The forecast model, MIROC-CHASER , contains detailed photochemistry in the troposphere and stratosphere by simulating tracer transport, wet and dry deposition, and emissions. The model calculates the concentrations of 92 chemical species and 262 chemical reactions (58 photolytic, 183 kinetic, and 21 heterogeneous reactions). Its tropospheric chemistry considers the fundamental chemical cycle of Ox-NOx-HOx-CH4-CO along with oxidation of non-methane volatile organic compounds (NMVOCs) to properly represent ozone chemistry in the troposphere. MIROC-CHASER has a T106 horizontal resolution (1.1∘×1.1∘) with 32 vertical levels from the surface to 4.4 hPa. This is coupled to the atmospheric general circulation model MIROC-AGCM version 4 . The simulated meteorological fields were nudged toward the 6-hourly ERA-Interim .

The a priori surface emissions of NOx, CO, and SO2 were obtained from bottom-up emission inventories. Anthropogenic NOx, CO, and SO2 emissions were obtained from the HTAP version 2 for 2010 , which combines regional inventories of the European Monitoring and Evaluation Programme (EMEP), Environmental Protection Agency (EPA), Greenhouse Gas-Air Pollution Interactions and Synergies (GAINS), and Regional Emission Inventory in Asia (REAS). For biomass burning emissions, we employed the monthly Global Fire Emissions Database (GFED) version 4 . Emissions from soils were based on monthly mean Global Emissions Inventory Activity (GEIA) . Lightning NOx sources were simulated using the convection scheme of MIROC-AGCM and the relationship between lightning activity and cloud top height . Methane concentrations were scaled on the basis of present-day values with reference to the surface concentration.

Data assimilation applied here is based upon on an EnKF approach, the Local Ensemble Transform Kalman Filter (LETKF) . The EnKF uses an ensemble forecast to estimate the background error covariance matrix and generates an analysis ensemble mean and covariance that satisfy the Kalman filter equations. In the forecast step, a background ensemble, xib(i=1,…,k), is obtained from the evolution of an ensemble model forecast, where x represents the model variable, b is the background state, and k is the ensemble size (i.e., 32 in this study). The observation operator H is applied to the background ensemble to convert them into the observation space, yib=H(xib), which is composed of a spatial interpolation operator and a satellite retrieval operator. The satellite retrieval operator uses an a priori profile and an averaging kernel of individual measurements (e.g., ). Using the covariance matrices of observation and background error as estimated from ensemble model forecasts, the data assimilation determines the relative weights given to the observation and the background and then transforms a background ensemble into an analysis ensemble, xia(i=1,…,k). The control vector, z=Dx, is a subset of the state vector (x) to be adjusted during assimilation, where D is a mapping matrix. The control vector z is updated at every analysis step by observations and then mapped back to the state vector x. Some variables in the state vector x are not parts of the control vector z for theoretical and practical reasons, as discussed below in this section. Then background error covariance is obtained from an ensemble forecast with the updated analysis ensemble, whereas the observation error is obtained from the satellite retrieval uncertainty information (see Sect. 3.1).

In the data assimilation analysis, a covariance localization and inflation was applied. The covariance localization was used to neglect the covariance among unrelated or weakly related variables, which results in removing the influence of spurious correlations resulting from the limited ensemble size. The optimization of the variable localization was based on a comparison against independent satellite and aircraft data, as described in Miyazaki et al. (2015). The analysis increments through the NO2 assimilation were limited to adjusting only the surface emissions of NOx, LNOx sources, and concentrations of NOy species (=NOx+HNO3+HNO4+PAN+MPAN+N2O5). The MOPPIT CO and OMI SO2 measurements were used for constraining surface CO and SO2 emissions only, respectively. Even in the short assimilation window (i.e., 2 h), data assimilation increments can be used to measure systematic model biases in emissions that could affect long-term model errors. For the LNOx sources, covariances with MOPITT CO data were neglected. Concentrations of NOy species and ozone were optimized from TES ozone, OMI, SCIAMACHY, and GOME-2 NO2 and MLS ozone and HNO3 observations. For NOx, concentration adjustments are quickly lost in the lower atmosphere due to the short lifetime, while emission adjustments are more efficient to store the information over longer time periods . Although the concentrations of VOCs are included in the state vector, they were not included in the control vector and thus were not optimized in the current setting because the current assimilated data sets did not improve their fields obviously. Consequently, the control vector in this study includes the concentration of NOx, HNO3, HNO4, PAN, MPAN, N2O5, and ozone, as well as the NOx, SO2, and CO emission sources.

