The press, blogosphere, and dKos have been echoing with scary headlines on a daily basis about the horrific events at Fukushima. However, you never see any actual analysis of what really matters: how many people will die because of this accident? Herewith a preliminary analysis.
We now have enough preliminary data to start making some decent first-cut estimates of the total population dose due to Fukushima. This is the real bottom line. All those scary stories don't add up to a hill of beans -- the only thing that matters for purposes of public policy is the casualty count. The financial costs of the accident will be carefully analyzed by power companies all over the world and will have their impacts on the financial planning of those companies; the public need not concern itself about such financial calculations because, if there's anything we can be certain of, it's that the power companies will keep a sharp eye on their bottom lines.
But OUR bottom line is this: how many people will come down with cancer because of this accident? We can estimate this number, because we have good data on the relationship between population dose and incidence of cancer, and we now have usable data on the total population dose.
What is that data? There are many sources. The Japanese government has been releasing radiation readings at several dozen sites every 3 to 7 hours for some weeks now; you can find that data here.
An excellent general source of data regarding the Fukushima accident can be found here. In particular, these graphs give us solid information for determining the total population dose. But the nucleartourist website is chock full of hard data on many aspects of the issue, and all of it is well-documented. I had spent some time compiling a list of such references, but when I saw what this guy had prepared, I gave up; his sources are excellent.
We also have aerial measurements of radioactivity from the US Department of Energy. These conform to the data from jaif, but have much higher spatial resolution. By combining the results from jaif -- which have high temporal resolution -- with the results from DOE, we can get an overall estimate of the total areal dose: the sum of all the radioactive exposure over all the affected areas.
I started with the jaif data. I eyeball-fitted the area under the highest curve (Iitate Village) with several rectangles and triangles, extrapolating out another few weeks. Then I calculated the total areas of those rectangles and triangles, obtaining a total dose of 16 mSv for the entire period.
Next, I turned to the DOE data. I fitted some more rectangles and triangles to the area enclosed by light blue, and obtained a total area of 13,000 km^2. Comparing a number of location values in the jaif data with the same locations in the DOE data, I obtained a correspondence of roughly 8 mSv total dose for a DOE reading of 1 mR/hr. This allowed me to arrive at the following correspondences:
DOE light blue zone: 0.12 mR/hr corresponding to 0.96 mSv total dose, 13,000 km^2
DOE green zone: 0.7 mR/hr corresponding to 5.6 mSv total dose, 3400 km^2
(However, about a third of the green zone is inside the evacuation radius, so we use only 2300 km^2)
DOE yellow and orange zone: ~6 mR/hr corresponding to 48 mSv total dose, 366 km**2 (However, about half of this zone is inside the evacuation radius, so we use only 183 km^2)
Next, we multiply the total dose for each zone by the total area of that zone, and add them all up:
0.96 mSv * 13,000 km^2 = 12480 mSv-km^2
5.6 mSv * 2300 km^2 = 12880 mSv-km^2
48 mSv * 183 km^2 = 8784 mSv-km^2
sum = 34144 mSv-km^2
Next, we use the population density of Fukushima Prefecture (154/km^2) to obtain the total population dose:
34144 mSv-km^2 * 154 people/km^2 = 5,258,176 mSv-people
Next, we apply the most pessimistic dose-rate relationship to assume that every 10,000 mSv will cause 1 case of cancer. This leads us to conclude that this accident will result in about 525 cases of cancer. Of these, about half will be fatal.
How accurate is this number? Not very. In the first place, whenever I had to make an assumption or guess, I used the most pessimistic reasonable value. For example, I assumed that the entire population was outdoors 24/7, when in fact most people spend most of their time indoors, where the dose is much lower. Second, the dose-rate value of 10,000 mSv/cancer is the most pessimistic value available. Third, there are many different nuclides of concern: I-131, Cs-137, Pu-239, and others. Each of these poses a different health risk. In particular, the I-31 radioactivity tends to bias the overall results in a pessimistic direction, but I cannot correct for this because I don't have good numbers for the percentage of radiation due to I-131.
My greatest concern with this calculation is with the linkage between the jaif data and DOE data. I suspect that a better result would be obtained by confining myself to the jaif data and carrying out a spatial integration based on the known distribution of emissions. Perhaps I'll do that calculation sometime; if so, I'll write up a new post.
There are lots of other problems with this estimate: the calculations are primitive and are based on many simplifying assumptions. Overall, I think we can take this value (525 cancers) as the upper limit of final cancers over the next 30 years. During this same period, approximately 138,000 people in Fukushima Prefecture will die of cancer, so the deaths arising from this accident will not be statistically detectable. For purposes of deciding between coal power plants and nuclear power plants, the best estimate for coal plants is several thousand deaths per coal power plant over its lifetime.
I anticipate three classes of response to this post:
1. The rational response: "This is a serious accident, but it doesn't change any of the bases for policy decisions regarding nuclear power."
2. The technical response: "Here is a technical detail you failed to take into account..." I expect most of these responses to be correct. This is a quick and rough estimate, not a final calculation. But if you want to apply your correction to my calculation and see how it affects the results, by all means do so; if it's sound, we get a better estimate.
3. The anti-nuclear response: "But what about this, and this, and this, and this..." all of which will be sensationalist facts that do not alter the calculation. As they said in "The Wizard of Oz", "Hydrogen explosions and spent fuel pond fires and water leaks, oh my!" All of those things contribute to the total population dose of radiation -- which is calculated here from actual data, not speculation.