## 3 Results and Discussion  
### Blank and Method Validations  
The results of the analytical tests for TGM isotope measurements using gaseous elemental mercury prepared from SRM 8610 showed recovery yields of 70 \(\pm\) 3%, 65 \(\pm\) 7%, and 90 \(\pm\) 8% for 5.2, 15.5, and 41.3 ng mercury introduced, respectively (Supplementary Table S4). The \(\delta^{\text{x}}\)Hg measurements of these samples for all the isotope ratios, except \(\delta^{199}\)Hg, showed significant differences between the measured and reference \(\delta^{\text{x}}\)Hg, and the average differences (\(\pm\)2 \(\times\) propagated uncertainty) were smallest for the test with 41.3 ng mercury, from \(-\)0.16 \(\pm\) 0.09% to \(-\)0.37 \(\pm\) 0.22%, while the differences for 5.2 ng and 15.5 ng were in comparable level, from 0.24 \(\pm\) 0.20% to 0.90 \(\pm\) 0.50% (Supplementary Table S4). For \(\delta^{199}\)Hg there was not a significant difference. The significant differences may have been due to unfavorable small fractionations for the heavy isotopes occurring during the TGM transfer from BAuTs to conventional gold traps, since we used air for the transfer. The results of the mercury transfer tests from BAuTs to conventional traps using either mercury-free air or pure nitrogen as the carrier gas showed recovery yields of 68 \(\pm\) 5% (\(n\) = 3) and 96% (\(n\) = 1), respectively. Thus, we speculate that the use of air as carrier gas caused an unfavorable reaction during the transfer. Unfortunately, dried mercury-free air was used to transfer TGM samples from the noyaki studies. Therefore, our \(\delta^{\text{x}}\)Hg data may have positive biases that needs to be corrected for \(\delta^{200}\)Hg, \(\delta^{201}\)Hg, \(\delta^{202}\)Hg, and \(\delta^{204}\)Hg when the captured TGM was between 5.2 and 15.5 ng. For the mass 41 g the biases are very small, slightly above 3\(\sigma\) for those isotope ratios. The analysis of backup BAuTs, which contained the breakthrough TGM from the front BAuTs, showed TGM of 100 pg or less. The minimum quantity of TGM captured by the front BAuT during noyaki and the background air sampling was 5 ng, indicating the breakthrough TGM was 2% or less. The analysis of eight blank filters resulted in nitrogen blank values lower than 1 \(\mu\)gN per filter. Due to the limited number of extracts, the stable nitrogen isotope ratio was not measured. The analysis of blank carbon showed an average blank value of 10 \(\mu\)gC per filter with \(\delta^{13}\)C of \(-\)23.9%. Further, the \({}^{14}\)C composition, or pMC, for the blank carbon was not measured due to the limited number of blank extracts, which were used for the \(\delta^{13}\)C analysis. The analysis of carbon mass and \(\delta^{13}\)C was conducted using the IAEA-C6 sucrose standard, which has \(\delta^{13}\)C of \(-10.8\)\(\pm\)\(0.5\)% (\(\pm\)uncertainty); see Supplementary Subsection S.2. for this evaluation. Briefly, within the range of carbon masses found in our LV-WSOC samples, the impact of the blank value was significant. Thus, the blank correction was needed for the yield of carbon masses and their \(\delta^{13}\)C values. The blank-corrected \(\delta^{13}\)C value agreed with the reference \(\delta^{13}\)C value within the propagated uncertainty (0.51 to 0.78%, depending on the spiked carbon mass). Due to the unknown pMC in the blank carbon, the blank correction was not made for \({}^{14}\)C data. Based on the blank value referred to previously, the blank carbon in the combined filter extracts for \({}^{14}\)C analysis accounted for 5% in the Daikanpou sample, 2% in the Namino sample, 1% in the Ubuyama sample, and 4% in the Kitayama sample. Considering the blank carbon as the dead carbon (assuming the petroleum originated organic material used in the production of PTFE-coated filters as the major source of blank carbon) and our sample carbon as modern carbon, the blank fractions would result in a maximum 1-5% bias in the pMC estimation.