Figure 1 shows the domain of the Lagrangian model (LM) with model terrestrial elevations, covering 138–143∘ E and 34–39∘ N. The model domain covers the southern part of the Tohoku region (the northern mountainous part of the domain, including Yamagata, Miyagi, and Fukushima prefectures), and includes the FDNPP and highly polluted areas such as the habitation-restricted zone (HRZ; 20–50 mSv yr-1) and difficult-to-return zone (DRZ; > 50 mSv yr-1; METI, 2012). It also covers the Kanto region (or Kanto Plain, the largest plain in Japan, approximately 120 km × 120 km), a highly populated region that includes low to moderately polluted areas such as Tokyo, Gunma, Tochigi, Ibaraki, Saitama, and Chiba prefectures.

The LM considers horizontal and vertical diffusion and advection, gravitational settling, dry and wet depositions, and radioactive decay. It uses simple parameterizations for dry and wet deposition schemes, and it can be driven by meteorological analysis datasets so that it does not require a meteorological model to predict detailed meteorological fields and variables. The model was designed to be easily handled and computationally efficient so that non-specialists of numerical simulations can conduct long-term assessments of atmospheric diffusion problems using their desktop or laptop computers. The LM was designed for rough budget estimates, as presented in the current study, or for sensitivity analyses using a large number of parameters (e.g., Groëll et al., 2014; Quérel et al., 2015; Girard et al., 2016), rather than for process-oriented analysis (e.g., Morino et al., 2013; Katata et al., 2015) or sensitivity analyses of the physical and chemical parameters of aerosols (Adachi et al., 2013). Details of each process and parameter are described in Appendix A. Statistical error of a Lagrangian simulation is inversely proportional to the square of the number of Lagrangian particles (LPs). The statistical accuracy of the current simulation setting is discussed in Appendix B.

The Grid Point Value-Mesoscale Model (GPV-MSM) of the Japan Meteorological Agency (JMA) was used for meteorological analysis to calculate the transport of LPs. It covers 120–150∘ E and 23–47∘ N and provides 3-hourly and 16 pressure levels of 3-D meteorological variables, from 1000 to 100 hPa, with a horizontal grid resolution of approximately 11 km (Δ longitude = 0.125∘ and Δ latitude =  0.1∘) and surface variables at twice the resolution of that for the 3-D variables (Δ longitude = 0.0625∘ and Δ latitude = 0.05∘). In the simulation, the whole model domain where LPs can travel is 138–143∘ E, 34–39∘ N and from ground surface to 500 hPa. For output of the model results, LP fields are converted to Eulerian concentration (Bq m-3) and deposition (Bq m-2) fields in the same horizontal space as the 3-D variables but are vertically allocated from the ground surface to an altitude of 1 km at 100 m intervals. The observed surface air concentration was compared with the simulated mean concentration at 0–100 m above ground level (AGL).

Ishizuka et al. (2016) developed a re-suspension scheme for radiocesium from bare soil based on measurements on the schoolyard at Namie High School, Tsushima Campus (denoted as Namie (Tsushima) in Table 1 and Fig. 1), in the DRZ. Fsoil=p20µmFM(1-fforest)B5mm(t), where Fsoil is the 137Cs dust re-suspension flux from soil (Bq m-2 s-1), p20µm is the surface area fraction of dust smaller than 20 µm in diameter against soil containing a maximum size of 2 mm particles and varies depending on soil texture (1.3 × 10-8 for sand, 0.19 for loamy sand, 0.45 for sandy loam, and 0.80 for silt loam), FM is the total dust mass flux (kg m-2 s-1), fforest is the forest area fraction, and B5 mm(t) is the specific radioactivity of surface soil (from the surface to a depth of 5 mm; Bq kg-1) as a function of time since March 2011. The formula is based on the assumption that dust particles smaller than 20 µm in diameter originating from the surface soil and to a depth of 5 mm were suspended and transported through the atmosphere. The surface area fraction was used for p20µm based on the assumption that radiocesium is bound to the surface of soil particles (Evrard et al., 2015). FM is formulated as being proportional to the cube of the friction velocity u∗ (m s-1) as described by Loosmore and Hunt (2002) and was applied to the dust emission: FM=3.6×10-9u∗3. Since u∗ is not available in GPV-MSM, u∗ was estimated using a wind speed at 10 m AGL by assuming neutral stratification conditions.

