Accepted on 28 Aug 2022
Submitted on 11 Feb 2022
Clouds play a remarkable role in the Earth’s radiation budget (Ramanathan et al., 1989). Cloud properties are modulated by atmospheric aerosols, as almost all the liquid cloud droplets form on an aerosol particle that can act as cloud condensation nuclei (Charlson et al., 1992; Twomey, 1974). Twomey (1974) hypothesized that an aerosol perturbation could modify the cloud droplet number concentration (Nd), which enhances the cloud albedo (now commonly referred to as the radiative forcing due to aerosol-cloud interactions, RFACIBellouin et al., 2020; Forster et al., 2021). At higher Nd, precipitation formation via collision-coalescence is slowed down or suppressed, implying a possible increase in the liquid water path (LWP) (Albrecht, 1989). Numerous further mechanisms, known as rapid adjustments to aerosol-cloud interactions (summarized, e.g., by Gryspeerdt et al., 2019), may lead to enhancements or decreases in LWP at larger Nd. Recent studies reveal that the time-dependency of these adjustment processes is crucial (Christensen et al., 2020; Gryspeerdt et al., 2021; Glassmeier et al., 2021). Besides their impact on LWP, adjustment mechanisms may also influence horizontal cloud extent (Gryspeerdt et al., 2016) or cloud-top temperatures (Rosenfeld et al., 2014; Bellouin et al., 2020). The combination of the radiative forcing due to the aerosol-cloud interactions, and these adjustments, is known as the effective radiative forcing due to aerosol-cloud interactions, ERFACI. Still, ERFACI constitutes the largest uncertainty among all forcing agents (Mülmenstädt & Feingold, 2018; Chen et al., 2014; Rosenfeld et al., 2014; Forster et al., 2021; Szopa et al., 2021).
Satellite observations play a crucial role in understanding and quantifying the RFACI (a component of effective radiative forcing, ERFACI) globally (Stephens et al., 2019) and in evaluating aerosol-cloud interactions in climate models (Saponaro et al., 2020). However, large uncertainties remain in satellite-based aerosol-cloud interaction estimates. This stems from retrieval artefacts in satellite products, asynchronous retrieval of aerosol and cloud properties, and limited abilities to observe the relevant processes (Stevens & Feingold, 2009; Christensen et al., 2017; Grosvenor et al., 2018; Quaas et al., 2020; Jia et al., 2021). Nevertheless, the co-variation in aerosol and cloud optical properties has been used to estimate aerosol-cloud interactions and, consequently, the RFACI (Feingold et al., 2003; Quaas et al., 2008; McCoy et al., 2017; Hasekamp et al., 2019). Recent studies proposed that the relationship between Nd and LWP is a vital metric for estimating the LWP adjustment to aerosol-cloud interactions (Gryspeerdt et al., 2019; Bulatovic et al., 2019). The relationship between Nd and LWP could constrain the role of the aerosols in adjustments to aerosol-cloud interactions if combined with an estimate of the anthropogenic perturbation to Nd (Michibata et al., 2016; Bellouin et al., 2020). Gryspeerdt et al. (2019) analyzed in much detail the relationship between satellite-derived Nd and LWP. They found that the Nd-LWP relationship is highly nonlinear over the Global Oceans, indicating that the LWP increases for lower Nd and the LWP decreases for higher Nd. A positive Nd-LWP relationship could result from precipitation formation delay or suppression (Albrecht, 1989; Suzuki et al., 2013). Also, warm cloud invigoration can lead to positive Nd-LWP relations (Koren et al., 2014). On the contrary, a negative Nd-LWP relationship may indicate an impact of cloud entrainment and mixing (Ackerman et al., 2004; Chen et al., 2014; Xue & Feingold, 2006; Michibata et al., 2016; Sato et al., 2018). A positive Nd-LWP sensitivity may, in turn, imply a negative contribution to ERFACI (additional cooling effect), while negative ones result in a positive (warming) contribution (Toll et al., 2019; Bellouin et al., 2020).
Although Nd is a crucial parameter for understanding aerosol-cloud interactions, none of the standard satellite retrieval algorithms directly provide this variable. A common method uses the cloud optical thickness and effective radius from passive satellite observations to infer Nd (Quaas et al., 2006). The satellite retrieved Nd is based on the adiabatic assumption, where Nd is assumed to be constant with height and the cloud liquid water content is assumed to increase linearly with height (Brenguier et al., 2000; Schüller et al., 2005). Applying these assumptions in satellite-based analysis reveals a negative RFACI (Twomey effect, a positive Nd-LWP sensitivity), which is partially offset by the LWP adjustment (negative Nd-LWP sensitivity) due to aerosol-cloud interaction (Toll et al., 2019). The magnitude and even sign of this LWP adjustment are very uncertain; this generates uncertainty in ERFACI (Forster et al., 2021). However, the adiabatic assumption and the satellite retrievals of cloud optical thickness and effective radius are uncertain (Grosvenor et al., 2018; Quaas et al., 2020), which also propagates to significant uncertainties in estimates of ERFACI.
This study investigates assumptions made to evaluate the Nd-LWP relationships from satellite observations by using the results of a large-domain large-eddy simulation. The idea is that a comparison of the Nd-LWP relationship between a high-resolution model and satellite retrieval allows an understanding of the impacts of biases and assumptions used in the satellite Nd and LWP retrievals.
In this study, we have analyzed available Large-eddy simulations (LES) using the ICOsahedral Nonhydrostatic (ICON) model (Dipankar et al., 2015; Zängl et al., 2015). The atmospheric model ICON is a unified model for numerical weather prediction and climate simulations. As an extension, Dipankar et al. (2015) configured the ICON to a large-eddy simulation framework, which has been validated against standard LES models and data (Heinze et al., 2017). Here, we have used the available ICON-LES simulation from the High Definition Clouds and Precipitation for advancing Climate Prediction (HD(CP)2) project. The simulation was carried out over a large domain over Germany in a weather prediction mode with realistic boundary conditions from the operational COSMOS-DE (Consortium for Small Scale Modelling, Baldauf et al., 2011), including a fully interactive land surface (Costa-Surós et al., 2020). The simulation was performed with a horizontal resolution of 156 m and 150 vertical levels with a model top at 21 km. Near the surface, the minimum layer thickness is 20 m, and the lowest 1000 m confines 20 layers (Heinze et al., 2017). The ICON-LES uses a new sub-grid scale turbulence scheme based on the classical Smagorinsky scheme, which also accounts for thermal stratification (Lilly, 1962). The LES uses a detailed two-moment liquid and ice-phase cloud micro-physics scheme implemented by Seifert & Beheng (2006). The Sommeria & Deardorff (1977) cloud fraction scheme assumes that within the grid box, the cloud fraction is either 1 or 0. CCN concentrations are prescribed in the study as a temporally and spatially varying distribution for the years 2013 and (at much larger pollution levels) 1985 (Costa-Surós et al., 2020). For this study, we have selected the simulation performed for 2 May 2013. It has been one of the extensive measurement campaigns for HD(CP)2 Observational Prototype Experiment (HOPE, Löhnert et al., 2015; Madhavan et al., 2016). A detailed description of the ICON-LES model and HD(CP)2 simulation can be obtained from Dipankar et al. (2015), Heinze et al. (2017), and Costa-Surós et al. (2020).
