Statistical evaluation of individual external exposure dose of outdoor worker and ambient dose rate at evacuation ordered zones after the Fukushima Daiichi Nuclear Power Station accident

Following the accident at the Fukushima Daiichi Nuclear Power Station, evacuation orders were issued for the surrounding communities. In order to lift the evacuation order, it is necessary to determine individual external doses in the evacuated areas. The purpose of this study was to determine the quantitative relationship between individual external doses and ambient dose rates per hour as conversion coefficients. More specifically, individual external doses of Tokyo Electric Power Company Holdings employees in difficult-to-return zone were measured broadly over a long period (fiscal year 2020 to fiscal year 2022). To obtain highly accurate estimates, we used not only ambient dose rates based on airborne radiological monitoring data, but also Integrated dose rate map data that had been statistically corrected to correspond to local ambient dose rate gradients on the ground. As a result, the conversion coefficients based on the ambient dose rate map measured by airborne radiological monitoring were 0.42 for the Evacuation-Order Lifted Zones (ELZs), 0.37 for the Special Zones for Reconstruction and Rehabilitation (SZRRs), and 0.47 for the Difficult-to-Return Zones without SZRRs (DRZs). On the other hand, the conversion coefficients based on the Integrated dose rate map which is a highly accurate dose rate map based on statistical analysis of various types of monitoring that have been studied in government projects in recent years, were 0.78 for the ELZs, 0.72 for the SZRRs and 0.82 for the DRZs. Using these conversion coefficients, the individual external dose can be estimated from two representative ambient dose rate maps provided by the government.


