Figure  shows a conceptual framework for trace-gas retrievals from a satellite spectrometer (e.g., Aura OMI); this quantifies trace-gas columns by analyzing spectral features in reflected sunlight. NO2 and other gases like ozone O3 and SO2 each have their own unique spectral absorption signature. The differential optical absorption spectroscopy (DOAS) algorithm converts these spectral signatures into a slant column density (SCD), the number of absorbing gas molecules along the effective photon path through the atmosphere to the satellite. The SCD is then converted into a vertical column density (VCD), the number of gas molecules in a vertical atmospheric column, using the concept of an air mass factor (AMF) that encapsulates the relationship between the measured SCD and VCD as VCD=SCD/AMF.

Theoretically, the relationship between SCD and VCD can be defined in terms of vertically resolved Jacobians, J(h)=-∂ln⁡I/∂τ(h), where I is the top-of-atmosphere (TOA) radiance and τ(h) is the gaseous absorption optical thickness at altitude h.

Generally, the AMF is calculated as 1AMF=∫0∞J(h)S(h)dh, where S(h) is the profile shape factor.

For O2-O2, absorption is a function of the square of the pressure, and S(h) is given by 2S(h)=σ(h)n2(h)/∫0∞σ(h)n2(h)dh, where σ(h) is the O2-O2 absorption cross section as a function of height (because of its dependence of temperature) and n(h) is the number density of O2.

Figure  shows an overall flow of our approach. The lower part of the diagram shows the trace-gas retrieval, in our case for NO2 but this could apply to other trace gases retrieved from UV–vis sensors. Spectral fitting is applied to both O2-O2 for the subsequent cloud retrieval and NO2. Cloud parameters are then used as inputs to the NO2 VCD algorithm. The other main inputs to the VCD algorithm are the clear- and cloudy-sky Jacobians. For the Jacobian calculations, surface bidirectional reflectance distribution function (BRDF) parameters from the MODerate-resolution Imaging Spectroradiometer (MODIS) instruments are used as inputs along with the UV–vis sensor (OMI) sun–satellite geometry as well as collocated aerosol optical properties. Details of the individual steps and input data are given below.

We use aerosol optical properties from the NASA Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing System version 5 (GEOS-5) system . The GEOS-5 global aerosol data assimilation system incorporates information from MODIS and recently completed a multi-decadal aerosol reanalysis, the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) , which includes assimilation of the aerosol optical depth (AOD) from various ground- and space-based remote sensing platforms . The analysis system is driven by a prognostic model comprising the global atmospheric circulation model, GEOS-5, radiatively coupled to the Goddard Chemistry, Aerosol, Radiation, and Transport model (GOCART) . The GOCART module simulates the production, loss, and transport of five types of aerosols (dust, sea salt, black carbon, organic carbon, and sulfate) treated as noninteractive external mixtures. The aerosol optical properties are described in and are primarily based on the Optical Properties of Aerosols and Clouds database , with updates to dust properties to account for nonsphericity .

The MERRA-2 global aerosol analysis data set provides vertically resolved 3D distributions of spectral aerosol layer optical depth, τ(h); single-scattering albedo (SSA), ωo(h); and scattering phase matrix, P(h,γ), as a function of the scattering angle γ, on 72 layers from the surface to the top of the atmosphere at a native resolution of 0.5∘ latitude by 0.625∘ longitude every 3 h. These parameters are needed for the radiative transfer (RT) computations of TOA radiance and trace-gas AMFs. The MERRA-2 aerosol analysis has been evaluated against independent (not assimilated) observations from ground-, aircraft-, space-, and shipborne measurements . For instance, comparisons of MERRA-2 analyzed AOD to historical (1982–1996) shipborne measurements show that the model has a mean bias in AOD of 0.009 and a strong correlation with the observations (r=0.71), while a comparison to the Marine Aerosol Network (MAN) observations from 2004–2015 showed a mean bias of 0.01 and a standard error of 0.002 (r=0.93). MERRA-2 analyzed AOD was also compared to airborne high-spectral-resolution lidar (HSRL) AOD observations during the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) campaign, which consisted of several flights during August–September 2013 over North America. Compared to HSRL observations, MERRA-2 AOD has a mean bias of 0.01 and standard error of 0.005 (r=0.85). The MERRA-2 aerosol analysis shows significant skill at representing dynamic global 3D aerosol distributions. For example, the MERRA-2 absorption aerosol optical depth (AAOD) and ultraviolet aerosol index (AI) compare well with OMI observations .

