A Comparison Study between Cmaq-simulated and Omi-retrieved No 2 Columns over East Asia for Evaluation of No X Emission Fluxes of Intex-b, Capss, and Reas Inventories

Comparison between the CMAQ (Community Multi-scale Air Quality Model)-calculated and OMI (Ozone Monitoring Instrument)-retrieved tropospheric NO 2 columns was carried out for 2006 over East Asia (100–150 • E; 20– 50 • N) to evaluate the bottom-up NO x emission fluxes of INTEX-B, CAPSS, and REAS v1.11 inventories. The three emission inventories were applied to the CMAQ model simulations for the countries of China, South Korea, and Japan, respectively. For the direct comparison between the two NO 2 columns, the averaging kernels (AKs) obtained from the Royal Netherlands Meteorological Institute (KNMI)/DOMINO v2.0 daily product were applied to the CMAQ-simulated data. The analysis showed that the two tropospheric NO 2 columns from the CMAQ model simulations and OMI observations (CMAQ,AK and OMI) had good spatial and seasonal correlation, with correlation coefficients ranging from 0.71 to 0.96. In addition, the normalized mean errors (NMEs) between the CMAQ,AK and OMI were found to range from ∼ 40 to ∼ 63 %. The CMAQ,AK were, on annual average, ∼ 28 % smaller (in terms of the NMEs) than the OMI , indicating that the NO x emissions used were possibly underestimated in East Asia. Large absolute differences between the CMAQ,AK and OMI were found, particularly over central eastern China (CEC) during winter (annual averaged mean error of ∼ 4.51 × 10 15 molecules cm −2). Although such differences between the CMAQ,AK and OMI are likely caused by the errors and biases in the NO x emissions used in the CMAQ model simulations, it can be rather difficult to quantitatively relate the differences to the accuracy of the NO x emissions, because there are also several uncertain factors in the CMAQ model, satellite-retrieved NO 2 columns and AK products, and NO x and other trace gas emissions. In this context, three uncertain factors were selected and analyzed with sensitivity runs (monthly variations in NO x emissions; influences of different NO x emission fluxes; and reaction probability of N 2 O 5 radicals). Other uncertain or possible influential factors were also discussed to suggest future direction of the study.


Introduction
There has been growing public concern about serious smog events in East Asia due to large amounts of anthropogenic pollutants in the atmosphere.Among the pollutants, nitrogen oxides (NO x ∼ = NO + NO 2 ) play a key role in tropospheric Asia during the winter season, which cannot be ignored in the estimation of direct radiative forcing in East Asia (Park et al., 2014).HNO 3 formation via the reaction of OH + NO 2 during the daytime and heterogeneous nitrate formation via the condensation of N 2 O 5 onto atmospheric particles during the nighttime are believed to be the main chemical and physicochemical processes removing NO x from the atmosphere (McConnell and McElroy, 1973;Platt et al., 1984;Dentener and Crutzen, 1993;Brown et al., 2006;Han and Song, 2012).
Recently, several studies have reported annual increases in NO x emissions in China (Zhang et al., 2007(Zhang et al., , 2009;;Kurokawa et al., 2013).For example, according to the Greenhouse gas and Air Pollution Interactions and Synergies (GAINS) model simulations, China makes the largest contribution to global NO x emissions, and its contribution was estimated to be 25 % for 2010 (Cofala et al., 2012).Also, when several emissions scenarios are applied to the GAINS simulations, the contribution of China is estimated to increase, to ∼ 29 % in the years between 2015 and 2035 (Cofala et al., 2012).However, large uncertainty in bottom-up NO x emissions over East Asia has been reported (e.g., Streets et al., 2003;Zhang et al., 2007;Klimont et al., 2009;Xing et al., 2011).
In the meantime, several studies have also reported rapid increases in atmospheric NO 2 columns over China, based on Global Ozone Monitoring Experiment (GOME), Ozone Monitoring Instrument (OMI), and SCanning Imaging Absorption spectroMeter for Atmospheric CHartogra-phY (SCIAMACHY) observations (Richter et al., 2005;van der A et al., 2006;Schneider and van der A, 2012;Hilboll et al., 2013;Itahashi et al., 2014).These satellite observations have provided useful global/regional information on the spatial distributions of NO 2 columns, and have also been used to investigate the accuracy of the global and regional NO x emissions (e.g., Martin et al., 2006;Uno et al., 2007;Wang et al., 2007;Han et al., 2009).
However, these satellite observations are not "real" or "true" values, having different vertical sensitivities at different altitudes in the atmosphere.To consider this vertical sensitivity of the satellite observations, averaging kernels (AKs) should be introduced into comparison studies between chemistry-transport model (CTM)-simulated and satelliteretrieved tropospheric NO 2 columns (hereafter, denoted as ).The introduction of AKs could correct the large systematic errors typically caused by assumed (or unrealistic) NO 2 vertical profiles used in the retrieval process of the NO 2 columns (Rodgers, 2000;Eskes and Boersma, 2003).In particular, Eskes and Boersma (2003) reported that the use of AKs is crucial in interpreting the retrieved , because of the low sensitivity of satellite observations of NO 2 near the surface areas.
In this context, several studies have used AKs to evaluate the surface NO x emissions over several regions (e.g., Herron-Thorpe et al., 2010;Lamsal et al., 2010;Huijnen et al., 2010;Ghude et al., 2013;Zyrichidou et al., 2013).The previous studies conducted by Han et al. (2009Han et al. ( , 2011) also compared the CTM-calculated tropospheric NO 2 columns with GOME-retrieved tropospheric NO 2 columns to evaluate the bottom-up NO x emissions over East Asia, but without using the AKs.Based on the comparison, Han et al. (2011) concluded that the bottom-up NO x emissions used in CTM simulations over East Asia may be overestimated.However, such a comparison without the application of AKs is like comparing apples with oranges, and is unreasonable.Therefore, one of the main objectives of this study was to correct our previous conclusions, using the state-of-the-science knowledge and methods, including the application of AKs to the CTM simulations.In this study, we intended to evaluate three bottom-up NO x emissions of INTEX-B, CAPSS, and REAS v1.11 inventories in East Asia, using OMI-retrieved tropospheric NO 2 columns ( OMI ) from KNMI/DOMINO v2.0 daily products and the CTM-calculated tropospheric NO 2 columns ( CTM ).To conduct this investigation, the AKs obtained from the KNMI algorithm were applied, and then direct comparison of the CTM,AK with OMI was carried out (refer to Sect.3.1).
However, evaluation of the bottom-up NO x emissions via comparison between CTM,AK and OMI may be hampered by many uncertain factors such as (i) uncertain temporal variations in NO x emissions in East Asia; (ii) uncertainty in meteorological fields; (iii) uncertain or missing photochemistries in the CTM; and (iv) errors in the retrieved NO 2 columns and AKs.Because of these errors and uncertainties, it can sometimes be difficult to directly and quantitatively relate the differences between the CMAQ,AK and OMI to the accuracy of the NO x emissions in East Asia.Some of these issues are therefore explored with several sensitivity analyses, and other factors are also discussed in Sect.3.2.

