The complex aerosol composition and the high aerosol concentrations render eastern China an interesting area for a variety of studies of processes involving aerosols, including the current study on the use of satellite data for the systematic assessment of aci, i.e., S, adjustments and confounding meteorological factors. The study focuses on two areas, i.e., the Yangtze River Delta (YRD, 26–35° N, 113–122° E) in eastern China and the East China Sea (ECS, 19–28° N, 125–134° E). The locations of the YRD and the ECS are shown in the map in Fig. 1.

The YRD has a developed economy, with much industrial activity, large harbors (sea and river) and related busy ship traffic, and dense population in large urban centers, all with high traffic intensity and high energy consumption. In addition to the direct emission of black carbon, also aerosol precursor gases such as NO2, SO2 and VOCs are emitted from the combustion of biomass, coal and petrochemical fuels, leading to the formation of secondary aerosol particles such as nitrate and sulfate aerosols, while agricultural activities result in the emission of dust, ammonia and biological VOCs (BVOCs) into the atmosphere. These activities and associated emissions result in the occurrence of high AOD over the YRD. Over the East China Sea (ECS) the main aerosol types are sea spray aerosol generated by the interaction between wind and waves and anthropogenic pollutants transported from the Asian continent over the ocean in the East Asian outflow. During transport over hundreds of kilometers, aerosol particles are removed by several processes such as dry and wet deposition, and hence the aerosol concentrations decrease and the AOD becomes relatively low and is dominated by sea spray aerosol. In view of the differences in aerosol composition and concentrations, the polluted YRD area and the relatively clean ECS area were selected as contrasting regions for the study of the influence of aerosols on cloud properties over land and over ocean.

In this study, aerosol and cloud properties were used (see Table 1), which were derived from measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Aqua satellite, for the period 2008–2022 (15 years). These data were selected because the MODIS data are widely used, and therefore they are well characterized. In addition, the Aqua satellite flies in an afternoon orbit with local overpass time around 13:30 local time (LT), when the atmospheric boundary layer is well developed. MODIS L3 Collection 6.1 daily aerosol and cloud parameters were downloaded from the LAADS website (Platnick et al., 2017a) with a spatial resolution of 1°×1°. Aerosol retrieval is only executed in clear-sky conditions, whereas cloud properties can only be retrieved in cloudy skies. Hence, it is not possible to obtain co-located aerosol and cloud data from satellite. For satellite-based aci studies it is assumed that, following, e.g., Jia et al. (2022), aerosol properties are homogeneous enough to be representative for those in adjacent cloud areas. Consequences of this assumption were discussed by McComiskey and Feingold (2012). The MODIS instrument has 36 spectral bands – aerosol properties are retrieved using the first seven of these (0.47–2.13 µm) (Remer et al., 2005; Levy et al., 2013; Sayer et al., 2014, 2017), while additional wavelengths in other parts of the spectrum are used for the retrieval of cloud properties (Platnick et al., 2003, 2017b). Detailed information on algorithms for the retrieval of aerosol and cloud properties is provided at http://modis-atmos.gsfc.nasa.gov (last access: 1 July 2021). In this study we use the AOD at 550 nm (referred to as AOD throughout this paper), CER, COT, cloud liquid water path (LWP), cloud top pressure (CTP), cloud fraction (CF) and cloud top temperature (CTT). The MODIS Collection 6.1 AOD product over China has been validated by, e.g., Che et al. (2019) and globally over land and ocean by Wei et al. (2019). MODIS C6.1 cloud products were evaluated by Platnick et al. (2017b). The validation of CER and LWP, the primary cloud products used in this paper, was described by Painemal and Zuidema (2011), who compared MODIS C5 with in situ data (aircraft), and likewise the MODIS C6.1 CER product was evaluated by Fu et al. (2022) by comparison with airborne measurements. Fu et al. (2022) concluded that their “validation, along with in situ validation of MODIS CER from other regions (e.g., Painemal and Zuidema, 2011; Ahn et al., 2018), provides additional confidence in the global distribution of bias-adjusted MODIS CER reported in Fu et al. (2019)”. It is noted that COT and CER are retrieved, whereas LWP is secondarily derived (e.g., Painemal and Zuidema, 2011). AOD is used as a proxy for the amount of CCN in the atmospheric column to investigate aci (Andreae, 2009), which seems to be the best alternative (Rosenfeld et al., 2014). As discussed in the Introduction, the use of an AE-based correction is not recommended over land (e.g., Kourtidis et al., 2015). Comparisons with surface-based sun photometer data show that Collection 6 improves upon Collection 5, and overall, 69.4 % of MODIS Collection 6 AODs fall within the expected uncertainty of ± (0.05+15 %) (Levy et al., 2013; Tan et al., 2017). To reduce a possible overestimation of the AOD (e.g., due to cloud contamination), cases with AOD greater than 1.5 were excluded from further analysis. The choice of this threshold is based on reports by Christensen et al. (2017) and Varnái and Marshak (2009), rather than 0.6 used by Brennan et al. (2005), who used MOD06 Collection 04 products. Christensen et al. (2017) used MOD06 C6 data (1km×1km) and reported that “large aerosol optical depths remain in the MODIS-observed pixels near cloud edges, due primarily to 3D effects (Varnái and Marshak, 2009) and the swelling of aerosols by higher relative humidity”. Varnái and Marshak (2009) noted that beyond 15 km contamination effects were minimized in MODIS data (1km×1km). Furthermore, we discarded scenes (1° × 1°) in which the aerosol distribution is heterogeneous, i.e., with a standard deviation higher than the mean value (Saponaro et al., 2017; Jia et al., 2022). As most aerosol particles are located in the lower troposphere (Michibata et al., 2014), to avoid deep convective clouds, the focus in this study is on warm clouds with CTT larger than 273 K and CTP larger than 700 hPa, while LWP larger than 200 gm-2 is excluded (Wang et al., 2014). Transparent–cloudy pixels (COT < 5) were discarded to limit uncertainties (Grosvenor et al., 2018). The solar zenith angle was restricted to SZA<65° and the viewing zenith angle to VZA < 55° to avoid the large biases in COT and CER retrievals at larger angles (Grosvenor et al., 2018). To ensure that the data used only included single-layer liquid clouds and nonprecipitating cases, the filtering criteria described by Saponaro et al. (2017) were applied.

