Inter-comparison of CO measurements from TROPOMI, ACE-FTS, and a high-Arctic ground-based FTS

The TROPOspheric Monitoring Instrument (TROPOMI) provides a daily, spatially-resolved (initially 7 × 7 km, upgraded to 7 × 5.6 km in August 2019) global data set of CO columns, however, due to the relative sparseness of reliable ground-based data sources, it can be challenging to characterize the validity and accuracy of satellite data products in remote regions such as the high Arctic. In these regions, satellite inter-comparisons can supplement modeland ground-based validation efforts and serve to verify previously observed differences. In this paper, we compare the CO products from TROPOMI, 5 the Atmospheric Chemistry Experiment (ACE) Fourier Transform Spectrometer (FTS), and a high-Arctic ground-based FTS located at the Polar Environment Atmospheric Research Laboratory (PEARL) in Eureka, Nunavut (80.05° N, 86.42° W). A global comparison of TROPOMI reference profiles scaled by the retrieved total column with ACE-FTS CO partial columns for the period from 10 November 2017 to 31 May 2020 displays excellent agreement between the two data sets (R = 0.93), and a small relative bias of −0.68 ± 0.25 % (bias ± standard error). Additional comparisons were performed within five 10 latitude bands; the north Polar region (60° N to 90° N), northern Mid-latitudes (20° N to 60° N), the Equatorial region (20° S to 20° N), southern Mid-latitudes (60° S to 20° S), and the south Polar region (90° S to 60° S). Latitudinal comparisons of the TROPOMI and ACE-FTS CO data sets show strong correlations ranging from R = 0.93 (southern Mid-latitudes) to R = 0.85 (Equatorial region) between the CO products, but display a dependence of the mean differences on latitude. Positive mean biases of 7.92 ± 0.58 % and 7.98 ± 0.51 % were found in the northern and southern Polar regions, respectively, while a 15 negative bias of−9.16 ± 0.55 % was observed in the Equatorial region. To investigate whether these differences are introduced by cloud contamination which is reflected in the TROPOMI averaging kernel shape, the latitudinal comparisons were repeated for cloud-covered pixels and clear-sky pixels only, and for the unsmoothed and smoothed cases. Clear-sky pixels were found to be biased higher with poorer correlations on average than clear+cloudy scenes and cloud-covered scenes only. Furthermore, the latitudinal dependence on the biases was observed in both the smoothed and unsmoothed cases. 20 To provide additional context to the global comparisons of TROPOMI with ACE-FTS in the Arctic, both satellite data sets were compared against measurements from the ground-based PEARL-FTS. Comparisons of TROPOMI with smoothed PEARL-FTS total columns in the period of 3 March 2018 to 27 March 2020 display a strong correlation (R = 0.88), however a positive mean bias of 14.3 ± 0.16 % was also found. A partial column comparison of ACE-FTS with the PEARL-FTS in the period from 25 February 2007 to 18 March 2020 shows good agreement (R = 0.82), and a mean positive bias of 25 1 https://doi.org/10.5194/amt-2021-190 Preprint. Discussion started: 6 July 2021 c © Author(s) 2021. CC BY 4.0 License.


TROPospheric Monitoring Instrument (TROPOMI)
TROPOMI is the exclusive payload aboard the European Space Agency's Sentinel 5-Precursor (S5-P) satellite, which was launched on 13 October 2017 into a high-inclination (98.7°), sun-synchronous orbit at an altitude of 824 km, with a 13:30 local 90 standard time Equator crossing time (Veefkind et al., 2012). The TROPOMI instrument is a nadir-viewing push-broom grating spectrometer array, comprised of four individual spectrometers (UV-Vis-NIR-SWIR), with a swath width of 2600 km, and a 7.2 × 7.2 km 2 footprint at nadir for CO (Veefkind et al., 2012). The footprint at nadir was further reduced to 7 × 5.6 km 2 from 6 August 2019 on-wards through improvements to the electronic read-out rate of the spectrometer analog-to-digital converter.
