Bayesian inference about nuclear disasters and press coverage

Via Brad DeLong, Clive Crook writes:

From the start of this calamity I have wanted to know, “What is the worst that can happen at these nuclear sites? Suppose everything that could go wrong does go wrong: what then?” I still don’t know the answer. In what I have read so far–dozens of articles–nobody who knows what he is talking about has spelt this out carefully.

I have had this same frustration.  The question is what to infer from this gap in the coverage.  Is it that newspapers have been asked by a government not to panic people?  Is it that newspapers are simply feckless?  Is it that we are in “uncharted waters,” relative to previous knowledge and previous nuclear disasters?  Or could it be “all of the above”?  Is there any hypothesis where this gap in coverage indicates the problem soon will be solved?  I don’t see it.

By the way, major evacuations are very difficult to pull off.  Nonetheless, will it be considered a moral failing that the Japanese are not currently trying to accomplish one?


Tyler, my frustration is that journalists and other amateurs are talking too much about the worst that can happen. There is no gap --there is too much noise and nonsense. Reading updates from IAEA and MIT Dep. Nuclear Sc.&Eng. my impression is that the experts are in "uncharted waters" but I know too little to judge their assessments. Rather than a problem of Bayesian inference, my impression is that experts are facing a situational awareness problem; from Wikipedia's entry on SA:

Situation awareness, situational awareness, or SA, is the perception of environmental elements with respect to time and/or space, the comprehension of their meaning, and the projection of their status after some variable has changed, such as time. It is also a field of study concerned with perception of the environment critical to decision-makers in complex, dynamic areas from aviation, air traffic control, power plant operations, military command and control, and emergency services such as fire fighting and policing; to more ordinary but nevertheless complex tasks such as driving an automobile or motorcycle.
Situation awareness (SA) involves being aware of what is happening around you to understand how information, events, and your own actions will impact your goals and objectives, both now and in the near future.[tone] Lacking SA or having inadequate SA has been identified as one of the primary factors in accidents attributed to human error (e.g., Hartel, Smith, & Prince, 1991; Merket, Bergondy, & Cuevas-Mesa, 1997; Nullmeyer, Stella, Montijo, & Harden, 2005). Thus, SA is especially important in work domains where the information flow can be quite high and poor decisions may lead to serious consequences (e.g., piloting an airplane, functioning as a soldier, or treating critically ill or injured patients).
Having complete, accurate and up-to-the-minute SA is essential where technological and situational complexity on the human decision-maker are a concern. SA has been recognized as a critical, yet often elusive, foundation for successful decision-making across a broad range of complex and dynamic systems, including aviation and air traffic control (e.g., Nullmeyer, Stella, Montijo, & Harden 2005), emergency response and military command and control operations (e.g., Blandford & Wong 2004; Gorman, Cooke, & Winner 2006), and offshore oil and nuclear power plant management (e.g., Flin & O'Connor, 2001).

"Allen has been at MTSU since 2007, but earlier in his career he worked more than 14 years at Sandia National Laboratories in New Mexico, where -- among other assignments -- he headed the federal lab's work on "severe accident phenomenology." That work included using a research reactor to actually melt the core of another reactor to better assess how the core relocates in an accident, as well as the release of fission products. He also conducted hydrogen and steam explosions at desert test sites outside Albuquerque, using reactor fuel simulants to assess the results."

"Much of his research directly addressed accident scenarios in which the nuclear fuel is no longer submerged in water, a situation that Japanese workers have been battling for days at the Daiichi reactor complex."


"You have an earthquake that lasts maybe a minute, a tsunami that lasts maybe 15 minutes. But these things could go on for months. You could lose all six of the reactors."

"If workers are unable to get additional cooling water into the reactor vessel, the molten fuel core will collapse into the water in bottom of the vessel. Eventually the heat from the decaying fuel would boil away the water that's left, leaving the core sitting on the vessel's lower head made of steel."

"Should that happen, "It'll melt through it like butter," Allen said."

"That, in turn, would cause a "high-pressure melt injection" into the water-filled concrete cavity below the reactor. Because the concrete would likely be unheated, the reaction created by the sudden injection of the reactor's ultra-hot content would be immense, he said."

