Great efforts have been made to simulate atmospheric
pollutants, but their spatial and temporal distributions are still highly
uncertain. Observations can measure their concentrations with high accuracy
but cannot estimate their spatial distributions due to the sporadic
locations of sites. Here, we propose an ensemble method by applying a linear
minimum variance estimation (LMVE) between multi-model ensemble (MME)
simulations and measurements to derive a more realistic distribution of
atmospheric pollutants. The LMVE is a classical and basic version of data
assimilation, although the estimation itself is still useful for obtaining
the best estimates by combining simulations and observations without a large
amount of computer resources, even for high-resolution models. In this
study, we adopt the proposed methodology for atmospheric radioactive caesium (Cs-137) in atmospheric particles emitted from the Fukushima Daiichi Nuclear Power Station (FDNPS) accident in March 2011. The uniqueness of this approach includes (1) the availability of observed Cs-137 concentrations
near the surface at approximately 100 sites, thus providing dense coverage
over eastern Japan; (2) the simplicity of identifying the emission source of
Cs-137 due to the point source of FDNPS; (3) the novelty of MME with the
high-resolution model (3 km horizontal grid) over complex terrain in eastern
Japan; and (4) the strong need to better estimate the Cs-137 distribution
due to its inhalation exposure among residents in Japan. The ensemble size
is six, including two atmospheric transport models: the Weather Research and
Forecasting – Community Multi-scale Air Quality (WRF-CMAQ) model and
non-hydrostatic icosahedral atmospheric model (NICAM). The results showed
that the MME that estimated Cs-137 concentrations using all available sites
had the lowest geometric mean bias (GMB) against the observations
(GMB
Great efforts have been carried out to simulate atmospheric pollutants, but the spatial and temporal distributions of simulated pollutants are still highly uncertain (e.g. Fuzzi et al., 2015). In contrast, observations are the most reliable method of monitoring the concentrations of atmospheric pollutants with high accuracy, but their spatial networks are usually sporadic. Even if these observations densely cover the target area, they cannot reveal the pathway of pollutants from the source to the sink. To analyse the measurements and deeply understand their behaviours in the atmosphere, we need to improve atmospheric transport models as well as optimal interpolations using observations. To understand the model performance, we have executed model intercomparison projects (MIPs) or multi-model ensembles (MMEs), which provide more reliable results than those by a single model for weather forecasting and climate prediction (e.g. Stensrud et al., 2000). To develop the optimal interpolation, we have also analysed the error and the variance between the simulations and observations to estimate more realistic distributions of the target materials (e.g. Rutherford, 1972; Talagrand, 1997; Robinchand and Ménard, 2014).
The MME technique is applied for weather forecasting (Stensrud et al., 2000; Gneiting et al., 2005), climate projections (Knutti et al., 2010; Taylor et al., 2012), short-lived climate forcer assessments (Lamarque et al., 2013; Myhre et al., 2013), air quality forecasting (Solazzo et al., 2012; Sessions et al., 2015) and atmospheric dispersion predictions (Draxler et al., 2015; Sato et al., 2018). The members of the ensemble are widely spread for the use of various numerical models with perturbed initial conditions and various physical and chemical modules. The ensemble method is generally divided into three types: pure average scheme (equal weighting), weighting scheme with all members and selected scheme with reduced members. The pure average method is a popular method for MME-based climate studies according to the concept of “one model, one vote” (Knutti et al., 2010; Weigel et al., 2010) or evidence of improvements in the concentrations of pollutants in air quality and atmospheric dispersion simulations (McKeen et al., 2005; van Loon et al., 2007; Sessions et al., 2015; Kitayama et al., 2018). The weighting scheme, especially with a relatively smaller ensemble size, can be adopted to eliminate the common biases and improve the ensemble results in the weather forecast (Krishnamurti et al., 1999), climate studies (Haughton et al., 2015), air quality forecasts (Casanova and Ahrens, 2009) and atmospheric dispersion predictions (Nakajima et al., 2017; Sato et al., 2018). The selected scheme is used in the air quality simulations (Solazzo et al., 2012, 2013; Solazzo and Galmarini, 2015a) and the atmospheric dispersion simulations (Riccio et al., 2012; Solazzo and Galmarini, 2015b). The use of the non-pure average scheme, i.e. weighting and selected schemes, is increasing, and the technique is a useful tool for estimating the reliable results among MMEs (Kioutsioukis et al., 2016).
