Warm boundary layer clouds, including stratus, stratocumulus, and cumulus clouds, are prevalent over the sub-tropical oceans and account for over 30 % of the global annual mean cloud coverage (Warren et al., 1988; Wood, 2012). These clouds cause a significant net negative radiative forcing on the surface radiation budget. However, our understanding of the aerosol indirect effect (AIE) on these clouds, particularly the impact of aerosols on cloud amount, brightness, and lifetime, remains a significant source of uncertainty in estimating the radiative forcing from human activities. The AIE plays a critical role in the Earth's radiation budget through its interactions with clouds. It consists of two effects: the Twomey effect, which involves an increase in the cloud droplet number from increasing aerosols and leads to an increase in cloud albedo (αc) from smaller droplets when the cloud liquid water path (LWP) is held constant (Twomey, 1977), and the cloud adjustment effect, which encompasses the impact of aerosols on cloud amount, cloud water, and αc through modulating cloud processes (e.g., Albrecht, 1989; Xue and Feingold, 2006; Chen et al., 2014; Gryspeerdt et al., 2019). The cloud adjustment effect is highly variable with large uncertainties in signs and magnitudes depending on the cloud state, boundary layer, and meteorological conditions among other factors (e.g., Han et al., 2002; Wang et al., 2003; Small et al., 2009; Sato et al., 2018).

Previous studies have made significant progress in identifying different cloud processes and feedback mechanisms to explain the responses of the cloud fraction (CF), LWP, and αc to aerosol perturbations (e.g., as summarized in Stevens and Feingold, 2009; Fan et al., 2016; Gryspeerdt et al., 2019). The cloud adjustment effect is influenced by two key feedback mechanisms: precipitation suppression and sedimentation–evaporation–entrainment.

Under clean conditions and for predominantly precipitating clouds, an increase in the cloud droplet number concentration (Nd) and an associated decrease in droplet sizes reduce precipitation efficiency and decrease water loss from precipitation. Consequently, this promotes an increase in cloudiness and cloud LWP (Albrecht, 1989; Qian et al., 2009; Li et al., 2011; Terai et al., 2012, 2015). For non-precipitating clouds, decreased cloud drop size due to increases in Nd impacts CF and LWP through their impact on the entrainment rate. A decrease in cloud droplet size diminishes the sedimentation rate in clouds, causing an accumulation of cloud water near the cloud top. This increased cloud water in the entrainment zone enhances cloud-top radiative cooling, the entrainment rate, and evaporation, resulting in a decrease in CF and cloud LWP (Bretherton et al., 2007; Chen et al., 2014; Toll et al., 2019; Gryspeerdt et al., 2019).

Additionally, the faster evaporation rates from smaller droplets enhance cloud-top cooling, downward motion in clouds, total kinetic energy, and the horizontal buoyancy gradient. The processes listed above, in turn, increase evaporation and the entrainment rate and, thus, form a positive feedback loop (Wang et al., 2003; Xue and Feingold, 2006; Small et al., 2009; Toll et al., 2019). Furthermore, among non-precipitating clouds, thick clouds with larger LWP exhibit stronger cloud-top longwave radiative cooling rates and therefore stronger cloud-top entrainment rates (e.g., Sandu et al., 2008; Williams and Igel, 2021). Therefore, the classification of cloud states (e.g., precipitating conditions and thickness) is essential for accurately quantifying the AIE and discerning opposing cloud processes. In this study, we classify cloud states based on the LWP–Nd parameter space, as these variables provide the most informative metrics for cloud susceptibility (Zhang et al., 2022).

