Eastern China (30–40° N, 112–122° E; Fig. 1) has undergone remarkable economic expansion over the past three decades, which was accompanied by a substantial increase in AOD. Eastern China presents a unique atmospheric laboratory due to its complex aerosol composition – featuring both anthropogenic pollutants from industrial emissions and natural mineral dust transported from Central Asian deserts, particularly during the spring (Proestakis et al., 2018; Liu et al., 2021). The multitude of sources and the persistent nature of these aerosol particles, which can remain suspended for days to weeks and be transported over long distances in the absence of precipitation (Costantino and Bréon, 2013; Li et al., 2016; Leung et al., 2023), makes eastern China an ideal study area for investigating aci. Our research leverages satellite observations to systematically evaluate the sensitivity of cloud properties (SCER and SNd) to the AOD variation, thereby revealing the scale-sensitive patterns of aerosol indirect effects and clarifying the regulatory role of LWP in aci over this region.

Data used in this study were acquired by the MODIS instrument aboard NASA's Aqua satellite, which features an extensive swath width of approximately 2300 km and comprehensive spectral coverage across multiple bands (King et al., 2003). The satellite's equator crossing time is 13:30 (Local time, i.e. in the early afternoon, coinciding with optimal development conditions for continental warm cloud systems (Wang et al., 2014; Liu et al., 2024). For aerosol characterization, we utilized the MODIS Collection 6.1 aerosol product (MOD04), generated from cloud-screened pixels with a native resolution of 500 m at nadir and subsequently aggregated to 10 km grid cells (Remer et al., 2005; Levy et al., 2010). AOD retrieval over land uses radiances measured at the top of the atmosphere (TOA) at wavelengths of 0.47, 0.66, and 2.13 µm (Remer et al., 2005). The MODIS AOD (at 550 nm) Level 2 product (10 km ×10 km) has been validated against ground-based remote sensing data and the results show that 69.40 % of the MODIS AOD data fall within the expected uncertainty of ± (0.05+15 %) over land (Levy et al., 2013). In this study, AOD larger than 1.5 was excluded from further analysis to mitigate potential retrieval overestimation. This threshold was selected based on two key considerations: (1) Christensen et al. (2017) used MOD06 C6 data (1 km ×1 km) and reported that “large aerosol optical depths remain in the MODIS-observed pixels near cloud edges, due primarily to 3D effects (Várnai and Marshak, 2009) and the swelling of aerosols by higher relative humidity”; (2) the threshold of 1.5 aligns with widely adopted thresholds in regional aci studies over eastern China, where high AOD often coincides with complex surface conditions (e.g., urbanization, heterogeneous land cover) that exacerbate retrieval biases (Wang et al., 2015; Liu et al., 2017, 2021).

The cloud properties used in this study, including CER, LWP, COT, CTP, and cloud phase infrared (CPI) index, were derived from the Collection 6.1 MODIS Level 2 cloud product (MYD06) (King et al., 2003). The retrieval of these cloud characteristics utilizes six spectral channels spanning wavelengths from the visible to the near-infrared (0.66, 0.86, 1.24, 1.64, 2.12, and 3.75 µm) as described by King et al. (1997). Uncertainties in the MODIS C6.1 cloud parameters over land originate from instrument calibration, atmospheric correction, land surface properties, and model assumptions (Platnick et al., 2017, 2018). For COT, these include scene-dependent Level 1B data errors (1.5 %–30 %), land surface albedo errors (±15%), and atmospheric correction errors (±20%). The C6.1 algorithm addresses some prior limitations by inheriting C6's optimized lookup table design, which reduces interpolation errors to 0.1 %–0.2 % for near-nadir views and corrects C5's overestimation of thin-cloud COT (Platnick et al., 2017). CER uncertainties, stemming from solar irradiance error (∼4% at 3.7 µm), atmospheric correction, and scattering differences, are mitigated as C6.1 retains C6's separate multi-band reporting, thereby eliminating C5's systematic bias (Platnick et al., 2017). LWP uncertainty is linked to COT/CER retrieval errors and cloud-phase classification accuracy; the latter is improved by C6's voting-based phase algorithm (preserved in C6.1), which reduces misclassification over complex surfaces like vegetation and deserts (Marchant et al., 2016; Platnick et al., 2017). For CTP (1 km resolution), uncertainties from viewing angles and cloud structure are partially countered in C6.1 by assigning fill values when the 1 km retrieval fails, avoiding surface parameter defaults. For land clouds above 3 km, CTP accuracy reaches ∼ 50 hPa (Baum et al., 2012). Finally, CPI adopts C6's weighted voting logic (replacing C5's sequential tree), with C6.1 maintaining an enhanced Phase Agreement Fraction against CALIOP/POLDER data, which reduces uncertainties from weak thin-cloud signals and complex land interference (Marchant et al., 2016; Platnick et al., 2017).

