# Validation of the aerosol optical property products derived by the GRASP/Component approach from multi-angular polarimetric observations

Xindan Zhang, Lei Li, Cheng Chen, Xingfeng Chen, Oleg Dubovik, Yevgeny

Derimian, Ke Gui, Yu Zheng, Hujia Zhao, Lei Zhang, et al.

► To cite this version:

Xindan Zhang, Lei Li, Cheng Chen, Xingfeng Chen, Oleg Dubovik, et al. Validation of the aerosol optical property products derived by the GRASP/Component approach from multi-angular polarimetric observations. Atmospheric Research, 2021, 263, pp.105802. 10.1016/j.atmosres.2021.105802. hal-03866971

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<figure><img src="image_1.png" /></figure>
1 Validation of the aerosol optical property products derived
2 by the GRASP/Component approach from multi-angular
3 polarimetric observations

4

5 Xindan Zhangª, Lei Liª*, Cheng Chenᵇ,ᶜ, Xingfeng Chenᵈ, Oleg Dubovikᵇ, Yevgeny

6 Derimianᵇ, Ke Guiª, Yu Zhengª, Hujia Zhaoᶜ, Lei Zhangª, Bin Guoª, Yaqiang Wangª, Brent

7 Holbenf, Huizheng Chea*, Xiaoye Zhangª

8

9 a State Key Laboratory of Severe Weather (LASW) and Key Laboratory of Atmospheric

10 Chemistry (LAC), Chinese Academy of Meteorological Sciences, Beijing, 100081, China

11 ᵇ Univ. Lille, CNRS, UMR 8518 – LOA – Laboratoire d'Optique Atmosphérique, 59000 Lille,

12 France

13 c GRASP-SAS, Villeneuve d'Ascq, France

14 d Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094,

15 China

16 e Institute of Atmospheric Environment, Shenyang, China

17 ᵈ Biospheric Sciences Branch, Code 923, NASA/Goddard Space Flight Center, Greenbelt, MD,

18 USA

19

20 Correspondence to:

21 L. Li (lilei@cma.gov.cn);

22 H. Che (chehz@cma.gov.cn)

23

24

25 Abstract

26 The multi-angle polarimetric satellite observations are helpful for improving the
27 retrievals of aerosol parameters. However, practical applications of polarization
28 technology are still limited because of complexity of measurement and interpretation
29 of polarimetric observations. In this study, we analyze the performance of a new
component approach developed in the frame of the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm. In addition to aerosol optical properties including particle size distribution, non-sphericity and index of refraction that are commonly derived from multi-angle radiance and polarization measurements, the GRASP/Component approach also provides some information about aerosol composition. Specifically, in this approach aerosol is modeled as an internal mixture of several components with distinctly different chemical compositions and known refractive indices. The approach is intended not only to provide additional insight on aerosol composition but also to improve retrieval of basic aerosol optical properties.
This study presents comprehensive validation and evaluation of Aerosol Optical Depth (AOD), Ångström exponent (AE), fine mode AOD (AODF), coarse mode AOD (AODC), and single scattering albedo (SSA) as retrieved by the GRASP/Component approach. The GRASP/Component products include aerosol retrievals using two different aerosol component mixing rules, i.e., Maxwell-Garnett (MG) effective medium approximation and a simple Volume-Weighted averaging (VW). The differences between the results obtained using these two assumptions are also discussed. The obtained results show that the aerosol optical property products of GRASP/Component approach have good agreement with the ground-based AERONET measurements, which is comparable to other PARASOL/GRASP approaches. Specifically, the AOD retrieved by GRASP/Component approach show high correlation and nearly no bias both over land and ocean, as compared with AERONET. The more detailed aerosol properties such as AE, AODF, AODC and SSA also show one of the best comparisons with AERONET. These improvements can probably be attributed to the use of the additional physical constraints on spectral dependence of the complex refractive index and the reduction of total number of aerosol parameters directly retrieved in the GRASP/Component approach. In addition, the choice of mixing rules had no significant effect on optical retrievals. With the exception of SSA, the results obtained based on the MG mixing rule were found to be slightly better over those obtained using VW mixing rule, especially for bias.
**Key words:** aerosol optical property, GRASP/Component approach, Maxwell-Garnett effective medium approximation, Volume-Weighted average effective medium approximation, POLDER-3/PARASOL

# 1 Introduction

The interaction between aerosol particles and solar radiation not only strongly affects the distribution of solar radiation in the atmosphere, but also affects the total energy budget of the atmosphere (Knapp et al., 2002; Liu et al., 2014; Sakaeda et al., 2011). Aerosol particles also have influences on the atmospheric visibility and climate dynamics (Charlson et al., 1992; Che et al., 2007, 2009; Ma et al., 2019; Kondratyev et al., 1982), as well as on the environment, air quality, ecosystems, human health and many other aspects (Chudnovsky et al., 2014; Jacobson et al., 2001, 2002; Zhang et al., 2012). However, atmospheric aerosol are one of the most complex atmospheric components; the spatial and temporal distribution of aerosol optical properties can be affected by many physical and chemical factors (Chen et al., 2021). Therefore, aerosol are very variable and hard to monitor reliably. As a result, the effects of aerosol particles on climate and environment are difficult to fully understand and quantify (Boucher et al., 2013; Hansen et al., 1997). For example, aerosol radiative forcing has been one of the most uncertain elements in climate change assessments (IPCC, 2013).

Satellite measurements and products are helpful for providing information on the spatial and temporal distribution of aerosol properties on large scale, which can be assimilated by climate models (Cameletti and Finazz, 2018; Formenti et al., 2018; Kaspar et al., 2009). The knowledge of atmospheric aerosol chemical composition derived from satellite measurements is helpful for aerosol pollution control and studying the aerosol optical properties and its radiation, weather and climate effects (Li et al., 2019). Multi-angular polarimetry is considered as one of the most promising types of remote sensing for improved characterization of atmospheric aerosol (Dubovik et al., 2019, 2021). It has been demonstrated that taking advantage of multi-angle, multi-spectral and polarization measurements could enhance the characterization of aerosol and surface properties (Deuzé et al., 1993, 2001; Dubovik
et al., 2019; Hasekamp et al., 2005, 2007; Wang et al., 2012; Waquet et al., 2009, 2013), and estimate aerosol composition (Li et al., 2019, 2020a; Chen et al., 2018, 2019). In recent years, the development of multi-spectral, multi-angle and polarization detection technology has significantly improved the types and precision of aerosol parameters derived from satellite observations. However, due to lack of available reliable polarimetric observation and apparent challenges in interpretation of these observations, the completeness and accuracy of aerosol data operationally derived from polarimetry do not yet appear to have reached the accuracy levels implied by theoretical sensitivity studies that analyzed the potential information content of satellite polarimetry (see discussion by Dubovik et al., 2019, 2021). Therefore, the most commonly used data set of aerosol satellite retrievals is provided by such satellite instruments as MODIS that has no polarimetric capabilities (Chudnovsky et al., 2014; Filonchyk et al., 2020; Jin et al., 2019; Kaufman et al., 1997; Lee et al., 2013; Tanré et al., 1997). The aerosol satellite retrievals provided by MODIS have been validated and evaluated using the accurate ground-based AOD measurements in previous studies. For example, MODIS AOD (660 nm) retrievals over land and ocean were separately compared to AOD (670 nm) products of more than 100 AERONET sites around the globe in the study of Ichoku et al. (2002) and the results showed that the MODIS AOD (660 nm) retrievals are significantly better over ocean (R = 0.936, Slope = 1.088, Offset = 0.009) than that over land (R = 0.729, Slope = 0.732, Offset = 0.063). A better correlation R = 0.882 was obtained for the validation of MODIS Collection 5 (C005) dark-target AOD (550 nm) products over land in the study of Levy et al. (2010). Recently, a long-term global validation of MODIS Aqua and Terra AOD (550 nm) products was conducted using the daily average of AOD products at 452 AERONET sites for the period 2000 – 2018 in the study of Bright and Gueymard (2019) and an absolute RMSE = 0.106 was obtained for the combined Aqua and Terra AOD (550 nm) products. At the same time, long-term validation of MODIS AOD products in China has also been conducted. Specifically, MODIS Collection 006 (C6) and 061 (C6.1) Dark Target (DT) AOD products in China for the period 2002 – 2014 were evaluated by Che et al. (2019) using AERONET and CARSNET (China Aerosol
Remote Sensing Network) AOD products and the results showed that the C6.1 DT AOD products with R = 0.901 and RMSE = 0.171 are better than the C6 DT products with R = 0.890 and RMSE = 0.185. A comprehensive evaluation and comparison of MODIS AOD (550 nm) products in China for the period 2000 – 2017, which includes multi-angle implementation of the atmospheric correction algorithm (MAIAC), Dark Target (DT), and Deep Blue (DB) products, were validated in the study of Liu et al. (2019) using AERONET AOD products and the results showed that MAIAC product achieved better accuracy than DT and DB products after the quality assurance filter. In addition, the validations of MODIS C005 AODF (550 nm) and AE were also shown in the study of Levy et al. (2010) with the correlation R = 0.807 and R = 0.554 respectively. A new look-up table-spectral deconvolution algorithm (LUT-SDA) was proposed by Yan et al. (2019) for improving the AODF retrievals from MODIS observations and AODF products at three AERONET sites (Beijing, Hong Kong, and Osaka) in Asia were used to validate the LUT-SDA AODF products with the changing of RMSE from 0.14 at Osaka site to 0.39 at Beijing site. At the same time, several new-generation retrieval approaches have recently been proposed to take advantage from polarimetric observations for aerosol monitoring. These methods were applied to available polarimetric observations such as those by POLDER instruments (Deuzé et al., 2001). For example, Fan (2008) verified the POLDER-3/PARASOL aerosol inversion scheme and showed that PARASOL inversion over land was mainly sensitive to fine-mode aerosols. Formenti et al. (2018) demonstrated the POLDER-3/PARASOL aerosol inversion products in the western Mediterranean, and the results showed that the inversion algorithm was able to evaluate the various components of aerosol optical depth (AOD) on a regional scale in the western Mediterranean very well. The study of Waquet et al. (2011, 2013) showed that the passive POLDER sensor with multi-angle, multi-spectral and polarizing abilities had a great potential in retrieval of the optical and microphysical characteristics of aerosols above cloud. Moreover, several new-generation retrieval approaches have recently been developed to provide more accurate retrievals of the main aerosol parameters such as aerosol optical depth and derive additional
parameters such as aerosol absorption. These methods use improved forward modeling of atmospheric (polarized) radiances and implement a search in the continuous space of solutions using rigorous statistically optimized inversions (Dubovik et al., 2019; Schutgens et al., 2021). For example, SRON-Netherlands Institute for Space Research has developed such retrieval based on an iterative fitting of a linearized radiative transfer model (Hasekamp and Landgraf, 2005) to the PARASOL data. The algorithm was applied to process the POLDER-3/PARASOL measurements for the year of 2006. The basic concept of the algorithm is described in Hasekamp et al. (2011), while several refinements were realized by Wu et al. (2015), Fu and Hasekamp (2018), Fu et al. (2020). Probably, the most extensive aerosol products available at present from multi-angular polarimetry are provided by GRASP algorithm (Dubovik et al., 2011, 2014). Indeed, 18 months of POLDER-1 and -2 and nine years of POLDER-3 observations have been processed and available at the AERIS/ICARE Data and Services Center (http://www.icare.univ-lille1.fr) and GRASP-OPEN site (https://www.grasp-open.com). It includes three different aerosol and surface products generated by GRASP algorithms using POLDER-3/PARASOL. The quality of these PARASOL/GRASP aerosol products was extensively evaluated and analyzed by Chen et al. (2020). This evaluation analysis suggested that the aerosol retrievals from multi-angle polarimetric observations (e.g. POLDER-3/PARASOL) allow solid retrievals of detailed aerosol properties such as aerosol optical depth (AOD) for the whole spectrum of observations from 443 nm to 1020 nm, and single scattering albedo (SSA) and absorbing AOD (AAOD) that are practically not accessible from mono- and bi-viewing photometric satellite observations, together with improved Ångström exponent (AE), fine mode AOD (AODF) and coarse mode AOD (AODC) on a global scale.

