Inverse modeling of SO2 and NOx emissions over China using multisensor satellite data – Part 1: Formulation and sensitivity analysis

SO2 and NO2 observations from the Ozone Mapping and Profiler Suite (OMPS) sensor are used for the first time in conjunction with the GEOS-Chem adjoint model to optimize both SO2 and NOx emission estimates over China for October 2013. Separate and joint (simultaneous) optimizations of SO2 and NO2 emissions are both conducted and compared. Posterior emissions, compared to the prior, yield improvements in simulating columnar SO2 and NO2, in comparison to measurements from the Ozone Monitoring Instrument (OMI) and OMPS. The posterior SO2 and NOx emissions from separate inversions are 748 Gg S and 672 Gg N, which are 36 % and 6 % smaller than prior MIX emissions (valid for 2010), respectively. In spite of the large reduction of SO2 emissions over the North China Plain, the simulated sulfate–nitrate–ammonium aerosol optical depth (AOD) only decrease slightly, which can be attributed to (a) nitrate rather than sulfate as the dominant contributor to AOD and (b) replacement of ammonium sulfate with ammonium nitrate as SO2 emissions are reduced. For joint inversions, both data quality control and the weight given to SO2 relative to NO2 observations can affect the spatial distributions of the posterior emissions. When the latter is properly balanced, the posterior emissions from assimilating OMPS SO2 and NO2 jointly yield a difference of −3 % to 15 % with respect to the separate assimilations for total anthropogenic SO2 emissions and ±2 % for total anthropogenic NOx emissions; but the differences can be up to 100 % for SO2 and 40 % for NO2 in some grid cells. Improvements on SO2 and NO2 simulations from the joint inversions are overall consistent with those from separate inversions. Moreover, the joint assimilations save ∼ 50 % of the computational time compared to assimilating SO2 and NO2 separately in a sequential manner of computation. The sensitivity analysis shows that a perturbation of NH3 to 50 % (20 %) of the prior emission inventory can (a) have a negligible impact on the separate SO2 inversion but can lead to a decrease in posterior SO2 emissions over China by −2.4 % (−7.0 %) in total and up to −9.0 % (−27.7 %) in some grid cells in the joint inversion with NO2 and (b) yield posterior NOx emission decreases over China by −0.7 % (−2.8 %) for the separate NO2 inversion and by −2.7 % (−5.3 %) in total and up to −15.2 % (−29.4 %) in some grid cells for the joint inversion. The large reduction of SO2 between 2010 and 2013, however, only leads to ∼ 10 % decrease in AOD regionally; reducing surface aerosol concentration requires the reduction of emissions of NH3 as well. Published by Copernicus Publications on behalf of the European Geosciences Union. 6632 Y. Wang et al.: Inverse modeling of SO2 and NOx emissions – Part 1

nitrate rather than sulfate as the dominant contributor to AOD and (b) replacement of ammonium sulfate with ammonium nitrate as SO2 emissions are reduced. Both data quality control and the weight given to SO2 relative to NO2 observations can affect the spatial distributions of the joint inversion results. When the latter is properly balanced, the posterior emissions from assimilating OMPS SO2 and NO2 jointly yield a difference of -3% to 15% 25 with respect to the separate assimilations for total anthropogenic SO2 emissions and ±2% for total anthropogenic NOx emissions; but the differences can be up to 100% for SO2 and 40% for NO2 in some grid cells. Improvements on SO2 and NO2 simulations evaluated with OMPS and OMI measurements from the joint inversions are overall consistent with those from separate inversions. Moreover, the joint assimilations save ~50% of the computational time than assimilating SO2 and NO2 separately when computational resources are limited to run one inversion at 30 a time sequentially. The sensitivity analysis shows that a perturbation of NH3 to 50% (20%) of the prior emission used in the bottom-up approach (Janssens-Maenhout et al., 2015). Moreover, the large uncertainty is compounded by possible discrepancies caused by the temporal lag of bottom-up emission inventories and the rapid changes of emissions over time.

