The Beijing Weather Modification Office (BJWMO) provided the data for this study, and nine flights of stratocumulus clouds and aerosols over Guangxi were conducted using the King Air 350 ER turbo aircraft. The aircraft is equipped with the Aircraft Integrated Meteorological Measurement System (AIMMS-20; AvenTech Inc., Canada), which provides meteorological elements such as temperature (T) and relative humidity (RH) with a time resolution of 1 s. A passive cavity aerosol spectrometer probe (PCASP-100X, DMT Inc, USA) was installed to provide aerosol number concentrations in the optical particle size range of 0.11 to 3 µm, with a time resolution of 1 s, particle size uncertainty of 20 %, and concentration uncertainty of 16 %. The Fast Cloud Droplet Probe (FCDP; SPEC Inc, USA) was used to observe the cloud droplet concentration, cloud particle concentration and cloud particle size distribution. Its principle is to detect particles with an optical diameter ranging from 2 to 50 µm using forward scattering technology with a time resolution of 1 s. The particle number concentration measured by the FCDP in the size range of less than 3 µm has significant uncertainty. In this study, the range of Nc is defined as 3–50 µm. Na and Nc are measured in volume units. All instruments were calibrated before observation. The detailed principles of the airborne instruments can be found in several studies (Collaud Coen et al., 2010; Strapp et al., 1992; Zhang et al., 2009).

Detailed data of this aircraft observation activity, including observation date, time, cloud thickness, and microphysical quantities, are summarized in Table 1. Compared with aircraft observation data in other regions, the average LWC in Guangxi was higher, 5.33 times that in north China, and the average cloud droplet diameter was larger, 2.58 times that in north China (Zhao et al., 2011). Compared with the marine stratocumulus (Lu et al., 2011; Miles et al., 2000), the stratocumulus in Guangxi had higher cloud base height and greater cloud thickness. The cloud microphysical characteristics of the stratocumulus observed in this study are similar to those of previous observations. Compared with stratocumulus (non-precipitation warm cloud) over eastern China, the Nc, LWC, and Ed of stratocumulus in the Guangxi region were larger. According to previous studies (Liu et al., 2024), there were no special weather processes in the upper air and on the ground in Guangxi during the observation period, which ensured the quality of the data and the universality of the conclusions.

To ensure data quality, this study selected the data that met the following conditions and the flight macro record as the in-cloud data: Nc ≥ 10 cm⁻³, LWC ≥ 10-3 g m⁻³ (Gunthe et al., 2009; Zhang et al., 2011). The observation records show that the clouds during the observation period were stratocumulus clouds (non-precipitation warm clouds). Therefore, the aerosol and cloud microphysical data met the following conditions: observation height ≤ 4000 m, T > 0 °C. The height of the PBL is determined by applying the gradient method to the vertical distribution of potential temperature (Kim et al., 2007; Su et al., 2017).

The microphysical quantities such as Nc, LWC, and Ed are calculated from the cloud droplet spectrum data detected by the FCDP. The calculation formulas are as follows: 1Nc=∑ni2LWC=∑43πri3ρwni3Ed=2∑niri3∑niri2. In the formulas, ni is the cloud number concentration for each bin, ri is the median particle size for each bin, and ρw is the density of water.

The relative heights of the cloud are defined as Zn: 4Zn=Z-ZbaseZtop-Zbase. In the formula, Zbase is the height of the cloud base, and Ztop is the height of the cloud top. The cloud heights have been normalized by setting the cloud base as 0 and the cloud top as 1.

Similar to previous studies, the first indirect effect (FIE) of aerosol or Twomey effect of aerosols and clouds is defined as 5FIE=-Δln⁡EdΔln⁡αLWC. In the formula, α represents the physical quantity of aerosols, which can be quantified using aerosol optical depth (Feingold et al., 2001), aerosol extinction coefficient (Feingold et al., 2003), cloud condensation nuclei concentration, and aerosol number concentration (Che et al., 2021; Zhao et al., 2012, 2018). The FIE value may vary with the variables representing the aerosol amount.

The vertical pressure velocity (Pa s⁻¹) was obtained from MERRA2, with a spatial resolution of 0.625° × 0.5° and 42 layers and a temporal resolution of 3 h. The data from the first to the 23rd layers, corresponding to pressure altitudes from 1000 to 200 hPa, were selected, covering the maximum altitude of aircraft observations. An average calculation was performed to obtain the vertical pressure velocity for the Guangxi region from 08:00 to 20:00 BJT during the observation period, reflecting the temporal variation characteristics of vertical airflow above the region. This dataset has been used in several studies (Ge et al., 2021; Kennedy et al., 2001; Painemal et al., 2021).

