Global Accuracy, Stability, and Consistency Assessment and Usage Recommendations of POLDER/PARASOL GRASP Aerosol Products

Highlights

What are the main findings?

• The GRASP/Components product achieves the lowest RMSE for AOD (0.114) and AE (0.321), outperforming GRASP/HP and GRASP/Models products in most global regions.
• None of the three POLDER-3/GRASP AOD products meet the Global Climate Observing System (GCOS) global stability requirement of 0.02 per decade.

What are the implications of the main findings?

• The GRASP/Components product is recommended as the primary choice for most aerosol-related research applications.
• Caution is required when using POLDER-3/GRASP AOD products in long-term climate and radiative balance studies.

Abstract

The Polarization and Directionality of the Earth’s Reflectances (POLDER)-3/GRASP (Generalized Retrieval of Aerosol and Surface Properties) aerosol products have been widely used in studies on radiative balance and climate change. However, the stability and consistency of the products have yet to be comprehensively evaluated, despite their critical importance for long-term studies. POLDER-3/GRASP products mainly consist of three variants: High-Precision (HP), Components, and Models. This study aims to evaluate the accuracy, stability, and consistency of these aerosol products at global and regional scales, and to provide usage recommendations. Compared with AERONET observations, the Components product shows the best performance for both aerosol optical depth (AOD) and Ångström Exponent (AE) retrievals, with Root Mean Square Error (RMSE) of 0.114 for AOD and 0.319 for AE. The Models AOD and HP AE also demonstrate relatively high validation accuracy, with RMSE of 0.138 for Models AOD and 0.366 for HP AE. Regionally, Components AOD and AE outperform those from the HP and Models products in 8 out of 10 regions. Stability evaluation shows that the stability metrics of the three AOD products range from 0.034 to 0.036 per decade, and none of them meet the Global Climate Observing System (GCOS) stability requirement (i.e., 0.02 per decade), which indicates that caution should be exercised when using POLDER-3/GRASP products for long-term analysis. In terms of consistency, Components AOD and Models AOD exhibit high agreement, while HP AOD is systematically higher than them. The AE retrieved by the three products shows considerable discrepancies, highlighting uncertainties in AE and spectral-AOD retrievals and pointing toward directions for future algorithmic improvements. In summary, considering global and regional accuracy, stability, and consistency, the Components AOD and AE products are generally recommended for use. For different regions, users can choose the appropriate product based on detailed validation and intercomparison results.

1. Introduction

Aerosols have significant climatic and environmental health impacts [1,2,3]. Satellites are a crucial means of obtaining the spatiotemporal distribution of aerosol properties. Common multispectral satellites, such as Moderate-resolution Imaging Spectro-radiometer (MODIS) and Visible Infrared Imager Radiometer Suite (VIIRS), can retrieve aerosol optical depth (AOD) over land with acceptable accuracy. However, other aerosol properties (e.g., fine mode AOD (AODF) and Ångström Exponent (AE)) over land retrieved from multispectral satellites lack quantitative accuracy [4,5]. Multi-angle polarization sensors are considered an important trend in aerosol remote sensing, and sensitivity analysis shows that multi-angle polarization sensors are more sensitive to various aerosol properties [6,7,8,9]. The Generalized Retrieval of Aerosol and Surface Properties (GRASP) algorithm, which shares the same principle as the AERONET inversion algorithm, has been used in the Polarization and Directionality of the Earth’s Reflectances (POLDER)-3 instruments with multi-angle polarization measurements to retrieve the aerosol properties, including multispectral AOD, AODF, coarse AOD, AE, Single Scattering Albedo (SSA), and other parameters [10,11,12]. In addition, the GRASP algorithm has been applied to other polarization observation sensors such as the Directional Polarimetric Camera (DPC) and Particulate Observing Scanning Polarization (POSP) aboard the Gaofen-5 satellite to retrieve aerosol properties [13,14].

The POLDER-3/GRASP products include four different variants: High Precision (HP), Optimized (OP), Models, and Components. Chen et al. [12] validated GRASP HP, OP, and Models products based on the global AERONET observation. The results showed that Models AOD and HP AE had the best overall validation accuracy over land. Zhang et al. [15] validated the GRASP Components product using a similar method, and its overall accuracy of land AOD and AE was comparable to that of Models AOD and HP AE. However, the validation of these products was spread across two different studies, making the comparison of these metrics lack a quantitative basis. In the China region, Wei et al. [16] used eight Sun–Sky Radiometer Observation Network (SONET) observation sites to validate GRASP Models and HP AOD. The result also showed that Models AOD had better accuracy. This study also lacks a validation comparison with the GRASP/Components product. Therefore, it is essential to quantitatively compare the accuracy and error characteristics of these different GRASP variants in a single study. In addition to overall accuracy, attention should also be paid to the accuracy of different regions, which may differ from the global average.

POLDER-3 GRASP’s aerosol properties are used in climate applications. For example, Li et al. [17] analyzed the climatology of spatiotemporal distribution patterns of fine and coarse mode AOD over East and South Asia. Jia et al. [18] used POLDER-3 AODF retrievals to reduce the uncertainty of estimating the radiation effect of aerosol-cloud interaction. However, the retrieval stability of POLDER-3 GRASP products has not yet been evaluated. This is important for long-term climate change studies, as unstable products could lead to erroneous trends and conclusions. The Global Climate Observing System (GCOS) defines stability metrics for AOD, namely a “Goal” target of 0.01/decade and a “Breakthrough” target of 0.02/decade. Achieving GCOS stability for satellite sensors is no easy feat. It requires not only high-accuracy, continuous, and consistent satellite observations, but also high-accuracy, continuous, and consistent aerosol retrieval algorithms [19,20]. POLDER-3 does not carry an onboard calibrator; it relies on pseudo-invariant targets to monitor and correct for radiative degeneration [21]. Even aerosol products used in radiation-stabilized MODIS sensor retrievals, such as DB, meet GCOS stability targets globally but not in East Asia [22,23]. MAIAC AOD retrievals also show that they do not meet GCOS stability targets in China, and their global stability is unknown [24]. Therefore, it is essential to assess the temporal stability of POLDER-3/GRASP aerosol products to better apply them to long-term trend and climate change studies. Furthermore, quantitatively comparing the consistency of different GRASP product variants can also demonstrate the stability and consistency of the GRASP algorithm.

