TROPESS data processing (Bowman, 2021) produces retrievals of temperature, water vapor, and trace gases such as ozone (O3), methane (CH4), carbon monoxide (CO), ammonia (NH3), and peroxyacetyl nitrate (PAN) from single and multiple instruments including AIRS and OMI as well as CrIS and TROPOMI. The MUSES retrieval algorithm used in TROPESS was developed with heritage from Aura/TES retrieval processing. Bowman et al. (2021) describe the sequential MUSES retrievals of temperature, water vapor, and effective cloud properties for each FOV that are necessary for the retrieval of CO. Each step in the sequence includes an iterative retrieval with a forward model and updated estimate of the state vector of atmospheric parameters following the maximum a posteriori (MAP) method. The forward model for radiative transfer at CrIS TIR wavelengths uses optimal spectral sampling (OSS, Moncet et al., 2015), which includes effective cloud optical depth and height parameters (Eldering et al., 2008; Kulawik et al., 2006).

Here we analyze TROPESS/CrIS TIR-only CO retrievals that use the 2181–2200 cm-1 spectral range. A priori profiles for TROPESS CO retrievals are taken from the model climatology used in Aura/TES processing (MOZART, Brasseur et al., 1998), with monthly variation over a 30∘ latitude and 60∘ longitude grid. The a priori uncertainty covariance matrix used to constrain the retrieval is the same as used for MOPITT profiles (Deeter et al., 2010) with 30 % uncertainty for vertical CO parameters at all levels and correlation lengths corresponding to 100 hPa between them in the troposphere.

The TROPESS CO products have quality flags for screening cases that did not converge or that have unphysical results. This screening checks the magnitude and spectral structure of radiance residuals, cloud retrieval characteristics, and deviation of surface emissivity from a priori values. Specifically, retrievals with good data quality of 1 have radiance residual standard deviation less than 12 times the radiance error, an absolute value of the radiance residual mean less than 0.7 times the radiance error, KdotDL (the normalized dot product of the Jacobians and the radiance residual) less than 0.8, LdotDL (the normalized dot product of the radiance and the residual) less than 0.6, cloud-top pressures below 90 hPa, mean cloud optical depths less than 50, cloud variability (variation with respect to wavenumber) less than 3, and mean surface emissivity that did not change by more than 0.06. These threshold values are based on comparisons with in situ data and other satellite data to determine when retrievals are valid.

Figure 1 shows an example of TROPESS/CrIS CO data for 12 September 2020 when there were significant fires in the western US. These retrievals are from a special data collection that processed scenes selected from 0.25∘×0.25∘ latitude–longitude subsampling to enable throughput with the available computing capacity (Bowman et al., 2021). The data in this collection are pre-filtered for quality (see Sect. 2.1), and Fig. 1a shows all available day and night retrievals. Figure 1b shows the data after higher cloudy scenes are removed (i.e., cloud tops with pressure <700 hPa and cloud effective optical depth >0.1). For reference, Fig. 1c shows the mid-tropospheric average CO volume mixing ratio (VMR) for the a priori profiles used in the retrievals, and Fig. 1d shows a NASA Worldview (https://worldview.earthdata.nasa.gov/, last access: 14 September 2022) image from SNPP/VIIRS (Visible Infrared Imaging Radiometer Suite) with clouds and smoke shown in true color and red areas indicating fire and thermal anomalies. Since vertical profile retrievals using TIR radiances have sensitivity to CO mainly in the free troposphere, Fig. 1 shows individual retrievals with average VMR from vertical layers between 700 and 350 hPa. When all scenes are included, the average number of degrees of freedom for signal (DFS) is 0.99 for the CrIS CO observations in Fig. 1a, and when cloudy scenes are removed (Fig. 1b) the average DFS is 1.14 for the remaining CrIS observations.

