The MOPITT instrument aboard the Terra satellite launched in December 1999 has been described elsewhere . Briefly, it is a gas-filter correlation radiometer with eight optical channels, of which three have been used since August 2001 for CO observations, two in the TIR band (channels no. 5 and no. 7; 4.617±0.055 µm), and one in the NIR band (channel no. 6; 2.334±0.011 µm). Each channel produces an “average” (A) and “difference” (D) radiance measurement. A linear detector array in each channel allows MOPITT to make observations at four different sounding locations simultaneously. The ground field of view is approximately 22km×22km for each sounding. Retrievals from among these four “footprints” or pixels were previously shown to have a bias compared to ground-based column measurements from the NDACC Infrared Working Group (IRWG) . A moving mirror scans cross track for 29 “stares” in each direction for a swath that is approximately 650 km wide, and one back-and-forth sweep takes approximately 26 s.

Terra is in a daytime-descending (nighttime-ascending) Sun-synchronous orbit at an altitude of about 700 km, with a local Equator crossing time at around 10:30 LT (22:30 nighttime) and an inclination angle of 98.4∘. Terra makes 14–15 orbits daily, with an exact repeat time of 16 d. However, with its wide swath width, MOPITT is able to achieve near-global coverage every 3–4 d. The redundancies built into the MOPITT mission allowed for continued measurements after a cooler failure in May 2001 eliminated one of the two optical boards and the usefulness of channels 1–4, leaving channels 5–8 . The impact of other early anomalies is minor. No abrupt changes since 2001 are expected to impact the retrievals, with the possible exception of annual hot calibrations, the latest of which being in March 2019 and a separate temporary cooler malfunction in July 2009. Due to the different instrument configuration from the early record, we only include MOPITT data from 2002 to 2017 (inclusive) in this study.

There are different retrieval products corresponding to TIR-only (T) retrievals, NIR-only (N) retrievals, and TIR–NIR (J – joint) retrievals. We chose to make comparisons with the level 2 Version 7 joint (L2, V7J) product because it should theoretically contain the most information. noted that the V6 TIR–NIR product has the greatest vertical resolution but has large retrieval errors and bias drift. The TIR-only product has the highest stability, and the NIR only is best at total column CO retrievals. The MOPITT retrievals are performed on a logarithmic scale due to the large variability in CO in the atmosphere (∼1 order of magnitude). The state vector includes up to 10 vertical layers of log⁡10(VMRCO) (dry volume-mixing ratios), surface temperature, and surface emissivity. Retrievals are performed on a grid of 100 hPa spaced layers up to 100 hPa (e.g., surface–900, 900–800 hPa; ). The top layer retrieved is 100–50 hPa, and above that the prior VMRCO from the model is used due to low sensitivity. The 50–0 hPa layer represents 1.2±0.4% (1σ) of the a priori CO column (1.3 % in SH and 1.0 % in NH). Fractions of CO in this layer compared to the total column are shown in Fig. S1 in the Supplement. The a priori value is from climatological output from the Community Atmosphere Model with Chemistry CAM-chem; and is described by . The a priori covariance matrix is described by . A total column is obtained by a weighted average of the layers, and this can be converted to a column-average dry-air mole fraction (denoted XCO) by dividing by the model total column of dry air included in the MOPITT V7 product that takes into account surface pressure and water content. We focus on only daytime soundings, which are defined as those with a solar zenith angle (SZA) less than 80∘ in the retrieval. In the V7J data product the 100–0 hPa layer is an average of the 100–50 and 50–0 hPa layers, and we use the 100–0 hPa values for our 100–50 hPa layer but use values that are 48 % of this amount for 50–0 hPa based on recommendations of the MOPITT V5 user's guide.

There are a number of previous studies that have compared MOPITT with different observing systems. Because the algorithm has been improved several times since the start of the mission, here we only list validation studies on Versions 6 (released in 2013) and 7 (released in 2016 and used in this study). Recently Version 8 was released (December 2018). Versions prior to 6 are no longer available (https://www2.acom.ucar.edu/mopitt/products, last access: 2 August 2018). noticed a bias between the MOPITT V6J column retrievals and aircraft observations of +4.3 ppb (assuming an average total air column density of 2.1×1025 molec. cm-2, roughly 5 % for a global 80 ppb average). They noted a correlation of r=0.89 between the systems and a drift of only 0.15±0.1 ppb yr-1 (∼0.18±0.12 %). The V6J retrievals had an overall positive bias at the surface and 800 hPa layers, a negative bias at the 600 and 400 hPa layers, and a positive bias again at the 200 hPa layer. The bias, drift, and correlation all depended on which data products were compared. Later, the V6J profiles were compared with aircraft measurements over the Amazon Basin . Limited maximum aircraft altitudes precluded column retrieval comparisons, but noted maximum biases at the 800 hPa of -27 %.

