A Fourier transform infrared trace gas and isotope analyser for atmospheric applications

Concern in recent decades about human impacts on Earth's climate has led to the need for improved and expanded measurement capabilities of greenhouse gases in the atmosphere. In this paper we describe in detail an in situ trace gas analyser based on Fourier Transform Infrared (FTIR) spectroscopy that is capable of simultaneous and continuous measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), nitrous oxide (N2O) and 13C in CO2 in air with high precision. High accuracy is established by reference to measurements of standard reference gases. Stable water isotopes can also be measured in undried airstreams. The analyser is automated and allows unattended operation with minimal operator intervention. Precision and accuracy meet and exceed the compatibility targets set by the World Meteorological Organisation – Global Atmosphere Watch for baseline measurements in the unpolluted troposphere for all species except 13C in CO2. The analyser is mobile and well suited to fixed sites, tower measurements, mobile platforms and campaign-based measurements. The isotopic specificity of the optically-based technique and analysis allows its application in isotopic tracer experiments, for example in tracing variations of 13C in CO2 and 15N in N2O. We review a number of applications illustrating use of the analyser in clean air monitoring, micrometeorological flux and tower measurements, mobile measurements on a train, and soil flux chamber measurements.


Introduction
Growing concern in recent decades about human impacts on Earth's climate has led to the need for improved understanding of the global carbon cycle and the sources and sinks of greenhouse gases in the atmosphere. The Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC, 2007) provides the most recent and extensive overview of the physical basis of human-induced climate change. Carbon dioxide (CO 2 ) and methane (CH 4 ) are the most important long-lived anthropogenic greenhouse gases (GHGs), accounting for 64 % and 18 %, respectively, of human-induced radiative forcing since the pre-industrial era (Hofmann et al., 2006, for update see http://www.esrl. noaa.gov/gmd/aggi/). Nitrous oxide (N 2 O) is the third most important greenhouse gas with a 6 % contribution that is becoming more important as the now-restricted chlorofluorocarbons decay in the atmosphere (Ravishankara et al., 2009). Major sources of anthropogenic CO 2 increases are fossil fuel combustion for energy; for CH 4 they are increased wetlands and agricultural livestock emissions; and for N 2 O the increased use of nitrogeneous fertilisers in agriculture. CO 2 emissions are partially taken up and recycled by the oceans, land and the biosphere, but approximately half of fossil fuel CO 2 accumulates in the atmosphere. CH 4 and N 2 O are ultimately chemically destroyed in the atmosphere, but increasing sources also mean that their atmospheric abundances are increasing (IPCC, 2007).
Measurements of greenhouse gases in the atmosphere provide the fundamental data on which our understanding is based. In situ measurements at the local or ecosystem level lead to "bottom-up" detailed understanding of the individual processes and magnitudes of GHG exchanges, but are necessarily sparse. They require significant up-scaling and extrapolation if they are to be used in global-scale models of GHG source-sink distributions and inventories. In the alternative "top-down" approach, time series of in situ and remote sensing measurements are combined with inverse models and atmospheric transport to infer source-sink distributions at global scales, but here the problem is mathematically illposed, and uncertainties are dominated by the sparseness of the available measurements. Both top-down and bottom-up approaches benefit from new techniques which can increase the density and accuracy of available measurements. In particular, the extension of measurements from occasional, often flask-based sampling programmes to continuous measurements near the ground, on tall towers, and from satellites is highly desirable. Continuous measurements resolve variability on diurnal and synoptic timescales, which is becoming increasingly accessible to high resolution modeling. However the accuracy requirements are stringent -the World Meteorological Organisation's Global Atmosphere Watch (GAW) specifies the required inter-station compatibility and lack of bias required for measurements to improve understanding of global greenhouse gas cycling. These requirements and approximate global mean atmospheric mole fractions (2010) are listed in Table 1 (GAW, 2011).
Regular atmospheric GHG measurements effectively began in the International Geophysical Year of 1957 with the establishment of CO 2 measurements by nondispersive infrared (NDIR) spectroscopy at Mauna Loa in Hawaii by C. D. Keeling (Keeling et al., 1995), and are now continuous at several global sites (e.g. Francey et al., 2010;, see also http://www.esrl.noaa.gov/gmd/). For other species, high accuracy greenhouse gas measurements have been dominated by gas chromatography (GC) techniques using various detectors. GC requires frequent calibration but can be automated and is commonly used to provide pseudocontinuous spot-measurements for most species in many stations and networks (see for example van der Laan et al., 2009;Vermeulen et al., 2011;Popa et al., 2010;Prinn et al., 2000;Langenfelds et al., 2011).
Optical techniques based on the absorption or emission of radiation are well suited to continuous measurements and have a robust physical basis for calibration. Recent advances in laser-based techniques have achieved the required precision in many cases and several instruments have become commercially available. Lasers are inherently singlewavelength devices that can be scanned over single absorption lines in a narrow wavelength interval. They are typically restricted to only one or two species, but high brightness of the laser source leads to low noise and high precision measurements. Earlier instruments used liquid nitrogen-cooled lead-salt mid-infrared lasers (MIR, λ > 2.0 µm), but these have been largely supplanted by cheaper, mass produced and readily available near-infrared lasers (NIR, λ ∼ 0.7-2.0 µm) operating near room temperature. While the NIR lasers are relatively cheap and freely available, absorption bands in the NIR are generally overtone and combination bands which are weak absorbers compared to the fundamental vibration bands in the MIR. The weak absorption cancels some of the advantage of high brightness and low noise, and long absorption paths are required to obtain the desired precision. Most recently, quantum cascade lasers operating near room temperature at MIR wavelengths have been developed, and these are becoming commercially available (e.g. Tuzson et al., 2011).
Fourier Transform InfraRed (FTIR) spectroscopy offers an alternative infrared optical technique to laser spectroscopy. FTIR uses broadband infrared radiation from a blackbody light source that covers the entire infrared spectrum simultaneously. In FTIR spectroscopy, the source radiation is modulated by a Michelson interferometer and all optical frequencies are recorded simultaneously in the measured interferogram (Davis et al., 2001;Griffiths and de Haseth, 2007). A mathematical Fourier transform retrieves the spectrum (intensity vs. frequency) from the interferogram. Compared to laser sources the blackbody source is less bright, but this disadvantage is largely offset by the multiplex advantage of measuring the whole spectrum simultaneously, and operation in the MIR region where absorption bands are strong compared to the NIR. The result is precision similar to or better than NIR-laser based instruments, but with the ability to determine several species, including isotopologues, simultaneously from the same measured spectrum. Figure 1 shows the mid infrared spectra of whole clean air, dried and undried, in a 24 m path absorption cell as recorded with the analyser described in this paper. The target gases, carbon dioxide (CO 2 ), methane (CH 4 ), nitrous oxide (N 2 O), carbon monoxide (CO), and water vapour (H 2 O) have absorption bands in this region. Infrared absorption frequencies depend on the atomic masses, and in the case of 13 CO 2 the ν 3 stretching vibration is shifted 66 cm −1 from the parent  (Parkes et al., 2012). Quantitative analysis of broad regions of the spectrum (typically 100-200 cm −1 wide) including whole absorption bands of the molecules of interest provides the concentrations of the target species. The spectral information from many ro-vibronic lines is included in each analysis, enhancing the information content of the measurement compared to narrow-band, single line laser methods, thus leading to high measurement precision and stability.
In this paper we describe the construction, performance and selected applications of a high precision trace gas analyser based on low resolution Fourier Transform Infrared (FTIR) spectrometry. The FTIR spectrometer is coupled to a multi-pass (White) cell and a gas sampling manifold and is principally intended for in situ sampling and analysis of ambient air. The analyser is fully automated and provides realtime concentration or mole fraction measurements of target gases including CO 2 , CO, CH 4 , N 2 O, H 2 O and the isotopologues 13 CO 2 , HDO and H 18 2 O. The analyser is an extension of earlier work (Esler et al., 2000a, b) and incorporates significant improvements in usability and performance. Parkes et al. (2012) describe optimisation of the analyser for stable water isotope measurements (Parkes et al., 2012).

