The Center for Climate System Research/National Institute for Environmental Studies/Frontier Research Center for Global Change (CCSR/NIES/FRCGC) Atmospheric General Circulation Model (AGCM)-based Chemistry Transport Model (i.e. JAMSTEC's ACTM) is used for simulating CH4 in the atmosphere (Patra et al., 2009). The model resolutions are T42 spectral truncations (∼2.8∘×2.8∘) in horizontal and 67 sigma-pressure vertical layers (surface to ∼90 km). In the control case, the ACTM meteorology is driven by interannually varying (IAV) sea-surface temperature (SST) and sea ice at monthly mean time intervals, based on the gridded analysis by the Hadley Centre (Rayner et al., 2003). The basic physical and dynamical features of the AGCM have been described in Hasumi et al. (2004). Advective transport of moisture and tracers is obtained from a 4th order flux-form advection scheme using a monotonic piecewise parabolic method (PPM) (Colella and Woodward, 1984) and a flux-form semi-Lagrangian scheme (Lin and Rood, 1996). Subgridscale vertical fluxes of heat, moisture and tracers are approximated using a non-local closure scheme in conjugation with the level 2 scheme of Mellor and Yamada (1974). The cumulus parameterization scheme is based on Arakawa and Schubert (1974). The updraft and downdraft of tracers by cumulus convection are calculated by using the cloud mass flux estimated in the cumulus parameterization scheme. We have checked that the AGCM simulated zonal-mean horizontal winds and temperatures in the troposphere are within ±5 ms-1 and ±1 K, respectively, when compared with ACTM simulations nudged to the Japan Meteorological Agency (JMA) 25 year reanalysis (JRA-25) (Onogi et al., 2007). These differences in meteorology do not appreciably affect our long-term simulation results, because only about 5 Tg CH4yr-1 (∼1 %) higher loss is simulated in the ACTM driven only by SST compared to when the ACTM is nudged to JRA-25. The ACTM also realistically represents interhemispheric transport, stratosphere–troposphere exchange, and SST driven climate variations such as the El Niño Southern Oscillation. Annual mean concentrations are used in this analysis, although the model integration time step is about 20 min.

We constructed global total CH4 emissions by combining: (1) the interannually varying annual mean anthropogenic emissions from the Emission Database for Global Atmospheric Research (EDGAR) – Hundred Year Database for Integrated Environmental Assessments (HYDE; version 1.4) (van Aardenne et al., 2001) and EDGAR 3.2 (Olivier and Berdowski, 2001), (2) interannually and seasonally varying emissions from rice paddies and wetland simulated by the Vegetation Integrative Simulator for Trace Gases (VISIT) terrestrial ecosystem model (Ito and Inatomi, 2012), and (3) natural emissions, such as those from biomass burning (including biofuels), termites based on the GISS inventory (Fung et al., 1991); emissions due to oceanic exchange near the coastal region (Lambert and Schmidt, 1993); and mud volcano emissions (Etiope and Milkov, 2004) as the major emission components (Fig. 1a). We apply scaling factors for emissions due to termites, oceanic exchange, mud volcano, biomass burning, rice paddies and wetlands, with values of 0.77, 0.40, 1.00, 0.4, 0.95, and 0.85, respectively (please refer to the Supplement, Table S1, for annual total emissions). Scaling factors are chosen to simulate the CH4 growth rate approximately for the first decade 1901–1910, and are in close agreement with Patra et al. (2011) for the period 1990–2008. For 1970–2000, interannually varying anthropogenic CH4 emissions from EDGAR 3.2 and EDGAR 3.2FT data are used and the data have been extended for 1901–1970 following the sector-wise trends recommended in EDGAR HYDE. For 2001–2010, the EDGAR 3.2FT emissions map for 2000 is used. EDGAR 3.2 and EDGAR 3.2FT emissions for biomass burning and rice sectors (SAV, DEF, AGR, AGL sectors) are excluded from the initial CH4 emissions (Eini), since they are given from different data sets as described above. The combination of different categories (Table 1) and interpolation/extrapolation of the EDGAR data set are similar to that used by Patra et al. (2011).

