The model used in this study is the System for Atmospheric Modeling SAM version 6.11.7. The microphysics scheme used is the two-moment bulk microphysics of . The aerosols available for activation are represented by a power law function of the super-saturation (SS): CCN = NaSSk, where Na is the concentration of CCN available at 1 % super-saturation and k is a constant, here equal to 0.4, representing typical maritime conditions. CCN activation at the cloud base is parameterized using the vertical velocity and CCN spectrum parameters . In this case, we use different Na concentrations for representing changes in aerosol concentration. Here, ice nucleation is not directly coupled to Na (i.e., changes in Na do not change the concentration of ice nucleating particles, INPs) but rather depends on the temperature and the supersaturation with respect to ice . We note that, in realistic conditions, changes in Na might cause changes in INPs, an effect that should be addressed in future research. In our simulations, freezing occurs through homogeneous freezing and heterogeneous freezing by contact or immersion freezing . Ice nucleation directly from vapor is not considered here, but depositional growth of cloud ice is enabled. Direct interactions between aerosols and radiation are also not considered here; however, aerosols could affect the radiation via the modification of the clouds' properties. In order to represent the Twomey effect , the model is configured to pass cloud water and ice-crystal effective radii from the microphysics scheme to the radiation scheme.

The simulations used here generally follow the Radiative-Convective-Equilibrium Model Intercomparison Project RCEMIP small domain protocol but with changes in aerosol concentration. The simulations are run in a small domain, of 96 km × 96 km, in order to avoid the effects of convective self-aggregation . The simulations are conducted with a horizontal grid spacing of 1 km, 68 vertical levels between 25 m and 31 km, and a vertical grid spacing increasing from 50 m at the surface to around 1 km at the domain top. To get solar insolation close to the tropical-mean value, the solar radiation is fixed at 551.58 Wm-2, with a zenith angle of 42.05° . A diurnal cycle is not considered here, and we note that it might affect the convective development to some extent even over the ocean . In order to initialize convection, a small thermal noise is added near the surface at the beginning of each simulation.

The concentration of CO2 is fixed at the pre-industrial level (280 ppm), while there are 25 different Na and SST combinations – five different values for each. Na ranges from 20 to 2000 cm-3 (20, 100, 200, 1000, and 2000 cm-3), following a recent observational data set , which showed the feasibility of this Na range. The SST ranges from 290 to 310 K in 5 K intervals. Snapshots of the different simulations are presented in Fig. S1 in the Supplement. This wide range of aerosol and SST conditions is used to maximize the effects and for establishing a better physical understanding. A fixed ozone profile, representing a typical tropical atmosphere, is used here . We note that using a fixed ozone profile under different SSTs is not entirely realistic and may have some effect on the cloud development . For simplicity, the effect of other trace gases (such as CH4 and N2O) is neglected. The temporal resolution of the simulations is 10 s, and that of the interactive radiative scheme is 5 min (using the CAM radiation scheme, ). All fields have an output resolution of 1 h; 3D fields are saved as snapshots, while domain statistics are saved as hourly averages. Each simulation was run for 150 d , and the last 30 d of each simulation was used for statistical analysis.

We start by examining the effect of changes in Na on the TOA energy gain under different SSTs (ΔR; Fig. a). Figure  illustrates that for all SSTs, an increase in Na decreases ΔR – an effect which becomes stronger with a decrease in the SST. The longwave (LW) and shortwave (SW) components of ΔR are negatively affected by Na (each declining by up to 4–5 Wm-2 for the entire Na range considered here, depending on the SST; Fig. b and c), with ΔRSW being more susceptible to SST changes (Fig. c), and ΔRLW decreases in a roughly similar manner across all SSTs (Fig. b). Moreover, the CRE (calculated as all-sky radiative flux minus clear-sky radiative flux) is identified as the main driver of ΔR variations, while changes in clear-sky radiation have a minimal impact, as indicated by Fig. d–f. This is true in our simulations as changes in Na do not directly affect radiation by aerosol–radiation interactions.