Confounding meteorological effects on aci were explored using the daily temperature at the 700 and 1000 hPa levels, RH at the 750 hPa level and PVV at the 750 hPa level. Low tropospheric stability (LTS), which is defined as the difference in potential temperature between the free troposphere (700 hPa) and the surface (1000 hPa), is used as a measure of the strength of the inversion that caps the planetary boundary layer (Klein and Hartmann, 1993; Wood and Bretherton, 2006). These meteorological data were retrieved from the ECMWF ERA-5 reanalysis data, which provide global meteorological conditions at 0.25°×0.25° resolution for 37 pressure levels in the vertical (1000–1 hPa), for every 1 h (UTC). The meteorological parameters were resampled to the MODIS/Aqua overpass time at 13:30 LT by taking a weighted average at the two closest times (05:00 and 06:00 UTC) provided by the ECMWF ERA-5 reanalysis data.

Changes in aerosol loading lead to an adjustment of cloud optical or microphysical parameters (COT, CER, etc.). Aerosol particles can become CCN or INP, depending on their chemical composition and ambient temperature. When these nuclei are activated, they become cloud droplets due to condensation of water vapor. When the concentration of aerosol particles increases, often also the number of CCN or INP may increase and thus the number of cloud droplets may increase. However, if the liquid water content in the cloud does not change (as indicated by a constant LWP), the condensable water will be distributed over more cloud droplets, which thus remain smaller; i.e., the CER decreases and the cloud albedo increases when the aerosol concentration increases. On the basis of findings of Kaufman and Fraser (1997), Feingold et al. (2001) pointed out that the sensitivity of cloud microphysical properties (e.g., CER) to changes in aerosol (e.g., AOD) can be described by the following formula: 1S=SCER-A=dln⁡redln⁡αLWP0<S<-0.33, where re represents the CER and α represents the AOD. Following Andreae (2009), AOD and CCN are correlated and AOD varies with CCN following a power law relationship. Equation (1) describes the relative change of CER with the relative change of the AOD for constant LWP. It is noted that this formulation differs from that used in recent studies (e.g., Bellouin et al., 2020), where S is expressed in Nd with no restriction in LWP. The sensitivity S of CER to AOD can be determined as the slope of a linear fit to a log–log plot of CER versus AOD. It is noted that S is a function of CER and effects on CER directly influence S. In this study effects on S and CER are used interchangeably. Relations between CER and AOD are determined through Eq. (1) and correlation coefficients R. The significance of these relations is determined by using the Student's t test; i.e., the results are statistically significant when the p value is smaller than 0.01, where p is defined as the probability of obtaining a result equal to or more extreme than what was actually observed.