For CO, total column densities are obtained from Earth radiance spectra in the shortwave IR spectral window around 2.3 µm, 95 where the first overtone absorption band of CO is located. Retrievals over land are performed for both clear-sky and cloudy conditions, however retrievals over oceans and other large bodies of water are only possible during cloudy conditions due to the low reflectivity of open water (Landgraf et al., 2016). The current TROPOMI CO processor uses spectroscopic parameters from the HITRAN 2008 line-list database (Rothman et al., 2009) with updates to the water vapor spectroscopy (Scheepmaker et al., 2013). 100 Vertically integrated CO column densities are retrieved from TROPOMI's shortwave infrared measurements using the Shortwave Infrared Carbon Monoxide Retrieval (SICOR) algorithm, which was developed specifically for the S5-P and S5 missions (Vidot et al., 2012). The SICOR retrieval algorithm employs a profile-scaling approach whereby the retrieval state vector contains a single scaling factor that represents the ratio of the retrieved CO total column to the a priori CO total column abundance. The a priori reference profiles are generated from the TM5 3D global chemical transport model (Krol et al., 2005), and 105 they vary based on location, month, and year. Thus, the final retrieved CO total column density corresponds to the verticallyintegrated scaled reference profile (Landgraf et al., 2016). The shape of the column averaging kernels of the CO retrievals varies based on the cloud fraction of a given measurement, reflecting the sensitivity loss of the retrieval due to cloud contamination. In general, for clear-sky retrievals over land, the averaging kernel of the SICOR retrieval is near unity for the entire vertical extent of the profile, meaning that it is relatively insensitive to the vertical distribution of CO. However, for retrievals 110 performed in the presence of cloud fractions greater than 0, the column averaging kernel values will decrease towards zero in the region below the clouds, while simultaneously increasing to values larger than one above the cloud, leading to an increased sensitivity to the CO partial column above the height of the clouds (Landgraf et al., 2016). This approach compensates for the effects of cloud shielding on the retrieved CO column, however for retrievals made in these conditions, the shape of the a priori profiles may introduce some additional error into the retrieved total columns (Borsdorff et al., 2014). The mission accuracy and 115 precision requirements for TROPOMI's CO product are 15 % and 10 %, respectively (Landgraf et al., 2016). Further details on the TROPOMI CO retrieval algorithm can be found in Landgraf et al. (2016).
In this work, we analyze TROPOMI CO measurements for the period from 10 November 2017 to 31 May 2020. We use either the reprocessed (RPRO) or offline (OFFL) data files from the most recent processor versions (010001, 010002, 010202, 010300, 010301, and 010302) depending on availability for a given day of observations. Individual pixels are filtered using the quality 120 4 https://doi. org/10.5194/amt-2021-190 Preprint. Discussion started: 6 July 2021 c Author(s) 2021. CC BY 4.0 License. flag variable ("qa_value"), which is a discrete value that provides a quality percentage (Landgraf et al., 2018). Pixels with a qa_value < 0.5 are removed prior to analysis as suggested in the algorithm theoretical baseline document (ATBD) (Landgraf et al., 2018). Furthermore, the quality values were also used to differentiate clear-sky scenes (qa_value = 1.0, representing an optical thickness < 0.5 and cloud height < 500 m) from cloudy scenes (0.5 ≤ qa_value ≤ 0.7, representing an optical thickness ≥ 0.5 and cloud height < 5000 m) for later analysis, as described in the CO product read-me file (Landgraf et al., 2020). −85° (Bernath et al., 2005). The FTS is the primary instrument aboard SCISAT, but it is also accompanied by Measurement of Aerosol Extinction in the Stratosphere and Troposphere Retrieved by Occultation (MAESTRO), a dual spectrophotometer 130 primarily aimed at improving our understanding of polar ozone chemistry (McElroy et al., 2007). In this work, we focus solely on measurements from ACE-FTS. ACE-FTS is an infrared Michelson interferometer which was designed and constructed by ABB Inc. in Quebec City, Canada.
It has a high spectral resolution of 0.02 cm −1 , and it covers the wavenumber range between 750-4440 cm −1 . ACE-FTS makes up to 30 measurements per day by solar occultation at sunrise and sunset, and provides vertical profile information (typically 135 between 5-110 km) of temperature, pressure and volume mixing ratios (VMR) for 68 molecules and isotopologues in the most recent data version (v4.1) (Boone et al., 2020). ACE-FTS has a variable vertical sampling of 1.5-6 km, and a mean vertical resolution of ∼3-4 km, which varies based on the orbit, beta angle, and instrument field-of-view (Boone et al., 2005).
CO VMR profiles from the latest version of the ACE-FTS data (v4.1) are used in this study (Boone et al., 2020). The VMR profiles are retrieved from the measured infrared spectra using a global-fit algorithm which employs a Levenburg-Marquardt been involved in the annual Canadian Arctic ACE-OSIRIS Validation Campaigns held during polar sunrise since Spring 2007, and has been previously compared with ACE-FTS and other satellite-borne instruments, for example: Clerbaux et al. (2008), The PEARL-FTS is a high-spectral-resolution (0.0035 cm −1 ) Michelson interferometer produced by Bruker Optics. Using a custom-built solar-tracker system and the sun as a source, it makes atmospheric solar-absorption measurements in the midinfrared region between 600-4300 cm −1 during the sunlit portion of the year (Batchelor et al., 2009). The interferograms are 160 collected using one of two liquid-nitrogen cooled detectors; a photoconductive mercury-cadmium-telluride (HgCdTe) detector or a photovoltaic indium-antimonide (InSb) detector. Additionally, seven internal narrow-bandpass filters are used, which limit the wavenumber range of the measured spectra, thus increasing the signal-to-noise ratio (SNR) (Batchelor et al., 2009 addition, the instrument is capable of near-infrared measurements using a third indium-gallium-arsenide (InGaAs) detector, and observations in the near-IR are contributed to the TCCON (Wunch et al., 2011). In this work, however, only the NDACC mid-infrared measurements of CO are used.