Modeling descriptions
First, for the CTM simulations, the US EPA/Models-3 CMAQ (Community Multi-scale Air Quality) v4.7.1 model was used (Byun and Schere, 2006).To drive CMAQ model simulations, two main drivers are needed: (i) meteorological fields and (ii) emission fields.For the former, PSU/NCAR MM5 (Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model 5) v3.7.1 was used with National Centers for Environmental Prediction (NCEP) reanalyzed data sets (Stauffer andSeaman, 1990, 1994).To prepare more accurate meteorological fields, fourdimensional data assimilation (FDDA) using QuickSCAT 10 m wind data sets was also carried out.For the latter, three anthropogenic emission inventories were used: INTEX-B (Intercontinental Chemical Transport Experiment-Phase B, Zhang et al., 2009), CAPSS (Clean Air Policy Support System, Hong et al., 2008), andREAS v1.11 (Regional Emis-sion Inventory in Asia, Ohara et al., 2007) emission inventories for the year 2006.Annual 0.5 • × 0.5 • -resolved INTEX-B and REAS v1.11 emissions were interpolated into the CMAQ grid cells in China and Japan, respectively.For biogenic emissions, the MEGAN-ECMWF (Model of Emissions of Gases and Aerosols from Nature-European Center for Medium-Range Weather Forecasts) inventory was obtained from the official website, at http://tropo.aeronomie.be/models/isoprene.htm(Müller et al., 2008).Biogenic emissions are an important factor during the summer, even in this type of NO x study, because the mixing ratios of biogenic species can influence the NO 2 -to-NO ratios via changing the levels of HO x and RO 2 radicals (Horowitz et al., 2007;Han et al., 2009).The accuracy of the biogenic emissions used in this study was also evaluated over the same domain, East Asia, as in our previous study (Han et al., 2013).
Table 1 summarizes the base-case simulation and several sensitivity runs for this study.For the base-case simulation, monthly variations of the anthropogenic NO x emissions from Zhang et al. (2009) were considered for China, while those from Han et al. (2009) were used for South Korea and Japan.The monthly factors were applied to the sectors of power generation, residential areas, industry, and transportation.As shown in Fig. 1, data on several monthly variations in NO x emissions over China were available.Among them, two representative and extreme monthly variations were chosen in this study, which were explored and discussed in Sect.3.2.1.
The modeling period was from 1 January to 31 December 2006.In this study, 2006 was chosen because the INTEX-B inventory was compiled for this year (the REAS v1.11 and CAPSS inventories were also chosen for 2006).The horizontal domain covers from 100 to 150 • E and from 20 to 50 • N with a grid-resolution of 30 km × 30 km.The vertical domain covers from 1000 to 118 hPa with 14 terrain following σ -coordinates.For considering aerosol dynamics and thermodynamics, the aerosol module of AERO4 was selected (Binkowski and Roselle, 2003).
For the consideration of gas-phase chemistry, the SAPRAC-99 (Statewide Air Pollution Research Center-99) mechanism was selected (Carter, 2000).Then, to consider unknown OH radical processes (Lelieveld et al., 2008), the SAPRAC-99 mechanism was modified partly, based on the work of Butler et al. (2008) in the following way.See Reaction (R1): Here, ISOPO2 and ISOPOOH represent isoprene-derived peroxy radical and peroxide, respectively.Other schemes used in the CMAQ model simulations were the global massconserving scheme (YAMO) for horizontal and vertical advection (Yamartino, 1993), the asymmetric convective model (ACM) algorithm for convective cloud mixing, and ACM (ver.2) for vertical diffusion (Pleim, 2007).
In the CMAQ modeling, initial conditions (ICs) were prepared from 1 week-long spin-up model simulations, and boundary conditions (BCs) were obtained from global CTM simulations, MOZART (Model for OZone And Related chemical Tracers) (Emmons et al., 2010).The MOZART model simulation data for the BCs were obtained from http://www.acd.ucar.edu/wrf-chem/mozart.shtml.Other details about the model setup were reported by Han et al. (2013).
For synchronization with the OMI , the CMAQ data were collected and then averaged between 13:00 and 14:00 local time (LT), because the OMI sensor scans the atmosphere over East Asia approximately at 13:45 LT.For further detailed analyses, eight highly populated focus regions were defined in this study, and are presented in Fig. 2.