Focusing on the above issues, this study comprehensively evaluates the accuracy, stability, and spatiotemporal consistency of AOD and AE retrieved from different GRASP variants at global, regional, and site scales. Section 2 describes the data and method, Section 3 presents the study results and discussion, and Section 4 summarizes the study.

2. Data and Method

2.1. PARASOL/GRASP Aerosol Products

POLDER-3 is a multi-angle, multi-polarization, and multi-spectral sensor onboard the PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) satellite, operated by the Center National d’Études Spatiales (CNES) on 18 December 2004. POLDER-3 provides an eight-year record of observations, spanning from March 2005 to October 2013. Radiometric measurements of POLDER-3 were collected in six spectral bands (443, 490, 565, 670, 865, and 1020 nm), and polarimetric measurements were collected in three bands (490, 670, and 865 nm), with up to 16 viewing angles per pixel [25]. POLDER-3 achieves near-global coverage approximately every two days, with a nadir spatial resolution of approximately 5 km × 6 km. Its capabilities in multi-angle and multi-polarization observations provide higher sensitivity for the retrieval of geophysical variables. GRASP is an aerosol retrieval algorithm designed to simultaneously retrieve aerosol and surface properties [10,26,27]. This study validates the POLDER-3/GRASP retrievals of AOD and AE. The POLDER-3/GRASP retrieval includes four distinct algorithm product variants:

(1)

GRASP “High-Precision (HP)”: Utilizes highly precise radiative transfer calculations [10].

(2)

GRASP “Optimized”: Employs optimized radiative transfer calculations to balance accuracy and efficiency [10].

(3)

GRASP “Models”: Assumes aerosols as external mixtures of several predefined aerosol component types [10].

(4)

GRASP “Components”: Models aerosol refractive index using internal mixtures of different aerosol components (including black carbon, brown carbon, organic carbon, etc.) based on the Maxwell Garnett effective approximation [11].

Since the Optimized and HP products only differ in the precision of the radiative transfer calculations [12], the HP product was selected in this study. Ultimately, three POLDER-3 products, including HP, Components, and Models, were evaluated.

The POLDER-3 Level 3 daily aerosol products were utilized, which have a spatial resolution of 0.1° and cover the period from 2005 to 2013. The analysis focuses on the global and regional accuracy and stability of AOD at 550 nm and AE at 440–870 nm. The AE, denoted as α, is a spectral derivative parameter of AOD and is calculated from AOD measurements at two different wavelengths, as defined in Equation (1). AE can qualitatively distinguish the relative size of aerosol particles. Since the POLDER-3 product does not provide 550 nm AOD, a quadratic polynomial in log space (Equation (2)) was used to calculate the POLDER-3 550 nm AOD. The 443 nm and 865 nm AOD of the POLDER-3 product can be used to calculate AE, and the difference with the AE bands of 440 nm and 870 nm of AERONET is negligible. Hereafter, unless otherwise specified, AOD refers to that at 550 nm, and AE refers to the wavelength range of 440–870 nm (443–865 nm for POLDER-3). These POLDER-3/GRASP products are publicly available and can be downloaded from the website: http://www.grasp-open.com/products (last accessed: 1 March 2026).

$$\alpha \approx -{\displaystyle \frac{\log \frac{{\tau }_{{\lambda }_1}}{{\tau }_{{\lambda }_2}}}{\log \frac{{\lambda }_1}{{\lambda }_2}}}$$

(1)

where ${\tau }_{{\lambda }_1}$ and ${\tau }_{{\lambda }_2}$ correspond to the AOD at wavelengths λ₁ and λ₂, respectively.

$$\log \left({\tau }_{\lambda }\right)={\mathrm{a}}_0+{\mathrm{a}}_1\log \left(\lambda \right)+{\mathrm{a}}_2{\log \left(\lambda \right)}^2$$

(2)

where ${\tau }_{\lambda }$ is the AOD at wavelength $\lambda$, ${\mathrm{a}}_0$, ${\mathrm{a}}_1$ and ${\mathrm{a}}_2$ are fitting coefficients, typically derived from the AOD observations or retrievals between 440 nm and 870 nm.

2.2. AERONET Data

AERONET is a global, standardized ground-based aerosol observation network established and maintained by NASA, aiming to provide high-accuracy, long-term, continuous observations of aerosol optical and microphysical properties [28,29]. AERONET data is widely used for the validation of satellite aerosol products. Its temporal resolution is typically 3–15 min, with spectral channels covering 340 nm to 1640 nm. The 440–870 nm AE and the 550 nm AOD are calculated using Equations (1) and (2), respectively. AERONET provides the data at three quality levels: Level 1.0 (raw data), Level 1.5 (cloud-screened but unvalidated data), and Level 2.0 (cloud-screened and validated data) [30]. This study uses the latest Version 3 of AERONET Level 2.0 direct-sun data, which features improvements in cloud screening and quality control techniques [29]. The data are publicly available through the AERONET website (https://aeronet.gsfc.nasa.gov, last accessed: 1 March 2026). The locations of the matched AERONET sites are shown in Figure 1.

2.3. Accuracy Validation Method

Spectral, temporal, and spatial matching are required for AOD and AE of AERONET and POLDER-3. In the spectrum, their AOD and AE were converted to wavelengths of 550 nm and 440–870 nm, respectively. The calculation accuracy of AE is affected under low AOD loadings. This is because, under low AOD conditions, even minor spectral differences in AOD at different wavelengths can significantly impact the calculated AE [31]. Therefore, when validating the AE from POLDER-3 aerosol products, a threshold for 550 nm AOD > 0.2 is applied to ensure the reliability of the results [12]. For spatiotemporal matching, the approach is to use the spatial median of satellite data within a spatial window of ±25 km centered on the AERONET site, and the temporal median of AERONET data within ±30 min of the satellite overpass time, for comparison [23,32,33]. The statistical criteria require that satellite retrievals contain at least 20% fraction of valid pixels within the spatial window, and AERONET observations include at least one valid observation within the temporal window [24,34].