From the measured solar absorption spectra, vertical profiles and total and partial column trace-gas abundances are retrieved using the SFIT4 v0.9.4.4 retrieval software (https://wiki.ucar.edu/display/sfit4/) which is based upon the Optimal Estimation 170 Method (OEM) of Rodgers (2000). The SFIT4 retrieval algorithm iteratively fits a calculated spectrum to the observed spectra by adjusting the VMR profile of the target gas on a 47-layer vertical grid (extending from 0.61 km (the altitude of the Ridge Lab) to 120 km) until a convergence criterion is met. For the retrieval of CO, the microwindows and interfering species recommended by NDACC were used (Table 1). The OEM retrieval procedure requires prior knowledge of the atmosphere as input, including daily atmospheric profiles of pressure and temperature from the US National Centers for Environmental 175 Prediction (NCEP, ftp://ftp.cpc.ncep.noaa.gov/ndacc/ncep/) interpolated to the location of PEARL, and a priori trace-gas profiles that are sourced from a 40-year average  of the Whole Atmosphere Community Climate Model (WACCM, https://www2.acom.ucar.edu/gcm/waccm) v4 for Eureka (Marsh et al., 2013). Above the 10 Pa pressure level (∼45 km) NCEP P-T profiles are unavailable, so in this region the mean pressure and temperature profiles from the aforementioned WACCM model run are used. Additionally, spectroscopic parameters used in the retrieval process for CO are from ATM16 (Toon, 2015), 180 while all other species are from HITRAN 2008 (Rothman et al., 2009). 3 Methods

Collocations and averaging
In this study, we consider a pair of instruments to be collocated when they are observing the same approximate airmass, at the same approximate time. For the comparisons presented here, broad collocation criteria of 24 hours in time, and 500 km 185 in space were used to maximize the quantity of data available. A range of stricter collocation criteria were tested, but no significant trend between the inter-instrument differences and the spatial and temporal collocation criteria was found. Similarly broad collocation criterion were used in previous ACE-FTS CO validation studies by Clerbaux et al. (2008) and Griffin et al. (2017).
In the determination of collocated measurements, we consider each ACE-FTS profile as a point measurement, using the  filtering and averaging (i.e., TROPOMI averages collocated with 6136 unique ACE-FTS observations). These collocations spanned a latitude range encompassing the polar, mid-latitude and equatorial regions, providing a broad basis for an intercomparison of the two instruments. For the collocated observations, the mean number of TROPOMI pixels included in the averages was 11 460, indicating that the computed TROPOMI averages are statistically robust, and that pixel-to-pixel variability or biases should be negligible. Given that each ACE-FTS solar occultation provides a CO VMR profile (typically in the altitude 215 range of 10-150km) instead of a total column value some additional steps are needed to allow for a direct comparison between these two instruments.
As previously mentioned in Sect. 2.1, the TROPOMI CO retrieval employs a profile-scaling approach, and a single scaling factor, which represents the ratio of the retrieved to the prior column, is applied to the reference profile to obtain the "retrieved" profile. However, these scaling factors are not provided in the TROPOMI CO product files, so these must be calculated.

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First, however, the CO reference profiles must be converted to partial columns, and then summed to obtain the total column concentration c using the following equation: where N = 25 is the number of layers in the TM5 a priori grid, ∆p is the thickness of a given partial column layer in Pa, x is the mean VMR in the layer above level i, M da = 0.02897 is the molar mass of dry air in kg mol −1 , andḡ is the column-averaged 225 gravitational acceleration. The scaling factors for each collocation are then calculated by taking the ratio of the retrieved to the a priori total column. The scaling factor is then applied to the TM5 reference profile to obtain the "retrieved" profile, allowing for a direct comparison against ACE-FTS profiles.
Following a similar approach to what was done for the TROPOMI reference profiles, since the ACE-FTS profiles are reported in VMR units, these must converted to partial columns as well. In addition to the VMR profiles, the ACE-FTS L2 product 230 includes retrieved profiles of temperature and pressure that can be used in accurately determining the partial column profile ρ.