The respective date of the study has been selected based on the evaluation results from Heinze et al. (2017) as a case in which a wide range of cloud regimes was present. Heinze et al. (2017) reported that the ICON-LES clouds are well represented compared to the satellite observations. They found a very good agreement between simulated cloud water paths and satellite retrievals. A slight underestimation in cloud fraction was observed, though. Additionally, the simulated vertical cloud profiles are in accordance with the satellite observations. Furthermore, Costa-Surós et al. (2020) documented that the LWP from the model and the satellite compare well. They also revealed that the simulated cloud profiles (effective radius, droplet number and liquid water content) are consistent with the ground-based observations. The above studies suggest that the simulated cloud micro-physical properties are consistent with both satellite and ground-based observations. Hence, the specific case simulated by the ICON-LES is conclusive for aerosol interaction studies and comparing it with the satellite analysis.
Although the ICON-LES simulation is performed with 156 m horizontal resolution, in our analysis, we have used coarse gridded data with a resolution of 1.2 km (grid size of 589 × 637) to approximately match the resolution of the satellite retrievals. The cloud-top is defined as the topmost level of the cloudy grid point with Nd > 2 cm–3. The corresponding cloud-top Nd are extracted for single-layered non-precipitating liquid clouds from the model. For the analysis, the cloud-top Nd is filtered for cloud fractions equal to 1 (at the 1.2 km scale) and cloud optical thicknesses greater than 2. To restrict the analysis to liquid clouds, we excluded the clouds with a cloud-top temperature of less than 268 K. Further, to avoid fog, cloud base heights greater than 300 m were selected for the analysis. For the chosen clouds, adiabatic cloud droplet number concentration (NAd) is calculated from cloud-top effective radius and cloud optical thickness using the relation suggested by Quaas et al. (2006). The cloud parameters are further filtered for the updraft regions and the cloud cores by choosing grid boxes with a positive vertical velocity (w > 0) and relative humidity greater than 100% (Heiblum et al., 2019). For the cloud regime classification, clouds with thicknesses between 100 to 600 m are considered shallow clouds; those with thicknesses greater than 1000 m are convective clouds. For the joint histogram analysis, hourly instantaneous model output from 0800 hrs to 2000 hrs is considered, and the corresponding data is compared with the satellite observation.
We use cloud optical properties from the Moderate Resolution Imaging Spectroradiometer (MODIS, Platnick et al., 2017) onboard the Aqua satellite. The cloud properties are obtained from MODIS Level2 collection 6.1 (MYDO6_L2) at 1 km × 1 km resolution (Menzel et al., 2015). The cloud droplet number concentration (NAd) is retrieved from cloud optical thickness and effective radius from this data set, which uses the adiabatic assumption (Quaas et al., 2006; Gryspeerdt et al., 2019). The NAd is then filtered for single-layer liquid clouds with a cloud-top temperature greater than 268 K and pixels with a cloud fraction greater than 0.9. Additionally, the cloud optical depth of less than two is excluded from the analysis (Gryspeerdt et al., 2019; Bennartz & Rausch, 2017; Grosvenor & Wood, 2014). The MODIS Level2 cloud fraction with 5 km resolution has been interpolated to 1 km by 1 km and used in the analysis. For the Northern hemispheric (0°N to 90°N) and the global analysis, cloud products from both MODIS Level2 and Level3 data sets are used. The MODIS Level3 (MYD08_D3) data from the period 2003–2020 and MODIS Level2 data from the period 2013–2017 are used.
Hereafter, Nd stands for the cloud droplet number concentration at the cloud-top (diagnosed in the model). Similarly, NAd indicates adiabatic cloud droplet number concentration (considered vertically uniform; from both model and satellite retrievals). The joint histograms analyzed in this study are constructed as conditional probabilities (CP [%]) following Gryspeerdt et al. (2016) and are defined as the probability of finding a certain LWP given that a certain Nd has been observed (CP = [P (LWP|Nd) × 100 ]). For the joint histogram analysis, 20 bins are used with varying sampling data in each bin. In the following text, the nonlinear relation implies that both negative and positive Nd/NAd-LWP sensitivities (positive and negative relation) coexist.
The sensitivity in NAd to LWP is investigated using a joint probability histogram analysis as described by Gryspeerdt et al. (2016). Figure 1 shows the comparison between the ICON-LES and satellite-derived NAd-LWP joint histograms over Germany. In both the model and the satellite, the peak (narrowest) CP is confined to the lower NAd (<100 cm–3). At these lower NAd, the model shows the peak CP is distributed between the LWP 30 and 60 g m–2, with no clear relation between NAd and LWP (Figure 1a). The satellite data, however, suggests that there is a high probability of observing a decreasing LWP with increasing NAd at these low NAd values (Figure 1b). For higher NAd (>100 cm–3), both the model and the satellite show a larger CP spread, with a tendency to increase LWP as NAd increases. In the joint histogramm, the change of the mean LWP (
) with NAd generally reflects the tendency of the NAd-LWP relation. For the ICON-LES, slightly increases with increasing NAd at lower values (NAd < 100 cm–3) and then it increases sharply until NAd ≈ 300 cm–3. Further, the shows a slight increase with increasing NAd (Figure 1a). In the case of the satellite-derived joint histogram, the shows a slight decrease with increasing NAd instead of an increase compared to the model, and it almost follows the peak CP. For higher NAd (>100 cm–3), the increases non-linearly with increasing NAd (Figure 1b). In both the model and the satellite, the selected continental boreal spring case (2 May 2013), the NAd-LWP relationship is positive and nonlinear; however, the relationship lacks, in particular, the negative relationship at higher NAd (where it is hypothesized that more entrainment at larger droplet concentrations may lead to depletion of LWP). However, Gryspeerdt et al. (2019) reported a highly nonlinear NAd-LWP sensitivity with increasing LWP at low NAd and decreasing LWP at high NAd over the Global Oceans using satellite data.
