An Estimation of Top ‐ Down NO x Emissions from OMI Sensor Over East Asia

: This study focuses on the estimation of top ‐ down NO x emissions over East Asia, integrating information on the levels of NO 2 and NO, wind vector, and geolocation from Ozone Monitoring Instrument (OMI) observations and Weather Research and Forecasting (WRF) ‐ Community Multiscale Air Quality (CMAQ) model simulations. An algorithm was developed based on mass conservation to estimate the 30km×30km resolved top ‐ down NO x emissions over East Asia. In particular, the algorithm developed in this study considered two main atmospheric factors—i) NO x transport from/to adjacent cells and ii) calculations of the lifetimes of column NO x ( τ ). In the sensitivity test, the analysis showed the improvements in the top ‐ down NO x estimation via filtering the data ( τ ≤ 2 hours). The best top ‐ down NO x emissions were inferred after the sixth iterations. Those emissions were 11.76 Tg N yr ‐ 1 over China, 0.13 Tg N yr ‐ 1 over North Korea, 0.46 Tg N yr ‐ 1 over South Korea, and 0.68 Tg N yr ‐ 1 over Japan. These values are 34%, 62%, 60%, and 47% larger than the current bottom ‐ up NO x emissions over these countries, respectively. A comparison between the CMAQ ‐ estimated and OMI ‐ retrieved NO 2 columns was made to confirm the accuracy of the newly estimated NO x emission. The comparison confirmed that the estimated top ‐ down NO x emissions showed better agreements with observations (R 2 = 0.88 for January and 0.81 for July).


Introduction
Smog events in East Asia have been recognized as severe air pollution problems, resulting in deteriorated air quality in the atmosphere [1][2][3] and harmful effects on human health and the ecological system [4][5][6]. With growing public concerns, air quality forecasts have become an important issue. In this context, forecasting the short-term particulate matters of 10 and 2.5 (PM10 and PM2.5) and ozone concentrations has been nationally implemented in South Korea since February 2014. However, there has been a lack of capability in more accurately forecasting the levels of pollutants due to many uncertainties related to the meteorological fields, anthropogenic and biogenic emissions, chemical and physical parameterizations, boundary, and initial conditions, and land uses and land covers [7][8][9]. Among these uncertainties, the accuracy of emissions is one of the most important for improving the performance of air quality forecasting.
Air quality forecast (and general air quality modeling) heavily depends on the accuracy of emissions. It has also been well understood that among the pollutants, nitrogen oxides (NOx=NO+NO2) are important precursors for producing ozone and secondary inorganic aerosols. Despite such importance, the NOx emissions in East Asia have still been highly uncertain [10][11][12][13][14].
Many investigators have used an advanced inversion method of 4D-variation data assimilation [42][43][44][45] and Kalman Filter [39,41,46,47] to estimate the top-down NOx emissions. However, the method is still computationally expensive despite better scalability on the hardware platform of parallel computing. On the other hand, the computational cost base on the mass balance approach is relatively low. Besides, in the comparison study, Cooper et al. showed that the mass balance approach for the NOx estimations produces similar results to those from the adjoint method [42]. Table 1 summarizes the various methodologies used for the estimations of NOx emissions from the satellite observations, based on the mass conservation approach. Leue et al. first estimated the top-down NOx emissions, using the Global Ozone Monitoring Experiment (GOME)-retrieved NO2 data with the conversion factor of NO2 to NOx and a constant NOx lifetime of 27 hours [48]. However, the simple assumption in the NOx lifetime possibly causes significant errors. ii) A posterior NOx (E, optimized NOx emissions) -εb: relative geometric error between a priori and EDGAR NOx emissions; -εt: relative geometric error between top-down and EDGAR NOx emissions Global/ Sep. 1996 -Aug. 1997 37.7 Tg N yr -1 (for the globe) 5.3 Tg N yr -1 (for East Asia) Boersma et al. [30] Basic concept from Martin et al. [35] Here, K (kernel) matrix defined as K Zhao and Wang [20] Assimilated a posteriori based on Martin et al. [35] East Asia/ Jul. 2007 9.5 Tg N yr -1 (for East Asia) Lamsal et al. [37,40] Top-down NOx estimation from Martin et al. [35] and Boersma et al. [30] N. America, Europe, and East Asia/ 2006-2007 7. 6-8.9 Tg N yr -1 (for N. America) 3.9-5.2 Tg N yr -1 (for Europe) 10.9-13.1 Tg N yr -1 (for East Asia) Lin et al. [21] Concept based on study of Leue et al. [42], using multi-satellite data observed at different scanning time -Et: top-down NOx emission; -Ωs|n: satellite NOx columns at nth hour; -Ωs|0: satellite NOx columns at 0th hour; -τ: NOx lifetime; -Δt: time interval; -Ei: NOx emission at ith hour; -Ē: daily mean of E China/ 2008 6.8 Tg N yr -1 (best estimate for China) Ghude et al. [22] Basic concept from Martin et al. [35] -Ωm: model-predicted NO2 columns w/ consideration of averaging kernel India/ 2005 1.9 Tg N yr -1 (for India) Goldberg et al. [34] Exponentially modified Gaussian fitting method [15] -  [35,36]. In their study, however, the transports of NOx molecules from/to neighbor grid cells were neglected via the uses of very coarse horizontal resolution (2°×2.5°) and relatively short NOx lifetimes, particularly during the summer months. For the consideration of NOx transport from/to the adjacent grid-cells, several investigators have introduced the smoothing kernels defined in Table 1 (e.g., references [30,37,40,49]). In Zhao and Wang [20], the issue of the NOx transport was treated indirectly by assimilation using the OMI (Ozone Monitoring Instrument)-retrieved NO2 columns on a daily basis. Another method was suggested by Lin et al. [21], who used multi-satellite NO2 columns observed at different scanning times (e.g., GOME-2 for ~ 9:30 LT and OMI for ~ 13:45 LT). The methodology applied to a summer case, based on the hourly differences between two satellite-derived NOx columns from the consistent retrieval algorithm and NOx chemical evolution. However, as pointed out in their study, significant limitations can be met, when the suggested methodology applies to the high-resolved chemistry-transport model (3D-CTM) simulations or the winter case, resulting in a sufficiently long NOx lifetime.
Many studies based on the mass balance approach have the relatively coarse-grid resolution (~1°) for the 3D-CTM simulations and focus on the estimations for summer episode. An alternative is required to estimate top-down NOx emissions with a finer grid-resolution, particularly during the cold seasons. Therefore, the challenging goal of this study is to develop an algorithm for the top-down estimation of NOx emissions with runs of 3D-CTM simulations in a 30 km × 30 km grid resolution and with the retrieval of OMI NO2 columns. The manuscript was organized as followed. First, the research methods for the CTM simulations and satellite data are described in Section 2.
The algorithm for the top-down estimations is fully described in Section 3. To evaluate and finally quantify NOx emissions over East Asia, the CTM-simulated NO2 columns are compared with the OMI-retrieved NO2 columns in Section 4. Summary and conclusions are given in Section 5.