All of the four main categories of anthropogenic emissions (oil and gas, coal, animals and landfills) have increased steadily in the last 110 years; according to the EDGAR inventories (HYDE, v3.2 and v3.2FT), oil and gas emissions increased from 12 to 78 Tgyr-1, coal from 9 to 33 Tgyr-1, animals from 30 to 89 Tgyr-1, and landfills from 6 to 59 Tgyr-1 for 1901–2010. The highest increases in these emissions took place during 1940–1990. Animal emissions were the dominant contributor to this rapid total increase for 1940–1960, while oil and gas controlled the increasing trend for the next 3 decades (1960–1990). There was a decrease in oil and gas emissions during the early 1990s from the former Soviet Union (Fig. 1a). We kept annual total biomass burning emissions constant over time (49.7 Tgyr-1; monthly varying GISS data set) because no consensus on the amplitude and trends has been achieved in the literature (see Sect. 3.4). The VISIT model simulated CH4 emissions from rice paddies and wetlands using a scheme by Cao et al. (1998). In the VISIT model, CH4 emission from wetlands is dependent on substrate availability, water table depth and temperature. The substrate availability was estimated from the decomposition rate of soil organic matter, assuming a certain part of carbon was used for methanogenesis. Water table depth was prescribed on the basis of inundation fraction, which varies seasonally. Aerobic soil fraction (i.e. above water table depth) is a sink of methane due to microbial oxidation, while anaerobic fraction (i.e. below water table depth) is a source of methane. Temperature (input data) explicitly affects methane production rate and implicitly affects gas diffusivity. The simulated total emissions from rice paddies increased from 18 to 37 Tgyr-1 and that from wetlands varied from 141 to 159 Tgyr-1 for the period 1901–2010. The trends in emissions from rice paddies are mainly due to the increase in rice cropping, and that for the wetlands are due to warming of the Earth's surface and inundation levels due to rainfall variations (Ito and Inatomi, 2012; Patra et al., 2013). The fraction of paddy field was derived from the cropland fraction in land use data (Hurtt et al., 2006).

The primary loss process for atmospheric CH4 (∼90 %) is oxidation by hydroxyl radicals (OH), mostly in the troposphere. The remaining ∼10 % of the sinks include consumption by methanotrophic bacteria in soils, and reactions with chlorine radicals (Cl) and electronically excited atomic oxygen (O(1D)) in the stratosphere. The following chemical removal reactions for CH4 are prescribed in the ACTM forward simulations. CH4+OH⟶kOHCH3+H2OkOH=2.45×10-12exp⁡(-1775/T)CH4+O1D⟶kO1DProductskO1D= 1.5×10-10CH4+Cl⟶kClCH3+HClkCl=7.3×10-12exp⁡(-1280/T). The temperature (T)-dependent reaction rates (k; units: cm3 molecule-1 s-1) are taken from Sander et al. (2006). The climatological monthly mean tropospheric OH concentrations are taken from Spivakovsky et al. (2000), and stratospheric OH and Cl concentrations are obtained from a stratospheric chemistry simulation by the CCSR/NIES AGCM (Takigawa et al., 1999). Concentration of O(1D) is calculated online in ACTM using climatological ozone distribution. Trends in Cl concentration over the period of our simulation are introduced using the estimated changes in effective equivalent tropospheric Cl for the period 1992–2012 (Montzka et al., 1999; updates on the NOAA/ESRL website) and by simple extrapolation to 1901 following the annual fluorocarbon production report of the Alternative Fluorocarbons Environmental Acceptability Study (AFEAS) (www.afeas.org). This method ignores the changes in Cl vertical distribution due to the differences in Cl production rate from different species, which is altitude dependent. A delay of about 5 years between emissions of the halocarbons at Earth's surface and Cl release in the stratosphere is used based on average “age” of stratospheric air in ACTM. No trends in OH are considered in this study because of the lack of consensus between models, e.g. 6 out of 14 models show increases in OH concentrations in the period of 1850–1980, even though the models used a consistent set of anthropogenic emissions since the preindustrial era (Naik et al., 2013).