As stated in the Introduction, the TROPESS single-FOV products are different from the NUCAPS and CLIMCAPS products that combine nine FOVs in a retrieval from a single cloud-cleared radiance (Susskind et al., 2003). These multiple-FOV products have the advantage of increased global coverage in the presence of partially cloudy scenes but with coarser spatial resolution. Figure 2 shows an example of SNPP CLIMCAPS (Barnet, 2019) compared to SNPP TROPESS/CrIS CO products (daytime only) on 13 September 2018 over the Pole Creek fire in Utah. For CLIMCAPS, trace gas products with less than 1 DFS report mass mixing ratio (MMR) on a single level at the retrieval pressure with peak sensitivity, which is 500 hPa for CO. We converted MMR to VMR for Fig. 2. This is compared to the tropospheric column average VMR from TROPESS, so the background VMR values are close but do not represent the same retrieved quantities. CrIS retrieval center locations are shown by the circles in Fig. 2a and b, which are not intended to represent the spatial extent of the observations. The CLIMCAPS retrievals show elevated CO from the fire, but these combined FOV retrievals would give an overestimate of the plume width and do not distinguish the larger plume from the smaller fires to the east in Colorado.

We note that retrievals of CO in the presence of smoke are not significantly affected by scattering for infrared observations at wavelengths λ ∼4.6 µm, such as in the CrIS CO band. This is because Rayleigh scattering, which decreases by 1/λ4, is completely negligible and Mie scattering would be significant only for particles larger than ∼λ/π=1.5 µm, (e.g., Seinfeld and Pandis, 1998), while the size distribution for biomass burning smoke particles peaks around 0.3 µm (e.g., Reid et al., 2005). For the same Pole Creek fire in Fig. 2, Juncosa Calahorrano et al. (2021) showed how SNPP/CrIS single-pixel MUSES retrievals of acyl peroxy nitrates, also known as PAN, along with CO, can be used to follow fire plume chemical evolution. After subtracting background amounts, the normalized excess mixing ratios (NEMRs) of PAN with respect to CO, computed from the CrIS observations for this plume, were consistent with in situ aircraft observations of smoke plumes from the summer 2018 WE-CAN (Western Wildfire Experiment for Cloud Chemistry, Aerosol Absorption, and Nitrogen) campaign.

Spanning 3 decades, NOAA GML aircraft network vertical profile observations are taken on semi-regular flights (approximately one per month) at fixed sites mostly in North America except for one site in Rarotonga, Cook Islands (Sweeney et al., 2015). These flights collect air samples using an automated flask system to obtain vertical profiles for each trace gas measured from near the surface to around 400 hPa, depending on aircraft limitations at each site. Flask samples are then sent for laboratory analysis of a multitude of trace gases including CO, which was measured with vacuum UV–fluorescence spectroscopy during the time period of this analysis. CO mixing ratios are reported relative to the WMO X2014A scale (https://gml.noaa.gov/ccl/co_scale.html, last access: 14 September 2022) and have reproducibility ∼1 ppb (Sweeney et al., 2015). NOAA GML aircraft profiles of CO have been used for the long-term validation of the MOPITT CO record, with updated validation for each new data version (Deeter et al., 2019, and references therein). For the current analysis, we use NOAA GML aircraft network observations of CO collected during 2016 and 2017 from seven locations (Table 1).

The Atmospheric Tomography Mission (ATom) was designed to study air masses in the most remote regions of the Pacific and Atlantic Ocean in each season (Thompson et al., 2022), which also makes the data valuable for validating satellite CO observations over a range of latitudes, with mostly background CO concentrations, except for where transported pollution plumes were encountered (Deeter et al., 2019, 2022; Martínez-Alonso et al., 2020; Hegarty et al., 2022). We use CO profiles from the quantum cascade laser spectrometer (QCLS) on ATom campaigns 1–4 (see Table 1). These NASA DC-8 flights obtained vertical profiles from 0.2 to 12 km altitude (∼290 hPa) by ascending or descending approximately every 220 km. CO was measured at 1 Hz with QCLS reproducibility around 0.15 ppbv (McManus et al., 2010; Santoni et al., 2014). The QCLS data were calibrated to the X2014A CO WMO scale maintained by the NOAA GML.

