Impact of aerosols on the OMI tropospheric NO2 retrievals over industrialized regions how accurate is the aerosol correction of cloud-free scenes via a simple cloud model?

. The Ozone Monitoring Instrument (OMI) has pro-vided daily global measurements of tropospheric NO 2 for more than a decade. Numerous studies have drawn atten-tion to the complexities related to measurements of tropospheric NO 2 in the presence of aerosols. Fine particles affect the OMI spectral measurements and the length of the average light path followed by the photons. However, they are not explicitly taken into account in the current operational OMI tropospheric NO 2 retrieval chain (DOMINO – Deriva-tion of OMI tropospheric NO 2 ) product. Instead, the operational OMI O 2 − O 2 cloud retrieval algorithm is applied both to cloudy and to cloud-free scenes (i.e. clear sky) dominated by the presence of aerosols. This paper describes in detail the complex interplay between the spectral effects of aerosols in the satellite observation and the associated response of the OMI O 2 − O 2 cloud retrieval algorithm. Then, it evalu-ates the impact on the accuracy of the tropospheric NO 2 retrievals through the computed Air Mass Factor (AMF) with a focus on cloud-free scenes. For that purpose, collocated OMI NO 2 and MODIS (Moderate Resolution Imaging Spec-troradiometer) Aqua aerosol products are analysed over the strongly industrialized East China area. In addition, aerosol effects on the tropospheric NO 2 AMF and the retrieval of OMI cloud parameters are simulated. Both the observation-based and the simulation-based approach demonstrate that the retrieved cloud fraction increases with increasing Aerosol Optical Thickness (AOT), but the magnitude of this increase depends on the aerosol properties and surface albedo. This increase is induced by the additional scattering effects of aerosols which enhance the scene brightness. The decreasing effective cloud pressure with increasing AOT primarily represents the shielding effects of the O 2 − O 2 column located below the aerosol layers. The study cases show that the aerosol correction based on the implemented OMI cloud model results in biases between − 20 and − 40% for the DOMINO tropospheric NO 2 product in cases of high aerosol pollution (AOT ≥ 0 . 6) at elevated altitude. These biases result from a combination of the cloud model error, used in the presence of aerosols, and the limitations of the current OMI cloud Look-Up-Table (LUT). A new LUT with a higher sampling must be designed to remove the complex behaviour between these biases and AOT. In contrast, when aerosols are relatively close to the surface or mixed with NO 2 , aerosol correction based on the cloud model results in an overestimation of the DOMINO tropospheric NO 2 column, between 10 and 20%. These numbers are in line with comparison studies between ground-based and OMI tropospheric NO 2 measurements in the presence of high aerosol pollution and particles located at higher altitudes. This highlights the need to imple-ment an improved aerosol correction in the computation of tropospheric NO 2 AMFs.

