Validation of GRASP algorithm product from POLDER/PARASOL data and assessment of multi-angular polarimetry potential for aerosol monitoring

Proven by multiple theoretical and practical studies, multi-angular spectral polarimetry is ideal for comprehensive retrieval of properties of aerosols. Furthermore, a large number of advanced space polarimeters have been launched recently or planned to be deployed in the coming few years (Dubovik et al., 2019). Nevertheless, at present, practical utilization of aerosol products from polarimetry is rather limited, due to the relatively small number of polarimetric compared to photometric observations, as well as challenges in making full use of the extensive information content available in these complex observations. Indeed, while in recent years several new algorithms have been developed to provide enhanced aerosol retrievals from satellite polarimetry, the practical value of available aerosol products from polarimeters yet remains to be proven. In this regard, this paper presents the analysis of aerosol products obtained by the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm from POLDER/PARASOL observations. After about a decade of development, GRASP has been adapted for operational processing of polarimetric satellite observations and several aerosol products from POLDER/PARASOL observations have been released. These updated PARASOL/GRASP products are publicly available (e.g., http://www.icare.univ-lille.fr, last access: 16 October 2018, http://www.grasp-open.com/products/, last access: 28 March 2020); the dataset used in the current study is registered under https://doi.org/10.5281/zenodo.3887265 (Chen et al., 2020). The objective of this study is to comprehensively evaluate the GRASP aerosol products obtained from POLDER/PARASOL observations. First, the validation of the entire 2005–2013 archive was conducted by comparing to ground-based Aerosol Robotic Network (AERONET) data. The subjects of the validation are spectral aerosol optical depth (AOD), aerosol absorption optical depth (AAOD) and single-scattering albedo (SSA) at six wavelengths, as well as Ångström exponent (AE), fine-mode AOD (AODF) and coarse-mode AOD (AODC) Published by Copernicus Publications. 3574 C. Chen et al.: Validation of GRASP algorithm product from POLDER/PARASOL data interpolated to the reference wavelength 550 nm. Second, an inter-comparison of PARASOL/GRASP products with the PARASOL/Operational, MODIS Dark Target (DT), Deep Blue (DB) and Multi-Angle Implementation of Atmospheric Correction (MAIAC) aerosol products for the year 2008 was performed. Over land both satellite data validations and inter-comparisons were conducted separately for different surface types, discriminated by bins of normalized difference vegetation index (NDVI): < 0.2, 0.2≤ and < 0.4, 0.4≤ and < 0.6, and ≥ 0.6. Three PARASOL/GRASP products were analyzed: GRASP/HP (“High Precision”), Optimized and Models. These different products are consistent but were obtained using different assumptions in aerosol modeling with different accuracies of atmospheric radiative transfer (RT) calculations. Specifically, when using GRASP/HP or Optimized there is direct retrieval of the aerosol size distribution and spectral complex index of refraction. When using GRASP/Models, the aerosol is approximated by a mixture of several prescribed aerosol components, each with their own fixed size distribution and optical properties, and only the concentrations of those components are retrieved. GRASP/HP employs the most accurate RT calculations, while GRASP/Optimized and GRASP/Models are optimized to achieve the best trade-off between accuracy and speed. In all these three options, the underlying surface reflectance is retrieved simultaneously with the aerosol properties, and the radiative transfer calculations are performed “online” during the retrieval. All validation results obtained for the full archive of PARASOL/GRASP products show solid quality of retrieved aerosol characteristics. The GRASP/Models retrievals, however, provided the most solid AOD products, e.g., AOD (550 nm) is unbiased and has the highest correlation (R∼ 0.92) and the highest fraction of retrievals (∼ 55.3 %) satisfying the accuracy requirements of the Global Climate Observing System (GCOS) when compared to AERONET observations. GRASP/HP and GRASP/Optimized AOD products show a non-negligible positive bias (∼ 0.07) when AOD is low (< 0.2). On the other hand, the detailed aerosol microphysical characteristics (AE, AODF, AODC, SSA, etc.) provided by GRASP/HP and GRASP/Optimized correlate generally better with AERONET than do the results of GRASP/Models. Overall, GRASP/HP processing demonstrates the high quality of microphysical characteristics retrieval versus AERONET. Evidently, the GRASP/Models approach is more adapted for retrieval of total AOD, while the detailed aerosol microphysical properties are limited when a mixture of aerosol models with fixed optical properties are used. The results of a comparative analysis of PARASOL/GRASP and MODIS products showed that, based on validation against AERONET, the PARASOL/GRASP AOD (550 nm) product is of similar and sometimes of higher quality compared to the MODIS products. All AOD retrievals are more accurate and in good agreement over ocean. Over land, especially over bright surfaces, the retrieval quality degrades and the differences in total AOD products increase. The detailed aerosol characteristics, such as AE, AODF and AODC from PARASOL/GRASP, are generally more reliable, especially over land. The global inter-comparisons of PARASOL/GRASP versus MODIS showed rather robust agreement, though some patterns and tendencies were observed. Over ocean, PARASOL/Models and MODIS/DT AOD agree well with the correlation coefficient of 0.92. Over land, the correlation between PARASOL/Models and the different MODIS products is lower, ranging from 0.76 to 0.85. There is no significant global offset; though over bright surfaces MODIS products tend to show higher values compared to PARASOL/Models when AOD is low and smaller values for moderate and high AODs. Seasonal AOD means suggest that PARASOL/GRASP products show more biomass burning aerosol loading in central Africa and dust over the Taklamakan Desert, but less AOD in the northern Sahara. It is noticeable also that the correlation for the data over AERONET sites are somewhat higher, suggesting that the retrieval assumptions generally work better over AERONET sites than over the rest of the globe. One of the potential reasons may be that MODIS retrievals, in general, rely more on AERONET climatology than GRASP retrievals. Overall, the analysis shows that the quality of AOD retrieval from multi-angular polarimetric observations like POLDER is at least comparable to that of single-viewing MODIS-like imagers. At the same time, the multiangular polarimetric observations provide more information on other aerosol properties (e.g., spectral AODF, AODC, AE), as well as additional parameters such as AAOD and SSA. Earth Syst. Sci. Data, 12, 3573–3620, 2020 https://doi.org/10.5194/essd-12-3573-2020 C. Chen et al.: Validation of GRASP algorithm product from POLDER/PARASOL data 3575


