Corresponding author: G. W. Santoni, Department of Earth and Planetary Sciences, Harvard University, 24 Oxford St., Cambridge, MA 02138, USA. (email@example.com)
 We have developed a mid-infrared continuous-wave quantum cascade laser direct-absorption spectrometer (QCLS) capable of high frequency (≥1 Hz) measurements of 12CH4 and 13CH4 isotopologues of methane (CH4) with in situ 1-s RMS precision of 1.5 ‰ and Allan-minimum precision of 0.2 ‰. We deployed this QCLS in a well-studied New Hampshire fen to compare measurements of CH4 isoflux by eddy covariance (EC) to Keeling regressions of data from automated flux chamber sampling. Mean CH4 fluxes of 6.5 ± 0.7 mg CH4 m−2 hr−1 over two days of EC sampling in July, 2009 were indistinguishable from mean autochamber CH4 fluxes (6.6 ± 0.8 mgCH4 m−2 hr−1) over the same period. Mean composition of emitted CH4 calculated using EC isoflux methods was −71 ± 8 ‰ (95% C.I.) while Keeling regressions of 332 chamber closing events over 8 days yielded a corresponding value of −64.5 ± 0.8 ‰. Ebullitive fluxes, representing ∼10% of total CH4 fluxes at this site, were on average 1.2 ‰ enriched in 13C compared to diffusive fluxes. CH4 isoflux time series have the potential to improve process-based understanding of methanogenesis, fully characterize source isotopic distributions, and serve as additional constraints for both regional and global CH4 modeling analysis.
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 Methane (CH4) is roughly 25 times more effective than carbon dioxide (CO2) in terms of its integrated greenhouse effect at hundred year timescales [Lelieveld et al., 1998]. After nearly a century of increasing atmospheric mixing ratios, growth rates of atmospheric CH4 leveled off between 1999 and 2006, stabilizing atmospheric concentrations at ∼1.8 μmol/mol [Lassey et al., 2007; Dlugokencky et al., 2009]. Subsequent data, however, suggested renewed growth [Rigby et al., 2008; Bousquet et al., 2011]. These changes in CH4 concentrations and trends were not predicted [Montzka et al., 2011]. Forward modeling based on emission inventories, reaction rates, OH distributions, and other source and sink parameters have shown limited success in recreating observed spatial distributions over time [Dlugokencky et al., 2003; Bousquet et al., 2006].
 Isotopic measurements of CH4 can help constrain source and sink uncertainties because processes related to methanogenesis and methanotropy fractionate differently. Isotopic composition, commonly expressed in units of per mil (‰), represents a ratio of two stable isotopes in a sample to that of a standard according to:
where Vienna Pee Dee Belemnite (VPDB) is the international standard for carbon isotopes. Different emission sources have distinguishing isotopic composition. The global mean of tropospheric CH4 is −47.3 ‰, with interhemispheric differences on the order of 0.2–0.6 ‰ and seasonal variations ranging between 0.1 ‰ and 0.6 ‰ depending on site proximity to CH4 sources with large seasonal changes in CH4 flux [Quay et al., 1999; Miller et al., 2002], representing the sum of the flux weighted average of individual CH4 source isotopic compositions and the mean sink fractionation [Gierczak et al., 1997; Lassey et al., 2000; Saueressig et al., 2001].
 The utility of isotopic characterization is limited by cumbersome measurement methods. measurements typically involve taking flask samples in the field and returning the flasks to a facility for analysis. Isotopic composition is determined by using a gas chromatograph (GC) to separate out CH4, a combustor (C) to fully oxidize CH4 to CO2 and an Isotope Ratio Mass Spectrometer (IRMS) to measure the 13Csample/12Csample ratio of that CO2. High accuracy can be achieved: GC-C-IRMS has reported precision of ∼0.1 ‰ with 0.2 L of air [Miller et al., 2002] and even better precisions of <∼0.05 ‰ for larger volumes of air (order ∼10 L) are achieved with ‘off-line’ techniques [Lowe et al., 1991]. Samples, however, are cumbersome to obtain, expensive to analyze, and require large masses of CH4 and consequently large sample volumes for atmospheric measurements. Long-term continuous measurements in remote areas are impractical, and consistent monitoring of source composition is costly and labor intensive.
 We present the first in situ ambient CH4 isoflux measurements by EC sampling using a tunable quantum cascade laser direct-absorption spectrometer (QCLS) at Sallie's Fen, a research fen in New Hampshire. We divide the isoflux measurements of CH4 by the mass flux measurements of CH4 to derive the isotopic composition of CH4 emitted from the fen. Using the QCLS to subsample an established automatic flux chamber network (autochambers) distributed throughout the fen, we compare Keeling plot regressions of the autochamber data to derived values from EC isoflux methods in order to further characterize the isotopic source composition of CH4 emissions from the fen. Potential improvements to instrumentation, sample conditioning, calibration, and data post-processing are discussed.
