1 Introduction

Atmospheric aerosols are solid and liquid particles with a size between 0.01 and 100 nm, which have complex physical, chemical, and optical characteristics (Nichol et al. 2020; Tian et al. 2018). Aerosols have a considerable impact on climate, atmospheric environment quality, human health, and related matters (Ali et al. 2020; Kaiser and Granmar 2005; Kaufman et al. 2002; Kulmala et al. 2013; Lelieveld et al. 2015; Sun and Ariya 2006). Aerosols can scatter or absorb solar radiation, causing changes in the earth–air radiation budget and affecting the radiation balance of the earth system (Butt et al. 2016; Dubovik et al. 2012). At the same time, due to the irregular spatial and temporal distribution of aerosols, which varies greatly with time, their optical and physical characteristics are unstable. Therefore, long-term observation of aerosols is a key requirement for studying the characteristics of aerosols (Bilal et al. 2014; Han et al. 2018; Miao et al. 2020; Misra et al. 2008). Aerosols are also responsible for environmental pollution; they are major components of haze, dust, and other extreme weather conditions. The study of aerosols can also deepen researchers’ understanding of their environmental effects and provide theoretical support for decision-makers to introduce corresponding environmental protection policies (Development 2014; Edenhofer and Seyboth 2013; Gong et al. 2015; Magistrale 1992; Tie et al. 2009; Zhang et al. 2014a).

Aerosol optical depth (AOD) is the most basic optical characteristic parameter of atmospheric aerosols and is the key factor in characterizing atmospheric turbidity and determining the climatic effect of aerosols(Zhang et al. 2014b). AOD is often used in studies of how aerosols affect regional climates and the temporal and spatial variation characteristics of the atmosphere (Jing et al. 2018; Kang et al. 2016; Rosenfeld 2000; Wang et al. 2019). At present, research on AOD depends mainly on satellite-based remote sensing and ground-based remote sensing dataset. The National Aeronautics and Space Administration (NASA) has established the ground-based aerosol robotic network (AERONET) around the world. Also, China has established the ground-based China aerosol remote sensing network (CARSNET) in the country to conduct a long-term observation of the aerosol's variation features. The results obtained from both these ground-based stations showed good findings (Che et al. 2014; Kleidman et al. 2005; Qin et al. 2018; Shi et al. 2019). The aerosol data observed by ground-based remote sensing are highly accurate, but the distribution of sites is very sparse, and the spatial distribution of aerosols features over large areas and at large scale cannot be obtained (Che et al. 2015; Ming et al. 2017). Satellite passive remote sensing can obtain AOD retrievals over large areas, as is done by the moderate resolution imaging spectroradiometer (MODIS) of onboard on Terra and Aqua satellites, which can make up for the deficiency that the ground observation data cannot represent the spatial distribution and the overall trend of aerosol changes. Besides, the active lidar remote sensing satellite CALIPSO (cloud-aerosol lidar and infrared pathfinder satellite observation), is equipped with cloud-aerosol lidar with orthogonal polarization (CALIOP), which provides not only large-scale, planar aerosol optical properties products but also three-dimensional spatial and temporal information of the aerosol vertical distribution (Marchant et al. 2020; Winker et al. 2007, 2003, 2009). This provides a powerful tool for the more comprehensive acquisition of aerosol optical and physical characteristics (Kato et al. 2012; Yu et al. 2015).

MODIS AOD products have the advantages of high retrieval accuracy, long time series, and good spatial coverage, which have been validated by a large number of international scholars to have significant application value in aerosol research (Ali and Assiri 2019; Ali et al. 2019; Tian et al. 2018). Since MODIS aerosol products are updated frequently, many scholars have carried out a large number of verification studies of new MODIS AOD products by comparing them with AERONET or CARSNET ground-based remote sensing data (Bilal et al. 2018; Che et al. 2015; Dubovik et al. 2012; He et al. 2017; Shi et al. 2019; Wang et al. 2019). Zhang et al. (2019b) evaluated the performance of MODIS Collection C6.1 (C6.1) AOD products over the Yellow River basin (YERB) by comparing the AOD data from ground-based CARSNET site and obtained good results (Zhang et al. 2019b). The study suggested that no single satellite AOD product performed satisfactorily over YERB. On the other hand, the verification of CALIPSO satellite products has been carried out less frequently by previous studies (Zhang et al. 2019a). The main reason might be that the location of the substellar point of CALIPSO is difficult to match precisely with the few ground-based sites, making it difficult to verify the CALIPSO aerosol products. Therefore, we decided to compare the MODIS and CALISPO products with each other to indirectly verify the performance of CALIPSO, based on the previous research results of MODIS-CARSNET obtained from the studies of Zhang et al. (2019a) and Zhang et al. (2019b). On the other hand, the performance of CALIPSO was good in studying the properties of the lowest aerosol layers over YERB. So it is important to the MODIS- and CALIPSO-derived AOD over YERB (Kumar et al. 2018; Shi et al. 2020; Yang et al. 2020).