In this study, the MME with the weighting scheme that minimizes the variance between the simulations and observations is carried out to derive a more realistic distribution of radioactive caesium (Cs-137) at the surface. The Cs-137 in atmospheric particles was emitted from the Fukushima Daiichi Nuclear Power Station (FDNPS) accident in March 2011. Thus far, many atmospheric dispersion models have simulated Cs-137 aerosols (e.g. Chino et al., 2011; Morino et al., 2011; Stohl et al., 2012), and several MIPs were conducted (Science Council of Japan, 2014; Draxler et al., 2015; Sato et al., 2018). Under the MIPs, the MMEs provided reliable results in the assessed models (10 or more). However, ordinary modellers cannot easily carry out such MMEs using only their own models. For such situations, we propose a useful method for limited ensemble size in MMEs by applying an analytical optimization to determine the weights for the ensemble. The optimization is based on a linear minimum variance estimation (LMVE), which is a classical and basic type of data assimilation similar to the Kalman filter (e.g. Talagrand, 1997; Kalnay, 2003).
This approach is unique from other MMEs of other species based on the
following four factors. (1) The observed Cs-137 concentration near the
surface is available at approximately 100 sites, providing dense coverage of
eastern Japan (Tsuruta et al., 2014; Oura et al., 2015). Since plumes
including Cs-137 particles are transported and diffused very
heterogeneously, dense measurements are essential to capture such plumes.
(2) The spatial distribution of Cs-137 distribution is captured relatively
easily since Cs-137 is emitted from the point source. For example, the PM
In a previous study, Nakajima et al. (2017), which comprises the basis of our proposed method, was applied using multi-models, including the Weather Research and Forecasting – Community Multi-scale Air Quality (WRF-CMAQ) model (Morino et al., 2013) and non-hydrostatic icosahedral atmospheric model (NICAM) (Goto et al., 2018), to derive a better Cs-137 distribution. However, the estimation is still uncertain, and its ensemble results were not greatly improved, which was mainly because the results of the original model were still highly uncertain. In addition, Nakajima et al. (2017) did not discuss the availability of the use of LMVE for more than three members and the uncertainty of the relevant parameters in LMVE. After the study of Nakajima et al. (2017), both models were further developed by using a finer horizontal resolution (3 km) grid and by nudging a new meteorological field provided by Sekiyama et al. (2017) with higher accuracy. In this study, the available results were increased to six members, including two atmospheric transport models and two or four sensitivity experiments. This proposed method using more than two members promises to be applicable for MIPs as a new ensemble method. Furthermore, the estimated Cs-137 concentrations are used for the estimation of inhalation exposure of Cs-137 emitted from FDNPS in March 2011 (Takagi et al., 2020).
Section 2 gives a description of two models, WRF-CMAQ and NICAM, including a design of the sensitivity experiments, an explanation of the ensemble method using LMVE, the used measurement datasets with designs to test several assumptions in the proposed ensemble method and statistical metrics for model evaluation. Section 3.1 shows the estimated Cs-137 concentrations and their comparison with the single-model results. Section 3.2 shows the tests used for the assumption of spatial interpolation in the LMVE equation using the distance between the nearest two sites, as shown in Sect. 2.2, by separating the measurement into learning and validation sites. In the proposed method, several parameters are assumed: the size, number and weighting values in the interpolation, the time window in the LMVE and the ensemble size. These parameters are investigated and discussed in Sect. 4. Section 5 shows a conclusion and the implication of this study.