Following the method of Holl et al. (2016), this is done using the ideal gas law (Clapeyron, 1834): where x is the VMR profile, p is the retrieved pressure in Pa, T is the retrieved ACE-FTS temperature profile in K, k = 1.380653 × 10 −23 J K −1 is Boltzmann's constant, and ∆h is the thickness of each layer in m. The resulting partial column 235 profiles only extend to the lowest ACE-FTS VMR measurement altitude, so for altitudes below this point, the partial column profile is filled using the nearest value from the TM5 reference profile, yielding a complete partial column profile from the surface to the top of the atmosphere (TOA).
Since ACE-FTS has a significantly higher vertical resolution than TROPOMI, the partial column profiles are linearly interpolated from the 1-km altitude grid of ACE-FTS, to the 50-layer retrieval grid used by the TROPOMI SICOR retrievals.

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As discussed in Sect. 2.1, for cloudy observations, TROPOMI retrievals are more sensitive to the above-cloud column than the below-cloud portion, which is reflected in the column averaging kernel values. As a result, to correctly inter-compare the measurements from ACE-FTS and TROPOMI, we must smooth the interpolated ACE-FTS partial column profiles with the TROPOMI column averaging kernels.
where A col is the TROPOMI column averaging kernel, and ρ true is the ACE-FTS partial column profile interpolated to the TROPOMI 50-layer retrieval grid. Generally, in comparisons such as this, the a priori profile of the higher-vertical-resolution instrument would typically be substituted with that of the lower-vertical-resolution instrument to reduce the smoothing error (Rodgers and Connor, 2003). However, since ACE-FTS performs solar occultation measurements, a sensitivity (i.e., the ratio 250 of information coming from the measurement versus the a priori) of 1 is assumed at each level with a negligible influence from the a priori profile except at the uppermost altitudes of the ACE-FTS grid, which is beyond the ACE-FTS retrieval and the range of the TROPOMI CO retrieval grid (which typically spans 0-50 km) (Boone et al., 2005). As a result, a full a priori substitution is not performed in the comparison of ACE-FTS with TROPOMI.
To minimize the influence of filling the missing lower altitudes of the ACE-FTS profile with the TROPOMI a priori profile, 255 the column from the lowest ACE-FTS altitude to the top of the TROPOMI retrieval grid is computed by integrating the smoothed ACE-FTS partial column profile above the altitude of the lowest ACE-FTS measurement. Similarly, to estimate the TROPOMI partial column in the same altitude range, the partial column below the lowest ACE-FTS altitude is computed by summing the scaled TM5 reference profile from the surface to the lowest measured ACE-FTS altitude. This "below-ACE" column is then subtracted from the retrieved TROPOMI total column, providing an estimate of the measured partial column 260 in the same altitude range as ACE-FTS, thus allowing a direct comparison of the two measurements. A similar method was applied in Martínez-Alonso et al. (2020) for comparisons of TROPOMI's CO measurements with above-cloud partial columns computed from ATom-4 in-situ airplane profiles.
Furthermore, to assess the retrieval error associated with using the shape of the TROPOMI TM5 reference profiles to approximate the shape of the atmospheric CO profile below the lowest ACE-FTS measurement, we calculate the null-space error where I is the corresponding altitude integral operator (a unit vector in the case of a profile in partial column units), and ρ true represents the true CO profile (Wassmann et al., 2015). For retrievals performed over clear, cloudless scenes, the null-space 270 error will be small since the column averaging kernel values are close to one at all altitude levels. For retrievals over cloudy scenes however, the magnitude of the null-space error is expected to be significantly larger. Here, we determine the relative nullspace error (in %) in reference to the coincident unsmoothed ACE-FTS columns. If the reference profile accurately represents the true vertical trace gas distribution ρ true , then we expect that e n should disappear and the column retrieved by TROPOMI should be an estimate of the true total column (Landgraf et al., 2016). Furthermore, the direction of the relative null-space Equatorial (20°S to 20°N), north Mid-latitudes (20°N to 60°N), and north Polar (60°N to 90°N) to investigate latitudinal trends in the differences.

TROPOMI versus PEARL-FTS
Ground-based instruments such as the PEARL-FTS provide context and a point of reference for instrument inter-comparisons such as that of ACE-FTS and TROPOMI. In the following section describes the methods used to compare the TROPOMI and 285 PEARL-FTS datasets. Since the PEARL-FTS only makes measurements during the period of polar sunlight, no collocations between these instruments occurred in 2017. The earliest collocation between TROPOMI and the PEARL-FTS dates to 3 March 2018, and the final collocation took place on 27 March 2020, after which mid-IR measurements by the PEARL-FTS were halted due to the lack of an on-site operator as a result of the current COVID-19 pandemic.
