We describe the development of an automated gas chromatography-isotope ratio mass spectrometry (GC-IRMS) system capable of measuring the carbon isotopic composition of atmospheric methane (δ13CH4) with a precision of better than 0.1‰. The system requires 200 mL of air and completes a single analysis in 15 min. The combination of small sample size, fast analysis time, and high precision has allowed us to measure background variations in atmospheric δ13CH4 through the NOAA Climate Monitoring and Diagnostics Laboratory Cooperative Air Sampling Network. We then present a record of δ13CH4 obtained from six surface sites of the network between January 1998 and December 1999. The sites are Barrow, Alaska (71°N); Niwot Ridge, Colorado (40°N); Mauna Loa, Hawaii (20°N); American Samoa (14°S); Cape Grim, Tasmania (41°S); and the South Pole (90°S). For the years 1998 and 1999, the globally averaged surface δ13C value was −47.1‰, and the average difference between Barrow and the South Pole was 0.6‰. Consistent seasonal variations were seen only in the Northern Hemisphere, especially at Barrow, where the average amplitude was 0.5‰. Seasonal variations in 1998, however, were evident at all sites, the cause of which is unknown. We also use a two-box model to examine the extent to which annual average δ13C and CH4 mole fraction measurements can constrain broad categories of source emissions. We find that the biggest sources of error are not the atmospheric δ13C measurements but instead the radiocarbon-derived fossil fuel emission estimates, rate coefficients for methane destruction, and isotopic ratios of source emissions.
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 Atmospheric CH4 is an important chemical component of both the stratosphere and the troposphere and is a major contributor to the enhanced greenhouse effect. In the stratosphere, methane is a major source of water vapor [Jones and Pyle, 1984] and is the primary sink for chlorine radicals [Cicerone and Oremland, 1988], and thus it plays an important role in the regulation of stratospheric ozone levels. In the troposphere, CH4 consumes about 25% of all hydroxyl radicals, and as a result it is an in situ source of CO and O3 [Thompson, 1992]. Models indicate that the contribution of methane emissions to greenhouse warming is 20 times that of CO2 on a per molecule basis [Lashof and Ahuja, 1990]. It is estimated that methane accounts for approximately 20% of the increase in radiative forcing by trace gases since the onset of the industrial era [Myhre et al., 1998].
 The amount of methane in the atmosphere has more than doubled in the last 150 years [Etheridge et al., 1992, 1998] and over that time is highly correlated with human population [Blunier et al., 1993]. The growth rate of methane in the atmosphere has averaged nearly 1% per year over the last 40 years [Cicerone and Oremland, 1988; Etheridge et al., 1998] but has been steadily decreasing over the last 15 years [Steele et al., 1992; Dlugokencky et al., 1998]. Neither the rapid increase nor the recent slowdown is fully understood, and this is directly related to the large uncertainties in the magnitudes and spatial distribution of identified methane sources. Estimates of the emission rates of various sources are typically based upon small-scale field measurements [Cicerone and Oremland, 1988, and references within] that are extrapolated to large spatial scales. A few studies have used forward [Fung et al., 1991] and inverse [Brown, 1993; Hein et al., 1997; Houweling et al., 1999] modeling approaches to estimate source distributions based on atmospheric measurements. Nonetheless, considerable uncertainties remain in the estimates of source strengths.
 The measurement of the stable carbon isotope ratio in atmospheric methane [e.g., Lowe et al., 1994; Quay et al., 1999] and in methane sources [e.g., Tyler, 1986; Conny and Currie, 1996] may allow for a significant reduction in the uncertainties of the magnitudes of various methane sources. If we can measure 13C/12C of atmospheric methane with sufficient precision and the kinetic fractionation associated with its consumption by the hydroxyl radical [Cantrell et al., 1990] and soil microbes [King et al., 1989], then we can determine the mass-weighted isotopic average of all methane sources at steady state. When the mole fraction or δ13C of CH4 is not at steady state, we also need to know their growth rates. If an isotopic “signature” can characterize different methane sources, then the mass-weighted average will be a constraint on the magnitudes of various methane sources. The ratio 13C/12C is commonly expressed as δ13C, which is defined as the part per thousand deviation of the 13C/12C ratio in a sample to that in a standard; i.e., δ13C ≡ [(Rsample/Rreference) − 1] × 1000‰, where R = 13C/12C and reference is Vienna Peedee belemnite (VPDB) [Craig, 1957].
 From a 13C point of view, the sources of methane may be divided into three categories: bacterially produced methane, like that from wetlands or ruminants; fossil methane, like that associated with coal and natural gas deposits; and methane produced from biomass burning. Each of these three classes has a fairly distinct isotopic signature, with bacterial methane δ13C ≅ −60‰, thermogenic methane δ13C ≅ −40‰, and biomass burning methane δ13C ≅ −25‰ [e.g., Quay et al., 1999]. Individual methane sources may differ significantly from their source type's characteristic signature, but the values above are averages that are probably valid on large spatial scales. In principle, we should be able to constrain the emissions from these three source types from global atmospheric measurements.
 A few studies have reported globally and temporally distributed values of δ13C in CH4 [Quay et al., 1991, 1999; Stevens, 1995]. Quay et al.  reported more than 600 measurements between 1988 and 1995 from biweekly sampling at Barrow, Alaska; Olympic Peninsula, Washington; Mauna Loa, Hawaii; and American Samoa in addition to less frequent sampling at Cape Grim, Tasmania, and from Pacific Ocean ship transects. Stevens  reported 201 measurements, mostly from the continental United States, between 1978 and 1989. In the Southern Hemisphere, δ13C of methane has also been regularly monitored at Baring Head, New Zealand, since 1990 [Lowe et al., 1994].
 The goal of this study is to establish high-precision measurements of δ13C of methane on a global basis, using a subset of sites in the National Oceanic and Atmospheric Administration's Climate Monitoring and Diagnostics Laboratory (NOAA/CMDL) Cooperative Air Sampling Network [e.g., Conway et al., 1994]. Since January 1998, we have measured δ13C of methane from six sites (Table 1) ranging in latitude from 90°S to 71°N, from pairs of flasks collected on a weekly basis. The NOAA network gives us the potential to measure δ13C of methane from more than 60 land-based and ship-based sites. In order to take advantage of the high temporal and spatial density offered by the network, we have designed an automated gas chromatography-isotope ratio mass spectrometry (GC-IRMS) system that analyzes samples using 200 mL of air in less than 15 min. Traditional analysis methods [e.g., Stevens and Rust, 1982], on the other hand, are severely constrained by the 15–60 L of air typically used and the labor intensive sample extraction and analysis. This paper describes the analysis system and presents data from the first 2 years of measurements.