The accuracy evaluation metrics are shown in Equations (3)–(11), including the number of matched site-satellite pairs (N), Pearson correlation coefficient (R), root mean square error (RMSE), mean bias (BIAS), relative mean bias (RMB), mean absolute error (MAE), the accuracy target defined by the Global Climate Observing System (GCOS) for long-term climate change studies [35,36], and expected error (EE). The expected error (EE) is defined separately by NASA’s Dark Target (DT) algorithm team (EE_DT), Deep Blue (DB) algorithm team (EE_DB) [33,36], and the expected error for AE (EE_AE) [33]. These expected errors are characterized by the percentage of retrievals falling within the error envelopes, with a typical expectation that this percentage exceeds 68% (i.e., the probability within one standard deviation).

$$\mathrm{R}=\sqrt{1-{\displaystyle \frac{{{\displaystyle {\sum }_{i=1}^n}{(\mathrm{AOD}}_{\left(\mathrm{satellite}\right)i}-{\mathrm{AOD}}_{\left(\mathrm{AERONET}\right)i})}^2}{{{\displaystyle {\sum }_{i=1}^n}({\mathrm{AOD}}_{\left(\mathrm{satellite}\right)i}-{\overline{\mathrm{A}\mathrm{O}\mathrm{D}}}_{\left(\mathrm{AERONET}\right)i})}^2}}}$$

(3)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{({\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{satellite}\right)i}-{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{AERONET}\right)i})}^2}$$

(4)

$$\mathrm{BIAS}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{satellite}\right)i}-{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{AERONET}\right)i}$$

(5)

$$\mathrm{R}\mathrm{M}\mathrm{B}={\displaystyle \frac{\overline{{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{satellite}\right)i}}}{\overline{{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{AERONET}\right)i}}}}$$

(6)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}\left|{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{satellite}\right)i}-{\mathrm{A}\mathrm{O}\mathrm{D}}_{\left(\mathrm{AERONET}\right)i}\right|$$

(7)

$$\mathrm{E}\mathrm{E}\_\mathrm{D}\mathrm{T}=\pm (0.05+15\mathrm{\%}\times {\mathrm{AOD}}_{\mathrm{AERONET}})$$

(8)

$$\mathrm{E}\mathrm{E}\_\mathrm{D}\mathrm{B}=\pm (0.05+20\mathrm{\%}\times {\mathrm{A}\mathrm{O}\mathrm{D}}_{\mathrm{AERONET}})$$

(9)

$$\mathrm{E}\mathrm{E}\_\mathrm{A}\mathrm{E}={\mathrm{A}\mathrm{E}}_{\mathrm{AERONET}}\pm 0.04$$

(10)

$$\mathrm{G}\mathrm{C}\mathrm{O}\mathrm{S}=\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}(0.03,10\mathrm{\%}\times {\mathrm{A}\mathrm{O}\mathrm{D}}_{\mathrm{AERONET}})$$

(11)

where AOD_satellite denotes the POLDER-3 AOD, AOD_AERONET and AE_AERONET denote AERONET AOD and AE, and n is the number of AOD matched.

2.4. Stability Assessment Method

Stability is defined as the maximum acceptable change in systematic error (uncertainty) over a given period, requiring less than 0.02 per decade [37]. Long-term stability assessments require the use of AERONET sites with long-term observations. Specifically, the AERONET sites with at least five years of observations between 2005 and 2013, and with more than six months of data per year, were used. The location of the long-term AERONET site is shown in Figure 1. The 10-year variation in the BIAS metric is used to quantify stability. In this study, two stability metrics, temporal slope and standard deviation, are used to quantify the range of variations in BIAS per decade. The strong correlation (R = 0.834) between the two metrics across different regions indicates their consistency and reliability (see Table 5). Since the fitted slope captures only the trend and not the variability, it tends to be smaller than the standard deviation in regions with large fluctuations but insignificant trends. In contrast, the standard deviation captures the degree of interannual variability. Since GCOS assesses stability on a 10-year scale, the fitted slope coefficient of yearly BIAS is scaled by a factor of 10 (i.e., 10 × fitted coefficient). Simultaneously, the standard deviation is doubled over the 10-year scale, i.e., (10/number of years) × 2 × standard deviation. Given that the data used in this study span 9 years (2005–2013), this becomes (10/9) × 2 × standard deviation.

3. Results and Discussion

3.1. Overall Accuracy

3.1.1. Aerosol Optical Depth

First, POLDER-3 AOD data from 2005 to 2013 were matched and compared with observations from all AERONET sites. Figure 2 shows the overall validation and error histograms of the three POLDER-3 AOD products against the AERONET AOD. Overall, three POLDER-3 AODs exhibit good agreement with AERONET AOD (R > 0.879). Component AOD shows the highest validation accuracy, with R = 0.906, RMSE = 0.114, and MAE = 0.064. These metrics are comparable to the validation results for Components AOD reported by Zhang et al. [15], with R of 0.912–0.931 and RMSE of 0.071–0.141. Previous results indicated that using fitting residual filtering has minimal impact on the validation results for the POLDER-3 GRASP products [38]. Therefore, we did not apply additional sample filtering, resulting in a larger number of matched samples in this study, which did not lead to a decrease in validation accuracy compared to prior studies [12,15]. The BIAS of −0.010 and RMB of 0.955 indicate that the Components product slightly underestimates AOD. The Models AOD shows a slight overestimation of AOD (BIAS = 0.009 and RMB = 1.036). HP AOD shows a more pronounced overestimation (BIAS = 0.071, RMB = 1.328), which is similar to previous studies [12]. Especially at low AOD loadings, HP AOD showed a significant positive bias. This is likely due to the insufficient sensitivity of other aerosol parameters at low AOD loadings, leading to larger retrieval errors that propagate to AOD retrieval. The fraction of Components AOD and Models AOD falling within the EE_DT envelopes of 77.3% and 75.1%, respectively, and the GCOS error envelope of 45.7% and 43.4%, respectively. These metrics demonstrate performance in quantitative applications and are significantly higher than those of HP AOD, with EE_DT of 55.0% and GCOS of 27.6%. As shown in Figure 2d–f, the error frequency histograms show that the Components AOD exhibits the highest frequency of errors close to zero and the smallest median difference, followed by Models AOD, while HP AOD shows the most scattered bias. Overall, the retrieval performance of HP AOD is significantly lower than that of Components and Models AOD, consistent with previous findings [12].

