Calibration of the Total Carbon Column Observing Network Using Aircraft Profile Data

. The Total Carbon Column Observing Network (TCCON) produces precise measurements of the column average dry-air mole fractions of CO 2 , CO, CH 4 , N 2 O and H 2 O at a variety of sites worldwide. These observations rely on spectroscopic parameters that are not known with sufﬁ-cient accuracy to compute total columns that can be used in combination with in situ measurements. The TCCON must therefore be calibrated to World Meteorological Orga-Correspondence nization (WMO) in situ trace gas measurement scales. We present a calibration of TCCON data using WMO-scale instrumentation aboard aircraft that measured proﬁles over four TCCON stations during 2008 and 2009. These calibrations are compared with similar observations made in 2004 and 2006. The results indicate that a single, global calibration factor for each gas accurately captures the TCCON total column data within error.


Introduction
The Total Carbon Column Observing Network (TCCON) is a ground-based network of Fourier transform spectrometers that precisely measure total columns of CO 2 , CO, CH 4 , N 2 O, H 2 O, HF and other gases . The TCCON instruments measure the absorption of direct sunlight by atmospheric gases in the near infrared (NIR) spectral region. To derive a total column measurement of the gases from these spectra, external information about the atmosphere (e.g. temperature, pressure, a priori mixing ratio) and NIR spectroscopy is required. A significant effort is put into minimizing errors in this external information, and the resulting total columns are precise (e.g. <0.25% in CO 2 ).
Due to systematic biases in the spectroscopy, the absolute accuracy of the column measurements is ∼1%, which is inadequate for use in combination with in situ measurements for carbon cycle science. In order to make TCCON column measurements useful for these combined analyses, they must be calibrated to the World Meteorological Organization (WMO) in situ trace gas measurement scales. To do this, we use profiles obtained with in situ instrumentation flown on aircraft over TCCON sites. A set of profiles were measured over the Park Falls, Wisconsin TC-CON site in 2004(Washenfelder et al., 2006 during the Intercontinental Chemical Transport Experiment-North America campaign (INTEX-NA, Singh et al., 2006) and the CO 2 Budget and Rectification Airborne -Maine experiment (COBRA-ME, Gerbig et al., 2003;Lin et al., 2006). A single profile was measured coincidently with the Darwin, Australia site in 2006 as part of the Tropical Warm Pool International Cloud Experiment (TWP-ICE, Deutscher et al., 2010;May et al., 2008). Since then, other TCCON sites have begun operational measurements. In this paper, we describe the first global calibration of five TCCON sites (Park Falls, Lamont, Darwin, Lauder and Tsukuba), using instrumentation calibrated to WMO scales aboard the HIA-PER aircraft, during the START-08 and HIPPO overpasses in 2008 and 2009, Learjet overflights of Lamont in 2009, and a Beechcraft King Air 200T aircraft profile over Tsukuba, Japan in 2009 (Tanaka et al., 2009). We present the calibration of CO 2 , CO, CH 4 , N 2 O and H 2 O.

