Exploring satellite-derived relationships between cloud droplet number concentration and liquid water path using large-domain large-eddy simulation

The semi-permanent stratocumulus clouds over the South-eastern Atlantic Ocean (SEA) can act as an “air conditioners” to the regional and global climate system. The interaction of aerosols and clouds become important in this region, and can lead to negative radiative effects, partially offsetting the positive radiative forcing of greenhouse gases. A key pathway of aerosols affecting cloud properties is by acting as cloud condensation nuclei (CCN). In this paper, we use the United Kingdom Earth System Model to investigate the sources of CCN (from atmospheric processes and emission sources) in the SEA, and the response of cloud droplet number concentration (CDNC), cloud liquid water path (LWP), and radiative forcing to those sources. Overall, total nucleation (binary nucleation) is the most important source of CCN0.2 % in the marine boundary layer, contributing an annual average of 50 % of CCN0.2 %. In terms of emission sources, anthropogenic emissions (from energy, industry, agriculture, etc.) contribute the most to the annual average CCN0.2 % in the marine boundary layer, followed by BB. In the free troposphere, however, BB becomes the dominant source of CCN0.2 %, accounting for 64 % of the annual average. The contribution of aerosols from different sources to CDNC is consistent with their contribution to CCN0.2 % within the marine boundary layer, with total nucleation being the most important source of CDNC overall. In terms of emissions, anthropogenic sources are also the largest contributors to the annual average of CDNC, closely followed by BB. The contribution of BB to CDNC is more significant than its increase to CCN0.2 %, mainly because BB aerosol also can increase CDNC by enhancing the maximum supersaturation through the radiative effect of shortwave absorption. For an aerosol source that shows an increase in CDNC, it also shows an increase in LWP resulting from a reduction in autoconversion. BB aerosol, due to the absorption effect, can enhance existing temperature inversions and reduce the entrainment of sub-saturated air, leading to a further increase in LWP. As a result, the contribution of BB to LWP is second only to total nucleation. These findings demonstrate that BB is not the dominant source of CCN within the marine boundary layer from an emission source perspective. However, its contribution to clouds increases due to its absorption effect (about the same as anthropogenic sources for CDNC and more than anthropogenic sources for LWP), highlighting the crucial role of its radiative effect on clouds. The results on the radiative effects of aerosols show that BB aerosol exhibits an overall positive RFari (radiative forcing associated with aerosol-radiation interaction), but its net effective radiative forcing remains negative due to its effect on clouds (mainly by absorbing effect). By quantifying aerosol and cloud properties affected by different sources, this paper provides a framework to understand aerosol sources effects on the marine cirrocumulus clouds and radiation in the SEA.

The semi-permanent stratocumulus clouds over the South-eastern Atlantic Ocean (SEA) can act as an “air conditioners” to the regional and global climate system. The interaction of aerosols and clouds become important in this region, and can lead to negative radiative effects, partially offsetting the positive radiative forcing of greenhouse gases. A key pathway of aerosols affecting cloud properties is by acting as cloud condensation nuclei (CCN). In this paper, we use the United Kingdom Earth System Model to investigate the sources of CCN (from atmospheric processes and emission sources) in the SEA, and the response of cloud droplet number concentration (CDNC), cloud liquid water path (LWP), and radiative forcing to those sources. Overall, total nucleation (binary nucleation) is the most important source of CCN0.2 % in the marine boundary layer, contributing an annual average of 50 % of CCN0.2 %. In terms of emission sources, anthropogenic emissions (from energy, industry, agriculture, etc.) contribute the most to the annual average CCN0.2 % in the marine boundary layer, followed by BB. In the free troposphere, however, BB becomes the dominant source of CCN0.2 %, accounting for 64 % of the annual average. The contribution of aerosols from different sources to CDNC is consistent with their contribution to CCN0.2 % within the marine boundary layer, with total nucleation being the most important source of CDNC overall. In terms of emissions, anthropogenic sources are also the largest contributors to the annual average of CDNC, closely followed by BB. The contribution of BB to CDNC is more significant than its increase to CCN0.2 %, mainly because BB aerosol also can increase CDNC by enhancing the maximum supersaturation through the radiative effect of shortwave absorption. For an aerosol source that shows an increase in CDNC, it also shows an increase in LWP resulting from a reduction in autoconversion. BB aerosol, due to the absorption effect, can enhance existing temperature inversions and reduce the entrainment of sub-saturated air, leading to a further increase in LWP. As a result, the contribution of BB to LWP is second only to total nucleation. These findings demonstrate that BB is not the dominant source of CCN within the marine boundary layer from an emission source perspective. However, its contribution to clouds increases due to its absorption effect (about the same as anthropogenic sources for CDNC and more than anthropogenic sources for LWP), highlighting the crucial role of its radiative effect on clouds. The results on the radiative effects of aerosols show that BB aerosol exhibits an overall positive RFari (radiative forcing associated with aerosol-radiation interaction), but its net effective radiative forcing remains negative due to its effect on clouds (mainly by absorbing effect). By quantifying aerosol and cloud properties affected by different sources, this paper provides a framework to understand aerosol sources effects on the marine cirrocumulus clouds and radiation in the SEA.