Three studies compared ground-based remote-sensing observations with those from MOPITT . made comparisons between MOPITT V6J L3 and various ground-based remote-sensing sites in Eurasia. There is significant variability in the unadjusted comparisons for different sites in their study, which could be from the influence of averaging kernels , but in general MOPITT observations were larger than ground-based observations. compared MOPITT V6J and IASI (Infrared Atmospheric Sounding Interferometer) satellite observations with ground-based observations in an urban site (Paris), a high-altitude site (Jungfraujoch), and a Southern Hemisphere site (Wollongong). They noted good agreement between space and ground-based observations with slopes of 0.91–0.99, with satellite observations being slightly lower. Recently, compared MOPITT V6 observations with those from 14 different ground-based NDACC sites between 78∘ S and 80∘ N and used data from August 2001 to February 2012 for comparisons with V6T, V6N, and V6J. We focus on their V6J comparison results. They found MOPITT to be generally biased high relative to the NDACC, and 11 sites have a bias less than 10 % over land. The all-station mean bias is 5.1 %, and the average correlation is r‾=0.78. They noted that the surface type (land or water) had little effect on validation statistics. However, they did note that validation results differed among pixels, and pixel 1 has the lowest correlation while pixel 3 has the highest correlation.

is the only systematic global validation study of the MOPITT V7 algorithm. They use aircraft measurements from the HIAPER Pole-to-Pole Observations (HIPPO) campaign and National Oceanic and Atmospheric Administration (NOAA) aircraft flask samples primarily over North America for their validation dataset. They describe the improvements included to create the V7 algorithm. They find that the V7J column observations have a smaller bias and larger r (1.4 ppb and 0.93, respectively) than the V6J product (3.8 ppb and 0.89).

While L1 includes radiance bias corrections, there are no empirical bias corrections to the physics-based retrieval in the L2 V7 MOPITT products. There are retrieval anomaly diagnostics included in the L2 product, but users need to define filters to use for their particular application. For L3, V7J daytime observations where both the signal-to-noise ratio (SNR) of channel no. 5A <1000 and the SNR of channel no. 6A <400 are excluded . All observations from pixel 3 are also excluded due to excessive and unstable noise from NIR measurements from that pixel . In this study suggested filters are developed along with a bias correction.

The TCCON is a global network of independently operated solar-viewing Fourier-transform spectrometers (SV-FTS) operated under a common set of standards. From measurements taken by these spectrometers, retrieved estimates of XCO are made . Because profiles are not a part of the TCCON data product, we focus on validating the MOPITT total columns rather than profiles. Data are quality screened by both individual site operators as well as a centralized team. From sensitivity tests perturbing the algorithm to each known source of uncertainty (e.g., a priori values of VMRs and temperature and surface pressure), GGG2014 XCO systematic errors for TCCON are below 4 % . The uncertainty in the scaling slope is 6 % (2σ).

One of the primary uses of the TCCON data has been satellite validation e.g.,. There are several reasons why TCCON data are considered more accurate than satellite observations and hence a good validation source. (1) Observations are directly pointed at the Sun, which increases the SNR, is insensitive to effects of surface properties, and is insensitive to the effects of both airglow and aerosol scattering e.g.,. (2) Instruments are operated at a resolution of at least 0.02 cm-1, which provides more information for spectral fitting than most satellite measurements. (3) The network was established in 2004 with contributions from many different institutions. This international collaboration has led to many discoveries on how to reduce errors in Xgas retrievals e.g.,.

Despite these advantages, there are known sources of uncertainty that could bias the measurements. For example, to tie this to the World Meteorological Organization (WMO) in situ scale, there is a 7 % scaling factor in GGG2014 for XCO . This factor is considered large compared to the current uncertainty in spectroscopy, and there is an ongoing effort to determine if this factor is appropriate. In this study we use both the official TCCON XCO product as well as a derived product without the empirical scaling factor applied. For a discussion and current comparison of unscaled TCCON data to the WMO scale, see Sect. S2 in the Supplement.

We compare MOPITT with TCCON from mid-2004 to 2017 (inclusive). Prior to 2007 there were only four TCCON sites (Table ). During 2007 and 2008 the TCCON grew to nine sites. Table  also lists the site locations and number of coincidence days after MOPITT data are filtered.