Description of WRF-CMAQ Model Simulations
The meteorological fields were generated by the Weather Research and Forecasting v3.4.1 (WRF) model [50] in conjunction with National Center for Environmental Prediction (NCEP) reanalysis data [51,52]. The WRF simulation was configured with the following atmospheric physical schemes: the Yonsei University (YSU) scheme for planetary boundary layer (PBL) physics [53], the five-layer thermal diffusion Land Surface Model (LSM) scheme for land surface, the Dudhia scheme for the shortwave radiation [54], the rapid radiative transfer model (RRTM) scheme for the longwave radiation [55]; and Kain-Fritsch scheme for the cumulus parametrization [56]. The output from the WRF simulations was then used to generate the model-ready meteorological input data via the meteorological chemistry interface process (MCIP) for the CMAQ model simulations.
The Community Multi-scale Air Quality (CMAQ) v4.7.1 model [57] was used over East Asia for January and July 2010. As shown in Figure 1, the CMAQ domain covered a region of East Asia (100° -145° E and 20° -50° N) including China, Korea, Japan, and some parts of Mongolia, Russia, and the northwest Pacific Ocean with a 30×30 km 2 horizontal resolution and 14 vertical levels from the surface to ~95 hPa. Lambert-conformal projection centered at 121° Longitude and 34° Latitude was applied. The main modules used in the CMAQ model simulations were the AERO4 for the aerosol dynamics and thermodynamics [58] and the Statewide Air Pollution Research Center-99 (SAPRC-99) mechanism for the gas-phase chemistry [59]. Other conditions for the CMAQ model simulations were described in the previous studies of Han et al. [14,60].
For emission inputs (i.e., a priori emission), the anthropogenic emissions from the Model Inter-comparison Study for Asia Phase III (MICS-Asia III) inventory compiled for the year 2010 were utilized for the CMAQ model simulations over East Asia. The MICS-Asia III emissions with 0.25°×0.25° resolution were combined from several regional emission inventories such as MEIC v1.0 for China, CAPSS for South Korea, JEI-BD/OPRF for Japan, and REAS v2.1 for others, to best describe the emissions from the countries. Further information on the MICS-Asia III inventory was described in the studies of Li et al. and Janssens-Maenhout et al. [61,62]. For the consideration of biogenic emissions, the 0.5°×0.5° resolved model of emission of gases and aerosols from nature-monitoring atmospheric composition and climate (MEGAN-MACC) emission inventory compiled for the same year of 2010 (http://eccad.sedoo.fr) were used [63]. Also, for fire emissions, the Quick Fire Emissions Dataset (QFED) v2.4 with 0.1°×0.1° grid resolution was obtained from the NASA Center for Climate Simulation (NCCS) for the year of 2010 [64]. The fire emissions injected from the high altitudes can have a considerable impact on the transport of NOx molecules in the model simulations [65,66]. However, we believe that such an effect is not significant in the monthly estimation of top-down NOx emissions because these biomass burning NOx emissions utilized in the current simulation account for ~0.01% of the total NOx emissions in the entire domain. Soil NOx emissions obtained from REAS v2.1 inventory [67] for the year of 2008 also accounted for 0.85 and 13.07% of the total NOx emissions in January and July, respectively. In the CMAQ model simulations, other NOx sources such as lightning and aircraft were not considered due to high uncertainties over East Asia [20].