The geographical detector method (GDM) is introduced to analyze which factors influence the aci and identify possible correlations between different factors. The GDM is based on the assumption that if an independent variable has an important influence on its dependent counterpart, their spatial distributions should also have evident similarities (Wang and Hu, 2012; Wang et al., 2016). The GDM not only accounts for the rank order of the variables as determined by the Spearman's rank method but also spatial information. The geographical detector provides four modules, including factor detector, interaction detector, risk detector and ecological detector. In this study, the first two modules are used to detect interactions between different parameters, based on their spatial variations, and thus reveal the driving factors for aerosol–cloud interaction over the target regions. The influencing factors (x) considered in this study are aerosol and meteorological parameters, and the dependent factors (y) are S and cloud parameters. In the GDM, for example, the CER data are recorded in a raster grid as illustrated in Fig. 2. The data in the raster grid are transformed into 2D point vector files, with each point containing a value for the CER and for one of the influencing parameters x. The dependent (CER) and influencing (x) parameters are separated into two layers with the same grid. In the x layer, the Jenks natural breaks classification method (Brewer and Pickle, 2002), aiming to minimize the variance within the group and maximize the variance between groups, was applied to categorize the whole region into i subregions (3 in Fig. 2), according to pre-defined ranges of influencing factors (e.g., AOD). In each subregion, the influencing factor (x) varies within certain limits, with variance σi. The power of determination q of x to y (also referred to as power of the influencing factor) determines the extent to which a factor (x) influences the dependent factor (y) over the whole study area and is calculated using Eq. (2): 2q=1-∑iLNiσi2Nσ2, where i (1,…,L) is the number of subregions of factor x, N represents the total number of spatial units over the entire study area, Ni denotes the number of samples in subregion i, and σi2 and σ2 denote the variance of the samples in the subregion i and the total variance in the entire study area, respectively. The value of q varies between 0 and 1, i.e., q[0,1], where 0 indicates that factor x has no influence on y and the closer q is to 1, the greater the influence of x. For instance, if q=0.5, x can explain 50 % of the variation of y. In this study, multi-years of mean values of influencing factors (x) and dependent factors (y) were calculated for each raster grid. Then, we classified the influencing factors (e.g., AOD and meteorological parameters) into five subregions by the Jenks natural breaks classification method (Brewer and Pickle, 2002). For example, AOD needs to be classified into five levels using the Jenks natural breaks classification method, and the AOD source data needs to be reclassified into one to five natural numbers from small to large and then counted into the grid. Therefore, the input of the independent variable AOD is a type variable. However, it should be noted that the GDM also has unstable characteristics. On the one hand, it is due to the MAUP (modified area unit problem) variable area unit problem, which can be understood as the influence of the scale effect. Due to the limitation of data resolution used in this study, the spatial statistical unit is 1°×1°. On the other hand, the methods used for data discretization can also have an impact. This study attempts to determine the optimal number of classifications by examining the impact of the number of classification levels (three to eight) on the GDM output results. The results show that the number of classification levels does not affect the relative importance of cloud factors on the cloud. Here we classify the values of each cloud factor into five levels during the period of 2008–2022.

The interaction detector can be used to test for the influence of interaction between different influencing factors, e.g., x1 and x2, on the dependent factor (y) and whether this interaction weakens or enhances the influence of each of x1 or x2 on the dependent variable, y, or whether they are independent in influencing y. For example, Fig. 3a shows the spatial distribution of the dependent variable, y. The factors x1 and x2 both vary across the study region, but in different ways, and for each factor different subregions can be distinguished by application of the Jenks classification method described above to each factor separately. This is illustrated in Fig. 3b and c where, as an example, three different subregions are considered for each factor. Usually, the dependent variable y is influenced by several different factors xi (Fig. 3), and the combined effect of two or more factors may have a weaker or stronger influence on y than each of the individual factors. The q values for the influences of factors x1 and x2 on y, obtained from the application of the factor detector method (Eq. 2), may be represented as q(x1) and q(x2). Hence, a new spatial unit and subregions may be generated by overlaying the factor strata x1 and x2, written as x1∩x2, where ∩ denotes the interaction between factor strata x1 and x2 as illustrated in Fig. 3d. Thus, the q value of the interaction of x1∩x2 may be obtained, represented as q(x1∩x2). Comparing the q value of the interaction of the pair of factors and the q value of each of the two individual factors, five categories of the interaction factor relationship can be considered, which are summarized in Table 2. If q(x1∩x2)>q(x1)+q(x2), this is referred to as a nonlinear enhancement of two variables. And if q(x1∩x2)>Max[q(x1),q(x2)], this is referred to as a bilinear enhancement of two variables. The occurrence of nonlinear enhancement and bilinear enhancement is indicated with the q values in Table 2 and in the caption of Fig. 7.