3.1.2. Ångström Exponent (AE)

The comparison of the AE of the three GRASP products with AERONET AE is shown in Figure 3. Note that only the AE matchups with AERONET AOD at 550 nm greater than 0.2 are retained. The result shows that the R for Components AE is 0.834, higher than that of HP (0.820) and Models (0.625). The RMSE and MAE for Components AE are 0.319 and 0.242, respectively, lower than those of HP (0.366 and 0.273) and Models (0.459 and 0.366). The fraction of Components AE retrievals falling within the EE_AE envelope is 0.820, higher than that of HP AE (0.769) and Models AE (0.638), indicating superior accuracy for Components AE. HP and Models both underestimate AE (BIAS < 0 and RMB < 1). The BIAS of Components AE is slightly greater than 0, and its RMB is slightly greater than 1, indicating a slight overestimation of the AE. Previous studies have shown that the Models product tends to overestimate low AE values and underestimate high AE values [12], which is consistent with the results of this study (Figure 2c). As shown in Figure 2b, when coarse modes dominate (i.e., AE < 1.0), HP captures the variation in the AE well; however, when fine modes dominate (i.e., AE > 1.0), HP tends to underestimate AE. In contrast, Components AE performs better under high AE values but overestimates low AE values. As shown in Figure 3d–f, the error frequency histograms indicate that most errors are concentrated within ±1.0. The AE for global matching data is approximately 1. Components AE exhibit the highest frequency of errors, close to zero. It shows the smallest median difference against AERONET. In summary, in terms of overall accuracy, Components AE performs best, followed by HP AE.

To reduce the potential impact of spatial and temporal variations in AERONET site distribution on validation metrics, this study selected long-term sites (i.e., sites with at least five years of data between 2005 and 2013, and more than six months of data per year) for validation of AOD and AE (see Figure 4). Compared with the validation results using all matched sites, there are no significant differences in the validation metrics for AOD and AE.

3.2. Temporal Validation

3.2.1. AOD Temporal Evaluation

An analysis of interannual variations in product accuracy at long-term observation sites is presented in Figure 5. Figure 5a shows the annual mean values and bias variations in AOD for the three GRASP AOD products matched with corresponding AERONET observations. The overall trends of the six curves are largely consistent; however, HP systematically overestimates AOD with a BIAS of 0.05–0.10, exceeding Components AOD by −0.023–0.018 and Models AOD by −0.006–0.032. Models AOD show the best agreement with AERONET, especially before 2010, with a BIAS close to 0. Components AOD exhibits a slight negative bias. Figure 5b shows that the fractions of Components and Models retrievals falling within the EE_DT are relatively high and stable over time. The fraction for HP remains relatively low each year, mostly below 60%. The fraction of Components and Models AOD meeting the GCOS accuracy target is approximately 45%, while that of HP AOD is less than 30%. The R, RMSE, and MAE metrics for Components and Models AOD show relatively stable interannual variations, while HP AOD exhibits a decreasing trend in R and increasing trends in RMSE and MAE, indicating larger year-to-year fluctuations in its accuracy. Year-by-year validation was consistent with overall validation. Components AOD and Models AOD showed high and comparable accuracy, while HP AOD showed lower accuracy, with an annual average significantly higher than other products. Noted that the validation metrics for HP AOD show greater interannual variation, indicating greater retrieval instability.

3.2.2. AE Temporal Evaluation

AE’s year-by-year validation metrics were also analyzed. Figure 6a shows the annual means and bias variations in the AE for the three POLDER-3 AE products against AERONET AE observations. HP AE is systematically lower than the other two products, approximately 0.16–0.23 below Components AE and 0.03–0.12 below Models AE. Components AE show the best agreement with AERONET, with the smallest bias (<0.05) each year. Both HP and Models products underestimate AE in each year, with bias ranging from −0.22 to 0. The largest underestimations occurred in 2013, with biases of −0.22 and −0.18, respectively. Figure 6b shows that Components and HP AE exhibit a relatively high fraction of retrievals within the EE_AE, both exceeding 70%. In contrast, Model AE consistently falls below 68% each year. For the R metric, Components and HP AE show relatively stable interannual variations, while Models AE exhibits an increasing trend. The RMSE and MAE of Model AE are significantly larger than those of HP and Components AE. Overall, the year-by-year validation was consistent with the overall validation, with Components AE and AERONET AE showing the highest consistency, while HP and Models AE showed an underestimation. The validation metrics of all the AE products showed time dependence, indicating that their accuracy was unstable.

3.2.3. AOD Stability Assessment

The BIAS metric is used to assess the stability of AOD products. As mentioned earlier, slope and standard deviation calculations each have their own advantages in terms of stability; subsequent analysis uses only the average of the two stability metrics. As shown in Figure 7, the BIAS metrics of all three AOD products exhibit an upward trend, which suggests that the product’s accuracy is time-dependent.

Table 1. Summary of stability metrics for AOD bias.

Product	Slope	Standard Deviation	Mean
Components AOD	0.039	0.030	0.035
HP AOD	0.039	0.029	0.034
Models AOD	0.042	0.030	0.036

summarizes the stability metrics for each AOD product. The results indicate that the stability of the three AOD products ranges from 0.034 to 0.036 per decade, which does not meet the GCOS stability requirement (i.e., 0.02 per decade). Previous studies have shown that the stability of MODIS and VIIRS AOD ranges from approximately 0.006 to 0.016 per decade [23,39]; therefore, the current POLDER-3 AOD products exhibit weaker stability compared to operational MODIS and VIIRS AOD products. This result indicates that caution should be exercised when using POLDER-3 AOD for trend analysis, as changes in AOD accuracy may exceed the actual changes in AOD itself. Further analysis of the correlation among the three AOD biases revealed a correlation coefficient exceeding 0.95. This suggests that the AOD bias may be systematically inherent in the GRASP algorithm or caused by POLDER-3 radiometric calibration drifts.

