Retrieving tropospheric nitrogen dioxide from the Ozone Monitoring Instrument: effects of aerosols, surface reflectance anisotropy, and vertical profile of nitrogen dioxide

Retrievals of tropospheric nitrogen dioxide (NO 2) from the Ozone Monitoring Instrument (OMI) are subject to errors in the treatments of aerosols, surface reflectance anisotropy, and vertical profile of NO 2. Here we quantify the influences over China via an improved retrieval process. We explicitly account for aerosol optical effects (simulated by nested GEOS-Chem at 0.667 ◦ long.× 0.5 lat. and constrained by aerosol measurements), surface reflectance anisotropy, and high-resolution vertical profiles of NO 2 (simulated by GEOS-Chem). Prior to the NO 2 retrieval, we derive the cloud information using consistent ancillary assumptions. We compare our retrieval to the widely used DOMINO v2 product, using MAX-DOAS measurements at three urban/suburban sites in East China as reference and focusing the analysis on the 127 OMI pixels (in 30 days) closest to the MAX-DOAS sites. We find that our retrieval reduces the interference of aerosols on the retrieved cloud properties, thus enhancing the number of valid OMI pixels by about 25 %. Compared to DOMINO v2, our retrieval better captures the day-to-day variability in MAX-DOAS NO 2 data (R2 = 0.96 versus 0.72), due to pixel-specific radiative transfer calculations rather than the use of a look-up table, explicit inclusion of aerosols, and consideration of surface reflectance anisotropy. Our retrieved NO 2 columns are 54 % of the MAX-DOAS data on average, reflecting the inevitable spatial inconsistency between the two types of measurement, errors in MAX-DOAS data, and uncertainties in our OMI retrieval related to aerosols and vertical profile of NO 2. Sensitivity tests show that excluding aerosol optical effects can either increase or decrease the retrieved NO 2 for individual OMI pixels with an average increase by 14 %. Excluding aerosols also complexly affects the retrievals of cloud fraction and particularly cloud pressure. Employing various surface albedo data sets slightly affects the retrieved NO 2 on average (within 10 %). The retrieved NO 2 columns increase when the NO2 profiles are taken from MAX-DOAS retrievals (by 19 % on average) or TM4 simulations (by 13 %) instead of GEOS-Chem simulations. Our findings are also relevant to retrievals of other pollutants (e.g., sulfur dioxide, Published by Copernicus Publications on behalf of the European Geosciences Union. 1442 J.-T. Lin et al.: Improved retrieval of tropospheric nitrogen dioxide from OMI formaldehyde, glyoxal) from UV–visible backscatter satellite instruments.

The retrieval of tropospheric NO 2 VCD from OMI is done by dividing the tropospheric slant column density (SCD) by the tropospheric air mass factor (AMF) (Boersma et al., 2011).(Hereafter we will focus the analysis in the troposphere.)The AMF is derived by radiative transfer modeling driven by ancillary assumptions on surface reflectance (Rs), surface pressure (Ps), pressure and temperature profiles, aerosol characteristics, cloud fraction (CF), cloud pressure (CP), and vertical profile of NO 2 .The calculation of AMF provides the dominant source of errors in the retrieved NO 2 columns over polluted areas (Boersma et al., 2007), with important consequences on emission constraints and other applications.
Current representative OMI products covering China, DOMINO v2 (Boersma et al., 2011) and OMNO 2 v2 (Bucsela et al., 2013), do not explicitly account for the effect of aerosols on the solar radiation.Rather, these retrievals assume that the cloud correction accounts for the effect of aerosols, as the OMI cloud retrieval provides effective cloud parameters sensitive to aerosol burdens (Boersma et al., 2011).Since aerosols affect the radiation field in retrieving both clouds (Boersma et al., 2011) and NO 2 (Leitão et al., 2010), the net effect on the retrieved NO 2 columns is unclear.This aerosol issue is particularly significant over East China due to its high aerosol loadings (Lin et al., 2010a;Cheng et al., 2013).This issue can be addressed by retrieving clouds and NO 2 columns that consistently account for the effects of aerosols (e.g., Martin, 2008).
In addition, the DOMINO and OMNO 2 products also assume Lambertian surface with no dependence of surface reflectance on the geometry of the light path (Boersma et al., 2011;Bucsela et al., 2013); the retrieved NO 2 VCDs are affected by 20 % or less over Europe (Zhou et al., 2010).DOMINO and OMNO 2 adopt the vertical profile of NO 2 simulated by coarse-resolution global chemical transport models (CTMs), TM4 at 3 • long.× 2 • lat.for DOMINO v2 and GMI at 2.5 • long.× 2 • lat.for OMNO 2 v2, which are unable to capture the variability of NO 2 at smaller scales.Russell et al. (2011) found differences in retrieved NO 2 columns of −75-10 % for individual OMI pixels around California in June 2008 when adopting NO 2 profiles from a WRF-Chem simulation at a resolution of 4 km × 4 km instead of a GEOS-Chem simulation at 2.5 • long.× 2 • lat.Furthermore, DOMINO and OMNO 2 adopt the cloud information from the OMCLDO2 cloud retrieval (Acarreta et al., 2004;Sneep et al., 2008) with consistent assumptions on reflective properties (Earth's surface and clouds are treated as Lambertian surfaces) and surface albedo (from Kleipool et al., 2008), but with differences in the assumed surface pressure (see more discussion in Sects.2.2 and 3).
Overall, research has found potentially large errors in the NO 2 products in comparison to independent measurements (Bucsela et al., 2008;Hains et al., 2010).For China, such evaluation is rare (Irie et al., 2012;Ma et al., 2013), and the effects of individual parameters have not been quantified.Since errors in one parameter may be related to (e.g., errors in surface reflectance and aerosol optical effects may be transferred to clouds) or enhanced/compensated by/for errors in another, it is necessary to account for the direct and indirect effects of various parameters together.
In this paper, we improve the retrieval of NO 2 over East China upon DOMINO v2 (hereafter referred to as DOMINO-2) by enhancing the assumptions on surface pressure, surface reflectance, aerosol optical effects, cloud properties, and vertical profile of NO 2 together.We calculate the tropospheric AMFs independently and adopt the tropospheric SCDs from DOMINO-2.Prior to the retrieval of NO 2 , we derive the cloud information through the O 2 -O 2 method (Acarreta et al., 2004;Sneep et al., 2008) but using improved ancillary parameters (Ps, Rs, aerosols, pressure levels, temperature profiles) consistent with our NO 2 retrieval.We compare our retrieval to DOMINO-2 using as reference the ground-based MAX-DOAS measurements from three urban/suburban sites in East China in various months of 2006, 2008, 2009, and 2011.We then evaluate the effects of aerosols, surface reflectance, and vertical profile of NO 2 on the retrievals of clouds and NO 2 columns.Our current analysis is focused on the OMI measurements spatiotemporally associated with the MAX-DOAS data.A later study will focus on the spatial and seasonal distributions of NO 2 over China (Lin et al., 2014).
Section 2 describes the NO 2 products retrieved from OMI and MAX-DOAS and presents the criteria for selecting suitable OMI and MAX-DOAS measurements for comparison.Section 3 compares the ancillary parameters employed by DOMINO-2 to those by our retrieval.Section 4 evaluates DOMINO-2 and our OMI retrieval using the NO 2 data retrieved from MAX-DOAS.Section 5 further evaluates the effects of individual ancillary parameters on the retrievals of clouds and NO 2 columns from OMI through a series of sensitivity tests.Section 6 concludes this study.
2 Retrievals of NO 2 and criteria for data selection

