Supplementary Information 1. The effect of the δ 13C(CH4) seasonal cycle

CH4 and δ13C(CH4) undergo seasonal cycles (Miller et al., 2002, Tyler et al., 2007, Dugoklencky et al., 2009), which are recorded in the upper firn. However, the inverse model cannot reconstruct the seasonal signal (see: Wang et al., 2012 for further discussion) thus it has to be assessed separately...

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Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.364.858
http://www.atmos-chem-phys.net/13/6993/2013/acp-13-6993-2013-supplement.pdf
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Summary:CH4 and δ13C(CH4) undergo seasonal cycles (Miller et al., 2002, Tyler et al., 2007, Dugoklencky et al., 2009), which are recorded in the upper firn. However, the inverse model cannot reconstruct the seasonal signal (see: Wang et al., 2012 for further discussion) thus it has to be assessed separately. The amplitude of the seasonal signal at the SH sites is very small and thus does not significantly affect the firn profiles from Antarctica. Therefore, the sensitivity to seasonality was only examined for the NH sites using the model in the forward mode. Model runs were performed for an atmospheric scenario with (Fig. S1: black lines) and without (Fig. S1: colored lines) seasonality and the difference between the two model results was used to correct the firn data for seasonality. These corrected values were used as input in the inverse model. Note that near-‐surface δ13C(CH4) data in Devon Island firn are distinctly lower than at other sites, although seasonality has a weak impact. Diffusivity at Devon Island is smaller than at all other sites, and stronger CH4 trends are observed in the upper firn than at other sites (Witrant et al., 2012). In relation with the melt layers, firn fractionation may already operate and be under-‐estimated by the model in the upper Devon Island firn. 2. Sensitivity to uncertainties on the CH4 scenario A reconstructed atmospheric CH4 scenario is used as input for the model. This scenario is based on direct atmospheric measurements from continuous 1 atmospheric monitoring from the NOAA-‐ESRL network and from high-‐resolution firn/ice core measurement from the high accumulation site of Law Dome, Antarctica (Etheridge et al., 1998, MacFarling Meure et al., 2006). Based on these data, two CH4 scenarios were built for the Northern (Buizert et al., 2012) and Southern (Witrant et al., 2012) hemispheres. As shown in Section 5.3 of the main paper, the temporal change in the CH4 mixing ratio is responsible for a large fraction of the δ13C(CH4) variations in the firn. In order to evaluate the ...