OMI-retrieved NO 2 columns and AKs
The OMI instrument on board the NASA/EOS-Aura satellite, a nadir-viewing imaging spectrometer, provides information on the properties of aerosols and clouds as well as global levels of atmospheric species such as ozone, NO 2 , SO 2 , OClO, BrO, and HCHO on a daily basis via observing backscattered UV-VIS radiances from 270 to 550 nm (Levelt et al., 2006).Two-dimensional charge-coupled device (CCD) detectors equipped in the OMI instrument observe the atmosphere with a spatial resolution of 13 km × 24 km at the nadir.CCD1 covers the UV channel of 270-310 nm and 310-365 nm.The visible channel, ranging from 365 to 500 nm, is covered by CCD2 to observe NO 2 .
In this study, daily levels of OMI-retrieved tropospheric NO 2 columns from KNMI/DOMINO v2.0 products were used (Boersma et al., 2007(Boersma et al., , 2011a)).The KNMI/DOMINO v2.0 algorithm (hereafter, KNMI algorithm) for retrieving the tropospheric NO 2 columns from the OMI radiance data proceeds in the following sequence.First, a slant NO 2 column density was determined from spectral fitting, using the differential optical absorption spectroscopy (DOAS) method.Second, the stratospheric NO 2 contribution was removed by subtracting the stratospheric portions of slant NO 2 columns from the total slant NO 2 columns.The stratospheric NO 2 slant columns were calculated by data assimilation of OMIobserved slant NO 2 columns in the global CTM (TM4) (Boersma et al., 2007).Finally, the tropospheric slant NO 2 columns were converted into vertical NO 2 columns, using the air mass factor (AMF), defined as the ratio of the measured slant column to the vertical column.This AMF is a function of several factors, such as the satellite viewing geometry, surface albedo, surface pressure, and vertical distributions of clouds, aerosols, and trace gases.In this study, to reduce retrieval errors, measured scenes with surface albedo values larger than 0.3 were excluded, as suggested by Boersma et al. (2011b).The surface albedo data was obtained from the OMI observations (Kleipool et al., 2008).Also, observed pixels with cloud radiance fractions (CRFs) larger than 50 % were filtered out, which are approximately equivalent to cloud fractions (CFs) smaller than 20 % (van der A et al., 2006).Thus, OMI-retrieved tropospheric NO 2 columns under almost "cloud-free" conditions were used in this study.
Errors in the retrieval of the OMI can mainly be caused by calculations of the AMFs.Boersma et al. (2011a) reported that errors of the OMI mostly due to calculations of the AMFs in KNMI/DOMINO v2.0 products were approximated to be ∼ 1.0 × 10 15 molecules cm −2 , with a relative error of 25 %.The other errors in the products were from the spectral fitting (∼ 0.7 × 10 15 molecules cm −2 ) and the stratospheric slant column (∼ 0.25 × 10 15 molecules cm −2 ).
The AKs were also applied to the CMAQ model simulations.The AKs are analytically expressed in Eq. (1) (Rodgers, 2000;Eskes and Boersma, 2003): where G y and K x represent the sensitivities of the retrieval (R) to the measurement (y) and the forward model (F ) to the state (x), respectively.Also, K x is known as a weighting function or Jacobian matrix.Thus, as shown in Eq. ( 1), the AKs represent the sensitivity of the retrieved quantities (here, vertical NO 2 column, x) to the true atmospheric state (x).Using the AKs, the retrieved quantity ( x) can be expressed by Eq. ( 2): where x a and ε represent a priori estimate and total error in measured signal relative to the forward model, respectively.Information on the AKs and retrieved quantity are included in the daily KNMI products (http://www.temis.nl/airpollution/no2col/no2regioomi_v2.php).Figure 3 presents the vertical distributions of the seasonally averaged AKs retrieved from the KNMI algorithms over Central East China (CEC) and other regions (defined in Fig. 2).As shown in Fig. 3, the AKs are strongly altitudedependent in the troposphere.For example, near the surface, the AKs are smaller than unity, ranging between 0.2 and 0.7 (based on seasonal averaged values).In contrast, in the upper troposphere, the AKs are larger than unity, ranging between 1.1 and 2.1 (an AK of unity means that the OMI instruments can directly measure the true NO 2 column densities).Additionally, the AKs are generally lower in warm seasons than in cold seasons.These low values in the AKs during the summer are probably related to low surface albedos, low concentrations of aerosols, and large uncertainty in cloud retrieval during the summer (Eskes and Boersma, 2003).
Figure 4 illustrates the main procedures of the comparison study.Once the CMAQ model simulations were done, all the vertically resolved NO 2 mixing ratios were interpolated to the OMI footprints on a daily basis since the AKs are defined for the OMI footprints.Interpolating AKs to model grid cells is not recommended because the AKs are sometimes sensitive to changes on small spatial scales (Boersma et al., 2011b).After this, the AKs under almost cloud-free conditions were applied to the NO 2 mixing ratios at different layers, and were then integrated from surface to tropopause in order to calculate CMAQ,AK .Meanwhile, the tropospheric NO 2 columns were retrieved from the OMI observations via the KNMI algorithms.A direct comparison study was then made between the two products (i.e., OMI vs. CMAQ,AK ).
For the purpose of this study, the seasonal average values of OMI and CMAQ,AK were calculated (in case of the CMAQ,AK , daily AK applications were first conducted and then seasonal average values were calculated).Seasonal averaging was carried out to reduce the "random errors" in the NO 2 retrieval process typically caused by instrument signal noise, fitting errors, and uncertainty in cloud information.It has been suggested and demonstrated that the random errors can be reduced by both temporal and/or spatial averaging (Fioletov et al., 2002;Monaghan et al., 2006;Johnson et al., 2007;Richter et al., 2011;Clarisse et al., 2013).
On the other hand, the application of AKs can reduce "smoothing errors" in the NO 2 retrieval process, which are mainly caused by bias in the a priori vertical NO 2 profiles.As mentioned previously, TM4-derived a priori profiles were used in the OMI NO 2 retrieval process, which can sometimes cause serious smoothing errors.In order to correct such errors, AKs were applied to the CMAQ model simulations in this study (Rodgers, 2000;Eskes and Boersma, 2003).After the application of AKs, a priori information from TM4 did not influence the comparison between OMI and CMAQ,AK .

