3.3. Base Year Budget
 We present results from three different inversions, in which: (1) the tropospheric OH sink strength was included as a parameter to be determined by the inversion, (2) the tropospheric OH sink strength was fixed at its a priori value (calculated using the parameterized OH), and (3) the tropospheric OH sink strength was fixed at a value derived from an inversion using observations of methyl chloroform (abbreviated as MCF here). Results from the third case are considered to represent our best guess for the budget. The first case yielded the surprising result that the a posteriori strength of the OH sink was much lower, by 38%, than the a priori value, outside the assigned 2σ uncertainty range. The equivalent tropospheric average OH concentration would be 10% lower than an estimate reported previously by Prinn et al.  and 27% lower than that of Spivakovsky et al. ; the resulting lifetime for MCF with respect to tropospheric OH is outside the 2σ uncertainty range of the estimate quoted by Prinn et al.  based on analysis of MCF observations. To understand this discrepancy, we conducted our own MCF inversions, taking advantage of the simpler budget of the gas and the relatively well-known spatial distribution of emissions. These calculations confirm that the a priori value for OH is too high, although the decrease in OH relative to previous studies is not as extreme, for example, ∼10% below the estimate of Spivakovsky et al. . A major difference between our method and those of previous MCF inversion studies [Prinn et al., 2001; Krol and Lelieveld, 2003] is that we optimized MCF emissions as well as the OH sink. The simultaneous optimization of the emissions and OH sink is justified by the observation that the averaging kernels (model resolution matrix) for the inversion show very little correlation between the global OH parameter and the MCF source parameters (the global source was divided into five geographic regions). This lack of correlation can be explained by the fact that the OH and source parameters have distinct spatial distributions (OH peaks in the tropics), while the vast majority of MCF emissions occurs in the middle to high latitudes of the Northern Hemisphere. The inversion results indicate that the MCF emissions assumed by previous studies for the 1980s (prior to the ban on the production of MCF in developed countries), based on the work of Midgley and McCulloch , may be too high, by about 10%. Assuming the MCF sales data of Midgley and McCulloch are accurate, the above result suggests that the time lag between sales and emissions may have been underestimated. The idea of a longer delay was proposed also by Krol et al.  and Barnes et al. . Another improvement over previous studies is that we use a transport model with meteorology specific to the period of the study and with higher spatial resolution. Krol and Lelieveld  demonstrated that inversions for OH are sensitive to the treatment of transport. There is evidence also from recent photochemical model calculations of tropospheric OH that previous estimates for OH may be too high. Full-chemistry simulations for various years with the GEOS-CHEM model that account for recent improvements in reaction rate coefficients and chemical mechanisms indicate a lifetime for MCF with respect to tropospheric OH of 6.2–6.6 years (I. Bey, H. Liu, and M. Evans, personal communication, 2004), longer than the lifetime of 5.99 ± 1.66 years computed by Prinn et al.  and the value of 5.7 years computed by Spivakovsky et al. . The improvements in the model include an upward revision of the rate coefficient for the O(1D) + N2 reaction based on the work of Ravishankara et al. , which results in a reduction in the rate for production of OH. The results of our MCF study indicate that current understanding of MCF emissions, global OH concentrations, and lifetimes of reactive trace gases may be subject to significant revision. The work on MCF will be presented in detail elsewhere.
 The second CH4 inversion (OH fixed at the a priori value) is included in the discussion in the rest of the paper to illustrate the sensitivity of the inversion results for CH4 sources as well as to demonstrate that the main conclusions regarding the interannual variability of CH4 are independent of the budget assumed for the base year. We refer to the first inversion as “Low OH,” the second as “High OH,” and the third as “Best Guess.”
