As described in B15, the MERRAero aerosol reanalysis arises from a “replay” of the GEOS-5 model driven by meteorology from the MERRA atmospheric reanalysis (Rienecker et al., 2011), followed by assimilation of 550 nm AOD retrievals derived from MODIS over ocean and dark target land retrievals. Details of the general AOD data assimilation algorithm can be found in Randles et al. (2017) with MERRAero specifics in B15. In practical terms this means the GEOS-5 model is initialized from the MERRA atmospheric state, performs a 6 h forecast, and subsequently has its meteorology instantaneously replaced by the balanced atmospheric state of the subsequent MERRA analysis. The MERRA meteorological analyses are inserted into our simulation at 03:00, 09:00, 15:00, and 21:00 UTC. The GEOS-5 system includes online aerosols via an implementation of the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) module (Colarco et al., 2010), with emissions as described in B15. The GOCART module produces a simulation of the 3-D distributions of the mass mixing ratios of dust, sea salt, sulfate, and black and organic carbon aerosols, which serves as a first guess for the 3-hourly aerosol analysis. With the assignment of lookup-table-based optical properties we can translate these mass mixing ratios into optical quantities, such as the spectral AOD or SSA.

The MERRAero-produced atmospheric state and aerosol mass mixing ratio distributions used here are identical to those described in B15. MERRAero was produced for the time period 2002–2015 at a global 0.625∘×0.5∘ longitude by latitude horizontal resolution with 72 vertical levels that vary from terrain following near the surface to pressure following near the tropopause, with a model top at about 80 km. Based on the analysis in B15 and parallel work, we have made two adjustments to the aerosol model lookup tables for computation of aerosol optical properties. First, we have adjusted the spectral dependence and absorption of dust aerosols as suggested in B15 and introduced dust non-spherical effects as described in Colarco et al. (2014). For our study this yields dust SSA of about 0.82 at 354 nm and 0.86 at 388 nm. Our second modification is to the optical properties of organic carbon (OC) aerosols in our model. Previously we have used the OPAC refractive (Hess et al., 1998) indices for the OC component, which presumed a weak and spectrally flat absorption for OC in the UV. Based on the analysis in B15 and the recent work by Hammer et al. (2016) we opt in this study to treat our OC as brown carbon (BrC) and reassign its optical properties accordingly. Here, we use the refractive indices from Hammer et al. (2016) for their 100 % BrC model (particle density ρp=1800 kgm-3, final column of their Table 5). This allows for a spectral absorption curve in our simulated radiances that is compatible with the assumptions in the OMAERUV retrieval algorithms. These results produce a SSA for our OC component that is about 0.82 at 354 nm and 0.84 at 388 nm. We stress that this solution is not in all cases ideal. In the implementation of GEOS-5 used in this study we do not distinguish carbonaceous aerosols from biomass burning sources from those arising from anthropogenic sources, which in general would have different optical properties, so it should be understood that in this study we are assigning the BrC optical properties to simulated OC mass everywhere in our model. The implications of these choices should be modest here because of the limited nature of our study. The model fields are being used to simulate the top-of-atmosphere radiance field, and since we limit this study to the investigation of the OMI aerosol index, our particular choices of refractive indices should be sufficiently realistic for that purpose. On the other hand, in the case that we extend this analysis to a critical evaluation of the OMAERUV AAOD and AOD products it would be important that our choices of refractive index for the forward model simulation of the radiances is compatible with the aerosol models assumed in the OMAERUV retrievals (Torres et al., 2007). In anticipation of that future study we have verified that the refractive indices used here in our aerosol models are within the bounds of the OMAERUV assumptions.

As in B15 we focus our study on the year 2007, specifically the period June–September 2007, and we note that the analysis is performed assuming a cloud-free atmosphere.

We simulate the OMI radiances at 354 and 388 nm using VLIDORT from the MERRAero fields following the approach in B15. The OMAERUV algorithms used here are an updated research version of the what was used for the officially released OMAERUV products, and are updated relative to what was used in B15. An important difference in this version vs. what was used in B15 is that the spectral surface albedo provided is no longer based on the heritage climatology derived from the OMI-predecessor TOMS series of instruments (i.e., Herman and Celarier, 1997), but now is determined from a new OMI surface climatology recently developed by the OMI aerosol team that will be implemented in the next release of the OMAERUV products. Additionally, while over land we continue to assume a Lambertian surface, in order to be consistent with corrections made to the over ocean reflectances in the OMAERUV algorithms we treat the ocean surface bidirectional reflectance function according to the Cox–Munk formulation (Cox and Munk, 1954). In principle, ocean surface reflectance is a function of surface wind speed, which could be provided by our model, but we have here made the simplifying assumption that the wind speed is a constant 6 ms-1, a choice consistent with what is used in the OMAERUV retrieval algorithms, where the observed radiances are corrected for surface reflectance based on the climatological OMI surface reflectance with an imposed Fresnel correction as if the surface wind speed was 6 ms-1 (see Sect. 2.3).