TCCON
The TCCON was developed to provide a long, nearly continuous time series to serve as a transfer standard between in situ networks and satellite measurements, and to provide insights into the carbon cycle (e.g., Yang et al., 2007;Keppel-Aleks et al., 2008;Wunch et al., 2009;Deutscher et al., 2010). TC-CON sites are located worldwide (Fig. 1). The first TCCON site, located in Park Falls, is described by Washenfelder et al. (2006).  Table 1. TCCON spectral windows and spectroscopy. If a single molecule is retrieved in multiple windows, the results are averaged. References are 1, Rothman et al. (2009); 1 a , Rothman et al. (2009, November update); 2, Toth et al. (2008); 3, Frankenberg et al. (2008);4, Smith and Newnham (2000); 5, Yang et al. (2005); 6, Gordon et al. (2010);7, Toth (2005); 8, Jenouvrier et al. (2007). Total column abundances are retrieved from spectra measured with the TCCON instruments using a nonlinear leastsquares spectral fitting algorithm (GFIT), which scales an a priori profile to produce a synthetic spectrum that achieves the best fit to the measured spectrum. We use the spectral windows and spectroscopic data listed in Table 1. Column-averaged dry-air mole fractions (DMF), denoted X G for gas G, are computed using the retrieved O 2 columns as a measure of the dry air column.
Dividing by O 2 improves the precision of the measurement by significantly reducing the effects of instrumental or measurement errors that are common to both the gases (e.g. solar tracker pointing errors, zero level offsets, instrument line shape errors, etc. described in Wunch et al., 2010). However, any errors specific to either column G or column O 2 will create errors in the DMFs of each gas. Atmospheric O 2 is not, as assumed by GFIT, constant. The seasonal cycle in the O 2 /N 2 ratio ranges globally by~10-30 ppm of O 2 (Bender et al., 1998), peaking in the summer, when the CO 2 amounts are at their minimum. Using a constant O 2 amount overestimates the seasonal cycle in X CO 2 by~0.05 ppm. The long-term depletion of O 2 is about twice the rate of the atmospheric CO 2 increase (Tohjima et al., 2005;Bender et al., 1998). Assuming a~2 ppm annual CO 2 increase, GFIT will overestimate the secular in-crease by~0.4%, or~0.01 ppm X CO 2 /year. This small timedependence will be built into a future version of our processing algorithm.
All TCCON X CO 2 data have an airmass-dependent artifact, which causes the retrievals to be ∼1% larger at low solar zenith angles than at high solar zenith angles . This artifact is caused primarily by spectroscopic inadequacies which are common to all TCCON instruments (e.g. line widths, neglect of line-mixing, inconsistencies in the relative strengths of weak and strong lines). The airmassdependent artifact is removed from the TCCON data with a single empirical correction factor before calibration. Airmass dependent artifacts have not been seen in X CH 4 , X CO , For comparison with the aircraft profiles, which are not measured instantaneously, averages are taken of TCCON X CO 2 , X CH 4 , X CO , and X N 2 O columns retrieved while the aircraft measurements were taking place, weather permitting. Typical durations are between 0.5-4 h. The standard deviations (1σ ) of the measurements are taken as the TCCON errors. One hour of TCCON measurements of X H 2 O are averaged to compare with each sonde profile, centered on the sonde launch time. Twice the standard deviations (2σ ) of the X H 2 O measurements are taken as the TCCON errors, because the atmospheric variability of H 2 O can be much greater than for the other molecules (Sussmann et al., 2009).

Aircraft campaigns
Three independent aircraft campaigns were held in 2008 and 2009 that included profiles over four TCCON stations. The instrumentation on each aircraft used for the calibration are listed in Table 2, and the dates of the profiles over TCCON sites are listed in Table 3. The WMO calibration scales used for the aircraft instrumentation are described for CO 2 in Zhao and Tans (2006) and Keeling et al. (2002), for N 2 O in Hall et al. (2007), for CH 4 in Dlugokencky et al. (2005) and for CO in Novelli et al. (1994). Demonstrated precision and accuracy for each instrument and each molecule are listed in Table 2.

START-08/pre-HIPPO and HIPPO-1
The NCAR/NSF High-performance Instrumented Airborne Platform for Environmental Research (HIAPER), is a modified Gulfstream V (GV) jet which hosted the Stratosphere-Troposphere Analyses of Regional Transport 2008 (START-08) campaign (Pan et al., 2010) and the preliminary HIA-PER Pole-to-Pole Observations (pre-HIPPO) campaign during 2008. The two campaigns shared flight time and instrumentation and made observations across North America, including a vertical profile above the Park Falls site in May, 2008. The HIAPER Pole-to-Pole Observations (HIPPO-1) campaign  covered a cross-section of the globe that spanned the Arctic to the Antarctic ( Fig. 1) with profiles over Lamont and Lauder in January, 2009. The START-08/pre-HIPPO and HIPPO-1 missions used similar in situ instrumentation ( Table 2). The water profiles are from the available H 2 O measurements on board the aircraft (e.g., VCSEL: Zondlo et al., 2010), with additional stratospheric information supplied by the noontime NCEP/NCAR specific humidity profile for that day. The HIPPO-1 profiles used in this analysis over Lamont are shown in Fig. 2.

Learjet
The NASA Glenn Lear-25 aircraft performed three profiles from 5-13 km altitude over the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) Lamont site during a campaign from 31 July 2009 to 5 August 2009 (Abshire et al., 2010). Lower altitude (0.3-5 km) profiles were measured with a Cessna 210 at essentially the same times and locations. On both aircraft, the CO 2 , CH 4 , N 2 O and CO measurements were made by flask samplers, which were analysed at the National Oceanic and Atmospheric Administration's Earth System Research Laboratory (NOAA's ESRL). Precisions and accuracies listed in Table 2 for the NOAA Flask Samplers are from Ness et al. (2010) (http://www.esrl.noaa.gov/gmd/ccgg/aircraft/qc.html). Water profiles were obtained from on-site sonde measurements taken at 11:30 a.m. LT.
Many years of bi-weekly Cessna 0-5 km flights are also available over Park Falls and Lamont and will be used in a future analysis to assess possible calibration drifts for those sites. The ceiling of these flights is insufficiently high for use in this analysis.