Similar to the methodology applied to the ACE-FTS and TROPOMI comparison, for each PEARL-FTS observation the 290 arithmetic mean of all collocated TROPOMI pixels within a 500 km radius of Eureka is computed to reduce the pixel-topixel variability and enhance the statistical robustness of the comparisons. However, unlike in the ACE-FTS and TROPOMI comparison, a priori information is provided for both the PEARL-FTS and TROPOMI, so we perform an additional step of prior substitution to place both retrievals on a common a priori (in this case, the TROPOMI a priori) (Rodgers and Connor, method was applied for the recent comparisons of ground-based TCCON and NDACC measurements in Zhou et al. (2019), and of TROPOMI and MOPITT by Martínez-Alonso et al. (2020). Following Rodgers and Connor (2003), the prior substitution to obtain the optimized retrieved profile x fts op is done by the following: where I is the identity matrix, A is the VMR averaging kernel of the PEARL-FTS, x s5p a is the TROPOMI a priori which has 300 been interpolated to the PEARL-FTS retrieval grid, and x fts a is the PEARL-FTS a priori profile. With the PEARL-FTS VMR profile optimized with respect to TROPOMI and its a priori profile, the former can be interpolated to the TROPOMI 50-layer retrieval grid and the partial column profile calculated using the right-hand portion of Eq.
1 and the TROPOMI pressure grid. The 'best estimate' of the PEARL-FTS total columnĉ fts is determined by smoothing the partial column profile by the TROPOMI column averaging kernel following the method of Rodgers and Connor (2003): where c s5p a is the TROPOMI a priori total column, A col is the TROPOMI column averaging kernel, ρ fts op is the optimized PEARL-FTS partial column profile interpolated to the TROPOMI retrieval grid, and ρ s5p a is the TROPOMI a priori partial column profile. In theory, this operation can be done in the opposite direction by bringing the scaled TROPOMI profile to the PEARL-FTS retrieval grid, to then be smoothed by the PEARL-FTS averaging kernel. However, these two approaches are not 310 symmetrical, and one way is expected to produce a better result than the other. This is because the higher resolution will more realistically reproduce the lower resolution measurement, rather than the other way around (Rodgers and Connor, 2003). Since TROPOMI is the lower vertical resolution measurement in this particular instance, we chose to bring the PEARL-FTS profiles to the TROPOMI retrieval grid.
Once the best estimate of the PEARL-FTS column with respect to TROPOMI is obtained, the bias in the retrieved TROPOMI 315 total columns relative to the PEARL-FTS is computed in the same manner as was done for the ACE-FTS and TROPOMI comparison described in Sect. 3.2.

ACE-FTS versus PEARL-FTS
As discussed in Sect. 2.3, earlier versions of the ACE-FTS CO data product have been validated against the PEARL-FTS and other ground-based FTSs in NDACC, namely by Clerbaux et al. (2008) and Griffin et al. (2017). Both of these studies showed 320 generally good agreement between ACE-FTS and the ground-based instruments. Since ACE-FTS profiles do not extend to the surface, these previous studies primarily focused on comparisons of partial column abundances instead of total columns. In this work, we employ a similar approach, which is described below.
Firstly, since we aim to compare the partial column abundances of ACE-FTS and the PEARL-FTS, we must determine the optimal altitude range for the PEARL-FTS in which to perform this comparison. This step is crucial because if the selected 325 range is too wide, then a priori information may dominate the partial column comparisons, and the true vertical information coming from the PEARL-FTS may be limited. On the other hand, if the selected altitude range is too small, then the comparison will essentially be reduced to a single layer. To achieve this, the sensitivity of the retrievals at each level k was first computed by summing the corresponding rows of the averaging kernel matrix, i A ki , following Vigouroux et al. (2008). The sensitivity density (i.e., the fraction of retrievals with sensitivity at a given altitude) of the PEARL-FTS retrievals was then investigated 330 for all collocated ACE-FTS measurements (Fig. 1). From an analysis of the sensitivity density, an optimal altitude range of 10.25 − 40.17 km was selected for the comparison of the partial columns. This chosen range is similar to the the altitude range of 9.0 − 48.5 km used by Griffin et al. (2017), albeit slightly more conservative. However, the SFIT4 CO retrieval has been modified in the meantime due to an NDACC-wide harmonization initiative, and the range used by Griffin et al. (2017) may no longer be ideal. A smaller altitude region with high sensitivity can be seen between 0.61 − 2.21 km, however ACE-FTS 335 retrieved profiles do not typically extend this close to the surface, and as a result this region was not used.
