Atmospheric aerosols play a significant role in the earth's radiation budget (IPCC, 2013). The climatic impact of aerosols depends on their absorption and scattering properties, quantified by single scattering albedo (SSA). Even a slight reduction in SSA can change the aerosol radiative forcing from cooling to warming, depending on the underlying surface albedo (Kaufman et al., 2001; Chand et al., 2009). However, the lack of an accurate global aerosol absorption database has led to SSA being the largest contributor to the total uncertainty in aerosol radiative impact assessment (IPCC, 2013).

The high spatiotemporal variability in aerosol properties entails the need for observations on a global scale (Dubovik et al., 2002; Levy et al., 2007b; Remer et al., 2008; Hammer et al., 2018). Satellite data, despite their inherent limitation associated with an inverse problem, can provide the global perspective required in analyzing spatiotemporal aerosol characteristics (Torres et al., 2002). However, it is difficult to quantify the absorption over bright surfaces (Kaufman and Joseph, 1982; Ahn et al., 2014; Jethva et al., 2018). Hence, quantifying the aerosol absorption over land regions using satellite-based remote sensing remains a challenge even now (Torres et al., 2013; Jethva and Torres, 2019).

Fraser and Kaufman (1985) developed a critical surface reflectance method to retrieve SSA using satellite data. Their method is based on radiative transfer simulations, which showed a particular surface reflectance where the top of atmosphere reflectance is independent of aerosol optical depth (AOD). Upward reflectance between a clear and a hazy day over a varying surface reflectance region are used, along with radiative transfer simulations, to derive SSA. This method has been widely applied to data from various satellites to derive SSA over particular regions (Kaufman, 1987; Kaufman et al., 1990, 2001; Zhu et al., 2011; Wells et al., 2012). Seidel and Popp (2012) have done extensive studies on the method's sensitivity to various parameters.

Various studies have ascertained the inadequacy of single-sensor data in the accurate retrieval of aerosol absorption (Kaufman et al., 2001; Zhu et al., 2011). The dawn of the A-Train satellite constellation (Anderson et al., 2005) with spatially and temporally near-collocated observations facilitates multi-satellite retrieval of aerosol absorption (Eswaran et al., 2019; Hsu et al., 2000; Hu et al., 2007, 2009; Jeong and Hsu, 2008; Narasimhan and Satheesh, 2013; Satheesh et al., 2009). However, all these multi-sensor retrievals are in the ultraviolet (UV) wavelengths, and SSA is extrapolated to visible wavelengths using spectral dependence of assumed particle size distribution. Satheesh and Srinivasan (2005) defined the concept of critical optical depth (τc) and introduced a method to retrieve SSA in the visible region by combining ground-based and satellite measurements. The method was validated and demonstrated over many locations, including the desert location of Solar Village in Saudi Arabia, using Aerosol Robotic Network (AERONET) data.

In this paper, we have utilized the concept of τc and further extended the methodology to develop the combined CERES-MODIS retrieval algorithm to derive regional and global maps of aerosol absorption (550 nm) using multi-satellite data. The critical optical depth method developed in this research shares a similar concept to the critical surface reflectance method (Fraser and Kaufman, 1985). For a particular parameter (such as surface reflectance or optical depth), there exists a critical value at which the top of atmosphere albedo or reflectance can be considered independent of variations in that parameter. Both methods retrieve SSA by parameterizing the critical value as a function of SSA using radiative transfer simulations. The critical reflectance method requires data from 2 d and large variations in surface reflectance over the region. It is suitable for retrieving daily SSA for a particular region, whereas the critical optical method developed in this paper is suitable for retrieving monthly or seasonal global maps of SSA.

The concept of τc, which forms the scientific basis for the development of this retrieval algorithm is illustrated in Sect. 2. The various steps involved in the retrieval algorithm are detailed in Sect. 3 on data and methodology. Sect. 4 presents the results and comparison with other satellite datasets. Uncertainty analysis is studied in Sect. 5. Comparison with aircraft measurements from various field campaigns are shown in Sect. 6. Comparisons with AERONET data from 15 sites are shown in Sect. 7. Summary and conclusions are provided in Sect. 8.

Let Δα be the difference between the top of the atmosphere (TOA) albedo and the surface albedo. Then, for a particular location with a given surface albedo, Δα variations are only due to changes in TOA albedo. The presence of absorbing aerosols over a bright surface decreases the TOA albedo. In contrast, scattering aerosols over a dark surface increase the TOA albedo. Thus, the increase (decrease) in aerosol loading due to scattering (absorbing) types of aerosols leads to an increase (decrease) in Δα. The rate of change in Δα with aerosol loading is dependent on SSA.