The NAd-LWP joint histogram in (a) the ICON-LES model, and (b) the MODIS-Level2 satellite retrieval, over Germany. The thick black line in each plot shows the mean LWP () at certain Nd bins (P (|Nd)). CP(%) is condition probability: the probability of finding a certain LWP given that a certain Nd has been observed.
The regime dependence of the NAd-LWP relationship and the representativeness of the particular case available for the joint satellite-LES analysis are further analyzed using MODIS satellite retrievals (Figure 2). Using the MODIS Level2, the NAd-LWP relationship over the Northern Hemisphere (NH) Land for the selected ICON-LES simulation date (2 May 2013) is illustrated in Figure 2a. The figure shows that the satellite retrieved NAd-LWP relationship over NH Land is very similar to that of the LWP-NAd relationship over Germany (Figure 1b). In both cases, for the lower NAd (<100 cm–3), the peak CP appears along the lower LWP as NAd increases, despite the NH Land showing a nonlinear pattern in (slight increase and decrease), especially at the lower NAd (NAd < 100 cm–3). Also, both cases show that the increases with increasing NAd (after the NAd > 100 cm–3). Further, the 2 May multi-year statistic of the NAd-LWP relationship over the NH Land (Figure 2b) is analogous to both relationships for the specific date over Germany and the NH Land. The NAd-LWP relationship over the NH Land, both for the selected day and the multi-year statistics, illustrates a similar relationship that persists irrespective of the sampling area and the period in spite of the diverse cloud pattern for the respective area/years. It lends credibility to the geographical representativeness of the evaluation between the satellite and the LES for the particular case. However, over the NH Ocean (the NAd-LWP climatology), the peak CP is more or less confined to the (Figure 2c). For low NAd (<20 cm–3), the peak CP appears along with increasing as the NAd increases. Beyond 20 cm–3, as the NAd increases, the higher CP is confined along decreasing until NAd is close to 500 cm–3. Finally, for the higher NAd, the CP shows a large spread between the LWP 10 and 800 gm–2. Over the NH Ocean, both CP and the show a nonlinear pattern; in particular, the shows positive and negative sensitivity with NAd compared to the continental case.
The NAd-LWP joint histogram for (a) the Northern hemisphere Land for the date 02 May 2013 using MODIS-Level2, (b) daily climatology (02 May 2013) for the Northern hemisphere Land for the period 2013–2017 using MODIS-Level2, (c) same as fig (b) but for the Northern hemisphere Ocean using MODIS-Level2, (d) daily climatology (02 May 2013) for the Northern hemisphere Land for the period 2003–2020 using MODIS-Level3, (e) same as fig (d) but for the Northern hemisphere Ocean using MODIS-Level3, and (f) daily climatology (02 May 2013) for the Global Ocean using MODIS-Level3. The figure description is the same as Figure 1.
In order to compare to published results (e.g., Gryspeerdt et al., 2019), we have assessed the relationships at aggregate, 1° × 1° scales corresponding to the scale of the MODIS Level3 products. The analysis is thus repeated with MODIS Level3 data. From this aggregated data, over the NH Land for the years 2003–2020, the NAd-LWP relationship is illustrated in Figure 2d. It also shows that the peak (narrowest) CP is bound to lower NAd, and then it appears along the increasing LWP with increasing NAd. The also follows the high CP, showing more or less a linear positive relation with NAd. When it comes to the NH Oceans, the peak CP is found at the lower NAd, similar to the NH Land, but for high NAd (<50 cm–3), the high CP appears mainly along the negative NAd-LWP slope (Figure 2e). Over the NH ocean, the Level3 NAd-LWP relationship is found to resemble the Level2 result but is less pronounced. Finally, over the Global Oceans, similar to the previous cases, the peak CP is bound to the lower NAd (<50 cm–3), and the relatively high CP appears along with the curve (Figure 2f). Furthermore, over the Global Ocean, the firmly follows a nonlinear relationship in which the LWP increases at lower NAd and decreases at higher NAd. Over the Ocean (Global and NH), the NAd-LWP sensitivity is more or less identical in all three cases; nevertheless, a more pronounced nonlinear sensitivity is observed in the Level3 Global Ocean. It is similar to the previous satellite analysis reported by Gryspeerdt et al. (2019), even if a longer time span is considered here. The above analysis clearly indicates that the marine clouds show a pronounced NAd-LWP sensitivity (nonlinear: increasing NAd leads to increasing/decreasing LWP at low/high NAd) irrespective of the data in contrast to continental clouds.
From the above satellite analysis of the NAd-LWP relationship, it is noticed that over the Ocean (global and NH), a highly nonlinear relationship persists. It indicates the increase with increasing NAd at low NAd, followed by a decrease in at higher NAd; at higher NAd, the further increase (Figure 2c, e, & f). However, in continental clouds, the negative NAd-LWP sensitivity is feeble (less nonlinear) compared to the marine clouds (highly nonlinear), which illustrates the diverse NAd-LWP relation in marine and continental clouds. Furthermore, in both MODIS Level2 and Level3 analyses, it is evident that a land-ocean contrast exists in the NAd-LWP relationship. Many reasons can lead to this distinction, such as the fact that continental clouds typically have higher cloud bases and are more heterogeneous than oceanic clouds (e.g., Unglaub et al., 2020), while marine clouds are affected by ship tracks with cleaner background conditions. In the case of continental clouds, at higher NAd, the NAd-LWP relations lack negative sensitivity due to the constraints in adiabatic assumption in deriving NAd. However, it persists in the marine clouds, which are highly susceptible to aerosol perturbation (significant reduction in higher LWP) compared to the continental clouds.
The ICON-LES simulated Nd may, however, not follow the adiabatic assumption; Nd may vary with height above the cloud base. The Nd-LWP relationship, this time using cloud-top Nd, is depicted in Figure 3a. At lower Nd (<100 cm–3), the CP shows a larger spread between LWP 10 and 800 gm–2 and the peak CP is confined to the lower LWP. At larger Nd (>200 cm–3), the spread of the CP decreases relative to the lower Nd, and the corresponding high CP occurs along a negative Nd-LWP slope. Further, at lower Nd (<100 cm–3), the increases with increasing Nd, and at higher Nd (>200 cm–3), the decreases as the Nd increases. The nonlinear Nd-LWP relationship is similar to what has been reported from previous studies analyzing satellite data over global Oceans, which uses NAd though (Gryspeerdt et al., 2019; Michibata et al., 2016). The discrepancies between the Nd-LWP and NAd-LWP relationship in the ICON-LES is further investigated by comparing Nd and NAd. Figure 3b shows the comparison between the model predicted Nd and model-derived NAd. The figure shows that peak CP occurs at Nd > 100 cm–3 and at NAd > 200 cm–3, with a significant correlation. At lower Nd, the CP shows a large spread for NAd, with less CP, which overestimates the actual droplet number concentration. The poorly correlated Nd-NAd relation indicates that sub-adiabatic clouds are common in the ICON-LES simulation. This is especially the case for clouds with low Nd.