Following the methodology of Platnick et al. (2017), CER and COT measurements at 3.7 µm were used to estimate Nd through adiabatic approximation principles (Quaas et al., 2006). Previous investigations have demonstrated that implementing filters based on cloud adiabaticity produced minimal effects on SNd estimates while significantly reducing the available dataset by up to 63.00 % (Gryspeerdt et al., 2022). Therefore, such filtering procedures were not adopted in the current analysis. Instead, Nd calculations are initially performed at the native pixel resolution (approximately 1 km) prior to spatial aggregation, thereby avoiding potential biases associated with deriving Nd from nonlinear combinations of CER and COT at coarser resolutions (Feingold et al., 2022). To maintain data quality, the analysis incorporated several quality control measures: only single-phase liquid clouds (CPI =1) with CTP exceeding 700 hPa and LWP smaller than 200 g m⁻² are considered, consistent with the typical atmospheric distribution of aerosols in the lower troposphere (Michibata et al., 2014). Pixels with CER values smaller than 4 µm or COT values smaller than 4 were excluded due to increased retrieval uncertainties (Sourdeval et al., 2016). Additionally, observations were restricted to solar zenith angles <65.00° and sensor zenith angles <41.40°. This constraint was intended to reduce the influence of well-documented biases, as elaborated in Grosvenor et al. (2018).

CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) operates within the A-Train constellation alongside the Aqua satellite and other NASA Earth-observing platforms. The primary instrument aboard CALIPSO is the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP). CALIOP is a two-wavelength, polarization-sensitive lidar specifically designed to provide high-resolution vertical profiles of aerosols and clouds on a global scale (Winker et al., 2009). The mission and its lidar instrument are described in Winker et al. (2009), and the associated Level 1 data products are detailed in Winker et al. (2010). This advanced sensor features an exceptionally narrow ground footprint of 70 m diameter for each laser pulse. The vertical resolution of CALIOP's products varies with altitude: 30 m within 0–8.2 km, 60 m between 8.2–20.2 km, and 180 m from 20.2–30.1 km, while maintaining a consistent 5 km horizontal resolution along the track direction (Liu et al., 2009).

The coordinated A-Train configuration ensures near-simultaneous observations (within 1–2 min) between MODIS/Aqua and CALIOP/CALIPSO for identical atmospheric targets (Stephens et al., 2002). This temporal synchronization guarantees data consistency when extracting coincident measurements, avoiding interferences such as aerosol diffusion and cloud evolution caused by observational time lags – an advantage unparalleled by positioning methods like random grid points and ground-based stations. For spatial compatibility, we resampled the higher-resolution MODIS cloud products (CER, LWP, and Nd at 1 km native resolution) to match CALIOP's 5 km along-track scale, while directly utilizing the 5 km-resolution CTP and CPI parameters. In cases where CALIOP detected aerosol presence, we computed spatial averages of MODIS aerosol and cloud retrieval products across multiple observation scales (detailed in Sect. 2.4) centred on CALIOP targets. This approach assumes reasonable homogeneity of aerosol properties between adjacent clear and cloudy regions (Anderson et al., 2003; Quaas et al., 2008). Table 1 provides a comprehensive overview of the aerosol and cloud datasets including the parameters used from each product, the resolution, and the data source, used in this study.