MAX-DOAS measurements
The MAX-DOAS measurements were conducted at three urban/suburban sites in East China, one at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS) in urban Beijing, one in Xianghe County to the southeast of Beijing, and one in the city of Tai'An.Figure 1 shows the locations of these sites with respect to the NO 2 columns in July 2008 retrieved from DOMINO-2.More information about the sites is described in Table 1.
The instrument operated in Beijing and Xianghe was designed at BIRA-IASB and is described extensively by Clémer et al. (2010).It is a dual-channel system composed of two thermally regulated grating spectrometers covering the ultraviolet and visible wavelength ranges (300-390 nm and 400-720 nm, respectively) by means of low-noise cooled CCD detectors.Scattered light is collected at various elevation angles within a field of view of about 0.5 • by a telescope mounted on a commercial sun tracker.The received light is guided to the spectrometers through depolarizing optical fiber bundles.The telescope points towards a fixed azimuth direction (north).A full MAX-DOAS scan, which requires ∼ 15 min, comprises nine elevation angles at 2 • , 4      , and 90 • (zenith).
The instrument at Tai'An employs a miniaturized ultraviolet-visible spectrometer (B&W TEK Inc., BTC111), a single telescope, and a movable mirror.It measures scattered sunlight sequentially every 30 min at five elevation angles: 5    , and 90 • .The telescope points to a fixed azimuth direction (north).The spectral resolution is about 0.4-0.5 nm for the fitting window of 460-490 nm.More information is given by Irie et al. (2008) and Irie et al. (2012).
For all sites, the VCD of NO 2 is retrieved from the radiation measurements around 477 nm.A profile approach based on an optimal estimation scheme (Rodgers, 2000) is taken that results in a companion vertical profile of NO 2 (Irie et al., 2012;Hendrick et al., 2013).The vertical profile may not represent the true distribution of NO 2 because there are only about 2 degrees of freedom for signal (DFS) (Hendrick et al., 2013) or less (Irie et al., 2011) from the retrieval process.Compared to space-based remote sensing, the MAX-DOAS measurements are insensitive to surface reflectance and are subject to better cloud screening.The total retrieval uncertainty on the tropospheric NO 2 column has been estimated at 11 % for the Beijing and Xianghe sites (Hendrick et al., 2013) and 14 % for the Tai'An site (Irie et al., 2012).These   (Mangshan, Rudong (Irie et al., 2012), and Beijing CMA (Ma et al., 2013): "x" signs).Overlaid on the background is the spatial distribution of NO 2 columns (10 15 molec cm −2 , at 0.05 • ) in July 2008 retrieved by DOMINO-2 together with a zoomed-in map around Beijing (116-117 • E, 39.5-40.5 • N; at 0.01 • ).OMI pixels are restricted to row-anomaly-free, ice/snow-free, CRF ≤ 0.5, and VZA ≤ 30 • .uncertainty estimates do not account for the spatial representativeness of MAX-DOAS measurements, an important factor when comparing to satellite retrievals that cover a larger area (see Sect. 2.4.1).
Prior to the retrieval of NO 2 , the MAX-DOAS remote sensing data are used to derive aerosol optical depth (AOD) and aerosol extinction profile (Clémer et al., 2010;Irie et al., 2011).We employed the AOD results at the Tai'An site to constrain the respective aerosol information in retrieving clouds and NO 2 columns from OMI (see Sect. 2.3).The retrieved aerosol extinction profile was not used considering its low DFS at 2.1 ± 0.6 (Irie et al., 2011).

DOMINO-2
For DOMINO-2, the AMF is interpolated from a precalculated look-up table (LUT) derived from the doubling-adding KNMI (DAK v3.0) radiative transfer model (RTM).The LUT provides layer AMFs (i.e., the sensitivity of SCD to VCD in individual atmospheric layers) that are determined by surface albedo (As), Ps, CF, CP, atmospheric pressure level, and the geometry of the light path.Table 2 summarizes the ancillary parameters used in deriving DOMINO-2.
DOMINO-2 adopts the monthly As data averaged from the OMI measurements between October 2004 and October 2007 (OMLER v1; Kleipool et al., 2008), not accounting for the effect of surface reflectance anisotropy.These As values are affected by the presence of aerosols (Herman et al., 2001;Kleipool et al., 2008).For a given ground pixel of OMI, the surface pressure is interpolated to the pixel center from TM4 simulations on a 3 • long.× 2 • lat.grid, and subsequently corrected for differences between the corresponding effective ground elevation and the high-resolution elevation obtained from the DEM_3KM database (Boersma et al., 2011).The vertical profile of NO 2 is adjusted subsequently by maintaining the volume mixing ratios (VMRs) of NO 2 in the individual layers so that the profile shape is not changed.The detailed formulation of the adjustments is presented by Zhou et al. (2009) and Boersma et al. (2011).DOMINO-2 takes the cloud fraction and cloud pressure information from the OMCLDO2 v1.1.1.3data set (Acarreta et al., 2004;Sneep et al., 2008).(Hereafter the version number of OMCLDO2 is dropped for simplicity.)Table 3 summarizes the ancillary parameters used for deriving OM-CLDO2.Compared to DOMINO-2, OMCLDO2 assumes a time-invariant relationship between pressure and height (i.e., the midlatitude summer profile from Anderson et al., 1986) and uses the pixel-specific ground elevation to determine the respective Ps.The effect of the inconsistent treatments of Ps between DOMINO-2 and OMCLDO2 is analyzed in Sects.3 and 4.
The retrieval processes of both DOMINO-2 and OM-CLDO2 do not explicitly account for the effect of aerosols (scattering, absorption, and vertical profile).The cloud fraction and cloud pressure retrieved from OMCLDO2 are thus considered as "effective" parameters that may include partial information about the presence of aerosols (Boersma et al., 2011).The implicit treatment of aerosols affects the retrieval of NO 2 over East China given its high aerosol concentrations.

