Minimizing aerosol effects on the OMI tropospheric NO2 retrieval - An improved use of the 477nm O2-O2 band and an estimation of the aerosol correction uncertainty

. Global mapping of satellite tropospheric NO 2 vertical column density (VCD), a key gas in air quality monitoring, requires accurate retrievals over complex urban and industrialized areas and under any atmospheric conditions. The high abundance of aerosol particles in regions dominated by anthropogenic fossil fuel combustion, e.g. megacities, and/or biomass-burning episodes, affects the space-borne spectral measurement. Minimizing the tropospheric NO 2 VCD biases caused by aerosol scattering and absorption effects is one of the main retrieval challenges from air quality satellite instruments. In this study, the reference Ozone Monitoring Instrument (OMI) DOMINO-v2 product was reprocessed over cloud-free scenes, by applying new aerosol correction parameters retrieved from the 477 nm O 2 − O 2 band, over eastern China and South America for 2 years (2006–

Abstract. Global mapping of satellite tropospheric NO 2 vertical column density (VCD), a key gas in air quality monitoring, requires accurate retrievals over complex urban and industrialized areas and under any atmospheric conditions. The high abundance of aerosol particles in regions dominated by anthropogenic fossil fuel combustion, e.g. megacities, and/or biomass-burning episodes, affects the space-borne spectral measurement. Minimizing the tropospheric NO 2 VCD biases caused by aerosol scattering and absorption effects is one of the main retrieval challenges from air quality satellite instruments. In this study, the reference Ozone Monitoring Instrument (OMI) DOMINO-v2 product was reprocessed over cloud-free scenes, by applying new aerosol correction parameters retrieved from the 477 nm O 2 −O 2 band, over eastern China and South America for 2 years (2006)(2007). These new parameters are based on two different and separate algorithms developed during the last 2 years in view of an improved use of the OMI 477 nm O 2 −O 2 band: 1. the updated OMCLDO2 algorithm, which derives improved effective cloud parameters, 2. the aerosol neural network (NN), which retrieves explicit aerosol parameters by assuming a more physical aerosol model.
The OMI aerosol NN is a step ahead of OMCLDO2 because it primarily estimates an explicit aerosol layer height (ALH), and secondly an aerosol optical thickness τ for cloud-free observations. Overall, it was found that all the considered aerosol correction parameters reduce the biases identified in DOMINO-v2 over scenes in China with high aerosol abundance dominated by fine scattering and weakly absorbing particles, e.g. from [−20 % : −40 %] to [0 % : 20 %] in summertime. The use of the retrieved OMI aerosol parameters leads in general to a more explicit aerosol correction and higher tropospheric NO 2 VCD values, in the range of [0 % : 40 %], than from the implicit correction with the updated OMCLDO2. This number overall represents an estimation of the aerosol correction strategy uncertainty nowadays for tropospheric NO 2 VCD retrieval from space-borne visible measurements. The explicit aerosol correction theoretically includes a more realistic consideration of aerosol multiple scattering and absorption effects, especially over scenes dominated by strongly absorbing particles, where the correction based on OMCLDO2 seems to remain insufficient. However, the use of ALH and τ from the OMI NN aerosol algorithm is not a straightforward operation and future studies are required to identify the optimal methodology. For that purpose, several elements are recommended in this paper.
Overall, we demonstrate the possibility of applying a more explicit aerosol correction by considering aerosol parameters directly derived from the 477 nm O 2 −O 2 spectral band, measured by the same satellite instrument. Such an approach can, in theory, easily be transposed to the new-generation of Published by Copernicus Publications on behalf of the European Geosciences Union.