Introduction
The magnitude 9.0 earthquake and accompanying tsunami that occurred on 11 March 2011 severely damaged the Fukushima Daiichi Nuclear Power Station (FDNPS) and released radioactive materials into the environment.Figure 1(a) shows the results of airborne radiological monitoring conducted by manned helicopter after the accident.As shown in figure 1(b), the ambient dose rate has been gradually decreasing [1].
The Japanese government issued evacuation orders for areas where an annual additional individual external dose of 20 mSv [2] could be exceeded in 2011.The evacuation order zones were redesigned in 2012, they were Evacuation Order Cancellation Preparation Zones, Restricted Residence Zones, and Difficult-to-Return Zones [3].In 2015, the Japanese government indicated three requirements for lifting the evacuation order [4].The first is certain that annual cumulative doses estimated based on ambient dose rates will become 20 mSv or lower; the second is that infrastructure and living-related services indispensable for daily lives have been almost restored and decontamination work has progressed sufficiently centred on children's living environments; and the third, consultations have been held sufficiently among the prefecture, municipalities and residents.It decontaminated to lift evacuation order in areas excluding the Difficult-to-Return Zones.These efforts reduced the individual external dose in these decontaminated areas, so the evacuation orders were lifted in 2020 except for the Difficult-to-Return Zones.
The Special Zones for Reconstruction and Revitalization (SZRRs) were established in Difficult-to-Return Zones to start the process of decontamination in 2017.In 2021, the Japanese government announced its policy for the return home of residents to the Difficult-to-Return Zones excluding SZRRs (DRZs) [5].In the future, to realize the return of those who are considering the decision to return to the SZRR and those who wish to return to the DRZ, it will be necessary to suitable estimate individual external doses, and to lift evacuation order based on their doses.Here, we define the evacuation order zones and others.ELZ is defined as the evacuation order lifted zones.It refers to former evacuation order zones that were once designated as Evacuation Order Cancellation Preparation Zones and Restricted Residence Zones.SZRR is defined as Special Zones for Reconstruction and Revitalization.In some municipalities, the evacuation order has been lifted and the SZRR setting has been lifted, but in this paper, to distinguish it from the ELZ, it is defined as SZRR even after the evacuation order has been lifted.The difficult-to-return zone excluding SZRR is defined as DRZ.
After the FDNPS accident, the ambient dose equivalent H * (10) [6] is expressed as the ambient dose rate, and the personal dose equivalent H p (10) [6] is expressed as the individual external dose in Japan.For this reason, we use the same expression in this study.The estimation of individual external dose includes methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20] based on individual external dose data and methods [21][22][23][24][25][26][27] based on ambient dose rate data.Estimation of individual external dose using individual external dose data has been conducted by the national government, local governments, researchers, and others [7][8][9][10][11][12][13][14][15][16][17][18][19][20].The values of individual external dose measured using personal dosimeter at chest level in evacuation-ordered zones where radioactive cesium is widely distributed have been reported by Hirayama [28], National Institute of Radiological Sciences and Japan Atomic Energy Agency (JAEA) [29] respectively to be almost equivalent to effective dose.In addition, because it can reflect active patterns, it is possible to estimate close to the annual additional individual external dose.Such measured data is effective for exposure control on an individual basis, but for area control and future projections, conversion from ambient dose rates, for which data is abundant, is required.
When estimating individual external dose from ambient dose rate data, it is important to use an estimation equation that does not deviate from actual exposure.The Japanese government has been estimating annual additional individual external dose based on ambient dose rate, establishing and reorganising evacuation zones, and proceeding with decontamination and the lifting of evacuation orders.It has been reported that the estimated annual additional individual external dose using Japanese government's model is evaluated to be safer in comparison to the estimated annual additional external dose using individual external dose data [13,14,16,17].The equation in the Japanese government's model [21] assumes 8 h are spent outdoors and 16 h indoors, respectively.The outdoor ambient dose rate is used as-is for the outdoor ambient dose rate, and the indoor ambient dose rate is found by multiplying the outdoor ambient dose rate by a reduction factor of 0.4.While this simplified model is useful for policymaking, estimating an individual external exposure dose requires detailed conditions that take into account individual life patterns.
After the FDNPS accident, studies have reported estimating individual external dose using the ambient dose rate data.Fukushima Prefecture estimated individual external doses over the first four months following the accident from activity logbooks and monitoring post measurements [25].Matsuo et al evaluated the annual additional individual external doses of returnees using the Japanese government's model [26].Yajima et al [27] used ambient dose rate from airborne radiological monitoring and re-examined various parameters in the government's model to improve the accuracy of individual external dose, such as the reduction factor for each building, the conversion coefficient from ambient dose rate to effective dose, and actual time spent indoors and outdoors.However, the individual external doses on which dose estimation equations were based are values measured by D-shuttles, which measure and record individual external doses every hour.D-Shuttle is a lightweight personal dosimeter that can measure and record hourly doses, but its inability to record location information limits the information obtainable from measurement data.Thus, it is necessary to verify dose estimates using individual external dose that can be separated by location and area to improve estimate accuracy.In order to estimate individual external doses in evacuation-ordered areas with high accuracy, it is important to continuously measure individual external doses over a broad area and evaluate the quantitative relationship between individual external doses and the ambient dose rates used to estimate individual external doses.
The authors [30] measured individual external doses in fiscal year 2020 (FY2020) for Tokyo Electric Power Company (TEPCO) Holdings employees working outdoors in SZRRs or DRZs, and evaluated individual external doses and conversion coefficients, which were obtained from ambient dose rates based on airborne radiological monitoring to individual external dose.These results confirmed that the individual external dose in the DRZs tends to be higher than Evacuation-Order Lifted Zones (ELZs) and SZRRs, that ambient dose rates from airborne radiological monitoring used to calculate the conversion coefficients have been affected by land use conditions, and that the conversion coefficients were different for ELZs, SZRRs, and DRZs.Also, decontamination of the SZRRs has continued, so conversion coefficients might have changed in these zones.Because the research was just conducted in FY2020, continuous and extensive measuring is important for verifying conversion coefficients trends in DRZs.
In addition to reconsidering various parameters of the government's model, JAEA developed an Integrated dose rate map with Wainwright et al [31] to improve the accuracy of individual external doses.The Integrated dose rate map is a statistical correction of the measurements from the airborne radiological monitoring, in-vehicle monitoring, and fixed-point monitoring to match to backpack survey at the same periods and same locations [32][33][34].Furthermore, the Integrated dose rate map has the characterisation similar to the measuring data based on airborne radiological monitoring, such as providing the ambient dose rates for widely and seamlessly within 80 km from FDNPS.To calculate the conversion coefficient using the Integrated dose rate map, it is expected to realise estimation to the individual external exposure for changes in local dose gradients on ground level.It is possible to be useful in DRZs for policies to the evacuation orders lifted and for the decision-making to return home.However, it was not reported in previous research for the conversion coefficients from ambient dose rates to individual external doses based on Integrated dose rate maps in SZRRs, and DRZs.
Therefore, individual external doses were measured from FY2020 to FY2022 in order to evaluate conversion coefficients from ambient dose rates to individual external doses in DRZs.The conversion coefficients were calculated from individual external doses and ambient dose rates based on airborne radiological monitoring and the ambient dose rates based on the Integrated dose rate map.