B5 mm (t) was derived from the combination of Bobs, the observed horizontal distribution of 137Cs deposition obtained from an airborne radiological survey (NRA, 2012; Bq m-2), and r5 mm, the surface soil activity ratio of 0–5 mm to 0–5 cm obtained from a vertical profile measurement of 137Cs in the ground soil at Namie High School (i.e., 0.57 Bq Bq-1), as B5mm(t)=Bobsr5 mmRdecay(t)5×10-3ρb, soil, where ρb, soil is the bulk density of soil particles per unit volume in the ground space (kg m-3) obtained from the porosity (0.4 m3 m-3) and the density of dust particles (2650 kg m-3). For Rdecay, which is the decreasing ratio of activity in the ground to its initial state (Rdecay(t=0) = 1), only radioactive decay was considered for the re-suspension calculation. The decreasing rate due to other processes such as land surface processes (e.g., runoff, erosion, percolation and all the processes resulting in migration of radiocesium in the soil and biota; Evrard et al., 2015; Matsuda et al., 2015) and decontamination were not considered here. Furthermore, suppression of dust emission due to soil moisture and snow cover was not considered. Therefore, it should be noted here that Fsoil in Eq. (1) is considered as the upper boundary of 137Cs re-suspension flux from surface soil. Effects such as land surface processes, decontamination, and dust emission suppression due to snow cover are extensively discussed in Sect. 5.3 using ambient gamma dose rate measurements obtained by the monitoring posts in Fukushima prefecture.

Equation (1) is a function of soil texture. The areal fraction of soil texture of the model grid was obtained from the database of the advanced research Weather Research and Forecasting model version 3 (WRFV3; Skamarock et al., 2008). Sixteen categories of soil texture (Miller and White, 1998) with a 30 arcsec resolution dataset can be obtained from the web after subscription at http://www2.mmm.ucar.edu/wrf/users/download/get_sources_wps_geog.html and were re-categorized into the above-mentioned four categories (i.e., sand, loamy sand, sandy loam, and silt loam) and interpolated to the LM resolution (∼ 11 km) as shown in Fig. 2a–c. Note that the loamy sand fraction is not presented because it is zero for the entire domain. The parameter fforest (Fig. 2d) was also obtained from the database of WRFV3 and was calculated based on the 24 United States Geological Survey (USGS) land use categories, which are constant over time. The land use category dataset can also be obtained from the above website.

Ishizuka et al. (2016) validated their dust emission module by using a 1-D model and observed the surface air concentration of 137Cs at Namie in the winter. After applying the module to our 3-D simulation, we found that the air concentration at Namie was underestimated by about factor of 5 for the same period. The module was formulated based on physical parameters (such as u∗) but contains parameters obtained at a single location (such as r5 mm and ρb, soil) and under a fixed atmospheric condition (Ishizuka et al., 2016), whereas ideally parameters in Eqs. (1)–(3) should have considered variations among locations and atmospheric conditions for the 3-D simulation. We simply multiplied the dust emission flux by 5 after adjusting the simulation results against the observed concentration of 137Cs at Namie in the winter. This is one of the simplest top-down approaches for adjusting the emission flux according to the air concentration. The module requires improvement in the future as more reliable parameters become available for various conditions and locations.

The re-suspension mechanism of radiocesium from land ecosystems remains unknown. Kinase et al. (2016) found substantial amounts of bioaerosols (rather than mineral dust particles) in samples collected for scanning electron microscopy in the summer, when the 137Cs concentration was high. This does not prove that the bioaerosol was carrying radiocesium but that it could be a potential carrier. The behavior of Cs in the environment can be inferred by analogy with K, a congener of Cs. Potassium is a necessary and abundant element in plants and circulates between land ecosystems. The addition of potassium fertilizer to a rice field in Fukushima significantly reduced the Cs content of the rice (Ohmori et al., 2014). Substantial amounts of K-salt-rich particles, possibly emitted by active biota such as plants and fungi, and coated with secondary organic aerosols, were observed in pristine Amazonian rainforest (Pöhlker et al., 2012). The major areal fraction of the contaminated area in Fukushima is covered by biota-rich mountain forests. Despite the differences in plant species and locations, it is plausible that water-soluble radiocesium circulating in the biota and soil in the forests was somehow re-emitted into the atmosphere and contributed to the surface air concentration. The re-suspension from the forest ecosystem was simply formulated as follows: Fforest=fforestfgreenrconstBobsRdecay(t), where Fforest is the 137Cs re-suspension flux from forest (Bq m-2 s-1); fforest is the forest area fraction; fgreen is the monthly green area fraction; rconst is the constant re-suspension coefficient (s-1); and, as in Eq. (3), Bobs and Rdecay are the observed 137Cs deposition (NRA, 2012; Bq m-2) and the decreasing ratio of activity in the ground, respectively. rconst is a tunable parameter to adjust the simulated air concentration of 137Cs to that observed. In the current study, rconst is set to 10-7 h-1 by adjusting the simulation data using the observed 137Cs concentration at Namie in the summer, when the re-suspension from soil was negligible due to the higher soil moisture content (following considerable rain) and lower wind speed. As with re-suspension from bare soil, only radioactive decay was considered for Rdecay and the other processes were not considered. The parameter fgreen was obtained from the database of WRFV3 and was originally derived from satellite Advanced Very High Resolution Radiometer (AVHRR) normalized difference vegetation index (NDVI) data (Gutman and Ignatov, 1998). Whereas fforest remains constant, the monthly averaged fgreen was used in order to reflect seasonal changes in the activity of the biota.