Hardware
The FTIR spectrometer is a Bruker IRcube, a modular unit built around a frictionless flex-pivot interferometer with 1 cm −1 resolution (0.5 cm −1 optional) and 25 mm beam diameter, globar source and CaF 2 beamsplitter. The modulated exit beam is coupled to a multipass White cell by transfer optics consisting of two flat mirrors. The White cell is a permanently aligned glass cell, f-matched to the FTIR beam with a total folded path of 24 m and volume 3.5 l. The beam exiting the White cell is directed back into the IRcube and fo- cussed onto a 1 mm diameter thermoelectrically-cooled Mercury Cadmium Telluride (MCT) detector with peak detectivity at 2000 cm −1 . The interferometer is scanned at 80 scans min −1 and normally spectra are coadded for 1-10 min according to the required time resolution and signal-to-noise ratio. The root mean square (RMS) signal-to-noise ratio in the spectra for a 1-min average measurement (∼ 80 coadded spectra) through the cell at 1 cm −1 resolution is typically 40 000-60 000:1 (measured as 1/noise where noise is the RMS noise from 2500-2600 cm −1 on the ratio of two consecutively collected spectra). The signal-to-noise ratio (SNR) increases as the square root of averaging time for coadded spectra up to at least 20 min. The White cell is fitted with a 0-1333 hPa piezo manometer to measure cell pressure and a type-J or type-T thermocouple in the cell for cell temperature measurement. Ambient water vapour, CO 2 , CO, CH 4 and N 2 O are removed from the internal volume of the IRcube and transfer optics with a slow purge of dry N 2 (0.1-0.2 l min −1 ) backed by a molecular sieve and Ascarite ® trap in the volume. The FTIR and sample cell are thermostatted, typically at 30 • C.
The evacuation and filling of the cell with sample or calibration gas is controlled by a manifold of solenoid valves, shown schematically in Fig. 2. A 4-stage oil-free diaphragm pump with ultimate vacuum of approximately 1 hPa is used to evacuate and draw sample gas through the cell. Sample or calibration gas streams are introduced through one of four equivalent inlets (V1-V4). To minimise uncertainty due to cross-sensitivity to water vapour lines in the spectra (Sect. 3), the airstream can be optionally dried by passing through a Nafion ® drier and Mg(ClO 4 ) 2 trap (selected by V9). The gas stream passes through a 7 µm sintered stainless steel particle filter into the sample cell (V6). Flow is controlled by a mass flow controller at the cell outlet which can optionally function as a cell pressure controller through a feedback loop to the cell pressure transducer. In earlier versions of the analyser, a needle valve and mass flow meter were used instead of the mass flow controller. In the most recent versions, the addition of a second mass flow controller at the cell inlet (not shown) allows both pressure and flow to be controlled simultaneously. Flow rate is typically 0.5-1.5 l min −1 and cell pressure is near ambient pressure. The dried sample gas stream leaving the cell provides the required backflush to the Nafion dryer at reduced pressure. The Nafion drier alone typically achieves water vapour mole fractions of 200-300 µmol mol −1 (dew point < −40 • C) in the sampled airstream, and the Mg(ClO 4 ) 2 typically reduces this to < 10 µmol mol −1 . Sample or calibration gas may also be analysed statically by evacuating and filling the cell without flow during the measurement. In this case a flow of dried air can be maintained through the Nafion drier via a cell-bypass valve (V5) to avoid step changes in water vapour levels that may occur if the Nafion drier is not continuously flushed. The cell can be evacuated directly through V8.
The solenoid manifold valves are switched by a digital output (DO) relay module connected to the controlling computer via a RS232-RS485 serial interface. An 8-channel, 16bit analogue-digital converter (ADC) module is connected via the same RS485 daisy-chain to log pressure, cell and room temperatures, flow and other desired analogue signals. The mass flow controller is controlled by an analogue output (AO) module. Additional DO, AO or ADC modules can be added as required to the RS485 daisy chain for special applications. Operation of the spectrometer, sample manifold, data logging, spectrum analysis (described below) and real time display of gas concentrations is controlled by a single program ("Oscar") written in Microsoft Visual Basic. The spectrometer communication is via Bruker's OPUS DDE interface over a private Ethernet network. The DO, AO and ADC modules are connected via the PC's serial RS232 port. Oscar provides for the configuration and fully automated execution of user-defined sequences of valve-switching for flow control, spectrum collection, spectrum quantitative analysis, logging and display. Different sequences may be executed in turn and looped to provide continuous automated operation, including periodic calibration tank measurements, without manual intervention. The instrument can be run remotely via an Ethernet connection to the PC.