2. Site Description
 Sallie's Fen is a Sphagnum-dominated peatland located in southeastern New Hampshire near the University of New Hampshire (43° 12.5′ N, 71° 03.5′ W). It is a mineral poor 1.7 ha fen with a peat depth range of 2–4.5 m. Ten automated Lexan flux chambers (autochambers) were interspersed in various plant communities in the fen and have been in operation since 2000. The chamber system and fen characterization is described in more detail by Bubier et al. . Figure 1 shows the distribution of the chambers in the fen, the boundary between the fen and surrounding forested lands and farms, the location of the EC tower sampling location, and the location of the QCLS during sampling. Ongoing measurements since 1989 have characterized gas exchange [Carroll and Crill, 1997; Bubier et al., 2003], seasonality [Melloh and Crill, 1996; Treat et al., 2007], vegetation [Frolking and Crill, 1994], and isotopic composition of carbon in CO2 [Shoemaker and Schrag, 2010]. Yearlong autochamber measurements from 2009 have used a Los Gatos Research (LGR) Integrated Cavity Output Spectrometer (ICOS) to record both CH4 and CO2 fluxes from the autochambers [Goodrich et al., 2011].
 In our sensor, a room temperature, mid-infrared, continuous-wave quantum cascade laser (QCL, Alpes Lasers) was housed in a hermetically sealed box, and its temperature (−14°C) and output frequency were controlled by a Peltier element in the box coupled to a recirculating chiller. Output power of the QCL was ∼30 mW. The output frequency was coarsely maintained by controlling the laser temperature while fine adjustments to the output frequency were made by modulating the current with a high-compliance source (ILX Lightwave 3232). Current to the QCL was linearly ramped, scanning the laser frequency across 480 channels at a rate of 909 kHz. The scan included absorption lines for 12CH4, 13CH4, N2O, and H2O in the 1294.1 to 1294.4 cm−1 region. The current supplied to the laser dropped below lasing threshold for an additional 40 channels during each scan so that a background ‘zero-light-level’ (detector output) was measured. This ramped current and shutoff pulse sequence was controlled by TDL Wintel ® software. A total scan of 520 channels took 5.72 · 10−4 seconds. Because the laser frequency did not respond linearly to the ramped current supplied to the laser, the laser frequency tuning rate was determined by fitting the spectrum of the system with a Germanium etalon in the beam path. The instrumental half-width at half-maximum (HWHM) line width for the laser was <0.001 cm−1, negligible compared to the molecular absorption line width.
 Light from the QCL was directed into an astigmatic multipass sampling cell operated at low pressure (<7 kPa) and detected by a thermoelectrically cooled detector. A long effective path length (210 m) was required to achieve sufficient precision on the 13CH4 line and achieved using 238 passes between mirrors spaced 88.23 cm apart. During EC measurements, a TriScroll 600 l/min pump (Varian TriScroll600) generated a flow rate of ∼11 slpm through the 5 L sample cell at 4.0 kPa, corresponding to a cell time constant of 1.08 s.
 Mixing ratios were derived by TDL Wintel ® at ∼1 s intervals using a Levenberg-Marquardt least squares fit to each sample spectrum. The fitting procedure treated each spectral line as a Voigt profile taking into account the line strength, line location, air broadening coefficient, pressure, and temperature. A sample ∼1 s spectrum representing the average of 1748 scans across the 480 channels is shown in Figure 2 along with the fit to the spectrum and a simulation using HITRAN line parameters and measured temperature, pressure, and mixing ratios. The baseline level (Io in the Beer-Lambert law) was modeled as a low-order polynomial. The fitting algorithm took ∼115 ms, making ∼8 Hz measurements possible, but not independent on account of the cell time constant.
 Removal of absorbance in the external path and baseline flattening was achieved by background subtraction using CH4-free air as determined with the QCLS spectra. Middlesex Gases 0.0001 Ultra Zero Air was passed through the sample cell and an average background spectrum was acquired over 20 s. Sample spectra were normalized by dividing by the mean of bracketing background spectra [Nelson et al., 2004].
Figure 3 shows an in-field time series of 12CH4, 13CH4, and their ratio expressed as for 30 min of sampling from a calibration tank. The 12CH4 and 13CH4 axes are each scaled by their relative abundance according to HITRAN, 0.0111031 and 0.988274, respectively, to illustrate the factor of ∼6 greater noise on the 13CH4 absorption line. Precision as a function of integration time gives a 1-s RMS precision of 1.5 ‰ Hz−1/2. The Allan minimum reaches <0.2 ‰ Hz−1/2 at order 102 seconds, approaching the precision of GCC-IRMS methods. In order to compare instruments measuring different tracers, it is useful to express performance as absorption precisions, which relate measurement precisions to line strengths and ambient mixing ratios [Nelson et al., 2002]. The absorption precisions for 13CH4 and 12CH4 are 4.5 · 10−6 Hz−1/2 and 1.5 · 10−5 Hz−1/2, respectively, determined using the corresponding line center absorbances of 0.25% and 8% calculated in the spectral simulation (Figure 2) and the 1 Hz Allan precisions at atmospheric abundance. Absorption precision on the major isotopologue (12CH4) is worse than for 13CH4 because the measurement of the 12CH4 is limited by noise proportional to its peak absorbance, a factor of 36 times greater than that of the 13CH4.
