A comparison of the impact of TROPOMI and OMI tropospheric NO 2 on global chemical data assimilation

. This study gives a systematic comparison of the Tropospheric Monitoring Instrument (TROPOMI) version 1.2 and Ozone Monitoring Instrument (OMI) QA4ECV tropospheric NO 2 column through global chemical data assimilation (DA) integration for the period April–May 2018. DA performance is controlled by measurement sensitivities, retrieval errors, and coverage. The smaller mean relative observation errors by 16% in TROPOMI than OMI over 60 ◦ N–60 ◦ S during April–May 2018 led to larger reductions in the global root mean square error (RMSE) against the assimilated NO 2 measurements in 5 TROPOMI DA (by 54%) than in OMI DA (by 38%). Agreements against the independent surface, aircraft-campaign, and ozonesonde observation data were also improved by TROPOMI DA compared to the control model simulation (by 12–84% for NO 2 and by 7–40% for ozone), which were more obvious than those by OMI DA for many cases (by 2–70% for NO 2 and by 1–22% for ozone) because of better capturing spatial and temporal variability by TROPOMI DA. The estimated global total NO x emissions were 15% lower in TROPOMI DA, with 2–23% smaller regional total emissions, in line with the observed 10 negative bias of the TROPOMI version 1.2 product compared to the OMI QA4ECV product. TROPOMI DA can provide city scale emission estimates, which were within 10% differences with other high-resolution analyses for several limited areas, while providing a globally consistent analysis. These results demonstrate


NASA ATom aircraft-campaign observations
Vertical profiles of NO 2 were obtained from the NASA Atmospheric Tomography mission 4 (ATom-4) aircraft campaign (Wofsy et al., 2018). The ATom-4 campaign was conducted using a NASA DC-8 aircraft from 24 April to 21 May 2018. The DC-8 flight tracks covered regions between 85 • S and 83 • N over the Pacific, Atlantic, and United States. The NO 2 concen-90 trations were measured via chemiluminescence with an overall uncertainty of 20 pptv (Weinheimer et al., 1994). To evaluate the DA performance for vertical NO 2 profiles over polluted areas, we used data averaged over coastal regions of the western United States (117.25-122.5 • W, 32-37 • N) from three flights on 24 and 27 April, and on 21 May.

Surface in-situ observations
We used surface NO 2 and ozone concentrations from 3,255 sites over Europe obtained from the European air quality database 95 (AirBASE) of the European Environmental Agency (EEA), 404 sites over the United States obtained from the Air Quality System (AQS) of the United States Environmental Protection Agency (US EPA), and 1,246 sites over Japan obtained from Japanese continuous measurement data of general air pollution at ground level compiled by the National Institute of Environmental Studies (NIES). We excluded sites in high-traffic and industrial locations, because the 0.56 • -resolution model grids cannot resolve NO 2 enhancement at roadside and individual point sources. For AirBASE and AQS, sites with station types 100 of "Industrial" and "Traffic" and with land use of "INDUSTRIAL" and "MOBILE" were excluded, respectively. For Japan, we excluded measurement sites for automobile exhaust gases. More than 97% of the observed NO 2 concentrations used in this study were measured by commercial chemiluminescence analyzers, with typical measurement errors of 1-5% (Gluck et al., 2003). These analyzers overestimate the ambient NO 2 concentrations, because the measurements contain interference from reactive nitrogen compounds other than NO 2 (e.g., Dickerson et al., 2019). Thus, correction factors proposed by Lamsal ANs were applied to the observations derived from the commercial chemiluminescence analyzers in the manner described by Sekiya et al. (2021): where AN is the sum of all alkyl nitrate concentrations, and PAN is the peroxyacetyl nitrate concentrations.

Ozonesonde observations 110
The observed vertical profiles of ozone were obtained from the World Ozone and Ultraviolet Data Center (WOUDC, http:// www.woudc.org), Southern Hemisphere Additional Ozonesondes (SHADOZ; Sterling et al. (2018); Thompson et al. (2017); Witte et al. (2017Witte et al. ( , 2018  2.3 Data assimilation system 2.3.1 CHASER chemical transport model We used the global chemical transport model, CHASER V4.0, at a resolution of 0.56 • with 32 vertical layers (Sudo et al., 2002;Sekiya et al., 2018) as the forecast model, which simulates tracer transport, emission, dry and wet deposition, and resolution substantially improves the model performance over polluted regions (Sekiya et al., 2018).
The a priori surface NO x emissions were obtained from the HTAPv2.2 anthropogenic emission inventory (at 0.1 • resolution) for 2010 (Janssens-Maenhout et al., 2015), the Global Fire Emission Database (GFED) version 4.1s monthly-based biomass burning emission inventory (at 0.25 • resolution) for 2018 (Randerson et al., 2018), and the Global Emission Initiative (GEIA) soil NO x emission inventory (at 0.5 • resolution) (Yienger and Levy, 1995). The a priori lightning NO x sources were calculated 130 in the model at each model time step using the parameterization proposed by Price and Rind (1992).