In order to understand the radiative effect of an increase in Na under the different SSTs, we first examine the domain- and time-mean cloud liquid water path, ice water path, and cloud fraction (L, I and CF, respectively; Fig. ). Figure  illustrates a monotonic increase in L with Na, which is generally stronger under lower SSTs, and a monotonic decrease in I, consistently across SSTs. In addition, Fig. c illustrates a general decrease in CF with Na, although not monotonic. We note that the CF trend is dependent on the choice of the cloud vs. clear-sky definition, as can be seen in Fig. S2.

Next, we examine vertical profiles of the different hydrometeors (Fig. ). We note that with an increase in SST, the freezing level increases. Since an increase in Na acts to push warm rain formation to higher levels , under lower SSTs, for which the freezing level is relatively shallow (about 1250 m above cloud base in the coldest case considered here), an increase in Na can inhibit warm rain (Fig. g). In contrast, under higher SSTs, for which the freezing level is relatively deep (about 6000 m above cloud base in the warmest case considered here), an increase in Na drives warm rain inhibition at the lower levels, which is compensated for at higher levels of the warm section (Fig. g). That is to say that under low SSTs the delay in warm rain is not being offset at higher levels within the warm section, while under high SSTs we do see such an offset. This explains the stronger rise in water content within the warm section (L), with an increase in Na under low-SST conditions compared to high-SST conditions (Fig. a).

In addition to resulting in an increase in L, the warm rain inhibition under higher Na results in more super-cooled water Fig. f, leading to higher production of snow Fig. j, and drives higher riming rates, thus producing more graupel Fig. i. We will get back to this observed trend for the explanation of the results presented in Fig.  below. In addition, cloud ice declines with Na consistently across SSTs (Fig. h). This trend is consistent with the decline in I and CF (Fig. b and c, respectively) and will be discussed further below (Fig. d).

Figures – examine the bulk cloud and radiative properties in the domain. However, as previously demonstrated, the impact of aerosols on clouds is cloud-regime-dependent . Therefore, it is crucial to analyze the distribution of cloud regimes in our simulations and discern how each specific cloud regime responds to the increase in Na. In this paper we define the cloud regimes based on different bins of L and I. For that purpose, Fig.  presents 2D histograms of the cloud occurrence (CO) at the different bins of L and I, as well as the average total, shortwave, and longwave CRE at these different bins, all for the coldest case considered here (SST = 290 K) as an example. Figure  also illustrates that the CF in these RCE simulations is mostly dominated by anvil clouds (e.g., ), i.e., clouds with negligible L and high (thick anvil clouds; denoted by marker 1 in Fig. a) or low (thin anvil clouds; denoted by marker 2 in Fig. a) I. However, Fig. a also illustrates the existence of two other types of clouds in these RCE simulations – shallow clouds (high L and low I; denoted by marker 3 in Fig. a) and deep convective clouds (high L and high I; denoted by marker 4 in Fig. a). We note that the shallow and deep cloud regimes may also consist of other types of clouds, such as cumulus congestus in the deep regime and two-layer-cloud conditions with cirrus clouds with relatively low I above shallow clouds. Furthermore, Fig. e and j present the radiative significance of each L and I bin (i.e., the CO times the CRE for each bin), which illustrates a strong heating by thin anvil clouds and cooling by other cloud regimes. Lastly, Fig. k–n illustrate the difference between simulations with the highest (2000 cm-3) and the lowest (20 cm-3) Na conditions. Specifically, Fig. k illustrates that an increase in Na drives thinning of the anvil clouds, i.e., an increase in the frequency of thin anvil clouds and a decrease in the frequency of thick anvil clouds. Additionally, Fig. l–n illustrate that with an increase in Na the CRE decreases for all L and I bins (and especially for medium–high L and low I; Fig. l), driven mostly by changes in the SW (Fig. m), with only minor changes in the LW (Fig. n). This SW difference with Na can be explained by the Twomey effect .