 Density fluctuations associated with water vapor fluxes are a concern for gas sampling systems because of the potential need for Webb-Pearlman-Leuning (WPL) corrections [Webb et al., 1980]. Because of the fast flow rates and large sample volumes during EC measurements, drying the sample was impractical. Instead, the QCLS scan was expanded to include an additional 40 channels to measure water content using a nearby absorption line seen in Figure 2. Tuzson et al.  used a similar instrument to show that in addition to density corrections, line broadening effects due to water vapor accounted for an additional correction of 16% of the total WPL correction. This additional correction is non-negligible in certain applications such as EC observations above areas of low CH4 flux. Tests using calibrated cylinder air run through a water-bubbler to generate air with varying H2O mixing ratios showed that H2O content did not modify the isotopic measurements since the line broadening effects were close to identical for both isotopologues.
3.2. Autochamber and Eddy Covariance Measurements
 The QCLS, calibration tanks, and other peripherals were located in an enclosed 6′ by 8′ trailer at the edge of the fen, approximately 40 m from the autochambers. The autochambers consisted of 10 chambers with closed loops of 3/8″ OD Synflex (Dekaron) tubing and total loop lengths ranging from 10–30 m depending on the chamber location relative to the valve manifold control box (Figures 1 and 4). A two-stage diaphragm pump drew ∼10 slpm of air through the autochambers in a closed loop via the valve manifold, spending 18 min on each individual chamber for a total autochamber sampling cycle of 180 min. Individual autochambers were automatically closed and opened at minutes 6 and 12, respectively, during which time a flux was calculated. Minutes 0–6 and 12–18 of a given 18 min cycle flushed the system with ambient air while the autochamber lid was open to the atmosphere. Measurements of CO2 and CH4 at 12 s intervals were obtained using the LGR-ICOS which subsampled ∼2 slpm from the main ∼10 slpm draw [Goodrich et al., 2011]. During autochamber subsampling, a second closed loop of 80 m using 1/4″ OD Synflex tubing brought air to the QCLS from the main ∼10 slpm autochamber flow (Figure 4). A 4-stage low pressure pump (Vaccubrand MD-4) was used to achieve a 2.5 slpm flow through the 5 L QCLS sampling cell volume at 5.3 kPa. A Licor (LI-7000) was positioned upstream in series of the QCLS and recorded CO2 and H2O at 1 Hz using a CO2-calibrated dry tank as the reference. Calibration additions were done upstream of the Licor and involved an additional solenoid valve to control return flow from the pump to the main autochamber draw so as not to return tank air to the main autochamber draw.
 The EC sampling location was positioned in the center of the fen, approximately 100 m from the QCLS. A sonic anemometer (Campbell CSAT-3) was mounted on a 3 m tower such that the sonic head was 2.0 m above the peat surface and oriented facing into the predominant wind-direction (N-NE). A sample inlet consisting of two 1-micron filters connected in parallel (to minimize the pressure drop across the filter and decrease the likelihood of blockage) was located 2.0 m above the peat surface and 0.2 m downwind from the CSAT head. The vegetation canopy was roughly 0.3 m above the peat surface. To minimize the pressure drop associated with a 100 m long sampling line, 1/2″ OD synflex tubing was used, requiring a 26 slpm flow to maintain fully turbulent conditions (Re ∼4000), and resulting in a pressure drop of only 3.3 kPa from the EC sampling inlet to the QCLS.
 To avoid wasting calibration gases associated with high flows during EC sampling, tank air was introduced upstream of the QCLS through a manifold equipped with a diaphragm check valve to reduce excess regulator pressure down to atmospheric pressure. During tank air additions the mass flow controller maintained instantaneous cell pressure fluctuations to within ∼100 Pa of sampling pressure, which stabilized within 2 s of switching from sample to calibration gas. A second two-head diaphragm pump (KNF Neuberger Model UA0026.1) pulled ∼13 slpm through the Licor measuring H2O and CO2 at 5 Hz. The cell volume of the Licor is 10.86 cm3, resulting in a sample cell time constant of 0.086 s. The ∼11 slpm QCLS draw (Section 3.1), the ∼13 slpm Licor draw, and a third draw of ∼7 slpm were connected in parallel for a total flow of ∼31 slpm through the main 100 m sampling line. This configuration, shown in Figure 5, minimized tank air consumption, ensured a ∼1 s response time, and maintained turbulence at the inlet even during tank-air additions to the QCLS.