Abstract. The Ozone Monitoring Instrument (OMI) has provided daily global measurements of tropospheric NO 2 for more than a decade. Numerous studies have drawn attention to the complexities related to measurements of tropospheric NO 2 in the presence of aerosols. Fine particles affect the OMI spectral measurements and the length of the average light path followed by the photons. However, they are not explicitly taken into account in the current operational OMI tropospheric NO 2 retrieval chain (DOMINO -Derivation of OMI tropospheric NO 2 ) product. Instead, the operational OMI O 2 −O 2 cloud retrieval algorithm is applied both to cloudy and to cloud-free scenes (i.e. clear sky) dominated by the presence of aerosols. This paper describes in detail the complex interplay between the spectral effects of aerosols in the satellite observation and the associated response of the OMI O 2 −O 2 cloud retrieval algorithm. Then, it evaluates the impact on the accuracy of the tropospheric NO 2 retrievals through the computed Air Mass Factor (AMF) with a focus on cloud-free scenes. For that purpose, collocated OMI NO 2 and MODIS (Moderate Resolution Imaging Spectroradiometer) Aqua aerosol products are analysed over the strongly industrialized East China area. In addition, aerosol effects on the tropospheric NO 2 AMF and the retrieval of OMI cloud parameters are simulated. Both the observationbased and the simulation-based approach demonstrate that the retrieved cloud fraction increases with increasing Aerosol Optical Thickness (AOT), but the magnitude of this increase depends on the aerosol properties and surface albedo. This increase is induced by the additional scattering effects of aerosols which enhance the scene brightness. The decreasing effective cloud pressure with increasing AOT primarily represents the shielding effects of the O 2 −O 2 column located below the aerosol layers. The study cases show that the aerosol correction based on the implemented OMI cloud model results in biases between −20 and −40 % for the DOMINO tropospheric NO 2 product in cases of high aerosol pollution (AOT ≥ 0.6) at elevated altitude. These biases result from a combination of the cloud model error, used in the presence of aerosols, and the limitations of the current OMI cloud Look-Up- Table (LUT). A new LUT with a higher sampling must be designed to remove the complex behaviour between these biases and AOT. In contrast, when aerosols are relatively close to the surface or mixed with NO 2 , aerosol correction based on the cloud model results in an overestimation of the DOMINO tropospheric NO 2 column, between 10 and 20 %. These numbers are in line with comparison studies between ground-based and OMI tropospheric NO 2 measurements in the presence of high aerosol pollution and particles located at higher altitudes. This highlights the need to implement an improved aerosol correction in the computation of tropospheric NO 2 AMFs. important reasons to improve our knowledge of the global distributions of NO x are (1) exposure to nitrogen dioxide leads to adverse health impacts; (2) the chemical budget of tropospheric ozone, also toxic for humans and the vegetation, is largely determined by the concentration of NO x (Jacob et al., 2006); (3) nitrogen oxides are the precursors of (ammonium) nitrate, an important component of particulate matter, and contribute to acidification and eutrophication of soils and surface waters; and (4) nitrogen oxides affect the global climate indirectly by affecting OH, and therefore modifying the residence time of the greenhouse gases O 3 and CH 4 (Shindell et al., 2009).
In 2004, the Dutch-Finnish Ozone Monitoring Instrument (OMI) (Levelt et al., 2006) was launched on the NASA EOS-Aura (National Aeronautics and Space Administration Earth Observing System) satellite. OMI is a nadir-viewing imaging spectrometer that provides with daily global coverage of key air quality components. The retrieval technique of the OMI tropospheric NO 2 Vertical Column Density (VCD) (Boersma et al., 2004) is common to all the other similar satellite missions Bovensmann et al., 1999). The backscattered solar radiation is captured in daylight in the visible spectral domain by the instrument at the Top Of the Atmosphere (TOA) and then processed through the Differential Optical Absorption Spectroscopy (DOAS) retrieval approach. The DOAS method is based on radiative transfer modelling of tropospheric NO 2 Air Mass Factor (AMF). The associated assumptions play a crucial role in the accuracy of the tropospheric NO 2 VCD.
The DOMINO (Derivation of OMI tropospheric NO 2 )  product contains worldwide concentrations of NO 2 in the troposphere derived from OMI. This product is used by a large number of air quality studies (e.g. Curier et al., 2014;Reuter et al., 2014;Ding et al., 2015). The computation of tropospheric NO 2 AMF is acknowledged as the dominant source of errors in the retrieved tropospheric NO 2 column over polluted areas (Boersma et al., 2007) with important consequences for emission constraints and other applications. The overall uncertainty of the latest version of individual retrieved DOMINO tropospheric NO 2 vertical column densities is estimated to be 1.0 × 10 15 molecules cm −2 ±25 % . This evaluation takes into account the slant column precision, between 0.7 and 1.1 × 10 15 molecules cm −2 (Boersma et al., 2007;Bucsela et al., 2006), and the uncertainty of tropospheric NO 2 AMF 10 − 40 % (depending on the impact of different parameters) (Boersma et al., 2007). Comparisons with in situ measurements from aircraft, ground-based observations from Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) and Pandora instruments has revealed that OMI tropospheric NO 2 retrievals generally agree within ±20 % (Lamsal et al., 2014). Several studies that investigated the accuracy of the DOMINO products over rural and urban areas in Russia, Asia, and Indonesia, by using different long-term network observations based on MAX-DOAS (Shaiganfar et al., 2011;Ma et al., 2013;Kanaya et al., 2014), found a negative bias between 26 and 50 % in urban and very polluted areas and when the Aerosol Optical Thickness (AOT) is high. These underestimations have been recently confirmed over Wuxi city, an area with high pollution adjoining Shanghai (Wang et al., 2015b). These low biases could be partially attributed to the inhomogeneity of NO 2 at the spatial scale of OMI observation, and incomplete accounting of NO 2 near the surface. However, the possible additional effects caused by aerosols cannot be ignored. Over industrial regions with comparable photochemical regimes, NO 2 and aerosol concentrations are very well correlated showing similar anthropogenic sources between aerosols and short-lived trace gases .
The current version of the DOMINO algorithm does not explicitly account for the aerosol effects on the tropospheric NO 2 AMF. Similarly, these effects are not explicitly considered in most of the other UV-Vis (ultraviolet-visible) satellite measurements (Valks et al., 2011). Martin et al. (2003) retrieved tropospheric NO 2 columns from the Global Ozone Monitoring Experiment (GOME) instrument by accounting for spatial and temporal variability of aerosols from monthly mean fields of aerosol mass concentration over 1 year simulated by the Global Ozone Chemistry Aerosol Radiation and Transport (GOCART) model. Aerosols affect the topof-atmosphere (TOA) radiances in the visible and O 2 −O 2 spectral bands Leitão et al., 2010) and the light path distribution -i.e. the distribution of distances travelled by photons in the atmosphere before leaving the atmosphere. Since the impacts of aerosols on the computation of tropospheric NO 2 AMF is a function of aerosol properties (Martin et al., 2003), NO 2 , and aerosol vertical distribution (Leitão et al., 2010;Bousserez , 2014), a proper characterization of aerosols' impact on the retrieval is then needed to accurately quantify trace gas amounts from satellite observations. The OMI cloud algorithm (Acarreta et al., 2004) derives the cloud fraction and cloud pressure from the O 2 −O 2 absorption in the spectral window between 460 and 490 nm. This cloud retrieval algorithm is applied both to cloudy and cloud-free scenes with aerosols. In other words, aerosols are treated as clouds. The correction for the aerosol impact cannot be simply separated from the effects of clouds and, if a cloud retrieval scheme is applied, it will account for a large part of the aerosol effect by retrieving modified cloud fraction and pressure (Boersma et al., 2004. Wang et al. (2015a) show that OMI cloud parameters are indeed perturbed in the presence of aerosols, by comparing with classified sky conditions using MAX-DOAS observations. Therefore, the cloud retrievals apply an implicit correction of aerosol presence in the computation of the tropospheric NO 2 . Recent studies reprocessed the OMI tropospheric NO 2 product, explicitly taking into account aerosols instead of effective cloud retrievals, either by considering model outputs or observations (Lin et al., 2014(Lin et al., , 2015Kuhlmann et al., 2015;Castellanos et al., 2015). These studies were performed over Atmos. Meas. Tech., 9, 359-382, 2016 www.atmos-meas-tech.net/9/359/2016/ urban areas in China or biomass-burning events in South America. Resulting changes mostly occurred in the case of high aerosol pollution (AOT > 0.8) with increased or decreased tropospheric NO 2 VCDs depending on the geophysical conditions and aerosol properties. All these studies considered the magnitude of the explicit aerosol correction on the computation of tropospheric NO 2 AMFs and highlighted that aerosol properties and distribution and OMI cloud retrievals are connected. Nonetheless, there is still not a comprehensive understanding of the interplay between aerosol effects on the observations and the associated response of the operational OMI cloud retrieval algorithm. Moreover, the dependence of the retrieved cloud parameters and the associated implicit aerosol correction to the geophysical conditions and the aerosol properties and distribution are not clear. The need to further investigate and understand the interplay between all these variables have been highlighted in different studies (Leitão et al., 2010;Lin et al., 2014). This has recently been emphasized in Castellanos et al. (2015) for the analyses of the implicit aerosol corrections in the case of biomass-burning aerosols. This paper aims to analyse how aerosols affect the current operational OMI cloud products and the derived tropospheric NO 2 AMFs. For that purpose, this study uses a model vs. observation approach focused on large industrialized areas in China. This work focuses on cloud-free scenes but dominated by aerosol pollution. The paper starts with a description of the expected aerosol net effects on the tropospheric NO 2 AMFs, based on simulations in Sect. 2. The importance of aerosols and NO 2 vertical profiles is highlighted. In Sect. 3, the OMI DOMINO v2 and collocated MODIS (Moderate Resolution Imaging Spectroradiometer) aerosol products are compared over a large industrial area in China. This provides insight into the behaviour of OMI cloud fraction and pressure, and tropospheric NO 2 AMFs in the presence of aerosols. We then evaluate the response of the DOAS O 2 −O 2 cloud algorithm on aerosol cases, as achieved by the operational OMI algorithm. The interplay between aerosol effects and the DOAS O 2 −O 2 cloud retrieval can be characterized. Finally, in Sect. 4, we show how an implicit aerosol correction is applied in the OMI retrieval chain through the Lambertian cloud model and evaluate its accuracy by comparing it to the explicit aerosol corrections simulated in Sect. 2.
2 Impact of aerosols on the tropospheric NO 2 AMF

Computation of the tropospheric NO 2 AMF
A two-step approach is used to determine the NO 2 VCD. First, the DOAS method (Platt and Stutz, 2008), based on the basic principle of absorption spectroscopy and the Beer-Lambert law, is applied to the measured spectra within 405-465 nm in order to derive a NO 2 Slant Column Density (SCD). This column gives the number of NO 2 molecules per cm 2 , integrated along the average light path. Then, the NO 2 SCD is converted into NO 2 VCD. This can be done by application of the AMF calculated with a radiative transfer model. Note that an intermediate step is to remove the stratospheric part in the NO 2 SCD part in order to derive the tropospheric SCD component. In the DOMINO product the stratospheric SCD is derived from measurements over remote regions that are assimilated into a transport-chemistry model for the stratosphere . The AMF A is defined as the ratio of the atmospheric SCD and VCD : where N s is the NO 2 SCD and N v is the NO 2 VCD. The computation of A( ) requires accurate knowledge concerning all the parameters affecting the optical properties of the atmosphere and then impacting the length of the average light path followed by the backscattered sunlight. The list of variables describing these conditions is summarized by and is detailed in Table 1.
The concept of altitude-resolved AMF was introduced by Wagner et al. (2007), Rozanov et al. (2010), and Richter et al. (2011). Also named block air mass factor or BAMF in other studies, it makes it possible to generalize this definition by computing the AMF variable at discrete atmospheric layers, as which describes the altitude dependence of A. The BAMF gives the change in the NO 2 SCD for a change in the vertical column density at one atmospheric layer p (Wagner et al., 2007;Platt and Stutz, 2008;Rozanov et al., 2010;Richter et al., 2011). The a is the altitude-resolved AMF at atmospheric pressure p. The n(p = p * ) refers to a change in the trace gas profile n at pressure level p * . N v and N s denote the resulting changes in VCD and SCD respectively. Currently only cloud parameters (and no aerosol parameters) are considered when computing a(p) in the DOMINO product: cloud (radiance) fraction and cloud pressure. A is then computed by weighting a(p) with the atmospheric vertical distribution of the trace gas profile: where n(p) is the vertical distribution of trace gas density, p top is the pressure at the top of the atmosphere, and p 0 is the surface pressure. In this paper, we define A tr as tropospheric NO 2 AMF, which can be calculated from Eq. (3) by integrating a vertical profile n(p) up to tropopause pressure.  Boersma et al. (2007) evaluated that an uncertainty of 0.05 on the cloud fraction and 60 hPa on the cloud pressure respectively contribute up to 30 and 15 % to the (relative) tropospheric NO 2 AMF. While inter-comparison studies show relative good agreements for the OMI cloud fractions Sneep et al., 2008) over cloudy scenes, the retrievals can be affected by aerosols. Thus, the degree of certainty is here evaluated between low (clear and cloudy scenes) and moderate (cloudy scenes). See Sect. 3 for further details. b Section 2 shows that the AOT and aerosol altitude are the key parameters when computing the tropospheric NO 2 AMF. Aerosols impact several parameters (e.g. surface albedo, cloud) in addition to the tropospheric NO 2 AMF. c Maasakers et al. (2013) and Lamsal et al. (2014) showed that using the high-resolution a priori NO 2 profiles impacts the OMI tropospheric NO 2 columns between −43 and 22 %. Aircraft and in situ measurements reveal that NO 2 profile shapes exhibit considerable day-to-day variation, such that the use of a monthly mean profile can cause significant errors in individual retrievals.
The ratio of the altitude-resolved AMF a(p) to the total AMF A (deduced from the NO 2 shape profile) gives the averaging kernel, i.e. the sensitivity of the satellite measurement to each atmospheric layer (Eskes et al., 2003;Richter et al., 2011). Therefore, A tr gives an indication of the sensitivity of the satellite measurement to the amount of NO 2 in the lowest atmospheric layers. Assuming an identical shape of the vertical NO 2 profile, a larger A tr value expresses a higher sensitivity of the measurement while a reduced A tr value indicates a decreased sensitivity. Indeed, in those cases, a change in A tr is directly associated with a change of a(p) at the atmospheric levels where the trace gas is present. The a(p) is in theory spectrally dependent, but the spectral dependence in the case of tropospheric NO 2 retrieval is very small. The reference wavelength considered in this paper is 439 nm . Note that in the case of real OMI tropospheric NO 2 retrievals, a temperature correction should be applied on the SCD. Since the temperature of the NO 2 absorption crosssection is assumed to be fixed at 221 K, a correction term is thus implemented in the computation of A such that it represents the ratio of the NO 2 SCD derived with a NO 2 crosssection 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.