Again drawing from Rodgers and Connor (2003), since the PEARL-FTS is of a lower vertical resolution than ACE-FTS the retrieved ACE VMR profiles must be interpolated to the coarser altitude grid of the PEARL-FTS. However, since the retrieval grid of the PEARL-FTS (0.61 km to 120 km) extends further towards the surface than ACE-FTS, the bottom-most altitudes of each coincident ACE-FTS VMR profile beneath the lowest measurement must first be filled in using the nearest value from the 340 PEARL-FTS a priori profile. In this case, since it is assumed that ACE-FTS has a sensitivity of 1 at each measured altitude, and no a priori information is provided with the ACE data, we do not perform any prior substitution step here. ACE-FTS VMR profiles are then smoothed using the VMR averaging kernel A of the PEARL-FTS using a similar form to Eq. 6 (Rodgers and Connor, 2003): 345 where x ace smooth is the smoothed ACE-FTS VMR profile, x fts a is the PEARL-FTS a priori, and x ace is the original ACE-FTS profile that has been interpolated to the PEARL-FTS retrieval grid. The partial column profile for ACE-FTS is calculated using Eq. 2, and then the partial columns between 10.25 − 40.17 km are summed. The difference between the ACE-FTS and the PEARL-FTS partial columns, δc pc , is found by:

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where c ace pc and c fts pc are the ACE-FTS and PEARL-FTS partial columns respectively, between 10.25 − 40.17 km.  Table 3 show the results of these comparisons. Globally, there is very strong correlation between the measurements from both instruments (R = 0.93), with a small mean bias of −3.70×10 15 ± 1.37×10 15 molec. cm −2 (−0.68 ± 0.25 %; bias ± SEM), and a standard deviation of the differences of 1.07×10 17 molec. cm −2 (19.79 %). The observed global mean bias between ACE-FTS and TROPOMI is well within the mission accuracy requirement of ± 15 % (Landgraf et al., 2016), and is consistent with global comparisons of the CO product to the ECMWF Integrated Forecasting System (IFS) by Borsdorff et al. (2018a) 365 who found a global mean relative bias of 3.2 ± 5.5 % (bias ± standard deviation). Fig. 2 and summarized in Table 3, it can be seen that the magnitude (as well as the sign) of the biases varies by latitude band. The largest positive relative biases are observed in the north and south Polar regions, with mean differences of 4.09×10 16 ± 2.99×10 15 molec. cm −2 and 2.30×10 16 ± 1.46×10 15 molec. cm −2 (7.92 ± 0.58 % and 7.98 ± 0.51 %) respectively, indicative of high TROPOMI 370  Table 3. Summary of the number of collocations, the mean partial column differences, and the standard deviations of the differences between ACE-FTS and TROPOMI globally, and in each latitude region. The relative bias and standard deviation values are computed with respect to ACE-FTS (i.e., 100×(TROPOMI−ACE-FTS)/ACE-FTS). The uncertainties provided for the absolute and relative biases corresponds to the standard error of the mean.

From the latitudinal comparisons between ACE-FTS and TROPOMI shown in
Region (   where anthropogenic CO sources are less influential, and overall no clear seasonal dependence of the biases is apparent. The aforementioned latitudinal variability in the biases, however, can still be observed in panels (c) and (d) of Fig. 3. The largest relative differences between the two instruments can be seen during March and September of each year when collocations are 385 occurring at high latitudes in both hemispheres (i.e., towards the polar regions), while generally smaller relative differences, conversely, are observed for collocations occurring at lower latitudes (i.e., nearer to the equator). It can also be noted that the dynamic range of ACE-FTS partial column values is noticeably larger than TROPOMI in both hemispheres.
To examine the relationship between the partial column differences and latitude, the differences versus the latitude of each collocation are shown in Fig. 4. On average, larger differences occur at the higher latitudes (most notably in the northern To assess whether any differences are introduced by the TROPOMI retrievals over cloudless versus cloud-covered scenes, the mean differences between ACE-FTS and TROPOMI were independently investigated for clear-sky and cloudy scenes (in addition to all scenes), and are shown in Fig. 5 for both the unsmoothed and smoothed cases. In general, smoothing ACE-FTS by the TROPOMI column averaging kernels reduces the mean relative bias by a significant margin both in the 400 global comparison as well as in all distinct latitude bands, but yields slightly poorer correlations in some regions (maximum difference of 0.03 in the Pearson correlation coefficients). The smoothing operation has a noticeably larger effect in the cloudcovered scenes than for the clear-sky pixels, and it shifts the mean biases in the Equatorial and mid-latitude regions from positive to slightly negative. Furthermore, in both the unsmoothed and smoothed cases, the clear-sky-only scenes tend to be biased higher than the clear+cloudy scenes and cloud-covered scenes only. It should also be noted that particularly in the 405 unsmoothed case, there is consistently better correlation between ACE-FTS and TROPOMI for cloud-covered vs. clear-sky scenes. This observed tendency is related to the aforementioned changes in the shape of the TROPOMI column averaging kernels over clear versus cloudy scenes. As outlined in Sect. 2.1, the shape of the TROPOMI column averaging kernels varies based on the cloud fraction of the measurement to reflect a reduction in sensitivity of the retrieval due to cloud contamination.
