2.1 POLDER/GRASP aerosol products

GRASP is a new-generation algorithm developed for deriving extensive aerosol properties from all remote sensing instruments. The overall concept of the algorithm is described by Dubovik et al. (2014), while specific technical aspects are detailed in Dubovik et al. (2011). GRASP is based on highly advanced statistically optimized fitting implemented as multi-term least-square minimization (Dubovik, 2004) which had earlier been successfully implemented for aerosol retrievals from ground-based AERONET radiometers (Dubovik and King, 2000; Dubovik et al., 2000, 2002a, b, 2006). GRASP inherits many methodological aspects in numerical inversion and aerosol modeling from the AERONET retrieval developments. In fact, all retrieval set-ups including modeling of aerosol microphysical and optical properties, surface reflectance, numerical inversion, utilization of multiple a priori constraints, etc., can be realized using GRASP. At the same time, the GRASP concept and algorithm are highly flexible and versatile. GRASP includes several additional original features and enables the implementation of advanced retrieval scenarios. A unique aspect of GRASP is that it can perform radiative transfer (RT) computations fully accounting for multiple interactions of the scattered solar light in the atmosphere online without the use of traditional LUTs. Several other algorithms of the new generation that have been or are being developed for interpretation of MAP observation use the online RT calculations and implement retrieval as a search in the continuous space of solution (e.g., Hasekamp et al., 2011; Xu et al., 2017, 2019; Fu and Hasekamp, 2018; Gao et al., 2018; Stamnes et al., 2018; Di Noia et al., 2019). Nonetheless, at present GRASP was the only algorithm that has been used to generate aerosol products for the full archive of POLDER observations (Dubovik et al., 2019).

The GRASP retrieval can utilize whatever information content is available. If there is sufficient information content of the observations, GRASP will find the aerosol solutions. In the case of any currently operational observations, GRASP can make optimal assumptions to constrain the solution. For example, GRASP can retrieve both aerosol and underlying surface properties simultaneously from multispectral satellite observations using additional a priori constraints on the spectral variability of the land bidirectional reflection distribution function (BRDF). Or (probably the most essential methodological novelty) it can operate by relying on the multi-pixel concept wherein the statistically optimized retrieval is performed simultaneously for a large group of pixels (Dubovik et al., 2011). This feature brings additional possibilities for improving the accuracy of satellite retrievals by using known constraints on the inter-pixel variability of retrieved aerosol and surface reflectance parameters. As a result, using this methodology GRASP provides reliable retrievals of detailed aerosol properties that traditionally have been difficult to obtain from satellites, for example, spectral AOD and AAOD over land including very bright deserts. The GRASP algorithm source code and detailed documentation are available from https://www.grasp-open.com (last access: 28 March 2020).

It should be noted that GRASP is a flexible inversion algorithm that can be applied to a wide variety of satellite, ground-based and laboratory observations. It has already been applied to ground-based AERONET photometers and lidars (Benavent-Oltra et al., 2017, 2019; Hu et al., 2019; Lopatin et al., 2013; Titos et al., 2019; Tsekeri et al., 2017), sky cameras (Román et al., 2017), polar-nephelometer data (Espinosa et al., 2017, 2019; Schuster et al., 2019), and surface measurements of AOD (Torres et al., 2017). In addition, GRASP is being used for several satellite instruments; aerosol products were generated for POLDER observations (discussed here) and for MERIS/Envisat, and there are ongoing developments for producing GRASP aerosol products from Sentinel-3 and Sentinel-5P observations and operational aerosol retrievals for future Sentinel-4 and 3MI/MetOp missions. GRASP is constantly being updated to produce many user-oriented products such as estimates of covariance matrices (Herrera et al., 2020), direct radiative forcing (Derimian et al., 2016) and so on.

For POLDER, GRASP utilizes radiance and polarization observations from all available spectral channels, including minor gaseous absorption for some of them, i.e., for total radiance five channels for POLDER-1 and 2 and six for PARASOL and for polarized radiances (three spectral channels for all instruments). The retrieval uses a unique global set of constraints (no location-specific assumptions) and a single initial guess globally. GRASP performs radiative transfer computations fully accounting for multiple interactions of the scattered solar light in the atmosphere online without using a traditional LUT. Since these RT computations are complex and time consuming, significant effort has been put into optimization and acceleration of the code for operational processing of voluminous datasets. At present, the speed of GRASP retrieval is appropriate for processing the full archive of POLDER observations at native resolution (POLDER-1 and 2 at ∼ 7 km and PARASOL at ∼ 6 km) using rather moderate computing resources, e.g., 3–4 s/pixel for GRASP/HP, 0.3–0.5 s/pixel for GRASP/Optimized and 0.1–0.2 s/pixel for GRASP/Models, in a single-core processor (the description of GRASP/HP, GRASP/Optimized and GRASP/Models will be detailed further in this section).

Since GRASP has been designed for use with different observations, it allows a variety of different possibilities on modeling aerosol scattering and surface reflectance and generally on implementing atmospheric radiative transfer calculations. As a result, different configurations of the atmospheric forward model can be used even for interpretation of the same data (as is the case here with POLDER). Currently, the full POLDER/PARASOL data archive is processed by GRASP using the three following retrieval configurations:

1. PARASOL/GRASP “Optimized” (in the sense that radiative transfer calculations were optimized to find the best trade-off between speed of processing and accuracy of results);

2. PARASOL/GRASP “High-precision” (radiative transfer calculations with high precision were used);

3. PARASOL/GRASP “Models” (the simplest, fastest processing; aerosol is assumed to be an external mixture of several aerosol models).

The Optimized and High-precision configurations are different only by the online precision of the RT calculations, while they are conceptually the same: aerosol size distribution, spectral values of complex index of refraction, fraction of spherical particles and the aerosol layer height (ALH) are retrieved simultaneously with the surface BRDF and bidirectional polarization distribution function (BPDF) parameters. The retrievals were performed using one aerosol component model with five bins of the size distribution and spectrally dependent complex refractive index. The aerosol vertical distribution was modeled using an exponential profile and scale height was retrieved. The details of implementation are discussed in Dubovik et al. (2011). The Models approach uses different assumptions for modeling aerosol properties (surface treatment is the same as above): aerosol is assumed to be an external mixture of several aerosol components, and only their respective concentrations are retrieved together with ALH and spectral BRDF/BPDF parameters. The size distribution, complex refractive index and non-sphericity parameter for each aerosol component are derived from the results of AERONET aerosol climatology for the main distinct aerosol types (Dubovik et al., 2002b) and improved in a series of sensitivity tests with satellite data. For retrievals over land, GRASP retrieves the parameters of the Ross-Li BRDF (Li and Strahler, 1992; Ross, 1981) and BPDF (Maignan et al., 2009) models under the assumption that the retrieved parameters are spectrally smooth (the strength of smoothness is different for each parameter) (Litvinov et al., 2011a, b). For retrievals over ocean, the wind speed and a spectrally dependent Lambertian albedo are included in the state vector. It should be noted that the Models approach firstly was intended to be used for mono-viewing satellite observations such as those from MERIS/Envisat. However, once the approach was tested with PARASOL data, the obtained results were quite appealing, especially in conditions of low aerosol loading, motivating the generation of the PARASOL/GRASP Models archive that is included in the consideration here.

The three archives (Optimized, HP and Models) are released publicly and can be found at the AERIS/ICARE Data and Services Center (http://www.icare.univ-lille.fr, last access: 16 October 2018) and on the GRASP-OPEN website (https://www.grasp-open.com/products/, last access: 28 March 2020) in slightly different formats. AERIS/ICARE is the official distributor of POLDER Level-1 and 2 data and allows the user to dive into the data using a web tool, which plots the results online. AERIS/ICARE provides detailed visualization of the data, while the GRASP-OPEN site is faster in releasing new products but with no visualization. The original PARASOL/GRASP retrievals are stored at Level-1, Level-2 and Level-3 products and are publicly available in the form of daily, monthly, seasonal, yearly and climatological datasets. The Level-2 data contain full-resolution data filtered following established quality criteria. Level-3 data are aggregated into a 0.1 and 1^∘ grid box using the sinusoidal projection and gdalwarp regridding technique (https://gdal.org/programs/gdalwarp.html, last access: 25 March 2020) from the arithmetic mean of Level-2 data. As discussed in Sayer and Knobelspiesse (2019), the arithmetic vs. geometric differences are likely significantly smaller for Level-3 0.1^∘ data used in this study. The list of retrieved aerosol parameters as well as derived aerosol characteristics can be found in Table 1. In this study, we adopt the current latest version of Optimized, HP (v1.2) and Models (v2.1) products.

In addition to the PARASOL/GRASP products, all observations of POLDER-1 and 2 were also processed (using the GRASP/Models approach only). These data records are much shorter than PARASOL and therefore not included in the following analysis. However, based on limited comparisons (not presented here), the quality of the POLDER-1 and 2/GRASP retrievals is expected to be similar to that of PARASOL/GRASP retrievals. Also, recently a new “GRASP/Component” approach has been developed (Li et al., 2019, 2020a, b). This approach retrieved the size-resolved fractions of aerosol components representing the different composition species, like black carbon, brown carbon, fine- and coarse-mode non-absorbing soluble and insoluble, coarse-mode absorbing, and aerosol water. The retrieved fractions drive the aerosol spectral index of refraction in modeling atmospheric radiances. This provides a fourth retrieval archive; however, the results have not yet been fully analyzed and are not released in a user-friendly format, so the GRASP/Component dataset will not be considered in this study.

PARASOL/GRASP aerosol products have already appeared in many studies, i.e., validation (Tan et al., 2019; Wei et al., 2019, 2020), data assimilation (Chen et al., 2018, 2019), AOD product merging (Li et al., 2020; Sogacheva et al., 2020). Despite these preliminary applications of the products, no systematic evaluation of the global PARASOL/GRASP aerosol products has been published. Moreover, most early studies are based on the GRASP/Optimized products, which were released first. The evaluation of PARASOL/GRASP surface properties, as well as aerosol microphysical parameters (size distribution, complex refractive indices, fraction of spherical particles) and aerosol layer height, will be the subject of separate studies.