ICON-LES diagnostics to assess the satellite assumptions in retrieving Nd. (a) same as Figure 1a, but using Nd diagnosed at cloud-top, rather than NAd (over Germany), and (b) A comparison between model predicted Nd and model derived adiabatic NAd at the cloud-top (over Germany). The thick black line (3b) shows the mean NAd at certain Nd bins (P (
|Nd)). CP(%) is condition probability: the probability of finding a certain NAd given that a certain Nd has been observed.
The comparison between Nd and NAd indicates that for lower Nd, there are occasions/grids boxes where the adiabatic assumption holds, in particular for the high Nd case. In other words, there are regions within the sub-adiabatic cloud regimes with a constant Nd profile or adiabatic. Cloud adiabaticity (α), the ratio of LWP to the adiabatic LWP (LWPAd, for an adiabatic cloud liquid water content (LWC), increases linearly with height), represents the adiabatic/sub-adiabatic cloud character. Clouds with α greater than 0.9, the cloud regimes are nearly adiabatic, and for α less than 0.9 implies sub-adiabatic or diluted clouds (Braun et al., 2018). Figure S1 shows the relation between cloud depth and LWP as a function of α. The figure illustrates that the cloud LWP increases with cloud depth, and the adiabatic clouds (α ≈ 1) are confined to lower cloud depth. The highest value of α is linked to geometrically thin clouds, and the lowest value of α is associated with relatively thick clouds in the simulated continental clouds (Figure S1). It further suggests that among the continental clouds, the shallow (thin) clouds tend to be adiabatic with less entrainment and mixing, compared to convective (thick) clouds that are sub-adiabatic and associated with stronger entrainment and mixing. Figure 4 shows the mean Nd profiles of shallow and convective clouds, respectively, as diagnosed from the ICON-LES. The shallow cloud regime (depth between 100 and 600 m) shows a more or less constant mean Nd profile with height (Figure 4a), except at the very bottom and top of the clouds. These shallow clouds can thus be considered approximately adiabatic with little lateral entrainment mixing. On the contrary, the thick convective clouds (depth greater than 1000 m) in the model have a varying mean Nd profile, within that particular decreasing Nd from the first third in cloud thickness onwards, implying a substantial mixing and sub-adiabaticity of these clouds (Figure 4b).
The ICON-LES Nd (cm–3) profile (over Germany) for (a) a shallow cloud regime, and (b) a convective cloud regime. The blue points indicate individual cloud profiles for the respective model grid, and the red points indicate the mean cloud profile with standard deviations.
The Nd-LWP relationship in the adiabatic and sub-adiabatic cloud regime in the ICON-LES model (over Germany) is shown in Figure 5. In the shallow or the adiabatic cloud regime, the Nd-LWP relationship shows a positive, almost linear relationship (Figure 5a); tends to increase with increasing Nd, and the peak CP occurs along the . For the shallow cloud regime, the CP is mainly confined to LWP between 2 and 200 gm–2. For the convective or the sub-adiabatic cloud regime, the Nd-LWP relation is nonlinear (Figure 5b). The slightly increases at the lower Nd and slightly decreases at the higher Nd (note the logarithmic axis). The peak CP appears for almost all Nd, and it is confined to higher LWP between 500 and 700 gm–2. Compared to the adiabatic cloud regime, in the sub-adiabatic clouds, the CP ranges between 10 to 800 gm–2 LWP. However, the sub-adiabatic Nd-LWP relationship is comparable to the ICON-LES simulated Nd-LWP relationship.
The Nd-LWP joint histogram (over Germany) for (a) the shallow cloud regime with the cloud depth between 100 to 600 m, and (b) the convective cloud regime with the cloud depth greater than 1000 m. The figure description is the same as Figure 1.
This work explores the relationship between cloud droplet number concentration and liquid water path using a large-domain large-eddy ICON-LES simulation and MODIS satellite. The satellite retrievals use adiabatic assumptions to retrieve NAd (adiabatic Nd) from cloud optical depth and effective radius (Quaas et al. 2006). The Nd/NAd-LWP relationship has the advantage of accounting for the confounding influence of relative humidity, compared to earlier studies that investigated aerosol impacts on LWP by correlating LWP to aerosol optical depth or relative aerosol retrievals (e.g., Nakajima et al., 2001; Sekiguchi et al., 2003; Quaas et al., 2004). However, the model-simulated Nd includes non-adiabatic conditions. Here we have demonstrated the issues in interpreting the satellite-retrieved NAd-LWP relationships using satellite forward-operator diagnostics (similar to the satellite retrieval, NAd is derived from the model) by a large-domain large-eddy simulation compared to corresponding satellite observation. Our analysis shows that, when using NAd in both model and the satellite, the NAd-LWP relationship is in approximate agreement; a positive NAd-LWP relationship is observed, especially at higher NAd (NAd > 100 cm–3) with a peak CP confined to the lower NAd and LWP in both cases. Additionally, for high NAd, the increases non-linearly with increasing NAd. However, both the model and the satellite NAd-LWP relationship lack, in particular, the negative relationship at higher NAd, reported in previous studies analyzing satellite data over Global Oceans (Gryspeerdt et al., 2019).
The model simulation output may be used to test the adiabatic assumption. This is particularly useful since the continental clouds are primarily sub-adiabatic, associated with entrainment and mixing, compared to marine clouds. The LWP increases at lower cloud-top Nd and decreases at higher levels, illustrating cloud lifetime (specifically for non-precipitating clouds) and entrainment effects. However, for the adiabatic cloud regime, in both model and the satellite, a positive NAd-LWP relationship dominates, with peak CP confined to the lower NAd and LWP bins of the joint histogram. Additionally, the NAd-LWP sensitivity is weak at the lower NAd, but it clearly shows a positive relationship at the higher levels. It implies that both model and the satellite could only explain the precipitation suppression; however, it lacks the entrainment effect on cloud droplets, which is associated with a negative Nd-LWP relation. A comparison between model-simulated Nd and NAd illustrates a nonlinear relationship, especially at the lower values. However, a relatively strong correlation is found at the higher Nd/NAd. It clearly indicates the constraints in the adiabatic assumption in inferring NAd and the subsequent NAd-LWP relationship.