Variations in aerosol loading significantly influence cloud optical properties (such as COT) and microphysical parameters (such as CER). Under specific environmental conditions, aerosol particles can transform into CCN or INP, a process primarily determined by their chemical composition and ambient temperature (Bellouin et al., 2020). When these nuclei are activated, water vapor condenses on their surfaces to form cloud droplets or ice particles. As the concentration of aerosol particles increases, the number of CCN or INP may rise correspondingly, leading to an increase in the number of cloud droplets. Notably, under conditions where the liquid water content in clouds remains constant (i.e., LWP), the same amount of water vapor is distributed across more cloud droplets, resulting in a reduction in the size of individual droplets. Specifically, as aerosol concentration increases, the CER decreases, while cloud albedo 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 the number concentration of aerosol particles (e.g., using AOD as a measure) can be described by the following formula: 1SCER=dln⁡redln⁡αLWP-0.33<S<0 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 terms of 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. The effect of aerosols on CER is analyzed by comparing the difference in SCER and correlation coefficients between AOD and CER under different spatial scales (Sect. 2.4) and LWPs (Sect. 3.2).

In this study, the variation in Nd with CCN is referred to as the susceptibility SNd. Following the method of Gryspeerdt et al. (2023), the sensitivity, SNd, of a cloud property, Nd, to α is defined here as 2SNd=dln⁡Nd/dln⁡α0<S<1 Relations between CER and Nd and AOD are determined through Eqs. (1) and (2) 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.

This method quantifies the sensitivity of CER and Nd to AOD variations via linear regression in log-log space, using Eqs. (1) and (2), respectively. Its core assumptions, uncertainties, and limitations are highly consistent: both rely on AOD as an aerosol proxy variable, assume constant cloud liquid water content and a linear sensitivity relationship, and depend on the reliability of satellite-retrieved parameters (Feingold et al., 2001; Gryspeerdt et al., 2023). However, AOD cannot distinguish aerosol size and hygroscopicity, retrieval errors are substantial in clean conditions, and linear fitting fails to capture nonlinear/non-monotonic responses. Both methods are constrained by satellite retrieval biases, limited scenario applicability (only valid for specific homogeneous clouds and aerosol types), the omission of key modulating factors (dynamical conditions, aerosol type) and feedback processes, and can only assess first-order direct effects. Reliability requires scenario constraints and uncertainty analysis; the only nuances come from the target variable (CER vs. Nd), which do not alter the shared methodological limitations.

This study was conducted at multiple spatial scales to examine the scale dependence of SCER and SNd in delineating aci (Fig. 2). Here, the spatial scales are described by two parameters: study area size (the geographic scope of the analysis) and buffer size (the local spatial extent around each observation point for aggregating aerosol and cloud data). To this end, the study area was divided into four congruent square research areas all centered at the same geographical location (35° N, 117° E) over Eastern China. Hence, spatial extent varies from the whole study area as defined in Sect. 2.1 (30–40° N, 112–122° E) to successively smaller areas simulated by decreasing the study area in steps of 2 to 4°×4° as illustrated in Fig. 2a.

Buffer size refers here to a circular spatial domain centered at each point in the study area where CALIOP detected the presence of aerosols. Within this circular domain, MODIS-retrieved cloud and aerosol data (AOD, CER, Nd, LWP) are spatially averaged to construct matched aerosol-cloud datasets at different local scales. As previously noted, this approach relies on the assumption that aerosol properties are reasonably homogeneous between adjacent clear and cloudy regions (Anderson et al., 2003; Quaas et al., 2008), and this premise is supported by the short-range transport of aerosols (e.g., 10–300 km) and the near-simultaneous observations (1–2 min) by MODIS and CALIOP within the A-Train constellation.