Quantitative spectrum analysis
Spectra are analysed to determine the amounts of selected trace gases in the cell by non-linear least squares fitting of broad regions (100-200 cm −1 ) of the spectrum selected for each target gas. The analysis is carried out automatically after spectrum collection, and the results logged and displayed on the controlling computer. Spectroscopic analysis fundamentally determines the total absorber amount (concentration × pathlength, C × L) of the target trace gas, from which the mole fraction χ of the trace gas in air is calculated from the molar concentration of air, n/V =P/RT where P is the measured sample pressure, T the sample cell temperature, and R the universal gas constant. From Eq. (1), χ is the mole fraction in whole air. χ can be converted to dry air mole fraction using the measured mole fraction of water vapour in the sampled air in the cell determined simultaneously from the FTIR spectrum, as in Eq. (2): . (2) For dried air, χ H 2 O is generally small (< 10 µmol mol −1 ) and the correction to dry air mole fraction is negligible. The quantitative spectrum analysis takes a computational approach in which the spectral region to be analysed is iteratively calculated and fitted to the measured spectrum by non-linear least squares.. The spectrum model, MALT (Multiple Atmospheric Layer Transmission), is described in detail elsewhere (Griffith, 1996) and only summarised here. For most trace gases of interest, the positions, strengths, widths and temperature dependences of relevant absorption lines are available in the HITRAN database (Rothman et al., 2005). From the HITRAN line parameters, the MALT spectral model calculates the absorption coefficients of the gas sample in the cell at the measured temperature and pressure. For samples containing gases that are not included in HI-TRAN, the absorption coefficients can be calculated from quantitative library reference spectra if available; for example, the Northwest Infrared Vapour Phase Reference Library provides such data for over 400 compounds (https://secure2. pnl.gov/nsd/nsd.nsf/Welcome, see also (Sharpe et al., 2004;Johnson et al., 2010). The monochromatic (i.e. true, infinite resolution) transmittance spectrum is calculated from the absorption coefficients and initial estimates of trace gas concentrations, then convolved with the FTIR instrument lineshape (ILS) function, which includes the effects of resolution (maximum optical path difference of the interferogram), apodization, and finite field of view (beam divergence in the interferometer). In addition, effects of imperfect alignment or optics can be included, for example wavenumber scale shift, loss of modulation efficiency at high optical path difference, and residual phase error, which may lead to shifted, broadened and asymmetric lineshapes, respectively. The resulting calculated spectrum simulates the measured spectrum, and is iteratively re-calculated using a Levenberg-Marquardt algorithm (Press et al., 1992) to update estimates of absorber amounts and ILS parameters until the best fit (minimum sum of squared residuals between measured and calculated spectra) is achieved. The transmittance model is not linear in the fitted parameters (absorber amounts and ILS), necessitating the iterative non-linear least squares fitting. This method is fundamentally different from methods commonly used in chemometric approaches to quantitative spectrum analysis, and in particular the classical least squares (CLS) or partial least squares (PLS) used in earlier work (Griffith, 1996). These chemometric approaches are applied to absorbance spectra and fit the spectrum as a linear combination of single component absorbance spectra (CLS) or factors (PLS). They inherently assume that Beer's Law (i.e. that absorbance is proportional to concentrations of absorbers) is obeyed or nearly obeyed, but cannot fit spectral variations due to ILS effects, and are restricted to regions of weak absorption to avoid non-linearities and breakdown of Beer's Law (Anderson and Griffiths, 1975;Haaland, 1987). In non-linear least squares the transmittance spectrum can be fitted in any region, not just one of weak absorption, because there is no assumption of linearity between transmittance and trace gas concentrations. All spectral points have the same measurement noise error independent of the transmittance, and therefore have equal weight in calculating and minimising the residual sum of squares.
The iterative fit normally takes 5-10 iterations and a few seconds of computation time on a typical personal computer. Figure 3 illustrates spectral fits to typical regions: (a) 2150-2310 cm −1 for CO 2 isotopologues, CO and N 2 O, (b) 2097-2242 cm −1 optimised for N 2 O and CO (c) 3001-3150 cm −1 for CH 4 , and (d) 3520-3775 cm −1 for CO 2 (all isotopologues) and H 2 O. Water vapour is fitted in all spectral regions because there are weak residual water vapour lines even in dried air. In undried air, H 2 O, HDO and H 18 2 O in the sample can be independently determined to provide the hydrogen and oxygen isotopic composition in water vapour (Parkes et al., 2012). In the region near 2300 cm −1 the 13 C and 12 C isotopologues of CO 2 are well resolved (the 13 CO 2 asymmetric stretching band is shifted 66 cm −1 from the corresponding 12 CO 2 band) and can be fitted independently, allowing a direct measurement of 13 C in atmospheric CO 2 . In general, overlap of absorption bands of different gases is accounted for by the MALT spectral model and isolated spectral features are not required for analysis. However, crosssensitivities may be significant with overlap of a weak band by a much stronger band, such as is the case for N 2 O and 13 CO 2 shown in Fig. 3a; in this case an additional window from 2097-2242 cm −1 shown in Fig. 3b can be used to minimise this cross-sensitivity.  All spectra are stored after measurement and archived. An advantage of the method is that spectra can be re-analysed at any later time, for example with a different choice of spectral regions or with improved line parameters when/if they become available.
The fitting procedure provides trace gas amounts and ILS parameters without any reference to calibration spectra of reference gases. For an ideal measured spectrum from a perfectly aligned spectrometer, the fitted spectrum residual should show only random detector noise, and absolute accuracy would depend only on the HITRAN line parameters, pressure, temperature and pathlength measurements. In reality, the raw FTIR determination of trace gas concentrations is highly precise, but typically uncertain to within a few per-cent of calibrated reference scales due to systematic errors in the spectrometer, MALT model, HITRAN data and measured pressure and temperature (Smith et al., 2011). Higher accuracy, equivalent to the precision of repeated measurements, is achieved by analysis of calibration standards that have known concentrations traceable to accepted standard scales such as the WMO scales for clean air (GAW, 2011). Calibration equations can be derived by analysis of such standards. Characterisation of the precision and accuracy is described in the following section.
The analyser and spectral analysis procedure has been developed and improved over several years since the first versions described by Esler et al. (2000a, b). Since 2011, the analyser described above, with refinements, has been available commercially as the Spectronus analyser from Ecotech Pty Ltd., Knoxfield, Australia.