Qualitative description of aerosol optical effects
Similarly to cloud particles, scattering and absorbing effects induced by the presence of aerosol particles affect the total radiance observed by the satellite sensor and the light path distribution of detected photons. The presence of aerosols leads in general to higher radiance levels captured by the satellite sensor. This increase has a spectral variability depending on the aerosol properties. Its magnitude is however smaller in cases of a very bright surface and absorbing aerosols. The change of light path distribution has consequences on the sensitivity of the remote sensing measurement to the tropospheric NO 2 amount. This sensitivity can be either increased or decreased. Qualitatively, one can distinguish two effects that aerosols/clouds can have on the NO 2 absorption signal at the TOA (Leitão et al., 2010): -Shielding effect: decreased sensitivity within and below the aerosol/cloud layers. The fraction of all detected photons coming from the top of the atmosphere that reaches the lowest part of the atmosphere (below the aerosol/cloud layer) is reduced compared to a cloud-or aerosol-free scene.
-Enhancement (albedo) effect: increased sensitivity within and above the aerosol/cloud layers. The fraction of all detected photons that sample the higher part of the atmosphere (above the aerosol/cloud layer) is in- creased, compared to a cloud-or aerosol-free scene, because more photons are scattered back towards the satellite. Figure 1 depicts an example of vertical distribution of a(p) for a cloud-free observation at 439 nm. With and without aerosols, a(p) values generally decrease close to the surface. Both shielding and enhancement effects can be seen relative to the line for τ = 0. The overall impact of aerosols on a measurement thus depends on the relative importance of the above-mentioned effects, which mainly results from the combination of aerosol optical properties (Martin et al., 2003), amounts, surface reflectance and vertical distribution of the particles, and the NO 2 gas. The geometry parameters like θ 0 (solar zenith angle or SZA) and θ (viewing zenith angle or VZA), and scattering angle (i.e. aerosol phase function) have an impact also as they modify the length of the light path.

Quantitative description of the impact of aerosols
properties, their vertical distribution, and NO 2 profile

Methodology
This section studies the direct effects of aerosols on the computation A tr without consideration of the O 2 −O 2 cloud retrieval. This study uses the Determining Instrument Specifications and Analyzing Methods for Atmospheric Retrieval (DISAMAR) software developed at Koninklijk Nederlands Meteorologisch Instituut (KNMI) (de Haan, 2011). This software package includes a radiative transfer model and can ap-ply different retrieval methods, such as direct fitting (within an optimal estimation framework) and DOAS. The radiative transfer model is based on the Doubling Adding KNMI (DAK) model (de Haan et al., 1987;Stammes et al., 2001) and thus computes the reflectance and transmittance in the atmosphere using the adding/doubling method. This method calculates the internal radiation field in the atmosphere at levels to be specified by the user and takes into account Rayleigh scattering, trace gas absorption, and aerosol and cloud scattering. Scattering by aerosols is simulated with a Henyey-Greenstein scattering phase function (cos ) (Hovenier and Hage, 1989): where is the scattering angle, and g = cos is the asymmetry parameter. In a standard case, an asymmetry parameter of g = 0.7 is used. Thus, in DISAMAR, the Ångström exponent α gives the spectral dependence of the AOT τ . In DISAMAR, a(p) is analytically determined, based on the weighting functions of the reflectances (i.e. derivatives of the reflectances to absorption cross-section and trace gas density). Indeed, a(p) for an atmospheric layer can be identified as the Jacobian of the forward model ∂F /∂n. This term is independent of the tracer distribution for optically thin absorbers. This methodology is conceptually equivalent to the approach discussed in Sect. 2.1.
The Henyey-Greenstein phase function is quite commonly used in the DOAS community for tropospheric NO 2 retrievals (Vlemmix et al., 2010;Castellanos et al., 2015) with explicit aerosol corrections. With an asymmetry parameter of g = 0.7, the Henyey-Greenstein function is known to reasonably well reproduce the Mie function. Thus, it can be used for the AMF calculation (Spada et al., 2006;Wagner et al., 2007, andP. Stammes, personal communication, 2015). Castellanos et al. (2015) found that decreasing g from 0.7 to 0.6 in DISAMAR impacts less than 5 % the tropospheric NO 2 AMF for AOT lower than 0.5. For larger AOT values, the impacts are almost negligible. It is noted that, for AOT retrievals, more realistic assumptions of the phase function should be used. However, this is not the case for an aerosol correction.
The simulations in this section are done with α of 1.5 for fine particles and 0.5 for coarse particles, asymmetry parameter 0.7 and Single Scattering Albedo (SSA) ω 0 = 0.95 and 0.9 respectively, assuming different altitudes, surface albedos 0.05 and 0.07 (surface reflectance is assumed Lambertian), SZA θ 0 = 25 • and VZA θ = 25 • . The ω 0 and τ values are considered at the reference wavelength of 550 nm.The NO 2 profiles are taken from a model run where atmospheric chemistry and transport model Tracer Model 5 (TM5) has been integrated into the global climate model EC-Earth version 2.4 (van Noije et al., 2014). We defined the tropospheric AMF aerosol factor f (τ ) as the ratio of the AMF with (A tr (τ )) and The f can be interpreted as the factor by which the tropospheric NO 2 AMF of a clear scene should be adjusted to represent aerosol effects. In practice, such a factor cannot accurately be determined as not all required information, associated with instantaneous individual measurement, are available. Similarly to the DOMINO product, A tr is computed at 439 nm.  Figure 3 demonstrates that f lies in the range between 0.7 and 1.3. The total effect of aerosols (shielding or enhancement) strongly depends on the location of the particles in the atmospheric layers, and results from the computed a(p) depicted in Fig. 2. Scattering of aerosols enhances the tropospheric NO 2 A up to 30 % for τ = 1.0 when they are located within or below the NO 2 bulk (between the surface and 900 hPa). When a given amount is lifted to higher altitudes, aerosols thus apply a shielding effect (i.e. reduced sensitivity to the tropospheric NO 2 amount) up to 30 %. The variability of the NO 2 vertical distribution impacts the magnitude of these effects, around 10 % for τ = 1.

