Optimal estimation of the present-day global methane budget

1. Introduction

[2] Despite the important role of methane (CH₄) in climate forcing, the magnitudes of its sources and sinks are still poorly quantified [Denman et al., 2007]. Anthropogenic emissions are diverse and include coal mining, natural gas use, agriculture, and waste treatment. Natural sources of CH₄, especially wetlands and geological seepage [Etiope et al., 2008] are particularly uncertain, as are biomass burning [van der Werf et al., 2006], which has both natural and anthropogenic origins, and the sinks of CH₄ (oxidation in soils and atmospheric chemistry). As a consequence, the future evolution of the CH₄ budget, and its response to climatic changes, remain highly uncertain. CH₄ observations can be used to constrain surface fluxes via inverse modeling [e.g., Mikaloff Fletcher et al., 2004a; Bruhwiler et al., 2005; Butler et al., 2005; Bousquet et al., 2006; Chen and Prinn, 2006; Bergamaschi et al., 2007; Meirink et al., 2006, 2008; Houweling et al., 1999; Hein et al., 1997]. The availability of satellite observations in particular has been shown to constrain the spatial structure of CH₄ flux to much higher resolution than surface stations, thereby decreasing the dependence on a priori assumptions [Bergamaschi et al., 2009]. Nonetheless, there is a strong spatial and temporal overlap between different source types that makes the differentiation between sources, based solely on spatial and temporal footprints, difficult. Other independent constraints are therefore needed to distinguish source types from one another.

[3] Additional constraints exist in the distinct “signatures” of carbon and hydrogen isotopes that characterize different CH₄ sources. The observed ratio of D/H in atmospheric CH₄ has been used by Whiticar and Schaefer [2009], Sowers [2010], and Mischler et al. [2010] to estimate the relative strength of thermogenic clathrate emissions, while Lassey et al. [2007a] examined the temporal record of ¹⁴CH₄ to constrain the relative fraction of fossil CH₄ sources. In this study we focus on the inversion of the observed ratio R = ¹³CH₄/¹²CH₄, typically quantified as δ¹³ = R/R_std − 1 (where R_std represents the Vienna PeeDee Belemnite standard [Craig, 1957; Lassey et al., 2007b]). The δ¹³ roughly differentiates fossil, biogenic, and pyrogenic methane sources. Observations of the spatial distribution of this ratio in the atmosphere (δ_A¹³) have been used previously to constrain the present-day spatial distribution of methane sources and sinks [Mikaloff Fletcher et al., 2004b], to distinguish source types [Mikaloff Fletcher et al., 2004a; Hein et al., 1997], and to extract information about the sources and sinks that were prevalent at different times [Fischer et al., 2008; Whiticar and Schaefer, 2009; Mischler et al., 2010].

[4] As will be shown below, a strong determinant of the net δ¹³ of emissions is the amount of CH₄ attributed to biomass burning and geological emissions, because these sources evidently both have high δ¹³ signatures. Geological seepage has recently come of interest as a strong CH₄ source that has been largely neglected in CH₄ budget studies [Kvenvolden and Rogers, 2005; Etiope et al., 2008]. Biomass burning is also an uncertain source, in part because fires are intermittent events with both natural and anthropogenic causes, but also because the CH₄ released depends on many interacting factors (fire type, vegetation type, etc.) that are difficult to estimate even at the present-day [Bowman et al., 2009].

[5] Inversions of the spatial variability of present-day CH₄ concentration by Bergamaschi et al. [2007], Houweling et al. [2008] and Bergamaschi et al. [2009] attribute 24–34Tg/a to biomass burning and around 18Tg/a to oceanic and geological emissions. This is in contrast to Mikaloff Fletcher et al. [2004a], who deduced a biomass burning source of around 88 Tg/a from present-day measurements of δ_A¹³. Similarly, but using the historical record of δ_A¹³, Lassey et al. [2007b] found that natural sources that are enriched in ¹³CH₄ (wildfires and/or geological seepage) may play a stronger role than generally assumed. A strong natural biomass burning and/or geological CH₄ source was also suggested by Fischer et al. [2008], based on the enhanced ¹³CH₄ found during cold climate periods over the last 20,000 years. These results reinforce the bottom-up estimate of Etiope et al. [2008], that geological CH₄ emissions may contribute as much as 53 ± 11Tg/a.