Precision
Precision may be quantified as repeatability (the closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement) or reproducibility (where the conditions of measurement may include different operators, locations and techniques). Accuracy is defined as the closeness of the agreement between the result of a measurement and a true value of the measurand (JCGM, 2008, see also http://gaw.empa.ch/glossary.html).
Repeatability of the FTIR analyser is determined as the standard deviation of replicate measurements of a gas sample of constant composition, for example a set of measurements of a constant air sample in the sample cell. Figure 4 illustrates the analyser's repeatability with time series (upper panels) and Allan deviation (lower panels) of consecutive 1min measurements of CO 2 , CH 4 , CO, N 2 O and δ 13 C in CO 2 in dry air. For these measurements the cell was slowly flushed with dried air from a high pressure tank, and spectra collected continuously for more than 2 days (54 h). Pressure in the cell was controlled at 1100 hPa.
Allan variance is commonly used to characterise noise in repeated measurements (Allan, 1966;Werle et al., 1993) and expresses the measurement variance as a function of averaging time. In Fig. 4 the plotted Allan deviation is the square root of the Allan variance. If the variance is dominated by white (Gaussian) noise, as should occur in the ideal case when the precision is detector noise limited, the Allan variance should decrease linearly with averaging time, and the log plots of Allan deviation in Fig. 4 should have slope of −0.5, as indicated by the dotted lines. From Fig. 4 it can be seen that in most cases the Allan deviation decreases with √ time for at least 30 min. Repeatabilities (as Allan deviations) for averaging times of 1 and 10 min are summarised in Table 1. These repeatabilities meet GAW compatibility requirements for baseline air monitoring (also listed in Table 1) for all species except δ 13 C in CO 2 .

Calibration and accuracy
The least squares fitting of spectra provides trace gas concentrations for which the accuracy depends on the FTIR instrument response, HITRAN line parameters, the MALT spectrum model and the accuracy of the least squares fitting procedure. The raw "FTIR" mole fraction scale also includes measurements of sample pressure and temperature (Eq. 1) and their associated uncertainties. The raw FTIR measurements are precise as described above, but absolute uncertainty may be up to a few percent (Smith et al., 2011). Cal- ibration of the analyser to an absolute or reference scale is achieved by measurements of two or more tanks of air independently calibrated for each trace gas on the reference scales. Calibration is described in detail in an accompanying paper by Hammer et al. (2012); combined uncertainty is shown to exceed GAW compatibility targets (Table 1) for all species except δ 13 C in CO 2 . Griffith et al. (2011) and Hammer et al. (2012) demonstrate that the raw FTIR scale is linear relative to WMO reference scales over a range of mole fractions typical of ambient air and above. While the calibration regressions are in general linear within the measurement error limits, they have small but significant non-zero y-axis intercepts, so the general calibration equation for each species is expressed as where a and b are the coefficients derived from slope and intercept of the regression. Figure 5 shows residuals from linear regressions of FTIRmeasured mole fractions against reference values from a suite of standard tanks maintained at the University of Heidelberg (data from Hammer et al., 2012). Similar measurements over wider mole fraction ranges for a suite of tanks at CSIRO's GASLAB also show no significant deviations from linearity (albeit with lower precision) . Possible effects of small non-linearities are observed in the calibration of δ 13 C in CO 2 measurements, described below.

Calibration stability
The Allan variance plots of Fig. 4 (upper panels) illustrate the uncalibrated variability of the FTIR response for continuous 1-min average measurements of a single tank gas over a two day period; in general the drift remained within the  . During this period, the FTIR analyser was based in Heidelberg except for two field campaigns at Cabauw, Netherlands (CBW) and Houdelaincourt, France (OPE). "Ecotech" refers to a rebuild of the instrument to include the mass flow controller (Sect. 2), and "EPC" refers to the addition of an electronic pressure controller upstream of the analyser in the sample airstream. "No evac" refers to a period where ambient and target gas in the cell was exchanged by switching flow alone, without evacuation of the cell.
repeatability summarised in Table 1 over the whole period. Hammer et al. (2012) show similar stability over six days but some species show small significant drifts at the precision limit. Figure 6, also from Hammer et al. (2012, Fig. 9), illustrates longer-term calibration stability with residuals of approximately daily measurements of a target tank relative to its nominal mole fractions over a 10-month period. The analyser was calibrated against 2 standards typically every day or two days. The calibration stability for all species except δ 13 C in CO 2 meets GAW compatibility levels (Table 1). Hammer et al. (2012) conclude that for most applications weekly calibrations would be sufficient to ensure total uncertainty meeting WMO-GAW targets in continuous measurements.

