Methane is one of the important greenhouse gases accumulating in the atmosphere today. The increased loading over the past 2 centuries is thought to be the result of increased anthropogenic emissions. Here we present records of the δ13C of CH4 in firn air from the South Pole and in trapped bubbles in a short ice core from Siple Dome, Antarctica, that help constrain historical emissions of various sources throughout the last 2 centuries. Using two firn air samplings in 1995 and 2001 we calculate that δ13CH4 has increased by an average of 0.06 ± 0.02‰/yr over the 6 years between samplings. Our ice core results suggest the δ13C of atmospheric CH4 has increased by 1.8 ± 0.2‰ between 1820 A.D. and 2001 AD. The δ13CH4 changes in both data sets are the result of an increase in the relative proportion of CH4 sources with elevated 13C/12C isotope ratios. One explanation for observed trends involves a 16 Tg/yr increase in CH4 emissions associated with biomass burning over the past 2 centuries.
 Methane (CH4) is a greenhouse gas that is currently accumulating in the atmosphere at a rate (now declining) of about 0.4% per year. Over the past 2 centuries, the atmospheric CH4 concentration has doubled in response to increasing anthropogenic related emissions. The primary anthropogenic CH4 sources are ruminants, rice paddies, landfills, natural gas release, and biomass burning. The largest natural source is wetlands followed by natural fires, termites, and oceanic emissions including clathrate destabilization (for a thorough review, see Reeburgh ). The total CH4 source strength at any point in time can be estimated knowing the rate at which CH4 accumulates in the atmosphere and the loss of CH4 via OH oxidation in the troposphere. This exercise does not, however, provide any information about the relative contributions of the various sources. In order to refine estimates of the magnitude of each individual source, measurements of the δ13C of atmospheric CH4 (δ13CH4) have been made. Knowing the characteristic isotope composition of the various sources, one can improve our understanding of the historical emissions with a δ13CH4 record in hand. Information of this type is important as we estimate future climate change that may result from anthropogenically mediated changes in the Earth's radiation budget [Hansen et al., 2000].
1.1. Previous Studies of Recent Atmospheric Methane Trends
 Ice cores provide the primary means of reconstructing the composition of past atmospheres. High-resolution atmospheric records have been reconstructed for the last 1000 years from the Law Dome ice cores [Etheridge et al., 1998]. Methane concentration records from Law Dome have documented atmospheric loadings that have increased in an exponential fashion starting from ∼670 ppb in 1000 A.D. to ∼1600 ppb in 1970 A.D. The major cause of this increase is thought to be the result of anthropogenic emissions (rice, cattle, biomass burning, and fossil fuels) with a smaller contribution from a net reduction in the primary atmospheric sink (tropospheric OH).
 To date, only one set of ice core analyses have been made to estimate the δ13C of paleoatmospheric CH4. Craig et al.  made δ13CH4 measurements on large ice samples from the Crete ice core (central Greenland) and concluded that atmospheric δ13CH4 increased by ∼2‰ over the past 2 centuries. Unfortunately, Craig et al.  failed to account for a number of important factors (gas age–ice age difference, gravitational and thermal fractionation, and the diffusional impact of increasing [CH4] on the δ13CH4 of firn air CH4) making their estimates of the net change in atmospheric δ13CH4 uncertain though the sense of the change is probably correct.
 Analyses of air from the interstitial spaces around snow near the surface of polar ice sheets (firn air) provides the means of splicing ice core records with direct measurements of the troposphere which began in the 1950s. Firn air δ13CH4 measurements indicate a positive recent trend of 0.03–0.10‰ per year for the later part of the twentieth century [Bräunlich et al., 2001; Francey et al., 1999]. By way of comparison, the current peak-to-peak amplitude of the seasonal δ13CH4 variations range from 0.1 to 0.4‰ in both hemispheres while the pole-to-pole difference is ∼0.5‰ with a tendency toward larger gradients during the boreal winter [Lowe et al., 1999; Platt et al., 2004; Quay et al., 1999; Rice et al., 2001]. Since loss of CH4 is controlled primarily by reaction with OH in the troposphere, the potential influence of isotope effects associated with loss processes in the stratosphere has been omitted in a number of budget studies [e.g., Craig et al., 1988; Francey et al., 1999]. Gupta et al.  pointed out, however, that the increase in the stratospheric Cl (with concomitant CH4 removal) should have raised tropospheric δ13CH4 by as much as 0.7‰ over the past century. Estimates suggest that stratospheric Cl loading may have increased by ∼200% owing to the introduction of chlorine containing freons [Flocke et al., 1999]. The magnitude of the Cl impact on tropospheric δ13CH4 has been recently reassessed indicating the net impact is probably between 0.2 and 0.5‰ [McCarthy et al., 2003; Wang et al., 2002].
 Recently, measurements of firn air from Dome C and Dronning Maud Land have yielded new δ13CH4 data that extend the atmospheric record back to ∼1950 A.D. Results indicate the δ13CH4 in the far Southern Hemisphere has increased by ∼1.7‰ since 1950 A.D. The trend toward higher δ13CH4 was thought to be the result of increased CH4 emissions from biomass burning and fossil fuel consumption [Bräunlich et al., 2001].