The Japan Atomic Energy Agency (JAEA)'s latest estimate of the primary emission from FDNPP, Katata et al. (2015), was applied for the emergency situation of March 2011 to evaluate the performance of the LM model against the horizontal distribution of 137Cs deposition of the airborne radiological survey (NRA, 2012; as shown later in Fig. 4a) and surface air concentrations measured at Tsukuba (Fig. 1a). We selected this inventory because it is JAEA's most up-to-date version. Based on an integrated understanding of environmental radioactivity, atmospheric dispersion, and the nuclear reactors, the JAEA team has carefully established a series of inventories for about 5 years, starting with Chino et al. (2011), followed by Katata et al. (2012a, b) and Terada et al. (2012), and finally the current inventory (Katata et al., 2015), which is substantially improved compared to the previous versions.

Ongoing emissions during the study analysis period after the emergency situation, i.e., January to December 2013, were obtained from the Tokyo Electric Power Co. Inc. (TEPCO) monthly mean emission flux from the reactor buildings (TEPCO, 2012, 2013, 2014a, b, 2015). Because only the sum of 134Cs and 137Cs was provided, the fractions of these two isotopes were calculated based on their half-lives and the assumption that their activities were equal in March 2011 (e.g., Katata et al., 2015), as shown in Fig. 3. The values range from 105 to 107 Bq h-1; however, for simplicity we set a constant value of 106 Bq h-1 in the current simulation.

In August 2013, unexpected re-suspension associated with debris removal operations was reported by TEPCO (2014c) and NRA (2014) and the gross amount was 1010–1011 Bq of 137Cs (TEPCO, 2014c; NRA, 2014; Steinhauser et al., 2015). The impact of this unexpected re-suspension is briefly discussed in Sect. 5.2 along with an additional finding, but this emission was not considered in the present LM simulation. In this study we focused on the ongoing and continuous emission, mostly from the natural environment, that is difficult to control.

Figures 4 and 5 show the observed and simulated distribution of 137Cs deposition in March 2011, and the scatterplot comparing the observational and simulation results. In the simulation shown in the figures, the “reference” sets used for dry and wet deposition parameters, namely the collection efficiency of aerosols using hydrometeors Ec (Eq. A1) and the dry deposition velocity over land vd (Eq. A3), were 0.04 and 0.1 cm s-1, respectively.

Since LM uses simple parameterizations for dry and wet deposition, as described in Appendix A, sensitivity tests were conducted for model validation, together with optimization of the deposition parameters. Table 2 summarizes the ranges of the deposition parameters for the sensitivity tests and the results of the 137Cs budget and statistical measurements between the observations and the simulation.

The parameter Ec was 0.05 for the JMA dispersion model (JMA, 1998) but the targeted species are different. For example, volcanic ash (particles larger than 1 µm in diameter) used for the JMA model was generally larger than the aerosols carrying 137Cs (around 1 µm in diameter observed in the downwind area, Tsukuba; Kaneyasu et al., 2012; Adachi et al., 2013). Since the inertia of these smaller 137Cs particles is likely to be smaller than that for volcanic ash, Ec could be smaller. The range of Ec was set as 0.02–0.06. The dry deposition velocity vd was selected as 0.1 cm s-1 for 137Cs in Furuno et al. (1999). The range for vd was set as 0.05 to 0.15 in the present study.