Results
In addition to the vertical distribution of the aerosol particles, the shape of the vertical NO 2 profile also significantly affects the magnitude of f . In winter (e.g. January in Fig. 1), such profile shows higher absolute values of concentrations near the surface with a higher variability. Moreover, the profile shape (obtained after normalization to the integrated vertical profile along the atmospheric layers) depicts a small difference with a higher dynamic between the surface and the atmosphere layer at 900 hPa. Figure 4a shows amplified enhancement effects (up to 40 % for aerosols between the surface and 950 hPa) and amplified shielding effects (up to 45 % for aerosols at very high altitude, between 600 and 700 hPa). The transition between a net shielding or enhancement effect is also closer to the surface compared to summer (close to 950 hPa) as the aerosols are well mixed with the tropospheric NO 2 bulk only below 950 hPa. The variability of the NO 2 profile, mostly in the tropospheric layers, have a larger impact in January, where the error bars indicate a variability of around 20 % for τ = 1.0. The altitudes of tropospheric NO 2 and aerosols, and so the relative altitude between both, are thus the key drivers of f .
Other parameters also contribute to the magnitude of this factor: -An increase of surface albedo (see Fig. 3b), from 0.05 to 0.07, reduces the enhancement effect by 10 % and enhances the shielding effect by less than 5 % for τ = 1.0.
-The size of particles specified through α has little impact on the factor (see Fig. 5a). Decreasing α from 1.5 (fine particles) to 0.5 (coarse particles) reduces the shielding and enhancement effects by between 2 and 5 % for τ = 1.0.
-A change of ω 0 from 0.95 to 0.9 (see Fig. 5b) leads to a reduction of the enhancement effect by 10 % (when aerosols are located below or well mixed with the tropospheric NO 2 bulk). The shielding effect is increased by 5 %.
-The increase of θ 0 from 25 to 50 • (typically Winter average over China), increases the shielding effects by 10 % for τ = 1.0 (assuming NO 2 profiles in January). Moreover, the enhancement effect increases between 5 and 10 % for τ between 0.3 and 0.7.
-The monthly variability of the NO 2 profiles increases the variability of f , expressed by the error bars in Fig. 3, when aerosols are located close to the surface between 900 and 1000 hPa. This is a direct consequence of the enhancement effect induced by aerosol particles that increase the sensitivity to the NO 2 in the lower part of the atmosphere.
Our results are consistent with previous findings by Leitão et al. (2010) and Bousserez (2014) who used different theoretical NO 2 and aerosol vertical distributions and optical properties. In particular, our present exercise considered various NO 2 profiles, as given by the TM5 model, representative of 2 distinctive months (July and January), and thus of 2 typical seasons, over urban areas in China. Moreover, the monthly variability of these profiles, and thus their impacts on the tropospheric NO 2 AMF variability, are investigated as a function of aerosol properties and vertical profile giving then complementary insights about explicit aerosol effects. These results are also in line with the work of Martin et al. (2003) where strongly absorbing aerosols reduced the AMF by 40 % (over biomass-burning regions) while scattering sulfate and organic aerosols increased the AMF by 5-10 %.  pressure based on the OMI O 2 −O 2 spectral band. This section is structured as follows: first the OMI DOMINO product is analysed in comparison with the MODIS Aqua aerosol product. Then, the OMI DOAS cloud O 2 −O 2 retrieval chain is analysed with simulated aerosol cases.

Comparison of OMI DOMINO-v2 with MODIS Aqua aerosol product
MODIS on-board EOS-Aqua observes the Earth's atmosphere approximately 15 min prior to OMI on-board EOS-Aura. The aerosol effects on the current OMI tropospheric NO 2 retrievals are investigated by comparing collocated OMI DOMINO with MODIS Aqua Level 2 (L2) aerosol products over large industrialized areas in China. Statistics are computed over 3 years (2005)(2006)(2007) and 2 seasons: summer (June, July and August) and winter (December, January and February). MODIS L2 aerosol products have a spatial resolution of 10 km × 10 km, therefore close to the OMI spatial resolution (13 km × 24 km at nadir). The OMI and MODIS data are paired on a pixel-by-pixel basis if the distance between pixel centres is less than 5 km and if both observations are acquired within 15 min. Observations with a cloud fraction (OMI and MODIS) higher than 0.1 are filtered out. This threshold is applied to both OMI and MODIS, although the parameters are not identical. Applying such a threshold on the observations increases the probability of identifying cloud-free scenes. Moreover, the availability of the MODIS aerosol product is a good confirmation of the identification of cloud-free scenes as MODIS Aqua AOTs τ are exclusively retrieved for cloud-free situations (Remer et al., 2008). However, it is well recognized, according to the analyses in the next section, that cloud-free observations with large presence of aerosols are filtered out as well. Tests were performed with higher cloud fraction thresholds ( The tropospheric NO 2 AMF (A) that is extracted from the OMI DOMINO database shows a decreasing trend with increasing τ in summer (see Fig. 6a). This decrease is on average 5 % for MODIS τ = 1, with a variability of 20 %. A small local positive trend (around 5 %) is however noticed for τ = 0-0.2. In contrast, in winter, there is on average no modification of the tropospheric NO 2 AMF A with increasing τ (see Fig. 6b). By making use of the Ångström coefficient α available in MODIS AQUA data (see Fig. 6c), it is found that A is larger for coarse particles than for fine particles (differences of 10 %). Such statistics also include spatial variability in τ and NO 2 , so that the apparent correlations between them may be affected by other spatial factors like surface albedo or elevation. Figures 7-9 depict the impact of aerosols on the OMI O 2 −O 2 cloud fraction and pressure. Under aerosol presence and no cloud contamination in the OMI measurement, the OMI cloud fraction shows a clear linear relation with respect to τ . On average, values increase from 0.01 to 0.07 with a variability of 30 % for τ = 1. The magnitude of this increase depends on the surface albedo (Kleipool et al., 2008) and MODIS Aqua aerosol properties: -The increase of cloud fraction with increasing AOT is higher over dark surfaces and lower over bright surfaces (average differences of 0.03 for τ = 1, between OMI surface albedos of 0.04 and 0.08; see Fig. 8). As analysed in detail in Sect. 3.3.1., this is a direct con-sequence of the aerosol effects on the continuum reflectance. The attenuation of surface reflectance by particles is stronger over bright surfaces than over dark surfaces. Over a brighter surface, aerosols play the role of a surface layer with a higher albedo as they increase the scene brightness. As a consequence, the retrieved effective cloud fraction value is higher. The cloud pressure values show a non-linear decrease from approximately 800 to 600 hPa for τ = 1, with a variability of around 100 hPa during summer (see Figs. 8 and 9). However, no decrease is observed during winter. The cloud pressure stays close to the surface (between 900 and 1000 hPa). The retrieved cloud pressure seems to have some sensitivity to the surface and aerosol properties. In particular, it decreases more over dark surfaces (difference of 100 hPa between surface albedo 0.04 and 0.07 for τ = 1) and in the presence of fine particles.
This section follows previous studies Lin et al., 2014;Castellanos et al., 2015) by analysing the OMI cloud and AMF parameters as present in the DOMINO product over scenes dominated by aerosols. It confirms that the cloud parameters respond to the presence of aerosols. The magnitude of this response is not only a function of aerosol properties but also of the atmospheric and sur-  face properties that impact the average light path (e.g. surface albedo). One may conclude that there is an implicit correction for the presence of aerosols in the tropospheric NO 2 retrieval chain since the OMI cloud algorithm cannot distinguish cloud and aerosol particles and retrieve effective cloud parameters. The computation of the tropospheric NO 2 AMF relies on the NO 2 vertical shape profile and aerosol properties (that drive the OMI cloud retrievals). Both parameters have different characteristics depending on the season. As a consequence, the implicit correction seems to show two different behaviours depending on the seasons. On average, this correction applies a shielding effect in summer: i.e. the measurements are assumed to have less sensitivity to tropospheric NO 2 in the presence of aerosols. In winter, this correction on average does not vary with increasing AOT values.