Our reference retrieval
Using the LIDORT v3.6 RTM (Spurr, 2008), we improved the AMF code by Palmer et al. (2001), Martin et al. (2002, 2003, 2006), and O'Byrne et al. (2010) to AMFv6 that simultaneously accounts for the coupled effects of aerosols and clouds on the NO 2 retrieval and for the angular distribution of surface reflectance.This code calculates the tropospheric AMFs of NO 2 for individual OMI pixels without the use of a LUT.We derived the VCDs of NO 2 by dividing the tropospheric SCDs from DOMINO-2 by the newly calculated AMFs.Prior to the retrieval of NO 2 , we derived the cloud information (CF and CP) based on the top-ofatmosphere reflectance and the O 2 -O 2 SCD data from OM-CLDO2 (Acarreta et al., 2004;Sneep et al., 2008) using ancillary parameters that are consistent with the NO 2 retrieval.Tables 2 and 3 summarize the ancillary parameters used in our retrieval processes for NO 2 and clouds, respectively.The retrieval here is referred to as our "reference retrieval" (case 0 in Table 4) in order to be distinguished from the sensitivity tests throughout the text (cases 1-17).
For surface reflectance, our reference retrieval accounts for the effect of surface bidirectional reflectance distribution function (BRDF) (Zhou et al., 2010).We adopted the MCD43C2 data set (Lucht et al., 2000) from the Moderate Resolution Imaging Spectroradiometer (MODIS) that provides the coefficients for three kernels (isotropic, volumetric, and geometric) determining the BRDF at 440 nm.MCD43C2 provides 16-day average coefficients for every 8 days of a year on a 0.05 • long.× 0.05 • lat.grid (the first file contains the average values over 1-16 January, and the second file represents 9-24 January, etc.).To fill the missing values, we interpolated the data temporally using the adjacent two data sets, spatially with the surrounding 5 × 5 grid cells, temporally using the respective data sets in the adjacent two years, and then temporally using the 2005-2011 average values representing the same days.The interpolation was done in the above order, and was exited once the missing value had been filled.We then conducted spatial smoothing (5 × 5 grid cells) on the coefficients to remove the influence of ice or snow that may not have been fully eliminated in MCD43C2.As a final step, we derived the kernel coefficients for an OMI pixel in a given day from the high-resolution data set by spatial mapping and temporal interpolation.
Our reference retrieval obtains surface pressure and NO 2 profiles from the nested GEOS-Chem model (0.667 • long.× 0.5 • lat.) with further adjustments in accordance to the pixelspecific surface elevation as done for DOMINO-2.(See Appendix A for a brief model description.)The nested GEOS-Chem NO 2 profiles are also used for Europe (Vinken et al., 2013).For surface elevation, we adopted the GMTED2010 data set at 30 arcsec (http://topotools.cr.usgs.gov/GMTED_viewer/).GEOS-Chem simulates vertical mixing in the planetary boundary layer (PBL) fairly well (Lin and McElroy, 2010).Compared to TM4, the nested GEOS-Chem has a much higher resolution, thus improving the representation of topography, emissions, and the nonlinear chemistry.We obtained the model outputs at the local time of OMI pixels.
Our reference retrieval explicitly accounts for the effect of aerosol optics by including in the RTM calculation the vertical profiles of aerosol extinction coefficient (EC), singlescattering albedo (SSA), and phase functions.We adopted the temporally and spatially varying aerosol information (EA, SSA, phase functions, and vertical profiles for individual aerosol types) at the local time of OMI pixels from the nested GEOS-Chem simulation (Lin, 2012).(See Appendix A for descriptions of the aerosol simulation.)GEOS-Chem captures the spatial distribution of AOD at 550 nm over East China in 2006 observed from MODIS, with a positive bias in winter and a negative bias in summer on average (Lin et al., 2012).Prior to our RTM calculation, we further constrained the model AOD using measurements from the AErosol RObotic NETwork (AERONET), MODIS, and MAX-DOAS.We scaled the simulated concentrations of all aerosol types simultaneously based on the ratio of observed to modeled AOD, and thus adjusted modeled AOD, SSA, and phase functions together.The same wavelength was ensured in comparing each pair of model and observation.For the Tai'An site, we used the AOD data at 476 nm retrieved from the MAX-DOAS measurements (Irie et al., 2011).For IAP and Xianghe (Liu et al., 2007), we used the AERONET data at 550 nm at the hour of the MAX-DOAS measurements.For seven days (34 pixels) without AERONET data, we used the MODIS AOD data at 550 nm from the MYD04 collection 5/5.1 level-2 product (Remer et al., 2008).For a given day, the MYD04 data were averaged over all valid values within 0.25 • of the respective MAX-DOAS sites.The MODIS AOD are affected by cloud contamination and errors in surface reflectance (Wang et al., 2010;Hyer et al., 2011).The consequent effects on our cloud and NO 2 retrievals are small compared to the effects of potential errors in modeled SSA and vertical distribution of aerosols.After the aerosol adjustments, the resulting AOD, when converted to 550 nm, ranges from 0.07 to 2.23, with a mean value of 0.61 for the 127 OMI pixels complying with our spatial constraints detailed in Sect.2.4.1.At 550 nm, the adjusted AOD is highly correlated to the GEOS-Chem simulated AOD (R 2 = 0.79) with an increase by 0.06 on average.The SSA at 550 nm is 0.934 on average (min = 0.870, max = 0.986), reflecting the high concentrations of black carbon in East China (Yang et al., 2011).
We converted the aerosol optics at 550 nm outputted from GEOS-Chem to other wavelengths (477 nm for comparison with AOD measurements at Tai'An, 475 nm for O 2 -O 2 cloud retrieval, and 438 nm for NO 2 retrieval).The conversion was based on the size distributions, refractive indices, and hygroscopic growth rates of individual aerosol types prescribed in GEOS-Chem (i.e., in the same manner as done in GEOS-Chem).For this purpose we also adopted the modeled relative humidity.
The GEOS-Chem aerosol vertical profile generally reproduces that observed by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) over East Asia, with a tendency for GEOS-Chem to underestimate the abundance of aerosols in the free troposphere (Ford and Heald, 2012;van Donkelaar et al., 2013).We thus test the effects of aerosol vertical profiles on the retrievals of clouds and NO 2 in Sect.5.3.2.

Spatial constraint and consistency between OMI and MAX-DOAS measurements
As the MAX-DOAS sites are located in the urban or suburban areas, the spatial variability of NO 2 needs to be considered in selecting suitable OMI and MAX-DOAS data for comparison.Parameters that can be used to adjust the spatial consistency between the space-and ground-based measurements include the viewing zenith angle (VZA) of OMI and the distance from the OMI pixel center to the respective MAX-DOAS site (hereafter referred to as pixel-center distance).For our analysis, the distance is restricted to be shorter than 25 km and the VZA smaller than 30 Note that the spatial constraints here cannot fully eliminate the spatial inconsistency between MAX-DOAS and OMI measurements, due to the inevitable spatial inconsistency between the ground-and space-based remote sensing.In particular, the MAX-DOAS sensors always face north and typically sample a horizontal distance of a few kilometers, while an OMI pixel represents an area of 13 × 24 km 2 or larger.Brinksma et al. (2008) showed that changing the azimuth angle of the MAX-DOAS sensor can result in differences by a factor of 10-350 % (by 50 % on average) in the retrieved NO 2 in Cabauw, the Netherlands, due to the influences of local sources and/or sinks (see their Fig. 6).Irie et al. (2012) also showed that the vicinity of the polluted Yokosuka site undergoes larger horizontal variability of NO 2 .For Chinese sites, the influence of horizontal inhomogeneity in NO 2 was suggested to be about 10-30 % for MAX-DOAS measurements taken at the Chinese Meteorological Administration in polluted urban Beijing (Ma et al., 2013) and about 10-15 % for less polluted Tai'An, Mangshan, and Rudong (Irie et al., 2012) (see Fig. 1 for locations and NO 2 pollution gradient at these sites).The effect of horizontal inhomogeneity is also in line with the pixel-specific comparison in Fig. 4a-c that show notable scattering in the OMI data in a given day corresponding to a MAX-DOAS site.
We tentatively estimate the overall effect of horizontal inhomogeneity (and spatial inconsistency between space-and ground-based measurements) to be 20-30 % for the OMI pixels analyzed here, considering that about 77 % of these OMI pixels are located near the polluted Beijing IAP with larger NO 2 gradient.This estimate is preliminary since previous studies suggested the spatial inhomogeneity to be strongly location-, time-, and meteorology-dependent (Brinksma et al., 2008;Irie et al., 2012;Ma et al., 2013).