Introduction
Long-time series of UV-visible (UV-vis) satellite measurements are a great asset for monitoring the distribution and evolution of pollutants such as NO 2 , HCHO, or SO 2 and aerosol particles in the troposphere. With the forthcoming new generation of sensors like TROpospheric Ozone Monitoring Instrument (TROPOMI) on board Sentinel-5-Precursor (Veefkind et al., 2012), Sentinel-4-UVN and Sentinel-5-UVNS within the Copernicus programme , they will become an important tool for verifying the effectiveness of implemented technology to protect the environment and population against air pollution (Duncan et al., 2016). While the last generation of space instruments have had a pixel size of 13 × 24 km 2 for the Ozone Monitoring Instrument (OMI) or 80 × 40 km 2 for the Global Ozone Monitoring Experiment (GOME-2), the new generation has smaller pixel sizes (about 7 × 3.5 km 2 for TROPOMI), allowing air quality mapping of complex urban and city areas. This is also expected to reduce the probability of cloud contamination. However, the significant probability of aerosol contamination in areas such as India, China or regions dominated by biomass-burning episodes will likely remain or may even increase. OMI is the Dutch-Finnish push-broom spectrometer flying on the National Aeronautics and Space Administration (NASA)'s Earth Observation Satellite (EOS) Aura platform since 15 July 2004. Its Sun-synchronous orbit has a local equator crossing time of approximately 13:40 LT. The operational tropospheric NO 2 product derived from the visible backscattered spectral light (405-465 nm), such as the OMI DOMINO-v2  or the very recent Quality Assurance for Essential Climate Variables (QA4ECV), is nowadays used as a reference. The related global mapping of tropospheric NO 2 concentrations has been used by many air quality research studies focusing on NO x emissions and secondary pollutant formation, as well as tropospheric NO x chemistry and transport, e.g. Curier et al. (2014), Reuter et al. (2014) and Ding et al. (2015).
A critical element for an accurate tropospheric NO 2 vertical column density (VCD) retrieval is our capability to reproduce the average light path along which the photons travelled before being detected by the satellite sensor at the top of the atmosphere (TOA) in the visible spectral window. In particular, scattering and absorption induced by atmospheric aerosol particles over cloud-free scenes are known to lead to very complex light paths. Because they are emitted by the same sources, high NO 2 and aerosol concentrations are often spatially correlated . Therefore, aerosol contamination needs to be properly addressed in the retrieval algorithms. In the frame of tropospheric NO 2 retrievals from visible spectral measurements based the differential optical absorption spectroscopy (DOAS) approach, the aerosol correction has to be applied to the air mass factor (AMF): a unitless number representative of the length of the average light path.
There are basically two strategies for achieving the aerosol correction in the AMF: 1. either by considering external data, or 2. by using the available particle parameters that can be simultaneously derived from the same UV-visible spectral space-borne measurement.
Studies that reprocessed DOMINO-v2 data set using external data usually relied either on atmospheric transport model outputs, e.g. GEOS-Chem in the Peking University OMI NO 2 (POMINO) (Lin et al., 2014(Lin et al., , 2015 or observations issued from different satellite platforms, e.g. the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) (Castellanos et al., 2015), or even both combined . Resulting changes mostly occurred in cases of high aerosol pollution (τ (550 nm) > 0.8) with increased or decreased tropospheric NO 2 VCDs depending on the geophysical conditions and aerosol properties and distributions. However, the resulting AMF computation becomes dependent on these data sources, their quality and the possibility (or not) to combine them. In general, spatial and temporal co-registration between the different instruments or due to different resolutions between the observation pixel and the model grid cell may become an issue. In the frame of an operational processing, it is generally preferred to maximize the exploitation of the spectral measurement acquired by a same instrument representative of the considered observation pixel. One of the main reasons is the need to have an indication of particle height representative of the average light path associated with every single OMI field of view (FOV). Such information is generally not easily and directly available from an external source. Exploitation of the 477 nm O 2 −O 2 absorption for aerosol retrieval is very promising.
Atmos. Meas. Tech., 12, 491-516, 2019 www.atmos-meas-tech.net/12/491/2019/ It is not only measured by OMI, but also by GOME-2, TROPOMI, Sentinel-4-UVN and Sentinel-5-UVNS. Several studies based on ground-based and satellite instruments have demonstrated its relatively high sensitivity to aerosols, in particular to ALH (Wagner et al., 2004;Castellanos et al., 2015;Park et al., 2016;Chimot et al., 2016Chimot et al., , 2017. Because of the difficulty of easily distinguishing clouds from aerosols and identifying the right aerosol model to use, it has always been preferred to retrieve effective clouds assuming a Lambertian and opaque reflector model (Joiner et al., 2004;Acarreta et al., 2004;Stammes et al., 2008;Vasilkov et al., 2018) and consequently to compute the resulting troposphere NO 2 AMF for all the OMI scenes, regardless of the type of particles present in the scene (clouds and/or aerosols). Such a correction is historically named an "implicit aerosol correction" (Boersma et al., 2004. Chimot et al. (2016) clearly demonstrated that, in spite of its implicit nature, the implicit aerosol correction mitigates biases in the OMI DOMINO NO 2 product over cloud-free scenes compared to an aerosol-free pixel assumption. However, limitations were identified: 1. A numerical artefact is present due to a too-coarse sampling employed in the OMI cloud look-up table (LUT), leading to a strong underestimation in the OMI tropospheric NO 2 VCD over scenes with τ (550 nm) ≥ 0.6 and aerosols located at high altitude.
2. The Lambertian cloud model, in spite of its benefits, somehow remains too simple and likely does not fully reproduce all the multiple scattering effects inherent to aerosol properties. The OMI effective cloud algorithm was then updated in order to remove these numerical artefacts (Veefkind et al., 2016). It also includes many additional relevant improvements related to the OMI 477 nm O 2 −O 2 measurement. But its impact on the correction for aerosols has not yet been evaluated.
To move one step further, Chimot et al. (2017) developed a novel machine-learning algorithm, based on the neural network (NN) technique, that allows ALH to be retrieved together with τ from the same OMI 477 nm O 2 −O 2 spectral band over cloud-free scenes. These retrievals were performed in various cases both over land and sea and compared with reference CALIOP observations and related climatology (Chimot et al., 2017(Chimot et al., , 2018. They benefit from a strong synergy with MODIS on board the NASA Aqua platform flying together with Aura in the same NASA A-Train constellation in order to identify the cloud-free scenes and to better constrain the ALH retrieval quality. For such a purpose, the 477 nm O 2 −O 2 band represents some advantages compared to the more traditional O 2 -A band at 760 nm, which is not measured by OMI: 1. It is spectrally closer to the NO 2 , HCHO, or SO 2 absorption features.
2. It has a wider spectral range but weaker signal, leading to high sensitivities in the case of high aerosol loading.
3. It has fewer radiative transfer challenges arising from strong absorption lines like in the near-infrared. Moreover, the NN technique development allows very fast OMI data processing, which is an important requirement within an operational environment. The aerosol retrievals performed with this algorithm are expected to lead to an explicit aerosol correction over cloudfree scenes by using the OMI 477 nm O 2 −O 2 measurement simultaneously acquired with the 405-465 nm NO 2 band.
This paper aims to evaluate the benefits of our improved use of the OMI 477 nm O 2 −O 2 band for correcting aerosol effects in tropospheric NO 2 VCD retrieval from the same visible observation. We evaluate the potential of directly using the OMI NN aerosol ALH (and τ ) in view of an explicit correction. We also assess the expected changes in the implicit aerosol correction based on the improved OMI effective cloud algorithm. To compare the different aerosol correction strategies, we reprocessed 2 years (2006)(2007) of the DOMINO-v2 data over different areas and seasons, dominated by different types of pollution episodes, and thus, NO 2 and aerosol sources: 1. the large urban and industrialized eastern China region dominated by a mix of continental polluted fine and weakly absorbing particles, and dust coarse and scattering particles in summertime (June-July-August), 2. the same area essentially dominated by continental polluted fine and weakly absorbing particles in wintertime (December-January-February), and 3. South America during the biomass-burning season associated with heavy load of strongly absorbing aerosol emission (August-September).
Given all the aerosol corrections available from our improved use of the OMI 477 nm O 2 −O 2 band, their comparison in this paper gives an estimation of the aerosol correction uncertainty in the OMI tropospheric NO 2 VCD retrieval. Sections 2 and 3 describe the algorithms and the reprocessing methodology. Section 4 evaluates the results of the applied aerosol corrections in the reprocessed tropospheric NO 2 retrievals. To complete the analyses, Sect. 5 includes specific discussions based on reference simulations to better understand the behaviour of the new OMI tropospheric NO 2 VCD. Similarly to Chimot et al. (2016), the advantage of such simulations is to determine, on well controlled cases, the expected new biases of the reprocessed OMI tropospheric NO 2 VCD and to identify the key geophysical factors driving them. At the end, in Sect. 6, we discuss the benefits and challenges of each aerosol correction. The DOAS method is a specific spectral fit approach following basic principle of absorption spectroscopy employed for UV and visible absorbing trace gases. The various DOAS techniques rely on the same key concept: a simultaneous fit of several trace gas slant column densities from the fine spectral features due to their absorption (i.e. the high frequency part) present in passive UV-visible spectral measurements of atmospheric radiation (Platt and Stutz, 2008). The assumed Beer-Lambert (or Bouguer-Lambert) law describes the light attenuation as a function of the travelled distance in the atmosphere, gas concentration and its spectral absorption intensity. It is commonly employed for absorption spectroscopy analyses of NO 2 , SO 2 , HCHO and O 3 from the OMI, TROPOMI, GOME, GOME-2 and SCIAMACHY sensors, e.g. Boersma et al. (2011) andDe Smedt et al. (2018). The spectral fit is achieved within a predefined spectral window and the slant column density N s is defined as the column density of a trace gas absorber along the average light path travelled by the detected photons from the Sun through the atmosphere, surface and back to the satellite sensor.
Here, the OMI 477 nm O 2 −O 2 DOAS fits together the absorption cross-section spectrum of O 2 −O 2 with a first-order polynomial over the (460-490 nm) spectral band (Acarreta et al., 2004;Veefkind et al., 2016). Note that the O 3 absorption, also present in this band, is taken into account. The continuum reflectance R c at the reference wavelength λ 0 = 475 nm is the reflectance which would be measured in the absence of O 2 −O 2 in the atmosphere.
In the absence of clouds, both OMCLDO2 and OMI aerosol algorithms rely on how aerosols affect the length of the average light path along which O 2 −O 2 absorbs. R c (475 nm) is known to represent the enhanced scene brightness due to the additional scattering effects induced by the particles. In particular, R c (475 nm) directly increases with increasing τ . The enhancement magnitude, however, depends on aerosol properties as well as the surface albedo Chimot et al., 2016;Castellanos et al., 2015). The aerosol layer height is the primary driver (Castellanos et al., 2015;Chimot et al., 2016Chimot et al., , 2017). An aerosol layer located at high altitudes causes a large shielding effect on the O 2 −O 2 located in the atmospheric layers below, by reducing the amount of photons coming from the top of the atmosphere and reaching the lowest part of the atmosphere, compared to an aerosol-free scene. As a second-order effect, aerosol properties such as τ and ω 0 , and surface reflectance also contribute to N s O 2 −O 2 (Castellanos et al., 2015;Chimot et al., 2016Chimot et al., , 2017.

OMI cloud algorithm OMCLDO2
The OMI cloud algorithm also named OMCLDO2 (Acarreta et al., 2004) derives the effective cloud fraction c f and cloud pressure c p assuming a single cloud layer as an opaque Lambertian reflector with a constant albedo of 0.8  and the independent pixel approximation (IPA) (Martin et al., 2002;Acarreta et al., 2004). The measured reflectance R is formulated as a linear combination of a clearsky R Clear and a cloudy reflectance R Cloud (Martin et al., 2002;Acarreta et al., 2004): (1) An LUT enables the conversion of R c (475 nm) and N s O 2 −O 2 into c f and c p . It requires knowledge of the surface reflectance and surface pressure in addition to the viewing and sun geometry configurations (Acarreta et al., 2004;Veefkind et al., 2016). Because of the low impact of small clouds on the O 2 −O 2 band, c p has large uncertainties in the case of low c f (Acarreta et al., 2004). The term "effective" here means that these cloud parameters do not represent actual clouds, but our best explanation of the measured radiance is obtained by combining these variables with the assumed approximate model Stammes et al., 2008). Therefore, the retrieved c f and c p values of each observed scene match the measurement summarized by (R c (475 nm)-N s O 2 −O 2 ), such that the (460-490 nm) radiance budget is comprehensively closed (apart from instrument noise). For example, true optically thin clouds will be retrieved as a an opaque and bright Lambertian reflector covering only a small part of the OMI pixel, mostly because of the large assumed cloud albedo value (Veefkind et al., 2016).
The main motivation of this cloud retrieval scheme has been the correction of cloud effects in trace gas retrievals . However, this algorithm is actually applied both to cloudy and cloud-free scenes with aerosols, without any prior distinction. Many studies demonstrated that OMCLDO2 accounts for a large part of aerosol effects in the retrieved c f and c p (Boersma et al., 2004Castellanos et al., 2015;Chimot et al., 2016;Wang et al., 2015). Under these conditions, the OMI cloud parameters then become more effective as they do not represent cloud any more but aerosol effects on the (460-490 nm) radiance. One could claim that OMCLDO2 then becomes an approximate aerosol model, independent of those considered in Sect. 1. c f is mostly driven by R c (475 nm) and increases with increasing aerosol load, regardless of its altitude. Its magnitude is weighted by aerosol properties and surface conditions.
2. c p represents beforehand the degree of shielding effect applied by aerosols, which results from a complex combination of ALH as a first order aerosol load τ and type, surface properties and geometry angles as a second order. A stronger shielding effect leads to a lower c p . In general, over scenes with high τ values, c p correlates well with ALH. Furthermore, regardless of true aerosol layer altitude, strongly absorbing particles lead to a decrease in c p , while the presence of more scattering particles increases c p values (Castellanos et al., 2015;Chimot et al., 2016). Veefkind et al. (2016) released a new version of the OMCLDO2 product. The new algorithm, here named OMCLDO2-New, includes several improvements such as a better consistency of gas absorption cross sections with the OMI NO 2 retrieval algorithm, outlier removal from the spectral fitting, etc. However, in the context of the implicit aerosol correction, the expected highest changes come from the higher number of nodes of the OMI cloud LUT. Indeed, the coarse sampling of the OMI cloud LUT associated with the OMCLDO2-Old version created a numerical artefact: c p was increasing with decreasing c f (or aerosol τ ) without any physical explanation (Chimot et al., 2016;Veefkind et al., 2016). This has strong impacts on the OMI tropospheric NO 2 product, DOMINO v2, in scenes dominated by aerosols (see Sect. 3.3). Furthermore, a temperature correction is implemented in OMCLDO2-New to take into account the densitysquared dependence of the O 2 −O 2 absorption. Its impact, however, depends on the temperature conditions and latitude area (Veefkind et al., 2016).