The emission inventory of Katata et al. (2015) amounted to 14.1 PBq from 12 March to 1 April 2013. The simulated deposition over the model domain (138–143∘ E, 34–39∘ N) ranged from 3.4 to 4.7 PBq, which is approximately 24–33 % of the emission from the FDNPP. Sixty percent of the total deposition occurred over land, for a total of 2.0–2.8 PBq, which is close to the observed value of 2.68 PBq, and the observed value is within the range of the sensitivity runs. Statistical measures such as the fractional bias FB, the correlation coefficient R (linear vs. linear), and FAx (fraction of the simulated values within a factor of x) are listed in Table 2. To find better combinations of (or to optimize) the dry and wet deposition parameters, sensitivity runs were screened based on the criteria FA10 > 0.9, FA5 > 0.7, R > 0.75, and an absolute value of FB < 10 %. Only one combination (Ec, vd)= (0.04, 0.1 cm s-1) satisfied the criteria, and thus this is referred to as the “reference” parameters. To evaluate the sensitivity (or uncertainty) of the re-suspension simulation for 2013 due to the deposition parameters, the range of the combination of parameters was set as (Ec, vd)= (0.03–0.05, 0.05–0.1 cm s-1) around the reference parameters (referred to as the “optimized range”) by excluding the parameters with the worse performances. The ranges of the statistical measures of the optimized runs are listed in Table 2. FB, R, FA2, FA5, and FA10 after the optimization had the ranges -0.18 to -0.036, 0.74–0.77, 0.26–0.30, 0.68–0.74, and 0.91–0.92, respectively. These statistical measures were comparable to those reported in previous multi-model comparison studies (R: 0.27–0.85; FB: -0.84–0.56; and FA2: 0.14–0.57, in SCJ, 2014; Draxler et al., 2015). The current model is thus shown to be sufficiently credible for the budget analysis in this study, despite the simple parameterization and the low resolution in space (∼ 11 km) and time (3 h).

In agreement with many previous studies, the simulated contribution of wet deposition was larger than that of dry deposition: the ratio of the amount of dry to wet deposition ranged from 0.12 to 0.23 for the optimized parameter ranges, indicating that the results were less sensitive to the dry deposition parameter. Generally speaking, R became higher as Ec became lower, whereas FAx became higher as Ec became higher for the various ranges of the sensitivity tests. Therefore, lower Ec did not meet the criteria of FAx and higher Ec did not meet the criteria of R. Consequently, after the optimization, the maximum values of the statistical measures were lower but the minimum values became higher, indicating that the optimization was successful in excluding the parameters with the worse performances (rather than selecting the best parameters). It should be noted here that the optimized deposition parameters are not necessarily physically valid but rather give simulation results consistent with the available observations. The results presented in this section indicate that the current LM simulation with these optimized parameters has the potential to reproduce consistent features of the radiocesium budget over the Tohoku and Kanto regions of Japan.

Figure 6 shows the temporal variation in simulated (red) and observed (black) 137Cs concentrations at Tsukuba in March 2011. The model reproduced the three major plumes arriving at Tsukuba on 15–16, 20–21, and 28–30 March; a plume on 23 March was not observed but only appeared in the simulation. The red shaded areas indicate the range of 137Cs concentrations obtained when the simulations were run using the optimized parameter ranges Ec= 0.03–0.05 and vd= 0.05–0.1 cm s-1. Due to differences in the parameters used, the surface air concentration could vary by approximately 1 order of magnitude in transported plumes that experienced wet scavenging along their pathway.

Figure 7 shows the observed and daily mean simulated (with the reference parameters) surface air concentrations at Namie and Tsukuba for the year 2013. The red, green, and blue lines indicate re-suspension from soil, re-suspension from forest, and emission from the FDNPP reactor buildings, respectively. Scatterplots between the observed and the simulated total concentrations are also shown in the figure and the statistical measures between them are listed in Table 3. The correlation coefficients (linear vs. linear) are low at the both sites, but the simulated and the observed medians are close to each other and FAx shows high values at the both sites. Consequently, the current simulation is credible enough for the quantitative assessment of the annual radiocesium budget.

As discussed in Sect. 2.2, note that the re-suspension flux due to the dust emission module (Ishizuka et al., 2016) is multiplied by 5 in this study in order to adjust to the observation level at Namie in the cold season (January to March, October to December). Also note that the re-suspension coefficient rconst in Eq. (4) was set as 10-7 h-1 in order to adjust to the observation level at Namie in the warm season (May to September). The emission flux reported by TEPCO varied from 105 to 107 Bq h-1 during the study period but we set it to 106 Bq h-1 for simplicity. We did not try to precisely adjust rconst to the observation by, for example, using inverse modeling, and instead we simply multiplied by power-of-10 values (except for dust emission, which is five), which are constant in time and space because (1) this facilitated straightforward interpretation of the simulation results by keeping the simulated variation solely originating from the variation in boundary conditions (i.e., emission and meteorology), and therefore (2) this provided simple but useful clues for understanding the re-suspension mechanisms, which remain unknown.