Description of OMI NO2 Columns
The OMI, one of four sensors on board the NASA/EOS-Aura satellite, has been used widely for the studies of atmospheric chemistry due to several advantages, particularly in the high spatial and temporal resolutions. The OMI instrument observes the atmosphere over East Asia at approximate 13:45 local time (LT) with a spatial resolution of 13 km × 24 km at the nadir.
The OMI-retrieved NO2 columns, their errors, and averaging kernels (AKs) used in the study were described in detail by Boersma et al. [68,69]. Therefore, here, we briefly introduce some information on the daily OMI dataset retrieved from KNMI/DOMINO v2.0 algorithm. The tropospheric NO2 columns from the OMI level-1b radiance data are retrieved in the following three steps. In the first step, NO2 slant columns are obtained from the OMI reflectance spectra with a fitting window ranging between 405 nm and 465 nm, on the basis of the differential optical absorption spectroscopy (DOAS) technique [70]. In the second step, the stratospheric contributions to the total NO2 slant columns are estimated to generate the tropospheric portions of the NO2 slant columns. Here, the stratospheric NO2 slant columns are calculated by assimilating OMI-measured NO2 slant columns in a chemical data assimilation system [71]. In the last, the air mass factor (AMF) is introduced to convert the tropospheric NO2 slant columns to the tropospheric NO2 vertical columns. The errors of the individual tropospheric NO2 columns in the DOMINO v2.0 are approximate 1.0×10 15 molecules cm -2 , which are mostly due to the AMF calculations [69]. AMF is a function of surface albedo, terrain height, vertical profiles of clouds and aerosols, and the presence of trace gases. In this study, in order to reduce retrieval errors, only OMI data with cloud radiance fraction (CRFs) smaller than 50% and surface albedo smaller than 0.3 was used, as suggested by Boersma et al. [68].
For the top-down NOx estimation in East Asia, we also took advantage of the "daily" levels of tropospheric OMI-retrieved NO2 columns (level 2 product) obtained from the TEMIS (http://www.temis.nl). The conversion of NO2 to NOx columns was fully described in Section 3.5. The total errors in the tropospheric NO2 columns applied to the estimations of NOx emissions were 3.05×10 15 and 7.47×10 14 molecules cm -2 , which accounted for approximately 65% and 48% of the tropospheric NO2 columns over the entire domain, in East Asia for January and July, respectively. Besides, several investigators identified significant low biases (e.g., 10% over Tokyo, 26-38% over Beijing) in the current OMI-retrieved tropospheric NO2 columns, comparing with the Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) observations over some regions in Canada, Greece, China, and Japan [72][73][74][75][76]. Accordingly, the top-down estimate in the study is likely underestimating the true one.

Algorithm for Top-Down Estimation of NOx Emissions
The current study can be characterized by two main components: the considerations of i) transport of NOx molecules among the grid-cells and ii) lifetimes of column NOx. Two issues are explained in detail.

General Concept
The NOx columns (ΩNOx) in the troposphere can be determined by the balance among emission (E), chemical production (F), chemical/physical losses (L), and columnar NOx transported from/to adjacent grid cells (Qin and Qout). The rate of change of ΩNOx with respect to time can be expressed by the following Equation (1): The above equation can be converted into Equation (2): where τ represents the lifetime of column NOx, which includes the photo-chemical, physical, and meteorological removals or disappearance at a given grid cell. For the estimations of NOx emissions (E), the data collected from the CMAQ model simulations were averaged between 13:00 and 14:00 LT for the i th time step, which is approximately consistent with the OMI scanning time over East Asia. The columnar NOx at the i th time step (ΩNOx,i) and emission (E) can be expressed via the following formulas (Equations (3) -(5)): where Δt represents a time interval, which is corresponding to 1 hour in this study. Other works can also be explained with Equation (5). For example, Lin et al. obtained ΩNOx,i and ΩNOx,i-1 from OMI and GOME-2 sensors, respectively, with Δt= 3 hours and ΔQ= 0 in terms of Equation (5), to calculate top-down NOx emissions [21].
The estimations of top-down NOx proceeded as followed: First, the amounts of NOx transported from/to adjacent cells (Qin and Qout) are calculated using the wind vectors and NOx concentrations of each layer at the i-1 th time step (refer to Figure 2 and Sections 3.2 and 3.3). Second, the variables such as columnar NOx at i th and i-1 th time steps, bottom-up NOx emission, and ΔQ are fed into the Equation (4) rearranged from Equation (3) to calculate τ. Third, we attempt to confirm whether the scientific approach chosen here is correct via re-calculating the bottom-up NOx emissions using Equation (5). The re-calculated NOx emissions should be equal to the bottom-up NOx emissions used in the CMAQ model simulations. In the fourth step, for conducting a sensitivity analysis of τ, the top-down NOx emission is estimated from Equation (5) using a columnar NOx (ΩNOx) based on the model results for the arbitrary satellite-observed data on the OMI footprint. In this step, the calculated top-down NOx emissions from the arbitrary data should be the same as the (bottom-up) model input emissions. The arbitrary data can be used for sensitivity tests of the here presented method. The statistical analysis between the two sets of data was carried out with respect to τ to find the optimal condition for the top-down NOx emissions in the final step. Finally, daily OMI-observed data are applied to the estimations of top-down NOx emission over East Asia. The procedure was repeated until the differences between CMAQ-calculated and OMI-retrieved NO2 columns are within the error tolerance. Further details can be found in the next sections.

NOx Transported from Adjacent Cells (Qin)
In many top-down NOx estimations, the influx and outflux into/out of grid cells have been neglected, because of the use of sufficiently large grid resolution in the global CTM simulations (typically, 2° × 2.5° in GEOS-CHEM), along with relatively short chemical lifetimes of NOx [21,35,38]. However, as discussed previously, the transports of NOx from non-local sources become an important issue in the top-down estimation of NOx emissions, particularly with a high spatial resolution.
In this study, with a grid resolution of 30×30 km 2 , the amounts of NOx molecules transported from adjacent cells (xi, yj) to a given cell (Xm, Yn) at each layer are estimated as illustrated in Figure 2a. During one hour of travel from i-1 th to i th time step (i.e., Δt = 1 hour), atmospheric NOx molecules that are assumed to be distributed homogenously in the black-dashed cell move to the blue dashed-cell centered at the position of xi,m and yj,n in Figure 2a. This movement of air parcel was calculated using the information on the wind vectors (u and v) (i.e., wind direction and velocity). The overlapped, red-shaded rectangle between the blue-and red-dashed cells in Figure 2a represents the area which NOx molecules are transported from the black-dashed cell into the given cell (i.e., red-dashed cell). The area (A) was calculated via Equation (6), using two (yellow) standard points shown in Figure 2a.
Here, the standard points can be changeable with the wind vectors at the adjacent cells. Accordingly, the red-shaded area can be overlapped differently with different wind vectors. The shaded area was then converted into the fractional area (fA) at the given cell via Equation (7): W represents the areas (30×30 km 2 ) of the given grid cell in the current CTM simulations. These calculations were applied to the entire grid cells via Equation (8) (except its own given grid cell), in order to estimate the total amounts of the NOx molecules (Qin(m,n)) transported into the cell centered at the Xm and Yn.
Here, C and Δh represent the number concentration of NOx (molecules cm -3 ) and vertical height (cm) of the layer, respectively. For the calculations, the number concentrations of NOx (C) and wind vectors were assumed to be constant during the travel of the air parcels. Finally, the Qin(m,n) (molecules cm -2 hr -1 ) at each layer was integrated vertically from surface to ~250 hPa.