Beechcraft King Air
The Beechcraft King Air 200T aircraft measures CO 2 continuously with a Li-COR (Li-840) non-dispersive infrared analyzer. CH 4 and other gases are measured using handoperated flask samplers, which are analysed at the National Institute for Environmental Studies (NIES). Precisions and accuracies for the Beechcraft King Air instrumentation listed in Table 2 are from Machida et al. (2008), Machida et al. (2007) and Zhou et al. (2009 Due to air traffic control restrictions, the higher part of the profile (2 to 7 km) was observed over Kumagaya, and the lower altitude range (0.5 to 2 km) was observed over Tsukuba. For the purposes of the FTS calibration, only data from the 15 January overflight is used, because of heavy cloud cover on 7 January. Water profiles were obtained from nearby radiosonde measurements taken at the Tateno Aerological Observatory near the time of the overpass.

Numerical integration of aircraft in situ profiles
To calibrate the total column measurements of the TCCON network, the aircraft in situ profiles must be integrated with respect to altitude. In order to properly compare the groundbased FTS measurements with the in situ aircraft measurement, which we consider the best measure of the true state of the atmosphere, the averaging kernels of the FTS measurements (A) must be taken into account. From the aircraft profiles (x h ), an averaging kernel-smoothed profile (x s ) can be computed that, when integrated, can be directly compared with the FTS retrieved total columns. The smoothed profile represents the profile that should be retrieved, if the FTS were measuring the true atmospheric profile without spectroscopic errors, given the GFIT a priori profile (x a ) and retrieved profile scale factor (γ ). We use Eq. (4) of Rodgers and Connor (2003), Note that for a GFIT scaling retrieval, the kernels are calculated for the solution mole fraction profile, not the a priori profile, so the point of linearization of the Taylor expansion producing Eq. (2) is γ x a and not x a .  For column measurement calibration, Eq.
(2) is integrated vertically: whereĉ s is the smoothed column-averaged DMF, c a is the column-averaged DMF from integrating the a priori profile and a is a vector containing the FTS dry pressure-weighted column averaging kernel (plotted in Fig. 3). The a T (x h −γ x a ) term represents the column averaging kernelweighted vertical integration of the difference between the in situ profile and the scaled a priori profile. Column averaging kernels vary as a function of pressure and solar zenith angle.
Integrating these profiles is done most accurately on a pressure grid, under the assumption that the atmosphere is in hydrostatic balance. The total vertical column for gas G (V C G ) is then defined in the following manner: where f G =f dry G ·(1−f H 2 O ) is the true mole fraction of gas G, P s is the surface pressure, and g is the gravitational acceleration, which is a function of altitude (z) and latitude (φ). We distinguish between the true mole fraction (f G ), and the dry mole fraction (f dry G ), which is what the aircraft in situ instrumentation measures. The mean molecular weight of air, m, can be expressed in terms of its wet and dry components as well: m=m H 2 O ·f H 2 O +m dry air ·(1−f H 2 O ). Substituting these into Eq. (4) and rearranging yields a useful, numerically integrable relationship to compute V C G . To compute the column averaging kernel-weighted vertical column (to satisfy the right-hand term in Eq. 3), the column averaging kernel (a(p)) must be included at every level in the integral.
The column of dry air (V C air ) is computed by setting the numerator in Eq. (6) to 1. The column-averaged DMF is computed by dividing the appropriate vertical columns by the column of dry air. Hence, Eq. (3) becomes: Aircraft measurements have good accuracy, but are limited in altitude floor and ceiling, and so we must use additional information for the surface and the stratosphere. When multiple instruments aboard the aircraft measure the same species, a running mean is applied. There is one instance where two CO measurements on HIPPO-1 disagree over Lauder in the upper troposphere (RAF and QCLS): in this case, QCLS is used.
Most TCCON sites are co-located with tower or surface in situ measurements. In the event that there were no surface or tower measurements available, and the aircraft did not measure down to the surface, the lowest measured aircraft value was assumed to be the surface value (e.g. Park Falls on 14 July 2004).
In general, the unknown state of the atmosphere above the aircraft ceiling is the largest source of uncertainty in the total integrated column (Table 4). For stratospheric CO 2 , the mole fractions are predictable at the 0.3% level. The CO 2 profiles in the stratosphere are empirically derived from in situ measurements on high-altitude balloons and include realistic latitude and time-dependencies. The stratosphere is set by an exponential decrease above the tropopause, based on the age of air measurements of Andrews et al. (2001). The tropopause pressure comes from the NCEP/NCAR fourtimes daily analysis, which is interpolated to local noon at the latitude and longitude of the site. A generous error of ±1 ppm is assumed for the GFIT stratospheric a priori profile. These stratospheric profiles are used as a priori information for all TCCON retrievals. A priori profiles for the troposphere are derived from GLOBALVIEW (GLOBALVIEW-CO 2 , 2006). Stratospheric