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Several methods have been developed to update SO2 and NOx emissions using satellite VCD retrievals of SO2 and NO2, which have global coverage and near-real-time access. The mass balance method, which scales prior emissions by the ratios of observed VCDs to Chemistry Transport Model (CTM) counterparts, was applied to SO2 retrievals from SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) and Ozone Monitoring Instrument (OMI) (Lee et al., 2011;Koukouli et al., 2018) and to NO2 from Global Ozone 70 Monitoring Experiment (GOME) and OMI (Martin et al., 2003;Lamsal et al., 2010) to estimate SO2 and NOx emissions, respectively. Lamsal et al. (2011) simulated the sensitivity of VCDs to emissions (the finite difference mass balance approach) using a CTM, which was applied to OMI NO2 retrievals to estimate NOx emissions. SO2 VCD retrievals from GOME, GOME-2, SCIAMCHY, and Ozone Mapping and Profiler Suite (OMPS) were used to estimate point sources through linear regression between VCDs and emissions or function fitting, although the 75 method can only detect about half of the total anthropogenic SO2 emissions (Li et al., 2017a;Zhang et al., 2017;Fioletov et al., 2013;Fioletov et al., 2016). With explicit considerations of chemistry, transport, and deposition, the four-dimension variational data assimilation (4D-Var) approach was applied to estimate emissions using SO2 data from OMI Qu et al., 2019a), and NO2 data from SCIAMCHY, GOME-2, and OMI (Kurokawa et al., 2009;Qu et al., 2017;Kong et al., 2019). The 4D-Var posterior has a smaller root mean 80 square error than the mass balance posterior, especially in the conditions when the initial guess and true emissions have different spatial patterns (Qu et al., 2017); this is because the spatial extent of source influences on modelled column concentrations (Turner et al., 2012) are only indirectly accounted for in the mass balance approach. Cooper et. al (2017), however, showed that the iterative finite difference mass balance approach has similar accuracy as the 4D-Var approach for global-scale models with coarse resolution. To combine the strengths of the 85 4D-Var and mass balance approaches, Qu et al. (2017) further introduced a hybrid 4D-Var-mass-balance approach, which can better capture trends and spatial variability of NOx emissions than the mass balance approach and save significant computational resources when applied to constrain monthly NOx emissions for multiple years. Other data assimilation approaches including the ensemble Kalman filter method (Miyazaki et al., 2012; and the Daily Emission estimates Constrained by Satellite Observation (DECSO) algorithm (Mijling and 90 van der A, 2012;Ding et al., 2015) have also been used to constrain NOx emissions. Here, we focus on the development and feasibility for joint 4D-var assimilation of satellite-based SO2 and NO2 data to optimize SO2 and NOx emission strengths simultaneously. Specifically, this study aims to conduct 4D-Var assimilation of VCDs of SO2 and NO2 from OMPS to constrain SO2 and NOx emissions over China using the 95 GEOS-Chem 4D-Var inverse modeling framework. In our companion study , we develop approaches to downscaling the optimized emission inventories for improving air quality predictions. Despite their numerous applications for top-down estimate of SO2 and NOx emissions in the past two decades, GOME and SCIAMCHY stopped providing data in 2004 and 2012, respectively, while OMI has been suffering from a row anomaly that leads to much less spatial coverage and larger data uncertainty (Schenkeveld et al., 2017). Hence, it 100 is important to study the potential of next-generation sensors such as OMPS toward continuously monitoring the change of SO2 and NOx emissions and their atmospheric loadings. Two OMPS sensors onboard Suomi NPP and NOAA-20 have been launched in 2011 and 2018, respectively, and the third one is expected to be launched in 2020. As OMPS will continue to provide SO2 and NO2 retrievals in the next two decades, this study seeks to provide a critical assessment of the extent to which the OMPS observations improve emissions estimates and air 105 quality forecast at the regional scale for the first time.
The novelty of this study lies not only in the first application of OMPS SO2 and NO2 retrievals to constrain emissions using the 4D-Var technique but also in the deployment of OMI data to assess the GEOS-Chem simulation with posterior emissions, thereby studying the degree to which OMPS and OMI retrievals, despite their 110 difference in sensor characteristics and inversion techniques, can provide consistent constraints for the model improvement. Qu et al. (2019a) showed that posterior SO2 emissions from different OMI SO2 products vary in strength and have consistent trend signs. Our study here using OMPS thus touches an important issue, which is whether or not there would be any artificial trends in our climate data record of atmospheric SO2 and NO2 due to the transition of satellite sensors. Our study is also different from past studies Qu et al., 2017;Qu 115 et al., 2019a;Qu et al., 2019b) that have applied the 4D-Var technique to OMI data with the GEOS-Chem adjoint model, but did not include evaluation with independent satellite data. Qu et al. (2019b) showed joint inversion using OMI SO2 and NO2 benefits from simultaneous adjustment of OH and O3 concentrations, which supports assimilating OMPS SO2 and NO2 observations simultaneously in this study. Additionally, considering that the uncertainty of NH3 emission inventories is up to 153% over China (Kurokawa et al., 2013) and NH3 emissions 120 are not constrained in our inversions, we also explore issues related to the co-variation among species that appear to be independent but indeed are connected through chemical processes and analyze the differences in responses of emissions and aerosols to NH3 emissions uncertainty between joint and single-species assimilations.
We describe OMPS and OMI data in Sect. 2. The GEOS-Chem model and its adjoint as well as the design of 125 numerical experiments are presented in Sect. 3. Results of case studies for October 2013 are provided in Sect. 4.
Sect. 5 consists of discussion and conclusions.