Results and discussions
The objective of this study is to evaluate the NO x emissions of the INTEX-B, CAPSS, and REAS v1.11 inventories over East Asia by comparing two obtained from the CMAQ model simulations and OMI observations (Sect.3.1).In addition, several sensitivity analyses were also conducted to examine the influences of the uncertainty factors on the discrepancies between CMAQ,AK and OMI (Sect.3.2).Obviously, not all the influential factors can be explored within the framework of this study.Thus, several selected issues that may be important are also discussed further in Sect.3.2.4.

Comparison between CMAQ-estimated and
OMI-retrieved NO 2 columns: Case 1

CMAQ-calculated vs. OMI-retrieved NO 2 columns
In this study, the analyses were conducted for four seasons: Figure 5 presents the comparison analysis between the CMAQ and OMI for the four seasons over East Asia before and after the applications of the AKs.As shown in Fig. 5, the CMAQ model simulations (the first and second columns) show spatially and seasonally consistent patterns with OMI observations (the third column).For example, the high values of the OMI over the densely populated and economically developed megacity regions such as Beijing, Shanghai, Hong Kong, Seoul, and Tokyo (refer to Fig. 2 regarding their locations) are well captured by the CMAQ model simulations.The levels of the during the winter are distinctly high.Also, the low values of the CMAQ during the summer are well matched with those from the OMI observations.The low levels of the during the summer are mainly caused by active NO x chemical losses via the reaction of NO 2 with OH radicals (McConnell and McElroy, 1973;Atkinson et al., 2004;Boersma et al., 2009;Han et al., 2009;Stavrakou et al., 2013).The uncertainties and unknown factors related to this reaction will be discussed further in Sect.3.2.4.
When panels (a) and (c) in Fig. 5 are compared, it can be seen that the CMAQ is in general greatly larger than the OMI over the regions with strong NO x emissions.This was also presented in Han et al. (2011).The large differences between the two NO 2 columns can be confirmed again in panel (d) of Fig. 5.However, such a comparison without apply- ing the AKs is like comparing apples and oranges, and is not reasonable.Such studies have been conducted over East Asia with misleading conclusions (e.g., Ma et al., 2006;He et al., 2007;Uno et al., 2007;Shi et al., 2008;Han et al., 2009Han et al., , 2011)).In this context, we now wish to correct our previous conclusions (Han et al., 2011) here, applying the AKs to the CMAQ model simulations, using the linear relationship presented in Eq. ( 2).
After the application of the AKs to the CMAQ model simulations, the comparison becomes independent of the a priori profile shape used in the NO 2 retrieval process (Eskes and Boersma, 2003).In this study, when the panels (b) and (c) in Fig. 5 are compared, it can be seen that the CMAQ-calculated NO 2 columns considering the AKs are much more compara-ble to the OMI-retrieved NO 2 columns, possibly indicating that the bottom-up NO x emission used in the CMAQ model simulations would not be very greatly overestimated, unlike the previous conclusion drawn by Han et al. (2011).Figure 5d and e more directly show the effects of the application of the AKs.When the AKs are applied, the differences are greatly diminished, and are even negative, particularly over the CEC regions.The CMAQ,AK becomes smaller than the OMI over the CEC, SC, SK, JP1, and JP2 regions.Also, possible overestimations of the bottom-up NO x emissions were found in the CEC2 and SB regions, particularly during the winter.Possible underestimations over the CEC and SC regions and overestimations over the SB and CEC2 regions were also presented in the study of Lin (2012).In Lin (2012), the GOES-CHEM,AK values were found to be about 20 and 36 % lower than the OMI over eastern China in summer and winter, respectively, whereas in the calculations herein, the respective CMAQ,AK values were about 57 % and 5 % lower than the OMI over eastern China.These differences would be caused by the constant NO x emission fluxes and relatively coarse horizontal resolutions (0.67 • × 0.5 • ) used in the GEOS-CHEM simulations performed by Lin (2012).
In Table 2, we summarize the seasonal average tropospheric NO 2 columns and normalized mean errors (NMEs, defined in Table A1) with and without considering the AKs for the eight focus regions.It can be seen that the NMEs (with AKs applied) ranged from 40.3 to 63.2 % over the entire domain in Table 2.Although the differences between CMAQ,AK and OMI were the smallest during the summer (as shown in Fig. 5), the NMEs showed the largest values during summer.The reasons for this are discussed in detail in Sect.3.1.2.
Collectively, the seasonal and regional (spatial) characteristics observed from the OMI sensor were found to be captured well by the CMAQ model simulations using the INTEX-B, CAPSS, and REAS emission inventories.However, some regional discrepancies between the two NO 2 columns were also found, particularly during winter, indi-cating possible underestimation of the NO x emissions over the CEC and SC regions as well as overestimation over the CEC2 and SB regions in the CMAQ model simulations.To further investigate the eight regions of interest, scatter plots and statistical analyses were carried out in Sect.3.1.2.