In recent years, as the environmental issues faced by China have grown to an unprecedented scale, researchers have placed much emphasis on studying the optical, physical, and distribution characteristics of aerosols in the Yangtze River delta, Beijing–Tianjin–Hebei, the Pearl River delta, and other important developed areas (Bilal et al. 2019, 2013, 2014; Deng et al. 2008; Jie et al. 2017; Liu et al. 2008; Shen et al. 2015; Xia et al. 2016). Those authors obtained the long-term temporal variation and spatial distribution of the aerosols, but less research has been carried out with regard to the aerosol distribution characteristics over YERB (Zhang et al. 2019b). The YERB is located in the north-central part of mainland China and lies in an east–west direction across the country. The sub-regions of the YERB have obvious differences in topographical distribution. The regional economies and industrial development of the YERB sub-regions have even more imbalance. Long-term accurate monitoring of aerosol optical physical characteristics and their spatiotemporal distributions over each sub-region of the YERB has important practical significance for the protection of the atmospheric environment over the YERB (Zhang et al. 2019b). According to the characteristics of the YERB, this paper evaluates the performance of the CALIPSO AOD product over the YERB by comparing it with the Aqua MODIS C6.1 AOD products. The study is organized as follows: the study area is described in Sect. 2, the data used and the methodology are described in Sect. 3, the results and discussion are presented in Sect. 4, and finally, the conclusions are summarized in Sect. 5.

2 Study Area

The YERB is located between 95° E and 120° E and between 30° N and 45° N (Fig. 1). Due to the large area of the YERB and to better study the characteristics of AOD in different sections of the YERB, this paper divides the YERB into three regions; the upper reaches of the Yellow River, with forest mountains and perennial snow on the mountain peaks (YERB1: 30° N–38° N, 95° E–105° E); the middle reaches of the Yellow River, dominated by the loess plateau (YERB2: 33° N–43° N, 105° E–112° E); and the lower reaches of the Yellow River, dominated by the plain (YERB3: 31° N–39° N, 112° E–119° E). The Yellow River originates from the northern foot of Bayan Kara Mountain in the central part of Qinghai province and flows through nine provinces and regions, namely Qinghai, Gansu, Sichuan, Ningxia, Inner Mongolia, Shaanxi, Shanxi, Henan, and Shandong, with a total length of 5464 km. It is about 1900 km long from east to west and 1100 km wide from north to south, draining a watershed area of about 795,000 km2 (Wang et al. 2007).

Fig. 1
figure 1

Geographical locations of the Yellow River Basin (YERB). The color bar represents the elevation

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The YERB is a vast area with complex terrain, spanning four geomorphic units: the Qinghai–Tibet plateau, the Inner Mongolia Plateau, the Loess Plateau, and the North China plain. The height difference between east and west is significant (the maximum height difference is 4480 m), and the range of climates along the basin is quite dramatic. From a monsoon perspective, the area west of Lanzhou in the upper reaches of the Yellow River (YERB1) belongs to the Qinghai–Tibet plateau monsoon region, while the other areas are temperate and subtropical monsoon regions. The temperature is warmer in the southeast (YERB3) than in the northwest (YERB1) and is cooler over mountains than over plains in the YERB. The economy of the YERB is relatively undeveloped except for the estuaries, especially in the upper reaches of the Yellow River in the west (YERB1), which is an area of lower elevation (Wang et al. 2007; Yang et al. 2020). Therefore, the study of the AOD characteristics in the YERB is of great scientific significance to reveal the influence of aerosols on climate under different regional environmental conditions.

3 Data Used and Methodology

3.1 MODIS C6.1 Data

The Aqua-MODIS Level 2 C6.1 aerosol products were downloaded from the Level-1 and Atmosphere Archive and Distribution System Distributed Active Archive Center (LAADS DAAC) (https://ladsweb.modaps.eosdis.nasa.gov/). The inversion of the MODIS C6.1 AOD product is based mainly on the dark target (DT) algorithm and the deep blue (DB) algorithm. The DT algorithm was developed to provide AOD retrievals over dark surfaces, and currently, it provides AOD retrievals over land at 3 km or 10 km resolutions. The results show that, on a global scale, more than 70.6% of DT retrievals are within the estimated confidence envelope of one standard deviation, which is approximately ± (0.05 + 15%) (Tian et al. 2018). The DB algorithm was developed to retrieve aerosol properties over the bright desert (Bilal et al. 2014; Gupta et al. 2016; Jie et al. 2017; Levy et al. 2013). The expected error (EE) of the DB algorithm for AOD over land is approximately ± (0.05 + 20%), and 79% of retrievals agree within the EE of the corresponding AERONET observation (Hsu et al. 2013; Shi et al. 2019). In this paper, Aqua-MODIS C6.1 (MYD04) DT AOD retrievals at 3 km (DT3K) and 10 km (DT10K) resolutions, the DB AOD retrievals at 10 km (DB10K), and combined DT and DB AO retrievals at 10 km resolution (DTB10K) are obtained for comparison with CALIPSO data. Table 1 shows the scientific data set of the Aqua-MODIS C6.1 AOD products used in this study between January 1, 2003, and December 31, 2017. In this study, only the best quality flag (QA = 3) data were considered.

