Global climate change is a major research topic of today's environmental sciences. Human activities, such as burning of fossil fuels, are the key drivers of the continuing increase of atmospheric greenhouse gases and the gases involved in their chemical production . Long-term measurements of the atmospheric composition provide the experimental data to quantify sinks and sources which are of utmost importance to understand the anthropogenic impact on global warming .

The Total Carbon Column Observing Network (TCCON) provides measurements of column-averaged abundances of greenhouse gases. TCCON is a ground-based network of Fourier Transform Infrared (FTIR) spectrometers initiated in 2004 by the California Institute of Technology, Pasadena, USA . The stationary high-resolution FTIR spectrometers measure total columns of CO2, CO, CH4, N2O, H2O, HF and other atmospheric gases. Precise and accurate column abundances are retrieved from near infrared (NIR) solar absorption spectra using direct sunlight. TCCON measurements are tied to the World Meteorological Organization (WMO) scale via in situ aircraft measurements flown over TCCON sites . For the greenhouse gases CO2 and CH4, TCCON achieves an accuracy and precision in total column measurements of about 0.2 % which is necessary to gain information about sinks and sources and for satellite validation . Currently, about 23 globally distributed sites are affiliated with TCCON. The network aims to improve global carbon cycle studies and to provide a primary validation data record of various gaseous atmospheric components for retrievals from space-based instruments. TCCON instruments measure the same quantities in the same spectral region as satellite-borne instruments – e.g., the Orbiting Carbon Observatory 2 OCO-2,, the Scanning Imaging Absorption Spectrometer SCIAMACHY, and the Greenhouse Gases Observing Satellite GOSAT,. Hence, for the validation, TCCON provides an ideal data set.

The TCCON strives to attain the best site-to-site precision and accuracy possible. Systematic biases that are consistent throughout the network are fully accounted for by scaling the TCCON retrieval results to the WMO scale via aircraft and AirCore profiles . Thus, the TCCON sets guidelines to ensure that the instrumentation at each site is as similar as possible, and that the retrieval software, including the spectroscopic line lists and line shapes, is identical for each site. For example, if a particular site used a different spectroscopic line list from the rest of the sites, the network consistency would decrease even if that line list is an improvement over the original. There are, however, several site-specific differences that can cause a degradation in the TCCON's consistency: differing instrument line shapes (ILS) between instruments , laser sampling errors (LSE) that differ between instruments , and differing optical component responses between instruments (beam splitters, detectors, filters, mirror coatings, etc.). The impacts of ILS differences are mitigated by requiring that all instruments maintain a near-perfect ILS at each TCCON station. The impacts of the LSE are minimized by applying a correction to the TCCON interferograms . TCCON partners typically use very similar optical components, and detectors which addresses the last of these issues. This approach to standardizing the optical components is imperfect, but the differences between spectra from different sites are generally small. The Karlsruhe system, however, has a significantly different optical setup, designed to allow for automated mid-infrared NDACC and TCCON measurements to be made from the same system. As shown here, using the standard TCCON retrieval approach for this setup causes biases of nearly 1 ppm in XCO2, which exceeds the precision requirements of the network.

In this paper, we discuss the particular instrumental setup of the Karlsruhe FTIR spectrometer and point out differences from the standard TCCON setup. We identify difficulties in the standard TCCON data processing when analyzing solar absorption spectra recorded by the Karlsruhe spectrometer and present a strategy for the Karlsruhe data set that improves its consistency with respect to TCCON.