N 2 O and CH 4 mole fractions are more difficult to estimate than CO 2 because they decrease rapidly with altitude, causing transport-driven variations in the strato-spheric column. To account for these transport-driven variations, columns of HF can be used, which are measured coincidently with N 2 O and CH 4 by the TCCON FTS instruments. Due to a complete absence of HF in the troposphere, HF is a sensitive indicator of ascent and descent in the stratosphere. Indeed, a 1 km vertical shift in the HF profile produces a ∼15% change in the total column, which is easily measureable. Furthermore, strong stratospheric CH 4 -HF and N 2 O-HF correlations have been observed globally by Luo et al. (1995) and Washenfelder et al. (2003), which we exploit in this analysis to determine the best stratospheric profile for a given overpass.
The GFIT CH 4 , N 2 O, CO and HF a priori profiles are generated from MkIV FTS balloon profiles (Toon, 1991). The profiles are shifted up or down in altitude depending on the tropopause pressure for local noon on that day. The CH 4 -HF and N 2 O-HF correlations in the a priori profiles are consistent with those observed by Luo et al. (1995) and Washenfelder et al. (2003) and are preserved under the vertical shifting. Since HF is a long-lived, stable stratospheric tracer, we assume that any difference in the retrieved HF column from the a priori value is due to the stratospheric dynamics and will be anti-correlated with the stratospheric N 2 O and CH 4 . The magnitude of the deviation of the HF column from the a priori HF column is used to adjust the CH 4 and N 2 O stratospheric profiles to generate our best estimate of the "true" stratospheric profile for a given overpass. An illustration of this is in Fig. 4. The average adjustment is 0.4 km, and the maximum adjustment is 1.8 km. Note that even small errors in the stratospheric a priori profile of N 2 O will be very important in this analysis, because the N 2 O column averaging kernels increase significantly in the stratosphere (Fig. 3). The stratospheric error contribution for both CH 4 and N 2 O is estimated by shifting the stratospheric profile up and down by 1 km and integrating the results, giving upper and lower bounds on the column due to errors in the stratospheric profile.
Unlike CH 4 and N 2 O, stratospheric CO is highly variable and does not have a simple relationship with HF. To estimate the CO stratospheric contributions, v2.2 profiles from the low-Earth orbiting ACE-FTS instrument (Bernath et al., 2005) were averaged within one month of the overpass and ±5 degrees latitude of the site. The work by Clerbaux et al. (2008) has shown that the ACE-FTS CO values are accurate to 30% in the upper troposphere/lower stratosphere, and 25% above. For our stratospheric error budget, we have taken the larger of the standard deviation of the ACE profiles and the estimated error by Clerbaux et al. (2008), and summed that in quadrature with shifting the stratospheric profile up and down by 1 km.
If water vapor profiles are not available from the aircraft in situ data (Tsukuba, Darwin and during the Learjet overpasses of Lamont), radiosonde measurements of H 2 O are used in Eqs. (5) and (6). Any additional stratospheric information is provided from GFIT a priori profiles, which are derived Table 4. Aircraft integration error budget. The mean errors (minimum, maximum errors) for the various overpasses indicate the contribution of the error source to the error in the integrated total column. The error is split into three sources: the contribution from the unknown stratospheric profile, the contribution from the unknown surface value (if applicable), and the contribution from the aircraft profile itself. The total error is the sum, in quadrature, of the three errors. The stratospheric error for CO 2 was estimated from a sum, in quadrature, of the errors from shifting the a priori stratospheric profile up by 1 km, and adding 0.3% error to the stratospheric profile. The stratospheric CO contribution was estimated by shifting the stratospheric profile by 1 km and adding 25% error to the stratospheric profile (due to the ACE-FTS profile uncertainty). For CH 4 and N 2 O, only the contribution of shifting the stratospheric a priori by 1 km is included. The surface contribution to the error in the total column is generally negligible, since most of these overpasses either had coincident surface in situ measurements available, or reached very close to the surface themselves. The aircraft error was estimated by adding twice the precision of the aircraft measurement to the profile and re-integrating the profile.  from NCEP profiles, and extended upwards using a model based on MkIV balloon profiles. Because most of the water column is located at altitudes below ∼5 km, errors in the upper altitude water profile do not significantly affect the total columns of CO 2 , CH 4 , N 2 O and CO.
To estimate the H 2 O calibration curve for the TCCON, the radiosonde profiles over Tsukuba, Darwin, Lamont, Lauder and Park Falls are used, which tend to reach higher altitudes than the aircraft (generally well above the tropopause). Water profiles are available from daily sonde measurements at Lamont and Darwin. The errors on the H 2 O columns are estimated to be ±5% of the total column.
Once full profiles of the gas of interest and H 2 O are generated on a fine altitude or pressure grid, the profiles are integrated via Eqs. (5) or (6), and the smoothed profile is computed via Eq. (7).