Further satellite analysis shows a regime dependency (marine and continental) in the NAd-LWP relation. The selected single-day limited-area case indeed is representative of NH Land areas in terms of the analyzed relationship. However, Oceanic clouds show nonlinear positive and negative NAd-LWP relationships at low and high NAd, respectively, comparable to the previous satellite analysis reported by Gryspeerdt et al. (2019), even if a longer period is considered here. A possible explanation for the regime dependency in the NAd-LWP relation is that the continental clouds can be more associated with sub-adiabatic Nd profiles due to entrainment and mixing than the marine clouds. However, a negative NAd-LWP relationship is lacking in the continental clouds, which attribute to the constraints in the adiabatic assumption in deriving the NAd.
Since the ICON-LES simulation is over the continental region and accounts for the regime dependency in the satellite-derived NAd-LWP relationship, further analysis explored the NAd-LWP relation in the adiabatic and sub-adiabatic parts of the cloud. Consequently, the regimes-based analysis could overcome the problems in diagnosing the LWP response from such statistical analysis. The model analysis demonstrates that comparatively thin (stratiform) clouds have a rather vertically uniform Nd profile, justifying the adiabatic assumption in the retrievals. However, for deeper clouds, the adiabaticity is violated considering all clouds in the joint histogram. In general, the NAd is almost always larger than Nd at the cloud-top, leading to differences in the Nd-LWP relationships between thick (convective) and thin (stratiform) clouds and between the relationships considering NAd and Nd, respectively. A reliable assessment is expected for comparatively thin, stratiform clouds that may be considered an approximately adiabatic cloud regime. In contrast, the convective continental clouds are mostly sub-adiabatic, associated with entrainment and mixing, compared to shallow clouds. In the ICON-LES, the shallow cloud regime shows a positive Nd-LWP sensitivity, similar to the satellite retrievals, while the convective cloud regime shows a nonlinear relationship identical to the entire model analysis over Germany. The diverse Nd/Ad-LWP relationship in adiabatic and sub-adiabatic cloud regimes further suggests that the regime-based analysis would be more relevant when model simulations are compared with satellite retrievals, especially in the warm continental clouds, which are subjected to more entrainment and mixing compared to the marine clouds.
In the boreal spring (2 May 2013) over Germany, the Nd(NAd)-LWP sensitivity has been explored between the ICON-LES and the satellite retrievals using a joint probability histogram method. Several studies suggest that the satellite inferred NAd-LWP relationship is consistent with high-resolution model results (Ackerman et al., 2004; Sato et al., 2018). However, this study demonstrated that the satellite-derived NAd-LWP relationship is inconsistent with the relation predicted by the high-resolution ICON-LES model (Nd-LWP). Conversely, the NAd-LWP sensitivity is consistent in the model and the satellite analysis. In both cases, the peak CP appears at the lower NAd values, and the increase with the increase in NAd, particularly above 50 cm–3. While, it lacks the entrainment effect on cloud droplets, associated with the negative NAd-LWP relationship at higher NAd. However, the Nd-LWP relationship in the ICON-LES shows a nonlinear relationship with peak CP confined to the , especially at the higher levels. The Nd-LWP sensitivity clearly illustrates the cloud lifetime and the entrainment effect. Thus the diverse NAd/Nd-LWP relation explains the constraints in adiabatic assumption deriving NAd and the resulting NAd-LWP relationship that lacks the negative sensitivity or the entrainment effect.
Our analysis suggests that regime-based analysis would be more relevant when comparing the model or observations with the satellite retrievals, especially in the warm continental clouds subjected to entrainment and mixing compared to the marine clouds. In principle, the NAd represents the adiabatic part of the clouds, which could be considered in both the model simulation and the satellite retrievals when comparing the NAd-LWP relation. We have demonstrated that, while using NAd in both model and the satellite, the NAd-LWP relationship is in approximate agreement. Alternatively, thin shallow clouds with relatively uniform vertical Nd profiles justify the adiabatic assumption, and it also shows a positive Nd-LWP sensitivity, similar to the satellite retrievals. Thus, the statistical relation between the model simulations and the satellite retrievals is comparable when using a consistent assumption. Since the Nd-LWP relationship significantly impacts effective radiative forcing, considering the appropriate cloud regime in the model simulations and its comparisons with the satellite observation would open a new avenue in studying the effect of clouds on climate change.
The model output data used for the development of the research in the frame of this scientific article is securely saved in tape archives at the Deutsches Klimarechenzentrum (DKRZ), which will be accessible for 10 years. Additionally, backup copies are stored in the University of Leipzig and University of Cologne backup services. The satellite-based observational data used in the present research are acquired from the Level1 and Atmosphere Archive & Distribution System (LAADS) Distributed Active Archive Center (DAAC), located in the Goddard Space Flight Center in Greenbelt, Maryland (https://ladsweb.nascom.nasa.gov/).
The additional file for this article can be found as follows:
Figure S1The relation between cloud depth (m) and LWP (g m–2) as a function of cloud adiabaticity (α) in the ICON-LES simulation over Germany. DOI: https://doi.org/10.16993/tellusb.27.s1
This study has been carried out under the project “FORCeS”, which is funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 821205. Further funding from the DFG-ANR project “CDNC4aci” (Deutsche Forschungsgemeinschaft, DFG GZ QU 311/27-1) is acknowledged. The Co-authors, Annica M. L. Ekman and Matthias Schwarz, also acknowledge the funding of the Swedish Science Foundation (VR) project 2020-04158. We thank the High Definition Clouds and Precipitation for Advancing Climate Prediction (HD(CP)2) project (funded by the German Federal Ministry of Education and Research (BMBF; http://www.fona.de/) under grant no. 01LK1504B) for providing the model simulations. EG was supported by a Royal Society University Research Fellowship (URF/R1/191602). We thank the anonymous reviewers for their valuable comments on an earlier version of this manuscript.
The authors declare that they have no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
All authors participated in the design of the study. DS & JQ conceived and refined the overall structure of the investigation based on discussions with and feedback from all co-authors. All authors assisted in the interpretation of the results and commented on the paper. All authors have read and agreed to the published version of the manuscript.