It is noted that the q values of multiple influencing factors are considered separately and they may sum up to larger than 100 %. However, when the variables are correlated they must be considered together and the interaction q value must be evaluated.

The geographical detector method has been used to detect influencing factors for several different purposes (e.g., Wang et al., 2018; Zhang and Zhao, 2018; Zhou et al., 2018). For example, the GDM was used to detect the influence of annual and seasonal factors on the spatial–temporal characteristics of surface water quality (Wang et al., 2018). Other examples are the application of the GDM to examine factors influencing regional energy-related carbon emissions (Zhang and Zhao, 2018) and to examine effects of socioeconomic development on fine particulate matter (PM2.5) in China (Zhou et al., 2018). In the current study, the GDM was used to detect the impact of nine variables and their interactions on S and cloud parameters over land and ocean. The advantages of using the GDM in this approach are the following: (1) stratified independent variables enhance the representation of a sample unit, so it has higher statistical accuracy than other models with the same sample size; (2) the use of a q-statistic value can afford a higher level of explanatory power but does not require the existence of a linear relationship between independent and dependent variables; (3) the GDM can determine the true interaction between two variables and is not limited to pre-established multiplicative interactions (Wang et al., 2010); (4) the use of the GDM does not need to consider the collinearity of multiple independent variables (Wang et al., 2010).

The spatial variations of the AOD and the cloud properties (CER, COT, CF, CTP and LWP) over the study area, averaged over the years 2008–2022, are presented in Fig. 4. Figure 4a shows a large difference between the AOD over land and ocean, with the highest values over the northern part of the YRD (averaged AOD larger than 0.5) and the lowest values over the southeastern part of the ECS (<0.1); the AOD decreases gradually from land to ocean. The spatial distributions of the CER, COT, CF, CTP and LWP over the YRD and ECS in Figs. 4b–f show that for each of them there is a distinct difference between those over land and over ocean both as regards the values and the spatial variation. Over the ECS, the CER is largest in the south and decreases toward the north of this area, and the values are overall substantially larger than over the YRD, where the CER varies somewhat and decreases from north to south. The variation of the CER with AOD over the YRD is opposite to what would be expected, which will be discussed in Sect. 4.2. The COT also varies somewhat over the YRD, but in contrast to the CER, COT increases from north to south. Over the ECS, the COT is generally lower than over the YRD, with the highest values in the northwest, which gradually decrease toward the southeast. Clearly, the CER is higher and the COT is lower over the ECS than over the YRD.

The spatial distributions of CF, CTP and LWP are clearly different. Over the ECS, CF increases from the southeast to the northwest, opposite to the variations of the CTP and the LWP, which are lower in the north of the ECS than in the south. Over ocean the clouds are generally lower (higher CTP) than over land, and CTP varies over the study area with the highest values over land, in the north. Over the YRD, the spatial patterns of the CF and CTP are opposite, with CF increasing from south to north and CTP decreasing. Over the YRD, the spatial distributions of COT and LWP are similar, with higher values toward the south. Over the ECS, the LWP varies, with the lowest values in the northwest and the highest values in the south. The high values of the CER over the ECS could be due to the dominance of sea spray aerosol, the high hygroscopicity of which makes these particles very efficient CCN, which in this environment over ocean with high water vapor concentrations results in larger CER. The influence of different factors on the sensitivity of cloud parameters to aerosol and the adjustments are discussed in the following sections, based on both statistical methods and the application of the GDM.