"It'll be like somebody dropped a bomb, and there'll be a big cloud of very, very radioactive material above the ground," Allen said, noting that it would contain uranium and plutonium, as well as the fission products."

"Should these events happen, the best outcome would be if the winds are blowing east and push the radioactive plume over the Pacific Ocean, he said. "It (the radioactivity) will fall out in the ocean and everything will be fine," he said."

?The worst case, Allen said, would be if winds pushed a radioactive cloud south toward Tokyo and Japan's highly populated cities. If that were to happen, he said, the consequences would likely be greater than the 1986 accident at Chernobyl, where an entire area of Ukraine had to be evacuated because of the radioactive conditions that increased the risk of developing cancer."

Mike, I read the interview yesterday and frankly I think that experts without specific knowledge of what is going on in Japan should not talk. For example, Allen could have said the worst case would be if both the winds he mentioned and a new 9.0 earthquake and tsunami were to happen, the consequences would likely be greater than WWII. So what?

I wish people would just talk without trying to signal meta-messages. But that's always true.

100% agreement here.

I'm a nuclear engineer. Worst case is always radioactive contamination throughout Tokyo and well beyond. Even now, though, I'd bet large amounts of money that nothing even remotely like that will happen - it's such a vanishingly small probability that it would be a "moral failing" to take action based on the chance that it *could* happen.

As someone that has worked in the sciences and on several projects that have had extensive media coverage, my guess is no reporter understands what they were told. Reporters take journalism classes - not science - and their ability to understand science is not great. There are rare exceptions.

mdb, this is exactly what I've been complaining about. In circumstances like this, the inherent silliness of being an expert in "standing in front of a camera and trying to reproduce what someone else told you" is exposed.

I'm a little more cynical: their ability to understand science is just this side of nonexistent. I was just shaking my head at the NYTimes' coverage:

"The development came as the authorities reached for ever more desperate and unconventional methods to cool damaged reactors, deploying helicopters and water cannons in a race to prevent perilous overheating in the spent rods of the No. 3 reactor."

Seriously, without mentioning once that time is on the side of containment? If we go another week without a full meltdown, we win.

If we go another week without a full meltdown, we win.

So, it's been a week. Japan is evacuating a wider area, they've found radiation in the water in Tokyo, and they've hospitalized several workers with radiation burns. Is this what winning looks like?


Ask Brad what's the absolute worst case scenario for the world economy?

Answer: collapse back to the Dark Ages.

Of course, that's not very likely, but is it the absolute worst case scenario.

I infer that a profit-maximizing newspaper gets substantial marginal gain (page views etc.) at little cost by publishing alarming but vague headlines, while there is insufficient market demand for clear explanation from knowledgeable experts to justify the subtantial marginal cost of researching and producing it.

Reactors give off radiation, and are extremely hot. If they get hot enough to melt through their (multiple) containers, that radiation is spewed directly into the atmosphere, and can contaminate wide areas much like a dirty bomb would. The size of the area, and density/duration of the contamination, would depend on many things such as wind and precipitation and terrain, and thus are not really predictable. If you want to say Tokyo could become forever uninhabitable, ok, I suppose you could say that. But you're probably just trying to get on television.

You can of course have reactors that merely overheat, or melt through some (but not all) of their containment vessels. This results in excess radiation and pressure buildup inside the plant, which can be released -- sometimes intentionally to relieve the pressure. This radiation is much less dangerous than what you would see from a meltdown that fully exposes the core. But the release itself can trigger an explosion when the radioactive gasses come into contact with the air. This has happened in Japan; it was not "the plant" exploding but rather hydrogen gas released from it.

The media is doing what it does best -- scaring the crap out of people while providing as little information as possible. It's rather hilarious to see a committed far-lefty like DeLing suddenly frustrated at the realization that CNN and the New York Times are nothing more than propaganda outlets.

I'll admit to being totally confused. Based on what I've read, the reactors themselves are no longer in danger; it's the containment pools for the spent fuel rods. Is that true?