Introduction
Over the past few decades, satellite remote sensing has provided essential advances in understanding the global distribution of atmospheric aerosols Remer et al., 2008) and constraining aerosol climate effects (Bellouin et al., 2005;Myhre, 2009;Yu et al., 2006). Nevertheless, aerosol effects remain the largest contributor to forcing uncertainty according to the Intergovernmental 95 Panel on Climate Change (IPCC) assessments (Boucher et al., 2013). Over the past few decades, satellite remote sensing techniques have developed rapidly and extensively, and various (primarily photometric) instruments have been developed and deployed to monitor atmospheric aerosols from space (Bréon et al., 2011;King et al., 1999;Kokhanovsky et al., 2015;Li et al., 2009;Tanré et al., 2011).
While the design and capabilites of the photometric observations are constantly evolving, the greatest 100 improvement has been in the form of Multi-Angular multi-spectral Polarimetry (MAP) measurements (Hansen et al., 1995;Knobelspiesse et al., 2012;Mishchenko et al., 2004;Waquet et al., 2009;Tanré et al., 2011). MAP measurements have enough inherent information content to greatly improve our understanding about aerosol properties. Several space-borne polarimeters have already been deployed and more advanced versions will be deployed soon . In addition, there are many airborne versions of 105 orbital polarimeters that have operated during field campaigns, which can be used to verify and improve the https://doi. org/10.5194/essd-2020-224 Open Access Earth System Science Data Discussions Preprint. Discussion started: 14 August 2020 c Author(s) 2020. CC BY 4.0 License. retrieval concepts (e.g. Knobelspiesse et al., 2020). Although the overall volume of polarimetric observations remains small compared to photometric observations, the potential for rapid advancement is large.
Several factors contribute to the current limited visibility of MAP observations and algorithms 110 including: (i) limited amount of polarimetric observations in comparison to photometric ones, (ii) general complexity of polarimetric observations, and (iii) consequent challenges in developing capable retrieval algorithms. As a result, at present, there is a lack of extensive aerosol products from satellite MAPs that attract the aerosol science community. This tendency is especially evident by the contrast with the increase of constantly improved aerosol products from mono-and bi-viewing photometric images. For example, the 115 archive of most popular Moderate Resolution Imaging Spectroradiometer (MODIS) observations has been processed using many different algorithms, and NASA distributes three complementary MODIS aerosol products: Dark Target (DT) by Remer et al. (2005) and Levy et al., (2013), Deep Blue by Hsu et al. (2004Hsu et al. ( , 2006Hsu et al. ( , 2013 and Multi Angle Implementation of Atmospheric Correction (MAIAC) by Lyapustin et al. (2018). Similarly, significant effort has been directed to improve aerosol products from European 120 ENVISAT satellite platform observations in frame of Climate Change Initiative (CCI) projects of European Space Agency (e.g. see de Leeuw et al., 2015;Holzer-Popp et al., 2013;Popp et al., 2016). As a result, the product archives of MEdium Resolution Imaging Spectrometer (MERIS) and especially Advanced Along-Track Scanning Radiometer (AATSR) missions are constantly updated and improved.
To date, only one space-borne MAP has a long and wide enough coverage to advance aerosol 125 science. The Polarization and Directionality of the Earth's Reflectances (POLDER) instrument was designed and developed by the French space agency Centre National d'Études Spatiales (CNES) to measure the spectral directional polarized solar radiation reflected by the Earth-atmosphere system (Deschamps et al., 1994). POLDER-1 and -2 flew on board of the Japanese Advanced Earth Observing  (Parkinson, 2003;Schoeberl et al., 2006;Tanré et al., 2011;Winker et al., 2010). The PARASOL imager has 3 gaseous absorption channels (763, 765 and 710 nm), in addition to 6 channels (443,490,565,670,865 and 1020 nm) measuring the total radiance, and 3 channels (490, 670 and 865 nm) measuring the polarization. The number of viewing angles 140 is similar for all spectral channels varying from 14 to 16 depending on solar zenith angle and geographical location. PARASOL provided global coverage about every 2 days with a nadir spatial resolution ~6 km (Tanré et al., 2011).
Several POLDER-1, 2 and PARASOL aerosol products were developed by the science team at LOA (Laboratoire d'Optique Atmosphérique, Lille, France). Hereafter, we refer to this aerosol product as 145 POLDER/Operational or Operational. The initial POLDER/Operational aerosol retrieval over ocean by Deuzé et al. (1999) provided total Aerosol Optical Depth (AOD) from the measured total and polarized radiances at 670 and 865 nm with expected accuracy of ±0.05±0.05AOD (Goloub et al., 1999). The updated algorithm by Herman et al. (2005) provided AOD of fine and coarse modes and, when geometrical conditions are optimal (scattering angle ranging between 90°-160°), the spherical/non-spherical separation 150 of coarse mode particles (Herman et al., 2005). Over land, the algorithm by Deuzé et al. (2001) retrieves only fine ("accumulation") mode AOD (AODF) using only polarized light at two wavelengths (670 and 865 nm) to capitalize on the small and fairly neutral polarized reflectance typical of land surfaces (Deuzé et al., 2001;Herman et al., 1997). These algorithms were designed to utilize the benefits of MAP information within the framework of a conventional MODIS like Look-up- Table (LUT) approach  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 210 fully accounting for multiple interactions of the scattered solar light in the atmosphere, and that it can perform it online without the use of traditional LUTs.
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, 215 GRASP can retrieve both aerosol and underlying surface properties simultaneously from satellite observations using additional a priori constraints on the spectral variability of 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 220 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. 225 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., 2017Hu 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(Espinosa 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 -5P observations and operational aerosol retrievals for future Sentinel-4 and 3MI/Metop missions. GRASP is constantly being updated to produce many useroriented products such as estimates of covariance matrices (Herrera et al., in preparation, 2020), direct 235 radiative forcing (Derimian et al., 2016), and so on.
For POLDER, GRASP utilizes radiance and polarization observations from all available spectral channels with minor gaseous absorption, i.e. for total radiance 5 channels for POLDER-1 and -2, and 6 for PARASOL, and for polarized radiances (3 spectral channels for all instruments). The retrieval uses a unique global set of constraints (no location-specific assumptions) and a single initial guess globally. 240 GRASP performs radiative transfer computations fully accounting for multiple interactions of the scattered solar light in the atmosphere on-line 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 245 and PARASOL at ∼6 km) using rather moderate computing resources, e.g. 3-4 sec/pixel for GRASP/HP, 0.3-0.5 sec/pixel for GRASP/Optimized and 0.1-0.2 sec/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 250 possibilities on modeling aerosol scattering, 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 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 external 260 mixture of several aerosol models).
The «optimized» and «high-precision» are different only by the precision of the RT calculations, while conceptually they are 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 265 performed using one aerosol component model with 5 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 by Dubovik et al. (2011). The «models» approach uses different assumption 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 270 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 275 al., 2009) models under assumption that the retrieved parameters are spectrally smooth (the strength of smoothness is different for each parameter) (Litvinov et al., 2011a(Litvinov et al., , 2011b. For retrievals over ocean, the wind speed and a spectrally dependent Lambertian albedo are included in the state vector. It should be noted that "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 280 https://doi.org/10.5194/essd-2020-224 results were quite appealing especially in conditions of low aerosol loading, motivating the generation of 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) and at GRASP-OPEN website (https://www.grasp-open.com/products/) in slightly different formats. The AERIS/ICARE is the official 285 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. The AERIS/ICARE provides detailed visualization of the data, while 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 -3 products and are publicly available in the form of daily, monthly, seasonal, yearly and climatological datasets. The Level-2 data contain full 290 resolution data filtered following established quality criteria. Level 3 data is aggregated into a 0.1° and 1° grid box using the sinusoidal projection from Level-2 data. The list of retrieved aerosol parameters, as well as derived aerosol characteristics can be found in the Table 1. In this study, we adopt the current latest version of Optimized, HP (v1.2) and Models (v2.1) products.
[ Table 1] 295 In addition to the PARASOL/GRASP products, all observations of POLDER-1 and -2 were also processed (using a single GRASP/Models approach). 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 those of PARASOL/GRASP retrievals. Also, recently a new "GRASP/Component" approach has been developed 300 (Li et al., , 2020a(Li et al., , 2020b. This approach retrieved the size resolved fractions of aerosol components representing the different composition species, like black carbon, brown carbon, fine/coarse mode nonabsorbing 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 https://doi.org/10.5194/essd-2020-224 archive; however, the results have not yet been fully analyzed and are not released in a user friendly format, 305 so the GRASP/Component data set 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., 2019Wei et al., , 2020, data assimilation (Chen et al., 2018, AOD products merging 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 310 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. 315 The MODIS sensors on board TERRA since 2000 (overpass ~10:30 local) and AQUA since 2002 (overpass ~13:30 local) 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 Dark Target, Deep Blue and MAIAC aerosol products
MODIS has a wider swath of 2330 km compared to ~1600 km of PARASOL, 36 spectral channels ranging from 410 to 15000 nm and higher spatial resolution for cloud mask. There are 3 mature aerosol products 320 produced operationally and distributed by NASA: Dark Target, Deep Blue and MAIAC.