 A data logger (Campbell CR-10 with new PROM for CSAT-3 sonic commands) located at the base of EC tower recorded wind velocities and sonic temperatures from the sonic anemometer at 8 Hz as well as air and water temperatures from two thermistors at 1 Hz. A PC in the instrument enclosure periodically collected data from the data logger via a short-haul modem (Campbell RAD-5). Unfortunately, data transfers every 3 min resulted in corruption of the CSAT data with spurious time-stamps. Exclusion of these artifacts resulted in the loss of 34% of the sonic data over the EC measurement period. The PC logging the CR-10 data also serially recorded the Licor data and was networked and time-synchronized to the QCLS computer.
4.1. QCLS Calibrations
 QCLS accuracy depended largely on the calibration procedure and the stability of the background laser spectrum in the absence of absorbing species. Ultra-zero air was introduced to the sampling cell every 10 min (background subtraction) in order to capture the influence on the baseline of small temperature and pressure variations that occurred over diurnal timescales. Calibrations were done using pairs of tanks that spanned the observed atmospheric range of CH4 above the fen, notably ∼1.8 to ∼10 μmol/mol, the latter of which was regularly observed during summer/fall nighttime inversions. During EC measurements, a low-span (LS, ∼1.8 μmol/mol) tank was sampled every 10 min and a high-span (HS, ∼10 μmol/mol) tank every 3 h. This was done because the LS tank was closer to ambient concentration and therefore had a greater influence on the calibration interpolation applied to the data. During autochamber measurements, when fluxes inside a closed chamber induced consistently higher mixing ratios, HS and LS tanks were alternately sampled every 18 min, coincident with the autochamber cycle. A cubic spline was interpolated to the 12CH4 and 13CH4 mixing ratios for both the HS and LS tanks. Each isotopologue of CH4 was treated as an independent measurement, separately calibrated. The range of variation of mixing ratios of CH4 obtained from spectral parameters only for one particular calibration tank over the course of a day, normalized by the atmospheric abundance of each, was roughly 30 ppb or 1.6%. The cubic spline interpolations versus time for 12CH4 and 13CH4 tracked each other well, largely because diurnal temperature variations affected each line similarly. The LS and HS tanks were calibrated to the VPDB scale by means of duplicate subsampled flasks of all calibration cylinders which were analyzed offline by means of GC-C-IRMS at Woods Hole Oceanographic Institute. Calibrated tank values for given by Scott Specialty Gases at 1% accuracy (i.e., ±18 nmol/mol for a ∼1.8 μmol/mol LS tank and ±100 nmol/mol for a ∼10 μmol/mol HS tank) and confirmed using the QCLS and spectroscopic parameters (line strength, pressure, temperature, broadening coefficients, etc.). QCLS mixing ratios of total CH4, 12CH4, and 13CH4 acquired by spectral fitting were then linearly interpolated to the cubic spline calibration interpolations, putting them on the VPDB scale. The interpolation was calculated as:
where and represent the 1 Hz dry air mixing ratios calculated by TDL Wintel ®, and the high-span spline interpolations to the 12CH4 and 13CH4 mixing ratios calculated by TDL Wintel ® from retrieved absorbance during the calibration tank additions, and the calibrated mole fraction values for the LS and HS tanks respectively, and and the GC-C-IRMS calibrated isotopic composition of the LS and HS tanks, respectively. The ratio of to computed using equations (3) and (2), respectively, represents the quantity and can be expressed in ‰ notation according to equation (1). The total mole fraction of CH4, is determined using equation (2) and the HITRAN isotopic abundances for the dominant isotopologue of CH4, [De Biévre et al., 1984].
4.2. Eddy Covariance Data Processing
 Continuous EC data were obtained on 18–19 July 2009. The CH4 flux was calculated from the covariance of and w′, the fluctuating parts of the CH4 mixing ratio and vertical wind velocity, respectively. Adopting the notation of Saleska et al. , we define the CH4 flux as:
where ρ represents the density of the sample, the overline represents the covariance of the two quantities, and the primes in the covariance term are fluctuations from the mean using Reynolds decomposition. Derivation of the isoflux has been presented by Saleska et al.  and Griffis et al.  who both focus on isofluxes of CO2 as a means of partitioning photosynthesis and respiration. The analog of equation (4) for isofluxes of CH4 is:
where is the fluctuating part of the Reynolds decomposition of the product of calculated from equations (1)–(3), and the calibration corrected mixing ratio from equation (2). We estimate the isotopic source composition of CH4 from the fen, by dividing equation (5) by equation (4). Isotopic data from the autochambers do not exist for these two days, but comparisons to Keeling plots were made with QCLS autochamber data later in the summer.