AirCore measurements are a novel way to vertically sample the atmosphere to obtain profiles of various gases and have been described elsewhere . Briefly, a coiled tube on the order of 100–300 m long, with an inner diameter on the order of 2–5 mm, is taken to altitude. One end of the tube is sealed, so during ascent it is evacuated and on descent the tube slowly fills with ambient air. Because diffusion is slow over the length of the tube but fast across the 2–5 mm diameter of the tube, air from different altitudes does not mix significantly. Upon landing the vertical profile of the gas is preserved along the length of the tube, with high altitudes near the closed end and low altitudes near the open end. On the ground, the AirCore is analyzed within a few hours, which minimizes molecular diffusion. By pulling the air through and measuring concentrations with a calibrated trace-gas analyzer, a vertical profile can be obtained. AirCore CO is still a developmental product with a sample measurement precision typically less than 5 ppb . However, stratospheric AirCore CO profile comparisons have shown differences as large as 20 ppb, which could be a result of diffusion in stratospheric AirCore samples, AirCore surface effects, or incorrect AirCore sample end-member assumptions. Accuracy is dependent on the quality of calibration and standards (see Sect. S2).

Often AirCores are flown on balloons that can reach a ceiling of around 30 km (∼10 hPa), depending on the type of balloon. Once altitude is reached, the payload is cut away from the balloon. Higher-altitude data (during rapid descent) often need to be discarded; hence 22 km (∼40 hPa) is the median highest altitude in this dataset. The vertical resolution depends on AirCore tubing dimensions, measurement altitude, recovery time, and temperature but is on the order of 200–1000 m. From 2012 to 2017 there are 36 AirCore profiles available. AirCore profiles are used among other profile measurements to tie TCCON retrievals to the WMO scale . Here we use them for sensitivity tests when an approximation of the true atmospheric profile is needed.

observed biases among the four MOPITT pixels. This bias significantly affects our SRA (Sect. ), as a biased value may be chosen as the median. We spatially grid the data in 2∘×2∘ bins and average for each pixel separately over monthly timescales to evaluate variability in the bias. Here and throughout, data are averaged as described in Appendix . We analyze multiple months but here show results from April and November 2016 in Fig.  for the difference between pixels 2 and 4. We choose these two pixels because the instrumental noise is larger for pixel 3 and pixel 1 has a known large global bias , and we would therefore expect the difference between pixels 2 and 4 to be a lower bound on pixel-to-pixel bias. We see large pixel-to-pixel bias polewards of 60∘. Comparing with scenes flagged as snowy or icy by retrievals from MODIS (Moderate Resolution Imaging Spectroradiometer; also aboard Terra), we see that there is some correlation between the bias with the snow or ice scenes. This bias can be positive or negative. For example, we see that pixel 2 is lower than pixel 4 towards the North Pole and is biased positively over land in Antarctica. Over sea ice around Antarctica, pixel 2 is lower than pixel 4. We also compare pixels 1 and 3 to the weighted mean and find that pixel 3 is biased low over land snow or ice and pixel 1 is biased high over both land and water snow or ice. These biases likely arise from the effects snow or ice have on the thermal contrast of the surface and hence affect the TIR channels. For the rest of our analysis, we filter for daytime scenes and remove soundings where the MODIS diagnostics indicate the presence of any snow or ice.

We examine temporal trends in MOPITT pixel bias compared to the weighted mean from all pixels (Fig. ). Data are averaged globally for each pixel and surface type separately for 15 d bins. This analysis relies on the assumption that on average each pixel samples the same area. We see that the absolute bias of pixel 1 is largest. However, in contrast with , we observe a negative rather than positive bias between pixel 1 and the mean in the TIR–NIR retrievals, which may be because their study was of V6 data. Pixel 3 has a smaller absolute bias that is positive. In 2002, the spread of the biases is larger than in 2017. On average, the land and water biases are similar (within 0.4 ppb); however, there is a larger seasonal cycle (∼1.5 ppb) in the bias for the land that may be an artifact of the sampling and averaging global 15 d bins.