Cross sensitivities
Raw measured mole fractions of trace gases from the FTIR analyser may show small but significant residual sensitivities to pressure, temperature, flow and water vapour in the sample that are not removed by the spectrum analysis and calibration procedures. These cross-sensitivities may be due to imperfections in the measured spectra, and systematic errors in the HITRAN database, MALT analysis procedure, temperature and pressure measurements. Hammer et al. (2012) have investigated and quantified these sensitivities in detail for one analyser, and provide a set of linear correction coefficients for sensitivity to cell pressure, cell temperature, cell flow and residual water vapour amount in the spectrum. These sensitivities are typical of all analysers we have built and tested to date, and are summarised in Table 2. The uncertainty in determining water vapour cross-sensitivities is such that drying the airstream to reduce the cross-sensitivity correction is recommended for the most accurate measurements. In almost all cases, the sensitivities for reasonable variations in the quantities are small and can be corrected to within GAW compatibility targets. These corrections are applied to raw measured mole fractions before calibration to reference mole fraction scales. Hammer et al. (2012) also found cross-sensitivity of CO and N 2 O measurements to CO 2 mole fraction in the sample when analysing spectra in the region shown in Fig. 3a. This sensitivity can be significant in situations where the CO 2 mole fraction may vary significantly between samples (for example chamber or nocturnal boundary layer measurements). However, this sensitivity can be reduced to insignificance by the use of the 2097-2242 cm −1 region (Fig. 3b), which avoids most spectral interference of the absorptions of N 2 O and CO with CO 2 .

Calibration for δ 13 C in CO 2
Chen et al.  isotopologues as individual species, from which the conventional δ values are directly calculated. In the following, we use International Union of Pure and Applied Chemistry (IU-PAC) recommendations (Cohen et al., 2007;Coplen, 2008) to distinguish the following quantities: C concentration, e.g. mol m −3 χ mole fraction of trace gas, e.g. µmol mol −1 , ppm X isotopic abundance of an isotope or isotopologue, mol mol −1 R isotope ratio Linestrengths in the HITRAN database (Rothman et al., 2005(Rothman et al., , 2009) are scaled by the natural abundance for each isotopologue, so that the actual measured isotopologue mole fractionχ iso for an individual isotopologue is reported as the scaled mole fraction χ iso : where X iso is the natural isotopologue abundance assumed in HITRAN, as shown in Table 3 for the major CO 2 isotopologues (Rothman et al., 2005). With this definition, FTIR analysis of a sample of CO 2 with all isotopes in natural abundance, as specified in HITRAN, and perfect calibration would report the same raw numerical value of χ iso for each isotopologue. δ 13 C in CO 2 is calculated from the individual mole fractions χ 636 and χ 626 and natural abundances X 636 and X 626 : where χ 636 /χ 626 is equivalent to the usual sample isotope ratio R 13 sample and X 636 /X 626 is equivalent to the standard isotope ratio R 13 std . δ 13 C is normally multiplied by 1000 and expressed in ‰, but for clarity the factor 1000 ‰ is not explicitly written in the following. The reference scale for δ 13 C in Eq. (5) is thus that of HITRAN. Calibration of isotopologuespecific measurements against reference standards calibrated to the standard Vienna Pee Dee Belomnite (VPDB) corrects simultaneously for both the difference between HITRAN and VPDB scales and calibration factors in the isotopologuespecific FTIR measurements of χ 636 and χ 626 , as detailed below.
In applying the calibration Eq.
(3) to individual isotopologues, we must know the individual isotopologue mole fractions in the reference standards. For parent and 13 C isotopologues of CO 2 , these can be calculated from the (assumed known) total CO 2 mole fractions and isotopic δ values for the standard as follows: The total CO 2 mole fraction is χ CO 2 = χ 626 + χ 636 + χ 628 + χ 627 + ...
From the definition of δ, Eq. (5), and Eq. (6) can be written where X = X 626 + i (1 + δ i )X i and the index iruns over all isotopologues except 626. Thus, and from Eq. (7) the mole fraction of 13 CO 2 is and similarly for the other isotopologues. To compute X, all values of δ i and X i must therefore be known. To calculate individual isotopologue mole fractions via Eq. (10), the total CO 2 mole fraction must also be known. For calibration standards δ 13 C and δ 18 O are usually known, and with sufficient accuracy for FTIR calibrations we can assume δ 17 O= 0.5 · δ 18 O and all δ = 0 for multiply-substituted isotopologues since their contributions to the sum are very small.
To generate an isotopologue-specific calibration following Eq. (3), the reference mole fractions χ ref should be calculated from Eqs. (9) and (10) for the regressions of χ meas vs. χ ref .
If calibrated measurements ofχ 626 and χ 636 are used to calculate δ 13 C following Eq. (5), the result should require no further calibration.
However, if uncalibrated χ 626 and χ 636 are used to calculate δ 13 C directly, the result is not simply a linear relation to the reference δ 13 , because in general it also depends on the mole fraction of CO 2 in the sample as follows from Eq. (5): which can be rearranged to If the intercepts b are zero, Eq. (12) reduces to a simple scale shift α where α = a 636 a 626 and the measured and reference δ scales are related by the ratio of isotopologue calibration scale factors a 636 and a 626 only. However, if b 636 and b 626 are non-zero, the slope and intercept of Eq. (12) become CO 2 mole fraction dependent and the regression over a range of CO 2 mole fractions is not linear.
To summarise, there are thus two methods to approach δ 13 C calibration, as specified below.