In this paper, we evaluate accuracy of aerosol retrievals from most recent developed GRASP/Component approach described in details by Li et al. (2019, 2020a, 2020b). In contrast with most of previous approaches, GRASP/Component derives not only aerosol optical properties but also some information about aerosol composition. Specifically, in this approach aerosol is modeled as internal mixture of
several aerosol components with different compositions including hydrated soluble particles embedded with black carbon, brown carbon, iron oxide, and other (non-absorbing) insoluble inclusions. The complex refractive indices of the dry components are fixed a priori (the refractive index of the soluble host is allowed to vary with hydration), and the complex refractive indices of the mixture are computed using mixing rules. The volume fractions of these components are derived along with the size distribution and the fraction of spherical particles. Thus, the GRASP/Component approach not only provides additional information about aerosol composition, but also provides a common comparability of aerosol optical properties (Li et al., 2019). The spatial and temporal distribution of black carbon (BC) and brown carbon (BrC) concentrations, as well as the climatological characteristics of total AOD, fine- and coarse-mode AOD (AODF, AODC) retrieved by the GRASP/Component approach over East and South Asia have been discussed in the study of Li et al. (2020a, 2020b). It should be noted that GRASP/Component retrieves aerosol component fractions together with size distribution and fraction of non-spherical particle that makes it essentially different to the traditional aerosol component inversion algorithm such as pre-assumed aerosol type in look-up-tables (LUT algorithm) or aerosol component estimation from aerosol optical properties products (e.g., refractive index, SSA, etc.) (Li et al., 2019; Kolven and Fung, 2006; Schuster et al., 2009, 2016; Russell et al., 2014; Chung et al., 2012; Bahadur et al., 2012).

This study aims to analyze how the assumptions used in GRASP/Component for modeling aerosol components affect the accuracy of aerosol optical properties such as AOD, AODF, AODC, AE and SSA. The evaluation of retrieval of aerosol component fraction is not considered here and expected to be done in a separate study. Thus, the paper presents comprehensive validation and evaluation of the GRASP/Component aerosol optical property products using the AERONET data over globe. The validation methodology follows similar strategy with one used by Chen et al. (2020) and described in details in Section 2. Section 3 presents a comprehensive comparison of satellite-derived products and ground-based measurements for AOD, Ångström
exponent (AE), AODF, AODC, and SSA over globe (land and ocean). The summary
and conclusions of this study is presented in Section 4.

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2 Data and methodology

2.1 POLDER-3 sensor description

The PARASOL (Polarization and Anisotropy of Reflectance for Atmospheric
Science coupled with Observations from a Lidar) was launched by the French
Aerospace Center on December 18, 2004. In addition to the commonly spectral
signature, POLDER-3 on PARASOL satellite can collect data with the polarized and
directional signatures (Tanre et al., 2011), which known to have higher information
content in respect with the size, shape and composition of aerosol particles. It
provided the longest record of multi-angle polarization and radiance observations
from March 2005 to October 2013. Besides 3 gas absorption channels (763, 765 and
910 nm), the radiance measurements are collected at six channels (443, 490, 565, 670,
865 and 1020 nm) and polarization measurements are collected at three channels (490,
670 and 865 nm) in up to 16 viewing directions per pixel. In addition, the POLDER-3
has ability to achieve global coverage approximately every two days with resolution
of about 5×6 km² at nadir.

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2.2 Description of the aerosol mixing rules in the GRASP/Component approach

GRASP is a versatile aerosol and surface parameters retrieval algorithm (Dubovik
et al., 2011, 2014, 2021) available publicly at https://www.grasp-open.com. (last
access: 24 March 2021). It was developed to enhance the characterization of aerosol
properties retrieved from multi-spectral, multi-angle, and polarization observations
(Dubovik et al., 2011, 2014). Recently, GRASP algorithm has been applied to a
variety of remote sensing observations (such as satellite, ground-based, laboratory
observation, etc.) to obtain a store of atmospheric aerosol parameters (Dubovik et al.,
2021; Torres et al., 2017; Titos et al., 2019; Hu et al., 2019; Lopatin et al., 2013, 2021;
Tsekeri et al., 2017; Schuster et al., 2019). The detailed descriptions of GRASP
algorithm can be found in Dubovik et al. (2011, 2014, 2021b). A complete archive of
POLDER/PARASOL data was processed by GRASP algorithm and three product sets of aerosol parameters were generated: GRASP/Optimized, GRASP/HP, and GRASP/Models. These products are generated with different approaches assuming using aerosol modeling and radiative transfer calculations. These aerosol products were extensively discussed and validated in the study of Chen et al. (2020).

Inspired by the study of Schuster et al. (2005, 2009, 2016) on retrieving aerosol components from aerosol optical properties provided by the ground-based Sun/sky photometer of AERONET network, a new aerosol component approach was realized in frame of the GRASP algorithm. The GRASP/Component approach differs from existing aerosol component inversion algorithms that estimate aerosol component indirectly through the complex refractive index, by allowing direct inference of aerosol components from measured radiation. A specific module was developed with the idea that aerosol complex refractive index is modeled as internal mixture of several aerosol components such as BC, BrC, fine/coarse mode non-absorbing soluble and insoluble, coarse mode absorbing and aerosol water with known spectral dependent refractive index and in the retrieval the values of refractive index are driven by fractions of each component. Thus, in this approach called GRASP/Component the aerosol components and aerosol optical properties are retrieved directly from measured radiance and polarization (Li et al., 2019, 2020a, 2020b). Here we only verify the retrieval quality of the optical products and the evaluation of retrieved aerosol component will be done in future study. Table A1 in the appendix shows the description of the aerosol components in GRASP/Component approach, together with the refractive index of each component at 0.440 and 0.865 µm. A full description of GRASP/Component approach can be found in Li et al. (2019). Here we provide some descriptions of different aerosol component mixing rules (MG: Maxwell-Garnet; VW: Volume-Weighted average) for the estimation of aerosol components in the GRASP/Component approach.

### (1) GRASP/Component_MG approach

In previous studies, MG mixing rule has been widely used to retrieve aerosol composition from remote sensing data (e.g., Schuster et al., 2005, 2016, 2009; Li et al., 2019, 2020b). Based upon the electromagnetic theory (Bohren and Hoffman, 1983),
the MG mixing rule could be used for the estimation of complex refractive index of each aerosol component and aerosol mixture. It is applicable to the situation where insoluble particles are suspended discretely in solution (Bohren and Hoffman, 1983).

The main assumption in GRASP/Component_MG approach is that the non-uniform aerosol particles are composed of insoluble inclusions and a homogeneous host.

Generally, the hygroscopic properties of soluble inorganic salts together with water content are used to calculate the complex refractive index of the host (Schuster et al., 2005; Li et al., 2019). When the host index of refraction is determined, MG equations are used to estimate the index of refraction of the mixture (Bohren and Hoffman, 1983).