NOx Transported to Adjacent Cells (Qout)
During 1-hr travel, the amounts of NOx molecules transported from the given cell (Xm, Yn) into the adjacent cells were quantified, as shown in Figure 2(b). The fractional area (fA) for NOx molecules transported into the adjacent cells was expressed by shaded-light blue in Figure 2b. In a convenient manner, the area (A') of the overlapped, dark-blue shaded rectangle between the red-and blue-dashed cells was calculated via Equation (9), using two yellow standard points in Figure 2b.
The area (A') was then converted into the fractional area (fA) at the given cell (see Equation (10)), and fA was applied to Equation (11) to estimate the amounts of NOx molecules (Qout(m,n)) transported from the given center of Xm and Yn into the adjacent cells. Finally, the Qout(m,n) at each layer was vertically integrated (molecules cm -2 hr -1 ).
Other issues described in Section 3.2 are skipped here but were applied to the Qout(m,n) calculations in the same manner with Qin(m,n). However, it should be noted that we did not considered the vertical transports, which is a possible source of error in the calculation.
The daily and spatial variability in the differences between Qin(m,n) and Qout(m,n) (ΔQ = Qin -Qout) was large because the daily wind vectors and the spatial distributions of NOx molecules are highly variable (refer to Figure S1 in the supplementary material). Also, it was somewhat obvious that the spatial and daily variability was stronger in January than in July due to strong winds in January. The strong variability in ΔQ originated from the meteorological influences can increase the degree of uncertainty in the estimation of the top-down NOx emissions, particularly during the winter seasons. This issue will be further discussed in Section 3.4.2.

Column NOx Lifetimes and Sensitivity Analysis
In the sensitivity test, arbitrary satellite data based on the simulation were utilized in the algorithm to reproduce the input of emission in the model simulations. The test aims at examining the accuracy and sensitivity of the method of top-down estimation.

Determination of Lifetimes of Column NOx (τ)
Determination of the lifetimes of column NOx (τ) is an indispensable component in the estimation of top-down NOx emissions. Many studies have conducted to estimate the NOx lifetime [77][78][79][80]. Recently, Laughner and Cohen report that NOx lifetime can be measured directly from satellite-observed NO2 columns [79]. It is well-known that the chemical NOx lifetimes are approximately several hours, depending on the latitudes and seasons [35,37]. The relatively short chemical NOx lifetimes in summer are mainly characterized by the active NOx chemical loss, leading to active HNO3 formation via the reaction of NO2 with OH radicals. The heterogeneous formation of nitrates through the N2O5 and NO3 condensations onto aerosol surfaces is another important removal process of NOx, particularly during winter. In the previous analysis of Han et al., the budget of NOx chemical loss via the heterogeneous nitrate formation of N2O5 condensation (~49%) during winter was almost equivalent to that through the NO2+OH reactions over the Korean peninsula [81]. Besides, the formations of peroxyacetyl nitrates (PANs) and alkyl nitrates (ANs) are another important possible pathways related to NOx chemical loss rates, and thus chemical lifetimes of NOx [78,82,83].
In this study, we defined the lifetimes of NOx columns (τ) as time how long columnar NOx molecules persist at the given grid cell. The lifetime of NOx columns was estimated from the mass balance equation with respect to the concentrations gradient of NOx between the i th and i-1 th time step, using several variables such as columnar NOx (ΩNOx), bottom-up NOx emissions (E), and ΔQ from the CMAQ model simulations. For the calculation of τ, Equation (4) was rearranged from Equation (3). To find a root (i.e., τ) of this implicit nonlinear Equation (4), an approach based on the bisectional method was employed [84]. The mean values of τ in this study are 7.44 and 5.22 hours over central-eastern China (covering Beijing, Tianjin, Hebei, Shanxi, Shandong, Henan, Jiangsu, Anhui, and Shanghai) in January and July, respectively. The values are slightly different to those from other studies [21,35,37]. For example, Martin et al. showed that the zonal mean lifetimes of NOx over the 30 -50 N° are ~10 -~ 20 hours in January and ~ 5 hours in July [35]. While Martin et al. considered only the chemical loss of atmospheric NOx via the oxidation to HNO3 in the continental boundary layer for the calculation of NOx lifetime (i.e., ), we employed entire fates of NOx including transport in the current estimation of τ. In other words, current τ considers all the processes of NOx such as chemical, physical, and meteorological removal from the given grid cells. Also, it should be noted that τ in the calculation covered only the time between 13:00 LT and 14:00 LT during the daytime. To more consistently compare chemical NOx lifetimes with other studies, monthly chemical lifetimes of columnar NOx without other effects (i.e., ΔQ=0 in Equation (4) (5) reproduces the bottom-up NOx emissions (Eb). The reproduced NOx emissions must be theoretically the same as the bottom-up NOx emissions. As shown in Figure S2 in the supplementary materials, the recalculated values are almost equal to the bottom-up NOx emissions. Their correlations (R 2 ) and slopes (S) are close to 1.00, although some negative values are found overs the remote areas such as Russia, Mongolia, and the northwestern parts of China. Some negative values or small differences were caused mainly by truncation error in the bisectional calculations of τ. Mean errors (MEs) due to the uncertainty were estimated to be 0.05×10 11 and 0.02 ×10 11 molecules cm -2 for January and July, respectively. The statistical analysis indicates that the total molecules of NOx are conserved almost entirely in the mass balance approach.