This study focuses on the eastern North Atlantic (ENA) region, where the US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program has deployed a ground-based user facility in the Azores archipelago (Mather and Voyles, 2013). During the summer over the ENA region, warm boundary layer clouds exhibit pronounced diurnal variations in their properties and cloud states. For example, based on ARM surface radar and lidar observations, the frequency of stratocumulus clouds is highest at night, accompanied by an increase in the fraction of precipitating clouds. Throughout the daytime, both the cloud fraction and the precipitation fraction experience a slight decrease, followed by an increase after sunset (Rémillard et al., 2012). The retrieved cloud microphysical properties from ARM ground-based observations show similar “U-shaped” diurnal variations in cloud LWP, liquid water content, and optical thickness (Dong et al., 2014). Additionally, numerical studies have revealed a distinct diurnal cycle of the AIE for marine stratocumulus clouds, attributed to changes in cloud properties and boundary layer thermodynamic conditions (e.g., Sandu et al., 2008, 2009). However, observational analyses based on the ground-based observations at the ENA site or in situ measurements from field campaigns are often based on a few cases with limited samples and insufficient spatial coverage (e.g., Liu et al., 2016; Wang et al., 2020; Zheng et al., 2022). There have been few observational studies investigating the diurnal cycle of the AIE in the ENA region. With recent advancements in the spatial resolution of geostationary satellites, this study aims to investigate the diurnal variation in the AIE in warm boundary layer clouds over the ENA region and give a better understanding of the underlying mechanisms.

Both cloud properties and meteorological conditions have substantial spatiotemporal variability and distinct diurnal variations. Furthermore, changes in meteorological conditions can in turn influence cloud and aerosol properties. One of the main challenges in understanding the AIE lies in isolating the impacts of the confounding meteorological drivers on clouds and aerosols from the AIE on clouds. To address this challenge, Gryspeerdt et al. (2016) proposed the use of Nd as an intermediary variable for the AIE, instead of using aerosol optical depth (AOD) or the aerosol index. The use of Nd circumvents the well-known dependency of AOD on CF and surface wind speed, which do not necessarily reflect actual changes in aerosol loading. Moreover, the control of relative humidity and aerosol type on AOD prevents the establishment of a direct link between AOD and aerosol concentration or cloud condensation nuclei (CCN).

Another common method to disentangle meteorological impacts is to sort the controlling meteorological factors of the cloud state, such as relative humidity, lower-tropospheric stability, or vertical velocity, and examine the AIE accordingly (e.g., Chen et al., 2014; Gryspeerdt et al., 2019). However, this approach overlooks important information, including the frequency of occurrence of specific environmental conditions, the spatiotemporal co-variation in meteorological factors, and the correlations among them. Zhou et al. (2021) and Zhang et al. (2022) proposed a new method to estimate the cloud susceptibility within a confined space (e.g., a 1° × 1° or 2° × 2° grid box) of each satellite snapshot by assuming consistent meteorological conditions within this spatial domain. Additionally, it is important to note that meteorological conditions influence albedo susceptibility by altering the frequency of occurrence of different cloud states (e.g., precipitating and non-precipitating). Specifically, within a particular cloud state, meteorological conditions offer limited information regarding cloud susceptibility (Zhang et al., 2022).

The second main source of uncertainty in observational AIE studies arises from inferring processes in a temporally evolving system based on snapshots of observations (Mülmenstädt and Feingold, 2018). Due to the limited temporal or spatial resolution of the observations, most studies assume a Markovian system, where clouds and the AIE are assumed to only relate to the current state of the system and have no memory of the past states. However, this assumption contradicts the nature of the cloud system. Observational and modeling studies have shown that aerosol–cloud interaction processes take hours to reach the equilibrium state and that the sensitivity of the AIE is time dependent. For instance, Glassmeier et al. (2021) utilized a Gaussian-process emulation and derived the adjustment equilibration timescale for LWP to be ∼ 20 h. By tracking the ship tracks in satellite observations, Gryspeerdt et al. (2021) found a similar AIE timescale of ∼ 20 h or longer and the magnitude of LWP susceptibility to increase with time. In addition, Christensen et al. (2020) discovered that the influence of aerosols on cloud LWP, CF, and cloud-top height persists for 2 to 3 d by tracking cloud systems in satellite observations. In summary, the sensitivity of cloud responses to Nd perturbations changes with time, and, thus, the assumption that the AIE has no memory of its past state is inadequate. Nonetheless, the direct evaluation of the impact of cloud memory on the quantified cloud susceptibility remains unexplored to the best of our knowledge.