Ensemble Kalman filter data assimilation
We developed a state-of-the-art chemical DA system (e.g., Miyazaki et al., 2019Miyazaki et al., , 2020a using the local ensemble transform Kalman filter (LETKF) technique (Hunt et al., 2007). The LETKF uses an ensemble model forecast to estimate background error covariance assuming that the background ensemble perturbations sample the forecast model errors. The background 135 ensemble model fields were converted into observation space by applying the observation operator which includes a spatial interpolation operator, and an averaging kernel. The inclusion of averaging kernels in the observation operator describes the vertically-dependent sensitivities and removes the influence of a-priori profile shape (Eskes and Boersma, 2003). The analysis ensemble mean x a was obtained by combining the background ensemble mean x b and assimilated observations y o with relative weights, which were determined using background and observation error covariance matrices X b and R, respectively: whereP a is the local analysis error covariance in the ensemble space, while y b and Y b are the background ensemble mean and error covariance in the observation space, respectively. The local analysis error covariance was estimated as where ∆ is a covariance inflation factor (= 7% per DA cycle) and k is the ensemble size (32 or 64 in this study, see Table 1 for details).
Surface and lightning NO x emissions were estimated based on a state argumentation method (e.g., Evensen, 2009) using the relationship between NO 2 concentrations and NO x emissions in the background error covariance matrix generated based on ensemble model simulations. The initial a priori error was set as 40% and 60% for the surface and lightning NO x sources, respectively. In the analysis step, the standard deviation of emission ensembles was artificially inflated to a predefined minimum 150 value obtained through sensitivity calculations (i.e., 56% of a priori emissions) to prevent covariance underestimation.
Our previous study (Sekiya et al., 2021) demonstrated that DA improvements were larger by factors of 1.5-3 at 0.56 • resolution than at 2.8 • resolution over polluted regions in comparison to the assimilated NO 2 observations. This high resolution leads to reduced spatial representativeness errors (due to an increased average coverage fraction per grid cell at 0.56 • resolution by a factor of two, compared to 2.8 • resolution). The 0.56 • -resolution ensemble model simulation also generates background 155 error covariance matrix which describes small(0.56 • )-scale features. Because of distinct non-linear transport and chemical processes, assimilation considering the background error covariance would also be essential for making the best use of observational information. The multi-constituent DA system have been used to assimilate ozone, NO 2 , CO, SO 2 , and HNO 3 (Miyazaki et al., 2020a). Nevertheless, in this study, only TROPOMI and OMI NO 2 were assimilated to emphasize the impact of assimilation of tropospheric NO 2 retrievals.

Super-observation approach
The super-observation approach (Eskes et al., 2003;Miyazaki et al., 2012a) was used for generating satellite observation data representative to the model grid size (i.e., 0.56 • ). The super-observation approach can minimize spatial representativeness errors for spatially varying concentrations of short-lived tracers on sub-grid scales, such as NO 2 , compared to the thinning approach which randomly selects an observation per grid cell (Boersma et al., 2016). The resolution of super-observation 165 was set to be identical to the forecast model resolution. The super-observation concentration was generated by averaging all data within a super-observation grid cell, while applying a weighting function based on the coverage area of overlap with the super-observation grid cell. The super-observation error was calculated as a combination of measurement and spatial representativeness errors √ σ m + σ r . In our approach, the super-observation measurement error σ m was estimated as

170
where σ m,i is the mean measurement error at individual pixels related to total slant column density (SCD), stratospheretroposphere separation (STS), and tropospheric AMF, c is the error correlation coefficient among the individual retrieval data for these error components, and n is the number of measurements with non-zero overlap with the chosen grid cell. This approach explicitly accounts for spatial correlations, c, between observation errors which depends on the error sources, compared to the conventional approach used in Miyazaki et al. (2012a). It is supposed that observation errors related to total SCD and 175 tropospheric AMF contain larger random components (by 85%, i.e., c = 0.15) than those related to STS (by 0%, i.e., c = 1.0).
The spatial representativeness error σ r was calculated as a function of coverage area fraction in the same way as Boersma et al. (2016).