Definition of individual external dose and ambient dose
The quantities related to external exposure are based on physical quantities such as absorbed doses in organs and tissues of the human body [6].These quantities are broadly classified into protective quantities, such as equivalent dose and effective dose, and operational quantities, such as ambient dose equivalent.The effective dose cannot be measured directly with measuring instruments, so it is estimated using measurable ambient dose equivalents such as ambient dose.A survey meter measures the ambient dose equivalent rates H * (10) (µSv h −1 ), and a personal dosimeter measures the personal dose equivalents H p (10).The value measured with personal dosimeter was integrated values (µSv).As mentioned above in section 1, in this paper, the value measured by a survey meter will be referred to as the 'ambient dose rate,' and the value measured by a personal dosimeter was referred to as the 'individual external dose.'It has been reported the radiation field caused in radioactive cesium in Fukushima has been the rotational irradiation field or the isotropic.In these irradiation fields, the value obtained with a personal dosimeter has been 30% lower than the ambient dose equivalent [17,[28][29][30], it has been known to be almost equivalent to the effective dose [28,29].Therefore, it is considered that the individual external dose measured by personal dosimeter to be an indicator of the effective dose due to external radiation exposure.In this study, we compared the case in which 'hourly individual external dose' and 'ambient dose rate' were used as measurable doses, and analyse the relationship between their doses.

Measurement of individual external doses
Measurements were taken from March 2020 to January 2023 of TEPCO Holdings employees working mainly in municipalities, including in DRZs.The measurements were taken outdoors during activities such as weeding and cleaning.All measurers were male.The number of persons for measurement was 201 in total (table 1).During the measurement period, decontamination was conducted in the SZRR, but not in other zones.Figure 2(a) shows the locations where doses were measured and the location of the SZRR, and figure 2(b) shows the land use map [35] around the measurement points.When working outdoors, personal dosimeters were worn on the chest and Global Positioning System (GPS) loggers were carried to measure individual external dose as well as latitude and longitude, respectively.The personal dosimeter was a DOSEe nano manufactured by Fuji Electric Co., Ltd., which measures and records at 1 min increments on the order of nSv (figure 3(a)).The GPS logger (K-18U) manufactured by ARKNAV International was used to measure latitude and longitude (figure 3(b)).Work locations, such as indoor and outdoor locations, were recorded by the workers themselves in their activity logbooks.
To identify the location where the workers stayed outdoors for a certain period of time, we used GPS data to locations where workers stayed at the same location for at least 5 min, and then confirmed the location was outdoors by comparing the GPS data with workers' activity logbooks.The individual external doses used for analysis were obtained from working outdoors locations where workers stayed at the same location for at least 5 min.The obtained number of datasets was 1884.On the other hand, they stayed at the office premises every day.The number of data was 320 at these outdoor places, which accounts for about 17% of the total.It was also confirmed, they did not sometimes wear the DOSEe nano.Therefore, it would cause bias in the analysis results.For this reason, the individual external doses used for analysis were excluded data at office premises measured in ELZs, SZRRs.The latitude and longitude information of the place where workers stayed was matched with map data entered into the Geographic Information System (GIS) to identify the zones where workers stayed.The number of datasets for individual external radiation doses at outdoor work sites was 1564 (table 1).The measurement sites vary each year, with relatively more data obtained at the DRZ in FY2022.