Buffer zones with sizes increasing from 10 to 300 km (10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 140, 150, 160, 180, 200, 250, and 300 km) were determined within the whole study area by using CALIOP data. Previous observations indicate that the typical horizontal scale of cloud clusters ranges from tens to hundreds of kilometers (Zhang et al., 2024; Cai et al., 2022), supported by CloudSat/CALIPSO satellite data showing power-law distributed cloud scales (10–1000 km fitting range) covering major cloud types (Zhang et al., 2024) and regional evidence of consistent multi-season, multi-latitude cloud extents (Cai et al., 2022). Meanwhile, aerosol spatial homogeneity varies with distance: local-scale aerosols (≤50 km) exhibit high homogeneity due to consistent sources and stable diffusion, while regional-scale aerosols (>100 km) show enhanced heterogeneity from multi-source mixing and atmospheric transport (Hassan et al., 2024; Mohebalhojeh et al., 2026). Thus, the 10–300 km buffer range covers both cloud characteristic scales and the aerosol homogeneity transition range, ensuring that MODIS data averaging effectively captures aci. This range avoids insufficient MODIS pixel coverage due to excessively small buffer sizes (<10 km). It also prevents conflation between regional meteorological variations and local aci signals arising from overly large buffer sizes (>300 km), as synoptic-scale circulation and other regional meteorological changes may interfere with local aci signals (Quaas et al., 2010). Meanwhile, this range aligns with the 50–150 km buffer sizes widely adopted in regional aci studies (Wang et al., 2015; Liu et al., 2017, 2024), enabling cross-validation of results and ensuring that MODIS data averaging effectively captures aci.

MODIS-retrieved cloud and aerosol data were averaged over a buffer area around each CALIOP data point with a radius varying from 10 to 300 km. Thus, a dataset including aerosol and cloud properties was constructed with different buffer sizes. The effect of buffer size on the sensitivity of CER and Nd to variations in AOD was determined in each study area varying from 4°×4° to 10°×10°. To this end, for each buffer size, the averaged AOD and cloud parameters were paired to calculate the sensitivities SCER (Eq. 1) and SNd (Eq. 2), as well as their correlation coefficients (R) between cloud properties (e.g., CER, Nd) and AOD. The optimal buffer size for each study area is defined as the one maximizing the R. This definition is adopted based on two core considerations. Firstly, it aligns with the statistical principle that a higher R value indicates a stronger linear correlation between the two variables in log-log space, minimizing the interference of random noise and non-aerosol confounding factors on the sensitivity estimation (Quaas et al., 2006; Gryspeerdt et al., 2022). This ensures that the derived SCER can reliably reflect the intrinsic relationship between aerosol loading and cloud droplet effective radius, rather than spurious correlations caused by inappropriate spatial scales. Secondly, this definition also facilitates comparability with existing literature, as it aligns with the methodological framework of satellite-based aci studies (Saponaro et al., 2017; Liu et al., 2021). In these studies, the optimal spatial scale is typically identified by maximizing the statistical robustness of variable correlations.

The dataset was used to study the characteristics of aerosol indirect effects as function of buffer size and study area, for two different periods: one with a high aerosol content (2008–2014) and another one with a decreasing aerosol content (2015–2022). This approach determined the optimal buffer size for aerosol indirect effect estimations as a function of study domain size, providing key observational constraints for constructing scale-adaptive parameterization frameworks suitable for different domain sizes over eastern China.

Figure 3 illustrates the spatial distributions of AOD and cloud properties (CER and Nd) across the study region, averaged for the periods 2008–2014 and 2015–2022. The AOD spatial patterns (Fig. 3a, d) show similar spatial distributions during both periods, but with notably reduced values during the latter. Pronounced spatial gradients in AOD are evident during both periods. The lowest AOD values occur over the mountainous regions of Shanxi province in the northwest, while elevated concentrations appear in the southeastern areas encompassing the Hebei and Shandong provinces. This geographical contrast arises from the mountain ranges that demarcate the heavily industrialized, densely populated North China Plain (NCP) in the east – characterized by substantial anthropogenic emissions – from the relatively cleaner western regions. Under prevailing southeasterly wind conditions, these topographic barriers effectively block transport of atmospheric pollutants which accumulate along their windward slopes (Sundström et al., 2012). The concentration of heavy industries and power generation facilities in the NCP are primarily responsible for the observed high AOD concentrations, together with meteorological and geographical conditions. Additionally, lower AOD values appear in southern Anhui and central Shandong relative to the surrounding regions.