The ensemble size is six, and it includes two different atmospheric
transport models, WRF version 3.1 (Skamarock et al., 2008) coupled with
CMAQ version 4.6 (Byun and Schere, 2006) and the NICAM (Tomita and
Satoh, 2004; Satoh et al., 2008, 2014) coupled with the
spectral radiation-transport model for aerosol species (SPRINTARS; Takemura
et al., 2005; Goto et al., 2011). According to the rule of Nakajima et al. (2017),
these models are hereafter referred to as the W-model and N-model,
respectively. The W-model analyses atmospheric processes, such as transport,
diffusion and deposition of particles, but it was modified for radioactive
particle use, such as Cs-137 emitted from the FDNPS accident in the target
area in Japan (Morino et al., 2013). The basic experimental design in this
study is widely used in this field, such as in Morino et al. (2013). The
N-model is a seamlessly multi-scaled model for air pollutants (Goto et al.,
2018) on a global scale with a quasi-uniform grid (Suzuki et al., 2008; Dai
et al., 2014), a semi-regional scale with a stretched grid (Goto et al.,
2015, 2019) and a perfect regional scale with a diamond grid
system (Uchida et al., 2017; Nakajima et al., 2017). The N-model also
considers the atmospheric processes of particles and focuses on the target
area in this study. The basic experimental design in this study is generally
common to Nakajima et al. (2017). Both the W-model and N-model participate
in the international MIP for Cs-137 emitted from the FDNPS accident (Sato et
al., 2018). The experimental design among the models was harmonized as best
as possible; that is, all experiments were carried out by using the same
emission inventory in Katata et al. (2015) and nudging the meteorological
fields using the operational model for regional weather forecasting around
Japan (the non-hydrostatic model, named NHM; Saito et al., 2006) coupled
with the local ensemble transform Kalman filter (NHM-LETKF) from Sekiyama et al. (2017), with almost a 3 km
grid resolution. Using the W-model and N-model, six experiments were
conducted, as shown in Table 1. The W-model was executed in four experiments
by considering differences in the meteorological fields used as nudging
data, the wet deposition process for Cs-137 and emission scenarios of
Cs-137 from Terada et al. (2012). The N-model was performed in two
experiments by considering only the difference in the meteorological fields.
The hourly Cs-137 concentrations simulated in all the experiments in the
lowest layer are linearly interpolated to a
Brief model description and the design of the experiments.
One of the optimization methods for the simulated Cs-137 concentration is a
multi-model ensemble. When the simulated concentration in model
Different from the previous study of Nakajima et al. (2017), the number of
ensemble members is not only two but also more than two. In this case, Eqs. (1) and (2) are generalized as follows:
In grids where an observation site or observed data at an observation site
are missing,
Test experiments in the ensemble method for linear interpolation (LIP).
The parameters
In Eq. (3),
Cs-137 observation sites used as a learning site in
Test experiments in the ensemble method using the selected sites.
The hourly measured Cs-137 concentrations at the surface are directly
estimated by using the aerosol sampling tapes of the national suspended
particulate matter (SPM) network (Tsuruta et al., 2014,
2018). There are almost 400 SPM sites in eastern Japan, but now 101 sites
have available data for Cs-137 (Oura et al., 2015). In this study, the
measured Cs-137 data at 100 sites (one site, Futaba, was eliminated because
the site is located in the same model grid as FDNPS, which is known as the
change-of-support problem; Gotway and Young, 2002) are used for the
ensemble. In addition, at an extra site, Tokai (36.45
The colours represent the sites used to learn or validate the data in the
extra ensemble estimation to examine the effect of the spatial interpolation
for the
The model evaluation should be carried out using multiple statistical
metrics (e.g. Chang and Hanna, 2004). In this study, we introduce the
geometric mean bias (GMB), root mean square error (RMSE) using the geometric
variance (GV), Pearson correlation coefficient (PCC), and the fraction of
data within a factor of 2 of observations (FAC2):
Temporal variations in Cs-137 at the relevant sites (Naraha, Haramachi, Furuga and Kawagoe). The locations in brackets represent the names of prefectures. The results are shown for the observations (“obs” in black), ensemble members (W1, W2, W3, W4, N1 and N2 in colours) and the ensemble model (red). The time is JST.