The covariance localization was also applied to avoid the influence of remote observations that may cause sampling errors. The covariance inflation was employed to inflate the forecast error covariance, in order to prevent underestimation of background error covariance and filter divergence caused by sampling errors associated with the limited ensemble size and by model errors. The cut-off radius was set to 1643 km for NOx emissions and 2019 km for CO emissions, lightning sources, and chemical concentrations based on sensitivity calculations. However, the optimal localization length may depend on the location, season, and species, reflecting meteorological conditions and the chemical lifetime.

The state vector includes several emission sources: surface emissions of NOx, CO and SO2, and lightning NOx (LNOx) sources, as well as the concentrations of 35 chemical species (see Fig. 3 in ). As described above, limited variables were included in the control vector and optimized by applying covariance localization in the reanalysis calculations. The emissions include both anthropogenic and natural (i.e., soil and biomass burning) sources, except for chemical productions of CO by the oxidation of methane and biogenic non-methane hydrocarbons (NMHCs). The emission estimation is based on a state augmentation technique, in which the background error correlations determine the relationship between the concentrations and emissions of related species for each grid point. We employed a scheme to correct diurnal emission variability from the simultaneous assimilation of multiple satellite measurements obtained at different overpass times . The simultaneous assimilation of multiple-species data and the simultaneous optimization of the concentrations and emission fields are important to propagate the observational information between various species and modulate the chemical lifetimes of many species, as demonstrated in our previous studies .

An observation operator is applied to assimilate individual measurements to map the model fields into the retrieval space. The operator includes the spatial interpolation operator, a priori profile for the satellite retrievals, and averaging kernel. See for more details.

Compared with the aircraft measurements (Fig. 4), the control run mostly overestimates SO2 concentrations in the lower troposphere by a factor of 2–5 for the DC-3, SEAC4RS, and KORUS-AQ profiles. The data assimilation greatly reduced the positive model biases and reproduced the observed profiles, with mean bias reductions of up to 90 %, mainly because of reduced surface SO2 emissions. The near-surface SO2 concentrations became too low (by about 20 %) after data assimilation for the SEAC4RS and KORUS-AQ profiles, which could be associated with the large uncertainty and assumptions made (e.g., constant observation errors; see Sect. 3.1.5) in the assimilated OMI SO2 retrievals and possible overestimation of an atmospheric sink of SO2 within the boundary layer in the model. Any errors in the assimilated retrievals and model processes could introduce biases in the estimated emissions (see Sect. 5.3). For the ARCTAS profiles, both the control run and reanalysis show excessively low SO2 concentrations throughout the troposphere, likely associated with the lack of observational constraints and large uncertainty in the model processes.

OH is directly linked to the concentrations of species determining the primary production (O3 and H2O), removal (CO and methane), and regeneration of OH (NOx). Because of the multi-constituent constraints for many key species, a positive impact is expected on global OH fields, given that the reactions are reasonably well described by the model. As shown in Fig. 9, the global tropospheric OH distribution is substantially modified in the reanalysis. Data assimilation mostly increased OH, with the largest increases in the SH tropics. The mean OH concentration in the SH tropics is increased over the reanalysis period by 20 %–25 % at 700 hPa and 30 %–45 % at 500 hPa. In the NH extratropics, the OH increases are about 15 %–20 % at 700 hPa and 20 %–30 % at 500 hPa. These increases are found throughout the reanalysis period, with the largest increases during spring–summer in both hemispheres. Both the concentration assimilation and the emission optimization were important in introducing these OH changes. The 14-year mean NH/SH OH ratio in the chemical reanalysis is 1.19±0.015 (1σ interannual variability), in contrast to 1.30 in the control run, which is closer to the estimates of 0.97±0.12 based on methyl chloroform observations . The NH/SH ratio is maximum in 2016 (1.23), reflecting relatively high OH concentrations over East Asia and low concentrations over South America (Figs. S3 and S4). The interannual variability can be associated with both human and natural activities, through changes in climate condition including lightning and in anthropogenic emissions, as discussed in and .