To facilitate a process-level understanding of the drivers behind the diurnal variation in the AIE for warm boundary layer clouds, we will classify these clouds into three states: precipitating clouds, non-precipitating thick clouds, and non-precipitating thin clouds. We investigate the changes in both the frequency of occurrence of cloud states and the magnitude of the AIE for different cloud states throughout the day. Additionally, we document the temporal changes in cloud state within each fixed 1° × 1° grid box and quantify the influences of cloud memory and state transition on the AIE. Section 2 describes the datasets as well as the methodology employed to quantify cloud susceptibilities, distinguish precipitating clouds from the satellite retrievals, and track cloud states. We present our results in Sect. 3. Section 3.1 characterizes the general conditions of warm boundary clouds over the ENA region during the summer. Section 3.2 introduces the LWP–Nd parameter space and illustrates the dependence of cloud responses to Nd perturbations on cloud states. We then discuss the mean daytime variation in cloud susceptibilities for all cloud states in Sect. 3.3, followed by an analysis of the AIE daytime variation for each cloud state and the impact of the state transition on the AIE in Sect. 3.4. In Sect. 3.5, we decompose the contributions to the daytime variation in cloud susceptibility into two components: one is from changes in the frequency of occurrence of different cloud states, and the other is from changes in the intensity of the AIE during the day. Section 4 includes discussions on the similarities and differences in findings between this study and previous studies of the AIE, and Sect. 5 gives the summary and conclusions of this study.

We use cloud retrievals derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on Meteosat-11, with a spatial resolution of 3 km at nadir and a half-hourly temporal resolution over the ENA region (33–43° N, 23–33° W). SEVIRI cloud products are derived using the Satellite ClOud and Radiation Property retrieval System (SatCORPS) algorithms (e.g., Painemal et al., 2021), based on the methods applied by the Clouds and the Earth's Radiant Energy System (CERES) project and specifically tailored to support the ARM program over the ARM ground-based observation sites (Minnis et al., 2011, 2020). Given the purpose of this study to quantify the AIE on warm boundary layer clouds, we focus on July over 4 years (2018–2021), a period that coincides with the highest frequency of occurrence of warm boundary layer clouds over the ARM ENA site (Rémillard et al., 2012; Dong et al., 2014, 2023).

The cloud mask algorithm implemented in SatCORPS is described in Trepte et al. (2019). SatCORPS cloud properties are based on the shortwave-infrared split-window technique during the daytime (VISST; Minnis et al., 2011, 2020), with the cloud optical depth (τ) and effective radius (re) being derived using an iterative process that combines reflectance and brightness temperatures from the 0.64 and 3.9 µm channels. Cloud LWP is computed from τ and re using the formula LWP=4reτ3Qext, where Qext represents the extinction efficiency and assumed constant of 2.0 (Minnis et al., 2011, 2020). The top-of-atmosphere (TOA) broadband shortwave αc is derived from an empirical radiance-to-broadband conversion using the satellite imager's visible channel and CERES Single Scanner Footprint (SSF) shortwave fluxes and dependent on the solar zenith angle and surface type (Minnis et al., 2016). Cloud-top height computation follows the methodology in Sun-Mack et al. (2014).

To validate the Meteosat-11-retrieved cloud mask and the detection of boundary layer clouds, we compare the boundary layer cloud fractions derived from Meteosat-11 with the ground-based observations at the ARM ENA site. As seen in Fig. S1 in the Supplement, both the diurnal variation and the mean CF of Meteosat-11 agree well with ARM observations. More details on the methodology for the evaluation study are included in the Supplement.