3.2.4. AE Stability Assessment

Similar to AOD, the stability of AE was also analyzed. Figure 8 shows the annual variation in bias for different AE products along with their fitted lines.

Table 2. Summary of stability metrics for AE bias.

Product	Slope	Standard Deviation	Mean
Components AE	0.019	0.036	0.028
HP AE	−0.017	0.066	0.042
Models AE	−0.067	0.087	0.077

summarizes all stability metrics for each AE product. Components AE exhibits the best stability with 0.028 per decade, followed by HP AE with a stability of 0.042 per decade. Model AE exhibits the poorest stability of 0.077 per decade. Since the GCOS does not specify stability targets for AE, it is necessary to coordinate efforts to establish AE stability targets suitable for climate change studies.

3.3. Regional Accuracy Validation

The accuracy of aerosol products exhibits spatial variability [4]. Since the availability of AERONET sites changes over time, using long-term AERONET sites can minimize the impact of site distribution changes. Therefore, this study employs long-term AERONET site observations to conduct regional accuracy validation of AOD and AE for the three POLDER-3 products. The study region boundaries and the distribution of long-term AERONET sites used are shown in Figure 1.

3.3.1. Regional Overall Accuracy of AOD

The validation results of the three AOD products against AERONET AOD for different regions are shown in Figure 9.

Table 3. Regional statistical metrics of Components, HP, and Models AOD products compared with long-term AERONET site observations. Bold values indicate the best-performing result among all products for each metric and region.

Region	Product (AOD)	Number	R	RMSE	BIAS	MAE	RMB	=EE DT	=EE DB	=GCOS
CSA	Components	3566	0.959	0.104	−0.007	0.059	0.964	77.5%	80.0%	50.1%
	HP	3580	0.945	0.165	0.061	0.092	1.334	58.8%	62.3%	30.9%
	Models	3295	0.951	0.175	0.019	0.073	1.098	75.2%	78.5%	46.6%
ENA	Components	5884	0.735	0.096	0.024	0.054	1.205	76.9%	79.6%	49.7%
	HP	5287	0.665	0.174	0.119	0.126	2.028	33.3%	35.9%	15.4%
	Models	5659	0.772	0.105	0.042	0.062	1.355	71.5%	73.9%	43.6%
EUR	Components	15,300	0.818	0.078	−0.003	0.049	0.982	82.2%	85.6%	48.4%
	HP	15,297	0.787	0.106	0.052	0.072	1.334	63.9%	67.6%	32.9%
	Models	14,269	0.817	0.089	0.010	0.052	1.065	80.8%	83.9%	46.8%
IND	Components	2063	0.867	0.170	−0.080	0.117	0.836	63.2%	71.3%	27.8%
	HP	2037	0.844	0.168	0.000	0.110	1.001	67.3%	75.9%	31.3%
	Models	2016	0.821	0.815	−0.053	0.118	0.892	66.4%	73.3%	31.2%
NAME	Components	11,006	0.914	0.118	−0.032	0.076	0.885	71.3%	77.0%	36.6%
	HP	10,817	0.862	0.165	0.059	0.106	1.211	58.2%	63.0%	27.5%
	Models	10,357	0.871	0.151	−0.020	0.082	0.930	70.7%	75.9%	37.1%
NEA	Components	4714	0.919	0.209	−0.035	0.112	0.918	70.4%	76.1%	38.6%
	HP	4686	0.911	0.240	0.124	0.177	1.288	34.7%	39.4%	15.8%
	Models	4627	0.909	0.222	0.026	0.112	1.060	71.0%	75.9%	38.2%
OCE	Components	1644	0.835	0.051	0.007	0.034	1.096	86.5%	88.2%	60.2%
	HP	1605	0.740	0.065	0.023	0.044	1.324	76.4%	77.9%	47.9%
	Models	1457	0.841	0.060	0.008	0.038	1.118	84.5%	86.0%	57.3%
SA	Components	840	0.807	0.076	−0.015	0.049	0.907	85.0%	88.0%	46.3%
	HP	715	0.690	0.118	0.045	0.071	1.250	71.5%	74.4%	41.8%
	Models	821	0.799	0.084	0.006	0.050	1.034	82.8%	85.5%	50.3%
SEA	Components	1328	0.886	0.153	−0.025	0.094	0.933	69.1%	74.9%	38.0%
	HP	1204	0.855	0.219	0.122	0.156	1.319	43.3%	49.8%	16.9%
	Models	1196	0.890	0.151	0.006	0.090	1.015	71.5%	77.3%	39.5%
WNA	Components	6139	0.692	0.076	0.006	0.039	1.077	85.2%	87.1%	58.4%
	HP	6197	0.690	0.110	0.067	0.076	1.804	53.7%	55.5%	29.9%
	Models	5583	0.736	0.084	0.011	0.043	1.123	82.8%	85.0%	54.0%

presents the validation metrics for each region. In OCE, WNA, SA, CSA, EUR, NAME, NEA and ENA regions (a total of 8 regions), Components AOD demonstrates the highest accuracy (R > 0.692, RMSE < 0.209, MAE < 0.112, EE_DT > 70.4%, EE_DB > 76.1%); Models AOD performs similarly to Components AOD (R > 0.736, RMSE < 0.222, MAE < 0.112, EE_DT > 70.7%, EE_DB > 73.9%); HP shows the lowest accuracy (R > 0.665, RMSE < 0.240, MAE < 0.177, EE_DT > 33.3%, EE_DB > 35.9%). Models AOD performs better in the SEA region (R = 0.890, RMSE = 0.151, MAE = 0.090, EE_DT > 71.5%, EE_DB > 77.3%). In the IND region, HP shows relatively better overall performance (RMSE = 0.168, MAE = 0.110, EE_DT > 67.3%, EE_DB > 75.9%). Except for the IND region, HP AOD is systematically overestimated in all regions (BIAS of 0.023–0.124; RMB of 1.211–2.028). In most regions, Models AOD showed a slight overestimation (Bias of 0.006–0.026), but a larger underestimation in the IND region (BIAS of −0.053) and a larger overestimation in the ENA region (BIAS of 0.042). In most regions, the overall bias of Components AOD is minimal, with a slight negative bias. The negative bias was significant in the IND, NAME, and NEA regions, exceeding −0.032. Overall, in terms of the EE_DT metric, Components AOD performed best in 7 out of the 10 regions. In terms of the RMSE metric, Component AOD performed best in 8 out of the 10 regions, Models AOD performed best in the SEA regions, while HP AOD performed best in the IND region. All products exhibited lower retrieval accuracy in East, South, and Southeast Asia, indicating that AOD retrieval remains challenging in regions characterized by high aerosol loading, complex aerosol sources, and diverse land cover types.

