CH4, CO, and H2O spectroscopy for the Sentinel-5 Precursor mission: an assessment with the Total Carbon Column Observing Network measurements

The TROPOspheric Monitoring Instrument (TROPOMI) will be part of ESA’s Sentinel-5 Precursor (S5P) satellite platform scheduled for launch in 2015. TROPOMI will monitor methane and carbon monoxide concentrations in the Earth’s atmosphere by measuring spectra of back-scattered sunlight in the short-wave infrared (SWIR).


Introduction
Methane (CH 4 ) and carbon monoxide (CO) have a large impact on climate variability and air quality. Accurate monitoring with high spatial and temporal coverage allows the scientific community to better model atmospheric chemistry, atmospheric transport, and land-atmosphere interactions (bush-fires, regional CH 4 emissions of wetlands and livestock, etc.). Both ground-based observations and satellite observations are currently used to monitor CH 4 and CO.
The Total Carbon Column Observing Network (TCCON) is a global network of ground-based Fourier transform spectrometers, established in 2004 (Wunch et al., 2011a). Its goal is to remotely measure column abundances of CO 2 , CO,CH 4 , N 2 O and other molecules that absorb in the short-wave infrared (SWIR) and near-infrared (4000-15 000 cm −1 ).
ESA's Sentinel-5 Precursor (S5P) satellite -due for launch in early 2015 -will complement a series of polar-orbiting satellites that monitor CH 4 and CO concentrations in the Earth's atmosphere. Its payload, the TROPOspheric Monitoring Instrument (TROPOMI) (Veefkind, 2012), is an imaging spectrometer that will measure back-scattered solar radiation spectra in the nadir and off-nadir directions. TROPOMI will feature a wide swath of 2600 km with a ground pixel area of 7 × 7 km 2 (for the sub-satellite point), which implies daily global coverage of the Earth's surface, with ∼7 × 10 6 measured spectra. The spectrometer will measure the SWIR range at 4190-4340 cm −1 with moderate spectral resolution (0.45 cm −1 ). This range covers strong absorption lines by CH 4 and water vapour (H 2 O) as well as weak absorption by CO and deuterated water (HDO).
During one decade of operations, the SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY) (Bovensmann et al., 1999) has demonstrated that this type of satellite observation allows for the retrieval of total atmospheric columns of CH 4 (e.g. Frankenberg et al., 2006;Bergamaschi et al., 2009) and CO (Buchwitz et al., 2007;de Laat et al., 2010). Since February 2009, the Greenhouse gases Observing SATellite (GOSAT) (Kuze et al., 2009) is providing CO 2 and CH 4 concentration measurements as well, which are currently subject to validation (Butz et al., 2011;Morino et al., 2011;Wunch et al., 2010;Parker et al., 2011). A satellite observation set of tropospheric CO is provided by the Measurements Of Pollution In The Troposphere (MOPITT) instrument, active since the year 2000. CO total columns and vertical profiles both from the SWIR and from the thermal-infrared near 2100 cm −1 are retrieved from the MOPITT data (Deeter et al., 2009). In the coming years, S5P will fill the gap between the currently orbiting satellites and later missions such as Sentinel-5. A common goal of these missions is to monitor atmospheric CH 4 concentrations with the accuracy and spatio-temporal coverage that enable inverse modelling of CH 4 sources on regional and weekly scales. S5P will also provide users with a CO product at high spatial and temporal sampling, a single measurement having an uncertainty of 10 % at most. In contrast, SCIAMACHY data have to be averaged in time (roughly one month) and space (∼5 • × 5 • ) to reach a comparable accuracy.
