## 3 Results and Discussion
### Tgm
For further analysis, the extent of mass independent fractionation (MIF) was evaluated. MIF can be evaluated by the deviation of the observed \(\delta^{\rm x}\)Hg from the predicted \(\delta^{\rm x}\)Hg using \(\delta^{\rm 202}\)Hg [36]:  
\[\Delta^{\rm x}\rm Hg\ (\%_{\rm x})\approx\delta^{\rm x}\rm Hg-\left(\delta^{ \rm 202}\rm Hg\times\beta_{\rm x}\right) \tag{3}\]  
where \(\beta_{\rm x}\) is the mass dependent fractionation factor for mass x (0.2520, 0.5024, 0.7520, and 1.4930 for mass 199, 200, 201, and 204, respectively). A scatter plot of \(\delta^{\rm 202}\)Hg against \(\Delta^{\rm 199}\)Hg showed negative values for both (Figure 4), which was a common feature of observed for Hg in plants [31; 33; 34; 35] and in soil [32; 35]. However, a plot of \(\Delta^{\rm 201}\)Hg versus \(\Delta^{\rm 199}\)Hg demonstrated scattered plots, regardless of the biases were corrected (Figure 5), even though reported plots display high correlations. Particularly, the noyaki sample collected on 6 April 2019 in Namino showed extreme \(\Delta^{\rm x}\)Hg values. This sample also showed unusual values in a plot of \(\Delta^{\rm 200}\)Hg versus \(\Delta^{\rm 204}\)Hg, and we do not know if these extreme \(\delta^{\rm x}\)Hg values were caused by the combustion. Even though this study could not distinguish the origins of Hg between plant and soil, the deposited mercury on the surface over a year still showed \(\delta^{\rm x}\)Hg values consistent with those observed by others. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{**Sample**} & \(\delta^{\rm 199}\)Hg & \(\delta^{\rm 200}\)Hg & \(\delta^{\rm 201}\)Hg & \(\delta^{\rm 202}\)Hg & \(\delta^{\rm 204}\)Hg \\ \hline \multicolumn{1}{c}{} & \multicolumn{5}{c}{\%\({}_{\circ}\)} \\ \hline \multicolumn{1}{c}{_Noyaki samples_} & & & & \\ \hline
24 March 2019, Daikanpou BAuT & \(-0.66\) & \(-0.91\) & \(-1.48\) & \(-1.62\) & \(-2.29\) \\ \hline
2019 April 6, Namino BAuT & \(-1.19\) & \(-1.02\) & \(-1.70\) & \(-2.06\) & \(0.29\) \\ \hline
23 March 2021, Ubuyama BAuT & \(-0.68\) & \(-0.99\) & \(-1.87\) & \(-2.03\) & \(-2.88\) \\ \hline
27 March 2021, Kitayama BAuT & \(-0.62\) & \(-0.90\) & \(-1.48\) & \(-1.72\) & \(-2.32\) \\ \hline \multicolumn{1}{c}{_Background air samples_} & & & & \\ \hline
31 March 2019, Namino BAuT & \(-0.13\) & \(0.11\) & \(-0.12\) & \(0.37\) & \(0.41\) \\ \hline
23 May 2019, Namino BAuT & \(-0.10\) & \(-0.20\) & \(-0.53\) & \(-0.53\) & \(-0.40\) \\ \hline
19 April 2021, Komezuka BAuT & \(-0.37\) & \(-0.48\) & \(-0.59\) & \(-0.80\) & \(-1.13\) \\ \hline
23 April 2021, Ubuyama BAuT & \(-0.42\) & \(-0.60\) & \(-0.58\) & \(-0.66\) & \(-1.06\) \\ \hline
10 May 2021, Kitayama BAuT & \(-0.29\) & \(-0.51\) & \(-0.76\) & \(-0.97\) & \(-1.21\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Biases corrected \(\delta^{\rm x}\)Hg. Figure 4: Scatter plot of \(\Delta^{199}\)Hg versus \(\delta^{202}\)Hg for TGM from noyaki and background air samples before and after the corrections for the measurement biases were made. Figure 5: Scatter plot of \(\Delta^{199}\)Hg versus \(\Delta^{201}\)Hg for TGM from noyaki and background air samples before and after the corrections for the measurement biases were made.