Key chemical NOx sink uncertainties and how they influence top-down emissions of nitrogen oxides

Triggered by recent developments from laboratory and field studies regarding major NO x sink pathways in the troposphere, this study evaluates the influence of chemical uncertainties in NOx sinks for global NOx distributions calculated by the IMAGESv2 chemistry-transport model, and quantifies their significance for top-down NO x emission estimates. Our study focuses on five key chemical parameters believed to be of primary importance, more specifically, the rate of the reaction of NO2 with OH radicals, the newly identified HNO3-forming channel in the reaction of NO with HO 2, the reactive uptake of N2O5 and HO2 by aerosols, and the regeneration of OH in the oxidation of isoprene. Sensitivity simulations are performed to estimate the impact of each source of uncertainty. The model calculations show that, although the NO2+OH reaction is the largest NO x sink globally accounting for ca. 60 % of the total sink, the reactions contributing the most to the overall uncertainty are the formation of HNO 3 in NO+HO2, leading to NOx column changes exceeding a factor of two over tropical regions, and the uptake of HO 2 by aqueous aerosols, in particular over East and South Asia. Emission inversion experiments are carried out using model settings which either minimise (MINLOSS) or maximise (MAXLOSS) the total NOx sink, both constrained by one year of OMI NO2 column data from the DOMINO v2 KNMI algorithm. The choice of the model setup is found to have a major impact on the top-down flux estimates, with 75 % higher emissions for MAXLOSS compared to the MINLOSS inversion globally. Even larger departures are found for soil NO (factor of 2) and lightning (1.8). The global anthropogenic source is better constrained (factor of 1.57) than the natural sources, except over Sou h Asia where the combined uncertainty primarily associated to the NO+HO 2 reaction in summer and HO2 uptake by aerosol in winter lead to top-down emission differences exceeding a factor of 2. Evaluation of the emission optimisation is performed against independent satellite observations from the SCIAMACHY sensor, with airborne NO2 measurements of the INTEX-A and INTEX-B campaigns, as well as with two new bottom-up inventories of anthropogenic emissions in Asia (REASv2) and China (MEIC). Neither the MINLOSS nor the MAXLOSS setup succeeds in providing the best possible match with all independent datasets. Whereas the minimum sink assumption leads to better agreement with aircraft NO2 profile measurements, consistent with the results of a previous analysis ( Henderson et al. , 2012), the same assumption leads to unrealistic features in the inferred distribution of emissions over China. Clearly, although our study addresses an important issue which was largely overlooked in previous inversion exercises, and demonstrates the strong influence of NOx loss uncertainties on top-down emission fluxes, additional processes need to be considered which could also influence the inferred source. Published by Copernicus Publications on behalf of the European Geosciences Union. 9058 T. Stavrakou et al.: Impact of NOx sink uncertainties on top-down NOx emissions


Introduction
Sources of nitrogen oxides in the atmosphere are predominantly anthropogenic. According to state-of-art estimates, anthropogenic NO x accounts for about 65 % of the annual global NO x flux, whereas natural emissions from fires, soils and lightning are less significant on the global scale, and are estimated at about 9 %, 17 % and 6 %, respectively (e.g. Jaeglé et al., 2005;Müller and Stavrakou, 2005). The uncertainties in these estimates are, however, significant, especially for natural sources. To narrow down these uncertainties, top-down or inverse modelling methods constrained by tropospheric NO 2 vertical column abundances observed from space have been widely used to evaluate and complement the bottom-up inventories used in atmospheric models (e.g. Müller and Stavrakou, 2005;Stavrakou et al., 2008;Zhao and Wang, 2009;Lin et al., 2010;Lin, 2012;Mijling and van der A, 2012;Miyazaki et al., 2012a).
Inverse modelling adjusts the emission fluxes used in a chemistry-transport model in order to reduce the mismatch between the predictions of the model and atmospheric observations. This is often realised iteratively by varying the emissions until the model/data biases are minimised within their assigned errors. This approach implicitly assumes that the relationship between the emission fluxes and the atmospheric abundances is reasonably well simulated by the model, so that the model/data mismatch can be mostly attributed to errors in the emission inventories. In other words, the uncertainties associated to the bottom-up emissions are assumed to be larger than errors in the model or in the measurements used to constrain the inversion. Nevertheless, a series of recent developments regarding chemical NO x sinks and the oxidising capacity of the atmosphere (Mollner et al., 2010;Butkovskaya et al., 2007Butkovskaya et al., , 2009Henderson et al., 2012;Brown et al., 2009;Lelieveld et al., 2008;Mao et al., 2013) point to flaws in the current mechanisms implemented in global models, implying potentially large impacts on simulated NO x concentrations, and consequently on top-down NO x emission estimates.
These developments concern firstly the main tropospheric NO x removal channel, i.e. the reaction of NO 2 with OH radicals, forming nitric acid. It was shown in a laboratory study that its reaction rate at room temperature is lower than previously recommended (Mollner et al., 2010), and further, aircraft observations were used to show that its reaction rate in the upper troposphere was even more largely overpredicted at the low temperatures typical of the upper troposphere (Henderson et al., 2012). Secondly, a series of laboratory experiments performed by Butkovskaya et al. (2007Butkovskaya et al. ( , 2009 suggested an additional loss process for NO x through a nitric acid formation channel in the NO+HO 2 reaction. Although this channel is quite minor compared to the traditional pathway forming NO 2 +OH (less than 0.5 % in dry air), it has the potential to represent a significant HNO 3 formation pathway (Cariolle et al., 2008); furthermore, it was found to pro-ceed much faster in the presence of water vapour. This could strongly affect the NO 2 concentrations, especially in the lower troposphere and in tropical regions. Thirdly, field measurements (Brown et al., 2009) suggested that reactive uptake of N 2 O 5 at the surface of aerosols proceeds at rates substantially lower than predicted by parameterizations widely used in global models (e.g. Evans and Jacob, 2005;Davis et al., 2008). Finally, the hydroxyl radical (OH) levels have possibly large errors in models. For example, field campaigns point to strong underpredictions of OH levels in low-NO x , high-isoprene environments , for reasons still unclear (Peeters et al., 2009;Crounse et al., 2011), although simple expedients have been proposed to crudely compensate for the model underprediction . In more polluted environments characterised by heavy aerosol loadings, the effect of HO 2 radical uptake by aqueous aerosols might be severely underestimated in models (Mao et al., 2013), leading to possibly large OH level overestimations, although field campaigns around Chinese megacities point to large OH underestimations by models (Hofzumahaus et al., 2009;Lu et al., 2013), for reasons still unclear.
A thorough discussion of the above sources of uncertainty is presented in Sect. 2, and their importance on the NO 2 abundances simulated with the IMAGESv2 global CTM is addressed in Sect. 4. Based on the above, two model setups are designed to either minimise (MINLOSS simulation) or maximise (MAXLOSS) the NO x sink in the model. These scenarios are meant to provide a measure of the overall uncertainty related to the major chemical NO x losses. They do not address other sources of uncertainty, however, such as errors related to meteorological fields or other model parameters. Recently, a systematic analysis of meteorological and chemical parameters affecting the NO x simulation over China in a CTM by Lin et al. (2012), showed that errors in meteorology affect significantly the modelled NO 2 columns, although their regionally-averaged overall reported uncertainty accounting for all parameters was lower than 20 %. Note that this estimation might be model-dependent.
The MINLOSS and MAXLOSS setups are used in an inverse modelling framework using the adjoint of the IM-AGESv2 model (e.g. Müller and Stavrakou, 2005;Stavrakou et al., 2008Stavrakou et al., , 2012. The inversion experiments are constrained by vertical NO 2 tropospheric columns retrieved from the Ozone Monitoring Instrument (OMI) (Boersma et al., 2011) (Sect. 3). Sensitivity calculations illustrating the effect of NO x sink uncertainties on the distribution of NO x sinks are presented in Sect. 4. The top-down estimates of NO x fluxes as derived from MINLOSS and MAXLOSS inversions are compared in Sect. 5. Evaluation of the results against independent measurements and inventories is presented in Sect. 6. More specifically, the model predictions before and after inversion are compared against (i) NO 2 column data from SCIAMACHY instrument aboard ENVISAT (Sect. 6.1), and (ii) airborne NO 2 profiles from INTEX-A T. Stavrakou et al.: Impact of NO x sink uncertainties on top-down NO x emissions 9059 Fig. 1. Zonally averaged vertical profiles at 40 • N of (a) the NO 2 + OH reaction rate in July, (b) the NO + HO 2 → HNO 3 reaction rate in July, and (c) the heterogeneous sink of N 2 O 5 on aqueous aerosols over continents in January. The continuous red line in panel (b) assumes that the NO-reaction rate of the HO 2 · H 2 O complex (k w ) is constant, whereas the dashed red line uses the temperature and pressure dependence of the rate in dry conditions (k d ).
and INTEX-B missions (Sect. 6.2). The top-down emissions are also directly compared with two state-of-the-art bottomup emission inventories for Asia and for China (Sect. 6.3). Finally, conclusions are drawn in Sect. 7.