OMPS data as constraints
We use OMPS Level-2 SO2 and NO2 tropospheric VCDs in October 2013 as constraints to optimize SO2 and NOx 130 emissions over China. The OMPS nadir mapper on board the Suomi-NPP satellite, launched in November 2011, observes hyperspectral solar radiance and earthshine radiance at 300-380 nm (Flynn et al., 2014). With 35 detectors of 50x50 km nominal pixel size in cross-track direction, OMPS has a swath of 2800 km flying across the equator at 1:30 PM local time ascendingly at the sunlit side of the Earth surface and providing global coverage daily. Both SO2 and NO2 are retrieved through the Direct Vertical Column Fitting (DVCF) algorithm with SO2 135 and NO2 atmospheric profile information from GEOS-Chem simulations and have a retrieval precision of 0.2 DU and 0.011 DU, respectively Yang et al., 2014).
Only pixels with both Solar Zenith Angle (SZA) and View Zenith Angle (VZA) less than 75° are used, as larger SZA or VZA result in longer light path length, and consequently less information content and lower data quality 140 for retrieving the change of SO2 or NO2 loadings in the Plane Boundary Layer (PBL) where the two trace gases from anthropogenic sources mainly concentrate. We also remove the pixels with Radiative Cloud Fraction (RCF) larger than 0.2 for SO2 and 0.3 for NO2 as a trade-off between the data amount and cloud impacts. Considering their large uncertainty, OMPS SO2 retrievals in the grid cell where the prior simulation is less than 0.1 DU will not be used, except in Quality Control (QC) sensitivity analysis experiments. 145 2.2 OMI data for assessment OMI Level-3 SO2 and NO2 tropospheric VCDs at a spatial resolution of 0.25°x0.25° from NASA are used for evaluating the model results. OMI is a UV-vis hyperspectral sensor that observes solar irradiance and earthshine radiance at 300-500 nm. The swath of OMI is 2600 km, consisting of 60 detectors with the nominal pixel size of 13x24 km 2 at nadir. OMI flies across the equator in the ascending node at 1:45 PM local time, which is very close 150 to the 1:30 PM local time for OMPS. Due to row anomaly (Schenkeveld et al., 2017), OMI takes more than one day to provide global coverage. The Level-3 product is derived from the Level-2 product; the latter is retrieved through the Principal Component Analysis (PCA) algorithm with a fixed Air Mass Factor (AMF) assumption for SO2 (Li et al., 2013) and variation of the Differential Optical Absorption Spectroscopy (DOAS) algorithm for NO2 Marchenko et al., 2015), with a precision of 0.5 DU (Li et al., 2013) and 0.017 DU 155 , respectively. In the Level-3 product, pixels affected by row anomaly are removed. For SO2, only the pixel with the shortest light path, SZA less than 70°, RCF less than 0.2, and detector number in the range of 2 to 59 (1-based) is retained in a 0.25°x0.25° grid cell and then corrected with a new AMF based on GEOS-Chem SO2 profile simulation (Leonard, 2017). For the OMI Level-2 NO2 product, the AMF calculation is based on Global Modeling Initiative NO2 profile simulation , and all pixels with SZA less than 160 85°, terrain reflectivity less than 30°, RCF less than 0.3 are averaged in a 0.25°x0.25° grid cell weighted by the overlapping area of grid cell and pixel to form Level-3 product (Bucsela et al., 2016). In the assessments, OMI observations are averaged at 2°x2.5° model grid cell, and model simulations are sampled by OMI observational time.