 The inversion results are compiled in Table 4. We verified that the a posteriori budgets are consistent with isotopic constraints. Model values for the average δ13C, δD, and fossil fraction of the source are compared in Table 4 with estimates based on atmospheric measurements of CH4 isotopic composition by Quay et al. . Quay et al. considered fractionation by tropospheric OH, soil oxidation, and stratospheric sinks in their calculations. The values for all three inversions lie well within the uncertainty ranges quoted by Quay et al. Also shown in Table 4 are the lifetimes of CH4 and MCF with respect to tropospheric OH and the tropospheric mean OH concentration for the three inversions along with corresponding estimates from the literature. The lifetime of CH4 with respect to OH for the Low OH case is 43% longer than the estimate by Prinn et al.  and outside the uncertainty range. The lifetime for the High OH case is 10% shorter than the estimate by Prinn et al. but within the uncertainty range. The lifetime for the Best Guess, 11.3 years, is 12% longer than the Prinn et al. value but within the uncertainty range. The Best Guess lifetime is 18% longer than the value of 9.6 years adopted by the Third Assessment Report of the Intergovernmental Panel on Climate Change (IPCC TAR) [Prather et al., 2001]; the lifetime with respect to all sinks is 9.9 years for Best Guess as compared with 8.4 years for the IPCC TAR. The strength of the OH sink is determined by the rate constant for the CH4 + OH reaction, the temperature distribution, and the concentrations and distributions of OH and CH4, all with associated uncertainties. Assuming that the concentration of OH is the dominant source of uncertainty, the Low OH inversion implies a mean concentration for OH 27% lower than the estimate by Spivakovsky et al. , outside the uncertainty range quoted in that study, but only 10% lower than and within the uncertainty range quoted by Prinn et al. . The average OH concentration for the High OH case is 17% higher than Spivakovsky et al. and 44% higher than Prinn et al., outside the uncertainty ranges of both. The average OH for the Best Guess is 7% lower than Spivakovsky et al. and 13% higher than Prinn et al. The OH concentrations for the Low OH, High OH, and Best Guess inversions translate into lifetimes for MCF with respect to tropospheric OH 42% longer, 10% shorter, and 12% longer than that of Prinn et al., respectively, and 49% longer, 5% shorter, and 18% longer than that of Spivakovsky et al. . Note that it is unclear why the OH averages of Spivakovsky et al. and Prinn et al. are so different while their lifetime estimates are quite similar. Most likely, the apparent inconsistency can be attributed at least in part to differences in the vertical and horizontal resolutions of the models; the model of Spivakovsky et al. has seven to eight tropospheric layers and a horizontal resolution of 4° latitude by 5° longitude, while the model of Prinn et al. has two tropospheric layers with four zonal bands in each layer. Similarly, differences in model resolution can probably explain the inconsistency between our results and those of Prinn et al. (i.e., higher OH at the same time as longer lifetime).
 Table 1 includes results from some previous methane inversion studies. Hein et al.  and Houweling et al.  estimated larger values for the OH sink than the result from our Low OH inversion, even though they allowed the OH sink to be adjusted by the inversion. We believe that the larger value obtained by Houweling et al. can be attributed to the fact that they assumed an extremely small a priori error for the OH sink, 5% (2σ). Regarding the Hein et al. study, use of large a priori estimates with small uncertainties for the sources (e.g., 270 ± 50 Tg for wetlands) may have resulted in the large OH sink in order to satisfy mass balance.
 The source estimates for swamps, biomass burning, and biofuels differ significantly between the Low OH and High OH inversions, with values being higher for the High OH case. The difference is particularly large for swamps: 80 Tg for Low OH and 230 Tg for High OH as compared to the a priori value of 195 Tg based on the work of Walter et al. [2001a]. Total wetland emissions, including bogs and tundra, are 107 Tg, 258 Tg, 176 Tg, and 260 Tg for Low OH, High OH, Best Guess, and a priori, respectively. Bottom-up estimates of total wetland emissions in the literature, excluding Walter et al., range from 80 to 156 Tg [Walter et al., 2001a; Cao et al., 1998, and references therein]. Walter et al. suggest that their estimate may be anomalously high because the wetland sites used to calibrate their process-based model exhibit high emissions that may not be representative of large regions. Only the estimate in the Low OH inversion lies within the range of most bottom-up estimates, but that for the Best Guess is close to the upper end of those estimates. The spatial distributions for swamps, biomass burning, biofuels, and tropospheric OH are similar, with maxima in the tropics. (Rice paddy emissions, in contrast, are centered around China and India at latitudes of around 30°N.) Examination of the averaging kernel, or model resolution function, for the OH parameter, included in Table 5, reveals a high degree of anti-correlation between the OH and biomass burning parameters and some anti-correlation of the swamps and biofuels parameters with the OH sink. The correlations indicate that the a posteriori strengths of the tropical sources depend on the strength of the OH sink. These sources are small in the Low OH inversion, balancing low OH, and large in the High OH inversion, balancing high OH. The correlations imply that these tropical sources are not well constrained by the available observations.