Our analysis focuses on warm boundary layer clouds with cloud tops below 3 km and a liquid cloud phase. To focus specifically on boundary layer cloud cases without including the edges of deep clouds, we apply a stricter threshold than merely using the pixel-level cloud-top height. We define boundary layer clouds as those with 90 % of their cloud tops below 3 km, labeling all contiguous cloudy pixels as distinct cloud objects.

Cloud Nd is retrieved based on the adiabatic assumptions for warm boundary layer clouds, as in Grosvenor et al. (2018), according to the following equation: 1Nd=52πkfadcwτQextρwre51/2.

In Eq. (1), k represents the ratio between the volume mean radius and re, assumed to be constant at 0.8 for stratocumulus; fad is the adiabatic fraction of the observed liquid water path and is assumed to be 0.8 for stratocumulus clouds (Brenguier et al., 2011; Zuidema et al., 2012); cw is the condensation rate, which is a function of temperature and pressure; Qext is the extinction coefficient, approximated as 2 in this study; and ρw is the density of liquid water. While the different components of Eq. (1) could contribute to the uncertainties in Nd, errors in re are the dominant drivers in Eq. (1) (Grosvenor et al., 2018).

To minimize uncertainties associated with bias in satellite cloud microphysical retrievals, we only select pixels with a minimum re of 3 µm, a minimum τ of 3, and a solar zenith angle (SZA) of less than 65° (e.g., Painemal et al., 2013; Painemal, 2018; Zhang et al., 2022). The SZA threshold of 65° was chosen to minimize biases observed at high solar zenith angles in re and τ (e.g., Grosvenor and Wood, 2014; Grosvenor et al., 2018).

In addition, to reduce uncertainties associated with the adiabatic assumption in the Nd retrieval, we implement a filtering process. For each cloud, we exclude cloudy pixels at the cloud edge, defined as those adjacent to cloud-free pixels, following a similar sampling strategy to that suggested by Gryspeerdt et al. (2022). Therefore, all cloud properties in this study refer to the properties of the cloud body without the cloud edge. It is worth noting that shallow cumulus clouds with diameters smaller than 9 km are not included. The removal of cloud-edge pixels accounts for ∼ 14 % of the cloudy pixels. Furthermore, we removed grid boxes containing islands due to the uncertainties in Meteosat retrievals over contrasting underlying surfaces. Lastly, to avoid unrealistically large retrievals, we eliminate pixels with the retrieved Nd values exceeding 1000 cm-3, which constituted only 0.002 % of the data.

Cloud susceptibility is quantified as the slope between cloud properties and Nd using a least-squares regression. As found by Arola et al. (2022) and Zhou and Feingold (2023), the retrieved cloud susceptibilities are sensitive to small-scale cloud heterogeneity, the co-variability between cloud properties and Nd, and the spatial scale of cloud organization. To reduce biases resulting from heterogeneity and co-variability, we first average the 3 km pixel-level cloud retrievals and Nd (Eq. 1) to a regular 0.25° × 0.25° grid for each half-hourly time step.

To further mitigate the impact from co-variability between cloud properties and Nd at larger spatiotemporal scales, cloud susceptibility is estimated within a 1° × 1° grid box at each satellite time step (e.g., Zhang et al., 2022). Moreover, estimating the cloud susceptibility over a confined space also helps to constrain the meteorological impacts on the AIE, with the assumption of a homogeneous meteorological condition within this spatial scale. Next, susceptibilities are calculated using the 0.25° smoothed data if the number of data points within the 1° × 1° box exceeds 6 (from a maximum of 16 data points). It is important to note that when computing the 0.25° × 0.25° averaged cloud properties, only data from cloudy pixels are used to ensure that the estimated susceptibility is not weighted by CF or impacted by satellite artifacts. Lastly, due to the minimal spatial variability in cloud susceptibility in the study region, the 1° cloud susceptibility is averaged over the study region (33–43° N, 23–33° W) to characterize the daytime variation in the AIE. Additionally, the results and conclusions of this study are not sensitive to the size of the box used in calculating the cloud susceptibility (e.g., over a 0.8° × 0.8° box or over a 1.5° × 1.5° box, not shown).