MODIS Dark Target
The Dark Target (DT) algorithm over land is based on an empirical surface reflectance relationship between blue and red channels with the shortwave infrared (2113 nm) radiance. The AOD is retrieved by 325 matching LUT values to observations at 466 nm, and then varying the weighting between two fixed aerosol models until the residual between LUT and observations are minimized at 645 nm. The main product is AOD at 553 nm with AOD reported at 466 nm, 645 nm and 2113 nm, consistent with the selected weighted aerosol model (Kaufman et al., 1997;Levy et al., 2007aLevy et al., , 2007b. Over ocean, the simplicity of the dark https://doi.org/10.5194/essd-2020-224 ocean surface permits the retrieval of AOD and aerosol particle size . In this situation 330 the algorithm chooses one fine mode out of four and one coarse mode out of five, along with the relative weight between fine and coarse mode by minimizing the summed difference between LUT and observations in six wavelengths (550, 660, 870, 1240(550, 660, 870, , 1610(550, 660, 870, , and 2130(550, 660, 870, nm) (Tanré et al., 1997Remer et al., 2005;Levy et al., 2013). The MODIS DT aerosol products are periodically updated to improve overall performance (Levy et al., 2003(Levy et al., , 2007a(Levy et al., , 2007b(Levy et al., , 2013Remer et al., 2005;Gupta et al. 2016). The widely 335 recognized limitation of the DT algorithm is the complex spectral structure of bright land surfaces (e.g. desert, bare soil, snow) that violates the assumptions of the empirical relationships between wavelengths and increases uncertainty in the aerosol retrievals to unacceptable levels. Therefore, DT does not provide coverage over these cases.