Satheesh and Srinivasan (2005) utilized this concept to retrieve SSA in the case of absorbing aerosols over a bright surface. In a pristine atmosphere (AOD = 0) over a bright surface, the Δα is positive for the solar zenith angle (SZA) = 0. Here, when absorbing aerosols become dominant, Δα decreases with an increase in AOD and eventually becomes negative. The AOD at which Δα equals zero is defined as τc. For a given surface albedo, τc is the AOD at which the scattering and absorbing effects of the aerosol cancel each other out. The rate of decrease in Δα with the increase in AOD is higher when SSA is high and consequently lowers the resulting values of τc. A radiative transfer (RT) model was then used to calculate the SSA that reproduces the same τc, given atmospheric conditions.

In this paper, the concept of τc is extended to retrieve SSA for all scenarios of surfaces (dark and bright) and aerosols (absorbing and scattering). For AOD less than 1, Δα is almost linearly dependent on AOD. Then τc is mathematically the x-intercept when parameterizing the linear relationship.

Figure 1 shows the estimation of τc for four different scenarios. Details of these RT simulations are given in Sect. 3.2. Unlike Satheesh and Srinivasan (2005), where simulations were carried out for SZA = 0, here the Δα is diurnally averaged. Therefore, it is possible to have negative Δα for AOD = 0 over relatively bright surfaces. It is difficult to retrieve SSA where the slope of the regression line is close to zero.

The combined CERES-MODIS retrieval algorithm consists mainly of two steps: (1) determining τc using MODIS and CERES data for a location, and (2) estimation of SSA that reproduces the same τc for the associated atmospheric conditions and surface albedo of that particular location. Figure 2 shows the flowchart illustrating the combined CERES-MODIS retrieval algorithm.

The TOA and surface fluxes used to determine Δα, are obtained from CERES SYN1deg-day, Edition 4.1 (Wielicki et al., 1996; Rutan et al., 2015). To avoid angular dependence of fluxes, the diurnally averaged flux data product from CERES is used, which is available only at 1∘ resolution. Hence, other satellite datasets in this study are also used at the same spatial resolution. The AOD and total columnar water vapor are obtained from the MODIS Daily Global Product (MxD08_D3 version 6.1). MODIS retrieves columnar AOD at 550 nm using two different types of algorithms – “Dark Target” (Levy et al., 2007a, 2013) and “Deep Blue” (Hsu et al., 2004, 2006; Sayer et al., 2013). Dark Target retrieves AOD over both land and ocean, whereas Deep Blue retrieves AOD only over land. In this study, we have used a combined Dark Target and Deep Blue product.

Figure 4 shows the seasonal-mean global maps of SSA (550 nm) retrieved by the combined CERES-MODIS algorithm for the 5 years of 2014–2018. Data are averaged for different seasons: December–January–February (DJF), March–April–May (MAM), June–July–August (JJA), and September–October–November (SON).

The retrieved SSA dataset (550 nm) was compared with other widely used global SSA datasets, OMI SSA (500 nm) and climatological POLDER SSA (565 nm). The OMAERUVd V3 (Torres et al., 2007, 2013; Ahn et al., 2014) for the corresponding period are shown in panels a, c, e, and g in Fig. 5. The POLDER v1.2 Level 3 (Dubovik et al., 2011, 2014, 2021) climatological seasonal mean SSA maps are shown in panels b, d, f, and h in Fig. 5. For a generalized qualitative comparison, we can assume that SSA does not vary much for the small 50 nm spectral difference between CERES-MODIS and OMI SSA (Zhu et al., 2011; Jethva et al., 2014).

From a quick comparison between Figs. 4 and 5 SSA maps, the following points can be noted:

Over the ocean, OMI retrieves SSA only for regions with high values of UVAI, leading to large data gaps. In comparison, we can notice that CERES-MODIS and POLDER have better data coverage on a global scale. In the CERES-MODIS maps, the absence of data is mostly due to the unavailability of MODIS AOD.

Global mean SSAs retrieved by combined CERES-MODIS over land and ocean are 0.93 and 0.97, respectively (OMI: 0.94 and 0.94; POLDER: 0.88 and 0.94). Accurate SSA estimations are also required over regions of interest such as deserts, oceans, biomass-burning forests, and highly polluted industrial areas. Hence, seasonal mean SSA values retrieved by the combined CERES-MODIS algorithm, OMI, and POLDER are reported in Table S2 for major regions of interest as shown in Fig. S1 and Table S1.