Table 1. NOAA/CMDL Air Sampling Sites Used in This Study
Cape Grim, Tasmania
Mauna Loa, Hawaii
Niwot Ridge, Colorado
 Sample analysis can be separated into six steps: sample introduction, methane preconcentration, cryofocusing, chromatographic separation, combustion, and mass spectrometric analysis. The details of the reference air used, batch analysis, and quality control will also be discussed below.
2.1. Sample Collection
 Ambient air is pumped through a pair of serially connected 2.5-L glass flasks fitted with two glass piston stopcocks sealed with Teflon O-rings. Conway et al.  have described the collection method in detail. Whole air reference gas is collected in aluminum high-pressure cylinders at the NOAA/CMDL cooperative site at Niwot Ridge, Colorado (40°N, 105°W, 3040 m).
 Samples are pressurized to roughly 0.2 bar above ambient pressure, resulting in 2.0 to 3.0 standard liters of air, depending on the altitude of the collection site. Upon arrival in Boulder, Colorado, flasks are analyzed for dry-air mole fractions of CH4, CO2, CO, H2, N2O, SF6, and the carbon and oxygen isotopic composition of CO2. On average, flasks contain less than 1.5 standard liters of air by the time they are analyzed for 13C/12C ratio of methane, which was a major constraint in the design of the analysis system. Air pressure in the flasks is also about 0.2 bar below ambient when extracted for measurement.
2.2. Sample Introduction
 Flasks are attached to a manifold described in detail by Lang et al.  in preparation for analysis. The circular manifold (Figure 1) is evacuated up to the flask stopcocks by a rotary pump (Edwards E2M5) to a pressure of less than 3 × 10−2 mbar. The stopcocks on the flasks are then opened, allowing the air inside to expand through tubing to an eight-port stream selection valve (Valco SD8, Valcon M rotor) fitted to a 16-position electric actuator. These extra actuation positions allow the manifold to be in a “blanked off” position between the analyses of samples. A diaphragm pump (KNF) then pulls air out of the flask at rate of 100 mL/min (STP), controlled by an electronic mass flow controller (Edwards 1605). The air then flows through an Ascarite II (NaOH on a silica substrate) and Mg(ClO4)2 trap to remove CO2 and water vapor from the sample. The CO2/water trap is a 15 cm × 6 mm ID glass trap consisting of a 6-cm layer of Ascarite II sandwiched between two 2-cm layers of Mg(ClO4)2, with small plugs of glass wool at each end. The Cajon Ultra-Torr fitting holding the trap on the downstream side also has a 10-μm stainless steel frit to prevent particles from entering the rest of the system. After leaving the trap, the air flows to a 40-mL sample loop positioned on a six-port, two-position injection valve (Valco 6-UW, Valcon E rotor). After flushing the sample loop and trap for 120 s, the injection valve is switched so that a flow of He (99.999% purity, further purified by Alltech “All-Pure” He purifier) flushes the contents of the sample loop to another six-port, two-position valve containing the preconcentrator (Figure 1). Note that the flow rate of the He stream is only pressure regulated, resulting in changing flow rates with temperature and flow path. The flow rates through the preconcentrator are 22 mL/min (STP) at room temperature and 30 mL/min (STP) at −120°C.
 The introduction of air from a reference tank has been designed to be as similar as possible to the introduction of flask air, so as to minimize any potential offset between analysis of reference air and sample air. The only difference is that reference air flows through the diaphragm pump while it is off. A downstream regulator pressure of at least 0.2 bar above ambient pressure on the reference air tank is needed to overcome the resistance of the water/CO2 trap and maintain a flow of 100 mL/min (STP). A total of approximately 200 standard mL is used in each sample analysis. This volume is more than 4 times the volume of tubing that is flushed but decreases the chances that the trap contains any “memory” of the previous sample from run to run.
2.3. Sample Preconcentration
 Preconcentration of the CH4 within the air sample is necessary to ensure that N2, O2, and Ar do not coelute with methane from the analytical column. N2 entering the combustion furnace can be oxidized to N2O, which interferes with the m/z = 44 and 45 signals that result from CH4-derived CO2. In general, we want only CH4-derived CO2 (and He) in the mass spectrometer during its analysis. The preconcentration step is to isolate methane on a substrate while N2, O2, and Ar are vented. Our preconcentrator is based on the design of Merritt et al.  and modified to ease automation. The preconcentrator is a linear 1/8 inch OD (0.085 inch ID) × 20 cm stainless steel column packed with 4 cm of 80/100 mesh Haysep-D surrounded by 5 cm of 60/80 mesh glass beads and 1 cm of glass wool on either side. The column is encased in a 12 cm × 6 mm ID glass tube, fitted with two 1/4 inch OD sidearms, as shown in Figure 2. A 1-cm-thick insulating layer of open-cell foam covers the glass tube. The column is centered within the glass tube by a pair of 1/2 inch to 1/4 inch Cajon Ultra-Torr reducing unions through which the column extends. The central 10 cm of the column is wrapped with fiberglass-insulated NiCr heating wire (0.23-mm diameter, Omega). The wire is wrapped over a narrow gauge K-type (alumel/chromel, Omega) thermocouple positioned about 2 cm from the center of the column, just beside the liquid N2 outlet (Figure 2). The column is fitted to the six-port, two-position valve with 1/16 inch stainless steel tubing and 1/16 inch to 1/8 inch reducing unions fitted with 10-μm screens (Valco) and sealed with Teflon ferrules.
 The column is maintained at −120°C by opening and closing a solenoid valve on a pressurized liquid N2 tank that is plumbed to the inlet of the jacket surrounding the preconcentration column. The valve is controlled by the central computer, which monitors the thermocouple at a frequency of about 5 Hz. Cold N2, mainly in the vapor phase, enters through one of the sidearms on the glass outer jacket and exhausts through the other sidearm and the gaps between the 1/8 inch OD column and the 1/4 inch ends of the Ultra-Torr fittings. Tests demonstrated that allowing liquid nitrogen to exhaust through the exit sidearm and both ends of the glass jackets provided the most uniform temperatures.