The time series of CH4 chemical loss as calculated with ACTM simulation with Eini for 1901–2010 is shown in Fig. 1b. Loss due to OH is the dominant contributor (244–466 Tgyr-1), followed by soil (18–36 Tgyr-1 as simulated by the VISIT model), O(1D) (4.6–8 Tgyr-1), and Cl (1.4–15.6 Tgyr-1) over 1901–2010. Consideration of trends in Cl concentration in the ACTM results in a dramatic increase in CH4 loss by Cl since the 1950s (Fig. 1b). We show later that the trends in stratospheric feedback of 13C-enriched CH4 cause a large imbalance in the tropospheric budget of the emission categories.

The observed CH4 concentrations in the Arctic and Antarctic regions were used for evaluating the ACTM simulations for two different emission scenarios. Two different types of data were used in the present study.

The global mass balance equation for total emissions (E), loss (L) and burden (B) of CH4 in the atmosphere is given by: dBdt=E-L. A conversion factor H can be calculated from the ratio of modelled B and an average CH4 concentration at the lower-most model level ([CH4]) as follows: B=H×[CH4]. This gives the value of 2.87±0.003 (average ± interannual variation) Tg CH4ppb-1 for the conversion factor H for the period 1910–2010. This value of H is about 4 % higher than common value of 2.77 calculated by Fung et al. (1991). This is mainly because in the present calculation we have used smaller than global mean CH4 concentration from Antarctica. L is calculated by summing up loss at all ACTM grids. Because our knowledge for developing accurate initial emissions (Eini) is incomplete, the simulated [CH4] time series is likely to deviate from the observation. The “correction” term ΔE to initial emission time series is calculated by applying Eq. () on the difference (Δ[CH4]) between observed and simulated [CH4]: Hd(Δ[CH4])dt+ΔL=ΔE, where ΔL is the difference in loss terms which is calculated using Δ[CH4] and the ratio L/[CH4] as a conversion factor (0.2907±0.0055) from model simulation for individual years. The optimized emissions (Eopt) are given by Eopt=Eini+ΔE. The calculation of global total Eopt is performed for each year. Emissions at all latitude-longitude grids are multiplied by a constant scaling factor (EoptEini) to prepare revised emission for running ACTM.

The contribution of different emission categories (Einii) to the bottom-up emissions as used in this study is prescribed (Fig. 1a and Table 1). However, the relative contribution of different emission categories to the emission correction ΔE is unknown. We thus introduce an additional constraint based on δ13C for distributing ΔE between two hypothetical source categories with lighter (13C-depleted) and heavier (13C-enriched) isotopic signatures.

The isotopic ratio of 13C to 12C in CH4 (δ13C) is defined as: δ13C=RsampleRstd-1×1000R=13C/12C, where Rsample is the isotopic molar ratio in the methane sample, and Rstd is the corresponding ratio in the international isotope standard (Vienna Pee Dee Belemnite (VPDB)) with an accepted value of 0.0112372 (Craig, 1957). δ13C is expressed in “per mil” (‰) notation.

We use a one-box model (e.g. Lassey et al., 2000) to estimate the isotopic signature for global emission E (δ13CE) using (1) global atmospheric burden (B) and loss (L) taken from the ACTM simulation and (2) observed atmospheric isotope ratio δ13Catmos. We used δ13Catmos observations from the Law Dome ice core (1885–1976)/firn (1944–1998) records (Ferretti et al., 2005); from air archive samples (1978–1994) (Francey et al., 1999); and NOAA-ESRL network direct observations (1998–2010) at CGO (Miller et al., 2002; White and Vaughn, 2011). Schmitt et al. (2013) reported a possible interfering effect by Kr on δ13C measurements using continuous-flow isotope ratio mass spectrometry systems. We assume that possible bias caused by the Kr-interference is not significant in deducing the observed δ13C trends over the past century.