Further, I'm confused about the outcome if the water in the containment pools boils off completely. I realize this means that the rods begin to break down, but can't more water be poured back into these pools (somehow?) or do they heat up so much that pouring water onto them becomes impossible because the water boils off faster than it can be added?

From what I can tell—and I am not a nuclear engineer—the water in the pools serves two purposes. It conducts heat away from the fuel rods, but it also shields the surroundings from their radiation. (That's why they're stored thirty feet deep.) As the water level falls, the radiation level rises, making it difficult to get pumping equipment near the pool. That's why they're using helicopters and water cannons—it allows them to put water in the pools without getting too close to them.

What's the worst that could occur? What's the minimum value of the Gaussian normal distribution?

By now, we're fairly confident that a chain reaction is unlikely to trigger all the deuterium and tritium in the environment into a fusion reaction. So if the reactor were to somehow explode and slam some fuel rods together in an utterly unanticipated way, a small nuclear explosion would probably be about as bad as it could get.

Utterly unanticipated in the "physically impossible to the best of our fairly good knowledge", you mean.

Not possible.
The chain reaction at a nuclear plant is too slow for a nuclear explosion. In nuclear reactors, a "moderator", slows down the neutrons to a 1/10,000 of its original speed. This is necesary to sustain a chain reaction because fast neutrons do not interact with the rest of the fuel and mostly escape through the walls.

For a nuclear explossion you need fast neutrons, so enrichment must be at least 30%. With slow neutrons the most you can have is the fuel to heat up rapidly, which may cause non-nuclear explosions due to gases or water vapor.

A reactor and a bomb are analogous to a piece of wood and dynamite. The speed of the burning in wood makes it impossible that it explodes like dynamite.

A reactor and a bomb are analogous to a piece of wood and dynamite. The speed of the burning in wood makes it impossible that it explodes like dynamite.

Uh oh.

The question is what to infer from this gap in the coverage. Is it that newspapers have been asked by a government not to panic people?

I bet that it is just he opposite. The news outlets are well motivated to try to keep viewers watching. If the worse case is a slightly elevated cancer rate in the area close to the plants people may not watch.

Worst case scenario is aliens invade.

Wait, even that's not the worst case, but I don't think that's what people really mean.

Ok, I'm no expert, but I know enough* to say that we are in uncharted territory.

*Yes, I know a bit of nuclear physics, very little. I know a bit of plant engineering too, again very little.

First, there is no risk of a nuclear explosion. None. At all. The fuel of those reactors simply can't explode, it doesn't matter the shape of any chemical explosion. The reactors were built in a way where, the core melting it should simply stay there, melted. It'd make a hellish scenario for cleaning the reactors and doing any kind of investigaion after that, but that's all. Now, theory is theory, and practice is another thing completely. They may explode after a meltdown, that is because they may react with the water at the botton of containment, a explosion could breach containment and release contaminants into the surrounding area (I have no idea how far). There may also be some thermal cracking or that containment is already breached, that would contaminate the near area, but not very far.

Now, the pool is another problem completely. Again, it was made in a way where if things go bad, the fuel will just melt there, quietly. I'd expect that the chance of an explosion at a pool be way lower than an explosion at a reactor meltdown. But again, practice is a different thing. If there is an explosion there, the consequences are way worse than at a reactor, because the pools store a much bigger amount of contaminants.

In other words, no big trouble is expected from the accident, and nobody can be sure about that. Coincidently, that is the same thing I'm hearing from everybody that claims to understand the situation.

NPR was talking a bit about this. From what I could gather, the worst case scenario has the fuel rods melt, forming a pile of radioactive sludge, and then that sludge can melt downward through the bottom of the facility and into the ground, contaminating ground water. I'm not sure how far down it is possible for the stuff to melt, maybe all the way to magma? Could that cause a volcanic eruption?

No, in several ways.

(1) Everything I've read says the plants were designed to contain a meltdown.

(2) Given that the plants are cooling down by the hour, every moment the Japanese pour water on the plants makes a full meltdown and criticality excursion less likely.