Based on the criteria of Nc ≥ 10 cm⁻³ and LWC ≥ 10-3 g m⁻³, aerosol, cloud droplet, and meteorological data were distinguished between inside and outside the cloud. The vertical averages were calculated at 10 m height intervals, resulting in the vertical distributions of physical quantities from nine observation flights, covering a height range of 0–4000 m and ensuring consistent vertical resolution for each physical quantity. Subsequently, the average vertical distribution of physical quantities from the nine observation flights was calculated, leading to the vertical distribution diagrams of each physical quantity during the observation period, as shown in Fig. 1. The average vertical profiles of Na (interstitial aerosol, aerosol particles too small to activate to cloud droplets), Na (outside cloud) (Fig. 1a), cloud microphysical quantities (Fig. 1b), and meteorological elements (Fig. 1c–d) during the observation period were obtained. Na (interstitial aerosol) decreased gradually with height and was affected by aerosols in the atmospheric environment. Below 1500 m, Nc first decreased and then stabilized with increasing height, following a trend similar to that of Na. This indicates that the number of cloud condensation nuclei capable of activating cloud droplets diminishes as altitude increases. Compared to the upper atmosphere (above 1500 m), there were more cloud condensation nuclei in the lower atmosphere, resulting in an average Nc value of 407 cm⁻³. Between 1500 and 3300 m, Nc showed little variation with height, remaining concentrated around 100 cm⁻³ at each altitude (Fig. 1a). The low Nc observed at certain altitudes may be due to the observation area being close to the edge of the cloud.

With the increase in height, Ed first increased and then remained unchanged and then increased (Fig. 1b). A large number of cloud droplets competed for water vapor below 1500 m, which is not conducive to the growth of cloud droplets, so the average Ed was only 11.21 µm. In Guangxi, the top of the PBL during autumn ranges from 1000 to 1500 m (Fig. 1c), where temperature inversion layers occur. This temperature structure increases the stability of the air, suppressing the formation of vertical airflow and hindering the growth of cloud droplets. Above 1500 m, Nc was lower than the near ground, and the lower atmospheric temperature was conducive to increasing cloud droplet particle size. The average value of Ed reached 22.78 µm. The value of LWC was independent of height, with an average value of 0.22 g m⁻³ in Guangxi (Fig. 1b). RH was consistently above 60 %, making it likely for the air to reach saturation and lead to cloud formation.

To understand the time variation of the vertical distribution of cloud microphysical quantities, the data were classified. Vertical profiles of interstitial aerosol (Na), Na outside the cloud (Fig. 2), cloud microphysical quantities (Fig. 3), and meteorological elements inside and outside the cloud (Fig. 4) were obtained at 10 times from 10:00 to 18:00 and at 20:00 BJT. The data collected inside the cloud were original, while the average values outside the cloud were calculated at 10 m intervals.

At 10:00 BJT, Nc below 900 m was less than 100 cm⁻³, and Na in the PBL was high (Fig. 2a). Although there were sufficient aerosols that can be activated into cloud condensation nuclei, RH > 60 %, and the atmospheric temperature was high, which was not conducive to the activation of small-size aerosol particles (Fig. 3a). At the same time, LWC was low, and it was difficult for the condensed cloud droplets to grow; the average Ed was only 8.01 µm (Fig. 3a). Between 900 and 1500 m, there were not only sufficient cloud condensation nuclei but also sufficient water vapor and temperature conditions, which are conducive to the formation of cloud droplets. The average Nc and Ed increased to 430 cm⁻³ and 11.15 µm. Above 1500 m, although the water vapor condition was sufficient (LWC = 0.16 g m⁻³), the cloud condensation nuclei were few, resulting in an average Nc value of only 35 cm⁻³. However, sufficient LWC was conducive to the growth of cloud droplets, and Ed was significantly higher than clouds below 1500 m, with Ed ranging from 13.82 to 37.26 µm. At 1500 m, Na (interstitial aerosol) was 34 cm⁻³, increasing to 134 cm⁻³ at 1600 m. RH remained nearly constant in this range, while LWC rose from 0.16 to 0.19 g m⁻³, promoting the hygroscopic growth of aerosols. However, Nc did not show a significant increase. Thus, the temperature inversion layer (Fig. 4a) within the cloud may contribute to the rise in Na (interstitial aerosol). This increase suggests more aerosols are inactive or unable to activate within the cloud. These aerosols may result from mixing warm air from outside the cloud at the cloud base (Lu et al., 2011). Furthermore, the temperature inversion layer may hinder vertical airflow within the cloud, suppressing cloud droplet growth.