In summary, MERRAero provides the vertical profiles of aerosol mixing ratio and relative humidity needed to compute the aerosol optical properties, and the vertical pressure profile needed to simulate molecular scattering. The GEOS-5 interface to VLIDORT translates the aerosol and molecular vertical profiles to the profiles of AOD, SSA, and phase scattering matrix input to VLIDORT. All of this information from MERRAero is sampled from the global model at the OMI pixel footprint using the OMI Level 2 product for the same day, which additionally provides needed information on the OMI viewing geometry associated with each pixel (i.e., solar zenith angle, sensor zenith angle, and relative azimuth angle) and the spectral surface reflectivity. In B15, the OMAERUV quality flags were used to discard cloudy pixels; here we are computing the synthetic radiances at the OMI footprints and providing them to the OMAERUV algorithms as if the atmospheric column is cloud-free.

Fundamental to calculating the aerosol index from the radiances is the computation of the so-called Lambertian equivalent reflectivity (LER), which is the surface reflectance that would be needed under a purely molecular atmosphere to explain the actual radiance (observed or simulated) at the top of atmosphere for the actual atmospheric profile. The LER at wavelength λ is computed as in B15 as follows: LERλ=Iλ-IλRayTλRay+SλRayIλ-IλRay, where Iλ is the actual (observed or simulated) radiance, IλRay is the calculated molecular-only radiance assuming a dark surface and the given atmospheric profile, and TλRay and SλRay are, respectively, the calculated transmission and spherical albedo for that molecular-only atmosphere. An important distinction between the MERRAero derivation of these parameters and the values used in the OMAERUV algorithms is that the MERRAero parameters are calculated using the modeled pressure profile, whereas in OMAERUV the parameters are interpolated from values pre-computed for a pair of atmospheric profiles generated assuming surface pressures of 600 and 1013.25 hPa (Torres et al., 2013). The pre-computed OMAERUV lookup tables have dimensions in scattering angle space (resolved into 7 solar zenith angle nodes, 14 viewing zenith angle nodes, and 11 azimuth angle nodes) that are interpolated between using the Lagrange method. The two surface pressure nodes are interpolated between linearly in log(pressure) space.

In this version of the OMAERUV algorithm, the LER is corrected by the spectral dependence of the surface as in B15, but here with two modifications: LER′388=LER388-Alb388-Alb354×f, where Alb388 and Alb354 are, respectively, the surface albedo at 388 and 354 nm. Over land these are just the Lambertian surface reflectivities from the long-term OMI climatology. Over ocean these albedos have here been corrected for the wind speed and viewing geometry-dependent Fresnel reflection of the surface based on a pre-computed table assuming a fixed surface wind speed of 6 ms-1. We did not investigate this assumption as the requirement to produce a Fresnel correction lookup table at arbitrary wind speed was beyond the scope of this work, but it should be stressed that the correction applied in the OMAERUV algorithm is consistent with what is done in the MERRAero AI calculation given the same radiances. Additionally, the factor f introduces an ad hoc correction for spectrally varying background (either cloud or surface) reflectance, needed for conditions of moderate-to-high reflectivity. f=1 for LER388<0.15, f=0 for LER388>0.8, and f varies linearly in between; in this experiment, in which we neglect clouds, LER388 is almost always <0.15, and so we almost always have f=1.

Finally, the definition of the aerosol index is as in B15: AI=-100×log⁡10I354I354RayLER388′, where I354 is in our case the simulated radiance at 354 nm and I354Ray is the calculated radiance for a molecular scattering atmosphere bounded by a surface reflectance of LER388′. Equation (3) assumes that both LERs at 388 and 354 nm are equal. Again, for OMAERUV the radiance I354Ray is interpolated from pre-computed tables performed for atmospheric profiles assuming surface pressures of 600 and 1013.25 hPa. The OMAERUV algorithms screen for sunglint regions over the ocean and do not retrieve AI (or other aerosol properties) where the glint angle is < 40∘. Accordingly we screen the simulated MERRAero AI results using the same criteria.