The CER spatial distributions (Fig. 3b, e) reveal distinct differences between the two periods. During 2008–2014, larger cloud droplets predominated in the northern sectors, particularly throughout Hebei and western Shandong. Notably, the spatial correspondence between AOD and CER maxima aligns with the anti-Twomey effect, suggesting that the high aerosol loading promoted cloud droplet growth rather than suppression – consistent with findings from Wang et al. (2014) and Liu et al. (2018). The 2015–2022 period shows markedly reduced CER values (typically <10 µm) with enhanced spatial homogeneity.

Similarly, Nd exhibits contrasting spatial patterns between the two periods (Fig. 3c, f). The earlier timeframe shows depressed Nd values in central regions surrounded by elevated concentrations peripherally. This pattern reverses during 2015–2022, with increases of Nd in the central area accompanied by overall reduction of the cloud droplet concentrations in the surrounding regions.

Before analyzing the influence of AOD on CER, the relationship between CER and LWP should be investigated. The values of the LWP were divided into 40 subsets with a width of 5 g m⁻², and then the average value of CER in each subset was calculated and plotted as function of LWP (Fig. 4).

The variation of CER with LWP shows three regimes. For LWP smaller than 55 g m⁻² (period 1) or 50 g m⁻² (period 2), CER increased rapidly with the increase of LWP. This first LWP regime is referred to as a rapid growth regime (LWP1). The second LWP regime, referred to as a decreasing regime (LWP2), applies to the LWP range from 55 to 135 g m⁻² (period 1) or 50–100 g m⁻² (period 2) and CER decreased with the increase of LWP. When LWP was greater than 135 g m⁻² (period 1) or 100 g m⁻² (period 2), CER increased with increasing LWP but at a much slower rate than during the first regime; the third LWP regime is therefore referred to as a slow growth regime (LWP3). These results show that CER is very sensitive to the changes in LWP, which is consistent with the study of Liu et al. (2021). Specifically, CER exhibited a three-stage variation with LWP: rapid growth when LWP <50 g m⁻² (with the fastest change rate), a stable state during 50–150 g m⁻² , and slow growth when LWP >150 g m⁻² (at a rate much lower than the first stage). This highlighted the necessity of fixing LWP conditions to accurately investigate the impact of AOD on CER. To separate the effects of changing LWP on CER from those of changing AOD on CER, relations between CER and AOD were evaluated for constant LWP (McComiskey and Feingold, 2012), for each of the three regimes mentioned above, by using double-logarithmic plots of AOD versus CER. The number of CER observations in the third regime is too small to achieve statistically meaningful results, therefore the sensitivity of CER to AOD was only analyzed for the rapid growth and decreasing regimes.

The sensitivity SNd is defined as the slope of a linear fit to a log-log plot of SNd versus AOD (Eq. 2). For each period, we binned the data into AOD intervals of 0.02 and averaged Nd within each bin. Figure 8 shows the variation of SNd with buffer size for different study areas. In contrast to SCER, SNd is predominantly positive (p<0.01) in both periods and decreases with increasing buffer size. During period 1 (2008–2014, high AOD), SNd for the 6°×6° study area decreases rapidly to a minimum at buffer sizes of 40–50 km, then increases to a maximum at a buffer size of 120 km. For buffer size ≥120 km, the two smallest study areas (4°×4° and 6°×6°) yield similar SNd values, which are substantially larger than those for the two larger study areas (8°×8° and 10°×10°). During period 2 (2015–2022, decreasing AOD), we can see an initial increase of SNd for the study area of 6°×6° and 8°×8°, and variation of SNd for the study area of 10°×10° and 4°×4°. After that, SNd for the study area of 4°×4° and 6°×6° decreases rapidly to a minimum for a buffer size of 80 km, followed by an increase to a maximum for a buffer size of 140 km.

The optimal buffer sizes (maximizing R) are larger for the 8°×8° and 10°×10° study areas than for the 8°×8° and 10°×10° areas (Fig. 9), reflecting different aci characteristics under varying AOD conditions. Estimates of SNd and R, stratified by optimal buffer size, for study areas ranging from 4°×4° to 10°×10° during the two periods are presented in the Appendix Table A2. Sample sizes of Nd and AOD across both study periods, all buffer sizes and study areas, are presented in Appendices Tables A7–A8.