OMI aerosol neural network
The OMI O 2 −O 2 aerosol algorithm relies on a NN multilayer perceptron approach to primarily retrieve ALH over cloud-free scenes, but also aerosol τ (550 nm) as a secondary parameter (Chimot et al., 2017(Chimot et al., , 2018. Since a fine characterization of aerosol vertical profiles cannot be retrieved from OMI UV-visible measurements, they are assumed as one box layer with a constant pressure thickness (100 hPa). ALH is the middle altitude of this layer in kilometres over sea level but can also be expressed in pressure. Here, the strategy differs from the OMI effective clouds of Sect. 2.2. The main motivation is to try to reproduce aerosol scattering and absorption in the visible spectrum via a more explicit aerosol model than the assumed opaque Lambertian reflector. Particle properties in this layer are considered to be homogeneous.
The ALH retrieval requires several input variables, the most critical being τ (550 nm), as both ALH and τ (550 nm) similarly affect N s O 2 −O 2 and need to be separated (Chimot et al., 2017). In theory, τ information may be available from diverse sources (e.g. atmospheric models, statistical prior guess or observations). In practice, the MODIS τ product has systematically been preferred due to its good spatial and temporal collocation with OMI measurements, and its recognized high quality. Retrieved OMI τ may also be used as they come from a same spectral measurement (same instrument). However, due to its higher uncertainty compared to MODIS, its use impacts the quality of OMI ALH (Chimot et al., 2017). For OMI τ retrieval, R c (475 nm) is considered instead of τ as prior input. Note that, in the next sections, we define NN MODIS when prior MODIS τ is considered, NN OMI based on the retrieved OMI τ , and NN True when the true τ value is considered for the synthetic cases (see Sect. 3.1).
The training data set was generated by full-physical spectral simulations, assuming explicit aerosol particles without clouds, and with the Determining Instrument Specifications and Analyzing Methods for Atmospheric Retrieval (DISAMAR) software by the KNMI (de Haan, 2011). Aerosol scattering phase function ( ) was simulated by the Henyey-Greenstein (HG) function parameterized by the asymmetry parameter g and the average of the cosine of the scattering angle (Hovenier and Hage, 1989). Aerosols were specified as standard fine particles with a typical value of the extinction Ångström exponent α = 1.5 and g = 0.7. They are assumed to fully cover the OMI pixel. To take into account the inaccuracies of the assumed aerosol singlescattering albedo ω 0 properties, two training data sets were generated with a different typical value: one with ω 0 = 0.95 and one with ω 0 = 0.9 in the visible spectral domain. Therefore, two separate OMI ALH NN algorithms were developed, one for each aerosol ω 0 value. The rational of these ω 0 values relies on those that are typically identified in the regions dominated by high NO 2 pollution, notably in eastern China (Lin et al., 2014(Lin et al., , 2015.
The HG phase function is known to have some limitations compared to more physical aerosol scattering models. Nevertheless, it was consciously chosen in Chimot et al. (2017) as the main motivation has been as exploratory development of an ALH retrieval algorithm, using the OMI 477 nm O 2 −O 2 absorption band, in view of correcting aerosol scattering and absorption effects in the visible spectral range for tropospheric NO 2 retrieval. For such a purpose, Chimot et al. (2016) quantitatively demonstrated that τ and ALH are the key needed parameters. Other aerosol parameters, that are more related to their optical properties, shape and size are of a secondary importance. This is supported by a significant number of additional studies (Boersma et al., 2004;Leitão et al., 2010;Castellanos et al., 2015). The main reason is that a comprehensive aerosol correction requires the length of the average light path in the presence of scattering and absorbing particles. This is primarily driven by τ and ALH (in addition to the shape of the NO 2 vertical profile), much less by the detailed properties of particles. Consequently, other details describing the shape of the scattering phase function are of secondary importance, even if they are not negligible. Moreover, geographical areas impacted by heavy NO 2 abundance are generally dominated by fine spherical particles, weakly absorbing (e.g. sulfate, and nitrate) or strongly absorbing (e.g. smoke) particles like in eastern China, South America, and Russia and include urban, industrial and biomass-burning pollution events (Chimot et al., 2017(Chimot et al., , 2018. Spheroid particles such as dust are sometimes mixed but do not dominate. The HG function is known to be smooth and reproduce the Mie scattering functions reasonably well with g = 0.7 for most aerosol types, especially for spherical particles (Dubovik et al., 2002). The evaluation results obtained in Chimot et al. (2017Chimot et al. ( , 2018 showed that this approximation is not oversimplified for all these cases over eastern China, Russia and South America. A similar approach is considered for the operational ALH retrieval algorithms for the Sentinel-4 Precursor and the Sentinel-5 Precursor (Leitão et al., 2010;Sanders et al., 2015;Colosimo et al., 2016;Nanda et al., 2018) and when applying various explicit aerosol corrections in the tropospheric NO 2 AMF calculation over urban and industrial areas dominated by anthropogenic pollution, for instance in eastern China (Spada et al., 2006;Wagner et al., 2007;Castellanos et al., 2015;Vlemmix et al., 2010).
Similarly to the high c p inaccuracy in the case of low c f , a high ALH bias is expected below a minimum particle load (i.e. threshold of τ (550 nm) = 0.5). This is directly due to the weak O 2 −O 2 absorption within the 460-490 nm spectral band. Below this threshold, low aerosol amounts eventually have negligible impacts on N s O 2 −O 2 . The ALH retrieval performance was assessed over areas in eastern China, South America and Russia with scenes including urban, industrial and biomass-burning pollution events and for different seasons (Chimot et al., 2017(Chimot et al., , 2018. These scenes are mostly dominated by fine spherical particles, weakly absorbing (e.g. sulfate, and nitrate) or strongly absorbing (e.g. smoke). Dust particles may sometimes be mixed. Over cloud-free scenes, OMI ALH has shown consistent spatial patterns with CALIOP level 2 (L2) ALH over urban and industrial areas in eastern China, with an uncertainty in the range of [500 : 700] m and for collocated MODIS scenes with τ (550 nm) ≥ 0.5 (Chimot et al., 2018). Additional analyses showed that differences between the LIdar climatology of vertical Aerosol Structure for space-based lidar simulation (LIVAS) and 3-year OMI ALH with MODIS τ (550 m) ≥ 1.0 were in the range of [180 : 800] m (Amiridis et al., 2015;Chimot et al., 2017). Finally, Chimot et al. (2018) showed the potential of OMI visible measurements to observe the height of thick and absorbing aerosol layers released by widespread fire episodes such as in South America. The aerosol model assumptions, in particular ω 0 , are the most critical as they may affect ALH retrieval uncertainty up to a maximum of 660 m. An accuracy of 0.2 is necessary in prior τ (550 nm) information to limit the ALH bias close to zero over scenes with τ (550 nm) ≥ 1.0, and below 500 m for τ (550 nm) values smaller than 1.0. A summary of all the OMI NN aerosol algorithms as well as related input and output parameters is given in Table 1.
3 From aerosol impacts to aerosol correctionmethodology

General methodology
Reprocessing of the OMI tropospheric NO 2 product is based on the DOMINO-v2 data set (see Sect. 3.3) in which the AMF (see Sect. 3.2) is recomputed with diverse aerosol correction strategies using the DISAMAR radiative transfer model, over cloud-free scenes contaminated by aerosols.
Recomputed AMF values then replace the original ones in DOMINO. They are applied to the available NO 2 SCD to derive consequently the tropospheric NO 2 VCD. The tropospheric NO 2 AMF computation follows the formulation detailed in Sect. 3.2, which relies either on an implicit or an explicit aerosol correction: the implicit correction considers the effective cloud retrievals obtained from OMCLDO2 (see Sect. 2.2); the explicit aerosol correction employs aerosol parameters: either OMI ALH and OMI τ from the OMI aerosol NN (see Sect. 2.3), or OMI ALH and MODIS τ . The complementary aerosol parameters (i.e. ω o , g, α) follow those specified in the associated training data set. The surface albedo is based on the OMI Lambertian equivalent reflectivity (LER) climatology (Kleipool et al., 2008). In DOMINO-v2, this climatology is derived from 3-year OMI time series measurements. However, it has evolved since then with an extended 5-year OMI time series (Veefkind et al., 2016). This evolved OMI LER is considered for all the reprocessed tropospheric NO 2 VCD of this study. All the other geophysical parameters associated with DOMINO-v2, such as the NO 2 vertical profile, remain identical.
To identify cloud-free OMI observation pixels with aerosols, a similar strategy to Chimot et al. (2016Chimot et al. ( , 2017 is considered. The DOMINO-v2 NO 2 scenes are collected together with the MODIS-Aqua aerosol τ (550 nm) from the combined Dark Target (DT) and Deep Blue (DB) products of Collection 6 available at a resolution of 10 km (Levy et al., 2013). They are collocated within a distance of 15 km. The probability of cloud-free OMI scene is a priori ensured by the availability of the MODIS aerosol product with the highest quality assurance flag. In this case, MODIS Aqua τ was then exclusively retrieved when a sufficiently high amount of cloud-free subpixels was available (i.e. at the MODIS measurement resolution of 1 km) (Levy et al., 2013). However, it is well recognized this may be not completely representative for the atmospheric situation of the OMI pixel. Therefore,  Chimot et al., 2016). Additional synthetic cases analysed in Sects. 4 and 5 are also based on the DISAMAR model, specified in a similar way to the NN training data set in Sect. 2.3. Either OM-CLDO2 or the OMI NN aerosol algorithms are used to determine the expected tropospheric NO 2 VCD biases.