Table 1 Scientific data set of the Aqua-MODIS C6.1 AOD products used in this study from January 1, 2003, to December 31, 2017
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3.2 CALIPSO Data

CALIPSO is an earth-probing satellite project started jointly by NASA’s Langley Research Center (LaRC) and the National Space Research Center of France in 2006. CALIPSO provides the three-dimensional distribution of clouds and aerosols at global scales every 16 days. CALIOP is one of the main instruments on the CALIPSO satellite. It has one 1064 nm wavelength channel and two 532 nm wavelength polarization channels. It can observe clouds and aerosols backscattering information between latitudes of 82° north and south (Huang et al. 2008; Winker et al. 2007, 2009; Yu et al. 2015). CALIOP can detect the vertical distribution of clouds and aerosols more accurately by utilizing the backscatter it receives at each level within the atmosphere. At the same time, CALIOP is an active remote sensing instrument that can operate during both day and night without interference from the earth’s surface, and free from the excessive dependence of passive remote sensing on short-wave solar radiation (Liu et al. 2008; Omar et al. 2009; Winker et al. 2007). Therefore, the CALIPSO satellite provides a clean and comprehensive set of measurements for the study of the vertical structure and transmission of aerosols.

The CALIPSO lidar has six main levels of data: levels 4, 3, 2, 1B, 1A, and 0. Level 2 data products include three types, namely: vertical feature layer products, layer products, and profile data products (Winker et al. 2003). The aerosol layer products are generated based on the raw CALIPSO profile data (https://www-calipso.larc.nasa.gov/about/atrain.php) using the selective iterated boundary locator (SIBYL) algorithm (Winker et al. 2009; Yu et al. 2015). Using SIBYL, the feature layers are detected in every raw data profile, then the amount (number) of aerosol feature layers (N) and the heights of the feature layer’s base (HBN) and top (HTN) are obtained. The data contain at most eight vertical layers (N ≤ 8) spanning the entire atmosphere in every raw data profile.

In this study, the AOD of the lowest aerosol layer (AOD1, if N = 1 in Eq. (1)) and the sum of the AOD from all the aerosol layers (AODS, Eq. (2)) were the main variables used for comparative analysis with the four MODIS products:

$${\text{AOD}}_{N} = \mathop \int \limits_{{{\text{HB}}_{N} }}^{{{\text{HT}}_{N} }} \delta \left( z \right){\text{d}}z; \quad N = 1,2, \ldots ,7,8,$$
(1)
$${\text{AOD}}_{{\text{S}}} = \mathop \sum \limits_{1}^{N} {\text{AOD}}_{N} ; \quad N = 1,2, \ldots ,7,8.$$
(2)

3.3 Comparison Methods

Since both CALIPSO and Aqua are part of the "A-Train" constellation and the data are spaced just a few minutes apart, there is only a small observation time difference between them, which allows them to be used for a comparative study. In this paper, CALIPSO and Aqua daytime Level 2 aerosol layer products at 550 nm were mainly used, and the selected data overlap time range was from January 1, 2007, to December 31, 2014. In the study area, MODIS produces multiple images every day, but they do not completely cover the study area, so multiple images need to be combined. Moreover, the CALIPSO data are vertical linear data, so the two types of data cannot be directly compared. Meanwhile, since the spatial resolution of each pixel in the MODIS image is 3 km or 10 km and there is no spatial resolution information of the substellar point of CALIPSO, it is very complex to match and screen the location of the MODIS pixel and the substellar point of the CALIPSO orbit transit. To facilitate data matching on the same time series, the MODIS and CALIPSO data applied in the research area were interpolated and resampled onto a grid of 1° × 1°, and the data over the research area were clipped out using a vector mask file. The linear mean interpolation technique is used, and if the latitude and longitude are in one grid, the mean value is considered as the final value. Then the data of the study area were statistically analyzed and compared on a seasonal and yearly basis for each of the three sub-regions of the YERB.