Ackerman, AS, Kirkpatrick, MP, Stevens, DE and Toon, OB. 2004. The impact of humidity above stratiform clouds on indirect aerosol climate forcing. Nature, 432(7020): 1014–1017. DOI: https://doi.org/10.1038/nature03174
Albrecht, BA. 1989. Aerosols, cloud microphysics, and fractional cloudiness. Science, 245(4923): 1227–1230. DOI: https://doi.org/10.1126/science.245.4923.1227
Baldauf, M, Seifert, A, Förstner, J, Majewski, D, Raschendorfer, M and Reinhardt, T. 2011. Operational convective-scale numerical weather prediction with the cosmo model: Description and sensitivities. Mon. Weather Rev., 139(12): 3887–3905. DOI: https://doi.org/10.1175/MWR-D-10-05013.1
Bellouin, N, Quaas, J, Gryspeerdt, E, Kinne, S, Stier, P, Watson-Parris, D, Boucher, O, Carslaw, K, Christensen, M, Daniau, A-L, Dufresne, J-L, Feingold, G, Fiedler, S, Forster, P, Gettelman, A, Haywood, JM, Lohmann, U, Malavelle, F, Mauritsen, T, McCoy, D, Myhre, G, Mülmenstädt, J, Neubauer, D, Possner, A, Rugenstein, M, Sato, Y, Schulz, M, Schwartz, SE, Sourdeval, O, Storelvmo, T, Toll, V, Winker, D and Stevens, B. 2020. Bounding global aerosol radiative forcing of climate change. Rev. Geophys., 58: e2019RG000660. DOI: https://doi.org/10.1029/2019RG000660
Bennartz, R and Rausch, J. 2017. Global and regional estimates of warm cloud droplet number concentration based on 13 years of aqua-modis observations. Atmos. Chem. Phys., 17(16): 9815–9836. DOI: https://doi.org/10.5194/acp-17-9815-2017
Braun, RA, Dadashazar, H, MacDonald, AB, Crosbie, E, Jonsson, HH, Woods, RK, Flagan, RC, Seinfeld, JH and Sorooshian, A. 2018. Cloud adiabaticity and its relationship to marine stratocumulus characteristics over the northeast pacific ocean. J. Geophys. Res. Atmos., 123(24): 13,790–13,806. DOI: https://doi.org/10.1029/2018JD029287
Brenguier, J-L, Pawlowska, H, Schüller, L, Preusker, R, Fischer, J and Fouquart, Y. 2000. Radiative properties of boundary layer clouds: Droplet effective radius versus number concentration. J. Atmos. Sci., 57(6): 803–821. DOI: https://doi.org/10.1175/1520-0469(2000)057<0803:RPOBLC>2.0.CO;2
Bulatovic, I, Ekman, AML, Savre, J, Riipinen, I and Leck, C. 2019. Aerosol indirect effects in marine stratocumulus: The importance of explicitly predicting cloud droplet activation. Geophys. Res. Lett., 46(6): 3473–3481. DOI: https://doi.org/10.1029/2018GL081746
Charlson, RJ, Schwartz, SE, Hales, JM, Cess, RD, Coakley, JA, Hansen, JE and Hofmann, DJ. 1992. Climate forcing by anthropogenic aerosols. Science, 255(5043): 423–430. DOI: https://doi.org/10.1126/science.255.5043.423
Chen, Y-C, Christensen, MW, Stephens, GL and Seinfeld, JH. 2014. Satellite-based estimate of global aerosol-cloud radiative forcing by marine warm clouds. Nat. Geosci., 7(9): 643–646. DOI: https://doi.org/10.1038/ngeo2214
Christensen, MW, Jones, WK and Stier, P. 2020. Aerosols enhance cloud lifetime and brightness along the stratus-to-cumulus transition. Proc. Nat. Acad. Sci. USA, 117b: 17591–17598. DOI: https://doi.org/10.1073/pnas.1921231117
Christensen, MW, Neubauer, D, Poulsen, CA, Thomas, GE, McGarragh, GR, Povey, AC, Proud, SR and Grainger, RG. 2017. Unveiling aerosol–cloud interactions – part 1: Cloud contamination in satellite products enhances the aerosol indirect forcing estimate. Atmos. Chem. Phys., 17(21): 13151–13164. DOI: https://doi.org/10.5194/acp-17-13151-2017
Costa-Surós, M, Sourdeval, O, Acquistapace, C, Baars, H, Carbajal Henken, C, Genz, C, Hesemann, J, Jimenez, C, König, M, Kretzschmar, J, Madenach, N, Meyer, CI, Schrödner, R, Seifert, P, Senf, F, Brueck, M, Cioni, G, Engels, JF, Fieg, K, Gorges, K, Heinze, R, Siligam, PK, Burkhardt, U, Crewell, S, Hoose, C, Seifert, A, Tegen, I and Quaas, J. 2020. Detection and attribution of aerosol–cloud interactions in large-domain large-eddy simulations with the icosahedral non-hydrostatic model. Atmos. Chem. Phys., 20(9): 5657–5678. DOI: https://doi.org/10.5194/acp-20-5657-2020
Dipankar, A, Stevens, B, Heinze, R, Moseley, C, Zn̈gl, G, Giorgetta, M and Brdar, S. 2015. Large eddy simulation using the general circulation model icon. J. Adv. Model. Earth Syst., 7(3): 963–986. DOI: https://doi.org/10.1002/2015MS000431
Feingold, G, Eberhard, WL, Veron, DE and Previdi, M. 2003. First measurements of the twomey indirect effect using ground-based remote sensors. Geophys. Res. Lett., 30(6): DOI: https://doi.org/10.1029/2002GL016633
Forster, P, Storelvmo, T, Armour, K, Collins, W, Dufresne, J-L, Frame, D, Lunt, D, Mauritsen, T, Palmera, M, Watanabea, M, Wild, M and Zhang, H. 2021. The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity. In Masson-Delmotte, V, Zhai, P, Pirani, A, Connors, SL, Péan, C, Berger, S, Caud, N, Chen, Y, Goldfarb, L, Gomis, MI, Huang, M, Leitzell, K, Lonnoy, E, Matthews, JBR, Maycock, TK, Waterfield, T, Yelekçi, O, Yu, R and Zhou, B (eds.), Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Chapter 7). Cambridge University Press. In Press.