 The present contribution extends the atmospheric record to the early 1900s with analyses of firn air from the South Pole that were drawn in January 1995 and 2001 [Battle et al., 1996]. Additionally, samples from a shallow ice core from the Siple Dome area are used to establish the δ13CH4 value during the nineteenth century. Moreover, the two separate firn air samplings provide an opportunity to establish the evolution of the firn air profiles over a 6-year period from the same locale. In the sections that follow, we initially discuss how firn air from South Pole has been sampled and used to reconstruct atmospheric records over the past century. We then discuss the methods we used to measure δ13CH4 and present results from two separate South Pole sampling expeditions measured in two labs. In order to establish a preanthropogenic δ13CH4 value, a new technique was developed to extract and analyze the δ13CH4 of air trapped in ice from a shallow core at Siple Dome. Finally, we discuss the significance of the results in terms of estimating historical CH4 emissions from anthropogenically mediated biomass burning.
1.2. Retrieving Interstitial Air From Polar Snow
 The composition of air within the interstitial spaces in polar snowfields is dictated by the historical atmospheric record and the rate at which air mixes in a vertical sense [Schwander et al., 1993]. At the South Pole, the firn/ice transition is located ∼123 m below the surface (mbs) [Battle et al., 1996]. Below 123 mbs, air is occluded in bubbles and can no longer communicate with the overlying atmosphere. Firn air at the South Pole is reasonably well mixed in the upper 2–5 m by wind and atmospheric pressure changes. Below 5 m, the air mixes solely by diffusion down to ∼116 m, corresponding to the top of the “lock-in” zone [Battle et al., 1996]. At this depth, the open porosity decreases to a level where the tortuous nature of the firn no longer allows the air within the lock-in zone to mix with the overlying firn air. The air becomes effectively sealed in the firn although very few bubbles are apparent. Below 116 m, the age of the air increases with depth at a rate that is dictated by the snow accumulation rate (∼8 cm of ice equivalent/year).
 Over time, atmospheric compositional changes are propagated down into the firn by diffusion. At the South Pole, the average age of CH4 molecules just above the bubble close-off region date to ∼1900 A.D. Moving up the firn column, the age of the air decreases rapidly between 123 and 116 m and then more slowly from 116 m to the surface. The composition of the air at any depth in the firn is therefore dependent on the atmospheric history and the diffusion processes controlling the movement of each constituent down into the firn [Battle et al., 1996].
 Two separate expeditions were mounted to retrieve firn air from the geographic South Pole. The first expedition occurred in January of 1995 where two holes (30 m apart) were drilled incrementally and sampled at 30 different depths using standard techniques to fill replicate flasks [Battle et al., 1996; Schwander et al., 1993]. In January 2001, a similar expedition was mounted using effectively the same equipment. In 2001, two additional holes were drilled incrementally and sampled at a total of 31 depths. A subset of flasks from both experiments was measured at NOAA/CMDL for trace gas species. Another suite of flasks was measured at Princeton for the elemental and isotopic composition of O2, N2, and Ar. The results from these analyses provide the basis for the firn air modeling that we discuss in a later section.
2. Analytical Methodology for Measuring δ13C of CH4
2.1. LGGE Analyses
 The δ13C measurements at LGGE were made with a Finnigan MAT 252 mass spectrometer coupled to a Finnigan GC/combustion interface in continuous flow mode (CF-IRMS). CH4 was initially isolated from other air constituents using a preconcentration device. Air samples are initially expanded into a pre-evacuated 150-mL sample loop that is subsequently flushed with pure He carrier gas for 20 min at 70 mL/min. The He carrier stream was passed through a HaySep D column (80/100 mesh, 20 cm length, 0.32cm OD) held at −130°C to trap CH4 and CO2 with the remainder of the air/He directed to vent. A six port Valco valve is then switched before the HaySep D column is instantaneously warmed to 50°C to release the trapped CH4 sample and other condensable gases from the HaySep D column. The CH4 and CO2 were then cryofocused onto a 3-m capillary column (fused silica Poraplot Q, 0.32 mm ID) at −130°C. Finally, the focusing column was warmed to 50°C to release the CH4 and CO2 into a 30-m Poraplot Q column where the CH4 was separated from CO2 and N2O. The effluent from the Poraplot column was then fed into an oxidation furnace (Ni, Pt, and Cu at 980°C) where CH4 was converted to CO2. The sample stream then passes through a reduction oven to remove N2O and O2 from the effluent stream. After a drying stage (Nafion membrane), the sample was transferred to the mass spectrometer using an open split design, where about one third of the effluent from the chromatographic column was admitted via a capillary into the ion source. The mass to charge ratio (m/e) for the 44-, 45-, and 46-isotopologue peaks were integrated before the 13C/12C ratio was then calculated using the 17O correction following Santrock et al. . The δ13CH4 values were reported on the VPDB scale using a pure CO2 working standard with a δ13CH4 value of −45.98 ± 0.02‰. System checks are performed daily using a compressed air standard (CSIRO 1636) that was filled at Cape Grim on March 1995 in collaboration with the Commonwealth Scientific and Industrial Research Organisation (CSIRO), who subsequently determined the δ13CH4 value as −47.12 ± 0.03‰. Throughout the 3 years over which measurements have been made at LGGE for this study, the average δ13CH4 on this tank was −47.07 ± 0.18‰ (N = 201).
2.2. PSU Analyses
 At PSU, we have developed a CF-IRMS technique to measure the δ13CH4 in air samples that is similar to previously developed techniques [Miller et al., 2002; Rice et al., 2001]. The analytical system consists of a substantially modified PreCon device (Finnigan MAT) that interfaces with a MAT 252 mass spectrometer (Figure 1).