Experimental setup
As summarized in known to be smaller in the summer season than those in the winter season (Lambert et al., 2020). We analyzed the DA results for the period 15 April-31 May after a 2 week-long spin-up.

Data characteristics
Super-observation concentrations and errors can affect DA results, which are compared in Figure 1 and averaged over 60 • S-60 • N were compared to those in OMI. The mean super-observation errors were 33% smaller in TROPOMI than in OMI, while the mean relative super-observation errors were 16% smaller in TROPOMI. These differences mainly result from improvements in SCD-related errors associated with improved S/N ratio of TROPOMI data, reduced random error components by increasing spatial resolution of TROPOMI data (i.e., an increasing number of observations per superobservation grid cell; see equation 4), and smaller TROPOMI stripes. Over polluted regions, because individual retrieval 200 uncertainties scale with tropospheric column amounts, the lower mean concentrations in TROPOMI than in OMI also led to the smaller super-observation errors in TROPOMI (by 33%). As an exception, over remote regions, reduced S/N ratio in SCD, rather than the lower concentrations, explain the smaller super-observation errors (by 32%) in TROPOMI. Over some remote areas, such as northern high latitudes, the Tarim basin, the tropical Pacific Ocean, and southern midlatitudes, relative errors were larger in TROPOMI than in OMI ( Figure 1i). The larger TROPOMI relative errros over these areas are influenced by 205 dominant contribution of the uncertainties in stratospheric column for TROPOMI because of reduced random error components in TROPOMI and the assumption of spatial correlation c = 1.
The spatial coverage per super-observation grid cell of TROPOMI (72%) was larger than those of OMI (69%) mainly because of OMI row anomalies, which led to smaller spatial representativeness errors of TROPOMI (7%) than those of OMI (10%). The mean relative super-observations errors of OMI were 8% smaller in 2005 than in 2018 (figure not shown), which 210 is attributed to the temporal changes in OMI row anomalies, stripes, and instrument radiometric degradation (see Section 2.1).
The averaging kernel values in the lower troposphere (below 850 hPa) were higher by 44% in TROPOMI averaged over 60 • S-60 • N than those in OMI, because mean CRF over 60 • S-60 • N is 15% smaller in TROPOMI due to better resolving small-scale cloud-free scenes.

215
The performance of TROPOMI DA and OMI DA was confirmed by the χ 2 test (Ménard and Chang, 2000;Zupanski and Zupanski, 2006). χ 2 value is diagnosed from the ratio of the Observation-minus-Forecast (OmF; i.e., y o −H( x b )) to estimated error covariance in the observational space (HP b H T +R) as 220 The mean values of estimated χ 2 over polluted regions (> 1×10 15 molecules cm −2 ) after inflation factor tuning was 0.99 for TROPOMI DA, which is close to the ideal value of 1. The mean χ 2 of 1.17 for OMI suggests underestimated background error covariance or observation errors.
We also evaluated the self-consistency with the assimilated observations based on reductions in root-mean-square error (RMSE) by DA (∆RMSE) using daily maps sampled at observation locations as where V and A are the observed tropospheric NO 2 column and corresponding averaging kernels, respectively, used for DA; c assim and c ctl are NO 2 concentration fields obtained from the DA runs and control model simulations, respectively; and N is the number of super-observation data. The level of significance of ∆RMSE was determined using the Mann-Whitney U test (Mann and Whitney, 1947).