To report accuracy and errors in the AOD retrievals, the following statistical parameters are used to evaluate the correlation of several values: the slope, y-intercept, Pearson’s correlation (R), root mean square error (RMSE, Eq. (3)), expected error (EE, Eq. (4)), the relative mean bias (RMB, Eq. (5)), and mean absolute error (MAE, Eq. (6)).

$${\text{RMSE}} = \sqrt {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {{\text{AOD}}_{{\left( {{\text{MODIS}}} \right)_{i} }} - {\text{AOD}}_{{\left( {{\text{CALIPSO}}} \right)_{i} }} } \right)^{2} } ,$$
(3)
$${\text{EE}} = \pm \left( {0.05 + 0.15{\text{AOD}}_{{{\text{MODIS}}}} } \right),$$
(4)
$${\text{RMB}} = \frac{{{\text{AOD}}_{{\left( {{\text{MODIS}}} \right)_{i} }} }}{{{\text{AOD}}_{{\left( {{\text{CALIPSO}}} \right)_{i} }} }},$$
(5)
$${\text{MAE}} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {{\text{AOD}}_{{\left( {{\text{MODIS}}} \right)_{i} }} - {\text{AOD}}_{{\left( {{\text{CALIPSO}}} \right)_{i} }} } \right|.$$
(6)

4 Results and Discussion

4.1 Comparison of Aqua-MODIS C6.1 AOD with CALIPSO AOD

Figure 2 shows scatter plots of the MYD04 C6.1 DT3K AOD against CALIPSO AOD for the period of January 1, 2007, to December 31, 2014, over the YERB in spring, summer, autumn, and winter. In Fig. 2, a total of 1427 observations of DT3K data are matched with the CALIPSO data. The results show poor correlation between DT3K and CALIPSO (AOD1 and AODS); for example, R is only 0.35 and 0.40 for AOD1 and AODS, respectively; RMSE was 0.35 for AOD1 and 0.34 for AODS; 35.18% of retrievals were within the EE for AOD1 and 52.07% for AODS; 7.71% and 12.89% of retrievals were below the EE, and 57.11% and 35.04% of retrievals were above, for AOD1 and AODS, respectively. Moreover, the values of RMB (1.90 and 1.37) and MAE (0.18 and 0.10) were significantly higher. According to these results, the DT3K AOD values were significantly greater than those of CALIPSO, and the differences between DT3K and AOD1 are significantly higher than the differences between DT3K and AODS. This is because AOD1 only represents the AOD of the lowest aerosol, while AODS represents the sum of the AOD over all layers. The AOD product of MODIS considers the whole atmosphere, not just the lowest aerosols, so the matching between AODS and C6.1 DT3K is better.

Fig. 2
figure 2

Validation of the CALIPSO AOD1 (a) and CALIPSO AODs (b) for the period of January 1, 2007 to December 31, 2014 against MYD04 C6.1 DT3K (a) AOD for the period of January 1, 2003 to December 31, 2017 over the YERB. The black solid line is the 1:1 line, the black dashed lines indicate the envelope of the EE, and the blue line is the regression line

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Table 2 provides the statistical parameters of MYD04 C6.1 DT3K versus the CALIPSO AOD for the four seasons. The comparison shows that the degree of matching of MYD04 C6.1 DT3K-CALIPSO AOD1 and MYD04 C6.1 DT3K-AODS in different seasons has a similar and large seasonal difference. Among these parameters, the value of the correlation coefficient R is within the range of 0.19–0.69 and 0.19–0.78 for AOD1 and AODS, respectively. The proportion of matching data falling within the EE is 24.40–45.76% and 43.16–63.24% for AOD1 and AODS, respectively. Furthermore, with the values of R being largest in summer (0.78) and the values within EE (63.24%) being largest in autumn, this numerical behavior indicates that, despite the good correlation coefficient, the C6.1 DT3K products still could not meet the EE standard. Almost 41.39–70.78% and 15.68–50.94% of the collocations fell below the EE for AODS and AOD1, respectively; at the same time, except for the value of the RMB in autumn, which is 1.02, the values are between 1.37 and 2.51, indicating that all of the C6.1 DT3K values match the CALIPSO AOD more closely in the YERB region.

Table 2 Comparison of the retrieval accuracy between the CALIPSO AOD for the period of January 1, 2007 to December 31, 2014 and the MYD04 C6.1 DT3K AOD for the period of January 1, 2003 to December 31, 2017 products in the four seasons
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Figure 3 shows the comparative results of MYD04 C6.1 DT10K and CALIPSO AOD. A total of 1211 matches are successfully obtained for CALIPSO AOD1 and AODS. Compared with AOD1, the matching result of the CALIPSO AODS are good, with high R values (0.78), nearly 51.78% of the AOD retrievals falling into the EE, and an RMB of 1.2, resulting in only 12% underestimation compared to the MYD04 C6.1 DT10K AOD.