Air mass factor computations
The computation of tropospheric NO 2 AMF A v NO 2 is a key step for converting NO 2 SCD N s NO 2 into tropospheric NO 2 VCD N v NO 2 , which represents the number of NO 2 molecules cm −2 integrated along the vertical direction from the surface P 0 to the tropopause P trop pressure. The application of A v NO 2 is crucial to correct the average light path variability contained in N s NO 2 . The A v NO 2 computation has generally been recognized as the principal source of errors in N v NO 2 determination in areas with a high level of air pollution (Boersma et al., 2007). This was emphasized even more by Lorente et al. (2017), who discussed how AMF structural uncertainty is driven by assumed prior information, and cloud and aerosol correction strategies: up to 42 % over polluted regions and 31 % over unpolluted regions.
In the context of OMI visible spectral measurements, A v NO 2 is defined as the ratio of the atmospheric SCD and VCD : with the list of input parameters prerequired for the radiative transfer model. Note that before performing this conversion, the stratospheric and tropospheric contributions to N s NO 2 must be separated. Therefore, A v NO 2 ( , λ) is only applied to the tropospheric NO 2 SCD. The OMI A v NO 2 formulation follows Palmer et al. (2001), Boersma et al. (2004) and the concept of altitude-resolved AMF a(z) (also named block AMF or BAMF) introduced by Palmer et al. (2001); Eskes and Boersma (2003) and then generalised by Wagner et al. (2007), Rozanov and Rozanov (2010) and Richter and Wagner (2011). The ratio of a to the total air mass factor A NO 2 (deduced from the NO 2 shape profile) gives the vertical averaging kernel AK, i.e. the sensitivity of the satellite measurement to each vertical atmospheric layer (Eskes and Boersma, 2003;Richter and Wagner, 2011). Overall, A v NO 2 can then be seen as a unitless number representative of the length of the average light path followed by the detected photons in the troposphere. It includes an indication of the sensitivity to the amount of NO 2 in the troposphere, with larger values indicating a higher sensitivity, assuming no change in vertical NO 2 profile. Indeed, in those cases, a change in A v NO 2 is directly associated with a change in a at the atmospheric levels where the trace gas is present. The reference wavelength considered in this paper is 439 nm, following the OMI NO 2 product (see Sect. 3.3) .
Aerosols may cause either a shielding or an enhancement effect. A shielding effect occurs when the length of the average light path is reduced leading to a decrease in A v NO 2 . Reciprocally, an enhancement effect results in an increase in A v NO 2 (Leitão et al., 2010;Chimot et al., 2016). Following Eq.
(2), any bias in the A v NO 2 calculation leads to a direct bias in N v NO 2 , with the same value but opposite sign. Note that, in the case of real OMI tropospheric NO 2 retrievals, a temperature correction is often applied as the temperature of the assumed NO 2 absorption cross section, fixed at 221 K, can differ from the actual temperature when deriving N s NO 2 . The correction term is thus implemented in the computation of A v NO 2 such that it represents the ratio of N s NO 2 derived with a NO 2 cross section at the real temperature T to the column derived at 221 K. European Centre for Medium-Range Weather Forecasts (ECMWF) temperature fields are used for this correction (Boersma et al., 2004. The computation of A v NO 2 requires accurate knowledge about all the parameters , affecting the optical properties of the atmosphere and the length of the average light path. For an aerosol and cloud-free scene, generally includes the satellite and solar geometries, ground pressure and the surface reflectance. In the presence of clouds and/or aerosols, adequate parameters describing their properties must be added. Among all these variables, many studies emphasized that ALH and τ are the most critical aerosol parameters primarily affecting A v NO 2 over cloud-free scenes dominated by aerosol particles (Leitão et al., 2010;Castellanos et al., 2015;Chimot et al., 2016). It was clearly demonstrated that other parameters describing aerosol properties, such as size, are generally of second order of magnitude for such a purpose. The main reason is because, to correct aerosol effects, we need the overall length of the average light path in the presence of scattering and absorbing particles. This is primarily driven by τ and ALH (in addition to the shape of the NO 2 vertical profile) and much less by the detailed properties of particles that affect the TOA radiance measurement more (Chimot et al., 2016).

OMI tropospheric NO 2 data set -DOMINO v2
DOMINO v2 ) is a reference worldwide tropospheric NO 2 product derived from the OMI visible measurements and can be downloaded from the Tropospheric Emissions Monitoring Internet Service (TEMIS) website (http://www.temis.nl, last access: 12 January 2019). Chimot et al. (2016) demonstrated that the implicit aerosol correction in DOMINO-v2 is better than the clear-sky assumption (Richter and Burrows, 2002), with remaining biases between −20 % and −40 % on tropospheric NO 2 VCD, especially in the presence of absorbing particles and for τ (550 nm) ≥ 0.5. One of the main identified limitations has been the coarse sampling of the OMI cloud LUT nodes used in OMCLDO2 (see Sect. 2.2). The effect of the OMCLDO2-New version on the implicit aerosol correction has not yet been analysed.
To our knowledge, no reprocessing has yet been done by applying an explicit aerosol correction based on (nearly) explicit aerosol parameters retrieved from the OMI 477 nm O 2 −O 2 spectral band. Thus, the use of OMI ALH and τ parameters from Sect. 2.3 is a first attempt to apply a (nearly) explicit aerosol correction in the A v NO 2 computation by using visible spectral measurements from the same sensor.
DOMINO has recently evolved through the Quality Assurance for Essential Climate Variables (QA4ECV) project (http://www.qa4ecv.eu, last access: 23 January 2019), which aims to address reliable and fully traceable quality information on some of the essential climate variables (ECVs), such as tropospheric NO 2 , as defined by the Global Climate Observing System (GCOS) (Lorente et al., 2017). This reprocessing contains numerous changes in the complete chain of retrieval, from the calibrated spectrum, spectral fitting with DOAS, to the AMF computation and all the ancillary data sets. This new generation of product is expected to represent one of the best NO 2 data sets. Since the reprocessing products of QA4ECV are still under thorough validation and were not completely available at the time of this paper (and its technical work), and given our specific objective focused on the aerosol scattering and absorption correction by using information from the O 2 −O 2 spectral band, the last version of DOMINO (v2) is preferred.
The OMI cloud algorithm configuration used at the time of DOMINO-v2 and its comparison with the other algorithms are summarized in Table 1. cussed in the previous sections and summarized in Table 1. The main differences between the different reprocessings are synthesized in Table 2 for all collocated OMI-MODIS aerosol scenes.