 The system was designed to measure δ13C of CH4 as well as the δ15N and δ18O of N2O from a single air sample. The details of the N2O analyses have been previously discussed [Sowers et al., 2002]. Initially, samples are loaded onto the PreCon between two 1/4″ ultratorr adapters. The connections are flushed with He for 3 min (15 cc/min) before the glass valves on the 100-cc sample flask are opened allowing the air to be flushed (30 cc/min) into a chemical trap containing ascarite and MgClO4 for CO2 and H2O removal. The air sample is then passed through a 1/32″ stainless steel (SS) loop in liquid nitrogen (LN2) where the N2O is trapped. The air +CH4 stream is then routed through trap 2 at −130°C (pentane slush) where the CH4 is trapped on a 0.32 cm × 10 cm SS column packed with 80/100 HaySep D material. The sample container is flushed for 1400 s to insure quantitative trapping of CH4 in trap 2. Valco valves 1 and 2 are then switched so the CH4 is transferred from trap 2 to trap 3, which contains a 1-m section of the 0.32-mm poraplot column immersed in the −130°C pentane bath. After 500 s, trap 3 is raised out of the pentane bath mobilizing the CH4 that is then separated from other trace impurities in the remainder of the poraplot column before entering the oxidation furnace (Pt, Cu, and Ni wires at 1050°C) for quantitative conversion to CO2. The effluent from the furnace passes through a 15-cm Nafion drying system cooled to −60°C for efficient water removal [Leckrone and Hayes, 1998]. The sample gas stream then enters the open split leading to the ion source of the mass spectrometer. The CO2 peak is monitored with three separate faraday cups that record each isotope of CO2 (m/e = 44,45 and 46). The area of each isotope peak was integrated before ratios of the peak areas were compared to CO2 standard peaks that were introduced before and after the sample for reference.
 The 13C/12C of the CH4 is referenced to a working standard of liquefied CO2 that was previously calibrated to VPDB using NIST CO2 reference standards (8563 and 8564). The δ13CO2 of the working standard was −33.26 ± 0.07‰ (1σ, N = 16) based on periodic analyses of the working standard against a primary lecture bottle of gaseous CO2. In all cases, the measured 45/44 ratios were corrected for 17O following Santrock et al. .
2.3. Ice Core Methodology for δ13C of CH4
 The analytical methodology for extracting and analyzing trapped gases in ice can be broken into two distinct parts: the liberation of the trapped gases from the ice core sample and the δ13CH4 analysis. The extraction of the gases from the 1–1.5 kg ice core samples was accomplished using a “wet” extraction technique. The outside of the ice samples were initially shaved to remove the outermost ∼5 mm of ice. The shaved samples were then inserted into a 7.6 cm × 35 cm stainless cylinder that was sealed with a copper gasket prior to evacuation. After 1 hour of evacuation, the cylinder was isolated and inserted into a warm water bath to melt the ice samples and liberate the trapped air into the headspace above the meltwater. The cylinder was then transferred to a large SS Dewar where the meltwater is refrozen using liquid nitrogen. After 30 min, the headspace was flushed with UHP He (60 cc/min) through a water trap (−110°C) and a HaySep D trap at −130°C where the CH4 was quantitatively removed from the air. After 1 hour, the CH4 trap was isolated and removed from the system. The trap was then connected to the PreCon and processed in an identical fashion as the air samples described above.
3.1. PSU Procedure Verification
 Each stage of the analytical procedure was checked to quantify the degree to which the measured δ13CH4 reflects the δ13C of CH4 in the original sample. To establish the integrity of the preconcentration/mass spectrometry, we analyzed 50–100 cc (STP) aliquots of two compressed air standards that had been previously calibrated by Stan Tyler (UCI) as part of their atmospheric δ13CH4 program [Rice et al., 2001; Tyler et al., 1999]. The assigned δ13CH4 values for the two standards (CH4 Std 1 and 2 in Table 1) are −19.6 ± 0.03‰ and −47.16 ± 0.04‰, respectively. Aliquots of these compressed air standards are routinely expanded into numerous 50–100 cc flasks at the beginning of each day to insure the complete analytical protocol provides accurate and precise δ13CH4 values. If the results on the daily standards are more than 0.2‰ away from the assigned value, system checks and additional standards are run until the results fall within the 0.2‰ tolerance. Over the 3-year period since we began measuring δ13CH4, we have measured 51 aliquots of CH4 Std 1 and 116 aliquots of CH4 Std 2 yielding average values of −19.6 ± 0.3‰ and −46.86 ± 0.2‰, respectively (Table 1). The difference between the average values and the assigned values is less than 0.2‰, suggesting that our analytical procedures provide accurate δ13CH4 data with an external precision of 0.2‰.
|Measured Quantity||N||δ13C, ‰ PDB||Measured – Accepted, ‰|
|Assigned δ13CO2 for liquid standard (NIST)b||16||−33.26 ± 0.07||N/A|
|CH4 Std#1 ([CH4] = 1441 ppb, δ13CH4 = −19.6‰)c||51||−19.6 ± 0.3||0.0 ± 0.3|
|CH4 Std#2 ([CH4] = 1776 ppb, δ13CH4 = −47.16‰)c||116||−46.86 ± 0.2||+0.3 ± 0.2|
|Simulated transfer of CH4 Std 2||8||−47.0 ± 0.3||+0.16 ± 0.3|
|Preanthropogenic air from Siple Dome ice core gas ages (1837–1907 A.D.)||10||−48.8 ± 0.3||N/A|
- a N/A denotes “not applicable.”
- b On the basis of CF-IRMS analyses of liquid CO2 via primary gaseous CO2 that was previously calibrated to VPDB via NIST SRM 8563 and 8564.
- c Assigned δ13CH4 value for the CH4 air standards were provided by Stan Tyler (University of California, Irvine).
