Aerosol particles, by acting as cloud condensation nuclei (CCN), can modify cloud properties and precipitation formation, altering the radiative flux at the top of the atmosphere, which is known as effective radiative forcing from aerosol–cloud interactions (ERFaci) . Additionally, absorbing aerosols can also alter the cloud distribution by perturbing the atmospheric temperature structure, known as semi-direct effects . ERFaci may be further subdivided into (i) the radiative forcing due to aerosol–cloud interactions (RFaci), also known as the Twomey effect describing the increased cloud albedo resulting from enhancement in cloud droplet number concentration (Nd) due to an increase in anthropogenic aerosol emissions , and (ii) rapid adjustments, which are essentially the consequent responses of liquid water path (LWP) and cloud horizontal extent to changed Nd via the Twomey effect . Although extensive investigations have been made to quantify the Twomey effect, significant uncertainties remain regarding its magnitude. This study will discuss the Twomey effect with a focus on the sensitivity of Nd to CCN perturbations due to its fundamental role in aerosol–cloud interactions. Note that the related radiative forcing will not be estimated here, as the anthropogenic perturbation to CCN concentrations is highly uncertain and not easily accessible from observational data.

Current climate models suggest diverse magnitudes of the Twomey effect even with identical anthropogenic aerosol emission perturbation . Thus, observational data at the climate-relevant scale, i.e., satellite retrievals, are required to quantify and constrain the Twomey effect globally, which is basically the sensitivity of Nd to CCN perturbations . As reviewed recently by , there are, however, several uncertainties in inferring the Nd-to-CCN sensitivity (S=dln⁡Nddln⁡NCCN, where NCCN means proxies for CCN number concentration) from satellite observations, hindering its applicability to further evaluate climate models or quantify RFaci from data. Most of them have been reported to bias S toward a lower value, in turn leading to an overall underestimated ERFaci, including (i) the instrument detectability limitations on aerosol loading in pristine environments , (ii) inadequate proxies (such as aerosol optical depth – AOD, or a variant thereof) for CCN owing to the lack of information on the aerosol size and chemical composition , (iii) the limited usability of the AOD–Nd relationship in the present day (PD) to determine the change in Nd caused by anthropogenic aerosol emission due to differing preindustrial (PI) and PD aerosol environments , and (iv) satellite sampling biases, which tend to discard clouds with a high cloud fraction due to the inability to retrieve aerosol under cloudy conditions, thereby resulting in an artificial cloud regime selection i.e., omitting more retrieval-reliable stratiform clouds;. Additionally, meteorological conditions, e.g., lower tropospheric stability , relative humidity , availability of water vapor , and wind shear , and vertical overlapping status of aerosol and cloud layers also play roles in regulating aerosol–cloud interactions. It is worth noting that most of these studies calculated S based on cloud effective radius rather than Nd, so they are subject to even more errors from the problem of stratification by liquid water path. Currently, a key difficulty in interpreting satellite-observed aerosol–Nd relationships is to isolate the causal impact of aerosols on Nd from other confounding factors modifying the variations of aerosol and cloud simultaneously, specifically (i) updraft, determining cloud development as well as the maximum supersaturation at cloud base and thus aerosol population that can be activated, (ii) precipitation processes, depleting cloud droplets via coagulation and scavenging sub-cloud aerosol particles, and (iii) retrieval errors, biasing retrieved aerosol and cloud properties concurrently. However, a clear understanding of how they affect the estimates of S quantitatively is lacking from the perspective of satellite observations .

In terms of the updraft, in situ aircraft measurements , ground-based remote sensing , and detailed parcel model simulations clearly showed the dependency of S on updraft, with generally larger S at stronger updraft. In particular, covariability of updrafts and aerosol concentrations has been found to result in a stronger S than keeping vertical velocity (w) constant . As noted by , the updraft may roughly explain 20 % of the variability in ΔNd from its PI–PD difference, adding to the uncertainty of the ERFaci estimate. Despite of the importance of dynamical constraint, it is not easily applicable to the analysis of satellite data due to the lack of updraft observations near cloud base at a global scale. As an alternative, cloud-base height (CBH) may potentially serve as a practical proxy for the updraft at the base of liquid cloud because of the tightly linear correlation illustrated by in situ observations of cumuliform clouds . Although data used to draw this conclusion by were collected from only three locations, they covered various boundary conditions over both continents and oceans. Moreover, a theoretical framework has also been established to support the observed empirical relationship , lending credibility to applying CBH as a proxy for the updraft. Building on this, recently developed CBH retrievals offer an opportunity to gain some insight into the potential role updraft variability may play in the global ERFaci assessment.