Equation (1) shows that the value of the sensitivity S of CER to AOD is determined by the slope of a linear fit to a log–log plot of CER versus AOD. To investigate S, we used correlated data pairs for 15 years, the data were binned in AOD intervals with a bin width of 0.02 and the CER data in each AOD bin were averaged. Logarithmic plots of the averaged CER data versus AOD over the YRD and the ECS are presented in Fig. 5. Figure 5a and b show different regimes for the variation of the CER with the AOD over the YRD and the ECS. The first regime, for AOD≤0.05, shows the increase in CER with AOD over both regions, followed by a variable CER over the YRD and a gradually stronger decrease over the ECS for AOD between 0.05 and 0.1. In view of this variability and the uncertainty of AOD of ± (0.05+15 %) over land and ± (0.03+5 %) over ocean (Levy et al., 2013), S will not be investigated for AOD<0.1. For higher AOD, S changes for AOD around 0.3. Thus, the second regime is selected as the part of the CER vs. AOD relationship where AOD varies between 0.1 and 0.3. In this AOD regime, the CER fluctuates a little with AOD over the YRD (Fig. 5a) and S is close to 0 (no discernible Twomey effect). In contrast, over the ECS the CER clearly decreases with AOD for AOD increasing from 0.1 to 0.3 (Fig. 5b), in good agreement with expectation based on the Twomey effect, and the correlation between CER and AOD is high with R=0.99 and statistically significant. Note, however, that no selection was made for LWP, and the condition of constant LWP was not fulfilled. This will be further discussed in Sect. 4.3.

In the third regime, where AOD>0.3, CER increases with increasing AOD over the YRD, with correlation coefficient R=0.79. In contrast, over the ECS the CER does not significantly change with increasing AOD for AOD>0.3 (very small S). However, the large uncertainty in the bin-averaged CER in this AOD regime, increasing with increasing AOD, indicates a very variable S between high-AOD events which on a statistical basis cannot be further analyzed and likely depends on the type of aerosol present during each event and the meteorological conditions. The reason for the increase in CER with increasing AOD (S positive) over the YRD may be similar to that described by Feingold et al. (2001), i.e., in the presence of a large number of aerosol particles (CCN) competing for a limited amount of water vapor, only a subset of aerosol particles is activated. Once activated, these particles continue to grow faster, thus preventing water vapor from condensing onto smaller aerosol particles that are less susceptible to activation. As a result, the amount of available water vapor is distributed over a subset of aerosol particles, which thus become cloud droplets with relatively large CER, and the CER in turn increases with further increasing AOD (Liu et al., 2017).

The CER sensitivity to AOD is stronger over the ECS (0.1<AOD<0.3) than over the YRD (AOD>0.3). It is anticipated that during the relatively low AOD over the ECS in AOD regime 2 (0.1<AOD<0.3) the aerosol number concentration is dominated by sea spray aerosol particles (de Leeuw et al., 2011), which are hygroscopic and thus provide good CCN, while over open ocean also the RH is generally high. Hence, the available water vapor will be readily distributed over all CCN, resulting in the decrease in the CER and a strong correlation with AOD. Further, the AOD over open ocean does not reach high values in the absence of continental influence, and even in very high wind speeds the AOD does not exceed 0.2 (Huang et al., 2010; Smirnov et al., 2012). Hence, AOD higher than 0.2 over the ECS is influenced by long-range transport of aerosol produced over land with lower hygroscopicity, and thus lower susceptibility to act as CCN, which explains the breakdown of the Twomey effect over the ECS for elevated AOD. In fact, the data in Fig. 5b show that the CER–AOD relationship starts to flatten for AOD∼0.2 and is flat for AOD larger than ∼0.3. Overall, Fig. 5 shows that the Twomey effect is clear in the second AOD regime over the ECS and the anti-Twomey effect in the third AOD regime over the YRD. For this reason, further analysis focuses on the aci over the ECS for AOD between 0.1 and 0.3, as well as over the YRD for AOD>0.3.