One consideration for bias corrections is whether accounting for differences in averaging kernels can account for the bias. noticed a large absolute bias for pixel 1 compared with NDACC observations even after accounting for averaging kernels. To examine the effects of averaging kernels, we find MOPITT soundings within an ellipse (±1∘ latitude, ±1.5∘ longitude) around the center location of AirCore flights on the same day. There are 20 flights with coincident observations and 1933 total corresponding MOPITT soundings. We apply averaging kernels to create simulated MOPITT column retrievals from AirCore profile measurements: 2c^=ca+aMTlog⁡10x-log⁡10xa, where c^ is the simulated XCO, and ca is the a priori column XCO. x is the dry VMR profile (from AirCore) and should not be confused with the state vector, which is log⁡10VMR for MOPITT. For this study we have defined the MOPITT column-averaging kernel for a pressure level i to be (Appendix ) 3aM,i=∂c^∂log⁡10xi=ln⁡10∑jnhjx^jAij. The pressure weighting function h has been described by and . We find that the maximum bias for the retrieved columns is between pixels 1 and 4 and is about 8 times larger for the retrieved (2.6 ppb) than for the simulated columns (0.3 ppb; Table ). For these soundings MOPITT is also biased high compared to the AirCore simulated columns by 3.3 ppb, which is greater than the bias of 0.5–1.4 ppb compared to other aircraft profiles .

We make a preliminary pixel bias correction by adjusting soundings over land and water for each pixel separately based on a linear fit to the overall time series shown in Fig. . This fit is later improved after filtering (Sect. ). After this adjustment we noticed some residual bias among the histograms, so we also apply a year-to-year pixel bias correction of up to 0.4 ppb that is the same for water and land.

We perform a SRA on the dataset with the preliminary filter for daytime and snow or ice free scenes and preliminary pixel bias correction. In a SRA, data within a specified area and time frame are assumed to be homogeneous, and variation within that area is assumed to be non-physical. There is always some real variation in the atmosphere; however, statistically, for a large sample size these variations are expected to average out. If the area is too small then there will be too few points for an unbiased median. If the area is too large then true atmospheric variability will be significant. A disadvantage of using this method as a “truth” proxy is that it is insensitive to bias on larger scales related to, for example, latitude and surface albedo e.g., for OCO-2 and CO2.

We use small regions that are approximately 89km×133km (0.8∘×1.2∘, latitude × longitude, at the Equator). Region size is a trade-off between having sufficient points per region and keeping regions small enough that real variations in XCO are small. The effects of different region sizes are described in Sect. S3. To calculate anomalies, we subtract the median from all the points within that region. If the median point does not have at least a degree of freedom (DOF) for the signal then the entire region is discarded. We also require at least 10 points in each region, which retains about 50 % of the SRA bins.

Using the SRA “truth” proxy, we can look for correlations of differences to the local median (i.e., anomalies) with various parameters that are or may be related to the retrieval. Table  lists parameters we consider for filtering and bias corrections. We make plots similar to those by and (though their studies were of XCO2) of anomalies versus one of the various parameters to aid in determining filter cutoffs (e.g., Fig. ). Such plots may reveal empirical relationships with features. Similar plots with additional parameters, including some we decided were inappropriate to use as filters, are available in the Supplement (Sect. S4). Several features can be examined in these plots to decide on where to set the filter limits, including the underlying histograms, systematic biases from zero in the mean including spikes, the spread among pixels – which indicates pixel-to-pixel bias, and the root-mean square (RMS) from the SRA – which includes systematic and random deviations from the truth proxy. We define filters based usually on one of the following criteria: (1) absolute mean bias is greater than 2 ppb, (2) the RMS is greater than 6 ppb, or (3) spread of pixel-to-pixel bias is greater than 5 ppb. These criteria are not strict, and we change thresholds if too few data are in a bin (due to possible sampling bias), if too many data are removed, or if the overall trend in the mean seems like it could be corrected by a bias correction.

Several features are apparent in the SRA diagrams (Figs.  and S4–S9) that indicate that data may be less reliable. For example, there is a step change in the bias for soundings over land going from day to night. The RMS is much smaller over snow or ice free scenes (flag of 1). We also note large anomalies for low channel 5A SNR which, in agreement with the L3 product filters, suggest it to be a good parameter to filter on. However, the bias is small for low channel 6A SNR soundings; so unlike the L3 product, we do not use it as a filter criterion. We also find that the sum of the retrieval anomaly diagnostics is a better indicator for suspicious data over land than over water. These particular tests also do not support excluding all pixel-3 soundings, though on average it does have a lower and more variable DOF . Maps of where data are filtered are available in Figs. S10 and S11. Using these filters reduces the number of daytime soundings to 3.50×108 (of 5.40×108) and reduces the RMS from 3.84 to 2.55 ppb. By comparison, when we apply the L3 filters it reduces data to 3.27×108 daytime soundings and an RMS of 3.02 ppb.

