Thursday, April 28, 2011

Expected Doses Over a Year and Evacuation of Fukushima Towns

A major part of the definition for an INES level 7 event is the use of "extended" emergency measures, like evacuation. Now I'm paraphrasing, but the basic idea is that long-term evacuations are sufficient to make it that level of an event. Obviously, the worst radiological consequences one could think of, aside from people dying, is an area being made uninhabitable by humans for a long time. The case of the area around Fukushima Daiichi, again, will not be anything like Chernobyl, and the speculation is that people will start returning to some areas in a few months. The picture isn't so simple because areas within about 3 km of the plant might take significantly longer. Either way, the government is currently mandating evacuations specifically due to long-term exposure in contaminated areas.

Several sources have evaluations for doses that come from long term exposure. A while ago the DOE/NNSA team in Japan used their aerial data (I think) to create a map of year-long exposure. The assumptions are very important to point out and compare. Their work assumed:
  • 8 hour per day exposure outside
  • Includes inhalation dose and ground accumulation
  • Conservative assumptions
The 2nd point there doesn't distinguish it from other analysis IMO. Ordinary monitoring points will include dose from accumulated isotopes on the ground... because they are on the ground. But since this group did an aerial survey, it might have been necessary for them to do additional calculations for ground accumulation.

DOE NNSA Dose Evaluation for 1 year
This paints a very clear picture of the expected dose, and the red area shows clearly what the 2 rem area is. Not much detail is given in their presentation, but I find it likely that this is a good example of an 'inferred' dose analysis from larger, more sweeping, data and independent of Japanese government reported numbers. But we do have data from the Japanese government agencies to compliment this. The Asahi newspaper published a map that represents the 1-year dose (Capacity Factor also blogged about this).

MEXT data for 1-year dose around the plant, from Asahi
Units of mSv

Fukushima Dose Over 1 Year from Government Sources
The units in the upper-right say mili-Sievert, and to convert, 20 mSv is 2 REM. Pretty simple, and matches up well with the other source. The 30 km mark is shown on both graphs, but the 20 km is the area that actually had mandatory evacuations, although the 20 to 30 km sliver had an optional evacuation. By now, the protrusion of the high-dose area to the North-West should be sticking out like a sore thumb to you. I wish that I had more information about the source of this graph and the assumptions with it, but I don't.

A week or so ago, they expanded the evacuated area to include that NW protrusion. I'm reporting on this a little late, but I've been trying to lag the news a little bit in order to give a more complete picture. The Asahi offered a fairly good graphic of the areas the government has evacuated, expanded the evacuation to, and applied a special status to. I've applied some English markup to share it here.

Evacuated areas and provisionally non-evacuated areas
Asahi image, English alterations mine
Fukushima Evacuation Area Expansion from North West Plume
I tried to apply a fairly literal translation, but I think that may lead to some confusion. I believe that the blue areas are more-or-less "on alert", in case the situation worsened and releases picked up again (although pragmatically I don't think many people remain). I am confused by the "no entry zone" myself, as the entire 20 km zone is prohibited from entry by law to the extent of my understanding. But that may be a result of this image being dated. Anyway, the gray dotted lines represent what I will call "political divisions". Japan has 3 types of designations that roughly translate as city, town, village, and all of the areas bounded by the lines here represent one of these. Obviously, cities tend to have larger populations. The designation comes at the end of the Japanese name as a suffix, but I won't reproduce them every time, I'll just summarize them here:

Name of place +
  • 市 - shi - city
  • 町 - machi - town
  • 村 - mura - village

In order to get a scope of the evacuation and its impacts, I wanted to look a more closely at those affected areas. I looked a Japanese government database and want to share that info here. The following is a table I've put together from that source.

Economy - Million yen per year (domestic product), known from tax base in 2007
Population - People by census in 2005

Overview of Evacuated Towns/Cities, source
English Economy Population Households Evacuation
76,893 72,837 23,003 partial
Futaba 9,261 7,170 2,342 complete
Ookuma 15,230 10,992 3,547 complete
Tomioka 20,937 15,910 5,646 complete
Kawamata 14,977 17,034 5,351 partial
Kawauchi 2,516 3,125 965 partial
Hirono 6,749 5,533 1,791 partial
Naraha 9,013 8,188 2,647 partial
Namie 23,020 21,615 6,984 complete
Tamura 37,852 43,253 11,902 partial
Katsurao 1,208 1,625 459 partial
Iitate 4,469 6,722 1,740 complete

I think this is useful, at least, to make conservative estimates or frame the discussion about the impacts. Asahi reports similar numbers for the people evacuated and such, but I wanted to make an independent assessment since this is pretty universal stuff and articulating assumptions is critically important. Below are some of the columns summed.