2.2 MODIS Dark Target, Deep Blue and MAIAC aerosol products

The MODIS sensors on board TERRA since 2000 (overpass ∼ 10:30 local) and AQUA since 2002 (overpass ∼ 13:30 local like PARASOL during the first 5 years) provide near-global coverage twice per day. In this study, we will employ products from MODIS Aqua only, which is on the same A-Train afternoon constellation orbit as PARASOL. MODIS has a wider swath of 2330 km compared to the ∼ 1600 km of PARASOL, 36 spectral channels ranging from 410 to 15 000 nm and higher spatial resolution for cloud mask. There are three mature aerosol products produced operationally and distributed by NASA: Dark Target, Deep Blue and MAIAC.

2.3 AERONET dataset

The Aerosol Robotic Network (AERONET) is a global distributed network of well-calibrated sun–sky photometers (Holben et al., 1998). By measuring direct sun radiance, AERONET provides high temporal (every 3 or 15 min in daytime depending on the operation mode of the instruments) multi-wavelength AOD products with high reliable accuracy (∼ ±0.01 to ±0.02) (Eck et al., 1999). Strict protocols for the calibration and maintenance assure homogeneity among all its instruments. Due to its high data quality, the AERONET AOD products are widely used as “ground truth” to evaluate satellite remote sensing aerosol products (Bréon et al., 2011; Chu et al., 2002; Kahn et al., 2005; Liu et al., 2004; Remer et al., 2005, 2002; Sayer et al., 2013).

In addition to direct sun observations, AERONET radiometers conduct routine measurements of the sky-scanning diffuse radiation. These observations are used to derive aerosol microphysical properties, e.g., single-scattering albedo, complex refractive index, size distribution and sphericity via Dubovik and King (2000). The accuracy of the AERONET inversion products has been analyzed in many studies (Dubovik et al., 2000; Sinyuk et al., 2020), and resulting recommendations were adopted for providing aerosol products of the highest quality (e.g., increase in quality of retrieval products with aerosol loading and range of observed scattering angles). The microphysical properties provided by AERONET contribute to aerosol and climatic applications. For example, the AERONET-derived aerosol particle property climatology (Dubovik et al., 2002b) is used in some form in nearly all satellite retrieval algorithms (including MODIS; see Levy et al., 2007b; Lyapustin et al., 2018) and feed the climate models used to characterize aerosol climate effects (Kinne et al., 2003; Sato et al., 2003).

In this study, the up-to-date AERONET Version 3 Level 2.0 dataset (http://www.aeronet.gsfc.nasa.gov, last access: 3 September 2019) (Giles et al., 2019) with standard cloud screening and quality control was used (Smirnov et al., 2000). We make use of all AERONET sites with data during the POLDER/PARASOL archive (2005–2013). The AERONET direct-sun AOD, Ångström exponent, fine- and coarse-mode AOD from the spectral deconvolution algorithm (SDA) (O'Neill et al., 2003), AAOD, and SSA product are chosen as references for satellite products comparison and evaluation.

2.4 Data quality assurance and matchup methodology

One of the main issues in satellite data validation is how to match the temporally varying AERONET point measurements with the spatially varying satellite remote sensing aerosol products at overpass time (Ichoku et al., 2002). This issue is compounded when multiple satellite products are involved that vary from ∼ 1 to ∼ 100 km pixel spatial resolution. There are some insightful studies (Kinne et al., 2013; Schutgens et al., 2017) that quantify the AERONET sites' spatial representativeness at scales from ∼ 50 to ∼ 300 km, which can be used for evaluation of chemical transport model simulations. However, the spatial resolutions (∼ 50 to ∼ 300 km) considered in those studies are seemingly too coarse for validation of satellite products of 1 km for MAIAC, 10 km for DB and DT, and ∼ 6 km data from PARASOL/GRASP.

This study considers aerosol products at 10 km spatial resolution, which is the native resolution of MODIS DB and DT products and seems to be the best compromise for comparing PARASOL/GRASP, MODIS DT, DB and MAIAC results. Also, 10 km is utilized by the aerosol community and other datasets (e.g., ESA CCI products mentioned earlier). This was also a reason for the generation of PARASOL/GRASP Level-3 products. Thus, we adopted PARASOL/GRASP Level-3 daily 0.1^∘ gridded aerosol products, MODIS/AQUA Level-2 daily DT and DB 10 km products, and the 1 km MODIS MAIAC aggregated to 0.1^∘ (MAIAC_0.1) and 0.01^∘ (MAIAC_0.01) resolution for the inter-comparisons. MAIAC_0.01 essentially represents the single 1 km pixel retrieval. The PARASOL/Operational L2 daily aerosol product is directly used for validation, which is at 18.5 km × 18.5 km spatial resolution.

The strategies to select PARASOL/GRASP retrieval products with the highest quality are presented in Table 2. The land pixel is defined only if 100 % of the 0.1^∘ by 0.1^∘ grid box has been identified as land, so an ocean pixel must contain 0 % land. Also, to guarantee proper coast elimination, the first pixel bordering ocean and land is removed (see Fig. 1). We selected the more reliable retrievals using “residual relative” (mean root square of relative error in fitting the measurements by the algorithm) for PARASOL/GRASP products. We adopted the same threshold for GRASP/Optimized and GRASP/HP (0.05 over land and 0.1 over ocean). These thresholds are suggested for general users. For the GRASP/Models product we did not use any filter because a stricter quality assurance filter has been applied in GRASP/Models product generation from L1 to L2 and L3 than for other GRASP datasets. In principle, the post-processing of all PARASOL/GRASP products was done in similar ways. At the same time, the L3 products were prepared and released not at the same time. For example, the L3 GRASP/HP and Optimized archives were generated and released much earlier than GRASP/Models. Therefore, the post-processing and quality screening approaches used for different data archives are not exactly the same. Unfortunately, most of the differences were identified after the release of the products, their extensive use and the full-scale validation. In these regards, the harmonization of all the archives is likely to be done in the future, but it will lead to the release of new products.

Table 2Strategies used to select quality-assured PARASOL and MODIS aerosol products.

¹ DB aerosol product is not available over ocean. ² MAIAC aerosol product is presently only available for tiles containing land, so the ocean retrievals are not considered in this study.

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Figure 1Schematic diagram for satellite data selection over (a) land and (b) ocean.

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In this study we tried to avoid additional filtering of PARASOL/GRASP L3 products, since most users utilize the products with no screening or with a very straightforward filtering. For MODIS DT, DB and MAIAC products, we select the data only with the highest quality assurance (QA) flag. The highest “quality index” was selected for PARASOL/Operational products (Bréon et al., 2011). Any pixel with a fitting residual higher than the threshold for PARASOL or QA lower than the highest flag for MODIS will be set to “no data”.

For validation with AERONET over land, we averaged all land satellite retrievals in a 3×3 window for the gridded satellite data centered over the AERONET station. For ocean sites, in order to select pure ocean pixels and keep a reasonably high number of validation points, we decided to use a 9×9 window over the AERONET site, using only pure ocean pixels. Any ocean pixels adjacent to land or land–ocean mixed pixels were omitted as represented in Fig. 1. The minimal number of accepted satellite data pixels within the window is 1 over land and 41 over ocean; otherwise, the data were excluded from comparison. The PARASOL/Operational product is treated a bit differently over ocean due to its relatively coarse resolution (∼ 18.5 km), with a similar land-like 3×3 window centered over the AERONET station.

The AERONET direct-sun AOD, AE, AODF and AODC data were averaged within ±30 min of the MODIS/AQUA and PARASOL overpass time, while AERONET SSA and AAOD (which have a lower sampling frequency) are averaged within ±180 min. In addition, AERONET station elevations greater than 3600 m above mean sea level and satellite 3×3 or 9×9 datasets with AOD standard deviation greater than 0.05 between window pixels were excluded.

2.5 Considered metrics for comparison statistics

For quantifying the validation results, we used standard statistical parameters, including Pearson's linear correlation coefficient (R), root-mean-square error (RMSE), slope and offset of linear regression and bias.

Here N is the number of matched data points i, O_satellite represents the observations from satellite and O_AERONET represents the referenced observations from AERONET; $\stackrel{\mathrm{‾}}{O_{\mathrm{satellite}}}$ and $\stackrel{\mathrm{‾}}{O_{\mathrm{AERONET}}}$ are the mean value for satellite and AERONET observations.

For MODIS validation, a commonly used metric is the fraction agreeing within and expected error (EE) envelope such as ±0.05 ± 0.15 AOD (Remer et al., 2005) or ±0.05 ± 0.1 AOD (Lyapustin et al., 2018). In this study, we adopted stricter requirements proposed by the Global Climate Observing System (GCOS) (the greater of 0.03 or 10 %), which have been adopted in the Aerosol_cci study (Popp et al., 2016) as well as the latest DB validation (Sayer et al., 2019). Following the Aerosol_cci study by Popp et al. (2016), the uncertainty of 0.01 for AERONET AOD has been taken into account and GCOS is defined as

Hence, the GCOS fraction (%) is the percentage of satellite-retrieved AOD satisfying the GCOS requirement.