 The preconcentrator is kept at −120° ± 3°C for 3 min prior to the sample injection to ensure that the entire diameter of the column has cooled. Once the sample air has been injected onto the preconcentrator, it is held at −120°C for 2 min allowing the bulk of the “air” to vent. Immediately after the cooling is stopped, the NiCr wire (total resistance of 19.7 Ω) is heated to 0°C by applying a 12-V potential across the NiCr wire. The central computer controls the warm temperature in the same manner as the cryogenic temperature. As soon as the heating begins, the six-port valve is switched so that the ∼30 mL/min (STP) of He through the preconcentrator is replaced by a 2.0 mL/min (STP) electronically controlled flow (Tylan FC-260). The low flow rate is required by the analytical column and ensures a reasonable split ratio prior to entering the mass spectrometer. We chose 0°C to minimize the amount of water vapor released by the preconcentrator onto the cryofocus stage. After the elution of CH4, the high He flow is returned to the preconcentrator, and it is heated to 110°C for 5 min to purge the column of H2O and any other remaining condensables.
 The temperatures and timings for the preconcentrator were determined by analyzing both the venting flow and the slow eluting flow by flame ionization detection (FID). At the measured temperature of −120°C, methane was retained indefinitely on the precolumn. Although the FID is not directly sensitive to air, the flow disturbance caused by its elution is evident at about 15 s. The additional 105 s was used to let the tail elute. A column heating rate of about 40°C/min, corresponding to an application of 12 V, resulted in the elution of methane at 45 s after the valve switch and the start of heating, with a peak width (full width at half maximum (FWHM)) of about 30 s. Tests using an NDIR analyzer (Li-Cor 6251) indicated that CO2 coelutes with methane in the absence of the presample loop CO2/H2O trap.
2.4. Sample Cryofocusing and Separation
 The methane eluting from the preconcentrator is transferred to the GC through a 0.32-mm ID deactivated fused silica transfer capillary (SGE). There it is cryofocused at the head of the analytical column (Molecular Sieve 5A, 0.32 mm × 25 m, Chrompack) so that its peak width can be reduced. The cryofocusing is achieved by cooling the first 10 cm of the column to about −150°C. The head of the column is encased in a section of 1/4-inch OD stainless steel tubing with a tee at one end and a cross at the other (Swagelok). The column is held in place by custom-drilled 1/4-inch-0.5 mm graphitized-vespel reducing ferrules. The tee is used as the inlet for liquid N2, while the cross is used as an outlet and as a port for a K-type thermocouple. The central computer controls the temperature in the identical manner as the preconcentrator. The head of the column is cooled 1 min prior to the heating of the preconcentrator to ensure that all eluting methane is trapped. It is held at −150°C for an additional 2 min, which corresponds to the FID-determined elution of methane from the precolumn plus one additional minute of “safety” time. The head of the column is heated by stopping the flow of liquid N2 and simply allowing the cryofocus device to warm to the GC temperature of 80°C. The column warms to 0°C within about 3 min, although design tests indicate that methane begins to desorb from the column at about −100°C.
 Methane and residual air from the preconcentration step, along with air from leaks and carrier gas impurities are cryofocused on the head of the analytical column. Some of this air passes through at −150°C, but the portion that is retained must be fully separated prior to combustion and analysis in the mass spectrometer. Although the dominant choice of analytical column in similar systems has been 0.32 mm × 25 m Poraplot Q [Zeng et al., 1994; Merritt et al., 1995; Sansone et al., 1997], we have found that the separation of CH4 from air is enhanced on Molecular Sieve 5A. At a GC oven temperature of 80°C, O2 elutes at 100 s, N2 elutes at 150 s, and CH4 elutes at 190 s after the warming of the cryofocus region. Furthermore, the strong retention of CH4 on Molecular Sieve 5A allows for a much smaller length of column to be used in cryofocusing.
 The GC effluent prior to the elution of CH4 is diverted from the source of the mass spectrometer through a changeover valve located downstream of the open split (Figure 1). The wide separation ensures that when CH4 is present in the combustion furnace and the analyzer section of the mass spectrometer, no other species (other than He carrier gas) are present. The width (FWHM) of the methane peak after conversion to CO2 is 5 s as measured by the mass spectrometer. The peak height is typically about 9 nA (Figure 3) but can vary depending upon both the sensitivity of the mass spectrometer and the temperature of the cryofocus unit. CO elutes at 350 s, but the ratio of its peak area to that of methane indicates that only a portion of the initial CO in the sample is trapped during methane preconcentration. Although the Molecular Sieve column has excellent separating characteristics, it irreversibly adsorbs water and CO2 at room temperature. The presence of the trap upstream of the sample loop prevents the majority of water and CO2 from reaching the column, but the column must be baked out after every ∼500 samples at greater than 200°C to remove adsorbed water and CO2.
2.5. Sample Combustion
 After eluting from the capillary column, the methane peak is transferred to the combustion furnace via a 20-cm section of 0.32-mm ID fused silica capillary. The combustion furnace is composed of a 3 mm OD × 0.5 mm ID × 300 mm high-density alumina tube (Alsint, Bolt Technical Ceramics) mounted coaxially within a 400-W cylindrical heater. The combustion tube is attached to transfer capillaries on either end by 1/8-inch–1/16-inch reducing unions (Valco), and the seal is made with 1/8-inch graphitized-vespel ferrules and 1/16-inch gold-plated stainless steel ferrules (Valco). The output of the heater is controlled by an electronic temperature controller (Omega 9000A) using an R-type (platinum and rhodium/platinum, Omega) thermocouple. The ceramic tube extends 6 cm beyond the edges of the heater to ensure that the fittings remain cool. Glass wool is used to plug both ends of the annulus between the combustion tube and the heater to minimize the temperature gradient within the heated zone.
 The combustion tube is filled with Ni and Pt wires that run the length of the furnace. The Ni wire is used as a substrate for oxygen required in combustion, and the Pt wire serves as a catalyst. In order to maximize the amount of oxygen available for combustion and the surface area available for catalysis, six 0.05-mm Ni (99.994% purity) and two 0.05-mm Pt wires (99.95% purity) are used (Alfa Aesar). All wires were braided together to facilitate insertion. The furnace is maintained at 1150°C; lower temperatures allow some methane to remain uncombusted. The Ni inside the furnace was initially oxidized by passing pure oxygen (99.999% purity) through the furnace at 5 mL/min (STP) at 500°C for 4–6 hours and then at 1150°C for 10–12 hours [Merritt et al., 1995]. However, repeated oxidation is not necessary. This is, most likely, because of the small amount of oxygen eluting through the column and passing into the furnace every time a sample is analyzed. The increased surface area of Ni wire, compared with that of Merritt et al. , may also provide a larger reservoir of oxygen available for combustion. This design yields a consistent amount of CO2, no CH4, and no CO, as measured by the mass spectrometer, FID, and reduction gas analyzer, respectively. On the basis of these tests we infer a combustion efficiency of 100%.