In addition to the updraft, precipitation formation further complicates the derivation of the strength of S, since it can efficiently deplete cloud droplets and scavenge aerosols from clouds . In such cases, the change in Nd is not necessarily related to actual aerosol perturbations but rather to the intensity of cloud sink, and thus in principle, it should not be directly applied to infer ΔNd driven by anthropogenic emissions. However, due to the lack of simultaneous observations of precipitation and aerosol–cloud properties from passive satellite remote sensing alone, most aerosol–cloud interaction (ACI) estimates do not consider the influence of precipitation or just roughly identify the occurrence of rain by relying on some simplified metrics, such as the threshold of 14 µm cloud effective radius (CER) for rain initiation or the difference of CER between retrievals employing the bands of 2.1 and 3.7 µm . Even though few studies have explicitly accounted for this by combining simultaneous precipitation observations from active remote sensing , how different treatments could influence the assessment of S remains unclear. Solving this problem is helpful to reconcile the current diverse ACI estimates in order to achieve a more confident observational constraint.

For satellite-based investigations, it is crucial but difficult to disentangle any physically meaningful attributable factors from artificial aerosol–cloud linkage induced by retrieval biases. In terms of Nd, retrievals for 3D-shaped clouds and partially cloudy pixels deviate from the retrieval assumptions of overcast homogenous cloud and 1D plane-parallel radiative transfer, thereby appearing to lead to an overestimation of CER , and in turn, an underestimated Nd . This issue was reported to be more pronounced for broken cloud regimes and could to some extent be addressed by only sampling Nd for pixels with either a high cloud fraction or large cloud optical depth COT;. In addition to the assumptions for clouds, the existence of aerosols above clouds can also affect the retrieval of cloud optical depth , in turn bias Nd calculation. Meanwhile, the retrieved AOD or aerosol index (AI) can be biased to a larger value due to inability to detect thin clouds in an aerosol retrieval scene or due to enhanced reflectance from neighboring clouds . It is noteworthy that the overestimation of AOD tends to be enhanced with increasing cloud fraction and COT as a result of both retrieval problems and aerosol swelling . Therefore, the potential covariations between biases in Nd and AOD (AI) modulated by cloud macrophysical properties could incur a spurious correlation between the two variables, obscuring the causal interpretation. While a few studies pointed out that the AOD(AI)–Nd correlation is substantially enhanced when analyzing reliable Nd retrievals , how and to what extent the satellite-diagnosed S varies with the retrieval biases in terms of both aerosol and Nd, respectively, has not been fully understood. Such understanding is quite important for reconciling the previous estimates and proposing a meaningful method applicable to satellite-based investigations.

While the problem of vertical co-location between retrieved CCN proxies and clouds has been noticed in many previous studies, most of them placed focus on its influence on the correlation between aerosol and cloud , i.e., a much higher correlation between Nd and aerosol extinction coefficients near cloud base compared to Nd vs. column-integrated aerosol quantity (AOD or AI), rather than the influence on S. The latter is usually quantified as a regression coefficient (regression slope in log–log space) between Nd and the CCN proxy and is a key determinant of radiative forcing estimates. Using AI as a CCN proxy, demonstrated a weaker cloud susceptibility for the case with separated aerosol–cloud layers than well-mixed ones. However, it is unclear how the S would change when switching commonly used column aerosol quantities to aerosol measures at cloud base. This understanding is particularly important for the intercomparison and further reconciliation between current ACI metrics relying on diverse CCN proxies, including column-integrated, near-surface, and cloud-level aerosol quantities.

In this study, we focus on the quantification of the impacts of three major confounders mentioned above, namely updraft, precipitation, and retrieval errors, as well as the problem of vertical co-location between aerosol and cloud, on the assessment of S in the context of marine warm clouds by combining multiple active and passive satellite sensors and reanalysis products. On the basis of current findings, this study further suggests several potential ways forward to practically account for, to the extent possible, the major influencing factors for the satellite-based quantification of S and hence the ERFaci.