Cs-137 simulated by parts of the ensemble six members, i.e. W1 and N1, is evaluated under an MIP (Sato et al., 2018). The performances of these two members are moderate among the MIP-participating models. Here, all of the ensemble members and the ensemble results are compared with the measurements of the surface Cs-137 concentrations. Figure 2 shows the temporal variation in both simulated and observed Cs-137 at the sites near FDNPS and in the Kantō region. Generally, the ensemble results at these sites are the closest to the observations compared to the results of the single-member model. For example, at Naraha (Fig. 2a), which is the closest site to FDNPS, the first and second largest peaks in the observed Cs-137 are noteworthy during 15–17 March. The results of the ensemble members are largely dispersed, so the ensemble results become very close to the observations. In the other peaks, such as those on 16 and 20–21 March at Furukawa (Fig. 2c), the ensemble results are almost completely matched with the observations. However, the ensemble results are not close to the observations when all the results of the ensemble members are underestimated compared to the observation, as is the case on 13 March at Haramachi (Fig. 2b). In this case, the ensemble result has a peak on 12 March, which is earlier than the timing captured by the observation. In contrast, on 12 March at Naraha, some of the members have a peak in the simulated Cs-137; thus, the ensemble result also has a small peak, whereas the observation does not have such a peak. These cases are also shown on 20 March at Kawagoe (Fig. 2d), which can be explained as follows: when the Cs-137 simulated by all members is underestimated compared to the observations, the variance in Cs-137 between the observations and the simulations, as defined in Eq. (3), must be too large, and thus the weighted coefficient of the members, as defined in Eq. (5), becomes very small. Because the cross terms of the Cs-137 concentration and the weighted coefficient are small, the Cs-137 concentrations estimated by the ensemble must be underestimated. In contrast, when Cs-137 simulated by some members is overestimated compared to the observations, the weighted coefficient becomes very small. However, because the cross terms of the Cs-137 concentration and the weighted coefficient are not small, the Cs-137 concentrations estimated by the ensemble are overestimated, which represents one of the disadvantages of the LMVE ensemble method and prevents it from obtaining more accurate ensemble results relative to the observations.
Relationship between the simulated Cs-137 and the observed
Cs-137 at all available sites using the
Statistical metrics defined in Sect. 2.4 using the
simulated Cs-137 and observed Cs-137 at the available 101 sites. The metrics
show the
Figure 3 shows scatterplots for the observed and simulated Cs-137 at all
sites using the ensemble results (a), the results of each member (b–g) and
the median results (h) among the ensemble members. The statistical metrics
are listed in Fig. 4, including the bias (GMB), uncertainty (RMSE),
correlation (PCC) and FAC2. The perfect model presents values of GMB
Temporal variations in Cs-137 at the independent sites (not learning but validation sites) using the LMVE ensemble method for CTL, SEN1, SEN2 and SEN3. The time is JST.
In Sect. 3.1, the results of the CTL are shown, and in this section, the sensitivity tests (SEN1, SEN2 and SEN3 as shown in Sect. 2.3) for the separation of learning and validation sites are conducted. The test results are evaluated at the sites that are independent (used as validation data) from the other sites (used as learning data) in the LMVE ensemble method (Table 3). At the independent sites, the temporal variations in the simulated Cs-137 are compared at the four sites near FDNPS and in the Kantō region (Fig. 5). The sensitivity depends on the location; the results of all sensitivity tests (SEN1, SEN2 and SEN3) are sometimes far from the observations at Fukushima, as shown in Fig. 5a and b, whereas those of all the sensitivity tests (SEN1, SEN2 and SEN3) are generally close to the observations at the sites in the Kantō region (Fig. 5c and d). This suggests that the interpolation of variance (and thus the Cs-137 concentrations) near the FDNPS is sometimes not applicable, which is probably because the plume of high-density Cs-137 near the FDNPS is very narrow and strongly depends on local winds (Nakajima et al., 2017). The wind, especially low wind speeds, tends to influence the results at the observation sites (Weil et al., 1992).