GEOS-Chem and its adjoint
GEOS-Chem is a 3-D chemistry transport model driven by emissions and GEOS-FP meteorological fields. The secondary sulfate-nitrate-ammonium aerosol formation in the model is introduced by Park et al. (2004). Both aerosols and gases are removed by wet deposition, including washout and rainout from large-scale or convective precipitation (Liu et al., 2001) and the dry deposition following a resistance-in-series scheme with aerodynamic 170 resistance and boundary resistance calculated from GOES-FP meteorological field and surface resistances based largely on a canopy model (Wang et al., 1998;Wesely, 1989). Anthropogenic SO2, NOx, and NH3 emissions used over East Asia are the mosaic emission inventory (MIX) (Li et al., 2017b) for year 2010. SO2 and NO2 VCDs are simulated at 2°x2.5° resolution with 47 vertical layers using both the prior and posterior emission inventories to compare with OMI retrievals. The GEOS-Chem adjoint model is a tool for efficiently calculating the sensitivity of a scalar cost function with respective to large numbers of model parameters simultaneously such as emissions (Henze et al., 2007). In this study, the cost function is defined as Eq. (1). estimate of σ, and Sa is the error covariance matrix for σa. Sa is assumed to be diagonal with a relative error of 50% for SO2 and 100% for NOx as used in Xu et al. (2013). γ is a parameter we introduce to balance the importance of the SO2 observation term (first term on the right side of Eq. (1)) and NO2 observational term (second term on the right side of Eq. (1)), given both the different sizes and observation errors of these two observation datasets.

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OMPS SO2 and NO2 tropospheric VCDs can be directly compared to GEOS-Chem tropospheric VCDs of SO2

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To optimize the emission inventories, σ is adjusted iteratively until the cost function is minimized. The minimization is conducted with the L-BFGS-B algorithm (Byrd et al., 1995), which utilizes the sensitivity of the cost function with respect to σ that is calculated by the GEOS-Chem adjoint model. The minimization process halts when the difference in the cost function between two consecutive iterations is less than 3%.

Experiment design
Several elements play a role in the inverse modeling of emissions, including data quality control, balancing the spatial distributions of observational frequencies for the same species, balancing the observation contributions from different species, and uncertainties in the NH3 emission inventory (because NH3 has impacts on SO2 and NO2 lifetimes). To investigate the impacts of these factors on the posterior emissions, we design a set of 220 experiments as summarized in Table 1 and

Control experiments
The first control experiment is E-SO2, in which only OMPS SO2 tropospheric VCDs are used to constrain SO2 emissions by removing the second additive term on the right side of Eq. (1). γ is just set to unity, as the issue of balancing the cost function contributions from SO2 and NO2 observations does not exist. If the OMPS SO2 tropospheric VCD error is set to 0.2 DU  for every pixel, the SO2 observational term in the cost 230 function (first term on the right side of Eq. (1)) over the North China Plain is much larger than that over Southwestern China (Fig. 2b), which thus has the high potential to over-constrain the former and under-constrain the latter. The spatially unbalanced cost function is caused by cloud screening, as the number of observations over Southwestern China is much less than that over the North China Plain (Fig. 2a) Both the SO2 and NO2 from OMPS are used simultaneously in E-joint for two reasons. Firstly, Qu et. al (2019b) showed that the change of SO2 or NOx emissions lead to the changes of O3 and OH concentrations, hence the 250 changes of SO2 and NO2 oxidations. Secondly, the computational time is reduced by ~50% in the joint assimilation as compared to separate assimilations when computational resource are restricted to running individual inversions sequentially (as opposed to in parallel), and energy usage is also saved; the latter require the realization of GEOSchem adjoint twice, while only once is needed by the former.

