During the characterization and calibration of the OCO-2 flight instrument at the JPL, a heliostat was used to direct sunlight onto a diffuser that was viewed by the flight instrument through a window in the TVAC chamber. Simultaneously, a TCCON instrument located at the same altitude about 200 m away recorded high-resolution solar spectra through essentially the same atmospheric column. The FTS spectra were acquired at an unapodized resolution of 0.013 cm-1 (45 cm optical path difference), which is approximately 20 times higher than the spectral resolution of the OCO-2 instrument. In addition, the FTS spectra had high SNR and were characterized by a single, well-determined ILS for the entire spectral range . Apart from the spectral resolution, there are a few other differences between the two measurements. First, the integration time of the OCO-2 instrument was 0.333 s (a continuous 3 Hz measurement) while the FTS required 79 s to complete a scan. Second, the OCO-2 instrument had a larger field of view (FOV) than the FTS, observing the full solar disk and some of the surrounding sky, while the FTS observed the center of the solar disk. The solar lines observed by OCO-2 were therefore broadened relative to those observed by the FTS due to Doppler shifts caused by the sun's rotation. For this reason, solar line pixels in the FTS fits were excluded in the following analysis, as we aimed at using exactly the same retrieval setup as for the OCO-2 fits.

For the spectral fits, we performed total column retrievals of trace gases for each band (O2A, WCO2, SCO2) independently. For this purpose, we used the fast IMAP-DOAS preprocessor in a special up-looking retrieval mode using a single temperature and pressure a priori profile for the entire day, which was extracted from the National Centers for Environmental Prediction (NCEP) data, but replacing the surface pressure with the one locally measured at JPL. In this up-looking mode, the IMAP-DOAS algorithm merely fits spectral dispersion, solar shift and continuum baseline as a third-order polynomial, as well as a total column scaling of a pre-defined O2, H2O and CO2 profile shape. Neither surface pressure nor a temperature scaling was retrieved.

In the following, we will show spectral fits for a low (1.1), typical (2.5) and high (5.1) air mass factor (AMF) in blue, red and black, respectively. The “typical” AMF will be very close to the lower end of AMFs encountered during flight, as the AMF in perfect nadir viewing simplifies to 1 + 1 / cos(SZA) with SZA denoting the solar zenith angle, and the instrument is required to return data at solar zenith angles between ∼ 21.5 and 85∘. To compare the OCO-2 spectral fit results (i.e., trace gas columns and fit residuals) to a high-quality reference, we used collocated FTS spectra and convolved them with the OCO-2 ILS, and performed fits on those spectra using exactly the same fitting routines as for the OCO-2 data. This ensures that differences in the fits are caused neither by differences in spectral resolution nor by specific software setups. Also, convolved spectral residuals of fits to high-resolution (e.g., FTS) data are not equal to residuals of fits to convolved spectra. In addition, solar lines were masked out for the FTS fits since, as noted above, the OCO-2 instrument, in TVAC mode, records full-disk solar spectra while the FTS records narrow FOV disk-centered spectra. In the following, we will display fit residuals in percent, normalized by a representative continuum level radiance, chosen as the maximum signal within each band. For the comparison, we chose OCO-2 and TCCON spectra where the zero-path difference (ZPD) was within a few seconds of the OCO-2 spectra acquisition. For the sake of clarity, we show residuals from only three of the eight footprints. However, we did verify that all footprints behave similarly. For all tests, we used the absorption coefficient (ABSCO) v4.2 spectroscopy database developed for OCO-2 .

Spectral fits to the oxygen A-band are shown in Fig. . The top panels show normalized residuals of the convolved FTS fits, followed by spectral residuals for 3 OCO-2 footprints (footprints 1, 4 and 7). The bottom panel shows normalized radiances for each air mass. At higher air masses, the R-branch from 760 to 762 nm saturates almost entirely even at OCO-2 spectral resolution, with near-zero transmission across 1–2 nm in wavelength range.

In general, fit residuals of the convolved TCCON spectra strongly resemble those of the OCO-2 flight instrument. Given the high SNRs for individual OCO-2 spectra in TVAC mode (600–1200 for all bands), purely noise-driven residuals should be on the order of 0.1–0.2 %. Systematic features appear in both TCCON and OCO-2 residuals with maxima of up to 1 %. Larger deviations in the R-branch are most likely caused by the choice of the a priori temperature and pressure profile. Given that the two instruments show very similar residuals, we conclude that they are still dominated by errors in the ABSCO tables of the O2 A-band absorption cross sections, specifically relating to line mixing, line-shape and collision-induced absorption. This can also be seen in the air mass dependence of systematic residuals. At higher air masses, the far line-wing shape becomes more important as line centers are entirely saturated. The periodic structures in the P branch residuals point to the importance of the line shape as residuals are smaller at lower air mass, at which the far wing line shape becomes less important.