3.1 Global validation of PARASOL/GRASP aerosol products

3.1.1 Aerosol optical depth

Figure 2 shows scatter plots of co-located PARASOL/GRASP AOD against AERONET AOD at 550 nm for the entire POLDER/PARASOL archive: Fig. 2a for GRASP/Optimized, Fig. 2b for GRASP/HP and Fig. 2c for GRASP/Models. Validation metrics for total spectral AOD (443, 490, 550, 565, 670, 865 and 1020 nm), as well as AOD separated for land and ocean, are presented in Table 3. As can be seen from Fig. 2 and Table 3, all retrievals present good agreement with AERONET spectrally. Overall, based on these metrics the quality of the comparison with AERONET is best for GRASP/Models. For example, for AOD (550 nm) GRASP/Models shows better performance than GRASP/Optimized and GRASP/HP: R=0.923 compared to 0.877 and 0.899 and RMSE =0.119 for GRASP/Models compared to 0.160 and 0.161 for GRASP/Optimized and GRASP/HP, respectively, at 550 nm (see in Fig. 2). GRASP/Optimized and GRASP/HP show a positive overall bias of 0.06–0.07 for all AOD conditions, which remains for low-AOD conditions (AOD< 0.2) and even increases to 0.08 (GRASP/Optimized). In comparison, GRASP/Models has a small overall bias (of 0.01 for AOD at 550 nm) that slightly increases to 0.03 for high-AOD conditions (AOD > 0.7). Because of the bias in GRASP/HP and GRASP/Optimized AOD, GCOS fraction for them is much lower than for GRASP/Models AOD: e.g., 55.3 % (AOD at 550 nm) for land + ocean vs. 28.2 % and 34.4 %, respectively. Over ocean, all three archives show good correlation with coefficients R > 0.93 at 550 nm. Nevertheless, GRASP/Models over ocean has the highest R=0.950 and offers the best performance for the other statistical metrics. As described in Sect. 2.4, the different post-processing scheme resulted in the difference for matched points between GRASP/Optimized, GRASP/HP and GRASP/Models. It can be noticed that applying a much stricter filter may improve the overall correlation against AERONET AOD for GRASP/HP and GRASP/Optimized products but leads to significant loss of points and, most importantly, does not improve the BIAS, which is considered to be a main issue for them.

Table 3Global statistics of PARASOL/GRASP spectral AOD vs. AERONET AOD over land and ocean. The best performing of three approaches by each metric is labeled in bold.

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Figure 2Evaluation of three archives of PARASOL/GRASP AOD at 550 nm against AERONET: (a) GRASP/Optimized, (b) GRASP/HP, (c) GRASP/Models. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The gray envelope indicates GCOS requirement: max (0.04 or 0.1 AOD). The probability density functions of differences (POLDER-AERONET) are present in the lower panel. The black, red, blue and green solid lines indicate all AOD conditions: any AOD, AOD < 0.2, 0.2 ≤ AOD ≤ 0.7 and AOD > 0.7, respectively.

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It is very important to note the robust performance of PARASOL/GRASP AOD retrieval in all spectral channels. For example, the GRASP/Models product shows only minor spectrally independent bias of 0.01 over land, and over ocean the bias is about 0.02 at 440 nm and decreases to zero at longer wavelengths, and the GCOS fraction for all wavelengths is at least ∼ 50 % over land and ∼ 60 % over ocean.

3.1.2 Ångström exponent

AE was determined from AOD at two different wavelengths ($\mathrm{AE}=\frac{\ln \left[\mathit{\tau }\right({\mathit{\lambda }}_{\mathrm{1}})/\mathit{\tau }({\mathit{\lambda }}_{\mathrm{2}}\left)\right]}{\ln ({\mathit{\lambda }}_{\mathrm{2}}/{\mathit{\lambda }}_{\mathrm{1}})})$. The accuracy of AE decreases for low AOD because even a small spectral bias of the AOD affects AE strongly (e.g., Wagner and Silva, 2008). Therefore, the threshold of PARASOL AOD (550 nm) > 0.2 was used in AE validation. For calculating the PARASOL AE (440∕870), the AOD retrieved at 443 and 865 nm is interpolated to nominal 440 and 870 nm wavelengths. Figure 3 shows the scatter plots of PARASOL/GRASP AE against AERONET AE (440∕870) for the whole archive (Fig. 3a: for GRASP/Optimized, Fig. 3b: for GRASP/HP and Fig. 3c: for GRASP/Models). GRASP/HP has a higher correlation R (0.845) than GRASP/Optimized (0.800) and GRASP/Models (0.692). In addition, GRASP/HP shows a lower RMSE (0.334) than GRASP/Optimized (0.356) and GRASP/Models (0.415). The statistics of separated land and ocean AE validation are presented in Table 4. Over ocean, the correlation coefficients are significantly higher (R > 0.93) than over land for all three datasets. Overall, the AE correlation statistical metrics are the best for GRASP/HP over both land and ocean. The GRASP/Models product has the smallest BIAS over land, which is counterpoised by overestimation of low and underestimation of high AE values due to assumed size distributions in the aerosol model-based approach. Both GRASP/Optimized and GRASP/HP capture AE well when large particles are dominant (AE < 1.0), while the products tend to slightly underestimate AE when small particles are dominant (AE > 1.0).

Table 4Global statistics of PARASOL/GRASP AE vs. AERONET AE (440∕870) over land and ocean. The best performing of three approaches by each metric is labeled in bold.

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Figure 3Evaluation of all archive PARASOL/GRASP AEs (440∕870) against AERONET: (a) GRASP/Optimized, (b) GRASP/HP, (c) GRASP/Models. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The probability density functions of differences (POLDER–AERONET) are present in the lower panels.

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3.1.3 Fine- and coarse-mode aerosol optical depth

Figure 4 shows the validation of PARASOL/GRASP AODF against SDA AODF provided by AERONET. AERONET SDA products (O'Neill et al., 2003) reported only at 500 nm; therefore here they were interpolated to AODF at 550 nm based on AE using a quadratic fit in log-log space (Eck et al., 1999). Over land + ocean, GRASP/HP AODF shows the best validation statistics with correlation R = 0.925; bias = 0.01 and slope = 0.892 compared to R = 0.922; bias = 0.02 and slope = 0.840 for GRASP/Optimized; and R = 0.867, bias = −0.02, and slope = 0.662 for GRASP/Models. The GRASP/Models AODF product has a slightly smaller RMSE (0.092) than GRASP/HP (0.097) and GRASP/Optimized (0.099). Even though the GCOS requirement is initially defined for total AOD, here we also applied the GCOS fraction to the AODF validation based on max (±0.04, ±0.1 AODF). The GCOS fraction for all AODF products is at least ∼ 55 % over land + ocean. The GCOS fraction is highest for GRASP/Models (65.2 %), which is dominant for low-aerosol-loading cases (AODF < 0.2). For moderate and high aerosol loadings (AODF > = 0.2), GRASP/Optimized and GRASP/HP show better performance than GRASP/Models, in terms of GCOS fraction and biases. The linear regression slope for GRASP/Models is weakest at 0.662 compared to 0.892 and 0.840 for GRASP/HP and GRASP/Optimized, respectively. These facts suggest a possible underestimation of fine-mode aerosol in high-AOD conditions for GRASP/Models. Caution is required in the interpretation of the regression slope as these data may not meet the assumptions behind the technique; however, the results are useful in a comparative sense. The statistics for separated land and ocean are presented in Table 5. As can be seen, overall, PARASOL/GRASP AODF products show very good agreement with AERONET SDA products. GRASP/HP AODF demonstrates the best performance in terms of the highest correlation and smallest bias.

Table 5Global statistics of PARASOL/GRASP AODF vs. AERONET SDA AODF at 550 nm over land and ocean. The best performing of three approaches by each metric is labeled in bold.

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Figure 4Evaluation of all archive PARASOL/GRASP AODF at 550 nm with AERONET SDA AODF: (a) GRASP/Optimized, (b) GRASP/HP, (c) GRASP/Models. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The gray envelope indicates the GCOS requirement applied for AODF: max (0.04 or 0.1 AODF). The probability density functions of differences (POLDER–AERONET) are present in the lower panel. The black, red, blue and green solid lines indicate all AODF conditions: any AODF, AODF < 0.2, 0.2 ≤ AODF ≤ 0.7 and AODF > 0.7, respectively.

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The coarse-mode AOD (AODC) is traditionally a difficult parameter to derive from satellite observations, especially over bright land surfaces, since nadir-looking satellite measurements are not very sensitive to large particles. The validation of all archived PARASOL/GRASP AODC with AERONET SDA AODC is presented in Fig. 5. Generally, the global (land + ocean) statistical metrics for AODC are less convincing than those for AODF but still reasonable: GRASP/HP has higher correlation R (0.745) and slope (0.936) than GRASP/Optimized (R = 0.689, slope = 0.748) and GRASP/Models (R = 0.579, slope = 0.657). GRASP/Models retrievals show a smaller bias (0.02) and RMSE (0.109) than GRASP/Optimized (bias = 0.04, RMSE = 0.116) and GRASP/HP (bias = 0.05, RMSE = 0.123). The GCOS fraction of AODC max (±0.04, ±0.1AODC) for GRASP/Models (65.4 %) is higher than GRASP/Optimized (44.3 %) and GRASP/HP (48.4 %). In line with AODF, GRASP/Models has better performance for low-aerosol-loading cases, which account for ∼ 90 % of the number of points. The statistics of separated land and ocean AODC validation, presented in Table 6, show a much higher correlation of retrieved AODC with AERONET over ocean. It is also interesting to note that the validation statistics for AODF seems to be superior to that for AODC over land, and the situation is reversed. This can be explained by the fact that the fine-mode aerosols have higher abundance over land while coarse-mode aerosol is dominant over ocean; i.e., dynamic ranges are different. Also, at longer wavelengths where the contribution of coarse particles to radiation is significant, the land surface is very bright while the ocean surface is practically dark. Over land AODC in GRASP/HP and GRASP/Optimized products exhibits rather high bias of 0.05 and 0.03 correspondingly, which probably dominates the bias for the total AOD in both. For the GRASP/Models product, biases in AODF and AODC over land have comparable magnitudes and different signs and therefore compensate for each other in the total AOD.

Table 6Global statistics of PARASOL/GRASP AODC vs. AERONET SDA AODC at 550 nm over land and ocean. The best performing of three approaches by each metric is labeled in bold.

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Figure 5The same as Fig. 4, but for AODC at 550 nm.