Sensitivity Analysis of τ
A small uncertainty in τ made a small impact on the estimation of top-down NOx emissions over the remote continental regions in East Asia, as shown in Figure S2. However, top-down NOx emissions can be highly uncertain when the small truncation error of τ is amplified with some errors caused by data interpolation. The interpolation of satellite data to model grid-cells inevitably produces some (small) errors, because the satellite-retrieved geophysical quantities do not accurately correspond to the model-gridded geophysical data [86]. To investigate such an impact on the estimation of the top-down NOx emissions or non-linear Equation (5), we prepared satellite columnar NOx (i.e., an arbitrary satellite data, ΩNOx) on the OMI footprint based on the daily CMAQ-modeled NOx columns. The daily satellite NOx was then interpolated back to the model grid-cells. Finally, we put the interpolated satellite NOx columns and other variables (i.e., τ and ΔQ) into Equation (5) to estimate the (arbitrary) top-down NOx emissions (Earb,t). It is expected that the arbitrary top-down NOx emissions should, in theory, be the same as the bottom-up NOx emissions (Eb), because the input data obtained directly from the CMAQ model simulations were used in this test. However, as shown in Figure S3, the Earb,t was much larger than the Eb. These large overestimations of top-down NOx emission were found, particularly over the low emissions areas of the bottom-up NOx emissions (< ~10×10 11 molecules cm -2 s -1 in x-axis), as shown in the scatter plots in Figure S3.
To explore the unexpected overestimations of top-down NOx emissions, the non-linear Equation (5) were analyzed in detail with respect to τ. Figure 3 presents a plot of the first and second terms on the right-hand side (f1(τ) and f2(τ)) of Equation (5), which are expressed by Equations (12) and (13), respectively. Equation (5) can be rearranged by Equation (14). Small changes in τ caused by truncation error in the bisectional method (discussed in Section 3.4.1) lead to a big difference in f1(τ) and f2(τ) around τ = 0 -2 hours in Figure 3, indicating that both the f1(τ) and f2(τ) can be highly uncertain around these ranges. The uncertain f1(τ) and f2(τ) are then multiplied by some error-involved ΩNOx owing to the spatial interpolation (in Equation 14). Eventually, the top-down NOx emissions can be highly uncertain around τ = 0 -2 hours. The results were presented in scatter plot analysis between Earb,t and Eb with respect to τ, as shown in Figure  4a,e). Eb with τ ≥ 0 for January and July, respectively; (b) and (f) Et vs. Eb with τ ≥ 1 for January and July, respectively; (c) and (g) Et vs. Eb with τ ≥ 2 for January and July, respectively; (d) and (h) Et vs. Eb with τ ≥ 5 for January and July, respectively (unit: 10 11 molecules cm -2 s -1 ).
Here, the color-coded circles represent τ at each grid cell. The large overestimations of Earb,t were estimated, particularly around τ = 0 -2 hours due to the combined errors by τ and data interpolation, as explained. To minimize such impact on the top-down NOx estimation, we filtered some data under the condition that τ is smaller than a specific value (i.e., 0, 1, 2, and 5 hours) in Figure 4. This sensitivity test strongly indicates that the analysis can be influenced significantly by the data filtering of τ. For instance, when the data were filtered, the correlations (R 2 ) generally improved from 0.21 to 0.98 for January (refer to more cases in Figure S4 and S5). Accordingly, mean errors (MEs) decreased from 1.67×10 11 to 0.23×10 11 molecules cm -2 s -1 (from 0.56×10 11 to 0.06×10 11 molecules cm -2 s -1 ) for January (July). Normalized mean errors also decreased, as shown in Figure 4. Furthermore, the slopes (S) were close to 1:1 line, 0.95 in the case of τ ≥ 5 hours. However, less data (i.e., 'N' in Figure 4) was available for constructing the top-down NOx emission. Figure 5 showed the arbitrary top-down NOx emissions (Earb,t) and the differences between Earb,t and Eb for the case of τ ≥ 5 hours. As expected from Figure 4d,h, the spatial distributions and magnitudes of Earb,t in Figure 5a,c were similar to those of Eb shown in Figure S2a for the entire domain in January and July, respectively. Also, the differences between Earb,t and Eb were small and ranged mostly from ~ -1×10 11 to ~1×10 11 molecules cm -2 s -1 for the entire domain (Figure 5b,d). In the seasonal perspective, data in July were denser than those in January for all the cases classified by the values of τ (Figure 4). More sparely scattered distributions in January were possibly caused by strong wind conditions in the cold seasons, as discussed in Section 3.3. From the sensitivity analysis, we, therefore, discarded some data showing τ smaller than two hours for the optimal estimation of the top-down NOx emissions.