Ambient dose rates used for calculating conversion coefficients 2.3.1. Ambient dose rates based on airborne radiological monitoring
Some of the published air dose rates were measured at monitoring posts on the ground [36].But the setting locations for them were limited, it was difficult to estimate for external exposure doses the entire 80 km radius of the FDNPS.On the other hand, airborne radiological monitoring can seamlessly cover within 80 km radius in FDNPS.As the result, the Japanese government used airborne radiological monitoring data to redesign for evacuation areas [37].In other words, the airborne radiological monitoring results is role for importance in considering the lifting of evacuation order zones.In addition, previous studies [11][12][13][14][15][16][17] used airborne radiological monitoring data to evaluate the relationship between ambient dose rate and hourly individual external dose.Therefore, in this study, to calculate the conversion coefficients from ambient dose rates to hourly individual external doses, ambient dose rates from airborne radiological monitoring [1] were used.The results of airborne radiological monitoring are published as 250 m mesh resolution and converted to ambient dose rates at 1 m above ground level [38].Airborne radiological monitoring was not conducted within 3 km of FDNPS. Figure 4(a) shows an example of a distribution map created using the 2022 airborne radiological monitoring data utilised in this paper.

Ambient dose rates based on Integrated dose rate map
To calculate the conversion coefficients from ambient dose rates to hourly individual external doses, ambient dose rates [32][33][34] from the Integrated dose rate map were used.The Integrated dose rate map is a 50 m mesh resolution data.It is that this data reproduces the situation of ambient dose rates on the ground better than airborne radiological monitoring.Therefore, this paper compared the results evaluated using airborne radiological monitoring does data presented in section 2.3.1 against Integrated dose rate map data.Figure 4(b) shows, as an example, the ambient dose rate map created by the Integrated dose rate map for 2022.

Dataset used for analysis
Ambient dose rates from airborne radiological monitoring corresponding to locations where workers stayed were identified by matching GPS data with the 14th-17th airborne radiological monitoring data [1] using GIS.The obtained ambient dose rates based on airborne radiological monitoring data were 1517 out of 1564 points for the locations (table 1).The remaining 47 points for ambient dose rates were not obtained, because airborne radiological monitoring did not measure within 3 km of the FDNPS.For ambient dose rates, airborne radiological monitoring measurement data appropriate to the timing of each individual external dose measurement were used, and only physical decay corrections were made to match the timing of individual external dose measurements [39].For ambient dose rates from the Integrated dose rate map [32][33][34], data from the same fiscal year as the year of individual dosimetry were used, and only physical decay correction was performed to match the timing of individual external dose measurements.

Analysis method 2.4.1. Individual external doses at locations where workers stayed
In order to compare the individual external doses obtained for each place where workers stayed with ambient dose rates, a summation of individual external doses at each place was converted into an hourly individual  external dose by dividing by the time spent at the place in accordance with equation (1-1).Because the individual external doses received from natural radionuclides at each place could not be determined [40], the individual external doses received from natural radionuclides were not removed from the measured values.Correlation between hourly individual external doses and the respective ambient dose rates was confirmed by Spearman's ordinal correlation coefficient.This was because the present study does not consider parametric analysis where D h is the hourly individual external dose (µSv h −1 ), D m is the accumulated individual external dose (µSv) and t s (h) is the time spent, respectively.

Calculation of conversion coefficients from ambient dose rates to hourly individual external doses
Relative deviation was defined as an index to compare existing monitoring data with measured individual external doses.The authors [30] calculated the conversion coefficients using the least-squares method, but the values calculated using the least-squares method are affected by outliers.In this study, conversion coefficients were calculated using 50%tile values, which are less susceptible to outliers, and conversion coefficient was calculated using the relative deviation shown in equation (2-1).The relative deviation has the of being able to be quantitatively the relationship between hourly individual external dose and ambient dose rate.Substituting equation (2-2) into equation (2-1), (2-3) is obtained, and conversion coefficient can be calculated from relative deviation.The conversion coefficient (50%tile value) was calculated by substituting relative deviations (50%tile value) for individual external dose, ambient dose rate from airborne radiological monitoring data, and ambient dose rate from Integrated dose rate map, respectively, for each year and each area into equation (2-3) ) ) where RD is the relative deviation, CC is the conversion coefficient, D a is the ambient dose rate from the airborne radiological monitoring and the Integrated dose rate map at the site where workers stayed, respectively.

Comparison of conversion coefficients in each zone
Non-parametric statistical analysis was performed for this study because the measurement locations did not account for parametric statistical analysis.Tests for differences in conversion coefficient for each zone calculated based on airborne radiological monitoring and Integrated dose rate map were confirmed using the Steel-Dwass multiple comparison method.