 Although water is produced in the combustion of methane, it is not removed from the He stream prior to admittance to the mass spectrometer. Normally, transient amounts of water are removed to limit the extent of the gas phase ion-molecule reaction between CO2 and H+ in the source of the mass spectrometer. In this reaction, a proton bonds to the CO2 resulting in a species of m/z = 45 that does not correspond to CO2 containing 13C. This reaction occurs in all IRMSs but is “invisible” when its contribution is the same for both running gas and sample gas. In our case the rate of this reaction is substantially higher when our CH4-derived CO2 peak enters the source than when our pure CO2 running gas does, resulting in a systematic error to our measurements. Such systematic errors can be accounted for by calibration. However, random variations in the H2O peak and drifts in the background concentration of H2O in the source over time do contribute to imprecision in our measurements. Fortunately, as is shown below, these random errors are small.
2.6. Mass Spectrometric Analysis
 After the CH4-derived CO2 peak leaves the combustion furnace, it is transferred to an open split. The split consists of a 0.11-mm ID capillary placed 4 cm within a 0.32-mm ID capillary that is bathed in He. A 1-m section of the 0.11-mm capillary leads through the changeover valve to the source region of the mass spectrometer (Micromass Optima or Micromass Isoprime), resulting in a pressure of 5–6 × 10−6 mbar. The split ratio is approximately 1:6. Although a larger split ratio would allow more CH4-derived CO2 to be analyzed, the mass spectrometer cannot operate at pressures greater than 1 × 10−5 mbar.
 Inside the mass spectrometer, the CH4-derived CO2 is ionized and the signals for m/z = 44, 45, and 46 are simultaneously measured. After the tail of that peak has disappeared, after about 1 min, a pulse of pure CO2 “running gas” (“bone-dry” quality) from the bellows of the dual-inlet portion of the mass spectrometer is mixed into the He stream and admitted to the source region (Figure 1). The purpose of the pure CO2 running gas is to track and correct for changes in the mass spectrometer ion source that occur over periods of half an hour to hours. This square peak of CO2 is 30 s wide with a height of about 6 nA. The CO-derived CO2 peak elutes about 20 s after the end of the running gas CO2 peak. Once the baseline has returned to normal after another 60 s, the signal collection is stopped.
 Each aliquot of air, from either a sample flask or reference tank, is measured in relation to running gas, so that drifts in the source or analyzer regions of the mass spectrometer at timescales of greater than a few minutes are taken into account. Specifically, the m/z = 44, 45, and 46 peaks are integrated for both the sample and running gas, and ratios of the areas are calculated. The data analysis software measures the current at the beginning and end of the data collection period, linearly interpolates between those points, and subtracts these “zero” lines from the raw signals. The m/z = 44, 45, and 46 peaks have slightly different elution times, requiring each peak to have unique integration limits. The software makes an “isotope shift” correction to the m/z = 45 and 46 peaks that are typically −40 ms and +20 ms, respectively. In order to correct for the contribution of 12C16O17O to the m/z = 45 signal, a “Craig correction” is made [Craig, 1957] on the basis of the area of the m/z = 46 peak. Finally, the δ13C value of the sample peak is calculated in relation to that of the running gas and then converted to the V-PDB scale using the user-entered V-PDB value of the running gas.
 The δ13C value of our running gas relative to V-PDB is −36.9‰ as determined on a dual inlet instrument (Micromass-Optima) in our lab. However, we cannot be certain that this is the δ13C value that is admitted to the source. The running gas is probably fractionated in the stainless steel capillaries between the bellows and the mass spectrometer, and the degree of fractionation can vary with the pressure in the bellows. In addition, it is possible that fractionation can occur in the introduction of running gas to the bellows from our CO2 source and through leaks in the dual inlet of the mass spectrometer. Other day-to-day variability may result from changing baseline conditions and their effect on zero subtraction. The consequence of these errors is that at this point the calculated delta values of both our samples and references differ from their true values by +1.0 ± 0.2‰, on average.
2.7. Reference Gases and Calibration
 In order to know the “true” value of our samples and references, our references have been externally calibrated by using traditional, dual-inlet, off-line techniques. Four references have been calibrated by Stanley Tyler at the University of California, Irvine (UCI), using a technique based on that of Stevens and Rust [Stevens and Rust, 1982; Tyler, 1986; Lowe et al., 1991]. The δ13CH4 of the reference air was measured in relation to pure CO2 reference gas that had been calibrated against IAEA-NZCH (see, e.g., Lowe et al. ). The isotopic compositions of our samples and one additional reference air tank have been determined in relation to these calibrated references. Our reference air is whole air that has been dried by Mg(ClO4)2 and pumped into aluminum cylinders to about 150 bar at Niwot Ridge, Colorado. In the future, at least one of our original reference air tanks will be remeasured by the Tyler group to check for drift in the δ13C value. All measurements are reported in relation to V-PDB [Coplen, 1995].
2.8. Analysis Sequence
 Each sample flask is measured as part of a batch of eight. The run starts with the analysis of five consecutive aliquots of reference air, of which the first is typically an outlier (greater than 2σ from the mean) and always rejected. The measurement of the flask samples then begins, and each sample analysis is alternated with a reference analysis until all eight samples have been measured. The batch analysis ends with the measurement of four consecutive aliquots of reference gas. Once the first reference measurement has been excluded, the reference measurements are averaged in three groups of five, i.e., runs 2, 3, 4, 5, and 7; runs 9, 11, 13, 15, and 17; and runs 19, 21, 22, 23, and 24. In this way, the drift of the total system over times of about 2 hours is tracked. Reference gas and sample gas are alternately introduced to the system to reduce the chances of “memory” of a previous sample affecting future samples. Standard gas δ13C values are linearly interpolated between the averages of groups 1, 2, and 3. Flask sample δ13C values are then recalculated in relation to the interpolated standard gas values to correct for drift. Drifts of about 0.1‰ are typically observed between the beginning and end of a run (about 6 hours), with the ending standard gas δ13C values heavier than those at the start. One possible explanation for this drift is the accumulation of water vapor in the source region of the mass spectrometer over the course of the run. Water produced as a result of methane combustion and admitted through leaks may not be pumped away from the tubing downstream of the furnace, and the source, as fast as it is produced. From one sample/standard analysis to the next, this effect would be difficult to observe, but over the 6-hour period of the run, we would expect to observe some accumulation. Regardless of the cause of the drift, our frequent use of reference gas gives us confidence in the accuracy of our measurements relative to that of the externally calibrated reference air.