Temporal constraint
Temporally, MAX-DOAS measures NO 2 much more frequently than OMI throughout the course of a day.In many days, it observes rapid changes in NO 2 within a short time period.To reduce the effect of the temporal variation of NO 2 in comparing the ground-and space-based measurements, here the measurement from an OMI pixel is considered to have a temporally consistent counterpart from MAX-DOAS only if (1) there exist two or more MAX-DOAS data within 1.5 h of the time of the OMI pixel and (2) the standard deviation of these MAX-DOAS data does not exceed 20 % of their mean value.In this case, the mean value of the MAX-DOAS data points is paired with the OMI value for comparison.

Other constraints
We excluded the OMI pixels affected by row anomaly, icy/snowy ground, or high cloud coverage.DOMINO-2 restricts valid NO 2 data to the pixels with cloud radiance fractions (CRFs) below 0.5.It also implicitly excludes the pixels with high aerosol loadings, since its cloud information is influenced by the presence of aerosols.This may not be desirable for aerosol-polluted regions such as East China, particularly when the effects of aerosols can otherwise be characterized.By comparison, our reference retrieval explicitly accounts for the effect of aerosol optics, thus providing information that is more specific to clouds.For example, there is a heavy aerosol loading near the IAP site on 28 December 2008 with the AERONET AOD close to 2. For this day, our reference retrieval suggests low cloud coverage in an OMI pixel with a CRF of 6 %, in contrast to the CRF at 55 % suggested by DOMINO-2.Detailed comparison of the cloud information is presented in Sect.3. Therefore, we used the CRF values derived from our reference retrieval to determine the OMI pixels with low cloud coverage (CRF ≤ 0.5) in comparing OMI to MAX-DOAS data.Had the CRFs from DOMINO-2 been used for constraint, the number of pixels would have decreased by 25 %.

Available data complying with all constraints
The constraints for spatial and temporal consistency, row anomaly, ground conditions, and cloud interference together result in 127 pixels of OMI over 30 days with suitable OMI and MAX-DOAS data.A total of 98 pixels (in 23 days) correspond to the IAP site, 27 pixels (in 6 days) correspond to the Tai'An site, and 2 pixels (in 1 day) correspond to the Xianghe site.The number of pixels (days) is 37 (10) in winter, 12 (4) in spring, 30 (7) in summer, and 48 (9) in fall, with relatively good seasonal representativeness.

Evaluating ancillary parameters for deriving DOMINO-2 and our reference retrieval
Unlike DOMINO-2, our reference retrieval accounts for surface BRDF.Here we used the respective bidirectional reflectance factor (BRF) to illustratively compare with the OMI albedo (OMLER v1) adopted by DOMINO-2.We neglected the scale factor π when deriving the BRF from the BRDF (Lucht et al., 2000).Figure 2a shows that the BRF is in the same range as the OMI albedo (0.03-0.08), while it is smaller than the OMI albedo by 0.023 averaged over the pixels.The two data correlate poorly with the coefficient of determination (R 2 ) below 0.05.Also, the MODIS BRF varies from one pixel to another more significantly than the OMI albedo (note the apparent horizontal lines in Fig. 2a).The lack of correlation highlights the spatial and angular dependence of surface reflectance not fully accounted for in the OMI albedo data.The Ps adjustment in deriving DOMINO-2 leads to unrealistically high Ps for most of the 127 pixels analyzed here, an apparent result of the likely overestimate in the TM4 Ps data.The adjusted Ps is larger than 1050 hPa (1100 hPa) in 76 % (24 %) of the pixels (Fig. 2b).It also exceeds the Ps assumed in OMCLDO2 by 57.7 hPa on average.For the 100 pixels near the IAP or Xianghe sites, the adjusted Ps overestimates the Ps observed at the Nanjiao (116.47 • E, 39.80 • N; 31 m) ground meteorological station in the southeast of urban Beijing (mean bias = 75.2hPa, R 2 = 0.35).Further analysis shows positive biases in the DOMINO-2 Ps data over various regions of East China with no clear dependence on land use types (Lin et al., 2014).By comparison, the Ps derived in our reference retrieval is consistent with the observed Ps at Nanjiao (mean bias = −9.1 hPa, R 2 = 0.65).Figure 2c-e compare the CF, CP, and CRF between DOMINO-2 and our reference retrieval.As mentioned in Sect.2.2, the DOMINO-2 CF and CP are taken from OM-CLDO2.The CFs and CRFs for DOMINO-2 are larger than those derived from our reference retrieval for most pixels (0.100 versus 0.063 for CF on average and 0.326 versus 0.180 for CRF), as explained by the different treatments concerning aerosols.On the other hand, our reference retrieval suggests higher CP than DOMINO-2 (OMCLDO2) with a mean difference by about 30 hPa.
For the assumed vertical profile of NO 2 , our reference retrieval differs from DOMINO-2 due to the differences between the coarse-resolution TM4 and high-resolution GEOS-Chem simulations as well as the different adjustments in accordance to the Ps. Figure 3b presents an illustrative example of the vertical profiles assumed by DOMINO-2 and by our reference retrieval for a pixel on 28 December 2008.Compared to our reference retrieval, the NO 2 profile in DOMINO-2 for this pixel is associated with much higher Ps and also assumes NO 2 to be more concentrated near the ground.The differences contribute partly to the much lower AMF in DOMINO-2 than our reference retrieval (0.32 versus 0.90).