The individual external dose and ambient dose rate
The individual external doses obtained were converted to hourly doses and shown as a histogram in figure 5(a).The range was from 0.33 to 56.6 µSv h −1 with a median value of 0.73 µSv h −1 .The ambient dose rates from the measurement points were identified using GPS data from the airborne radiological monitoring (figure 4(a)) and the Integrated dose rate map (figure 4(b)), respectively.The distribution of ambient dose rates obtained from the airborne radiological monitoring ranged from 0.14 to 13.0 µSv h −1 with a median of 1.51 µSv h −1 in figure 5(b).The distribution of ambient dose rate obtained from the Integrated dose rate map ranged from 0.09 to 11.1 µSv h −1 with a median value of 0.88 µSv h −1 in figure 5(c).We attempted to compare these data for the same location using relative deviation as an indicator.

The correlation between ambient dose rate and hourly individual external dose
In figures 6(a) and (b), the scatter plot shows correlation coefficient r calculated from all measurement points.The r is Spearman's rank correlation coefficient.It is 0.85 (p < 0.01 ) based on airborne radiological monitoring data, and 0.86 (p < 0.01 ) based on Integrated dose rate map data.In Figures 7(a   Comparing the relative deviation and conversion coefficient calculated from airborne radiological monitoring and Integrated dose rate map, the correlation between individual external dose and ambient dose rate.Table 2 shows the statistical parameters of relative deviation and conversion coefficient calculated based on airborne radiological monitoring data.Table 3 shows the conversion coefficients calculated based on Integrated dose rate map data.Table 4 shows the results of the Steel-Dwass multiple comparison method. The ambient dose rate and individual external dose measured above a height of 1 m above ground are the ambient dose equivalent and personal dose equivalent, respectively.Various values for conversion coefficients have been reported from operational quantities to individual external dose in previous studies.The conversion coefficients from ambient dose equivalents to personal dose equivalents have been calculated for radiation fields on a ground contaminated with radioactive cesium.Hirayama [28] reported that the conversion coefficient from ambient dose to individual external dose was about 0.7, and also reported that the individual external dose and effective dose were almost the same.Satoh et al [41] and International Commission on Radiological Protection (ICRP) [42] reported a conversion coefficient from environmental dose equivalents to effective dose on a ground contaminated with radioactive cesium, which was reported to be about 0.6.Some previous studies have shown that the conversion coefficients obtained from measurements using personal dosimeters and NaI(Tl) scintillation survey meters are 0.7 [17,29].The authors [30] investigated the conversion coefficient and confirmed that it was 0.7 by measuring individual external doses with DOSEe nano and ambient dose rates with NaI(Tl) scintillation survey meter, respectively.Since DOSEe nano is also used in this study, the ideal Relative deviation and conversion coefficient are expected to be −0.3 and 0.7, respectively.As shown in tables 2 and 3, the median conversion coefficient based on airborne radiological monitoring was 0.44, and 0.77 based on the Integrated dose rate map.Median of conversion coefficient based on the Integrated dose rate map was close to conversion coefficient 0.7 based on the fixed-point survey on the ground and about 10% higher.On the other hand, the Integrated dose rate map has been statistically corrected to backpack survey value on the ground.The backpack survey values have been reported to be 10% lower than fixed-point survey data at same periods [32][33][34].This is the reason for the conversion coefficient based on the Integrated dose rate map being about 10% higher than conversion coefficient based on the fixed-point survey on the ground.This suggests conversion coefficient based on the Integrated dose rate map is expected to be more accurately estimated for individual external dose than when based on airborne radiological monitoring.