Table 5. Averaging Kernels (Model Resolution Matrix) for the CH4 Inversiona
 The results for the High OH inversion are similar to those of the Low OH case for animals + fossil + waste − soil sink, bogs + tundra, and rice paddies, with values for all of these except for the rice source lower than the a priori. The a posteriori values for the animals + fossil + waste − soil sink parameter are 30 Tg (15%), 19 Tg (9%), and 23 Tg (12%) lower than the a priori for the Low OH, High OH, and Best Guess inversions, respectively. These are sizable decreases, although the a posteriori values still lie within the large a priori uncertainty range. The decreases in the bogs + tundra parameter are even larger in relative (and absolute) terms, 59%, 57%, and 58% for the three inversions, and place the estimates outside the a priori uncertainty range. The increases in the rice paddy source are 40%, 45%, and 46%, with the a posteriori strengths lying within the a priori uncertainty range. The agreement among the three inversions suggests that the estimates for these sources are robust. Furthermore, the reductions in uncertainty obtained through the inversion procedure are large for these parameters, ∼88% for animals + fossil + waste − soil sink, ∼65% for rice, and ∼76% for bogs + tundra for all three inversions, signifying that the parameters are well constrained by the observations.
 Figure 3 presents comparisons of a priori and a posteriori (Low OH and High OH) model CH4 concentrations with observations at selected sites. It can be seen that the a posteriori agreement between model and observations is improved. A notable improvement is the latitudinal gradient; the a priori concentrations are generally too high in the extratropical Northern Hemisphere (NH) and too low in the rest of the world. The latitudinal gradient can be seen more clearly in Figure 4, in which latitudinal profiles of annual mean concentration are plotted. In both the Low OH and High OH cases, decreases in the animal, fossil fuel, waste, bogs, and tundra sources, located primarily in middle and high latitudes of the Northern Hemisphere, help to eliminate the positive model bias at these latitudes. In Low OH, a decrease in OH contributes to an increase in concentrations of CH4 in the tropics and in the extratropical SH. In High OH, where the OH sink is not allowed to change, tropical sources, especially swamps, are increased significantly to raise the concentrations in the tropics and the extratropical SH. Included in Table 4 is the percentage of global emissions occurring in the SH for each of the budgets. As may be seen, the Low OH budget has a relatively small proportion of emissions in the SH, while the High OH budget has a larger proportion in the SH. This result reflects the fact that 57% of global emissions from swamps and 44% of global emissions from biomass burning occur in the SH, while the proportion for most of the other sources is 25% or less. An interesting implication of these results is that the discrepancy between bottom-up (80–156 Tg) and top-down (e.g., 190–230 Tg from Hein et al. ) estimates for wetlands can be explained perhaps by the overestimate of OH in the top-down budgets, which requires high tropical wetland emissions for mass balance.
Figure 3. Comparison of model a priori (thin solid lines) and a posteriori (Low OH (dotted lines) and High OH (dashed lines) inversions) CH4 monthly means for 1994 with observations (thick solid lines) at selected CMDL sites.
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Figure 4. Latitudinal profiles of 1994 annual mean CH4 for model a priori and a posteriori versus observations at selected CMDL sites. (a) Low OH inversion. (b) High OH inversion. Squares connected by solid lines represent observations, crosses with dotted lines represent the a priori, and pluses with dashed lines represent the a posteriori. CMDL site codes are displayed at a constant offset from the observation values.
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 Agreement between model and observed amplitudes of the seasonal cycle is improved also with the Low OH inversion, especially in the mid- and high-latitude Southern Hemisphere (SH), for example, at Easter Island, Cape Grim, and Palmer Station, and at certain high-latitude NH sites, including Baltic Sea and Station M. In contrast, the amplitude of the seasonal cycle is overestimated in these regions with the High OH simulation. According to results of our tagged simulations of individual sources/sinks, the seasonal cycle of CH4 in these regions is shaped largely by OH. Hence the overestimate of the seasonal cycle further supports the idea that OH is too high in the High OH case. The chi-squared (cost function) value provides a quantitative measure of the goodness of fit to the observations and to the a priori constraints, with the expected value for a satisfactory retrieval being 1. The values of χ2 for the three main inversions, included in Table 4, indicate that the model fit is improved in all three cases, with the Low OH and Best Guess a posteriori budgets fitting the constraints better than the High OH budget.