Satellite-Derived NOx Columns
To apply the OMI-retrieved NO2 columns to the top-down NOx estimations, both OMI-derived NOx columns at the i th and i-1 th time steps are necessary for Equation (5). Since the OMI sensor does not provide the NOx columns, but NO2 columns only at the i th time step, two assumptions were made for the use of Equation (5). First, to convert OMI-retrieved NO2 columns to the OMI-derived NOx columns at the i th time step ( i OMI NO x , ,  ), it was assumed that the ratios of NOx columns to NO2 columns in the CMAQ model simulations are the same with those in the OMI observations (Equation (15 )), i.e.,:      (15) In this calculation, the averaging kernels (AKs) are also implicitly considered. Secondly, for the OMI-derived NOx columns at the i-1 th time step, it was assumed that the differences (ΔΩNOx,CMAQ) between the CMAQ-calculated NOx columns at the i th and i-1 th time steps were the same with those from the OMI observations (ΔΩNOx,OMI) as the following Equation (16): The OMI-derived NOx columns from the above calculations were finally applied to the top-down estimations of NOx emissions (Equation (17)) over East Asia.
Shortly, the second assumption will not be necessary since the Korean geostationary environmental satellite of the Geostationary Korea Multi-Purpose Satellite/Geostationary Environmental Monitoring Spectrometer (GEOKOMPSAT/GEMS) provides us with hourly resolved 2 NO  for Asia [87]. Also, this will be true for other geostationary satellite missions such as Sentinel 4 and TEMPO (Tropospheric Emissions: Monitoring of Pollution) over Europe and North America, respectively [88,89].

Optimal Conditions for the Top-Down NOx Estimation
The OMI-retrieved data mentioned in Sections 2.2 and 3.5 were utilized for the estimation of the top-down NOx emissions over East Asia, using Equation (17). As shown in Figure 4, the top-down estimation of NOx emissions showed generally acceptable results under the conditions of τ ≥ 2 hours. However, to find optimal conditions at each grid cell, we prepared the 25 databases of the monthly top-down NOx emissions (Ei,τ in Figure 6) at different conditions which are depending on τ. Despite conducting estimations of top-down NOx emissions, some areas of the grid cells remain unoccupied (for example, white pixel areas in Figure 5). These white colors represented the areas where i) OMI observations were not conducted during the periods because of large cloud fractions and/or high surface albedo, and/or ii) τ shorter than the specific values were estimated. The unoccupied areas were then filled by spatial interpolation. Furthermore, the other remaining pixels after interpolations were replaced by the bottom-up NOx emissions (i.e., Ei-1 in Figure 6) used in the previous CMAQ model simulations.
As shown in Figure 6, the optimal condition at each grid cell was then determined by combinations of ΔΩNO2 (= ΩNO2,CMAQ -ΩNO2,OMI) and ΔE (= Ei-1 -Ei,τ). Here, averaging kernels (AKs) were applied to the ΩCMAQ for absolute differences. Also, the Ei-1 is the bottom-up NOx emission (or top-down NOx emission used in the previous CMAQ model simulation). Error tolerances are between -1.0×10 15 and 1.0×10 15 molecules cm -2 . Error tolerances are related to the uncertainties associated with the observation. Since the uncertainties in observations depend on the season and pixel, it should be applied differently to the algorithm. However, we fixed reference values to ±1.0×10 15 molecules cm -2 in this study because the error of the individual tropospheric NO2 columns of the DOMINO v2.0 used in this application is ~1.0×10 15 molecules cm -2 [69]. For example, the top-down NOx emission (Ei) at iteration step, i can be Ei-1 under the condition of 1.0×10 15 > ΔΩNO2 > -1.0×10 15 molecules cm -2 . If ΔΩNO2 is larger than 1.0×10 15 molecules cm -2 , Ei should be reduced because NOx emissions (Ei-1) utilized in the CMAQ simulations are overestimated. Therefore, Ei can be Ei,τ at the minimum case among the cases of positive ΔE (i.e., P_ΔE). In the case of ΔΩNO2 < -1.0×10 15 molecules cm -2 , Ei can be Ei,τ at the maximum case, among the cases of negative ΔE (i.e., N_ΔE). Finally, estimated NOx emissions were used in the next CMAQ model simulation to validate the NOx emission fluxes and iterate the procedure.

Comparison Between ΩNO2,CMAQ and ΩNO2,OMI from Initial CMAQ Simulation
The NO2 columns (ΩNO2,CMAQ) calculated from the initial CMAQ simulation with the consideration of the bottom-up NOx emission were compared with the OMI-retrieved NO2 columns (ΩNO2,OMI) over East Asia. For the sake of this comparison, the modeled concentrations of NO2 at each layer were multiplied by the averaging kernels (AKs) from the KNMI/DOMINO products and were then vertically integrated from the surface to ~ 250 hPa for direct comparison between ΩNO2,CMAQ and ΩNO2,OMI. Figure 7 (b1, c1, e1, and f1) present the direct comparison for January and July. From the scatter plot analysis, the ΩNO2,CMAQ were spatially well correlated to ΩNO2,OMI with good correlation coefficients in January (R 2 = 0.82) and July (R 2 = 0.64). However, the absolute differences (ΔΩNO2 = ΩNO2,CMAQ -ΩNO2,OMI) showed large negative biases (i.e., bluish colors, approximate -0.8×10 15 molecules cm -2 over the entire domain) in both January and July over most regions of East Asia, except over some inland in January (e.g., Shanghai and Jiangsu province). For example, the absolute differences ranged approximately from -2×10 15 to -1×10 15 molecules cm -2 over China, North Korea, South Korea, and Japan. In more detail, the highest absolute differences of -8.09×10 15 and -8.02×10 15 molecules cm -2 were found over Beijing in January and Tianjin in July, respectively.  (c2 and f2) scatter plots with the use of top-down NOx emissions in the CMAQ simulations. The R 2 , S, N, ME, and NME indicate the correlation coefficient, slope, number of available data, mean error (unit: 10 11 molecules cm -2 s -1 ), and normalized mean error (unit: %), respectively.
We also found the significant absolute differences ranging from -6×10 15 to -3×10 15 molecules cm -2 over other regions such as Hebei, Shanxi, Guangdong, Shandong, and Hunan provinces. These negative biases (i.e., bluish colors) and some linear regression slopes less than unity (i.e., S < 1) in both January and July indicated that the bottom-up NOx emission used in the initial simulations was possibly underestimated over most regions of East Asia. The bottom-up NOx emissions used in the initial CMAQ simulations were 814 and 914 Gg N month -1 over the entire domain for January and July, respectively.