Because of the nonlinear relationships between LWP and Nd, the LWP susceptibility is defined as the slope in logarithmic scale, that is dln(LWP)/dln(Nd) (e.g., Gryspeerdt et al., 2019). The albedo susceptibility is estimated as the slope between αc and ln(Nd), equivalent to dαc/dln(Nd) (e.g., Painemal, 2018). Lastly, the CF susceptibility is estimated as dCF/dln(Nd). The mean CF is defined as the cloudy pixels excluding the cloud edge as a fraction of the sum of cloudy and clear pixels within each 0.25° × 0.25° box. Due to the highly variable nature of CF, the variability in the 0.25° CF could arise from quantifying edges or centers of the same cloud layer rather than Nd perturbations. To assess the potential influence of cloud morphology on the retrieved CF susceptibility, we did a sensitivity test to exclude any 1° × 1° scene meeting the following three criteria: (1) the difference between the maximum and minimum 0.25° CF is greater than 0.9, (2) the variation in the 0.25° Nd is less than 60 cm-3, and (3) the 0.25° CF in the 1° × 1° box samples the same cloud. The 0.9 and 60 cm-3 thresholds represent ∼ 45 % of the data. With the three thresholds combined, a total of 17 000 scenes were removed, which accounts for ∼ 24 % of the total samples. Removing these scenes does not change the conclusions of CF susceptibility in this study (not shown), which demonstrates that cloud morphology has minimal impact on the retrieved CF susceptibility. Furthermore, as we removed Nd retrievals at the cloud edge where Nd likely suffers large uncertainties, cloudy pixels at the cloud edge are set as clear for consistency in the calculation of the CF susceptibility. Removing the cloud edge decreases the 4-month mean CF for warm boundary layer clouds from 21.6 % to 19.0 %.

The susceptibility of the shortwave radiative fluxes to Nd (F0) is estimated as the sensitivity of the TOA shortwave upward radiative flux (SWTOAup) to Nd perturbations (e.g., Chen et al., 2014; Painemal, 2018; Zhang et al., 2022). The mean SWTOAup over a 1° × 1° grid box is estimated using Eq. (2), with the assumption that the clear-sky albedo over the ocean is small compared to the cloud albedo: 2SWTOAup‾=SWTOAdn‾⋅αc‾⋅CF‾, where SWTOAdn is the grid-box mean TOA shortwave downward radiative flux, which is estimated based on the latitude, longitude, date, and overpass time of each pixel, and αc and CF are the grid-box mean values. Then, F0 is estimated using the calculated αc and CF susceptibilities and the 1° × 1° grid-box mean cloud properties as shown in the equation below: 3F0=-dSWTOAupdln(Nd)=-SWTOAdn‾⋅dαcdln(Nd)⋅CF‾+dCFdln(Nd)⋅αc‾.

F0 is in units of Wm-2ln(Nd)-1, and a positive value indicates a decrease in the SWTOAup, which is a warming effect at the surface.

To minimize uncertainties in the linear regression for the estimated susceptibility, we analyze regressions that exhibited a goodness of fit exceeding the 95 % confidence interval (i.e., χ2<χ0.95,c2) and an absolute correlation coefficient greater than 0.2 (e.g., Painemal, 2018; Zhang et al., 2022). There are a total of ∼ 115 000 samples of the 1° cloud susceptibilities in this study; applying the goodness-of-fit thresholds results in exclusions of ∼ 33 000–43 000 samples for different susceptibilities, which comprise ∼ 28 %–37 % of the data. Sensitivity test shows that including cases that fail the goodness-of-fit test will not change the results and conclusions of this study (not shown). Specifically, including these cases decreases the magnitude of cloud susceptibilities for all three cloud states, but the signs of cloud responses to Nd perturbations remain consistent.