 Aliquots of CH4 Std 2 air standards were processed through the entire ice core procedure using degassed ice from Siple Dome. We performed eight simulated trapped gas transfers between October 2002 and November 2003 using 100–150 cc (STP) aliquots of CH4 Std 2 with an assigned δ13CH4 value of −47.16‰ (Table 1). The resulting average δ13CH4 was −47.0 ± 0.3‰. The results are indistinguishable from the assigned value, indicating that the complete procedure did not measurably alter the isotopic composition of CH4. The standard deviation about the mean for the simulated transfers is ∼0.1‰ higher than that based on replicate analyses of the standards expanded directly into glass flasks. We attribute the added uncertainty to variable amounts of water that get transferred to the PreCon with the fossil air sample. Small changes in the water background in the source accompanying the sample CO2 influence the measured 45/44 ratio through protonation of CO2 to HCO2+ (m/e = 45) in the ion source [Leckrone and Hayes, 1998].
3.2. South Pole Firn Air
 The NOAA/CMDL [CH4] data show a gradually decreasing trend with depth to 114 m with a much steeper rate of decrease below 114 m to the final bubble close off at 122 m where the measured CH4 was 910 ppb (Figure 2). The 114-m horizon represents the top of the lock-in zone below which exchange with the overlying firn is substantially restricted. The δ13CH4 data show a gradually decreasing trend between the surface and 110 m. Between 110 m and 122 m, the δ13CH4 values exhibit an interesting oscillation that has not previously been observed in firn air studies because of their younger firn air age. The minimum values approach −51.7‰ at 117 m with increasing δ13CH4 values below 117 m. This oscillation is generated by the faster diffusion coefficient of 12CH4 in air compared to 13CH4, superimposed on a present-day atmospheric δ13CH4 value which is comparatively heavier than the pre-industrial one.
 There are three firn air δ13CH4 data sets from the South Pole plotted in Figure 2. Two of the three δ13CH4 data sets were generated at LGGE, one on each of the two expeditions (1995 and 2001). At each depth, multiple flasks were collected to provide enough firn air for all analyses. All data plotted in Figure 2 are average results from all flasks that were measured at each depth by each lab (generally duplicate flasks with duplicate or triplicate analyses on each flask in each laboratory). The δ13CH4 measurements were also made at PSU on the same 2001 flasks as an intercalibration exercise. These data, along with the corresponding LGGE data for each flask, are tabulated in Table 2. All data have been corrected for gravitational fractionation using the δ15N of N2 measured on each flask at Princeton (M. Bender, personal communication, 2002). Eleven flasks were measured at PSU before shipping 20 flasks to LGGE for analyses. Five of those flasks were remeasured at PSU after the LGGE analyses to check for alterations associated with the trans-Atlantic shipments and the LGGE analyses. The average difference between the PSU analyses performed before and after the LGGE analyses was −0.05‰, indicating no measurable change in the δ13CH4 values.
|Flask ID||Depth, mbs||δ15N2,a ‰ Atm N2||PSU δ13CH4, ‰ PDB||LGGE δ13CH4, ‰ PDB||Corr. LGGE δ13CH4,b ‰ PDB||PSU–LGGE, ‰|
|775||0||−0.001||−46.84 ± 0.15||−46.67||−46.87 ± 0.12||0.04|
|SDF-49||19.99||0.107||−46.98 ± 0.02||−47.01||−47.32 ± 0.18||0.34|
|SDF-27||19.99||0.102||−47.14 ± 0.06||−47.03||−47.34 ± 0.14||0.20|
|523||44.47||0.242||−47.57 ± 0.06||−47.55||−48.00 ± 0.17||0.43|
|O2/CO2 8||53.61||0.260||−47.09 ± 0.04||−46.81||−47.28 ± 0.19||0.19|
|SP-335||69.61||0.338||−48.30 ± 0.01||−47.83||−48.38 ± 0.07||0.07|
|SP-141||69.61||0.354||−48.30 ± 0.17||−47.96||−48.53 ± 0.14||0.22|
|TF-23||79.4||0.412||−48.61 ± 0.08||−48.19||−48.81 ± 0.11||0.20|
|818||100.16||0.536||−49.15 ± 0.11||−48.72||−49.46 ± 0.20||0.32|
|SP-64||100.2||0.555||−49.77 ± 0.08||−49.17||−49.94 ± 0.21||0.16|
|SP-2||102.8||0.538||−49.18 ± 0.01||−49.17||−49.92 ± 0.21||0.74|
|SP-20||108||0.581||−50.32 ± 0.05||−49.78||−50.57 ± 0.10||0.25|
|SP-37||110||0.626||−50.27 ± 0.06||−49.95||−50.79 ± 0.41||0.52|
|SP-38||110||0.610||−50.65 ± 0.08||−49.89||−50.71 ± 0.08||0.07|
|SP-45||113.1||0.624||−50.75 ± 0.18||−50.34||−51.17 ± 0.12||0.42|
|TF-40||116.2||0.598||−51.27 ± 0.01||−50.75||−51.56 ± 0.03||0.29|
|668||119.87||0.611||−50.57||−51.39 ± 0.13|
|SP-43||119.9||0.621||−50.56 ± 0.01||−49.55||−50.38 ± 0.13||−0.17|
|O2/CO2 4||121.3||0.619||−50.05 ± 0.03||−50.22||−51.05 ± 0.22||1.00|
|O2/CO2 6||121.3||0.649||−49.66 ± 0.16||−49.55||−50.41 ± 0.13||0.75|
|Average||PSU-LGGE||0.32 ± 0.28|
- a The δ15N2 of N2 measurements were made by M. Bender at Princeton and are reported with respect to atmospheric N2.