[6] Sowers [2010] suggests that enhanced ¹³CH₄ during cold climate periods over the past 10,000 years can also be explained by the reduction of emissions from boreal wetlands, the changing ratio of C3 and C4 vegetation, and changing emissions from methane clathrates in the ocean. Houweling et al. [2008] explain the historical record of δ_A¹³ over the last millenium as the combined effect of decreasing natural emissions (during the Little Ice Age), superimposed on increasing anthropogenic emissions (first from agriculture and then from industry). Thus, fundamentally different CH₄ storylines exist in the literature to explain the available observations of δ_A¹³.

[7] In this study we formulate the relationship between observed δ_A¹³ and the isotopic signatures of CH₄ sources and sinks as an optimal estimation problem that takes into account the existing uncertainties in surface fluxes, chemical sinks, δ¹³ signatures of the sources, and isotopic fractionations of the sinks. Because this amounts to a very underconstrained problem wherein four observations are used to constrain over 20 variables, we avoid looking for a definitive most probable CH₄ source/sink scenario. Instead we select three substantially different scenarios from the recent literature, adjust them relative to the observed information, and examine the resulting corrections in order to understand the remaining uncertainties in the present-day CH₄ budget. The optimization is described in section 2. The baseline results are given in section 3, along with a physical interpretation and tests of the sensitivity of our results to various assumptions. Section 3 also gives a set of distinct, isotopically consistent emission scenarios and uncertainty ranges, which can be used as a priori esimates in spatially constrained inverse modeling, e.g., using satellite observations. Conclusions and points for further research are given in section 4.

2. Methods

[8] Table 1 shows the net ¹³CH₄ isotopic signature in the atmosphere, δ_A¹³, and the corresponding CH₄ concentrations, measured at the South Pole in 2005 (GLOBALVIEW-CH4, NOAA Earth System Research Laboratory, Boulder, Colorado, anonymous ftp to ftp.cmdl.noaa.gov), in Antarctic ice cores for the years 1000 and 1900 [Ferretti et al., 2005] and at the Last Glacial Maximum (LGM) [Fischer et al., 2008]. The 2005 measurements represent the combined influence of present-day natural, industrial, and agricultural emissions, as well as the removal of CH₄ from the atmosphere by various sinks (all of which result in ¹³CH₄ enrichment). The year 1900 represents the early industrial (EI) era, when anthropogenic CH₄ emissions were dominated by agricultural and burning sources. Here both atmospheric CH₄ and δ_A¹³ were low relative to the present-day. During the early agricultural era (EA, represented by the year 1000), when anthropogenic emissions were still low relative to natural emissions, observed atmospheric CH₄ is correspondingly lower but δ_A¹³ is close to the present-day level. During the drastically different climate conditions of the LGM, the average CH₄ concentration was roughly half the EA level, but δ_A¹³ was higher than at any post glacial time.

[9] The net δ_A¹³ results from the balance of global source and sink totals (E_iS_j, respectively, representing mass over time), with the sink fluxes multiplied by the fractionation factors α_j specific to each process, and the emission fluxes by the isotopic ratios δ_i¹³ that characterize each source type. Assuming that both the atmospheric methane concentration and δ_A¹³ are in steady state gives the following relationship between δ_A¹³ and methane sources, sinks, and their respective δ_i¹³ signatures and sink fractionation factors α_j (see Appendix A):

[10] Equation (1) is used to optimize the global annual fluxes (in Tg/a) of ten sources (rice agriculture, domestic ruminants, waste, oil and natural gas production, coal mining and biofuel, biomass burning, wetlands, oceans, termites/wild animals, and terrestrial and marine geological seepage) and four sinks (soil consumption and reactions in the atmosphere with OH, Cl, and O(¹D)), as well as their respective source signatures (δ_i¹³) or sink separation factors (ε_j = α_j − 1). This is done by (1) formulating a priori estimates of present-day sources, sinks, and assumed uncertainties; (2) extrapolating these estimates to the past climatic periods defined above; (3) computing δ_A¹³ for each period using (1); and (4) adjusting the source and sink totals and their isotopic factors to minimize the misfit between implied and observed δ_A¹³.