Evaluating DOMINO-2 and our reference retrieval using MAX-DOAS measurements
The scatter plots in Fig. 4a and b compare the NO 2 columns derived for the 127 OMI pixels with their MAX-DOAS counterparts.There is significant scattering in the DOMINO-2 data when the MAX-DOAS values are large (> 60 × 10 15 molec cm −2 , Fig. 4a).The scattering is due largely to errors in the assumed ancillary parameters, and is much reduced by our reference retrieval (Fig. 4b).The remaining scattering is due likely to the actual NO 2 variability in the vicinity of the MAX-DOAS site.The scatter plots in Fig. 4d and e compare the daily NO 2 data derived from OMI to MAX-DOAS measurements.Here each OMI value represents the average over all pixels in a day.Our reference retrieval captures the day-to-day variability of MAX-DOAS NO 2 (R 2 = 0.96).However, the retrieved NO 2 columns are about half of MAX-DOAS, with a normalized mean bias (NMB) at −46 % and a reduced major axis (RMA) slope at 0.51.The magnitude of NO 2 columns in DOMINO-2 is closer to MAX-DOAS (NMB = −5 %) with a reduced correlation (R 2 = 0.72).Note that the correlation for DOMINO-2 here is comparable to the findings from previous studies (e.g., Irie et al., 2012).
To further evaluate the consistency between MAX-DOAS and OMI NO 2 data, we mimicked the retrieval process of DOMINO-2 by adopting its ancillary parameters including As, Ps, CF, CP, pressure levels, and vertical profiles of tem-perature and NO 2 (case 1 in Table 4).However, we performed pixel-specific LIDORT radiative transfer modeling to calculate the layer AMFs instead of using the LUT produced with the DAK RTM (see Appendix C for detailed analyses).The mimicked retrieval process largely reproduces the NO 2 columns in DOMINO-2 (Fig. 4c, f), with a negative mean difference of 4 % for the 30 daily data.It better captures the day-to-day variability of MAX-DOAS (R 2 increases from 0.72 to 0.85 for the 30 daily data pairs), due to the remaining differences in the retrieval process detailed in Appendix C.
We then analyzed the effects of the overestimated Ps in DOMINO-2.As detailed in Sect.3, DOMINO-2 overestimates the observed Ps by 75.2 hPa on average and adjusts the pressure dependence of NO 2 accordingly.It adopts the CP from OMCLDO2 (that assumes lower Ps) without additional adjustments.Thus it puts more NO 2 below the cloud top, consequently lowering the AMF.In addition, DOMINO-2 adopts the OMCLDO2 CF data that are overestimated due to the influence of aerosols.This further enhances the sensitivity to the treatments of Ps and CP.As a result of changing the retrieval process of case 1 by adopting the Ps from OM-CLDO2 (case 2 in Table 4), the resulting NO 2 columns are lower than MAX-DOAS by 27 % on average.Therefore, that the mean DOMINO-2 NO 2 column is close to the MAX-DOAS value is contributed in part by the overestimate in Ps.

Effects of ancillary assumptions in retrieving NO 2 columns from OMI
Section 4 shows that our reference retrieval is highly correlated to MAX-DOAS with a significant underestimate in magnitude.This section explores the extent to which our retrieval is affected by ancillary assumptions.Sections 5.1-5.3evaluate the impacts of individual ancillary parameters on the retrievals of clouds and NO 2 , including surface reflectance, vertical profile of NO 2 , and aerosol characteristics.The sections start with conceptual analyses of individual parameters, followed by various sensitivity tests perturbing the parameters upon our reference retrievals of clouds and NO 2 (cases 3-17 in Table 4, with statistics for NMB, RMA slope, and R 2 ).Section 5.4 summarizes the sensitivity tests, identifying the relative contributions of individual factors affecting the comparisons between OMI and MAX-DOAS NO 2 .

Effects of surface reflectance
Figure 5 shows that, in retrieving the cloud information, an increase in Rs will enhance the AMF of O 2 -O 2 that is compensated by a decrease in CP.The increased Rs also enhances the reflectance at top of atmosphere (R TOA ) with a consequent reduction in the retrieved CF.The reduction in CF will further reduce the retrieved CP if the amount of AMF in the cloudy portion of the pixel (AMF cl ) is smaller than the AMF in the clear-sky portion (AMF cr ), whereas it has an opposite effect when the AMF cl exceeds the AMF cr .In retrieving NO 2 , the increased Rs also enhances the AMF of NO 2 .
Table 4 describes various sensitivity retrievals with perturbed surface reflectance.Cases 3 and 4 assume blue-sky albedo and black-sky albedo, respectively, derived from the MODIS BRDF data.The black-sky albedo accounts for the incident solar radiation reflected by isotropic surface, while the blue-sky albedo accounts for both direct and diffuse radiation reaching the ground.The relative contributions of direct and diffuse radiation are determined using the LUT developed by Lucht et al. (2000).The resulting blue-sky albedo and black-sky albedo differ insignificantly from the MODIS BRF, with a difference within ±0.01 for all pixels.They thus result in cloud properties and NO 2 columns very close to our reference retrieval (Table 4).
Case 5 adopts the monthly climatological surface albedo data set based on the OMI measurements over 2005-2009 (OMLER v3, 0.5 • long.× 0.5 • lat.).During our retrieval process, the albedo for a given day is interpolated from the closest two months.The resulting albedo is larger than the MODIS BRF for 78 % of the pixels with a positive mean difference of 0.023.On average, it leads to a lower CF (CRF) by 0.01 (0.04) than the reference retrieval.The consequently retrieved NO 2 columns deviate further from the MAX-DOAS data (NMB = −51 % versus −46 % for the reference retrieval).Pixel by pixel, changes in NO 2 columns due to the Rs changes can reach 45 %.
Case 6 uses the same albedo as DOMINO-2 (OMLER v1).The resulting changes in CF are within ±0.05 for all pixels (within ±0.1 for CRF).On average, adopting the albedo from DOMINO-2 has a small impact on the AMF and VCD of NO 2 due to the changes in clouds compensating for the effects of the perturbed Rs.Nonetheless, the consistency between the retrieved NO 2 and MAX-DOAS is reduced slightly (R 2 decreases from 0.96 to 0.93 for the 30 daily data pairs).Had the CF and CP not been modified in accordance to the perturbed Rs, the influence of Rs would have been larger.
Overall, various sets of surface reflectance data lead to NO 2 columns within 10 % on average for the OMI pixels investigated here.The effects of different surface reflectance data sets are smaller than found for entire Europe (within 20 %; Zhou et al., 2010).

Effects of the vertical profile of NO 2
The assumed vertical profile of NO 2 affects the NO 2 retrieval because the layer AMFs decline with height in the troposphere (e.g., Fig. 3a).For example, assuming NO 2 to be closer to the ground reduces the AMF with a positive effect on the retrieved NO 2 column.The cloud retrieval is not affected.Cases 7-11 perturb the vertical profile of NO 2 .The   resulting profiles are illustrated in Fig. 3b for a pixel on 28 December 2008.
As described in Table 4, case 7 adopts the vertical profiles derived from the MAX-DOAS retrieval.Compared to the reference retrieval, it reduces the AMFs of NO 2 for 85 % of the pixels, consequently enhancing the retrieved NO 2 columns.This is because the MAX-DOAS profile assumes a larger fraction of NO 2 near the ground than the fraction simulated by GEOS-Chem (see the illustration in Fig. 3b).The resulting NO 2 columns are closer in magnitude to MAX-DOAS (NMB = −36 %).Similarly, case 8 adopts the vertical profiles simulated by TM4 (as in DOMINO-2); this leads to a 13 % increase in retrieved NO 2 column on average, because TM4 assumes NO 2 to be more concentrated near the surface.
Cases 9-11 further test extreme situations for the vertical shape of NO 2 , aiming to analyze the range of influences of vertical profile on the NO 2 retrieval.Case 9 assumes the mixing ratio of NO 2 to decline exponentially with height from the surface to 1.5 km (with a scale height of 0.25 km and with the column density conserved).Such a gradient is probably overestimated, based on a recent study for urban Paris (i.e., with strong surface emissions) by Dieudonné et al. (2013) showing the NO 2 concentration at 300 m height to be about 50-60 % of the concentration near the surface at the overpass time of OMI.By concentrating NO 2 near the ground, case 9 enhances the retrieved NO 2 columns with smaller differences from MAX-DOAS (NMB = −24 %).Case 11 further increases the retrieved NO 2 by assuming an unrealistic exponential decrease of NO 2 from surface to 3 km.In contrast, case 10 assumes NO 2 to be fully mixed within 0-1.5 km above the ground, thus lowering the retrieved NO 2 columns (NMB = −52 %); this case represents the lower end   of retrieved NO 2 columns due to the effect of its vertical profile alone.