The tropospheric mean OH concentrations averaged during the reanalysis periods are estimated at 8.7×105 molec.cm-3 for the control run and 11.5×105 molec.cm-3 for the reanalysis. By applying the obtained tropospheric OH burden to the ACCMIP multi-model mean estimates of tropospheric chemical methane lifetime (τOH(chemical)) from for 2000, with the mean OH concentrations of (11.7±1.0)×105 molec cm−3, τOH(chemical) of 9.3±1.6 years, and total lifetime (τOH(total))) of 8.6 years, we estimated τOH(chemical) for 2005–2018 at 12.5 years for the control run and 9.5 years for the reanalysis. The large changes in methane lifetime have a strong implication for the methane budget estimate including emission inversions.

The model bias against the aircraft profiles varies largely among the campaigns. For the INTEX-B profile, the control run captured the observed profile well, whereas the data assimilation puts too high OH throughout the troposphere, likely corresponding to increased ozone. For the ARCTAS-A, ARCTAS-B, and KORUS-AQ profiles, the model negative bias is strongly reduced by data assimilation in the free troposphere, mainly due to the increased NOx emissions and resultant increased ozone. The large negative bias near the surface remains for the ARCTAS-B profiles. Remaining large errors in HO2 could influence the performance of the simulation of OH for some profiles, including ARCTAS-B. Observed OH concentrations are also largely uncertain (e.g., ). estimated the absolute accuracy for aircraft HOx measurements to be ±32 % at 2σ confidence.

The ATom measurements provide great data to evaluate remote tropospheric OH, for instance, those derived from OMI CH2O measurements . Compared with all the profiles during the ATom-1 and ATom-2, the RMSE is reduced by up to 30 % above about 600 hPa in the reanalysis than in the control run (Fig. 10a). Improved agreements can be found for many profiles throughout the troposphere (Fig. S5), whereas a few profiles (e.g., on 6 August 2018, 2 February 2017, and 5 February 2017) led to a degradation in the agreements in the lower troposphere. The ATom measurements provide comprehensive pictures of interhemispheric ratios of OH and its seasonal changes over remote oceans (Fig. 10b, c). The observed interhemispheric ratio is about 2 near the surface and exceeds 7 in the middle troposphere in boreal summer (ATom-1), whereas it is 0.4–0.8 throughout the troposphere in boreal winter (ATom-2). The control run mostly overestimated the ratios by a factor of up to 2.5 for ATom-1 and by up to 1.6 for ATom-2, with the largest overestimation in the lower troposphere. Data assimilation decreased the ratio and shows improved agreements from the surface to the upper troposphere. Because the chemical lifetimes of many species are affected by the amount of OH, the improved representation of OH profiles and its global distributions suggests that multi-constituent assimilation improves the simulation of concentrations and emissions of various species. Decadal changes in the tropospheric OH derived from the reanalysis will be discussed in Sect. 6.

Although no aerosol observations were assimilated, improved representations of aerosol fields can be expected through corrections made to trace gas concentrations, such as NOx and SO2, that affect the formation of secondary aerosols. Figure 11 shows the scatter plots of ammonium (NH4), nitrate (NO3), and sulfate (SO4) aerosols from in situ observations, control run, and reanalysis. The control run overestimates ammonium and sulfate aerosol concentrations and underestimates the nitrate aerosol concentrations for most of the CASTNET (the US), EANET (East Asia), and EMEP (Europe) sites, while the estimated mean biases (Table 6) are dominated by large biases for a few stations. The median biases are lower than the mean biases for many cases. The multi-constituent data assimilation substantially modified the aerosol concentrations. The RMSE is decreased by 7 %–61 % for ammonium aerosols, 2 %–11 % for nitrate aerosols, and by 5 %–38 % for sulfate aerosols, while the correlation improved for many cases, for instance, from 0.27 to 0.42 for ammonium aerosols compared to the EMEP observations. The median bias also became smaller (by up to 75 %) for most cases. For urban stations, the model representativeness errors may prevent data assimilation improvements, which may have caused degradation for some cases. An assessment of global particulate nitrate and ammonium aerosols in the MIROC-CHASER simulation is also given in .