For observations over clear-sky scenes, the values of the column averaging kernel will be close to one at all levels, and the 410 influence of the reference profile on the computation of the scaling factor will be minimal. However, for measurements made over cloud-covered scenes, the column averaging kernel values rapidly decrease towards zero below the height of the cloud, while simultaneously increasing above the cloud. Because of this, in cloudy scenes, the above-cloud column (which is in the same approximate altitude range that ACE-FTS measures) is used to estimate the total column, and a greater reliance is placed on the TM5 reference profiles. If the reference profiles are underestimating the CO column below the height of the cloud, 415 then the resulting retrieved total column value will be biased lower, which is broadly consistent with the observed relationship. All pixels Clear pixels Cloudy pixels Despite the differences between the unsmoothed and smoothed comparisons, both cases still display a latitudinal bias, with the largest mean differences occurring in the NH and SH polar regions.
As discussed in Sect. 3.2, the null-space error e n can be helpful in diagnosing the error associated with the choice of the a priori profile shape on the retrieved CO column in a profile-scaling approach, particularly for measurements made over 420 cloudy scenes. The null-space error was computed for all collocated cloudy pixels (0.5 ≤ qa_value ≤ 0.7) relative to the true (unsmoothed) ACE-FTS profiles, as shown in Fig. 6. The values of the relative null-space error are entirely negative across all latitudes, with a global mean of −28.58 ± 9.98 % (bias ± standard deviation). The negative nature of the null-space errors suggests that the TM5 references profiles are generally underestimating CO concentrations in the vertical extent with respect to the retrieved ACE-FTS columns. Furthermore, a pattern in the relative null-space error with respect to latitude can also be 425 observed, with the most strongly negative values occurring between 60°to 90°in both the NH and SH. The larger observed difference in this latitude band may be due to differing cloud properties relative to lower latitudes regions, such as cloud height and optical thickness. This implies that the magnitude of the error associated with this choice of reference profile is on average larger in these high latitude regions. In general, for collocations where the null-space error is more strongly negative (i.e., the below-cloud column is more largely underestimated), a larger positive bias in the TROPOMI partial column relative to 430 ACE-FTS is anticipated.
The correlation between the relative differences and the relative null-space errors was also investigated in the same latitude bands as the partial column comparisons, and this is shown in Fig. 7. In the upper left panel of Fig. 7, no clear relationship between the relative null-space errors (R = 0.04) can be seen in the global comparison. However, within the latitude bands, weak correlations between the null-space error and the partial column differences can be observed. In particular, in the N Polar,

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Equatorial, and S Polar regions, the relative partial column differences increase with relative null-space errors, with Pearson correlation coefficients of R = 0.22, R = 0.41, and R = 0.20, respectively. The north and south Polar regions display the most strongly negative mean relative null-space errors, with −33.18 ± 10.68 % and −29.36 ± 7.92 %, respectively, while the Equatorial region has the least negative mean null-space error with −23.15 ± 7.98 %. In the northern and southern Mid-latitude regions, no notable correlation between the relative null-space error and the relative partial column differences is observed, with   To ascertain whether there is a seasonal dependence in the biases between TROPOMI and the PEARL-FTS, the time-series 460 of the TROPOMI and smoothed PEARL-FTS total columns is shown in the top panel of Fig. 9, along with the total column and relative differences. From Fig. 9, it can be seen that with the exception of a few collocations during the late spring and early summer of 2018 and 2019, a positive systematic bias is present in the TROPOMI CO total columns with respect to the smoothed PEARL-FTS CO total columns. Furthermore, the differences display some seasonal variability, with the largest differences typically present during the spring, and the lowest differences occurring in the summer months. The larger CO 465 column biases in the early spring may be a result of polar vortex conditions accompanied by the descent of mesospheric airmasses containing high concentrations of CO as the vortex begins to dissipate, an event previously observed over Eureka in Manney et al. (2008). Furthermore, larger differences may arise during the spring months from a mismatch in the TROPOMI footprint and the broader spatial extent of the PEARL-FTS measurements at high solar zenith angles (i.e., the slant-path of the PEARL-FTS covers a greater horizontal distance in high SZA conditions). In general, both instruments capture the same 470   temporal patterns in the CO total columns across all months for which comparisons were possible, however TROPOMI displays a consistent systematic high bias in the high-Arctic region within 500 km of Eureka.