The NO 2 +OH → HNO 3 reaction
Despite its crucial role as the primary sink of NO x in the troposphere, the rate constant for the termolecular association reaction, NO 2 + OH + M → HNO 3 + M, has remained very difficult to measure with accuracy under atmospheric conditions. Recently, its expression has been revised by Mollner et al. (2010) based on room temperature experiments performed using improved experimental methods relying on the simultaneous measurement of all reactants and products in the reaction (Donahue, 2011). The measured rates at 298 K were significantly lower than in previous recommendations, by 23 % compared to IUPAC-2004(Atkinson et al., 2004 and by 13 % compared to JPL (Sander et al., 2011). Since the temperature dependence of the rate was not investigated by Mollner et al. (2010), the recommendation of Sander et al. (2011) is adopted to extrapolate the experimental result of Mollner et al. (2010) at all temperatures, resulting in the following expressions for the low-and high-pressure limits of the reaction: k 0 = 1.48 × 10 −30 × (T /300) −3 cm 6 molecule −2 s −1 , and k inf = 2.58 × 10 −11 cm 3 molecule −1 s −1 .
Using upper tropospheric airborne measurements of NO 2 , HNO 3 , O 3 , OH, and HO 2 from the Intercontinental Chemical Transport Experiment -North America (INTEX-NA) in a Bayesian modelling framework designed to constrain reaction rates, Henderson et al. (2012) found that the HNO 3 formation rate in the upper troposphere is overestimated by 22 % when adopting the rate recommendation of Sander et al. (2011). Assuming the experimental rate at 298 K by Mollner et al. (2010) to be correct, Henderson et al. (2012) deduced an updated temperature dependency: k 0 = 1.48 × 10 −30 × (T /300) −1.8 cm 6 molecule −2 s −1 .
The altitude dependence of the rate calculated using four different recommendations is displayed in Fig. 1 for midlatitude summer conditions (left panel). Note that the IUPAC rate is overestimated in part because it represents the total NO 2 + OH + M rate constant, including the minor channel leading to pernitrous acid, HOONO. The latter channel cannot be considered a true NO x sink, because HOONO rapidly decomposes back to NO 2 and OH in lower tropospheric conditions (Sander et al., 2011). A reasonable estimation for the uncertainty on the nitric acid-forming channel in NO 2 + OH is the difference between the expressions provided by JPL and Henderson et al. (2012). The impact of this uncertainty is explored through CTM simulations carried out following either Sander et al. (2011) or Henderson et al. (2012 (JPL and MINLOSS, cf. Table 1).
The overall reaction rate under dry conditions (k d ) is the product of this branching ratio by the Sander et al. (2011) recommended value for the NO + HO 2 reaction rate: Recent modelling studies have investigated the impacts of the addition of the new channel on the distribution of HNO 3 , NO x , HO x and O 3 (Cariolle et al., 2008), on the trends of atmospheric species and radiative forcing (Søvde et al., 2011), and on the effects of aviation on atmospheric composition (Gottschaldt et al., 2013).
Further experiments showed that the HNO 3 yield is strongly enhanced in presence of water vapour (Butkovskaya et al., 2009). Assuming that this effect is due to the reaction of NO with the HO 2 · H 2 O complex, the rate of the reaction NO + HO 2 · H 2 O → HNO 3 was estimated under their experimental conditions (298 K, 200 Torr): This value is equal to about 42 times the reaction rate under dry conditions at those experimental conditions. Unfortunately, the temperature and pressure dependence of this rate is unknown. The complexed fraction f c of the hydroperoxyl radical HO 2 is estimated from the equilibrium constant of HO 2 +H 2 O ↔ HO 2 · H 2 O:  (Sander et al., 2011). The overall rate of the NO + HO 2 → HNO 3 reaction in moist air is estimated using Under the assumption that k w is temperature-and pressureindependent (i.e. k w = k exp w ), the H 2 O-assistance in the HNO 3 -forming channel leads to a factor of 2-3 increase of the rate constant below 4 km ( Fig.1, middle panel), whereas the gap closes at higher altitudes as air becomes drier. However, this enhancement reaches much larger values (factor of 8) if the temperature-and pressure-dependence of k d is adopted (i.e. k w = 42 · k d ), as assumed in a recent modelling study (Gottschaldt et al., 2013).
The implications of the new reaction on the global modelled NO 2 columns are investigated in three simulations (BUTKO1, BUTKO2, BUTKO3) differing by their treatment of H 2 O-assistance, as detailed in Table 1.

Heterogeneous reaction on sulfate aerosols
The heterogeneous hydrolysis of N 2 O 5 at the surface of aerosols is an important NO x loss process during nighttime. Its overall impact is largest in polluted environments (where aerosol loadings and N 2 O 5 formation rates are high) during winter (when nights are longer and hydroxyl radical levels are at their lowest). Among different aerosol types, sulfatecontaining aerosols are putatively characterised by the highest reaction probability (e.g. Evans and Jacob, 2005). Two commonly used parameterizations for the reaction probability on sulfate-containing aerosols (γ N 2 O 5 ) by Evans and Jacob (2005) and by Davis et al. (2008), are based on laboratory measurements and account for the effect of temperature and relative humidity. Davis et al. (2008) includes a dependence on aerosol (dry/wet) state and provides a further distinction between different sulfate-and nitrate-containing aerosols, including sulfuric acid, ammonium sulfate, bisulfate and nitrate. Evans and Jacob (2005) also propose recommendations for the reaction probability on organic and black carbon, dust and sea-salt. The possible influence of organics on γ N 2 O 5 is, however, neglected in both parameterizations. Brown et al. (2009) determined reactive uptake coefficients for N 2 O 5 using field measurements of O 3 , NO x , and aerosol surface area obtained during the night flights of the TexAQS II (Second Texas Air Quality Study) campaign in 2006. This study revealed that γ N 2 O 5 (i) lies in the range 0.5-6 × 10 −3 , i.e. much lower than previously reported laboratory-based values, and (ii) contrary to current belief, does not exhibit a clear dependence on relative humidity or aerosol composition. The average value for the uptake coefficient derived by these measurements is equal to 0.003, by up to an order of magnitude lower than in parameterizations currently utilised in atmospheric models. Supporting evidence for the low value of the uptake coefficient is provided by direct N 2 O 5 reactivity measurements on ambient aerosol parti-cles (Bertram et al., 2009), where the observed values were found to be by a factor of ten lower compared with current parameterizations. Organic material at the aerosol surface has been identified as a candidate explanation for the reduction of the accommodation coefficient (McNeill et al., 2006).
The N 2 O 5 sink rate on aerosols calculated for mid-latitude winter conditions using different parameterizations are compared in Fig. 1 (right panel). Note that the uptake coefficient on hydrophilic carbonaceous aerosols is taken to be 0.003 in all cases; for simplicity, only the uptake coefficient on sulfate/ammonium/nitrate aerosol has been varied. Overall, the Brown et al. (2009) value leads to a sink lower by a factor of 2-3 compared to the Davis et al. (2008) parameterization, and by an order of magnitude compared to Evans and Jacob (2005). To evaluate the impact of these differences on the NO x budget and distribution, we contrast the results of two simulations, one using a constant value of 0.003 for the uptake coefficient, as suggested by Brown et al. (2009), and one using the Davis et al. (2008) parameterization (MINLOSS and DAVIS simulations, respectively).