Expanding the study area inevitably increases spatial heterogeneity in aerosol loading, meteorology, and cloud type, while also introducing larger satellite retrieval uncertainties. This spatial mixing blends clean and polluted air masses, thereby introducing a statistical dilution effect on the estimated SNd. Therefore, the decrease in SNd with increasing study area size (Fig. 8) reflects not only a genuine weakening of aerosol-cloud interactions but also the combined effects of meteorological confounding, cloud regime transitions, and retrieval limitations. It is noted that SCER and SNd exhibit distinct anomalies in large buffer zones, which may be associated with all these factors.

Changes in aerosol chemical composition between the two periods may also modulate SNd. During 2008–2014, aerosols over eastern China were dominated by sulfate (30 %–40 % of PM_2.5 mass; Huang et al., 2014; Zheng et al., 2018). Given the strong hygroscopicity of sulfate-dominated aerosols (Zhang et al., 2012; Liu et al., 2023), their CCN activation efficiency was likely high, providing a favorable physical basis for aci (Lee et al., 2009). In contrast, during 2015–2022, policy interventions (e.g., the Air Pollution Prevention and Control Action Plan; Zheng et al., 2018) drove a structural transition: the sulfate mass fraction dropped sharply to 15 %–25 % (an absolute reduction of >50%), while less hygroscopic components (nitrate, carbonaceous aerosols, and secondary organic aerosols) increased in relative proportion (Huang et al., 2014; Zheng et al., 2018). As these components generally exhibit weaker hygroscopicity compared with sulfate (Zhang et al., 2012; Liu et al., 2023), this compositional shift may have reduced CCN activation efficiency under the same AOD, thereby weakening the sensitivity of Nd to AOD and altering aci intensity (Lee et al., 2009).

LWP is a critical parameter governing cloud radiative properties (Murray-Watson and Gryspeerdt, 2022). The quantification of albedo effects strongly depends on the spatial scale and the LWP. Neglecting LWP constraints in aci studies can weaken microphysical signals, leading to underestimation of radiative forcing (McComiskey and Gryspeerdt, 2012). To address this, we first systematically investigated the dynamic relationship between CER and LWP before analyzing CER sensitivity to AOD. The results demonstrate pronounced CER sensitivity to LWP variations, which can be categorized into three distinct regimes (Fig. 4).

In the first LWP regime, CER increases rapidly with LWP, i.e. the evolution of CER is predominantly driven by changes in LWP. This dominance may lead to overestimation of the influence of the AOD on CER (Liu et al., 2021).

In the second LWP regime, CER decreases with increasing LWP. In this regime, the regulatory effect of LWP on CER weakens significantly, and CER variations become increasingly governed by aerosol-related processes, indicating the growing dominance of aerosol indirect effects.

The third regime contains an insufficient number of CER observations to yield statistically significant results, which excludes the analysis of the sensitivity of CER to AOD.

Comparative analysis of scale-conditioned SCER across LWP regimes in periods 1 and 2 revealed markedly enhanced sensitivity of SCER to AOD in the second LWP regime. A trade-off exists between AOD and LWP under conditions of insufficient water vapor. This trade-off leads to smaller CER values. As suggested by Costantino and Bréon (2013), the LWP response to aerosol invigoration is influenced by two competing mechanisms: a drying effect caused by enhanced entrainment of dry air at cloud top (dominant in optically thin clouds) and a moistening effect from precipitation suppression (dominant in optically thick clouds). For larger LWP, the supply of cloud water is sufficient. The increase in aerosol number concentrations significantly affects the distribution of cloud droplet number concentrations and sizes. This further enhances the sensitivity of CER to AOD. For small aerosol concentrations, the values of |SCER| (Figs. 5b, 7b) decreased overall with expanding buffer size within the same study area. For fixed buffer size, |SCER| decreased as the study area increased. The ranges of |SCER| values across different study areas showed a convergent pattern. These values typically remained small and close to zero. During the high AOD period (2008–2014), anthropogenic emissions and dust transport provided abundant CCN. This laid the material foundation for strong aci. It enhanced the synergistic effect of “sufficient liquid water + abundant CCN” in the second LWP regime. This synergistic effect amplified the difference in SCER between the two LWP regimes. In the period of decreasing AOD (2015–2022), CCN concentration decreased following the implementation of clean air policies (de Leeuw et al., 2021, 2023). This reduction weakened the direct impact of aerosols on CER. However, the LWP-driven microphysical differences persisted. Thus, SCER in the second regime remained significantly smaller than that in the first regime, albeit with a smaller difference. Additionally, the complexity of aerosol types during the high AOD period (e.g., mixing of anthropogenic pollutants and natural dust) may have adjusted the value of SCER. However, it did not alter the dominant role of LWP. This aligns with the theory that “aerosol indirect effects are jointly regulated by concentration and type” (Liu et al., 2017).