Implicit aerosol correction -benefits of the updated OMI cloud algorithm
Among all the main changes that are included in the updated version of OMCLDO2, the increased sampling of the OMI cloud LUT is expected to show the most important impacts on the aerosol correction (see Sect. 2.2). Indeed, the coarse sampling of the OMI cloud LUT in the former version was clearly identified by Chimot et al. (2016) as a limitation regarding the behaviour and the magnitude of c p , and thus, when deriving N v NO 2 in the presence of aerosols (see Sect. 3.3). As depicted by Fig. 1, differences in c p are now quite significant for low τ . On average, c p from OMCLDO2-New are about 200 hPa lower than from OMCLDO2-Old (with a large standard deviation) over scenes with MODIS τ (550 nm) ≤ 0.5. Indeed, the low aerosol load has a very limited effect on N s O 2 −O 2 and does not dominate the measured radiance signal. This results in large uncertainties in the retrieved c p and a large sensitivity of the resolution at which the LUT interpolation is performed for these cases. Over scenes with high aerosol load (MODIS τ (550 nm) ≥ 1.0), differences are more minor and may even reverse sign. We attribute the small reverse sign to the application of the temperature correction of N s O 2 −O 2 (see Sect. 2.1), which, depending on the temperature difference compared to the assumed midlatitude summer atmosphere, may apply a positive or negative small modification of c p in cases of high τ . However, as analysed by Veefkind et al. (2016), the impact of the temperature correction of c p remains minor in cases of high c f and thus aerosol load, compared to the updated OMI cloud LUT. Overall, all these changes are consistent with those analysed by Veefkind et al. (2016) over cloudy scenes, with low and high c f .
Based on synthetic cases, Fig. 2 illustrates the expected improvements of the implicit aerosol correction of N v NO 2 due to the higher OMI cloud LUT sampling. While remaining N v NO 2 biases were contained between −20 % and −40 % with OMCLDO2-Old, they should be now limited to the range of [0 : 20] with the use of OMCLDO2-New over scenes with relatively scattering or weakly absorbing aerosol particles (i.e. ω 0 = 0.95) and assuming a typical NO 2 summer vertical profile over north-eastern China. Such improvements are particularly good in the case of aerosols located at an elevated altitude (i.e. more than 1 km). However, although they were improved, the biases could be higher in the case of strongly absorbing particles: in the range of [−10 : 20] % for ω 0 = 0.9. Additional geophysical parameters, in particular the NO 2 profile shape, may affect these biases and are therefore of high importance (see further discussions in Sect. 5.2). Overall, the future changes when applying the new implicit aerosol corrections from DOMINO will result from a combination of different parameters, mainly the higher sampling of the OMI cloud LUT, the temperature correction of N s O 2 −O 2 and the updated OMI surface albedo database. To quantify the resulting changes in the reprocessed OMI N v NO 2 , the results are separated into two categories. Firstly, Fig. 3a, c and e illustrate the changes in reprocessed N v NO 2 from DOMINO to OMCLDO2-Old. As indicated in Table 1, these changes result from two consequences: 1. the temperature correction of N s O 2 −O 2 and the new OMI surface albedo, which both directly modify the retrieval of the effective cloud parameters, and 2. the direct application of this new albedo when computing A v NO 2 .
A higher surface albedo should result in an increased length of the average light path and therefore an enhanced A v NO 2 . However, this can become more complex when combined with the new effective cloud parameters as they may either enhance, reduce or even counterbalance this effect. On average, N v NO 2 is lower (i.e. higher A v NO 2 ), between −1 %±9 % in China in summertime and −15.6 %±29.8 % in China in wintertime. The quality of these changes, however, depends on the accuracy of the new surface albedo climatology, which is primarily expected to be more robust due to the longer time series considered in the OMI reflectance observations (see Sect. 3.3).
Secondly, Fig. 3b, d and f depict the impacts of the implicit aerosol correction evolution from OMCLDO2-Old to OMCLDO2-New. They are directly driven by the improved c p (see Table 1). Over scenes with MODIS τ (550 nm) in the range of [0.0 : 0.5], a decreased c p (see Fig. 1) results in a stronger shielding (or reduced enhancement) effect from particles: N v NO 2 generally increases. In contrast, larger c p over scenes with MODIS τ (550 nm) ≥ 1.0 leads to a lower shielding (or stronger enhancement) effect: N v NO 2 decreases. Stan- China -summer 6.5 ± 11.9 China -winter 11.2 ± 18.4 South America -−3.0 ± 14.0 biomass burning NO 2 (NN OMI,ω 0 =0.9 ) −NO 2 (NN OMI,ω 0 =0.95 ) China -summer 8.5 ± 13.7 China -winter −1.9 ± 24.3 South America -1.0 ± 14.6 biomass burning dard deviation of these changes is between 15% and 20% in China in wintertime and South America, and lower than 10% in China in summertime and South America. Averages are in the range of [1.3 % : 7.9 %]. Regional and seasonal differences may reflect the implicit dependencies on the aerosol types, the combined effects on c f − c p , spatially variable surface albedo and the impacts of seasonal NO 2 vertical profile. All these observed changes are in line with the analyses deduced from the synthetic cases in Fig. 3b, d and f, confirming the improvements thanks to the updated OMI cloud LUT. Interestingly, these overall changes seem to be in line with the average AMF uncertainty of 11 % evaluated by Lorente et al. (2017) due to a different cloud correction scheme in polluted conditions and assuming c f ≤ 0.2.
Overall, maps in Figs. 4c-6c show that the total changes in N v NO 2 , from DOMINO to OMCLDO2-New, mostly occur in the eastern part of China, where the NO 2 pollution is higher. Spatial patterns of these overall changes mostly result from a complex combination with MODIS aerosol horizontal distribution as suggested by Fig. 3, but also aerosol types and vertical distribution: a decrease over Beijing areas in summertime and an increase in the same area in wintertime.

Explicit aerosol correction results
In this study, there are four possibilities for applying an explicit aerosol correction from the OMI 477 nm O 2 −O 2 band. Each of them differ regarding the assumed aerosol properties (i.e. ω 0 ), aerosol τ observations (i.e. MODIS or OMI) and the consequent fitted ALH (see Sect. 2.3). All these possibilities were individually applied when reprocessing the OMI DOMINO product to quantify their overall differences.
Similarly to the benefits of the new implicit aerosol correction based on OMCLDO2-New evaluated in Sect. 4.1, Fig. 7 shows the benefits of the applied explicit aerosol corrections. Provided that the aerosol model (e.g. ω 0 ) is in line with the actual aerosol type present in the observed scene (i.e. biases after application of the implicit aerosol correction as a function of true aerosol optical thickness (AOT) τ (550 nm) and based on synthetic cases including different true ALH, surface albedo = 0.05, µ 0 = 25 • , µ = 25 • and a typical TM5 NO 2 vertical profile for 1 July 2006 at 12:00 over China (van Noije et al., 2014;Chimot et al., 2016). True aerosol properties are defined by α = 1.5, ω 0 = 0.95 or 0.9 and g = 0.7. Implicit aerosol correction is derived from the retrievals given by OMCLDO2-Old or OMCLDO2-New, which, among other elements, includes the new OMI cloud LUT with a higher sampling (see Sect. 2.2 and Table 1 ideal scenario), remaining biases in N v NO 2 are below 20 % and are slightly dependent on aerosol parameters (τ , ω 0 and ALH) when assuming a NO 2 vertical profile representative of a typical summer day over the east of China (van Noije et al., 2014;Chimot et al., 2016). In such a scenario, using either the retrieved OMI τ value or a more accurate one is not expected to make a major difference. However, in practice, these results may vary with respect to the NO 2 profile shape and additional errors in the employed aerosol model (see next subsections). Figure 8 shows that all reprocessed N v NO 2 with implicit or explicit corrections are larger by [10 % : 50 %] than if no correction was performed, especially over scenes with MODIS τ (550 nm) ≥ 1.0. This suggests that both corrections converge in the same direction (i.e. same sign) in spite of some different magnitudes of the aerosol correction. Since all the considered strategies attenuate the N v NO 2 biases due to aerosols from an aerosol-free scene assumption, it is worth emphasizing that all of them, without distinction, are an aerosol correction, regardless of their implicit or (more) explicit nature.

Atmos
Overall, over OMI pixels collocated with MODIS τ (550 nm) ≥ 0.5, Fig. 9 depicts that most of the reprocessed N v NO 2 values are generally higher with the explicit aerosol correction than with the implicit aerosol correction from OMCLDO2-New. This suggests a stronger shielding effect leading to lower A v NO 2 (439 nm). The differences increase with increasing MODIS τ as aerosol effects consequently amplify along the average light path.
In eastern China, by using the explicit aerosol correction with NN MODIS,ω 0 =0.95 , N v NO 2 values are higher than with the implicit aerosol correction, with OMCLDO2-New at about 12 ± 12.5 % in summer and 40 ± 26.1 % in winter over scenes with MODIS τ (550 nm) ≥ 0.5 (see Fig. 9). The larger increase in wintertime is likely due to different NO 2 profile shapes, with NO 2 molecules being closer to the surface (see further discussions in Sect. 5.2). The differences with OMCLDO2-New are somehow reduced when assuming a lower aerosol ω 0 . In such a configuration, the main differences are as follows: 1. a lower ALH due to an assumed lower ω 0 value (Chimot et al., 2017), combined with

