*This piece assumes some familiarity with two radiation harm models, Linear No Threshold (LNT), and Sigmoid No Threshold (SNT). At a minimum, you will need to be familiar with LNT is Nonsense and A Sigmoid No Threshold Primer. The Policy Implications of SNT might also be helpful.*

Figure 1. Fukushima ambient air dose rates, 2011-04-29.

#### Imagining a fixed compensation scheme at Fukushima

Suppose a fixed compensation scheme had been enforced at Fukushima. We'd have enough radiation monitors around to be able to estimate reasonably accurately the ambient air dose rate anywhere in the surrounding area through time.1 We'd know the population distribution quite precisely. We'd know a great deal about the behavior of people: how much time they spend indoors, how much time they spend in paved areas, how much time they spend in open fields. We'd calibrate our estimates by distributing personal dosimeters to a sample of the population.2 We'd end up doing a pretty good job of estimating the daily dose for each person in the area for every day since the release.

I can do none of the above. Despite that, I have made a stab at estimating the total Lost Life Expectancy (LLE) associated with the radiation release at Fukushima. My guesstimate is based on the following heroic assumptions.

1) I cut the analysis off after 40 years.

2) We have ambient air dose rate measurements for some 120 measuring points in the area. From these measurements, we can estimate the minimum and maximum initial dose rate for each town in the plant's vicinity.

3) We have a pretty good idea of the isotopic composition of the release. Given the initial max/min air dose rates for each town, we can estimate the corresponding ambient dose rates through time. Figure 2 shows the dose rate range for Okuma, the hardest hit town right next to the plant. Figure 3 shows the dose rate range for Tamura City, a town 20 or more kilometers from the plant and away from the main radioactive trace to the northwest of the plant.

For the hard hit towns, the 40 year cumulative dose can be very large. LNT claims the only thing that counts is cumulative dose. But for models which recognizes our ability to repair radiation damage, what counts is the dose within the repair period, which SNT assumes is a day. For the worst of the worst, the initial ambient air dose rate is 8 mGy/d and within a week it is below 5 mGy/d. This corresponds to a probable initial max absorbed dose of less then 2 mSv/d,. This drops below 1 mSv/d, the pre-1950 tolerance dose rate, within a week. All these dose rates are well below the 20 mSv/d level at which we start to see harm in chronic situations.

Figure 2. Okuma ambient air dose range,

Figure 3. Tamura City ambient air dose range

4) We know the population at the time of each town. We split the town's dose rate range into 11 evenly spaced dose rates; and assume 1/11th of the town get each dose rate.3 A kind of linear interpolation over the town's population, assuming no evacuation. This is obviously a very rough approximation; but let's see where it takes us.

Once we have concocted a dose rate profile through time for everybody in the area, we can apply a radiation harm model to estimate the cancer incidence associated with that dose rate distribution. Our two contenders are Sigmoid No Threshold (SNT) and Linear No Threshold (LNT). Once we have the cancer incidence distribution, we can estimate each individual's Lost Life Expectancy, and compensate him or her for that loss.

An important variable here is the gray to sievert factor (Gy2Sv), which is the fraction of the ambient air dose that is actually absorbed by an individual. This will depend on each person's behavior: time spent indoors, type of building, outdoors activity, etc. At Fukushima, the Japanese assumed a Gy2Sv factor of 0.6. But when they gave everybody in Date-shi, just outside the evacuation zone, dosimeters, the measured average Gy2Sv was 0.15+/-0.03.\cite{ishikawa-2015} Golikov modeled the behavior at Chernobyl for 20 different subgroups. He also came us with an average Gy2Sv of about 0.2 but with a much larger range.\cite{golikov-2002} In a properly instrumented release, we should be able to come up with a decent estimate of a person’s Gy2Sv; but for now we will look at just two possibilities:

1) Gy2Sv = 0.20 as a likely average.

2) Gy2Sv = 1.00 as an upper bound.