The Karlsruhe TCCON FTIR spectrometer was initiated in 2009 at the Karlsruhe Institute of Technology (KIT) – Campus North (49.1∘ N, 8.4∘ E, 110 m a.s.l.). Karlsruhe is an extensive urban region in central Europe and experiences an oceanic, mild climate similar to most cities in the mid-western part of Europe. The flat terrain is a favorable scene for nadir-looking satellite overpasses as well as model studies. Solar spectra are acquired by operating a Bruker IFS 125HR spectrometer (Bruker Optics, Germany). The automated instrument is housed in an air-conditioned 20 ft sea transport certified shipping container. The spectrometer features a precise cube-corner Michelson interferometer containing a semi-transparent calcium fluoride (CaF2) beam splitter and a linearly moving scanner. An InSb detector covers the spectral range from 1900–5250 cm-1 and an InGaAs detector covers the 5250–11 000 cm-1 spectral range. The InSb diode is cryogenically cooled using a liquid nitrogen (LN2) microdosing autofill cooling system (Norhof, Netherlands). A dichroic mirror (Optics Balzers Jena GmbH, Germany) is installed with a cut-on wavenumber of 5250 cm-1. The instrument features a camera-based solar tracker developed by KIT with gold-coated optics to minimize photon noise induced by the visible spectrum. TCCON measurements are routinely recorded at a maximum optical path difference (OPDmax) of 45 cm leading to a spectral resolution of 0.02 cm-1. In addition, solar spectra are also recorded at OPDmax=64 cm and OPDmax=120 cm leading to spectral resolutions of 0.014 and 0.0075 cm-1, respectively.

Within TCCON, the recorded interferograms are processed and analyzed with the GGG2014 Software Suite which includes GFIT, a non-linear least-squares spectral fitting algorithm . In general, all TCCON sites use the same software and retrieval analysis strategy to minimize algorithmic biases between sites. The calibration of the spectral radiances, exact modeling of the far line wing contributions, and continuum transmission variability will cause consistent errors for all TCCON stations, because the line shape and continuum models are identical, thus negligibly impacting the TCCON precision. However, surface temperatures and signal-to-noise ratios can differ significantly from site to site, and therefore these errors are much more important to minimize.

The standard GGG2014 retrieval strategy fits a level and a tilt to the continuum of a spectral window. However, GFIT has also the ability to fit an Nth-order discrete Legendre polynomial basis function to the continuum . This continuum fit option is meant to fit curvatures in the continuum of the spectrum that are caused by instrumental features that cannot be neglected in the data processing.

We invoke the higher-order continuum level fit option in GGG2014. We determine the basis function order, N, for every affected spectral window individually using spectral fits of cavity measurements since their residuals are free from atmospheric absorptions. Different continuum basis function orders are tested to achieve the best fit in the continuum level. An example of how the continuum fit improves residuals of atmospheric spectral fits for the O2 and N2O spectral windows is given in Fig. . Spectral fits for all affected target gases are depicted in Fig.  in the Appendix.

We compare Karlsruhe TCCON data to aircraft overflights recorded as part of the EU project Infrastructure for Measurement of the European Carbon Cycle (IMECC) in 2009 to provide evidence that the higher-order continuum level fit option improves the consistency of the Karlsruhe data set with other TCCON sites. IMECC was the first airborne campaign to calibrate the European TCCON FTIR sites with respect to the WMO standards.

For our comparison, we rely on IMECC and TCCON data which were presented in detail in, e.g., , and , where numerous CO2 in situ profiles were obtained via instruments on an aircraft and compared to CO2 column amounts from TCCON spectrometers. An update of the calibration curve which has already been discussed in the aforementioned publications with combined results using the IMECC campaign and other aircraft profiles is shown in Fig. . The calibration curve contains North American, Australian, Asian and European TCCON sites (see legend within Fig. ). There is no significant bias between the Karlsruhe data and the aircraft data when comparing the integrated in situ profiles and the Karlsruhe TCCON data (with the higher-order continuum fit option). Karlsruhe data are in good agreement with the other geographically nearby TCCON stations of Orleans (France), Bialystok (Poland), Jena and Garmisch-Partenkirchen (both Germany). Without the higher-order continuum fit, Karlsruhe data is slightly elevated and exhibits an overestimation with respect to the best fit as seen in Fig. .