230
As shown in Figure 2 and Table 3, the RMSE for TROPOMI DA over 60 • S-60 • N was reduced by 54% compared to that for the control model simulation, with larger RMSE reductions over polluted regions (by 60%) than over remote regions (by 37%).
The RMSE reductions were substantial over most regions in the tropics and northern midlatitudes, whereas improvements are not clear over the northern high latitudes, Tarim Basin, Arabian Sea, northern Australia, South America, and parts of the southern mid-latitudes. Mean RMSE reductions were larger for TROPOMI DA than OMI DA (by 38%). The differences in 235 RMSE reductions between TROPOMI DA and OMI DA over the tropics and northern midlatitudes were statistically significant at the 95% confidence level. These differences can be explained by the reduced relative super-observation errors in TROPOMI.
In contrast, the differences in RMSE reduction between TROPOMI DA and OMI DA were statistically insignificant over most regions with larger relative super-observation errors in TROPOMI.
shows clear decreases in RMSE reductions with increasing relative super-observation errors for both TROPOMI and OMI DA.
Steep RMSE decreases occurred around relative super-observation errors of 20-50%, which reflected areas over and downwind of polluted regions. Over polluted regions, observational information is more effectively assimilated into the model, because of the large uncertainty (i.e., background error covariance) of estimated NO x emissions over these regions. As shown in Figure 3c, mean relative super-observation errors at individual grids were smaller than those in TROPOMI in OMI by 16%. Corresponding 245 to these smaller super-observation errors, the mean RMSE reductions by TROPOMI DA at individual grids (by 54%) were larger than those by OMI DA (by 38%), with large differences in frequency of RMSE reductions between TROPOMI DA and OMI DA for RMSE reductions of > 10% ( Figure 3d). These results confirm that improved RMSE reductions by TROPOMI DA compared to OMI DA can be attributed to the reduced relative super-observation errors in TROPOMI. Meanwhile, the obtained result suggests that DA efficiency by TROPOMI is determined by the amount and quality of TROPOMI data, regardless of the 250 TROPOMI low bias.

Validation against independent observations
3.3.1 ATom aircraft-campaign data On 24 April, TROPOMI DA increased negative bias at 850 hPa, while it reduced positive bias at 750 hPa, which could also be attributable to model biases in PBL height. The mean bias in the lower troposphere (below 700 hPa) was largely reduced by TROPOMI DA (by 84%) on 24 April. The improvements were small (by 17%) on 27 April when the DC-8 aircraft NO 2 measurements were conducted in the early morning before the TROPOMI overpass time, whereas TROPOMI DA reduced 265 positive model biases by 78% in the lower troposphere on 21 May. In the middle and upper troposphere, TROPOMI DA reduced the model biases by 12-53%. These bias reductions were larger by 52-70% for the lower troposphere and by up to 31% for the middle and upper troposphere in TROPOMI DA than OMI DA, except for the lower troposphere on 27 April.
Because of the large variability in the observed concentrations, these differences in bias were statistically insignificant based on a two-sample t test, except for the upper troposphere on 21 May.

Surface in-situ data
Surface in-situ observation data at 14:00 LT was used for validation to evaluate assimilation impacts just after their overpass times. Validation was conducted after filtering out model grids where water bodies cover >50% of a grid box area using annual Moderate Resolution Imaging Spectrodadiometer (MODIS) land cover data (Friedl and Sulla-Menashe, 2015) for 2018, considering large representativeness errors. Over Europe, the regional mean model bias and RMSE of NO 2 were −18% and 275 145%, respectively (absolute errors are shown in Table 5). The model biases vary with regions, with positive biases of 12-115% over the United Kingdom (UK), Belgium, and the Netherlands and negative biases of 42-78% over Italy, Serbia, and Romania ( Figure 5). Over the United States, regional mean model bias and RMSE were 37% and 268%, respectively, with larger positive biases over urban areas such as New York, Los Angeles, and Chicago. The regional mean bias and RMSE over Japan were −23% and 124%, respectively.

280
TROPOMI DA reduced the regional RMSE over Europe by 29%, with larger RMSE reductions by 45% and 47% over the UK and the Netherlands, respectively, reflecting improvements in spatial and temporal variability by TROPOMI DA ( Figure   6). Because of the small RMSEs in the control model simulation, RMSE reductions by TROPOMI DA were not obvious over Italy, Spain, and Portugal. Over the United States, TROPOMI DA reduced the regional mean bias and RMSE by 46% and 50%, respectively. In contrast to the large RMSE reductions over the eastern United States and western coastal areas, RMSEs 285 increased over Colorado and Wyoming again due to the small RMSEs in the control model simulations. Over Japan, TROPOMI DA reduced RMSE by 23%, but increased negative model bias by 68%. Error reductions were smaller in OMI DA overall. The RMSE over Europe was increased by OMI DA by 5% mainly due to the increased errors over the Netherlands. Over the United States and Japan, the RMSE reductions for megacities such as New York, Los Angeles, and Tokyo were 25-70% larger in TROPOMI DA than in OMI DA. The regional RMSE reduction was comparable between the two runs (by 47% for the United