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3.1.4 Single-scattering albedo

Figure 6 shows the validation of PARASOL/GRASP SSA (670 nm) with AERONET L2 inversion products. The SSA products in the AERONET L2 database provide the values only for moderate- and high-AOD cases (AOD at 440 nm ≥ 0.4) to assure the highest quality of the inversion products (Dubovik et al., 2000, 2002b). Following the same strategy, PARASOL/GRASP L2 and L3 products of SSA for low-AOD cases are also filtered out (land: AOD 443 nm < 0.3; ocean: AOD 443 nm < 0.02). The threshold for filtering SSA over ocean is very low because using higher values would eliminate a significant fraction of the retrievals. This low-AOD filtering is done over L2 products, and then L3 SSA is generated from filtered L2 products. The validation shows convincing correlation of all SSA PARASOL/GRASP products with those from AERONET, although due to a rather small dynamic range (mostly 0.7–1.0) of SSA, the correlation coefficients for SSA (670 nm) in Fig. 6 are notably lower than for other parameters. The highest correlation is for GRASP/HP with R = 0.536 and RMSE (0.056) compared with GRASP/Optimized (R = 0.511; RMSE = 0.065) and GRASP/Models (R = 0.324; RMSE = 0.057), while GRASP/Models has the smallest bias (−0.02) compared to GRASP/HP (bias = −0.03) and GRASP/Optimized (bias = −0.04).

Figure 6Evaluation of all archive PARASOL/GRASP SSA values at 670 nm with AERONET SSA at 675 nm: (a) GRASP/Optimized, (b) GRASP/HP, (c) GRASP/Models. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line.

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Table 7 shows the statistics of PARASOL/GRASP spectral SSA (443, 670, 865 and 1020 nm) against AERONET SSA at four wavelengths (440, 675, 870 and 1020 nm). The statistics are given for combined land and ocean, because of the limited number of validation points over ocean. The SSA correlation coefficients for GRASP/Optimized and GRASP/HP L3 products increase from 440 nm (∼ 0.25) to 1020 nm (∼ 0.60), which is likely due to the increased dynamic range of SSA at longer wavelengths (e.g., see Dubovik et al. (2002b); SSA at 1020 can change from very low values for biomass burning aerosol to nearly unity for desert dust). Consequently, the RMSE also increases from 440 to 1020 nm.

Table 7Global statistics of PARASOL/GRASP spectral SSA vs. AERONET SSA stratified by PARASOL AOD (565 nm) levels. The best performing at each wavelength of three approaches by each metric is labeled in bold.

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In addition, Table 7 reports the statistics of SSA validation at different PARASOL AOD levels. The results clearly illustrate the improvement of retrieved SSA with the increase in aerosol abundance, in agreement with the results of AERONET sensitivity studies by Dubovik et al. (2000). For example, the correlation coefficient for GRASP/Models SSA at 670 nm with AERONET significantly improves from 0.321 for all PARASOL/GRASP L3 products to 0.814 for PARASOL AOD greater than 1.5. Meanwhile, the RMSE decreases from 0.056 to 0.029.

3.1.5 Aerosol absorption optical depth

Aerosol absorption optical depth (AAOD) is related to SSA and total AOD as

$$\begin{array}{}\text{(5)}& \mathrm{AAOD}\left(\mathit{\lambda }\right)=\mathrm{AOD}\left(\mathit{\lambda }\right)\times \left[\mathrm{1}-\mathrm{SSA}\left(\mathit{\lambda }\right)\right].\end{array}$$

In the current PARASOL/GRASP L3 dataset, the AAOD value of each grid box (0.1^∘ or 1^∘) is calculated based on Eq. (5) using average AOD(λ) and SSA(λ) of the grid box. Note that the PARASOL/GRASP L3 SSA(λ) values are aggregated based on moderate- and high-AOD cases (land: AOD 443 nm ≥ 0.3; ocean: AOD 443 nm ≥ 0.02), and again the very low threshold for filtering SSA over ocean was chosen in order to retain a sufficient number of SSA and AAOD retrievals. Choosing even slightly higher values would eliminate the majority of retrievals over ocean. Thus, the direct use of L3 climatology of AAOD may lead to overestimation of the global aerosol absorption, because the low-AOD cases are filtered. Similarly, the AERONET L2 database provides AAOD products only for moderate- and high-AOD cases (AOD at 440 nm ≥ 0.4) to assure their highest quality (Dubovik et al., 2000).

The statistics of PARASOL/GRASP spectral AAOD (443, 670, 865 and 1020 nm) validation versus AERONET AAOD (440, 675, 870 and 1020 nm) are shown in Table 8. The correlation coefficients of AAOD are relatively low (0.4–0.55), which is certainly due to the low absolute value of AAOD, and most cases are less than 30 % of total AOD. GRASP/HP and GRASP/Models AAOD products show the RMSE equal to 0.042–0.018 from 443 to 1020 nm for Models and 0.047–0.025 for HP. The bias is lowest for GRASP/Models AAOD: 0.00 at 440, 870 and 1020 nm and 0.01 at 670. Thus, PARASOL/GRASP AAOD provides rather useful information about global AAOD values; even the uncertainties are rather significant given the generally low magnitudes of AAOD. In contrast with SSA, the attempts to analyze the AAOD accuracy for different AOD levels did not show any consistent improvement in accuracy with increase in abundance.

Table 8Global statistics of PARASOL/GRASP spectral AAOD vs. AERONET AAOD. The best performing at each wavelength of three approaches by each metric is labeled in bold.

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3.2 Comparison of results obtained from validation of PARASOL and MODIS aerosol products against AERONET

In order to place the PARASOL/GRASP validation results into perspective, here we compare the PARASOL/GRASP ability to retrieve AOD, AE, AODF and AODC with other satellites. Specifically, these products from MODIS, PARASOL/Operational and PARASOL/GRASP products are validated using the same approach for all of 2008 and validation results were compared. MODIS aerosol products have been extensively evaluated globally by the MODIS team in multiple studies (Gupta et al., 2018; Levy et al., 2010, 2013, 2018; Lyapustin et al., 2018; Sayer et al., 2013, 2014, 2019), and PARASOL/Operational aerosol products have been evaluated in Bréon et al. (2011); the present analyses is performed for reader convenience and consistency of methodology across products. We confirmed that the statistic metrics that we found for MODIS and PARASOL/Operational aerosol product validation in 2008 is similar to these studies. This section is therefore focusing on a comprehensive evaluation of the consistencies and differences between PARASOL and MODIS aerosol products using examples from 1 year. The year 2008 was chosen because it presents generally good statistics of observations, and all types of aerosol are clearly present. The validation figures for the satellite products over land and ocean are presented separately, because over land there are three MODIS products (DT, DB and MAIAC), while only the DT product is provided over ocean. MAIAC products cover some land-containing ocean tiles; however due to limited coverage of these retrievals, we do not consider MAIAC ocean products here. PARASOL/Operational AODF products are provided over land and ocean and total AOD products only over ocean.

Figure 7 shows validation results for AOD at 550 nm for three PARASOL/GRASP products over land with collocated AERONET measurements. Figure 8 shows the validation results for MODIS DT, DB and MAIAC AOD products over land. The products called MAIAC_0.1 and MAIAC_0.01 correspond to the MODIS MAIAC original product aggregated to 0.1^∘ and 0.01^∘ grid boxes, respectively. In general MODIS products have more matched points than PARASOL products due to MODIS' wider swath and higher spatial resolution of measurements allowing better cloud detection. From low to high values the sequence of obtained global correlation coefficients is 0.870 (DB), 0.874 (MAIAC_0.01), 0.875 (GRASP/Optimized), 0.895 (MAIAC_0.1), 0.898 (DT), 0.908 (GRASP/HP) and 0.924 (GRASP/Models). The GCOS fraction sequence is 28.8 % (GRASP/Optimized), 32.4 % (GRASP/HP), 46.1 % (DT), 48.1 % (MAIAC_0.01), 48.8 % (DB), 52.8 % (MAIAC_0.1) and 53.2 % (GRASP/Models). The high to low RMSE sequence is 0.157 (GRASP/HP), 0.150 (GRASP/Optimized), 0.126 (DB), 0.121 (GRASP/Models), 0.120 (DT) and 0.112 (MAIAC_0.1). The large to small total bias sequence is 0.06 (GRASP/HP), 0.04 (GRASP/Optimized), −0.03 (MAIAC_0.01 and MAIAC_0.1), 0.02 (DT), −0.01 (DB) and 0.00 (GRASP/Models). The low to high sequence of regression slope values is 0.780 (GRASP/Optimized), 0.793 (MAIAC_0.1), 0.794 (MAIAC_0.1), 0.841 (DB), 0.938 (GRASP/HP), 0.988 (DT) and 0.989 (GRASP/Models). The results illustrate that the overall accuracy of these AOD products is generally comparable on a global scale. Note, however, that different products may have different regional strengths and weaknesses (e.g., Sayer et al., 2014), motivating the mapped analysis later. The GRASP/Models AOD yields overall the largest number of the best statistical indicators over land: with the highest correlation (R = 0.924), the highest GCOS fraction (53.2 %), correlation slope (0.989) and the smallest total bias (bias = 0.00). The detailed statistics of PARASOL and MODIS AOD products against referenced collocated AERONET AOD at 550 nm over land and ocean are presented in Table 9.

Figure 7Validation of PARASOL/GRASP AOD at 550 nm over land in 2008: (a) GRASP/Optimized, (b) GRASP/HP, (c) GRASP/Models. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The gray envelope indicates GCOS requirement: max (0.04 or 0.1 AOD). The probability density functions of differences (POLDER–AERONET) are present in the lower panels. The black, red, blue and green solid lines indicate all AOD conditions: any AOD, AOD < 0.2, 0.2 ≤ AOD ≤ 0.7 and AOD > 0.7, respectively.

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Figure 8Validation of MODIS AOD at 550 nm over land in 2008: (a) DT, (b) DB, (c) MAIAC_0.1, (d) MAIAC_0.01. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The gray envelope indicates GCOS requirement: max (0.04 or 0.1 AOD). The probability density functions of differences (MODIS–AERONET) are present in the lower panels. The black, red, blue and green solid lines indicate all AOD conditions: any AOD, AOD < 0.2, 0.2 ≤ AOD ≤ 0.7 and AOD > 0.7, respectively.