Other losses
In addition to the previous pathways of NO x removal, the following processes are also considered.
-Dry deposition of NO 2 The dry deposition of NO 2 to vegetation and soils is a direct NO x sink, computed with the resistance-inseries scheme of Wesely (1989).
-Wet and dry deposition of organic nitrates NO x is converted to organic nitrate through reactions of NO 3 with alkenes, as well as through reactions of peroxy radicals with NO and acyl peroxy radicals with NO 2 . Organic nitrates are temporary NO x reservoirs with lifetimes of the order of minutes to weeks which can be transported away from the source regions, where they can either release NO 2 through decomposition or oxidation, or undergo wet and/or dry deposition. Besides peroxy acyl nitrates (PANs), isoprene and monoterpene nitrates are believed to represent the largest contribution to the total organic nitrate budget (Beaver et al., 2012;Browne and Cohen, 2012). Their precise yields and fate remain poorly understood despite recent advances regarding the further oxidation of nitrates produced in the OH-and NO 3 -oxidation of isoprene Kwan et al., 2012). Their role is relatively limited in IMAGESv2 due to their short lifetimes and their oversimplified reaction scheme which follows the MIM2 mechanism (Taraborrelli et al., 2009). In itself, nitrate formation and export should not be considered a NO x sink, even though it might significantly deplete NO x levels in the formation region . Therefore, only the 9062 T. Stavrakou et al.: Impact of NO x sink uncertainties on top-down NO x emissions deposition of organic nitrate will be considered a NO x sink in this study.
-Reaction of NO 3 with aldehydes and with dimethylsulfide (CH 3 ) 2 S NO 3 can be converted to nitric acid by reaction with aldehydes, NO 3 + RCHO → HNO 3 + RCO·, or by reaction with dimethylsulfide, NO 3 + (CH 3 ) 2 S → HNO 3 + CH 3 SCH 2 . Whereas the reaction with aldehydes is only a minor sink in our model calculations, the reaction with (CH 3 ) 2 S is significant above oceans.
According to our model calculations, the sum of the above sinks represents only a small part (ca. 20 %) of the global tropospheric NO x sink (Table 1). Uncertainties related to these sinks will not be addressed in this study, although they might be substantial. As a result, the overall NO x sink uncertainty derived in this study should only be seen as a lower limit. In particular, a more detailed treatment of organic nitrate chemistry could result in increased NO x sinks in regions influenced by biogenic isoprene emissions.

OH radical concentration
An additional source of uncertainty resides in the abundances of OH radicals, responsible for the conversion of NO 2 to nitric acid as well as for the removal of most reactive compounds in the troposphere. We discuss briefly below three possibly major reasons for this uncertainty, namely, the degradation chemistry of isoprene, the production of HONO, whose photolysis provides a direct OH source, and the heterogeneous HO 2 loss on aerosols.
There is strong evidence from field campaigns in midlatitude forests, tropical forests and other rural environments (e.g. Lelieveld et al., 2008;Ren et al., 2008;Hofzumahaus et al., 2009) that OH levels are largely underestimated in models when using traditional isoprene chemical chemistry Kubistin et al., 2010;Stone et al., 2011). Furthermore, the model underprediction is found to increase for increasing isoprene concentrations as well as for decreasing NO levels . Although the causes of this behaviour are still under heated debate, they imply the existence of OH recycling processes counteracting the OH suppression due to reaction with isoprene and its degradation products. Lelieveld et al. (2008) suggested that between 2 and 4 OH radicals are formed in the reaction of isoprene peroxy radicals with HO 2 as implemented in the MIM2 chemical mechanism (Taraborrelli et al., 2009). Although this approach allowed to better align the model to the data, it was not supported by theoretical or experimental evidence. A substantial progress towards the elucidation of the high observed OH concentrations was provided by the theoretical studies of Peeters et al. (2009) and Peeters and Müller (2010), proposing that the isomerization of specific isoprene peroxy radicals leads to substantial HO x regeneration. Tested in global models (e.g. Stavrakou et al., 2010), the mechanism was found to be very efficient in enhancing HO x concentrations in the boundary layer, providing good agreement with available data. However, several open issues merit further investigation, e.g. the subsequent degradation chemistry of the isomerization products, as well as the reconciliation of theoretical findings with experimental evidence from the laboratory (Crounse et al., 2011).
The second source of uncertainty in OH levels originates in the primary OH radical source through HONO photolysis, which has been identified from field observations as quite significant in the lower troposphere, especially in the early morning (e.g. Elshorbany et al., 2009). A strong missing source of HONO has been invoked by recent studies to reconcile the large discrepancies found between observed and modelled HONO abundances during daytime (Sörgel et al., 2011;Su et al., 2011). The formation processes leading to these unexpectedly enhanced HONO concentrations are still under investigation, like nitrate photolysis following HNO 3 deposition on forest canopy surfaces , heterogeneous conversion of NO 2 on ground and aerosol surfaces (Su et al., 2008), or HONO release from soil nitrites (Su et al., 2011). However, evidence favouring one or the other process is still partial, and therefore, the atmospheric impact of HONO, in particular its contribution to the production of OH radicals, remains an open issue.
Finally, the reactive uptake of HO 2 by aerosols is a potentially important yet very uncertain HO x sink. This reaction is generally assumed to form H 2 O 2 with a yield (Y H 2 O 2 ) equal to 0.5, and a reaction probability (γ HO 2 ) value of 0.2 has been recommended for use in atmospheric models (Jacob, 2000). Laboratory measurements at atmosphericallyrelevant conditions revealed that the uptake coefficients for dry (NH 4 ) 2 SO 4 and NaCl aerosol were lower than 0.05, whereas for wet aerosols, measured γ HO 2 ranged between ca. 0.1 and 0.2 (Taketani et al., 2008). Much lower values (< 0.01) by more than an order of magnitude over both dry and wet aerosols were derived in a recent laboratory study (Matthews et al., 2012), possibly reflecting a saturation effect. On the other hand, values higher than 0.2 were observed in the presence of transition metal ions, most notably copper, in aqueous aerosols (Cooper and Abbatt, 1996;Taketani et al., 2008;Matthews et al., 2012). Furthermore, the presence of iron favours pathways leading ultimately to (Mao et al., 2013), thereby increasing the overall HO x depleting effect of aerosols. Under molar concentrations of copper and iron typically found in fine aerosols in the United States and in other (moderately) polluted areas, Mao et al. (2013) estimated using a detailed aerosol model that the reactive uptake coefficient of HO 2 should be close to unity, with H 2 O as main reaction product. This result was found to be consistent with HO x measurements in field studies in various environments. Its impact on the global tropospheric composition was calculated using a global CTM and found to be substantial (Mao et al., 2013), although the adopted assumptions (γ HO 2 = 1 and Y H on all aerosol types) clearly represent an exaggeration, since the HO 2 uptake cannot be expected to be efficient on dry aerosols, and since laboratory determinations of γ HO 2 indicate values significantly lower than unity even for Cu-doped aerosols. Nevertheless, this efficient uptake scenario is also adopted in our baseline simulation (MINLOSS), except that only fine mode aqueous aerosols (i.e. hydrophilic carbonaceous and sulfate/ammonium/nitrate aerosols) are allowed to promote the HO 2 uptake. Neglecting the effect of coarse mode aerosols should not lead to large errors, since sulfate and organic aerosols largely dominate the aerosol loading and therefore the aerosol surface area over most continental areas, especially over NO x source regions (Jimenez et al., 2009). In order to test the uncertainties related to isoprene chemistry, we performed a sensitivity simulation denoted MIM2+ (Table 1), which includes the recycling mechanism proposed by Lelieveld et al. (2008). The OH production from HONO is not considered in the current version of the model. We test the sensitivity of the model with respect to uncertainties in HO 2 aerosol uptake by carrying out a simulation where γ HO 2 is set to a lower value (0.2), and Y H 2 O 2 is set equal to 0.5 (HO2L run of Table 1).

Tropospheric NO 2 columns from OMI
OMI (Ozone Monitoring Instrument) is a Dutch-Finnish nadir viewing imaging spectrometer flying on a sunsynchronous orbit crossing the local equator at ca. 13:40 LT (Levelt et al., 2006). Launched aboard the Aura platform in 2004, OMI measures in the UV-visible spectral window (270-500 nm) at a nadir resolution of 13 × 24 km. The Dutch OMI tropospheric NO 2 version 2 (DOMINO v2) data product (Boersma et al., 2011), publicly available through the TEMIS portal (http://www.temis.nl), is used in this study. This version constitutes a major improvement compared to the previous DOMINO v1 tropospheric NO 2 columns (Boersma et al., 2011). DOMINO v2 has been used thus far in assimilation studies (Miyazaki et al., 2012a, b), air quality assessments (McLinden et al., 2012), as well as for validation purposes (Irie et al., 2012;Ma et al., 2013). DOMINO v2 tropospheric NO 2 columns are reduced by 20 % in winter, and by 10 % in summer over polluted regions, compared to the DOMINO v1 product. Larger discrepancies between DOMINO v2 and v1 occur, however, on regional scales. Cloudy pixels (i.e. with cloud fraction > 0.2) and pixels affected by the so-called row anomaly (i.e. track positions 53-54, since June 2007) were excluded. The OMI tropospheric NO 2 retrieval error for individual, cloudfree pixels comprises the uncertainties on the slant and on the stratospheric slant column, estimated at 0.7 × 10 15 and 0.15×10 15 molec. cm −2 , respectively, and the uncertainty on the tropospheric AMF, lying between 10 and 40 % (Boersma et al., 2007). The total error of the DOMINO v2 product is estimated to be lower, from 1.0 × 10 15 molec. cm −2 + 30 % for v1, to 1.0 × 10 15 molec. cm −2 + 25 % for DOMINO v2 (Boersma et al., 2011).