It is noted that the dielectric functions of aerosol particles are not typically tabulated in the literature, thus they must be calculated from the index of refraction firstly. Then a homogeneous material (for example, a 2-component mixture) can be computed by the MG dielectric function, which is written as (Bohren and Hoffman, 1983):

$$ \epsilon_{MG} = \epsilon_m \left[ 1 + \frac{3 \left( f_1 \frac{\epsilon_1 - \epsilon_m}{\epsilon_1 + 2\epsilon_m} + f_2 \frac{\epsilon_2 - \epsilon_m}{\epsilon_2 + 2\epsilon_m} \right)}{1 - f_1 \frac{\epsilon_1 - \epsilon_m}{\epsilon_1 + 2\epsilon_m} - f_2 \frac{\epsilon_2 - \epsilon_m}{\epsilon_2 + 2\epsilon_m}} \right], \quad (1) $$

where $\epsilon_m$, $\epsilon_1$, and $\epsilon_2$ are the complex dielectric functions of the host matrix and inclusions and $f_1$, $f_2$ are the volume fractions of the inclusions. At the same time, the corresponding complex refractive index of the mixture can be obtained by Eqs. (2) - (3):

$$ m_r = \sqrt{\frac{\epsilon_r^2 + \epsilon_i^2 + \epsilon_r}{2}}, $$
$$296 \qquad m_i \\ 297 \qquad = \sqrt{\frac{\varepsilon_r^2 + \varepsilon_i^2 - \varepsilon_r}{2}},$$

where $\varepsilon_r$ and $\varepsilon_i$ denote the real and imaginary components of the mixture dielectric function, $\varepsilon_{MG}$.

### (2) GRASP/Component_VW approach

Unlike the MG approach mentioned above, the VW is an empirical approach for the estimation of aerosol component using the complex refractive index of each component. The main assumption in the VW mixing rule is that all ingredients are fully mixed and not based on the complex calculation of dielectric function. The mixed aerosol index of refraction is estimated by the volume-weighted average based on the proportion of each component. Therefore, the VW mixing rule is easy to calculate and it was also used and tested for the estimation of mixed aerosol index of refraction (Wang et al., 2013; Koven and Fung, 2006). Considering that the selection of mixing rules in the GRASP/Component approach probably imposes some influences on aerosol property retrievals, a simple VW mixing rule also was incorporated in the GRASP/Component approach (Li et al., 2019). Therefore, the estimation of aerosol components and refractive index for fine and coarse models can be written as:

$$316 \qquad m_F(\lambda) \\ 317 \qquad = \frac{\sum_{i=1}^{j} \text{Frac}(F_i) m_{F_i}(\lambda)}{\sum_{i=1}^{j} \text{Frac}(F_i)},$$

$$318 \qquad m_C(\lambda) \\ 319 \qquad = \frac{\sum_{i=1}^{j} \text{Frac}(C_i) m_{C_i}(\lambda)}{\sum_{i=1}^{j} \text{Frac}(C_i)},$$
321

322

where “F” and “C” indicates fine and coarse mode, respectively.

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## 2.3 AERONET products

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The Aerosol Robotic Network (AERONET) of ground-based Sun/sky photometers that have been installed at hundreds of stations around the world (Holben et al., 1998, 2001). Sun/sky photometer at each AERONET site measures direct Sun radiance and sky-scanning diffuse radiation at several wavelengths mostly between 340 nm and 1020 nm. Based on these measurements, a set of aerosol optical and microphysical properties (e.g., AE, SSA, index of refraction, size distribution, sphericity, etc.) can be derived (Dubovik and King, 2000). The highly reliable accurate AERONET direct-sun AOD products with uncertainty of 0.01 to 0.02 (Eck et al., 1999) are extensively used as reference for verifying aerosol satellite retrievals (e.g., Ahn et al., 2014; Bréon et al., 2011; Kahn et al., 2010; Kumar et al., 2015; Mao et al., 2019; Melin et al., 2009; Remer et al., 2002, 2005; Sayer et al., 2018, 2019). In this study, the latest AERONET Version 3 Level 2.0 data set (Giles et al., 2019; Sinyuk et al., 2020), which is available at http://www.aeronet.gsfc.nasa.gov (last access: 5 January 2021), are used to validate and evaluate the GRASP/Component optical products.

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## 2.4 Validation concept

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Matching the satellite-derived aerosol products to the ground-based AERONET products with an appropriate spatial and temporal resolution is a primary issue for the evaluation and validation of satellite retrievals (Ichoku et al., 2002). The overall concept of comparison follows similar strategy as in study by Chen et al. (2020). However, the data sampling has been changed due to some differences in data archiving of GRASP/Component compare to other GRASP products. In this study, the satellite retrievals and ground-based AERONET products are selected to coincide within a space-time window as following: 1) For the time matching, the average window including the 30 min before and after the satellite transit time is used to
extract the ground-based AERONET products of AOD, AODC, AODF and AE.

Considering the low sampling frequency of the SSA, the AERONET SSA was averaged within ±180 min before and after the satellite transit time. 2) We use the algebraic mean of retrievals within a 2x2 pixels grid (about 10 ~ 15 km) centered on the corresponding AERONET site (Li et al., 2019, 2020a) to represent satellite products. At the same time, only if the 100% land percentage pixels are considered as land pixels; similarly, the 0% land percentage is a criterion for ocean data. To further select high quality data, we use GRASP/Component retrievals with the “relative residual” smaller than 5% over land and 10% over ocean (Chen et al., 2020).

We use standard statistical parameters, including Pearson's linear correlation coefficient (R), root mean square error (RMSE), slope and offset of linear regression and deviation to quantitatively assess the validations, which is similar to the study of Chen et al. (2020). The values can be calculated from Eq. (6) – Eq. (8):

$$R = \frac{\sum_{i=1}^{N} (X_{i,satellite} - \bar{X}_{satellite})(X_{i,AERONET} - \bar{X}_{AERONET})}{\sqrt{\sum_{i=1}^{N} (X_{i,satellite} - \bar{X}_{satellite})^2 \sum_{i=1}^{N} (X_{i,AERONET} - \bar{X}_{AERONET})^2}}, \quad (6)$$

$$RMSE = \sqrt{\frac{\sum_{i=1}^{N} (X_{i,satellite} - X_{i,AERONET})^2}{N}},$$

$$BIAS = \frac{1}{N} \sum_{i=1}^{N} (X_{i,satellite} - X_{i,AERONET}), \quad (8)$$

where N is the number of matched data points i, $X_{satellite}$ represents the observations from satellite, and $X_{AERONET}$ represents the reference observations of AERONET. $\bar{X}_{satellite}$ and $\bar{X}_{AERONET}$ represent the mean values of satellite and
378 AERONET observations, respectively.

379 The more stringent requirements imposed by the Global Climate Observing System (GCOS) (Croom, 1994; Zillman, 2009) are also considered and shown in our evaluation of satellite products. According to Popp et al. (2016), the uncertainty of 0.01 for AERONET AOD was considered. Therefore, GCOS was calculated as:

$$384 \qquad GCOS = \max(0.04 \text{ or } 10\%\text{AOD}), \qquad (9)$$

385 where GCOS fraction (%) shows that the percentage of AOD retrieved from satellites observations satisfies the requirements of GCOS.

388
389 **3 Results and discussions**

390 In order to comprehensively characterize and understand the quality and accuracy of aerosol optical property products retrieved by the GRASP/Component approaches (MG and VW) for the entire POLDER-3/PARASOL data archive (2005-2013), the parameters of aerosol optical property (e.g., AOD, AE, AODF, AODC, SSA) were selected for comparison with the AERONET standard products. The AERONET products are available at four wavelengths (440, 675, 870, and 1020 nm) and GRASP/Component approach can provide retrievals at six wavelengths (443, 490, 565, 670, 865, and 1020 nm) inverted from POLDER-3/PARASOL observations. Although the direct comparisons of AERONET and GRASP/PARASOL products can be done for the wavelengths of 440, 670, 870 and 1020 nm, considering that aerosol properties at mid-visibility (550 nm) are mainly used for comparison and analysis of satellite AOD retrievals (Sogacheva et al., 2020) and it should be consistent with the wavelengths used by Chen et al. (2020) for the comparison of AERONET and GRASP, the comparison of GRASP/Component products with AERONET products also uses 550 nm aerosol products by interpolations in log-log space from the available products at the closest wavelengths. Similarly, aerosol products at 565 nm for AERONET are also obtained using this interpolation method.

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407 **3.1 Aerosol optical depth**
Figure 1 shows the comparisons of AOD derived by the GRASP/Component approach (the upper parallel figures (a-b) for MG mixing rule and the lower parallel figures (c-d) for VW mixing rule) with AERONET AOD at 550 nm for the whole POLDER-3/PARASOL archive (2005-2013). The results in two different cases of over land and ocean are presented respectively from left to right panels. We can see that GRASP/Component AOD (550 nm) are consistent with AERONET AOD (550 nm) and the performances of GRASP/Component_MG approach are slightly better than GRASP/Component_VW approach for R, RMSE, and GCOS. Over land, the bias (-0.02) of GRASP/Component_MG is slightly higher than that for GRASP/Component_VW (bias = 0.01), however, over ocean the opposite is true (bias = 0.01 for GRASP/Component_MG and bias = 0.02 for GRASP/Component_VW). In principle, these values for biases are quite small considering common result of satellite data validation (e.g. Sogacheva et al., 2019; Chen et al., 2020). It is noted that the results of GRASP/Component approach (MG and VW mixing rules) demonstrated that the performance of the relevant statistical parameters is slightly better over ocean than over land, for GRASP/Component_MG approach at 500 nm with the highest R (0.93) and GCOS (69.5%), while the smallest RMSE (0.07) and bias (0.01) over ocean; for GRASP/Component_VW approach at 500 nm also with the highest R (0.93), GCOS (63.0%), and the smallest RMSE (0.08) over ocean. In addition, the validation metrics for all spectral AOD (443, 490, 550, 565, 670, 865, and 1020 nm) over land and ocean are listed in Table 1 and Table 2. It can be seen that all GRASP/Component AOD retrievals (MG and VW mixing rules) show good agreement with AERONET standard AOD products with biases within ±0.03 for all wavelengths and surface types. At all wavelengths, the GCOS of GRASP/Component are about 40 – 60% over land and about 60 – 80% over ocean.