Following the method outlined in , we calculate the total regime's CF as the 2D integral over the regime's L and I bins as defined in Table S1 in the Supplement. Figure a illustrates a monotonic decrease across SSTs in thick anvil cloud fraction (CFthick) with increasing Na, consistently with the domain mean CF reduction (Figs. c and S8a). On the other hand, thin anvil cloud fraction (CFthin) mostly increases with Na, which is generally stronger for lower SSTs (Fig b), and illustrates a general thinning of anvil clouds. We note that the entire distribution of I is shifted to lower values with Na, demonstrating this thinning of the anvil clouds (Figs. k, b, and h). A decrease in CFthick and thinning of the anvil clouds leads to more outgoing LW radiation out of the atmosphere and reduces ΔRLW, as can be seen in Fig. b. In addition, Fig. c presents the relative change in the shallow cloud fraction (CFshallow). It illustrates a rise in CFshallow with Na for low SST, while for high SST it illustrates a decrease in CFshallow with Na (the change in the shallow cloud fraction is not observed in Fig. k due to the dominance of ice clouds, which inflates the color-bar range). We note that although the relative changes in CFthick, CFthin, and CFshallow have similar magnitudes, the baseline (i.e., referring to the simulated value and not the difference between the most polluted and cleanest runs) CFthick and CFthin are an order of magnitude larger than CFshallow (Fig. S8). Lastly, deep cloud fraction (CFdeep) changes in a non-monotonic trend with Na (Fig. d), while also covering a small fraction of the domain (Fig. S8d).

Figure  illustrates that the response of the CRE to an increase in Na is driven both by changes in CO (Fig. k) and by changes in CRE for a given bin of L and I (Fig. l). Next, we aim to quantitatively separate these two effects. Thus, we write the total CRE as the 2D integral over the different bins of L and I of the CF times the CRE in each bin: 4CRE=∫0∞∫0∞CRE(L,I)CF(L,I)dLdI.

In the simulations presented here ΔCRE ≊ ΔR (Fig. ). Thus, following a somewhat similar method to that presented in and , we decompose the mean ΔR into three contributions: 5ΔCRE≊ΔR=∫0∞∫0∞ΔCRE(L,I)CF(L,I)dLdI︸Opacity+∫0∞∫0∞CRE(L,I)ΔCF(L,I)dLdI︸Shift+∫0∞∫0∞ΔCRE(L,I)ΔCF(L,I)dLdI︸Nonlin. In this decomposition, the first term on the right-hand side, the “Opacity” term, represents changes in ΔR due to changes in the CRE per L and I bin, while the distribution of L/I is held fixed; i.e., this term is calculated by multiplying Fig. a with Fig. l. This term represents changes in the cloud's opacity (reflectance and absorption) for a given liquid and ice amount (for example, by the Twomey effect). We note that this term could also be influenced by changes in clear-sky fluxes . The second term on the right-hand side, the “Shift” term, represents changes in ΔR due to changes in the distribution of L/I occurrence, while the CRE per L and I bin is held fixed; i.e., this term is calculated by multiplying Fig. b with Fig. k. The Shift term is contributed by both changes in the total CF and by a shift between the different cloud regimes (for example, thinning of ice clouds). The last term on the right-hand side, the nonlinear (“Nonlin”) term, represents the combined effect of changes in the CRE and the cloud occurrence in the different L/I bins; i.e., this term is calculated by multiplying Fig. k with Fig. l.

Figure a–c illustrate the decomposition presented in Eq. () for the domain mean (i.e., integrating over all L and I bins, excluding the no-cloud regime as defined in Table S1) for all the different SSTs. Figure a–c also present the simulated response as presented in Fig.  (referred to as “Model”) and the sum over the three terms presented in Eq. () (referred to as “Total”). These panels illustrate that the Opacity term is the main driver for the decline in ΔR with Na (Fig. a), occurring mostly through the SW (Fig. b). In addition, Fig.  illustrates that the Opacity term is the main driver for the SST sensitivity, demonstrating a generally weaker response as the SST increases, consistent with Fig. c. The Shift term, on the other hand, demonstrates similar magnitudes but opposite sign in the SW and LW (Fig. b and c, respectively), with a weak SST dependence, thus making this term negligible in the total (Fig. a). The nonlinear term shows close to zero contributions to ΔR and its SW and LW components, thus justifying focusing on the linear decomposition in Eq. (). We note that the decomposition results in a similar magnitude and SST trend to the model (comparing Total to Model in Fig. a–c), thus justifying its use. However, we also note a slight overestimation of ΔR using the decomposition at the lower SSTs (Fig. a).

In addition to the domain mean, ΔR is decomposed per cloud regime by integrating over the relevant part of the L and I phase space (Fig. d–f and Table S1). These panels illustrate that deep convective clouds have negligible contributions to ΔR, ΔRSW, and ΔRLW, mostly due to their small coverage (Figs. a and S8d). Therefore, most of the contribution to ΔR comes from anvil cloud and shallow cloud changes.