TROPESS/CrIS CO profiles are selected for comparison if they have retrieval quality of 1 and effective cloud optical depth less than 0.1 to ensure non-cloudy CrIS observations. We then find all eligible CrIS and aircraft profile pairs within 9 h and 50 km distance. This has been a standard coincidence distance criterion for several validation studies (e.g., Deeter et al., 2019, 2022; Hegarty et al., 2022). Tang et al. (2020) found very little sensitivity in MOPITT CO validation results for 25, 50, 100, and 200 km coincidence except for the cases with a 25 km radius that resulted in an insufficient number of matches for meaningful statistics. The Tang et al. (2020) study also tested the time coincidence criterion (12, 6, 2, and 1 h) with similar conclusions. Application of the 9 h–50 km coincidence criteria yielded 2092 CrIS–aircraft profile pairs for NOAA GML flights from 2016 and 2017 and 1052 profile pairs for the ATom 1–4 campaigns. Since the aircraft profiles used for validation do not span the full vertical range of satellite-retrieved profiles, we must extend these with a reasonable approximation of atmospheric CO to facilitate the comparison as described below in Sect. 4.2. Here we use the TROPESS a priori profiles (from model climatology, described above) to extend the in situ profiles above the highest altitude sampled. The a priori profile is scaled to match the CO abundance of the aircraft measurement at the highest altitude. The choices of model and approach for extending the aircraft profiles are examined more in Tang et al. (2020) and Hegarty et al. (2022), with similar conclusions that the impacts apply mostly to bias estimates in the middle to upper troposphere. Martìnez-Alonso et al. (2022) compute the uncertainty introduced by this extension explicitly using NOAA AirCore in situ balloon profiles that sample into the stratosphere (Karion et al., 2010). This uncertainty is computed for validation using aircraft profiles (with top samples around 400 hPa for NOAA/GML) by comparing MOPITT profiles to truncated and extended AirCore profiles vs. the true full AirCore profiles. The comparison error introduced by the extension was at most 3 % around 300 hPa and much less than the standard deviation of MOPITT and full AirCore profile differences (∼7%–10 %) in the upper troposphere. We also note that for ATom profiles, the highest-altitude samples are normally taken around 12 km (∼200 hPa), and the profile extension therefore has a minimal impact on tropospheric validation results.

In order to account for the satellite observational and retrieval approach, including prior information, when comparing satellite retrieval products to in situ measurements of CO, we apply the instrument operator to convert the in situ profile into the values that would be retrieved for the same air mass assuming the satellite instrument and retrieval (Jones et al., 2003, Rodgers and Conner, 2003, Worden et al., 2007): 1x^val=xa+A(xval-xa), where xval is the aircraft or sonde in situ profile being used for validation (following extension, described above, and linear interpolation to the satellite vertical grid), xa is the a priori profile used in the TROPESS retrieval, A is the averaging kernel matrix that describes the observation and retrieval vertical sensitivity to the true state, and x^val is the in situ validation profile transformed by the satellite instrument operator. This operation accounts for both the broad vertical resolution (or “smoothing”) of remotely sensed measurements and the influence of the a priori, which is especially important in the vertical ranges where satellite observations have low sensitivity to CO abundance. Figure 3 shows an example of the averaging kernel A and a validation comparison with Eq. (1) applied to an ATom in situ profile.

Following Bowman et al. (2006, 2021), for retrieved parameter x^ (e.g., CO abundance) with a priori covariance Sa, radiance measurement covariance Se, Jacobian matrix K=∂L∂x, radiance L(x), gain matrix G=KTSe-1K+Sa-1-1KTSe-1, and averaging kernel A=GK, the a posteriori error covariance can be written as the sum of 2Sx^=Ssmoothing+Sobservational, with Ssmoothing=I-AxxSaI-AxxT and 3Sobservational=Snoise+Scross-state+Ssystematic, where Snoise=GSeGT, Scross-state=∑b_retAxsSab_retAxsT, and 4Ssystematic=∑bGKbSbGKbT. In this notation, b variables are parameters that are held constant in the CO retrieval (such as temperature and water vapor) but affect the radiance observation and are propagated through Jacobian Kb, while b_ret variables are retrieved along with CO (such as surface emissivity) and have corresponding off-diagonal terms in the full retrieval averaging kernel matrix. When we apply the satellite instrument operator in Eq. (1) to the in situ aircraft profile, we are accounting for the smoothing error term. Thus, we expect differences between x^val and our retrieved x^ to be due to observational error terms (Eq. 3) and to geophysical differences from the sampling of different air masses and surface locations because of imperfect coincidence.