<caption>**Table 1.** The validation metrics for all spectral AOD over land and ocean. The AOD at 550 nm and 565 nm for AERONET products, and AOD at 550 nm for PARASOL/GRASP retrievals were interpolated in log-log space from the closet wavelengths.</caption>
<table><thead><tr><th>Type</th><th>Band (nm)</th><th>Mixing rules</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>GCOS (%)</th><th>Bias</th><th>Std</th></tr></thead><tbody><tr><td rowspan="10">Land</td><td rowspan="2">443</td><td>MG (22577)</td><td>0.92</td><td>0.87</td><td>0.01</td><td>0.17</td><td>40.9</td><td>-0.04</td><td>0.17</td></tr><tr><td>VW (23542)</td><td>0.91</td><td>0.92</td><td>0.04</td><td>0.19</td><td>39.4</td><td>0.01</td><td>0.19</td></tr><tr><td rowspan="2">490</td><td>MG (22577)</td><td>0.91</td><td>0.89</td><td>0.01</td><td>0.15</td><td>43.7</td><td>-0.03</td><td>0.15</td></tr><tr><td>VW (23542)</td><td>0.90</td><td>0.94</td><td>0.03</td><td>0.17</td><td>41.4</td><td>0.01</td><td>0.17</td></tr><tr><td rowspan="2">550</td><td>MG (22706)</td><td>0.91</td><td>0.89</td><td>0.01</td><td>0.14</td><td>46.6</td><td>-0.02</td><td>0.14</td></tr><tr><td>VW (23681)</td><td>0.90</td><td>0.94</td><td>0.03</td><td>0.16</td><td>43.8</td><td>0.01</td><td>0.16</td></tr><tr><td rowspan="2">565</td><td>MG (22577)</td><td>0.91</td><td>0.89</td><td>0.01</td><td>0.14</td><td>47.2</td><td>-0.02</td><td>0.14</td></tr><tr><td>VW (23542)</td><td>0.89</td><td>0.94</td><td>0.03</td><td>0.16</td><td>44.4</td><td>0.01</td><td>0.16</td></tr><tr><td rowspan="2">670</td><td>MG (22577)</td><td>0.90</td><td>0.86</td><td>0.01</td><td>0.13</td><td>51.0</td><td>-0.02</td><td>0.12</td></tr><tr><td>VW (23542)</td><td>0.88</td><td>0.92</td><td>0.03</td><td>0.14</td><td>47.5</td><td>0.01</td><td>0.14</td></tr><tr><td rowspan="2">865</td><td>MG (22577)</td><td>0.89</td><td>0.80</td><td>0.02</td><td>0.11</td><td>55.7</td><td>-0.02</td><td>0.11</td></tr><tr><td>VW (23542)</td><td>0.86</td><td>0.86</td><td>0.04</td><td>0.13</td><td>51.9</td><td>0.01</td><td>0.13</td></tr><tr><td rowspan="2">1020</td><td>MG (22200)</td><td>0.88</td><td>0.78</td><td>0.02</td><td>0.11</td><td>57.4</td><td>-0.02</td><td>0.11</td></tr><tr><td>VW (23170)</td><td>0.86</td><td>0.83</td><td>0.04</td><td>0.12</td><td>53.9</td><td>0.01</td><td>0.12</td></tr><tr><td rowspan="10">Ocean</td><td rowspan="2">443</td><td>MG (1280)</td><td>0.93</td><td>0.92</td><td>0.03</td><td>0.08</td><td>61.5</td><td>0.01</td><td>0.08</td></tr><tr><td>VW (1334)</td><td>0.92</td><td>0.96</td><td>0.04</td><td>0.09</td><td>55.8</td><td>0.02</td><td>0.09</td></tr><tr><td rowspan="2">490</td><td>MG (1280)</td><td>0.93</td><td>0.96</td><td>0.02</td><td>0.08</td><td>65.4</td><td>0.01</td><td>0.08</td></tr><tr><td>VW (1334)</td><td>0.92</td><td>1.00</td><td>0.03</td><td>0.09</td><td>58.5</td><td>0.03</td><td>0.08</td></tr><tr><td rowspan="2">550</td><td>MG (1280)</td><td>0.93</td><td>1.00</td><td>0.01</td><td>0.07</td><td>69.5</td><td>0.01</td><td>0.07</td></tr><tr><td>VW (1334)</td><td>0.93</td><td>1.03</td><td>0.02</td><td>0.08</td><td>63.0</td><td>0.03</td><td>0.07</td></tr><tr><td rowspan="2">565</td><td>MG (1280)</td><td>0.93</td><td>1.00</td><td>0.01</td><td>0.07</td><td>69.8</td><td>0.01</td><td>0.07</td></tr><tr><td>VW (1334)</td><td>0.93</td><td>1.04</td><td>0.02</td><td>0.08</td><td>65.2</td><td>0.03</td><td>0.07</td></tr><tr><td rowspan="2">670</td><td>MG (1280)</td><td>0.93</td><td>1.03</td><td>0.01</td><td>0.07</td><td>74.3</td><td>0.01</td><td>0.06</td></tr><tr><td>VW (1334)</td><td>0.93</td><td>1.07</td><td>0.01</td><td>0.07</td><td>70.5</td><td>0.02</td><td>0.07</td></tr><tr><td rowspan="2">865</td><td>MG (1280)</td><td>0.93</td><td>1.06</td><td>-0.00</td><td>0.06</td><td>82.4</td><td>0.01</td><td>0.06</td></tr><tr><td>VW (1334)</td><td>0.93</td><td>1.10</td><td>0.01</td><td>0.06</td><td>78.0</td><td>0.02</td><td>0.06</td></tr><tr><td rowspan="2">1020</td><td>MG (1240)</td><td>0.92</td><td>1.05</td><td>-0.01</td><td>0.06</td><td>84.5</td><td>0.00</td><td>-0.06</td></tr><tr><td>VW (1292)</td><td>0.93</td><td>1.09</td><td>0.002</td><td>0.06</td><td>82.7</td><td>0.01</td><td>0.06</td></tr></tbody></table>

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<caption>**Table 2.** The validation metrics of the probability density functions of differences for all spectral AOD over land and ocean.</caption>

The AOD at 550 nm and 565 nm for AERONET products, and AOD at 550 nm for PARASOL/GRASP retrievals were interpolated in log-log space from the closet wavelengths.

<table><thead><tr><th>Type</th><th>Band</th><th>Mixing</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th></tr></thead></table>
<table><thead><tr><th></th><th>(nm)</th><th>rules</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th></tr></thead><tbody><tr><td rowspan="10">Land</td><td rowspan="2">443</td><td>MG</td><td>0.00</td><td>0.07</td><td>59.6</td><td>-0.05</td><td>0.13</td><td>27.1</td><td>-0.14</td><td>0.36</td><td>27.0</td></tr><tr><td>VW</td><td>0.03</td><td>0.09</td><td>51.4</td><td>-0.00</td><td>0.15</td><td>30.2</td><td>-0.04</td><td>0.41</td><td>30.4</td></tr><tr><td rowspan="2">490</td><td>MG</td><td>0.00</td><td>0.06</td><td>61.0</td><td>-0.04</td><td>0.13</td><td>28.7</td><td>-0.12</td><td>0.35</td><td>27.1</td></tr><tr><td>VW</td><td>0.03</td><td>0.09</td><td>53.5</td><td>0.00</td><td>0.15</td><td>30.8</td><td>-0.03</td><td>0.39</td><td>29.7</td></tr><tr><td rowspan="2">550</td><td>MG</td><td>0.00</td><td>0.06</td><td>63.1</td><td>-0.04</td><td>0.13</td><td>29.6</td><td>-0.11</td><td>0.33</td><td>25.7</td></tr><tr><td>VW</td><td>0.03</td><td>0.08</td><td>55.5</td><td>-0.00</td><td>0.15</td><td>31.5</td><td>-0.03</td><td>0.38</td><td>29.3</td></tr><tr><td rowspan="2">565</td><td>MG</td><td>0.00</td><td>0.06</td><td>63.7</td><td>-0.04</td><td>0.13</td><td>29.3</td><td>-0.11</td><td>0.33</td><td>25.9</td></tr><tr><td>VW</td><td>0.03</td><td>0.08</td><td>56.3</td><td>-0.00</td><td>0.15</td><td>31.3</td><td>-0.03</td><td>0.38</td><td>29.0</td></tr><tr><td rowspan="2">670</td><td>MG</td><td>0.00</td><td>0.06</td><td>66.6</td><td>-0.04</td><td>0.13</td><td>29.2</td><td>-0.12</td><td>0.32</td><td>23.0</td></tr><tr><td>VW</td><td>0.03</td><td>0.08</td><td>59.7</td><td>-0.01</td><td>0.15</td><td>30.4</td><td>-0.05</td><td>0.38</td><td>24.6</td></tr><tr><td rowspan="2">865</td><td>MG</td><td>0.01</td><td>0.06</td><td>70.5</td><td>-0.05</td><td>0.13</td><td>26.3</td><td>-0.18</td><td>0.30</td><td>19.6</td></tr><tr><td>VW</td><td>0.03</td><td>0.07</td><td>63.7</td><td>-0.02</td><td>0.15</td><td>28.1</td><td>-0.10</td><td>0.38</td><td>23.6</td></tr><tr><td rowspan="2">1020</td><td>MG)</td><td>0.01</td><td>0.06</td><td>71.2</td><td>-0.05</td><td>0.13</td><td>24.3</td><td>-0.21</td><td>0.28</td><td>17.7</td></tr><tr><td>VW</td><td>0.02</td><td>0.07</td><td>65.0</td><td>-0.03</td><td>0.15</td><td>26.4</td><td>-0.14</td><td>0.31</td><td>23.4</td></tr><tr><td rowspan="10">Ocean</td><td rowspan="2">443</td><td>MG</td><td>0.02</td><td>0.04</td><td>79.9</td><td>0.01</td><td>0.09</td><td>47.0</td><td>-0.07</td><td>0.18</td><td>46.4</td></tr><tr><td>VW</td><td>0.03</td><td>0.04</td><td>70.3</td><td>0.03</td><td>0.10</td><td>44.8</td><td>-0.03</td><td>0.21</td><td>38.2</td></tr><tr><td rowspan="2">490</td><td>MG</td><td>0.01</td><td>0.04</td><td>80.8</td><td>0.01</td><td>0.09</td><td>49.3</td><td>-0.03</td><td>0.18</td><td>47.8</td></tr><tr><td>VW</td><td>0.03</td><td>0.04</td><td>72.8</td><td>0.03</td><td>0.10</td><td>43.2</td><td>0.01</td><td>0.22</td><td>44.4</td></tr><tr><td rowspan="2">550</td><td>MG</td><td>0.01</td><td>0.03</td><td>83.9</td><td>0.02</td><td>0.10</td><td>48.6</td><td>-0.00</td><td>0.16</td><td>46.9</td></tr><tr><td>VW</td><td>0.02</td><td>0.04</td><td>76.2</td><td>0.04</td><td>0.10</td><td>43.2</td><td>0.03</td><td>0.19</td><td>48.4</td></tr><tr><td rowspan="2">565</td><td>MG</td><td>0.01</td><td>0.04</td><td>83.2</td><td>0.02</td><td>0.09</td><td>48.1</td><td>0.00</td><td>0.16</td><td>46.7</td></tr><tr><td>VW</td><td>0.02</td><td>0.04</td><td>77.8</td><td>0.04</td><td>0.10</td><td>44.4</td><td>0.03</td><td>0.19</td><td>44.8</td></tr><tr><td rowspan="2">670</td><td>MG</td><td>0.01</td><td>0.05</td><td>83.7</td><td>0.01</td><td>0.08</td><td>50.0</td><td>0.05</td><td>0.15</td><td>47.4</td></tr><tr><td>VW</td><td>0.02</td><td>0.06</td><td>79.4</td><td>0.03</td><td>0.08</td><td>47.3</td><td>0.10</td><td>0.17</td><td>42.1</td></tr><tr><td rowspan="2">865</td><td>MG</td><td>0.00</td><td>0.05</td><td>88.6</td><td>0.01</td><td>0.08</td><td>53.1</td><td>0.06</td><td>0.16</td><td>50.0</td></tr><tr><td>VW</td><td>0.01</td><td>0.05</td><td>83.8</td><td>0.03</td><td>0.08</td><td>50.5</td><td>0.11</td><td>0.16</td><td>37.5</td></tr><tr><td rowspan="2">1020</td><td>MG</td><td>-0.00</td><td>0.05</td><td>90.3</td><td>0.01</td><td>0.08</td><td>48.5</td><td>0.09</td><td>0.15</td><td>63.6</td></tr><tr><td>VW</td><td>0.01</td><td>0.05</td><td>88.0</td><td>0.03</td><td>0.08</td><td>49.7</td><td>0.13</td><td>0.15</td><td>36.4</td></tr></tbody></table>
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