This work is based on observational data from multiple instruments on board Terra, Aqua, and CloudSat platforms as well as reanalysis data from the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) and the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) . Table  summarizes the aerosol, cloud, and precipitation parameters and their corresponding sources, temporal–spatial resolutions, and time periods analyzed in the present study. Note that due to the requirement for co-located aerosol–cloud–precipitation observations, the data used in Sect. 3.2 are obtained from the A-Train constellation of satellites (Aqua and CloudSat), which are then interpolated to 5×5 km2 resolution for analysis, while the remaining parts are based on the observations from Terra, for which all data are interpolated to 1∘×1∘ resolution. The combination of datasets used in each section is summarized in Table . It is worth mentioning that, as S was found to vary with the spatial resolution of data , the different data resolutions between Sect. 3.2 and other sections can lead to a difference in S, but this is not the focus here. This study is restricted to the global ocean with latitude between 60∘ S and 60∘ N because of limited quality of retrievals of aerosol size parameters and Nd over land and polar regions.

Aerosol properties are obtained from the level 3 Moderate Resolution Imaging Spectroradiometer (MODIS) Dark Target product MOD08 and MYD08;. In order to collect co-located (adjacent) aerosol and cloud retrievals for analysis, aerosol retrievals on a coarsely resolved grid (1∘ × 1∘ on a latitude–longitude grid) are used to match cloud pixels (1×1 km2), assuming that aerosol properties in adjacent clear areas are homogeneous enough to represent those under cloudy conditions (). Note that this assumption would be questionable, especially when aerosol is scavenged by precipitation . In addition to commonly used AOD, the aerosol index (AI = AOD × Ångström exponent) containing information on aerosol size is also employed since it is considered a better proxy for CCN . The Ångström exponent is calculated from AOD at wavelengths of 460 and 660 nm. To eliminate 1∘ by 1∘ scenes in which the aerosol distribution is heterogeneous, retrievals with a standard deviation higher than the mean values are discarded . As suggested by , the lowest 15 % of data for AOD (AI) at a global scale are excluded to avoid large retrieval uncertainty at low aerosol concentrations . Note that leaving out the low AOD (AI) yields a larger S compared to using all data .

Cloud optical properties, including CER and COT at 3.7 µm , are obtained from the MODIS level 2 cloud products MOD06 and MYD06; and then applied to compute Nd based on the adiabatic approximation . It was found that the filtering of cloud adiabaticity only has a negligible impact on the estimate of S, but in turn results in a reduction of up to 63 % in the data volume . For this reason, we do not apply such filtering here. Note that Nd is calculated on the level of the satellite pixel (order 1 km) before being aggregated to larger scales. Thus, the aggregation bias caused by the derivation of Nd from the highly nonlinear function of CER and COT as shown by does not affect the results presented here. To ensure confident retrievals, the Nd is filtered to include only single-layer liquid clouds with top temperature higher than 268 K. Pixels for which CER<4 µm and COT<4 are discarded due to the large uncertainty of retrievals . In addition, only pixels with a cloud fraction at 5 km resolution (CF5×5km2) > 0.9 and with a sub-pixel inhomogeneity index (cloud_mask_SPI) < 30 are used to reduce the retrieval errors induced by cloud edges and broken clouds . Further, we only consider pixels with a solar zenith angle of less than 65∘ and a sensor zenith angle of less than 41.4∘ to minimize the influence of known biases as detailed in . With the above sampling strategy, the random uncertainty in Nd was reported at 78 % on a pixel level, and this dropped substantially when averaged to a 1∘ by 1∘ region . However, as stated in , the systematic bias in the Nd retrievals for in situ measurements is low, with determination coefficients of 0.48 for all cloud types and 0.5–0.8 for stratocumulus clouds.

To overcome the lack of global updraft observations, we utilize satellite-based retrievals for CBH as a proxy for cloud-base updraft for cumuliform clouds based on the finding that these two quantities exhibit an approximately linear correlation for convective clouds . Here, clouds are considered convective for lower troposphere stability (LTS) less than 16 K . Additionally, cloud geometrical thickness (CGT; the difference between cloud-top height and CBH) is used as an alternative proxy for the updraft regardless cloud types, since it has been observed to be associated with the cloud-base updraft for shallow cumuliform clouds and also correlated with cloud-base updraft for stratiform clouds via modulating cloud-top cooling . To obtain CBH and CGT, we apply a recently developed retrieval algorithm 0.25∘ × 0.25∘ resolution, based on Multi-angle Imaging SpectroRadiometer (MISR)/Terra observations, i.e., the MISR Level 2 Cloud Product MIL2TCSP;. The best performance of this algorithm is achieved for clouds with CBH around 1 km and CGT below 1 km. For such heights, which are characteristic for oceanic clouds considered in this analysis, the root mean square error ranges 300–350 m. It is important to note that the MISR cloud-base height retrieval is limited to CBH > 560 m . At this lower end of the detection range, a slight underestimation of the CBH is expected . The ERA5 reanalysis is employed here to calculate LTS as the difference in potential temperature between 700 and 1000 hPa . The hourly LTS is then matched to 10:30 local solar time to approximate the overpass time of the Terra satellite.