The δ13C signature for the global source δ13CE can be calculated in two different ways: top-down and bottom-up methods. First, the top-down estimation is based on using the observed atmospheric isotope ratio δ13Catmos and mass balance Eq. () as follows: 13E=ddt(13B)+∑13Li13B=δ13Catmos×0.001+1×Rstd×B13Li=Li×αi×Ratmosδ13CE=13EE×Rstd-1×1000, where Li are the loss processes due to reactions with OH, O(1D), Cl and soil oxidation, αi=13ki/12ki is the isotopic fractionation factors for different loss processes, k is the rate coefficient of chemical reactions. The choice of αi used in this work and their uncertainties are addressed later in this section. Superscript 13 refers to the carbon isotopologue 13C in CH4. In the one-box model, we assume that burden [12CH4] is identical to [CH4], which however is the sum of [12CH4], [13CH4] and other minor isotopologues. We confirmed that this assumption has a negligible effect on our results. Our results are consistent with the calculation of δ13CE under non-steady-state conditions (Lassey et al., 2000).

Secondly, δ13CE can be calculated by considering the relative fractions of individual emission categories (Ei) as follows (bottom-up estimation): δ13CE=∑δ13CEi×Ei/E, where E=∑Ei and δ13CEi is the isotopic signature for emission category Ei. For the optimized case, E=Eopt=∑Einii+ΔE, and Li=Lopti and B=Bopt from the ACTM simulation should represent the observed condition. Using Eqs. ()–(), we calculate the isotope signature for Eopt(δ13CEopt). Again δ13CEopt can be estimated using Eq. () with Eopt=∑Einii+ΔE. Here we assume that ΔE is distributed between two hypothetical emissions ΔEl and ΔEh with lighter (δ13CΔEl) and heavier (δ13CΔEh) isotopic signatures, respectively. The δ13CEi are taken from Monteil et al. (2011) and references therein (Table 1). Using Eq. (), we obtain, δ13CEopt=∑δEinii13×Einii+δ13CΔEl×ΔEl+δ13CΔEh×ΔEhEopt. And we have an additional constraint on ΔEl and ΔEh as follows: ΔE=ΔEl+ΔEh. The value of δ13CEopt as calculated using Eq. () is substituted into Eq. (). There is, however, no unique solution for Eqs. () and () as they contain four unknown variables (ΔEh, ΔEl, δ13CΔEh and δ13CΔEl). In order to remove the underdetermination, we assume that δ13CΔEh and δ13CΔEl represent emissions from biomass burning (δ13C is -21.8 ‰ from Monteil et al., 2011) and residual biogenic sources (e.g. wetland, rice, animals, etc., mean δ13C near to -60 ‰ from Sapart et al., 2012), respectively. Equation () can now be modified to: ΔEl=δ13CEopt×Eopt-∑δEinii13×Einti-δ13CΔEh×ΔEδ13CΔEl-δ13CΔEh Using Eq. () we can estimate ΔEl and then ΔEh is calculated using Eq. (). Estimation of emissions due to biomass burning is our primary interest here because no direct statistics are available over the past century and it was assumed constant at 49.7 Tgyr-1 in Eini. It may be reiterated here that the anthropogenic emissions varied as per the EDGAR inventories, and wetland and rice emissions are taken from a terrestrial ecosystem model simulation.