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Table 9Statistics of PARASOL and MODIS AOD products against collocated AERONET AOD at 550 nm over land and ocean.

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Figure 9 presents validation of PARASOL/GRASP (Optimized, HP and Models), PARASOL/Operational and MODIS/DT AOD products versus collocated AERONET measurements over ocean in 2008. The detailed statistic metrics are presented in Table 9. The matching methodology is the same as described in Sect. 2.4. The total matched points in 2008 range from minimum GRASP/Optimized 116 to maximum MODIS/DT 218. In general, all AOD products show high correlation over ocean, of which GRASP/Models has the highest R (0.963), following by Operational (0.954), DT (0.952), GRASP/Optimized (0.950) and GRASP/HP (0.947). The high to low sequence of RMSE is 0.092 (GRASP/HP), 0.089 (GRASP/Optimized), 0.081 (DT), 0.077 (Operational) and 0.061 (GRASP/Models). The slopes are quite similar: 1.165 (Operational), 1.145 (GRASP/Optimized), 1.074 (GRASP/HP), 0.965 (GRASP/Models) and 0.974 (DT). Overall, GRASP/Models shows slightly better bias (0.02) and GCOS fraction (62.9 %), following by DT (bias = 0.03, GCOS fraction = 55.0 %), Operational (bias = 0.03, GCOS fraction = 52.2 %), GRASP/Optimized (bias = 0.06, GCOS fraction = 42.2 %) and GRASP/HP (bias = 0.07, GCOS fraction = 26.6 %). Altogether, GRASP/Models, PARASOL/Operational and DT AOD yield quite similar performance over ocean with better statistics than GRASP/Optimized and GRASP/HP AODs that correlate well with AERONET measurements but present a significant positive bias (0.06–0.07).

Figure 9Validation of PARASOL/GRASP, PARASOL/Operational and MODIS/DT AOD at 550 nm over ocean in 2008. (a) GRASP/Optimized; (b) GRASP/HP; (c) GRASP/Models; (d) Operational; (e) DT. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The gray envelope indicates GCOS requirement: max (0.04 or 0.1 AOD). The probability density functions of differences (satellite–AERONET) are present in the lower panel. The black, red, blue and green solid lines indicate all AOD conditions: any AOD, AOD < 0.2, 0.2 ≤ AOD ≤ 0.7 and AOD > 0.7, respectively.

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In order to obtain more information about the quality of the retrieval products over different land surfaces, the statistics of satellite validation against AERONET were also analyzed separately for different land covers. Table 10 shows the statistic metrics for land surfaces with different normalized difference vegetation index (NDVI) values. The statistics are presented for several categories: bare soil/desert surfaces (NDVI < 0.2), mixture of bare soil and vegetated surfaces (0.2 ≤ NDVI < 0.4) and surfaces covered different types of vegetation (0.4 ≤ NDVI < 0.6 and NDVI ≥ 0.6). The global NDVI dataset is adopted from GRASP/Models L3 annual mean products for the year 2008 (Fig. 10). The statistic metrics in Table 10 show that, in general, all products show better performance over surface type with 0.2 ≤ NDVI < 0.6 than bright, bare surfaces (NDVI < 0.2) and somewhat better than for dense vegetation surface (NDVI ≥ 0.6). Overall the AOD product of GRASP/Models seems to show the best correlation with AERONET, with the highest R over three of four surface classes. Over bright surfaces (NDVI < 0.2), GRASP/HP has the highest R (0.915), but also rather high bias of 0.06. The GRASP/Models AOD also has zero bias for three surface classes except the dense vegetation surface (NDVI ≥ 0.6), where GRASP/Models AOD has total bias of 0.03, higher than that in any MODIS AODs.

Table 10Statistics of PARASOL and MODIS AOD products against collocated AERONET AOD at 550 nm classified by NDVI. In each individual NDVI level, the best performing metric is indicated in bold. The number of matched pairs is included in brackets.

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Figure 10Spatial distribution of annual mean NDVI for 2008 from GRASP/Models L3 products.

Figure 11Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models) and MODIS (d DT and e DB) AE over land in 2008. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The probability density functions of differences (satellite–AERONET) are present in the lower panels.

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Figure 11 shows the validation of AEs for PARASOL/GRASP and MODIS DT and DB products over land versus collocated AERONET measurements. The MODIS AE for DT and DB products were calculated based on 470 and 660 nm that are reported in both products; an equivalent for AERONET was calculated using AOD interpolated to 470 and 660 nm. PARASOL/GRASP products contain AOD at 440 and 870 nm; therefore AE (440∕870) was directly used for validation of PARASOL/GRASP results. MAIAC AE was not included because MAIAC reports AOD at two rather close wavelengths (470 and 550 nm), and calculation of AE using these such close channels could produce substantial uncertainties in AE. The threshold of satellite AOD (550 nm) > 0.2 was used in validation of AE over land and ocean. In general, PARASOL/GRASP (Optimized, HP and Models) AE agrees notably better with AERONET than MODIS (DT and DB), which is likely caused by the lower information content in regards to aerosol size in mono-viewing MODIS observations. In addition, both DT and DB algorithms rely on climatology for the aerosol model selection; i.e., AE is rather predetermined than retrieved to some extent. For example, although AOD over land is reported by DT at 470 and 660 nm, the spectral dependence of the DT land retrieval is mostly imposed by assumed aerosol models. The DT team makes a specific point of not reporting AE over land for that reason, and at best the spectral dependence might allow a binary inference of either fine-mode or coarse-mode-dominated particles but not a quantitative measure of the true spectral dependence. The DT over ocean algorithm has greater flexibility in its mixing of models and does return a quantitative AE. The weaker performance of the GRASP/Models approach compared to GRASP/HP and GRASP/Optimized is caused by the limitation of maximum and minimum AE values allowed by the mixture of aerosol components used, even though the GRASP/Models approach allows mixing of different components freely with no location-specific constraints. As a result, GRASP/Models tends to overestimate AE for large particles (low AE values) and underestimate AE for small particles (high AE values). Hence, GRASP/Models AE products are less appealing than those from GRASP/Optimized and GRASP/HP in terms of evaluation metrics. GRASP/HP tends to provide the most reliable AE products over land.

Figure 12 presents the validation of AE over ocean from PARASOL/GRASP, PARASOL/Operational and MODIS/DT products against AERONET measurements. PARASOL/Operational AE was calculated based on 670 and 870 nm that are reported in the product, and AE (670∕870) of AERONET was calculated using AOD interpolated to 670 and 870 nm. Although there are not many available points, the satellite-derived AE values over ocean are much better than those over land. GRASP/Models shows R (0.949) higher than Operational (0.891), GRASP/HP (0.890), GRASP/Optimized (0.840) and DT (0.832). GRASP/Models and MODIS DT AEs show an overestimation for large particles. Operational AE tends to overestimate for both large and small particles. At the same time, GRASP/HP AE correlation has the slope closer to 1:1 line with AERONET AE than other products, with the best linear fitting slope (0.810) and intercept (0.051). The statistic metrics of AE validation over land and ocean are listed in Table 11.

Figure 12Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models), (d) PARASOL/Operational and (e) MODIS/DT AE over ocean in 2008. The gray dashed line and the red solid line are the 1:1 reference line and the linear regression line. The probability density functions of differences (satellite–AERONET) are present in the lower panels.

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Table 11Statistics of PARASOL and MODIS AE products against collocated AERONET AE over land and ocean, with a threshold of satellite AOD (550 nm) > 0.2.

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AODF is often used to estimate anthropogenic aerosol climate effects (Bellouin et al., 2005) and surface air quality (e.g., PM_2.5) (Zhang and Li, 2015). MODIS started to report the fine-mode weighting parameter (η) in the products from the second-generation DT operational algorithm (Levy et al., 2007b), though η is weighted for reflectance not for AOD. Consequently η over land is a diagnostic that has little physical meaning and the resulting AODF and AODC do not have physical meaning and generally are not recommended to be used. Therefore, it is not considered in the analysis. However, over ocean, based on single-scattering approximation, η is also weighted for AOD (Remer et al., 2005). Therefore, MODIS fine- and coarse-mode AODs at 550 nm over ocean are derived according to the equations below:

Figure 13 shows the validation of AODF at 550 nm for PARASOL/GRASP and PARASOL/Operational AODF products over land against AERONET AODF products from the SDA algorithm. It is noticeable that the AODF products over land are only available from PARASOL MAP measurements. The results in Fig. 13 indicate the PARASOL/GRASP and PARASOL/Operational AODF products are in good agreement with AERONET SDA products, for example, R > 0.86. The GCOS fraction of AODF for PARASOL/GRASP and PARASOL/Operational products is at least 50 %. GRASP/HP AODF shows the best correlation among all four AODF products over land, with rather similar performance for GRASP/Optimized AODF.

Figure 13Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models) and (d) PARASOL/Operational fine-mode AOD at 550 nm over land in 2008. The gray envelope indicates GCOS requirement applied for AODF: max (0.04 or 0.1 AODF). The probability density functions of differences (POLDER–AERONET) are present in the lower panels. The black, red, blue and green solid lines indicate all AODF conditions: any AODF, AODF < 0.2, 0.2 ≤ AODF ≤ 0.7 and AODF > 0.7, respectively.

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The AODF validation over ocean is shown in Fig. 14, and statistical metrics over land and ocean are presented in Table 12. GRASP/Optimized and GRASP/HP AODF show generally consistent performance over ocean and over land, with correlation R around 0.9, while the bias for GRASP/Optimized and GRASP/HP AODF is higher over ocean than over land. At the same time, GRASP/Models AODF shows significant improvement over ocean; for example, the fitting line is much closer to 1:1 (dotted line), and the RMSE decreased dramatically. PARASOL/Operational AODF shows a slight decrease in R from land (R = 0.886) to ocean (R = 0.780), also reported in Bréon et al. (2011), while the fitting line, RMSE and bias show improvement from land to ocean. This is likely due to higher information content about aerosols in satellite observations over dark ocean surfaces compared to brighter land surfaces.