2.9. Quality Control
2.9.1. Flask tests
 In order to quantify systematic biases in the measurement of air from underpressure flasks versus that from overpressure tanks, we conducted systematic flask tests. Eight flasks were filled from a tank of standard gas to about 0.5 bar, which is the typical pressure in flasks when they are analyzed. The δ13C values of these flasks were measured, in the manner stated above, and compared with the δ13C values of the standard aliquots of the same batch analysis. Analysis was repeated twice more on these flasks to simulate three total measurements. No systematic bias was detected within the noise (1σ ≅ 0.05‰) to which all samples and standards were subject. Additionally, the δ13C values of the flasks from the first and third runs were not distinguishable, implying that we can analyze a flask at least 3 times without error.
2.9.2. Flask pair differences
 One measure of the precision of flask analyses is the difference between the δ13C values of a single flask and its mate. The mean pair difference is −0.018‰ (first flask measured minus the second), and the mean of the absolute values of pair differences is 0.118‰ (n = 630). The distribution of pair differences is well approximated by a normal distribution centered on zero (Figure 4), indicating that there is no systematic bias in the order in which a pair of flasks is measured. Among good pairs, defined as those pairs with a difference of less than 0.2‰, the mean pair difference is −0.009‰, and the mean absolute difference is 0.071‰ (n = 554).
2.9.3. Precision of standards
 We can also use the standard deviation of the standards in a batch analysis as a proxy for the precision of flask measurements. The mean standard deviation of aliquots from standards in any given run is 0.08‰ ± 0.02‰ (1σ, n = 172) (Figure 5). Since all measurements are corrected for the drift of standards during a run, we also calculate the absolute difference between the measured δ13C value and the δ13C value of the linearly interpolated drift line, at the same point in time. The standard deviation of these differences is 0.07‰ ± 0.02‰. Using a 40-mL air sample, the shot-noise limited precision of our measurement is ∼0.02‰; so we are within a factor of 4 of this limit.
2.9.4. Sample size versus δ13C relationship: “Linearity”
 The relationship between sample size and δ13C value was checked by making repeated measurements from a single standard tank using 40-mL and 25-mL sample loops. Although peak area as measured by the mass spectrometer varied in proportion to sample loop size, the δ13C value was constant to within typical experimental uncertainty of ∼0.05‰. Given that the mole fraction of methane in sample flasks varies by a maximum of ±15%, we are confident that “nonlinear” effects in the chromatographic/combustion system or ion source do not compromise our measurements.
2.9.5. Internal comparison of reference tanks
 We have measured the δ13CH4 values of our standard tanks relative to one another and compared the measured differences to the differences between tanks as originally measured at UCI. Since the δ13C values encompass a range from −47.17‰ to −47.27‰, we measured only the two tanks at the ends of the scale. These two tanks are also the tanks that have provided the standard gas for close to 90% of our sample measurements. Treating the tank “Harpo” as the standard and the tank “Lucy” as an unknown, the δ13C value of Lucy was determined to be −47.14 ± 0.01‰ (standard error of the mean, n = 16), whereas the assigned δ13C value of Lucy as determined at UCI is −47.17 ± 0.04‰ (standard deviation, n = 2).
2.9.6. Contamination levels
 We intermittently assess the level of contamination in our analysis system by injecting a sample loop filled with He instead of air. Such blank runs never yield CH4-derived CO2 peak areas of greater than 0.1% of the sample peak area. As an alternative test, we inject a He-filled sample loop into the system but bypass the preconcentration device. These tests yield peak areas only 0.03% of sample peak area. Thus the contamination that is present is mostly due to condensation of leaks and carrier gas impurities during sample preconcentration.
2.10. Future Measurements of D/H
 The system described above is well suited for adaptation to make measurements of δD in atmospheric methane. The oxidation furnace currently in line could be replaced by a furnace that would directly convert CH4 to H2 [Burgoyne and Hayes, 1998; Hilkert et al., 1999]. The hydrogen isotopic ratio could then be analyzed by an isotope ratio mass spectrometer appropriately tuned. The other change that would have to be made would be to increase the size of the sample loop to account for the lower relative abundance of D compared with 13C and the lower ionization efficiency of H2 relative to CO2. Assuming a CH4 to H2 conversion efficiency of near 100% and using a 100-mL sample loop, precision close to 1‰ should be attainable.
3. Results and Discussion
3.1. Editing and Selection of Data
 Sample data are shown in Figure 6. Most data are averages of a single aliquot taken from each member of a pair of flasks, and less than 1% of the data are from unpaired flasks. At some sites, samples are collected by different methods on the same day. The observed variations in the value of δ13C are a composite of large-scale and small-scale spatial variations, sampling errors, and analytical errors. Following the convention of Dlugokencky et al. , data are first “edited” for sampling and analytical problems. Methane data exclusion on the basis of sampling and analytical problems has been discussed previously [Lang et al., 1990; Dlugokencky et al., 1994] but can involve problems associated with incomplete flushing of sample flasks and obvious contamination from local sources. Data are then edited for analytical problems that occurred during methane mole fraction measurements. Any sample determined to have either a problem in sampling or in the analysis of methane mole fraction is similarly flagged in the δ13C data set. Samples analyzed during batch analyses where the standard deviation of the standard gas aliquots exceeded 0.12‰ are also flagged. Samples from these analyses are typically rerun. Data are also flagged and excluded from further analysis if the difference in δ13C values from a flask pair exceeds 0.2‰. Pair differences greater than 0.2‰ most likely indicate analytical problems and not natural variability. Note that all data, including those flagged for sampling and analytical problems are available at ftp://ftp.cmdl.noaa.gov/ccg/ch4c13/.
 After editing, data are “selected” to ensure that they are representative of a very large volume of well-mixed air. Air samples determined to be “nonbackground” on the basis of the methane mole fraction, as described by Dlugokencky et al. , are flagged as such in the δ13C data set. Air samples are also determined to be nonbackground if the δ13C value lies beyond a 3σ window around the smooth curve (see section 3.3) shown in Figure 6. Most often, a sample is considered background if it was collected when winds were coming from a predetermined clean-air sector. In the first two years of data, 2% of samples were excluded because of sampling problems and mole fraction analysis problems, 12% of the data were excluded because of δ13C analysis problems, and 2% were determined to be nonbackground on the basis of δ13C values.