Although CH4 losses due to reactions with Cl and O(1D), which mainly take place in the stratosphere, are small compared to the total loss, the strong isotopic fractionations (εi=(αi-1)×1000; εi is also known as “kinetic isotope effect” (KIE)) in these reactions have a large impact on the isotopic budget (Lassey et al., 2007a; Wang et al., 2002). The isotopic fractionation factors (αi) for the CH4+Cl reaction (αCl=0.935) is much smaller than that of the CH4+OH and CH4+O(1D) reactions, e.g. αOH=0.9961 and αO(1D)=0.9872, respectively (Saueressig et al., 1995). Previous studies have shown that there exists a large vertical gradient in δ13C from the troposphere to the stratosphere due to the stronger fractionation effects in CH4+O(1D) and CH4+Cl reactions during passage through the stratosphere (Rice et al., 2003; Röckmann et al., 2011; Sugawara et al., 1997). Stratosphere air returning to the troposphere is enriched in 13CH4, but the re-entry flux and consequent 13CH4 enrichment in the troposphere are not well quantified (Lassey et al., 2007a). In a modelling study, Wang et al. (2002) estimated that the tropospheric 13CH4 enrichment for 1992 due to stratospheric Cl without assuming steady state was 0.23 ‰ (0.18–0.54 ‰). If the αi for Cl and O(1D) loss processes as mentioned above (Saueressig et al., 1995) are used in the one-box model, because of the strong isotopic fractionations, the isotopic effect of stratospheric CH4 loss on the tropospheric δ13C budget will be overestimated. To avoid such overestimation, we assume that αi in the troposphere are mainly due to OH loss, and a smaller fractionation effect of the stratospheric loss on δ13C at the surface. In fact, the magnitude of fractionation during CH4 loss, both in the troposphere and stratosphere, is uncertain since the published values of αi in the literature are significantly different. The values of αCl range from about 0.935 (Saueressig et al., 1995) to 0.966–0.974 (Tanaka et al., 1996; Gupta et al., 1997), αO1(D) from 0.9872 (Saueressig et al., 2001) to 0.999 (Davidson et al., 1987) and αOH from 0.9946 (Cantrell et al., 1990) to 0.9961 (Saueressig et al., 2001). In the present study, αOH is the mean of two published αOH values (Cantrell et al., 1990; Saueressig et al., 2001). We scaled αCl so that the reaction with Cl has an impact of +0.23 ‰ on surface δ13C in 1992, to be consistent with Wang et al. (2002). αO(1D) is also adjusted by keeping the ratio (αCl-αOH)/(αO(1D)-αOH) and total loss by reactions with Cl and O(1D) unchanged. The weighted mean isotopic fractionation factor (α¯¯) for all loss processes is 0.9943 and the global mean δ13CE value in 1990 is -52.1 ‰, which are in agreement with other estimates, e.g. 0.9941 and -52.3 ‰, respectively (e.g. Lassey et al., 2000). The values of αCl and αO1(D) used in this study are now much closer to that of αOH producing the smaller fractionation effect of stratospheric loss on the estimation of δ13C at the surface (Table 1). Due to the increase in atomic Cl in stratosphere, the effect of αCl on surface δ13C is estimated to increase from +0.01 to +0.38 ‰ during the period 1910–2010.

The model simulations are compared with the observed CH4 concentration time series constructed from ice core, firn air, air archives and ambient air measurements (Fig. 2). The first 9 years (1901–1909) of the simulation are used to spin-up the ACTM, to guarantee that the results are independent of the initial conditions. The initial ACTM simulation using Eini (Fig. 2) underestimates the growth rate by 0.6 ppbyr-1 (4.8 ppbyr-1) for the period of slow (rapid) growth during 1910–1950 (1950–1990), and it also fails to capture the slowdown of the observed CH4 growth rate during the 1990s. Apparently, the Eini is a better first-guess in the first half of the 20th century compared to the latter half, when the CH4 growth rate changed dramatically. The model-observation mismatches are attributed to incomplete knowledge of Eini as used in the ACTM simulations, assuming no significant uncertainties in chemistry and transport. Thus we have estimated optimized global total CH4 emissions using the mass balance calculation as described in Sect. 2.5.

