Explicit and consistent aerosol correction for visible wavelength satellite cloud and nitrogen dioxide retrievals based on optical properties from a global aerosol analysis

We discuss an explicit and consistent aerosol correction for cloud and NO2 retrievals that are based on the mixed Lambertian-equivalent reflectivity (MLER) concept. We apply the approach to data from the Ozone Monitoring Instrument (OMI) for a case study over norththeast Asia. The cloud algorithm reports an effective cloud pressure, also known as cloud optical centroid pressure (OCP), from oxygen dimer (O2−O2) absorption at 477 nm after determining an effective cloud fraction (ECF) at 466 nm. The retrieved cloud products are then used as inputs to the standard OMI NO2 algorithm. A geometry5 dependent Lambertian-equivalent reflectivity (GLER), which is a proxy of surface bidirectional reflectance, is used for the ground reflectivity in our implementation of the MLER approach. The current standard OMI cloud and NO2 algorithms implicitly account for aerosols by treating them as non-absorbing particulate scatters within the cloud retrieval. To explicitly account for aerosol effects, we use a model of aerosol optical properties from a global aerosol assimilation system and radiative transfer computations. This approach allows us to account for aerosols within the OMI cloud and NO2 algorithms with 10 relatively small changes. We compare the OMI cloud and NO2 retrievals with implicit and explicit aerosol corrections over our study area.

. Conceptual diagram showing various paths of scattered and/or absorbed sunlight relevant to an NO2 retrieval that may be observed from satellite along with standard terminology used for UV/Vis trace-gas retrievals. Stutz, 2008), converts these spectral signatures into a slant column density (SCD), the number of absorbing gas molecules 90 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) = −∂lnI/∂τ (h), where I is the top-of-atmosphere (TOA) radiance and τ (h) is the gaseous absorption optical thickness at 95 altitude h. Generally, the AMF is calculated as (Palmer et al., 2001) where S(h) is the profile shape factor. For O 2 −O 2 , absorption is a function of the square of the pressure, and S(h) is given by 100 where σ(h) is the O 2 −O 2 absorption cross-section as a function of height and n(h) is the number density of O 2 . Figure 2 shows an overall flow of our approach. The lower part of the diagram shows the trace-gas retrieval, in our case for NO 2 but this could apply to other trace-gases retrieved from UV/Vis sensors. Spectral fitting is applied to both O 2 −O 2 for the subsequent cloud retrieval as well as to NO 2 . Cloud parameters are then used as inputs to the NO 2 VCD algorithm.  The other main inputs to the VCD algorithm are the clear-and cloud-sky Jacobians. For the Jacobian calculations, surface 105 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.

Assimilated aerosol parameters
We use aerosol optical properties from the NASA Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing

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System version 5 (GEOS-5) system (Randles et al., 2017). The GEOS-5 global aerosol data assimilation system incorporates information from the MODIS and recently completed a multi-decadal aerosol reanalysis, the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) (Gelaro et al., 2017), that includes assimilation of the aerosol optical depth (AOD) from various ground-and space-based remote sensing platforms (Randles et al., 2017). The analysis system is driven by a prognostic model comprising the global atmospheric circulation model, GEOS-5, radiatively coupled to the God-115 dard Chemistry, Aerosol, Radiation, and Transport model (GOCART) (Colarco et al., 2010). 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 non-interactive external mixtures. The aerosol optical properties are described in Colarco et al. (2010) and are primarily based on the Optical Properties of Aerosols and Clouds database (Hess et al., 1998), with updates to dust properties to account for non-sphericity (Colarco et al., 2014).

RT calculations 135
For RT calculations here and elsewhere, we use the Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT) code (Spurr, 2006). 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 (SZA) and viewing zenith angles (VZA). This pseudo-spherical mode of VLIDORT was used in all our computations including on-line calculation and generation of lookup tables.

Surface reflectivity treatment
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 LER (GLER) in Vasilkov et al. (2017). The GLER is derived from TOA radiance computed with Rayleigh scattering and surface BRDF for the particular geometry of a satellite instrument pixel and has been evaluated with OMI over 145 both land (Qin et al., 2019) and ocean (Fasnacht et al., 2019). 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 NO 2 algorithms (Vasilkov 150 et al., 2017(Vasilkov 150 et al., , 2018. Climatological LER values have inevitable cloud/aerosol contamination because they are derived from TOA radiance measurements by removing the Rayleigh scattering contribution only (Kleipool et al., 2008). The cloud/aerosol contribution is minimized by selecting lower values of the residuals, however it cannot be removed completely, partially due to 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 155 scattering effects at the much higher spatial resolution of MODIS as 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 (Lin et al., 2015).

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According to the IPA, the measured TOA radiance is a sum of the clear sky and overcast sub-pixel radiances that are weighted with an effective cloud fraction (ECF or f ), i.e., where the aerosol optical properties, aer = [τ (h), ω 0 (h), P (h, γ)], are from the MERRA-2 global aerosol analysis. The ECF is calculated by inverting Eq.
(3) at 466 nm, a wavelength little affected by gaseous absorption or rotational-Raman scattering.