Effects of aerosol optical effects
Aerosol optics affect the retrievals of cloud properties and NO 2 columns (Boersma et al., 2004(Boersma et al., , 2011;;Leitão et al., 2010).In retrieving the cloud information, aerosol scattering enhances the R TOA , thus reducing the CF (Fig. 5).It increases the AMF of O 2 -O 2 with a negative effect on the CP.Aerosol scattering also enhances the AMF of NO 2 when aerosols are collocated with or located below NO 2 .Aerosol absorption has opposite effects by enhancing the CF and CP and reducing the AMF of NO 2 .Furthermore, the height of aerosols is important for their influences on the R TOA and on the AMFs of O 2 -O 2 and NO 2 .Scattering aerosols located above NO 2 will attenuate the radiation reaching NO 2 (i.e., acting like clouds) with a negative effect on the AMF of NO 2 , as opposed to if scattering aerosols are below or collocated with NO 2 .When a given amount of absorbing aerosols are lifted to higher altitudes, their absorption effect is enhanced.
Section 5.3.1 evaluates the effects of aerosol scattering and absorption in retrieving clouds and NO 2 based on the simulated vertical shape of aerosols (cases 12-14 in Table 4).Section 5.3.2analyzes the influences of the vertical shape of aerosols, keeping the AOD and SSA unchanged (cases 15-17 in Table 4).

Effects of aerosol scattering and absorption based on the simulated vertical shape of aerosols
Compared to the reference retrieval, case 12 does not include the optical effects of aerosols, as is done in the retrieval processes of OMCLDO2 and DOMINO-2.As shown in Fig. 6a  the amounts of incremented CF, and there is large scattering in the increments of CF when AOD exceeds 1.0.The changes in CP do not correlate with the amounts of decremented AOD (R 2 = 0.10, middle panel), due to the compensating effect of excluding aerosol absorption versus excluding aerosol scattering.These results suggest complex effects of aerosol optical characteristics on the cloud retrieval.Comparisons of the cloud properties between case 12 and DOMINO-2 (OM-CLDO2) are presented in Appendix D.
Figure 7a shows the effects of excluding aerosols on the retrieved NO 2 in case 12.As discussed above, aerosols affect both the cloudy-sky and clear-sky AMFs of NO 2 .Moreover, aerosol scattering and absorption lead to different effects on the radiation fields relevant to the AMFs of both O 2 -O 2 and NO 2 .Thus, the exclusion of both aerosol scattering and absorption has large and complex impacts on the retrieved NO 2 columns for individual pixels, particularly when AOD is high.Of the 44 pixels with AOD of 0.8 or more, case 12 results in larger NO 2 columns than the reference retrieval by 0-50 × 10 15 molec cm −2 for 18 pixels, with negative effects by 0-20×10 15 molec cm −2 for the other 26 pixels (mid-dle panel).The percentage changes in NO 2 columns are as large as −40-90 % for the 44 pixels (right panel).Compared to the reference retrieval, assuming no aerosol optical effects in case 12 leads to a smaller mean bias relative to MAX-DOAS NO 2 data (NMB decreases from −46 % to −39 %) with lowered capability in capturing the day-to-day variability of MAX-DOAS NO 2 (R 2 decreases from 0.96 to 0.90).
The capability of aerosols to absorb solar radiation is determined mainly by black carbon.Emissions of black carbon in China have been under debate recently (Fu et al., 2012;Wang et al., 2013).The top-down constraint by Fu et al. (2012) suggested Chinese black carbon emissions to be underestimated by about 60 % by the INTEX-B inventory.In contrast, Wang et al. (2013) suggested consistent magnitudes of emissions between their top-down calculation and the INTEX-B data after filtering out high pollution plumes and large precipitation events (for which cases they determined that the CTM was limited by model resolution and wet deposition errors).In light of these studies, we test the effects of aerosol absorption in retrieving clouds and NO 2 by excluding or doubling the absorption in cases 13 and 14, respectively.Assuming no aerosol absorption in case 13 reduces the amounts of CF and CRF (Fig. 6c).It leads to reduced NO 2 columns in many but not all pixels (Fig. 7c), with a NMB of −54 % relative to MAX-DOAS NO 2 .Doubling aerosol absorption in case 14 has opposite effects on the retrieved clouds and NO 2 .
Figures 6b and 7b further present the sole effect of aerosol scattering by contrasting case 12 (neglecting both scattering and absorption) to case 13 (neglecting absorption).Neglecting aerosol scattering is compensated by increases in CF and CRF (Fig. 6b) with high correlation: R 2 = 0.84 (0.82) for the incremented CFs (CRFs) against the amounts of decremented scattering.This is consistent with the analysis by Boersma et al. (2011) for the southeastern US.The changes in CP do not correlate with the amounts of aerosol scattering omitted (Fig. 6b).Furthermore, Fig. 7b shows that neglecting aerosol scattering can either increase or decrease the retrieved NO 2 columns, with no obvious dependence on the amounts of aerosol scattering neglected (R 2 < 0.20 and the percentage changes range from −40 % to +160 %).This is because aerosol scattering increases the absorption both by black carbon and by NO 2 with compensating effects on the AMFs of NO 2 (Lin et al., 2012).Also, aerosol scattering affects the AMFs of NO 2 indirectly through its impacts on cloud fraction and cloud pressure.(Depending on the cloud pressure, the existence of clouds can either increase or decrease AMFs of NO 2 .)Our results suggest complex influences of aerosol scattering on the NO 2 retrieval.

Effects of the vertical shape of aerosols under given AOD and SSA
The MAX-DOAS sites are located in urban or suburban areas; therefore aerosols and NO 2 are dominated by anthropogenic sources and are collocated in the lower troposphere.Figure 3c illustrates the vertical distributions of aerosol EC and SSA assumed in the reference retrieval for a pixel on 28 December 2008.Cases 15-17 test the influences of the vertical shape of aerosols on the retrievals of clouds and NO 2 without altering AOD and SSA (Table 4).
Case 15 assumes constant EC and SSA of aerosols throughout the troposphere as an extreme situation for the vertical distribution of aerosols.It enhances both scattering and absorption of aerosols at high altitudes, thus reducing the AMF of O 2 -O 2 that is compensated for by an increase in CP.This case increases the CFs for 71 % of the pixels in compensating for the effect of enhanced aerosol absorption on the R TOA .Overall, putting more aerosols above NO 2 enhances the retrieved NO 2 columns with a NMB of −32 % relative to MAX-DOAS.
Case 16 puts all aerosols at the PBL top, thus lowering the contributions of O 2 -O 2 and NO 2 in the PBL.It increases the CFs for half of the pixels with negative effects for one-third of the pixels, due to the competing effects of aerosol scattering and absorption.Compared to the reference retrieval, case 16 increases the retrieved NO 2 columns with a reduction in NMB relative to MAX-DOAS (from −46 % to −39 %).Putting all aerosols to the tropopause (case 17) further reduces the NMB to −29 %; this test acts as another extreme case for analyzing the effect of aerosol vertical shape on the NO 2 retrieval.The artificial adjustments in aerosol vertical shape in cases 16 and 17 significantly reduce the correlation to MAX-DOAS NO 2 data (Table 4).