A new ACTM simulation using optimized emissions (Eopt) was performed and the modelled CH4 concentrations for the Arctic and Antarctic regions (blue and green, respectively) are shown in Fig. 2. Simulated and observed CH4 are in good agreement for the ACTM using Eopt (see Table 2 for detailed statistics). Observations in the Antarctic region reveal that the growth rates are: moderate (5.1 ppbyr-1) during 1910–1950; fastest (13.6 ppbyr-1) during 1950–1990; moderate (6.7 ppbyr-1) during the 1990s; near-steady in the early 2000s; and moderate again (5.7 ppbyr-1) since 2007. These are all simulated well by ACTM within the measurement uncertainties of 2–5 ppb. CH4 observations in the Arctic region only cover 1945–2010. The ACTM simulated growth rates for the Arctic region follow a similar trend as the Antarctic region: 5.6 ppbyr-1 during 1910–1950; 15.2 ppbyr-1 during 1950–1990; 5.2 ppbyr-1 during the 1990s; near-steady state during the early 2000s; and 5.8 ppbyr-1 since 2007. The inter-polar difference (IPD) of CH4 is, however, smaller in the model simulation (102.2±17.9 ppb) compared to observations (117±16.7 ppb) for the period 1949–2010. A detailed discussion on IPD is given in Sect. 3.3.

As no consensus has been reached for the trends in global mean OH concentration simulated by state-of-the-art CTMs (e.g. John et al., 2012), we used monthly varying climatological OH concentrations for our ACTM simulations. This OH distribution, from Spivakovsky et al. (2000), also fits well with ACTM transport for simulating inter-hemispheric gradients in CH3CCl3 and CH4 for the period 1988–2010 (Patra et al., 2011, 2014). The OH field is scaled by 0.92 for simulating the decay rate of CH3CCl3 in Earth's atmosphere (Krol and Lelieveld, 2003). For Eopt the total CH4 lifetime is given by τTotal=BoptEopt-dBoptdt. The trends in CH4 lifetime and tropospheric mean temperature anomaly are shown in Fig. 3. The average CH4 total lifetime during 1910–1919 and 2000–2009 are 9.4±0.09 and 9.0±0.09 years, respectively. The ACTM simulated air temperature anomaly is very similar to that of the observed temperature anomaly produced at GISS (Hansen et al., 2010). This illustrates that the long-term simulation of CH4 by ACTM, driven by analysed SST only, is close to that simulated by ACTM nudged to the reanalysis meteorology. To examine the factors causing change in the CH4 lifetime, we have calculated the temporal change of “apparent reaction rate” ka,i=Li/B, where i is the CH4 reaction with OH, O(1D), Cl or soil oxidation. Between the 1910s and the 2000s, contributions of Cl, OH, O(1D) reactions and soil oxidation to CH4 lifetime change are +61.7, +48.7, -1.6 and -8.8 %, respectively. Thus, the ∼4 % shorter average CH4 total lifetime from the first to the last decades of the last 100 years (1910–2009) is mainly caused by the large increase in Cl concentration and the increase in the tropospheric air temperature.

Global total CH4 emissions are optimized by minimizing the model-observation mismatches of CH4 concentrations over the Antarctic region (combined measurements from Law Dome ice core/firn air and direct air sampling from Cape Grim). Figure 4 shows a comparison of both the initial and optimized emissions with TransCom-CH4 emissions (CH4_EXTRA) for 1988–2010 (Patra et al., 2011). The increase rate of global total emissions is underestimated (overestimated) by ∼30 % (∼380 %) during 1940–1989 (1990–2009) in the initial emission scenario. Optimized emissions (Eopt) are in overall agreement with TransCom CH4 emissions for 1988–2010. This indicates robustness of the mass-balance based optimization used in this study. For quantitative assessment of ACTM simulations with all the emissions scenarios (Eini and Eopt), the model-observation CH4 concentration biases and SDs (1σ) (in ppb) of the biases over the Antarctic region, and averages of Eini, Eopt and Bopt for each decade are summarized in Table 2. Both the bias and 1σ are reduced drastically when optimized global total emissions are used in ACTM (Table 2). It may be reiterated here that the global total emissions for mass balance is dependent on the CH4 loss rates as parameterized in ACTM (Eq. 1).