MODIS Deep Blue
The Deep Blue (DB) algorithm retrieves over both bright (except snow) and vegetated land surfaces. It is able to retrieve over brighter surfaces than DT because it makes use of the much darker surface reflectance in the deep blue (412 nm) channel (Hsu et al., 2004(Hsu et al., , 2006. Depending on the processing path, determined by observed reflectance and vegetation indices, the algorithm will invoke 345 empirical spectral relationships of surface reflectance similar to DT (vegetation), rely on a pre-calculated data base of surface reflectance (arid/deserts) or apply a hybrid method (urban surfaces). The MODIS DB aerosol products have also gone through several version updates Sayer et al., 2015).
Within the MODIS official products, the DB algorithm is applied for only land aerosol retrieval. Over vegetated surfaces DT tends to provide more retrievals in the tropics, and DB more retrievals at mid-350 latitudes, due to different pixel selection and cloud screening criteria (Sayer et al., 2014). The Multi Angle Implementation of Atmospheric Correction (MAIAC) algorithm has been developed and applied to MODIS (Lyapustin et al., 2011a, 2011b, 2012, 2018, and is running 355 operationally in the NASA system. The MAIAC algorithm uses the minimum reflectance method to dynamically characterize spectral ratios of the surface reflectance (which are prescribed in the DT) and separate aerosol and surface contributions to the measurements. The accumulation of up to 16 days of the last observations in the operational memory allows MAIAC to derive spectral surface BRDF. The MAIAC aerosol product is available at higher spatial resolution of 1 km, in comparison to DT and DB that provide 360 aerosol products at 3 km and 10 km. As a more recent addition to the MODIS family of aerosol products than DT and DB, MAIAC has shown itself to produce an AOD product as accurate or better than the older algorithms over all types of land surfaces (Jethva et al., 2019), and thus offers a complementary/alternative product to those from the original DT and DB algorithms. 365 All three MODIS algorithms (DT, DB and MAIAC) are developed based on LUT approaches with a fixed certain number of aerosol models. Over ocean, DT assumes 9 aerosol models (4 fine models plus 5 coarse models); any retrieval corresponds to one of total 20 combinations of one fine mode and one coarse mode (Levy et al., 2003;Remer et al., 2005;. Over land, DT algorithm adopts aerosol models from AERONET retrievals, clustering down to three possible spherical fine-mode dominant models 370 (non-absorbing, moderately-absorbing and absorbing) and 1 spheroid coarse-mode dominant model (Levy et al., 2007a). In addition, the fine-and coarse-mode dominant aerosol models over land are defined as a function of season and location (Levy et al., 2013). The DB algorithm makes use of prescribed dust, and smoke/sulfate aerosol models in the LUT . For example, over vegetated surfaces, AE is limited to some extent (0.0≤ AE≤1.8), and fixed at 1.5 for low AOD conditions. Over bright arid/desert 375 surfaces the AE is limited to a maximum of 1.0 Sayer et al., 2013). A geographic distribution of aerosol models is also adopted in the MAIAC algorithm, where the aerosol model parameters are regionally, and may be parameterized as a function of AOD (dynamic models) for regions https://doi.org/10.5194/essd-2020-224 with high humidity variations. The detailed description of the MAIAC regional aerosol models can be found in Lyapustin et al., (2018). Hence, the MODIS aerosol products do not have the ability to retrieve 380 aerosol particle properties with known uncertainties, with the exceptions of size parameter (over ocean in DT), SSA for dust (in DB), and AE (with known caveats).