NO 2 simulated by IMAGESv2 CTM
The IMAGESv2 global chemistry-transport model simulates the concentrations of 132 trace species at a resolution of 2 • × 2.5 • , and at 40 sigma-pressure levels between the Earth's surface and the lower stratosphere (44 hPa). As a drawback of the global model domain, its relatively coarse resolution should be acknowledged as a possible source of error in NO 2 abundances and sensitivities, given the nonlinear character of tropospheric chemistry. The model includes the chemistry of 22 precursor NMVOCs, as detailed in the Supplement. Meteorological fields are obtained from ERA-Interim analyses of the European Center of Medium-Range Weather Forecasts (ECMWF) for the year of the simulation (2007). Convection follows the parameterization of Costen et al. (1988) constrained by ERA-Interim updraft mass fluxes. Turbulent mixing in the planetary boundary layer (PBL) is parameterized as vertical diffusion (Müller and Brasseur, 1995) based on ERA-Interim boundary layer heights. Details about the model, including its evaluation against radionuclide data ( 222 Rn and 85 Kr), airborne and satellite measurements, and other CTMs can be found in previously published work (e.g. Müller and Brasseur, 1995;Müller and Stavrakou, 2005;van Noije et al., 2006;Stavrakou et al., 2008Stavrakou et al., , 2012. The chemistry is solved by the fourth order Rosenbrock solver of the Kinetic Preprocessor software tool (KPP, Sandu et al., 2006). The model time step for the forward simulations is taken equal to 4 h. Note that the chemical solver uses an adaptable internal timestep, which is often much shorter than the external timestep of 4 h. As described in more detail in Stavrakou et al. (2009a), the effects of diurnal variations are accounted for through correction factors calculated from a detailed model run with a 20 min time step, which is also used to estimate the NO 2 column diurnal shape profile. This diurnal cycle simulation accounts for diurnal variations in the photolysis and kinetic rates, in the meteorological fields, and in the emissions.
The model uses anthropogenic emissions of NO x , CO, SO 2 and NH 3 from the EDGAR 3.2 FT2000 inventory for year 2000 (http://themasites.pbl.nl/tridion/en/themasites/ edgar/), overwritten by the REAS version 1 (Ohara et al., 2007) inventory over Asia, and EMEP emissions over Europe (http://www.ceip.at/). Over the US, the EDGAR emission is scaled to the National Emission Inventory (NEI, http://www.epa.gov/ttn/chief/eiinformation.html) values for each year. Anthropogenic emissions of NMVOCs (ethane, propane, ethene, propene, acetylene, methanol, benzene, toluene, xylenes, formic and acetic acids, and the sum of other NMVOCs) are provided by the RETRO inventory for The seasonality of anthropogenic emissions accounts for (i) a temperature dependence of vehicle emissions from the MOBILE 6 algorithm (Giannelli et al., 2002), and (ii) the seasonal variation of residential heating. In MOBILE 6, the effect of cold starts on CO road transport emissions is accounted for by a correction factor applied for temperatures lower than 18 • C, equal to 1 + (18 − T C ) · 0.05, with T C the temperature in Celsius. Road emissions of NO x are only slightly temperature-dependent, a correction factor equal to 1 + (24 − T C ) · 0.0072 being applied only for temperatures above 24 • C. The sectoral split of anthropogenic emissions is obtained from EDGAR. The seasonal variation of heating emissions is estimated by assuming that these emissions are proportional to the number of heating degree-days, with a threshold of 18 • C.
Diurnal and weekly profiles of CO, NO x and VOC anthropogenic emissions for OECD countries are obtained from Jenkin et al. (2000). A diurnal cycle is also applied to biomass burning emissions (Stavrakou et al., 2009a) as well as to lightning emissions, assumed to follow the diurnal cycle of convective updraft fluxes.
For  (Price and Rind, 1993;Martin et al., 2007) which uses cloud top heights and convective precipitation rates from ECMWF. The lightning emissions are vertically distributed according to Pickering et al. (1998).
Soil emissions are calculated according to the algorithm of Yienger and Levy (1995). Biome data are taken from the compilation of Matthews (1983) (http://data.giss.nasa. gov/landuse/vegeem.html), and cropland distribution from the land use database of Klagenfurt University (Erb et al., 2007). Total fertilizer consumption per year and per country is obtained from the International Fertilizer Association (IFA, http://www.fertilizer.org), and the fraction of fertilizer consumption which is used in rice paddies is obtained from the Food and Agriculture Organization (FAO, http://faostat. fao.org). The fraction of the applied fertilizer assumed to be lost as NO is equal to 1 % for all crops (Steinkamp and Lawrence, 2011), except for rice paddies where it is assumed to be zero (Yienger and Levy, 1995). The total soil emission is scaled to 8 Tg N globally.
Inorganic (i.e. sulfate/ammonium/nitrate/water) aerosols are calculated using EQSAM (Metzger et al., 2002). The calculation of organic aerosols (OA) and black carbon (BC) fol-lows Stavrakou et al. (2012). Since, however, the model using unadjusted POA anthropogenic emissions (Bond et al., 2004) and SOA parameterization (Ceulemans et al., 2012) largely underestimates organic carbon (OC) measurements over polluted areas, an additional OA source is included, of magnitude equal to three times the POA source over the United States, and five times the POA source in other regions. Moreover, the parameterized SOA production due to monoterpene oxidation in low-NO x conditions is reduced by a factor of 5 in order to provide a better match with observations in biogenically-influenced regions. Although crude, this adjustment strongly reduces the biases with the measurements, as detailed in the Supplement. Previous model-based analyses (Spracklen et al., 2011;Heald et al., 2011) have pointed to the existence of a large OA source over anthropogenicallyinfluenced regions, of the order of 100 Tg yr −1 . The precise nature of the additional source is currently unclear, although SOA very likely makes up for a large fraction of it (Yuan et al., 2013). The additional source included in IM-AGESv2 amounts to 68 Tg(OA) per year, whereas the global SOA source amounts to 53 Tg yr −1 , primarily due to biogenic emissions. More details on the treatment of inorganic and carbonaceous aerosols in IMAGESv2 is provided in the Supplement.
The wet removal scheme for gases and aerosols (Stavrakou et al., 2009c) is based on ECMWF analyses for cloud fraction, cloud ice and liquid/mixed water content, convective and stratiform precipitation data.
Nine forward global simulations are performed (Table 1)  The simulated monthly averaged NO 2 columns are compared to the corresponding DOMINO v2 averages binned at the horizontal resolution of the model. The monthly averages are calculated from daily values accounting for the number of measurements and averaging kernel for each day (also binned onto the model resolution) and for the sampling times of observation at each location.
The errors associated to the monthly DOMINO v2 averages are estimated from the reported retrieval errors, following a super-observation approach as in Eskes et al. (2003). The super-observations are the measurement averages at the model resolution. The super-observation errors account for an assumed error correlation of 50 % between retrieval errors on individual measurements contributing to the same super-observation. The total monthly error combines this super-observation retrieval error and an assumed model/representativity error of 0.5 × 10 15 molec. cm −2 .

The inversion setup
The discrete adjoint of the IMAGESv2 model is used to infer top-down NO x emission estimates constrained by Atmos. Chem. Phys., 13, 9057-9082 OMI columns. This method, described in previous work (Stavrakou et al., 2006, allows for deriving monthly emission estimates at the resolution of the model (2 • × 2.5 • ) for each of the NO x emitting categories (anthropogenic, biomass burning, soil and lightning). The assumed error on the anthropogenic emissions by country is set equal to a factor of 1.6 and 2 for OECD and other countries, respectively, to a factor of 2 for soil emissions, and 2.5 for vegetation burning and lightning.
Two optimizations are carried out, which use NO x sink assumptions of either the MINLOSS and MAXLOSS simulations (Table 1). They are performed at 2 • × 2.5 • model resolution and use one year (2007) of OMI NO 2 global columns as constraints. The total number of control variables to be optimized in these source inversions is approximately equal to 70 000.