For RT calculations here and elsewhere, we use the vector linearized discrete ordinate radiative transfer (VLIDORT) code . VLIDORT computes the Stokes vector in a plane-parallel atmosphere with a Lambertian or non-Lambertian underlying surface. It has the ability to deal with attenuation of solar and line-of-sight paths in a spherical atmosphere, which is important for large solar zenith angles (SZAs) and viewing zenith angles (VZAs). This pseudo-spherical mode of VLIDORT was used in all our computations including online calculation and generation of lookup tables. VLIDORT computes the single-scattering contribution exactly in a spherically curved atmosphere using the full scattering matrix. For multiple scattering, VLIDORT treats the direct solar beam attenuation in the pseudo-spherical approximation. This study used the delta-M scaling option to treat sharply peaked aerosol phase functions . We used 12 discrete ordinate streams in the polar hemisphere half space for the computation.

The Earth's surface reflectance depends on illumination and observation geometry. The surface reflection anisotropy is described by the BRDF. To account for surface BRDF in our satellite algorithms, we have introduced the concept of a surface geometry-dependent Lambertian-equivalent reflectivity (GLER) in . The GLER is derived from TOA radiance computed for Rayleigh scattering and full surface BRDF for the particular geometry of a satellite instrument pixel. The TOA radiance computed by VLIDORT is then inverted to derive GLER using the following exact equation: 3ITOA=I0+GLER⋅T1-GLER⋅Sb, where I0 is the TOA radiance calculated for a black surface, T is the total (direct+diffuse) solar irradiance reaching the surface converted to the ideal Lambertian-reflected radiance (by dividing by π) and then multiplied by the transmittance of the reflected radiation between the surface and TOA in the direction of a satellite instrument, and Sb is the diffuse flux reflectivity of the atmosphere for the case of its isotropic illumination from below . All quantities, I0, T, and Sb are calculated using a known surface pressure for a given OMI pixel. The GLER concept has been evaluated with OMI over both land and ocean .

The GLER approach provides an exact match of TOA radiances with the full BRDF approach, i.e., the TOA radiance calculated with the full surface BRDF is equal to the radiance calculated with GLER. This approach does not require any major changes to existing MLER trace-gas and cloud algorithms. It simply requires replacement of the static LER climatologies with GLERs pre-computed for a specific satellite instrument.

We have incorporated GLERs based on a MODIS BRDF product and use these GLERs within OMI cloud and NO2 algorithms . Climatological LER values have inevitable cloud and aerosol contamination because they are derived from TOA radiance measurements by removing the Rayleigh scattering contribution only . The cloud–aerosol contribution is minimized by selecting lower values of the residuals; however it cannot be removed completely, partially due to the relatively large OMI footprint. The OMI GLER is computed using the MODIS BRDF product, which is derived from the atmospherically corrected TOA reflectance, that is after applying the MODIS cloud mask algorithm and removing aerosol scattering effects at the much higher spatial resolution of MODIS compared with OMI.

Therefore, the use of the GLER product in trace-gas algorithms over heavily polluted regions greatly benefits from an explicit account of aerosols .

Aerosols can both increase and decrease sensitivity to trace-gas absorption in satellite trace-gas retrievals depending on their optical properties and vertical distributions relative to the trace-gas vertical profile . Aerosol scattering and absorption may shield photons from the atmosphere below, decreasing sensitivity to trace-gas absorption. This effect is particularly pronounced when the primary layer of aerosols is located above the region of the atmosphere that contains the trace gas of interest. Aerosol scattering within the trace-gas layer increases photon path lengths and therefore may also enhance sensitivity to trace-gas absorption.