In addition, to test how DMFs from other sites are affected when a higher-order continuum fit in the retrieval strategy is applied, we update the calibration curve from, e.g., , and using the Karlsruhe retrieval approach to process data of the other TCCON stations which contribute to the TCCON XCO2 calibration curve (of the particular day of the aircraft overflight).

The differences between XCO2 retrieved from both retrieval strategies are depicted in Fig. . The change in XCO2 for Karlsruhe is about three times larger than for the other TCCON sites. This shows that a continuum fit to the Karlsruhe spectra is required to improve its consistency with the other TCCON data. The change in XCO2 is not negligible for the other stations which mainly follow the standard FTIR instrumental setup as recommended by TCCON. However, the changes are consistent (to within 0.1 ppm) for all other TCCON sites, suggesting that the addition of higher-order continuum terms is likely accommodating error that is common across the network. Such error is currently accounted for in scaling to the aircraft/AirCore profiles and thus do not impact the overall accuracy of the TCCON. This suggests that although adding such higher-order terms reduces the site-specific bias at Karlsruhe, it likely has not done so completely. In the next version of the TCCON retrieval software, we will seek to produce a uniform recommendation for modeling the continuum that will accommodate the unique aspects of the Karlsruhe implementation.

As seen in the previous sections, the non-standard Karlsruhe data set requires a modification to the standard GGG2014 TCCON retrieval setup. Instrumental features and the particular optical setup of the Karlsruhe FTIR induce variations of non-atmospheric origin in the recorded solar absorption spectra. The GGG2014 standard retrieval does not take into account continuum curvature in the spectral fitting routine, and thus leads to detrimental curvature in the spectral fits of several spectral windows in the Karlsruhe spectra. Hence, Karlsruhe TCCON data are processed using a higher-order continuum fit for the affected spectral windows by fitting higher-order discrete Legendre polynomial basis functions. We apply three slightly different retrieval approaches for different time periods of the data set because three different narrowband spectral filters were used for the InSb detector since the instrument was initiated in 2009. The different narrowband spectral filters have different optical properties which affect the spectral fits of several spectral windows in a different way. Again, we follow the strategy described in Sect.  to determine the polynomial order, N, for affected spectral windows for the different filters. An overview of the determined N values for filter 1 (used until 15 November 2011) and filter 2 (used until 10 August 2012) is given in Table . For filter 2, one additional spectral window is affected, namely N2O (cw: 4395.2) and for filter 1 two more spectral windows are affected, namely CO (cw: 4233.0) and N2O (cw: 4330.1).

Table  summarizes the modified retrieval strategy for Karlsruhe. Gases which are not listed in Table  remain unchanged.

The results achieved with the modified retrieval setup developed for Karlsruhe in this work indicate that the spurious air-mass dependence of O2 retrievals is mainly induced by the overlaying collision-induced absorption (CIA). This corroborates earlier studies by using PROFFIT , which also indicated reduced air-mass dependence when using a refined treatment of the background continuum level. The approach includes a fit of the empirical background based on a user-selectable number of baseline points which are evenly distributed across the fitted spectral window. A single point is equivalent to a scaling factor, two points are used to create a linear fit, three or more points create a smooth background, very similar to a cubic spline fit through these guiding points. This choice has been made because each associated derivative is spectrally localized, whereas the fitting of parameters shaping a global polynomial fit across the spectral window results in derivatives which are all strongly interwoven. Dohe demonstrated that a detailed model of the O2 CIA which overlaps the 1.26 µm absorption band is not required if a sufficiently flexible empirical background fit is included in the fit.