AERONET Dataset
The Aerosol Robotic Network (AERONET) is a global distributed network of well-calibrated sunsky photometers (Holben et al., 1998). By measuring direct Sun radiance, AERONET provides high temporal (every 3 or 15 minutes in daytime depending on the operation mode of the instruments) multiwavelength AOD products with high reliable accuracy (~±0.01 to ±0.02) (Eck et al., 1999). Strict protocols 395 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., 2005Remer et al., , 2002Sayer et al., 2013).
In addition to direct Sun observations, AERONET radiometers conduct routine measurements of the 400 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 https://doi.org/10.5194/essd-2020-224 Open Access Earth System Science Data Discussions Preprint. Discussion started: 14 August 2020 c Author(s) 2020. CC BY 4.0 License. al., 2000;Sinyuk et al., 2020) and resulting recommendations were adopted for providing aerosol products of highest quality (e.g. increase of quality of retrieval products with aerosol loading and range of observed 405 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), are used in some form in nearly in 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 (Smirnov et al., 2000). We make use of all AERONET sites with data during the POLDER/PARASOL archive (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013). The AERONET direct-sun AOD, Ångström Exponent, fine and coarse mode AOD from spectral deconvolution algorithm (SDA) (O'Neill et al., 2003), 415 AAOD and SSA products are chosen as references for satellite products validation.

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 over pass time (Ichoku et al. 2002). This issue is compounded when multiple satellite products are involved that 420 vary from ~1 km to ~100 km pixel spatial resolution. There are some insightful studies Schutgens et al., 2017) that quantify the AERONET sites spatial representativeness at the scales from ~50 km to ~300 km, which can be used for evaluation of chemical transport model simulations. However, the spatial resolutions (~50 km 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. 425 This study considers aerosol products at 10 km spatial resolution; that 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). That also was a reason for the generation of PARASOL/GRASP Level 3 products. Thus, we adopted PARASOL/GRASP Level 3 daily 0.1° gridded 430 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 x 18.5 km spatial resolution.
The strategies to select PARASOL/GRASP retrieval products with highest quality are presented in 435 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 0.1 440 over ocean). These thresholds are suggested for general users. For GRASP/Models approach, we did not use any filter, since L3 products were generated from L2 using filtering. GRASP data filtering and quality assurance schemes are likely to be improved in the future. Nonetheless, in this study we tried to avoid additional filtering of PARASOL/GRASP L3 products, since most of users would utilize the data with no screening or with a very straightforward filtering. For MODIS DT, DB and MAIAC products, we select the 445 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 fitting residual higher than the threshold for PARASOL or QA lower than the highest flag for MODIS will be set to "no data".
[ Table 2] For validation with AERONET over land, we averaged all land satellite retrievals in a 3x3 window 450 for the gridded satellite data centered over the AERONET station. For ocean sites, in order to select pure ocean pixels and keep reasonably high number of validation points, we decided to use a 9x9 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 Figure 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 455 PARASOL/Operational product is treated a bit differently over ocean due to its relatively coarse resolution (~18.5 km), with a similar land-like 3x3 window centered over the AERONET station.
The AERONET direct-sun AOD, AE, AODF and AODC data were averaged within ±30 minutes of the MODIS/AQUA and PARASOL overpass time, while AERONET SSA and AAOD (which have a lower sampling frequency) are averaged within ±180 minutes. In addition, AERONET station elevations greater 460 than 3600 m above mean sea level, satellite 3x3 or 9x9 data sets with AOD standard deviation greater than 0.05 between window pixels were excluded.