From Eqs. (1) and (3) we see that the AI depends on a calculation of the atmospheric molecular scattering, which in turn depends on an assumption of the atmospheric pressure profile. The assumption of the atmospheric pressure profile is handled differently in OMAERUV vs. in MERRAero. In OMAERUV, the surface pressure is nominally assumed to have a fixed value of 1013.25 hPa at sea level that is adjusted by a high-spatial-resolution topography data set in order to account for differences in the molecular scattering over high mountains vs. the oceans, and the molecular atmosphere radiance is recovered by interpolating the pre-computed atmospheric radiance lookup tables between their 600 and 1013.25 hPa values, as discussed in Sect. 2.3. In MERRAero, the atmospheric pressure profile used is based on the model grid-box mean surface pressure and the radiative transfer of the molecular atmosphere is solved exactly for that pressure profile. It is important to point out that with the approximately 50 km grid scale of MERRAero we are certainly not resolving the actual spatial variability in topography that is assumed in the OMAERUV pressure scaling. For our purposes, it does not matter that MERRAero does not resolve those high-spatial-resolution topographic features since our objective is simply to put MERRAero and OMAERUV on as much of the same footing as possible, but we will revisit this point later.

Figure 1a shows the MERRAero AI on 5 June 2007, showing major absorption features across Saharan Africa, the Arabian Peninsula, and much of southern Asia. Other absorption features are present over southern Africa, in the Pacific Ocean immediately west of Mexico, and near Beijing and across the northern Pacific. Note the wide areas, mainly over the ocean, that are shaded grey. Because the OMAERUV algorithms rely on pre-computed lookup tables of the atmospheric radiance profile bounded by surface pressures of 600 and 1013.25 hPa, we have here and for the remainder of this paper excluded grid points where the MERRAero grid-box mean surface pressure is outside of those bounds. Figure 1c shows the OMAERUV–MERRAero difference in the AI, both using the MERRAero simulated radiances. The differences in the AI are small, mainly less than 0.2 in magnitude, and not obviously associated with the aerosol features shown in Fig. 1a. Mostly the AI differences are positive (OMAERUV AI > MERRAero AI, green shading), although there are some regions showing negative AI differences (MERRAero AI > OMAERUV AI, red shading) over the land in southern Australia and northern Europe.

For Fig. 1c, the OMAERUV AI is computed with the algorithm using its default assumption of the surface pressure. Thus the assumed surface pressure in the OMAERUV algorithm is constant over the oceans and static in time, and so differs from the actual surface pressure at any given moment, where spatial and temporal variability in the surface pressure in the MERRAero simulation is assured by the MERRA meteorology (i.e., surface pressure in the real atmosphere changes with weather patterns). Figure 1b shows this OMAERUV–MERRAero difference in the surface pressures on 5 June 2007, and it is clear that differences of tens of hPa are possible. Negative pressure differences (red shading) in Fig. 1b are apparent over the land, mainly in southern Australia and northern Europe, and so coincident with the negative AI differences shown in Fig. 1c. (It is worth noting here that most of the greyed-out region over the oceans occurs in places where MERRA has surface pressures greater than 1013.25 hPa, and so are screened out in this analysis. See Supplement Fig. S1 for a version of Fig. 1 where the surface pressure screening is not applied.)

In Fig. 1d we show the OMAERUV AI–MERRAero AI difference where the OMAERUV calculation was performed using the MERRAero grid-box mean surface pressure, and indeed we see that much of the AI difference apparent in Fig. 1c is reduced in magnitude in Fig. 1d. The negative bias over the land is much reduced, as is the noise near topographic features. Residual positive discrepancies in the AI as high as ΔAI∼2 remain, however, and these seem mainly to be associated with regions of high topographic variability. For the approximately 538 000 AI pixels on this day, only about 5 % of them have an AI discrepancy greater than 0.2 for the calculation where the OMAERUV AI is computed using the MERRAero pressure vs. 20 % for the case where OMAERUV used its own pressure.