Since precipitating and non-precipitating clouds exhibit distinct responses to aerosol perturbations due to the effect of precipitation suppression and the wet-scavenging feedback, it is critical to distinguish between these two cloud states when estimating the AIE. Previous studies have utilized various methods based on the effective radius threshold (e.g., Gryspeerdt et al., 2019; Toll et al., 2019; Zhang et al., 2022) and the rain rate threshold (e.g., Duong et al., 2011; Terai et al., 2015) from satellite retrievals. In our study, we validate these two methods using the precipitating mask estimated from ground-based observations with a radar reflectivity threshold together with the lidar-defined cloud base at the ARM ENA site (e.g., Wu et al., 2020a). The thresholds of re > 12 µm and re > 15 µm yield hit rates of 0.79 and 0.73, respectively. However, the false alarm rate is higher for re > 12 µm (0.21) compared to re > 15 µm (0.1). The rain rate is computed using the empirical relationships derived from ground-based measurements in Comstock et al. (2004) as R=0.0156(LWP/Nd)1.75. Using a threshold of R > 0.05 mmh-1 results in a hit rate of 0.65. Consequently, we use the re > 15 µm threshold to define precipitating clouds in this study.

To investigate the dependencies of cloud susceptibility on previous cloud states and quantify the influence of cloud memory on the estimated cloud susceptibility, we track the historical cloud state over a 1° × 1° grid box for a 2 h period. During the summer in the study region, low-wind conditions prevail in the boundary layer, with the mean wind speed being less than 10 ms-1 for 85 % of the time and less than 7 ms-1 for 60 % of the time. Therefore, in most cases, fewer than half of the clouds exit the grid box within the 2 h, allowing us to track the previous cloud state within the same grid box (i.e., from the Eulerian perspective). The influence of cloud memory is assessed by comparing the cloud susceptibilities of clouds that undergo a transition in cloud state with those that do not experience such a transition. Section 3.4 provides more details and discussion on the sensitivity of tracking time and the influence of advection on our classification.

In this study, we quantify the susceptibility of warm boundary layer clouds to Nd perturbation using the pixel-level SEVIRI cloud retrievals of each time step. For heavily precipitating clouds, LWP increases under pristine conditions (e.g., Nd < 30 cm-3, Fig. 2a). For lightly precipitating and non-precipitating clouds, LWP decreases with Nd. The Nd–LWP relationship found in this study is consistent with that in Gryspeerdt et al. (2019) using global mean cloud retrievals from MODIS and AMSR-E at a coarser resolution of 1° × 1° and daily timescale. This consistency between different satellite measurements at different temporal and spatial scales greatly enhances our confidence in the retrieved relationship.

This study further separates non-precipitating clouds into thin and thick clouds based on their LWP. A consistent decreasing trend in cloud water is found for both states, yet non-precipitating thick clouds exhibit more negative LWP susceptibility dln(LWP)dln(Nd)=-0.94 compared to thin clouds dln(LWP)dln(Nd)=-0.71. The LWP susceptibilities estimated in this study are more negative than those in Zhang et al. (2022) and Zhang and Feingold (2023), based on a similar classification of cloud states. Particularly, we found that non-precipitating thin clouds have a decreasing trend in cloud water and a warming effect at the surface radiation while these are opposite in Zhang et al. (2022) and Zhang and Feingold (2023). This is due to different seasons and study regions between our study and their studies. The summer boundary layer in the ENA region is deeper and less stable with higher cloud tops (e.g., Klein and Hartmann, 1993; Ding et al., 2021; King et al., 2013) compared to the NE Pacific in Zhang et al. (2022) and the NE Atlantic region in Zhang and Feingold (2023). The less stable condition, deeper boundary layer, and deeper clouds could lead to a stronger cloud-top entrainment rate and result in a more negative LWP susceptibility (Possner et al., 2020; Toll et al., 2019).

