Tuesday, April 12, 2011

Fukushima Daiichi to INES Level 7 - Some Numbers on Why

During a disaster, we should certainly strive to deliver the best available information as quickly as possible. If not done correctly, public distrust increases, and while directly avoiding sensationalism, others will step up their own sensationalism. The Fukushima Daiichi disaster was not as bad as it could have been, but it may fit the INES category 7 for nuclear emergencies, which is the most severe type of accident. The Japanese government has made very strong statements indicating it will announce they've upgraded it to that level. I find the borderline between the INES categories to have at least some amount of gray area, and the major component that is required for this to be a level 7 event is vaguely worded as widespread health and environmental effects, or the use of extended countermeasures. I will address a subset of those criteria in this post.

In assessing the impacts of low-level radiation on a large population, a linear no-threshold model is used to determine the predicted increase in cancer incidence. This simply means that the cancer from low radiation doses is extrapolated from the known cancer risk from high radiation doses that we know from things like post-Hiroshima studies and other historical nuclear events. This may or may not be correct, but past studies have either confirmed this or didn't have the statistical significance to tell. Because of that reason, I find this to be a correct and reasonable application of the precautionary principle, which deals with risks we accept to our health from things that are scientific unknowns. A common value for the this correlation for the radiation is:

0.005 cancers / mSv of radiation

That is to say, we assume (for better or worse), that any given radiation dose will cause a given number of cancers by multiplying by the above number. This number will be for expected fatal cancers, and can be applied to a large population. It is "expected" because cancers have a latency period of 2-60 years between when the exposure happens and when the cancer develops. It is my contention that seriously addressing this for nuclear accidents (and informing the public) is important for recognizing the full scale of the accident based on best-available-information.

If one uses this assumption for the Fukushima Disaster, how many cancers are expected to result from the accident? I have found no estimates for this, if you know of any let me know. So I had to make my own.

  1. Integrate the dose rate readings from start of the disaster to now at all cities affected by the spread of radiation - obtain total dose
  2. Multiply this by the population of the town or area to get the expected fatal cancers in that town or area
  3. Do this for all towns and areas affected by the radiation spread and sum them all up
This is fairly general and would apply for a more advanced study than what I'm able to offer here, but to be fully accurate, modeling of the transport of the radioactive particles through the environment is very important too, and completely neglected here. The concept of internal dose is a very major topic that will become more and more important as the scale of the accident comes into focus, and it is a notable and intentional omission in this post.

The above steps are actually fairly straight-forward once one has very well organized data for the dose readings. Thankfully, other productive netizens have done this work for me. See Phillip Mills's page with up-to-data readings and all kinds of goodies. This is of great help because they've provided comma separated files that make this an easy task, particularly, the task of integrating the dose rates over time at the recorded locations, as portrayed in their graphs:

Step #1: Get Dose Rates from Monitoring, Integrate to get Dose

Pragmatically, the dose rates are often given in μSv/h. That is, micro-Sievert per hour. It also so happens that dose rates are often recorded once every hour. That means the above task is accomplished by adding all the numbers. Yeah. Not that special. But sometimes they are not taken every hour, and appropriate adjustments must be made. The real world is, of course, complicated and messy. It is even more messy after a record-setting earthquake just hit your town, and that is the environment that these measurements were taken in. The following are 3 different sets of data are for the Fukushima Prefecture alone. They might look nice and well-behaved, but they are from very different kinds of information sources and do not follow the same methods at all.

Note: Doses are calculated from start of monitoring until April 8th or 9th.

These three data sets provide a wide range of monitor locations, but there are difficulties. To begin with, they are spaced out in an extremely non-uniform pattern. Some are redundant while other large areas lack readings altogether. I can help illustrate this to a limited extent by offering some maps from other crowd-sourcing radiation monitoring efforts, here I'll use RDTN and Pachube.

The Fukushima Prefecture border is slightly hard to make out, but just know that it goes very far into the mountains and the nuclear plants are about midway along the coast. These two projects are using most of the same sources of information that Phillip used (who I got information from). I just hope this gives a good general picture.