ACE-FTS versus the PEARL-FTS
Comparison of ACE-FTS and PEARL-FTS CO partial columns provides additional context for the TROPOMI results presented above. Here, a total of 2906 unique collocations between ACE-FTS and the PEARL-FTS were analyzed spanning the period  isons performed in this work (i.e., both TROPOMI and ACE-FTS are biased high relative to the PEARL-FTS, but TROPOMI is biased higher relative the PEARL-FTS than ACE-FTS), which suggests that the observed high bias in TROPOMI over the high Arctic is a genuine feature in the TROPOMI CO product.
The TROPOMI instrument provides a highly spatially-resolved global data set of CO columns. However, the validity and accuracy of TROPOMI's CO product in remote regions such as the high Arctic has previously not been well characterized.
In this work, we have compared TROPOMI, ACE-FTS and a high-Arctic ground-based FTS located in Eureka, Nunavut. A global comparison of TROPOMI with ACE-FTS CO partial columns was performed for the period from 10 November 2017 to 31 May 2020, resulting in excellent agreement, with a Pearson correlation coefficient of R = 0.93, and a mean relative bias 500 of −0.68 ± 0.25 % globally. The agreement between TROPOMI and ACE-FTS was also investigated in five latitude bands including: the north Polar region (60°N to 90°N), the northern Mid-latitudes (20°N to 60°N), the Equatorial region (20°S to 20°N), the southern Mid-latitudes (20°S to 60°S), and the south Polar region (60°S to 90°S). A latitudinal dependence on the mean differences was observed, with positive mean relative biases of 7.92 ± 0.58 % and 7.98 ± 0.51 % in the north and south Polar regions, respectively, while a negative bias of −9.16 ± 0.55 % was found in the Equatorial region. This observed trend 505 is generally consistent with earlier comparisons of the TROPOMI CO product with the ECMWF-IFS model in Borsdorff et al. (2018a). Furthermore, to highlight any differences introduced by cloud contamination in the TROPOMI CO measurements, the latitudinal comparisons were repeated independently for cloud-covered and clear scenes only, and for the unsmoothed and smoothed cases. Clear-sky pixels were found to be biased higher with slightly poorer correlations on average than clear+cloudy scenes and cloud-covered scenes only, which suggests that the TM5 reference profile shape used in the retrieval can have a 510 measurable effect on the TROPOMI columns in the comparisons. Additionally, the latitudinal dependence of the biases is present in both the unsmoothed and smoothed cases. Despite the observed variability in the magnitude and direction of the mean biases, strong correlations ranging from R = 0.93 (SH mid-latitude region) to R = 0.85 (Equatorial region) were found between TROPOMI and ACE-FTS across all latitude bands.
To provide additional context to the global comparison of TROPOMI with ACE-FTS in the Arctic, both satellite data 515 products were compared against NDACC measurements from the PEARL-FTS in Eureka, Nunavut (80.05°N, 86.42°W).
Comparisons of TROPOMI with smoothed PEARL-FTS total columns in the period from 3 March 2018 to 27 March 2020 showed that the datasets were strongly correlated (R = 0.88, slope of linear fit = 1.07), however a systematic mean positive bias of 14.3 ± 0.16 % was also observed. These results are consistent with recent ground-based validation efforts by Sha et al. (2021) who found a comparable mean bias of 12.96 ± 4.56 % (bias ± standard deviation) for the PEARL-FTS while 520 using stricter collocation criterion than in this study. A small degree of seasonal variability in the differences was found, with larger mean biases on average occurring during the spring months, and the lowest biases present during the summer months.
However, with the exception of a few collocations during the late spring and early summer of 2018 and 2019, TROPOMI was consistently biased higher than the PEARL-FTS. Lastly, a partial column comparison between ACE-FTS and the PEARL- In general, the magnitude and sign of the mean relative differences are consistent across all inter-comparisons presented in this work, suggesting that the current TROPOMI CO product exhibits a high bias in the high-Arctic region that is consistent with the recent ground-based validation results of Sha et al. (2021). The observed mean differences fall within the TROPOMI mission accuracy requirement of ± 15 %, indicating that the data quality of the CO product in these high-latitude regions meets the specifications. Proposed updates to the TROPOMI CO retrieval spectroscopy and de-striping methods described 535 in Borsdorff et al. (2019) are expected to improve the latitudinal bias that is currently present in the operational product. It is suggested that a similar validation exercise be repeated following the release of the upcoming version 2 TROPOMI CO product to verify that the observed latitudinal bias has been corrected.