Glassmeier, F, Hoffmann, F, Johnson, JS, Yamaguchi, T, Carslaw, KS and Feingold, G. 2021. Aerosol-cloud-climate cooling overestimated by ship-track data. Science, 371: 485–489. DOI: https://doi.org/10.1126/science.abd3980
Grosvenor, DP, Sourdeval, O, Zuidema, P, Ackerman, A, Alexandrov, MD, Bennartz, R, Boers, R, Cairns, B, Chiu, JC, Christensen, M, Deneke, H, Diamond, M, Feingold, G, Fridlind, A, Hünerbein, A, Knist, C, Kollias, P, Marshak, A, McCoy, D, Merk, D, Painemal, D, Rausch, J, Rosenfeld, D, Russchenberg, H, Seifert, P, Sinclair, K, Stier, P, van Diedenhoven, B, Wendisch, M, Werner, F, Wood, R, Zhang, Z and Quaas, J. 2018. Remote sensing of droplet number concentration in warm clouds: A review of the current state of knowledge and perspectives. Rev. Geophys., 56(2): 409–453. DOI: https://doi.org/10.1029/2017RG000593
Grosvenor, DP and Wood, R. 2014. The effect of solar zenith angle on modis cloud optical and microphysical retrievals within marine liquid water clouds. Atmos. Chem. Phys., 14(14): 7291–7321. DOI: https://doi.org/10.5194/acp-14-7291-2014
Gryspeerdt, E, Goren, T and Smith, TWP. 2021. Observing the timescales of aerosol–cloud interactions in snapshot satellite images. Atmos. Chem. Phys., 21: 6093–6109. DOI: https://doi.org/10.5194/acp-21-6093-2021
Gryspeerdt, E, Goren, T, Sourdeval, O, Quaas, J, Mülmenstädt, J, Dipu, S, Unglaub, C, Gettelman, A and Christensen, M. 2019. Constraining the aerosol influence on cloud liquid water path. Atmos. Chem. Phys., 19(8): 5331–5347. DOI: https://doi.org/10.5194/acp-19-5331-2019
Gryspeerdt, E, Quaas, J and Bellouin, N. 2016. Constraining the aerosol influence on cloud fraction. J. Geophys. Res. Atmos., 121(7): 3566–3583. DOI: https://doi.org/10.1002/2015JD023744
Hasekamp, OP, Gryspeerdt, E and Quaas, J. 2019. Analysis of polarimetric satellite measurements suggests stronger cooling due to aerosol-cloud interactions. Nat. Commun., 10(1): 5405. DOI: https://doi.org/10.1038/s41467-019-13372-2
Heiblum, RH, Pinto, L, Altaratz, O, Dagan, G and Koren, I. 2019. Core and margin in warm convective clouds – part 1: Core types and evolution during a cloud’s lifetime. Atmos. Chem. Phys., 19(16): 10717–10738. DOI: https://doi.org/10.5194/acp-19-10717-2019
Heinze, R, Dipankar, A, Henken, CC, Moseley, C, Sourdeval, O, Trömel, S, Xie, X, Adamidis, P, Ament, F, Baars, H, Barthlott, C, Behrendt, A, Blahak, U, Bley, S, Brdar, S, Brueck, M, Crewell, S, Deneke, H, Di Girolamo, P, Evaristo, R, Fischer, J, Frank, C, Friederichs, P, Göcke, T, Gorges, K, Hande, L, Hanke, M, Hansen, A, Hege, H-C, Hoose, C, Jahns, T, Kalthoff, N, Klocke, D, Kneifel, S, Knippertz, P, Kuhn, A, van Laar, T, Macke, A, Maurer, V, Mayer, B, Meyer, CI, Muppa, SK, Neggers, RAJ, Orlandi, E, Pantillon, F, Pospichal, B, Röber, N, Scheck, L, Seifert, A, Seifert, P, Senf, F, Siligam, P, Simmer, C, Steinke, S, Stevens, B, Wapler, K, Weniger, M, Wulfmeyer, V, Zängl, G, Zhang, D and Quaas, J. 2017. Large-eddy simulations over germany using icon: a comprehensive evaluation. Q. J. R. Meteorol. Soc., 143(702): 69–100. DOI: https://doi.org/10.1002/qj.2947
Jia, H, Ma, X, Yu, F and Quaas, J. 2021. Significant underestimation of radiative forcing by aerosol–cloud interactions derived from satellite-based methods. Nat. Commun., 12(1): 3649. DOI: https://doi.org/10.1038/s41467-021-23888-1
Koren, I, Dagan, G and Altaratz, O. 2014. From aerosol-limited to invigoration of warm convective clouds. Science, 344(6188): 1143–1146. DOI: https://doi.org/10.1126/science.1252595
Lilly, DK. 1962. On the numerical simulation of buoyant convection. Tellus, 14(2): 148–172. DOI: https://doi.org/10.1111/j.2153-3490.1962.tb00128.x
Löhnert, U, Schween, JH, Acquistapace, C, Ebell, K, Maahn, M, Barrera-Verdejo, M, Hirsikko, A, Bohn, B, Knaps, A, O’Connor, E, Simmer, C, Wahner, A and Crewell, S. 2015. Joyce: Jülich observatory for cloud evolution. Bull. Amer. Meteor. Soc., 96(7): 1157–1174. DOI: https://doi.org/10.1175/BAMS-D-14-00105.1
Madhavan, BL, Kalisch, J and Macke, A. 2016. Shortwave surface radiation network for observing small-scale cloud inhomogeneity fields. Atmos. Meas. Tech., 9(3): 1153–1166. DOI: https://doi.org/10.5194/amt-9-1153-2016
McCoy, DT, Bender, FA-M, Mohrmann, JKC, Hartmann, DL, Wood, R and Grosvenor, DP. 2017. The global aerosol-cloud first indirect effect estimated using modis, merra, and aerocom. J. Geophys. Res. Atmos., 122(3): 1779–1796. DOI: https://doi.org/10.1002/2016JD026141
Menzel, W, Frey, R and Baum, B. 2015. Terra/modis cloud product 5-min l2 swath 1 km and 5 km, c6, nasa level-1 and atmosphere archive & distribution system (laads) distributed active archive center (daac). Greenbelt, MD: Goddard Space Flight Center. DOI: https://doi.org/10.5067/MODIS/MOD06_L2.006
Michibata, T, Suzuki, K, Sato, Y and Takemura, T. 2016. The source of discrepancies in aerosol–cloud–precipitation interactions between gcm and a-train retrievals. Atmos. Chem. Phys., 16(23): 15413–15424. DOI: https://doi.org/10.5194/acp-16-15413-2016
Mülmenstädt, J and Feingold, G. 2018. The radiative forcing of aerosol-cloud interactions in liquid clouds: Wrestling and embracing uncertainty. Curr. Clim. Chang. Rep., 4(1): 23–40. DOI: https://doi.org/10.1007/s40641-018-0089-y
Nakajima, T, Higurashi, A, Kawamoto, K and Penner, JE. 2001. A possible correlation between satellite-derived cloud and aerosol microphysical parameters. Geophys. Res. Lett., 28(7): 1171–1174. DOI: https://doi.org/10.1029/2000GL012186
Platnick, S, Meyer, KG, King, MD, Wind, G, Amarasinghe, N, Marchant, B, Arnold, GT, Zhang, Z, Hubanks, PA, Holz, RE, Yang, P, Ridgway, WL and Riedi, J. 2017. The modis cloud optical and microphysical products: Collection 6 updates and examples from terra and aqua. DOI: https://doi.org/10.1109/TGRS.2016.2610522