Fig. 3
figure 3

Validation of the CALIPSO AOD1 (a) and CALIPSO AODS (b) for the period of January 1, 2007 to December 31, 2014 against MYD04 C6.1 DT10K AOD for the period of January 1, 2003 to December 31, 2017 over the YERB. The black solid line is the 1:1 line, the black dashed lines indicate the envelope of the EE, and the blue line is the regression line

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As shown in Table 3, the matching result is a little different for the four seasons, with the R values (AOD1: 0.69–0.78; AODS: 0.72–0.84), the RMSE values (AOD1: 0.12–0.17; AODS: 0.11–0.16), and the within-EE values (AOD1: 23.38–43.38%; AODS: 44.40–60.78%), respectively, and the best matches are observed in spring. On the whole, the C6.1 DT10K AOD tends toward overestimation compared to CALIPSO AOD retrievals for the spring, summer, and winter, except for the AODS with MAE = 0.01 and RMB = 0.96 in autumn.

Table 3 Comparison of the retrieval accuracy between the CALIPSO AOD for the period of January 1, 2007 to December 31, 2014 and the MYD04 C6.1 DT10K AOD for the period of January 1, 2003 to December 31, 2017 products in the four seasons
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Compared with MYD04 C6.1 DT3K, the MYD04 C6.1 DT10K product has fewer matches in every season but shows large overestimations. This phenomenon is caused mainly by the fact that the MYD04 C6.1 DT3K images had higher resolutions. On the other hand, the reason could be that C6.1 DT10K has few retrievals for the water system over the YERB, as mentioned by (Zhang et al. 2019b).

Figure 4 shows the validation of the MYD04 C6.1 DB10K AOD and CALIPSO AOD over the YERB area. As shown in Fig. 4, a total of 1799 MYD04 C6.1 DB10K-CALIPSO matches are available for AOD1 and AODS. The C6.1 DB10K AOD is well-matched with the CALIPSO AOD1 and AODS, respectively. That is, the R values are 0.78 and 0.84 and the percentages within the EE are 34.24 and 53.25%, respectively. A slight overestimation occurs accompanied by MAE values of 0.12 and 0.05, respectively.

Fig. 4
figure 4

Validation of the CALIPSO AOD1 (a) and CALIPSO AODS (b) for the period of January 1, 2007 to December 31, 2014 against MYD04 C6.1 DB10K AOD for the period of January 1, 2003 to December 31, 2017 over the YERB. The black solid line is the 1:1 line, the black dashed lines indicate the envelope of the EE, and the blue line is the regression line

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Table 4 provides the accuracy statistics for the MYD04 C6.1 DB AOD and CALIPSO AOD products for each season. The accuracy of both products shows apparent seasonal variation in AOD1 and AODS. Comparing the result for all seasons with DT3K and DT10K, there is some degree of improvement in the result of matching of the CALIPSO AOD (AOD1 and AODS) and MYD04 C6.1 DB10K product, with R values of 0.77–0.88 for AOD1 and 0.85–0.90 for AODS, respectively, except for DT10K in spring. Comparing the MYD04 C6.1 DB AOD and CALIPSO AOD1 or AODS, the best matches are observed in winter (AOD1 = 0.88) and autumn (AODS = 0.90), with higher R values, but the MAE (0.07, 0.12), RMB (1.38, 1.73), and within-EE (50%, 36.97%) values are comparatively better in autumn than in winter for the CALIPSO AOD1, while the lowest matches are observed in spring. Moreover, unlike the MYD04 C6.1 DT3K and MYD04 C6.1 DT10K products, the MYD04 C6.1 DB10K products show good retrieval accuracy: 450, 450, 450, and 449 matches are found for the four seasons, as the DB algorithm can retrieve AOD over complex and bright urban surfaces, whereas the DT algorithm cannot retrieve AOD over such areas. A similar result was also reported by Zhang et al. (2019b).

Table 4 Comparison of the retrieval accuracy between the CALIPSO AOD for the period of January 1, 2007 to December 31, 2014 and the MYD04 C6.1 DB10K AOD for the period of January 1, 2003 to December 31, 2017 products in the four seasons
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The evaluation of the MYD04 C6.1 DTB10K AOD and the CALIPSO AOD products over the YERB is presented in Fig. 5. We found 1788 matches of AOD retrievals from MYD04 C6.1 DTB10K and CALIPSO products, with high R values (0.76 and 0.83 for CALIPSO AOD1 and AODS products, respectively, and low RMSE values (0.14 and 0.12 for CALIPSO AOD1 and AODS products, respectively. Meanwhile, 51.06% and 59.01% of AOD1 and AODS retrievals, respectively, fell within the EE. At the same time, the RMB values are 1.47 and 1.07, respectively, for AODs and AOD1, indicating that the C6.1 DTB10K AOD product is overvalued by only 47% and 7% for CALIPSO AODS and AOD1 products, respectively. These results indicate that the value of C6.1 DTB10K AOD is slightly larger than that of CALIPSO, and the degree of matching between AODS and C6.1 DTB10K is better.