 Non-sonic scalars were measured ∼100 m from the EC tower at the QCLS trailer. Lag-times were determined by maximizing the covariance of each scalar etc.) with w′ as a function of Δt over 100 s intervals. 42 of the 96 half-hour intervals with u* > 0.1 m/s and a clearly identifiable maximum/minimum covariance in the lagged covariance plot were linearly interpolated to determine the sampling lag time (typically ∼6–8 s) through the tubing for each half-hour time segment. The standard deviation of the covariances of the first and last 20 s of the 100 s interval is reported as measurement error, a method often used for closed-path sensors [Wienhold et al., 1994; Kormann et al., 2001; Smeets et al., 2009]. Other relevant quantities calculated have been summarized elsewhere: Kormann et al.  provide a detailed overview of the important quantities, Smeets et al.  discuss CH4–specific EC calculations, and both Webb et al.  and Ibrom et al. [2007a] discuss WPL corrections.
 We performed two coordinate rotations to force the mean horizontal and vertical winds to zero. Rotation of the vertical axis resulted in a mean angle of rotation for the 96 half-hourly segments of 0.56° with a 95% CI of 1.1°. EC averaging time was set to be 30 min, long enough to capture the fast and slow eddies up to the spectral gap beyond which diurnal and synoptic variability influenced the power spectrum of winds, momentum, and heat flux. Spectral analysis showed that the ogives – the cumulative power densities of the cospectra – of our flux data asymptote well before frequencies associated with 30 min [Lee et al., 2004]. Because of the gaps in the data every 3 and 10 min associated with data logger transfers and calibrations, respectively, Lomb-Scargle methods were used instead of traditional spectral analysis to compute cospectra [Press et al., 1992].
 The frequency spectrum of w′ for 57 of the 96 half-hour intervals over the two days, each having a friction velocity (u*) greater than 0.1 m/s is shown in Figure 6. Relevant cospectra calculated by Lomb-Scargle methods are shown in Figure 7 and represent half-hour averages with power averaged into exponentially increasing frequency bins. The spectra are approximated by the model [Lee et al., 2004]:
where A is a normalization parameter, fx is the frequency at which the frequency-weighted power co/spectrum reaches a maximum (here 0.09 Hz for w′ and w′T′, and 0.064 Hz for μ is a broadness parameter (here 2/3, consistent with a slightly unstable atmosphere), and m is set to 3/2 for spectra and 3/4 for cospectra to describe the −5/3 and −7/3 power laws in the inertial subrange, respectively. Peak power was well predicted by the Kaimal curve for the spectra using a measurement height of 2.0 m, a vegetation height of 0.3 m, and a mean horizontal wind velocity of 0.45 m/s [Kaimal and Finnigan, 1994]. Cospectra in Figure 7, approximated from equation (6) with m = 3/4, show some evidence of differential spectral attenuation and illustrate the different eddy length scales responsible for the fluxes of the different scalars.
 We calculated CH4 fluxes and isofluxes from equations (4) and (5) using two methods: WPL corrected fluxes and dry-mole fraction fluxes. The first used the water vapor measurement of the Licor and applied WPL corrections to the wet-mole fraction CH4 fluxes. The second used the QCLS water measurement to correct the 12CH4 and 13CH4 mixing ratios to dry-mole fraction. The two methods produced statistically indistinguishable results at the p = 0.05 level and the latter method is presented in the results. Because measurements such as and did not occur at frequencies as high as that of the sonic anemometer, degradation of the cospectrum (vertical wind velocity and sonic virtual temperature) from 8 Hz ‘raw’ data to 5 Hz Licor and 1 Hz QCLS data was used to calculate the correction factor for high-frequency loss [Ibrom et al., 2007b] according to:
For Licor sampling at 5 Hz, the mean F1 was 100.05 ± 0.85 (95% C.I.) % showing that the high-frequency loss due to degradation of an 8 Hz signal into a 5 Hz was negligible. Correction factors for high frequency loss of CO2 and H2O fluxes were therefore not applied to the data. The corresponding high frequency correction factor for the 1 Hz QCLS data was 92.87 ± 6.59% indicating a loss of ∼7% of the covariance at high frequency. We corrected for this loss using equation (7), substituting CH4 for Tv and rearranging, to solve for the true covariance as [Ibrom et al., 2007b; Kroon et al., 2007]:
Horst  calculate F1 using spectral transfer function analysis according to F1 = 1 + (2πfmτc)α where fm represents the peak of the logarithmic cospectrum (0.064 Hz for τc represents the time constant of the sensor (1.08 s for the QCLS), and α =7/8 for neutral and unstable stratification within the surface-flux layer, giving a high frequency attenuation correction factor of 1.48, much larger than the correction factor derived from equation (7).