Substantial changes in the aerosol concentrations suggest considerable potential of trace gas data assimilation for constraining secondary aerosol formation processes. Among numerous factors, optimizations of NOx and SO2 emissions are considered to be essential to improve secondary aerosol formation in our framework. Our comparisons show improved agreements against various aircraft measurements for many key species relevant to aerosol formations, such as NO2, HNO3, and SO2 (see Sect. 4.8). Meanwhile, assimilation of aerosol optical depth (AOD) and aerosol concentration observations are required to further improve the representation of primary aerosol emissions and concentrations e.g.,. Simultaneous assimilation of trace gas and aerosol observations would be a powerful approach to fully represent aerosol–gas interactions in the data assimilation framework, which would improve both trace gas and aerosol data assimilation analysis.

As shown in Fig. 4, the observed main structures of HNO3 are generally captured well by the control run, with increasing errors toward the surface for some profiles. The increase in HNO3 toward the surface is driven mainly by the oxidation of NOx in polluted areas for most profiles except for the ARCTAS-A. The control run overestimated the lower tropospheric HNO3 concentrations by a factor of more than 2 for the INTEX-B, DISCOVER-AQ, and KORUS-AQ profiles, whereas it mostly underestimated HNO3 concentrations throughout the troposphere for the ARCTAS-B, DC3–DC8, DC3-GV, and SEAC4RS profiles. For ARCTAS-A, the control run largely overestimated HNO3 above about 600 hPa. The data assimilation mostly increases the HNO3 concentrations throughout the troposphere except for the ARCTAS-A and DISCOVER-AQ profiles, which is primarily attributed to the increased NOx emissions and NO2 concentrations. The data assimilation increase largely reduced the negative model biases in the free troposphere and lower stratosphere for the ARCTAS-A and DC3–DC8 and DC3-GV profiles. In contrast, it increased the positive model bias in the lower troposphere for INTEX-B and KORUS-AQ. For DISCOVER-AQ, the positive model bias in the lower troposphere is greatly reduced. To improve the lower tropospheric HNO3 concentrations, corrections for its removal processes including deposition and direct assimilation of tropospheric HNO3 measurements could be important. In the UTLS region, the MLS HNO3 data assimilation mostly removed the positive model bias in HNO3 for the ARCTAS-AQ profile.

The tropospheric HO2 profiles mainly reflect variations in water vapor. The control run generally overestimates HO2 throughout the troposphere except for the ARCTAS-B profile. The control run overestimates the tropospheric HO2 concentrations. As an exception, the model negative bias is found in the lower troposphere for the ARCTAS-B and in the upper troposphere for KORUS-AQ. Data assimilation slightly increases HO2 in the lower troposphere and decreases it in the upper troposphere for most cases. The increased HO2 in the lower troposphere could be associated with increased CO through the reaction of OH with CO that converts OH into HO2. The remaining errors could be associated with model errors for instance in the heterogeneous loss of HO2 on cloud droplets.

Both the control run and reanalysis capture the tropospheric CH2O profiles well for most campaigns, except for the ARCTAS-A where CH2O concentrations are underestimated by a factor of 2 throughout the troposphere. The data assimilation influences on CH2O concentrations are small because of the lack of assimilation of direct measurements. Interspecies correlations with CH2O in the state vector were neglected for all the assimilated measurements, which also prevented data assimilation adjustments to CH2O.

The multi-constituent data assimilation framework has been used to improve estimates of global NOx emissions . In this framework, the simultaneous optimization of concentrations and emissions of many species reduces the model-observation mismatches that arise from model errors other than those related to emissions. Meanwhile, the simultaneous assimilation of multiple satellite measurements obtained at different overpass times was employed to constrain diurnal emission variability . Thus, the estimated emissions in TCR-2 can be expected to provide unique information on decadal changes in anthropogenic and natural emission sources. The global surface NOx emissions averaged over the 14 years are estimated at 49.2 TgN yr-1 from the data assimilation, which is 17.4 % larger than the a priori emissions (41.9 TgN). The mean total emissions are estimated at 29.0 TgN (12.0 % larger than the a priori emissions) for the NH (20–90∘N), 16.8 TgN (22.6 % larger) for the tropics (20∘ S–20∘ N), and 3.5 TgN (29.6 % larger) for the SH (20–90∘ S), as summarized in Table 7.