Figure 2 presents a similar analysis for the entire month of June 2007. In Fig. 2a we present the joint histogram of the OMAERUV AI–MERRAero AI difference for the case of OMAERUV calculating AI with its own surface pressure assumption vs. the OMAERUV–MERRAero surface pressure difference for all OMI pixels during the month (again, excluding those where the MERRA surface pressure is out of bounds of the OMAERUV lookup tables). It is clear in Fig. 2a that most of the pixels are near the origin, where the differences on both axes are nearly zero. The excursions toward high surface pressure differences are relatively infrequent (ten to hundreds of points vs. the hundreds of thousands of points with near-zero pressure differences) and are mainly associated with the difference of the MERRAero resolved surface pressure from the OMAERUV values in highly variable topography (i.e., the noise in the mountainous regions shown in Fig. 1b). Also clear from Fig. 2a is the sense in which a difference in the assumed surface pressure propagates to a difference in the derived AI. Where OMAERUV assumes a higher surface pressure than MERRAero it also systematically derives a higher AI. The opposite is also true: OMAERUV derives a lower AI for pixels in which its surface pressure is assumed lower than MERRAero provides.

Figure 2b presents the same results sorted differently, showing the AI difference as a function of the MERRAero AI. Colored points are for the case where the OMAERUV AI is calculated using the OMAERUV surface pressure, with the color indicating the OMAERUV–MERRAero surface pressure difference. Grey points are for the case where OMAERUV AI is calculated using the MERRAero surface pressures. It is immediately apparent that much of the scatter in the AI difference is reduced when OMAERUV calculates the AI using the MERRAero surface pressure. Most of the discrepancy in the OMAERUV AI calculation where OMAERUV uses its own surface pressure occurs for low positive values of the MERRAero AI, with low AI values indicating either low aerosol loading, low aerosol altitude, or the presence of non-absorbing aerosols. The discrepancy is also clearly a function of the surface pressure discrepancy, with the greatest negative AI differences occurring at pixels where the surface pressure difference is most negative, and vice versa for the high AI differences. On the other hand, at high values of the MERRAero AI the AI difference is nearly zero. It follows that as aerosol loading decreases, the radiative transfer becomes more sensitive to the molecular profile, and so especially to differences in the pressure profile implied by the OMAERUV surface pressure relative to what is provided by MERRAero. For the baseline case of OMAERUV using its own surface pressure, 18 % of the pixels have an absolute difference in the simulated AI from MERRAero greater than 0.2. When OMAERUV uses the MERRAero surface pressure only 5 % of the pixels have an absolute difference in the AI greater than 0.2. The results for the full month shown in Fig. 2 are thus very similar to the results for the single day shown in Fig. 1.

Figure 3 continues this analysis, showing maps of the monthly mean OMAERUV AI–MERRAero AI difference for June 2007 for both the cases where OMAERUV calculates AI using its own surface pressure (Fig. 3a) and where OMAERUV uses the MERRAero grid-box mean surface pressure (Fig. 3b). Over the ocean there are large regions that are again excluded (grey shading) because MERRAero persistently has surface pressure >1013.25 hPa (Fig. S2 shows the same figure but without the high-pressure areas screened). The AI differences are generally positive (OMAERUV AI > MERRAero AI) and can be as large as 0.1–0.2 over the oceans, and greater than 0.2 over the land. The only apparent negative differences are in southern Australia again. (For comparison, Fig. S2 highlights the dominant high-pressure regions over the ocean in the MERRA meteorology; although the OMAERUV retrieval of AI when forced with these high surface pressures is extrapolated outside the bounds of the lookup tables the sense is that these are places where substantial negative AI biases would exist in the actual OMAERUV products.) In Fig. 3b, where the MERRAero surface pressure was used to calculate the OMAERUV AI, the over-ocean AI discrepancy is greatly reduced. Over land the residual AI difference is larger and mostly positive (i.e., OMAERUV > MERRAero). Figure 3b shows also the 1000 m height contour over the land surface, from which it is apparent that the residual AI difference is spatially correlated with topographic features. The results are similar for our analysis of July, August, and September (Fig. 4; see also Fig. S3), with the land residual difference remaining basically the same from month to month, while the ocean residual moves with the changing months. We do not explore the geometric nature of this small seasonal dependence further here. Possibly it would be resolved by improved lookup tables of the OMAERUV radiative transfer (see next section) or could be characterized further by simulating a longer period of time (e.g., an annual cycle).