3.2. Latitudinal Gradient of δ13C
 The north-south gradients in methane mole fraction and its isotopic composition are important constraints on the location and strength of methane sources and sinks [Fung et al., 1991]. The mole fraction latitudinal gradient is well established [e.g., Steele et al., 1987; Dlugokencky et al., 1994], and Quay et al. [1991, 1999] have reported an annual mean gradient for δ13C. Figure 7 shows the annual mean gradients for 1998 and 1999 between 90°S and 71°N. The average difference between SPO and BRW (BRW - SPO) was −0.65 ± 0.1‰ in 1998 and −0.56 ± 0.1‰ in 1999. Quay et al.  reported a mean annual average difference of −0.54 ± 0.05‰ between BRW (71°N) and CGO (41°S) during the years 1989–1995. We calculate the annual mean hemispheric difference by fitting a cubic curve to the latitudinal profile, as a function of sine of latitude, and take the average δ value north and south of the equator. For the period 1998–1999 the mean hemispheric difference was 0.30‰.
 As expected, the δ13C values in the Southern Hemisphere are consistently higher than δ13C values in the Northern Hemisphere. This occurs because the majority of sources are located in the Northern Hemisphere, and the reaction with OH enriches the methane remaining in the atmosphere. Methane in the Southern Hemisphere has had more time to react with OH than methane in the Northern Hemisphere, leaving it more enriched in the heavy isotope. Another prominent feature of the interhemispheric gradient is the near uniformity of Southern Hemisphere δ13C values. This is also observed in the interhemispheric gradient of methane mole fraction and is a function of a paucity of surface emissions and rapid atmospheric mixing in the Southern Hemisphere [Law et al., 1992].
3.3. Seasonal Variations in δ13C
Figure 8 shows monthly mean δ13C values and mole fractions for the triad of sites in each hemisphere. Monthly mean δ13C values are calculated from the smooth curves shown in Figure 6. The smooth curve for each site is represented by a function composed of a linear term to represent the long-term trend in the data and four harmonic terms, which capture the average seasonal variation.
The function is fit to the data by using a least squares technique, which has been described in detail previously [Thoning et al., 1989; Steele et al., 1992; Dlugokencky et al., 1994]. We average monthly portions of the smooth curve to give monthly mean δ13C values, because the data are not evenly spaced. Samples are not collected every week, and sampling problems or nonbackground conditions may occur at a site during a given month. Monthly mean values remove some of the short-term natural variability and analytical variability in the data and allow for a more straightforward comparison to the mole fraction data.
3.3.1. Southern Hemisphere sites
 In our record, Southern Hemisphere sites SPO (90°S), CGO (41°S), and SMO (14°S) do not exhibit strong seasonal variability. During 1998, however, substantial decreases in monthly mean δ13C values are present during August, September, and October, especially at SMO and CGO. The conventional assumption is that seasonal variations in Southern Hemisphere mole fractions are driven mostly by OH oxidation, but the magnitude of the dip in δ13C values is too large to be explained by OH alone. One possible contribution to the observed dip is the positive 12 Tg/yr anomaly in tropical wetland emissions during 1998 proposed by Dlugokencky et al. . A + 12 Tg/yr anomaly would result in a −0.13‰ anomaly in the lower southern atmosphere (0°–30°S) if the emissions mixed evenly through the entire semihemisphere and if the signature of the wetland source were −60‰. The seasonal cycle amplitudes at CGO, based on the smooth curve fit to the data, were 0.26‰ in 1998 and 0.12‰ in 1999. Thus anomalously large tropical wetland emission could help to explain the presence of the dip at SMO and CGO in 1998.
Lowe et al.  showed distinct seasonal cycles in δ13C between 1989 and 1997 from air collected at Baring Head. As was discussed by Lowe et al. , the amplitude of the observed seasonal cycle was too large to be explained solely on the basis of OH oxidation. If the methane mole fraction seasonal amplitude were controlled completely by OH destruction (as might be the case for SPO), we would expect the amplitude in δ13C value to be approximately 0.1‰ according to the following Rayleigh model of CH4 consumption:
Here δ and δ0 are the original and final isotopic ratios, expressed in δ notation (per mil units), ε is the kinetic fraction factor due to reaction with OH (ε = −5.4‰ [Cantrell et al., 1990]), and ΔM/M is the fraction of total methane destroyed (ΔM/M = 30 ppb/1700 ppb). Given the analytical noise in our measurements of ∼0.1‰, we may not be able to clearly observe a seasonal cycle with an amplitude of the same order. However, the Lowe et al.  measurements indicate the presence of a seasonal cycle with an amplitude of at least 0.2‰. It is unclear at this point in our measurement record whether or not we are observing a seasonal cycle in δ13C values at our Southern Hemisphere sites, because of the brevity of our record and the possible anomaly we may have observed in 1998. Conversely, seasonal cycle amplitudes in δ13C much greater than 0.1‰ are an indication that processes other than destruction by OH are at work.
3.3.2. Northern Hemisphere sites
 Seasonal variations of δ13C are more distinct in the Northern Hemisphere than in the Southern Hemisphere. Roughly 75% of methane emissions are from the Northern Hemisphere [Fung et al., 1991]. Mean Northern Hemisphere mole fractions average about 90 ppb higher than those in the Southern Hemisphere, and in both 1998 and 1999 δ13C values averaged about 0.3‰ lower in the Northern Hemisphere than in the Southern Hemisphere. The relative proximity of Northern Hemisphere sampling sites to source regions also results in a greater degree of variability in the seasonal variations of both mole fractions and isotopic ratios than is observed in the Southern Hemisphere.
 Seasonal variations are most evident at BRW, where the seasonal cycle amplitude has averaged 0.65‰, with the maximum in May and the minimum at the end of September. Values of δ13C start to decrease in May and continue through the summer despite the fact that destruction of CH4 by OH is largest during this time of year. This probably occurs because emissions from isotopically light sources like wetlands are greatest during the summer, and bacterial emissions have 2–3 times the impact on δ13C values than OH for the same change in mole fraction. Seasonal patterns at NWR and MLO are less distinct than those at BRW but, as is the case in the Southern Hemisphere, exhibit deeper minima in 1998. The amplitudes are also substantially smaller than those at BRW, which may be a result of BRW being closer to strong wetland emission regions.