[11] We adapt three CH₄ emission scenarios from the recent literature as prior emission scenarios; they are summarized in Table 2. Scenarios B07 and BQT are based on two recent inversions of satellite observations, Bergamaschi et al. [2007] and Bousquet et al. [2006], respectively. While these scenarios have similar nonburning natural emissions, BQT attributes about 40Tg/a less to anthropogenic biogenic emissions (rice, domestic ruminants, and waste), and correspondingly more to anthropogenic “fossil” sources (oil/gas production and coal mining/biofuel) and biomass burning (which has both natural and anthropogenic components). We additionally adapt BQT into a third scenario, GEO, by adding an additional 40Tg/a for geological seepage, thus taking into account the possible strong geological CH₄ source suggested by Etiope et al. [2008]. We neglect aerobic emissions from terrestrial plants. To avoid adding a difficult-to-constrain unknown to the optimization, we refrain from separating biomass burning into natural and anthropogenic components. We assume the same prior values for the isotopic characteristics δ_i¹³ of each source. These are also listed in Table 2.

[12] In order to focus this study on sources, the same prior magnitudes and sink separation factors are assumed for three of four CH₄ sinks. We assume 29Tg/a for the bacterial consumption of CH₄ in dry soils [Curry, 2007], 10Tg/a for the reaction of CH₄ with O(¹D) [Denman et al., 2007], and 25Tg/a for the reaction of CH₄ with Cl. The assumed Cl sink is an estimate based on the marine boundary layer Cl sink estimate of Allan et al. [2007], together with the stratospheric Cl sink, which is estimated to comprise around 20–35% [Röckmann et al., 2004] of the 40Tg/a total stratospheric sink of CH₄ [Denman et al., 2007] (the sensitivity of our results to this assumption is tested in section 3.2). The strongest CH₄ sink, the reaction with OH, is both highly uncertain and variable [Krol et al., 1998], and is therefore estimated such that the total sink equals the total emission for each scenario, in keeping with our assumption of steady state.

[13] A prior uncertainty of 25% is assumed for all sources and sinks. This is sometimes less that the range between scenarios, but is done because the problem is too weakly constrained to converge to a single “best fit” scenario. We shall see that this choice of errors preserves the fundamental differences between the scenarios, allowing us to examine the physical parameters under which each scenario can be reconciled with the isotopic observations.

[14] For the δ_i¹³ per source, an uncertainty of 5‰ is assumed for all sources except biomass burning, where we assume an uncertainty of 8‰ in order to account for possible differences between anthropogenic and natural burning, which we examine in more detail in sections 3.3 and 3.4. For the isotopic separation factors ε_j of the sinks, we adopt the uncertainties estimated by Lassey et al. [2007b], assuming uncertainties of 2‰, 0.75‰ and 1.0‰ for soil consumption, the reaction with OH, and the reaction with Cl, respectively. In addition, we assume a 2‰ uncertainty for the reaction with O(¹D). Thus the optimization gives more freedom to change the isotopic signature of sources, which are the focus of our study.

[15] The ten sources and four sinks at the present-day, plus their respective δ_i¹³ or ε_j, comprise the 28-element optimization vector, x. To optimize x, a given present-day source/sink configuration is first mapped to the three past times (EI, EA, and LGM) by making the following five assumptions: (1) that anthropogenic emissions (not accounting for biomass burning) were negligible at LGM, and at EI and EA were given by the nonindustrial source totals, multiplied by relative population factors a_EI = 0.24 and a_EA = 0.12, respectively [United Nations Population Division, 1999]; (2) that wetland emissions at LGM were proportional to the present-day wetland emission by a factor w_LGM; (3) that total biomass burning emissions at past times were proportional to the present-day total burning emission by factors p_EI, p_EA, and p_LGM; and (4) that all other (nonburning) natural emissions remained constant relative to each other in time; and (5) that the sinks changed in proportion to the total emission, but not relative to each other. As an experiment baseline, we assume w_LGM = 0.62, following [Weber et al., 2010], and examine other values in section 3.5. For pyrogenic emissions, we begin with baseline values of p_EI = p_EA = 1.0 and p_LGM = 0.8, examining other values in sections 3.3 and 3.4.