Figure 5 shows inter-polar differences (IPD) of CH4 concentration using the ACTM simulations with Eini and Eopt over Arctic and Antarctic regions for 1910–2010. For the observations, we used a combination of data sets from Arctic (NGRIP firn air: 1953–2001, NEEM firn air: 1945–1996 and direct measurements at SUM since 1998) and Antarctic (Law Dome ice cores: 1901–1980, DE08-2 and DSSW20K firn air: 1978–1993, and direct measurements and archive tanks at CGO since 1978) regions. It is noted that no observation for 1910–1945 is available from the Arctic region, so the IPD of observed CH4 concentration is limited to 1945–2010. Uncertainty in the IPD before direct measurements is of order 20 ppb (1-σ), as indicated by the vertical uncertainty bars on the 20-year mean values (filled circles in Fig 5). This uncertainty in IPDs is consistent with that arising from the uncertainty (about 1.5 years) in effective age estimation of firn air, considering that CH4 growth rates were varying between 7–15 ppb in the period of 1950–1990. The ACTM simulation with Eini generally underestimated the observed CH4 IPD, and statistically significantly for the period 1970–2011. This underestimation reduces significantly (Fig. 5, refer to the black and blue lines) when the global total emission is optimized (Eopt) using observations from the Antarctic region. This suggests that the northern–southern hemispheric totals of CH4 emissions in Eini were incorrect, particularly for the period of 1970–2011. We assumed that the other factors affecting the IPD of CH4 concentration such as the latitudinal distribution of CH4 sinks and the mixing rates between hemispheres remained unchanged. Considering these uncertainties, we conclude that the ACTM simulations using Eopt successfully reproduce the observed CH4 IPD during 1950–2011. We found a high correlation (R=0.99) between differences of IPDs (IPDopt-IPDint) and difference of NH–SH emissions (ΔENSopt-ΔENSint) in optimized and initial guess cases (Fig. 5 inset), i.e. the larger the change in difference of NH–SH emissions, the larger the change in IPD. The change in latitudinal distribution of emissions is the dominant driver of IPD, which is in agreement with a previous study (Mitchell et al., 2013).

The difference between initial and optimized emissions (ΔE=Eopt-Eint) ranges from -15 to 0 and from 0 to 60 Tgyr-1 for the first and second halves of the last 100 years, respectively (Fig. 4). Though Eopt reproduces the CH4 concentration for the last 100 years fairly well, it does not verify how individual source categories have evolved over the period. Here we constrain different emission categories based on evolution of δ13C by separating ΔE into isotopically lighter and heavier sources (Sect. 2.6). We set the goal here to infer trends in emissions from biomass burning, because this emission category was kept constant over the whole simulation period due to the lack of consensus among different estimations (Mieville et al., 2010; Ito and Penner, 2005). The detailed interannual variability cannot be calculated from δ13Catmos over the Antarctic region, because a smoothed fitted curve is used to interpolate between observations. For the sake of consistency, we also fitted smoothed curves for δ13CEopt and ΔE, and then redistributed the smoothed ΔE between ΔEl and ΔEh. Observations and smooth time series of δ13Catmos and δ13CEopt are shown in Fig. 6a. We assumed δ13CΔEl and δ13CΔEh values of -60 ‰ (representing biogenic sources) and -21.8 ‰ (representing biomass burning emissions), respectively (Table 1). The corrected biomass burning emission now becomes Ebb=49.7 (initial biomass burning emission) +ΔEh (correction term) Tgyr-1. We have taken this approach because the level of confidence for estimations of emission variations from biomass burning is relatively low compared to all other emission categories, which are either estimated based on statistical data of human activities or model simulations. Ebb is also shown in Fig. 6b. Ebb has an increasing trend (varies from 23 to 51 Tgyr-1) during the period 1910–1990, followed by a decreasing trend (from 51 to 38 Tgyr-1) from the 1990s onward.