(3) Groundwater contamination is the worst plausible scenario. Melting down to the magma would require being hot enough to melt through several dozen miles of rock. Exercise: Assume the crust is composed of granite. Look up its thickness, specific heat, melting point, and average temperature, and figure out how much energy the sludge would have to produce to get to the mantle. Compare to the current rate of energy production (conservatively assume constant 5% of full thermal output).

Worst case scenario is that aliens have already invaded, provoked the earthquake and our now awaiting further orders..

This just in! Proceed to quadrant number 4,execute Plan B.

I guess we need to design plants to withstand 9.01 earthquakes and 30.01 foot tsunamis. Then we'll NEVER have a problem.

Sorry Andrew but I live in Chile so please be sure that your plants can withstand at least 9.6 earthquakes.

And make sure all nuclear plants are designed to those standards, even if they're 500 miles inland in a place that's never seen an earthquake larger than 3.0.

It seems that the NRC chairman is not drinking from the same bottle of Happy Juice that some of our commenters, or the Japanese government for that matter, appear to be chugging.

If the American analysis is accurate and emergency crews at the plant have been unable to keep the spent fuel at that inoperative reactor properly cooled — it needs to remain covered with water at all times — radiation levels could make it difficult not only to fix the problem at No. 4, but to keep servicing any of the other problem reactors at the plant. In the worst case, experts say, workers could be forced to vacate the plant altogether, and the fuel rods in reactors and spent fuel pools would be left to melt down, leading to much larger releases of radioactive materials. * * *

The spent fuel pools can be even more dangerous than the active fuel rods, as they are not contained in thick steel containers like the reactor core. As they are exposed to air, the zirconium metal cladding on the rods can catch fire, and a deadly mix of radioactive elements can spew into the atmosphere. The most concern surrounds Cesium-137, which has a half-life of 30 years and can get into food supplies or be inhaled.

And then there's the reactor with the plutonium in its fuel.

I'm pro-nuclear myself, faute de mieux, but the defensive quality of much of the commentary by experts is not any better than the scary exaggerations of the media.

Since all these cores were running at some point in time, all 6 reactors have plutonium in them.

I was going by this from the article I linked:

The decision to focus on the No. 3 reactor appeared to suggest that Japanese officials believe it is a greater threat, since it is the only one at the site loaded with a mixed fuel known as mox, for mixed oxide, which includes reclaimed plutonium.

Well, there are multiple standards here. The earth just killed 10,000 people and we don't want to do away with that. And yet, we hold nuclear to a much higher standard and understandably so, because any accident is by definition a nuclear accident with the public relations fallout resulting in more nuclear bombs than nuclear reactors going forward, even if the harm is similar to what might happen at a coal power plant.

"and then that sludge can melt downward through the bottom of the facility and into the ground, contaminating ground water. I’m not sure how far down it is possible for the stuff to melt, maybe all the way to magma? "

No, that was a movie with that well known nuclear engineer, Jane Fonda, in it.

Try three or four inches of the concrete underneath the reactor. Concrete which is 2-3 metres thick.

We've had tests of this: enough people have dropped 100 tonne crucibles of molten steel over the years.

Funny, because I would say we have heard the worst case scenario many times, even though that information is meaningless and really is barely an intelligible concept. Everyone says worst case scenario is meltdown through containment, massive release of radioactive material into the atmosphere. But unless we know how likely it is, what does it matter? After all, as others have pointed out, the true worst-case scenario is that malevolent AI comes back from the future to torture us all for eternity.

We cannot know everything that can go wrong although it is natural to poke in that direction.
My personal fear is that nuclear paranoia stalls newer and probably safer power plants.

A central failure seems our squeamishness and irrationality at assigning a price to human life. The probability and magnitude of disaster scenaros can be much reduced if only we were willing to expend some lives early on in the situation.

Note that the radiation exposure to crews so far is much less than what is lethal. Not even close. If only we were more aggressive at initial damage control even at the cost of radiation mortality to a select few workers. The key obstacle in flooding has been the inability to get crews close. Even in helicopters.

We are more accepting of elevated cancer death rates than crew deaths at this moment.