Method 1: Absolute calibration
If a suite of reference gases of known CO 2 mole fraction and isotopic composition is available to generate individual isotopologue calibrations, δ 13 C can be calculated from Eq. (5) directly using the true, calibrated values of χ 626 and χ 636 obtained following Eqs. (9), (10) and (3). This requires calibration of both χ 626 and χ 636 to the same level of uncertainty as required for δ 13 C, typically < 0.1 ‰.

Method 2: empirical calibration
If a suite of reference gases is not available, calibration for δ 13 C can still be established from one or more calibration gases of known CO 2 mole fraction and isotopic composition, provided the CO 2 mole fraction dependence in Eq. (12) is taken into account. Equation (12) can be rearranged in terms of the measured CO 2 mole fraction χ 626 as where β = b 636 −α·(1+δ 13 C ref )·b 626 . Equation (14) reduces to Eq. (13) if the b values are zero. In Eq. (14) α describes a scale shift determined by the ratio of isotopologue-specific calibration scale factors α = a 636 /a 626 , while β quantifies an inverse CO 2 dependence, determined principally by the difference between b 636 and b 626 (since α ∼ 1 and δ ∼ 0). If δ 13 C meas is first corrected by subtracting the CO 2 dependence (determined empirically as described below), the scale shift α can be determined from FTIR measurements of one or more reference tanks of known δ 13 C ref .  . 7. (a) Empirical dependence of raw measured δ 13 C in CO 2 on the inverse CO 2 mole fraction, 1/χ CO 2 , following Eq. (14). Each point is from a 1 min average spectrum measured during the stepwise stripping sequence from 800 to 330 µmol mol −1 CO 2 . (b) Fit of Eq. (13) to δ 13 C measured by FTIR and corrected for CO 2 dependence (see text) against reference values for five reference tanks with CO 2 mole fractions 350-800 µmol mol −1 and δ 13 C values −8 to −23 ‰. Each point is from a 1-min average spectrum after filling the measurement cell with reference gas. From the fit α = 1.0199, equivalent to a scale shift of 19.9 ‰.
The CO 2 dependence of δ 13 C meas can be determined empirically by varying CO 2 mole fraction at constant δ 13 C ref . Figure 7a illustrates such a measurement, where CO 2 is gradually stripped stepwise from a flow of sample air from a tank. The flow is split into two streams in variable portions, one of which is scrubbed completely of CO 2 with Ascarite or soda lime, and the two streams are recombined. Samples taken from the recombined flow and analysed independently by Isotope Ratio Mass Spectrometry (IRMS) confirm that there is no fractionation in the stripping process. The observed dependence on CO 2 mole fraction is approximately proportional to 1/χ CO 2 , as expected from Eq. (14) with a fitted value of β = −1715 ‰ ppm. However, there is residual curvature in the plot against 1/χ CO2 , which can be accounted for by including a linear term γ · χ CO 2 in the empirical fit.
One possible source of this linear term is a very small nonlinearity of the analyser response; Eq. (14) assumes that the calibration equation, Eq. (3), is linear, but a small nonlinearity, represented by a quadratic term cχ 2 ref in Eq. (3), would lead to an additional linear term γ · χ 626 in Eq. (14) with the coefficient γ determined approximately by the difference between c 636 and c 626 . The value of c 636 − c 626 required to account for the residual curvature in Fig. 7a, approximately 0.005 ‰ ppm −1 , is small enough to be consistent with the observed residuals in the individual 636 and 626 linear calibration regressions. The calibrations of Griffith et al. (2011) andHammer et al. (2012) which showed the analyser to be "linear" would not have resolved a small non-linearity of this magnitude.
With δ 13 C meas measured by FTIR corrected for the empirical CO 2 dependence as above, α can be determined from Eq. (13) from measurements of one or more reference gases of known δ 13 C ref . Fig. 7b shows such a case as a regression for five reference tanks, with CO 2 mole fractions 350-800 µmol mol −1 and δ 13 C values spanning −8 to −23 ‰. The tanks were provided by MPI for Biogeochemistry, Jena. The best fit α = 1.0199, equivalent to a scale shift of 19.9 ‰.

Results and selected applications
The FTIR analyser has been used in a variety of applications for atmospheric measurements. An earlier version of the analyser is described by Esler et al. (2000a, b) and some earlier applications are reviewed by Griffith et al. (2002) and Griffith and Jamie (2000). Here we review recent applications as examples in clean air monitoring, tower profile measurements and chamber flux measurements which exploit the high precision and stability of the FTIR analyser.

Clean air monitoring
A core application of the FTIR analyser is in continuous monitoring of air at background and clean air sites. From November 2008-February 2009 we operated an analyser at the Cape Grim Baseline Air Pollution Station on the NW tip of Tasmania, Australia. At Cape Grim, unpolluted Southern Hemisphere marine air is sampled when the airflow is from the SW sector; Cape Grim is a key station of the GAW and AGAGE networks. The detailed results of the 3-month comparison between the FTIR analyser, LoFlo NDIR CO 2 measurements and AGAGE GC measurements for CH 4 , CO and N 2 O have been reported previously . Comparisons with LoFlo and AGAGE GC measurements for the 3-month period are shown in Fig. 8. For these data the CO calibration offset evident in Griffith et al. (2011) has been corrected for non-linearity in the AGAGE GC mercuric oxide reduction detector and the CO data are now in good agreement. While the LoFlo analyser clearly shows higher precision (less scatter) than the FTIR, for the AGAGE GC system  the FTIR is more precise for each species. Calibration biases were less than the scatter in the AGAGE data.