Economy: 222,125 million Yen / year = 2.72 billion USD / year
People: 214,004 people
Homes: 66,377 households

Now, this reflects more than strictly "evacuated" areas, and that is much harder to assess. But then again, maybe that isn't of great interest. Minamisoma, for instance, has been gravely affected by the optional evacuation order. According to Asahi, however, the new mandatory evacuation order only applied to 7 households and 10 people in that city, which is the small yellow area in that area on the map. Seriously. This is a testament to just how non-uniformly Japan is populated - they have huge cities but very few people living in the mountainous regions. So, let's say for a minute that we don't include the 2 major cities on the periphery in summing up the people and economy. This is removing Minamisoma and Tamura cities.

Economy: 107,380 million Yen / year = 1.31 billion USD / year
People: 97,914 people
Homes: 31,472 households

All the numbers have been cut about in half. In fact, I don't even understand how this works, because the news had reported that about 200,000 people were evacuated with the original 20 km zone was established, which isn't consistent with the census numbers I'm reporting here. The only way the numbers climb to 200,000 people is if the relatively major cities that never had an evacuation order are included. Again, I think most people still left those places, and I know for a fact that they had problems getting supplies and managing the relief effort due to being within 30 km.

My Last Post on This Was Wrong

I realize that I made a very embarrassing error. I very quickly looked for a place to get the Linear-no-Threshhold coefficient from, this source, which was right, but I used it wrong. The smallest dose for which a measurable increase in cancer has been measured is 100 mSv, or 10 REM. The cancer risk increase is 0.5% to 1% for that dose, depending on the source. The source I quoted had 0.5% for 100 mSv, which is what the literature says, but this divides to 0.00005 cancers / mSv, and not 0.005 cancers / mSv that I so embarrassingly put. This means that while I reported 300 expected cancers, that should have been 3.


Comparison of Evacuation Cost and Health Cost

Now we have a some idea of the dose and risk from initial air-dose exposure as well as the long-term exposure for a year. The trade-offs for evacuation can now be quantified to some degree. Firstly, we can find the number of expected cancers, but in order to compare in some sense, that would have to be given an economic value. I've heard this addressed in classes before by looking at previous litigation dealing with life-or-death choices that automobile makers deal with in regard safety features. Payouts have been in the range of 5 million dollars in the past for compensation for death of a loved one. Obviously, no amount of money can replace someone we love, but risk is something that we make trade-offs for in our own lives. If I lived in that area, I would seriously consider the health trade-off with going back home, especially if I owned a farm or a business where the choice would impact my livelihood.

If we consider the evacuated 2 REM and greater area, I would pick about 40 mSv as a average dose by eyeballing it (for the full year). This only applies for the 97,914 population number (less actually). Let's say that they didn't leave - what is the value of the risk they would accept? I will use 1% increase cancer risk per 100 mSv and all those numbers.

(97,914 people) x (40 mSv / person) x (1e-4 cancers / mSv) = 391 cancers
(note this is similar to my previous wrong numbers, but because the coefficient is lower and the dose is higher, about canceling each other out)

(391 cancers ) x (5 million USD / cancer) = 1.96 billion USD

This number has all kinds of assumptions attached to it, but at least it is based on analysis that has fairly good radiation science behind it for dose and the number of people is fairly straightforward. This is the economic cost of staying, so to speak (my own evaluation of it).

What is the economic cost of leaving? Well, I think that the economic product of the area is a good number to start with, because we're at least fairly sure that individuals can not be as productive at their ordinary work when they've been evacuated from where they work and live. Obviously. But there are other factors, so many we can not consider them all. Either way, I will make the bold claim here that the cost of staying is comparable to the cost of leaving, based on the inferred health risk cost and the economic activity of the area alone.

Conclusion: The decision to evacuate is a hard decision with empirical analysis returning a toss-up, the errors in these two costs, 1.31 and 1.96 dwarfs the difference between them. In other words, the numbers show that:

(cost of staying) ≈ (cost of evacuating)

I'm mostly happy to point out, and back up, the obvious. But I should stress that this applies to the evacuation zones already discussed in this post. If it is a toss up for that area, then the cost of evacuating more distant areas is almost certainly higher than the cost of staying. Now granted, the government has supposedly made their decision based on regulation/policy that dictates that no member of the public should get more than 20 mSv / year in such an accident situation like this. But it is possible that that criteria itself is a fairly reasonable mark for the balance between the cost of staying and the cost of going.


  1. You wrote: (97,914 people) x (40 mSv / person) x (1e-4 cancers / person) = 391 cancers

    I suppose it should be:

    (97,914 people) x (40 mSv / person) x (1e-4 cancers / mSV) = 391 cancers

  2. Yes, that would be a careless error. Thanks for pointing it out.