Regarding the CF adjustment to Nd perturbation, a daytime mean positive response is found for precipitating and non-precipitating thin clouds and a negative response for non-precipitating thick clouds (Fig. 2c). Few studies have quantified the CF adjustment rate at 30 min intervals for a direct comparison of CF susceptibility. However, similar results are found using measurements and retrievals from different platforms at various spatial scales and timescales, which greatly increases our confidence in the observed CF responses toward Nd perturbation. For example, using MODIS measurement, Kaufman et al. (2005) found an increase in the longitudinal mean cloudiness for warm boundary layer clouds with increasing AOD in all four regions of the Atlantic Ocean characterized by distinct aerosol types. Using the natural experiment of volcanic eruption at Holuhraun in Iceland, Chen et al. (2022) found that aerosols from the eruption increase the monthly mean cloud cover by 10 % over the North Atlantic. By tracking the cloud trajectory using geostationary satellites, Christensen et al. (2020) found that aerosols enhance both CF and cloud lifetime at the timescale of 2–3 d, especially under stable conditions. It is worth noting that a decrease in CF was not observed in these studies, likely due to the prevalence of non-precipitating thin clouds and precipitating clouds in the Atlantic or the NE Pacific (e.g., Zhang and Feingold, 2023) that mask the signal from non-precipitating thick clouds without distinguishing cloud states.

Lastly, the distinct U-shaped daytime variation in all three cloud properties found in this study (Fig. 3a–c) is unlikely to be due to the systematic bias in re and τ retrievals at large SZAs based on the following two aspects. Firstly, if the daytime variation were driven by retrieval bias at large SZAs, we would expect the susceptibility to exhibit a symmetric pattern at local noon. As shown in Figs. 10 and 6, the LWP and αc susceptibilities for precipitating and non-precipitating thick clouds exhibit asymmetric patterns at local noon: with a decreasing trend from 13:00 LST and daily minimum at 16:00 LST and a continuously increasing trend from 11:00 to 18:00 LST, respectively. In addition, the CF susceptibilities for all three cloud states show asymmetric patterns at local noon. Secondly, if the retrieval uncertainty were to dominate the signal, we would expect less variation in cloud susceptibilities for overcast clouds, which suffer lower uncertainties in cloud retrievals from the plane-parallel assumption and the cloud 3-D effect. However, the opposite is found from the sensitivity test where overcast clouds exhibit stronger daytime variation in cloud susceptibilities (not shown).

Using Nd as an intermediary variable, this study investigates the aerosol indirect effect (AIE) for warm boundary layer clouds and its daytime variation over the ENA region with the half-hourly and 3 km cloud property retrievals from SEVIRI on Meteosat-11. To constrain meteorological impacts on clouds and aerosol–cloud interaction, cloud susceptibilities are estimated within a 1° × 1° grid box for each satellite time step. Based on the daytime mean cloud susceptibilities in the LWP–Nd parameter space, the sign and magnitude of cloud susceptibilities strongly depend on the cloud states (Fig. 2). Accordingly, warm boundary layer clouds are classified into three states: precipitating clouds (re > 15 µm), non-precipitating thick clouds (re < 15 µm, LWP > 75 gm-2), and non-precipitating thin clouds (re < 15 µm, LWP < 75 gm-2).

Precipitating clouds exhibit contrasting responses in cloud LWP, with increases observed for heavily precipitating clouds and decreases for lightly precipitating clouds. Positive αc and CF susceptibilities are identified for both heavily and lightly precipitating clouds. The net all-sky radiative forcing of the AIE on precipitating clouds is estimated to be -13 Wm-2ln(Nd)-1, with contributions from the CF and αc effects of -9.5 and -3.5 Wm-2ln(Nd)-1, respectively. For non-precipitating clouds, both thick and thin clouds show negative LWP susceptibility with more negative values found for thick clouds with higher LWP and Nd. This is likely attributable to the stronger shortwave absorption, larger cloud-top radiative cooling rate, and stronger entrainment for thick clouds. Consistent with the evaporation–entrainment feedback, non-precipitating thick clouds exhibit a decrease in CF and αc with increasing Nd and result in a net warming effect at the surface and a radiative forcing of +4.4 Wm-2ln(Nd)-1. On the other hand, non-precipitating thin clouds show an increasing response in CF and a less negative αc susceptibility. Additionally, the radiative effect from increasing CF (-8.3 Wm-2ln(Nd)-1) outweighs that from a darker cloud (+3.1 Wm-2ln(Nd)-1) and leads to a net cooling effect of -5.2 Wm-2ln(Nd)-1.