Comparison of conversion coefficients of each zone 3.4.1. Conversion coefficients based on airborne radiological monitoring
Previous studies [11][12][13][14][15][16]30] have discussed conversion coefficient in central tendency such as mean and median.For this reason, as discussed in section 2.4.2, we evaluated conversion coefficient using the median value, which is not affected by outliers.As shown in tables 2 and 3, the median of conversion coefficient are 0.42 for ELZs, 0.37 for SZRRs, and 0.47 for DRZs.Previous studies [14,15,30] reported that the median of conversion coefficient was 0.16-0.50 in each ELZ and outdoor evacuation ordered area, respectively.Previous study was also similar to be tendency this study.The previous study and this study results are notably lower than the expected conversion coefficient 0.7.Because approximately 90% of measurements based on airborne radiological monitoring contributed to radiation sources within a 470 m radius range [43], airborne radiological monitoring values tend to have difficulty reflecting decontamination [14,16,37] and weathering effects [44][45][46][47] on the ground.On the other hand, about 90% of ground-based measurements were contributed by radiation sources with a diameter of 100 m [43], so these measurements reflect gradient dose Measurements by airborne radiological monitoring might have been higher than actual due to the topographical effects at mountainous regions [37,48].In particular, the DRZs had more mountainous areas than the ELZs and SZRRs, so the topographical effects might have been significant.
The conversion coefficient varies from area to area as dictated by these considerations.As shown in table 4, it was confirmed that the conversion coefficients calculated from airborne radiological monitoring were significantly different (1%) among all zones.The conversion coefficients were different in each of these zones because the state of decontamination and human activities varied according to the zone [30].It was reported the individual external doses measured on the ground have decreased in area of decontamination, while measurement data for ambient dose rates based on airborne radiological monitoring data were not confirmed to be decreased in these areas [14,16,30].This was because it is difficult for such ambient dose rate data based on airborne radiological monitoring to reflect decontamination and weathering effects on the ground.As a result, similar to previous study [30], it was considered the conversion coefficients for the ELZs and SZRRs decontaminated were lower than for the DRZs non-decontaminated.
The relationship between the conversion coefficients of SZRRs and ELZs is considered.Although decontamination was underway in the SZRRs, neighbourhood areas had not been decontaminated.It was considered that airborne radiological monitoring data would not decrease at decontaminated locations, and it was possible that the conversion coefficient measured at decontaminated locations was lower than in the ELZs.By contrast, in places where decontamination was not carried out, it was expected that individual external doses were higher than in places that had been decontaminated.So, the conversion coefficient for non-decontaminated places was considered to be higher than in the ELZs.In this study, because it was confirmed the conversion coefficient to be lower than in the ELZ, it was thought that more measurements were taken of decontaminated places.The conversion coefficient was confirmed to be lower in zones where decontamination has progressed and there were more human activities.This factor is affected by the difference in the extent that radiation source range contributed to measured values between those taken by aircraft and those on the ground.In other words, this indicates the difficulty that airborne radiological monitoring has in reflecting local dose gradient changes on the ground due to decontamination and human activities.Although the air dose rate is measured at a height of 1 m above the ground, the measured value is affected by approximately 90% of the radiation source contribution within a 100 m radius [43].Malins et al also reported on the relationship between distance and the radiation source contribution in ground measurements.At a height of 1 m above the ground, 80% of the measured values are influenced by sources within a 30 m radius.In other words, if there is a change in the distribution of radioactive cesium within 30 m, a dose gradient will occur.Previous studies [44][45][46][47]49] have reported that the radiation source distribution was different in each land use situations.So, it is considered that a dose gradient occurs under conditions where different land use conditions were close.Therefore, these results indicate that if measurements based on airborne radiological monitoring are used, conversion coefficients would have changed depending on conditions at the measurement locations.While they may be expected to be useful as the conversion coefficients for wide areas, conversion coefficients based on airborne radiological monitoring have been not stable.Therefore, if conversion coefficients based on airborne radiological monitoring are applied to estimate the approximate individual external dose for a zone, such as a DRZ, it suggests the need to understand for conversion coefficient.

Recommended individual external dose estimation method
In concluding this study, we propose a conversion coefficient for estimating individual exposure doses based on the Integrated dose rate map.Conversion coefficients based on the Integrated dose rate map was 0.78 for ELZs, 0.72 for SZRRs, and 0.82 for DRZs.These values were close to 0.7.This value of 0.7, as reported in previous studies, is based on a fixed-point survey, measured with a typical survey meter on the ground [17,29,30].The Integrated dose rate map data was statistically corrected to match the backpack survey data [31], so it was thought to be 10% higher than conversion coefficient based on fixed-point survey data [32][33][34].Therefore, in consideration of fixed-point measurements, the results were 0.71 for ELZs, 0.65 for SZRRs, and 0.75 for DRZs, which could be predicted to be even closer to the values of previous research.
In this study, it was confirmed that outdoor individual external doses can be estimated accurately with the Integrated dose rate map using individual external doses data from SZRRs and DRZs.This result suggests that Integrated dose rate maps can estimate correctly external exposure doses in SZRRs and DRZs.