The thick and thin ice clouds' response drives a negative net total ΔR, which is stronger under lower SSTs (Fig. d). This trend is dominated by the Opacity term, which is driven almost entirely by the SW part of the spectrum (Fig. e). This term represents an increase in the reflectivity of the ice clouds for a given L and I distribution and can be explained by a similar mechanism to the Twomey effect but for ice particles. We note that this result might differ under coupling of Na to ice nucleating particles, which is not considered here. This term becomes stronger (more negative) with a reduction in SST, especially for thick clouds, due to an increase in the baseline CF of these clouds (Fig. S8). The Shift term in thick ice clouds is strongly positive in the SW (Fig. e) and negative in the LW (Fig. f) due to the thinning of the ice clouds and the general reduction of the occurrence of these thick clouds (Figs. k and a). Thin ice clouds exhibit an opposite trend to thick clouds in the Shift term due to them increasing in CO with an increase in Na (Figs. k and b). However, the combined net effect of thick and thin ice clouds on the Shift term is low due to them being similar in magnitude but opposite in sign (Fig. d).

Similarly to the ice clouds' response, the shallow clouds' response also drives a negative net total ΔR, which becomes stronger under lower SSTs (Fig. d). As expected, changes in shallow clouds have a small impact in the LW (Fig. f) but a significant effect in the SW (Fig. e). As in ice clouds, the negative net total ΔR in the shallow cloud case is driven mostly by the Opacity term, which in this case can be explained by the classical Twomey effect. Unlike ice clouds, the Opacity term demonstrates a low sensitivity to the underlying SST, but the shallow clouds' Shift term exhibits strong SST sensitivity. This term, while having a relatively small magnitude, is negative under low SSTs and positive under high SSTs, consistent with the relative change in CFshallow, which is positive under low SSTs and negative under high SSTs (Fig. c). The contrasting response of CFshallow to Na under the different SSTs can be explained by warm rain inhibition at varying depths of warm layers. As was noted above, with an increase in SST, the warm layer depth increases, while an increase in Na acts to push warm rain formation to higher levels . Thus, under lower SSTs, for which the warm layer depth is relatively shallow, an increase in Na can inhibit warm rain (see Fig. g) and hence lead to an increase in CFshallow. In contrast, under higher SSTs, for which the warm layer depth is relatively deep, an increase in Na drives warm rain inhibition at the lower levels, which is compensated for at higher levels of the warm section (Fig. g), thus eliminating the positive effect on CFshallow.

The combined response of ice and shallow clouds to an increase in Na, as explained in this section, can explain the reduction in ΔRLW with Na, the reduction in ΔRSW with Na and its SST sensitivity, and hence the reduction in ΔR with Na and its SST sensitivity (Fig. ).

As was noted above, a decrease in CFthick with Na (Fig. a) leads to more outgoing LW radiation out of the atmosphere (Fig. b). In order to understand the reduction in CFthick and the ice cloud thinning with Na, next we examine the sensitivity of the maximum (in the vertical dimension – see Fig. d) of the radiatively driven mass divergence Dr to Na under the different SSTs (Fig. ). Figure a illustrates that the CFthick is strongly correlated with Dr (Pearson correlation coefficient ≈ 0.93 with p value < 0.01). While the general decrease in Dr with SST has previously been demonstrated , here we show that for a given SST, Dr generally decreases with Na (Fig. b). The general reduction in Dr with Na drives a general reduction in CFthick with Na for a given SST (Figs. a and c). This reduction in Dr and CFthick with Na explains the reduction in I and cloud ice (Figs. b and h, respectively) with Na, which in turn can explain the reduction in ΔRLW (Fig. b).

In addition to modifying Dr, an increase in Na also affects the lifetime of anvil clouds by perturbing the sedimentation rate . Specifically, high-aerosol conditions lead to smaller ice crystals, which sediment slower from the cloud (i.e., the sedimentation flux becomes less negative; Fig. S13), thus acting to increase CFthick. However, Fig. a shows a decrease in CFthick with Na in our simulations, thus making this only a secondary effect compared with the effect of Dr (agreeing with previous results regarding the effect of warming on anvil clouds; ).