Inverse cloud model
In the context of trace gas measurements from space, the purpose of a cloud model is to describe the clouds in a way that reproduces the reflectance spectrum, and thus the distribution of photon paths, within the cloudy scenes. cloud optical thickness, cloud top altitude, and cloud vertical extent. However, instruments like OMI have limited spatial resolution (13 km × 24 km at nadir view) and do not resolve individual clouds. Therefore, cloud fraction and cloud optical thickness cannot be separated. Furthermore, OMI cannot give information on cloud microphysical properties such as cloud phase, cloud particle shape and size, and cloud vertical structure.
Because clouds are a correction step in trace gas retrievals, both the cloud retrieval algorithm and the cloud correction algorithm have to use the same cloud model. As a consequence, a simple model is used in the OMI tropospheric NO 2 retrievals, describing a cloud as a Lambertian reflector with a fixed albedo through which no light is transmitted. The associated effective cloud fraction is thus not a geometric cloud fraction but the radiometrically equivalent cloud fraction which, in combination with the assumed cloud albedo, yields a TOA reflectance that agrees with the observed reflectance. While scattering clouds have two main optical properties in the UV-Vis (namely reflection and transmission -their absorption being negligible), a Lambertian reflector has only reflection properties, determined by the cloud albedo, and no transmission properties. The OMI cloud retrieval algorithm assumes a cloud albedo of 0.8 . This value has been found suitable to correct NO 2 and O 3 retrievals for partially cloudy scenes. The missing transmission of optically thin and medium thick clouds in the Lambertian cloud model is compensated for by the cloud-free part of the pixel.
Based on the properties of an opaque Lambertian cloud model, the effective cloud fraction is mainly constrained by the brightness of the cloud and how much a brighter cloud would outshine the observation scene. The effective cloud pressure is mainly constrained by the perturbation of the clouds on the O 2 −O 2 collision complex absorption. A cloud located at high altitude shields the O 2 −O 2 complexes that are below the cloud. As a consequence, the O 2 −O 2 absorption signal, and so the associated slant column density, are attenuated (Acarreta et al., 2004;Stammes et al., 2008;Sneep et al., 2008).

Description of the O 2 −O 2 DOAS retrieval algorithm
The OMI cloud retrieval chain (Acarreta et al., 2004) exploits the 460-490 nm absorption band of O 2 −O 2 , a collision pair of oxygen. The retrieval algorithm is based on the DOAS method and consists of two steps. In the first step, the absorption cross-section spectrum of O 2 −O 2 is fitted together with a first-order polynomial to the negative logarithm of the measured reflectance spectrum. The window of the spectral fit is 460-490 nm. This step can be summarized as follows: where γ 1 + γ 2 · λ defines the first-order polynomial, In the absence of absorbers, one may define the continuum reflectance R c at the reference wavelength λ 0 : The reference wavelength is fixed at the middle of the DOAS fit window at λ 0 = 475 nm.
In the second step, a Look-Up- Table (LUT) is used to convert the retrieved N s O 2 −O 2 and R c into the cloud pressure C p and cloud fraction C f . This inversion step requires prior information about surface albedo, surface altitude, and geometry angles (θ 0 , θ and the relative azimuth angle φ − φ 0 ).

OMI cloud algorithm applied to aerosol scenes
To test the sensitivity to aerosols, the current version of the OMI DOAS O 2 −O 2 algorithm was applied to simulated spectra for scenes dominated by aerosols. The implementation was performed in such a way that it is almost identical to the operational DOMINO chain at KNMI. The effective cloud fraction and cloud pressure parameters are derived following Eqs. (6) and (7) and through linear interpolation in the LUT, assuming thus an opaque Lambertian cloud model as described previously. Reflectance spectra are simulated by including only aerosol particles with the DISAMAR software. No clouds are included in the simulated reflectances. The sensitivity of the retrievals are investigated as a function of surface albedo, aerosol properties (α, ω 0 , vertical distribution), θ 0 , and θ . Simulated reflectances are noise-free. All the parameters (including surface albedo) are identical in the simulated spectra dominated by aerosols and the retrieval of effective cloud parameters. Figure 10a shows that the effective cloud fraction increases with increasing τ in cloud-free scenes up to 0.09 for τ = 1.0 at the wavelength of 550 nm, assuming fine particles (α = 1.5), high single scattering albedo (ω 0 = 0.95), θ 0 = 25 • (summer in China), and θ = 25 • . Here, aerosols are located between 700 and 800 hPa in the atmosphere (between approximately 2 and 3 km). Similarly to what has been observed in the DOMINO product, the increase of the effective cloud fraction, in the presence of aerosols, is linear and higher with lower surface albedo (i.e. over dark surfaces). In this case, with a surface albedo of 0.07, the effective cloud fraction stays below 0.09 for τ = 1.0 while, with a surface albedo of 0.03, the value is close to 0.1. Such an increase is consistent with the impact of the aerosol particles on the continuum reflectance as a function of τ and surface albedo. For these surface albedos and aerosol properties, the scattering effects of aerosols dominate over their extinction. Figure 10b and c illustrate that aerosol properties (size and absorption) drive the magnitude of the increase of effective cloud fraction. Notably, low α and ω 0 values have smaller impact on the increase of the effective cloud fractions. This illustrates the reduction of scattering effects of aerosols under these conditions. Indeed, low ω 0 values increase the probability of absorption of the photons and so reduce the scattering within the layers and towards the satellite sensor. Coarse particles reduce also the scattering effects by increasing the probability of forward scattering of the pho-tons towards the top of the atmosphere or towards the surface. With fine particles, the effective cloud fraction varies between 0.06 (ω 0 = 0.9) and more than 0.1 (ω 0 = 0.97) for τ = 1.0.

Response of the cloud fraction to aerosol scenes
As a consequence, a higher cloud fraction is understood from the excess TOA reflectance caused by the additional scattering due to aerosols and the impact of the surface reflection. This represents the significant enhanced brightness of the scene (or enhanced scene albedo). Figure 11 shows that the retrieved effective cloud pressure decreases with increasing τ (or AOT). This decrease is linked to the O 2 −O 2 shielding effect which strongly depends on τ . The O 2 −O 2 absorption, below the optically thicker aerosol layer, is reduced since a high amount of particles decreases the fraction of photons reaching the lowest part of the atmosphere and increases the attenuation of the surface reflectance signal. Therefore, the length of the average light path is shortened. At high τ values, the retrieved cloud pressure correlates with the aerosol layer height. Overall, the values are close to or smaller than the mean aerosol layer height which may be caused by the model error (i.e. difference between the cloud model and the aerosol spectral effects). Surprisingly, at small τ values, the mean aerosol layer height has no effect on the retrieved cloud pressure. The retrieved values stay very close to the surface pressure.