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**Figure 1.** Evaluation of GRASP/Component AOD at 550 nm against AERONET. The AOD at 550 nm were interpolated in log-log space from the closet wavelengths. The figures (a-b) in the upper parallel present the results for GRASP/Component_MG and the figures (c-d) in the lower parallel present the results for GRASP/Component_VW. (a) and (c) represent the validation over land; (b)
and (d) represent the validation over ocean. The 1 : 1 reference line and the linear regression line are labeled as gray dashed line and the red solid line. The GCOS requirement of max (0.04 or 0.1AOD) is labeled as gray envelope region. The probability density functions of differences (POLDER-AERONET) are shown in the lower panel for each figure. Different AOD conditions (all AOD, AOD < 0.2, 0.2 ≤ AOD ≤ 0.7 and AOD > 0.7) are marked as black, red, blue and green solid lines.

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## 3.2 Ångström exponent

Ångström exponent (AE) was calculated from using wavelengths of AOD by the equation of $AE = \frac{\ln[\tau(\lambda_1)/\tau(\lambda_2)]}{\ln(\lambda_1/\lambda_2)}$. Since the accuracy of AE retrieval could decrease if the corresponding AOD is low (Wagner and Silva, 2008). As in study by Chen et al. (2020), a threshold of GRASP/Component AOD (550 nm) > 0.2 was used for the validation of AE. The comparisons of GRASP/Component AE (440/870) with corresponding AERONET AE (440/870) are shown in Figure 2 (the upper parallel figures (a-b) for MG mixing rule and the lower parallel figures (c-d) for VW mixing rule) and the validation metrics are summarized in Table 3. It can be seen that the GRASP/Component AE retrievals present good agreement with AERONET AE products and the AE retrievals were quite comparable in both cases, although the MG bias is somewhat better than the VW bias (see validation metrics of R, RMSE, Slope, bias, etc. in Table 3) for both over land and ocean. In addition, for both of GRASP/Component approaches (MG and VW) the correlation over ocean (R>0.9) is significantly higher than that over land (R≤0.84). Specifically, for MG mixing rule, the correlation R = 0.92 over ocean is higher than that over land, R = 0.84 which is similar to VW mixing rule with R = 0.91 over ocean and R = 0.80 over land. However,

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it should be pointed that AE bias over land is lower than that over ocean for both of
GRASP/Component approaches (MG and VW). This probably could be attributed to
the fact that multi-angle, multi-spectral and polarimetric measurements not only
enhance the characterization of aerosol properties, but also improve the terrestrial
inversion and estimations of surface properties (Deuzé et al., 1993, 2001; Dubovik et
al., 2019; Hasekamp et al., 2005, 2007; Wang et al., 2012; Waquet et al., 2009, 2013).
<figure><img src="image_10.png" /><figcaption>**Figure 2.** Evaluation of GRASP/Component AEs (440/870) against AERONET. The figures (a-b) in the upper parallel present the results for GRASP/Component_MG and the figures (c-d) in the lower parallel present the results for GRASP/Component_VW. (a) and (c) represent the validation over land; (b) and (d) represent the validation over ocean. The 1 : 1 reference line and the linear</figcaption></figure>
regression line are labeled as gray dashed line and the red solid line. The probability density functions of differences (POLDER-AERONET) are shown in the lower panel for each figure.

<table><caption>**Table 3.** The validation metrics for AEs over land and ocean.</caption><thead><tr><th>Type</th><th>Mixing rules</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>Bias</th></tr></thead><tbody><tr><td rowspan="2">Land</td><td>MG (9781)</td><td>0.84</td><td>0.80</td><td>0.16</td><td>0.32</td><td>-0.02</td></tr><tr><td>VW (11727)</td><td>0.80</td><td>0.72</td><td>0.22</td><td>0.36</td><td>-0.05</td></tr><tr><td rowspan="2">Ocean</td><td>MG (526)</td><td>0.92</td><td>0.93</td><td>0.03</td><td>0.24</td><td>-0.06</td></tr><tr><td>VW (593)</td><td>0.91</td><td>0.92</td><td>0.01</td><td>0.26</td><td>-0.10</td></tr></tbody></table>

## 3.3 Fine- and coarse- mode aerosol optical depth

Figure 3 shows the comparison of the GRASP/Component AODF with the AERONET SDA AODF. Due to the fact that the AERONET SDA products only provide retrievals at 500 nm (O'Neill et al., 2003), the AODF at 550 nm was interpolated based on AERONET SDA fine mode AE ($\alpha_f$) using a quadratic fit of the AODF through log-log space (Eck et al., 1999; Chen et al., 2020). The analysis of two different cases (land and ocean) are shown in Table 4 and Table 5. We can see that in all these two cases the GRASP/Component_MG approach performs comparably to GRASP/Component_VW approach. For example, GRASP/Component_MG shows the values of correlation coefficient R=0.93, offset=0.00, RMSE=0.09, Bias=-0.01 over land; GRASP/Component_VW has correlation coefficient R=0.92, offset=0.02, RMSE=0.10, Bias=0.02 over land. Here, the GCOS fraction is applied to the AODF validation based on max (±0.04 or 0.1 AODF). GRASP/Component_MG shows higher GCOS fraction than GRASP/Component_VW with at least ~56% GCOS fraction over land, and ~64% GCOS fraction over ocean. Overall, the GRASP/Component AODF products show good agreement with the AERONET SDA AODF products and the GRASP/Component_MG AODF shows comparable results with GRASP/Component_VW AODF retrievals. It is noted that the correlation coefficient of AODF over ocean is significantly lower than that over land for both of two aerosol component mixing rules (MG: 0.66 over ocean and 0.93 over land; VW: 0.63 over ocean and 0.92 over land), which might be related to the predominance of coarse-mode aerosol particles over ocean and AODF over ocean are quite low (see
<table><caption>**Table 4.** The validation metrics for AODF over land and ocean.</caption><thead><tr><th>Type</th><th>Mixing rules</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>GCOS Fraction (%)</th><th>Bias Total</th><th>Std</th></tr></thead><tbody><tr><td rowspan="2">Land</td><td>MG (17611)</td><td>0.93</td><td>0.94</td><td>0.00</td><td>0.09</td><td>62.8</td><td>-0.01</td><td>0.09</td></tr><tr><td>VW (18397)</td><td>0.92</td><td>0.98</td><td>0.02</td><td>0.10</td><td>56.7</td><td>0.02</td><td>0.10</td></tr><tr><td rowspan="2">Ocean</td><td>MG (1045)</td><td>0.66</td><td>0.89</td><td>0.04</td><td>0.09</td><td>68.7</td><td>0.02</td><td>0.09</td></tr><tr><td>VW (1093)</td><td>0.63</td><td>0.95</td><td>0.03</td><td>0.10</td><td>64.1</td><td>0.03</td><td>0.10</td></tr></tbody></table>