- b LGGE δ13CH4 were corrected for an additional 0.21‰ shift that was related to a change in the primary liquid CO2 reference tank value.
 Comparison of the δ13CH4 results from each flask measured at LGGE and PSU showed the average difference between the 19 flasks was 0.32 ± 0.28‰. This value is comparable to the external precision associated with replicate analyses on a given flask (∼0.1‰). We interpret this close agreement as indicating the analytical procedures and working standards at the two laboratories are consistent within our external precision.
 In order to compute the net change in the δ13CH4 between the two firn air expeditions (2001–1995 = Δδ13CH4), we interpolated the 1995 δ13CH4 profile at depths for which samples were taken during the 2001 expedition. We then used the average LGGE data at each depth for the two samplings to calculate the difference (Δδ13CH4, Figure 2). With the exception of the 53 mbs sample, the upper 100 m showed the 2001 values to be ∼0.3‰ higher than the 1995 values. The δ13CH4 values below 100 mbs are effectively identical given our sample resolution. This was expected as the air in the deeper portions of the firn has not communicated with the overlying atmosphere during the 6 years that separate the two expeditions. We interpret this close agreement below 100 mbs as evidence that the sampling and analytical techniques employed during the two expeditions are indistinguishable from one another.
3.3. Siple Dome Ice
 We have analyzed 10 individual samples of ice from a shallow Siple Dome ice core that was drilled during the 1996/1997 field season (81°24.18′S, 148°18.14′W, elevation = 621 masl, mean annual temp = −25.4°C, accumulation ∼11 cm ice/yr [Taylor et al., 2004]). The depths ranged from 62.4 m to 70.6 m, with corresponding gas ages between 1837 and 1907 A.D. The average δ13CH4 was −48.8 ± 0.37‰ (1σ). This value has been corrected for gravity with three measurements of the σ15N of N2 (δ15N2 = 0.22 ± 0.02‰) (1σ) using a previously described technique [Sowers et al., 1989; Sowers and Jubenville, 2000]. One sample from 66.5 mbs (gas age = 1873 A.D.) provided a δ13CH4 value of −49.8‰. While we cannot attribute the anomalous result to any identified artifact associated with the extraction, we consider this value questionable given that it falls more than 1‰ below the average of the other nine samples (−48.7 ± 0.1‰). We consider the average of the nine samples (−48.7 ± 0.1‰) to be the best estimate of the average δ13CH4 for the later part of the nineteenth century.
4. Firn Air Modeling
 In order to extract the atmospheric history of δ13CH4 from our firn air measurements, we have employed two 1-D gas diffusion models that account for the main factors influencing the firn air composition. The upper few meters of firn are advectively mixed with the overlying atmosphere by barometric fluctuations and wind pumping. Below this convective zone, air mixes solely by diffusion in an isothermal environment where gravitational fractionation occurs down to the top of the “lock-in” zone. Within the lock-in zone, air cannot communicate with the overlying firn air/atmosphere so no additional gravitational fractionation occurs. Finally, as bubbles are pinched off, a small amount of air is forced upward because bubbles are closing off in a region of increasing hydrostatic load.
 The two key features of a firn air model are the effective diffusivity and the open porosity profiles. For both models, temperature, accumulation rate, and firn structural parameters are held constant for the duration of the simulations. Battle et al.  developed records of open porosity based on the measured density profile following Schwander et al. . The effective diffusivity for CO2 was initially based on the open porosity following Schwander et al. . The CO2 diffusivity profile was subsequently tuned until the model CO2 profile matched the measured profile using the Law Dome CO2 record as the atmospheric CO2 forcing function. Once the CO2 effective diffusivity was established, other trace gas species can be modeled in a forward sense using the ratio of their molecular diffusivities relative to CO2 [Trudinger et al., 1997].
- gram molecular weight of CO2 (0.044 kg/mole);
- gram molecular weight of each CH4 isotopomer (i);
- = 0.01604 kg/mole;
- = 0.01704 kg/mole;
- gram molecular weight of air (0.028966 kg/mole);
- CO2 diffusivity in air at the South Pole (1.07 m2/day);
 In order to validate the diffusivity profile deduced from CO2 measurements, we utilized the well-known atmospheric CH4 record from Law Dome. We constructed an atmospheric methane record for the past 300 years using ice core measurements from DE08 and DSS ice cores from 1700 to 1978 A.D. [Etheridge et al., 1998], atmospheric measurements at Cape Grim from 1978 to 1983 [Langenfields and Fraser, 1996], and direct atmospheric measurements at South Pole between 1983 and the date we recovered the firn air [Dlugokencky et al., 1994, 1998] (NOAA/CMDL, ftp://ftp.cmdl.noaa.gov/ccg/ch4/flask/month/spomm.ch4). This atmospheric record was run through both the Battle and LGGE firn models with the resulting CH4 profiles plotted in Figure 2 along with the measured values in 1995. The agreement between the firn CH4 data and the model reconstructions is good, as seen in Figure 2, thus validating the open porosity and diffusivity profiles used in the model. The average difference between the two model CH4 profiles is 11 ± 10 ppb. The depth-averaged differences between the measured and modeled CH4 data are 22 ± 30 ppb and 11 ± 36 ppb for the LGGE and Battle models, respectively. We interpret the strong similarity between the measured and modeled CH4 profiles as evidence that (1) the parameterizations of the physical nature of gas mixing and trapping in the two models are virtually identical, and (2) the models capture the important factors controlling gas movement in the firn.