The larger SCER observed at larger spatial scales (Figs. 5 and 7) may be attributed to meteorological confounding effects. In addition, clouds with larger LWP are usually associated with strong updrafts (such as convective clouds), and stronger turbulence and vertical transport will bring more aerosols into the clouds, increasing CCN concentration and a decrease in particle size, making them more sensitive to changes in AOD (Jones et al., 2009; Han et al., 2022; Fan et al., 2025). Therefore, this phenomenon is the result of the combined action of cloud microphysical processes (CCN activation, cloud droplet competition growth) and dynamic processes (updrafts, turbulent mixing). If the characteristics of aerosols (such as composition) change in the second LWP regime, this sensitivity may be further amplified. Consequently, the LWP-stratified SCER quantification framework enables precise characterization of scale-dependent aci, providing robust physical insights for climate effect assessments and effectively reducing uncertainties in future climate projections.

The central hypothesis of this study – that LWP is relatively consistent between the two periods (2008–2014 and 2015–2022), supporting valid comparisons of the spatial sensitivity of AOD-CER relationships –is well-supported by the following analysis. The differences in the mean, median, 25th, and 50th percentiles of LWP between the two periods are all less than 5 %, indicating a stable overall water vapor supply level. The spatial patterns of high-LWP regions (e.g., southeastern areas) and low-LWP regions (e.g., the mountainous areas in northern Shanxi) remained stable across the two periods (see Appendix Fig. A1), demonstrating that LWP spatial distribution characteristics are highly consistent. The sample proportions of LWP in the rapid growth regime are 59.30 % (period 1: 0–55 g m⁻²) and 55.36 % (period 2: 0–50 g m⁻²), while those in the decreasing regime are 29.64 % (period 1: 55–135 g m⁻²) and 24.59 % (period 2: 50–100 g m⁻²), suggesting that there is no systematic temporal shift in the LWP distribution. Meanwhile, short-term fluctuations are smoothed by multi-year averaging and large-sample statistics, resulting in a weak indirect impact of aerosols on LWP (LWP only increased by 5.6 %, much smaller than the 24 % decrease in AOD). Additionally, LWP-stratified analysis (i.e., binning LWP into 5 g m⁻² intervals) further isolates interference. The validation of the core hypothesis provides a reliable premise for accurately quantifying the impact of aerosol concentration changes on the sensitivity of cloud parameters and their spatial scale dependence.