4.3. Autochamber Data Processing
 Eighty autochamber closures per day were observed by the QCLS data over eight days (12–13, 28–31 August 2009, 1–2 September 2009). Each chamber closing was treated as an independent measurement of (a) the CH4 flux, calculated from chamber ground temperature (Tground), volume (Vchamber), surface area (Achamber), and a regression of the CH4 time series using a Type I simple linear regression (SLR, e.g., blue lines on the left of Figure 10) according to:
where R is the ideal gas constant, and the molecular mass of CH4, and (b) isotopic source composition for that chamber, derived from the y-intercept of a Keeling plot (e.g., x =0 on the right side of Figure 10) in which is plotted against The regression is a mixing line assuming two end-members: CH4 from the fen and atmospheric CH4. In this case, Type II regressions which use independent error constraints on ordinate and abscissa variables were indistinguishable from Type I regression because the measurement error on was negligible compared to the measurement error of
 Of the 640 chamber closings observed with the QCLS, 585 were used to calculate fluxes and isotopic composition; 217, 139, and 229 of which were categorized as linear, ebullitive, and random fluxes, respectively. Linear buildups were defined as having residual variances on the flux regression <0.05 nmol/mol/s. CH4 fluxes both by diffusion from the water surface and by plant mediated transport exhibited linear buildups of CH4 in chambers whereas ebullitive fluxes showed sudden jumps, categorized by a CH4 flux regression >8 nmol/mol/s that were between 10 and 120 s in duration as defined in Goodrich et al. . In order to differentiate the isotopic composition of ebullitive fluxes in the autochambers, Keeling regressions using the ebullitive events were compared to the Keeling regression of the entire flux interval using 83 definitive ebullitive events which lasted between 10 and 60 s. Random buildups showed oscillations in the CH4 time series having amplitudes >50 nmol/mol, a result of improper sealing of the chamber due to emergent vegetation and/or inadequate mixing of the chamber headspace.
Figure 8 shows the mean mixing ratios of CH4, CO2, and along with relative humidity, temperature, u*, wind speed, and wind direction. Half hour mean CH4 and CO2 mixing ratios were correlated, showing a diurnal pattern consistent with nighttime inversion of the Planetary Boundary Layer (PBL). These inversions typically involve stable atmospheric conditions, u* < 0.1 m/s and low mean wind speeds. Wind direction averaged −35 degrees N-NW over the two days. Mean half-hourly values approached the free tropospheric northern hemisphere value of −47 ‰ during the periods of highest wind speed. During periods of lower mean wind speeds, the influence of the fen on the mean was apparent with deviations toward more 13C depleted CH4 values, consistent with a biogenic CH4 source.
 The flux time series is shown in Figure 9 where solid dots represent fluxes calculated during periods in which u* exceeded 0.1 m/s (fluxes for periods with u* < 0.1 m/s are artifacts not used in our analysis but are shown as open gray circles). The mean CH4 flux for the two days using only data with u* > 0.1 m/s (solid dots) was 6.5 ± 0.7 (95% C.I.) mg CH4 m−2 hr−1, in excellent agreement with the mean autochamber CH4 flux of 6.6 ± 0.8 (95% C.I.) mg CH4 m−2 hr−1. Mean CH4 isofluxes were −518 ± 73 (95% C.I.) ‰ mg CH4 m−2 hr−1 and the resulting distribution of inferred had a mean of −79 ± 9 (95% C.I.) ‰.
Figure 10 shows examples of chamber closing cycles illustrating the buildup of CH4 following chamber closing at minute 1 and the abrupt return to near-ambient concentrations after minute 7 when the chamber opens (the lag is residual high CH4 data from the closed QCLS loop not sampled during QCLS calibration). The linear regression to minutes 2–6 used to calculate the flux is shown in blue. High concentrations of CH4 during the chamber closure intervals correspond to depletions, consistent with a biogenic CH4 source. Keeling analysis is well suited to chamber data, as large enhancements from ambient concentrations of CH4 that accumulate during a chamber closure improve regression statistics for extrapolation to infinite concentrations → 0) [Pataki et al., 2003]. The linear increase in shown in Figure 10 corresponds to a flux that is half the mean August fluxes yet still shows enhancements of ∼1 μmol/mol above ambient CH4 concentrations. The regression shown has a standard deviation on the intercept of 0.9 ‰, representing the error estimate of the isotopic source composition, Uncertainties in the Keeling intercept decrease with increasing CH4 enhancements, as shown in Figure 11. The 25, 50, and 75 quartiles of CH4 fluxes have associated 1σ uncertainties on the isotopic source of 2.3 ‰, 1.6 ‰, and 1.1 ‰, with minimum uncertainties of <0.6 ‰ associated with the largest fluxes.
 Variability in Keeling intercepts largely represent real differences in the isotopic composition of CH4 from the fen in the individual chambers. The distributions of derived from EC isoflux methods and autochamber Keeling analysis are compared in Figure 12. Mean from Keeling regressions (n = 332 chamber closings of linear and ebullitive fluxes with q-statistic >0.5) was −64.5 ± 0.8 (95% C.I.) ‰, statistically indistinguishable (at p = 0.05) from −71 ± 8 (95% C.I.) ‰ for EC isoflux methods. Neither CH4 fluxes nor exhibited a significant diurnal pattern. Mean CH4 fluxes for each of the individual 10 chambers highlighted the heterogeneity of the fen. Chambers with large percentages of Carex plants, for instance, had larger fluxes because plant mediated transport occurred faster than diffusion through surface water. The distributions of by chamber, however, were statistically indistinguishable at p = 0.05.