Importance of uncertainties in NO x losses addressed with IMAGESv2
Using MINLOSS as our baseline run, the influence of the chemical uncertainties discussed in Sect. 2 is illustrated by their impact on the sink rate of the tropospheric NO x column in January and July (Figs. 2 and 3). Note that for simplicity, the results given in this section concern the daily averaged sink rate of the tropospheric column calculated without averaging kernels; in some cases, however, the sensitivity of the sink rate in the hours preceding the satellite overpass time and weighted by the altitude-dependent instrument sensitivity might differ markedly from the sensitivity shown here. This is most evident in the case of the sink due to N 2 O 5 uptake by aerosols, which is primarily a nighttime process. By far the largest impact on the sink rate is the change due to the HNO 3 forming channel in the reaction NO+HO 2 , especially when H 2 O-assistance is included (BUTKO1-3). The impact reaches up to a factor of two over tropical oceans, as a result of the high abundance in HO 2 and water vapour in these regions (Fig. 2d). Over polluted regions, the relative impact of this loss process is found to be lower, due to the predominance of other sinks (OH+NO 2 in summer and N 2 O 5 +H 2 O in winter) in those regions. Overall, the relative contribution of this reaction to the global tropospheric NO x sink amounts to 12 % in the case of BUTKO1 scenario, and reaches 26-43 % when water-assistance is taken into account (BUTKO2-3). As a result, the global NO x lifetime is reduced by 18, 32 and 75 % in BUTKO1, BUTKO2 and BUTKO3, respectively, compared to the base run, whereas the lifetime of methane due to reaction with OH in the troposphere (8.1 yr in MINLOSS) is increased to 9.2, 10.6 and 14.3 yr (i.e. by 14, 31 and 76 %), respectively. These results imply a very large uncertainty associated to the temperature and pressure dependence of the rate k w in humid conditions. The methane lifetime changes are slightly larger than the lifetime increases (11 % and 50 % without and with H 2 O-assistance, respectively) estimated in the modelling study of Gottschaldt et al. (2013) which adopted the same T-and p-dependence of k w as in our BUTKO3 simulation. Part of the discrepancy with that study might be due to the lower equilibrium constant for the complexation of HO 2 adopted by Gottschaldt et al. (2013).
Including the new channel in the HO 2 +NO reaction results in an overall decrease of NO 2 columns by up to 45 % (60 %) at remote oceanic regions, and by 15 % (30 %) over the continental Tropics in BUTKO1 (BUTKO2) cases, whereas the decrease over polluted continental regions is less important (ca. 15 % in the US in BUTKO2). Note that the instrument averaging kernels and satellite overpass time are taken into account in the calculated NO 2 columns. Over Eastern China, the calculated NO 2 column changes in July in the BUTKO3 case (20-40 %) are only slightly lower than the corresponding changes (20-50 %) calculated by Lin et al. (2012) when assuming a 5 % HNO 3 yield in the HO 2 +NO reaction. This good agreement reflects the HNO 3 yield in the BUTKO3 case, reaching 5 % near the surface at mid-latitudes, even though it decreases to much lower values (about 2 %) in the upper troposphere (Fig. 1).
As expected, and in qualitative agreement with Lin et al. (2012), the impact of the additional sink is largest for chemically aged air masses, far away from the emission regions. Calculated changes in the surface NO 2 mixing ratios generally do not exceed 15 % over continents in the BUTKO2 simulation. As an effect of the lower NO x abundances, O 3 production is reduced by 4-6 % at mid-latitudes near the surface, and by up to 16 % at remote environments to southward of 50 • S in the BUTKO1 run, in very good agreement with the changes reported by Cariolle et al. (2008). The enhanced NO x sink in BUTKO2 run leads to more pronounced decreases of model surface O 3 , by 5-10 % in mid-latitudes and by 20-25 % over oceans in the Southern Hemisphere.
The replacement of the low value for γ N 2 O 5 (0.003) by the Davis et al. (2008) parameterization for the uptake of N 2 O 5 on inorganic aerosols (DAVIS simulation) leads to substantial increases in the loss rate of the NO x column in the northern extratropical latitudes during winter. This is attributed to the low wintertime HO x levels and to high NO x and aerosol sources in these regions. The enhancement of the sink rate reaches 70 % in these regions in January. Note that the increased NO x sink e.g. over Europe leads to decreased NO x levels over neighbouring areas (e.g. Northern Africa) and therefore to decreased OH levels, explaining the decreased NO x sink rate in those areas. Over Northern China, the very low effect of N 2 O 5 uptake is explained by dry and Atmos. Chem. Phys., 13, 9057-9082, 2013 www.atmos-chem-phys.net/13/9057/2013/ cold conditions causing inorganic aerosols (dominated by ammonium sulfate and ammonium nitrate) to be predominantly solid in the model in this region. The heterogeneous uptake is believed to be very slow on dry particles (Davis et al., 2008). A comparatively stronger sensitivity to N 2 O 5 uptake was calculated by Lin et al. (2012), with NO 2 column changes exceeding 10 % when decreasing the uptake coefficient by a factor of 10. This is explained by the fact that the reduction was applied by Lin et al. (2012) to all aerosol types, i.e. not just to inorganic aerosols as in the DAVIS simulation. Furthermore, the parameterization of Evans and Jacob (2005) used in the reference run by Lin et al. (2012) does not account for the suppression of γ N 2 O 5 on dry particles. In July, the importance of the N 2 O 5 sink on aerosol is low due to the dominance of the NO 2 +OH sink (Figs. 2, 3e). The sensitivity is weak in the Tropics. Globally, the N 2 O 5 sink on (both inorganic and carbonaceous) aerosol, which accounts for 14 % of the sink in the baseline simulation, is increased to 19.3 % in the DAVIS case, and is responsible for a reduction of the global NO x lifetime by 4 % (Table 1). This weak sensitivity is due to the importance of organic aerosols, which contribute significantly to the total N 2 O 5 uptake, in spite of the low assumed γ N 2 O 5 . Note that the contribution of N 2 O 5 uptake on inorganic aerosols is increased from 4.2 % in MIN-LOSS to 10.6 % in DAVIS.
The reaction of NO 2 with OH constitutes the major loss of NO x in the troposphere. The use of the JPL recommendation for its rate constant (JPL run) leads to increased NO x loss rate by about 10-15 % in most areas, and by up to 20 % over the remote Southern Ocean (Table 1, Figs. 2, 3). This appears consistent with the 15-20 % difference in the rate constants in the boundary layer (Fig. 1), given that this reaction represents ca. 60 % of the total NO x sink.
The calculated changes are comparatively lower when the Mollner et al. (2010) rate constant is used (generally < 10 %) (MOLLNER). This is explained by the fact that the rate constant adopted in the MINLOSS and MOLLNER cases are very similar in the boundary layer ( Fig. 1), where most of the NO 2 column resides. Globally, the calculated NO x lifetime is found to decrease by 5 % and 11 % in the MOLLNER and JPL simulation, respectively.
The effect of the model changes in the MIM2+ simulation is found to be small. The increased OH concentrations over low-NO x forested areas lead to increased NO x loss rates. The sink increase amounts to less than 1 % on the global scale, although it can reach 20 % in low-NO x , isoprene-rich regions. Finally, the model using a less efficient HO x loss (γ HO 2 = 0.2 and Y H 2 O 2 = 0.5) due to HO 2 uptake by aerosols (HO2L simulation) exhibits a strong sensitivity in regions with high aerosol concentrations, in particular over East and South Asia as well as over biomass burning areas such as Africa in the winter hemisphere and Central Canada during summer (Fig. 2-3f). In fact, HO 2 uptake appears to be the largest source of uncertainty over much of Europe and the Northeastern US in July, as well as over China in both seasons, where the NO x sink rate is increased by up to 30 % (up to 50 % in January) when HO 2 uptake is assumed to be less efficient. Those changes are primarily due to the strong impact of the reaction on OH levels, as shown by the 11 % decrease in mass-weighted tropospheric OH concentration in the HO2L run, very similar to the 12 % change in tropospheric OH reported by Mao et al. (2013) between simulations either ignoring HO 2 uptake or adopting the same efficient uptake scenario (γ HO 2 = 1 and Y H 2 O 2 = 0) as in MIN-LOSS. Annually averaged OH and HO 2 concentrations are increased by factors of up to 2 and 3, respectively, over both China and India; those changes over China are lower than in the modelling study of Mao et al. (2013), as expected since HO 2 was allowed to react on all aerosol types in the latter study, irrespective of the aerosol state. In contrast, the calculated changes over India are much lower in Mao et al. (2013), presumably due to lower organic aerosol loadings in GEOS-Chem compared with IMAGESv2. The NO 2 column changes calculated in IMAGESv2 over China are larger in January (20-35 %) compared to July (between 10 % in Southern China and almost 20 % in Northern China), in qualitative agreement with Lin et al. (2012) where the impact of a reduction of γ N 2 O 5 from 0.2 to 0.05 was estimated.
As seen from this analysis, the base run MINLOSS realises the lowest NO x loss rates and the largest global tropospheric NO x lifetime among the sensitivity tests. The MAXLOSS scenario is designed by adopting the choices which maximise the NO x loss. This is realised by using the JPL recommendation for the NO 2 +OH reaction rate, by including the HNO 3 forming channel in NO+HO 2 , based on Butkovskaya et al. (2009) (with T-and p-independent k w ), γ N 2 O 5 on sulfate aerosols from Davis et al. (2008), γ HO 2 = 0.2 on aqueous aerosols (with Y H 2 O 2 = 0.5), and the MIM2+ chemistry. The combination of these settings causes a strong reduction of the global NO x lifetime, by a factor of 1.8 with respect to MINLOSS (Table 1). Note that other model uncertainties could affect the modelled NO x columns, e.g. in meteorological parameters, in the emissions of other compounds (e.g. NMVOCs) or in chemical parameters other than those considered in this study . The comparison of our MINLOSS and MAXLOSS simulations should, nevertheless, provide a measure of the uncertainties associated to the major chemical NO x pathways. The analysis of Lin et al. (2012) suggests that the uncertainties due to other factors are generally much lower than overall uncertainty considered in this study.
The daily averaged NO x lifetimes calculated for MIN-LOSS and MAXLOSS cases are shown in Fig. 4 and the contribution of the main individual NO x sinks to the total sink is illustrated in Fig. 5 for MAXLOSS. Lifetimes of less than one day are calculated in the case of MAXLOSS over most continental regions, especially in summertime and in high-NO x environments, due to the dominance of the loss via OH. In essence, the distribution of the NO 2 +OH sink reflects mainly the boundary layer OH concentration field pattern (Fig. 5). The loss via NO+HO 2 occurs mostly over tropical regions, and is, on average, roughly two times lower than the loss due to NO 2 +OH. In January, N 2 O 5 uptake by aerosols is significant in regions with high aerosol concentrations and long nights, and is estimated to be three times more important than in July at the global scale (Fig. 5). Over oceans and high-latitude regions the lifetime can reach several days due to lower OH and NO 2 levels.