Fig. 5
figure 5

Validation of the CALIPSO AOD1 (a) and CALIPSO AODS (b) for the period of January 1, 2007 to December 31, 2014 against MYD04 C6.1 DTB10K AOD for the period of January 1, 2003 to December 31, 2017 over the YERB. The black solid line is the 1:1 line, the black dashed lines indicate the envelope of the EE, and the blue line is the regression line

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Table 5 provides the accuracy statistics for the MYD04 C6.1 DTB10K products in each season compared to the CALIPSO AOD products over the YERB region. In the comparison of the MYD04 C6.1 DTB10K product and CALIPSO AOD products, 444, 450, 450, and 444 matches are found for the four seasons. Taking the comparison of AODS and MYD04 C6.1 DTB10K as an example, it reveals high accuracies, with within-EE values of 45.05, 53.33, 69.33, and 68.24% for the four seasons (spring, summer, autumn, and winter), along with high R values (0.76, 0.90, 0.93, 0.88) and small RMSE values (0.14, 0.11, 0.17, 0.10). The seasonal variation of the maximum within-EE value is 69.33% during autumn and the minimum is 45.05% for spring. Unlike the above products, the overall value of CALIPSO AODS is slightly higher than that of MYD04 C6.1 DTB10K product, as shown by a negative MAE (0.01, 0.04), while the RMB (0.96, 0.83) is less than 1 in both summer and autumn, respectively. The reason might be that the DTB algorithm not only considers the volume of the target but also includes the dark blue algorithm, which is relatively comprehensive, making for better agreement between the two in their estimates of AOD.

Table 5 Comparison of the retrieval accuracy between the CALIPSO AOD for the period of January 1, 2007 to December 31, 2014 and the MYD04 C6.1 DTB10K AOD for the period of January 1, 2003 to December 31, 2017 products in the four seasons
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By comparing the matching of products with AOD1 and AODS in different seasons in Tables 2, 3, 4, 5, it is found that the degree of matching between MODIS products and CALIPSO AOD varies to a certain extent, depending on the different MODIS algorithms and resolutions used.

Figures 6 and 7 show box diagrams of the bias between the MYD04 C6.1 AOD retrievals and the CALIPSO AOD retrievals. As shown in Fig. 6, the bias between all MYD04 C6.1 products (with different algorithms or resolutions) and CALIPSO AOD1 is often greater than 0. According to Fig. 7, although, on the whole, the AOD value of the MYD04 C6.1 product is also larger than the CALIPSO AODS, within the range of MODIS AOD < 0.30, most of the CALIPSO AODS values are greater than or equal to MYD04 C6.1, indicating that the measured AOD values of the two products are in good agreement there. However, the difference between all MODIS products and CALIPSO AODS becomes increasingly negative as MODIS AOD increases for values of MODIS AOD > 0.30. This also indicates that in clean environmental conditions, when atmospheric aerosol levels are low, the difference is small. Algorithmically, the MODIS product considers the radiation extinction of the whole atmosphere (aerosols and gas molecules), while the AODS of CALIPSO only considers the extinction of the aerosol layer. Therefore, in clean environmental conditions with low aerosol content, the difference between the two is small. In severe air pollution conditions, the aerosol content is large, both types of AOD are larger, and the difference between the two is also larger.

Fig. 6
figure 6

Box plots of the CALIPSO AOD1 retrievals for the period of January 1, 2007, to December 31, 2014, against the MYD04 C6.1 AOD retrievals for the period of January 1, 2003, to December 31, 2017, over the YERB. The EE envelopes are within the dashed lines. The number above each box refers to the corresponding matches in the different intervals of the MODIS AOD (0–0.2, 0.2–0.4, 0.4–0.6, 0.6–0.8, and > 0.8). The DT3K, DTB10K, DB10K, and DT10K retrieval biases are presented in (a)–(d), respectively

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Fig. 7
figure 7

Box plots of the CALIPSO AODS retrievals for the period of January 1, 2007 to December 31, 2014 against the MYD04 C6.1 AOD retrievals for the period of January 1, 2003 to December 31, 2017 over the YERB. The EE envelopes are within the dashed lines. The number above each box refers to the corresponding matches in the different intervals of the MODIS AOD (0–0.2, 0.2–0.4, 0.4–0.6, 0.6–0.8, and > 0.8). The DT3K, DTB10K, DB10K, and DT10K retrieval biases are presented in (a)–(d), respectively

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4.2 Time Series and Regional Variation of AOD Retrieval Bias

Due to large differences in topography, climate, and economic development in the YERB, the region is divided into three sub-regions to study further the comparison between the two products in the time series of these sub-regions.