 A variety of tests were implemented to assess the sensitivity of the inversion results to our methods and assumptions. For example, polluted continental sites (all located in the NH) were excluded in one inversion in order to assess the influence of possible inaccuracies in the model's simulation of pollution episodes. The OH sink was included as an inversion parameter. The results, shown in Table 4, are generally similar to those of the standard Low OH inversion, other than a higher estimate for the (animals + fossil + waste − soil sink) parameter and a lower estimate for the rice parameter. The smaller a priori-to-a posteriori decrease in the animals + fossil + waste − soil sink parameter relative to the standard inversion can be explained by the fact that the decrease is driven largely by an a priori overestimate of annual mean CH4 at high-latitude NH sites, especially continental ones. The lower estimate for the rice parameter relative to the standard inversion is driven perhaps by mass balance requirements, considering that the estimates for the animals + fossil + waste − soil sink parameter and swamps are higher than in the standard inversion. Overall, possible inaccuracies in model simulation of pollution episodes do not affect significantly the main conclusions from our inverse analysis.
 We examined results also for a different year, 1993. The parameter estimates are generally similar to those for 1994, suggesting that they are robust. A significant difference is that the estimate for the OH sink for 1993 is 16 Tg higher than that for 1994. This may indicate that the inverse calculation captures the effect of Mount Pinatubo on OH concentrations in 1993. (The effect of Pinatubo on OH is discussed further in section 3.4.4.) Another difference is that the estimate for emissions from rice paddies is 24 Tg higher than for 1994. An actual change of this magnitude from one year to the next is unlikely. The estimate for 1993 is probably less accurate than for 1994, since the South China Sea shipboard observations, which help to constrain the source from rice paddies, are lacking for the former year.
 Other sensitivity tests included use of a different set of a priori source estimates, compiled by the EPA [2001, 2002] (see Table 1 for these source estimates); exclusion of sites located close to other sites in order to minimize possible effects of correlation of observation errors; use of a different spatial and seasonal distribution for OH [from Spivakovsky et al., 2000]; and a decrease in the a priori uncertainty for the OH parameter by a factor of 2. In all cases, the a posteriori budgets (not shown in Table 4) are similar to that obtained with the standard Low OH inversion.
 Our analysis suggests that the sum of the EDGAR values for animals, fossil fuels, and landfills, which are based partly on the default methodologies of the IPCC , may be high, although a large uncertainty range is attached to these estimates. There is additional evidence supporting this conclusion. For the source from animals, the default IPCC approach overestimates the contribution from cattle since all animals are treated as full-sized adults, despite the fact that a significant portion are immature and emit less CH4 (E. Matthews, personal communication, 2003). With regards to landfills, the EDGAR estimates were obtained using a sophisticated first-order decay model. However, the IPCC default value for the fraction of degradable organic carbon ultimately dissimilated (DOCf), 0.77, was used, and the fraction of methane produced that is oxidized within landfills was assumed to be 0 for Organization for Economic Cooperative Development (OECD) countries and 0.1 for economies in transition (the IPCC default being 0 everywhere). Bogner and Matthews  recommend a revision of the IPCC default values to 0.5 for DOCf and to 0.1 for fraction oxidized for the entire world. Application of these recommended values would lower the EDGAR global estimate by around 40%, or around 9 Tg. Furthermore, Bogner and Matthews suggest that the revised parameter values may still result in an upper-bound estimate for emissions. Our results for the anthropogenic sources, especially oil and gas and animals, are more in line with those from the global inventory compiled by the EPA [2001, 2002] (Table 1). The EPA included for many sources IPCC “Tier 2” and “Tier 3” estimates, which involve detailed methods and country-specific emission factors rather than the default methods adopted in “Tier 1” estimates. Our rice paddy source however is higher than the EPA's result, as is the case for the comparison with EDGAR. Recent bottom-up estimates for this source, including those of EDGAR and EPA, are significantly lower than earlier estimates. For example, earlier estimates include 63 Tg (for Asia alone) [Neue et al., 1990; Bachelet and Neue, 1993], and 60 Tg [Olivier et al., 1999], while the latest EDGAR estimate is 39 Tg, the value from the EPA is 30 Tg, and Denier van der Gon  estimated 39 Tg. Reasons for the decrease in estimated emissions include use of a lower factor for the conversion of soil-returned carbon to net emitted CH4 [Denier van der Gon, 2000] and measurements over a whole growth period rather than on a few individual days [Sass et al., 1999]. Our inversion results, with a best guess of 56.6 ± 8.4 Tg, suggest that the recent estimates may be too low.