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In the E-joint experiment, observational terms for SO2 and NO2 in the cost function should be balanced through setting γ in Eq. (1). If they are not balanced, it is likely to under-constrain for one observational term. One approach is to set γ to be the ratio of number of NO2 observations to the number of SO2 observations. This approach is not feasible here as the SO2 observational error in E-SO2 is much larger than the NO2 observational error in E-NO2; not only does the number of observations play a role, but the observation error also has important impacts on 260 balancing the cost function. If γ is simply set as unity, the NO2 observational term in Eq.
(1) is a factor of ~200 larger than the SO2 observational term, which can lead to OMPS SO2 in the E-joint experiment to be negligible.

Self-consistency check
The cost functions are reduced by 41.6%, 27.6%, and 28.6% for E-SO2, E-NO2, and E-joint, respectively, and the results are shown in Fig. 3. Noticeably, hot spots of SO2 VCDs over the North China Plain and the Sichuan Basin are shown in the OMPS observations (Fig. 3a), prior (Fig. 3b), posterior E-SO2 (Fig. 3c), and posterior E-joint 310 ( Fig. 3d) simulations, however the prior simulation has an NMB of 106.5% (Fig. 3i) when compared with OMPS.
This large positive NMB decreases to 13.0% and 38.3% in the posterior E-SO2 (Fig. 3j) and E-joint (Fig. 3k) simulations with an RMSE decreasing from 0.42 DU to 0.13 DU and 0.20 DU and R increasing from 0.62 to 0.72 and 0.64, respectively. Large NO2 values are found over the North China Plain and Eastern China with large NOx emissions from the transportation sector ( Fig. 3e-h). Comparing with OMPS NO2, GEOS-Chem results have an 315 RMSE of 0.05 DU in the prior simulation (Fig. 3l) and reduce to 0.02 DU and 0.03 DU for E-NO2 (Fig. 3m) and E-joint (Fig. 3n), with R increasing from 0.95 to 0.99 and 0.98, respectively. In general, the E-SO2 and E-NO2 posterior simulations show better results than E-joint, which may be affected by the value of γ, which we will discuss in Sect. 4.3.

Emissions
The anthropogenic SO2  over China (Fig. 4e), but the difference can be up to 100% in some model grid cells (Fig. 4f). Anthropogenic NOx 330 emissions over China are reduced by 5.8% and 6.5% , from 714 Gg N in prior MIX for October 2010 (Fig 4g) to 672 Gg N (Fig. 4h) in E-NO2 and 667 Gg N ( Fig. 4i)  underestimation of this study for October. Although the relative difference between E-joint and E-NO2 proved to 335 be less than 2% in terms of total anthropogenic NOx emissions over China (Fig. 4k), it is up to 40% for some model grid cells (Fig. 4 l).