3.3.2. Regional Overall Accuracy of AE

Satellite-AERONET AE matchups with AERONET AOD < 0.2 were excluded [40,41]. Figure 10 shows the validation results of POLDER-3 AE retrievals against AERONET AE observations across different regions.

Table 4. Regional statistical metrics of the AE for Components, HP, and Models products compared with long-term AERONET AE observations. Bold values indicate the best-performing result among all products for each metric and region.

Region	Product (AE)	Number	R	RMSE	BIAS	MAE	RMB	=EE AE
CSA	Components	800	0.812	0.361	−0.126	0.276	0.906	77.0%
	HP	788	0.840	0.437	−0.303	0.348	0.776	62.6%
	Models	727	0.695	0.511	−0.304	0.450	0.780	44.0%
ENA	Components	777	0.533	0.451	−0.153	0.349	0.902	65.3%
	HP	683	0.487	0.631	−0.476	0.539	0.696	36.9%
	Models	756	0.338	0.699	−0.531	0.608	0.662	30.4%
EUR	Components	3883	0.699	0.356	−0.085	0.262	0.938	78.1%
	HP	3896	0.703	0.436	−0.286	0.345	0.791	66.4%
	Models	3799	0.594	0.543	−0.397	0.451	0.709	48.4%
IND	Components	1850	0.868	0.240	0.084	0.182	1.096	90.3%
	HP	1836	0.817	0.260	−0.032	0.199	0.963	88.8%
	Models	1829	0.634	0.336	0.009	0.261	1.010	79.7%
NAME	Components	5316	0.785	0.311	0.156	0.252	1.337	80.9%
	HP	5237	0.820	0.234	0.007	0.175	1.015	91.8%
	Models	5193	0.566	0.442	0.277	0.351	1.597	69.0%
NEA	Components	2799	0.772	0.268	0.024	0.203	1.022	89.0%
	HP	683	0.487	0.631	−0.476	0.539	0.696	80.0%
	Models	2740	0.664	0.334	−0.163	0.265	0.853	79.9%
OCE	Components	107	0.777	0.358	0.081	0.281	1.059	73.8%
	HP	99	0.760	0.400	0.131	0.307	1.097	77.8%
	Models	104	0.686	0.408	−0.162	0.326	0.880	67.3%
SA	Components	250	0.705	0.438	0.167	0.331	1.165	68.4%
	HP	250	0.865	0.300	−0.094	0.214	0.908	85.6%
	Models	253	0.766	0.364	−0.060	0.278	0.942	78.3%
SEA	Components	843	0.607	0.277	−0.073	0.204	0.949	86.5%
	HP	805	0.649	0.413	−0.324	0.337	0.773	65.8%
	Models	772	0.579	0.443	−0.362	0.387	0.749	56.5%
WNA	Components	364	0.722	0.376	−0.088	0.279	0.942	77.2%
	HP	393	0.820	0.431	−0.299	0.352	0.798	63.9%
	Models	383	0.594	0.586	−0.412	0.503	0.726	37.3%

presents the statistical metrics for each region. The results show that Components AE achieves the highest R (0.868) in IND, while HP and Models show their highest R in SA (0.865 and 0.766, respectively). In the ENA region, all three products exhibit the lowest R, with 0.533 for Components, 0.487 for HP, and 0.338 for Models. Based on the EE_AE metric, Components AE performs best in 7/10 of the regions (EE_AE = 65.3–90.3%), and HP achieves the best performance in the remaining 3/10 (EE_AE = 77.8–91.8%). The bias of Components AE is small across all regions, below 0.17. The bias of HP AE varied considerably across different regions (−0.476 to 0.131), primarily exhibiting negative bias, indicating its underestimation of AE and spatial instability in retrieval. Models AE showed a larger negative bias and greater variability in bias across different regions (−0.531 to 0.277). The RMSE of AE ranges between 0.23 and 0.7, so setting EE_AE to ±0.4 appears reasonable.

3.3.3. Regional Stability Assessment

The stability of POLDER-3 AOD in each region was analyzed (see

Table 5. Summary of stability metrics for AOD bias across regions. Bold values indicate that the metric meets the Global Climate Observing System (GCOS) requirement (less than 0.02 per decade).

Region	Product	Slope	Standard Deviation	Mean
CSA	Components	0.018	0.030	0.024
	HP	−0.042	0.067	0.055
	Models	−0.053	0.067	0.060
ENA	Components	0.038	0.028	0.033
	HP	0.034	0.030	0.032
	Models	0.032	0.023	0.028
EUR	Components	0.046	0.034	0.040
	HP	0.021	0.023	0.022
	Models	0.053	0.036	0.045
IND	Components	0.106	0.079	0.093
	HP	0.101	0.084	0.093
	Models	0.129	0.091	0.110
NAME	Components	0.059	0.048	0.054
	HP	0.080	0.067	0.074
	Models	0.068	0.052	0.060
NEA	Components	0.005	0.031	0.018
	HP	0.023	0.024	0.024
	Models	0.019	0.021	0.020
OCE	Components	0.015	0.019	0.017
	HP	0.002	0.029	0.016
	Models	0.026	0.024	0.025
SA	Components	0.011	0.032	0.022
	HP	0.064	0.048	0.056
	Models	−0.001	0.036	0.019
SEA	Components	0.062	0.053	0.058
	HP	−0.036	0.065	0.051
	Models	0.072	0.061	0.067
WNA	Components	0.041	0.028	0.035
	HP	0.043	0.031	0.037
	Models	0.042	0.030	0.036

). POLDER-3 AOD shows potential to meet the GCOS stability target of 0.02 in the NEA, OCE, and SA regions. However, attention should still be paid to regions where the two metrics differ, specifically, where the slope is small, but the standard deviation is large, indicating that although the bias trend is not significant, the interannual bias varies widely. In the remaining seven regions, stability ranges between 0.022 and 0.110 per decade, with stability exceeding 0.05 per decade in the CSA, IND, NAME, and SEA regions. Note that the temporal bias trends are positive in most regions except CSA. Therefore, POLDER-3-derived AOD trends should be interpreted with caution over most global regions. The differences in AOD stability across different regions are related to regional aerosol and surface conditions. Previous studies have also shown that MODIS and VIIRS DB products exhibit stability differences across different regions [22,23].