Data assimilation largely increased surface NOx emissions over major polluted areas such as most parts of China, Southeast Asia, and Europe (Fig. 12). The increments vary from year-to-year over these regions. For instance, they decreased in more recent years over China. This is associated with the assumptions applied to the a priori emissions, such as the use of 2010 anthropogenic emissions in the estimations for 2011–2018. The complex spatial structure of the increments over India and eastern China suggests that the emissions evolved differently among the grid points while the bottom-up inventories exhibited large uncertainty. The seasonal variations are also largely modified for many regions. The bottom-up inventories did not consider seasonal variability for anthropogenic emissions, such as emissions from wintertime heating. Over agriculture and desert areas such as the western and central US, Sahara, western China, and southern Europe, the summertime large positive increments can be attributed to underestimated soil emissions, as commonly suggested by and . By applying the ratio of different emission categories within the a priori emissions for each grid point, the global total a posteriori NOx emissions by soils is estimated at 8.7 TgN, which is about 58 % larger than the a priori emissions (5.5 TgN) and closer to other recent estimates of around 10 TgN . The large positive increments over north and central Africa, South America, and Southeast Asia suggest general underestimations in biomass burning emissions in the GFED v4 inventories.

Figure 15 depicts the decadal trend of the estimated NOx emissions over major polluted regions, updated from our previous estimates . The detailed spatial maps of the NOx emissions for an individual year are shown in Fig. S6, and the regional yearly emission values are summarized in Table S3. For China, the estimated emissions increased from 2005 to 2011 by 30 % and decreased rapidly after 2013. Since 2016, the Chinese country-total emissions started to increase again, while exhibiting substantial spatial differences in the estimated trends. For India, the emissions show a continuous increase by 30 % over 14 years. The Middle East also exhibits an emissions increase from 2005 to 2014 of 24 %. After 2014, it exhibits a flattened or a slight negative trend, however with substantial spatial variations. For the US, the emissions show a reduction of 25 % from 2005 to 2010. The emission reduction is slowed down afterwards, as suggested by using our previous emission estimates based on the TCR-1 system . The estimated emissions for Europe show a negative trend during 2005–2014 (by 13 %), followed by a flattened trend. Our estimates also reveal substantial emission increases for most parts of southeastern and southern Asia and Mexico after 2014. In spite of the substantial changes for many regions reflecting a combination of effects of environmental policies and economic activities, the global total emissions did not change obviously over 2005–2018 (49.2±2.8 TgN).

The 14-year mean of global total emissions of CO is increased by 26 % by data assimilation (1104 Tg CO yr-1 vs. 877 Tg CO yr-1), which is attributable to a 35 % increase in the NH and 18 % increase in the tropics. The large positive increments are found over eastern and southern China, northern parts of southeastern Asia, India, and central Africa (Fig. 12). The emissions increase in the NH is large in the boreal late winter–spring period, especially over polluted areas at NH midlatitudes, which enhanced the seasonal amplitude for industrialized countries.

The estimated emissions show strong negative trends over most parts of China (by -0.6 % yr-1), Japan (-2.2 % yr-1), Europe (-0.8 % yr-1), and the US (-1.8 % yr-1) and positive trends over India (1.5 % yr-1) during 2005–2018 (Fig. 14). As seen in the underestimated decreasing trends of surface CO concentration for the NH in the current estimates (see Sect. 4.3), the obtained CO emissions could underestimate a long-term decreasing trend in CO emissions in NH as compared with other estimates e.g.,. For biomass burning areas, such as Southeast Asia, Amazon, and central and north Africa, the estimated emissions exhibit a strong year-to-year variability, such as enhanced emissions over southeastern Asia in 2006–2007 and 2015 and over South America in 2007 and 2010 (Fig. S7). The regional total surface CO emission values are summarized in Table S4.

In the multi-constituent data assimilation framework, the assimilation of non-CO observations influences various chemical species including OH, which provides additional constraints on the CO emission estimation. As suggested in Sect. 4.6, possible underestimations in OH in the control run could lead to underestimations in the estimated CO emissions for many regions. Assimilation of ozone and NO2 measurements exerts a substantial influence on OH and thus on CO emission estimates. Nevertheless, insufficient corrections for the NH extratropical CO suggest requirements for further improving CO emission estimates, as will be discussed in Sect. 7.4.