Using the dust emission module (which has a physical basis), 137Cs flux re-suspended from soil could account for the level of the observed surface air concentration of 137Cs at Namie in the cold season. Under the influence of the northwesterly winter monsoon, the surface wind speed is high over the contaminated area compared to the summer (as shown later in Fig. 10). Note that the flux might be a maximum estimate since it does not consider land surface processes (such as soil moisture, snow cover, or migration of 137Cs in the soil and biota) and decontamination, which could reduce the 137Cs re-suspension flux. In contrast, in the warm season, the estimated flux significantly underestimated the observation by 1 to 2 orders of magnitude due to the weak surface wind, indicating that the dust emission process may not be the sole process involved in sustaining the air concentration of 137Cs during this period. Introducing the 137Cs re-suspension component from forest with a resuspension coefficient of 10-7 h-1 and a monthly variation in the green area fraction (derived from NDVI) could quantitatively account for the observed air concentration together with its seasonal variation at Namie. Even though both the simulated re-suspension from soil and forests reproduced the quantity and seasonal variation in the background concentration (in other words, concentrations originating from continuously presenting emissions, such as natural emissions, and not accidental ones) at Namie, sporadic peak events, such as the daily mean 137Cs concentration exceeding 10 mBq m-3 as observed in June and August at Namie, were not simulated. Some specific re-suspension events might occur from the highly contaminated areas such as the premises of FDNPP (e.g., debris removal operations) or very close to FDNPP on these days, as indicated later in Sect. 5.2. The simulated 137Cs concentrations due to the monthly mean emission from the reactor buildings (i.e., 106 Bq h-1) significantly underestimated the observed concentration by more than 3 orders of magnitude at Namie and by 2 orders of magnitude at Tsukuba. Even the maximum estimate of 107 Bq h-1 does not reach the observed level. The emission from FDNPP may not have been the sole process sustaining the air concentration of 137Cs in 2013, supporting the discussion in Igarashi et al. (2015), which concluded that direct emission from the FDNPP played a minor role in the observed atmospheric radiocesium concentrations over Tsukuba during 2013–2014.

The observed air concentration of 137Cs at Tsukuba was about 1 to 2 orders of magnitude lower than that at Namie. The simulated difference between the two sites inside and outside of the contaminated areas was consistent with the observed difference. This finding indicates that the current LM simulation provided consistent features of re-suspension, transport, and re-deposition in the Tohoku and Kanto regions of Japan of 137Cs originating from Fukushima.

Figure 8 illustrates the simulated (with the reference parameters) annual amounts of total re-suspension and re-deposition of 137Cs, together with their ratios to the observed deposition (Fig. 4a). The simulated areal total re-suspended amount was 1.28 TBq, which was equivalent to 0.048 % of the total deposited amount, 2.68 PBq. The areal total re-deposited amount (with the reference parameters) was 0.22 TBq (0.18–0.23 TBq for the optimized range of the deposition parameters), corresponding to approximately 17.2 (14.1–18.0) % of the re-suspended amount deposited mainly in the Tohoku region, with the remainder being transported out of the model domain. Therefore, the regional mean rate in the decrease of the land surface 137Cs concentration due to re-suspension was estimated to be 0.040 (0.039–0.041) % yr-1

The amount re-suspended, excluding re-deposition (1.28 TBq minus 0.22 (0.18–0.23) TBq) for the year 2013, divided by the total deposited amount of 2.68 PBq.

The discussion in this section expands on that in Sect. 4.2. Figure 9 shows the same temporal variation as Fig. 7 but for simulated (using the optimized ranges of parameters) results for 137Cs from dust and FDNPP in winter (January to March) and from forest and FDNPP in summer (June to August).