Weak CO2 band (WCO2) fits are shown in Fig. . At OCO-2 spectral resolution this band is not saturated even at high air masses. Most of the information content is thus in the line centers as measured by OCO-2, and the continuum can be isolated much more easily from well-separated CO2 lines. Again, we observe residuals that strongly resemble those from TCCON fits (with many solar features masked), pointing to small remaining errors in CO2 absorption cross sections. There is a strong similarity between footprints but, in general, most features are below 0.5 %, similar to measurements from the GOSAT satellite as well as TCCON. Some residual features, such as the slope at the short-wavelength edge of the fit window, can also be caused by broad spectral variations in the solar spectrum that are not accurately represented here.

SCO2 fits are shown in Fig. . Line centers at OCO-2 resolution now gradually saturate at higher air mass and the continuum level radiances are harder to define than in the other bands because of overlapping line wings. In general, conclusions for this band are similar to the other bands, with spectral residuals roughly resembling the TCCON residuals. The only exception may be at the short-wavelength edge where OCO-2 residuals are somewhat higher, potentially caused by either dispersion or ILS changes at the band edge, where the instrument calibration is less well characterized.

In summary, spectral fits to OCO-2 data yield expected fitting results but, as with all other current instruments measuring this spectral range, systematic residuals still appear. Given the high SNR of the OCO-2 instrument, this would result in unrealistically high χ2 values for spectral fits, which is why we will implement a residual fitting technique based on empirical orthogonal functions derived from systematic features as is currently done for data from GOSAT. Using these basis functions, as additional fit parameters, we expect fit residuals to be mostly noise driven, resulting in realistic χ2 values that will help the fit converge, allow us to use χ2 as quality criteria, and result in more realistic a posteriori uncertainty estimates, as the true OCO-2 measurement noise can be provided to the weighted least squares fit.

To determine whether the variability in spectral residuals can be explained by OCO-2 detector noise, we computed the standard deviation of spectral residuals using 2000 OCO-2 fits and define this as a surrogate for empirically derived noise in the OCO-2 data. Using the mean of the 2000 radiance spectra as signal level surrogate, we then derive a set of SNR points at varying signal levels within a spectrum, mostly caused by CO2 and O2 absorptions. Figure  shows the empirically derived SNR points as well as a typical SNR relationship based on the launch-ready OCO-2 calibration . There is excellent agreement between calibration curves and empirically derived SNR based on spectral fits. The spread of the individual data points for each band is due to the behavior of the detector, with varying gain coefficients and shot noise in each pixel. This is reflected in the OCO-2 launch-ready calibration curves as well but, for clarity, the theoretical SNR curve of just a typical pixel is shown in transparent lines, and corresponds very well with the empirical noise estimates. After accounting for the systematic residual features, expected χ2 distributions of the residuals are thus attained.

Two advantages of the OCO-2 grating spectrometer are its high dynamic range and relatively low noise at low signal levels. This results in much lower noise levels within deep absorption lines of the O2A and the SCO2 bands than would be possible with space-based FTS data, which exhibit a constant absolute noise level across the entire spectrum (which would yield a straight line through the origin in the SNR vs. signal level curve when plotting individual spectral points within a single acquisition).

The OCO-2 spectrometer records spectra separately in the spatial domain of the focal plane array. To increase SNR, photons collected in 20 adjacent spatial rows are averaged to define a footprint, hence the 160 spatial detector rows produce eight spatial footprints (see Fig. ). Given that each footprint spans a considerable fraction of the focal plane array, instrument calibration (most importantly dispersion and ILS) varies from footprint to footprint. With the unprecedented accuracy requirements in the sub 1 % range for atmospheric CO2 measurements, inter-footprint difference in retrieved quantities for imaging spectrometers will cause challenges in using this data.

In Fig. , we show differences between the total column CO2 estimates from each footprint and the all-footprint average, for the weak and strong CO2 bands. Two main features are apparent: (1) there is a very small inter-footprint variation but at least six to seven of the footprints agree to within ±0.5 ppm; (2) the inter-footprint variations are somewhat unstable and appear to be influenced by how the heliostat is illuminating the OCO-2 instrument, as can be seen by some jumps around 16:00, when the heliostat was realigned. In the test setup, the heliostat was not large enough to fill the entire OCO-2 pupil, which can slightly affect the characteristics . This effect, which will not happen in orbit, might change when the heliostat is realigned. Hence, it is not yet clear what fraction of the variation is merely caused by the experimental setup and what is caused by potential small calibration inconsistencies. In orbit, the inter-footprint differences are not expected to vary in time and the variability of ±0.5 ppm can be characterized using in-orbit data and corrected for using constant correction factors. It should be mentioned that the OCO-2 pupil during calibrations using the integrating sphere was fully illuminated.