Table 1 identifies the major sources of error in the retrieval and summarizes their individual contribution. Uncertainty in the retrieved SSA was estimated by calculating retrieval sensitivities to perturbations in the possible error sources. The range of perturbation was based on published literature or reasonable assumptions for possible variations. Also, since SSA is computed from τc, which depends on the slope of the regression, uncertainties due to each error source were computed by perturbing them for different cases of SSA (0.8–1 in steps of 0.01). For example, uncertainties in surface albedo were calculated by perturbing it by ±0.01 for different cases of surface albedo (dark–bright: 0.05–0.5 in steps of 0.05) and SSA (absorbing to scattering: 0.8–1 in steps of 0.01). The mean value of the uncertainties obtained from all these cases is shown as retrieval uncertainty in Table 1.

Uncertainty in shortwave integrated surface albedo from CERES results in the maximum uncertainty in SSA of ±0.03. MODIS-retrieved AOD contains considerable uncertainties due to assumed aerosol models (Jeong et al., 2005). The MODIS AOD uncertainty is 20%±0.05 over land (Chu et al., 2002) and 5%±0.03 over the ocean (Remer et al., 2002). The corresponding error in our retrieval is ±0.02%. For a typical variation of the Ångström exponent (±0.4) and the imaginary part of the refractive index (±0.01), the uncertainties vary depending on the surface albedo and are mostly around ±0.01.

Changes in aerosol height can vary the TOA radiances due to Rayleigh scattering interactions, which depend on pressure. Sensitivity to aerosol height was estimated by conducting a synthetic retrieval of SSA over a range of aerosol height values and perturbations from those heights. The average uncertainty observed for an aerosol height variation of ±1 km was ±0.01. Many methods have been developed for detecting aerosol type, especially smoke vs. dust, to improve the uncertainties of various AOD and SSA retrievals.

Uncertainties due to possible variations on scales of the regions used for linear fitting were estimated as residuals of the fit. The uncertainty on the linear intercept is spatially dependent and is mostly around ±0.02, with higher values for those combinations having a slope close to zero during the regression. For highly correlated cases (i.e., correlation coefficient |r|>0.5), the probability of obtaining a slope close to zero is ∼ 20 % over the ocean and <5 % over land. These cases are mostly formed over regions where AOD variations are less. Regions having large variations in AOD values have lower uncertainty due to residual fit. Adding in quadrature, the total uncertainty estimated for the CERES-MODIS algorithm is around ±0.044.

Overall, the algorithm is most sensitive to variations in surface albedo, followed by higher sensitivity towards AOD values used in the linear fit. Seasonal mean maps of surface albedo are shown in Fig. S3. The uncertainties are higher for scattering aerosols over bright surfaces and absorbing aerosols above dark surfaces. Sensitivity to water vapor is almost negligible, except in very few cases where the uncertainty is ±0.008. The CERES-MODIS algorithm is most effective over regions with large AOD variations and less surface albedo variations.

For the comparison of columnar SSA values thus retrieved, we have used aircraft-based measurements of SSA from three campaigns: South West Asian Aerosol Monsoon Interactions (SWAAMI), Regional Aerosol Warming Experiment (RAWEX), and SWAAMI-RAWEX, to obtain column-integrated SSA. Available data points over India and adjoining oceanic regions (Arabian Sea and Bay of Bengal) from these field campaigns were compared with the retrieved SSA.

Babu et al. (2016), as part of RAWEX (Moorthy et al., 2016), derived SSA at 520 nm from aircraft measurements of scattering and absorption coefficients over the IGP and Central India during winter 2012 and spring/premonsoon 2013. Various measurements of aerosol properties were carried out in an instrumented Beechcraft B200 aircraft of the National Remote Sensing Centre, India. Manoj et al. (2019) estimated vertical profiles of SSA during the SWAAMI campaign conducted during monsoon (June-July) 2016 over the IGP, thee Arabian Sea, and the Bay of Bengal. Aerosol scattering coefficients were measured aboard the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146 aircraft. Vaishya et al. (2018) estimated vertical profiles of SSA (520 nm) using an instrumented Beechcraft B200 during the SWAAMI-RAWEX campaign (June 2016). Instrument design and calibration were based on Anderson et al. (1996) and its application for Indian field experiments was as described by Nair et al. (2009). Uncertainties in the scattering coefficient measurement by a nephelometer are ∼±10 %, as reported by Anderson et al. (1996). As stated by Babu et al. (2016) uncertainties in the columnar SSA values estimated from RAWEX aircraft measurements depend mainly on instrumental uncertainties, sampling errors, and large spatial averaging.