A reduction in Dr with Na could be attributed to changes in Qr (the radiative cooling rate; Fig. b) and/or in the static stability (S; Fig. a). Thus, in order to understand the reasons behind the decrease in Dr with Na (for a given SST), in Fig.  we calculate the change in Dr with Na for the different SSTs, assuming that either Qr or S are held fixed at the value it attains at a reference Na of 200 cm-3 for each SST. This calculation is similar to that presented in Fig. 4 of but for changes in Na instead of changes in SST. Figure  illustrates that the reduction of Dr with an increase in Na can mostly be attributed to changes in S. This result is illustrated by the consistent reduction in Dr with Na for all SSTs when only S (or the temperature, T) is varied. However, when only Qr is varied, the trend of Dr with Na is not consistent across the different SSTs, and for some of the SSTs, the trend is not monotonic.

The domain and time mean temperature vertical profiles for the different simulations and their response to an increase in Na are presented in Fig. . This figure illustrates that, for a given SST, an increase in Na drives strong warming of the upper troposphere and in some cases a weak cooling of the lower troposphere. This trend demonstrates an increase in S with Na, which in turn explains the reduction in the anvil cloud fraction.

A remaining open question concerns the reasons behind the strong warming of the upper troposphere (or the increase in S) with Na. In the model, a central prognostic variable is the liquid/ice water static energy (hL). The hL tendency equation contains five terms: advection (adv), radiation (rad), latent heating (lat, includes latent heating from freezing), turbulence, and large-scale tendency . In an RCE configuration, by definition, the large-scale tendency is set to zero, thus having no effect here. In addition, in our simulations the turbulence term is negligible compared to the rest of the terms. Hence, in Fig.  we present vertical profiles of the domain and time mean ∂hL∂t due to latent heating, advection, and radiation of the different simulations. Figure  illustrates that under equilibrium conditions, the latent heating acts to heat the upper troposphere; advection acts to cool it, although by a smaller magnitude; and radiation acts to weakly cool the entire troposphere almost uniformly. This trend is enhanced with an increase in Na (Fig. d–f), suggesting that the increase in temperature of the upper troposphere with Na is mostly driven by a stronger latent heat release, which is consistent with the higher production rates of graupel and snow with Na (Fig. i and j). Graupel and snow, unlike small ice crystals, efficiently sediment out of the cold portion of the cloud, thus leaving behind the heat they released in their formation, resulting in a net warming effect. In addition, at higher altitudes, the air density drops. Thus, a given amount of latent heating will cause a larger temperature change at higher altitudes than low altitudes . Therefore, higher production of graupel and snow with Na is identified as the main driver of the observed temperature increase in the upper troposphere.

Next, we examine the response of the surface precipitation to Na under the different SSTs. Figure a illustrates an increase in surface precipitation (in energy units, LΔSP, where L is the latent heat of vaporization and SP is the surface precipitation) with Na across SSTs. In order to understand this increase, we use the atmospheric energy budget perspective and decompose the changes in LΔSP to changes in LW atmospheric radiative cooling (ΔLWC, calculated as the TOA's LW radiation flux minus the surface's net LW radiation flux; Fig. b), changes in surface sensible heat flux (ΔSHF; Fig. c), and changes in atmospheric SW absorption (ΔSWA, calculated as the TOA's net SW radiation flux minus the surface's net SW radiation flux; Fig. d), following the notations of : 6LΔSP=ΔLWC-ΔSWA+ΔSHF.

We note that Eq. () holds under equilibrium conditions, as simulated here . Following the notations of Eq. (), Fig. a can be reconstructed by summing Fig. b–d. Hence, we note that the increase in LΔSP could mostly be explained by enhanced ΔLWC (Fig. b), while changes in ΔSWA produce only a small positive contribution, and changes in ΔSHF present a small contribution and a non-consistent contribution across SSTs. The enhanced ΔLWC with Na is driven by clear-sky radiative cooling, which is in turn driven by the decreased CFthick with Na across SSTs, as illustrated in Fig. a. The enhanced ΔLWC is also consistent with the reduction in ΔRLW presented in Fig. b. These results suggest that under equilibrium conditions, higher Na concentrations drive higher LW cooling rates of the atmospheric column, which supports the production of more precipitation.