Summary of sensitivity tests and consistency between OMI and MAX-DOAS NO 2
That our reference retrieval captures the day-to-day variability of MAX-DOAS NO 2 much better than DOMINO-2 (R 2 = 0.96 versus 0.72) is caused by multiple factors.The largest contribution comes from the pixel-specific RTM calculation in place of the use of a LUT (R 2 increases from 0.72 to 0.85; see Sect. 4 and Appendix C).Additional improvements are derived from the inclusion of aerosol optical effects (R 2 decreases by 0.06 when excluding aerosols, case 12) and surface reflectance anisotropy (R 2 decreases by 0.03 when adopting the OMI albedo instead of the MODIS BRDF, case 6).Changes in vertical profile of NO 2 alone do not affect the correlation significantly for the OMI data analyzed here (case 8).There may be nonlinear interactions between the effects of these individual factors affecting the overall retrieval results.
Our reference retrieval leads to lower NO 2 columns than MAX-DOAS by 46 % on average.The difference is caused largely by the inevitable spatial inconsistency between OMI and MAX-DOAS measurements (effects roughly estimated at 20-30 %).This factor can be weakened in future studies using MAX-DOAS measurements taken at places with a more homogeneous horizontal distribution of NO 2 (e.g., rural areas).Other possible factors include errors in MAX-DOAS measurements (by 11-14 %; Irie et al., 2012;Hendrick et al., 2013) and uncertainties in our reference retrieval associated with SSA of aerosols (by 15 % based on cases 13-14), vertical distribution of aerosols (by 15 % based on case 16), and vertical profile of NO 2 (by 10-20 % based on cases 7-8).The uncertainties in a given parameter may also influence the importance of other parameters in retrieving NO 2 .
On average, the magnitude of NO 2 columns in DOMINO-2 is higher than our reference retrieval by 76 % and is close to MAX-DOAS.This is caused in part by a significant overestimate in surface pressure adopted in DOMINO-2 (the effect is estimated at 25 % in Sect.4).The higher NO 2 columns in DOMINO-2 are contributed also by the exclusion of aerosols (effect at 14 %, case 12), a stronger vertical gradient of NO 2 (effect at 13 %, case 8), and possibly the use of a DAK-based LUT (effect at 4 %, case 1).

Conclusions
Based on LIDORT v3.6, we improved the AMF calculation ("AMFv6" code) in order to retrieve VCDs of tropospheric NO 2 from OMI and to evaluate the effects of aerosols, surface reflectance anisotropy, and vertical profile of NO 2 in the retrieval process.To derive the VCDs, our reference retrieval calculated the AMFs of NO 2 independently after adopting the tropospheric SCDs from the widely used DOMINO-2 product.We retrieved the cloud properties prior to the retrieval of NO 2 using consistent ancillary parameters including but not limited to surface pressure, surface reflectance, and aerosols.We accounted for surface reflectance anisotropy by adopting the MODIS BRDF data.We used vertical profiles of NO 2 simulated by the nested GEOS-Chem model.Also, we explicitly accounted for the effect of aerosols on the solar radiation during the retrieval process by incorporating aerosol information from GEOS-Chem simulations and observations.
We compared DOMINO-2 to our NO 2 retrieval, using the ground-based MAX-DOAS measurements at three urban/suburban sites in East China as reference and focusing on the 127 OMI pixels in 30 days complying with our spatial constraints (pixel-center distance ≤ 25 km, VZA ≤ 30 • ).Compared to DOMINO-2, our reference retrieval better captures the day-to-day variability in MAX-DOAS NO 2 (R 2 = 0.96 versus 0.72 for the 30 days).This is due to the LIDORTbased pixel-specific radiative transfer calculations instead of interpolation from a DAK-derived LUT (R 2 increases by 0.13), the explicit inclusion of aerosols (R 2 increases by 0.06), the inclusion of surface reflectance anisotropy (R 2 increases by 0.03), and the potential interactions between the effects of these factors.
Our reference retrieval leads to NO 2 columns about 54 % of MAX-DOAS data on average.The difference is due to the inevitable spatial inconsistency between the ground-and space-based remote sensing (by 20-30 %, a rough estimate), errors in MAX-DOAS measurements (by 11-14 %), and uncertainties in our OMI NO 2 retrieval associated with aerosols (SSA and vertical distribution, by 15 % each) and vertical shape of NO 2 (by 10-20 %).The magnitude of NO 2 columns retrieved by DOMINO-2 is closer to the MAX-DOAS measurements, due in part to the overestimate in surface pressure, the exclusion of aerosols, a stronger vertical gradient of NO 2 , and possibly the adoption of a DAK-based LUT in the retrieval process.Note that our estimate for the effect of spatial inconsistency is preliminary since the spatial inhomogeneity of NO 2 strongly depends on the locations, time, and meteorological conditions (Brinksma et al., 2008;Irie et al., 2012;Ma et al., 2013).Comparisons with MAX-DOAS measurements and NO 2 sondes (Sluis et al., 2010) in places with a more homogenous distribution of NO 2 will be less subject to the effect of spatial inconsistency, and will help separate the effects of individual ancillary assumptions in retrieving NO 2 .
When excluding aerosols in the cloud retrieval, the increase in retrieved cloud fraction is highly correlated to the amount of aerosol scattering omitted (R 2 = 0.84).However, the effect of omitting aerosol scattering on retrieved cloud pressure and the effect of omitting aerosol absorption on both cloud fraction and cloud pressure are complex and nonlinear.Compared to DOMINO-2, the inclusion of aerosols increases the number of valid OMI pixels with low cloud coverage (CRF ≤ 50 %, the criterion for cloud screening) by about 25 % for the data set investigated here.
In retrieving NO 2 , the inclusion or exclusion of aerosol optical effects results in very different AMFs and VCDs of tropospheric NO 2 for individual pixels.Particularly when AOD exceeds 0.8, the retrieved NO 2 columns differ by −70-90 % with versus without the inclusion of aerosols.This supports a better treatment of aerosols in retrieving NO 2 , with important implications for further applications such as emission inversion at fine spatial or temporal scales.Meanwhile, the difference is about 14 % for the 30-day average NO 2 column with or without explicitly accounting for aerosols in the retrieval process, suggesting that the effect of aerosols may be reduced by spatiotemporal averaging.
Adopting the vertical shape of NO 2 from TM4 or MAX-DOAS increases the retrieved NO 2 columns by 13-19 % on average.This sensitivity calls for a better representation of NO 2 vertical profile in the retrieval process.In addition, a variety of assumptions on surface reflectance (e.g., MODIS BRDF, MODIS black-sky or blue-sky albedo, and OMI albedo) lead to similar NO 2 columns on average (within 10 %).This reflects the compensation between the direct effect of surface reflectance errors in retrieving NO 2 and its indirect impact through the cloud retrieval for the OMI pixels investigated here.Zhou et al. (2010) suggested larger sensitivity of the NO 2 retrieval to surface reflectance data over Europe.
As a concluding remark, the effects of aerosols and surface reflectance anisotropy found here also have important implications for retrievals of other species (sulfur dioxide, formaldehyde, glyoxal, etc.) from OMI and/or other UVvisible backscatter instruments.We recommend that aerosols and surface reflectance anisotropy be explicitly accounted for in future satellite retrievals, especially when a near-real-time retrieval (fast computation) is not required, so that these factors can be well characterized for individual pixels in the retrieval process without the use of a LUT.Aerosol information can be adopted from observations or model simulations (especially after constrained by independent measurements).Even when accurate aerosol information is not available, a retrieval that explicitly accounts for the effects of aerosols can provide an alternate product for comparisons with a nearreal-time product with no explicit consideration of aerosols.In addition, we suggest using high-resolution vertical profiles of tracers in the retrieval process to better characterize their spatial inhomogeneity.   of TM4 (with 34 layers) to the coordinate assumed in the LUT (with 24 layers).The projection introduces certain errors due to the large vertical variability in the layer AMFs (e.g., Fig. 3a).Our AMF calculation adopted the TM4 pressure coordinate with no need of a coordinate projection.A LUT also means that layer AMFs are obtained by linear interpolation based on various parameters (As, Ps, CF, CP, and light path geometry), as opposed to our pixel-specific RTM simulations.Further research is required to quantify the effects of these individual factors.