Although there are dozens of reported locations, I cut it down to just 15 that represent some definable population center, and when multiple readings were available I took the highest (actually doesn't matter as much as you would think). Of course, these did not add up to the entire population of Fukushima Prefecture, in fact, only about 1.4 million of the people in the prefecture of 2.0 million are represented by a radiation reading in the data set. So when I multiply the expected dose to an individual by the population, I also multiply by 2.0/1.4, doing so introduces the assumption that the average dose of the unrepresented population is the same as the represented population. This overestimates in the areas not important enough to take readings in, and underestimates in areas in the exclusion zone (although the population numbers are blown there anyway). Here is what I got.

Interpretation: Both high-population and low-population cities and towns had high doses, but long term health risk is mainly accounted for in large cities because of the large population exposed.

I could not give enough provisos for the interpretation of this chart with 10 more pages. I offer it only because I have not seen anyone else offer this information. I expect a highly modified pictures when official sources address the issue, but this is a good first shot.

Fukushima city, where the largest expected collective cancer risk lies, expects about 34 additional cancer deaths from the radiation from this accident. I just want to point out that the city has a population of 290,000 people, which brings me to my first point: We will probably never detect an increased rate of cancer incidence from the Fukushima disaster. Ever. Even if the type of cancer is narrowed down, the statistical noise will probably swamp those 34 deaths. It is still tragic, but in terms of assessing the damages, Fukushima city is the best bet for detecting long cancers caused in the general public, and it is simply not going to happen.

Finally, the larger region: People in Ibaraki Prefecture received notably a high dose and Tokyo received several times background for a while, what are the wider consequences? I applied a similar methodology for neighboring prefectures of Ibaraki and Tochigi, again from Phillip (thank you again). In order to obtain a "high" value, I took the location with the highest dose and assumed the entire population was exposed to that.

Predicted Long Term Cancer Deaths from Fukushima Daiichi Radiation Releases



Could be much lower due to evacuations, data done by convolution

Probably reliably close to high number, due to population distribution

Convolution by city looks good, largest unknown is unlisted cities
Kanto plus Tohoku126120

Fairly reliable minimum attainable considering only metro Tokyo area


I'll provide just a few notes about this. The same method as described for Fukushima Prefecture was applied for Ibaraki and Tochigi, which was actually easier since there is less information. Then I wanted to include effects on the larger population, so I integrated dose rates in Tokyo, but only for 3 locations. Out of those locations, they varied from 0.05 mSv to 0.06 mSv so I wasn't strongly concerned about the maximum versus average, the main problem is extrapolating this number for a larger area. It is clear from my general knowledge and sense about this (see prior posts) that the entire Kanto region (Tokyo metro, if you will) was subject to similar doses from the passing clouds. Now, it seems absurd to extrapolate to the entire Kanto and Tohoku regions on this basis, but it isn't. The Tokyo metro area is around 30 million, and even including all of Tohoku (everything North of Kanto on the main island) only adds 10 million. For the level of detail I'm concerned with, that 10 million at the same low dose really doesn't matter much to me. What I'm more concerned about is the mid-range doses delivered to prefectures not next to Fukushima, but one over (Miyagi for instance). That can affect the numbers some, but no greater scale than what is already seen on the table, and the entire reason I used Ibaraki and Tochigi in the first place is because I could see on the plots that they had high levels.

Here I leave with the final word. Chernobyl was estimated at 4,000 to 6,000 total premature deaths due to the radiation spread. Three Mile Island is estimated at around 1, just 1. Fukushima is somewhere in the middle - we already knew that. Now, I wouldn't be surprised to see a tally of 20 people or a final tally of 1,500 people. Mainly, I don't know where people were, and I don't know how much internal dose they received. These are still people's lives, and I think it allows for classification in the same stratum of accident that Chernobyl was. Aside from these, the complications of relief efforts also had a cost in human lives that I believe could be on a similar scale as the premature cancer deaths. Then there are industries and farmers who lost their livelihood and the people who are wondering when they can return home. Mainly, I want the true cost to be seriously considered by the reasonable people out there.