In the winter, the simulated trend for dust agreed well with the observed trend (Fig. 9a), and the surface air concentration during this period was positively correlated with the surface wind speed in both the simulation (R = 0.88 on an hourly basis) and the observations (R = 0.32 on a daily basis). There was a sporadic peak in the observational data of 6.7 mBq m-3 from the 17 March at 13:00 local time (LT) to 18 March at 13:00 LT that could not be reproduced by the dust module, and this peak coincided with a plume arriving from FDNPP, as shown in Fig. 9c. Therefore, the observed peak could be accounted for by specific re-suspension events on the order of 109 Bq h-1 (the left axis divided by the right axis multiplied by 106 Bq h-1 in Fig. 9c) if they occurred on the premises of FDNPP or close to the area. There are also two events exceeding 2 mBq m-3, one in January and another in February. It is unlikely that the two peaks originated from the direct emission from FDNPP and likely that they originated from the dust emission because the observed peaks coincided with the simulated dust peaks (Fig. 9a) and not with the simulated peaks due to the FDNPP emission (Fig. 9c).

In the summer, the simulated quantity as well as the variation in the forest data agreed well with the observed data (Fig. 9b). Because there is only monthly variation in the simulated emission, the simulated daily trend solely originated from variations in the meteorological parameters (wind field, turbulent mixing, and wet scavenging). A significant peak of 60.4 mBq m-3 is observed from 14 August at 13:00 LT to 15 August at 13:00 LT. This observed level was approximately 2 orders of magnitude larger than the simulated level and 1 to 2 orders of magnitude larger than the observed level for the other days in this period. Therefore, continuous emission such as re-suspension from forest is less likely to be the origin of the peak. Because the observed peak and the simulated peak of 137Cs from FDNPP coincided (Fig. 9d), the observed level could be accounted for by specific re-suspension events on the order of 1010 Bq h-1 either on the premises of FDNPP or close to the area. There have been several arguments that the observed peaks in August 2013 were associated with debris removal operations at FDNPP, and this is discussed separately in Sect. 5.2.

Figure 10 illustrates the seasonal mean surface wind vector and surface air 137Cs concentration (simulated using the reference parameters) due to (a) dust re-suspension in the winter and (b) forest re-suspension in the summer. Due to the prevailing northwesterly winter monsoon, 137Cs was carried southeastward in the winter. In the summer, under the influence of the Pacific high-pressure system, 137Cs was carried inland. The monthly mean wind speed is high in winter and low in summer. The upper panels of Fig. 11 illustrate the observed and simulated (using the optimized ranges of parameters) total (from soil, forest, and FDNPP) 137Cs concentration at Namie and Tsukuba. The time resolutions of the simulation are daily for Namie and weekly for Tsukuba to be consistent with the sampling intervals of the two respective sites. The simulation successfully reproduced the quantity and variation in the observed background concentration at Namie and Tsukuba but could not reproduce the sporadic peak events observed at Namie, as discussed above. The simulation also significantly underestimated the observations at Tsukuba from January to March, 2013. Due to the northwesterly monsoon (Fig. 10a), there was less air mass transported from FDNPP to Tsukuba in the winter and therefore this underestimation is probably due specifically to underestimation of the simulated re-suspension around Tsukuba. The lower panels of Fig. 11 show the relative contributions of 137Cs from soil and forests at Namie and Tsukuba. The contribution from FDNPP was negligible throughout the year. At both sites, the contribution from dust was high (0.7–0.9) in the cold season and low (0.2–0.4) in the warm season due to higher surface wind speed in the cold season.

Figure 12a shows the observed and simulated (with the reference parameters) monthly Namie to Tsukuba 137Cs concentration ratios. The mean concentration ratio exceeded 100 in June and 200 in August due to the sporadic peak events. The monthly median would be relevant for comparing the background observation with the simulation results by considering only continuous emission sources. The values of the simulated concentration ratio and its seasonal variation agreed fairly well with the observed monthly median ratio: the observed and simulated annual means were 38.9 and 31.1, respectively. Figure 12b shows the monthly mean simulated re-suspension source area contributions to the 137Cs air concentration at Namie and Tsukuba. The re-suspension source area is defined as the model grid where the observed deposition amount exceeded 300 kBq m-2 (Fig. 4a) and includes the Namie grid (2300 kBq m-2). Eighty to 90 % of the 137Cs air concentration at Namie originated from the source region, and there was no clear seasonal variation in the value. In contrast, Tsukuba is characterized as a downwind region and there was clear seasonal variation in the source contribution ratio: high in summer and low in winter, due to the summer and winter monsoons, as discussed above. Nonetheless, the highest value at Tsukuba was 0.4 in July, and so more than half of the 137Cs concentration at Tsukuba originated locally or from areas other than the contaminated regions throughout the year. As shown in Fig. 11a and b, the variability in the simulated concentration at Tsukuba due to uncertainty in the deposition parameters was much larger than that at Namie. The differences in the variability indicated that the Namie and Tsukuba sites can be characterized as the source area and the downwind area, respectively: as the time required for the plume to move from the emission site to the observation site increases, the variability becomes larger due to the increased chance for the plume to experience dry and wet scavenging.