Quaas, J, Arola, A, Cairns, B, Christensen, M, Deneke, H, Ekman, AML, Feingold, G, Fridlind, A, Gryspeerdt, E, Hasekamp, O, Li, Z, Lipponen, A, Ma, P-L, Mülmenstädt, J, Nenes, A, Penner, JE, Rosenfeld, D, Schrödner, R, Sinclair, K, Sourdeval, O, Stier, P, Tesche, M, van Diedenhoven, B and Wendisch, M. 2020. Constraining the twomey effect from satellite observations: issues and perspectives. Atmos. Chem. Phys., 20(23): 15079–15099. DOI: https://doi.org/10.5194/acp-20-15079-2020
Quaas, J, Boucher, O, Bellouin, N and Kinne, S. 2008. Satellite-based estimate of the direct and indirect aerosol climate forcing. J. Geophys. Res. Atmos., 113(D5). DOI: https://doi.org/10.1029/2007JD008962
Quaas, J, Boucher, O and Bréon, F-M. 2004. Aerosol indirect effects in polder satellite data and the laboratoire de météorologie dynamique–zoom (lmdz) general circulation model. J. Geophys. Res. Atmos., 109(D8). DOI: https://doi.org/10.1029/2003JD004317
Quaas, J, Boucher, O and Lohmann, U. 2006. Constraining the total aerosol indirect effect in the lmdz and echam4 gcms using modis satellite data. Atmos. Chem. Phys., 6(4): 947–955. DOI: https://doi.org/10.5194/acp-6-947-2006
Ramanathan, V, Cess, RD, Harrison, EF, Minnis, P, Barkstrom, BR, Ahmad, E and Hartmann, D. 1989. Cloud-radiative forcing and climate: Results from the earth radiation budget experiment. Science, 243(4887): 57–63. DOI: https://doi.org/10.1126/science.243.4887.57
Rosenfeld, D, Sherwood, S, Wood, R and Donner, L. 2014. Climate effects of aerosol-cloud interactions. Science, 343(6169): 379–380. DOI: https://doi.org/10.1126/science.1247490
Saponaro, G, Sporre, MK, Neubauer, D, Kokkola, H, Kolmonen, P, Sogacheva, L, Arola, A, de Leeuw, G, Karset, IHH, Laaksonen, A and Lohmann, U. 2020. Evaluation of aerosol and cloud properties in three climate models using modis observations and its corresponding cosp simulator, as well as their application in aerosol–cloud interactions. Atmos. Chem. Phys., 20(3): 1607–1626. DOI: https://doi.org/10.5194/acp-20-1607-2020
Sato, Y, Goto, D, Michibata, T, Suzuki, K, Takemura, T, Tomita, H and Nakajima, T. 2018. Aerosol effects on cloud water amounts were successfully simulated by a global cloud-system resolving model. Nat. Commun., 9(1): 985. DOI: https://doi.org/10.1038/s41467-018-03379-6
Schüller, L, Bennartz, R, Fischer, J and Brenguier, J-L. 2005. An algorithm for the retrieval of droplet number concentration and geometrical thickness of stratiform marine boundary layer clouds applied to modis radiometric observations. J. Appl. Meteorol., 44(1): 28–38. DOI: https://doi.org/10.1175/JAM-2185.1
Seifert, A and Beheng, KD. 2006. A two-moment cloud microphysics parameterization for mixed-phase clouds. part 1: Model description. Meteorol. Atmos. Phys., 92(1): 45–66. DOI: https://doi.org/10.1007/s00703-005-0112-4
Sekiguchi, M, Nakajima, T, Suzuki, K, Kawamoto, K, Higurashi, A, Rosenfeld, D, Sano, I and Mukai, S. 2003. A study of the direct and indirect effects of aerosols using global satellite data sets of aerosol and cloud parameters. J. Geophys. Res. Atmos., 108(D22). DOI: https://doi.org/10.1029/2002JD003359
Sommeria, G and Deardorff, J. 1977. Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34: 344–355. DOI: https://doi.org/10.1175/1520-0469(1977)034<0344:SSCIMO>2.0.CO;2
Stephens, GL, Christensen, M, Andrews, T, Haywood, J, Malavelle, FF, Suzuki, K, Jing, X, Lebsock, M, Li, J-LF, Takahashi, H and Sy, O. 2019. Cloud physics from space. Q. J. R. Meteorol. Soc., 145(724): 2854–2875. DOI: https://doi.org/10.1002/qj.3589
Stevens, B and Feingold, G. 2009. Untangling aerosol effects on clouds and precipitation in a buffered system. Nature, 461(7264): 607–613. DOI: https://doi.org/10.1038/nature08281
Suzuki, K, Stephens, GL and Lebsock, MD. 2013. Aerosol effect on the warm rain formation process: Satellite observations and modeling. J. Geophys. Res. Atmos., 118(1): 170–184. DOI: https://doi.org/10.1002/jgrd.50043
Szopa, S, Naik, V, Adhikary, B, Artaxo, P, Berntsen, T, Collins, W, Fuzzi, S, Gallardo, L, Scharr, AK, Klimont, Z, Liao, H, Unger, N and Zanis, P. 2021. Short-Lived Climate Forcers. In Masson-Delmotte, V, Zhai, P, Pirani, A, Connors, SL, Péan, C, Berger, S, Caud, N, Chen, Y, Goldfarb, L, Gomis, MI, Huang, M, Leitzell, K, Lonnoy, E, Matthews, JBR, Maycock, TK, Waterfield, T, Yelekçi, O, Yu, R and Zhou, B (eds.), Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Chapter 6). Cambridge University Press. In Press.
Toll, V, Christensen, M, Quaas, J and Bellouin, N. 2019. Weak average liquid-cloud-water response to anthropogenic aerosols. Nature, 572: 51–55. DOI: https://doi.org/10.1038/s41586-019-1423-9
Twomey, S. 1974. Pollution and the planetary albedo. Atmos. Environ., 8(12): 1251–1256. DOI: https://doi.org/10.1016/0004-6981(74)90004-3
Unglaub, C, Block, K, Mülmenstädt, J, Sourdeval, O and Quaas, J. 2020. A new classification of satellite-derived liquid water cloud regimes at cloud scale. Atmos. Chem. Phys, 20(4): 2407–2418. DOI: https://doi.org/10.5194/acp-20-2407-2020
Xue, H and Feingold, G. 2006. Large-eddy simulations of trade wind cumuli: Investigation of aerosol indirect effects. J. Atmos. Sci, 63(6): 1605–1622. DOI: https://doi.org/10.1175/JAS3706.1
Zängl, G, Reinert, D, Rṕodas, P and Baldauf, M. 2015. The icon (icosahedral non-hydrostatic) modelling framework of dwd and mpi-m: Description of the non-hydrostatic dynamical core. Q. J. R. Meteorol. Soc., 141(687): 563–579. DOI: https://doi.org/10.1002/qj.2378