The absorption lines of CH 4 and CO in the SWIR can be used to infer the total atmospheric concentration with high sensitivity to the Earth's surface and lower atmosphere where sources are located. Measurements in the thermal-infared are usually less sensitive to CO in the lower troposphere. The main challenge for the inversion technique is the desired accuracy: for CH 4 , residual retrieval biases as small as ∼0.4 % could be detrimental to inverse modelling of sources and sinks (Bergamaschi et al., 2009). The scientific objective for CO -an overall accuracy of better than 15 % (Vidot et al., 2012) -seems less demanding, but the CO absorption lines are hard to detect among the strong absorption lines of CH 4 and H 2 O. The retrieval accuracy depends on accurate knowledge of the light path of the back-scattered sunlight through the Earth's atmosphere. Scattering by particles such as aerosols, water and cirrus clouds can modify the light path and induce retrieval errors. The two studies published recently by Butz et al. (2012) and Vidot et al. (2012) focused on this error source and -using synthetic input spectra -concluded that the scientific goals of TROPOMI can be achieved with the predicted instrumentation. Butz et al. (2012) cautioned, however, that a few other, unrelated, error sources had not yet been assessed. One of them, which is hard to assess by means of synthetic input spectra alone, is the inaccuracy of the assumed molecular absorption lines of CH 4 , CO, and H 2 O. This error source is the topic of this study. It is representative for the spectroscopy-related errors in TROPOMI retrievals with a low density of scatterers in the forward model.
To assess these errors, we will retrieve CH 4 and CO columns from the spectra of ground-based Fourier transform spectrometers at two different locations, both at their native high resolution (0.02 cm −1 ) and convolved with the TROPOMI instrument response function to produce lowerresolution spectra (0.45 cm −1 ). The results of the retrievals in the 4190-4340 cm −1 range will then be compared to the reference values obtained from 5880-6174 cm −1 (for CH 4 ), and from 4209-4313 cm −1 (for CO) at the native resolution. The paper is structured in the following way: in Sect. 2, we will characterise the measurements and the inversion method to evaluate them. The results and their implications for the spectroscopic databases of CH 4 , H 2 O, and CO will be presented in Sect. 3. Section 4 will conclude the paper with recommendations for the S5P mission.

Methodology
In this section, we present the TCCON observations and the different spectral ranges used for this study (Sect.  Washenfelder et al., 2006). Each of the 100 spectra was measured on a different day, the days being evenly distributed in time. The Park Falls data cover a large range of solar zenith angles (SZA) between 20 and 80 degrees. The Darwin spectra have a narrower spread in observation geometry (35 < SZA < 45 degrees for 48 of 50 spectra). For evaluation, we split the spectra into the ranges listed in Table 1 and, whenever TROPOMI spectra were to be simulated, convolved them with the expected TROPOMI instrument response function (Sect. 2.2). Table 1 summarises all spectral windows referred to in this study. The windows used for GFIT are windows 1, 2, and 3 for CH 4 , the windows labelled 4 for H 2 O, and the windows labelled 5 for CO. Windows 6a and 6b cover the expected spectral range for TROPOMI. The original resolution corresponds to a full width half maximum (FWHM) of 0.0134 cm −1 (window 6a), and the TROPOMI resolution has a a FWHM of 0.45 cm −1 (window 6b).

Forward model
In contrast to the more elaborate forward model required to invert back-scattered sunlight spectra (Hasekamp and Butz, 2008), the forward model in this study neglects scattering processes. The TCCON spectrometers measure direct sunlight, which is, to a good approximation, only affected by molecular absorption on its way through the atmosphere (Wunch et al., 2011a). The modelled signal F (k) can be written as an integral over the entire height h of the atmosphere S denotes the solar radiance, for which we adopted the solar line list used by the TCCON science team (G. C. Toon, private communication, 2010). The other terms in Eq. (1) are the instrument gain g, the wave number of the spectrum k, the pressure and temperature p and T , the molecular cross-sections σ (p, T , k), the particle density of the considered absorber molecules n(h), and finally f (µ 0 ), the airmass as a function of µ 0 = cos(SZA) (Kasten and Young, 1989). After integrating over height and atmospheric constituents, one needs to convolve the modelled absorption spectrum with the instrument response function R before comparing it to the measurements. To reproduce the TC-CON retrieval values, we assumed the instrument line shape to be a sinc function convolved with a rectangular function, with 0.02 cm −1 between the first zero-crossings (corresponding to FWHM = 0.0134 cm −1 ) and an oversampling rate of 1.9 × FWHM. To simulate TROPOMI-like spectra, we convolved the TCCON spectra with a Gaussian instrument line shape with a coarser FWHM of 0.45 cm −1 and an oversampling rate of 2.5 × FWHM. Figure 1 shows the two spectral resolutions in the SWIR window between 4190 and 4340 cm −1 .