Results
Aircraft overflights of the Park Falls, Darwin, Lamont, Lauder and Tsukuba TCCON stations are listed in Table 3, including their dates and which molecules were measured on the aircraft. Sample profiles from the HIPPO aircraft over Lamont are shown in Fig. 2 and the derived column-average calibration data are shown in Figs. 5-9. Errors computed for the smoothed, integrated aircraft measurements are the sum in quadrature of estimated stratospheric and surface measurement uncertainties and the estimated error on the aircraft or sonde profiles in the troposphere (Table 4). In all cases (except H 2 O), the stratospheric uncertainty is a significant component of the total error. The slopes of the calibration curves are listed in Table 5. Errors on the slopes are quoted as standard errors on the best fit, calculated using the errors in both the x and y axis (York et al., 2004) and as 2 standard deviations of the individual measurement ratios.
Our retrieval method is predicted to be both linear and have no intercept. We thus fit the data with a linear leastsquares and force a zero intercept. When the least-squares fits are allowed a nonzero y-intercept, all have a y-intercept that is zero within the uncertainty. To attempt to remove any biases added from errors in the GFIT a priori information, the aircraft profile with our best estimate of the stratospheric profile was input as the a priori profile. The same spectra were processed using the standard GFIT a priori profiles as well. The calibration coefficient for both cases have identical slopes within standard error, suggesting that the GFIT a priori profiles do not add a significant bias to the retrievals. Figures 5-9 show the calibration curves calculated using the aircraft profile as the a priori profiles.
For all molecules, there is excellent consistency between the TCCON calibrations obtained from different sites and seasons. Within measurement error, all stations can be described by a single regression line and hence single calibration factor, with variations around the regression line being explicable by instrumental and site differences. Hence, the reported TCCON columns are produced by dividing the retrieved columns by the values listed in Table 5. With the exception of H 2 O, all the calibration values are <1. This is because the O 2 spectroscopy has an error that causes the O 2 columns to be~2% high. The largest uncertainties in the calibration coefficients are for H 2 O. The H 2 O calibration curve shows that over a large range of humidities, the FTS instruments are capable of measuring water columns to a good degree of accuracy, but due to the high variability of tropospheric H 2 O, we do not expect calibration errors as small as for CO 2 , CH 4 , CO or N 2 O.
The uncertainties on the slopes, listed in Table 5, are used to compute the species uncertainty of each molecule, and can be compared with the WMO-recommended intercomparability for the molecules (WMO, 2007). The calibrated TCCON data, though less precise and accurate than the in situ data, provide long time series of total column measurements of atmospheric CO 2 , CH 4 , CO and N 2 O.

Conclusions
The TCCON column-averaged dry-air mole fractions of CO 2 , CO, CH 4 and N 2 O have been calibrated to the WMO scale using aircraft profiles measured between 2004 and 2009. The TCCON H 2 O columns have been calibrated using radiosonde measurements. The calibration curves show excellent consistency between the different TCCON sites and seasons, and can be described by a single calibration factor for each molecule. Future plans include extending this calibration set using additional HIPPO campaigns and other aircraft programs. We expect that all TCCON sites will eventually be calibrated using WMO-scale in situ measurements.