Here, we revisit the O2 spectral window (cw: 7885.0) and investigate the impact of the number of guiding points, G, on the retrieved column of molecular oxygen in greater detail using PROFFIT. We expect that a small number of guiding points requires explicit modeling of the CIA, and that a rather flat plateau area is reached for a larger number of guiding points where fits with or without taking CIA into account are essentially equivalent until a further increase finally results in an empirical continuum so flexible that it starts to interact with individual spectral lines, spoiling the retrieved column. The result of this investigation is shown in Fig. . Note that the flat plateau area extends at least up to G=400 – at this value the dimension of the state vector becomes so large that the executable runs out of memory. The retrieved column is slightly decreasing with increasing G, probably due to the fact that the continuum starts to curve into some broader absorption bands, as the solar H absorption line or the Q-branch of the O2 band (see Fig. ). A further improvement of the approach might be achievable by allowing for a variable spacing of guiding points, allowing for a higher degree of flexibility as function of the position in the spectral window. Although the retrieval seems stable for up to the maximum number of guiding points we were able to test, a small number of guiding points is clearly preferable from the technical point of view. In the standard PROFFIT setup for this window G=25 is used (this setup is currently used for the analysis of low-resolution spectra as recorded with the EM27/SUN, ).

Note that the required basis function order empirically determined for the operational TCCON retrieval is smaller (e.g., N=5 for the O2 spectral window) than the number of guiding points required for PROFFIT (larger than 20). This discrepancy might be due to the use of a superior model of the CIA in the GGG2014 Software Suite and due to the fact that the retrieval strategy differs: both algorithms retrieve the O2 column from the line absorption alone, but GGG2014 in addition allows a scaling of the CIA, whereas PROFFIT only performs a forward calculation of the CIA without any further adjustments of this absorption contribution in the retrieval.

Whereas the Karlsruhe instrumental setup deviates from the standard TCCON setup, it is quite typical from the NDACC perspective. Several narrow filter bands are defined by use of optical filters in the MIR region covered by the InSb detector. In general, NDACC sites do not use lamp or cavity measurements for correcting a spectral variability of filter transmissions. Traditionally, the analysis of solar absorption spectra using the NDACC methodology relies on narrow spectral fitting regions, typically a couple of tenths up to several wavenumbers wide. The spectral window atlas edited by provides a comprehensive collection of spectral windows as used for the analysis of MIR spectra. Due to the fact that (1) far line wing contributions emerging from outside the spectral window can only be modeled with limited reliability, (2) the continuum transmission of the atmosphere is variable, and (3) the knowledge of the solar brightness temperature in the spectral region under consideration is limited, an empirical fit of the background continuum is generally included in a retrieval of that window. A single scaling factor is always required – typically a linear slope is also taken into account – and for wider spectral windows encompassing several lines, a second-order polynomial might be appropriate.

The retrieval strategy favored by TCCON prefers much wider spectral fitting regions, which might encompass a whole molecular band of the target gas. This is a superior approach especially in the NIR because using whole absorption bands minimizes any temperature sensitivities, and for a given noise level in the spectrum, this approach significantly reduces the noise error of the retrieved column abundances because many absorption lines contribute. In the future, selection of wider spectral windows might prove useful for NDACC applications as well. From this perspective our investigation might be useful for future NDACC work also when fits over wider spectral regions are attempted.

In this work we present a modified retrieval strategy for the Karlsruhe TCCON data set. The Karlsruhe FTIR spectrometer has an extended spectral range and does not conform with the standard TCCON setup. Karlsruhe's particular optical setup induces stronger variations of the spectrum continuum that need to be correctly fitted using a higher-order polynomial fit than provided in the standard GGG2014 Software Suite. Our modified retrieval strategy uses higher-order discrete Legendre polynomial basis functions to fit the continuum which improve spectral fits and air-mass dependencies for affected spectral windows. After this modification, the Karlsruhe data are in good agreement with other European TCCON data sets. A new version (R1) of the Karlsruhe TCCON data is available through CDIAC (http://tccon.ornl.gov). Future scientific studies should use this superior R1 data , instead of the obsolete R0 data. The setup of the Karlsruhe instrument provides valuable findings for the entire network.