The HITRAN 2008 molecular spectroscopic database (HI-TRAN08, Rothman et al., 2009) served as our default crosssection database, with the exception of the H 2 O line lists. For H 2 O in windows 1 to 4, we combined the line list by Jenouvrier et al. (2007) with HITRAN08 by selecting for each absorption line the version that produced the smaller spectral fit residuals. For the TROPOMI range at 4190-4340 cm −1 , we used the line list developed by Scheepmaker et al. (2012). These line lists are not identical to the H 2 O spectroscopy used by the TCCON science team. The latter improved the fit quality in spectral window 1, whereas it led to larger fit residuals in the TROPOMI range. To keep the paper short, we will only present retrievals obtained with the H 2 O line lists developed for this study. The CH 4 , CO, and CO 2 line lists used in the GFIT algorithm are the HITRAN08 line lists that were also used for this study. Figure 2 shows the relative strength of the CH 4 , H 2 O, and CO absorption features in the range of 4190-4340 cm −1 . The cross-sections were evaluated at p = 1000 hPa, T = 296 K and multiplied with columns N i representative for observations at Darwin to obtain approximate optical depths (Eq. 1).

Inverse method
We used the same inversion approach as described by . We optimised the state vector x, subjected to the forward model F (Eq. 1), from the TCCON measurements y by minimising Eq.
(2). The state vector x contained the following elements: total column number density N i = n i (h) for CO and H 2 O, a profile for CH 4 , three parameters to fit a wave number dependent instrumental gain g, and two auxiliary parameters to compensate for a spectral shift of the measured spectrum with respect to the tabulated cross-sections. By default, pressure, temperature, and the height profiles of the absorbing species were not retrieved in the state vector. We assumed a fixed a priori atmospheric profile for CH 4 , H 2 O, and CO, and fitted only a scalar correction factor to the initial N i . The exception to this rule was CH 4 . The spectral fit residuals decreased by 10 % when the CH 4 column was retrieved as a 12-layer height profile. The state vector thus contained twelve instead of one entry for CH 4 . They were summed up in the end to yield a total CH 4 column. As for all other species, the degrees of freedom of the inversion (between 1.8 and 1.9) were insufficient to retrieve a meaningful profile.
To retrieve x, regularisation is required because the inverse problem is ill-posed, i.e. the measurements y contain insufficient information to retrieve all state vector elements independently. The Phillips-Tikhonov regularisation method (Phillips, 1962;Tikhonov, 1963) finds the optimised state vectorx by minimising a cost function that is the sum of the least-squares cost function and a side constraint weighted by the regularisation parameter γ ≥ 0 according tô W is the weighting matrix, and S y is the diagonal measurement error covariance matrix containing the noise estimate. For S y we assumed a signal-to-noise ratio of 1000 (Wunch et al., 2011a). The set-up of the atmospheric input was not changed with respect to Butz et al. (2012): the atmosphere was divided into a grid of 72 planar atmospheric layers (equidistant steps in terms of pressure). By default, temperature, pressure, and height were kept constant. The initial values for pressure, temperature and the H 2 O profile were taken from the ECMWF (European Centre for Medium-Range Weather Forecasts) ERA-Interim analysis, provided 6-hourly on a 1.5 • × 1.5 • latitude × longitude grid. We checked that the surface pressure agreed within 0.1 % to the pressure measured at the TCCON stations. For the CH 4 and CO a priori profiles, we relied on the chemistry transport model (TM4) profiles . The a priori were obtained from a one-year average at the corresponding geolocation of the observation sites.

Reference retrievals
Throughout this paper we used the atmospheric total columns N i (in molecules cm −2 ) obtained from the spectral ranges 5880-6174 cm −1 (for CH 4 ) and from 4209-4319 cm −1 (for CO) as reference values. These spectral ranges are also used by the TCCON science team for their retrievals with the GFIT nonlinear least squares spectral fitting algorithm. GFIT is a profile scaling retrieval which fixes the a priori profile shape of the absorber, and scales the profile to produce a calculated spectrum that best matches the measured spectrum. The surface pressure is measured at each TCCON station with a barometer (Wunch et al., 2011a). Dedicated effort in the past years to improve CH 4 and H 2 O spectroscopy in the 5880-6174 cm −1 range (Frankenberg et al., 2008;Tran et al., 2010;Jenouvrier et al., 2007) has enabled accurate retrieval of CH 4 columns from this spectral range. This has been confirmed by validation of GFIT retrievals with independent aircraft measurements. Similarly, the accuracy of retrieved CO columns from the 4209-4319 cm −1 spectral range by GFIT has also been confirmed by validation with aircraft measurements .