At 11:00 BJT, aerosols were transported by updrafts (Fig. 5a) to around 1500 m (near the top of the PBL) and activated into cloud condensation nuclei. Below 1500 m, the average Nc value was 102 cm⁻³ (Fig. 2b), while the average LWC value was only 0.03 g m⁻³ (Fig. 3b). Cloud droplets were competing for water vapor. The Ed value was only 8.20 µm, similar to the cloud microphysical characteristics near the PBL at 10:00. Between 1500 and 3150 m, Na was less than 10 cm⁻³, indicating insufficient CCN, and the average Nc was only 29 cm⁻³. Compared to 10:00 BJT, the LWC was higher (mean 0.19 g m⁻³), resulting in a larger Ed in the upper part of the cloud, with an average of 28.95 µm.

At 12:00 BJT, the height of the PBL top rose to 1000 m; the near-surface aerosol was transported to 1200–1500 m (Fig. 2c; the mean value of Na outside the cloud was 578 cm⁻³); the mean value of Nc reached 399 cm⁻³; and the mean value of Ed was only 9.41 µm (Fig. 3c), higher than at 11:00 BJT. Stratocumulus clouds above 1800 m had low Nc (mean 35 cm⁻³) and large Ed (mean 26.14 µm).

At 13:00 BJT, the Nc ranged from 13 to 2052 cm⁻³ below 1200 m (Fig. 2d), which may be attributed to the uneven development of clouds within the detection range. The increase in solar radiation leads to high near-surface temperatures (Fig. 4d, T > 25 °C), which enhances turbulent activity within the PBL and is favorable for cloud droplet formation. Therefore, Nc at 13:00 BJT was larger than that at 10:00 BJT, and many cloud droplets hindered their particle size growth, with an average Ed value of 9.23 µm (Fig. 3d). From 1200 to 1500 m, the mean values of Nc and Ed were 155 cm⁻³ and 12.29 µm. At this height, a strong temperature inversion layer appeared (Fig. 4d), and cloud droplet evaporation activity was enhanced (Li et al., 2003), resulting in a higher Na (interstitial aerosol) than Na (outside cloud). For stratocumulus clouds above 1500 m, the Nc varied little with height, and the average Ed was 21.45 µm.

At 14:00 BJT, the Nc range below 1500 m was 11 to 1109 cm⁻³ (Fig. 2e), with the highest PBL top height at 1500 m, which diluted the Na (out of the cloud) within the PBL, resulting in a decrease in the maximum Nc (Nc = 1109 cm⁻³). The average LWC was 0.29 g m⁻³ (Fig. 3e), higher than at 13:00 BJT, providing moisture conditions for cloud droplet growth, while the upward airflow was strong (Fig. 5b). Consequently, the average Ed was 13.75 µm. A temperature inversion layer was present at 2500 m (Fig. 4e), hindering aerosol diffusion and enhancing the evaporation of cloud droplets near the cloud top, leading to a peak in Na (interstitial aerosol) at that height.

At 15:00 BJT, the Nc and Na (interstitial aerosol) between 1600 and 2000 m were higher than those at 14:00 BJT with average values of 720 and 249 cm⁻³ (Fig. 2f). Due to the increase in Nc, the average Ed was only 13.72 µm (Fig. 3f). The increase in Na (outside cloud) above 2000 m provided CCN, resulting in an average Nc of 146 cm⁻³. Although the moisture conditions were sufficient, with an average LWC of 0.23 g m⁻³, which was higher than the 0.05 g m⁻³ recorded at 14:00 BJT (Fig. 3f), and RH was 52 % (Fig. 4f), the average Ed decreased to 16.73 µm. This decrease was due to the competition for moisture among cloud droplets, which led to an increase in small-particle-size cloud droplets.