[16] Figure 1a compares the δ_A¹³ implied within the above framework by each scenario for the four time periods. The uncertainty of the implied δ_A¹³ is estimated via a 20,000-member ensemble of perturbations generated around each scenario, using Gaussian distributions with standard deviations given by the assumed uncertainties. It can be seen that, given the above assumptions, none of the emission scenarios fit all four periods equally well, with scenarios BQT and GEO overestimating δ_A¹³ for all times except LGM. Scenario B07, which is the most biogenically dominated, in general fits the observed δ_A¹³ best, but does not really capture the variation in δ_A¹³ across PD, EI, and EA. Given our assumed wetland and pyrogenic LGM emission factors, scenario BQT reproduces the observed high δ_A¹³ at LGM best.

[17] To see how each scenario changes when constrained to fit these observations, we compute the optimal state x^a for each scenario using the Bayesian update equation:

[18] (x) represents the mapping of the elements of x to the observations of δ_A¹³, using (1) and the backward extrapolation described above. The difference between the observations of δ_A¹³ (y), and the result implied by a prior estimate of the state [(x^b)] is weighted by an optimal weight matrix (K), which represents the prior uncertainty modulated by the total prior and observational uncertainty, and added to the background estimate. Because K includes the nonlinear operation ℋ, it is approximated using a 20,000-member ensemble of normally distributed random perturbations with standard deviations given by our prior assumed uncertainties. Having computed K, each ensemble member is adjusted via (2); the ensemble mean analysis is then taken as the optimized state.

[19] We define y to contain the δ_A¹³ observations for PD, EI, and EA, as well as the assumed present-day total emission, E. Since the only distinguishing factors between EA and LGM emissions in our framework are the wetland and pyrogenic emission reduction factors, the LGM observation only constrains these factors and does not give additional information about the other variables. We therefore perform the optimization without the LGM observation, and treat the relationship between assumed w_LGM and p_LGM and the implied δ_A¹³ in section 3.5.

[20] In section 3 we perform two main optimizations, not counting sensitivity tests: first, the scenarios are optimized such that their prior source and sink total is preserved. This shows how an enhancement of one source/sink requires a reduction in another in order to balance both the total emission and the net implied δ_A¹³. Then, all scenarios are optimized to a common total of 583Tg/a, which corresponds to the observed global average concentration for 2005 (Table 1), assuming no net growth of CH₄ in 2005 and a present-day lifetime of 8.45 years [Denman et al., 2007] This yields three comparable scenarios for discussion.

3. Results

3.1. Optimization

[21] Figure 1b shows the four values of δ_A¹³ that result for each scenario following optimization. The optimization manages to fit all scenarios to the observed δ_A¹³ at PD, EI, and EA, but worsens the fit to the LGM observation, which was not assimilated. This implies that our choice of factors p_LGM = 0.8 and w_LGM = 0.62 is not consistent with the adjusted scenarios for the LGM (to be discussed in section 3.5). Figure 2 compares the prior and optimized present-day source totals per scenario. For the sake of simplicity, and to filter out small differences in sources that are isotopically similar, the sources have been aggregated into five categories: natural and anthropogenic biogenic (NBIO, ABIO), natural and anthropogenic fossil (NFOSS and AFOSS) and pyrogenic (PYRO). It is clear that even though all scenarios are reconciled with the observations, their fundamental differences are retained.

[22] A common adjustment across all scenarios is an enhancement of anthropogenic fossil emissions (coal mining, biofuel, and oil/gas production) and biogenic emissions (rice, waste, and domestic ruminants), with concomitant reductions in natural biogenic (wetlands, termites, wild animals, and oceans) and pyrogenic emissions. This result can be explained by considering that the adjustment toward observations requires that the reduction of δ_A¹³ at EI must be stronger than for PD and EA. The fit to the EI observation is in part achieved by decreasing geological (NFOSS) and burning emissions (PYRO), but this adjustment affects the δ_A¹³ implied for PD, EI, and EA equally. As a consequence, AFOSS is increased in all scenarios while NBIO is lowered, which increases δ_A¹³ at PD relative to EI and EA. Increasing ABIO also raises δ_A¹³ at EA relative to EI, since fewer anthropogenic biogenic sources (which have low δ¹³) are assumed to exist at EA. Thus we have the overall result that to simultaneously satisfy both the present-day global δ_A¹³ and that of past times, assuming no change in biomass burning emissions since the early agricultural era, and no changes in the relative magnitudes of sinks or the isotopic signatures of sources and sinks over time, requires fossil fuel (or biofuel)-related emissions to be near the upper end of the uncertainty range.