We observe trends in the mean bias with various parameters (e.g., Figs.  and S4–S9). To reduce the likelihood of overfitting, used linear fits as bias corrections only if they removed at least 5 % of the variance for XCO2 from OCO-2. For XCO from MOPITT, the ratio between the scatter (indicated by RMS) and bias is larger than for XCO2 from OCO-2; however, over our period of analysis there are about 400 times more data over water and about 100 times more over land. Fitting concerns here primarily relate to how representative the SRA is as a truth proxy and how much the biases would already be accounted for by adjusting individual soundings using averaging kernels.

Even with a criterion of only a 3 % reduction in the overall RMS, the only parameter to meet this is the maximum difference between adjacent levels over land (see Fig. S5j). This feature is larger for strong gradients between levels, which can appear when there are strong surface fluxes or when the retrieval is unstable and oscillates. This instability may be caused by bias related to, for example, spectroscopic errors. Following we make piecewise linear fits to the overall mean over two regimes, split at 100 ppb for a bias correction. The Multivariate Adaptive Regression Splines (MARS) algorithm could also be used to make a piecewise linear fit over a multidimensional dataset. However, it is more likely to overfit the data. When we applied it to the top three most variable fields the RMS for land soundings was not significantly reduced compared with our piecewise fit, so we did not use those results.

In addition to the single “feature” bias correction above, we apply a pixel-to-pixel bias correction after the filtering, described in Sect. . We perform a second SRA on the filtered data without a pixel bias correction. SRA data are binned separately for each pixel and land or water surface type and averaged over 10 d. On 28 July 2009 one of the coolers on MOPITT malfunctioned, which caused a 2-month instrument shutdown. We separate the period before and after this event and make 16 different linear fits of the bias relative to the all-pixel mean with time (2 for land and water, 4 for pixels, and 2 for time), following the method of . These linear fits are used to define the pixel-to-pixel bias.

Various coincidence criteria have been used to match MOPITT soundings with other datasets, such as aircraft measurements, other satellites, or ground-based sensors. For example, used a colocation radius of 50 km for aircraft profiles primarily over North America and a colocation radius of 200 km for aircraft profiles primarily over remote ocean. Over the Amazon, also used a colocation radius of 200 km and a colocation time of 24 h. used criteria of ±0.15∘ latitude and ±0.23∘ longitude, corresponding to 33km×33km over Paris. used a 1∘ radius and ground-based measurements within the same day. Criteria could also include fields such as the temperature of the free troposphere e.g., around 700 hPa,. used a sampling cone based on the solar azimuth angle at the time of measurement for comparing TCCON with TROPOMI. This is likely unimportant for MOPITT given the larger footprint size (22km×22km versus 7km×7km). For example, at a 60∘ SZA for a MOPITT pixel centered on a TCCON site at sea level, the TCCON ray would leave the MOPITT pixel at around 11 km or above 250 hPa. For a comparison of SCIAMACHY with NDACC–TCCON, found it to be necessary to deweight observations that were further away in time and space from points of comparison. This is likely much less of an issue for this study due to differences in retrieval errors and coincidence scales. For MOPITT the median retrieval error is about 3.5 ppb versus 24.8 ppb for SCIAMACHY. For SCIAMACHY temporal averaging was on the order of a month compared to this study, where we only use TCCON observations within ±30 min. We apply spatial averaging to the MOPITT data typically over areas of 2∘×4∘ (with exceptions noted below). Spatial weighting is not as much of a concern here as for with SCIAMACHY because they used coincidence criteria of 500–2000 km radii, which are significantly larger in terms of area (about 8–100 times). However, despite using smaller areas, heterogeneities in CO sources that MOPITT averages over may occasionally introduce bias for real reasons e.g.,.

We make exceptions to the ±1∘ latitude ±2∘ longitude spatial coincidence criteria for several sites. For sites poleward of 60∘ (eu, sp, and so) we expand the area to 4∘×8∘ because the atmosphere is expected to be well mixed and retrievals are more sparse. For sites in the Los Angeles Basin (ci, jc, and jf), we limit the area to 33.4–34.3∘ N, 116.7–118.8∘ W, because we expect XCO within the basin to be much larger than the surrounding area due to urban emissions. We set the minimum latitude to 34.5∘ N for the AFRC site to avoid the polluted Los Angeles Basin. We average soundings over land and water separately.