6.1. Error Estimates
 The precision of 12CH4 and 13CH4 compare well to other reported instrument precisions [Hendriks et al., 2008; Kroon et al., 2007; Lee et al., 2009; Nelson et al., 2004]. The selection of spectral sampling features between 1294.1 and 1294.5 cm−1 combined with CW operation of a 30 mW QCL light source, a high D* thermoelectrically cooled 8 μm detector, and a 210 m effective path length resulted in a precision <0.2 ‰ at order 102 s averaging times. Reductions in isoflux error could be achieved with higher sampling rates accompanied by shorter sample cell residence times, and a more complete micrometeorological data set. We attribute 20% of our isoflux error to incomplete micrometeorological data, and estimate an upper limit on an improvement factor of ∼2.2 (√5) for 5 Hz sampling. Recent improvements in cell design have resulted in a 2.1 L sampling cell volume with effective path lengths of up to 260 m using 554 passes between mirrors spaced ∼47 cm apart where losses from mirror reflectivity due to higher pass numbers are mitigated by using wavelength specific mirror coatings [McManus et al., 2011]. This reduced sampling volume would allow for independent sampling at ≥2 Hz and would decrease F1, the high-frequency loss term of our EC measurements. It is hard to predict actual isoflux error improvements because 5 Hz measurement noise will also be ∼2.2 (√5) times higher than that of 1 Hz sampling due to the acquisition of fewer spectra over a given sampling interval. The upper limit improvement with faster sampling could decrease the standard deviation of the measurement distribution, from 25 ‰ to 9 ‰, approaching the real variability of the fen depicted in Figure 12 with the autochamber QCLS data.
 For comparison, the 1σ error estimate on was 0.97 mg CH4 m−2 hr−1, as calculated from the standard deviation of for the first and last 20 s of a 100 s lag-time interval. This corresponded to a signal to noise (S/N) ratio of ∼7. Smaller by a factor of two, the S/N of the isoflux was ∼3.5 with a corresponding 1σ error estimate of 158 ‰ mg CH4 m−2 hr−1 (or in alternate units, 66.4 ‰·nmol/mol·m/s). We characterized the error on the resultant by dividing the isoflux error estimate by the range of mean CH4 fluxes observed giving a mean of 25 ‰. This error is the same order as the deviation between the isotopic composition of CH4 from the free troposphere (−47 ‰) and CH4 from biogenic sources (−60 to −70 ‰) and illustrates how a decrease in the to 9 ‰ from a smaller sampling volume would improve the retrieved EC isoflux calculations.
 Similar to Hendriks et al. , we observed that mean CH4 fluxes derived using vegetation-type-by-surface-area weighted fluxes of chamber data were statistically indistinguishable (at the p = 0.05 level) from EC measurements over the same period. Autochambers were distributed to be representative of the fen [Bubier et al., 2003], and it is reassuring that the two methods produce similar CH4 flux estimates. Schuepp et al.  define a footprint function for fluxes in terms of local meteorological conditions and sampling height that predict a maximum surface sensitivity of the EC observations ∼10 m upwind from the EC tower at Sallie's Fen, roughly 4 times smaller than the nearest edge of the fen. We estimate that 90% of the cumulative footprint lies within the area of the fen [Kormann and Meixner, 2000].
 Differential attenuation of scalar measurements such as H2O and CO2 by closed-path EC systems must be accounted for when using WPL corrections [Ibrom et al., 2007b]. Attenuation is particularly of concern for stable isotope measurements where there is potential for fractionation due to sampling. Griffis et al.  characterize this sampling effect with a CO2 isotope spectrometer and find attenuation <0.5 ‰ for both and We maintained fully turbulent conditions throughout our sampling system as fractionation has been demonstrated insignificant in turbulent conditions [Griffis et al., 2008].
6.3. Isofluxes and
 CH4 from anaerobic environments is released to the atmosphere largely by three different processes: diffusion through peatland pore water, plant mediated transport, and ebullition. Depth profiles of pore water CH4 show that CO2 reduction to CH4 is the dominant pathway of methanogenesis at depth while acetate fermentation is more prevalent closer to the surface [Popp et al., 1999, 2000]. At the oxic-anoxic interface, CH4 oxidation results in 13C enrichment because methanotrophs preferentially oxidize 12CH4 by roughly 5–20 ‰ [King et al., 1989; Whiticar, 1999]. Of the three transport pathways, ebullition is perhaps the most poorly quantified and least understood. Goodrich et al.  estimated that ebullition accounted for up to 12% of CH4 fluxes at Sallie's Fen by separating linear fluxes (pore water diffusion and plant-mediated fluxes) from ebullitive fluxes using the same methods described in section 4.3.