There have been several scientific studies and governmental reports on the unexpected re-suspension from FDNPP in August 2013. The high-dose-rate alarm was activated on August 19 within the premises of FDNPP associated with the debris removal operation. Matsunami et al. (2016) related the radiocesium contamination of brown rice in Fukushima in 2013 to this operation, whereas MAFF (2015) denied any association. The NRA estimated the 137Cs emission rate during the debris removal operation as 6.7 × 1010 Bq h-1 and the cumulative amount as 1.1 × 1011 Bq (NRA, 2014). TEPCO (2014c) estimated the emission rate during the operation as 5.8 × 1010–1.2 × 1011 Bq h-1 and the cumulative amount as 1.3–2.6 × 1011 Bq. Steinhauser et al. (2015) estimated the gross amount as 2.8 × 1011 Bq using measurements of weekly air filter sampling and monthly deposition, and a numerical simulation. Their estimates are similar in magnitude to our estimate (1010 Bq h-1; see Sect. 5.1) but the dates are different: our observed peak was earlier than the reported removal operation.

Our daily sampling showed a peak concentration (60.4 mBq m-3) from 14 August at 13:00 LT to 15 August at 13:00 LT before the reported operation but did not detect high concentrations in the 19 August (0.33 mBq m-3 for August 18 at 13:00 LT to 19 August at 13:00 LT and 1.2 mBq m-3 for 19 August at 13:00 to 20 August at 13:00 LT). Figure 13 shows the forward trajectories predicted by the LM (statistical locations of LPs) starting from FDNPP on 14 August (left) and 19 August (right). The sky-blue lines and red dashed circles indicate areas containing approximately two-thirds of the LPs within 1 km AGL: the extent of the area reflects horizontal and vertical atmospheric diffusion. The highest dose rate peaks were observed from 13:50 to 14:10 LT on 19 August at 2.8–8.3 km north and north-northwest of FDNPP on the leeward side, as reported by Fukushima prefecture (https://www.pref.fukushima.lg.jp/download/1/20130827moni.pdf.pdf). The forward trajectories on 12 August indicated that plumes during the debris removal operation traveled north-northwest to north of FDNPP (Fig. 13b and d), rather than towards the west-northwest, where the Namie site is located. On 14 August, on the other hand, plumes were transported towards the west (starting at 12:00 LT, Fig. 13a), and then to the north (starting at 15:00 LT, Fig. 13c) due to fast changes in wind direction, resulting in the simulated peak concentration shown in Fig. 9d during this period. Our simulation and observations together indicated that the same order of magnitude of 137Cs emission occurred on August 14–15 and on 19 August. Alarm activation was not reported on August 14–15, but debris removal operation was also conducted on August 14 and 16 (MAFF, 2015).

Figure 14 presents the time series of ambient gamma dose rates measured at the monitoring posts in Fukushima prefecture indicated in Fig. 1b. The data were obtained from the Nuclear Regulation Authority (NRA), Japan, website (http://radioactivity.nsr.go.jp/map/ja/index.html). A total of six monitoring posts, two from each of the three geographical areas (Hamadori coastal area, Abukuma highland area, and Nakadori valley area), were selected. There are tens to hundreds of monitoring posts in each municipality (village, town, and city) in Fukushima prefecture. We selected a monitoring post in each municipality by applying the following conditions: a post showing the highest dose rate of all posts in the municipality at the time of downloading (around 11:00, 28 December 2015), data are available since 1 April 2012, and the instruments are situated 100 cm above the ground.

In April 2012, the government of Japan designated the evacuation-directed zones as a difficult-to-return zone (DRZ; > 50 mSv yr-1; 9.55 µSv h-1), a habitation-restricted zone (HRZ; 20–50 mSv yr-1; 3.85–9.55 µSv h-1), and a zone being prepared to have the evacuation directive lifted (< 20 mSv yr-1; 3.85 µSv h-1) (METI, 2012). The two sites in the Hamadori area, Okuma and Omaru, have been designated DRZ (13.6 and 11.8 µSv h-1 on 28 December 2015). The dose rates at the two sites in the Abukuma area, Iitate and Kawamata, dropped below the HRZ level during the analysis period in this study (1.17 and 0.521 µSv h-1 on 28 December 2015). The dose rates in the Nakadori area are below 1 µSv h-1 (0.242 and 0.201 µSv h-1 on 28 December 2015).