Top-down NO x emissions
This section focuses on the results of the two emission inversions constrained by 2007 OMI data performed using either the MINLOSS or the MAXLOSS model settings (Table 1). The a priori and optimized tropospheric NO x budget is summarised in Table 2, and the annual total NO x emission update is shown in Fig. 6.
The differences between the emissions inferred by both inversions are found to be substantial, with the total NO x source being 75 % higher in MAXLOSS compared to MIN-LOSS. The top-down estimates, 38 Tg N from MINLOSS against 68 Tg N from MAXLOSS, correspond to a slight de-crease of the source (15 %) in the former case, and a substantial increase by 50 % in the latter, with respect to the a priori source. The annual total NO x emission update, i.e. the ratio of a posteriori to the a priori emissions (Fig. 6), is found to be generally lower than one at mid-latitudes in MINLOSS. In tropical regions, the emissions are increased by up to a factor of two, mainly due to increased natural sources. Similar patterns are found in the case of MAXLOSS, but with much higher emission updates, generally between 1 and 2 over polluted regions, and between 2 and 5 in the Tropics.
In a relative sense, the largest discrepancies between the two inversions concern natural emissions. Global NO x emissions from lightning and soil differ by 80 % and 125 % between MAXLOSS and MINLOSS, respectively. This is the consequence of the large difference in NO x lifetimes between the two inversions in tropical regions (Fig. 4). This difference is further amplified by chemical feedbacks. In most tropospheric conditions, a NO x emission increase leads to an increase in OH (through the HO 2 +NO→OH+NO 2 reaction) and therefore in the NO x sink rate. In the context of inverse modelling, this implies that larger emission increments are required in order to match the observations, to compensate for this negative chemical feedback, compared to an emission inversion neglecting feedbacks. Since the NO x emission increments are larger in MAXLOSS compared to MIN-LOSS, the NO x lifetime decreases (relative to the a priori) are also larger in MAXLOSS compared to MINLOSS, which amplifies the differences between the emission increments in MAXLOSS and MINLOSS.
In comparison to most global inversion studies, soil NO emission is found to be generally underestimated by the algorithm of Yienger and Levy (1995). Top-down studies derived estimates for the global soil NO source ranging between 8.9 Tg N (Jaeglé et al., 2005) and 10-12 Tg N (Müller and Stavrakou, 2005;Stavrakou et al., 2008). More recently, improvements upon the algorithm of Yienger and Levy (1995) resulted in new parameterizations yielding global above-soil NO x emission of 10.7 Tg N , and an above-canopy soil NO x source at 8.6 Tg N (Steinkamp and Lawrence, 2011), in better agreement with satellite-derived fluxes. In the latter study, which was based on a compilation of a large number (ca. 600) of flux measurements, the emission factors for the different ecosystems were estimated from the geometrically averaged observed fluxes. However, the use of an alternative, equally plausible averaging method (the plain arithmetic average) resulted in an annual estimate of 27.6 Tg N, much higher than all previous values. This find-ing underscores the high uncertainty of this source, whereas the wide range of our OMI-derived estimates for soil emissions, 9-20 Tg N per year (Table 2), could be regarded as a (probably conservative) top-down uncertainty range for this source.
The global NO x production from lightning derived in this study is estimated at 3.3-5.9 Tg N yr −1 , i.e. 10-100 % higher than the a priori source, with the strongest increases predicted in the Tropics. This result is in line with previously reported top-down values, ranging between 1.1 and 6.4 annually (Müller and Stavrakou, 2005;Stavrakou et al., 2008;Boersma et al., 2005). Recently, Murray et al. (2012), based on satellite lightning data, estimated a global annual source of 6 ± 0.5 Tg N, in agreement with the best estimate of 6 Tg N by Martin et al. (2007) derived through comparisons of satellite observations of NO 2 , O 3 and nitric acid with a global CTM, and with the study by Schumann and Huntrieser (2007) reporting a range of 2-8 Tg N per year, based on a literature review suggesting that a thunderstorm flash produces 15(2-40) × 10 25 molecules NO per flash on average. However, this result was contradicted by a more recent study (Beirle et al., 2010) using SCIAMACHY NO 2 columns, which suggested that the production efficiency is of the order of 2 × 10 25 molecules NO per flash, at the low end of the range derived by Schumann and Huntrieser (2007). Table 2. Annual NO x emissions and tropospheric sinks (Tg N) in the MINLOSS and MAXLOSS scenarios. Global anthropogenic includes shipping and aircraft. The total source given between brackets includes the production due to HNO 3 photolysis and reaction with OH. Regional anthropogenic emissions are italicized. This lower estimate for NO production efficiency translates to an annual lightning NO x source of 1 Tg N. The biomass burning source is also highly sensitive to the NO x sink scenario: global annual emissions are found to be 3.7 Tg N in MINLOSS and 6.7 Tg N in MAXLOSS, compared to 4.3 Tg N in GFEDv3. The strongest emission increments are derived over Southern Africa (factor of 2-3 in MAXLOSS) and Oceania, whereas fire emissions in South America are either close to the prior (in MAXLOSS) or significantly lower in MINLOSS). Support for higher NO x emissions from fires is provided by an independent global database of fire emissions (Fire Inventory from NCAR, Wiedinmyer et al., 2011), where the global 2007 emissions are estimated at 6.7 Tg N.