The CO based reference for open biomass burning by Ito et al. (2005), which is scaled using the ratio of CH4 and CO emissions from biomass burning based on the Global Inventory for Chemistry-Climate studies (GICC) data set (Mieville et al., 2010), shows a similar increasing trend. However, both the trend and mean values in the present study are larger than the GICC data set. The variation in biomass burning emissions during the 20th century is influenced by both the warmer climate and human activities (e.g. agricultural expansion, land-use change, domestic fuel use, fire management). The human population increased at the fastest rate since 1950 as per the United Nations statistics. However, saturation in cropland expansion in Asia, shift in domestic fuel use and improved fire management practices since the late 1980s would have suppressed the growth of CH4 emissions due to biomass burning caused by human activities (Patra et al., 2013; Li et al., 2002; Hurtt et al., 2006; Sathaye and Tyler, 1991; Montiel and Kraus, 2010). Uncertainties remain in the estimation of biomass burning emissions for the 20th century due to assumptions of δ13CEi and αi values. However, a sensitivity analysis using the estimated biomass burning emissions by varying δ13CΔEl from -55 to -65 ‰ (Sapart et al., 2012) suggests the trends in CH4 emissions from biomass burning are robust and only the magnitude of this emission could change by ± (5–15) % (Appendix A). The decreasing trend in biomass burning emission has also been reported for recent years but typically at lower absolute levels (Fig. 6) (e.g. Kirschke et al., 2013). The inclusion of δ13C in inversions and global mass balances has also in the past yielded higher emissions for global biomass burning than inventories (Miller et al., 2002; Bousquet et al., 2006).

The supplement biogenic source (ΔEl) follows a similar trend (a slow increasing trend during 1910–1950 and a rapid increase for the period 1950–1980, Fig. 6b) to that of the biogenic sources in the initial emissions (Eini) for the period 1910–1980 (Fig. 1a). Between 1981–2006 ΔEl shows a decreasing trend, followed by an increase from 2007 onward (Fig. 6b), which is different from the biogenic sources in Eini showing an increasing trend during this whole period (Fig. 1a). Recent studies suggested a likely reduction in emissions from wetlands (e.g. due to more frequent El Niño events in the last three decades compared to the decades before 1980, Hodson et al., 2011, or due to the cooling effect of increased anthropogenic sulphur pollution, Gauci et al., 2004, or volcanic eruptions, Hogan et al., 1994) and changes in rice agricultural practices (Li et al., 2002). The increase in atmospheric CH4 since 2007 may be ascribed to enhanced emissions from wetlands combined with an increasing trend of fossil fuel use (Dlugokencky et al., 2009; Bousquet et al., 2011; Kirschke et al., 2013; Bergamaschi et al., 2013). Apparently, ΔEl is able to capture these detailed features of biogenic emissions in recent decades, which are otherwise different in Eini. On the contrary, the rapid increase in emissions during 1950–1980, which is reflected in both ΔEl and biogenic sources in Eini, is likely to be driven by increasing anthropogenic activities (e.g. agriculture, ruminants and termites, organic waste deposits etc.) related to increasing human population during this period.

The present analysis limits the unaccounted emissions ΔE to only be from biomass burning (heavy) and biogenic (light) sources, but there could be other combinations of different categories of emissions. As we have two Eqs. () and (), unique solutions are only possible for two unknown categories of emissions assuming the rest of the emissions are all known. One reasonable scenario is distributing ΔE into biomass burning and biogenic sources as examined in this study. To calculate for other possible combinations, such as fossil fuel (heavy) and biogenic (light) sources, we need to know the correct biomass burning emissions in Eini and leave the correction terms ΔEl and ΔEh uncertain. We also attempted a combination of biomass burning and fossil fuel sources, but it produced unrealistic emission values (negative). We need additional constraints such as the 14C (Lassey et al., 2007b) and hydrogen isotopic ratio (δD) of CH4, which are presently very limited, to find solutions for more than two variables, e.g. distributing ΔE among biomass burning, fossil fuel and biogenic sources.