Response of the cloud pressure to aerosol scenes
The OMI cloud LUT has been intended for representing the cloud spectral effects and not those of thin aerosol layers. Thus, the sampling may be not high enough in the case of low cloud fraction values (i.e. smaller than 0.1). Such values have limited effects on the average light path and the actual designed LUT is not sensitive enough to small changes on the O 2 −O 2 absorption (Acarreta et al., 2004). Since low amounts of aerosol have little effect on the O 2 −O 2 SCD and the continuum reflectance, the overestimation of the retrieved cloud pressure, in those cases, may be caused by the coarse sampling of the employed LUT. When τ increases, the considered entry in the LUT moves from this undetermined regime to a regime where meaningful cloud pressure value can be interpreted. This can be seen in Fig. 10a-c where the transition between both regimes is located between τ = 0.6 and τ = 0.8, assuming θ 0 = 25 • and θ = 25 • . This demonstrates a non-linear behaviour between the cloud pressure retrieval and the AOT. Such behaviour is consistent with the analyses of Boersma et al. (2011), over southern and eastern USA, which show that reduced OMI O 2 −O 2 cloud pressure values are observed only with high AOTs. Wang et al. (2015a) found that in general the effective cloud fraction of up to 15 % and cloud top pressure from the surface to 900 hPa from OMI are assigned to the condition of "clear sky with presence of aerosol particles".
The value of τ at which the retrieved cloud pressure starts being sensitive to the aerosol layer height mainly depends Atmos. Meas. Tech., 9, 359-382, 2016 www.atmos-meas-tech.net/9/359/2016/  on the geometry. Figure 12 shows that for larger θ 0 and θ values (i.e. more than 25 • ), this transition triggers at smaller τ values (around τ = 0.4). This can be understood as an increased average path length travelled by the photons in the atmosphere and higher retrieved effective cloud fraction values (up to 0.15). Note that change of relative azimuth angle may have similar effects. The effects of aerosol microphysics properties on the effective cloud pressure retrieval mainly depend on the aerosol amount and the geometry. While smaller α and ω 0 values lead to smaller O 2 −O 2 SCDs (see Fig. 10b and c), the associated effective cloud pressure only decreases: for τ well above 1 in the case of small angles (θ 0 = 25 • and θ = 25 • ); or between τ = 0.6 and τ = 1 in the case of large angles (θ 0 = 50 • , or θ = 45 • ). Finally, cases with high surface albedo show smaller retrieved effective cloud pressure. The brighter the surface, the more the average photon path length is reduced by a thin aerosol layer. This also highlights that a bias on the assumed surface albedo can perturb the effective cloud pressure retrieval in cases of high aerosol amount. For in-stance, an overestimated surface albedo (because of scattering aerosol affects) can lead to reduced effective cloud pressure.

General inter-comparison of cloud and aerosol impacts on the O 2 −O 2 spectral band
The previous analyses clearly show the limitation of the response of the current OMI cloud algorithm, in particular the effective cloud pressure retrieval, due to the not-optimized OMI cloud LUT over clear-sky scenes dominated by aerosol particles. The use of a LUT cannot be avoided since it is required to convert the continuum reflectance and the O 2 −O 2 SCD into effective cloud parameters. Since different LUTs may give different results, the following exercise (summarized in Fig. 13) illustrates in a general way how aerosols and OMI effective cloud retrievals should be connected. O 2 −O 2 spectra (from 460 to 490 nm) were simulated containing either an opaque Lambertian cloud (albedo = 0.8) assuming different cloud fraction and pressure values, or box fine and scattering aerosol layers with different AOT and aerosol pressure values (see list of values in Table 2). A very high sampling in the simulation nodes (i.e. cloud fraction, cloud pressure, AOT, and aerosol pressure values) is considered. Then a DOAS fit is achieved as described in Sect. 3.3.2. Finally, a linear interpolation/extrapolation, based on the radial basis function, is performed in order to have a global overview of the variation of the simulation nodes as a function of the DOAS fit variables. The accuracy of the linear interpolation/extrapolation is here ensured thanks to the very high sampling of the simulation nodes. As expected, Fig. 13 confirms that the effective cloud fraction is primarily constrained by the continuum reflectance, while the O 2 −O 2 SCD mainly drives the effective cloud pressure. Similarly, following the previous analyses, AOT mostly impacts the continuum reflectance while the aerosol altitude (or aerosol pressure) mostly results in a change of O 2 −O 2 SCD. Furthermore, in the case of low-continuum reflectance (below than 0.2), which corresponds to aerosol cases and low effective cloud fraction, some correlations are observed between both DOAS fit variables.
Therefore, in the case of an ideal O 2 −O 2 cloud retrieval (i.e. without the specific limitation of the current employed OMI cloud LUT), the following is expected: -For a given aerosol altitude value, increasing AOT should result in a larger continuum reflectance and thus increase the effective cloud fraction; -For a given AOT value, increasing the aerosol altitude (or decreasing pressure) should result in smaller O 2 −O 2 SCD and thus decrease the effective cloud pressure; -Since increasing AOT primarily impacts the continuum reflectance but also simultaneously impacts the O 2 −O 2 SCD, retrieved effective cloud pressure could theoretically either increase, decrease or stay constant depending on the aerosol altitude. This demonstrates that the magnitude of the O 2 −O 2 shielding effect by aerosols is a combination of aerosol amount and altitude.
The high sampling of simulation nodes in Fig. 13 shows that the variation of effective cloud pressure, in the case of low-continuum reflectance, has very small impact on the O 2 −O 2 SCD. However, it is theoretically still possible to retrieve small values (not only values close to the surface). Low sampling of simulations would result in inaccuracy of the interpolation/extrapolation. This is why the current OMI cloud LUT only exhibits high effective cloud pressure values, i.e. close to the surface pressure.

Tropospheric NO 2 AMF factor based on effective cloud parameters
The behaviour of the OMI cloud algorithms in response to aerosols, as analysed in Sect. 3.3, has consequences on the computation of the tropospheric NO 2 AMF. Indeed, as effective cloud parameters are sensitive to the presence of aerosols, their properties, and their location in the atmosphere, they apply an implicit aerosol correction as observed in the DOMINO product (Sect. 2). This implicit aerosol correction is obtained through the altitude-resolved AMF a( , p) which uses the retrieved effective cloud fraction and cloud pressure, that are impacted by the presence of aerosols, and no explicit aerosol information. This differs from an explicit aerosol correction in which explicit aerosol parameters would be used. Similarly to Fig. 3, Fig. 14 depicts the resulting tropospheric NO 2 AMF factor f following Eq. (5) at 439 nm, based this time on effective cloud parameters: i.e. the computation of A tr is not based on τ and other aerosol properties, but on effective cloud fraction values between 0. and 0.1 and different cloud pressures. The denominator of f corresponds here to cloud-free cases (i.e. effective cloud fraction = 0). Two surface albedo values are considered (0.05 and 0.07), θ 0 = 25 • , θ = 25 • and NO 2 profiles from TM5 in July at 12:00 p.m. (see Fig. 1). In the case of strong aerosol contamination (i.e. effective cloud fraction = 0.1), the implicit aerosol factor lies in the range of 1.15-0.6: i.e. 15 % enhanced sensitivity if the cloud is retrieved close to the surface and likely well mixed (even below) the tropospheric NO 2 bulk; 40 % reduced sensitivity if the cloud is retrieved at elevated altitude. In cases of high τ values, the decrease of effective cloud pressure has more impact on the magnitude of f than the increase of cloud fraction. Indeed, an increase of effective cloud fraction from 0.08 to 0.1 has an impact of less than 10 %. At the same time, a change of cloud pressure from 900 to 700 hPa can induce a change of 20 % in the AMF factor.
Finally, the variability of the NO 2 profiles causes a higher variability of f , between 10 and 15 %, for cloud pressures between the surface and 700 hPa. It is highly reduced for very high clouds (i.e. cloud pressure between 300 and 500 hpa). This reduction is caused by the absence of scattering properties in the inverse cloud model which results in an almost complete mask of the tropospheric NO 2 bulk below the supposed cloud layer. This is contrary to f based on explicit aerosol properties, where even particles with strong shielding effects show a non-negligible sensitivity to the variability of tropospheric NO 2 vertical shape.
Following the sensitivity analyses of the O 2 −O 2 cloud retrieval algorithm, the behaviour of tropospheric NO 2 AMFs observed in the DOMINO products, over China, can be un-Atmos. Meas. Tech., 9, 359-382, 2016 www.atmos-meas-tech.net/9/359/2016/ derstood as follows: on average, a decrease of tropospheric NO 2 AMF in summer with increasing AOT is caused by the simultaneous increase of effective cloud fraction and decrease of effective cloud pressure. Qualitatively, this behaviour is in line with the expected aerosol shielding effect on tropospheric NO 2 in summer. Indeed, Vlemmix et al. (2015) have shown that in summer in China, aerosol particles are generally located above the tropospheric NO 2 layers. The probability that aerosol layers are located higher than tropospheric NO 2 bulks is also mentioned in other studies. For instance, Li et al. (2013) performed MAX-DOAS measurements during the PRIDE-PRD2006 campaign in the Pearl River Delta region, in China, for 4 weeks in July 2006. The considered site is located at 60 km north of Guangzhou in a rural area. It is clearly shown that (for these data) aerosol mixing layers are most often deeper/higher than NO 2 mixing layers. Mendolia et al. (2013) retrieved tropospheric NO 2 vertical column densities from OMI and MAX-DOAS measurements over Canada. One key conclusion of this work is that NO 2 diurnal profiles can even be systematically lower in summer and do not follow the expected pattern of the convective boundary layer (higher in summer than in winter). Aerosols do follow this seasonal pattern since they have a longer life time.
The absence of statistic increase/decrease of tropospheric NO 2 AMF in winter with increasing AOT is mainly caused by the smaller effective cloud fraction (compared to summer) and no variation of effective cloud pressure values which stay close to 900 hPa on average. The accuracy of the implicit aerosol correction is evaluated in the next section.