Table 12Statistics of PARASOL and MODIS AODF products against collocated AERONET AODF over land and ocean.

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Figure 14Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models), (d) PARASOL/Operational and (e) MODIS/DT fine-mode AOD at 550 nm over ocean in 2008. The gray envelope indicates GCOS requirement applied for AODF: max (0.04 or 0.1 AODF). The probability density functions of differences (satellite–AERONET) are present in the lower panels. The black, red, blue and green solid lines indicate all AODF conditions: any AODF, AODF < 0.2, 0.2 ≤ AODF ≤ 0.7 and AODF > 0.7, respectively.

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The validation of AODC over land and ocean is shown in Figs. 15 and 16, respectively. Even though AODC products over land are only provided for PARASOL/GRASP, for completeness we present this over land for the year 2008 in Fig. 15. Similarly to the results from the total PARASOL/GRASP archive, AODC over ocean is more accurate than over land. The overall best results of AODC are provided by GRASP/HP with the highest R (0.771) and the best linear fitting (slope is reaching 1 and intercept is close to 0) over land. Yet, the bias of GRASP/HP AODC is 0.05, which is higher than GRASP/Models (0.01) and GRASP/Optimized (0.03), which result in a higher GCOS fraction for GRASP/Models AODC (63.7 %) than GRASP/HP (45.8 %) and GRASP/Optimized (45.6 %). At the same time, as mentioned above, over dark ocean the sensitivity of the observed signal to aerosol is stronger, allowing for retrieval of particle size information that is more challenging over land. The GRASP/Models AODC shows the best R (0.966) and RMSE (0.040) while MODIS/DT AODC has the smallest bias (0.00) against AERONET over ocean, followed by Operational (0.01), GRASP/Models (−0.01), GRASP/Optimized (0.03) and GRASP/HP (0.05). Although AODC is not included in the PARASOL/Operational product list, over ocean we subtract AODF from total AOD to obtain Operational AODC, which shows a rather good agreement with AERONET (R = 0.936, slope = 0.971, RMSE = 0.045, bias = 0.01). However, over land, only AODF is provided in the PARASOL/Operational product.

Figure 15Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models) coarse-mode AOD at 550 nm over land in 2008. The gray envelope indicates GCOS requirement applied for AODC: max (0.04 or 0.1 AODC). The probability density functions of differences (POLDER–AERONET) are present in the lower panel. The black, red, blue and green solid lines indicate all AODC conditions: any AODC, AODC < 0.2, 0.2 ≤ AODC ≤ 0.7 and AODC > 0.7, respectively.

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Figure 16Validation of PARASOL/GRASP (a GRASP/Optimized, b GRASP/HP and c GRASP/Models), (d) PARASOL/Operational and (e) MODIS/DT coarse-mode AOD at 550 nm over ocean in 2008. The gray envelope indicates GCOS requirement applied for AODC: max (0.04 or 0.1 AODC). The probability density functions of differences (POLDER–AERONET) are present in the lower panels. The black, red, blue and green solid lines indicate all AODC conditions: any AODC, AODC < 0.2, 0.2 ≤ AODC ≤ 0.7 and AODC > 0.7, respectively.

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The statistics in comparison of each single product vary due to the differences in product coverage: coverage of MODIS Aqua is wider than PARASOL; at the same time, the products have different limitations and availability:

• MODIS/DT has limited products over bright land surfaces, and AODF and AODC are only available over ocean;

• MODIS/DB and MAIAC AOD products are only over land and do not include AODF and AODC;

• PARASOL/Operational over land provides only AODF;

• quality screening is different (even between PARASOL/GRASP products).

Therefore, the approaches chosen in this paper for considering all above factors could have some effects on the results and their interpretation. At the same time, the correlations with AERONET obtained in these studies for known products including MODIS DT, DB and MAIAC and PARASOL/Operational in general agree with the results of previously mentioned studies.

3.3 Evaluation of PARASOL and MODIS validation results over different AERONET sites

In this section, we compare the validation metrics of PARASOL/GRASP and MODIS aerosol products over spatially distributed AERONET sites. PARASOL/Operational AOD products are provided over ocean only and hence are not included in this section. The AOD validation was conducted over all AERONET sites that had available data in 2008. At the same time and to increase statistical robustness only sites with at least 10 matchup points were included in the analysis. However, the different products can also have a different number of matchup points over different AERONET sites due to various factors (as discussed previously). Therefore, to evaluate the validation performance of different products, the percentage (%) of the cases when the product of each algorithm showed the best statistic metrics, observed among all the products (e.g., the highest R and GCOS fraction and the lowest RMSE and bias), was used as an indicator for the performance evaluation.

Figure 17 shows the percentage score for each algorithm at AERONET sites for statistical metrics R, RMSE, bias and GCOS fraction, respectively. The detailed statistics for the performance of each AOD product are shown in Fig. 18 (only the first ranking statistics over each site are present in the maps.). All PARASOL/GRASP products have fewer sites with at least 10 matchup points than MODIS AOD products. There are 102, 124 and 95 sites having sufficient matchup points for GRASP/Optimized, GRASP/HP and GRASP/Models, respectively, lower than DT (153), DB (172), MAIAC_0.1 (169) and MAIAC_0.01 (172) by 20 %–45 %. Regarding the correlation coefficient R, GRASP/Models, DT and MAIAC_0.1 are the three algorithms showing higher scores for 37.9 %, 28.1 % and 24.9 % sites where respective products were provided. As shown in Fig. 18a, these three algorithms show good performance worldwide, e.g., North America, Europe and East Asia. There are no MODIS AOD products showing the best R over Australia (only four sites are available there). The three GRASP algorithms show high percentage for products over dust and biomass burning regions, e.g., South America, southern Africa and central Africa, central Australia. At the same time, the GRASP/Optimized and GRASP/HP AOD products performed less well over North America.

Figure 17Percentage of the AERONET sites where each product shows the best statistical metric (R, RMSE, bias and GCOS fraction) between seven PARASOL/GRASP and MODIS AOD products. The number on top of each product is the number of sites where this product has sufficient matchup points for the comparison.

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In terms of the percentage of sites with the best RMSE, GRASP/Models and MAIAC_0.1 are the top two algorithms showing the best RMSE results over 60.0 % and 33.1 % of AERONET sites with available GRASP/Models and MAIAC_0.1 retrievals. Thus, overall, all these results indicate that GRASP/Models presents a strong ability to provide AOD that agrees well with AERONET measurements. Both GRASP/Models and MAIAC_0.1 show the best RMSE over Europe and North America (Fig. 18b), which also have the highest density of AERONET sites. GRASP/Models shows the best bias over 36.8 % sites, followed by DB (27.3 %) and MAIAC_0.01 (23.3 %). For the best GCOS fraction, GRASP/Models leads with 57.9 % over its total 95 sites. Then, MAIAC_0.1 has the highest GCOS fraction for 30.8 % over a total of 169 sites. In Fig. 18d, the best GRASP/Models sites are globally distributed. Over the eastern United States, DB and MAIAC_0.1 products tend to have more sites with the best GCOS fraction.

Figure 18Maps showing statistical metrics (a) R, (b) RMSE, (c) bias, (d) GCOS fraction (%) for the best performing AOD products (first ranking statistics among seven PARASOL/GRASP and MODIS products) over each AERONET site. Note that only the first ranking statistics over each site are present in the maps.

Using a similar concept as the AOD analysis above, the PARASOL/GRASP and MODIS (DT and DB) AE validations over AERONET sites were compared. Only cases with satellite AOD (550 nm) > 0.2 were included in the analysis; due to the reduced data volume from this threshold, the requirement on minimum matchups was reduced to 5. Figure 19 shows the detailed statistics for the performance of each AE product. Figure 20 shows the best performing algorithm at each site according to R and RMSE, respectively. In general, GRASP/HP and GRASP/Optimized AE products outperform the other AE products in the site level validation. The best sites are globally distributed (see Fig. 20). There are 44.1 %, 38.6 % and 34.7 % sites showing the best R for GRASP/Optimized, GRASP/HP and GRASP/Models, somewhat higher than DT (12.0 %) and DB (8.2 %). GRASP/HP AE has the best RMSE over 43.0 % AERONET sites, higher than GRASP/Optimized (34.3 %), DB (28.6 %), GRASP/Models (24.5 %) and DT (17.0 %).

Figure 19Percentage of the AERONET sites where each product shows the best statistical metric (R and RMSE) between five PARASOL/GRASP and MODIS AE products. The number on top of each product is the number of sites where this product has sufficient matchup points for the comparison.

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Figure 20Maps showing statistical metrics (a) R and (b) RMSE for the best performing AE products (first ranking statistics among five PARASOL/GRASP and MODIS products) over each AERONET site. Note that only the first ranking statistics over each site are present in the maps.

4.1 Comparisons between PARASOL/GRASP and PARASOL/Operational aerosol products

To begin, we investigate two independent aerosol products derived from PARASOL measurements, PARASOL/GRASP and PARASOL/Operational, globally for 2008. As mentioned above, PARASOL/Operational provides only AODF over land, while over ocean AOD, AE and AODF are available. We subtract AODF from total AOD to obtain Operational AODC over ocean.

Table 13Statistics of PARASOL and MODIS AODC products against collocated AERONET AODC over land and ocean.

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Table 14Pixel-to-pixel (0.2^∘ × 0.2^∘) statistical metrics between PARASOL/Operational and PARASOL/GRASP aerosol products; the statistics for only AERONET pixels are presented in brackets.

