## 3 Results and Discussion
### Methodology Tests  
Analysis of the ambient samples collected in the Aso region showed that the atmospheric TGM concentrations during Noyaki on 24 March and 6 April were 3.7 and 1.4 ng m\({}^{-3}\), respectively, while those in the background air were 0.7 and 0.8 ng m\({}^{-3}\), respectively (Table 4), indicating that the Noyaki events increased the TGM concentrations. The TGM concentrations in the background air were slightly lower than the expected--approximately 1 ng m\({}^{-3}\)--which is the minimum GEM concentration observed at the Japanese background sites [20]. The filtering of the air through the PTFE filter kept the trapping material clean and avoided its deterioration; however, airborne particulate matter trapped on the PTFE filter may have adsorbed TGM and lowered the TGM concentration. The obtained extract concentrations of the Noyaki and background air samples using the plastic bag extraction method were in the range of 3.1-1.0 ng g\({}^{-1}\), and the results of the isotope ratio measurements for these analyses are shown in Table 3. It should be noted that according to the linearity of the isotope measurements discussed in Section 2.3, the \(\delta^{\rm x}\)Hg for the 6 April sample may have up to a \(\pm\) 0.4% bias. The samples collected during the Noyaki events were mixtures of TGM from Noyaki and background air; therefore, we subtracted the averaged background concentrations and isotopic compositions to calculate the true \(\delta^{\rm x}\)Hg of TGM emitted during the Noyaki using the mass balance for the isotope ratios [21]. Except for \(\delta^{\rm 204}\)Hg of the 6 April sample, the background-corrected \(\delta^{\rm x}\)Hg values were of light isotopic compositions (Table 5), which may refer to the isotope fractionation associated with the burning during Noyaki. To further investigate the observed \(\delta^{\rm x}\)Hg values, we compared them to the predicted \(\delta^{\rm x}\)Hg values based on the theory of mass-dependent fractionation using the \(\delta^{\rm 202}\)Hg value and the scaling factor for the mass \(x\), \({}^{\rm x}\beta\). The deviation from the predicted value--\(\Delta^{\rm x}\)Hg--is an indicator for evaluating the mass-dependent and independent isotope fractionations (MDF and MIF, respectively) and can be approximated as follows when \(\delta^{\rm x}\)Hg values are smaller than 10% [7]:  
\[\Delta^{\rm x}\rm Hg\approx\ \delta^{\rm x}\rm Hg-\ \delta^{\rm 202}\rm Hg\times ^{\rm x}\beta \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**n**} & **Spiked Hg** & **Extraction** & **Recovery** & \(\delta^{\rm 199}\)Hg \(\delta^{\rm\lx@sectionsign}\) & \(\delta^{\rm 200}\)Hg \(\delta^{\rm\lx@sectionsign}\) & \(\delta^{\rm 201}\)Hg \(\delta^{\rm\lx@sectionsign}\) & \(\delta^{\rm 202}\)Hg \(\delta^{\rm\lx@sectionsign}\) & \(\delta^{\rm 204}\)Hg \(\delta^{\rm\lx@sectionsign}\) \\  & & **(mg)** & **(h)** & **Yield (\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline
20\% inversed & 2 & \(103\pm 2\) & 6 & \(92\pm 6\) & \(-0.15\pm 0.01\) & \(-0.19\pm 0.05\) & \(-0.28\pm 0.09\) & \(-0.33\pm 0.14\) & \(-0.49\pm 0.34\) \\
40\% inversed & 3 & \(103\pm 2\) & 3 & \(87\pm 11\) & \(-0.15\pm 0.01\) & \(-0.21\pm 0.03\) & \(-0.38\pm 0.04\) & \(-0.46\pm 0.08\) & \(-0.69\pm 0.21\) \\
30\% inversed & 2 & \(103\pm 2\) & 3 & \(96\pm 5\) & \(-0.15\pm 0.05\) & \(-0.24\pm 0.09\) & \(-0.44\pm 0.17\) & \(-0.50\pm 0.20\) & \(-0.74\pm 0.30\) \\ \hline \hline \end{tabular}  
* Recommended isotope ratios according to NIST. \(\dagger\) N.A.: not applicable. \(\lx@sectionsign\) The measured \(\delta^{\rm x}\)Hg values shown are average \(\pm\) standard errors form the 50 replicate measurements.  
\end{table} 
Table 2: _Cont._