Extensive studies have demonstrated a significant spatial scale dependence of aerosol indirect effects (McComiskey and Feingold, 2012; Possner et al., 2016; Glotfelty et al., 2020; Ekman et al., 2023). Failure to explicitly define the scale-dependent behavior of aerosol indirect effects may introduce systematic biases and inconsistencies in subsequent process analyses. Based on satellite observations, this study confirms statistically significant negative correlations between CER and AOD, as well as positive correlations between Nd and AOD during periods with different aerosol concentrations, aligning with classical aci theory (Quaas et al., 2009). Analysis of scale-conditioned SCER and SNd reveals that for fixed buffer size, an increase in the size of the study area leads to a systematic reduction in SCER (less negative) and SNd, corroborating the nonlinear attenuation of aerosol signals with spatial domain expansion (Quaas et al., 2009). The results from this study suggest that AOD-cloud property correlations in large study areas are susceptible to meteorological confounding effects (Quaas et al., 2010; Boucher and Quaas, 2012; Gryspeerdt et al., 2014; Liu et al., 2024). Theoretically, aerosol regulation of cloud microphysics is strongly local: smaller domains (e.g., 4°×4°) feature homogeneous meteorological conditions (humidity, updrafts), preserving undiluted aci signals and yielding larger |SCER| (pronounced Twomey effect). In contrast, expanded domains (e.g., 10°×10°) encompass heterogeneous meteorological conditions (circulation differences, boundary layer variability) that independently modulate cloud droplet growth. For example, strong updrafts enhance liquid water supply, offsetting aerosol-induced radius reduction (Altaratz et al., 2014), weakening aerosol-CER correlations and reducing |SCER|. Consistent with Grandey and Stier (2010), large-scale domains introduce “dilution bias” via non-target meteorological variability. This scale-dependent confounding mechanism elucidates uncertainties in aerosol indirect effect assessments at regional scales.

Multi-scale spatial analysis identifies different optimal buffer sizes for SCER and SNd in different periods. These findings align closely with satellite-based aerosol indirect effect studies (Wang et al., 2015; Liu et al., 2017), providing critical scale benchmarks for satellite product validation. Wang et al. (2015) reported an inverse “Twomey” effect between aerosols and CER in eastern China by analyzing aerosol and CER within a 50 km buffer zone around CALIOP samples. Similarly, Liu et al. (2017) systematically examined the response mechanisms of warm cloud macro- and microphysical parameters to increasing AOD in the Yangtze River Delta region, also using CALIOP samples within a 50 km buffer zone. The present study further shows that, as aerosol concentrations decrease, SCER values across different study areas with the same buffer size exhibit convergence characteristics, with generally smaller SCER (closer to zero). This indicates a significant weakening of aci intensity and reduced spatial extent dependency in low aerosol loading conditions. This phenomenon is consistent with the simulated behavior of aerosol-limited cloud regimes, where aci are quantitatively modulated by moisture availability and lose their sensitivity to large-scale dynamical stability, leading to a weaker and more homogeneous effect (Zhao et al., 2025).

By systematically quantifying the scale-response characteristics of aerosol indirect effects, this work not only elucidates the dynamic scale behavior of aci, but also, more critically, establishes criteria for determining optimal buffer size in regional aerosol indirect effect studies. These results provide quantitative observational constraints for refining scale-dependent parameterization modules in climate models, particularly for representing the modulation of ACI by spatial scale and LWP, thereby improving model predictive reliability.

A comprehensive comparison of the sensitivity SCER and SNd reveals that the responses of CER and Nd to AOD exhibit distinct yet inherently interconnected characteristics. These characteristics are jointly modulated by spatial scale and LWP regimes (Figs. 5, 7, 8; Appendices Tables A1–A2), which profoundly reflect the core microphysical mechanisms of aci. Details are elaborated as follows.

This study has three significant limitations. Firstly, similar to most previous studies (Wang et al., 2015; Liu et al., 2021), this study only utilized MODIS data with a resolution of 10 km to explore scale effects, ignoring finer or coarser resolution data. Therefore, using a 10 km buffer size as the minimum observation unit, this limitation makes the indirect effects of aerosols on smaller scales still unknown, which may lead to inaccurate evaluation of aerosol indirect effects. Therefore, future research can improve the sensitivity of aerosol indirect effects to scale changes by using observation data with higher accuracy or model simulations. Secondly, the current research focuses on the influence of buffer size and study areas, the potential impact of spatial aggregation methods (especially zoning directionality) on the quantitative results of aerosol indirect effects has not been systematically evaluated. Future research should further investigate the sensitivity of aerosol indirect effects to zoning direction. Moreover, the current study employs a uniform buffer size for both aerosol and cloud parameters, failing to account for potential interaction effects arising from discrepancies of buffer size between them. Therefore, clarifying scale dependence will avoid directly extrapolating local observation results to a larger study area when downscaling climate models or formulating regional environmental policies.