# Methane Emission Estimates by the Global High-Resolution Inverse Model Using National Inventories
## 2 Materials and Methods
### Prior Fluxes and Observations  
Prior methane fluxes used in the coupled model included anthropogenic emissions, biospheric emissions of wetlands, soil sinks, emissions from biomass burning, and other natural sources from the ocean, geological sources, and termites. EDGAR provides an annually gridded anthropogenic emission dataset that is available at a resolution of \(0.1^{\circ}\times 0.1^{\circ}\)[19]. The seasonal cycle was found to have effects on the top-down emission estimation [33]. In this study, monthly variation of anthropogenic emissions was prepared based on the climatology data issued by EDGAR for 2010. The ratio of monthly emissions to annual emissions was calculated for each grid. Then, for other years, the grid value for each month was calculated proportionally to the annual grid emission of the corresponding year. The VISIT model simulations for wetlands (Cao mechanism [51]) and soil sink (Curry mechanism [52]) are available at \(0.5^{\circ}\)[53]. For simulations in this study, we updated the data by remapping the wetland emissions from \(0.5^{\circ}\) to \(0.1^{\circ}\) using the Global Lakes and Wetlands Database (GLWD) wetland area map at a resolution of 30 arcseconds [54], while soil sink data were remapped to a resolution of \(0.1^{\circ}\) using the gross primary productivity (GPP) maps by the MODIS MOD17 GPP product [55]. For emissions from biomass burning, daily Global Fire Assimilation System (GFASv1.2) [56] data were used. The oceanic, geological, and termite emissions were taken from [PERSON] et al. [57].  
The total column-averaged dry-air mole fraction (XCH\({}_{4}\)) retrieved from the Greenhouse Gas Observing Satellite (GOSAT) (NIES Level 2 retrievals, v. 02.72) from 2010-2012 was used to constrain methane emissions. The vertical sensitivity of the GOSAT observations given by the column averaging kernel [58] was examined using 2010-2012 simulations. The root-mean-square error (RMSE) of the total methane flux was 4.5 Tg CH\({}_{4}\) yr\({}^{-1}\), or 0.82% of the mean total flux, and the retrieval-averaging kernel of GOSAT retrievals was not applied in this study.  
In addition to the GOSAT retrievals, ground-based atmospheric methane observations from global surface sites, aircrafts, and ship tracks were used in the inversions (see Appendix A). The data contained weekly and continuous samples. The continuous observations were analyzed at the hourly scale, which was further averaged to daily means using 12:00-16:00 LT (except for mountain sites, where 0:00-4:00 LT was used). Where sampling flags were available, we pre-filtered the continuous weekly and hourly observations by selecting those with well-mixed conditions. Data uncertainty, used as the diagonal of \(R\) in Equation (1), included both the observation uncertainty (e.g., measurement error and spatial representativeness) and the transport model error. For the ground-based sites, data uncertainty was defined based on the average RMSE between the observations and prior atmospheric CH\({}_{4}\) generated by the NTFVAR model with the prior emissions (original EDGAR plus natural sources) for each site. The minimum uncertainty was set to 6 ppb in order to allow more freedom for the inversion in the southern hemisphere. Note that we did not apply any temporal variations to the data uncertainty. The rejection threshold of the ground-based sites was set to two times the data uncertainty. The data uncertainty for the GOSAT retrieval was set to 60 ppb with a rejection threshold of 30 ppb. Large data uncertainty was applied to the GOSAT retrievals, because the amount of GOSAT data is generally much larger than that of ground-based observations and using an insufficient data uncertainty may result in over-fitting the GOSAT data, although the measurement precision is higher for ground-based observations.