Scatter plots and statistical analyses
Figure 6 presents the seasonal scatter plot analysis between the CMAQ,AK and OMI for the eight focus regions defined in Fig. 2. The statistical analysis related to the scatter plots was also conducted in terms of the Pearson correlation coefficient (R), linear regression slope (S), and y intercept (Y-I).As mentioned in Sect.2.2, seasonal average of the daily was taken to reduce the random errors which have occurred during the NO 2 measurement and retrieval processes (Fioletov et al., 2002;Monaghan et al., 2006;Johnson et al., 2007;Richter et al., 2011;Clarisse et al., 2013).The use of seasonally averaged data improved the correlation coefficients from 0.49-0.63 to 0.78-0.88over the entire domain (DM) (regarding this issue, readers can compare Fig. 6 with Fig. S1 in the Supplement).Although the correlation coefficients were sometimes lower than 0.7 in Fig. 6, the two NO 2 columns correlated well, with R values between 0.71 and 0.96 (also, refer to the "R" values colored in Fig. 7).Slopes lower than 1.0 (see dashed lines in Fig. 6) were found in the "blue" regions in Fig. 5e such as the CEC, SC, SB, JP1, and JP2 regions.These low slopes indicate the possible "underestimation" of the bottom-up NO x emissions used in the CMAQ model simulations, as discussed in Sect.3.1.1.Further statistical analyses were conducted.For absolute differences, mean error (ME) and mean bias (MB) were utilized.For relative differences, mean normalized gross error (MNGE), mean normalized bias (MNB), normalized mean error (NME), normalized mean bias (NMB), mean fractional error (MFE), and mean fractional bias (MFB) were used.The Pearson correlation coefficient (R) and index of agreement (IOA) were also analyzed to assess the degrees of correlations and agreement, respectively.These 10 performance metrics are defined and described in Table A1 (see Appendix A).
Figure 7 summarizes the seasonal statistical analyses for eight focus regions.Light colors were used to indicate good agreements, while dark colors marked poor agreements.As shown, the IOAs (as a measure of the degree of model prediction errors, Willmott, 1981) showed high values, between 0.78 and 0.93, over the entire domain.However, the IOAs sometimes showed relatively low values during the summer over several regions where large relative differences were found (e.g., SB, JP1, and JP2 regions during the summer), because the IOA decreased with the large differ- ence between CMAQ,AK and OMI .As shown in Fig. 7, large MEs were found over the CEC region (2.03 × 10 15 to 4.51 × 10 15 molecules cm −2 ) and MBs mostly ranges between −1.78 × 10 15 and 1.88 × 10 15 molecules cm −2 in East Asia, except in CEC.Again, the negative values of the MBs in Fig. 7 indicate that the NO x emissions used were possibly underestimated.
In the seasonal perspective, all statistical parameters of the relative differences (i.e., MNGE, MNB, NME, NMB, MFE, and MFB) showed large values for the summer in all the regions, because the OMI-retrieved quantity in the denominator of the equations (see Table A1) for the summer were relatively small versus the values of the absolute differences in the numerator.In this study, the CMAQ,AK values over the entire domain were 7.3 and 59.7 % smaller than OMI in terms of the NMB during the summer and winter seasons, respectively.In the regional perspective, the relative differences showed large values in the SC, SB, JP1, and JP2 re-gions, where the were relatively low (i.e., the same reason leading to larger relative errors and biases in the summer).In this study, the CMAQ,AK values during winter were found to be 21.8 % smaller than the OMI over CEC, but 32.3 % and 54.7 % larger over CEC2 and SB, respectively.Collectively, the statistical analyses showed that the CMAQ,AK were, on annual average, ∼ 28 % (from 7 % to 60 % with seasonal variation) smaller than the OMI , indicating that the NO x emissions for East Asia were possibly underestimated.

Sensitivity analyses
After the application of the AKs, both the CMAQ,AK and OMI became much more comparable with each other as shown in Fig. 5.Even so, this comparison study still has several uncertainties.Because of the uncertainties, it is difficult to directly relate the differences between the CMAQ,AK and OMI to under-or over-estimations in the NO x emissions.Therefore, examination of the uncertainty issues was carried out herein.The issues selected for examination in this study were as follows: (i) the monthly variation in NO x emissions; (ii) influences of the different magnitude of NO x emissions; and (iii) different parameterizations of the reaction probability of N 2 O 5 onto aerosols in the CMAQ model simulations.These three issues were selected for the following reasons: (i) the emission flux in East Asia is believed to be one of the most uncertain factors, and its magnitude can vary greatly depending on monthly variation as well as methodology and activity data used to estimate the emission fluxes (Cases 2 and 3) (Wang et al., 2007;Zhang et al., 2007Zhang et al., , 2009;;Han et al., 2009;Klimont et al., 2009;Xing et al., 2011); and (ii) although the condensation of N 2 O 5 radicals is a major NO x loss processes during the winter and thus may significantly influence the tropospheric NO 2 columns, the magnitudes of γ N 2 O 5 remain highly uncertain, ranging between 0.1 and 0.001 (Case 4) (Dentener and Crutzen, 1993;Jacob, 2000;Brown et al., 2006;Davis et al., 2008;Macintyre and Evans, 2010).Sect.3.2 is therefore devoted to these issues, which are addressed with sensitivity analyses.