Independent evaluation with OMI data
The while OMI only observes hot spots over the former region ( Fig. 5a-d). When validating with OMI SO2 VCDs, the NMB is ~300% in the prior simulation, and it reduces to ~100% in E-SO2 and ~130% in E-joint (Fig. 5i). Not only is the NMB reduced, but the spatial distributions are also improved with the NCRMSE reducing from ~1.6 345 in the prior simulation to ~0.7 in E-SO2 and ~0.8 in E-joint, which is much closer to ~0.6 when comparing OMPS observations with OMI observations (Fig. 5i). For NO2, OMI observations and the prior and posterior simulations show large NO2 concentrations over the North China Plain and Eastern China (Fig. 5e-h). The improvements for E-NO2 and E-joint are reflected in terms of R when evaluating with OMI tropospheric VCDs, although the two experiments show larger negative NMB than the prior simulation (Fig. 5j).
Although OMPS observations and GEOS-Chem simulations are compared with OMI observations as an evaluation of posterior emission inventories, it is not assumed that OMI provides the true status of SO2 and NO2 in the atmosphere. OMPS SO2 average is ~0.14 DU, or ~95% larger than OMI SO2, and the R of the two products is 0.81 (Fig. 6b). Thus, it is reasonable that posterior SO2 is larger than OMI observations by ~100% in E-SO2 and 355 ~130% in E-joint. OMPS NO2 is ~24% smaller than OMI (Fig. 6d), which explains why the posterior NO2 simulations have larger negative NMB than the prior simulation when compared with the OMI observations. Our analysis also shows that the systematic difference among various satellite products for the same species (such as SO2 or NO2) can lead to biases in constraining emissions, but the posterior GEOS-Chem simulations still show in terms of the spatial distribution of SO2 and NO2. Plain becomes smaller than that over grid cells M and S. Grid cell M becomes more reasonable after conducting the data quality control by removing OMPS SO2 in any grid cells where prior GEOS-Chem SO2 VCDs are less than 0.1 DU (e.g., as in E-SO2-noBL, as shown in Fig. 7d). QC helps to improve grid cell M, as the data removed are close to Inner Mongolia, and are generally less than 0.1 DU, which are comparable to the retrieval error. SO2 over grid cell S from E-SO2-noBL (Fig. 7d) is, however, still larger than that over the North China Plain, compared 370 with the better spatial pattern from E-SO2 (Fig. 3c). Thus, QC and spatial balancing of the cost function together improve the spatial pattern of the posterior GEOS-Chem SO2 VCD simulation.

The impacts of γ on joint assimilations
In addition to setting γ as 200 in E-joint, we test the impacts of using various γ values on joint assimilation in Ejoint-dγ for October 2013. All the SO2 and NO2 VCDs from prior and posterior E-joint and E-joint-dγ simulations 375 are compared with OMPS counterparts (Fig. 8a-b). Regardless of the γ values used, all the posterior simulations of SO2 show smaller NMB and NCRMSE than the prior simulation when validating against OMPS and OMI counterparts, but the extents vary. When γ is 20, 50, or 100, the SO2 terms are obviously under-constrained, and the range of ~1.4 to ~1.7 in the posterior E-joint-dγ simulations, which are much larger than ~0.7 in E-SO2 (Fig.   380 8a). Similarly, when γ is no larger than 100, the bias of GEOS-Chem SO2, validated with OMPS observations, only reduces from ~100% to ~75%, compared to ~25% in E-SO2 (Fig. 8a), and the posterior SO2 emissions are in the range of 1055 Gg S to 1143 Gg S, which are much larger than 748 Gg S from E-SO2 (Table 3). When γ is in the range of 200 to 2000, the SO2 simulation results and emissions from joint assimilations are more similar to that from E-SO2 than that with γ no larger than 100 ( Fig. 8a and Table 3). Similar to SO2, the NO2 GEOS-Chem 385 simulations in the sensitivity experiments improve in terms of R and NCRMSE in all joint assimilation tests, but the significance of γ is less than that for SO2. NO2 NCRMSE is ~0.4 in the prior simulation when evaluating with OMPS counterparts, compared to the range of ~0.2 to ~0.25 in E-joint, E-joint-dγ and E-NO2 (Fig. 8b). The posterior NOx emissions are in the range of 662 Gg N to 682 Gg N, compared with 672 Gg N in E-NO2 (Table 3).

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The impacts of γ are also reflected when evaluating SO2 and NO2 simulations with OMI retrievals (Fig. 8c-d).
Small γ values of 20, 50, and 100 lead to a much larger bias and NCRMES for SO2 from E-joint-dγ than that from E-SO2. For NO2, these small γ values make results from E-joint-dγ very similar to that from E-NO2.
Considering all of the above analyses, the results with γ in the range of 200 to 2000 are deemed acceptable. The 395 E-joint-dγ (200≤ γ ≤2000) emissions are within -3% to 15% of E-SO2 for SO2 and ±2% of E-NO2 for NOx in terms of total anthropogenic SO2 and NOx emissions over China. When evaluating with OMPS observations, the NCRMSE of using the posterior emissions from the separate and joint (200≤ γ ≤2000) inversions are ~60% and ~45%-60% smaller than that of using the prior emissions for SO2, respectively, and ~50% and ~38%-50% smaller than that of using the prior emissions for NO2, respectively. 400