Considered metrics for comparison statistics
For quantifying the validation results, we used standard statistical parameters, including Pearson's (2) where is the number of matched data points ; satellite represents the observations from satellite, and AERONET represents the referenced observations from AERONET; satellite ̅̅̅̅̅̅̅̅̅̅ and 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±0.15AOD (Remer et al., 2005)  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.

Validation of satellite observation by comparison with AERONET data: results and discussion
In order to characterize the quality of the retrieved aerosol parameters from PARASOL, the set of main aerosol parameters including AOD, AE, AODF, AODC, SSA and AAOD were evaluated for the 485 entire PARASOL ~9 years (2005-2013) data archive. This list includes all main aerosol parameters expected to be retrieved from MAP instruments in general . In addition, the validation results of AOD, AE, AODF and AODC were compared with the results of validation of these (where available) from the standard MODIS products for the year 2008.
PARASOL/GRASP retrievals are available and validated at six wavelengths (443,490,565,670,490 865 and 1020 nm). The MODIS retrievals and even PARASOL/Operational have different spectral coverage and, therefore, the comparisons of the GRASP product focused on the aerosol properties at midvisible (550 nm) that is commonly used in the satellite data comparisons and analysis (e.g. Sayer et al., 2018;Sogacheva et al., 2020). Therefore, for PARASOL/GRASP and PARASOL/Operational data the aerosol products were generated at 550 nm by interpolations in log-log space from the closest channels 495 available from the products. Similarly, AERONET aerosol products were also interpolated to 550 nm since the ground-based radiometers do not have a 550 nm channel.   (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 It is very important to note the robust performance of PARASOL/GRASP AOD retrieval in all spectral channels. For example, 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.  ln ( 2 / 1 ) ). The accuracy of AE decreases for low AOD because even a small spectral bias the AOD affects AE strongly (e.g., Wagner 525 and Silva, 2008). Therefore, the threshold of PARASOL AOD (550 nm) > 0.2 was used in AE validation.  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 is the best for GRASP/HP both over land and ocean. GRASP/Models product has the smallest BIAS over land, which is  Table 4] AERONET. AERONET SDA products (O'Neill et al, 2003) reported only at 500 nm, therefore here were interpolated to AODF at 550 nm based on AE using a quadratic fit in log-log space (Eck et al., 1999 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. 560 GRASP/HP AODF demonstrates best performance in terms of the highest correlation and smallest bias.

Fine-and Coarse-mode Aerosol Optical Depth
[ Figure 4] [ 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 575 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 difference. Also, at longer wavelengths where the contribution of coarse particles to radiation is significant, the land surface is very bright while ocean surface is practically dark. Over land 580 AODC in GRASP/HP and GRASP/Optimized products exhibit rather high BIAS of 0.05 and 0.03 correspondingly, that probably dominates the bias for the total AOD in both. For GRASP/Models product biases in AODF and AODC over land have comparable magnitudes and different signs, and therefore compensate each other in the total AOD.
[ Figure 5] 585 [ Table 6] Single Scattering Albedo  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 amount 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. 605 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.
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 of aerosol abundance, in ageement with the results of AERONET sensitivity studies by Dubovik et al., (2000). For example, the 610 correlation coefficient for GRASP/Models SSA at 670 nm with AERONET significantly improves from 0.321 for all L3 products to 0.814 for AOD greater than 1.5.
[ Figure 6] [ Table 7] Aerosol absorption optical depth 615 Aerosol absorption optical depth (AAOD) is related to SSA and total AOD as: In the current PARASOL/GRASP L3 dataset, the AAOD value of each grid box (0.1° or 1° degree) is 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 625 cases (AOD at 440 nm ≥ 0.4) to assure their highest quality .
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, most cases are less than 30% of total AOD. GRASP/HP and GRASP/Models AAOD products show the RMSE equal 630 to 0.042-0.018 from 443 nm to 1020 nm for Models, and 0.047-0.025 for HP. The BIAS is lowest for PARASOL/Models AAOD: 0.00 at 440, 870 and 1020 nm and 0.01 at 670. Thus, PARASOL/GRASP AAOD provide 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 635 increase of abundance.