Monthly variation in NO x emissions: Case 2
First, the monthly variations of NO x emissions over China were investigated, choosing different monthly variations from the base-case emission.In this sensitivity run (see Table 1), we applied a more drastic/extreme monthly variation of the NO x emissions (thick black line in Fig. 1) (Han et al., 2009) to the CMAQ model simulation over China in this 1year run.The main reason we did this is that, as shown in Figs. 5 and 6, the CMAQ,AK was smaller than the OMI , over several main regions (such as CEC and main megacity areas like Hong Kong and Shanghai) in China, particularly during the "cold months".It should be noted that during the cold months, the NO x emission fluxes reported in Han et al. (2009) for China were 1.20 times larger than those from the INTEX-B inventory.
The results are presented in Fig. 8.The spatial distributions of the CMAQ,AK and OMI are shown in Fig. 8 for the four seasons.As indicated in Table S1 in the Supplement, the application of the AKs again greatly reduced the errors and biases between the two tropospheric NO 2 columns in this sensitivity test.As expected, the CMAQ,AK in Fig. 8a generally increased for the spring and winter, whereas it decreased for the summer and fall, compared with the values in Fig. 5b.These increases in the CMAQ,AK for the winter produced better agreement with the OMI , particularly over the CEC region, showing that the MBs over CEC during the winter decreased from −3.10 × 10 15 to −7.42 × 10 14 molecule cm −2 (see the average NO 2 columns and NMEs in Tables 2 and  S1).However, as shown in Tables 2 and S1, the situations became worse, except for the CEC region, showing significant increases in NMEs, compared with the NMEs in cases using the monthly variation of the INTEX-B inventory taken from Zhang et al. (2009).Even larger (more serious) differences between the two NO 2 columns in Fig. 8c were found over other regions of China (CEC2, SC, and SB) than those shown in Fig. 5e in terms of errors and biases.For example, the MBs during the winter increased from 2.74 × 10 15 , −2.92 × 10 13 , and 1.88 × 10 15 molecule cm −2 to 5.26 × 10 15 , 7.10 × 10 15 , and 5.35 × 10 15 molecule cm −2 over CEC2, SC, and SB, respectively.
Further detailed analyses over the eight focus regions were carried out, and the scatter plots and statistical analyses are presented in Figs.S2 and S3.Collectively, the sensitivity test showed that the monthly variations of the OMI observations were better captured by the CMAQ model simulations using the monthly variations of the INTEX-B inventory than those from Han et al. (2009)

Another NO x emission inventory (REAS v1.11): Case 3
There is another NO x emission inventory available in China: the REAS v1.11 emission inventory for 2006 (Ohara et al., 2007).Thus, in this section, the REAS emission inventory, a frequently used bottom-up inventory established by the National Institute of Environmental Studies (NIES) in Japan, was tested over China for January (a cold month) in order to determine the influence of different NO x emissions on the tropospheric NO 2 columns.Because the REAS v1.11 inventory does not include monthly variation, the same monthly variation of the INTEX-B inventory was also applied to this sensitivity study.The NO x emissions between the INTEX-B and REAS inventories differed greatly over China.For example, the annual NO x emissions from the INTEX-B inventory were 2.48, 2.22, 1.60, and 0.57 Tg N yr −1 over the CEC, CEC2, SC, and SB regions, respectively, whereas those from the REAS inventory were 1.93, 1.56, 1.40, and 0.40 Tg N yr 1 , respectively, over the same regions.
The results are presented in Fig. 9 and Table S2.The application of the AKs to the CMAQ model simulations were also taken into account in this comparison (see Table S2).As expected, the CMAQ,AK decreased significantly over China, when the REAS NO x emissions were used (refer to Table S2).Although the absolute differences between the CMAQ,AK and OMI became smaller over the CEC2 and SB regions, much large underestimates were found over the CEC region, compared with the case of the INTEX-B inventory as shown in Fig. 9.
Collectively, our results indicate that (i) the NO x emission fluxes from the REAS inventory are also underestimated over China (particularly, over the CEC region), (ii) both NO x emission inventories (INTEX-B and REAS) showed under-estimation over the CEC region and the Hong Kong area, and (iii) accurate spatial distributions of NO x emissions and the magnitude of NO x emissions were important factors to reduce the degree of disagreement between the CTM-estimated and satellite-retrieved NO 2 columns.For better agreement between the CMAQ,AK and OMI over China, a combination of the two emission inventories may be a good practical attempt in the CMAQ model simulations over East Asia, based on this result.That is, the INTEX-B NO x emissions data tended to produce better results over the CEC region, whereas the REAS NO x emissions data tended to generate better results over the CEC2 and SB regions.However, this issue (i.e., the combination of the two emission inventories) needs to be examined using a more sophisticated approach, and should be investigated further.