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Table 14 presents the pixel-to-pixel statistic metrics (R, slope, intercept, RMSE and bias) between Operational and GRASP aerosol products (note here the bias should be interpreted as an offset rather than true bias as the “truth” is unknown; we retain the name of the metric for consistency with the earlier analysis). We took Operational products as a reference as these were the original PARASOL aerosol products released by AERIS/ICARE; hence, the bias is defined as GRASP – Operational. All the statistics for AOD, AODF and AODC are given for the midvisible wavelength (550 nm), while AE is calculated based on 670 and 870 nm. The statistical metrics are reported both for global comparisons and over AERONET pixels only (the numbers in the brackets). It can be seen from Table 14 the global comparison between PARASOL/GRASP and PARASOL/Operational is rather consistent for AOD over ocean and AODF over land, for which, the global pixel-to-pixel correlations between GRASP/HP, GRASP/Models and Operational products are generally higher than 0.85 based on more than 5 million pairs. However, the agreement of AODF over ocean decreases to 0.63–0.73 for R. The slight decrease in correlation against AERONET from land to ocean for Operational AODF products is also recorded in Table 12 and a previous study by Bréon et al. (2011). The AODC over ocean for the Operational product is derived from AOD and AODF; hence, the number of matched pairs is lower than for AODF. The overall agreement has a correlation coefficient of ∼ 0.7. GRASP/HP AODC is ∼ 0.05 higher than Operational, but the difference between GRASP/Models and Operational is ∼ 0.0, which is in line with the validation against AERONET in Table 13. The pixel-to-pixel agreement for PARASOL/GRASP and PARASOL/Operational AE is less convincing (R < 0.6) than any other parameters, even though they are all well correlated with AERONET (R > 0.8) over ocean. One possible reason is that the AE here is calculated at different wavelengths (670 and 870 nm) than for the comparisons with AERONET (470∕660 nm and 440∕870 nm). Besides, the decrease in AE agreement for global correlation (R) compared to that over AERONET pixels is more notable than other parameters. This may explain why the AE products resulting from LUT-based algorithms are more determined by climatological assumptions about the aerosol models than retrieved.

4.2 AOD comparisons between PARASOL/GRASP and MODIS products

In order to further clarify the level of consistency of satellite products (PARASOL/GRASP and MODIS), the global correlations of different satellite products were extensively analyzed for the year 2008 at a spatial resolution of 0.1^∘ × 0.1^∘. Figure 21 shows the seasonal pattern of AOD (550 nm) from PARASOL (GRASP/HP and GRASP/Models) and MODIS (DT, DB and MAIAC) products. Any grid box with fewer than three measurements for a season was omitted. Figure 22 shows the differences of mean AOD (550 nm) by season between PARASOL and MODIS aerosol products using GRASP/Models as the reference. A positive value indicates that the MODIS product had a higher mean value. Since the analysis in Sect. 3 suggested that the AOD products over land and ocean from the GRASP/Models processing have the lowest biases, this was used as a reference product in Fig. 22. Since GRASP/HP AOD shows non-negligible bias (land: +0.06; ocean: +0.07) from AERONET validation (see Table 9), in order to show the intrinsic, the bias was subtracted from the GRASP/HP AOD products before obtaining the seasonal differences shown in Fig. 22.

Figure 21Spatial distribution of 0.1^∘ × 0.1^∘ seasonal AOD (550 nm) from PARASOL (GRASP/HP and GRASP/Models) and MODIS (DT, DB and MAIAC) products. DJF: December–January–February; MAM: March–April–May; JJA: June–July–August; SON: September–October–November.

Figure 22Spatial distribution of 0.1^∘ × 0.1^∘ seasonal AOD (550 nm) differences between PARASOL and MODIS aerosol products, referenced to GRASP/Models.

In addition, the global correlations between different satellite products and GRASP/Models data at 550 nm were calculated for the complete year of 2008. Also, in order to evaluate the consistency of different MODIS products over land, the inter-comparisons were done against the MAIAC AOD (Land) product chosen as a reference, as MAIAC provides the most universal coverage over land. Table 15 presents the pixel-to-pixel statistic metrics (R, slope, intercept, RMSE and bias) between AOD products compared to the reference of GRASP/Models (Land and Ocean) and MAIAC AOD (Land) products. The statistical metrics are reported both for global comparisons and over AERONET pixels only (numbers in brackets).

Table 15Pixel-to-pixel (0.1^∘ × 0.1^∘) statistical metrics between AOD (550 nm) products based on references of GRASP/Models (land and ocean) and MAIAC AOD (land); the statistics for only AERONET pixels are presented in brackets.

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Each of these global correlations was based on several dozens of millions of pairs and less noisy compared to the AERONET correlations (based on only a few thousand points). In spite of this significant difference in volume, the outcome of the global satellite comparisons is rather consistent with the results of validation against AERONET. For example, all AOD products are in close agreement over ocean, with the correlation coefficients above 0.9 and slope lines close to 1:1 (Table 15). Specifically, the three aerosol products (GRASP/HP, GRASP/Models and DT) over ocean agree with R > 0.92 for any two products. Also, in line with the validation over AERONET sites, GRASP/HP AOD (550 nm) consistently has a positive offset ∼ 0.05–0.16 from low- to high-AOD conditions with respect to GRASP/Models. DT and GRASP/Models AOD values show good agreement over ocean, R = 0.92 for all points and R = 0.97 for AERONET pixels; in addition, the bias (DT–GRASP/Models) equals −0.01 for all points and 0.00 for low AOD (< 0.2), while the negative bias of −0.06 appears when AOD is greater than 0.7. Statistics over ocean rely on ∼ 65 million pairs between GRASP/HP and GRASP/Models and ∼ 32 million pairs between DT and GRASP/Models.

However, over land surfaces the situation is quite different, and MODIS/MAIAC and DB AOD products show evidently better agreement with GRASP/Models over AERONET pixels than the rest of globe. The correlations over AERONET pixels for both MAIAC versus GRASP/Models and DB versus GRASP/Models are of ∼ 0.89, which is generally in line with the correlation coefficient values with AERONET shown in Table 9. In a contrast, the corresponding correlation coefficients decrease to 0.76 and 0.77 for global statistics. The other statistical parameters (e.g., slope, offset, RMSE and bias) showed the same trend, indicating a better agreement over AERONET pixels. For comparisons of GRASP/HP and DT versus GRASP/Models AOD, such tendency is not evident. Even though the correlation coefficient drops from 0.90 over AERONET to 0.85 globally, the rest of statistical indicators do not show significant changes, whether over an AERONET site or elsewhere. It is interesting to note that MODIS products show better agreement (especially in correlations) with other MODIS products over AERONET stations and globally than between PARASOL and MODIS products over AERONET stations and globally (Table 15). This phenomenon can be explained by several factors. First, the inputs from the two satellites differ significantly. The multi-angle polarization information from PARASOL offers algorithms many more degrees of freedom from which to constrain environmental factors and invert aerosol parameters than does a single-view radiometer like MODIS. Second, because of this extra information the PARASOL/GRASP retrievals do not have location-specific assumptions about aerosol and conduct their retrievals in exactly the same manner globally. In contrast, all three MODIS retrievals use some regional assumptions over land about aerosol types, surface properties, etc. Even though each algorithm's assumptions are different, the need for a priori constraints could draw the MODIS products closer together. Therefore, the similarities in global performance of three algorithms can probably be explained by somewhat similar a priori assumptions about aerosol types used in MODIS algorithms. Third, as can be seen from Table 15 and Fig. 21, GRASP/Models, GRASP/HP and MAIAC have wider coverage over land than DB and DT, because of the lack of retrievals over bright surfaces for DT and reduced number of retrievals over dark vegetation for DB (although some of this was improved in DB Collection 6.1; Sayer et al., 2019). Specifically, for the year 2008, there are more than 64 million pairs of MAIAC–GRASP/Models AOD over land, which is much higher than the number of pairs obtained with other two AOD products. Thus, the collocation statistics for MAIAC/GRASP, DT/GRASP and DB/GRASP as well as MAIAC/DT and MAIAC/DB were based on different datasets. Fourth, the different representation of various natural conditions in the global statistics and statistics over AERONET can be non-identical and, therefore, the average performance indications can differ. For example, there is only a certain fraction of AERONET sites in desert areas while land cover with bright surface may have a notably higher or lower fraction in global statistics. Correspondingly, if the product agreement is non-identical over different land surfaces, then the statistics with different representations of various surfaces can differ.

In order to explore the last factor, the statistics of the comparisons were sorted by land surface type. Tables 16 and 17 show pixel-to-pixel statistic metrics with reference AOD from GRASP/Models and MAIAC, respectively, over different land coverage using four classes of land surface by NDVI (as before, NDVI < 0.2, 0.2 ≤ NDVI < 0.4, 0.4 ≤ NDVI < 0.6 and NDVI ≥ 0.6).

Table 16Pixel-to-pixel (0.1^∘ × 0.1^∘) statistical metrics between AOD products based on reference of GRASP/Models over land pixels with four classes of surface (NDVI < 0.2, 0.2 ≤ NDVI < 0.4, 0.4 ≤ NDVI < 0.6 and NDVI ≥ 0.6); the statistics for only AERONET pixels are presented in brackets.

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Table 17The same as Table 16, but for reference of MAIAC AOD.

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Table 18Pixel-to-pixel statistical metrics between AE products based on references of GRASP/HP; the statistics for only AERONET pixels are presented in brackets.

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Tables 16 and 17 show that over very bright land surfaces (NDVI < 0.2), the global correlations between MODIS (especially DB and MAIAC) with PARASOL/Models products were significantly lower than over other surfaces and showed the most notable drop (> 0.1) in global correlations compared to the correlation over AERONET sites. Such a large drop was not seen between different PARASOL products or between different MODIS products. Therefore, these differences are likely related to the fact that MODIS retrievals rely on regional climatological aerosol assumptions or surface assumptions derived from atmospheric correction at (unevenly distributed) AERONET sites while in PARASOL/GRASP retrievals no location-specific assumptions are used. Another issue that may be related is that MODIS has much higher spatial resolution for cloud detection than PARASOL. The possible sub-pixel cloud contamination for PARASOL may affect the global inter-comparison statistics, since the validation against AERONET brings an additional cloud clearing filter from AERONET. As a result, PARASOL/GRASP retrievals are expected to be rather consistent globally, while MODIS retrievals are more closely tied to AERONET statistics and may perform less well in the areas with a lack of AERONET sites. At the same time, the fraction of pairs over bright surfaces in inter-satellite product comparisons is higher than in AERONET statistics since there are only a limited number of AERONET sites in desert areas. This latter statement does not necessarily apply to MODIS DT because it often does not retrieve over deserts; however, although the sample size is very small, Table 16 shows that it actually matches GRASP/Models less well at AERONET sites than globally for NDVI < 0.2.