After extending the in situ profiles vertically (described in Sect. 4.1) and applying Eq. (1), we compute the differences between satellite retrievals and transformed aircraft profiles. Figure 4 shows the bias (% relative difference) of the CrIS CO retrieved profiles with respect to NOAA GML aircraft profiles (x^val). A similar pattern of positive bias in the lower to middle troposphere and negative bias in the upper troposphere is observed for MUSES/AIRS profiles compared to NOAA GML flights (Hegarty et al., 2022). However, MOPITT (version 9, TIR-only data) comparisons to NOAA GML (Deeter et al., 2022) have almost the opposite vertical bias pattern with a negative bias (-1.6 %) in the lower to middle troposphere and a positive bias (0.6 %) in the upper troposphere. Since TROPESS and MOPITT retrievals both use optimal estimation algorithms and a similar prior CO error covariance, this different vertical bias pattern is most likely due to instrument differences. MOPITT uses gas filter correlation radiometry instead of spectroscopy to detect CO absorption in the atmosphere with corresponding differences in vertical sensitivity that are determined from gas cell pressure rather than spectral resolution. After accounting for retrieval differences in a priori profiles and covariances between MOPITT and IASI (another FTS instrument), George et al. (2015) find a similar positive bias for MOPITT in the upper troposphere.

Table 2 gives the mean bias and standard deviations for selected pressures and partial column average VMRs over different observing conditions (land, ocean, day, and night). The partial column refers to the CO column between the minimum and maximum flight altitudes of each aircraft profile. The average VMR over this range is computed by interpolating both the CrIS retrieval and the aircraft x^val profile to these end points. Since aircraft flights normally occur during daytime, there are fewer coincident pairs for CrIS night retrievals. Tang et al. (2020) find larger bias and variance for nighttime MOPITT data in comparisons with in situ aircraft data, especially for flights over urban regions, suggesting that more night validation flights are needed to properly evaluate night satellite retrievals.

Figure 5 shows how the observed partial column average VMRs and CrIS retrieval bias with respect to NOAA GML x^val profiles vary with latitude, and Fig. 6 shows how these vary with time. No significant bias dependence on latitude is observed for the NOAA GML flight sites. Although a bias drift of -0.007±0.001 % d-1 is detected, we recognize that our comparison time range is not sufficient for a reliable estimate of bias drift, and more years of comparisons would be required.

Figure 7 shows the bias (% relative difference) of the CrIS CO retrieved profiles with respect to ATom x^val in situ profiles for all latitudes and three latitude ranges: 30∘ S to 30∘ N, 90 to 30∘ S, and 30 to 90∘ N. The vertical behavior of the bias is similar to the above CrIS comparisons with NOAA GML flights, with a positive bias in the lower troposphere and a negative bias in the upper troposphere, and is also similar to the MUSES/AIRS CO profiles compared to ATom flights (Hegarty et al., 2022). However, for MOPITT V9T comparisons to ATom flights (Deeter et al., 2022), the vertical bias pattern is again mostly opposite, with a negative bias (∼4 %) in the lower to middle troposphere and a positive bias (∼2 %) in the upper troposphere. This TROPESS/CrIS CO bias also differs from Nalli et al. (2020), who examined the bias of NUCAPS profiles (including CO) with respect to ATom in situ profiles. That study, using the multiple-FOV NUCAPS retrievals, found a small positive bias (∼2 %) for SNPP/CrIS CO with respect to ATom CO at all tropospheric vertical levels after applying their averaging kernels.

CrIS CO comparisons with ATom have less variance than comparisons with NOAA GML, especially for 90 to 30∘ S. Table 3 gives the mean bias and standard deviations for selected pressures and partial column average VMRs over different observing conditions (land, ocean, day, and night) and latitude ranges. As described above, the partial column average VMR is computed over the altitude ranges of each aircraft profile. Due to the nature of the ATom campaign, there are fewer observations over land.