The 14-year mean global total surface SO2 emissions are decreased by about 30 % by data assimilation from 50.9 to 35.1 TgS, with large reductions in the NH (by 37 %). The negative data assimilation increments are also large over China (by -50 %), India (-64 %), and Southeast Asia (-75 %), suggesting overestimated emissions in the bottom-up inventories for most industrialized areas. In contrast, the mean increments are positive over western Europe and the western US (by up to 50 %). These large adjustments suggest large uncertainties in the current inventories, as suggested by and . The increments changed greatly during the 14 years for many regions, according to substantially temporal changes in the observed SO2 columns.

The a posteriori SO2 emissions show substantial reductions during the years 2005–2018 over China (by -6.1 % yr-1 for the country total), some parts of Europe (by up to -6 % yr-1 at grid scale), the eastern US (up to -3 % yr-1),, and Japan (up to -8 % yr-1), whereas it shows strong increase over India (up to 5 % yr-1), the Middle East (up to 4 % yr-1), and Mexico (about 4 % around Mexico city). The negative trends are particularly large over central and southwestern China, which is due to strong emission reductions after 2010 (Fig. S8), as reported by and . In contrast, the reductions are smaller for northwestern China, which could be attributed to the exceptional positive trend in this region after 2010 . The obtained strong emission changes (summarized in Table S5), along with changes in NOx emissions, have strong implications into the secondary aerosol formation processes for many polluted regions.

The a posteriori SO2 emissions seem excessively high in 2011 for many regions (see Fig. S8), which seems unrealistic and could be due to potential problems in data assimilation setting or assimilated retrievals. Volcanic eruptions also affected a temporal increase in the estimated emissions, as shown by using the OMI SO2 measurements. This requires additional careful verification before used in detailed trend analysis. The estimated emissions should have a large uncertainty associated with large retrieval uncertainty (e.g., random noise of ∼0.5 DU for remote areas, as described in ) and the assumed constant retrieval errors and air mass factor. Because the optimized emission factors were applied to the a priori emissions, any missing sources in a priori inventories e.g., could also lead to systematic biases in the estimated emissions.

The multi-constituent data assimilation with different vertical sensitivities provides strong constraints to distinguish between surface and lightning NOx sources and to correct the vertical profiles of lightning NOx sources. The a posteriori global total lightning NOx source is 7.5 TgN, which is about 32 % higher than in the control run (5.7 TgN). The estimated global total emission is about 17 % larger than our previous estimates (6.4 TgN) based on the TCR-1 system . The differences between two estimates can primarily be attributed to change in the forecast model and its resolution. The resolution improvement affected the representation of cumulus convection and lightning frequency distributions. Nevertheless, both estimates suggest common problems of the lightning parameterizations, such as the requirements of modifying the C-shape assumption and land–ocean contrasts.

The long-term trends of lightning NOx are mostly insignificant and dominated by multi-year-scale variability rather than linear increase or decrease (Fig. S9 and Table S6). The interannual variability of lightning NOx during 2005–2018 is large over southeastern and southern Asia, central and southern Africa, central America, and the Amazon (Fig. 14). Over central Africa, the lightning NOx sources are large in 2006 and 2008 and small in 2016. The lightning NOx sources also show strong interannual variations over the Amazon, with a maximum in 2009 and minimum in 2015. These changes are considered to be connected with climate variability such as El Niño–Southern Oscillation (ENSO) , associated with variations in convective activity, thunderstorm type, and cloud distributions. The lack of TES ozone measurements after 2010 introduced artificial changes, whereas the variations are considered to be consistent during 2005–2009 and 2010–2018 in the reanalysis when the observation density is nearly constant. Further detailed analyses are required to understand the possible causal mechanisms of the multi-year variability, which would provide important implications into chemistry–climate interaction processes. The regional total values of the estimated lightning NOx sources for major source regions.