At 16:00 BJT, Nc and Na (interstitial aerosol) below 2000 m were relatively large, 458 and 468 cm⁻³, respectively (Fig. 2g). The temperature inversion layer at the top of the PBL hinders the condensation growth of cloud droplets. The average Ed was only 11.00 µm (Fig. 3g). Similar to the observations at 15:00 BJT, Na (outside cloud) and Na (interstitial aerosol) near 3000 m were higher. The low temperature (T = 7.75 °C) and high humidity (RH = 70 %) of the cloud environment (Fig. 4g) were conducive to the activation of aerosol. The maximum value of Nc reached 395 cm⁻³. However, the average of Ed was only 17.13 µm due to water vapor contention between cloud droplets.

At 17:00 BJT, the height of the PBL decreased to 730 m. Aerosols were transported above the PBL (Fig. 2h), providing CCN above 2000 m. Nc remained constant with an average of 134 cm⁻³ (Fig. 2h), while Ed averaged 17.12 µm (Fig. 3h). Under the cooling of the atmosphere and the cooling of the cloud tops at sunset, the Ed near the cloud tops was greater than 30 µm. The temperature inversion layer of 1600–2000 m (Fig. 4h) enhanced cloud droplet growth and hindered aerosol diffusion, causing the Na (interstitial aerosol) to be higher than the Na outside cloud.

At 18:00 BJT, the height of the PBL decreased to 500 m, resulting in the accumulation of aerosols between 900 and 1400 m (Fig. 2i), which led to the formation of small-particle-size cloud droplets, with an average Nc of 273 cm⁻³ and an average Ed of 16.67 µm (Fig. 3i). Similar to the observations at 17:00 BJT, the atmospheric temperature above 1400 m was high (Fig. 4i), and cloud droplet evaporation caused Na (interstitial aerosol) to be close to or greater than Na (outside cloud).

At 20:00 BJT, there were upward flows between 1000 and 1500 m (Fig. 5d). The abundance of CCN and low temperature (Fig. 4j) promoted the formation and growth of cloud droplets. The average Nc was 194 cm⁻³ (Fig. 2j), higher than the Nc observed from 10:00 to 13:00 BJT. LWC and Ed gradually increased with height (Fig. 3j). LWC rose from 0.02 to 0.64 g m⁻³. Ed increased from 7.52 to 29.59 µm.

The cloud height is normalized, and the relative height of the cloud is set as Zn (0 ≤ Zn ≤ 1). Zn < 0.33 is the lower cloud layer, 0.33 ≤ Zn < 0.67 is the middle cloud layer, and Zn ≥ 0.67 is the upper cloud layer. The concentration spectra of cloud interstitial aerosol numbers (Fig. 6a–c) and cloud droplet numbers (Fig. 6d–f) at different locations at different times were obtained.

From 10:00 to 13:00 BJT, the interstitial aerosol particle size in the cloud's lower layer was concentrated below 0.4 µm. In comparison, the cloud droplet diameter was primarily concentrated below 20 µm, with few large-particle-size cloud droplets (Fig. 6a, d). In the middle cloud layer, Na across all particle size ranges had decreased to below 1000 cm-3µm-1. Nc for particles smaller than 20 µm has decreased, while Nc for particles larger than 20 µm exceeded 0.1 cm-3µm-1 (Fig. 6b, e). Na in the upper cloud layer was minimal compared to the middle and lower layers. Sufficient water vapor (LWC = 0.14 g m⁻³, Fig. 3a–c) and low temperature (T = 11.72 °C, Fig. 4a–c) promote the growth of cloud droplets, resulting in fewer Nc for particles larger than 20 µm in the upper layer (Fig. 6c, f) compared to the middle layer.

From 14:00 to 16:00 BJT, aerosols diffused upward with the increase in the PBL, leading to a decrease in Na in the cloud's lower layer (Fig. 6a, d). The upward transport of aerosols caused the upper-level Na of the cloud to be higher than that observed from 10:00 to 13:00 BJT. This change increased the Nc of droplets with diameters greater than 20 µm (Fig. 6b–c, e–f). Newly formed cloud droplets competed for water vapor. Nc of droplets larger than 30 µm decreased, while Nc of smaller droplets increased.

From 17:00 to 20:00 BJT, the height of the PBL decreased. Na increased, and Nc of large droplets decreased. Aerosols retained at the top of the PBL provided CCN for the cloud's middle and upper layers (Fig. 6b–c, e–f). During this period, Nc was higher than observed from 10:00 to 13:00 BJT. The increase in Nc may be attributed to the rise in Nc of droplets smaller than 20 µm.