  1. This analysis is based on the linear, no threshold assumption. I don't agree with that assumption, as there is too much evidence to the contrary. But let's leave that aside for the moment.

    A more complete analysis would also include deaths avoided by Fukushima Daiichi complex during its operational life. Had the reactors not been built, it is almost certain that coal-fired power plants would have been built instead. Those coal-fired power plants would have caused deaths in their normal operation due to emissions of particulates, sulphur dioxide, oxides of nitrogen, etc. Plus additional deaths would have come from coal mining. I wonder if the number of deaths avoided by building nuclear power plants might not outweigh the deaths from radiation exposure, even using the linear, no threshold model.


  2. "0.005 cancers / mSv of radiation"
    Do you mean 0.005 cancers per mSv of radiation AND PER INHABITANT ?

  3. donb,

    If one compares the deaths caused to the public using nuclear power versus not using it in general, the numbers unambiguously favor nuclear. By a long shot. If the Fukushima I Plant ITSELF was a coal plant, would it have killed more people? Yes. Not only that, I will show that if FFI was a coal plant, it would have killed about the same number of people JUST LAST YEAR!

    Now, I'm going to take the 24,000 estimate for preventable deaths in the US due to coal power. In 2009 FFI produced 29.9 TW-h of energy, averaging to 3.4 GW. Coal in the US produces 227 GW average power.

    If FFI was a coal plant during 2009, it would have caused this many early deaths:

    24,000*3.4/227 = 360

    Just think about that. The nuclear disaster of our generation probably caused as many untimely deaths as if the same size coal plant had operated for just one year. The worst year for all nuclear plants all over the world, for a generation, is an average year for a coal plant. Now, Japan tends to have better technology than the US, but they still have coal plants and they are higher density than the US, so I find this number to still be close to the real value.

    The LNT model is what it is. Some people believe that higher background radiation levels, in fact, should be avoided. I can't argue much with that. Again, this is based on the precautionary principle. Even if the analysis right up to the LNT assumption is completely perfect, I'm not saying that those people were actually killed. Instead, I'm saying that for the purposes of the civic discussion about energy we should make decisions assuming that number to be a reasonable estimate. Note that the only way to dethrone this approach is to have an alternative model with broad acceptance. We do not have that.

  4. Alan, thanks for the additional analysis. It certainly puts things in perspective.

    In a case like the Fukushima plant disaster, the potential victims are more easily identified than in the case of (say) someone dying from an asthma attack caused by fine particulates from a coal plant. We then arrive at the dilemma similar to that of spending $X to support an orphan drug to keep an identifiable individual alive, vs. spending the same $X on a road improvement that saves 10 lives when those traffic accidents don't happen. The lives saved cannot be identified in the second case. The first case tugs at our heart-strings, and may be the one more likely to be funded.

    In addition, radiation is 'mysterious' and thus more frightening. It is interesting how a cancer death 20 years down the road is somehow more severe than a death right now from an asthma attack.


  5. Dear Alan,
    I am very interested (by simple intelectual curiosity)in your research, which follows the same orientation that led to the 4000 deaths estimate for Chernobyl. I know, the LNT theory is not confirmed, but I am not here do discuss that. By the way, I am a Power Systems Professor in Lisbon, Portugal, 59 years old.
    My question is: there is a distinction between radioactivity emission (Bq), exposure, and ingestion.
    The measured Sv are for the soil and the air, which is what can be easily measured. However, it is not sure that all that radioactivity in the environment will be ingested or inhaled by the people. You have to consider also some probability function that maps the present radioactivity to the really absorbed one. This seems to me to be a very important point, perhaps capable to partially explain the difference between the estimates for Chernobyl and the actual verified deaths (very few).
    Searching for this topic, I found a PhD thesis on it, which may deserve your atention, here: http://www.zsr.uni-hannover.de/arbeiten/drharb.pdf
    As you can see, the most important elements are I-131, Cesium and Stroncium. I-131 can be prevented by evacuating the areas for a few months, as is being done. Cs is in the air, but probably will not be inhaled all the year long, since people travell.