Section 3.1 identified the surface pressure assumptions as a significant driver of the MERRAero AI and OMAERUV AI differences given the same input radiances. When OMAERUV was forced to use the MERRA-provided surface pressure the residual AI differences were greatly reduced, as shown in Figs. 3 and 4, particularly over the ocean. As shown in Figs. 3b and 4, however, the AI residual over land in cases where OMAERUV used the MERRAero surface pressure remains and is a persistent, stationary feature, apparently spatially correlated with topographic features. We explore here the nature of this residual difference. Our hypothesis is that this difference results largely from differences in the treatment of the molecular atmosphere scattering between MERRAero and OMAERUV, as discussed above in Sect. 2.3.

We examine this here for a region in the central United States, extending from roughly western Illinois to western Nevada (120–90∘ W, 38–42∘ N) and transitioning from relatively flat, lower elevations in the east to higher elevations crossing the Rocky Mountains. Figure 5a shows the mean and 1 SD about the mean of all the MERRAero and OMAERUV coincident aerosol index points in this region during June 2007, sorted by longitude. Again, here the OMAERUV AI is computed using MERRAero surface pressure. The high bias of the OMAERUV aerosol index relative to MERRAero is consistent with Figs. 3b and 4, and shows this bias increasing toward the west, i.e., for the higher topography portion of the region. This is made explicit in Fig. 5b where we show the OMAERUV AI–MERRAero AI difference plotted with the topographic elevation. The correlation of the AI difference with elevation is clear.

Having identified a high bias in the OMAERUV AI over land with respect to MERRAero and finding an apparent correlation with surface elevation, we explore further with a simple sensitivity analysis. We construct a synthetic orbit of the OMI Level 2 data in which a spectrally invariant surface albedo of 0.05 (a typical value for the surface reflectivity) is prescribed and we define a range of viewing geometries that encompasses typical OMI viewing angles (solar zenith angle between 8 and 96∘; sensor zenith angle between 0 and 70∘; relative azimuth angle of 0, 90, and 180∘). The atmosphere is assumed aerosol free; that is, we only consider molecular scattering. We perform calculations of the top-of-atmosphere (TOA) radiance with the MERRAero OMI simulator code for each viewing geometry considered and for variations in 50 hPa increments of the surface pressure between 1000 and 600 hPa. As in the previous AI comparisons we provide the simulated TOA radiances to the OMAERUV algorithms and look at the derived parameters returned. The MERRAero calculations return AI =0 and LER =0.05. This result is expected by construction of the problem: in a molecular-only atmosphere with a spectrally invariant Lambertian surface the LER is equivalent to the surface albedo and the AI is expected to be zero according to Eq. (3).

Figure 6 presents the results of this sensitivity analysis as applied to the OMAERUV calculation. The LER as derived in Eq. (1) depends on the “observed” TOA radiance (i.e., what MERRAero provides) and properties of the molecular atmosphere: IλRay, TλRay, and SλRay. Differences between the MERRAero and OMAERUV transmissivity are very small, but more sizable differences in the spherical albedo and atmospheric radiance are found. Figure 6a and b show these as a percent difference (OMAERUV–MERRAero)/MERRAero for the spherical albedo and atmospheric radiance I388Ray, respectively, presented as a function of scattering angle and surface pressure. Differences are very small at the end-point surface pressures at 600 and 1000 hPa, but are about 1.5 % in the spherical albedo and 2.5 % in the atmospheric radiance at the mid-point 800 hPa surface pressure. These errors percolate through the calculation so that the LER from OMAERUV is not identical to the surface albedo (=0.05) as expected, but instead is too low, varying between about 0.04 and 0.05, as shown in Fig. 6c. Finally, the bias in the AI is revealed in Fig. 6d, where the error in the LER propagates through to a high bias in the OMAERUV AI that can be as much as 0.5 at scattering angles near 120∘ and surface pressures near 700 hPa. More typically the AI bias is smaller, but the sensitivity analysis performed offers an explanation of the AI bias shown over the central US (and more generally over land) in Fig. 5. We contend that ultimately this error emerges from the simple interpolation of the pre-computed atmospheric radiance calculations between the 600 and 1013.25 hPa nodal points used in the OMAERUV algorithms. We note additionally that there is an apparent scattering angle sensitivity to the results shown in Fig. 6. This applies particularly to the atmospheric radiance (Fig. 6b) and the resultant aerosol index (Fig. 6d). Because the differences shown in Fig. 6 are based on the interpolation from the two pressure nodes of the OMAERUV lookup tables it follows that the apparent scattering angle sensitivity also results from the interpolation of the lookup tables to the specific viewing geometries used in our analysis. We do not explore this further here, but suggest that additional nodes in the OMAERUV lookup tables will mitigate these kinds of uncertainties.