Significant temporal changes in the reanalysis quality can partly be attributed to discontinuities in the observing systems. As discussed in Sect. 6, the reduced number of assimilated TES ozone retrievals after 2010 substantially influenced the usability of the reanalysis products for trend analyses. Meanwhile, changes in the NO2 observing system, including the OMI row anomaly after December 2009 and the limited temporal coverage of SCIAMACHY and GOME-2, are also considered to affect long-term consistency. The reanalysis ozone bias against the ozonesonde measurements was relatively large in the tropical lower and middle troposphere, which could partly be attributed to the positive biases in the assimilated TES measurements. tested a bias correction scheme for assimilation of TES ozone based on evaluation results using ozonesonde measurements ; however, the results were not always positive because of the difficulty in estimating the detailed bias structure. The reanalysis ozone bias can also be affected by biases in ozone precursors measurements such as NO2 measurements. Nevertheless, we did not apply any bias correction to any assimilated measurements in the reanalysis because of the difficulty in estimating the bias structure, including inter-measurement biases. To improve the temporal consistency, a detailed assessment of biases in individual retrievals e.g., and between different retrieval products would be helpful, as already tested in the CAMS reanalysis .

The availability of the ozonesonde measurements for the most recent years was also limited at the time of this research, which limits the evaluation of the reanalysis performance. The mean ozonesonde concentrations at SH midlatitudes show rapid changes after 2017, which were associated with the reduced number of available ozonesonde observations at the time of this research and consequent increased representativeness errors of the ozonesonde network for the large domain. The current ozonesonde network is also too sparse to capture the regional and monthly representative ozone fields, especially in the tropics, which can lead to substantial sampling biases in the reanalysis performance, as discussed for evaluations of chemistry climate models .

Even though the assimilation of multi-species data influences the representation of various chemical fields, including precursor emissions, the remaining model errors (such as chemical reaction rates and deposition rates) and the limited representation of atmospheric chemistry and meteorology limit the data assimilation improvements. developed a MOMO-Chem framework using four global chemical transport models (CTMs) and an EnKF data assimilation that directly accounts for model error in transport and chemistry. They demonstrated that the observational density and accuracy was sufficient for the assimilation to reduce the influence of model errors in data assimilation analysis; i.e., multi-model spread of ozone analysis is reduced by 20 %–85 % in the free troposphere. Model negative biases in the tropospheric NO2 column and surface CO in the NH are also greatly reduced by more than 40 % in all models. MOMO-Chem provides integrated unique information on the tropospheric chemistry system and its uncertainty ranges, which would benefit future development of chemical reanalysis.

Meanwhile, a strong reanalysis dependence on forecast model performance was found on the near-surface concentrations and precursor emissions, associated with insufficient observational constraints . The ozone response to precursor's emissions was also found to be strongly sensitive to the chemical mechanisms in the model, which varied by a factor of 2 for end-member models, revealing fundamental differences in the representation of fast chemical and dynamical processes . The emissions of ozone precursors other than NOx and CO, such as VOCs, have a pronounced influence on the tropospheric chemistry. Adjusting additional model parameters such as VOC emissions, deposition, and/or chemical reactions rates could help reduce model errors. Furthermore, a simultaneous assimilation of trace gas and aerosol measurements would also reduce systematic model errors and provide more comprehensive information on various applications. Meanwhile, high-resolution modeling is also essential for accurate modeling of nonlinear chemistry and resolving rapid variations in air pollution and emissions around cities , which is also needed to improve the reanalysis performance.

Next-generation satellite data products, which have improved vertical sensitivity and accuracy and improved spatial sampling, have great potential to further improve emissions and surface ozone analyses. The exploitation of existing sounders and development of multispectral retrievals is expected to add constraints on the reanalysis and to remove remaining model errors. For instance, as demonstrated in Sect. 3.2.2, the multispectral AIRS/OMI ozone retrievals provide decadal records of tropospheric ozone. demonstrated that assimilation of AIRS/OMI ozone data, together with precursors and stratospheric measurements, improved the tropospheric ozone analysis over East Asia during the KORUS-AQ campaign for any meteorological conditions. This would provide important constraints on the decadal ozone variations in the reanalysis.

Tropospheric PAN retrievals from TES were used to evaluate the reanalysis fields over both polluted and remote regions (see Sect. 4.1.2). Cross-Track Infrared Sounder (CrIS) on Suomi-NPP also provides tropospheric PAN retrievals with improved coverage and accuracy compared with TES . Assimilating PAN retrievals from TES and CrIS can be expected to improve the representation of the global nitrogen cycles, which would also benefit surface and lightning NOx emission estimates combining with tropospheric NO2 column measurements. Meanwhile, TROPOMI provides global maps of the tropospheric NO2 column on a daily basis with improved accuracy and higher spatial resolution compared with OMI . Assimilating TROPOMI NO2 has potential for improved evaluation of the changing landscape of emissions on urban-to-regional and regional-to-global scales . Assimilation of other retrievals such as OMI and TROPOMI CH2O; CrIS Isoprene ; and TES, CrIS, and IASI NH3 would also help improve the model chemistry and tropospheric ozone reanalysis.