290
States and 20% for Japan by OMI DA).

Regional performance over Los Angeles
The magnitude of improvements by DA can be affected by meteorological conditions (e.g., Miyazaki et al., 2019). We eval-  The top-down estimates provided by TROPOMI DA significantly differed from the a priori emissions (Figure 9 and Table 7).
TROPOMI DA tends to decrease emissions over the eastern United States, China, northern India, and Central Africa. Large positive increments (by 42% on average) were found over regions where soil emissions are dominant (> 50% in a priori emissions), such as over remote areas of Spain, Turkey, the Midwest United States, Kazakhstan, and the Sahel regions. This suggests underestimated soil emissions in a prior inventories, as commonly reported by previous studies (Vinken et al., 2014;Oikawa et al., 2015;Visser et al., 2019). The country and regional total emissions were decreased by 14% in the United States, 38% China, 17% in India, and 22% in Central Africa, and increased by 12% in Europe, 39% in the Middle East, and 44 % in Southeast Asia.
The global total NO x emissions were 15% smaller in TROPOMI DA than in OMI DA, with 3-18% smaller regional total emissions for polluted regions and 22-23% smaller regional total emissions for biomass burning regions, reflecting the low 340 bias of TROPOMI retrievals compared to OMI retrievals. The low bias of the TROPOMI retrievals compared to the OMI retrievals also affects OH concentrations. Assimilation of lower NO 2 retrievals, through NO x emission and NO 2 concentration optimization, led to weaker chemical production of HO x and conversion from HO 2 to OH. This effect resulted in 2-21% smaller regional-mean OH concentrations in the lower troposphere in TROPOMI DA, except for South Africa. In contrast, differences in the regional total emissions over India and the Middle East between TROPOMI DA and OMI DA were small 345 (4-5%), reflecting small differences in regional-mean concentrations between the TROPOMI and OMI retrievals (4-6% lower in TROPOMI). Compared to the EDGARv5 (Crippa et al., 2019) and REASv3.2 (Kurokawa and Ohara, 2020) bottom-up emission inventories for 2015, the regional total emissions from TROPOMI DA and OMI DA over major polluted regions, except for Europe, were smaller by 17-35% and 9-21%, respectively. These results suggest that the emission estimates from OMI DA are closer to the EDGARv5 and REASv3.2 bottom-up emission inventories than those from TROPOMI DA (using 350 the TROPOMI v1.2beta product).
The Cloud-covered scenes of satellite NO 2 retrievals were used to optimize lightning NO x sources following the method of As a result, the difference between TROPOMI DA and OMI DA can be attributed to 75-92% higher vertical sensitivities above the cloud height for cloud-covered scenes (CRF > 0.5). As shown in Table 7, the global total production of lightning NO estimated by TROPOMI DA was 13% larger than that estimated by OMI DA, with larger regional total production by 14-52% over North and South America, Southeast Asia, the Atlantic, and Indian Ocean. The impacts of TROPOMI on lightning NO x source estimation will be investigated in more detail in a separate study.

Impacts on ozone analysis
The NO 2 DA plays an important role in improving the representation of tropospheric chemistry, including ozone. We evaluated 375 the relative values of TROPOMI and OMI NO 2 DA on surface and tropospheric ozone analysis.

Validation using surface in-situ data
Daily maximum 8-h average (MDA8) ozone concentrations were validated using surface in-situ observation data in the same manner as NO 2 . As summarized in Table 5, the regional mean bias and RMSE of the control model simulation against surface in-situ ozone observations over Europe were 22% and 29%, respectively, with large RMSEs over southern Europe ( Figure   380 10). Over the United States, the mean model bias and RMSE were 10% and 22%, respectively, reflecting large model biases over the eastern United States. The mean bias and RMSE over Japan were 7% and 18%, respectively. Positive model biases in surface ozone over polluted regions are commonly reported in other global CTMs (Schnell et al., 2015;Turnock et al., 2020).
TROPOMI DA increased the mean bias and RMSE of surface ozone over Europe by 14% and 8%, respectively, with large error increases over southern Europe. Increased bias and RMSE were also found over the western United States. Many 385 factors can lead to increased errors in ozone, including model errors in ozone precursors' emissions other than NO x , chemical processes, and meteorological processes such as PBL vertical mixing. For example, ozone responses to NO x emissions strongly depend on the choice of CTMs (Miyazaki et al., 2020c), which affects the impacts of NO x emission corrections on ozone analyses. Over the eastern United States, RMSEs were typically reduced by 5-10 ppbv by TROPOMI DA, resulting in improved bias by 14% and RMSE by 16% at country scale. Over Japan, the mean bias and RMSE were reduced by TROPOMI DA by 390 54% and 7%, respectively.
For most regions, better agreement with surface ozone data was obtained from TROPOMI DA than from OMI DA. OMI DA resulted in larger increases in the positive bias and RMSE over Europe by 32% and 22%, respectively. Over the United States, the mean bias and RMSE were slightly increased by OMI DA by 8% and 1%, respectively. The bias reduction over Japan by TROPOMI DA was larger than that by OMI DA (by 18%), while RMSE over Japan was increased by OMI DA (by 395 4%). The better agreement in surface ozone by TROPOMI DA coincides with that in surface NO 2 (c.f., Section 3.3.2). This confirms that the better representation of NO 2 through assimilation of advanced NO 2 satellites is essential to improve surface ozone analysis for many regions of the world. Meanwhile, any biases in satellite NO 2 retrievals affect surface ozone analysis.
Surface ozone analysis bias could be improved by using updated retrievals with reduced TROPOMI NO 2 negative biases.
TROPOMI DA greatly reduced the mean model biases and RMSE by 98% and 24% at 500 hPa, respectively, and 82%