Limitations
In this study, several limitations need to be considered.First, the data are not representative of the region because measurements were not taken in all ELZs, SZRRs, and DRZs throughout the region; second, the data do not represent daily life exposure in the area because they are data from workers in outdoors not from residents; third, the data were not removed radiation doses from natural sources, so there are uncertainties due to the variability of such doses; and fourth, the data do not include individual external dose data measured in indoors.To estimate more accuracy the individual external dose using the conversion coefficient in SZRRs and DRZs, we think that individual external dose data in indoor is obtained at these zones an issue for the future.

Conclusion
In this study, we evaluated the quantitative relationship between ambient dose rates and individual external doses.The conversion coefficients based on the airborne radiological monitoring were 0.42 for ELZs, 0.37 for SZRRs, and 0.47 for DRZs.All conversion coefficients based on airborne radiological monitoring in this study were lower than 0.7 at a height of 1 m above ground as reported previous studies.In contrast, when ambient dose rates based on the Integrated dose rate map were used, the values were 0.78 in ELZs, 0.72 in SZRRs, and 0.82 in DRZs.The conversion coefficients in each area were near 0.7 at a height of 1 m above ground.This indicates that estimation of individual external doses that uses the conversion coefficients based on the Integrated dose rate map data is expected to reflect local changes on the ground.We will continue to contribute to the reconstruction of Fukushima by elucidating actual exposure conditions through the measurement of individual external doses.

Figure 1 .
Figure 1.Maps show the ambient dose rate at 1 m above ground estimated based on (a) the 20 October 2012 airborne radiological monitoring and (b) the 3 February 2022 airborne radiological monitoring [1].

Figure 2 .
Figure 2. (a) Locations where individual external doses were measured.(b) Land use map around measurement locations [35]; the land use map for the period 2018 to 2020 was provided from Japan Aerospace Exploration Agency.

Figure 3 .
Figure 3. Instruments for measuring individual external dose and location.

Figure 4 .
Figure 4. Monitoring data used for dose estimation (a) Airborne radiological monitoring (b) Integrated dose rate map.

3 . 3 .
) and (b), the scatter plot shows correlation coefficient r calculated from data measured in the ELZs.It is 0.56 (p < 0.01 ) based on airborne radiological monitoring data, and 0.70 (p < 0.01 ) based on Integrated dose rate map data.In figures 8(a) and (b), the scatter plot shows correlation coefficient r calculated from data measured in the SZRRs.It is 0.58 (p < 0.01) based on airborne radiological monitoring data, and 0.69 (p < 0.01 ) based on Integrated dose rate map data.In figures 9(a) and (b), the scatter plot shows correlation coefficient r calculated from data measured in the DRZs.It is 0.78 (p < 0.01 ) based on airborne radiological monitoring data, and 0.74 (p < 0.01 ) based on Integrated dose rate map data.These results indicate a positive correlation between individual external dose and ambient dose rate.Conversion coefficient from ambient dose rate to individual external dose As shown above, the ambient dose rate maps officially presented by the government (airborne radiological monitoring and Integrated dose rate map) and the individual exposure dose data obtained in this study were found to be positively correlated.In addition, as shown in figures 6(a), (b), 7(a), (b), 8(a), (b) and 9(a), (b),

Figure 5 .
Figure 5. Distribution of hourly individual external dose, ambient dose rate based on airborne radiological monitoring and Integrated dose rate map.

Figure 6 .
Figure 6.Relationship between hourly individual external dose and ambient dose rate in this study.

Figure 7 .
Figure 7. Relationship between hourly individual external dose and ambient dose rate in ELZs.

Figure 8 .
Figure 8. Relationship between hourly individual external dose and ambient dose rate in SZRRs.

Figure 9 .
Figure 9. Relationship between hourly individual external dose and ambient dose rate in DRZs.

Table 2 .
Statistical parameters for comparative results of airborne radiological monitoring.

Table 3 .
Statistical parameters for comparative results of Integrated dose rate map.

Table 4 .
Test results for differences in conversion coefficient for each zone.