[23] Table 3 shows the optimized source/sink totals, their optimized isotopic signatures, and the totals and estimated uncertainties of each, when the optimization is repeated while constraining the total source and total sink in all three scenarios to 583Tg/a. This upscaling of all three scenarios was found to preserve the optimized δ_A¹³ values and the relative magnitudes of the individual sources. Comparing Table 3 to Table 2 shows that the range of prior estimates has largely been reduced for emissions from oil/gas production and waste. The fraction of natural emissions, not counting natural biomass burning, has been lowered overall, and constrained from 36–41% to 33–35%. Even though the scenarios fit the observations equally well, substantial differences between them remain.

Table 3. Optimized Global Totals for Sources, Sinks, and Their Corresponding Isotopic Factors, Optimized to a Total Source and Sink of 583 Tg/a

Sources (Tg/a)	B07	BQT	GEO	B07 δ13 (‰)	BQT	GEO
Coal, biofuel	34 ± 6	70 ± 13	68 ± 13	−30.5 ± 4.8	−32.9 ± 4.4	−31.9 ± 4.4
Oil, gas	72 ± 11	74 ± 14	71 ± 14	−31.2 ± 4.3	−37.9 ± 4.4	−36.7 ± 4.3
Waste	75 ± 17	60 ± 13	58 ± 13	−58.4 ± 4.6	−60.4 ± 4.6	−60.7 ± 4.7
Dom. ruminants	118 ± 22	118 ± 19	113 ± 19	−66.7 ± 4.0	−70.8 ± 3.9	−71.2 ± 4.0
Rice agriculture	67 ± 14	35 ± 8	34 ± 8	−66.8 ± 4.7	−67.0 ± 4.9	−67.1 ± 4.9
Bio. burning	24 ± 6	38 ± 9	33 ± 9	−18.3 ± 7.8	−19.0 ± 7.6	−21.0 ± 7.6
Termites/wild rum.	24 ± 6	23 ± 6	23 ± 6	−56.9 ± 5.0	−57.1 ± 5.0	−57.6 ± 5.0
Geol. seepage	5 ± 1	0 ± 0	36 ± 10	−39.9 ± 5.0	−39.9 ± 5.0	−40.8 ± 4.9
Wetlands	155 ± 27	147 ± 23	127 ± 23	−59.9 ± 2.3	−61.1 ± 3.2	−63.9 ± 3.4
Ocean	10 ± 2	19 ± 5	19 ± 5	−59.8 ± 5.0	−59.9 ± 5.0	−60.2 ± 5.0
Sinks (Tg/a)	B07	BQT	GEO	B07 ε (‰)	BQT	GEO
Soil	30 ± 7	28 ± 7	28 ± 7	−20.1 ± 2.0	−19.9 ± 2.0	−19.9 ± 2.0
CH4 + OH	518 ± 10	522 ± 10	522 ± 10	−4.6 ± 0.7	−4.4 ± 0.7	−4.3 ± 0.7
CH4 + Cl	26 ± 6	23 ± 6	22 ± 6	−60.0 ± 1.0	−60.0 ± 1.0	−59.9 ± 1.0
CH4 + O(1D)	10 ± 2	10 ± 2	10 ± 2	−13.0 ± 2.0	−12.9 ± 2.0	−12.9 ± 2.0
Total Source Ea	583	583	583	−54.5 ± 1.0	−54.0 ± 1.0	−53.7 ± 1.1
Total Sink Sa	583	583	583	−8.0 ± 0.9	−7.5 ± 0.9	−7.3 ± 0.9
N/Ea	0.33	0.32	0.35

• a Optimized total source (E) and sink (S) and their respective isotopic factors, as well as the natural source fraction N/E (N excluding biomass burning).