Figure 8 shows how the observed partial column average VMRs and CrIS retrieval bias with respect to ATom x^val profiles vary with latitude. It appears that tropical and Northern Hemisphere subtropical latitude ranges have a slightly higher positive bias than what is observed for higher latitudes, potentially indicating a TROPESS/CrIS retrieval issue with water vapor or some other interferent that is not fully characterized and requires further investigation. For example, Deeter et al. (2018) found that an empirical correction to MOPITT radiances resulting from a linear dependence on water vapor removed most of the latitude-dependent bias in MOPITT CO profiles. Another gas interferent in the TIR CO band is N2O, and we will also need to consider the latitude-dependent N2O anomalies observed by ATom (Gonzalez et al., 2021) when assessing the contributions to this latitude dependence in TROPESS/CrIS CO bias.

In Fig. 9, we examine the seasonal behavior of CO sampled by ATom and CrIS in mostly remote ocean regions. In the high-latitude Southern Hemisphere (SH), we see the lowest values in summer and fall (Jan–Feb and Apr–May) as expected due to the chemical destruction of CO in a region with few local combustion sources. In the tropics, we find high values corresponding to African and South American biomass burning plumes over the Atlantic in all seasons except Northern Hemisphere (NH) spring. Lower values of CO in the tropics for NH summer and winter correspond to profiles over the Pacific Ocean (e.g., Strode et al., 2018; Bourgeois et al., 2020). The close alignment of the CrIS and ATom x^val partial column average values in Fig. 9 indicates that CrIS is able to capture the seasonal, latitudinal, and hemispherical variations observed by ATom.

For both the NOAA GML and ATom flights we find a small negative dependence of TROPESS/CrIS retrieval bias with respect to CO amount, with magnitude less than 0.1 % ppb-1. Figure 10 shows how the partial column average VMR bias varies with CO VMR for the two validation data sources, and we can also see how ATom flights sampled air with lower CO concentrations. Figure 10 indicates that TROPESS/CrIS CO average column VMRs have very little dependence on CO amount, and we find similar results for CrIS-retrieved CO at vertical levels 511 and 750 hPa (shown in the Supplement).

Here we compare the observed variance of differences between retrieved CrIS CO profiles and in situ aircraft profiles, after applying Eq. (1), with the TROPESS reported observational errors defined in Eqs. (3) and (4). As described in Sect. 4.3, we expect the differences between retrieved CrIS and aircraft CO profiles (x^val) to have a variance due to the combination of observational errors and geophysical variation from imperfect coincidence. Figure 11 shows comparisons of individual and average computed observational fractional errors to the standard deviation (SD) of CrIS–x^val profile differences as well as the diagonal for the a priori covariance and the SD of prior–x^val profile differences. As expected, the average observational errors are less than SD(CrIS–x^val), but in some vertical ranges, they are much less and could be underestimated via instrument and systematic error assumptions in the TROPESS retrieval as Hegarty et al. (2022) suggest. Additional studies to test the sensitivity of the comparison variance to a range of coincidence criteria are needed to confirm a retrieval underestimate, but these would require several repeated validation measurements for the same observing conditions.

Despite the potential for underestimated observational errors, the general behavior of the error comparison is what we expect from Eq. (1), and we can see the retrieval influence on the shape of SD(CrIS–x^val). Near the surface, where there is less retrieval sensitivity as indicated by the averaging kernel, we see that SD(prior–x^val) becomes smaller than SD(CrIS–x^val). This is expected for vertical ranges with less retrieval sensitivity since the priori contribution becomes more dominant in x^val. In contrast, for the middle troposphere where we have the most sensitivity for TIR remote sensing, it is clear that SD (CrIS – x^val) represents an improvement over SD (prior–x^val). In Fig. 12, the error comparison is shown separately for three ATom latitude ranges, and we can see that the agreement between observational errors and SD (CrIS–x^val) is closest for ATom flights in the mostly clean middle- to high-latitude Southern Hemisphere, where it is most likely that the aircraft and satellite are observing similar air masses with background CO concentrations. These results give confidence that TROPESS single-retrieval error characterization can be used to weight data for averaging and inverse analysis applications.