Figure 8 shows the change curves of MODIS products over the YERB1 region from 2003 to 2017, and CALIPSO products from 2007 to 2014, with different AOD values during each of the four seasons. As can be seen from Fig. 8, the inter-annual variation of the AOD1 and AODS curves in the four seasons are similar, with only a small difference, indicating that the bottom AOD over the YERB1 region undergoes little change over the four seasons, the difference value of AOD in the whole layer remains stable, and the corresponding AOD has a small range of change between different years. This is because the YERB1 region is in the eastern part of the Qinghai–Tibet plateau, where the mountains are cold, the atmosphere is clean, and the overall aerosol content is low. Besides, there is less aerosol stratification there, and the bottom layer of AOD is representative of the full profile of AOD (Zhang et al. 2019b). Also, the value of the bottom layer of AOD over the YERB1 region is relatively high and is close to the value of AOD for the entire atmospheric depth. This might be since the YERB1 region is located in the plateau area, with an average elevation of 3000 m and a high aerosol concentration at low altitude. We found that in summer and fall, there are high and low levels of MODIS products in different years, but in spring and winter, CALIPSO products reported small values throughout the study period. Comparing the four types of MODIS products, for summer and autumn, the difference between them is small, but for spring and especially winter, they exhibit a bigger difference, mainly because the spring and winter DT algorithm products give smaller AOD values, and the obtained data values are all large; at the same time, this also shows that the use of different algorithms in different seasons for the retrieval of AOD leads to a certain difference. Excluding the values of DT3K and DT10K in winter, the overall AOD values were higher in spring and summer than in autumn and winter. Another reason might be that in spring and winter in the mountain plateau areas, the temperature difference is large, which has a certain influence on the change of atmospheric aerosol content, resulting in a large difference in spring and winter products.

Fig. 8
figure 8

Time series of AOD changes for the MYD04 C6.1 product from January 2003 to December 2017 and CALIPSO AOD product from January 2007 to December 2014 in the four seasons over the YERB1 region

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Figure 9 shows the change curves of MODIS products over the YERB2 region from 2003 to 2017, and CALIPSO products from 2007 to 2014, with different AOD values during each of the four seasons. As can be seen from Fig. 9, the change between the four seasons in the same region generally follows the order: summer > spring > winter > autumn. Among them, the inter-annual variation of the AOD1 and AODS curves for the four seasons are similar, and the changes in different values are relatively small, but the difference value of AOD1 and AODS in each year is greater than that of the YERB1 region. This might be because the YERB2 region is predominantly loess plateau. Compared with the YERB1 region, the altitude is lower and the vertical stratification of the atmosphere is stronger. As a result, the aerosol stratification intensity is relatively high, and consequently, the AOD of the bottom layer is less than that of the full profile (Zhang et al. 2019b).

Fig. 9
figure 9

Time series of AOD changes for the MYD04 C6.1 product from January 2003 to December 2017 and CALIPSO AOD product from January 2007 to December 2014 in the four seasons over the YERB2 region

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Comparing the curves of the two products, it is found that the AODS values in summer, autumn, and winter are slightly greater than those of DTB10K AOD in almost all years (this might be caused by DTB’s combination of the dark target and dark blue algorithms). Other DT10K, DB10K, and DT3K products in different years have high and low values, but for the spring, in almost all years, the AOD values given by the four MODIS products are greater than those obtained by CALIPSO. This might be because a large number of sandstorms occur in the loess plateau area in spring, and thus a large number of dust aerosols will appear. As stated earlier, this increase in dust aerosol content will cause the AOD by MODIS to be greater than that of CALIPSO. By comparing the four MODIS products, it is found that the AOD values of DTB are the smallest in almost every year, in each of the four seasons over the YERB2 region, while DT10K AOD is maximal and DT3K AOD is medium in different seasons, respectively. This pattern is completely different from that of the YERB1 region, indicating that the inversion of AOD by MODIS products over different regions is quite different, as is also reflected in our previous research results (Zhang et al. 2019a; b).

Figure 10 shows the change curves of MODIS products over the YERB3 region, from 2003 to 2017, and CALIPSO products, from 2007 to 2014, with different AOD values during each of the four seasons. As can be seen from Fig. 10, the inter-annual variation curves of AOD1 and AODS are similar for the four seasons, but the differences between AOD1 and AODS are larger than over the YERB1 and YERB2 regions, indicating that the difference value between AOD1 and AODS increases with the decrease in altitude, for the reasons explained above. MODIS AOD is greater than CALIPSO AOD in the four seasons in almost all years, but the difference between the four MODIS products varied significantly among the four seasons. Among them, the difference between DT3K and DT10K products in the four seasons is smaller, except that the DB10K AOD value in spring is found to the smallest in each year, while the other three seasons exhibit the highest values and show a different pattern than over the YERB1 and YERB2 regions, indicating that the aerosol load of DB and DT algorithm products has a large correlation over the region. A comprehensive picture can be observed from Figs. 8, 9, and 10; on the whole, the degree of matching of the MODIS and CALIPSO products follow the order: YERB1 > YERB2 > YERB3, indicating that under the lower aerosol load, the AOD retrieval values of the two products are closer.