<table><caption>**Table 5.** The validation metrics of the probability density functions of differences for AODF over land and ocean.</caption><thead><tr><th></th><th>Mixing rules</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th></tr><tr><th></th><th></th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th></tr></thead><tbody><tr><td rowspan="2">Land</td><td>MG</td><td>-0.00</td><td>0.05</td><td>71.4</td><td>-0.01</td><td>0.12</td><td>34.4</td><td>-0.08</td><td>0.33</td><td>30.9</td></tr><tr><td>VW</td><td>0.02</td><td>0.06</td><td>63.8</td><td>0.02</td><td>0.13</td><td>33.1</td><td>-0.01</td><td>0.33</td><td>31.9</td></tr><tr><td rowspan="2">Ocean</td><td>MG</td><td>0.02</td><td>0.09</td><td>72.1</td><td>0.01</td><td>0.09</td><td>44.0</td><td>-0.26</td><td>0.00</td><td>0.0</td></tr><tr><td>VW</td><td>0.03</td><td>0.10</td><td>67.6</td><td>0.02</td><td>0.09</td><td>39.6</td><td>---</td><td>---</td><td>---</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>**Figure 3.** Evaluation of GRASP/Component AODF at 550 nm against AERONET. The AODF at 550 nm were interpolated in log-log space. The figures (a-b) in the upper parallel present the results for GRASP/Component_MG and the figures (c-d) in the lower parallel present the results for GRASP/Component_VW. (a) and (c) represent the validation over land; (b) and (d) represent</figcaption></figure>
the validation over ocean. The 1 : 1 reference line and the linear regression line are labeled as gray dashed line and the red solid line. The GCOS requirement of max (0.04 or 0.1AODF) is labeled as gray envelope region. The probability density functions of differences (POLDER-AERONET) are shown in the lower panel for each figure. Different AODF conditions (all AODF, AODF < 0.2, 0.2 ≤ AODF ≤ 0.7 and AODF > 0.7) are marked as black, red, blue and green solid lines.

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Similarly, Figure 4, Table 6 and 7 show the validation of the GRASP/Component AODC retrievals against the AERONET SDA AODC products for the two different cases (land and ocean). It is noted that for the separated over land and over ocean cases (in Figure 3 and 4) the performances of GRASP/Component approaches (MG and VW) on AODF and AODC are different. That is, the statistic values of the AODC over ocean are better than that over land (Figure 4), while it is a opposite scenario for AODF that the statistics values of the AODF over land are better than that over ocean, which is also seen from other PARASOL/GRASP products. This probably is related to the fact that aerosols over ocean are mainly dominated by coarse mode particles and the AODF over ocean is small. At the same time, polarization measurements have a rather weak sensitivity to the index of refraction of coarse particles (Mishchenko et al., 1997; Dubovik et al., 2006).

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<table><caption>**Table 6.** The validation metrics for AODC over land and ocean.</caption><thead><tr><th>Type</th><th>Mixing rules</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>GCOS Fraction (%)</th><th>Bias Total</th><th>Std</th></tr></thead><tbody><tr><td rowspan="2">Land</td><td>MG (17612)</td><td>0.824</td><td>0.749</td><td>0.015</td><td>0.084</td><td>65.5</td><td>-0.01</td><td>0.08</td></tr><tr><td>VW (18398)</td><td>0.763</td><td>0.813</td><td>0.017</td><td>0.103</td><td>63.3</td><td>-0.00</td><td>0.10</td></tr><tr><td rowspan="2">Ocean</td><td>MG (1044)</td><td>0.916</td><td>1.104</td><td>-0.012</td><td>0.061</td><td>84.1</td><td>-0.00</td><td>0.06</td></tr><tr><td>VW (1092)</td><td>0.927</td><td>1.182</td><td>-0.008</td><td>0.062</td><td>84.6</td><td>0.00</td><td>0.06</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Figure 4.** Evaluation of GRASP/Component AODC at 550 nm against AERONET. The AODC at 550 nm were interpolated in log-log space. The figures (a-b) in the upper parallel present the results for GRASP/Component_MG and the figures (c-d) in the lower parallel present the results for GRASP/Component_VW. (a) and (c) represent the validation over land; (b) and (d) represent</figcaption></figure>
the validation over ocean. The 1 : 1 reference line and the linear regression line are labeled as gray dashed line and the red solid line. The GCOS requirement of max (0.04 or 0.1AODC) is labeled as gray envelope region. The probability density functions of differences (POLDER-AERONET) are shown in the lower panel for each figure. Different AODC conditions (all AODC, AODC < 0.2, 0.2 ≤ AODC ≤ 0.7 and AODC > 0.7) are marked as black, red, blue and green solid lines.

<table><caption>**Table 7.** The validation metrics of the probability density functions of differences for AODF over land and ocean.</caption><thead><tr><th></th><th>Mixing rules</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th><th>Bias</th><th>Std</th><th>GCOS (%)</th></tr><tr><th></th><th></th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>τ<sub>f</sub>(550) &lt; 0.2</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th><th>τ<sub>f</sub>(550) &gt; 0.7</th></tr></thead><tbody><tr><td rowspan="2">Land</td><td>MG</td><td>0.00</td><td>0.06</td><td>72.6</td><td>-0.07</td><td>0.14</td><td>20.7</td><td>-0.19</td><td>0.30</td><td>16.5</td></tr><tr><td>VW</td><td>0.01</td><td>0.07</td><td>70.0</td><td>-0.07</td><td>0.15</td><td>19.2</td><td>-0.07</td><td>0.57</td><td>20.8</td></tr><tr><td rowspan="2">Ocean</td><td>MG</td><td>-0.01</td><td>0.05</td><td>87.9</td><td>0.02</td><td>0.10</td><td>48.9</td><td>0.15</td><td>0.13</td><td>16.7</td></tr><tr><td>VW</td><td>-0.00</td><td>0.05</td><td>89.2</td><td>0.06</td><td>0.10</td><td>39.8</td><td>0.21</td><td>0.14</td><td>16.7</td></tr></tbody></table>

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### 3.4 Single scattering albedo

Figure 5 and Table 8 present the comprehensive comparisons of GRASP/Component SSA retrievals with AERONET SSA retrievals at four wavelengths (440, 670, 870, and 1020 nm) for all points. In order to ensure that the AERONET SSA products are of the highest quality, the SSA products in the AERONET L2 database are only available for medium and high AOD cases (Dubovik et al., 2000). Similarly, considering that high threshold would eliminate a significant fraction of the inversion data over ocean, we use a threshold of 0.3 (AOD 443 nm < 0.3) over land and a threshold of 0.2 (AOD 443 nm < 0.2) over ocean (Chen et al., 2020) to filter our GRASP/Component SSA products. As shown in Figure 5 and Table 8, the correlations for GRASP/Component_MG approach are higher than that for GRASP/Component_VW approach at all four wavelengths, however, smaller biases at all four wavelengths are found for GRASP/Component_VW approach. In addition, whether GRASP/Component_MG approach or GRASP/Component_VW approach, the correlation coefficient of SSA increases with the increase of wavelength, which may be related to the increase of dynamic range for longer wavelength (Chen et al., 2020). At the same time, the slope, RMSE, increases with wavelength along with the
growth of the correlation coefficient. It is noted that SSA is significantly less correlated at four bands than the other parameters, which can be attributed to the more concentrated dynamic range of the SSA.

<figure><img src="image_13.png" /><figcaption>**Figure 5.** Evaluation of GRASP/Component SSA (670 nm) against AERONET. From left to right, they represent GRASP/Component_MG and GRASP/Component_VW, respectively. The 1 : 1 reference line and the linear regression line are labeled as gray dashed line and the red solid line. The probability density functions of differences (POLDER-AERONET) are shown in the lower panel for each figure.</figcaption></figure>

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<table><caption>**Table 8.** The validation metrics for SSA at 4 bands for all points.</caption><thead><tr><th>AOD Level</th><th>Band(nm)</th><th>Mixing Rules</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>Bias</th></tr></thead><tbody><tr><td rowspan="8">All V3 L2 data</td><td rowspan="2">440</td><td>MG (4978)</td><td>0.36</td><td>0.30</td><td>0.65</td><td>0.05</td><td>0.02</td></tr><tr><td>VW (5140)</td><td>0.30</td><td>0.30</td><td>0.65</td><td>0.05</td><td>0.01</td></tr><tr><td rowspan="2">670</td><td>MG (4978)</td><td>0.61</td><td>0.49</td><td>0.51</td><td>0.05</td><td>0.03</td></tr><tr><td>VW (5140)</td><td>0.52</td><td>0.53</td><td>0.45</td><td>0.05</td><td>0.01</td></tr><tr><td rowspan="2">870</td><td>MG (4978)</td><td>0.63</td><td>0.48</td><td>0.52</td><td>0.06</td><td>0.04</td></tr><tr><td>VW (5140)</td><td>0.56</td><td>0.53</td><td>0.45</td><td>0.05</td><td>0.02</td></tr><tr><td rowspan="2">1020</td><td>MG (4978)</td><td>0.64</td><td>0.48</td><td>0.51</td><td>0.06</td><td>0.04</td></tr><tr><td>VW (5140)</td><td>0.59</td><td>0.55</td><td>0.44</td><td>0.05</td><td>0.02</td></tr></tbody></table>

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## 3.5 Discussions on the evaluation of GRASP/Component retrievals