The semi-permanent stratocumulus clouds over the South-eastern Atlantic Ocean (SEA) can act as an “air conditioners” to the regional and global climate system. The interaction of aerosols and clouds become important in this region, and can lead to negative radiative effects, partially offsetting the positive radiative forcing of greenhouse gases. A key pathway of aerosols affecting cloud properties is by acting as cloud condensation nuclei (CCN). In this paper, we use the United Kingdom Earth System Model to investigate the sources of CCN (from atmospheric processes and emission sources) in the SEA, and the response of cloud droplet number concentration (CDNC), cloud liquid water path (LWP), and radiative forcing to those sources. Overall, total nucleation (binary nucleation) is the most important source of CCN0.2 % in the marine boundary layer, contributing an annual average of 50 % of CCN0.2 %. In terms of emission sources, anthropogenic emissions (from energy, industry, agriculture, etc.) contribute the most to the annual average CCN0.2 % in the marine boundary layer, followed by BB. In the free troposphere, however, BB becomes the dominant source of CCN0.2 %, accounting for 64 % of the annual average. The contribution of aerosols from different sources to CDNC is consistent with their contribution to CCN0.2 % within the marine boundary layer, with total nucleation being the most important source of CDNC overall. In terms of emissions, anthropogenic sources are also the largest contributors to the annual average of CDNC, closely followed by BB. The contribution of BB to CDNC is more significant than its increase to CCN0.2 %, mainly because BB aerosol also can increase CDNC by enhancing the maximum supersaturation through the radiative effect of shortwave absorption. For an aerosol source that shows an increase in CDNC, it also shows an increase in LWP resulting from a reduction in autoconversion. BB aerosol, due to the absorption effect, can enhance existing temperature inversions and reduce the entrainment of sub-saturated air, leading to a further increase in LWP. As a result, the contribution of BB to LWP is second only to total nucleation. These findings demonstrate that BB is not the dominant source of CCN within the marine boundary layer from an emission source perspective. However, its contribution to clouds increases due to its absorption effect (about the same as anthropogenic sources for CDNC and more than anthropogenic sources for LWP), highlighting the crucial role of its radiative effect on clouds. The results on the radiative effects of aerosols show that BB aerosol exhibits an overall positive RFari (radiative forcing associated with aerosol-radiation interaction), but its net effective radiative forcing remains negative due to its effect on clouds (mainly by absorbing effect). By quantifying aerosol and cloud properties affected by different sources, this paper provides a framework to understand aerosol sources effects on the marine cirrocumulus clouds and radiation in the SEA.

Increased anthropogenic aerosols result in an enhancement in cloud droplet number concentration (Nd), which consequently modifies the cloud and precipitation process. It is unclear how exactly cloud liquid water path (LWP) and cloud fraction respond to aerosol perturbations. A volcanic eruption may help to better understand and quantify the cloud response to external perturbations, with a focus on the short-term cloud adjustments. The goal of the present study is to understand and quantify the response of clouds to a selected volcanic eruption and to thereby advance the fundamental understanding of the cloud response to external forcing. In this study we used the ICON (ICOsahedral Non-hydrostatic) model in its numerical weather prediction setup at a cloud-system-resolving resolution of 2.5 km horizontally, to simulate the region around the Holuhraun volcano for one week (1–7 September 2014). A pair of simulations, with and without the volcanic aerosol plume, allowed us to assess the simulated effective radiative forcing and its mechanisms, as well as its impact on adjustments of LWP and cloud fraction to the perturbations of Nd. In comparison to MODIS (Moderate Resolution Imaging Spectroradiometer) satellite retrievals, a clear enhancement of Nd due to the volcanic aerosol is detected and attributed. In contrast, no changes in either LWP or cloud fraction could be attributed. The on average almost unchanged LWP is a result of some LWP enhancement for thick, and a decrease for thin clouds.

