# Methods

## Release Rate Estimation

Estimation of the release rate is based on the principle that the atmospheric dispersion model can calculate a spatial distribution of relative values of deposition rates on the ground although their absolute values are unknown. According to this principle, the ratio of deposition rate to the release rate can be assumed to be the same for both measurements and calculations as follows:

where *S*m is the release rate used for model calculation (Bq h−1), *Q*r is the measured deposition rate (Bq m−2 day−1), and *Q*m is the calculated deposition rate (Bq m−2 day−1). The subscripts *t* and *i* denote the sampling time and sampling point, respectively. The release rate was estimated with Eq. (14.1) by solving it for *S*r (Bq h−1). To estimate a release rate at the time when discharged into the atmosphere, a release time was determined by calculating a fractional contribution that represents how much of the release during a unit-time period contributes to each sampling time and sampling point. The contributions were determined by using a series of calculations with an atmospheric dispersion model for every 12-h continuous release. The calculation for each release was carried out until the released radionuclides went out of the calculation domain.

Equation (14.1) does not strictly hold, primarily because of errors in the atmospheric dispersion calculation. For a given time, there might be more than two different release rate values estimated from independent monitoring data. In this case, a geometric mean was applied to estimate a single value for the time.

## Atmospheric Dispersion Model

A Lagrangian particle random-walk model (LPRM) [7] coupled with a nonhydrostatic atmospheric dynamic model, MM5 [8], was used to calculate the dispersion of the radioactive plume released from FDNPP. MM5 calculates the threedimensional wind field and the vertical diffusion coefficient. Radioactive decay, dry deposition, and wet deposition were calculated using LPRM. Iodine-131 and cesium-137 were modeled as passive tracers with half-lives of 8.04 days and 30 years, respectively. Dry and wet depositions were parameterized in terms of a dry deposition velocity and a washout (or scavenging) coefficient, respectively.

**Fig. 14.1 Location of deposition measurement site on calculation domain**

As a standard pair of these removal parameters, according to [9], the dry deposition velocity, *V*d, was set to be 1.0 mm s−1 and the scavenging coefficient, *Λ*, was expressed as *Λ* = *α*(*I*/*I*0)β, where *I* is the precipitation intensity, *I*0 = 1.0 mm h−1, *α* = 8.0 × 10− 5 s−1, and *β* = 0.8. Dry deposition velocity and *α* can vary within a range of approximately 0.1–10 mm s−1 and 10−6–10−3 s−1, respectively, depending on the physicochemical characteristics of the nuclides, gas–particle partitioning, and particle-size distribution of aerosols (see [10, 11] for an overview). The removal parameters were changed by a factor of 3 in the sensitivity analysis.

## Environmental Monitoring Data

To estimate the release rate, this study used the daily deposition measured at Chigasaki, Hitachinaka, Ichihara, Maebashi, Saitama, Sinjuku, Utsunomiya, and Yamagata with a 24-h sampling time from 18 March 2011 by MEXT [12]. The sampling sites are plotted in Fig. 14.1. The following criteria were set for data selection to eliminate the influence of resuspended radionuclides: the deposition rate of 131I and 137Cs is greater than 5.0 × 102 and 1.0 × 102 Bq m−2 day−1, respectively. Altogether, 56 measured deposition rates of 131I and 137Cs were adopted in this study.

## Calculation Condition

The calculation domain of the atmospheric dispersion was a 600-km square with a 6-km depth above the ground to cover most of Tohoku and Kanto Regions. The same physical processes of MM5 as the previous study [5] were used. For initial and boundary conditions and the four-dimensional data assimilation of the meteorological fields, the JRA-25 reanalysis data provided by Japan Meteorological Agency (JMA) and Central Research Institute of Electric Power Industry (CRIEPI) were used. Topography and land-use data were obtained from the United States Geological Survey global database. The radar-AMeDAS precipitation analysis data from JMA were used for the precipitation intensity in the wet deposition calculation. The MM5 calculation was conducted for the period from 09 Japanese Standard Time (JST), 8 March to 00 JST, 1 April. The dispersion of 131I and 137Cs from FDNPS started at 15 JST, 17 March and ended at 00 JST, 1 April. The release height was set to be 15 m above the ground. A constant release rate of 1 TBq h−1 was assumed.