Mobile platforms
The FTIR analyser is portable, robust and automated, and well suited to field applications. We have made FTIR measurements on eight N-S transects of the Australian continent between Adelaide (34 • S) and Darwin (12 • S) onboard the Ghan train since 2008 (Deutscher et al., 2010). For these measurements the analyser is mounted in a nonairconditioned luggage van and draws air from an inlet on the side of the train. Figure 9 illustrates results for CH 4 during the late wet season of 2008, covering 6 days in which the train travels from Adelaide in the south to Darwin in the north and returns. Although the train has diesel locomotives, there is no evidence for CH 4 emissions from the engines. The observed CH 4 mole fractions are distinctly different in three regions: variable in the agricultural and more populated southern section south of 30 • S; low variability and a distinct latitudinal gradient through the arid and unpopulated centre of the continent; and large, irregular enhancements north of 23 • S affected by high seasonal monsoonal rainfall. Spikes at 23 • S, 14 • S and 12 • S coincide with long pauses at Alice Springs, Katherine and Darwin, respectively, where urban emissions are sampled. The enhanced CH 4 concentrations are attributed mostly to ephemeral emissions from wetlands and are being used to improve methane budgets in the Australian region (Deutscher et al., 2010;Fraser et al., 2011).

Point source emissions detection
The detection, location and quantification of leaks from potential carbon capture and storage (CCS) sites is of paramount importance for assessing the effectiveness of CCS technology for removing CO 2 from the atmosphere. In an experiment to assess the possibility of remotely detecting such a leak through atmospheric measurements, Humphries et al. (2012) combined FTIR measurements with a novel tomographic analysis to locate and quantify a point source release of CO 2 and N 2 O in a flat, homogeneous landscape. Using both CO 2 and N 2 O simultaneously enabled the effect of background variability on the source retrieval to be assessed, since the background of CO 2 is highly variable while that of N 2 O is not. The point source was located within a 50 m circle of 8 sampling points in a bare soil paddock. The sampling points were sequentially sampled and analysed by a common  FTIR analyser every 30 min continuously for several months, building up a catalogue of atmospheric concentrations at the 8 sampling points under a range of wind speeds and directions. A Bayesian analysis of the concentration and wind data was used to "find" the location and emission strength for each gas without detailed prior knowledge of either location or emission strength. Figure 10 shows the results of the analysis for the CO 2 release. The analysis located the correct position of the release within 0.7 m and the strength within 4 %. Similar results were obtained for the N 2 O release. The FTIR analyser allowed the continuous autonomous operation of the sampling system for CO 2 , N 2 O, CH 4 and CO over several months.

Tower profile and flux measurements
Vertical profiles of trace gas concentrations measured from tall towers and flux towers probe boundary layer mixing processes and trace gas exchange between the atmosphere, surface and plant/forest communities. The Australian Ozflux tower at Tumbarumba (Leuning et al., 2005) is situated in a mature eucalypt forest in SE Australia to investigate the exchanges of energy, water and carbon in this representative biome. The tower is 70 m high and extends above the canopy top, which is ∼ 40 m above ground level. In November 2006 we operated two FTIR analysers at the Ozflux tower over a 3week campaign, one sampling dried air for precise trace gas measurements, and one sampling undried air for stable water vapour isotope analysis. Seven inlets on the tower from 2 to 70 m above ground were sampled sequentially by both FTIR analysers every 30 min to provide vertical profiles of trace gases, δ 13 C in CO 2 and δD in water vapour. The general intent of the campaign was to use vertical profiles of carbon and water isotopic compositions to partition water vapour between evaporation and transpiration, and CO 2 between photosynthetic uptake and release by respiration. The campaign setup and water vapour isotope analysis have been described in detail elsewhere (Haverd et al., 2011). Time series of trace gases and δ 13 C are shown in Fig. 11. For CO 2 and δ 13 C in CO 2 (Fig. 11a) strong vertical gradients are observed in the canopy at night when canopy turbulence is low, but above the canopy the air is generally better mixed and gradients are much smaller. There is strong anti-correlation between CO 2 and δ 13 C because the added respired CO 2 is depleted in 13 C. Figure 12 shows a typical Keeling plot of data collected over two nights; the y-intercept is −26.8 ‰ (±0.4 ‰ 1σ random uncertainty), consistent with respiration from the predominantly C3 plants that dominate this forest. However during daytime, when canopy turbulence and boundary layer mixing is stronger, the air is well mixed in and above the canopy and vertical gradients are smoothed out, making the determination of partitioning from isotopic profiles during daytime impractical. Figure 11b shows vertical profile data for CH 4 and N 2 O, indicating clear uptake of CH 4 at the surface (decreasing mole fractions near the ground), and barely detectable N 2 O emission (increasing mole fractions near the ground). Vertical gradients of trace gas concentrations can be used to calculate surface exchange fluxes if the turbulent diffusion can be quantified (e.g. Monteith and Unsworth, 1990). This technique was not practical in the forest environment, where turbulence within the canopy was high during the day and concentration gradients were small, or gradients were high at night but turbulence was suppressed. Flux gradient measurements are suited to agricultural environments above a uniform surface such as grass or crop. Here the high precision of the FTIR analyser is well suited to measurement of the small concentration gradients that exist. An early application to agricultural flux gradient measurements was able to quantify CO 2 fluxes, but was not sufficiently precise for background N 2 O or CH 4 fluxes except following rain when N 2 O emissions are enhanced . Based on the Fick's Law relationship between flux and concentration gradient where F = flux, K = diffusion constant, z = height and C = concentration. With the measurement precisions described in Table 1, a typical turbulent diffusion constant of 0.1-0.2 m 2 s −1 , and a vertical scale for measuring gradients of the order of 1 m, Table 4 provides estimates of minimum detectable fluxes for the FTIR analyser using the flux gradient technique. Eddy accumulation methods such as Relaxed Eddy Accumulation (REA) or Disjunct Eddy Accumulation (DEA) allow more measurement time to achieve higher trace gas measurement precision, and hence improved flux detection limits. We have applied the FTIR analyser in both REA and DEA techniques, which will be reported in forthcoming publications.