Increased anthropogenic aerosols result in an enhancement in cloud droplet number concentration (Nd), which consequently modifies the cloud and precipitation process. It is unclear how exactly cloud liquid water path (LWP) and cloud fraction respond to aerosol perturbations. A volcanic eruption may help to better understand and quantify the cloud response to external perturbations, with a focus on the short-term cloud adjustments. The goal of the present study is to understand and quantify the response of clouds to a selected volcanic eruption and to thereby advance the fundamental understanding of the cloud response to external forcing. In this study we used the ICON (ICOsahedral Non-hydrostatic) model in its numerical weather prediction setup at a cloud-system-resolving resolution of 2.5 km horizontally, to simulate the region around the Holuhraun volcano for one week (1–7 September 2014). A pair of simulations, with and without the volcanic aerosol plume, allowed us to assess the simulated effective radiative forcing and its mechanisms, as well as its impact on adjustments of LWP and cloud fraction to the perturbations of Nd. In comparison to MODIS (Moderate Resolution Imaging Spectroradiometer) satellite retrievals, a clear enhancement of Nd due to the volcanic aerosol is detected and attributed. In contrast, no changes in either LWP or cloud fraction could be attributed. The on average almost unchanged LWP is a result of some LWP enhancement for thick, and a decrease for thin clouds.

<strong class="journal-contentHeaderColor">Abstract.</strong> Increased anthropogenic aerosols result in an enhancement in cloud droplet number concentration (<span class="inline-formula"><i>N</i>_d</span>), which consequently modifies the cloud and precipitation process. It is unclear how exactly the cloud liquid water path (LWP) and cloud fraction respond to aerosol perturbations. A volcanic eruption may help to better understand and quantify the cloud response to external perturbations, with a focus on the short-term cloud adjustments. The goal of the present study is to understand and quantify the response of clouds to a selected volcanic eruption and to thereby advance the fundamental understanding of the cloud response to external forcing. In this study we used the ICON (ICOsahedral Non-hydrostatic) model in its numerical weather prediction setup at a cloud-system-resolving resolution of 2.5 km horizontally, to simulate the region around the Holuhraun volcano for 1 week (1–7 September 2014). A pair of simulations, with and without the volcanic aerosol plume, allowed us to assess the simulated effective radiative forcing and its mechanisms, as well as its impact on adjustments of LWP and cloud fraction to the perturbations of <span class="inline-formula"><i>N</i>_d</span>. In comparison to MODIS (Moderate Resolution Imaging Spectroradiometer) satellite retrievals, a clear enhancement of <span class="inline-formula"><i>N</i>_d</span> due to the volcanic aerosol is detected and attributed. In contrast, no changes in either LWP or cloud fraction could be attributed. The on average almost unchanged LWP is a result of some LWP enhancement for thick clouds and a decrease for thin clouds.

A two-moment cloud microphysical scheme, to predict both the mass and number concentrations of cloud droplets and ice crystals, is implemented into the aerosol-climate model BCC_AGCM2.0.1_CUACE/Aero. The model results for aerosols, cloud properties, and meteorological fields are evaluated, and the anthropogenic aerosol indirect effect (AIE) is estimated. The new model simulates more realistic aerosol mass concentrations and optical depth compared with the original version using a one-moment bulk cloud microphysical scheme. The global annual mean column cloud droplet number concentration (CDNC) from the new model is 3.3 × 1010 m−2, which is comparable to the 4.0 × 1010 m−2 from satellite retrieval. The global annual mean cloud droplet effective radius at the cloud top from the new model is 8.1 µm, which is smaller than the 10.5 µm from observation. The simulated liquid water path (LWP) in the new model is significantly lower than that in the original model. In particular, the annual mean LWP is lower in the new model by more than 100 g m−2 in some midlatitude regions and hence much more consistent with satellite retrievals. Cloud radiative forcing and precipitation are improved to some extent in the new model. The global annual mean radiation budget at the top of the atmosphere is −0.6 W m−2, which is considerably different from the value of 1.8 W m−2 in the original model. The global annual mean anthropogenic AIE is estimated to be −1.9 W m−2 without imposing a lower bound of CDNC, whereas it is reduced significantly when a higher lower bound of CDNC is prescribed.