Reaction probability of N 2 O 5 : Case 4
We explored the issue of reaction probability of N 2 O 5 (γ N 2 O 5 ) onto aerosols, because a relatively large discrepancy between the CMAQ,AK and OMI was found, particularly during the winter season.During the winter season, the condensation of N 2 O 5 into atmospheric particles is an important NO x loss process (Dentener and Crutzen, 1993;Brown et al., 2004Brown et al., , 2006)).Thus, it can affect the CMAQ-simulated NO 2 columns ( CMAQ,AK ).Although it is an important physicochemical NO x loss process during the winter, the magnitude of γ N 2 O 5 has been a controversial issue.In this study, five CMAQ,AK from the CMAQ model simulations with five different γ N 2 O 5 parameterizations were compared with the OMI over East Asia.These five parameterizations are from the works of (i) Dentener and Crutzen (1993), (ii) Riemer et al. (2003), (iii) a combination of Riemer et al. (2003) and Evans and Jacob (2005), (iv) Davis et al. (2008), and (v) Brown et al. (2006).The mathematical expressions for these    parameterizations are summarized briefly in Table 3.In the Dentener and Crutzen's parameterization (1993), they used a fixed value of γ N 2 O 5 of 0.1 in their global CTM simulation (Scheme I in Table 3).In Riemer et al.'s parameteriza-tion (2003), γ N 2 O 5 is a main function of the acidity of the particles (Scheme II).In the combined parameterization of Evans and Jacob (2006) and Riemer et al. (2003), γ N 2 O 5 is a function of relative humidity (RH), temperature, and the acidity of the particles (Scheme III, standard scheme).In Davis et al.'s (2008) parameterization, γ N 2 O 5 is a function of all the factors, such as RH, temperature, the acidity of the particles, and the mixing state (Scheme IV).Finally, for Brown et al.'s (2006) parameterization, we used a fixed minimum value of γ N 2 O 5 of 10 −3 in the CMAQ model simulation (Scheme V).
The comparison results are presented in Fig. 10.As shown in Fig. 10 and Table 4, the CMAQ,AK with the Brown et al. (2006) parameterization were ∼ 19 % larger than those with the standard Scheme (III) over East Asia.This indicates that Brown et al.'s parameterization resulted in the smallest NO x loss rates (or nitrate formation rates) via this physicochemical reaction pathway.
In contrast, the application of the Dentener and Crutzen's parameterization to the CMAQ model simulation produced the smallest CMAQ,AK in East Asia, indicating the fastest NO x loss rates, due to the large γ N 2 O 5 .These results suggest that Brown et al.'s γ N 2 O 5 (= 0.001) may be smaller than the real value, while Dentener and Crutzen's γ N 2 O 5 (= 0.1) is probably larger.Other than Brown et al.'s and Dentener and Crutzen's parameterizations, it was found that there was almost no significant or practical difference in the CMAQ,AK among the other three Schemes, II, III, and IV (also, refer to Table 4).
As shown in Fig. 10 and Table 4, Schemes II, III, and IV tended to produce better CMAQ,AK data over East Asia than Schemes I and V, compared with OMI .More recently, Brown et al. (2009) and Bertram et al. (2009) also discussed that the γ N 2 O 5 values being used currently in regional/global CTMs were generally larger than those from their observed γ N 2 O 5 .In addition to the issue of γ N 2 O 5 , it should be noted that the aerosol surface density (A) is another uncertain factor that can influence the CMAQ,AK , because the rate constant (k N 2 O 5 ) of the physicochemical reaction also depends on the aerosol surface density (refer to the Schwartz formula, k ).Although all of these issues are arguable, our results show that the γ N 2 O 5 parameterizations can certainly influence the levels of NO 2 in East Asia, particularly during the winter season.