 Although routinely used for mixing ratios, the implementation of the inverse technique developed by Rommelaere et al.  for isotope ratios has been hampered by the nonlinearities associated with modeling two isotopes simultaneously. In order to construct atmospheric δ13CH4 records that were consistent with our firn air δ13CH4 data, we utilized a Monte Carlo approach with a wide range of hypothetical atmospheric δ13CH4 histories that were tested using the forward firn air model. The input scenarios were parameterized as third-order polynomial functions that provide acceptable trends of CH4 isotopic ratios (obviously, for example, low-frequency sinusoidal functions would not be compatible with our knowledge of trace gas trends and their budgets). The validity of each tested scenario, through the agreement between the modeled and experimental firn profiles, is evaluated with a chi test [Aballain, 2002]. Scenarios are accepted when the difference between modeled and experimental data is less than 0.6‰ (that is, χ2 ≤ 0.36).
 The maximum and minimum atmospheric δ13CH4 values from the Monte Carlo simulations are plotted in Figure 3. The color coding for the lines represents the percent of air of a specific age that is represented in the South Pole firn. For example, ∼25% of air from 1900 A.D. still resides in the firn with the balance (75%) either mixed out of the firn or trapped in bubbles below. The lower percentage values are located just above the bubble close-off region and the highest percentages are located at the surface. This information is important in assessing the degree to which the Monte Carlo results can be applied to paleoatmospheric reconstructions. As the percent of fossil surface air that is represented in the firn goes down, so does our confidence in the inferred paleoatmospheric δ13CH4 from the firn air analyses. Thus we are less confident in the paleoatmospheric reconstructions before ∼1900 A.D. based on firn air data alone.
5.1. Evolution of δ13CH4 Between 1995 and 2001 at the South Pole
 One advantage of performing multiple firn air experiments at the same locale is the fact that seasonal variations in surface air are smoothed out in the firn by diffusion. Resampling firn air thereby provides a unique means of deciphering the compositional changes without having to continually sample and measure air from a site. In this case, we sampled the interstitial firn air at South Pole in January of 1995 and again in January of 2001, providing a 6-year integrated window.
 To determine the net change in δ13CH4, we utilized the 1995 and 2001 δ13CH4 data generated at LGGE (Figure 2b). To calculate the δ13CH4 difference, we interpolated the 1995 profile at depths sampled in 2001. The resulting Δδ13CH4 profile is plotted in Figure 2c. Discounting the anomalous 2001 sample at 53 mbs, the average Δδ13CH4 between 20 and 103 m is 0.56 ± 0.14‰ (N = 6). This value should represent the true δ13CH4 change over the 6-year period as it was determined by measurements made in the same laboratory using identical equipment and procedures. However, we have documented a measurable offset between the CSIRO air standard cylinder measurements that were made during the two analytical windows. For the 1995 suite, 43 measurements of the CSIRO standard were made with a mean δ13CH4 value of −47.22 ± 0.08‰. This value is 0.21‰ lower than the corresponding δ13CH4 value obtained from the same tank in 2001 (−47.01 ± 0.012‰, N = 25). We attribute the different results to slightly higher water background levels associated with the 2001 samples [Leckrone and Hayes, 1998], and a drift in the δ13C value of the liquid CO2 tank that served as the working reference. We have thus applied the 0.21‰ correction to all 2001 LGGE δ13CH4 values (Table 2). Applying this difference to the measured Δδ13CH4 values, we calculate that the net change in atmospheric δ13CH4 over the 6-year period was 0.35 ± 0.2‰. This value translates to +0.06 ± 0.03‰/yr for our best estimate of the average annual δ13CH4 change recorded in the firn at South Pole. This value is slightly higher than that determined by Bräunlich et al.  and Francey et al.  of +0.04 ± 0.01‰/yr for the last 2 decades of the twentieth century. The increasing δ13CH4 trend is thought to be the combined result of an increase in the proportion of Δδ13CH4 emissions with elevated 13C/12C values and/or simply the added time needed for atmospheric δ13CH4 to adjust to a change in sources/sinks [Tans, 1997].
5.2. Preliminary Tests With an Atmospheric Isotope Model
 The twentieth century δ13CH4 record from the South Pole firn air provides additional constraints on the cause of the 150% mixing ratio increase. Given the plethora of sources, sinks, and their characteristic isotope fingerprints, it is not possible to derive a single set of historical emission records that will satisfy the δ13CH4 data. To address this problem, we utilized an eight-box atmospheric CH4 model (BOSCAGE-8) that was constructed for performing long-term sensitivity tests of various emission scenarios [Marik, 1998]. Briefly, the BOSCAGE-8 model consists of eight boxes: six boxes cover the troposphere in 30° meridional bands and two for each hemisphere of the stratosphere with the boundary between the troposphere and stratosphere set at 200 hPa. Model dynamics were tuned with SF6 following Levin and Hesshaimer . The model is based on seasonal and latitudinal variations in the emission and sink terms as well as the tabulated characteristic isotopic values adopted from the inverse modeling of Hein et al. . Starting with an initial inventory of sources and their distribution (Table 3), the model calculates the mixing and isotopic ratios inside each box taking into account the exchange times and the methane lifetime (about 8 years) estimated from the sinks. The free parameters of the model are the strengths of each source and sink and the characteristic isotope value of each source group (animals, rice, bogs, swamps, landfills, biomass burning, coal, oil/gas). In order to reproduce the industrial increase of CH4 mixing ratio, Marik  keeps the natural sources constant and sets the anthropogenic sources (animals, rice, landfills, coal, oil/gas, and part of the total biomass burning) proportional to human population, as suggested by Khalil and Rasmussen . The BOSCAGE-8 model does not have a chemical module to predict changes in [OH] that result from increased CH4 and CO loadings. To account for the decreasing [OH] levels, we adopt a 25% linear decrease between 1885 A.D. and the present that was suggested by Marik  in line with results from Khalil and Rasmussen . Model runs with these settings compared extremely well with direct measurements of [CH4], δ13CH4, and δDCH4 during the 1990s from three sites: Alert (82°N), Izana (28°N), and Neumayer Station (70°S) [Marik, 1998].