Aerosol-cloud interactions remain one of the largest uncertainties in quantifying anthropogenic impacts on climate, particularly through their influence on cloud liquid water path (LWP), cloud droplet number concentration (CDNC), and cloud susceptibility to aerosol perturbations. This presentation synthesizes insights from satellite observations, large-eddy simulations, global climate models, long-term in-situ observations, and advanced statistical analyses to address biases and uncertainties in these interactions. Satellite-based studies often report a decreasing LWP with increasing CDNC, yet retrieval errors and natural spatial variability can mask positive LWP adjustments, leading to an underestimation of the cooling effects of aerosol-cloud interactions. Large-eddy simulations of marine stratocumulus clouds reveal that assumptions of adiabaticity and spatial variability in cloud properties contribute to biases in satellite-derived LWP-CDNC relationships. However, with careful case selection and well-defined meteorological conditions, satellite-based estimations can be improved. Building on these findings, global climate modeling and machine learning analyses highlight the importance of updraft velocity and aerosol size distributions in shaping the CCN-CDNC relationship. Advanced methods such as Elastic Net Regression isolate these confounding factors, refining susceptibility estimates and enhancing consistency with physical expectations. Further, long-term in-situ observations of aerosols and clouds at high-latitude locations reveal that the susceptibility of CDNC to CCN is significantly higher for low-level stratiform clouds than suggested by global oceanic satellite data. This implies stronger aerosol radiative forcing than current satellite-based estimates assume. Comparisons with Earth system models reveal large inter-model variability in susceptibility, driven by differences in sub-grid scale updraft velocities and aerosol size distributions. Even models with relatively accurate susceptibility values exhibit unrealistic underlying physics, highlighting areas for improvement in model representation. Lastly, combining satellite, reanalysis, and in-situ ACTRIS observations, we evaluate the roles of aerosol size distributions and updrafts in warm cloud formation, bridging gaps between microphysical processes and large-scale variability. This comprehensive approach emphasizes the need for integrating multi-platform observations with advanced modeling and statistical methods to reduce biases and improve the fidelity of aerosol-cloud interaction estimates. These advancements are crucial for more accurately quantifying aerosol radiative forcing and its implications for climate prediction.

Abstract. The response in cloud water content to changes in cloud condensation nuclei remains one of the major uncertainties in determining how aerosols can perturb cloud properties. In this study, we used an ensemble of large eddy simulations of marine stratocumulus clouds to investigate the correlation between cloud liquid water path (LWP) and the amount of cloud condensation nuclei. We compare this correlation directly from the model to the correlation derived using equations which are used to retrieve liquid water path from satellite observations. Our comparison shows that spatial variability in cloud properties and instrumental noise in satellite retrievals of cloud optical depth and cloud effective radii results in bias in the satellite-derived liquid water path. In-depth investigation of high-resolution model data shows that in large part of a cloud, the assumption of adiabaticity does not hold, which results in a similar bias in the LWP–CDNC (cloud droplet number concentration) relationship as seen in satellite data. In addition, our analysis shows a significant positive bias of between 18 % and 40 % in satellite-derived cloud droplet number concentration. However, for the individual ensemble members, the correlation between the cloud condensation nuclei and the mean of the liquid water path was very similar between the methods. This suggests that if cloud cases are carefully chosen for similar meteorological conditions and it is ensured that cloud condensation nuclei concentrations are well-defined, changes in liquid water can be confidently determined using satellite data.