To identify the role of precipitation, CloudSat radar precipitation observations co-located with AOD and AI as well as Nd from MODIS/Aqua are adopted as well. Here, we use the precipitation flag from the 2B-CLDCLASS product to distinguish precipitating (with the flags of “liquid precipitation” and “possible drizzle”) and non-precipitation clouds (with the flag of “no precipitation”). As a sink of Nd, drizzle could also affect the aerosol–cloud interactions even without rain falling on ground , so we also include drizzling clouds in precipitating cases. The CloudSat data at a 1.4×2.5 km2 resolution are matched to the nearest MYD06 5×5 km2 pixels for further analyses.

The MERRA-2 product assimilates observations of the atmospheric state as well as remotely sensed AOD so that it can generate reasonable aerosol horizontal and vertical distributions . The use of aerosol reanalysis also largely avoids the spuriously high AOD near clouds caused by retrieval artifacts from the satellite . Given that variability in sulfate aerosols contributes the most strongly to variability in Nd among all aerosol species , the sulfate concentration is considered be to the CCN proxy here. We utilize vertically resolved sulfate mass concentrations from MERRA-2 reanalysis in combination with the MISR CBH retrieval to obtain sulfate mass concentrations near cloud base (SO4B). In addition, sulfate surface mass concentrations (SO4S) and column mass density (SO4C) are also used to investigate if there will be different behaviors of Nd-to-CCN sensitivity when applying CCN proxies at different levels. The MERRA-2 3 h averaged fields are interpolated to 10:30 local solar time to approximate the overpass time of the Terra satellite.

Figure  illustrates the regression procedure for calculating the S. After excluding the lowest 15 % AOD (AI), the data are then divided into 20 bins of CCN proxy, with each bin having an equal number of samples. The same number of samples ensures the same statistical representativeness within each bin. The values of Nd and the CCN proxy for a certain bin are the medians of all values in that bin. The generated 20 paired values of Nd and CCN proxies are then used in linear regression to determine S unless otherwise stated. The uncertainties of estimated S are reflected by the 95 % confidence interval of the regression slope. We also tried 100 and 1000 bins and found that the derived susceptibilities do not change significantly with the number of bins. Additionally, the linear regression on all data points is also shown (yellow dashed line) in Fig.  for comparison with the pre-binned approach, since both approaches have been used extensively by previous studies , but it is still unclear how large the difference in estimates between the two approaches could be. Figure  illustrates that the pre-binned approach has a larger slope than lumping together all data points by 18 %, suggesting that attention should be paid when comparing S derived from different approaches. In our study, both approaches lead to similar conclusions; as such, we will only focus on the results from the pre-binned approach in the main text. Meanwhile, we also put the results associated with the all-data approach in the Supplement.

Although this study has demonstrated the significant impacts of major confounders on the estimation of Nd-to-CCN sensitivity, some caveats remain. In order to achieve an optimal estimate of radiative forcing from the remote sensing perspective, the following sources of uncertainty should be accounted for in future investigations.

The derivation of Nd from satellite observations relies on a number of assumptions , making it prone to systematic biases. While some sampling strategies have been applied to side-step the biases in Nd retrieval (see Sect. 2), the uncertainties remain. To further ensure the cloud adiabaticity, there are two practical methods for use, including comparing the CER at different wavelengths and locating the cloud “core” . Appropriate Nd sampling strategies are beneficial in future investigations, though they have relatively little impact on S (and the implied RFaci) .