[24] In particular, optimized scenario GEO is still distinguished by a strong geological source (though now with a small reduction in anthropogenic fossil sources relative to BQT), and BQT by a strong biomass burning source. Comparison of the optimized δ¹³ signatures of the sources reveals that the differences in the scenarios are made possible by compensating adjustments in source isotopic signatures, for which we assumed prior standard deviations of 5‰. For example, in BQT and GEO, where fossil and pyrogenic emissions are stronger, the δ¹³ of domestic ruminants is decreased by 6‰ (i.e., it is assumed to be more depleted in ¹³CH₄). The largest change in the prior isotopic signature is for oil and gas in scenario B07, from the typically observed ratio for fossil fuels of −40‰ to −31‰. It can also be seen that the optimized total sink fractionations are within one standard deviation of each other, and within the estimate of −7.7 ± 1.4‰ made by Lassey et al. [2007b], with scenario B07 requiring a slightly stronger total sink fractionation to offset the slightly higher total δ¹³ of emission.

3.4. Temporal Variation in Pyrogenic Emissions

[27] It was found in section 3.1 that, in order to satisfy both the EI δ_A¹³ minimum and the PD observation, optimization increases anthropogenic fossil emissions relative to the prior. This happens in part because pyrogenic emissions, which are isotopically heavy and were estimated above to be unchanged between EI/EA and PD, constitute a much larger part of EI/EA emissions, thus requiring a strong adjustment in the other emission types, which is in turn compensated for by large increases in anthropogenic fossil emissions at the present-day.

[28] This result is therefore related to our assumed pyrogenic emission factors p_EI and p_EA, and is examined more closely in Figure 3, which shows how the optimized present-day AFOSS changes as we change the value assumed for p_EI and p_EA from 0.5 to 1.5. Superimposed in Figure 3 are the results of two alternative optimizations, one (dashed lines) where the isotopic signature of biomass burning is lowered to −25‰ (reflecting a possible reduction in anthropogenic biomass burning), and one (dot-dashed lines) where the isotopic signature of wetland emissions is increased to −52‰, which considers the extreme possibility that wetland emissions are dominated by inundated trees instead of grasses [Rice et al., 2010]. The baseline value (p_EI = p_EA = 1.0) is indicated by a vertical line. As predicted, estimated AFOSS increases with p_EI/p_EA. Assuming the high extreme value of δ¹³ for wetlands results in an optimized AFOSS that is about 3Tg/a lower, while assuming the higher value for biomass burning raises the optimized AFOSS by at most 1Tg/a.

[29] Charcoal records [Power et al., 2008] suggest that pyrogenic CH₄ emissions were slightly higher at EI and EA than PD (presumably due to more aggressive agricultural burning), though the actual CH₄ emissions for these eras depend strongly on vegetation and fire type and are therefore far less clear. If EI/EA biomass burning emissions differed from the present-day by 20%, the impact on estimated present-day anthropogenic fossil emissions is within about 5Tg/a, while the range between scenarios is much larger. The BQT prior total for AFOSS (122Tg/a) results from inverse modeling of present-day measurements of both concentration and δ_A¹³, and is thus substantially backed up by observation. It is indicated by a horizontal solid line in Figure 3. It is not possible to achieve this total in the optimization of our three scenarios without a change in EI/EA pyrogenic emissions that exceeds 50%.

3.5. Implication for LGM Emissions

[30] We now turn our attention to the observed δ_A¹³ at LGM. Clearly, our assumption that w_LGM = 0.62 (62% wetland emissions relative to PD) and p_LGM = 0.8 (80% pyrogenic emissions relative to PD) is no longer consistent with this observation given the optimized scenarios (Figure 1). If p_LGM is increased, the implied LGM emissions will be isotopically heavier, which means that the w_LGM required to satisfy the observation will increase. In other words, if there are substantial natural fossil emissions, the required wetland emission reduction will be less. Figure 4 shows the change in implied δ_A¹³ at LGM as a function of w_LGM, for unchanged LGM burning emissions (p_LGM = 1), and a 20% reduction and enhancement of emissions at LGM (p_LGM = 0.8 and 1.2, respectively). The plot is shown for scenarios B07 (Figure 4a) and GEO (Figure 4b), omitting BQT because it shows values in between those of B07 and GEO. The observed LGM δ_A¹³ is indicated by a horizontal black line.