A new operational retrieval of cloud droplet number concentration (ND) at cloud base has been produced from surface remote sensors at the Atmospheric Radiation Measurement (ARM) Southern Great Plains site for 13 years from January 1998 to January 2011. The retrieval is based on surface radiometer measurements of cloud optical depth from the multifilter rotating shadow band radiometer and liquid water path from the microwave radiometer (MWR). It is only applicable for single‐layered overcast warm (stratus or stratocumulus) clouds. Evaluation with in situ aircraft measurements during the extended‐term aircraft field campaign, Routine ARM Aerial Facility (AAF) Clouds with Low Optical Water Depths (CLOWD) Optical Radiative Observations (RACORO), shows that the retrieved ND robustly reproduces the primary mode of the in situ measured probability density function (PDF) but produces too wide a distribution, primarily caused by frequent high cloud droplet number concentration. Our analysis shows that the error in the MWR retrievals at low liquid water paths is one possible reason for this deficiency. Modification through the diagnosed liquid water path from the coordinate solution improves not only the PDF of the retrieved ND but also the relationship between the cloud droplet number concentration and cloud droplet effective radius. Consideration of entrainment effects rather than assuming an adiabatic cloud improves the values of the ND retrieval by reducing the magnitude of cloud droplet number concentration. Aircraft measurements and retrieval comparisons suggest that retrieving the vertical distribution of cloud droplet number concentration and effective radius is feasible with an improvement of the parameter representing the mixing effects between environment and clouds and with a better understanding of the effect of mixing degree on cloud properties.

By combining measurements from MODIS and the CloudSat radar, we develop a parameterization scheme to quantify the combined microphysical controls by liquid water path (LWP) and cloud droplet number concentration (CDNC) of the probability of precipitation (PoP) in marine low cloud over tropical oceans. We demonstrate that the spatial‐temporal variation of grid‐mean in‐cloud <PoP> can be largely explained by the variation of the joint probability density function of LWP and CDNC in the phase space specified by the bivariate PoP (LWP and CDNC) function. Through a series of sensitivity tests guided by this understanding, we find that in the Southeastern Pacific and Atlantic the stratocumulus to cumulus transition of the <PoP> is mainly due to the variation of CDNC while the annual cycle is mainly due to the variation of LWP. The results of this study provide a viable way to diagnose the root cause of warm rain problems in global climate models.

Abstract. Marine stratocumulus (Sc) clouds play an essential role in the earth radiation budget. Here, we compare liquid water path (LWP), cloud optical thickness (τ), and cloud droplet effective radius (re) retrievals from 2 years of collocated Spinning Enhanced Visible and Infrared Imager (SEVIRI), Moderate Resolution Imaging Spectroradiometer (MODIS), and Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) observations; estimate the effect of biomass burning smoke on passive imager retrievals; and evaluate the diurnal cycle of South Atlantic marine Sc clouds.The effect of absorbing aerosols from biomass burning on the retrievals was investigated using the aerosol index (AI) obtained from the Ozone Monitoring Instrument (OMI). SEVIRI and MODIS LWPs were found to decrease with increasing AI relative to TMI LWP, consistent with well-known negative visible/near-infrared (VIS/NIR) retrieval biases in τ and re. In the aerosol-affected months of July–August–September, SEVIRI LWP – based on the 1.6 µm re – was biased low by 14 g m−2 ( ∼ 16 %) compared to TMI in overcast scenes, while MODIS LWP showed a smaller low bias of 4 g m−2 ( ∼ 5 %) for the 1.6 µm channel and a high bias of 8 g m−2 ( ∼ 10 %) for the 3.7 µm channel compared to TMI. Neglecting aerosol-affected pixels reduced the mean SEVIRI–TMI LWP bias considerably. For 2 years of data, SEVIRI LWP had a correlation with TMI and MODIS LWP of about 0.86 and 0.94, respectively, and biases of only 4–8 g m−2 (5 %–10 %) for overcast cases.The SEVIRI LWP diurnal cycle was in good overall agreement with TMI except in the aerosol-affected months. Both TMI and SEVIRI LWP decreased from morning to late afternoon, after which a slow increase was observed. Terra and Aqua MODIS mean LWPs also suggested a similar diurnal variation. The relative amplitude of the 2-year-mean and seasonal-mean LWP diurnal cycle varied between 35 % and 40 % from morning to late afternoon for overcast cases. The diurnal variation in SEVIRI LWP was mainly due to changes in τ, while re showed only little diurnal variability.

Changes in marine boundary layer cloud (MBLC) radiative properties in response to aerosol perturbations are largely responsible for uncertainties in future climate predictions. In particular, the relationship between the cloud droplet number concentration (Nd, a proxy for aerosol) and the cloud liquid water path (LWP) remains challenging to quantify from observations. In this study, satellite observations from multiple polar-orbiting platforms for 2006–2011 are used in combination with atmospheric reanalysis data in a regional machine learning model to predict changes in LWP in MBLCs in the Southeast Atlantic. The impact of predictor variables on the model output is analysed using Shapley values as a technique of explainable machine learning. Within the machine learning model, precipitation fraction, cloud top height, and Nd are identified as important cloud state predictors for LWP, with dynamical proxies and sea surface temperature (SST) being the most important environmental predictors. A positive nonlinear relationship between LWP and Nd is found, with a weaker sensitivity at high cloud droplet concentrations. This relationship is found to be dependent on other predictors in the model: Nd–LWP sensitivity is higher in precipitating clouds and decreases with increasing SSTs.