Table 6. Summary of stability metrics for AE bias across different regions.

Region	Product	Slope	Standard Deviation	Mean
CSA	Components	0.231	0.227	0.229
	HP	0.146	0.202	0.174
	Models	0.328	0.241	0.285
ENA	Components	0.066	0.109	0.088
	HP	−0.008	0.149	0.079
	Models	−0.059	0.134	0.097
EUR	Components	−0.054	0.112	0.083
	HP	−0.066	0.153	0.110
	Models	−0.167	0.157	0.162
IND	Components	−0.034	0.068	0.051
	HP	−0.148	0.134	0.141
	Models	−0.199	0.173	0.186
NAME	Components	0.095	0.070	0.083
	HP	0.066	0.072	0.069
	Models	−0.020	0.086	0.053
NEA	Components	−0.073	0.069	0.071
	HP	−0.118	0.112	0.115
	Models	−0.046	0.073	0.060
OCE	Components	−0.310	0.539	0.425
	HP	−0.512	0.961	0.737
	Models	−0.583	0.421	0.502
SA	Components	0.346	0.327	0.337
	HP	0.068	0.176	0.122
	Models	0.542	0.393	0.468
SEA	Components	−0.055	0.059	0.057
	HP	−0.253	0.248	0.251
	Models	0.000	0.101	0.051
WNA	Components	−0.231	0.218	0.225
	HP	−0.102	0.200	0.151
	Models	−0.251	0.262	0.257

presents the statistical results of AE stability metrics. HP performs best overall in four regions (CSA, ENA, SA, and WNA regions), with stability of 0.174, 0.079, 0.122, and 0.151 per decade, respectively. Components AE performs best overall in three regions (EUR, IND, and OCE), with stability of 0.083, 0.051, and 0.425 per decade, respectively. Model AE achieves the best performance in three regions (NAME, NEA, and SEA), with stability of 0.053, 0.060, and 0.051 per decade, respectively. All POLDER-3 AE exhibits lower stability in the CSA, OCE, and WNA regions, exceeding 0.15/decade. Its stability in the ENA and NAME regions is relatively better, better than 0.10/decade.

3.4. Site-Scale Comparison of POLDER-3 Aerosol Products

To better illustrate the performance comparison among the three products, validation metrics across different sites are compared. To enhance statistical robustness, data with fewer than 20 satellite-site matches were discarded, resulting in a total of 338 sites for AOD and 204 sites for AE.

3.4.1. Site-Scale Comparison of AOD

Among the POLDER-3 AOD products, the percentage of AERONET sites where each product achieves the best statistical performance is shown in Figure 11. In terms of the R metric, Components AOD performs best at 45.0% of the sites, followed by Models AOD, which performs best at 41.7% of the sites, while HP AOD performs best at only the remaining 13.3% of the sites. For error metrics (including RMSE and MAE), Components AOD performs best at approximately 70% of the sites, Models AOD at approximately 20% of the sites, and HP AOD at approximately 10% of the sites. Then, all sites were grouped by region to analyze their regional performance. As shown in Figure S1, for the R, Components AOD performs best in 5/10 of the regions (including IND, CSA, NEA, OCE, NAME), while Models AOD performs best in the other 50% of regions (including EUR, SA, SEA, WNA, and ENA). HP AOD does not perform best in any region. For RMSE, Components AOD performs best in all regions. These results demonstrate that Components AOD not only outperforms HP and Models AOD in overall performance, but also consistently achieves superior results in most regions of the world.

3.4.2. Site-Scale Comparison of AE

A site-by-site comparison of the POLDER AE products is shown in Figure 12. Components AE performs best at 45.6–69.6% of the sites globally, depending on the statistical metric used, followed by HP AE (25.5–41.7%), and Models AE performs worst (4.9–12.7%). Similarly, all sites were then statistically grouped by region to analyze their regional performance. As shown in Figure S2, for the R metric, Components AE performs best in 7/10 of the regions (including IND, CSA, SEA, NEA, OCE, WNA, and ENA); HP AE performs best in 6/10 of the regions (EUR, CSA, SA, OCE, WNA, and NAME); and Models AE performs worst in all regions. For RMSE, Components AE performs best in 8/10 of the regions (EUR, IND, CSA, SEA, NEA, OCE, WNA, and ENA); HP AE performs best in 2/10 of the regions (SA and NAME).

3.5. Spatial Distribution Pattern

The spatiotemporal distributions of the retrievals from the three products are compared to elucidate their consistency.

3.5.1. AOD Spatial Distribution Patterns

The multi-year means and differences among the three AOD products were compared at a spatial resolution of 0.1° (see Figure 13). Overall, the spatial distribution patterns of the three AOD products are largely consistent. The North Africa and the Middle East region is dominated by natural dust aerosols, South Africa by biomass burning aerosols, Northeast Asia and the Indian subcontinent by anthropogenic pollution. Therefore, the AOD in these regions is relatively high, exceeding 0.4. In contrast, Eastern and Western North America, Europe, and Oceania generally exhibit lower AOD loadings. As shown in Figure 13d,f, the annual mean differences between HP AOD and the other two AOD products are relatively large and positive. In 69.37% (60.31%) of global pixels, the difference between HP AOD and Components (Models) AOD is within ±0.05. In some regions, including Western North America, Central and South America, North Africa and the Middle East, South Africa, and Northeast Asia, the differences between HP and the other two products exceed 0.15. As shown in Figure 13e, Models and Components AOD are largely consistent, with 95.84% of pixels showing AOD differences within ±0.05. The seasonal mean AOD and its differences for the three POLDER-3 GRASP products globally were analyzed, as shown in Figures S3 and S4. The differences in seasonal mean AOD distribution patterns among different products are similar to the differences in annual mean AOD distribution patterns.