Our inversion algorithm being not identical to GFIT, we first verified our algorithm. We checked if it reproduces the CH 4 and CO total columns derived with GFIT when the same spectral ranges and spectral resolution were used (see Table 1). A complication arose when inter-comparison of our CH 4 results from windows 1, 2, and 3 showed that the retrieval quality from window 1 (5880-5996 cm −1 ) was unsatisfying. A closer inspection revealed that there were several strong H 2 O absorption lines not well captured by our line list. We therefore decided to discard window 1 altogether and reproduce the GFIT values for CH 4 from the average of windows 2 and 3. For all observation windows, the spectrum measured at Park Falls on 21 June 2005 turned out to produce much larger spectral fit residuals than the average. The GFIT retrieval also assigns large error bars to the columns retrieved from this spectrum. This data point was therefore omitted from further analysis.
Comparing our retrieved CH 4 values from windows 2 and 3 to the GFIT values, we found a bias between the two datasets of 0.1 % for both Parkfalls and Darwin and standard deviations of 0.26 % and 0.18 % for Park Falls and Darwin, respectively. These differences are not larger than the average uncertainty of the CH 4 column retrieved with the GFIT algorithm. The latter is 0.28 % for the Park Falls time-series and 0.22 % for the Darwin time-series. For CO, we found biases of 1.6 % and −2.8 %, and standard deviations of 1.1 % and 1.8 % for Park Falls and Darwin, respectively. The small differences between our algorithm and GFIT can be explained by the differences in averaging kernels and a priori profiles for CH 4 , CO, and H 2 O (smoothing and interference errors), and the differences in the H 2 O line list. Therefore, we considered our retrieved columns from the 5880-6174 cm −1 range (for CH 4 ) and from 4209-4319 cm −1 range (for CO) as reference values and the standard deviations between the algorithms as the associated error σ ref .

Analysis of the results
To discuss the retrieval accuracy, we used the following four diagnostic quantities throughout this study. They quantify by how much the quality of the retrieved columns decreased when CH 4 , CO, and H 2 O columns were retrieved from 4190-4340 −1 at the TROPOMI resolution compared to the reference results (spectral ranges listed in Table 1). For the standard deviation, the bias, and the correlation coefficient, we interpreted the columns of CH 4 , CO, and H 2 O retrieved at Park Falls or Darwin as a time-series and compared it to the time-series of the reference values: 1. The reduced fit residual χ 2 /ν: the sum of the residuals between modelled and measured spectrum, divided by the degrees of freedom ν (number of spectral pixels minus the degrees of freedom of the fit): The fit residual χ 2 equals the least-squares part of the cost function in Eq.
(2). In the results section, we will list the average χ 2 /ν over all spectra.
2. The σ N standard deviation of the differences between the retrieved columns at TROPOMI-like settings and the reference values. This number serves as an estimate of the accuracy of our results including systematic errors.
In the tables, we will always compare it to the error σ ref of the reference retrievals. If σ N is not much larger than σ ref , the differences between the two retrievals are statistically insignificant.
3. The bias b of the new retrieval values with respect to the reference values, calculated from the median of the relative differences.
