Figure  shows the time evolution of the key cloud-topped boundary layer properties for the original reference case in (red lines), henceforth referred to as the PD case, and its warmer-world counterpart at the EoC (black (SSP3) and green (SSP1) lines). We start by presenting the impact of warming on the SCT (solid lines) and then discuss the effect of aerosol perturbation (dashed lines). Note that SSP1 has fewer cloud droplets (120 mg⁻¹) compared to the other two cases (150 mg⁻¹) and thus will be discussed separately. Additionally, we use a new metric for determining the onset of cumulus activity. Earlier studies have used various metrics to define the magnitude of this transition. defined SCT based on reduction in scene albedo (A). In and , the transition is defined on the basis of a sustained reduction (6 to 24 h) in the cloud fraction fc. The latter definition is applicable for the cases in which precipitation plays a prominent role in the transition. Here, we use the spatial variance in the cloud base (zb) as a metric for the onset of cumulus clouds in the boundary layer. For nearly horizontally homogeneous stratocumulus clouds, the variance in zb will be near zero. However, with the onset of cumulus activity, i.e., for cumulus-under-stratocumulus, the variance will increase as the number of cumulus columns increases.

The evolution of PD (solid red line) is similar to the results in . The diurnal cycle is clearly evident in the LWP and cloud fraction (fc) time series (Fig. b, d). Note that cloud breakup in PD occurs earlier (by approximately 10–12 h) than in . We attribute this to the additional 12 h spin-up in the current simulations, which causes the boundary layer to deepen by an additional 200 m during this time period. The rapid reduction in fc (around 52 h in Fig. d) is triggered by the onset of strong precipitation at the cloud base (Fig. f), and is correlated with a rapid reduction in cloud droplet concentration Nd (Fig. c). In the strongly warmer-world (SSP3), the LWP is substantially lower than its PD counterpart (Fig. b). Note that the entrainment velocity is also lower in SSP3, which is evident from the inversion layer height zi time series (Fig. f). This is due to weakening of the boundary layer turbulence due to climate change . zi in the warmer world is lower than in the PD scenario until the onset of precipitation below zb (≈ 55 h). The reduction in LWP, despite the reduction in entrainment velocity, is an outcome of the entrainment-liquid flux (ELF) feedback associated with the increase in humidity jump across the inversion layer due to warming . This increase in the humidity jump across the inversion layer enhances the evaporative cooling rate at the cloud-top, which translates to enhanced buoyancy production at cloud-top, thus increasing the entrainment flux despite a lower entrainment velocity (see for a detailed discussion of the ELF feedback mechanism). Additionally, fc undergoes a stronger diurnal cycle in a warmer climate due to the strong reduction in cloud-top radiative cooling as well as the ELF feedback . Interestingly, the onset of cloud breakup in the warmer world (SSP3) around 50 h (Fig. d) is also driven by precipitation, and the timing of the onset of precipitation is a bit earlier than in PD. Post cloud breakup (after 64 h), the cloud properties and consequently the short wave upward (SWUP) flux for these two cases converge. The LWP and fc converge within a few hours while the inversion heights take longer. Another variable of interest is the variance of the cloud base height zb (Fig. e). We see that cumulus activity is initiated earlier in SSP3 (enhanced value of the variance around 43 h), which is consistent with the earlier onset of precipitation. Note that the boundary layer coupling strengthens after sunset on day 2 and then weakens again after the onset of precipitation. Subsequently, in the remaining days, the magnitude of the zb variance continues to increase. Thus, apart from the onset of precipitation and the reduction in fc, the variance in zb is also a good indicator of cumulus activity in this system.

In the muted warming scenario (SSP1), the effect of warming on cloud properties (solid green line in Fig. ) is a lot weaker compared to SSP3. This is an obvious outcome of weaker forcing associated with climate change (see Table ). However, there are additional contributions from the lower aerosol concentration. The LWP and fc are similar to the PD case on days 1 and 2. A possible explanation is that the effects of the ELF feedback associated with warming are offset by the lower aerosol concentration within the marine boundary layer, i.e., the reduction in LWP associated with the effects of climate change (warming and weakened radiative cooling) and the increase in LWP due to the reduction in Nd (weakened sedimentation-entrainment and evaporative-entrainment feedbacks), offset each other. Here too, the lower aerosol concentration results in a slightly earlier onset of precipitation compared to PD. The evolution of cloud properties post-transition is similar to SSP3 but does not show any signs of convergence towards the PD values. fc and SWUP flux are consistently higher in SSP1 after the transition (after ≈ 65 h).