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 640 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 the entire 2008 year 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., 2010Levy et al., , 2013Levy et al., , 2018Lyapustin et al., 2018;Sayer et al., 2013Sayer et al., , 2014Sayer et al., , 2019 and PARASOL/Operational 645 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 products validation in 2008 is similar to these studies. This section is therefore focusing on a comprehensive evaluation of the consistencies and products are provided over land and ocean, and total AOD products only over ocean.  Table 9. [ Table 9] 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.  (Fig. 10). The correlation 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 705 (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 highest R over 3 of 4 surface classes. Over bright surfaces (NDVI<0.2), GRASP/HP has a highest R (0.915), but also rather high BIAS of 0.06. The GRASP/Models AOD also has zero BIAS for 3 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 710 AODs.
[ Figure 10] [ 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 best AE products over land.   Table 11. 750 AODF is often used to estimate anthropogenic aerosol climate effects (Bellouin et al., 2005) and surface air quality (e.g. PM2.5) (Zhang and Li, 2015). MODIS started to report 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 755 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 AOD at 550 nm over ocean are derived according to the equations below: [ Figure 13] [ Figure 14] [  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 highest R (0.771) and the best linear fitting (slope is reaching 1 and intercept is close to 0) 785 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 results in 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

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 815 over ocean only, 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 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 820 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, GCOS Fraction, and the lowest RMSE, BIAS, etc.) was used as an indicator for the performance evaluation.  were included in the analysis; due to the reduced data volume from this threshold, the requirement on minimum matchups was reduced to 5. Fig. 19 shows the detailed statistics for the performance of each AE products. Fig. 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% 855 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 19] section since GRASP/Optimized shows rather similar results to GRASP/HP. Since the focus of this section is global pixel-to-pixel comparison of satellite aerosol products, we use all available data of the highest quality for each dataset (Table 2).

Comparisons between PARASOL/GRASP and PARASOL/Operational aerosol products
To begin, we investigate two independent aerosol products derived from PARASOL measurements, 875 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.  Operational and GRASP aerosol products (note here the BIAS should be interpreted as an offset rather than 880 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 885 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 decreasing of correlation against 890 AERONET from land to ocean for Operational AODF products is also recorded in Table 12 and 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 are in line with the validation against AERONET 895 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 increase of AE agreement for global correlation (R) compared to that over AERONET pixels is more notable than 900 other parameters. This may explain that the AE products resulting from LUT-based algorithms are more determined by climatological assumptions about the aerosol models than retrieved. [

AOD comparisons between PARASOL/GRASP and MODIS products
In order to further clarify the level of consistency of satellite products (PARASOL/GRASP and 905 MODIS), the global correlations of different satellite products were extensively analyzed for the year 2008 at a spatial resolution of 0.1° x 0.1°. Fig. 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 less than 3 measurements for a season was omitted. Fig. 22 shows the differences of AOD (550 nm) by season between PARASOL and MODIS aerosol products using GRASP/Models as the reference. A positive value 910 indicates that the MODIS product had a higher mean value. Note that Fig. 22 is not a simple difference of the seasonal means shown in Fig. 21. Instead, to decrease sampling-related differences, a difference between the products was calculated at the pixel level, and these pixel-to-pixel differences were then averaged for a season. In addition, we require at least three matched points in a season to be plotted on the map. Since the analysis in Section 3 suggested that the AOD products over land and ocean from the 915 GRASP/Models processing have the lowest biases, this was used as a reference product in Fig. 22. It should be noted that in order to show the intrinsic difference between the products, the overall bias from AERONET values (using validation metrics in Table 9) were subtracted from the AOD products before obtaining the seasonal differences shown in Fig. 22.
In addition, the global correlations between different satellite products and GRASP/Models data at 920 550 nm were calculated for the complete year 2008. Also, in order to evaluate the consistency of different MODIS products over land, the inter-comparisons were done against MAIAC AOD (Land) product chosen as a reference, as MAIAC provides the most universal coverage over land. Table 15 presents   Each of these global correlations was based on several dozens of millions of pairs, and less noisy 930 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)  This phenomenon can be explained by several factors. First, the inputs from the two satellites differ 955 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 assumption about aerosol and conduct their retrievals in the exactly the same manner globally. In contrast, all three MODIS retrievals use some regional assumptions over land 960 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, etc. used in MODIS algorithms. Third, as can be seen from the Table 15 and In order to explore the last factor, the statistics of the comparisons were sorted by land surface type.
The Tables 16 and 17 show pixel-to-pixel statistic metrics with reference AOD from GRASP/Models and 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 maybe related is that MODIS has much higher 990 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 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 995 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. 1000 Interestingly, the maps in Fig. 22  DT retrievals also show this negative bias against PARASOL/GRASP in the African biomass burning ( Figure 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.