Warm boundary layer clouds manifest distinct and significant (p < 0.05) daytime variations in LWP, αc, and CF susceptibilities. All three cloud susceptibilities exhibit U-shaped diurnal patterns with clouds being less susceptible in the morning and evening and more susceptible at local noon (Fig. 3).

Daytime variation in LWP and αc susceptibilities is likely attributable to the transition in cloud state with clouds sustaining the memory of responses to Nd of the previous state (H1 in Table 1). From morning to noon, with increasing solar radiation, non-precipitating thick clouds evolve into thin clouds. Thin clouds decayed from thick clouds show significantly more negative LWP and αc susceptibilities than thin clouds that were previously thin (Fig. 5). Therefore, LWP and αc susceptibilities decrease from morning to noon for thin clouds and reach their daily minima at noon (Fig. 4). In the afternoon, thin clouds develop into thick clouds while retaining the memory of being less susceptible to Nd perturbations (Fig. 7), and therefore this leads to an increase in LWP and αc susceptibilities for non-precipitating thick clouds in the afternoon (Fig. 6). Meanwhile, daytime variation in CF susceptibility for non-precipitating thick clouds is more likely driven by changes in cloud morphology rather than the transition of cloud state (Fig. 8, H3 in Table 1). Compared to non-precipitating clouds, precipitating clouds exhibit smaller daytime variation in cloud susceptibility (Fig. 10).

The daytime variation in cloud susceptibility is primarily driven by changes in the intensity of cloud susceptibilities from morning to noon, rather than changes in the frequency of occurrence of different cloud states (Fig. 12). As the polar-orbiting satellites only observe cloud susceptibilities across different cloud states during a specific overpass time, they overlook the change in the intensity of cloud susceptibilities during the day. More specifically, based on the daytime variation in cloud susceptibilities found in this study, LWP susceptibility estimated at 13:30 LST could underestimate the daytime mean value by 26.3 % (-0.76 compared to -0.60), underestimate the αc susceptibility by 475 % (-0.023 compared to -0.004), and underestimate the CF susceptibility by 120 % (-0.019 compared to +0.055). It is worth noting that both the daytime variation and the daytime mean values of cloud susceptibilities in this study are estimated based on the regression analysis on spatial data within each satellite time step, with the assumption that the temporal change in cloud properties from Nd perturbations can be represented by the spatial relationships.

This study underscores the importance of considering the diurnal cycle of cloud susceptibilities when quantifying the AIE and its impacts on clouds and radiation. The classification of cloud states enables us to distinguish the sign and magnitude of cloud susceptibility and the underlying processes driving the diurnal variation in the AIE.

To further advance our understanding of the diurnal variation in the AIE, several avenues for future research can be pursued. Firstly, it is important to address uncertainties associated with satellite retrievals, which can propagate into uncertainties in the retrieved Nd, as discussed in Grosvenor et al. (2018). Future study could utilize active sensors to reduce these uncertainties, particularly during nighttime conditions. Moreover, using the retrieved Nd as a proxy for aerosol concentration may introduce uncertainties related to cloud processes that can act as sources or sinks of Nd, potentially buffering the relationships between Nd and cloud condensation nuclei. Future investigations are needed to better understand the relationships and how they vary with different cloud processes and throughout the day. Lastly, this study encompasses all warm boundary layer clouds without considering the highly diverse meteorological regimes and the associated cloud types in the ENA region. Classification of the synoptic and meteorological conditions associated with different cloud states and aerosol properties would contribute to a more comprehensive understanding, allowing for the disentanglement of the impacts of meteorology from the AIE.