Chamber measurements
Micrometeorological flux measurement techniques are usually not able to resolve background fluxes of methane, nitrous oxide and trace gases other than CO 2 because the small vertical gradients cannot be resolved with sufficient speed or precision by existing measurement techniques. In many cases, chamber measurements offer the only feasible method to estimate small fluxes, despite their limitations (e.g. site inhomogeneity and disturbance, microclimate perturbation) (Livingstone and Hutchinson, 1995). The FTIR analyser coupled to automated surface flux chambers provides a useful technique for greenhouse gas exchange measurements at the Earth's surface with several advantages: -Simultaneous measurement of greenhouse gases CO 2 , CH 4 and N 2 O, as well as CO and δ 13 C in CO 2 -High precision enabling the measurement of small fluxes -Continuous measurements with 1 min averaging time or better, allowing assessment of the linearity of concentration changes and hence chamber leakage or other secondary processes occurring in the chamber -Continuous fully automated operation -The isotopic specificity of FTIR analysis allows the option to include isotopic labelling to elucidate the mechanisms of trace gas emissions.
We have carried out several FTIR-chamber flux studies in a variety of agricultural and natural settings. A fully automated system has operated continuously since 2004 measuring N 2 O fluxes from irrigated and non-irrigated pasture in Victoria, Australia (Kelly et al., 2008), and another system was deployed over a complete sugar cane growth cycle in northern Australia (Denmead et al., 2010). Both studies were based on earlier FTIR systems but provided continuous measurements over periods of months to years.
Here we briefly describe two current examples of chamber flux measurements with the FTIR analyser -full details will be published elsewhere. The Quasom field experiment at the Max Planck Institute for Biogeochemistry in Jena, Germany, (https://www.bgc-jena.mpg.de/bgp/index. php/Main/QuasomFieldExperiment) investigates the cycling of carbon through an entire growing cycle of an annual crop by measurements of all carbon pools and fluxes, including isotopic 13 C labelling and discrimination measurements. The FTIR analyser is coupled to 12 soil flux chambers in the field experiment and sequentially samples air from the chambers as each goes through a closure cycle. The sampled air is recirculated back to the chambers. The system has operated continuously since June 2011, with a 1-min measurementaveraging time and typically ninety 15-min chamber closures per day. The 13 CO 2 isotopic measurements were calibrated using the procedures described in Sect. 3, based on measurements of whole air reference gases provided by MPI-BGC. Results agree well for both absolute and empirical calibration methods, with 1σ precision of better than 0.1 ‰. Figure 13 illustrates trace gas measurements from a sequence of closures of seven individual chambers, made in the evening when there is no photosynthetic CO 2 uptake. Individual chambers show considerable variability, but all are sources for CO 2 and N 2 O, sinks for CO, and show complex  Fig. 14. Keeling plot of δ 13 C vs. 1/χ CO 2 for a typical single chamber closure from the data of Fig. 13. The two plots are derived from the absolute and empirical δ 13 C calibration methods described in Sect. 3.
behaviour for CH 4 . CO 2 emissions correlate with decreasing δ 13 C because the respired CO 2 is depleted in 13 C. Figure 14 shows a typical night-time Keeling plot of δ 13 C vs. 1/(CO 2 mole fraction) from a single chamber closure. The δ 13 C signature of the respired CO 2 in the chamber is equal to the yintercept of the plots, −31.8 and −32.1 ‰ (±0.3 ‰ 1σ random uncertainty) for the empirical and absolute calibrations, respectively. The second example of chamber flux measurements includes novel measurements of N 2 O isotopologues in the field (Phillips et al., 2012). Fluxes of 14 N 14 NO, 14 N 15 NO, 15 N 14 NO and 15 N 15 NO were measured pre-and postaddition of 15 N labelled substrate (potassium nitrate or urea) to the soil at a pasture site with a pneumatically-controlled, automated chamber system. Chambers were controlled and sampled sequentially by the FTIR analyser for 30 min each, with analysed air recirculated back to the chamber in a closed  loop. Each chamber closed for 18 min out of the 30 min cycle and spectra were measured continuously with 1-min averaging time. Isotopologue amounts were determined by analysis of a spectral window near 2200 cm −1 in the strong ν 3 band of N 2 O. A total of 40 flux measurements (chamber closures) were collected each day from the five chambers between 1 December 2011 and 30 January 2012. Four chambers received 15 N in solution and one chamber received water only. Only 14 N 14 NO was detected for the water-only chamber; 15 N isotopologues in natural abundance were below quantification limits. All four isotopologues were quantified with better than 1 nmol mol −1 precision for the four chambers dosed with 15 N. Figure 15 shows the instantaneous and cumulative fluxes of all N 2 O isotopologues from 4 days before 15 N addition to 8 days after. 15 N-labelled N 2 O emissions decreased to near-zero levels after 8 days, while emissions of unlabelled N 2 O continued from the unlabelled soil nitrogen pool. This experiment enabled the measurement of additional N 2 O emitted due to nitrogen addition independent of the background N 2 O emission flux. Approximately 1-2 % of the added N was emitted as N 2 O.

Conclusions
The FTIR trace gas analyser provides simultaneous, continuous, high precision analysis of the atmospheric trace gases CO 2 , CH 4 and N 2 O and CO in air. A 1-5 min averaging time is sufficient to achieve repeatability meeting GAW measurement compatibility targets for clean air measurements, and with careful calibration the accuracy is of similar magnitude (Hammer et al., 2012). In addition, parallel measurements of δ 13 C in CO 2 from the same air samples with precision only slightly less than GAW targets are obtained. The analyser is suited to a wide range of applications in atmospheric trace gas measurements, including composition monitoring at clean air baseline stations and on mobile platforms, micrometeorological and chamber flux measurements, and isotopic measurements of atmospheric trace gases.