3.4. Constraints on the Global Budget
 The global atmospheric average 13C/12C (RA) is related to the flux-weighted isotopic ratio of all sources (RS) by
where C is the average atmospheric methane mole fraction, prime denotes time derivative, k12 is the inverse of the methane lifetime, and α is k13/k12. The denominator is simply the total of all methane sources. Lassey et al.  have formulated the same expression in the more usual δ notation:
where ε = 1000(α − 1). These exact formulations differ from the common first-order approximation
 Using average values for the parameters in (4) over the period of our measurements (Table 2), δs = −52.68‰. Using (5), the value would be −53.32‰. Global average δs is clearly sensitive to the approximations used in its calculation. As would be expected simply from (5), δs is most sensitive to δA and ε, although δA is better known than ε; ε requires knowledge of OH, soil, stratospheric and possibly Cl sink fractionation factors and their relative reaction rates, whereas δA can be directly measured; δs is not very sensitive to methane mole fraction and δ growth rates, but if we assume that they are zero, i.e., that the atmosphere is at steady state with respect to both 13CH4 and 12CH4, the δs estimate may be in error by up to 1‰.
Calculated as k12 = kOH + kSOIL + kSTRAT; kOH is 1/10.5 and is taken from Montzka et al. ; kSOIL is 1/484.2 and is calculated as a first-order loss assuming a 30 Tg/yr soil sink and a global CH4 burden of 1750 ppb. We assume that 2/3 of the soil sink is in the Northern Hemisphere. Parameter kSTRAT is 1/110 and is taken from Scientific Assessment of Ozone Depletion (1998).
Calculated as α = (αOHkOH + αSOILkSOIL + αSTRATkSTRAT)/k12; αOH is 0.9946 and is taken from Cantrell et al. ; αSOIL is 0.979 and is taken from King et al. ; αSTRAT is 0.988 and is calculated by weighting αOH and αCl by the strengths of Cl and OH sinks in the stratosphere according to Hein et al. . Errors were determined only by propagating errors in k12 and assigning an error to αOH of 0.0009, the error estimate of Cantrell et al. .
FFP (fossil fuels plus) is the sum of the Fung et al.  categories: gas venting, gas leaks, coal mining, and landfills. The total of the fossil fuel categories was 100 Tg/yr and was calculated from Quay et al. 14CH4 data. Landfill emissions are taken as 35 Tg/yr, which is the average of the Hein et al.  and Fung et al.  estimates. The north/south division (92%/8%) is based on Table 4 of Fung et al. . Error estimates are derived from the range in landfill emission estimates (20 Tg/yr) and the range for fossil fuel emissions of 50% given by Quay et al. .
Bacterial emissions (B) are defined as the sum of the Fung et al.  categories: bogs, swamps, tundra, rice, animals, termites, and clathrates; BMB is biomass burning; FFP is defined as above; δ values are calculated by using source signatures from Table 1 of Quay et al.  with weightings from the global totals of the Fung et al. categories listed above. We assume that source signatures are the same for each hemisphere.
0.02 ± 0.02
1.0 ± 0.1
0.1071 ± 0.01
0.9936 ± 0.0008
124 ± 47
−61 ± 2
−24 ± 2
−43 ± 2
0.02 ± 0.02
1.0 ± 0.1
0.1057 ± 0.01
0.9938 ± 0.0008
11 ± 4
−61 ± 2
−24 ± 2
−43 ± 2
3.4.1. An inverse two-box model
 We can use the annual average of observed values of δ13C and CH4 mole fraction in each hemisphere to constrain the global methane budget by simultaneously solving equations (6) and (7) and equations (8) and (9) for bacterial and biomass burning emission strengths in each hemisphere, if we calculate the strength of fossil fuel emissions on the basis of radiocarbon measurements [e.g., Quay et al., 1999] and assume emissions of other small sources in each hemisphere. Equations (6)–(9) are mass balances for 12CH4 and 13CH4 in each hemisphere:
Here the subscripts N and S refer to each hemisphere; C is total methane mole fraction, i.e.,13CH4 + 12CH4; prime denotes the time derivative; and R is the isotopic ratio 13C/(13C + 12C). Note that this is not the standard way of defining R; so we must redefine RPDB = 13C/(13C + 12C) = 0.01111. Constant kex is the interhemispheric exchange constant; B is the total of all bacterial emissions; BMB is the total of biomass burning emissions; and FFP is the total of fossil fuel related emissions, plus other emissions, especially those from landfills. Fossil fuel and landfill sources were grouped together because of their very similar source distributions: both are estimated to be more than 90% in the north. A composite isotopic ratio was created for this category by weighting their isotopic source signatures by emissions.
Table 2 lists values of parameters used in the equations. The left-hand sides of (6)–(9) contain only known quantities, and the four unknown fluxes are on the right-hand sides. When we solve our two systems of two linear equations using our best estimates for the terms on the left-hand side, the global emission totals are as follows: bacterial, 355 ± 48 Tg/yr; biomass burning, 56 ± 37 Tg/yr. The hemispheric totals are BN = 250 ± 33 Tg/yr, BS = 106 ± 21 Tg/yr, BMBN = 23 ± 30 Tg/yr, and BMBS = 31 ± 10 Tg/yr. We calculate the ratio of the B, FFP, and BMB emissions as 65/25/10. This ratio is similar to the ratios obtained by Fung et al.  of 64/25/11, Crutzen  of 72/22/6, and Hein et al.  of 70/22/7.
 We estimated errors by using a Monte Carlo approach in which all parameters not determined from NOAA/CMDL measurements were assigned errors listed in Table 2. The dominant source of error appears to be the uncertainty in our assumption of fossil fuel emission rate, especially for Northern Hemisphere sources. Uncertainty in source δ values and rate coefficients for sinks are the next most important sources of error. The interhemispheric exchange constant kex does not influence global partitioning, but it has a big impact on partitioning of a source between hemispheres. For example, although our stronger BMBS source contrasts with other estimates [e.g., Fung et al., 1991], we can adjust the north/south partitioning by choosing a different value of kex.
 The sensitivity of our model to changes in individual parameters is shown in Table 3. It is evident that improving the precision of our atmospheric measurements will not dramatically alter our ability to partition sources, at least when using annual hemispheric average δ13C values. Changing the global average δ by 0.1‰ would only alter emissions partitioning by about 1.5 Tg/yr in our model. The hemispheric gradient in δ13C can be an important constraint on hemispheric partitioning of sources provided that the interhemispheric exchange rate is well known, but the gradient does not strongly constrain global emission totals, only their north/south partitioning. The biggest improvements in emission partitioning will come from better constraining fossil fuel emissions as stated earlier by Quay et al.  and by better understanding the isotopic ratio of source emissions and how and why they vary. Unless the value of εOH is in error by more than 2–3‰, the most important way we can improve the sink side of the equation is by better determining the lifetime of CH4 in the atmosphere, including the magnitude of the soil sink. Our box model does not make use of seasonal and interannual variations in the data. As our monitoring effort continues and more data accumulate, seasonal variations and eventually long-term trends should provide additional constraints on the global budget.