Table 9 and Table 10 show the statistics of the validation of GRASP/Component retrievals and previous PARASOL/GRASP retrievals for aerosol optical property (AOD, AODF, AODC, AE, and SSA). The values for previous PARASOL/GRASP approaches (GRASP/Optimized, GRASP/HP and GRASP/Models) adopted from Chen et al. (2020) and the values for GRASP/Component approaches (MG and VW) in this study are listed. We can see that aerosol retrievals of GRASP/Component approaches (MG and VW) show a comparable agreement with AERONET products comparing to previous PARASOL/GRASP approaches in Chen et al. (2020). Specifically, all of these different GRASP approaches provide AOD retrievals consistent with ground-based AERONET measurements. At the same time, the retrievals of GRASP/Component AODF and AODC show rather similar results with the PARASOL/GRASP approaches in Chen et al. (2020), with some improvements of AODC retrievals but worse retrievals of AODF over ocean. In addition, the GRASP/Component approaches (MG and VW) provide some improvements of AE retrievals. That is, GRASP/Component AE products over land present better correlation metrics than GRASP/Optimized, Models and HP in terms of relevant statistical indicators such as correlation coefficient, bias, offset, slope, this is related to the multi-angle, multi-spectral and polarization measurements that enhance the surface properties. Similarly, the GRASP/Component SSA products present a higher
correlation, lower RMSE, but lower slope than the PARASOL/GRASP products.
Therefore, GRASP/Component approaches (MG and VW) present some
improvements of the aerosol optical property retrievals derived from
POLDER-3/PARASOL observations. This improvement probably relates with the
following new aspects in GRASP/Component approach i) constraining complex
refractive index retrieval (12 parameters for real and imaginary parts of the complex
refractive indices) by aerosol component retrieval (6 parameters for aerosol
components in MG approach or 7 parameters for aerosol components in VW approach)
is helpful to reduce the total number of directly inverted aerosol parameters (Li et al.,
2019, 2020a); ii) the aerosol component conversion model employed in the MG or
VW approaches imposes additional physical constraints on the spectral dependence of
the complex refractive index (Li et al., 2019, 2020a), which is probably more realistic
for the aerosol retrievals. At the same time, it should be noted that validation of
GRASP/Component approaches (MG and VW) have about 30-50% fewer points
matching AERONET data than that of previous PARASOL/GRASP, in particular for
the matching points over ocean. This is because the mean of original retrieved
parameters for 2 x 2 pixels centered on the AERONET sites is selected in this study
for the GRASP/Component approach, however, the mean within 3 x 3 and 9 x 9
windows of Level 3 0.1_degree products is used in the previous three
PARASOL/GRASP approaches over land and ocean respectively. The differences of
matching points method and numerical statistics between this study and Chen et al.
(2020) could have some influence on the statistics of validation. Further
comprehensive inter-comparison of aerosol optical property products inverted by
these different GRASP approaches is planned in future study.

<caption>**Table 9.** Statistics of different approaches in the GRASP algorithm for AOD, AODF, AODC products at 550 nm validated by the collocated AERONET over land and ocean. The products at 550 nm were interpolated in log-log space from the closet wavelengths. The values for GRASP/Optimized, GRASP/HP, and GRASP/Models in the study of Chen et al. (2020) within 3 x 3 pixels over ocean and 9 x 9 pixels over land, and the values for GRASP/Component_MG and</caption>
GRASP/Component_VW within 2 x 2 pixels in this study are listed.

<table><thead><tr><th></th><th>Type</th><th>Products</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>GCOS<br>Fraction(%)</th><th>Bias</th><th>Bias<br>τ<sub>f</sub>(550) &lt; 0.2</th><th>Bias<br>0.2 ≤ τ<sub>f</sub>(550) ≤ 0.7</th><th>Bias<br>τ<sub>f</sub>(550) &gt; 0.7</th></tr></thead><tbody><tr><td rowspan="5">AOD</td><td rowspan="5">Land</td><td>MG (22706)</td><td>0.91</td><td>0.89</td><td>0.01</td><td>0.14</td><td>46.6</td><td>-0.02</td><td>0.00</td><td>-0.04</td><td>-0.11</td></tr><tr><td>VW (23681)</td><td>0.90</td><td>0.94</td><td>0.03</td><td>0.16</td><td>43.8</td><td>0.01</td><td>0.03</td><td>-0.00</td><td>-0.03</td></tr><tr><td>Optimized (41268)</td><td>0.88</td><td>0.85</td><td>0.10</td><td>0.16</td><td>27.5</td><td>0.06</td><td>0.08</td><td>0.05</td><td>-0.08</td></tr><tr><td>HP (42202)</td><td>0.90</td><td>0.97</td><td>0.07</td><td>0.16</td><td>34.0</td><td>0.07</td><td>0.07</td><td>0.07</td><td>0.04</td></tr><tr><td>Models (28449)</td><td>0.92</td><td>1.02</td><td>0.01</td><td>0.12</td><td>54.2</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.03</td></tr><tr><td rowspan="5">Ocean</td><td rowspan="5">Land</td><td>MG (1280)</td><td>0.93</td><td>1.00</td><td>0.01</td><td>0.07</td><td>69.5</td><td>0.01</td><td>0.01</td><td>0.02</td><td>-0.00</td></tr><tr><td>VW (1334)</td><td>0.93</td><td>1.03</td><td>0.02</td><td>0.08</td><td>63.0</td><td>0.03</td><td>0.02</td><td>0.04</td><td>0.03</td></tr><tr><td>Optimized (1495)</td><td>0.94</td><td>1.06</td><td>0.04</td><td>0.07</td><td>48.4</td><td>0.05</td><td>0.04</td><td>0.06</td><td>0.04</td></tr><tr><td>HP (1551)</td><td>0.94</td><td>1.08</td><td>0.04</td><td>0.07</td><td>46.4</td><td>0.05</td><td>0.04</td><td>0.07</td><td>0.11</td></tr><tr><td>Models (2064)</td><td>0.95</td><td>0.96</td><td>0.02</td><td>0.05</td><td>70.3</td><td>0.01</td><td>0.01</td><td>0.01</td><td>-0.05</td></tr><tr><td rowspan="5">AODF</td><td rowspan="5">Land</td><td>MG (17611)</td><td>0.93</td><td>0.94</td><td>0.00</td><td>0.09</td><td>62.8</td><td>-0.01</td><td>-0.00</td><td>-0.01</td><td>-0.08</td></tr><tr><td>VW (18397)</td><td>0.92</td><td>0.98</td><td>0.02</td><td>0.10</td><td>56.7</td><td>0.02</td><td>0.02</td><td>0.02</td><td>-0.01</td></tr><tr><td>Optimized (31902)</td><td>0.92</td><td>0.84</td><td>0.04</td><td>0.10</td><td>54.9</td><td>0.02</td><td>0.03</td><td>0.01</td><td>-0.16</td></tr><tr><td>HP (32973)</td><td>0.92</td><td>0.89</td><td>0.03</td><td>0.10</td><td>60.9</td><td>0.01</td><td>0.02</td><td>0.01</td><td>-0.10</td></tr><tr><td>Models (23653)</td><td>0.87</td><td>0.66</td><td>0.03</td><td>0.09</td><td>64.5</td><td>-0.02</td><td>0.00</td><td>-0.07</td><td>-0.37</td></tr><tr><td rowspan="5">Ocean</td><td rowspan="5">Land</td><td>MG (1045)</td><td>0.66</td><td>0.89</td><td>0.04</td><td>0.09</td><td>68.7</td><td>0.02</td><td>0.02</td><td>0.01</td><td>-0.26</td></tr><tr><td>VW (1093)</td><td>0.63</td><td>0.95</td><td>0.03</td><td>0.10</td><td>64.1</td><td>0.03</td><td>0.03</td><td>0.02</td><td>---</td></tr><tr><td>Optimized (1074)</td><td>0.90</td><td>0.96</td><td>0.04</td><td>0.06</td><td>56.7</td><td>0.04</td><td>0.04</td><td>0.05</td><td>-0.24</td></tr><tr><td>HP (1155)</td><td>0.91</td><td>0.93</td><td>0.03</td><td>0.04</td><td>76.3</td><td>0.02</td><td>0.02</td><td>0.03</td><td>-0.27</td></tr><tr><td>Models (1338)</td><td>0.83</td><td>0.75</td><td>0.04</td><td>0.05</td><td>77.5</td><td>0.02</td><td>0.02</td><td>-0.03</td><td>-0.33</td></tr><tr><td rowspan="5">AODC</td><td rowspan="5">Land</td><td>MG (17612)</td><td>0.82</td><td>0.75</td><td>0.02</td><td>0.08</td><td>65.5</td><td>-0.01</td><td>0.00</td><td>-0.07</td><td>-0.19</td></tr><tr><td>VW (18398)</td><td>0.76</td><td>0.81</td><td>0.02</td><td>0.10</td><td>63.3</td><td>-0.00</td><td>0.01</td><td>-0.07</td><td>-0.07</td></tr><tr><td>Optimized (31903)</td><td>0.69</td><td>0.74</td><td>0.06</td><td>0.12</td><td>43.1</td><td>0.04</td><td>0.05</td><td>-0.03</td><td>-0.18</td></tr><tr><td>HP (32973)</td><td>0.74</td><td>0.93</td><td>0.06</td><td>0.12</td><td>47.7</td><td>0.05</td><td>0.05</td><td>0.03</td><td>-0.02</td></tr><tr><td>Models (23651)</td><td>0.57</td><td>0.65</td><td>0.04</td><td>0.11</td><td>64.3</td><td>0.02</td><td>0.03</td><td>-0.08</td><td>-0.28</td></tr><tr><td rowspan="5">Ocean</td><td rowspan="5">Land</td><td>MG (1044)</td><td>0.92</td><td>1.10</td><td>-0.01</td><td>0.06</td><td>84.1</td><td>-0.00</td><td>-0.01</td><td>0.02</td><td>0.15</td></tr><tr><td>VW (1092)</td><td>0.93</td><td>1.18</td><td>-0.01</td><td>0.06</td><td>84.6</td><td>0.00</td><td>-0.00</td><td>0.06</td><td>0.21</td></tr><tr><td>Optimized (1076)</td><td>0.87</td><td>0.94</td><td>0.01</td><td>0.05</td><td>77.6</td><td>0.01</td><td>0.00</td><td>0.01</td><td>0.03</td></tr><tr><td>HP (1156)</td><td>0.92</td><td>1.12</td><td>0.02</td><td>0.05</td><td>70.0</td><td>0.02</td><td>0.02</td><td>0.06</td><td>0.20</td></tr><tr><td>Models (1337)</td><td>0.92</td><td>0.75</td><td>0.01</td><td>0.04</td><td>84.8</td><td>-0.01</td><td>0.00</td><td>-0.06</td><td>-0.09</td></tr></tbody></table>