Figure 23Spatial distribution of 0.1^∘ × 0.1^∘ seasonal AE from PARASOL (GRASP/HP and GRASP/Models) and MODIS (DT and DB) products.

Figure 24Spatial distribution of seasonal AE differences between PARASOL and MODIS aerosol products, referenced to GRASP/HP.

Interestingly, the maps in Fig. 22 of seasonal AOD difference indicate lower AOD (550 nm) for PARASOL/Models over bright surfaces compared to MODIS products, while the global comparisons of PARASOL/Models and MODIS DB and MAIAC products did not show significant bias in AOD (550 nm). At the same time, the global comparisons (Table 16) between PARASOL/Models, MODIS DB and MAIAC show a significant bias for different ranges of AODs. MODIS DB and MAIAC had a positive bias of ∼ 0.06–0.04 for the situation with lower aerosol loadings (AOD 550 nm < 0.2) and a notable negative bias (0.02–0.06) for moderate AOD (0.2 < AOD 550 nm < 0.7) and an especially large bias for high aerosol loadings (AOD 550 nm > 0.7) that reached ∼ 0.3. A very similar tendency can be seen from the statistics of validation against AERONET in Table 10: both PARASOL/Models and MODIS/DB have very small bias of −0.01, while the distribution of bias is quite different for the situations with different loadings: 0.01 and 0.03 for low AODs, −0.03 and −0.05 for moderate AODs, and 0.01 and −0.16 for high AODs. This suggests that the observed positive differences when MODIS/DB and MAIAC show higher AOD over bright surfaces occur mainly during low-AOD conditions. This conclusion is supported by the fact that seasonal means from all products do not show high AOD over the northern Sahara between 20 and 30^∘ N latitude. Also, both DB and MAIAIC show significant underestimation of AOD over the Taklamakan desert where seasonal mean AOD retrieved by PARASOL is high, which agrees with the negative offset between MODIS DB, MAIAC and PARASOL/Models products over bright and bare soil land surfaces (NDVI < 0.4).

The negative bias between MODIS and PARASOL products is clearly seen on the maps of seasonal AOD from different products for African biomass burning events. The results of correlation analysis over green vegetation (NDVI ≥ 0.6) in Table 16 also show a significant negative bias in all MODIS products compared to PARASOL/Models over green vegetation that increases for medium and high aerosol loading. The validation against AERONET in Table 10 shows the highest bias of 0.06 to 0.07 for PARASOL/Models is over green vegetation (NDVI ≥ 0.6) when 0.2 < AOD < 0.7, while the MODIS products tend to be less biased (DT bias = 0.03) or negatively biased (MAIAC bias = −0.04 to −0.06 and DB bias = −0.04) for this surface type and AOD range. This pattern continues for DB and MAIAC through all the vegetated surfaces with NDVI > 0.2. MODIS DB and MAIAC continue to be more negatively biased against AERONET for moderate to high aerosol loading than PARASOL/Models is. Thus, the results suggest that observed differences for African biomass burning events can be explained by two potential reasons: a combination of overestimations of AOD by PARASOL/GRASP retrievals and underestimation of AOD by MODIS products for cases of moderate to high aerosol loading. However, the DT retrievals also show this negative bias against PARASOL/GRASP in the African biomass burning (Fig. 22) but do not follow the same trends against MODIS as DB and MAIAC. Other factors, such as differences in cloud screening, data amount, aggregation and quality-screening approaches must also contribute to these differences and need to be investigated in future analysis.

Table 19Pixel-to-pixel statistical metrics between AE products based on references of GRASP/HP over land pixels with four classes of surface (NDVI < 0.2, 0.2 ≤ NDVI < 0.4, 0.4 ≤ NDVI < 0.6 and NDVI ≥ 0.6).

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4.3 AE comparisons between PARASOL/GRASP and MODIS products

The seasonal pattern of AE from PARASOL (GRASP/HP and GRASP/Models) and MODIS (DT and DB) products is presented in Fig. 23, as well as AE differences by season between PARASOL and MODIS aerosol products in Fig. 24. Table 18 shows the global pixel-to-pixel statistic metrics between AE products based on references of GRASP/HP; in the brackets, the values corresponding to validation results over AERONET pixels only are shown. As before, the statistic metrics split into four classes of land surface by NDVI are presented in Table 19. The GRASP/HP AE products are chosen to be a reference taking into account the highest obtained correlation in the validation with AERONET in the Sect. 3. Again, note that although AOD over land is reported by DT at 470 and 660 nm, the spectral dependence of the DT land retrieval is mostly imposed by assumed aerosol models, and thus DT AE over land is at most a binary indication of fine and coarse particles and not a quantitative parameter. We expect no correlation with GRASP/HP over land. AE over land from DB is similarly prescribed, not retrieved, when AOD < 0.2 (Hsu et al., 2013). On the other hand, the DT AE over ocean is a true quantitative measure.

The differences between PARASOL/GRASP and MODIS DT and DB AE products are pronounced in all comparisons. From Fig. 23, the seasonal variations for DB and DT are minor, which likely implies utilization of similar climatological information in the DB and DT algorithms. Even though the differences for GRASP/Models and GRASP/HP shown in Fig. 24 are not small (mainly due to the limited dynamic range of aerosol components used in the GRASP/Models approach), the overall pixel-to-pixel correlation between GRASP/Models and GRASP/HP is the highest between any two products (0.70 over land, 0.74 over ocean), and the RMSEs are 0.39 over land and 0.45 over ocean. The correlations for AE over land between MODIS DT and DB AE versus GRASP/HP are lower than 0.5 and RMSEs are higher than 0.59 for all land surface types (Table 19), which is not surprising for the aforementioned reasons. Over ocean, all available products (GRASP/HP, GRASP/Models and DT) show good agreement with AERONET measurements, with R > 0.8 (Fig. 11 and Table 11); however, the pixel-to-pixel correlation between DT and GRASP/HP for ocean pixels globally decreases to 0.46, with RMSE = 0.53. The cause of the drop for global statistics is presently unknown. It could be due to assumptions in the DT retrieval but could also be linked to differences in calibration between POLDER and MODIS, as AE is particularly sensitive to nuanced spectral changes in calibration in the lower-AOD conditions often seen over ocean.

4.4 AODF and AODC comparisons between PARASOL/GRASP and MODIS products

This section compares AODF and AODC at 550 nm from PARASOL/GRASP (GRASP/HP and GRASP/Models) and MODIS DT algorithms. As discussed earlier, the quantitative fine-mode fraction (η) provided by the DT algorithm can be used to derive AODF and AODC only over ocean. Therefore, the comparison of AODF and AODC over land is between GRASP/HP and GRASP/Models. The seasonal distribution of AODF and AODC is shown in Figs. 25 and 27, respectively. The seasonal differences between GRASP/Models, DT and GRASP/HP are shown in Fig. 26 (AODF) and Fig. 28 (AODC). GRASP/Models AODF is higher than GRASP/HP over dust source and downwind regions, while it is lower than GRASP/HP over biomass burning and urban areas, which is consistent with the validation versus AERONET measurements in Figs. 13–16.

Figure 25Spatial distribution of 0.1^∘ × 0.1^∘ seasonal AODF (550 nm) from PARASOL (GRASP/HP and GRASP/Models) and MODIS (DT) products.

Figure 26Spatial distribution of seasonal AODF (550 nm) differences between PARASOL and MODIS aerosol products, referenced to GRASP/HP.

Figure 27The same as Fig. 25, but for AODC (550 nm).

Figure 28The same as Fig. 26, but for AODC (550 nm).

Globally, GRASP/Models and GRASP/HP AODF show a consistent agreement over land (R = 0.87, bias = −0.01) and ocean (R = 0.89, bias = 0.00), as presented in Table 20. MODIS/DT AODF and AODC over ocean have good agreement with GRASP/HP with R 0.86 and 0.84, respectively. GRASP/Models AODC shows a better agreement with GRASP/HP over ocean than over land, while differences are less pronounced, R of 0.89 and 0.71, respectively. As was mentioned above, this tendency can be explained by a stronger sensitivity of the observed signal to aerosol over dark ocean surface. Another interesting tendency is that correlations for AODF over land are generally higher than for AODC, while over ocean the situation is inversed and the correlations are higher for AODC, especially over AERONET. This can probably be explained by the two facts that dominating oceanic aerosol has a pronounced coarse mode and that at the longer wavelengths, where the contribution of coarse mode is the strongest, the ocean is practically dark. The land reflectance is, however, higher than ocean at long wavelengths, even for relatively dark vegetated surfaces. The statistics of pixel-to-pixel comparison (GRASP/HP and GRASP/Models) over different land surface types, as discriminated by different NDVI categories, are also reported in Table 22 (AODF) and Table 23 (AODC).

Table 20Pixel-to-pixel statistical metrics between GRASP/HP AODF with other AODF products; the statistics for only AERONET pixels are presented in brackets.

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In conclusion, the differences in more detailed aerosol characteristics including AE, AODF and AODC (Tables 18–23) derived from PARASOL and MODIS are pronounced over both land and ocean. This is in contrast to the results for the total AOD from PARASOL and MODIS, which are close over ocean and in reasonable agreement over land. This conclusion can likely be generalized by the fact that retrieval accuracy of detailed aerosol properties is expected to be significantly higher from MAP products than from mono-viewing photometric imagery.

Table 21The same as Table 20, but for AODC.

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Table 22Pixel-to-pixel statistical metrics between AODF products based on references of GRASP/HP over land pixels with four classes of surface (NDVI < 0.2, 0.2 ≤ NDVI < 0.4, 0.4 ≤ NDVI < 0.6 and NDVI ≥ 0.6); the statistics for only AERONET pixels are presented in brackets.

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Table 23The same as Table 22, but for AODC.

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