Application of linear minimum variance estimation to the multi-model ensemble of atmospheric radioactive Cs-137 with observations
Authors: Goto Daisuke , Morino Yu , Ohara Toshimasa , Sekiyama Tsuyoshi Thomas , Uchida Junya , Nakajima Teruyuki 
Published: March 2020

Abstract. 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 =1.53), the lowest uncertainties based on the root mean square error
(RMSE) against the observations (RMSE =9.12 Bq m−3), the highest
Pearson correlation coefficient (PCC) with the observations (PCC =0.59) and
the highest fraction of data within a factor of 2 (FAC2) with the
observations (FAC2 =54 %) compared to the single-model members, which
provided higher biases (GMB =1.83–4.29, except for 1.20 obtained from one
member), higher uncertainties (RMSE =19.2–51.2 Bq m−3), lower
correlation coefficients (PCC =0.29–0.45) and lower precision
(FAC2 =10 %–29 %). At the model grid, excluding the measurements, the
MME-estimated Cs-137 concentration was estimated by a spatial interpolation
of the variance used in the LMVE equation using the inverse distance weights
between the nearest two sites. To test this assumption, the available
measurements were divided into two categories, i.e. learning and validation
data; thus, the assumption for the spatial interpolation was found to
guarantee a moderate PCC value (> 0.4) within an approximate
distance of at least 70 km. Extra sensitivity tests for several parameters,
i.e. the site number and the weighting coefficients in the spatial
interpolation, the time window in the LMVE and the ensemble size, were
performed. In conclusion, the important assumptions were the time window and
the ensemble size; i.e. a shorter time window (the minimum in this study
was 1 h, which is the observation interval) and a larger ensemble size
(the maximum in this study was six, but five is also acceptable if the
members are effectively selected) generated better results.