The validation results of CO concentrations suggested under-corrected surface emissions of CO, especially in the NH extratropics (see Sect. 4.3). There are several reasons for this. First, while our previous estimates in TCR-1 used MOPITT TIR-only CO profile data at 700 hPa, TCR-2 used TIR/NIR total column retrievals. The truly optimal settings of data assimilation parameters probably differ between the two setups. The TCR-2 setting might require further optimization. Second, the chi-square and observation-minus-forecast statistics suggested underestimated background errors of CO for many regions. Considering different systematic model errors and the increased model resolution between TCR-1 and TCR-2, background error inflation settings need to be further optimized for TCR-2. Third, the data assimilation window (2 h) used is clearly too short for CO emission estimates, considering its relatively long chemical lifetime and the coverage and limited near-surface sensitivity of MOPITT measurements. A longer data assimilation window for CO emission estimates, while keeping the short window for short-lived species such as NOx and ozone, would be required. Finally, CO is produced by the oxidation of methane and biogenic NMHCs . These components can account for part of the missing CO concentrations. Adding more observational constraints, such as for CH2O and methane, would help improve CO emission estimates (e.g., ). We have already tested some of the developments and obtained improved estimates of CO concentrations and emissions, which will be implemented in the next-generation chemical reanalysis.

Important information regarding the reanalysis product is provided by the error covariance. Within the EnKF assimilation framework, the analysis ensemble spread is estimated from the standard deviation across the ensemble and provides a measure of the uncertainty of the reanalysis product. The information on the analysis uncertainty is included in the TCR-2 reanalysis products. For instance, as shown in Fig. S14, the analysis spread for ozone is about 1–3 ppb in the tropics and subtropics and 3–12 ppbv in the extratropics before 2011. These variations may be related to spatial variations in observation errors, the number of assimilated measurements, and model errors. After 2011, the spread mostly becomes smaller than 3 ppb for the globe. The analysis uncertainty after 2011 seems excessively small as compared with the validation results against the ozonesonde measurements (see Sect. 4.1.1), which is likely associated with the stiff tropospheric chemical system and lack of observational constraints. The obtained results indicate the requirements for additional observational information and/or stronger covariance inflation for measuring the analysis spread corresponding to actual analysis uncertainty. At 200 hPa, the analysis spread is about 1–4 ppb in the tropical upper troposphere and about 20–80 ppb in the extratropical lower stratosphere. The relative value (compared to the analysis ozone) is smaller in the extratropics because of the high accuracy of the MLS measurements. For other species, further investigations would be required to clarify the usefulness of the estimated uncertainty (i.e., analysis spread).

The long-term reanalysis products allow detailed evaluations of interannual and decadal variations in atmospheric composition simulated by chemistry climate and chemistry transport models in association with changes in human activities and natural processes. Employing TCR-1, evaluated the ACCMIP tropospheric ozone simulations and investigated sampling biases in model evaluation results when using the ozonesonde network. Evaluations of ozone simulations using chemical reanalyses provide important information on the performance of the simulated radiative forcing (e.g., ), attribution of radiative forcing , and emergent constraints on future projections . Validation of short-lived species can be used to identify potential sources of error in model fields and is also important for evaluating the radiative forcing because simulated OH fields influence simulated climates through their influences on methane . The optimized precursor emission fields can be used to validate bottom-up emission inventories and lightning parameterizations. As changes in tropospheric ozone burden and NOx emissions show a close relation in different future scenarios , evaluations using the estimated emissions and evaluated model response to emissions have the potential to evaluate preindustrial, present-day, and future model simulations. Short-lived climate pollutants (SLCP) are an increasingly important component of greenhouse gas budgets that limit warming to target temperatures, e.g., 1.5 or 2 ∘C . Chemical reanalysis can play a crucial role in assessing the changes and efficacy of SLCPs.