[31] Charcoal records indicate LGM fire activity that is lower than the present-day [Power et al., 2008]. Assuming that p_LGM = 0.8 we find that emissions from wetlands had to be 30% of the present-day value in scenario B07, and about 42% in scenario GEO, in order for the implied δ_A¹³ to meet the observed value. For comparison, the finding of Weber et al. [2010], that LGM wetland emissions were by 58–65% of the PD emission, is indicated in Figure 4 by a dashed line at 0.62. Similarly, the result of Kaplan [2002], that wetland emissions at LGM were reduced to 76% of the PD value, is indicated by a dot-dashed line. For the biogenically dominated scenario B07, simultaneously fitting the observed δ_A¹³ and either estimate of wetland emissions reduction requires increases in biomass burning that are likely to be unrealistic (p_LGM > 1.2). However, with the strong geological emissions of scenario GEO, the Weber et al. [2010] value can be reconciled with the observations for a 20% enhancement of pyrogenic emissions.

3.6. Implication for Changing CH₄ Lifetime

[32] Our optimizations do not include as a constraint the observed atmospheric CH₄ concentrations for the past time periods (Table 1), and thereby avoid making assumptions about changes in CH₄ lifetime between the four climate periods. However, if for example our implied past time sources and sinks are small compared to the observed burden at each time (along with the assumption of a steady state), then we are required to assume either an overall enhancement of natural emissions at the past times (EI or EA) and/or a change in the atmospheric lifetime of CH₄. To see this, one can relate the total emission for periods T = EI and EA to the corresponding approximate burden, divided by lifetime:

Here τ represents the present-day CH₄ lifetime, and A′, P and N represent the nonindustrial-anthropogenic, pyrogenic, and natural emission totals, respectively, for present-day; these are scaled by the factors a_T and p_T (assumed a priori), and n_T and s_T, which represent the ratio between past time and present-day natural emissions (n_T), and lifetime (s_T). B_T represents the atmospheric burden at each time period, and can be approximated by scaling the present-day burden of 4932 Tg by the ratio of present-day and past time Antarctic/South Pole concentrations in Table 1. This neglects the difference between global mean and Antarctic CH₄ resulting from the latitudinal gradient, which is estimated as 1–4% for LGM [Chappellaz et al., 1997; Brook et al., 2000] and 2–4% for EA and EI [Dällenbach et al., 2000; Brook et al., 2000], and thus translates to at most about 5% difference in the estimated burden. Having assumed values for a_T it is possible to use equation (3) to infer either n_T or s_T, while assuming the other is unity, as a function of p_T.

[33] We find that the maximum implied changes for both periods, if p_EI and p_EA are varied from 0.5 to 1.5, is a 3% reduction of either the CH₄ lifetime or natural CH₄ emissions at EI or EA, which is marginal. A somewhat reduced EA/EI lifetime is certainly plausible [e.g., Crutzen and Brühl, 1993].

4. Summary and Conclusions

[34] We have presented an optimal estimation of the present-day methane budget using the observed δ_A¹³ isotopic record, taking into account the uncertainties in sources, sinks, and δ_i¹³ and ε_j factors. It was found that it is possible to fit the observations by slightly adjusting three present-day CH₄ emission scenarios, without changing the fundamental properties that distinguish each scenario. This yields three distinct ways of partitioning the present-day CH₄ emission budget, all of which satisfy the δ_A¹³ record: scenario B07 is dominated by biogenic sources, especially anthropogenic ones (rice and waste), while BQT and GEO feature more prominent contributions from biomass burning (33–38Tg/a), and GEO an additional strong contribution (36 ± 10Tg/a) from geological seepage. The 14Tg/a range of biomass burning emissions covered by these scenarios is within the interannual variability estimated for biomass burning emissions [e.g., Butler et al., 2005]. Comparing the scenarios to the approximate CH₄ burden, all three imply only marginal changes in CH₄ lifetime or nonpyrogenic natural emissions over the last millenium.

[35] In order to differentiate the δ_A¹³ implied for the present-day from the early industrial and early agricultural eras, we find that present-day anthropogenic emissions related to fossil fuels (coal mining and biofuel, oil and gas production) need to be on the high end of the assumed uncertainty range, especially if biomass burning in the past was high relative to the present-day. This, along with relatively lower present-day natural biogenic emissions than were assumed a priori, was a common result in the optimization of all scenarios; even in the presence of strong geological emissions, which contribute to the total fossil fraction of emission. The optimization of scenario GEO shows that, while the geological source helps to explain the high δ_A¹³ at LGM, geologic emissions do not readily explain the difference in δ_A¹³ between, e.g., the early industrial period and present-day. For scenario B07, the shift from biogenic to anthropogenic fossil emissions is primarily pronounced as an increase of estimated oil/gas emission to 72Tg/a, in line with scenarios BQT and GEO. The posterior estimate for anthropogenic emissions in B07 is in agreement with the recently published Emission Database for Global Atmospheric Research (EDGAR) version 4 emissions [EDGAR, 2010].