Statistical metrics (GMB, RMSE, PCC and FAC2) at the
available sites for CTL, SEN1, SEN2 and SEN3. The statistical metrics are
calculated using all sites (in black) and the independent sites (in grey),
which are not used in the LMVE ensemble method. The names of the experiments
are shown in each panel. The
Figure 6 summarizes the statistical metrics among the sensitivity tests.
This figure indicates that the GMB and RMSE values are larger and the PCC
and FAC2 values are smaller as the distance between the learning and
validation sites increases. The figure also shows that the differences in
these metrics between the results using all and independent sites are small
and thus clearly show the success of the linear interpolation of variance
between the simulation and the observation in the LMVE ensemble method.
These results are consistent with the results shown in the Kantō region of
Fig. 5c and d, indicating that the largely spread plumes are
generally reproduced by the ensemble method. As shown in Fig. 6, the
relationship between the two axes, i.e. distance vs. PCC, can be fitted as a
linear line with a slope of 0.18 for the results using all sites and 0.36
for the results using only the validation sites. The slope indicates that
the PCC decreases by 0.02–0.04 when the distance from the learning site to
the validation site increases by 0.1
This section discusses the uncertainties caused by several assumptions in the LMVE ensemble method. As described in Sect. 2.2, the spatial interpolation of variance defined in Eq. (3) assumes IDW. The selection of the sites is also uncertain and is investigated in Sect. 4.1. The time window used in Eq. (3) is assumed to be 1 h, which is discussed in Sect. 4.2. The ensemble size defined in Eqs. (4) and (5) is also discussed in Sect. 4.3. In Sect. 4.4, the spatial distribution of the Cs-137 surface concentrations estimated by the LMVE ensemble method is shown as an example for estimating the impact of Cs-137 on inhalation exposure of residents in Japan.
Statistical metrics (GMB, RMSE, PCC and FAC2) for the
three sensitivity tests (SEN1, SEN2 and SEN3) as described in Table 3 using
the five interpolation methods (nearest, LIP1, LIP2, LIP3 and LIP4)
described in Table 2. The
The spatial interpolation of variance defined in Eq. (3) adopts IDW using
two of the nearest sites as denoted by LIP1 in Table 2. Here, four extra
methods in Table 2 are used for testing SEN1, SEN2 and SEN3, as shown in
Sect. 3.2. Figure 7 illustrates the statistical metrics for 15 tests using
the validation sites, which are not used in the LMVE ensemble method as
learning data. For SEN1, all metrics in the five interpolation methods are
estimated as
Same as Fig. 2 except for the use of the ensemble results with various time windows ranging from 1 h (tw01hr) to 49 h (tw49hr).
To investigate the sensitivity of the time window in Eq. (3), the temporal variations in Cs-137 simulated by the ensemble methods are shown in Fig. 8 using various time windows ranging from 1 to 49 h (not all results are shown in Fig. 8). The difference in the estimated Cs-137 concentrations is generally small but sometimes very large. In Fig. 8a, for example, at Naraha on 20 March, the observed peak is sharp, whereas the sharpness of the estimated peaks depends on the time window values. As the time window increases, the sharpness of the peak becomes weak, i.e. the peak is broadly distributed. At Kawagoe (Fig. 8d) on 20–22 March, the estimated Cs-137 concentrations using the longer time window are far from the observations and estimations using the shorter time window. Such situations are found at the other sites and during other periods (not shown). This also indicates that the peak in Cs-137 is very sharp temporally and spatially, so the time window must be shortened. The dependency of the time window on the results is investigated using the statistical metrics at all sites used in the LMVE ensemble method, as shown in Fig. 9. The dependency of the time window on the GMB, RMSE, PCC and FAC2 was found to be strong; moreover a shorter time window tends to provide higher PCC and FAC2 values and lower GMB and RMSE values. Therefore, the time window in the standard experiment is set to the shortest time, i.e. 1 h.