Yeah, I don't understand why a country that invented the kamikaze pilot can't get some workers to be heroes by risking radiation exposure. Sounds easier than flying planes into boats -- and more heroic.

Presumably it's because the people in charge think the good they would do in possibly preventing further radiation release is not worth the single digit number of lives that would be lost.

That could be a bet on the expected severity of release, or on the probability of success, or both.

Good point about thinking of it as a calculated bet.

Or it is a principal agent problem. If there is a large radiation leak at this stage (aka Chernobyl) we can agree that the responsibility will be pretty diffuse or none at all. Who would you blame?

On the other hand, any brave plant manager taking the decision to deliberately send some firefighters into the no-go zone would be immediately berated for being a monster. Lots of moral outrage would presumably follow if these guys should die.

So rather than a calculated risk I suspect it is the typical bureaucratic ploy of never allowing precise accountability for any actions.

I sympathize with the question but the worst scenario would be that after

- a magnitude 9 earthquake,
- a large tsunami,
- several hydrogen explosions in the secondary containments of unit 1 thru 3

we could foresee a situation where six planes, full of expats, taking off from Narita, were to crash directly into each of the reactors. You could conceive that if they aim right, they could get some type of criticality and have six low yield nuclear bombs. The dispersal would be equivalent to about 60 atomic bombs. We have done that in the sixties in Nevada...

This scenario is ABSOLUTELY ABSURD. It provide good TV ratings for the 24 hours channels to imagine a worst case scenario but why would a technically competent person even discuss this ? There is nothing to gain out of that discussion. This is the reason most rational experts are reluctant to talk about a "worst scenario".

To technically competent people, the worst scenario is the release of any radioactivty off-site. Since this is already the case, the next worst case scenario is any additional release of radioactive material off-site.. We are in unchartered territory in that there seems to be an inability to do a simple thing: cool these things for a facility that is 200 feet away from the Pacific ocean.

We are in unchartered territory because:
- one incident in one of the six places of interest stops operations on the remaining five.
- the operating crew seems exhausted.
- we are not sure of the robustness of the cooling capabilities for each units.

Taking those elements into account, from the outside, you have to deal with some of things that are not said, i.e.we just learned yesterday that they were getting a power line restore power to the diesel generators (what;s taking so long!)

Oh I forgot, the worst case scenario would continue in that North Korea, seeing nuclear plumes coming their way, sends their nukes on Japan. The US would respond in kind and send nukes on North Korea. Except a few US nukes would be detected by the Russian and the Chinese detection system and now we have 5000 nuclear weapons thrown in the air aimed at Russia, China and the US. The worst would really be when an asteroid, the size of Texas, hit us 10 years after the nuclear winter subsides.

"But unless we know how likely it is, what does it matter?"

But that's what they aren't telling us, and it seems like (I said seems like) every day it's worse than they told us it would get. So, we tend to assume it's worse than they tell us it could get.

"the true worst-case scenario is that malevolent AI comes back from the future to torture us all for eternity."

Holy Shit! I think it may be time to panic!

What I'm wondering about is when they get the problem under control what is going to be the impact of all this water they are spraying into these reactors and containment pools with exposed uranium?

Isn't that water going to be radioactive waste spilling all over the place?

This water is considered high level waste and then usually go through some decontamination process.Everything that goes in is treated as radioactive waste. It's not dumped.

I should have been more specific, I understand it will be de-contaminated, but how are they going to collect it all?

The way they are spraying water all over the thing haphazardly with fire houses and even helicopters I can't see how they'll have anything but a huge mess on their hands.

I guess there isn't really any alternative at this point, but couldn't this be biggest culprit as far as a negative environmental impact (assuming they get the possible meltdown contained?)