East Asia
To more accurately estimate NOx emissions over East Asia, the estimation of the top-down NOx emissions was conducted, using Equation (17) under the optimal condition described in Sect. 3.6. In this estimation, a six-iteration was performed for the final emission product, which presented in Figure 7 (a2 and d2) (refer to Figures S6 and S7 for all estimations). The spatial distributions of the top-down NOx emissions were, in general, similar to those of the bottom-up NOx emissions. For example, both the NOx emissions showed high emission fluxes over central-eastern China (CEC) as well as in the megacities of Beijing, Shanghai, Hong Kong, Seoul, and Tokyo. Despite the spatial similarity, the top-down NOx emissions were large by 19-34% in January and 19-47% in July over the entire domain, respectively, compared to the bottom-up NOx emissions. Table 2 summarizes the top-down NOx emission fluxes by country. The final estimates of the NOx emissions over the entire domain were 991 Gg N month -1 and 1346 Gg N month -1 in January and July, respectively. As in the bottom-up NOx emissions, the top-down NOx emission fluxes in July were also larger than those in January because of possible contributions from soil microbiological activity during summer.
The direct comparisons between ΩNO2,CMAQ and ΩNO2,OMI were made in order to determine the optimal NOx emissions for the next estimation and also to confirm how much the estimated top-down NOx emissions were improved. Figure 7 presents the absolute differences and scatter plots between the two ΩNO2 in the second and third columns, respectively (also, refer to Figures S6 and  S7). According to the comparison analysis, there were significant improvements in the final estimation of the top-down NOx emissions, in terms of the linear regression slopes, correlation coefficients, and absolute differences between ΩNO2,CMAQ and ΩNO2,OMI, during both January and July. For example, the linear regression slopes for the final estimation of the top-down NOx emissions were close to the 1:1 line (S= 0.97 for January and 0.84 for July), compared to those for the initial simulations with the bottom-up NOx emissions (S= 0.81 for January and 0.45 for July). Also, the correlation coefficients (R 2 ) increased from 0.82 to 0.88 in January and from 0.64 to 0.81 in July. Furthermore, absolute differences over the entire domain decreased from -0.83×10 15 molecules cm -2 to 0.31×10 15 molecules cm -2 in January, and from -0.82×10 15 to -0.38×10 15 molecules cm -2 in July. We believe that there are marked improvements.

China, North Korea, South Korea, and Japan
For a more detailed analysis, we investigated the variations of the absolute differences (△Ω= ΩCMAQ -ΩOMI) after individual iteration over Chinese regions, North Korea, South Korea, and Japan, as shown in Figure 8. In January, variations were substantial after each iteration over several polluted regions such as Beijing, Tianjin, and Hebei, Henan, Shandong, Anhui, Jiangsu, and Shandong provinces. The fluctuations in △Ω over Beijing, Tianjin, and the Shanghai provinces were even higher than those over other regions, due to a relatively small number of pixels for the analysis.
However, △Ω in January was reduced rapidly after the first iteration (also, refer to the second column of Figure S6). Eventually, the differences after the final (sixth) iteration were within the error tolerance of ±1.0×10 15 molecules cm -2 over most of the Chinese provinces. On the other hand, in July the variations of △Ω from the first to the sixth iterations were almost constant within the error tolerance over most of the Chinese provinces, except over Tianjin and Shanghai provinces, indicating that our estimations represent real NOx emission fluxes over most of China with considerable accuracy. For North Korea, positive biases in January were substantial at the third to fifth iterations (refer to Figure S6 (b4, b5, and b6)). Those were mainly due to abnormally high NOx emissions from a specific pixel over North Korea. Accordingly, in South Korea, the positive biases for the same period appear to be influenced by such NOx plumes transported from North Korea (refer to Figure S6). The final estimation showed a slight overestimation over South Korea. In July, the absolute differences over North Korea and South Korea were getting close to zero. Over Japan, all the estimations showed good performances in January and July.
To validate the top-down NOx estimation, it is also required to make a comparison using independent observation data. For the comparison, we used in-situ NO2 measurement data for the Seoul metropolitan areas, which are quite densely distributed and only available open data for study periods. In South Korea, NO2 measurements have been carried out using the commercial chemiluminescent detector. In the analyzer, ambient NO2 passing through a molybdenum converter operating under 300-350°C is converted to NO. However, other species like HNO3 and PANs are converted together [90,91]. Nevertheless, we compared the CMAQ-calculated NO2 data with in-situ NO2 observation over Seoul Metropolitan areas. As shown in Figure S8 and Table 3, the magnitudes of NO2 calculated from the CMAQ simulation using the top-down emission is more close to the in-situ observation than those of CMAQ simulation with the bottom-up emissions, particularly in January. More studies will be required for South Korea and some Chinese provinces such as Hebei and Shandong because they still have high biased pixels (refer to Figure 7b2). Even so, Table 2 showed the best top-down NOx emissions estimated by the country. The annual estimation was calculated linearly from the monthly top-down NOx emissions in both January and July. The best top-down NOx emissions over China were 11.76 [20,37,92]. Our emission is close to those from Lamsal et al. [37]. These differences may be attributed to different periods, grid resolutions, methodologies, and chemical mechanisms in the CTM simulations [93]. In terms of the different time windows, Miyazaki et al. reported +0.73 Tg N yr -1 of annual increase rate from 2008 to 2010 in top-down NOx emissions over China [41]. Thus, we believed that considering the annual increase rate, our estimated NOx emissions are much closer to the other estimates for China.
Our best estimates of top-down NOx emissions over North Korea, South Korea, and Japan are 0.13, 0.46, and 0.68 Tg N yr -1 , which were approximately 62%, 60%, and 47% larger than the bottom-up NOx emissions, respectively. The estimates of the top-down NOx emissions over S. Korea and Japan in this study are close to the bottom-up emissions from EDGAR v4.3.2 [94], showing 0.45 Tg N yr -1 and 0.64 Tg N yr -1 of the bottom-up NOx emissions from South Korea and Japan, respectively. Figure 9 presents spatial distributions of the bottom-up and top-down NOx emission fluxes and the differences between these two NOx inventories by country and Chinese province. Figure 9c shows large increases in the top-down NOx emissions found over the Guangdong, Shanxi, Sichuan, and Hunan provinces. On the other hand, top-down emissions are lower than the bottom-up NOx emissions in January over central-eastern China (e.g., Tianjin, Hebei, Henan, Anhui, Jiangsu, Shanghai, and Zhejiang), indicating decreases in the top-down NOx emissions by -6.8% to -56.7%, compared with the bottom-up NOx emissions (also, refer to Table S1 for the detailed regional bottom-up and top-down NOx emission fluxes and their differences). Considering possible underestimations of bottom-up NOx emissions in Figure 7b1, this is an unexpected decrease in the top-down NOx emissions over the Tianjin, Hebei, Henan, and Anhui provinces. Despite the decreases, the CMAQ-calculated levels of NO2 over central-eastern China were enhanced by NO2 transported from adjacent provinces, such as Shanxi, Shaanxi, Inner Mongolia, and others where the top-down NOx emissions increase, as shown in Figure 9c. Again, this indicates that the considerations of NOx transport from/to adjacent cells can be a crucial factor in the fine-grid resolved top-down estimation, based on a mass balance approach because this type of detailed NOx transport occurring over central-eastern China would not be shown in coarse grid-resolution. In July, an increase in the top-down NOx emissions was found over most Chinese provinces, particularly over the Hebei and Shandong provinces (approximately 22-23 Gg N month -1 ).

