take to be ash (I have some skylight-type windows as well as vertical ones). The temperatures in Bielefeld, Germany, where I am (about 100km west of Hannover) have also been unusually low for this time of year, say 10° during the day in the sunshine (though with significant wind chill) and getting near zero at night. Indeed, it even snowed briefly in some places near here yesterday (Wednesday). The light is unusually white in the sunshine, an effect particularly pronounced in the evening. People used to smoggy atmospheres (Los Angeles, San Francisco Bay Area) will be familiar with this phenomenon.

The debates now seem to be concentrating on whether governments (rather, their regulatory agencies) were too cautious, not cautious enough, or just right. The consensus appears to be that the reaction, essentially to close the airspace where the highest concentrations were known to be until Wednesday, may have been more cautious than the facts warranted, as the UK Minister for Transport, Andrew Adonis, said in this report on Wednesday. The political fallout has started, as in this report from The Times.

For the record, I think the reaction to this environmental phenomenon has been exemplary. First, the dangers of flying gas turbines through volcanic ash can be catastrophic, as I noted (with reference) in my first post on this topic. (David Crocker pointed out to me an article in Boeing Aero magazine from before the current phenomenon, which gives the necessary background information for those still searching for it.) Second, this phenomenon, that a major part of the world for commercial air traffic at all altitudes was affected, was unprecedented. Third, over the course of a few days, test flights taking measurements were organised and flown by the only organisations capable of producing believable results. Fourth, everyone was involved: manufacturers, regulators, and government. Fifth, the outcome so far has been as good as it could be for safety: no commercial air passengers have been killed or severely injured; there have been no train accidents injuring people who would have flown but were forced to take the train; ditto for ships.

And, sixth, the main point of this note: if everything is done “right” (whatever “right” may mean), and safety is prioritised, it follows with high likelihood that, in hindsight, when more is known, it will be seen that we have erred noticeably on the side of caution. This note is a qualitative argument using probability theory (but no math!) that this is so.

When the facts come in, hindsight is a wonderful thing. Safety is paramount to the regulators, by their charter, and also to the manufacturers of the equipment because of liability. The national governments chose to prioritise safety. The result could not have been better for safety. There was, last week, virtually perfect uncertainty as to the potential effects of this particular cloud. Standard industry practice, for many years if not decades, is to avoid all volcanic ash. So, at the beginning, this practice, evolved over decades of experience, was followed, in the face of considerable uncertainty. Within a very few days, various organisations had determined that it was likely safe to fly, say, research aircraft. Data were gathered, uncertainty was reduced, we are back to flying.

What could have been done differently? Safety was prioritised in the face of uncertainty. Should we not have prioritised safety? My answer is that prioritising safety was exactly the right move.

So what does prioritising safety involve? Risk is generally construed as a combination of likelihood and severity of untoward events. What was the risk involved in flying? Likelihood of a volcanic ash encounter over most airspace in Western Europe was certain (the various meteorological offices knew it was there), so there is no uncertainty there. The uncertainty with this risk resides, then, exclusively with the severity of the phenomenon (the effects of the ash cloud). Previous experience shows that the “worst case” is catastrophic, both for the people involved and (as it would be) for the government and agencies that would be said to have “allowed” an accident to happen. (Although severe accidents have not happened directly, losing all of one’s engines is defined to be a “catastrophic” in aircraft-certification terms, because after a loss of all engines only environmental circumstances can affect whether one lands on-airport or off-airport, and the least favorable plausible environmental circumstances, here an off-airport forced landing and its likely deadly consequences, are taken to define the severity.) Since experience had shown that severity (defined as worst-case) over the sample (all volcanic-ash-encounter incidents) is catastrophic, one can attempt to define the sample more narrowly, to reduce the uncertainty if you like. What is the range of possible effects? Let us say, from mildy increased maintenance costs on gas turbine engines, to heavily increased maintenance costs, to flame-outs and the ensuing necessary tear-down of all engines of that type on all aircraft, up to the consequences of any accident resulting from near-simultaneous flame-outs of all engines on an airframe. We could presume on general physical principles that these effects are some function of the type of ash (known, and variable, in the current eruption), its density, and the length of exposure. But we don’t know what function. Furthermore, for all flights, there is going to be a range of densities encountered as well as a variety of lengths of exposure.

Now comes a little qualitative reasoning about likelihoods. This is the bit that people who haven’t studied the basics of probability and statistics don’t necessarily grasp, despite the best efforts of us professional educators over the decades. I am going to talk about a “bell curve”, and having just searched the WWW for “bell curve” it seems to me that we professional educators are somewhat to blame for this state of affairs, because the typical WWW explanations are technical enough to alienate anyone who doesn’t have a degree in higher mathematics, as we shall see in the reference immediately below! I will be avoiding any math here, but I do want to talk about “bump curves”.