Because of the long (13+ year) comparison between MOPITT and TCCON, random representation error is much less important than systematic error. and noted that systematic biases can arise from comparing total column observations (in molec. cm-2) from MOPITT and NDACC when the surface altitudes differ significantly. This effect will be diminished in column averages (XCO) in locations away from strong local surface fluxes; however, different surface altitudes can lead to biases because CO profiles are not completely uniform. Between two TCCON sites only ∼10 km apart in an urban region, noted an XCO2 difference of nearly 1 ppm. They attributed part of this to the different site altitudes. We estimate the ratio between observations at the surface pressure of TCCON versus the surface pressure of MOPITT soundings. The total column-average dry mole fraction is 4XCO,ppb=∑hjxj. The vector x here can be either the retrieved profile or the a priori VMR profile. We use the MOPITT profiles because they are likely more representative of the true atmosphere than TCCON a priori profiles and apply Eq. () to find the retrieved and prior MOPITT XCO at the MOPITT sounding surface pressure. We then recalculate h based on the daily average TCCON site surface pressure. When TCCON altitude is lower, the MOPITT surface level is uniformly extended. For higher-altitude sites, the lowest-altitude MOPITT levels are either unused (hj=0) or deweighted. We then calculate XCO based on TCCON surface pressure. Figure  shows the ratios between the MOPITT retrieved XCO using the TCCON surface pressure compared to the MOPITT sounding surface pressure for 10∘×10∘ areas. Larger areas are used to get a larger variety in surface pressures. We see that for the high-altitude Zugspitze site, this scaling is particularly large (around 15 %). Over these areas the overall scaling for all sites is 0.996±0.023 (1σ). A scaling factor less than unity is usually due to larger CO mixing ratios near the surface than the rest of the column and lower TCCON site pressure . In this intercomparison, we implicitly account for differences in surface pressure using the h vector. This can make a difference for individual sites by as much as -10.5±4.1 ppb (1σ) (for Zugspitze). However, we have found in practice that accounting for differences in surface pressure makes little difference here on the overall comparison (compare Fig. S12c and f). In aggregate the difference is only -0.2±1.5 ppb (1σ).

MOPITT and TCCON use different a priori VMR profiles and have different averaging kernels (AKs; Sect. ), and these differences in sensitivity need to be taken into account when comparing retrievals from the different instruments. Here we account for differences in AKs and a priori profiles following the methods of , which are formally described as method II in Sect. S6.1. Retrievals are also on different vertical grids, and regridding is described in Appendix . Figure  shows the comparison for all sites. We find that MOPITT observations are higher than TCCON by about 6.4 %. This is similar to the 5.1 % positive bias between MOPITT V6J and NDACC total column observations .

We perform a variety of sensitivity tests on the overall global comparison. There are different approaches to account for different a priori VMR profiles and AKs such as the choice of comparison ensemble (Sect. S6). Figure S12 shows the comparison for a variety of tests when AKs are applied differently or not at all. Generally all comparisons show MOPITT to be about 6 %–9 % higher than TCCON, with some exceptions. For method III, where AKs are applied in a manner opposite to method II, the bias is as high as 15 % but is closer to ∼10 % or less. Figure S13 is a series of bar charts of how the different methods compare for each site. We also examine how the scaling changes for different colocation criteria in Figs. S12d and e by halving and doubling the coincidence areas. We find that MOPITT is biased higher than TCCON in these tests by 5 %–7.4 %. Doubling the area decreases R2 for the global comparison.

Next we test sensitivity to pressure scaling. Our vertical regridding (Appendix ) accounts for differences in surface pressure, so we use a basic comparison without AK corrections (method 0) for this test. Between these two, the overall offset is not significantly different (9 %–10 %).

Finally we test whether filtering and bias corrections affect the comparison (Fig. S12g–i). The pixel and feature bias correction have little effect on the overall global comparison (∼5.8 %–6.8 %). Without filtering, the scatter in the comparison increases, leading to a smaller R2. Due to a large intercept, the percent difference spans about 3 %–8 %. Figure S12g shows the comparison for a derived TCCON product without empirical corrections for airmass and without correction to the WMO scale . In this comparison the TCCON data do not have the standard scaling to aircraft. Due to uncertainties in the TCCON WMO scaling (Sect. S2), some comparisons are made without it. Here the bias between the datasets is significantly different and is less than 0.5 %. When MOPITT V7J data were compared directly with NOAA flask measurements from aircraft, found a positive bias of less than about 1 %.

Figure shows boxplots of the MOPITT to TCCON differences (using method II) for each site for land-only and water-only soundings. We do not note an overall bias between land and water. For all sites the TCCON-MOPITT bias is positive and usually on the order of about 3–10 ppb with a few exceptions. For example, MOPITT observations compared to the AFRC (df) TCCON are particularly high (∼14 ppb). This could be related to the high albedo or high surface temperatures of this desert site.