a more absorbing aerosol model used to compute
A NO 2 (439 nm).
In both cases, NN MODIS,ω 0 =0.9 and NN MODIS,ω 0 =0.95 , prior τ (coming from MODIS) remains unchanged. As illustrated in Figs. 9, resulting N v NO 2 using NN MODIS , ω 0=0.9 over China are smaller (i.e. A v NO 2 (439 nm) higher) by about −0.2 ± 7.8 % in summer, and −8.2 ± 22.3 % in winter compared to N v NO 2 with NN MODIS,ω 0 =0.95 . These numbers represent a first evaluation of the impact of aerosol model uncertainty, assuming one may use a very accurate prior τ information for both the ALH retrieval and the A v NO 2 (439 nm) computation. Over scenes in South America with MODIS τ (550 nm) ≥ 0.5, the difference between N v NO 2 from NN MODIS,ω 0 =0.95 and from OMCLDO2-New is on average close to zero with a standard deviation of 16.8 %. The use of NN MODIS,ω 0 =0.9 reduces N v NO 2 by about −1.3 ± 8.7 %. Interestingly, Castellanos et al. (2015) reported an average change of 0.6 ± 8 % on A v NO 2 after reprocessing DOMINO N v NO 2 over cloud-free scenes during the biomass-burning season in South America and applying an explicit aerosol correction based on the OMI near-UV aerosol algorithm (OMAERUV) and CALIOP aerosol ALH.
When using the retrieved OMI τ as prior input instead of MODIS τ over eastern China, N v NO 2 differences with respect to the use of OMCLDO2-New differ by 5-10 % on average over scenes with MODIS τ (550 nm) ≥ 0.6 (higher in summer but lower in winter). This suggests a higher sensitivity to the combination of OMI τ and ALH when used together for the A v NO 2 computation. Figures 4-6 show that most of the changes in N v NO 2 are located on the eastern part and over areas dominated by heavy NO 2 pollution such as the megacities and the Pearl River delta. The horizontal distribution of aerosol load adds some complex patterns. Overall, the quantitative N v NO 2 differences between the applied explicit aerosol corrections and the improved implicit aerosol correction can be considered an average uncertainty related to the choice of an aerosol correction approach. Similar numbers are reported by Lorente et al. (2017), who indicated an average aerosol correction uncertainty of 45 % over highly polluted scenes and with large aerosol loading (τ (550 nm) ≥ 0.5). Furthermore, it was found that N v NO 2 from the POMINO data set over China (Lin et al., 2015) is 55 % higher (A NO 2 smaller) than if no explicit aerosol correction was considered when the aerosol layer is located above the tropospheric NO 2 bulk. The main identified reason was a reduced shielding effect applied by the effective cloud parameters resulting from a higher effective cloud pressure (c p = 350 hPa); i.e. the Lambertian reflector Atmos. Meas. Tech., 12, 491-516, 2019 www.atmos-meas-tech.net/12/491/2019/ was defined at a lower altitude. The reduction of this shielding effect may of course be attenuated when aerosols are mixed with NO 2 , as their multiple scattering effects increase, then the average light path length increases and so does the NO 2 absorption.
Finally, over scenes with a small amount of aerosol (i.e. MODIS τ (550 nm) ≤ 0.2), the difference in N v NO 2 between the explicit aerosol correction assuming prior MODIS τ and the implicit aerosol correction with OMCLDO2-New is systematically lower and non-null: about an average of −10 % over all the considered regions. This difference may seem strange as small aerosol amounts are expected to have an almost negligible effect on the light path and thus on A v NO 2 . When OMI τ is instead considered, this difference becomes positive over China, but is reduced everywhere (less than 10 %). Note that NN MODIS,ω 0 =0.95 and NN MODIS,ω 0 =0.9 algorithms differ from OMCLDO2 by using an external geo-physical parameter (i.e. MODIS τ ). Although it is more accurate than using the retrieved OMI τ , the combination of an external MODIS aerosol parameter derived from different assumptions about the scattering model and surface reflectance may in the end lead to inconsistencies when combined with the OMI NN model: the 477 nm O 2 −O 2 radiance budget is likely not closed. This radiance budget is always closed with OMCLDO2 (apart from the instrument noise), since it simultaneously adjusts both c f and c p to match the R c (475 nm) − N s O 2 −O 2 combination. The topic of radiance closure budget and its impacts on A v NO 2 are further discussed in Sect. 5.5.

Explicit vs. implicit aerosol correction -main reasons for the differences
As discussed in Sect. 3.2, ALH is the first crucial parameter for the computation of A v NO 2 (439 nm). Therefore, as a first assumption, it is expected that the accuracy of the OMI ALH retrieval, and its difference with c p , may be one of the first causes (although not unique) of the difference between the applied implicit and explicit aerosol corrections. Figure 10 compares the average OMI ALH (retrieved with the NN trained with aerosol ω 0 = 0.95) and c p from OMCLDO2-New, both converted into metric unit (km) over cloud-free scenes and for collocated MODIS scenes with τ (550 nm) ≥ 0.5. Overall, both variables are quite well correlated, with similar spatial and seasonal distributions. Values are higher in China in summertime and over South America and lie in the range of [1.5 : 5.0] km. They are lower in China in wintertime, between 0.4 and 2.0 km. Quantitatively, ALH values from NN MODIS,ω 0 =0.95 show that the fitted aerosol layers are located higher than the fitted opaque Lambertian clouds; i.e. aerosol pressures are smaller than c p with average differences in the range of [−0.49 : −50.3] hPa. Standard deviation of the differences are of the order of 120 hPa. The sign of the differences is reversed when employing NN MODIS,ω 0 =0.9 (average differences 12.9-59.3 hPa).
As a first assumption, when ALH values are higher than c p , the explicit aerosol corrections shall generally apply a stronger shielding effect to A v NO 2 . Therefore, the resulting N v NO 2 should be larger. However, this element alone is likely insufficient to explain the differences observed in Sect. 4.2. The combined impacts of the assumed prior τ value also play a significant role. Furthermore, the assumed Lambertian cloud and the aerosol Henyey-Greenstein models differ for the horizontal coverage of the OMI pixel: the opaque pixels (optical properties can be changed, fraction coverage is fixed). The transmission and multiple scattering properties are included within the aerosol layer and vary as a function of the optical properties. Therefore, one can assume that, in the case of optically thick layers, the aerosol model generally applies a stronger screening effect by fully covering the scene and thus obstructing the surface transmission signal. By opposition, the surface transmission signal is more or less always ensured with the Lambertian opaque model by the non-covered pixel fraction.

Advantages and challenges of an explicit aerosol correction based on the 477 nm O 2 −O 2 measurement
This section discusses specific elements in order to evaluate the relevancy of the developed explicit aerosol correction strategy over cloud-free scenes from OMI, but also in general from all UV-vis satellite measurements. In particular, we wish to draw the reader's attention to the advantage of using an explicit aerosol correction based on the exploitation of the 477 nm O 2 −O 2 spectral band from a satellite measurement, but also the remaining difficulty of implementing it in practice. The next subsections focus on the significance of the aerosol model error, the importance of the NO 2 vertical profile, the cases with absorbing particles, the NO 2 vertical averaging kernels and the OMI visible radiance closure budget issue.

Impact of aerosol model error on tropospheric NO 2 air mass factor
When applying an explicit aerosol correction, the accuracy of each variable describing aerosol properties, once combined with the NO 2 vertical profile (see Sect. 5.2) and surface reflectance, drives the overall A v NO 2 (439 nm) computation uncertainty. The A v NO 2 uncertainty due to this whole set of vari-  ables, not only ALH, can be defined as the aerosol model error for OMI N v NO 2 retrieval.
To understand the quantitative impact of each aerosol model variable uncertainty, Fig. 11 shows the A v NO 2 (439 nm) biases resulting from some aerosol model inputs. A single Atmos. Meas. Tech., 12, 491-516, 2019 www.atmos-meas-tech.net/12/491/2019/  Table 1) and the implicit aerosol correction based on OMCLDO2-New (improved effective cloud parameters, up-to-date version): bias in ALH of 100 hPa directly affects N v NO 2 within the range of [60 % : 70 %] when absorbing aerosols (ω 0 = 0.9) are located below 0.5 km, assuming a wintertime NO 2 profile and with τ (550 nm) = 1.4. The uncertainties are below 50 % for τ (550 nm) ≤ 0.5 and overall below 10 % when particles are located at elevated altitudes (i.e. true ALH ≥ 1.4 km). This quantitatively emphasizes how essential ALH information quality is when particles are actually mixed with NO 2 molecules due to the complexity of reproducing the enhancement of the average light path caused by scattering effects. A bias of 0.2 in the assumed τ (550 nm) mostly impacts scenes with a small aerosol load: while resulting N v NO 2 uncertainties lie in the range of [−20 % : 20 %] for τ (550 nm) ≤ 0.5, they decrease to the range of [0 % : 10 %] for τ (550 nm) = 1.4. Finally, an overestimation of aerosol scattering efficiency (i.e. ω 0 bias of 0.05) leads to an underestimation of N v NO 2 up to −20 % over scenes with high τ as a consequence of an underestimation of aerosol shielding effect and therefore a A v NO 2 (439 nm) that is too large. Overall, ALH uncertainty is the key driver of the AMF computation quality. ALH uncertainty must be better than 50 hPa to limit N v NO 2 bias below 40 %. With τ uncertainty, they form the most important set of aerosol parameters prerequired for a high quality of the A NO 2 (439 nm) computation. Although it is not negligible, the uncertainty of aerosol model parameters that are more related to the particle optical and scattering properties, such as ω 0 , g and α, is of secondary importance provided that both the ALH and τ qualities are ensured.