To study the spatial variation of S over the study area, S has been calculated in each grid cell by application of Eq. (1) to all observations over the YRD for which AOD>0.3 and to all observations over the ECS for which 0.1<AOD<0.3. The results are plotted in Fig. 6, which shows maps of S, the correlation coefficient R between CER and AOD, and the statistical P value for each grid cell over the study area. Figure 6b shows that over the ECS, for the second AOD regime (0.1–0.3), S is negative, with large negative correlation coefficients (-0.66 to -0.98) which mostly are statistically significant (p<0.01). These results show the good correlation between CER and AOD, consistent with the cloud albedo effect. In contrast, over the YRD, for the third AOD regime (>0.3), S is mostly positive and the correlation between CER and AOD is positive; i.e., high aerosol loading results in larger CER for AOD>0.3, as was also concluded from Fig. 5. The data in Fig. 6a also show that, over the YRD, S is largest over the area to the north of Shanghai but R is relatively weak (0.11 to 0.35), and for the majority of the cells the correlations are not statistically significant (p∼0.1 or larger). South of Shanghai the correlations are small and not statistically significant. The observed anti-Twomey effect of aerosols over the YRD has also been reported in earlier publications such as Jin and Shepherd (2008), Yuan et al. (2008) and Liu et al. (2017). Factors influencing the relationship between AOD and cloud parameters have been reported in the literature, such as hygroscopic effects (e.g., Qiu et al., 2017), atmospheric stability, cloud dynamics, cloud height (Shao and Liu, 2005) and land cover type (Jin and Shepherd, 2008; Ten Hoeve et al., 2011). The effects of competing mechanisms and their possible influence on the observed response of CER to high AOD in the YRD will be further discussed in the following sections.

In the data presentation and discussion of S in Sect. 4.2, the condition of constant LWP for the application of Eq. (1) and the occurrence of the cloud albedo effect were not considered. In this section the effect of LWP on S will be further investigated. To this end, the condition of constant LWP is approached by stratifying LWP into five intervals, each with a width of 40 gm-2, for the LWP range of [0 gm-2, 200 gm-2]. S was calculated over the YRD and the ECS, for each LWP interval using Eq. (1) for all observations over the YRD for which AOD>0.3 and for all observations over the ECS for which 0.1<AOD<0.3. The results are presented in Table 3, together with the corresponding correlation coefficients R between CER and AOD in the relevant AOD regimes. The data in Table 3 show that over the ECS, S is negative and statistically significant for all four LWP ranges between 40 and 200 gm-2. The sensitivity becomes stronger as LWP increases, i.e., S changes from -0.19 (LWP 40–80 gm-2) to -0.46 in the highest LWP range (160–200 gm-3), with corresponding R of -0.98 to -0.99. Thus, the magnitude of the LWP has a substantial influence on the albedo effect. Over the YRD, S is positive and statistically significant in the first three LWP regimes, with values varying between 0.06 and 0.10 and a correlation R between 0.57 and 0.81. These data show that, in contrast to the ECS, over the YRD the variation of the LWP has little influence on S, and thus the magnitude of the LWP has little influence on the cloud albedo effect.

In summary, the data show that both over the ECS and the YRD the relationships between the CER and the AOD are significant, but for different LWP intervals ([0 gm-2, 120 gm-2] over the YRD and [40 gm-2, 200 gm-2] over the ECS) and for different AOD regimes (0.1<AOD<0.3 over the ECS and AOD>0.3 over the YRD), and that the CER–AOD relation follows the Twomey effect over the ECS and the anti-Twomey effect over the YRD.

The variation of S with changes in LWP indicates that the condition of constant LWP is not truly satisfied: if the data would be stratified according to smaller LWP intervals (quasi-constant LWP, Ma et al., 2018), S would likely vary more smoothly with LWP. As mentioned in the Introduction, LWP is not directly retrieved but calculated form CER and COT, and thus also the calculation of S is to some extent affected by LWP. We further note the results by Ma et al. (2018); i.e., the slope of CER versus AI (comparable to S in this paper) varies little with LWP, with positive values over land and negative values over ocean, and thus behaves similar to the data in Table 3 for YRD and ECS.

In the following study on the effects of the AOD and different cloud and meteorological properties on S and adjustments, these differences will be taken into account; i.e., over the YRD only data with AOD>0.3 and LWP in the range from 0 to 120 gm-2 will be used, and over the ECS only data with AOD in the interval [0.1,0.3] and LWP in the range from 40 to 200 gm-2 will be used.