The retrieved AOD (AI) as well as reanalyzed SO4 were treated as CCN proxies in this study. However, the usability is limited due to the lack of information on the aerosol size and/or hygroscopicity for AOD (AI) and also due to the fact that SO4 cannot fully explain the variability of CCN since organic aerosols also contribute significantly , particularly in the remote marine boundary layer . Therefore, the application of direct CCN retrievals from polarimetric satellites is promising in future investigations of aerosol–cloud interactions. However, it would need to be combined with an estimate of the contribution of above-cloud aerosol, especially in regions unaffected by continental outflow. More importantly, the PD CCN–Nd relationship has been shown to be a better approximation of the PI and hence the “actual” sensitivity of Nd to aerosol perturbations than the AOD (AI)–Nd relationship, as it is not affected by the differing PI and PD aerosol environments . This again highlights the importance of directly retrieved CCN in the assessment of the radiative forcing from the Twomey effect.

Notably, using a linear regression slope from an ordinary least-squares (OLS) line-fitting method to describe the actual nonlinear aerosol–Nd (Fig. ) can introduce additional uncertainties related to the problem of regression dilution . The OLS method is also likely to overestimate the change in Nd from PI to PD over polluted continents, as a saturation effect will occur as aerosols keep rising under a polluted background. A joint histogram method proposed by can be useful to account for the nonlinearity.

In addition to the precipitation, entrainment mixing is a crucial droplet sink process . However, given that it is practically difficult to infer a quantitative measure of the strength of entrainment mixing from satellite observations, its impacts were not explicitly considered here. It has been proven that entrainment mixing process is associated with dynamical and cloud regimes , so the updraft constraint in this study would also incorporate the effect of entrainment mixing to some extent. Although there have been some attempts to characterize entrainment mixing via the combination of lower tropospheric stability and relative humidity near cloud top or the Nd–LWP relationship at a certain phase relaxation timescale describing evaporation–entrainment feedback , they are relatively rough approximations or qualitative differentiations. An updated approach for deriving measures of entrainment mixing at the global scale would be highly beneficial.

It was found that S can vary not only with the spatial resolution of data but also with the spatial scale at which the regression is performed . demonstrated that conducting analysis over large regions could induce spurious aerosol–cloud correlations, mainly owing to the spatial covariations in aerosol type, cloud regime, and meteorological conditions. Despite the global analyses employed in this study, the applied updraft constraint may make our results less susceptible to this issue. It is expected that, with joint use of an updraft constraint and CCN retrieval that greatly eliminate the spatial gradient effects, global analysis would be preferable compared to a regional or local method, since the latter could lead to a large bias in the aerosol–Nd slope over pristine oceans where either the instrument detectability limitations on aerosol or the inability of column-integrated measure to represent aerosol near cloud base for low aerosol conditions (see Sect. 3.4) could play a major role.

Given the impossibility of combining all datasets used in different sections together (e.g., the CBH and CGT from Terra are observed at 10:30 but the precipitation from Aqua at 13:30 local solar time), this work evaluates the individual impact of each bias on the estimate of S separately. Nevertheless, the sources of bias could also be correlated with each other; thus, an optimal estimate of S with all biases constrained is desirable. Future studies are being planned to make use of CALIOP/CloudSat satellite observations, which provide simultaneous retrievals of aerosol extinction profiles, precipitation, and cloud-base height such that an analysis accounting for all potential sources of bias can be performed.

By employing a statistically robust dataset from multiple active and passive satellite sensors as well as a reanalysis product, we systematically assessed the aerosol impact on marine warm clouds and found that the Nd-to-CCN sensitivity (S) shows a strong dependence on (a) updraft proxy, (b) precipitation, (c) satellite retrieval biases, and (d) vertical co-location between aerosol and cloud layer. The key results and the corresponding implications are summarized as follows, and the impacts of issues highlighted here on the overall estimation of S are listed in Table .

SAOD and SAI are found to increase remarkably with both CBH and CGT (treated as proxies for vertical velocity at cloud base), suggesting that stronger aerosol–cloud interactions generally occur under larger updraft velocity conditions. Although a similar dependency has been reported by some previous studies utilizing in situ aircraft measurements or ground-based remote sensing, they were limited to certain time periods and regions. Instead, S here is characterized as a function of CBH (CGT) based on 4 years of global satellite observations, which can thus reflect the full variability of cloud dynamic conditions. This functional relationship, as a better alternative to large-scale meteorological condition constraints (less directly linked to cloud dynamics on a cloud scale), could be promising in application to the estimation of global aerosol–cloud radiative forcing, by which the change in Nd from the PI to the PD may be inferred based on CBH (CGT) climatology from satellite and anthropogenic aerosol emission perturbation assuming first-order unchanged CBH distributions.