The importance of the relative layer height
A comprehensive aerosol correction for an accurate A NO 2 (439 nm) computation also requires the actual NO 2 vertical profile. Figure 12a shows the accuracy of the aerosol corrections in A NO 2 (439 nm), based on a synthetic case, assuming the presence of absorbing aerosol particles (ω = 0.9) but a typical NO 2 vertical profile of wintertime (1 January, 12:00) over China. The main difference with Fig. 2 and Fig. 7 is the presence of a more abundant tropospheric NO 2 bulk closer to the surface and a stronger decrease rate to higher altitudes (Chimot et al., 2016). In such a case, relative N v NO 2 biases with the implicit aerosol correction are strongly 40 %] (winter). As already identified in Sect. 4.1 with the summertime NO 2 profile, the insufficient shielding effect applied by the effective cloud parameters from OMCLDO2-New in the case of aerosol layers located at elevated altitude is severely degraded here (from −10 % to −80 %). The insufficient enhancement effect when particles are mixed with the tropospheric NO 2 molecules is also amplified here (from 20 % to 40 %).
When considering an explicit aerosol correction using NN True,ω 0 =0.9 , the N v NO 2 bias is changed to 0 %-40 %. Similarly to summertime, they are lower in the case of particles at high altitude, suggesting strong benefits of such a correction scheme in wintertime and/or in the presence of absorbing particles. The cases of aerosols close to the surface (i.e. lower than 0.5 km) remains an issue due to the difficulty of distinguishing the scattering effects from the surface and the adjacent aerosol layer when retrieving ALH. The retrieval seems, in such a case, to overestimate the aerosol layer altitude.
The observed positive difference of about 40 % between explicit and implicit aerosol corrections is in line with the analyses over China in wintertime (see Sect. 4.2 and Fig. 9). All these elements strongly remind us and emphasize that the quality of the aerosol corrections and their differences for N v NO 2 retrieval are actually more dependent on the relative height between the particles and the tropospheric NO 2 bulk than the absolute values of ALH or c p themselves. The evolutions of operational aerosol correction schemes in present and future air quality UV-visible space-borne sensors, such as TROPOMI on board Sentinel-5 Precursor, then need to consider a proper joint characterization of trace gas vertical profiles together with aerosol vertical distribution and related optical properties.

Explicit vs. implicit aerosol correction -focus on absorbing particles
In this study, the cases with absorbing particles, i.e. aerosol ω 0 = 0.9, brings more challenges to the implicit aerosol correction than scenes dominated by more scattering aerosols. Such difficulties were also identified by Castellanos et al. (2015). As a reminder, the presence of absorbing particles leads to a reduced c p (increasing the shielding effect) but a lower c f (lower shielding effect) with a higher transmittance coming from the clear part of the pixel. Part of the insufficient shielding effect observed with the implicit correction in Sect. 4.1 and 5.2 may thus be explained by insufficient coverage of the observation scene by the Lambertian opaque cloud layer; i.e. a higher fraction of the cloud-free part of the OMI scene, including the surface, is assumed to lead to a higher transmittance of the associated atmospheric layers. This last element likely overall limits the potential of the effective cloud model to apply an adequate shielding effect to A v NO 2 . However, these biases still remain lower than if no aerosol correction was achieved (Chimot et al., 2016). Figures 7 and 12a showed the potential of the explicit aerosol correction but by assuming no bias in the assumed τ and ω 0 parameters. To investigate this further, Fig. 12c-d depict the impacts of a wrong prior aerosol ω 0 (overestimation of 0.05) when applying the explicit aerosol correction through the use of the OMI aerosol NN. When the true prior τ value for both the ALH retrieval and the A v NO 2 computation is conserved, the increases in N v NO 2 biases are limited from 0 %-40 % (see Fig. 12a) to 0 %-60%. This reflects how the quality of prior τ knowledge helps to constrain both ALH retrievals and then limit the perturbation of A v NO 2 . However, this may be more severely degraded when inaccurate prior biases after application of the implicit or explicit aerosol correction (see Table 2) as a function of true aerosol optical thickness (AOT) τ (550 nm). Synthetic cases are similar to Fig. 2, except the summer NO 2 profile was replaced by a typical winter one. Furthermore, only absorbing aerosols with true ω 0 = 0.9 are considered. Finally, the impact of a bias on the assumed ω 0 through the application of the explicit aerosol correction is illustrated: (a) implicit aerosol correction based on OMCLDO2-New, (b) explicit aerosol correction, true τ and assumed ω 0 = 0.9, (c) explicit aerosol correction, true τ and assumed ω 0 = 0.95 and (d) explicit aerosol correction, retrieved OMI τ and assumed ω 0 = 0.95. τ is considered (see Sect. 5.5). Figure 12d shows the impacts of replacing true τ by the retrieved OMI one. N v NO 2 biases are higher, about [−40 % : 60 %]. This is a direct result of a degradation of ALH retrieval due to an overly biased aerosol τ and the resulting impact on the A v NO 2 . As discussed in Sect. 5.1, although the ω 0 parameter is of secondary importance for A v NO 2 (439 nm) itself compared to the (ALH-τ ) combination, its direct impact on τ retrieval consequently affects the ALH determination accuracy and then indirectly affects A v NO 2 . In spite of these drawbacks, N v NO 2 biases remain smaller than if the derived effective cloud parameters were employed through the implicit aerosol correction (see Fig. 12a). Thus, even if imperfect, the explicit aerosol correction based on OMI ALH and τ retrievals seem to remain advantageous for an efficient aerosol correction in tropospheric NO 2 VCD retrieval from visible satellite radiance. Nevertheless, true horizontal distributions of aerosols within the observation pixel may actually be quite heterogeneous. Such problems should be further investigated with a focus on areas where absorbing particles are expected, such as in wintertime in China, or during large biomass-burning episodes. Future studies should also determine how often such an effect occurs and its overall impact depending on the NO 2 vertical profile variability.

Aerosol model and NO 2 vertical averaging kernel
Theoretically, the application of an explicit aerosol model is expected to simulate more realistic scattering and absorption effects due to particles when computing A NO 2 (439 nm). Figure 13 illustrates the vertical averaging kernel (AK) (see Sect. 3.2) assuming τ (550 nm) = 1.0 and from the application of OMCLDO2-New, NN MODIS,ω 0 =0.95 and true aerosol conditions, assuming no bias in prior aerosol assumptions. AKs are very important for estimating the surface NO x emissions by convoluting the NO 2 vertical profiles from the used atmospheric models to match the OMI N v NO 2 observations (Eskes and Boersma, 2003;Ding et al., 2015). AKs based on OMCLDO2-New display a sharp distinction between the enhanced atmospheric layers located above aerosols and the shielded layers located below. On the contrary, AKs from NN MODIS,ω 0 =0.95 depict a smoother transition, which is then enhanced at the shielded layers. This transition is more in line with the actual AKs (Fig. 13a) and results from the scatter-Atmos. Meas. Tech., 12, 491-516, 2019 www.atmos-meas-tech.net/12/491/2019/ ing effects induced by the more or less wide aerosol particle layer. A bright Lambertian reflector is by nature fully opaque and does not induce multiple scattering effects. This is partly compensated by the transmission of the clear fraction of the pixel through the IPA assumption (see Sect. 2.2). This suggests that applying an explicit aerosol correction leads to the consideration of more realistic physical assumptions and AK productions. However, such a suggestion critically depends on an ensemble of other parameters that contribute to the AK generation: the accuracy of the retrieved ALH which triggers the location of the enhancement/shielding transition, the potential aerosol model biases (e.g. ω 0 , scattering phase function, etc. . . ) and the difference between actual and assumed aerosol vertical profiles.