|Source||Amount, Tg/yr||δ13CH4, ‰ PDB||δDCH4, ‰ SMOW||Box 1 90°S–60°S, %||Box 2 60°S–30°S, %||Box 3 30°S–0°, %||Box 4 0°–30°N, %||Box 5 30°N–60°N, %||Box 6 60°N–90°N, %|
|Animals||84.1||−61.5 ± 2.9||−330||0||4.94||18.73||41.13||35.20||0.0|
|Rice||71.9||−62.5 ± 2.8||−335||0||0.18||13.9||77.50||8.42||0.0|
|Bogs||56.1||−62.9 ± 2.7||−350||0||0.18||5.25||5.75||64.79||24.03|
|Swamps||141.3||−62.6 ± 3.3||−330||0||2.9||50.19||38.36||8.21||0.35|
|Landfills||23.1||−50.7 ± 2.0||−280||0||0.25||1.95||16.35||80.83||0.62|
|Biomass||53.2||−25.8 ± 2.9||−40||0||0.2||55.95||43.85||0.0||0.0|
|Coal||39.8||−34.3 ± 2.9||−180||0||0.0||9.95||25.93||61.02||3.10|
|Oil gas||47.1||−39.6 ± 2.0||−190||0||0.72||8.22||40.70||50.36||0.0|
|Siberian gas||10.0||−39.9 ± 2.0||−205||0||0.0||0.0||0.0||58.33||41.67|
|FW δDCH4,b ‰||−263||0||−321||−260||−277||−279||−307|
- a The source/sink distribution for each box was determined from an adaptation of the Hein et al.  3-D inversion to the 2-D construct of BOSCAGE-8. Characteristic δ13C and δDCH4 values were taken from the literature as stipulated by Hein et al.  and Marik .
- b FW represents the flux-weighted isotope value for each atmospheric box. The value is determined by multiplying each individual source delta value by the percent in the latitude box and then averaging all the sources.
- c CH4 loss via OH and Cl in each box is reported as in terms of the lifetime of CH4 in each box. Units are yr−1. For the two stratospheric boxes (7 and 8), the corresponding values are 0.046 yr−1 and 0.039 yr−1.
- d The isotope effect of each sink term is reported as an isotope fractionation factor (α) with respect to the CH4 in each box. For tropospheric OH, αOH = 1.0054 is taken from Cantrell et al. . αsoils, and αstratosphere (including stratospheric Cl) are model tuned parameters which are very close to literature values (αsoils = 1.021 ± 0.005 [King et al., 1989]), and (αstratosphere = 1.0154 ± 0.008, [Rice et al., 2003]).
- e The latitudinal distribution of soil uptake was adopted from Dörr et al.  and is reported as a percentage of the total emissions (33 Tg/yr) in each box.
5.3. Sensitivity Tests With the BOSCAGE-8 Model
 There are effectively two bacterial processes that liberate methane. In terrestrial ecosystems, acetate fermentation is the dominant pathway whereby methanogenic bacteria produce methane with characteristic δ13CH4 values between −55 and −65‰ [Francey et al., 1999; Quay et al., 1999, 1991; Whiticar, 2000, 1993]. In deep sea marine sediments, CO2 reduction is the primary pathway yielding δ13CH4 values between −55 and −70‰ [Whiticar et al., 1986]. The large δ13CH4 overlap between these two metabolic pathways makes it difficult to ascribe a given change in the atmospheric δ13CH4 to any particular source. However, CH4 associated with biomass burning has a distinct δ13CH4 value (−27 ± 3‰ [Quay et al., 1991]) relative to the dominant bacterial sources. Thus, while we cannot rule out changes in the characteristic δ13CH4 value for any of the anthropogenically mediated sources that would account for the increasing δ13CH4 values we recorded over the past 150 years, we suggest that the more likely explanation for the increasing δ13CH4 values is increased CH4 emissions from biomass burning. To assess the magnitude of the expected increase in biomass burning that would account for the δ13CH4 increase, we performed three sensitivity tests involving changes in the percentage of total biomass burning CH4 that is associated with anthropogenic activities.
 The optimum scenario from Marik  identified 30% of the total biomass burning CH4 as being anthropogenic in origin. In our first scenario, we assumed that 70% of the 53.2 Tg/yr of biomass burning methane in 1985 was related to anthropogenic activities. Two other runs were made in which we assigned the anthropogenic contribution as 20% and 30% of total. In all runs, the natural emissions were held constant for the duration of the model run. To maintain the atmospheric loading for all three runs, the OH sink term during the nineteenth century had to be increased by 40%, 35%, and 25% relative to today's value for the simulations in which anthropogenic biomass burning accounted for 20%, 30%, and 70% of the total.