Statistical metrics (GMB, RMSE, PCC and FAC2) at the 101
available sites against various time windows (
The previous study of Nakajima et al. (2017) used only two members for the
LMVE ensemble method, and the ensemble results were better than the original
results for each member, but the difference in the PCC was very small
(0.03–0.05; Table 1 in Nakajima et al., 2017). Therefore, this study
increases the number of LMVE ensembles to six members and investigates the
sensitivity of the ensemble size to the results. Figure 10 shows the
relationship between the ensemble size and the statistical metrics (GMB,
RMSE, PCC and FAC2). The results clearly show that as the ensemble size
increases, the GMB and RMSE decrease, and the PCC and FAC2 increase. This
tendency can also be found in previous studies (e.g. Pennell and Reichler,
2010; Kioutsioukis and Galmarini, 2014; Solazzo and Galmarini, 2015a). Using
two members, the average GMB is calculated to be 1.95, which is smaller than
that obtained using a single member by 0.76; the average RMSE is calculated
to be 10
Statistical metrics (GMB, RMSE, PCC and FAC2) at the
available sites against the number of the ensemble members, the median and
the average (
Even in the best estimate using selected five or six members, the PCC value is less than 0.7, which means the ensemble results are moderately (not strongly) correlated with the observations. Therefore, to obtain values much closer to the observations, a new ensemble member is required. As explained in Sect. 3.1, when one of the members provides results close to the observations even at 1 h, the ensemble results proposed in this study become closer to the observations.
For the median and average values using six members, the PCC is calculated to be 0.42 and 0.46, respectively, similar to the ensemble results obtained using two members. By contrast, the GMB, RMSE and FAC2 values for the median and average results obtained using six members are close to the results for the single members. Since the median and average values obtained using many members are generally closer to the best estimate compared to the original members, the original members used in this study are not independent of each other. Therefore, these results indicate that the LMVE ensemble method is applicable even when the ensemble size is only two and even when they are not independent, although the bias, uncertainty, correlation and precision dramatically decrease as the ensemble size increases. The proposed ensemble method is very useful for properly estimating Cs-137 concentrations, even under a limited ensemble size.
Spatial distribution of the
The above discussion indicates that the LMVE ensemble method can better estimate the Cs-137 distribution; the spatial distributions of Cs-137 concentrations that are integrated daily on 15 March 2011 are also shown (Fig. 11). In the Fukushima prefecture, including the FDNPS, the results of Cs-137 simulated by each member are largely spread, so the ensemble results, especially in the area far from the observation sites, are very important. Figure 5 suggests that the ensemble results are moderately correlated with the observations around the area where the distance from the observation site is approximately 20–30 km. Therefore, in the Fukushima prefecture, which presents a complex terrain, parts of the results of Cs-137 in this area are still uncertain, even when using models with a 3 km horizontal grid, because part of the area is far (30 km away the coast of Fukushima, which is called Hama-dori in Japan), and the inner area is the location of many observation sites (called Naka-dori in Japan). By contrast, although the difference in the simulated plumes among each member is very large over the Kantō region, the conclusion from Sect. 3.2 supports the results that the ensemble Cs-137 results are closer to the observations, with PCC > 0.4, compared to the results of each member. This result is obtained because in the Kantō region, most areas are within 70 km of any observation site. However, some of the prefectures in the Kantō region do not have measurement sites, so in these prefectures, the ensemble results are still uncertain. This suggests that in the future, it should be required to observe Cs-137 at distance intervals of 20–30 km distance near the source region and 70 km in other areas to properly estimate the best results of the Cs-137 spatial distribution.