To illustrate these effects, we conduct a theoretical study of the aerosol effects on NO2 scattering weights for two model aerosol profiles. We perform calculations for a case where aerosols are elevated near the surface and another case where aerosols are present in an elevated layer (with a Gaussian shape and peak near 3 km altitude). For all computations, we use a single NO2 profile that corresponds to a polluted region. For each aerosol profile we perform calculations for two values of ω0. We use ω0=1.0 for a case of nonabsorbing aerosol, and for the case of absorbing aerosols, we used ω0=0.88. For both cases we assumed that ω0 is uniform throughout the atmosphere. For these computations, we set the surface albedo to 0.05, the VZA to zero (nadir), and the SZA to 45∘. Based on the computed Jacobians, we calculate the NO2 AMFs for the four different aerosol scenarios (two profiles and two values of ω0).

Figure  (left) shows the two model aerosol profiles along with a typical vertical profile of NO2 number density for polluted areas. The total aerosol optical depth (AOD) for both aerosol profiles is equal to 1.0.

Figure b compares the Jacobians with respect to NO2 layer optical depth computed for nonabsorbing aerosol profiles with the Jacobian for the aerosol-free atmosphere. Here, elevated aerosol clearly exhibits enhanced sensitivity to NO2 above the aerosol layer and the shielding effect below. As a result of the shielding effect of the elevated aerosol, the values of NO2 AMFs are lower than that for the aerosol-free NO2 AMF. The near-surface aerosol enhances the sensitivity to NO2 for almost all altitudes; however, the enhanced sensitivity drops abruptly towards the surface owing to the increasing shielding effect.

Similarly, Fig. c compares the Jacobians computed for absorbing aerosols with the Jacobian for the aerosol-free atmosphere. In general, aerosol absorption decreases the NO2 sensitivity for both aerosol profiles. However, the qualitative dependence of the Jacobians on height remains similar to the nonabsorbing aerosol Jacobians.

To demonstrate our explicit aerosol correction effects on the OMI cloud and NO2 retrievals, we selected a cloud-free area over land in the Shenyang region of northeastern China. Figure  shows a map of OMI TOA reflectance over northeastern China calculated at 440 nm for orbit 3843 on 5 April 2005. The selected cloud-free area is shown by a square on this map. The GEOS-5 MERRA-2 aerosol optical properties were collocated over nominal OMI pixels within the area. There are in total 114 OMI pixels within the selected area. The selected area has low cloud fractions (ECF<0.1) but significant aerosol loading, AOD≈0.5–0.6, according to the MERRA-2 data set.

Figure  shows vertical profiles of the layer AOD, SSA, and asymmetry parameter of a scattering phase function for different OMI pixels from the MERRA-2 data set within this selected area. The asymmetry parameter characterizes the anisotropy of the phase function, i.e., a size of aerosol particles. According to the MERRA-2 aerosol analysis, most aerosol is located in the planetary boundary layer (PBL) with significant increase in aerosol loading towards the surface. There is some enhancement of aerosol loading at altitudes of about 11 km. This aerosol plume at 11 km has distinctive optical properties with increased SSA (lower aerosol absorption) and increased asymmetry parameter (larger aerosol particles). The PBL aerosol has relatively low SSA within 0.83–0.88 and a slightly increased asymmetry parameter (however lower than in the high-altitude plume).

NO2 profiles (shown in Fig. a) and other model-derived information (e.g., temperature profiles, tropopause pressure) used in the computations are taken from the Global Modeling Initiative (GMI) model. The GMI simulation is driven by the meteorological fields from MERRA-2. We use the GMI model because the simulations have been run consistently from the start of the OMI mission, and this allows us to reprocess results from the entire OMI mission with the proposed aerosol correction.