Fig. 10
figure 10

Time series of AOD changes for the MYD04 C6.1 product from January 2003 to December 2017 and CALIPSO AOD product from January 2007 to December 2014 in the four seasons over the YERB3 region

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By comparing the AOD values of different regions for the same season in Figs. 8, 9, and 10, it is found that, in spring and winter, the overall average value of MODIS products generally follows the order: YERB3 > YERB1 > YERB2. In summer and autumn, MODIS products generally follow the order YERB3 > YERB2 > YERB1, indicating that the value of AOD acquired by MODIS products is influenced by both seasonal and regional factors. In all four seasons, CALIPSO products follow the order: YERB3 > YERB2 > YERB1. This pattern occurs because the YERB3 region is located in the north China plain, which has a high aerosol load (Che et al. 2013; Chen et al. 2017; He et al. 2018; Tao et al. 2017). Overall, the results (Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10 and Tables 2, 3, 4, 5) show that there are degrees of variation for several MODIS C6.1 products. Previously, we reported the comparison between MODIS products and the ground-based CARSNET data and found that currently no MODIS aerosol product is suitable for the whole YERB region and that it is a challenging task to obtain high-quality AOD retrievals for such large areas. In this paper, the results of CALIPSO also show a big difference over each region. On the whole, it can be concluded that the retrieval and measurement values of AOD of several products have an excellent relationship with the different seasons, sub-regions, and terrains.

4.3 Spatial Distribution of MYD04 C6.1 and CALIPSO AOD

To the best of our knowledge, the optical and physical properties of aerosol in the YERB given by MODIS products have not yet been studied. Figure 11 shows that the AOD values of the three sub-regions have obvious regional characteristics; AOD values over the YERB3 sub-region are significantly higher than those over the other two areas. This pattern might be due to the fact that relative to the YERB1 and YERB2 regions, the YERB3 region has a relatively well-developed economy, and so industrial and vehicle aerosol emissions are higher there. First, AOD1 is the AOD of the lowest aerosol layer, so AOD1 is all lower than other products. Second, the eastern part of YERB (YERB3) is the plain area, the economy is developed, anthropogenic emissions are high, especially in winter. The summer and autumn also are the harvest season, crops Straw burning activities were also frequent and leading to high aerosol emissions and high AOD.

Fig. 11
figure 11

Spatial distribution of the MYD04 C6.1 AOD for the period of January 1, 2003 to December 31, 2017 and the CALIPSO AOD1 retrievals for the period of January 1, 2007 to December 31, 2014 in the four seasons over the YERB. The color scale refers to the AOD values

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Several products generally show that the AOD values in spring and summer are greater than that in autumn and winter, which might be due to the straw burning in the YERB3 region, which might, in turn, lead to an increase in anthropogenic aerosol content in spring and summer. High AOD values over the YERB1 and YERB2 sub-regions might be due to the increase of natural aerosol content caused by wind-blown sand in spring and summer, and due to the increase of dust emitted from the loess plateau.

Furthermore, MYD04 C6.1 DT3K and DT10K aerosol products have not retrieved the corresponding AOD values in some areas in the north and east of the basin, especially in winter. This large area has no data, which might due to the low single scattering reflectance over the snow surface. Because the Qinghai–Tibet plateau and part of the loess plateau are often covered by snow in winter.

5 Conclusions

In this paper, CALIPSO AOD products from 1 January 2007 to 31 December 2014 are evaluated in comparison with MODIS MYDO4 C6.1 AOD products from 1 January 2003 to 31 December 2017 over the YERB. This study concludes that: The distribution of AOD values obtained from CALIPSO and MODIS are significantly different over three different regions of YERB, and this difference is closely related to the season, sub-region, and topography. As a whole, the CALIPSO products’ AOD retrievals underestimate the MODIS AOD products, while no single satellite AOD product is suitable for the whole of the YERB region. The degree of matching between the CALIPSO AODS and the MODIS product is significantly higher than that of AOD1; the MODIS and the CALIPSO AODS products are well matched within the range of MODIS AOD < 0.30, while the degree of matching decreases as MODIS AOD increases within the range of MODIS AOD > 0.30. All the products we investigated here generally reveal the pattern that the AOD retrievals of spring and summer are larger than those of autumn and winter and the difference in AOD retrievals by all these products is the smallest in autumn. In spring and winter, the overall average value of MODIS products generally follows the order: YERB3 > YERB1 > YERB2, while in summer and autumn, MODIS products generally follow the order: YERB3 > YERB2 > YERB1. For all four seasons, CALIPSO products follow the order: YERB3 > YERB2 > YERB1. This is closely related to the topographic factors of the YERB. Based on the season, sub-region, and other factors, the CALIPSO AOD retrievals have the best consistency with the MYD04 C6.1 DTB10K product, while they have the lowest consistency with MYD04 C6.1 DT3K. The performance of DTB10K is better than DT3K although it has the coarser spatial resolution, it has the best consistency with CALIPSO. CALIPSO AOD products can be used for AOD retrieval analysis for such large and diverse topographic areas.