#### Gray to Sievert = 0.20

Table 1 summarizes the results for Gy2Sv = 0.20. For compensation, I have assumed $350 per lost day, based on the US dialysis limit. I have used 12 Lost Life Years per fatal cancer, about the US average. For LNT these assumptions lead to 9500 Lost Life Years which is roughly equivalent to 238 air crash deaths assuming 40 years lost life per air crash fatality.4 At $350 per lost life day, the total LNT compensation comes to about 1.2 billion dollars. The three towns that were hit the hardest represent 70% of the harm.

The SNT numbers are entirely different. The total lost life is less than 2 years. This lack of mortality is consistent with UNSCEAR’s finding no detectable increase in cancer in the area 10 years after the release.\cite{unscear-2021} The total compensation is a paltry $250,000. The SNT harm is about 1/5000th of the LNT harm. The three hardest hit towns experience 97% of the harm. The LLE of the hardest hit group in Okuma is 140 minutes. Evacuation was a net benefit for nobody.

The timing of the harm is also quite different. Figure 4 shows that for SNT, 23% of the harm is experienced in the first 30 days and 55% in the first year. For LNT, 3% of the harm is inflicted in the first month and 18% in the first year. Half of the harm is incurred after 5 years. If you are an LNTer and decide to evacuate, expect a very long exile.

Figure 4. Okuma high end fractional Cancer Incidence (CI)

#### Gray to Sievert = 1.00

Table 2 assumes a Gy2Sv of 1.00. LNT is linear in the cumulative dose, so all the harm and compensation numbers go up by a factor of 5. SNT is more than quadratic in the dose rate. All the harm and compensation numbers are up by a factor of over 30. I suppose one could argue for a **regulatory** Gy2Sv of 1.00, on the grounds some one will approach that number; or all should be free to spend as much time outdoors doing whatever they want, even if that's not their normal behavior. If a release restricts that freedom, compensation is called for. **But do not confuse such legalistic logic with actual harm**. Even if we adopt such a charitable policy, the SNT compensation at Fukushima is less than ten million dollars. For LNT it's over 6 billion dollars.

#### Take Away

In this exercise, there is a 1000 fold difference between the SNT harm and the LNT harm at Fukushima. Of course, this illustrative analysis involved a great deal of hand waving and multiple heroic assumptions. But a far more accurate estimate of the dose rate profiles is quite unlikely to change this difference very much. If we adopt a harm model that recognizes our bodies' ability to repair radiation damage, the radiation risk of a nuclear plant release is easily insurable. If we stick with LNT which denies that capability, the computed radiation risk is probably uninsurable, even if we have a fixed compensation scheme. **For nuclear power to achieve its promethean promise, we need both a fixed compensation scheme and a reasonably realistic radiation harm model.**

And the sensors would have battery back up. At Fukushima, when the grid went down, so did the sensors.

This will have to be done carefully. It is an easy matter to blow up dosimeter readings by a factor of 20 or a lot more. A tiny piece of monazite held next to the instrument will do the trick.

This split into sub-groups by dose rate is required by SNT's non-linear nature. SNT gives far more weight to the high end victims than the low end. LNT does not care how a given dose is distributed.

This mortality is in the same ballpark at TenHoeve and Jacobson, who came up with a mean of 130 deaths with a range of 15 to 1100 using LNT and a plume dispersion model.\cite{tenhoeve-2012}

Following the link for SNT, I find "page not found".

I'm curious because in biology, most dose-response curves are sigmoids if you use a semi-log plot, which corresponds to a hyperbola if you use a linear rather than a logarithmic x-axis (i.e. it's a supra-linear model).

edited Nov 14, 2023I should have highlighted the Tamura City numbers in Table 1. At Tamura City, the PEAK dose rates were less than the AVERAGE dose rates in high natural background areas such as portions of the Kerala coast.\cite{nair-2009} Nair et all found no increase in cancer in the high dose rate districts. SNT is consistent with this non-effect. The SNT total compensation for the 40,000 citizens of Tamura is $105. But for LNT, the collective dose results in a total compensation of 29 million dollars.