 The three corresponding δ13CH4 trends calculated with the BOSCAGE-8 model for the southern tropospheric box since 1790 A.D. are shown in Figure 3. The output from the BOSCAGE-8 scenarios with 20 and 30% of total biomass burning attributable to anthropogenic activities envelopes both the 1995 A.D. and 2001 A.D. Monte Carlo envelopes as well as the Siple Dome δ13CH4 results. One interpretation of these results holds that between 20% (11 Tg/yr) and 30% (16 Tg/yr) of total CH4 from biomass burning in 1985 AD is attributable to anthropogenic activities. It is, however, noteworthy that this result assumes (1) no anthropogenic biomass burning emissions at 1800 A.D. whereas savanna burning and wood use for cooking and heating were already significant contributors, and (2) that all natural CH4 emissions have remained constant and the characteristic δ13CH4 values that we have assigned to the various sources and sinks (Table 3) have also remained constant (thus assuming no shift of the anthropogenic biomass burning signature from “heavy” savanna burning to “lighter” forest burning).
 We finally utilized the δ13CH4 output from the BOSCAGE-8 model as the input for the forward firn model to compare the predicted firn δ13CH4 profile with our measurements. This test effectively evaluates the internal consistency between the BOSCAGE model assumptions and the most accurate estimates of the atmospheric δ13CH4 record over the last century. We utilized the BOSCAGE model output that resulted from assuming that 30% of total biomass burning CH4 emissions were anthropogenically produced. This BOSCAGE atmospheric record was used as the surface forcing along with the CH4 loading record from Etheridge et al.  in the Battle model ending in January 2001. The resulting δ13CH4 profile is plotted in Figure 2b (black line). The difference between the BOSCAGE predicted δ13CH4 profile and the measured data (omitting the 53 mbs sample) is 0.08‰ with the upper portion of the model curve having slightly lower δ13CH4 values and the lower portion of the model curve having slightly higher δ13CH4 values relative to the measured values. Overall, we consider the close agreement between the BOSCAGE model profile and the measured profile as support for the atmospheric δ13CH4 history resulting from the chosen scenario.
 The BOSCAGE-8 model does not include a separate term for methane decomposition by stratospheric Cl. Rather, we have modeled the stratospheric uptake via both OH and Cl with a single fractionation factor (αstrato = 1.16). This tuned parameter is very close to the empirically determined value (αstrato = 1.153 ± 0.008) from Rice et al. . As the stratospheric fractionation factor is held constant throughout the model run and stratospheric Cl levels must have been lower during the eighteenth and nineteenth centuries, the model predicted tropospheric δ13CH4 values during the nineteenth century are slightly higher than model runs in which the Cl effect had been treated separately. The magnitude of this oversimplification must be less than the total effect attributable to Cl today (0.2–0.5‰) [McCarthy et al., 2003; Platt et al., 2004; Wang et al., 2002].
 These preliminary tests using our reconstructed δ13CH4 trends thus suggest that a significant contribution of natural biomass burning to the CH4 budget must be invoked for the last 2 centuries. Our results also suggest that the source/sink scenario developed by Marik  is compatible with our δ13CH4 data over the last century. Testing other scenarios was beyond the scope of our study and will motivate future research.
 We have reconstructed a record of δ13CH4 over the past 2 centuries (nineteenth and twentieth) from a Siple Dome shallow ice core and two separate firn air samplings at the South Pole. Our results suggest the δ13CH4 was −48.8 ± 0.2‰ in the early 1800s and has increased exponentially to present-day values of −47.0‰ in 2001 A.D. The 1.8‰ δ13CH4 change must be related to an increase in the proportion of CH4 emissions with elevated 13C/12C ratios.
 In order to evaluate the reconstructed δ13CH4 record in terms of historical emissions, we applied an eight-box atmospheric model (BOSCAGE) that accounts for meridional transport and cross-tropopause mixing in addition to a prescribed OH sink distribution. The inputs for the model are the time-dependent anthropogenic CH4 emissions (tied to world population) and their assigned δ13CH4 value. One scenario that is in agreement with our isotope data invokes an increase in biomass burning CH4 emissions from 37 to 53 Tg/yr over the last 2 centuries. For this scenario, we maintained natural biomass burning values at 37 Tg/yr throughout the simulation and held the isotopic composition of all sources and sinks constant. Increased emissions throughout all simulations were tied to world population. It is important to note that this scenario is one of many possible solutions that are consistent with our δ13CH4 record combined with the atmospheric loading record from Etheridge et al. . We expect to be able to add additional constraints to this problem with future D/H measurements of CH4 trapped in ice.
 Finally, we sampled firn air from the South Pole station in 1995 and again in 2001 to establish the net change in δ13CH4 over a 6-year period. Because the seasonal δ13CH4 signal is damped within the firn, periodic measurements at a single firn site provide an ideal means of determining the average δ13CH4 change over multiple years. Over the 6 years separating the two samplings (1995 and 2001), we measured a change of 0.35 ± 0.2‰. This implies the average annual increase in δ13CH4 was 0.06 ± 0.03‰. This value is slightly higher than previous firn air estimates (0.04‰/yr) from single firn air reconstructions at Law Dome, Dronning Maud Land, and Dome C [Bräunlich et al., 2001; Francey et al., 1999].
 This research was supported by the NSF (OPP 95-26556, OPP 01-25981, and ATM-0117291 to TAS) and the National Institute of Global Environmental Change (NIGEC). It is a contribution to the European Commission project CRYOSTAT (EVK2-CT2001-00116) funded under the Energy, Environment and Sustainable Development Programme, 1998–2002. Additional support was provided by the French national program ECLIPSE. We thank Ingeborg Levin for providing access to the BOSCAGE model and Dave Scerbo for analytical support. We also thank P. Tans (NOAA/CMDL) for his continued support of the U.S. firn air program.
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