[36] Overall, optimization constrains the present-day natural fraction of emissions to 32–35%, not counting natural biomass burning. In contrast, the optimized scenarios differ in the fossil fraction of sources. B07 has 19% fossil sources, BQT has 25%, and GEO 30%. This range is possible within the allowed uncertainty range of the δ¹³ signatures of the sources; that is, scenario B07 tends to estimate these to be on the high, and scenario GEO on the low end, of the uncertainty range. From observations of atmospheric radiocarbon, Quay et al. [1999] estimate that fossil emissions, which are devoid of radiocarbon, make up 18 ± 9% of total present-day emissions, while more recent work by Lassey et al. [2007a] argues that a fossil fraction of 30 ± 2.3% is more likely. Thus, while fossil fractions of about 20–29% can evidently be accommodated within the global δ¹³ budget, the results of Lassey et al. [2007a] would suggest that the BQT and GEO scenarios are more likely, though it would mean that the present-day emissions from coal mining and biofuel are about 34Tg/a stronger than estimated by B07, and also much larger than assumed in the recent EDGAR 4 inventory [EDGAR, 2010].

[37] We find the maximum feasible wetland emissions at LGM to be ∼ 60% of present-day wetland emissions, in agreement with Weber et al. [2010], but this requires a ∼ 36Tg/a geological CH₄ source (scenario GEO), and a ∼ 20% enhancement in LGM biomass burning emissions relative to the present-day. For the biogenically dominated scenario B07, and without any LGM enhancement of biomass burning, estimated wetland emissions are about 40% the present-day value.

[38] The interpretation of the LGM observations in section 3.5 neglects possible relative changes in CH₄ sinks at LGM. For example, both Kaplan [2002] and Schaefer and Whiticar [2008] estimate that the soil sink was reduced at the LGM relative to PD. Schaefer and Whiticar [2008] estimate that this would result in a ∼ 1.7‰ weaker total sink fractionation, which would require a corresponding increase in the δ¹³ of emission. In our framework this translates to roughly a 0.15 reduction of w_LGM for a given p_LGM, i.e., an additional 15% reduction of LGM wetland emissions relative to the present-day, which, given reasonable estimates of biomass burning at LGM, would increase the disagreement between our results and the wetland emission reductions estimated by Kaplan [2002] and Weber et al. [2010]. A more exact number would require an in-depth analysis of LGM atmospheric chemistry, and is beyond the scope of this study. Observations of δD may offer further constraints on the past and present time CH₄ budgets; here we point to the recent work of Sowers [2010] and Mischler et al. [2010]. As mentioned above, in order to avoid convoluting the results with too many unknown factors, this study has not in detail considered changes in the δ¹³ signatures of the individual sources over the last 25,000 years, which could have arisen from various climatic effects, with several complex possibilities [Whiticar and Schaefer, 2009]. We have also not explicitly accounted for possible isotopic differences in emissions from boreal peatlands (which are dominated by C3 plants, Still et al. [2003]) and tropical wetlands, though the experiment of section 3.4 suggests that even strong changes in the δ¹³ of wetland emissions would have a small effect on the outcome of this study. The optimal estimation approach outlined here could be extended to take these factors into account, though such an approach would also increase the degrees of freedom of an already underconstrained problem, which further increases the necessity for more observations and better prior knowledge of the relevant sources and sinks (as well as their isotopic signatures) at each point in time.

[39] It remains to be seen how the scenarios resulting from this analysis compare to observations with spatial and temporal structure, in particular from satellites. Inversions of satellite measurements by Bergamaschi et al. [2007], Meirink et al. [2008] and Bergamaschi et al. [2009] have suggested that an emission budget similar to scenario B07 is likely, though these studies did not test alternative a priori scenarios. Accounting for geological emissions in an inversion of high-resolution spatial observations requires an a priori inventory of the global distribution of geological seepage, which to our knowledge has not yet been published.