4. The correlation coefficient ξ between the new retrieval values and the reference values.

Results
In this section, we compare the inversion results (CH 4 in Sect. 3.1, CO in Sect. 3.2) for the TROPOMI spectral range to the reference retrievals. An option to improve the CO retrieval accuracy is presented in Sect. 3.3.  Figure 3 shows the time-series of CH 4 columns (upper panel) and the differences (lower panel) between the results from the TROPOMI range and the 5996-6147 cm −1 range. The Darwin observations are coloured red, the Park Falls observations are shown in blue. In the lower panel, solid lines belong to retrievals at TROPOMI resolution (window 6b in Table 1), dotted lines denote results from the original resolution (window 6a). The dashed lines illustrate the biases for window 6b. Table 2 lists the fit diagnostics. Those are from left to right: average spectral fit residuals ( χ 2 /ν ), standard deviation of the differences in columns (σ N ) versus the reference error σ ref (see Sect. 2.4), bias b, and correlation coefficient ξ . Table 2 shows that the CH 4 columns were well reproduced for TROPOMI-like settings. The average scatter of retrieved columns increased only from 0.18 to 0.24 % at Darwin, and from 0.26 to 0.28 % at Park Falls. Neither the standard deviation nor the correlation changed significantly when the original spectral resolution was assumed. The difference between the values derived from TROPOMI-like settings and the reference values from spectral windows 2 and 3 was not significant except for the two outliers in summer 2005 at Park Falls (Fig. 3). The error bars assigned to these values by the GFIT algorithm are also three times larger than the average value. The positive bias of roughly 1 % at both sites thus is the only evidence for spectroscopy-related errors affecting the CH 4 columns. This bias increased for the lower spectral resolution, which is consistent with interference errors due to inaccurate CH 4 or H 2 O spectroscopy. The spectral fit residuals increased from ∼30 at the 6000 cm −1 range to ∼100, but they cannot be directly related to a column error. To see if H 2 O interference errors could account for the 1 % bias, we investigated the dependence of the CH 4 retrieval errors on the H 2 O abundance. Figure 8, upper panel, shows CH 4 retrieval errors against H 2 O dry air mole fraction (DMF) at Darwin, the air-mass being between 1.2 and 1.4 for all observations. The dashed line is the linear regression (correlation coefficient = 0.22), the dotted lines show the 1-σ uncertainty level of the slope. The slope is not significantly larger than zero at a 2-σ level and it increases only from 0.9 to 1.1 % for the range of observed H 2 O DMF. This may be enough to account for the increase of the bias for the lower spectral  resolution, but both effects are on the order of the reference retrieval accuracy.

CH 4 retrieval accuracy
Since there are no plans to retrieve O 2 from TROPOMI spectra, the surface pressure was treated as a fixed parameter in the inversion method up to this point. The TCCON spectra cover several strong O 2 absorption regions and can thus also be used to derive total O 2 columns and -if one assumes a constant atmospheric oxygen ratio -a surface pressure. To study the pressure-dependence of the spectroscopic line lists, we chose a different approach to avoid an assessment of O 2 spectroscopy. Instead of retrieving surface pressure and trace gas species separately, our inversion algorithm also allows for a simultaneous retrieval. For such a retrieval, the observation windows need not include O 2 absorption lines, since the line shape of any absorber depends on pressure. At each iteration step, then, the total dry air column is optimised with respect to the cross-sections of all retrieved molecules. When we retrieved the surface pressure from the CH 4 and H 2 O absorption features in the 5996-6145 cm −1 range, the dry air columns agreed with the in-situ measurements within 2 %. The same approach resulted in errors larger than 10 % when we chose the 4190-4340 cm −1 range. The difference in retrieved CH 4 columns were smaller (0.3 to 0.8 %), but still significant. Figure 4 shows the relative differences of retrieved dry air columns versus the value measured at the Park Falls site. Results from windows 2 and 3 (circles) are compared to the column errors from the TROPOMI spectral range (crosses). The dry air columns derived from the ECMWF pressure profile, which serve as our default, agree with the measured dry air columns within 0.1 % standard deviation (black curve in Fig. 4).
The failure to retrieve surface pressure from the SWIR band was probably caused by inaccurate pressure-broadening parameters of the CH 4 and H 2 O line lists. As long as the pressure was kept fixed, these shortcomings manifested themselves primarily in the spectral fit residuals (see Fig. 5). If, however, the surface pressure was treated as a free parameter, the inversion routine optimised for a pressure which compensated for inaccurately predicted absorption line shapes. This resulted in values as far as 10 % away from the true surface pressure (see Fig. 4). CH 4 and H 2 O were found to yield a comparable pressure over-estimation when only one of them was retrieved. The only region exempt from these problems was the 4318-4328 cm −1 region where strong CH 4 and H 2 O absorption bands are absent (see Fig. 1). For the CH 4 absorption bands in the 5996-6145 cm −1 , the pressure retrieval yielded accurate results. The CH 4 HITRAN08 database for this range relies on the line list published by Frankenberg et al. (2008) who focused on pressure-broadening effects.
We also inverted 45 spectra from one single observation day at Park Falls to check for air-mass dependent errors. Up  to SZA ≈65 degrees, no systematic influence of air-mass was found for CH 4 , nor for CO columns. For larger SZA, the discrepancies caused by different averaging kernels increased to the extent to which they masked any potential spectroscopyrelated errors.