Radiance closure budget issue and potential impacts
The discussions about the model error in the previous subsections implicitly made the assumption that the whole set of parameters such as (c f , c p and surface reflectance) on the one hand, or (τ , ALH, ω o , g, α and surface reflectance) are fully consistent in the sense that they form one unique particle model. However, when external data are used to constrain ALH retrieval accuracy, such as MODIS aerosol τ , one may combine inconsistent model assumptions, leading to complex artefacts such as the issue of the OMI closure radiance budget.
The radiance closure budget is not only important in the 477 nm O 2 −O 2 band, but also in the NO 2 absorption band at the wavelength where the AMF is computed. Aerosol τ combined with surface reflectance are expected to drive OMI R c (475 nm). As discussed in Sect. 2.2, OMCLDO2 simultaneously adjusts both c f and c p based on the same prior surface reflectance, such that their combination allows the (R c (475 nm)-N s O 2 −O 2 ) budget to be closed and thus the OMI 477 nm O 2 −O 2 radiance occurs independently of the accuracy of the selected model. On the contrary, by using MODIS τ , only OMI N s O 2 −O 2 is exploited, not R c (475 nm). If all the prior parameters are accurate and derived from a unique set of aerosol model and surface reflectance parameters, the (R c (475 nm)-N s O 2 −O 2 ) budget should be closed. However, any mismatch between the model employed for MODIS τ determination and the one used in the OMI NN training data set, between MODIS and OMI instrument radiance, and/or the surface reflectance hypothesis, may leave this budget open. In particularly, it is worth remembering that the surface reflectance data set behind MODIS τ , OMI c f and A v NO 2 (439 nm) are not identical: for OMI, a multi-spectral surface Lambertian equivalent reflectance (LER) was used (Kleipool et al., 2008), while MODIS aerosol retrieval uses a directional surface spectral reflectance (Levy et al., 2013).
Therefore, the strategies of the implicit vs. explicit aerosol correction analysed in Sect. 4.2 do not only differ in terms of assumed particle optical and scattering property model but also on how much the whole OMI radiance budget is eventually fitted. This last difference likely explains the strange systematic difference (about −10 %) identified over OMI scenes with MODIS τ (550 nm) ≤ 0.2, where aerosol effects could be assumed to be almost insignificant (see Fig. 9). When. MODIS τ is replaced by the retrieved OMI τ (see Table 1), which is, like c f , mostly constrained by R c (475 nm), prior OMI surface albedo and the same aerosol model used for ALH retrieval and A v NO 2 (439 nm) calculation, resulting N v NO 2 are higher than with the use of MODIS τ (see Table 2). Moreover, as analysed in Sect. 4.2, the differences between the implicit and explicit aerosol corrections are smaller everywhere over scenes with small aerosol load confirming the consistency in the employed models for each set of parameters and an almost complete closure of the OMI visible radiance budget (except instrument noise).
At the end, one might wonder what the best option is for an optimal aerosol correction: 1. using the best aerosol and surface parameters available for the most accurate correction at the cost of not closing the satellite radiance budget, or 2. applying a less accurate correction but with an ensemble of aerosol and surface parameters that eventually comprehensively fit the spectral measurement.
The first option gives more weight to the used auxiliary data, while the second option maximises the weight of the amount of information contained in the satellite measurement. Due to the differences in the OMI-derived LER and the MODIS surface reflectance, it may be very tempting to select primarily both the OMI τ and ALH variables to avoid inconsistencies when correcting aerosol effects. However, in this study, such a choice is not necessarily obvious for everyone, as the accuracy of the ALH retrieval is strongly dependent on the requested prior τ (Chimot et al., 2017). The most accurate OMI ALH retrievals were obtained with collocated MODIS τ , not with the derived OMI AOT. This would naturally suggest first that the combination of OMI ALH and MODIS τ shall give the most accurate tropospheric NO 2 AMF. However, the apparent inconsistencies due to the different algorithms employed for each physical product are mostly observed in the present study through the discussion on the TOA radiance closure budget issue. They do not necessarily mean that the aerosol correction is less accurate.
The answer to such a problem is, in our opinion, not clear at this stage. But, given the fact that several studies prioritise the application of multiple parameters from very diverse sources (models, ancillary instruments with different techniques, etc.) to satellite spectral measurements, we think that the issue of radiance closure budget should be kept in mind by the scientific community and further investigated in future research studies. At the end, an optimal trade-off must be found between the quality of the N v NO 2 product and the weight given to the original satellite measurement.

Conclusions
This paper reprocesses the reference OMI tropospheric NO 2 vertical column density N v NO 2 for cloud-free scenes over eastern China and South America for 2006 and 2007. These regions are dominated by high aerosol loadings. The goal of this study is to evaluate the benefits of the recently achieved developments during the last years to improve the aerosol correction in the tropospheric NO 2 air mass factor A v NO 2 , a crucial parameter when retrieving N v NO 2 from visible air quality satellite backscattered measurements. In particular, the tested aerosol correction strategies rely on our recent experiences with the 477 nm O 2 −O 2 spectral band: a key spectral band present in current and future air quality UVvis satellite instruments such as OMI, GOME-2, TROPOMI, Sentinel-4-UVN and Sentinel-5-UVNS. The use of this band is important in view of operational data processing, as it allows parameters to be derived that, in principle, could reproduce the particle scattering and absorption effects on the average light path in the visible spectral window and represent the sensor field of view. Regardless of the type of algorithm employed here, these parameters can all be derived using computationally inexpensive methods, are directly representative of the OMI pixel in terms of spectral measurement, spatial coverage and temporal acquisition, and can directly be used for the A v NO 2 computation. The two tested algorithms are the OMI cloud software OMCLDO2 (Veefkind et al., 2016) and the OMI aerosol neural network (NN) approach (Chimot et al., 2017(Chimot et al., , 2018. The most important difference between these methods is the assumed aerosol model, not only for the retrieval of the aerosol parameters in the O 2 −O 2 band, but also how they represent aerosol effects in the tropospheric NO 2 air mass factor. The OMCLDO2 represents the aerosols as effective cloud parameters and thus implicitly correct the aerosol effects, whereas the NN approach explicitly models and corrects for aerosols. The most recent OMCLDO2 update from (Veefkind et al., 2016) includes, among many elements, an increased number of nodes in the LUTs and the necessary temperature correction of the O 2 −O 2 slant column density.
For both methods, the reprocessed N v NO 2 shows smaller biases over cloud-free scenes dominated by aerosol pollution, compared to the standard DOMINO retrieval and its related aerosol correction. Previous studies showed an underestimation of the OMI N v NO 2 between −20 % and −40 % over scenes with MODIS aerosol optical thickness τ (550 nm) ≥ 0.6, assuming scattering aerosol particles with aerosol singlescattering albedo ω 0 = 0.95 and summertime NO 2 vertical profile. In similar conditions, these biases are expected to be contained in the limit of [0 % : 20 %] for both the most recent OMCLDO2 method and the NN method. On average, the applied explicit NN correction leads to higher N v NO 2 values compared to the implicit OMCLDO2 correction up to 40% depending on the seasons, regions and aerosol pollution episodes. This represents our best estimate of the aerosol correction uncertainty for the OMI N v NO 2 retrieval due to the possible choices of the algorithm correction. They are at-Atmos. Meas. Tech., 12, 491-516, 2019 www.atmos-meas-tech.net/12/491/2019/ tributed to the model differences and the associated output variables.
Although both the implicit OMCLDO2 and explicit NN methods are a significant improvement over the current OMI DOMINO retrieval, we also found limitations that need to be further studied: -If absorbing aerosols (i.e. single-scattering albedo ω 0 ≤ 0.9) are present, the implicit aerosol correction still leads to substantial biases in N v NO 2 due to an insufficient applied shielding effect: between −80 % and 20 % assuming a typical NO 2 wintertime profile. This is most severe when particles are located at high altitude (above 1.4 km) and with heavy aerosol load. In similar conditions, the explicit aerosol correction allows us to mitigate the biases to the range of [0 % : 40 %] if accurate τ and aerosol model are available, or [−40 % : 60 %] with inaccurate τ (e.g. retrieved OMI τ ) and aerosol model.
-Biases remain high when particles are located close to the surface, regardless of the aerosol correction methodology. The distinction between aerosol scattering and surface reflectance is challenging under such conditions. Since particles are close to the tropospheric NO 2 bulk (either mixed or slightly above), small errors in the retrieved aerosol height or effective cloud pressure have a significant impact on the derived NO 2 column.
-All aerosol correction methodologies are sensitive to the NO 2 vertical profile and the employed surface albedo or reflectance. Future improvements need to address both these parameters together with any evolution that can still be done in the aerosol or effective cloud retrievals from the 477 nm O 2 −O 2 .
-Although the OMI aerosol NN algorithms lead to a promising ALH retrieval, its use for an explicit aerosol correction is not straightforward. Indeed, ALH is only one variable (although a key one) of a set of aerosol parameters that need to be applied for the required explicit aerosol correction. Its combination with other aerosol parameters (size, ω 0 , τ ) can lead either to model errors and/or to the risk of not closing the OMI radiance budget if any of these parameters were issued from an external source (model or instrument) that is not consistent with the OMI ALH retrieval.
Based on its estimated performances, we recommend an operational processing of OMI data, where no distinction is made between cloudy, cloud-free and aerosol-contaminated scenes, to first use the implicit aerosol correction based on OMCLDO2. It allows both cloud and aerosol particle effects to be adequately corrected on the average light path. If cloudfree scenes can be carefully identified and collected in the same way as has been done here, then the explicit aerosol correction based on the OMI NN aerosol algorithms should be considered. We demonstrated in this study, for the first time, its high performance and the realism of the simulated physical effects. Moreover, the developed NN approach can ensure a fast cloud-free data processing.
Overall, the considered aerosol corrections can in principle be transposed to the future generation of air quality UV-vis satellite sensors, such as TROPOMI, Sentinel-4 and Sentinel-5-UVNS. It can also be considered for other trace gases of interest, e.g. SO 2 or HCHO. However, such an approach has to be adapted to the specificities of this new generation of instruments.
Code and data availability. All the data results and specific algorithms created in this study are available from the authors upon request. If you are interested in having access to them, please send a message to julien.chimot@eumetsat.int and pepijn.veefkind@knmi.nl. The pybrain library code is available at http://pybrain.org/ (last access: 23 January 2019). Finally, The OM-CLDO2 data set is available from the NASA archives: https://disc. gsfc.nasa.gov/uui/datasets/OMCLDO2_003/summary (last access: 23 January 2019).
Author contributions. JC is the main contributor to this research work, supported by the guidance of PV and PL. JdH developed the DISAMAR code used in this study. PS provided support in radiative transfer simulations and key analyses.
Competing interests. The authors declare that they have no conflict of interest.