Retrieved SSAs for the same period as the campaign over a 2∘×2∘ region around the campaign location, were utilized for comparison. Figure 4 shows the comparison of collocated aircraft measurements and CERES-MODIS retrieved SSA. The ideal 1:1 case (solid line), the absolute difference of 0.03 (dotted lines), and regression coefficients are also provided.

Most of the points were within the absolute difference of 0.03; however, there were a few exceptions. The SSA values over the Bay of Bengal during SWAAMI campaign were reported as 0.84 ± 0.07 during June–July by Manoj et al. (2019), whereas CERES-MODIS retrieved a higher SSA of ∼ 0.89 for the same time period. This large variation could be due to frequent cloud cover during the monsoon season, leading to fewer SSA points retrieved over the ocean and land. The SSA estimated over Nagpur in Central India during RAWEX was ∼ 0.8, while CERES-MODIS retrieved ∼ 0.85. This inconsistency is due to the large surface albedo variations (standard deviation > 0.05) over Central India, which leads to fewer points available for retrieval. Except for a few such cases, most of the other points lie within an absolute difference of 0.03.

For comparison purposes, many previous studies have used ground-level SSA data from AERONET obtained through inversion methods (Zhu et al., 2011; Jethva et al., 2014). Even in this study, only very few points were available for comparison due to the limited number of direct measurements of columnar SSA. Despite this limitation, this comparison exercise provided confidence to generate global maps of SSA following this method.

The Aerosol Robotic Network (AERONET) is a ground-based worldwide federated network of Cimel Sun photometers that measure extinction AOD from direct Sun measurements (Holben et al., 1998). The spectral diffuse sky radiations measured at different angles are inverted in conjunction with direct Sun measurements to derive the spectral SSAs (440, 675, 870, and 1020 nm) and size distribution (Dubovik and King, 2000). The estimated uncertainty in retrieved SSA is largely attributed to the uncertainties in instrument calibration and is within 0.03 for AOD (440 nm) larger than 0.4. (Dubovik et al., 2000, 2002).

The AERONET version 3, level 2.0 monthly average values from selected sites were compared with corresponding CERES-MODIS SSA data. Sites were chosen to represent various types of aerosols following that of Giles et al. (2012). The location of the sites is shown in Fig. S2 and Table S3. Scatterplots of the comparison of AERONET SSA and CERES-MODIS SSA are shown in Fig. 7. AERONET SSA at 550 nm was estimated by interpolation between the values at 440 and 675 nm.

Most AERONET SSA values are above 0.85, even in the case of biomass burning aerosols. For dust type aerosols (sites: Caboburning aerosols. For dust type Verde, Dakar, and Banizoumbaou) and mixed type aerosols (sites: Sede Boker, Kanpur, Xiang He and Illorin) as shown in Fig. 7a and b respectively, the AERONET and CERES-MODIS data shows good agreement. For urban (sites: Goddard Space Flight Center (GSFC), Mexico City, Shirahama, Ispra, and Moldova) and biomass (sites: Alta Floresta, Lake Argyle, and Mongu), only very few data were available during the study period of 2014–2018 as shown in Fig. 7 panels c and d. Data points combined from all the sites are plotted together in Fig. 7e, showing a RMSE of 0.026. Overall, the resulting comparisons are in agreement within the uncertainties of both AERONET and CERES-MODIS datasets.

Global maps of aerosol absorptions were generated using the newly developed combined CERES-MODIS algorithm based on the concept of critical optical depth. The CERES-MODIS dataset was compared with OMI and POLDER SSA datasets. The retrieved SSA values were also compared with available aircraft measurements over India and surrounding oceanic regions, which showed that most retrieved SSA values are within ±0.03. We showed that the combined CERES-MODIS algorithm captures the spatial and seasonal variations in aerosol absorption better and the resultant maps provide an improved global SSA database with fewer data gaps. Global mean SSA was estimated to be 0.93 and 0.97 over land and ocean, respectively. Sensitivity analysis to various parameters indicate a mean uncertainty around ±0.044 and shows maximum sensitivity to changes in surface albedo. The algorithm is shown to be the most effective over regions with large aerosol optical depth (AOD) variations and less surface albedo variations. Comparison with SSA from 15 AERONET sites showed an acceptable agreement between AERONET and CERES-MODIS SSA within their uncertainties. These global maps provide valuable input to models for assessing the aerosol-climate impacts on both regional and global scales.