The dose rate significantly dropped when the ground was covered with snow, in January and December 2013 in Hamadori and Nakadori, and from January to early March and December 2013 in Abukuma (the elevation of Abukuma is 500–1000 m and higher than Hamadori and Nakadori). Snow cover suppresses re-suspension due to dust emission. Namie (Tsushima) is located in Abukuma and the ground was covered with snow until early March (Ishizuka et al., 2016). The observed air concentration of 137Cs at Namie (Tsushima) was correlated with the wind speed in the winter from January to March, indicating that re-suspension during the period was mechanically induced. In the winter, dust re-suspension from outside Abukuma, such as from Hamadori and Nakadori, or from land surface where the snow cover was partly melted due to solar radiation, might be the dominant source contributing to the 137Cs surface air concentration at Namie (Tsushima) when the ground was covered with snow.

The first-order decreasing rates fitted by the least-squares approximation for the period without snow cover, May to October 2012 and 2013, are presented in Fig. 14. The rates ranged from 5.2 to 12.1 × 10-4 day-1. The monthly mean radioactive decay rates of total radiocesium (134Cs + 137Cs), determined by assuming that the activities of 134Cs and 137Cs were equivalent in March 2011, were 4.2 × 10-4 and 3.0 × 10-4 day-1 in April 2012 and March 2014, respectively, due to the difference in half-life of 134Cs and 137Cs (2.07 and 30.1 years, respectively). By assuming that the gamma dose rate primarily originated to radiation from the land surface radiocesium, the radioactive decay accounted for 35–50 % of the decreasing rate of total ground radioactivity; the exception was Shirakawa, where radioactive decay accounted for 55–80 % of the decrease. In other words, 50–65 % of the ground radioactivity decrease was likely due to land surface processes, decontamination, and re-suspension to air. As discussed in Sect. 4.3, the estimated decreasing rate due to re-suspension was 2.7 × 10-7–8.2 × 10-6 day-1, which is 2 to 3 orders of magnitude smaller than the decreasing rates due to the other processes (10-4–10-3 day-1).

It is difficult to distinguish the contributions of land surface processes and decontamination. By subtracting the radioactive decay rate (3.0–4.2 × 10-4 day-1) and the decreasing rate due to re-suspension (2.7 × 10-7–8.2 × 10-6 day-1) from the gross decreasing rate (5.2–12.1 × 10-4 day-1), the estimated decreasing rates due to land surface processes and decontamination ranged from 1.0 to 7.9 × 10-4 day-1. Matsuda et al. (2015) summarized the depth profiles of radiocesium in soil at more than 80 locations in Fukushima, including Hamadori, Abukuma, and Nakadori. They found that the radiocesium levels have been slowly migrating downward, with rates ranging from 1.7 to 9.6 kg m-2 yr-1 (equivalent to 1.1–6.0 mm yr-1 for a dust particle density of 2650 kg m-3 and a porosity of 0.4 m3 m-3, for example). Evrard et al. (2015) summarized that significant transfer of particulate-bound radiocesium occurs during major rainfall and runoff events (e.g., typhoons and spring snowmelt). Together with the relaxation depth–dose rate relationship provided by Saito and Petoussi-Hess (2014), the decreasing rate due to land surface processes such as downward migration, runoff, and erosion could be quantified and thus the decontamination effect could be separately extracted.

Issues that remain to be resolved in future research are summarized in this section. First of all, re-suspension from biota could be predominant in the warm season, but the re-suspension sources as well as mechanisms remain essentially unknown. Further study is needed to understand the mechanism based on field experiments and numerical simulations. The current estimation could account for the measured background concentration (0.1–1 mBq m-3) but could not reproduce the observed sporadic peak concentration (1–10 mBq m-3) at the Namie site. Further study is needed to identify the cause. The dust flux module has been validated at a single location. The module needs to be improved to be applicable to various land use and soil texture conditions. The decontamination may reduce resuspension afterward, whereas the resuspension may occur during decontamination-related work. This effect should be evaluated in the future. The current estimation was based on a single model simulation. Variability in multi-model simulations is rather large (SCJ, 2014; Draxler et al., 2015) and therefore multi-model assessment will be indispensable for long-term re-suspension analysis.