<table><caption>**Table 10.** Statistics of different approaches in the GRASP algorithm for AE and SSA validated by the collocated AERONET over land and ocean. The values for GRASP/Optimized, GRASP/HP, and GRASP/Models in the study of Chen et al. (2020) within 3 x 3 pixels over ocean and 9 x 9 pixels over land, and the values for GRASP/Component_MG and GRASP/Component_VW within 2 x 2 pixels in this study are listed.</caption><thead><tr><th>Type</th><th>Products</th><th>R</th><th>Slope</th><th>Offset</th><th>RMSE</th><th>Bias</th></tr></thead></table>
<table><tbody><tr><td rowspan="5">AE (440/870)</td><td rowspan="5">Land</td><td>MG (9781)</td><td>0.840</td><td>0.801</td><td>0.156</td><td>0.325</td><td>-0.02</td></tr><tr><td>VW (11727)</td><td>0.804</td><td>0.715</td><td>0.218</td><td>0.355</td><td>-0.05</td></tr><tr><td>Optimized (18594)</td><td>0.797</td><td>0.680</td><td>0.213</td><td>0.358</td><td>-0.10</td></tr><tr><td>HP (19093)</td><td>0.843</td><td>0.716</td><td>0.139</td><td>0.336</td><td>-0.14</td></tr><tr><td>Models (11468)</td><td>0.681</td><td>0.415</td><td>0.511</td><td>0.420</td><td>-0.04</td></tr><tr><td rowspan="5">Ocean</td><td>MG (526)</td><td>0.918</td><td>0.929</td><td>0.026</td><td>0.244</td><td>-0.06</td></tr><tr><td>VW (593)</td><td>0.909</td><td>0.917</td><td>0.005</td><td>0.264</td><td>-0.10</td></tr><tr><td>Optimized (363)</td><td>0.935</td><td>0.773</td><td>0.199</td><td>0.210</td><td>0.01</td></tr><tr><td>HP (391)</td><td>0.949</td><td>0.817</td><td>0.092</td><td>0.193</td><td>-0.05</td></tr><tr><td>Models (522)</td><td>0.958</td><td>0.620</td><td>0.451</td><td>0.292</td><td>0.16</td></tr><tr><td rowspan="5">SSA (670 nm)</td><td rowspan="5">All points</td><td>MG (4978)</td><td>0.614</td><td>0.488</td><td>0.505</td><td>0.047</td><td>0.03</td></tr><tr><td>VW (5140)</td><td>0.518</td><td>0.527</td><td>0.451</td><td>0.046</td><td>0.01</td></tr><tr><td>Optimized (7192)</td><td>0.511</td><td>0.608</td><td>0.324</td><td>0.065</td><td>-0.04</td></tr><tr><td>HP (7450)</td><td>0.536</td><td>0.648</td><td>0.299</td><td>0.056</td><td>-0.03</td></tr><tr><td>Models (6095)</td><td>0.321</td><td>0.334</td><td>0.602</td><td>0.057</td><td>-0.02</td></tr></tbody></table>

621

622

## 4 Summary and conclusions

We evaluated the accuracy of aerosol optical retrievals using the AERONET data over globe and analyzed how the assumptions on the aerosol component mixing affect the accuracy of aerosol optical properties (i.e., AOD, AODF, AODC, AE and SSA) in the GRASP/Component approach, which can be applied not only for other multi-angular polarimetric observations such as Directional Polarimetric Camera (DPC) on Chinese GaoFen-5 satellite, but also for AERONET ground-based measurements with some modifications (Li et al., 2019; Dubovik et al., 2019). The results demonstrated that GRASP/Component approaches (MG and VW) can provide reliable aerosol optical products, with the following key findings:

1. GRASP/Component AOD products have good agreement with the ground-based AERONET measurements for all two different cases (land and ocean) and the retrievals of GRASP/Component_MG AOD are generally slightly better than those of GRASP/Component_VW. The GRASP/Component_MG approach provides the most solid AOD products, such as the AOD (550 nm) is unbiased and has the highest correlation (R ~ 0.912) and highest GCOS fraction (~47.8%), as compared to AERONET observations. In addition, the retrievals of GRASP/Component AODF
and AODC have comparable results with the previous PARASOL/GRASP approaches in Chen et al. (2020), showing some improvements of AODC retrievals but worse retrievals of AODF over ocean.

(2) GRASP/Component AE retrievals also show good agreement with AERONET products for all surface types and AE bias over land is lower than that over ocean for both of GRASP/Component approaches (MG and VW), demonstrating the ability of multi-angle, multi-spectral, polarimetric measurements to retrieve aerosols.

(3) Similar to the previous PARASOL/GRASP approaches in the study of Chen et al. (2020), GRASP/Component SSA retrievals are consistent with AERONET SSA products and the correlation coefficient have an increase with wavelength. For the validations of SSA retrieval, the performance of GRASP/Component_VW is better than GRASP/Component_MG except for the correlation coefficient (R), which is a different situation for the validations of AOD, AODF, AODC, and AE retrievals. It probably could be attributed to the differences of these two mixing rules (MG and VW) for the complexity and assumption of aerosol component calculation, as well as their applicability and practicability in satellite aerosol retrievals.

GRASP/Component approaches (MG and VW) could provide a globally reliable aerosol optical property datasets derived from multi-angular polarimetric POLDER/PARASOL observations. The analysis shows that the data from multi-angle, multi-spectral and polarimetric observations are able to provide not only conventional aerosol products, such as AOD at 550 nm, but also provide detailed aerosol information applicable to the entire observed spectrum (e.g., 443-1020 nm) including AOD, AODF, AODC, AE, and SSA on a global scale. An important finding of this study is that the GRASP/Component approach can provide aerosol products with considerable accuracy, and that different mixing rules have no significant effects on the optical retrieval results, with GRASP/Component_MG inversions being slightly better than GRASP/Component_VW (e.g., AOD, AODF, AODC, and AE). Although the evaluation of aerosol component retrievals still has to be done in a future study, the study already shows the GRASP/Component approach improves the accuracy and
reliability of aerosol optical property retrievals by the means of additional physical constraint on the spectral dependence of the complex refractive index and the reduction of the number of unknown parameters.

673

## Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 41905117), National Science Fund for Distinguished Young Scholars (No. 41825011) and National Key Research and Development Program (2019YFC0214603). The GRASP/Component approach development was supported by the CaPPA project (Chemical and Physical Properties of the Atmosphere), funded by the French National Research Agency through the Programme d'Investissement d'Avenir under contract "ANR-11-LABX-0005-01" and by the Regional Council Nord Pas de Calais-Picardie and the European Funds for Regional Economic Development. We would like to thank the following agencies for providing data: The POLDER data, POLDER/PARASOL Level-1 data were provided by CNES and AERIS/ICARE Data and Services Center (http://www.icare.univlille.fr/). The AERONET team for their efforts in maintaining the instruments and providing available data (http://www.aeronet.gsfc.nasa.gov). We also acknowledge the entire GRASP team for the algorithm development.

689

## Appendix

<table><caption>**Table A1.** Description of aerosol components and refractive indices at 440 and 865 nm (courtesy of Li et al., 2019).</caption><thead><tr><th rowspan="2">Abbreviation</th><th rowspan="2">Component</th><th colspan="2">Complex refractive index</th><th rowspan="2">Reference</th></tr><tr><th>440 nm</th><th>865 nm</th></tr></thead><tbody><tr><td>BC</td><td>Black carbon, representing wavelength-dependent strong absorption</td><td>1.95 + 0.79<i>i</i></td><td>1.95 + 0.79<i>i</i></td><td>Bond and Bergstrom (2006)</td></tr><tr><td>BrC</td><td>Brown carbon, representing wavelength-dependent absorption</td><td>1.54 + 0.07<i>i</i></td><td>1.54 + 0.003<i>i</i></td><td>Sun et al. (2007)</td></tr><tr><td>FNAI</td><td>Fine-mode non-absorbing insoluble, representing fine non-absorbing dust and organic carbon</td><td>1.54 + 0.0005<i>i</i></td><td>1.52 + 0.0005<i>i</i></td><td>Ghosh (1999)</td></tr><tr><td>FNAS</td><td>Fine-mode non-absorbing soluble, representing inorganic salts</td><td>1.337 + 10<sup>-9</sup><i>i</i></td><td>1.339 + 10<sup>-8</sup><i>i</i></td><td>Tang et al. (1981), Gosse et al. (1997)</td></tr></tbody></table>
<table><tr><td>FAWC</td><td>Fine-mode aerosol water content</td><td>1.337 + 10<sup>-9</sup><i>i</i></td><td>1.329 + 10<sup>-6.5</sup><i>i</i></td><td>Hale and Querry (1973)</td></tr><tr><td>CAI</td><td>Coarse-mode absorbing insoluble, representing iron oxides</td><td>2.90 + 0.345<i>i</i></td><td>2.75 + 0.003<i>i</i></td><td>Longtin et al. (1988)</td></tr><tr><td>CNAI</td><td>Coarse-mode non-absorbing insoluble, representing coarse non-absorbing dust And organic carbon</td><td>1.54 + 0.0005<i>i</i></td><td>1.52 + 0.0005<i>i</i></td><td>Ghosh (1999)</td></tr><tr><td>CNAS</td><td>Coarse-mode non-absorbing soluble, representing inorganic salts</td><td>1.337 + 10<sup>-9</sup><i>i</i></td><td>1.339 + 10<sup>-8</sup><i>i</i></td><td>Tang et al. (1981), Gosse et al. (1997)</td></tr><tr><td>CAWC</td><td>Coarse-mode aerosol water content</td><td>1.337 + 10<sup>-9</sup><i>i</i></td><td>1.329 + 10<sup>-6.5</sup><i>i</i></td><td>Hale and Querry (1973)</td></tr></table>

691

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