CO retrieval accuracy
In contrast to CH 4 and H 2 O, the CO absorption maxima are relatively sharp and well separated from each other. Nonetheless, inversion of CO in the SWIR is non-trivial because the CO signature has to be separated from the much stronger background of CH 4 and H 2 O absorption. If possible, we would like to retrieve all three species at the same time, using the entire spectral range of 4190-4340 cm −1 . This approach worked reasonably well for CH 4 . Figure 6 shows the time-series of retrieved CO (upper panel) and the relative differences of CO columns retrieved at the TROPOMI resolution compared to window 5 at the original resolution (lower panel). The two biases were added  as dashed lines in the lower panel. Table 3 lists the corresponding fit diagnostics. The CO retrieval accuracy obviously deteriorated for TROPOMI-like settings. First, the bias b increased from a few to roughly ten percent. Second, the standard deviation of the retrieved CO column error, σ N , increased by a factor of two to three compared to the reference uncertainty. The increase of bias and standard deviation was more pronounced at Darwin than at Park Falls. An explanation might be that the average H 2 O abundance at Darwin was two times higher. We will examine this conjecture in the following. The impact of CH 4 spectroscopic errors on CO retrievals is hard to identify because the atmospheric CH 4 abundance varies little compared to H 2 O. We fitted H 2 O and HDO as interfering absorbers while retrieving the CH 4 and CO columns. Figure 7 compares the H 2 O columns retrieved from the TROPOMI range to the columns retrieved from window 4 (around 6200 cm −1 ). The upper panel shows the time-series; the lower panel shows the relative differences to the reference results from window 4   We first replaced our default line list with the HITRAN08 line list to test how sensitively the CO retrieval results reacted to the H 2 O spectroscopy. The spectral fit residuals increased by a factor of 2.2 and the H 2 O columns were equally biased, whereas the bias of the CO columns changed from 14.8 to 6.7 % at Darwin, and from 4.6 to 1.1 % at Park Falls. On the other hand, the standard deviation of column errors did not decrease significantly.
The CO bias would be of little consequence for the S5P mission if it were constant for all observation sites and atmospheric conditions. A further examination revealed, however, that it strongly depended on the H 2 O vapour content. This dependence would introduce undesired seasonal and latitudinal biases for the S5P mission. Figure 8 demonstrates for the Darwin observations the extent to which the CO and CH 4 retrieval errors increased with H 2 O abundance. In the lower panel, the CO retrieval errors for the nominal TROPOMI range and for an optimised sub-window (see In this study, spectroscopic errors are primarily characterised by their impact on retrieved columns. Spectral fit residuals allow us to track down inaccurate absorption lines but do not directly relate to a column inversion error. We correlated the spectral fit residuals to the molecular absorption spectra by calculating Spearman's rank-order correlation coefficient (Press et al., 1986). The correlation with the H 2 O absorption spectrum was significant (significance >10 σ ) for all measurements. The actual correlation strength increased with atmospheric H 2 O abundance. For dry atmospheric conditions (H 2 O DMF < 0.1 %), the correlation with the CH 4 absorption lines dominated over the H 2 O correlation, whereas it became non-significant for wet atmospheric conditions. Figure 5, upper panel, shows a part of the fit residuals for an observation at Darwin with H 2 O DMF = 1 %. The cross-sections of H 2 O and CH 4 , evaluated at p = 1000 hPa and T = 296 K, are shown as blue and black lines. The residuals peak to the immediate left and right of the absorption maxima of H 2 O, whereas the line centres seem to be correct. Inadequate pressure broadening parameters of the strong H 2 O absorption lines are an obvious interpretation for this deficiency (see the results on pressure retrievals in Sect. 3.1), but other effects, such as line mixing, probably also contributed to the residuals. There were also fit residuals peaking around CH 4 absorption lines (the lower panel in Fig. 5 shows a Park Falls spectrum for a dry Winter day) but these fit residuals were much more variable in shape and size than their H 2 O counterparts.
For the CO retrievals, the 15 % threshold accuracy (Vidot et al., 2012) was met for all 100 examined spectra, but this would be the full error budget for the S5P mission. Moreover, the retrieval errors varied systematically with H 2 O and additional errors due to scattering processes of aerosols and clouds are to be expected for a TROPOMI observation geometry. An improvement of the CO retrieval accuracy is therefore necessary.