The impacts of NH3 emission
In the single-species inversions, NH3 emission uncertainty has weaker impacts on posterior SO2 emissions than NOx emissions. Posterior SO2 emissions over China are 748 Gg S in the 100% NH3 emission scenario (E-SO2), and they only slightly reduce to 747 Gg S and 745 Gg S when NH3 emissions are 50% (E-SO2-0.5NH3) and 20% (E-SO2-0.2NH3) of the original values, respectively (Table 4). The largest relative changes at model-grid-cell 405 scale are only -2.5% (Fig. 9a) for E-SO2-0.5NH3 for and -4.7% (Fig. 9b) for E-SO2-0.2NH3. All these results can be explained by considering how changes of NH3 can potentially impact the lifetimes of SO2 and NO2 and hence affect SO2 and NO2 VCD simulations. When the NH3 emissions decrease to 50%, and 20% SO2 VCDs only increase up to 3.8% and 6.1%, respectively, in some grid cells over the Sichuan Basin in the prior simulations, and these changes are even much smaller over the North China Plain (Fig. 10a-b), as NH3 has no direct effect on 410 the life cycle of SO2. This is understandable because in GEOS-Chem, once SO2 is oxidized to H2SO4, SO4 2remains as particulate sulfate regardless it is neutralized by NH3 or not (Wang et al., 2008). Hence, the reductions of NH3 to 50% and 20% overall has minimal (negligible) impact on SO2 amount in the prior simulation, hence on the posterior separate SO2 emission inversion.
N2O5 normally forms at night by reaction between NO2 and NO3, and thermally decomposes back to NO2 and NO3 (Seinfeld and Pandis, 2016), and hence the amount of N2O5, NO2, and NO3 are in equilibrium through the reversible reaction. Since the hydrolysis of N2O5 to form HNO3 mainly occurs on hydrated aerosol particles 425 (Seinfeld and Pandis, 2016), the decrease of hydrated aerosol surface area (due to reduction of NH3 emission) leads to less hydrolysis of N2O5 (an important sink for atmospheric NOx) and subsequently more NO2 to be in the equilibrium with N2O5 at night. As a result, the reduction of NH3 emissions further increases the positive bias in the prior NO2 simulations when comparing with OMPS observations, and to compensate such large positive bias, non-negligible decreases in the posterior NOx emissions are required ( Fig. 9 e and f). The reduction of nitrate and 430 ammonium aerosols can also increase sunlight reaching troposphere, hence photolysis O3 and NO2. Figure S1 separates the impacts of increase of photolysis O3 and NO2 and decrease heterogeneous N2O5 chemistry on NO2 lifetime and shows that the former is negligible compared the latter.

Aerosol responses to emission changes
Although SO2 emissions over the North China Plain (E-joint-dγ (γ=500)) have decreased by more than 50%, and NOx emissions have also been reduced, reductions of Sulfate-Nitrate-Ammonium (SNA) Aerosol Optical Depth 445 (AOD) over the same region are only up to 10% (Fig. 11). This is because the North China Plain is mainly polluted by nitrate rather than sulfate ( Fig. 12a-l), and the reduction of SO2 emissions will increase nitrate loadings in the atmosphere ( Fig. 12g-l), which is also consistent with Kharol et al. (2013)'s research that shows nitrate concentrations decrease as SO2 emissions increase; the reduction of SO2 emissions lead to less H2SO4 to react with NH3, which further favor the reaction of HNO3 and NH3 to form nitrate. As NH3 emissions change reduce 450 by 50% and 80% ammonium column loadings decrease by ~40% and ~70% (Fig. 12g-l), respectively, and nitrate column loadings decrease even by ~70% and ~90%, respectively ( Fig. 12m-r).

Discussion and conclusions
We