Summary and Conclusions
In this study, an algorithm for the estimation of top-down NOx emissions in a horizontal resolution of 30×30 km 2 was developed based on the mass balance approach. Key components considered in this algorithm were i) the estimation of NOx molecules transported from/to adjacent cells, and ii) the calculation of the lifetimes of column NOx (τ). The wind vector estimated from WRF simulations was analyzed, as discussed in Sections 3.2 and 3.3 to quantify the amounts of NOx molecules. For the calculations of τ, an implicit nonlinear equation (Equation (4)) derived from the mass conservation equation (Equation (3)) was solved (Subsection 3.4.1). The mean values of τ calculated from the nonlinear equation are approximate seven and five hours over central-eastern China in January and in July, respectively. In Subsection 3.4.2, the top-down NOx estimations were significantly influenced (or overestimated) by combined uncertainties from truncation error in the τ calculation and the interpolation of satellite data. The sensitivity test showed the improvements in the top-down NOx estimation via filtering the data under the conditions that columnar NOx lifetimes (τ) are smaller than two hours. The optimal estimation of top-down NOx emissions at each grid cell was determined based on the combinations of differences in NO2 columns (ΔΩNO2 = ΩNO2,CMAQ -ΩNO2,OMI) and NOx emissions (ΔE = Ei-1 -Ei,τ). Then, the algorithm applied to estimate of the top-down NOx emissions over East Asia in conjunction with OMI observations. In the estimation, a six-iteration was conducted to generate the best top-down NOx emissions over East Asia.
To check all the procedures taken in this study (e.g., corrections, interpolation of satellite NO2 data, and calculations of τ and ΔQ), direct comparisons between ΩNO2,CMAQ and ΩNO2,OMI were also made for January and July. The comparison analysis showed significant improvement over the CEC regions, particularly in January, when the final top-down NOx emissions were used in the CMAQ model simulation. The absolute differences decreased from -0.83×10 15 to 0.31×10 15 molecules cm -2 in January and from -0.82×10 15 to -0.38×10 15 molecules cm -2 in July.
The best estimates of the top-down NOx emissions were 11.76, 0.13, 0.46, and 0.68 Tg N yr -1 over China, North Korea, South Korea, and Japan, which were large by 34%, 62%, 60%, and 47%, respectively. From the regional analysis in Chinese provinces, the best top-down NOx emissions varied considerably according to regions and seasons. It was shown that for January, the best top-down NOx emissions decreased, compared to the bottom-up NOx emissions over the central-eastern China regions of Tianjin, Hebei, Henan, Jiangsu, Anhui, Shanghai, and Zhejiang. On the other hand, for July, the top-down NOx emissions were large, compared to the bottom-up NOx emissions, over most Chinese provinces. However, it should not be excluded that the top-down estimate in the study can underestimate the true value because of significant low biases in the current OMI-retrieved tropospheric NO2 columns, compared with MAX-DOAS observations.
In the future, it is expected that the hourly top-down NOx and SO2 emissions for much finer grid resolution can be estimated with the currently developed algorithm, using the data from the geostationary satellite sensors, such as GEMS onboard GEO-KOMPSAT-2B over Asia, TEMPO onboard TEMPO over North America, and Sentinel-4 onboard Meteosat Third Generation-Sounder (MTG-S) over Europe [87][88][89]. Such efforts to retrieve the hourly concentrations of atmospheric pollutants via the data from geostationary satellite sensors, to estimate the emission fluxes, and to evaluate their accuracies, could improve the future performance of air quality modeling. For example, in using Equation (17), the previous concentrations (ΩNOx,i-1) will no longer be obtained from the CTM simulations, but directly from GEO monitoring data. Therefore, after the successful launch of the GEO sensors, we will revisit this issue.