For the pre-launch OCO-2 calibration, two sets of instrument line shapes were tested , of which one will eventually be implemented for official OCO-2 retrievals. One set is derived from tunable diode laser measurements and a second, enhanced set (see ) using direct comparisons against the high-resolution FTS spectra, where the ILS was optimized to best match the FTS data. In Fig. , the inter-footprint variations averaged over a longer time-period are shown independently for the FTS enhanced ILS (solid lines) and the original laser-based ILS (dashed lines). The impact is not large and mostly affects footprint #1, at the edge of the FOV. For this particular footprint, both CO2 bands would behave somewhat abnormally but deviate in opposing directions (positive or negative). This could have implications for a joint three-band retrieval. The enhanced ILS largely mitigates this problem to the best possible degree. Once OCO-2 is collecting in-orbit data, both ILS models will be evaluated in order to decide whether the FTS-enhanced ILS mitigated only an issue associated with the TVAC test setup or a real calibration issue. In any case, most footprints agree very well with each other for both choices of ILS and provide confidence, especially given the small fitting residuals discussed earlier. However, even this small footprint dependence will have to be scrutinized since the accuracy requirements of better than 1 ppm are very stringent. This also has implications for future imaging spectrometers with hundreds of spatial pixels, for which a careful per-footprint calibration as for OCO-2 might not be feasible.

The OCO-2 retrieval strategy imposes stringent requirements on knowledge about the detector linearity and dark current. Any imperfections can slightly modify the fractional depths of absorption lines depending on the detector fill level, which can create regional and/or seasonal biases in retrieved XCO2. For OCO, the so-called “Matador test” was devised to detect any apparent non-linearities or dark offsets .

The general TVAC setup was used with direct sunlight illuminating a diffuser viewed by the OCO-2 spectrometers via a series of mirrors. For the Matador test, special sheets with varying transmission were optionally inserted into the optical path. To create a spectrally uniform reduction in the solar intensity, aluminum sheets with small holes were fabricated with different hole-densities in a hexagonally packed pattern to create effective transmissions of approximately 75, 50, 25 and 10 %. For the test, the sheets were rapidly (and manually) inserted into and removed from the heliostat optical path, hence the name “Matador test” due to the visual analogy to a matador's cape. The test was performed near local noon on 20 April 2012.

Figure shows results for both CO2 bands and the O2 A-band independently, for each footprint, expressed as deviations in XCO2 or O2 column from the average across all footprints at the initial 100 % transmission level (i.e., before the sheets were inserted). The periods with reduced transmission are indicated with a gray background, as each sheet, in descending order of transmission, was inserted and removed three times.

For the 75, 50 and 25 % transmission levels, changes on the order of much less than 0.5 ppm occur. More importantly, deviations are neither consistent across footprints nor consistent across all three independent Matador tests per transmission level. This behavior hints at subtle changes in how the OCO-2 pupil was illuminated for each of these tests, which can also cause minor variations in the ILS and, hence, XCO2. This is even more obvious at the < 10 % transmission levels, in which jumps in retrieved CO2 are considerably higher but without any consistent pattern across all three independent tests.

For O2 columns, all footprints agree to about 0.05 %, which would translate to better than 0.5 hPa or 0.2 ppm if errors propagate linearly into XCO2. In general, the O2 A-band appeared to be somewhat more consistent than the CO2 bands. It is, however, not clear whether calibration parameters are the cause of the very small variations in the O2 fits or whether these can be merely attributed to the shape of the oxygen absorptions itself, where a lot of information is also coming from the deep Q-R-branch, which is less sensitive to ILS variations as no individual lines are sampled.

As an additional test, we derived radiance ratios of the full illumination level and two separate Matador tests for the 25 % transmission level, as shown in Fig. . No absorption features can be detected in the CO2 band ratios, which confirms an accurate OCO-2 calibration in terms of linearity and dark subtraction. However, the two separate tests exhibit ratios with some broad-band features that differ between tests and might be causing slight changes in XCO2 between tests, potentially due to changes in the pupil illumination. Similarly, there appears to be a small change in the ILS for the O2 A-band, most likely also related to the illumination changes.

In summary, all of the three spectral bands show very good consistency, but achieving a near perfect consistency is currently not possible and small calibration factors for each footprint may need to be included for OCO-2. At this stage, we have gained confidence that the OCO-2 behaves well at variable illumination levels but also that we have obtained the maximum amount of information possible from the TVAC setup. For these pre-launch tests, it is hard to reach the stability in terms of instrument thermal control or illumination that will be achieved in orbit.