Measures to improve on CO retrieval accuracy
The performance of the CO inversion at TROPOMI resolution is limited by the strong overlapping of the CO with neighbouring CH 4 and H 2 O lines, both of which have systematic errors (Fig. 5). Sussmann and Borsdorff (2007) reported that the H 2 O interference errors on CO in the 2050-2160 cm −1 range were reduced when they retrieved an H 2 O profile instead of a scalar value. We experimented with a similar approach for the TROPOMI range, but we did not achieve a notable decrease in CO column error. One reason might be that we relied on an H 2 O prior profile already close to the optimum profile.
Another means to reduce interference errors is to restrict the retrieval to a sub-window where the CO absorption lines are more pronounced relative to the CH 4 and H 2 O lines. The main drawback of this approach is the loss of information, making the inversion potentially more vulnerable to instrumental effects. For the inversion of back-scattered sunlight, we also have to keep in mind that those parts of the spectrum without CO absorption lines may be needed to retrieve information on scattering particles (Vidot et al., 2012). We defined an overlapping function ω in terms of the spectral sensitivity as (4) From Eq. 4 we optimised the CO sub-window by choosing wave number limits k 0 , k 1 such that k 1 k=k 0 k 1 − k 0 ω(k) became maximal. This criterion led to an optimised range of 4231.3-4302.6 cm −1 if one contiguous spectral range was to be used. Replacing the nominal TROPOMI range by this sub-window reduced the dependency of the CO retrieval errors with humidity. This is illustrated in Fig. 8, where the retrieval results from the CO sub-window (circles) are compared to the nominal retrieval results (crosses). The bias of the CO columns decreased by 3 to 5 % for both observation sites, and σ N decreased from 4.8 % to 3.9 % at Darwin and from 3.3 % to 2.7 % at Park Falls.

Conclusions
The current H 2 O spectroscopy affected, due to interference errors, the CO retrieval accuracy at 4190-4340 cm −1 when the TROPOMI resolution was assumed. For wet conditions, the retrieved CO columns deviated by almost 15 % from the result at high spectral resolution. This error correlated with H 2 O content in the atmosphere. Because the atmospheric H 2 O abundance is highly variable, this would lead to seasonal and latitudinal biases of CO columns for the S5P mission. The CO bias reacted also very sensitively to a different H 2 O line list. No shortcomings of the CO spectroscopy itself were detected. The impact of inaccurate CH 4 spectroscopy on CO retrieval errors could not be quantified because of the small variations of atmospheric CH 4 . We presented a way to mitigate the impact of interference errors from H 2 O and CH 4 by reducing the retrieval window, but a further improvement on H 2 O and CH 4 spectroscopy is required for the S5P mission. The loss of information due to a reduced spectral range may pose a problem to the inversion of back-scattered sunlight, for which also scattering properties of the atmosphere need to be retrieved.
For CH 4 column errors, no strong correlation with H 2 O abundance was found. The combined H 2 O and CH 4 spectroscopy errors caused CH 4 retrieval errors consisting of a constant bias of about 1 % and a standard deviation of about 0.3 %. This is better than the threshold accuracy requirement of 1 % for the S5P mission. Spectroscopy-related errors also manifested themselves in an increase of spectral fit residuals when we compared the TROPOMI spectral range to the 6000 cm −1 . This can be caused both by H 2 O and by CH 4 spectroscopy. We caution that the intrinsic retrieval accuracy of CH 4 from TCCON spectra is a few tenths of a percent. This means we can only identify spectroscopic deficiencies that result in column errors with the same order of magnitude as the intended accuracy for the S5P mission. For CO, the reference accuracy is an order of magnitude better than the S5P requirement.
Both H 2 O and CH 4 showed an incorrect pressuredependence at 4190-4340 cm −1 . This implies that not only the H 2 O but also the CH 4 line list is less accurate at the TROPOMI range than around 6000 cm −1 . For atmospheric inversion this shortcoming would become important if the surface pressure was to be retrieved from the spectra. Currently, we do not intend such a pressure retrieval for TROPOMI spectra. To improve on the general accuracy of spectroscopic databases, we recommend a similar effort to be directed at the pressure broadening and pressure shift of absorption lines as done by Frankenberg et al. (2008) for CH 4 at 5860-6185 cm −1 .