More uncertainties and outlooks
As mentioned previously, in this type of analysis all types of temporal variation are potentially important and should therefore be taken into account.A sensitivity analysis on the monthly variation in the NO x emissions in China was performed in Sect.3.2.1,showing that the monthly variations in NO x emissions were an important factor.In contrast, there is only limited information on other temporal variation, such as daily and weekly variation in NO x emissions in East Asia.Unfortunately, no emission inventory in East Asia can provide us with this level of information.Regarding the issue of the temporal variation, the future Korean Geostationary Environmental Monitoring Spectrometer (GEMS) sen-sor, which is planned to be launched in 2018, will be able to help to obtain such information on daily and weekly variation in the NO x emissions over East Asia (Kim, 2012).
There is also some level of uncertainty in the NO 2 -to-NO ratios, as discussed previously by Richter et al. (2005) and Han et al. (2009).This factor may be important, because every satellite remote-sensor monitors only NO 2 columns, not NO x columns.The NO 2 -to-NO ratios are affected seriously by anthropogenic and biogenic VOC (AVOC and BVOC) emissions and their mixing ratios.For example, if we assume a photostationary state, the NO 2 -to-NO ratios can be influenced by the mixing ratios of ozone and HO 2 , CH 3 O 2 , and RO 2 radicals, as shown in the following formula: where J 1 is the NO 2 photolysis rate constant (s −1 ) and k 1 (= 1.81 × 10 −14 at 298 K), k 2 (= 8.41 × 10 −12 at 298 K), k 3 (= 7.29 × 10 −12 at 298 K), and k 4 (= 9.04 × 10 −12 − 2.80 × 10 −11 at 298 K) are the reaction rate constants (cm 3 molecules −1 s −1 ) for NO + O 3 , NO + HO 2 , NO + CH 3 O 2 , and NO + RO 2 reactions, respectively.Although k 1 is the smallest among the 4 reaction rate constants, the NO 2 to-NO ratio tends to be determined by the NO + O 3 reaction, together with the photolysis of NO 2 (J 1 ), because ambient O 3 mixing ratios usually occur in several tens of ppb.However, the NO + HO 2 and NO + RO 2 reactions during summer have almost equivalent (non-negligible) contribution to the NO 2 -to-NO ratios, for example, over the SC region where BVOC emissions are active.In addition, the mixing ratios of ozone, HO 2 , CH 3 O 2 , and RO 2 in Eq. ( 3) can be affected by AVOC and BVOC emissions and their mixing ratios, which are believed to be highly uncertain in East Asia (Fu et al., 2007;Lin et al., 2012;Han et al,. 2013).
Recently, modeling uncertainties including meteorological parameters were discussed comprehensively by Lin a Scheme I (Dentener and Crutzen, 1993), Scheme II (Riemer et al., 2003), Scheme III (combination of Riemer et al., 2003 andEvans andJacob, 2005), Scheme IV (Davis et al., 2007), Scheme V (Brown et al., 2006); b The number of data; c Unit, × 10 15 molecules cm −2 ; d Standard deviations of the distributions of tropospheric NO 2 columns.et al. (2012).They reported that when tropospheric NO 2 columns from several sensitivity simulations were compared with those from standard simulations, the largest impact on the tropospheric NO 2 columns was caused by modifying the reaction probability of HO 2 onto aerosols (i.e., γ HO 2 ), fol-lowed by the modifications of cloud optical depth, HNO 3 formation rate via NO 2 +OH, γ N 2 O 5 , and aromatic species emissions.It was also reported in their study that modification of all the parameters could increase the tropospheric NO 2 columns by 18 % during July and by 8 % during Jan--As shown in  Riemer et al. (2003) and Evans and Jacob (2006).In this study, the conventional γ N 2 O 5 parameterizations (Schemes II, III, and IV) showed almost no practical differences in the CMAQ,AK and tended to produce better CMAQ,AK data over East Asia than Schemes I and V.
One of the main driving forces of this study was to correct our previous conclusions (Han et al., 2011), in which AKs were not employed for the comparison between the OMI and CMAQ .Again, this study indicated that the bottom-up NO x emissions of the INTEX-B, CAPSS, and REAS v1.11 inventories used in the CMAQ model simulations would be rather underestimated over East Asia.In the sensitivity studies, the influences of different NO x emissions and monthly variation in NO x emissions can also significantly influence the levels of the CMAQ,AK in East Asia.Moreover, we showed that the γ N 2 O 5 parameterization could be another important factor in the winter.Because other possible uncertainty factors still exist, as discussed in Sect.3.2.4,further analyses are definitely necessary in future studies.
The estimation of "top-down" NO x emissions has also been carried out in East Asia (Stavrakou et al., 2008;Lin et al., 2010;Mijling et al., 2013) using satellite-derived NO 2 columns.However, in such top-down estimations, other uncertain (limiting) factors exist, such as the lifetime of NO x (i.e., τ NO x ).The uncertainty in τ NO x is also linked with the factors discussed herein in Sect.3.2.4.In addition, even in the top-down NO x emission, the random and smoothing errors should be reduced/minimized via temporal and/or spatial averaging and the application of AKs, respectively, as demonstrated herein.
Improvements in the NO x emissions data or evaluation of the accuracy of bottom-up NO x emission fluxes in East Asia can improve air quality modeling and chemical weather forecasting over East Asia.Thus, much effort should be focused on this issue in the future, particularly on the circumstances over East Asia.In this context, efforts in inverse modeling to improve the NO x emissions data over East Asia, such as adjoint modeling with measured data and top-down estimations of the NO x emissions with satellite observations, could also contribute to improving the performance of air quality modeling and the accuracy of chemical weather forecasting over East Asia (Park et al., 2013).
The Supplement related to this article is available online at doi:10.5194/acp-15-1913-2015-supplement.
Figure 4. Flow diagram for direct comparison between CMAQ-estimated and OMI-retrieved NO 2 columns.

Figure 5 .
Figure 5. Spatial and seasonal distributions of CMAQ-calculated tropospheric NO 2 columns (a) without the applications of the AKs and (b) with the AKs and (c) OMI-retrieved NO 2 columns from the KNMI algorithm.Differences between OMI-retrieved and CMAQ-calculated NO 2 columns (d) before the applications of the AKs and (e) after the applications of the AKs.

Figure 6 .Figure 7 .
Figure 6.Seasonal scatter plots between CMAQ-calculated and OMI-retrieved NO 2 columns (Unit: × 10 15 molecules cm −2 ) using seasonally averaged data sets over the CEC, CEC2, SC, SB, SK, JP1, JP2, and DM regions.Here, the AKs were applied to the CMAQ model simulations.R, S, Y-I, and N represent the correlation coefficient, linear regression slope, y intercept, and the number of data points, respectively.

Figure 8 .Figure 9 .
Figure 8. Spatial distributions of (a) CMAQ-calculated NO 2 columns with the AKs and (b) OMI-retrieved NO 2 columns and (c) their differences for four seasonal episodes.Here, the monthly variations of NO x emissions from Han et al. (2009) were applied to the CMAQ model simulations.

Table 1 .
Description of CMAQ model simulations conducted in this study.

Table 2 .
Average tropospheric NO 2 columns, standard deviations, and the normalized mean error (NME) with and without the application of AKs for four seasons.Unit, × 10 15 molecules cm −2 ; c Standard deviations of the distributions of tropospheric NO 2 columns.
a The number of data; b

Table 3 .
Reaction probabilities of N 2 O 5 onto aerosol surfaces.

Table 4 .
Average tropospheric NO 2 columns, standard deviations and the ratios of the CMAQ,AK to the OMI , when different γ N 2 O 5 parameterizations were applied to the CMAQ model simulations for January.
Table 5, when REAS v1.11 inventory data over China were used in the CMAQ model simulations, the CMAQ,AK become −31.45 to −58.44 % lower over China than those from the case with the INTEX-B inventory.Based on this, the NO x emissions from the REAS v1.11NO x emissions appeared to be more underestimated over China than the INTEX-B NO x emissions.-In the sensitivity test of γ N 2 O 5 , it appeared that the γ N 2 O 5 parameterization would not be a negligible factor, particularly during the winter.The CMAQ,AK from Brown et al.'s (2006) parameterization were ∼ 19 % larger over East Asia than the CMAQ,AK from the combined parameterization of