Scatterplots of CER versus other cloud properties (COT, CF and CTP), with AOD as third parameter (color-coded), over the ECS and the YRD, are presented in Fig. 7. Over the ECS, the CER and CTP decrease (the cloud top height increases) with the increase in AOD, and the COT and CF increase. The increase in AOD indicates an increase in the aerosol concentration and thus potentially the number of CCN, which in turn, upon activation, results in the increase in the number of cloud droplets and thus an increase in the COT. The positive correlation between COT and AOD over the ECS suggests that the thicker clouds contain more water droplets and are formed in a more polluted atmosphere, which, as discussed in Sect. 4.2, results from the influence of long-range transport of aerosol produced over land on the aerosol burden over ocean. But at the same time, as Fig. 7a shows, CER decreases with increasing AOD, resulting in the increase in cloud albedo and thus also in the increase in COT. The increase in cloud top height with AOD indicates that both the horizontal and vertical expansion of the clouds are also enhanced. These observations are in agreement with the strong correlation between aerosol loading and cloud vertical development for convective clouds over the North Atlantic reported by Koren et al. (2005). Although there is a strong correlation between AOD, CF and CTP, this does not imply evidence of an aerosol effect (Quaas et al., 2010; Gryspeerdt et al., 2014a).

In contrast to the situation over the ECS, over the YRD the increase in AOD results in an increase in the CER and CTP (the cloud top height decreases) and a decrease in the COT. These observations are consistent with those proposed by Liu et al. (2017) in the same study region. The decrease in the CF with increasing AOD could be explained as follows. Due to the high concentration of smoke particles over the YRD (Shen et al., 2021), aerosol particles absorb solar radiation, which results in local heating of the aerosol layer and cooling of the surface (Li et al., 2017). This in turn stabilizes the temperature profile and reduces the relative humidity and surface moisture fluxes (evapotranspiration) (Koren et al., 2008) and thus also cloudiness. Reduced cloud cover exposes greater areas of the aerosol layer to direct irradiation from the Sun and therefore produces more intense heating of the aerosol layer, further reducing cloudiness (Koren et al., 2008). It is noted that this process is different from that proposed by Liu et al. (2017), i.e., that the CF increases with increasing AOD in polluted and heavily polluted conditions (AOD>0.3). In the study of Liu et al. (2017), the LWP range was not constrained; i.e., aerosol–cloud interaction was studied considering the whole LWP range. The data presented in Table 3 show that S significantly changes between the three LWP intervals between 0 and 120 gm-2 where S is positive (anti-Twomey effect), and for a larger LWP it is negative but statistically not significant. Figure 8 shows that CER and CTP substantially increase, whereas COT and CF decrease with increasing AOD in the two LWP intervals between 40–120 gm-2. However, in the other three LWP intervals the relationships between these cloud parameters and AOD are not evident. The different explanations offered here and in Liu et el. (2017) may be related to the different aerosol and cloud data sets used by Liu et al. (2017) and in the current study. On the one hand, the data sets have a different spatial resolution and cover a different time period. The data sets used in the study of Liu et al. (2017) are MYD04 Level 2 Collection 5 and MYD06 Level 2 Collection 5 in the period from 2007 to 2010. During that period the AOD over the YRD was at a maximum and decreased substantially in later years (Y. Liu et al., 2021; de Leeuw et al., 2022, 2023). On the other hand, in the study of Liu et al. (2017), the MODIS-retrieved AOD was averaged over an area with a radius of 50 km from the CALIOP target, and the MODIS-retrieved cloud data were averaged within a radius of 5 km from the CALIOP target. Hence, the AOD and cloud parameters were not representative for the same area, in particular in cases with inhomogeneous spatial distributions.

Scatterplots of the CER versus AOD over the ECS and the YRD, with meteorological factors (LTS, RH, PVV) (color coded) as a third parameter, are presented in Fig. 9. Over the ECS (Fig. 9a), the AOD is inversely related to LTS, whereas the CER increases with increasing LTS. This observation is different from the findings of Saponaro et al. (2017), who reported that there is no significant influence of atmospheric stability (LTS) on the relationship between CER and AOD. Likewise, the AOD is inversely related to RH, whereas CER increases with increasing RH. These two observations indicate that RH and LTS have a similar effect on the relationship between AOD and CER. In contrast, with the increase in PVV, the AOD becomes larger but the CER becomes smaller. The CER vs. AOD curves show that, overall, the meteorological conditions do not change the functional relationship between AOD and CER, but quantitatively they do have an effect. The change of meteorological conditions plays an important role in the variation of CER.

Different from the situation over the ECS, over the YRD the effect of meteorological conditions on the CER is weak as shown in Fig. 9d–f. RH and PVV have an inverse effect on the relationship between AOD and CER. There is no significant influence of atmospheric stability (LTS) on the relationship between CER and AOD as suggested by Saponaro et al. (2017). Overall, aerosol concentration plays a more important role in the effects of different factors on CER over the YRD.