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The clear subpixel radiance, I g , is computed on-line with the VLIDORT code for a given pixel geometry and surface pressure, P s . The cloud radiance, I c , is calculated using a pre-computed lookup table (LUT).
Our OMI cloud and NO 2 algorithms are based on the MLER model, ground and cloud being treated as Lambertian surfaces with pre-defined reflectivities. The ground reflectivity, R g , is assumed to be represented by GLER that effectively accounts for surface BRDF (Vasilkov et al., 2017). The cloud reflectivity, R c , is equal to 0.8 which is a common assumption (Stammes 175 et al., 2008). Within the MLER model, here we explicitly account for aerosol for the clear-sky part of pixel only. This is due to the simplifying treatment of cloud as an opaque surface, i.e. aerosol below the cloud does not contribute to the TOA radiance. SCD calculated using spectral fitting of the absorption band at 477 nm. The OCP, here also denoted as P c , is estimated using the MLER method to compute the appropriate air mass factors (AMF) (Vasilkov et al., 2018). To solve for OCP, we invert the following equation SCD =AMF g (P s , R g , aer) VCD(P s ) (1 − f r )+ (4) ω 0 = 1.0 for a case of non-absorbing aerosol and for the case of absorbing aerosols, we used ω 0 = 0.88. For both cases we assumed that ω 0 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 NO 2 AMFs for the four different aerosol 220 scenarios (two profiles and two values of ω 0 ).  above the aerosol layer and the shielding effect below. As a result of the shielding effect of the elevated aerosol, the values of NO 2 AMFs are lower than that for the aerosol-free NO 2 AMF. The near-surface aerosol enhances the sensitivity to NO 2 almost for all altitudes; however, the enhanced sensitivity drops abruptly towards the surface owing to the increasing shielding effect.
Similarly, Figure 3(right) compares the Jacobians computed for absorbing aerosols with the Jacobian for the aerosol-free 230 atmosphere. In general, aerosol absorption decreases the NO 2 sensitivity for both aerosol profiles. However, the qualitative dependence of the Jacobians on height remains similar to the nonabsorbing aerosol Jacobians.

Case study over northeast Asia
To demonstrate our explicit aerosol correction effects on the OMI cloud and NO 2 retrievals, we selected a cloud-free area over land in the Shenyang region of northeastern China. Figure 4 shows a map of OMI TOA reflectance over northeastern China     Figure 6 shows both the climatological LER (Kleipool et al., 2008) and GLER for the selected area for OMI orbit 3843 on April 5, 2005. We used the climatological LER for our cloud and NO 2 retrievals in the following figures for the purpose of demonstrating the BRDF effects on the retrievals. It is seen from Fig. 6 that values of GLER are noticeably lower that climatological LER values because the latter include inevitable aerosol contamination. On average, the difference between the 250 climatological LER and GLER for this area is about 0.03.  (3) and subsequently higher retrieved ECFs. Explicit account of the aerosol contribution increases the computed clearsky 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 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 260 AOD derived for this particular day is slightly lower than climatological AOD (and possibly residual cloud optical depth) for those pixels.
Similarly, Figure 8 compares OCP retrievals computed using the climatological LER with those calculated using the GLER and either implicit or explicit aerosol corrections. The GLER effect only 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.

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It is not straightforward to explain the GLER effect on OCP because the retrieved OCP depends on both ECF and clear-sky Finally, Figure 9 compares tropospheric NO 2 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 NO 2 amounts as has been shown previously for polluted areas in Vasilkov et al. (2017Vasilkov et al. ( , 2018. The explicit aerosol correction additionally enhances the NO 2 vertical column density for all OMI pixels. This enhancement is caused by the combined effect of the explicit aerosol correction on the cloud parameters and clear-sky NO 2 AMFs. This  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 NO 2 enhancement is mostly caused by decreasing the clear-sky AMF. The MERRA-2 aerosol data show absorbing aerosols for the selected area (see Fig. 5) particularly for near-surface aerosol. According to our RT simulations, the absorbing aerosols mostly decrease NO 2 AMFs for polluted regions.   about 100 hPa. The OCP increase is approximately 50 hPa for mid-altitude clouds with OCP of about 800 hPa. An interesting feature of the explicit aerosol correction on OCP is that the OCP can be reduced for a small fraction of the pixels. Particularly it is true for high altitude clouds with OCP values of about 500 hPa. The explicit aerosol correction increases the tropospheric NO 2 VCDs for all OMI pixels of the selected area by approximately 20% on average. This indicates that the aerosol shielding 300 effect prevails over the effect of aerosol enhancement of photon path length for the selected area.
The uncertainties in tropospheric NO 2 retrievals arise from the uncertainties in NO 2 slant column retrievals, in the AMF calculations, and from the stratosphere-troposphere separation scheme. The uncertainty in NO 2 slant columns is about 0.8 × 10 15 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 back background areas. Uncertainties in the AMF are 20-80%, 305 and dominate the overall retrieval uncertainties (Martin et al., 2002;Boersma et al., 2011;Bucsela et al., 2013;Lin et al., 2014) Errors in the a-priori vertical NO 2 profile shape, surface reflectivity, and cloud-aerosol treatment are the largest error sources (Boersma et al., 2011;Lamsal et al., 2014;Lin et al., 2014Lin et al., , 2015Vasilkov et al., 2017Vasilkov et al., , 2018Liu et al., 2019). The uncertainty in the stratosphere-troposphere separation is expected to be less than 0.3×10 15 molec cm −2 , especially in polluted areas (Bucsela et al., 2013). Consistent with prior studies by Lin et al. (2014) and Liu et al. (2019), our study suggests that the 310 aerosol effect over China is significant, and is similar to that of a-priori NO 2 profile shape and surface reflectivity.