The spatial variability of the microphysical fields in stratocumulus clouds is documented in this paper with statistics of droplet number concentration, droplet mean volume radius, and liquid water content for eight cases of the second Aerosol Characterization Experiment. Statistics are calculated in five sublayers, from cloud base to cloud top, and they are utilized for deriving estimates of cloud optical thickness and liquid water path, by assuming either random or maximum overlap. The resulting in situ frequency distributions of optical thickness and liquid water path are validated against distributions of these two parameters retrieved from independent remote sensing measurements of cloud radiances. They are also used for testing parameterizations of optical thickness based on liquid water path and either the droplet effective radius or the cloud droplet number concentration. This unique data set of extensive, concomitant, and independent measurements of cloud microphysical and radiative properties is finally used for assessing the detectability of the aerosol indirect effect through examination of the correlation between cloud optical thickness and droplet effective radius. If only cases of comparable values of geometrical thickness are considered, the correlation between optical thickness and effective radius is negative, as anticipated by Twomey [1977]. However, if the most polluted cases are also accounted for, the trend suggests a positive correlation. In fact, the most polluted cloud systems sampled during ACE‐2 were slightly drier, hence thinner, than the marine and intermediate cases, hence producing a positive correlation between optical thickness and droplet effective radius. This study demonstrates that the monitoring of the aerosol indirect effect with satellite observations requires an independent retrieval of the liquid water path together with the cloud optical thickness and droplet effective radius.

Abstract. Aerosol–cloud interactions (ACIs) are uncertain and the estimates of the ACI effective radiative forcing (ERFaci) magnitude show a large variability. Within the Aerosol_cci project the susceptibility of cloud properties to changes in aerosol properties is derived from the high-resolution AATSR (Advanced Along-Track Scanning Radiometer) data set using the Cloud–Aerosol Pairing Algorithm (CAPA) (as described in our companion paper) and compared to susceptibilities from the global aerosol climate model ECHAM6-HAM2 and MODIS–CERES (Moderate Resolution Imaging Spectroradiometer – Clouds and the Earth's Radiant Energy System) data. For ECHAM6-HAM2 the dry aerosol is analysed to mimic the effect of CAPA. Furthermore the analysis is done for different environmental regimes. The aerosol–liquid water path relationship in ECHAM6-HAM2 is systematically stronger than in AATSR–CAPA data and cannot be explained by an overestimation of autoconversion when using diagnostic precipitation but rather by aerosol swelling in regions where humidity is high and clouds are present. When aerosol water is removed from the analysis in ECHAM6-HAM2 the strength of the susceptibilities of liquid water path, cloud droplet number concentration and cloud albedo as well as ERFaci agree much better with those of AATSR–CAPA or MODIS–CERES. When comparing satellite-derived to model-derived susceptibilities, this study finds it more appropriate to use dry aerosol in the computation of model susceptibilities. We further find that the statistical relationships inferred from different satellite sensors (AATSR–CAPA vs. MODIS–CERES) as well as from ECHAM6-HAM2 are not always of the same sign for the tested environmental conditions. In particular the susceptibility of the liquid water path is negative in non-raining scenes for MODIS–CERES but positive for AATSR–CAPA and ECHAM6-HAM2. Feedback processes like cloud-top entrainment that are missing or not well represented in the model are therefore not well constrained by satellite observations. In addition to aerosol swelling, wet scavenging and aerosol processing have an impact on liquid water path, cloud albedo and cloud droplet number susceptibilities. Aerosol processing leads to negative liquid water path susceptibilities to changes in aerosol index (AI) in ECHAM6-HAM2, likely due to aerosol-size changes by aerosol processing. Our results indicate that for statistical analysis of aerosol–cloud interactions the unwanted effects of aerosol swelling, wet scavenging and aerosol processing need to be minimised when computing susceptibilities of cloud variables to changes in aerosol.