3.5.2. AE Spatial Distribution Patterns

The multi-year means and differences among different AE products were analyzed, as shown in Figure 14. The AE in the North Africa and the Middle East regions is generally low (typically less than 0.5), primarily due to strong dust emissions. Among the three products, Components AE shows generally higher values across regions, while Models and HP exhibit relatively lower values, consistent with the validation results shown in Figure 3 and Figure 4. As shown in Figure 14d, the annual mean difference between Components and HP AE is relatively large: 55.95% and 79.32% of pixels fall within ±0.2 and ±0.4. The annual mean difference between Components and Models AE falls within ±0.2 and ±0.4 for 83.32% and 93.18% of pixels. The annual mean difference between Models and HP AE falls within ±0.2 and ±0.4 for 62.75% and 87.58% of pixels. This indicates significant discrepancies and poor consistency among AE retrievals from three products. Compared to AOD, AE retrieval is more sensitive to the setting of aerosol types (components or parameters). The HP algorithm retrieves all aerosol parameters used for radiative transfer simulation, the Components algorithm is set to an internal mixture of five aerosol components [11], and the Models algorithm uses an external mixture of four aerosol models [12]. Different GRASP algorithms have different aerosol model settings, which lead to differences in AE retrieval. Figures S5 and S6 show the seasonal mean AE and their differences for the three POLDER-3 GRASP products across global regions. The seasonal mean difference is similar to the annual mean difference.

4. Conclusions

In this study, the global and regional accuracy, consistency, stability, and spatiotemporal distribution patterns of AOD and AE retrievals from the three POLDER-3 GRASP products were comprehensively evaluated and inter-compared. The major findings are summarized as follows:

(1)

Global and regional accuracy validation: the overall validation results indicate that the three POLDER-3 GRASP AOD products show good consistency with observations from all AERONET sites and long-term AERONET sites (R > 0.879). Components AOD demonstrates superior overall statistical metrics (BIAS within −0.011, RMSE = 0.114, and Within GCOS = 45.7%), followed by Models AOD (BIAS within 0.009, RMSE < 0.138, and Within GCOS > 43.4%), and the HP AOD showed the worst validation metrics (BIAS within 0.071, RMSE < 0.158, and Within GCOS > 27.6%). The BIAS metric shows that the HP product overestimated AOD. For AE, the Components AE performs best (R > 0.834, RMSE < 0.321, and Within EE_AE > 81.7%), followed by HP AE (R > 0.820, RMSE < 0.366, and Within EE_AE > 76.9%), and Models AE shows relatively lower accuracy (R < 0.629, RMSE > 0.459, and Within EE_AE < 63.8%). Both HP and Models products underestimate the AE (BIAS < −0.1), and the Components product slightly overestimates AE (BIAS = 0.018). Components AOD performs best in 8/10 regions globally, Models AOD performed best in the SEA region, and HP AOD performed best in the IND region. For AE, Components AE performs best in the 8/10 regions globally. In the remaining two regions, the HP AE shows the best performance. The site-by-site RMSE comparison results show that the Components AOD performs best in 69.8% of the sites, and the Components AE performs best in 68.1% of the sites.

(2)

Global and regional stability assessment: The results show that the stability metrics of the three AOD products range from 0.034 to 0.036 per decade, and none of them meet the GCOS stability requirement (i.e., within 0.02 per decade). However, in the Oceania region, both Components and HP meet the GCOS requirement (0.017 per decade and 0.016 per decade); in the South Africa region, Models AOD meets the GCOS requirement (0.019 per decade); and in the Northeast Asia region, Components and Models AOD meet the GCOS requirement (0.018 per decade and 0.020 per decade). For the AE, the stability metrics are 0.028 per decade for Components, 0.042 per decade for HP, and 0.077 per decade for Models. In this study, slope and standard deviation are used, each with its own advantages. Therefore, it is necessary to combine the two metrics to comprehensively assess stability.

(3)

Regarding spatiotemporal distribution patterns, regions such as North Africa-Middle East, South Africa, and Northeast Asia exhibit relatively high AOD loadings, while North America, Europe, and Oceania generally show lower AOD loadings. The spatial distribution patterns of Components AOD and Models AOD show high consistency, with over 95.84% of pixels exhibiting differences smaller than ±0.05. HP’s AOD difference from the other two products is within ±0.05 in less than 70% of global pixels. Spatial distribution pattern of HP AOD is systematically higher than that of Components AOD and Models AOD, which is consistent with the validation results indicating that HP overestimates AOD. For the AE parameter, the three products showed significant spatial distribution divergence. The difference between Components AE and HP AE is less than ±0.2 (±0.4) at 55.95% (79.32%) of pixels. This indicates inconsistent AE retrievals among GRASP algorithm variants, which is due to the different aerosol model setting strategies of the GRASP algorithms.

(4)

Product usage recommendation: overall, Component AOD demonstrates the highest validation accuracy globally and across 8 out of 10 regions, making it the recommended choice for the application. Users should exercise caution when applying POLDER-3/GRASP products to long-term trend analyses due to their relatively poor temporal stability. The long-term accuracy variations in these products may obscure true temporal changes in AOD and AE. The time-dependent bias characteristics of different AOD products are highly correlated (R > 0.95), suggesting that the AOD bias may be systematically inherent in the GRASP algorithm or caused by POLDER-3 radiometric calibration errors. The differences in spatial distribution patterns among the three products show higher consistency between Components AOD and Models AOD, suggesting reasonable spatial representativeness. In contrast, the poor agreement in AE among the three products indicates a need to develop a unified GRASP algorithm to improve the accuracy and spatiotemporal representation of AE retrieval.