Post aerosol injection (≥ 12 h) and prior to cloud breakup (≲ 50 h), the in-cloud (τ≥1, where τ is cloud optical thickness) LWP is reduced relative to the unperturbed case (dashed lines in Fig. ). The reduction in LWP is more substantial in PD and SSP1. In SSP3, a combination of weaker boundary layer turbulence and lower LWP reduce the magnitude of sedimentation-entrainment feedback. In PD and SSP3, fc is weakly affected by aerosol perturbation prior to cloud breakup (≈50 h). However, in SSP1, suppression of weak precipitation around sunrise on day 2 causes a substantial reduction in fc (between 40–45 h, Fig. d, f). This results in a reduction in the scene albedo as is evident from the SWUP flux time series (green dashed line in Fig. a). A similar observation was reported in . This precipitation-suppression induced darkening (albedo reduction) was attributed to the effects of enhanced SW absorption.

Injection of aerosol into the boundary layer delays the onset of cloud breakup through precipitation suppression in all scenarios. Despite the reduction in LWP, the suppression of precipitation maintains overcast conditions for an additional day, leading to substantial cloud brightening on day 3. However, the reduction of fc in the warmer world means that a reduced amount of cloud is available for brightening. This leads to a weaker enhancement of the SWUP flux in SSP3 on day 3 (Fig. a).

To quantify the impact of aerosol perturbation on cloud properties, we explore aerosol-induced changes to the SW cloud radiative effect (dCRE =CREunperturbed-CREaerosolperturbed), where positive values indicate cloud brightening. Following and , we decompose dCRE into contributions from fc, Nd, and LWP: 1dCRE=Fin{fc[(Ac,Nd,aP-Ac)]︸dCRE-Nd+fc[(Ac,LWP,aP-Ac)]︸dCRE-LWP+(fc,aP-fc)(Ac,aP-Aclr)︸dCRE-fc}, where Fin is the incoming solar radiation at top-of-the-atmosphere (TOA), Aclr is the clear-sky albedo, Ac,Nd/LWP is the cloud albedo contribution from changes in Nd or LWP, fc is cloud fraction, and aP in the subscript indicates aerosol perturbation, respectively. dCRE -Nd or dCRE - LWP represent the change in CRE while LWP or Nd is unperturbed (with respect to aerosol), respectively. Both terms are directly proportional to the unperturbed fc. dCRE -fc is a product of cloud abedo changes and fc changes in response to aerosol perturbation.

Figure  shows the evolution of dCRE and its components in all scenarios, and Table  shows the daytime average for the same quantities. Similar to , dCRE increases from day 1 to day 3 in all scenarios (Fig. a). On day 1, dCRE is highest for SSP1 and PD and lowest for SSP3 (Fig. a and Table ). By day 2, the dCRE is highest for the SSP1 case and lowest for the PD case. On day 3, the highest dCRE is for SSP1 followed by PD and then SSP3. These trends suggest a combined influence of warming and the background aerosol concentrations in determining aerosol-induced CRE changes.

To gain a deeper understanding of these trends on each day, we examine the decomposition of dCRE (Fig. b, c, and d). In the first two days, the positive contribution to dCRE is dominated by dCRE -Nd with SSP1 having the highest value. On day 3, dCRE -fc is the dominant contributor to dCRE in all scenarios. This is associated with the suppression of precipitation-induced cloud breakup. As in dCRE -Nd, SSP1 has the highest magnitude, and SSP3 the lowest. The dCRE - LWP component is predominantly negative on all days as a result of the reduction in LWP from increased entrainment flux and SW absorption. This substantially offsets the brightening from the Twomey and lifetime effects. On most days, the highest magnitude is for PD followed by SSP1 and SSP3 (Table ).

Figure , similar to Fig. , shows the time series of key boundary layer properties in all scenarios with dry FT humidity (entrainment-driven transition). In this case, precipitation does not play a dominant role in the transition to a cumulus-topped boundary layer. This is evident from Fig. f, which shows that the precipitation flux at zb is negligible prior to the onset of cumulus activity (around 66 h) in all unperturbed scenarios. As noted previously, we use the variance in zb as a metric to assess the onset of cumulus activity.