A “bell curve” associates a range of possible values for a parameter (along the horizontal axis) with the frequency with which those values occur (on the vertical axis). The term itself is taken by technical people to refer specifically to the so-called Gaussian or Normal Distribution, in tech-speak. But actually I want to be more general than this. Take a look at the first graphic in that Wiki article, of “probability density function”, and you see four examples, in green, blue, red and yellow, of graphs I want to talk about. They are small at the ends and have a bump somewhere in the middle. Most uncertain phenomena look like this when you show values (horizontal) against frequency (vertical). When I say “like this”, I want now to allow that the “bump” can be pushed to one side, kinked, in all sorts of ways. Imagine that you had a Plasticine “bump” sitting on the floor, and you let your one-year-old stick hisher thumbs into it, push it around and so on, then you cut it in the middle with a knife and trace the outline of the cut on a piece of paper. It is going to be thicker nearer the middle and thinner near the edges. Let me call all these things “bump curves” for the sake of this note.

The particular “bump curve” I want to talk about is the “distribution” of severities of ash-cloud encounters. So on the “right hand side” we have all-engine flameouts (“catastrophic”); going to the left of that we have one-engine flameouts and consequent flight bans and tear-downs of all engines of that type; going further to the left we have highly increased maintenance (involving large costs and effort); moving further left we have mildly-increased maintenance; moving further we have insignificantly increased maintenance. Remember, we don’t know quite what this “bump curve” looks like, even whether it has “one bump or two”, and where the “bump” or “bumps” are. But let me assume it has, for all intents, one “bump”, to make it easier to follow my reasoning.

First, I want to make the “bump curve” more like a bell curve. I can do this as follows. Imagine I have drawn the bump curve on a rubber sheet. I have a metal frame, consisting of a horizontal track into which are inserted a succession of vertical rods. I can’t bend the rods or take them out of the track, but I can fix them anywhere I want on the track, as well as slide them left and right and then fix them in their new position. I glue my rubber sheet with the bump curve onto this frame of rods. Now, I slide the rods left and right, to stretch the sheet sideways more or less, to make it look more like the bell curve. So, for example, if the “bump” is to the right of center, then I stretch the sheet on the right of center until the curve on the right looks more like the curve on the left of the bump.

Now I have something that looks like the bell curve, but the scale on the horizontal is all distorted, because I have moved the rods around.

And now I draw a vertical line on the rubber sheet, at the point which divides the consequences which are not deleterious to safety (on the left) from those consequences which are deleterious (people killed or injured).

Suppose you are blindfolded, and some supernatural agent performs this manoeuvre I just described. You are blindfolded; you can’t see the curve, but you know it is more or less a “bell curve” because that is what the agent made it look like. You can feel the edges of the white board, so you know where the left side and right side of the curve lie (left edge: “insignificant”; right edge: “catastrophic”), and you can find the middle. But you don’t know how the rubber has been stretched, so you don’t actually know where the vertical “safety boundary” line is; whether it is to the left or to the right of middle.

Now you are given the following task. Put a mark on the board, as far to the right as possible, but to the left of the safety boundary line. Remember you don’t know where this line lies, because the agent has pulled the rubber in a way you didn’t and can’t observe. So you give it your best guess.

And behind you in line are another ninety-nine people who will try to perform the same task. All of you are perfect “rational agents”. In other words, you all think straight, think deep, are perfect at statistical and probabilistic reasoning, and do as well as you can at the given task. You are all trying to put your point as close to, but left of, the safety boundary line as you can guess. In other words, you are basically trying to guess where the line is.

I predict the outcome: almost all of you are going to place your point well left of center. If you don’t believe me, try it out with your “perfectly rational” group of friends!

Let us see what this means. Remember, we don’t actually know how the agent has stretched the curve, because we don’t know how the curve looked to start with. Suppose we now ask for the likelihood distribution of the position of the vertical “safety boundary” line. What is it going to look like? On general principles, it is going to look like some sort of “bell curve”. The bell curve is symmetric about its middle. But you and all your pals put your best guess as to where this line is on the left. That means that most of the area under the curve (which represents likelihood) is going to lie to the right of where you all put your points. That means that, when you don’t know where it is, it is most likely that the safety boundary line lies to the right of where you all put your points.

That means that your conjoint best guess as to where the safety boundary lies most likely errs noticeably towards the cautious (left) side. When somebody removes your blindfolds and you can see the curve (translated into our problem terms: somebody does the research so we know more about concentrations of ash in the atmosphere as well as what such concentrations might do to engines) you would expect to see that your choices are well to the left of the safety boundary line.

The moral of this story: if everybody were perfectly rational and used an appropriate risk-based approach with safety paramount, Lord Adonis’s statement is to be expected: the authorities should expect that they have guessed well left of the safety boundary line.

I hope to have shown you the following. Erring definitively on the side of caution is an expected outcome of a rational approach, in a situation of great uncertainty, to a risk of which the value ranges from insignificant to catastrophic.

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