MINLOSS
The differences in anthropogenic global totals inferred by the inversions are significant, 22.3 Tg N in MINLOSS vs. 35.1 Tg N in MAXLOSS (cf. Table 2). Pronounced differences are also derived on the continental scale, as illustrated in Table 2. In most regions, the posterior emissions are lower than the a priori in the MINLOSS inversion, but higher when the maximum loss scenario is considered.
Over China, the anthropogenic emission total is 3.8 Tg N in MINLOSS, by a factor 1.6 lower than in MAXLOSS (6 Tg yr −1 ). The latter total is close to the 2006 top-down anthropogenic flux estimate derived from SCIAMACHY NO 2 columns, 6.3 Tg N yr −1 , and is slightly lower than reported in a recent inversion study for East  • N), 7.1 Tg N yr −1 , also constrained by DOMINO v2 NO 2 columns (Lin, 2012). Based on a bottom-up methodology for China, Zhang et al. (2007) estimated the anthropogenic emission in 2004 at 5.7 Tg N yr −1 . Extrapolating this value based on the emission growth rate derived by Zhang et al. (2007) between 1995-2004 (6.1 % yr −1 ) would result in an emission estimate of 6.8 Tg N in 2007, close to the MAXLOSS result. Two recently available bottom-up inventories, namely, the latest version of the Regional Emission inventory in ASia (REAS version 2) and the Multi-resolution Emission Inventory in China (MEIC) will be compared with the OMI-derived emissions in Sect. 6.3.
The flux estimates for North America and Europe depend strongly on the inversion setup. In North America, they are found to be lower (4.7 Tg N) or higher (7.1 Tg N) in comparison with the a priori (6 Tg N) in MINLOSS and MAXLOSS, respectively, whereas the previous top-down estimate for the same region in 2006 by Stavrakou et al. (2008) lies within the above range, and is very close to the a priori (6.1 Tg N yr −1 ). In Europe, based on data assimilation of DOMINO v2 NO 2 columns, Miyazaki et al. (2012a) reported an anthropogenic annual flux equal to 4.6 Tg N, close to our a priori value.
South Asia is the region where NO x sink uncertainties have the largest impact: the anthropogenic emission total according to MAXLOSS (6.3 Tg N yr −1 ) is a factor of 2.4 larger than in MINLOSS. Over India, the difference even exceeds a factor 3. This strong discrepancy over India is primarily due to the new channel in NO+HO 2 (in summer) and even more to the uptake of HO 2 by aerosols (in winter), as seen from the calculated sensitivity of NO x sink rates to those processes (Figs. 2-3). Note that, although the uptake of N 2 O 5 by aerosol is a large contribution to the daily averaged NO x sink over East and South Asia in January (Fig. 5), it has little influence on top-down emissions because OMI samples NO 2 columns in the early afternoon. The emission update over India is highest (> 3) in January (Fig. 7), when the effect of HO 2 uptake is strongest due to high aerosol loadings and relatively slow photochemistry.
The global sources and sinks of NO x are summarised in Table 2. Note that the direct NO x sources are not exactly balanced by the sinks due to the conversion of HNO 3 back to NO x totaling > 5 Tg N yr −1 in the troposphere. The calculated global photochemical lifetime of tropospheric HNO 3 ranges between 23 and 27 days, depending on the simulation. About 55 % of the photochemical sink is due to photolysis, the rest being due to reaction with OH.
The percentage differences between inferred total NO x emissions in simulations MINLOSS and MAXLOSS (Fig. 7) T. Stavrakou   are less pronounced over Europe and North America in January (generally less than 30 %) than in July (40-100 %). This relatively weak sensitivity of winter fluxes is partly explained by the longer NO x lifetimes and increased role played by transport in determining NO x columns over emission regions in winter. Furthermore, the winter losses are dominated by the uptake of N 2 O 5 on aerosols (Fig. 5) which has only a modest influence on NO x columns at the overpass time of OMI (13:40 LT).
Both inversions are found to modify the seasonality of anthropogenic emissions over China (Fig. 8), improving the agreement with the bottom-up inventory of Zhang et al. (2007). The December-to-July emission ratio, equal to 1.33 in MINLOSS is close to the ratio reported in Zhang et al. (2007) (1.26). However, the weaker seasonal dependence of the emissions in MAXLOSS (ratio of 1.13) agrees well with the more recent inventories (cf. Sect. 6.3). In North America and Europe, the inversions keep the main seasonality features of the a priori almost unchanged. The February peak of the a priori seasonality, due to the low temperatures and the heating-degree day approach applied to the residential emis-sions, is consistent with the satellite observations, especially in the MINLOSS inversion.

SCIAMACHY NO 2 vertical columns
We evaluate the modelled a priori and a posteriori NO 2 columns against NO 2 column abundances retrieved from the SCIAMACHY UV-visible nadir sounder crossing the local equator at ca. 10h00 local time. SCIAMACHY has a ground pixel of 30 × 60 km 2 and achieves global coverage within six days. For these comparisons we use SCIAMACHYv2 data distributed via the TEMIS website (www.temis.nl, . This product is reprocessed using the same basic algorithm for satellite observations used for DOMINO v2. Comparisons above selected regions between SCIAMACHY and modelled NO 2 columns before and after inversion and columns from OMI and SCIAMACHY are illustrated in Figs. 9 and 10. Overall, the model/OMI data discrepancy is efficiently reduced after the optimization. Whereas relatively small changes are inferred in summer over Northern China, the column increases are more substantial in wintertime (up to factor of two in MAXLOSS), despite the reduced seasonality of anthropogenic emissions (Fig. 8). As discussed in Stavrakou et al. (2008), different photochemical regimes in summer and in winter lead to different responses of the NO x lifetime to an emission increase, primarily because OH levels increase with NO x in summer (due to the HO 2 +NO reaction), resulting in a negative feedback, whereas the opposite effect prevails in winter (due to OH+NO 2 ). The role of N 2 O 5 is limited because it operates only at night, as noted above.
The bias between the model and the SCIAMACHY data is significantly reduced in the a posteriori solution in Northern China, despite remaining underestimations during winter, especially in the MINLOSS case. In Western Europe and Eastern US, the optimized columns are still lower than OMI (up to 25 %), but in good agreement with SCIAMACHY data, although the MAXLOSS inversion leads to an overestimation of the columns over Europe in summertime. In Southeast Asia, the a priori columns capture quite well the seasonal pattern of the observed columns from OMI and SCIAMACHY, but their magnitudes are strongly different due to the importance of the NO+HO 2 sink in the Tropics in the MAXLOSS case. After inversion, the match between the modelled and OMI columns is excellent, however, a systematic model overprediction persists with respect to SCIAMACHY data. This overestimation is also found over tropical America and trop-ical Africa. It might be related to biases in the satellite products or, for example, in the diurnal cycle of emissions and/or oxidants in the model.

Aircraft campaign measurements
Modelled NO 2 profile shapes before and after inversion are evaluated against the two Intercontinental Chemical Transport Experiments INTEX-A and INTEX-B. The INTEX-A field mission (Singh et al., 2006) was undertaken between 1 July to 15 August 2004 over North America (http://www-air. larc.nasa.gov/missions/intexna/intexna.htm) The NO 2 profiles obtained in this mission are described in Singh et al. (2007). The INTEX-B two-phase mission (Singh et al., 2009)  Over North America (Fig. 11), the a priori NO 2 model profiles are quite similar with slight differences (less than 20 %) in the continental boundary layer. Both inversions succeed in reducing the bias with the observations in summertime. In spring, the MAXLOSS inversion results lead to large overestimations in the boundary layer. Over oceans (Fig. 12), the changes inferred by the inversions are small in all cases. Although biased high, the MINLOSS profiles lie closer to the measurements, especially over the North Pacific. The assumed strong sink in the MAXLOSS setup leads to significant NO 2 underestimation over all oceanic regions, especially in the mid-and upper troposphere. Figure 13 compares the annual inversion results from MIN-LOSS and MAXLOSS with the latest version of the Regional Emission inventory in ASia (REAS version 2) and the Multiresolution Emission Inventory in China (MEIC) for the year 2007. The a priori inventory used for Asia is REASv1, except for the seasonality which has been calculated as described in Sect. 3.2. REASv2 was developed recently by updating the REASv1 database, which was a first historical anthropogenic emission inventory in Asia covering the period from 1995 to 2003, whose major emission sources are fuel combustion, industrial process, and agricultural activities. The new REAS inventory includes most of major air pollutants and greenhouse gases: SO 2 , NO x , CO, NMVOC, PM 10 , PM 2.5 , BC, OC, NH 3 , CH 4 , N 2 O, and CO 2 . Target years are from 2000 to 2008 and areas are expanded from East, Southeast and South Asia of REASv1 to Central Asia and Asian part of Russia (Ural, West and East Siberia, and Far East). Emissions are estimated on a monthly basis for each country and region and are allocated to grids at a 0.25 • × 0.25 • resolution. Both spatial and temporal resolutions are finer than in REASv1. Activity data such as energy consumption and industrial production were obtained from new statistics and database of power plants as point sources are fully updated. Country-and region-specific parameters such as emission factors and removal efficiencies were also updated by surveying recently published literature for Asian emission inventories. As for Japan, South Korea, and Taiwan, inventories of other research works based on detailed activity data and information were used in REASv2 (Kurokawa et al., 2013).