Retrieval of cloud properties assuming no aerosols: our retrieval versus DOMINO-2 (OMCLDO2)
Our case 12 assumes no aerosols with consequences on the retrieved cloud properties.Figure A2 shows that the CRFs in case 12 are close to those in DOMINO-2, and that the CFs in case 12 are similar to OMCLDO2 averaged over all pixels.However, notable differences exist for individual pixels, due to differences in surface reflectance, pressure and temperature profiles, RTMs, and whether or not to use a LUT (Tables 2 and 3 and Appendix C).
The CP produced by case 12 is larger than OMCLDO2 (Fig. A2).The difference is not caused by the different Ps data used according to our test cloud retrieval adopting the Ps data from OMCLDO2.Further research is needed to determine the causes of the difference.

Fig. 2 .
Fig. 2. Scatter plots between DOMINO-2 (y axis) and our reference retrieval (x axis) for surface reflectance, surface pressure, cloud fraction, cloud pressure, and cloud radiance fraction across the individual pixels.For (a), the OMLER v1 albedo data (y axis) are compared to the MODIS bidirectional reflectance factors (BRF, x axis).The criteria for pixel selection are presented in Sect.2.4.The number of pixels is smaller for cloud pressure because cloud fraction is 0 in some pixels.Also shown are the statistics from the RMA regression; the dashed line indicates the regression curve and the dotted line denotes the 1 : 1 relationship.

Fig. 3 .
Fig. 3. (a) The pressure dependence of layer AMFs for an OMI pixel on 28 December 2008.The derived cloud radiance fraction (CRF) and AMF are depicted as well, together with the AMF from DOMINO-2 (with respect to the red dashed line).(b) The vertical shape of NO 2 (i.e., VMRs of NO 2 normalized to the maximum VMR).(c) The vertical distributions of aerosol extinction coefficient (EC, km −1 ) and SSA assumed in our reference retrieval (case 0).The thickness of the individual layers is shown in the EC line.The horizontal grey line depicts the PBL top.

Fig. 4 .
Fig. 4. Scatter plots for NO 2 columns (10 15 molec cm −2 ) from MAX-DOAS measurements and OMI retrievals.Each "+" corresponds to an OMI pixel in (a-c), as well as to the mean value from all OMI pixels in a day in (d-f).The criteria for pixel selection are presented in Sect.2.4.Also shown are the statistics from the RMA regression; the dashed line indicates the regression curve and the dotted line denotes the 1 : 1 relationship.The RMA regression in (a-c) should be interpreted with caution since there may be multiple OMI pixels/data in a day corresponding to a single MAX-DOAS value.

Fig. 5 .
Fig. 5. Effects of surface reflectance (Rs), aerosol scattering optical depth (ASOD), and aerosol absorption optical depth (AAOD) on the retrieval of cloud fraction (CF) and cloud pressure (CP).Aerosols are assumed to be concentrated in the lower troposphere, as for the OMI pixels examined in this study.Grey denotes a secondary effect of the changed CF on the CP; the effect depends on the amount of O 2 -O 2 AMF in the cloudy portion of the pixel (AMF cl ) relative to the AMF in the clear-sky portion (AMF cr ).The changes in CP have a relatively small effect on the CF (not depicted here). 1

Fig. 6 .
Fig. 6.Absolute changes in the retrieved cloud properties for the 127 OMI pixels by neglecting (a) AOD, (b) aerosol scattering, and (c) aerosol absorption.The criteria for pixel selection are presented in Sect.2.4.The number of pixels is smaller for cloud pressure because cloud fraction is 0 in some pixels.Also shown are the statistics from the RMA regression; the dashed line indicates the regression curve.

Fig. 7 .
Fig. 7. Similar to Fig. 6 but for the absolute changes in the AMF of NO 2 (left column) and the absolute (middle column) and percentage (right column) changes in the VCD of NO 2 .

Fig. A1 .
Fig. A1.Dependence on pixel-center distance and VZA of the RMA regression (slope and R 2 ) for the daily NO 2 columns between MAX-DOAS and OMI retrievals.The lower left tile in each panel represents distance ≤ 25 km and VZA ≤ 30 • .The rest of the criteria for pixel selection are unchanged (row-anomaly-free, ice/snow-free, CRF ≤ 0.5).Overlaid on (d) is the number of days with suitable NO 2 data for conducting the RMA regression.
Fig. A2.Scatter plots between DOMINO-2 (y axis) and our case 12 (assuming no aerosols, x axis) for cloud properties across the individual pixels.DOMINO-2 adopts cloud fraction and cloud pressure from OMCLDO2.The criteria for pixel selection are presented in Sect.2.4.The number of pixels is smaller for cloud pressure because cloud fraction is 0 in some pixels.Also shown are the statistics from the RMA regression; the dashed line indicates the regression curve and the dotted line denotes the 1 : 1 relationship.

Table 2 .
RTMs and ancillary parameters in deriving tropospheric NO 2 columns from OMI.

Table 3 .
RTMs and ancillary parameters in deriving cloud properties from OMI.The pressure levels are recalculated according to the elevation-adjusted surface pressure.

Table 4 .
Retrieving VCDs of NO 2 from OMI by altering the ancillary parameters * .
• , unless stated otherwise.A stricter spatial constraint would significantly reduce the number of days with suitable data, not allowing for a meaningful analysis.The dependence on distance and VZA of the comparison between OMI and MAX-DOAS data is discussed in Appendix B.