Evaluation of the implicit aerosol correction on tropospheric NO 2 AMF
In this section, AMFs computed with the cloud model used in the OMI O 2 −O 2 retrieval (Sect. 3.3) are compared with AMFs computed assuming aerosols instead of clouds. This comparison is applied to cloud-free scenes dominated by aerosols. Thus, the implicit aerosol correction accuracy is here evaluated and discussed through the computation of the relative bias S A (τ ) expressed as a percentage: where A tr exp (τ ) is the tropospheric NO 2 AMF explicitly taking into account aerosols. This relative bias is computed in two ways: (1) assuming that A tr (τ ) includes an implicit aerosol correction (based on the retrieved effective cloud parameters), and (2) that no aerosol correction at all (i.e. A tr (τ ) = A tr (τ = 0)). Then, the implicit aerosol correction can be compared to the case of no aerosol correction. Figures 15-17 show that the relative biases S A induced by the implicit aerosol correction vary from −10 to 30 % in most of the simulated cases. These biases are negative (i.e. underestimation of the AMFs) and minimal when aerosols are mixed with the tropospheric NO 2 bulk at the surface. They are generally positive and maximal (i.e. overestimation of the AMFs) when aerosols are elevated in the atmosphere and so not mixed with the tropospheric NO 2 peak (i.e. between 950 and 600 hPa depending on the analysed cases). In most of the simulations, the higher biases are found over scenes with elevated and high aerosol pollution, with τ ≥ 0.6. This is a consequence of an insufficient shielding effect applied in the computation of A tr by the implicit aerosol correction through the OMI cloud algorithm. This results from too large effective cloud pressure values. When the effective cloud pressure value significantly decreases with increasing AOT, the implicit aerosol correction is then able to reproduce the aerosol shielding effect with a better accuracy. For example, in Fig. 15, when geometry angles are small (θ 0 = 25 • and θ = 25 • ), with very high aerosol pollution (τ close to 1), fine particles (α = 1.5), and high SSA (ω 0 ≥ 0.95), the biases S A decrease from 30 to around 10 %. This improvement is related to the fact that only for higher AOT is the impact on the O 2 −O 2 signal sufficient to dominate over artifacts related to interpolation and limited sampling of the LUT. In cases of aerosols mixed with NO 2 , the biases are likely related to the discrepancy between the opaque Lambertian cloud model and the aerosol properties.
Overall, the relative biases induced by the implicit aerosol correction are generally better than if no aerosol correction was applied in the computation of tropospheric NO 2 AMF. No aerosol correction would induce biases from −20 to 60 % on A, assuming small geometry angles (θ 0 = 25 • and θ = 25 • ) and summer NO 2 profiles (see Figs. 15 and 16). Assuming winter NO 2 profiles (e.g. Fig. 17a) or larger angles (e.g. θ 0 = 50 • in Fig. 17c), these relative biases can even increase up to 150 % depending on the aerosol altitude. Indeed, in those cases, aerosols apply a stronger shielding effect on the tropospheric NO 2 bulk.  but with NO 2 profiles for January and SZA = 50 • : (a) S A assuming no aerosol correction is applied, January NO 2 profiles, (b) S A assuming implicit aerosol correction through the OMI cloud retrieval algorithm, January NO 2 profiles, (c) S A assuming no aerosol correction is applied, aerosols, January NO 2 profiles and SZA = 50 • , (d) S A assuming implicit aerosol correction through the OMI cloud retrieval algorithm, January NO 2 profiles and SZA = 50 • .

Atmos
Aerosol altitude and amount (i.e. AOT) are the key drivers of the magnitude of the relative biases S A . Effects of aerosols microphysics, such as associated SSA or size, have a second order of magnitude. Compared to Fig. 15, Fig. 16 shows that coarser particles (α = 0.5 instead of 1.5) and reduced SSA (0.9 instead of 0.95) mostly increase the relative biases induced by the implicit aerosol correction for very large AOT (τ ≥ 1) by increasing values from around 10 to 40 %. However, these values still remain lower than if no aerosol correction was applied: S A values are close to 55 % in the case of high aerosol altitude. For lower AOT values, no significant changes are visible. Figure 16 depicts that the shape of NO 2 vertical profile and large angles do not significantly change the S A values of implicit aerosol corrections for elevated aerosol layers (from 900 to 600 hPa). Only in the specific case of aerosols located between 900 and 950 hPa are the values increased (between 50 and 70 %). The cause is an enhancement effect produced by too large effective cloud pressure while aerosols actually apply a strong shielding effect.
The monthly variability of the NO 2 profile shape induces a variability on the relative biases for implicit aerosol correction between 10 and 20 % (indicated by the error bars in Figs. 14-16). The magnitude of this variability depends on the distance between the aerosol layer and the peak of the tropospheric NO 2 bulk. It is generally larger when the aerosol layer is close to the maximum in the NO 2 profiles.
Relative biases associated with implicit aerosol correction shows an irregular behaviour with respect to increasing AOT values: i.e. they do not smoothly increase or decrease with increasing AOT. They somewhat either increase or decrease depending on AOT (and aerosol altitude) values. This differs from the smooth increase of relative biases assuming no aerosol correction with respect to AOT. This is probably caused by the coarse sampling of the designed cloud LUT combined with the fact that the cloud model cannot describe aerosol-dominated scenes in a perfect way. A higher sampling should be designed and tested through the OMI cloud algorithm over scenes dominated by aerosols. The behaviour of these biases could lead to complex spatial and temporal patterns of the individual DOMINO tropospheric NO 2 products over highly polluted areas, not consistent with the physical NO 2 and aerosol patterns. The potential impacts on the estimation of NO x surface fluxes should be investigated. . Tech., 9, 359-382, 2016 www.atmos-meas-tech.net/9/359/2016/