Comparison with REASv2 and MEIC emission inventories
MEIC is based on a dynamic, technology-based methodology to estimate anthropogenic emission fluxes in China beyond 1990 and until the present date. Emissions are estimated for all anthropogenic sources for ten chemical species: SO 2 , NO x , CO, NMVOC, NH 3 , CO 2 , PM 10 , PM 2.5 , BC, and OC. Total NMVOC emissions are further speciated into species for five chemical mechanisms: CBIV, CB05, RADM2, SAPRC99, and SAPRC07. MEIC updates and improves upon the inventories developed by the same group (Zhang et al., 2007Lei et al., 2011a). The major improvements of MEIC inventory include unit based emission inventory for power plants  and cement plants (Lei et al., 2011b), updates of recent activity data and emission factors from literature, and an on-line emission process database (http://www.meicmodel.org). Emissions are available for four aggregated sectors, namely, power generation, industry, residential and transportation, with monthly temporal variation and 0.25 • spatial resolution.
The REASv2 and MEIC distributions are very similar both geographically and temporally over China. At the resolution of the CTM (2 • × 2.5 • ), REASv2 and MEIC are highly correlated (r = 0.96). Only the MAXLOSS optimization brings the model total emissions closer to REASv2 and MEIC: 6.0 Tg N yr −1 vs. 7.2 and 7.6 Tg N yr −1 in REASv2 and MEIC, respectively, whereas the MINLOSS value is only 3.8 Tg N yr −1 . In terms of seasonal variation (Fig. 8) of December to July emissions, 1.13 in MAXLOSS, agrees very well with the values derived from REASv2 (1.06) and MEIC (1.13). The a priori seasonality (too high in late winter, and too low in summer) is therefore not supported by the satellite observations.
Regarding the spatial distributions of the emissions (Fig. 13), the MINLOSS inversion leads to an emission enhancement in the North China Plain, and to emission decreases in other regions, leading to a deterioration of the correlation with the MEIC and REASv2 inventories ( Table 3). The MAXLOSS inversion realises a better match with the recent inventories, as seen by the reduced root-mean-square deviations shown in Table 3.

Conclusions
We have investigated the influence of major uncertainties in NO x chemical sinks on the NO x columns simulated with the IMAGESv2 model and on the top-down NO x emission strengths derived by inverse modelling. Uncertainties in five key processes were addressed, namely, (i) the rate of the re-  1. Including the reaction NO+HO 2 →HNO 3 in the model leads to NO x column decreases estimated at ca. 60 % in oceanic regions and at 30 % over the continental Tropics, whereas the tropospheric NO x lifetime is reduced globally by 32 %, and the lifetime of methane is decreased by 2.5 yr. Even larger impacts are obtained when adopting the same temperature-and pressuredependence of the H 2 O-assisted rate as in the study of Gottschaldt et al. (2013).
2. The use of laboratory-based rates for the uptake of N 2 O 5 by aerosols, instead of the low value suggested by field data, is found to enhance the total NO x column sink by almost 70 % during winter at mid-and at high latitudes. However, this uncertainty is of little consequence for the comparison of model columns with satellite data obtained around midday local time.
3. The model sensitivity to the rate constant of the NO 2 +OH reaction is found to be relatively weak. Compared to a simulation which uses a rate expression constrained by field data (Henderson et al., 2012), the use of the JPL recommendation (Sander et al., 2011) results in a global decrease of NO x lifetime by 11 %. Furthermore, the influence of OH recycling in isoprene oxidation, as represented in the MIM2+ mechanism, is found to be small on the global scale, although it leads to increased (by up to 20 %) loss rates over remote forested environments.
4. The uptake of HO 2 by fine mode aerosols is found to be the largest source of uncertainty over China, with NO 2 column differences reaching 35 % in winter and 20 % in summer, but also over Europe and the United States in summer, and especially over South Asia during the winter, where the efficient uptake scenario increases NO 2 columns by up to 50 %. The calculated impacts on HO x species are consistent with the study of Mao et al. (2013) in spite of our neglect of HO 2 uptake on dry or coarse mode aerosols.
The consequences of those sink uncertainties on top-down emissions are explored through emission inversion using model settings which either minimise (MINLOSS) or maximise (MAXLOSS) the total sink. Top-down flux estimates for 2007 are obtained from OMI DOMINO v2 NO 2 columns using the IMAGESv2 model and its adjoint.
Major differences are inferred in the NO x sources derived in both inversions, by virtue of their substantial differences in NO x loss rates. More specifically, the global NO x flux from the MAXLOSS inversion is by almost 80 % higher than in MINLOSS. The largest discrepancies are deduced for soil NO and lightning fluxes (about a factor of two) as well as for anthropogenic emissions in South Asia (factor of 2.4), reflecting the large sink uncertainties in tropical regions. The global anthropogenic source exhibits somewhat weaker differences, 22 vs. 35 Tg N yr −1 .
Between the two inversions, MAXLOSS realises by far the best match with two new anthropogenic inventories for China (REASv2 and MEIC), both in terms of total emission (underestimation by 20-30 % in MAXLOSS, by almost a factor of 2 in MINLOSS) and in terms of spatiotemporal correlation (0.92 for MAXLOSS, 0.75-0.80 for MINLOSS). Over Europe and North America, the choice of the scenario has a large impact on the top-down flux estimates, and results in either lower or higher emissions than in the a priori. Comparisons with INTEX-A and INTEX-B aircraft measurements suggest that the MINLOSS scenario provides the best match with observations both over continents and over ocean, thereby (i) comforting the NO 2 +OH rate expression recommended by Henderson et al. (2012), which was also based on INTEX-A data analysis, and (ii) indicating that the formation of HNO 3 in NO+HO 2 might be slower than proposed by Butkovskaya et al. (2009). Note that the latter process was neglected by Henderson et al. (2012) in their Bayesian inversion of rates based on aircraft data; had it been taken into account, an even lower rate constant would have been derived for NO 2 +OH in upper tropospheric conditions.
Neither optimization scenario succeeds in improving the agreement with all independent datasets. Whereas comparisons with aircraft measurements and SCIAMACHY data point to MINLOSS as the most likely scenario, an opposite conclusion could be drawn from our analysis of top-down emissions over China. Reasons for this apparent contradiction might be multiple. It should be first pointed out that the formation of HNO 3 in NO+HO 2 has very little influence on NO x sink rates over China; results essentially similar to those of MAXLOSS would have been obtained if this process had been completely neglected. Secondly, the main reason for the very low Chinese emissions in MINLOSS is the very efficient HO 2 uptake adopted in that scenario. This process has comparatively much less influence in North America, especially in summer, and is therefore not well constrained by INTEX-A and INTEX-B. The poor agreement of MINLOSS with the Chinese inventories might therefore reflect an overestimation of HO 2 uptake on Cu-doped aqueous aerosols, as also suggested by laboratory studies; furthermore, the uptake on organic aerosols (which make up a large fraction of the aerosol surface area over polluted continental regions) might be inhibited in cold or dry conditions (Mikhailov et al., 2009;Virtanen et al., 2010) due to physical changes, more precisely the appearance of a semi-solid or very viscous amorphous state affecting hygroscopic growth and the uptake of radicals. The fact that OH radical levels are strongly underestimated by models in large Chinese cities during summer (Hofzumahaus et al., 2009;Lu et al., 2013) is another indication that the sinks of HO x might be too strong in the MINLOSS scenario. However, other error sources may bring additional uncertainties. For example, still unknown mechanisms affecting NMVOC oxidation and HONO emissions and/or heterogeneous formation could also contribute to increase OH levels in polluted areas in summer as well as in winter.
In conclusion, the substantial influence of NO x sink uncertainties on the satellite-derived fluxes shown by our study raises an important issue, largely overlooked in previous inversion studies. Clearly, more research is needed to constrain the relevant processes which might affect NO x removal. Among these processes, the nitric acid forming channel in NO+HO 2 and the uptake of HO 2 by aerosols were found to represent the largest sources of uncertainty. In view of their potential importance, confirmation by further experimental studies is urgently needed.