Figure  shows both the climatological LER and GLER for the selected area for OMI orbit 3843 on 5 April 2005. We used the climatological LER for our cloud and NO2 retrievals in the following figures for the purpose of demonstrating the BRDF effects on the retrievals. It is seen from Fig.  that values of GLER are noticeably lower than climatological LER values because the latter represent the most probable values of LER, which implicitly account for persisting aerosol layers. On average, the difference between the climatological LER and GLER for this area is about 0.03. It should be noted that the differences include both BRDF effects and biases between the MODIS and OMI-based surface reflectance data sets. This is because the BRDF data and thus the GLERs are derived from atmospherically corrected MODIS radiances while the climatological LERs are inherently affected by residual aerosols. Additionally, climatological LERs can be contaminated by clouds due to the substantially larger OMI pixel size compared with MODIS footprints. Calibration differences between OMI and MODIS are discussed in , and specific details are provided in Appendix D: “Relative calibration of OMI and MODIS” of that paper. To summarize, MODIS Collection 5 radiances (used to derive BRDF kernel coefficients and thus GLER values) are higher than OMI Collection 3 radiances by approximately 1 %. A sensitivity analysis of the equation used to compute GLER shows that a 1 % error in TOA radiances will produce errors in LER of up to 0.003 in surface reflectivity. This value is much lower than the reported average difference between the climatological LER and GLER of 0.03. The atmospheric correction for MODIS band 3 used in this study has a theoretical error budget of about 0.005 reflectance units . Again, this error is much lower than the reported average difference, suggesting that neither the calibration differences nor the MODIS atmospheric correction are major contributors to the observed difference between climatological LER and GLER.

Figure  compares ECF retrievals computed using climatological LERs with those computed using GLER and either implicit or explicit aerosol corrections. The comparison of ECFs retrieved with the climatological LER and the GLER and implicit aerosol correction shows the effects of replacing the surface climatological LER with the GLER only. As discussed earlier in , the GLERs are lower than the climatological LERs, thus resulting in lower computed clear-sky radiances in Eq. () and subsequently higher retrieved ECFs. Explicit account of the aerosol contribution increases the computed clear-sky radiance, thus reducing the retrieved ECF. The combined effect of GLER and explicit aerosol correction leads to ECFs slightly higher than those retrieved with the climatological LER for most pixels. The climatological LER is contaminated by aerosols and possibly clouds owing to the substantially larger size of OMI pixels compared with those of MODIS data that are used for computation of GLER. That is why the lower ECFs retrieved with the climatological LER may indicate that the MERRA AOD derived for this particular day is slightly lower than climatological AOD (and possibly residual cloud optical depth) for those pixels.

Similarly, Fig.  compares OCP retrievals computed using the climatological LER with those calculated using the GLER and either implicit or explicit aerosol corrections. The GLER effect on OCPs is mixed. For most OMI pixels, replacing the climatological LER with GLER results in lower OCPs. However for some pixels, this replacement leads to higher OCPs. It is not straightforward to explain the GLER effect on OCP because the retrieved OCP depends on both ECF and clear-sky O2-O2 AMF, both of which are affected by replacing the climatological LER with GLER. The comparison of OCPs retrieved with either implicit or explicit aerosol correction (Fig. b versus Fig. c) shows that the explicit aerosol correction significantly increases values of the OCPs for the overwhelming majority of OMI pixels. Again, this is a complex effect with multiple factors including the ECF calculation.

Finally, Fig.  compares tropospheric NO2 VCD retrievals computed using the climatological LER with those computed using the GLER and either implicit or explicit aerosol corrections. Replacing the climatological LER with GLER significantly increases the retrieved NO2 amounts as has been shown previously for polluted areas in . The explicit aerosol correction additionally enhances the NO2 vertical column density for all OMI pixels within the selected area. This enhancement is caused by the combined effect of the explicit aerosol correction on the cloud parameters and clear-sky NO2 AMFs. This aerosol correction is in line with low biases in the satellite NO2 retrievals as documented in several publications . For instance, compared total NO2 column retrievals from OMI with the ground-based Pandora at multiple sites in the US and South Korea and found up to a factor of 2 lower column estimates by OMI. Assessment of OMI NO2 retrievals with ground- and aircraft-based NO2 observations during the DISCOVER-AQ (Deriving Information on Surface conditions from Column and Vertically Resolved Observations Relevant to Air Quality) and KORUS-AQ (Korea-United States Air Quality Study) field campaigns suggested that OMI NO2 retrievals are about 20 % lower compared to validation measurements even after accounting for the effect of a priori NO2 profiles and spatial mismatch using high-resolution NO2 simulations . Both studies point to surface reflectivity and other factors in the NO2 AMF for the low biases in OMI NO2 retrievals. The application of our approach of the explicit aerosol correction to the selected area shows that the NO2 increase due to the correction is in the direction of reducing the documented low biases in the NO2 retrievals with respect to ground- and aircraft-based observations.