A seasonal variation in bias may be indicative of differences in sensitivities between the instruments to some feature, such as airmass or water content, that varies seasonally. Figure  shows the time series of the difference averaged in 1-month 5∘ latitudinal bands. Though there is significant scatter among individual comparisons, we find a long-term trend of -0.06±0.06 % yr-1 in the MOPITT–TCCON difference using the Theil–Sen estimator. reported a bias drift of -0.04±0.10 % yr-1 for V7J, though bias drifts for individual layers were larger. Including a correction trend to the L1 radiances significantly reduced the bias drift for the layers . Seasonalities of the difference for each site are in Fig. S14. There does not appear to be a persistent seasonal trend for all sites, though there is some seasonal variability for individual sites. For Lamont and AFRC the bias is larger in July–October, while for Białystok the bias is larger in April–June. At Ascension the bias is largest in January–February, while for Réunion it is largest in September–November. We do not make a seasonal bias correction.

There appears to be some latitudinally dependent bias, with a larger bias in the Northern Hemisphere. Part of this could be related to stratospheric CO (Sect. S1). also showed some latitudinal variation in MOPITT retrievals compared with aircraft. They suggested that part of the variability could arise from interfering species such as N2O, which has spectral lines that overlap with the TIR channels. Before V7 a constant value of N2O was assumed, which was determined to cause biases on the order of a few parts per billion . In V7 a global average is used based on a linear fit to monthly in situ observations. Figure S14 shows the bias as a function of column N2O measured by the TCCON. There is a slope of -0.40XCOppbXN2Oppb, though the overall correlation is small (R2=0.08). There also appears to be a small dependence on column H2O, which was likely reduced in V8 . We do not make bias corrections for any of these systematic features.

According to Sect. 2 therein, an intercomparison of two observing systems should also include a comparison of (1) averaging kernels, (2) retrieval noise covariance, (3) degrees of freedom, and (4) the Shannon information content. In conjunction with the comparison of averaging kernels, we think that it is also helpful to compare a priori profiles, which is done in Appendix . Because the MOPITT retrievals are of logarithmic profiles and the TCCON uses a linear scaling retrieval, some aspects of the comparison are inherently different.

Example AKs for MOPITT and TCCON are shown in Fig. . Because the MOPITT retrieval is on a log scale, we make an assumption that the a priori VMRs represent the true profile to obtain unitless AKs (Appendix ). We find that the TCCON AKs are more sensitive than MOPITT. Shaded regions in Fig. a show a wide variability in MOPITT column AKs. In addition, the typical state significantly affects the MOPITT AKs (e.g., compare Pasadena and Lauder). TCCON CO column AKs are most sensitive to the stratosphere and are assumed to be consistent at all sites. We make a sensitivity test where the AKs were explicitly calculated in GGG2014 for days with a wide range of XCO at the East Trout Lake site. In general the difference from the standard AKs is small, on the order of 5 % at most.

A priori profiles and MOPITT retrieved profiles along with their differences for select sites are shown in Appendix . We compare MOPITT and TCCON a priori profiles. In general, MOPITT a priori profiles are influenced more by localized emissions, as they are based on 1∘ simulated monthly climatologies from the CAM-chem model . This can be seen especially at Pasadena and to a lesser extent at Lamont and Tsukuba. Ascension Island shows a special case where enhanced CO in the lower free troposphere is seen coming from biomass burning and rainforest VOC emissions in Africa. At sites far removed from local emissions (e.g., Ny-Ålesund and Lauder) the MOPITT and TCCON a priori profiles are in better agreement with each other see e.g.,.

We take differences in a priori profiles and averaging kernels into account following method II, described in Sect. S6.1. Corrections are applied to each MOPITT retrieval and to daily averages of TCCON retrievals within coincidence criteria. We find in practice that corrections change the comparison by about 3 %. TCCON data are adjusted by 0.7±1.8 ppb (1σ), and MOPITT data are adjusted by -1.0±3.1 ppb (1σ).

Rather than comparing the retrieval noise covariance, we compare reported errors and measures of precision and accuracy. Histograms of total reported retrieval error for MOPITT are shown in Figs. S4o and S5o. With our prescribed filtering, global mean uncertainty values are 2.60±1.27 ppb (1σ) for smoothing, 2.68±1.40 ppb (1σ) for measurement, and 3.86±1.63 ppb (1σ) for the total error. The average of the errors reported in the TCCON files is 0.62±0.50 ppb (1σ). However, these errors are more a measure of repeatability than the total error or the accuracy. The 2σ uncertainty for TCCON (GGG2009) was reported as 4 ppb , and the uncertainty budget from a range of sensitivity tests is less than 4 % .