Previous studies have shown two sources of aerosols in Guangxi, namely the land and the ocean, where air masses from land will bring higher aerosol particle number concentrations (Liu et al., 2024). According to the classification of air mass sources, the frequency distributions of Na (interstitial aerosol), Nc, LWC, and Ed under the influence of land and ocean air masses were obtained (Fig. 7).

Under the influence of land air mass, Na (interstitial aerosol) was less than 500 cm⁻³, and Nc was high. The frequency distribution of Ed was unimodal, mainly concentrated in the range of 16–18 µm (Fig. 7a). Under the influence of ocean air mass, Na (interstitial aerosol) was mainly less than 20 cm⁻³. Nc was primarily distributed in the range of 10 to 50 cm⁻³. Ed was significantly higher than that under the influence of land air mass. Ed presented a bimodal distribution with peak values of 17.75 and 34.25 µm (Fig. 7b).

In addition to the influence of the air mass source, the vertical distribution of Na is also affected by PBL. We selected two aircraft observation data on 29 October and 2 November to analyze the influence of the PBL on the cloud microphysical quantities. The observed cloud base height was lower than the heights of the PBL, and the cloud top height was > 1500 m. The clouds crossed the top of the PBL, and the cloud thickness was similar (about 2500 m).

According to the vertical profiles of the aerosol number concentration spectrum (Fig. 8a–b), there were significant differences between the two Na profiles. In the height affected by the PBL (below 1500 m), aerosol pollution occurred on 29 October (Na > 1000 cm⁻³), and the atmosphere was clean on 2 November (Na < 600 cm⁻³). In the upper atmosphere (above 1500 m), aerosol pollution (Na < 200 cm⁻³) occurred on 2 November compared to 29 October (Na < 100 cm⁻³).

On 29 October, the aerosol pollution in the PBL was severe (Fig. 9a, Na = 1331 cm⁻³). The aerosol number concentration spectrum exhibited a bimodal distribution, with peak diameters of 0.14 and 0.22 µm (Fig. 8a). The atmosphere contained sufficient CCN, resulting in a large Nc (Fig. 9a, Nc = 460 cm⁻³). As shown in the cloud droplet number concentration spectrum (Fig. 8c), most cloud droplets were concentrated in the size range of 3–24 µm (Fig. 8c). Ed was 9.69 µm (Fig. 9e), primarily because many cloud droplets competed for water vapor, making it difficult for them to grow into larger droplets. A strong inversion layer at 1500 m (Fig. 9c) hindered the upward transport of aerosols. Consequently, Na above 1500 m was low, leading to a reduced Nc, with an average of only 35 cm⁻³. Figure 8c showed that cloud droplet sizes within the PBL primarily range from 8 to 21 µm. In contrast, above the PBL, cloud droplet sizes are mainly distributed below 8 µm and above 21 µm, with an average effective diameter (Ed) of 25.28 µm (Fig. 9e). These large-particle-size cloud droplets likely originated from the collision and growth of droplets within the 8.0 to 21 µm range.

On 2 November, Na in the PBL (Fig. 9b, Na = 405 cm⁻³) was slightly higher than Na in the upper air (Na = 220 cm⁻³). The Nc in the PBL (Nc = 243 cm⁻³) was higher than that above the PBL (Nc = 124 cm⁻³). The concentration spectra of cloud droplet numbers exhibited a bimodal distribution (Fig. 8d). The presence of a large number of small cloud droplets in the PBL hinders the growth of larger droplets, resulting in a lower number of large cloud droplets (Dp > 18 µm) in the PBL compared to the upper air. Ed in the PBL (Fig. 9f, Ed = 12.89 µm) was lower than in the upper air (Ed = 17.94 µm). The inversion layer (Fig. 9d, about 750 m in thickness) above the top of the PBL enhanced the evaporation activity of cloud droplets, leading to a lower Nc at this height compared to other heights and a higher Na (interstitial aerosol) than that observed at other heights.

To understand whether the relationship between aerosol and cloud in Guangxi is consistent with the Twomey effect, we classified the in-cloud data below 1000 m on 29 October and 2 November. We calculated the FIE index of LWC in different ranges (Fig. 10). The equation within each panel of Fig. 10 represents a fitted curve for the data, indicating the relationship between Na and Ed. The relationship between Na and Ed can be expressed as Ed = NaFIE. The results showed that Na and Ed were always negatively correlated, regardless of low LWC conditions or high LWC conditions. Therefore, the relationship between aerosol and stratocumulus in Guangxi is consistent with the Twomey effect, and Ed decreases with the increase in Na.