Table 3. Sensitivity of Source Partitioning to Parameter Changes in the Inverse Box Model
For all other source sensitivities, biomass burning (BMB) is simply of the opposite sign as bacterial (B), such that total global emissions remain constant. Adding a Cl sink increases the total emissions in the model, which requires that BMB and B sensitivities not be of equal magnitude.
 One way to improve our understanding of the lifetime of CH4 is to establish the extent to which atomic Cl in the marine boundary layer (MBL) consumes CH4. A variety of studies have suggested the possibility of CH4 oxidation by Cl in the marine boundary layer [Gupta et al., 1996; Vogt et al., 1996; Wingenter et al., 1999; Allan et al., 2001]. Wingenter et al.  estimated that 2% of CH4 in the MBL is consumed by Cl. Because of the unusually large isotopic fractionation that results when CH4 reacts with Cl [Saueressig et al., 1995], atmospheric δ13C is a good tracer for the presence of Cl radical. In a model experiment, we introduced a Cl sink for atmospheric CH4 that was scaled according to ocean surface area in each hemisphere. Using the parameters in Table 2, our results indicate that a small tropospheric Cl sink cannot be ruled out (Figure 9). If the Cl sink in the troposphere were greater than 6 ± 4% of the total sink, then the biomass burning source would be less than 20 Tg/yr, which is unlikely from an inventory point of view. We generate the error estimate by incorporating the 50% error in our fossil fuel emission estimate into our calculation.
3.5. Comparison of NOAA/INSTAAR Data With Other Records
 Maximal use of our measurements will come when they can be confidently integrated with existing records [Quay et al., 1991, 1999; Lowe et al., 1994; Francey et al., 1999; Tyler et al., 1999]. At present, no common standard scale for δ13CH4 in air exists, making comparisons between different laboratories difficult. Nonetheless, we present a comparison of our data from BRW, MLO, SMO, and CGO with those of Quay et al.  from 1988 to 1996 in Figure 10. A line is fit through the Quay data to represent the small positive trend. Extrapolating the trend in the δ13C data to bridge the 1.5-year gap between our data and the Quay data suggests that our data are heavier than the Quay data by about 0.1‰. The atmospheric δ13C trend may have changed markedly in the 1.5-year period when δ13C values were not being measured at MLO, SMO, and BRW, but without a direct intercomparison of standards and air samples, the magnitude of the offset between the two labs will be difficult to determine.
 At CGO, our 1998 annual mean value of −46.96‰ is also about 0.1‰ heavier than the fitted trend curve of the CGO archived air samples [Francey et al., 1999]. Figure 11 shows our 1998 CGO data alongside the 10-year record from Baring Head, New Zealand (41°S), and shorter records from CGO. After extrapolating the positive δ13C trend between 1992 and 1998, our CGO data appear to be about 0.1‰ heavier. Our CGO data also appear to be about 0.1‰ heavier than data from Baring Head, New Zealand, during 1998 and 1999 (D. Lowe, personal communication, 2000). Samples collected at NWR by our lab and the Tyler lab during 1998 compare well (S. Tyler, personal communication, 2000). Samples were collected on different days, at different times, and at a different location on Niwot Ridge, precluding a direct comparison, but there is no obvious offset in the data. This is expected because both labs use a scale prepared by the Tyler lab. The apparent agreement between our lab and the Tyler lab exists despite the good agreement on samples measured in common between the Tyler lab and the NIWA lab [Tyler et al., 1999]. These offsets emphasize the need to intercompare measurements between different laboratories through joint measurements of whole air in both reference tanks and sample flasks.
 We have presented a spatially and temporally dense data set of atmospheric δ13C values. This was enabled by the development of an automated, high-precision gas chromatography-isotope ratio mass spectrometry technique that was coupled with the NOAA/CMDL global air sampling network. The global mean δ13C value during 1998–1999 was −47.10‰, and the Northern Hemisphere and Southern Hemisphere means were −47.28‰ and −46.93‰, respectively. Southern Hemisphere δ13C values show very little meridional variability, while in the Northern Hemisphere, there is a difference of about 0.4‰ between MLO and BRW. The annual average difference measured between SPO and BRW was 0.6‰.
 Northern Hemisphere seasonal variations are more complex than those in the Southern Hemisphere, reflecting the proximity to seasonally varying source emissions and more complex atmospheric circulation. Summertime δ13C variations at all of the Northern Hemisphere sites, but especially BRW and NWR, appear to be dominated by changes in isotopically light emissions, possibly from wetlands. In the Southern Hemisphere, seasonal variations have been less consistent. During 1998, δ13C variations are too large to be explained solely by changes in OH and may be the result of enhanced tropical wetlands emissions. In other years, our level of measurement precision may be preventing us from observing seasonal cycles in the Southern Hemisphere.
 Since January 1998, we have analyzed more than 600 pairs of flasks with analytical precision sufficient to determine the meridional gradient and observe seasonal variations in the Northern Hemisphere. One of the principal challenges in the near future will be to establish the magnitude of any offsets of our measurements relative to other laboratories making similar measurements. All of our current measurements are based on reference air tanks calibrated by the Tyler lab at the University of California, Irvine. However, there are some preliminary indications that our values may be heavier than those of the Quay lab [e.g., Quay et al., 1991, 1999] and the NIWA (New Zealand) lab [Lowe et al., 1994; Francey et al., 1999] by 0.1‰, but without direct comparisons, this is difficult to establish.
 We have used a two-box model to show how our δ13C measurements coupled with methane mole fraction measurements made on the same samples can provide some constraints on the global methane budget. Making use of the more detailed spatial and seasonal variations present in our data should provide better constraints on the global methane budget. Prediction of future amounts of methane in the atmosphere is predicated on a detailed understanding of the global source and sink processes and how they change over time. Atmospheric δ13C measurements can help to achieve this goal, if we can (1) improve our understanding of the isotopic ratio of emissions from sources, (2) better define CH4 lifetime with respect to different sinks and their fractionation factors, and (3) couple δ13C measurements with radiocarbon and δD measurements.
 We thank Stanley Tyler for providing us with δ13C measurements of our reference air tanks, which were crucial to the completion of this study. We also thank Mark Dreier for help in the maintenance and operation of the δ13C analysis system and thank the numerous sample collectors who are part of the NOAA/CMDL Cooperative Air Sampling Network. John Miller was supported by U.S. EPA graduate fellowship U-914748-01 and a National Research Council postdoctoral fellowship during the course of this study.