 Ebullition exhibited a diurnal cycle at Sallie's Fen, with more ebullitive events occurring at night [Goodrich et al., 2011]. Keeling intercepts of ebullitive fluxes measured during the 8 days of QCLS subsampling were on average 1.2 ± 0.7 ‰ (95% C.I., 1σ = ± 3.2 ‰) enriched in 13C compared to the Keeling intercept using the entire chamber subset. We hypothesize that bubbles which can form and grow on plant vascular tissue are more likely to encounter more oxic conditions due to plant pathways that facilitate oxygen exchange. CH4 oxidation to CO2 leaves residual CH4 in the bubble enriched in 13C which can later outgas via ebullition. A complementary effect proposed by Chanton et al.  is that plants relying on passive gas transport act as restrictive pipes that discriminate against 13C. In rice paddies, this effect, combined with a fraction of total CH4 being oxidized, produced what they refer to as ‘bubble CH4’ enriched in 13 C by roughly 5 ‰ [Chanton et al., 1997]. This diffusional fractionation, theoretically a 19.5 ‰ effect in air but a smaller effect in water, could also explain the observed difference as ebullitive fluxes originating from depth would tend to bypass diffusional fractionation in the water column [Popp et al., 1999; Cerling et al., 1991].
 The mean calculated by bootstrapping using resampled data (1000 times, with replacement) to construct a population distribution of the Keeling plot autochamber analysis was −64.5 ± 0.8 (95% C.I.) ‰. This agrees with the isotopic content of CH4 from similar ecosystems as presented by Popp et al. [1999, 2000] and Whiticar . Bootstrapped mean by EC isoflux techniques were −71 ± 8 (95% C.I.) ‰, −79 ± 9 ‰, and −82 ± 12 ‰ using subsets of the total 96 half-hour intervals, representing n = 90 intervals with within 3σ of the mean calculated n = 55 intervals with u* > 0.1 m/s, and n = 32 intervals with the stability parameter z/L <0 [see Kormann et al., 2001], respectively (Figure 12). Because the covariance terms in equations (4) and (5) contain the same scalar measurements (w′ and dividing the two equations to calculate results in error cancellation such that the retrieved distribution by EC is statistically indistinguishable (at p = 0.05) from the autochamber Keeling plot derived distribution when all the data (n = 90) are used. When filters typically applied to EC data are used (e.g., n = 55 or n = 32 subsets), the retrieved is distinguishable (at p = 0.05) from the Keeling plot derived though we note that these filters preferentially remove nighttime data, thereby biasing the distribution toward depleted 13C values by partially removing the influence of 13C enriched nighttime ebullitive fluxes. In the present study, Keeling plots provide a more robust constraint on the real distribution of from the fen as our EC isoflux sample size is limited and the isoflux error is similar in magnitude to the variability of the distribution from 332 Keeling plot intercepts.
 We presented measurements using a QCLS capable of in situ precisions of 1.5 ‰ and <0.2 ‰ at 1 s and 102 second averaging times, respectively, demonstrating that both EC isoflux methods and autochamber Keeling analysis achieve consistent characterization of producing statistically indistinguishable CH4 flux estimates. Fast-response in situ atmospheric 13CH4 and 12CH4 measurements can robustly quantify the distributions of from various CH4 sources and characterize seasonal changes in these distributions. They can also therefore provide additional constraint for modeling efforts that use atmospheric data to quantify emission sources in global inventories [Allan et al., 2001; Lassey et al., 2007]. Modeling efforts to date have shown limited improvements from using both and CH4 data, as opposed to CH4 data alone, largely because GG-C-IRMS instrumentation limitations make data very scarce [Fletcher et al., 2004a, 2004b; Bousquet et al., 2006].
 Longer time series of EC or flux chamber 12CH4 and 13CH4 measurements may elucidate the seasonal dependence of processes affecting CH4 fluxes, particularly in regions such as the arctic [Dlugokencky et al., 2009, 2011] which have diverse CH4 sources potentially susceptible to large scale environmental changes. In this study of a Sphagnum-dominated fen in New Hampshire, we used a week of automatic flux chamber measurements to characterize the bulk isotopic composition of late-August CH4 emissions. We observed enrichment of ebullitive fluxes at night, which may be related to changes in oxygen status near plant roots. Continuous data, including over a year from autochambers can potentially identify the biogeochemical drivers of changes in both CH4 fluxes and their isotopic composition at various timescales.
 Parts of this research were supported by the Department of Energy, Small Business Innovation Research Award DE-FG02-07ER84889 and the National Science Foundation Graduate Research Fellowship Program. The authors acknowledge Sean Sylva at the Woods Hole Oceanographic Institute for isotopic analysis of our calibration cylinders. We would also like to thank Jack Dibb, Nicola Blake, and Sallie Whitlow for all their help at the fen. We thank Ryan McGovern, Daniel Glenn, Stanley Huang, Scott Herndon, Ezra Woods, and Bob Prescott of Aerodyne, and Bill Munger, Bruce Daube, Josh McLaren, Rodrigo Jimenez, and Elaine Gottlieb of Harvard University. Last, we acknowledge the contributions of John B. Miller and two additional anonymous reviewers.