Probably not. Look up the half-lives of the isotopes that would be released with the steam. As I recall (I read this on the Register's website, I think) the longest-lived isotope has a half-life of several minutes. It's practically gone after a quarter of an hour. (


even if everything goes wrong - nothing will happen now.

the heat from reactors decrease exponentially. after the reactor is switched off - it retains 5% of 'working' energy output - in few days it is just 0.1% - this cannot melt reactor, though can damage it. But reactors are designed for complete melting - the floor should keep it.

what we seen - hydrogen explosions - are due to zirconium chemical reaction ( the cladding is made of zirconium as it is most suitable metal for the purpose, though now there are substitutes - but it lasts for only 15 minutes being exposed in exterme heat ( >>1000C ) - so no more hydrogen build up for now.

all available radioactive gasses are already went to air.

and while iodine was a problem at Chernobyl - but there the graphite core was in fire - which made iodine and cesium to evaporate - no graphite is in this reactor - so no iodine flaring here.

so nothing really can happen. The worst we seen in Chernobyl - is very difficult to replicate even if one tries very hard - there was no containment, there was complete destruction of reactor, there was graphite in fire.

nuclear is dangerous - but it is not evil dangerous - or it will never even start to be built.

Barry Brook at Brave New Climate, who certainly has been no alarmist:

In sum, this accident is now significantly more severe than Three Mile Island in 1979. It resulted from a unique combination of failures to plant systems caused by the tsunami, and the broad destruction of infrastructure for water and electricity supply which would normally be reestablished within a day or two following a reactor accident. My initial estimates of the extent of the problem, on March 12, did not anticipate the cascading problems that arose from the extended loss of externally sourced AC power to the site, and my prediction that ‘there is no credible risk of a serious accident‘ has been proven quite wrong as a result. It remains to be seen whether my forecast on the possibility of containment breaches and the very low level of danger to the public as a result of this tragic chain of circumstances will be proven correct. For the sake of the people there, I sure hope it does stand the test of time.

Boldfacing his. For his links and the entire 3/17 morning update, read the whole thing.

See, "significantly more severe than Three Mile Island in 1979" isn't saying much. It's like saying "quite a bit smarter than Forrest Gump" or "lots poorer than Warren Buffet".

Anyway, I'd emphasize "the very low level of danger to the public" --- even in his forecast, there's not much danger to the public. Not anything like Chernobyl.

Well, yes, agreed: not as bad as the worst nuclear accident ever. It took Soviet-level incompetence for Chernobyl to happen (tho I'm sure that Terry Eagleton can explain why it's the fault of "the West," partially).

But too many people are saying "no danger," and I think that's pernicious.

Actually, I got the opposite feeling. I feel that the media are deliberately ignorant with the desire to hype the potential danger beyond anything that could actually happen. There is no government conspiracy to cover up the far worse than has already been published potential of these reactors, if anything, the government is providing voices to the media that are unashamedly biased against nuclear energy. Every worst case scenario printed so far has been through a nuclear "expert" of the rabidly anti nuke fringe.

The reporting I've seen for this crisis is much more balanced and realistic than the reporting that followed 911 and continued on for more than two years until after the US was committed to spending a trillion dollars to deal with the result from the horrible reporting on the threat from terrorism.

Reporting on previous nuclear disasters have generally under played the problems, with the exception of TMI. Chernobyl might have been about right with to risks overstated balanced by others that were ignored. And the things learned from Chernobyl haven't been well reported. For example, I didn't know until "leftist" NPR reported it, but after Chernobyl they figured out who to send into a high radiation environment based on the data from Chernobyl workers: older experienced workers who would die of old age before they suffered cancer from radiation, and, I'm guessing, get to enjoy retiring early because they have exceeded their lifetime exposure on the job.

Back to terrorism vs nuclear accident - far more people become experts on terrorism and what Saddam or Iranians or bin Laden will do or are capable of than we see nuclear disaster experts who speak as passionately and with such certainty as Rumsfeld, Cheney, Bush, et al.

this calamity I have wanted to know, “What is the worst that can happen at these nuclear sites? Suppose everything that could go wrong does go wrong: what then?” I still don’t know the answer. In what I have read so far–dozens of articles–nobody who knows what he is talking about has spelt

Here ya go, a "reasonable" worst case:

Worst case is that there is a complete nuclear meltdown, and some large group of fanatics forces each man, woman, and child to ingest a fatal dose of the stuff....along with all cherished pets.

I'm not sure what this accomplishes.

I'm a bit late to the party here, but this article has a good overview of the possible worst case scenario:

Comments for this post are closed