Histograms of the MOPITT DOF for the signal for water and land are shown in Figs. S4d and S5k. The DOF for the signal (ds) can be determined from 5ds=Ex^-xaTSa-1x^-xa, where E is the expected value operator Eq. 2.46 therein. However, ds is usually determined from the trace of the averaging-kernel matrix Eq. 2.80 therein, which is equivalent to Eq. () for profile retrievals. Because GGG2014 is a scaling retrieval, we treat TCCON measurements as having ds=1. With a profile retrieval we would expect ds>1, as was the case for CO2 . The DOF gives an indication of how many independent parameters can be improved compared with the a priori profile. MOPITT DOFs are between 1 and 2, which indicates that total column measurements may be reasonable, but individual layer measurements may not always be accurate.

Finally, the information content Hs is a measure of how accurate a measurement is to how well a value is known a priori. expresses it on a natural log scale (Eqs. 2.73 and 2.80 therein): 6Hs=12ln⁡S^-1Sa=-12ln⁡In-A, where In is the identity matrix. Here we express Hs on a log⁡2 scale instead. Histograms of Hs for MOPITT profile retrievals are shown in Figs. S6a and S8a, and values are on the order of 2.5–5.5 bits over water and 2.5–7 bits over land. If model values of XCO are accurate to about 32 ppb, and if the TCCON accuracy is about 4 ppb, then the TCCON XCO information content is about log⁡2324≈3 bits.

In addition to the formal aspects of intercomparing retrievals from different remote sounding retrievals, there are a variety of practical aspects to consider. For several of these aspects, an entire study could be devoted to them for each intercomparison. We summarize our comparison methodology in Table  and give examples of other studies that provide additional details or alternative methods. Though it is impractical to test all combinations of different considerations, we test some as described in Sect. , such as coincidence criteria, filtering, bias corrections, and applications of averaging kernels.

Several lessons learned in this study may be useful for future versions of MOPITT data products or users assimilating the data. Additional fields used in the retrieval, such as the a priori mixing ratio from 50 to 0 hPa and the water vapor profile, would be useful outputs when converting mixing ratios from whole air to dry air. Though the prior covariance matrix is fixed , a single matrix per daily file may be helpful. The retrieved surface emissivity over land is on average about 0.007, or about 0.75 % larger than the prior emissivity, and the retrieved surface temperature is on average about 6 K larger than the prior temperatures (see histograms in Fig. S5f and S5m). This suggests that prior surface emissivity and temperature values should perhaps be reconsidered, as they may be biased low over land. Further updates to prior values of CO, N2O, and H2O are expected to further improve the retrievals. For example, the retrieved column CO is slightly larger than the a priori column globally (Fig. S16), but the difference depends on the level and could be related to uncertainties in model transport, sinks, and sources.

Filtering can reduce spurious values. MOPITT files include parameters that could be used in filtering, such as a retrieval anomaly diagnostic, various cloud indicators, and the DOF. Data users should consider creating a QC flag for their analyses, or a binary flag could be included in future versions, e.g., based on parameters in Table  or based on the recommendations of the MOPITT team (e.g., the L3 filters). Often highly deviant retrieved surface temperatures show up around coastlines (especially western coastlines; Fig. S10) that did not pass our quality screening. These may be related to sounding definitions of surface type. SNR 6A is used to filter MOPITT data when creating the TIR–NIR L3 product to maintain consistency with the NIR product and increase stability of the DOF, but we do not find sufficient evidence to use it as a TIR–NIR filter criterion based on XCO stability alone.

When biases are found in the MOPITT L2 data, the strategy is to correct the L1 radiances or the retrieval algorithm e.g.,. MOPITT data users of L2 XCO may consider implementing a bias correction before analysis or model assimilation. In terms of XCO, pixel-3 data agree with pixels 2 and 4; however, this agreement may not necessarily hold for retrieved profiles, and pixel-3 data are excluded in the L3 product due to excessive NIR noise and in order to increase stability in the DOF e.g.,. A bias correction should be considered when assimilating pixel 1. There is a bias in the SRA for large retrieval errors on XCO above about 8 ppb (Figs. S4o, S5o). This bias suggests that perhaps these data should be excluded or deweighted further, which we did not do here. A bias adjustment field could also be included as a field in future MOPITT files. Such an adjustment could account for empirical biases noted with various parameters; pixel-to-pixel biases (Sect. ); and an overall bias compared with NDACC , aircraft flights , and/or TCCON.