Summary and conclusion
We compared DA analyses of NO 2 , ozone concentrations, and NO x emissions derived from the assimilation of the TROPOMI and OMI tropospheric NO 2 column retrievals. To generate observation data representative to the model grid size, we employed a super-observation approach that explicitly accounts for spatial correlations between observation errors. Because of 16% smaller relative super-observation errors in TROPOMI than in OMI, the DA self-consistency, as measured by RMSE reductions 420 against the assimilated observations, was improved in TROPOMI DA by 54%, which was larger than OMI DA (by 38%).
Agreements against the independent ATom-4 aircraft-campaign and surface in-situ NO 2 data were also improved by 12-84% and 23-50%, respectively, which was larger than those for OMI DA (by up to 70% and 47%, respectively) for many cases.
The improved NO 2 led to improved agreement with surface in-situ MDA8 ozone over United States and Japan in TROPOMI DA (by 7-40%) than in OMI DA (by 1-22%). Agreements with ozonesonde data at 500 and 800 hPa were also improved by 425 TROPOMI DA by 14-40% for most regions, except for the tropics, which was larger than those by OMI DA (by 12-22%).
Global total NO x emission was increased from 43.5 Tg N yr −1 in a priori emissions to 46.2 Tg N yr −1 by TROPOMI DA, which was 15% smaller than those derived from OMI DA (54.2 TgN), with 3-23% smaller regional total emissions for major polluted and biomass burning areas. The city-scale emissions derived from TROPOMI DA were generally consistent with previous estimates using limited-area high resolution analyses (within 10% differences for Riyadh, New York, and Chicago).

430
The global emission estimates constrained by the more accurate and dense TROPOMI measurements provide complementary information about emission variability, especially where accurate and detailed information on activity data and emission factors is missing when developing bottom-up inventories (Elguindi et al., 2020). This would also benefit model simulations of tropospheric ozone (e.g., Miyazaki et al., 2019;Visser et al., 2019;Bae et al., 2020;Qu et al., 2020), and estimations of nitrate aerosols and their deposition flux (Nowlan et al., 2014;Geddes and Martin, 2017). These improvements are important 435 for productivities and diversities of terrestrial and marine ecosystems.
The DA performance comparisons provide a systematic evaluation of TROPOMI and OMI retrievals, independent from their averaging kernels and a priori profiles. The improved agreements with independent observations in TROPOMI DA demonstrate the importance of improved spatial coverage and reduced retrieval uncertainty for many science applications. Meanwhile, validation against surface NO 2 measurements showed lower bias in TROPOMI retrievals compared to OMI retrievals by 15% 440 for the United States, Europe, and Japan. The smaller estimated NO x emissions also confirm the low biases in TROPOMI NO 2 relative to OMI NO 2 globally, which also affected ozone analysis. This systematic bias is largely attributed to a negative cloud height bias in the FRESCO cloud retrieval algorithm (van Geffen et al., 2021).     DA (middle), and the differences between them (right). For the right panel, grids with a gray color indicate differences between RMSE reductions by TROPOMI DA and OMI DA that are statistically insignificant at the 95% confidence level using the Mann-Whitney U test.   Probability distribution [%] Relative super-observation error [%] TROPOMI DA OMI DA Probability distribution [%] RMSE reduction [%] TROPOMI    TROPOMI DA-OMI DA [%] Root-square-mean error (RMSE) reduction: windy conditions (wind speed > 2.5 m/s over Los Angeles)        Table 7. Global and regional total surface and lightning NOx emissions (