The LMVE ensemble method is based on a classical idea but is still useful for estimating the best results using MMEs and observations without requiring a large amount of computer resources for high-resolution models. This method was first applied to estimate the Cs-137 distribution by Nakajima et al. (2017) and is extended in this study. The uniqueness of this approach compared with other MMEs for other species is based on the following: (1) the availability of observed Cs-137 concentrations near the surface at approximately 100 sites, thus providing dense coverage over eastern Japan; (2) the simplicity of identifying the emission source of Cs-137 associated with the point source of FDNPS; (3) the novelty of implementing the MME approach with a high-resolution model over complex terrain in eastern Japan; and (4) the strong need to better estimate the Cs-137 distribution due to its inhalation exposure risk among residents in Japan. However, Nakajima et al. (2017) did not thoroughly discuss the availability of this method in depth, show the biases, uncertainties, precision and generalizability of this method under varying time windows, space windows and ensemble sizes. Radioactive Cs-137 was released from the FDNPS in March 2011, and many studies have investigated the distribution of Cs-137, but the proper estimations of Cs-137 are not still adequate. Therefore, this study first extended the LMVE ensemble method to an ensemble size of six for simulating Cs-137, including two models, the WRF-CMAQ and NICAM models, and observations and then investigated their uncertainties to confirm their performances to generalize this method and attempt to give the best estimate for the estimation of their inhalation impacts on humans, which is a companion study by Takagi et al. (2020). The results of the ensemble members are also updated from Nakajima et al. (2017) by using a finer horizontal resolution (3 km grid) and by nudging an improved meteorological field provided by Sekiyama et al. (2017).
The proposed LMVE ensemble method provides the best results among the single
members of the ensemble. This shows that the MME-estimated Cs-137
concentrations at all available 101 sites have the lowest bias against the
observations, with GMB
It should be noted, however, that the LMVE ensemble method presents certain limitations. When Cs-137 simulated by all members is too underestimated compared to the observations, the variance in Cs-137 between the observations and the simulations, as defined in Eq. (3), must be too large, and thus the weighted coefficient of the members, as defined in Eq. (5), becomes very small. Because the cross terms of the Cs-137 concentration and the weighted coefficient are small, the Cs-137 concentrations estimated by the ensemble must be underestimated. By contrast, when Cs-137 is overestimated by some members, the weighted coefficient becomes very small. However, because the cross terms of the Cs-137 concentration and the weighted coefficient are not small, the Cs-137 concentrations estimated by the ensemble are overestimated.
In addition, the spatial interpolation used in this study does not obtain a moderate PCC value (> 0.4) in the areas where the distance from the observation sites exceeds approximately 70 km. Therefore, the estimated results over the area with very sporadic site locations are very uncertain, especially for the inner areas of the Kantō region, e.g. Gunma and Tochigi prefectures. The assumption of the spatial interpolation using IDW is difficult to apply to broadly distributed materials, such as Cs-137 emitted from the FDNPS, which is spatially and temporally distributed very heterogeneously (Nakajima et al., 2017). It can be said that it is difficult to use any spatial interpolation, which basically assumes the spatial smoothness of the target's concentrations based on the best estimation of the Cs-137 distribution. In the future, Cs-137 should be observed at distance intervals of 20–30 km near the source region, including in complex terrain, and at intervals of at least 70 km in other areas to properly estimate the best results of the Cs-137 spatial distribution.
This study only applies the LMVE ensemble method to radioactive Cs-137 in
the atmosphere, but this method can be applied to Cs-137 deposition and
atmospheric pollutants, such as PM
The WRF-CMAQ and NICAM model results used to support this article can be
obtained from the corresponding author upon request
(goto.daisuke@nies.go.jp). The observational data of Cs-137 are freely
accessible in Appendix A of Oura et al. (2015) at
DG designed the experiments, conducted the ensemble calculation and drafted the manuscript. YM and JU conducted model simulations. TO, TTS and TN contributed to the discussion of the ensemble results. All authors contributed to writing the manuscript and all of the discussions.
The authors declare that they have no conflict of interest.
We acknowledge Haruo Tsuruta and Yasuji Oura for measuring the Cs-137 concentrations at the monitoring sites and Mai Takagi for checking our ensemble results to estimate the inhalation exposure.
This research has been supported by the Environmental Research and Technology Development Fund (fund nos. 5-1501 and 1-1802) of the Environmental Restoration and Conservation Agency, Japan; the Ministry of the Environment, Japan; Japan Society for the Promotion of Science (JSPS) KAKANHI (grant no. JP17H04711); and the Japan Aerospace Exploration Agency (JAXA)/Earth Observation Research Center/GCOM-C.
This paper was edited by Jianping Huang and reviewed by two anonymous referees.