Impact of the implicit aerosol correction on observed data: comparison with recent studies
An overestimation of the tropospheric NO 2 AMF results in an underestimation of the tropospheric NO 2 VCD with the same absolute magnitude according to Eq. (1). The findings here identified on the biases related to the implicit aerosol correction are consistent with those identified by Shaiganfar et al. (2011), Ma et al. (2013), and Kanaya et al. (2014). These studies found negative biases between −26 and −50 % on the OMI tropospheric NO 2 VCDs over areas with high aerosol pollution, in particular in summer. Investigations led by Ma et al. (2013) show that these underestimations can be explained by the presence of elevated aerosol layers, which are mostly observable in summer in this region (Vlemmix et al., 2015;Li et al., 2013;Mendolia et al., 2013). Very recently, Wang et al. (2015b) analysed MAX-DOAS data over Wuxi city, an area with high pollution adjoining Shanghai. It is clearly shown that, under aerosol pollution, by using the modified cloud parameters in the collocated DOMINO products, tropospheric NO 2 AMFs are overestimated. This mostly happens when the effective cloud pressure value is larger than 900 hPa. Kuhlmann et al. (2015) recalculated tropospheric NO 2 AMFs using high-resolution aerosol parameters over the Pearl River Delta region in southern China by the Models-3 Community Multiscale Air Quality (CMAQ) modelling system. Resulting tropospheric NO 2 VCDs increased by +6.0±8.4 %, likely because of polluted cases where the employed aerosol and NO 2 profiles show aerosol particles located higher in altitude compared to tropospheric NO 2 . In addition, Lin et al. (2014) explicitly took into account aerosol optical effects from the Goddard Earth Observing System -Chemistry (GEOS-Chem) simulations where model AOT is constrained by monthly MODIS Aqua AOT data and validated by ground-based AOT measurements. This study shows that excluding both aerosol scattering and absorption lead to changes between −40 and 90 % with AOD ≥ 0.8. Castellanos et al. (2015) have reduced the OMI NO 2 VCDs by 10 % on average by using aerosol extinction vertical profile observations from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument and AOD and SSA from the OMI/Aura level-2 near UV Aerosol (OMAERUV) database for scenes over South America including absorbing biomass-burning aerosols. According to the figures of CALIOP and collocated Tracer Model 4 (TM4) NO 2 profiles, the processed cases seem to include aerosol particles mixed (in parts) with the tropospheric NO 2 bulk. Finally, the new Peking University OMI NO 2 (POMINO) data set which takes aerosol properties from GEOS-Chem simulations, and which is based on the reprocessing of all the DOMINO product, show on average a reduction of the tropospheric NO 2 VCDs by 0-40 % over most of China (Lin et al., 2015). However, it is mentioned that individual reductions or enhancements depend strongly on location and season, and thus on the oc-currence of the relative altitude between aerosol particles and tropospheric NO 2 .
Overall, all these references which performed real retrievals show consistent numbers and conclusions with the sensitivity study performed here, and highlight the crucial role played by the actual OMI cloud algorithm and the derived implicit aerosol correction. This emphasizes that high aerosol pollution has currently large impacts on the individual OMI tropospheric NO 2 products over industrialized regions and cloud-free scenes.

Conclusions
In this paper, the behaviour of the OMI cloud model over cloud-free scenes dominated by aerosols was studied as well as the accuracy of the cloud-model-based aerosol correction of tropospheric NO 2 AMFs. This study focused on the operational OMI DOMINO product for cloud-free scenes, its behaviour in the presence of aerosol-dominated scenes that were selected based on collocated MODIS Aqua aerosol products, and the comparison with numerical simulated study cases. The goals were to understand the behaviour of the implicit aerosol correction based on the OMI cloud retrieval, and to investigate how much it improves the accuracy of the tropospheric NO 2 AMFs compared to performing no correction (and assuming clear-sky conditions with no aerosols). Analyses relied on a model vs. observation approach and have specifically focused on the industrialized part of East China.
The OMI cloud algorithm cannot distinguish aerosol and cloud signals. Effective cloud parameters are retrieved over cloud-free scenes but including aerosol particles. This implies that these retrievals include considerable aerosol information (AOT, optical properties, particles size, altitude) but they are treated as an opaque Lambertian reflector (albedo of 0.8). The effective cloud fraction linearly increases with increasing AOT and can reach values between 0.1 and 0.15 for AOT = 1. This represents the aerosol scattering effects on the 460-490 nm continuum reflectance. The slope of the linear regression of AOT vs. cloud is, however, dependent on the aerosol properties, the surface albedo, and the SZA and VZA. The response of effective cloud pressure to aerosol scenes represents the O 2 −O 2 shielding effect induced by the attenuation of photons by optically thicker aerosol layers, shortening the length of the average light path. In the case of high aerosol pollution, retrieved effective cloud pressure values correlate with the mean aerosol layer height. Values smaller than the mean aerosol layer pressure may be related to the cloud model error over aerosol scenes. In cases of low AOT or effective cloud fraction values, aerosols have little effect on O 2 −O 2 absorption, leading to effective cloud pressure values close to the surface pressure independently of the altitude of the aerosol layer. This overestimation can be caused by the coarse sampling of the cloud LUT used by the OMI cloud algorithm to convert the O 2 −O 2 continuum reflectance and slant column into effective cloud fraction and pressure. Indeed, this LUT was initially intended for retrievals over cloudy scenes, not for cloud-free scenes dominated by aerosols.
Aerosols can either decrease (shielding) or increase (enhancement) the sensitivity to tropospheric NO 2 bulk. Such effects simultaneously depend on the aerosol altitude and the shape of the NO 2 vertical profile. Shielding effects mostly occur when particles are above the NO 2 layers which should mostly happen during summer in China. Generally, if no aerosol correction was performed in the DOMINO products, relative biases of the tropospheric NO 2 VCDs would range from −60 to 20 % for large AOT values. These values could even decrease to −150 % in cases of large angles (e.g. SZA ≥ 50 • ) or very large vertical separation between aerosols and the tropospheric NO 2 bulk.
An implicit aerosol correction is applied in the computation of the tropospheric NO 2 AMF through the use of the retrieved effective cloud fraction and pressure over scenes dominated by aerosols. After the implicit aerosol correction, relative biases in the VCDs are negative and in the range of −40 to −20 % in the case of elevated aerosol particles and high pollution (AOT ≥ 0.6). In the case of aerosols located close to the surface or mixed with the tropospheric NO 2 bulk, relative biases in the VCDs are positive and in the range of 10 to 20 %. These values are smaller than if no aerosol correction was applied in the OMI DOMINO products. AOTs and aerosol altitude are the key drivers of these biases, while aerosol microphysical properties are of secondary importance. Note that geometry angles and shape of the NO 2 profile can either increase or decrease these values. For elevated aerosols, the main cause of these biases is an underestimation of the aerosol shielding effect by the cloud algorithm. The reason for this underestimation is probably a combination of the cloud model error, used in the presence of aerosols, and the employed numerical approach to convert the O 2 −O 2 continuum reflectance and SCD into effective cloud fraction and pressure through a LUT. Furthermore, the coarse sampling in the employed cloud LUT leads to complex behaviours between these biases and AOT. An improved LUT with a higher sampling should be implemented and evaluated. The impact on the ability to estimate the NO x surface fluxes should be further studied. The biases in the presence of aerosols located at the surface or mixed with tropospheric NO 2 are likely a consequence of the difference between the opaque Lambertian cloud model and aerosol properties.
The present analyses considered box aerosol layers (i.e. discrete atmospheric layers with constant aerosol extinction value) and assumed that aerosols cover completely the OMI pixels. It is recognized that a more realistic description of the vertical distribution of aerosols and assumptions of OMI pixels partially covered by aerosols would result in different biases. Nevertheless, biases found here compare quite well with biases found in various ground-based comparison studies. Finally, all the sensitivity studies performed here assume that, in the case of highly polluted regions, only non-explicit aerosol correction impacts the current individual OMI tropospheric NO 2 products. It should be noted that uncertainties in the shape of vertical NO 2 profile and climatology surface albedo can also play a significant role in the estimated biases when aerosols are present in the measurement.
The results described in this paper indicate that it is worthwhile to design and evaluate an improved aerosol correction in view of retrieving tropospheric NO 2 vertical column densities. This is needed in the context of OMI measurements, but even more in the future for TROPOMI (Veefkind et al., 2012). Since the spatial resolution will be higher (7 km × 7 km), there is a significant probability that a scene will be fully covered by aerosol particles.