1035
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. As before, the statistic metrics split into four classes of land surface by NDVI 1040 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 Section 3. Again, note that although AOD over land is reported by DT at 470 nm 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 1045 GRASP/HP over land. AE over land from DB is similarly prescribed, not retrieved, when AOD < 0.2 . On the other hand, the DT AE over ocean is a true quantitative measure.  for GRASP/Models and GRASP/HP shown in Fig. 24 are not small (mainly due to the limited dynamic 1055 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). The correlations for AE over land between MODIS DT and DB AE versus GRASP/HP are lower than 0.5 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 1060 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. The cause of the drop in correlation 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.

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 1070 distribution of AODF and AODC are shown in Fig. 25 and Fig. 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.  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 1085 AODF over land are generally higher than for AODC, while over ocean the situation is inverse 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 1090 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).
[ 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 a reasonable agreement over land. This conclusion can likely be generalised by the fact that 1100 retrieval accuracy of detailed aerosol properties is expected to be significantly higher from MAP products than from mono-viewing photometric imagery.

Summary and conclusions
The new PARASOL/GRASP products were extensively evaluated using validations against In terms of data volume and geographic extent, the global comparisons analyses are more representative of the global aerosol system than the subset based on colocations with AERONET. 1120 The results show that the PARASOL/GRASP retrieval provided reliable aerosol products, and important advancement over the reference MODIS aerosol products: -Total AOD  the PARASOL spectral products including AOD for six wavelengths in the range 443 to 1020 nm agree well with AERONET AOD measurements, e.g. for PARASOL/Models AOD correlation Analysis presented in this paper suggests that the data from PARASOL, and therefore from multi-angle polarimeters (MAP) in general, allow not only solid retrievals of conventional aerosol products (e.g. AOD at 550 nm), but also detailed aerosol properties such as AOD for the whole spectrum of observations (e.g. for PARASOL from 443 to 1020 nm), and aerosol SSA and AAOD that are practically not accessible from mono-and bi-viewing photometric satellite observations, as well as improved AE, AODF, and AODC at a 1170 global scale. It is also important to emphasize that PARASOL/GRASP retrievals are based on rigorous optimized inversion that searches for statistically optimized fitting in a continuous space of solution without using widely used Look-up-Tables. As a result, it provides a globally-consistent product using exactly the same aerosol modeling approach over land and ocean, unique set of a priori constraints and initial guess, while retrieving surface reflectance properties simultaneously with aerosol. It is expected that 1175 similar type of approaches will become more common and evolve further in the coming era of multiple 2019). The multi-dimensional aerosol information derived from MAPs is expected to improve quality and utility of atmospheric aerosol characterization from space.
One key finding of this work is that the best retrieval of total AOD is provided by the 1180 GRASP/Models approach, which restrains the retrieval to a priori aerosol model components, vastly reducing the number of free parameters for retrieval. The more complex GRASP/HP retrieval with many more retrieval parameters seemed to offer more accurate detailed aerosol parameters such as AE, AODF, AODF and SSA. Future efforts on improving the GRASP retrieval will be aimed at achieving accurate retrievals within one approach. However, this situation also reveals the challenge of a developing unique 1185 approach that can provide a retrieval of all parameters with highest accuracy from MAP observations.
Indeed, multi-angular polarimetric observations have sensitivity to different aerosol properties, and therefore the MAP algorithms tend to be designed for the retrieval of large number of parameters, while in the situations with low aerosol presence the information may be not sufficient to retrieve all parameters reliably. Nonetheless, the presented results demonstrate an overall clear advantages of MAP aerosol 1190 retrievals compare with photometric mono-viewing product and support high expectations from future MAP missions with improved instrumental and algorithmic developments.

Data availability
The PARASOL/GRASP Optimized, HP and Models products are publicly available the official GRASP algorithm website (https://www.grasp-open.com/products) and the AERIS/ICARE Data and Services 1195 Center (http://www.icare.univ-lille.fr). The dataset used in the current study is registered under: http://doi.org/10.5281/zenodo.3887265 .

Author contribution
The GRASP aerosol products evaluation exercise has been implemented and investigated by the GRASP AH and CF carried through the POLDER data processing based on the GRASP-OPEN software.