Given that the cloud fractions are very low for the selected area (ECF<0.1), it is reasonable to suppose that the effect of the explicit aerosol correction on the NO2 enhancement is mostly caused by decreasing the clear-sky AMF. The MERRA-2 aerosol data show absorbing aerosols for the selected area (see Fig. ), particularly for near-surface aerosol. According to our RT simulations, the absorbing aerosols mostly decrease NO2 AMFs for this case. However, our preliminary analysis outside of the selected area reveals a more complex picture demonstrating both shielding and enhancement aerosol effects. A global analysis of the aerosol effects will be a subject of our follow-up paper.

Figure  further elucidates the effect of explicit aerosol correction on cloud and NO2 retrievals. It shows scatter plots of ECF, OCP, and tropospheric NO2 computed with GLER and implicit versus explicit aerosol corrections. The explicit aerosol correction consistently decreases the retrieved ECF within the whole range of ECFs. This ECF decrease does not depend on an ECF value and is equal to approximately 0.015 on average. OCP changes due to the explicit aerosol correction generally depend on the value of OCP. The OCP increases with explicit account of aerosol for the overwhelming majority of pixels. This OCP increase is most pronounced for high values of OCP, i.e., for low-altitude clouds. For such clouds, the OCP increases by about 100 hPa. The OCP increase is approximately 50 hPa for mid-altitude clouds with OCP of about 800 hPa.

An interesting effect of the explicit aerosol correction on OCP is that OCP values for high-altitude clouds are lower for a few pixels within the selected area, while in general OCPs are higher for the remaining bulk of pixels. In particular this is true for high-altitude clouds with OCP values of about 500 hPa. It should be noted that an OCP error is amplified with lower cloud fraction values. This is true for all cloud pressure algorithms. In addition to OCP, we retrieve the so-called scene pressure . In the absence of clouds and aerosols, the scene pressure should be equal to the surface pressure. A difference between the scene pressure and surface pressure can be considered an estimate of the OCP retrieval bias. This bias is about 40 hPa. Thus an increase of 50 hPa is comparable to the expected accuracy of the OCP retrievals. However, in our work we compare the OCP retrievals with and without the explicit aerosol correction. Even though these retrievals possess bias, difference between them, e.g., increase of 50 hPa due to the implicit aerosol correction, does make sense.

The explicit aerosol correction increases the tropospheric NO2 VCDs for all OMI pixels of the selected area by approximately 20 % on average. This indicates that the aerosol shielding effect prevails over the effect of aerosol enhancement of photon path length for the selected area.

The uncertainties in tropospheric NO2 retrievals arise from the uncertainties in NO2 slant column retrievals, in the AMF calculations, and from the stratosphere–troposphere separation scheme. The uncertainty in NO2 slant columns is about 0.8×1015 molec.cm-2, which is typically less than 7 % in high slant column cases (either over polluted areas or for observations at high solar zenith angle) and reaches up to 20 % in clean areas. Uncertainties in the AMF are 20 %–80 % and dominate the overall retrieval uncertainties . Errors in the a priori vertical NO2 profile shape, surface reflectivity, and cloud–aerosol treatment are the largest error sources . The uncertainty in the stratosphere–troposphere separation is expected to be less than 0.3×1015 molec.cm-2, especially in polluted areas . Consistent with prior studies by and , our study suggests that the aerosol effect over China is significant and is similar to that of a priori NO2 profile shape and surface reflectivity.

It should be noted that we used the vector VLIDORT code to calculate TOA radiances and vertically resolved O2-O2 and NO2 Jacobians in our case study. Such calculations have been too computationally expensive for online use in global processing of multi-year satellite data records. A scalar approximation to the radiative transfer equation implemented using the LIDORT code is much faster than VLIDORT and saves computational costs by about an order of magnitude. However the LIDORT produces errors in TOA radiance as large as 10 % due to neglect of polarization effects. Recently, an artificial neural network (NN) technique to correct TOA radiances from the LIDORT to within 1 % of vector-calculated radiances has been developed . We plan to optimize the NN technique for the OMI cloud and NO2 algorithms and extend it to calculate vertically resolved Jacobians.