The reduction in FT humidity substantially lowers the cloud LWP (Fig. b) compared to the corresponding cases in Fig. . Over time, the increase in SST enhances the LWP in the cloud layer in all the unperturbed cases. The LWP is lowest in SSP3 until the onset of precipitation, and similar in the PD and SSP1 cases on day 1 and most of day 2. The relatively low LWP in SSP3 results in weak precipitation below the cloud base until the end of the simulation (Fig. f). The fc time series is substantially altered by the degree of climate change (Fig. d). The increase in SST due to climate change and the weakening of radiative cooling at cloud-top, enhances the magnitude of changes in fc over the course of a diurnal cycle. Consequently, SSP3 has the lowest fc, followed by SSP1 and the reference case. It is interesting to note that the minimum value in fc is similar on all three days in SSP3, while, in the SSP1 and PD scenarios, the minima in fc decrease from day 1 to day 3. On day 3, the value of the minimum in fc is similar in all three cases around 66 h, marking the onset of cumulus activity. This is evident from the sharp increase in the cloud base variance time series (≈ 66 h in Fig. e). The onset of precipitation in the final 12 h of the simulation results in the breakup of the stratocumulus layer, lowers fc and zb, and further increases the variance in zb (Fig. d, e, and f). Note that despite the similarity in the onset times of cumulus clouds across scenarios, the cloud breakup timings are quite different. Substantial precipitation occurs first in SSP1 due to a lower Nd, followed by PD, and then SSP3 (Fig. f). Substantially lower LWP in SSP3 results in a delayed and weaker precipitation flux (20 %–50 % lower compared to PD). Consequently, cloud breakup is slower in SSP1 (Fig. d) and the SWUP flux is highest for SSP1 on day 4 (Fig. a). Note that precipitation only plays a secondary role in this entrainment-driven transition case. However, we will see later that the aerosol-induced changes in CRE are dominated by processes associated with precipitation.

The injection of aerosol lowers the LWP in all three scenarios until the onset of precipitation (dashed lines in Fig. b). The magnitude of the change in LWP increases with time until the onset of precipitation (Fig. b). Additionally, during the daytime, fc also decreases weakly due to the increase in aerosol concentration prior to the onset of precipitation (Fig. d). Furthermore, aerosol injection does not influence the onset of cumulus activity (see the variance of zb time series in Fig. e). Notable effects related to aerosol perturbation are evident only post precipitation suppression. This enhances fc in PD and SSP1 scenarios. Note that in SSP3, the increase in fc post aerosol injection is weaker compared to SSP1 and PD due to the weaker precipitation flux at zb.

Figure  and Table  show the dCRE and its components for the entrainment-driven transition cases. Until the onset of precipitation (day 3/day 4), the enhancement in CRE is weaker compared to the high-humidity cases (Fig. a). This is an outcome of lower LWP and fc. However, post precipitation onset on the final day, the enhancement in CRE is comparable to the moist FT case. dCRE is comparable in PD and SSP1 on days 1 and 2. On day 3, the dCRE in SSP1 is substantially higher than in PD. For SSP3, the dCRE values are substantially lower than the other two cases on all days. The decomposition of dCRE offers further insights into the evolution of dCRE across scenarios. In SSP3, dCRE -Nd is the lowest on all three days, and the values are similar in SSP1 and PD on each day with slightly higher values for SSP1 due to its lower baseline Nd (Fig. b). dCRE - LWP and dCRE -fc are largely negative with similar magnitude in both SSP1 and PD in the first two days (Fig. c and d). Additionally, the lowest magnitude for dCRE - LWP on each day is for SSP3. On day 3, there are strong fluctuations in dCRE - LWP and dCRE -fc due to strong cumulus activity (Fig. c, d). The substantially higher dCRE on day 3 for SSP1 is the outcome of strong positive LWP and fc contribution due to cumulus activity which is stochastic in nature and thus cannot be directly attributed as a response to aerosol perturbation. A more detailed discussion on ACI after separating the effects of climate change will be presented in Sect. .

It is tempting to interpret the differences between scenarios in dCRE (Figs.  and ) as an outcome of changes in ACI due to climate change. Instead, these trends are a combination of warming-induced changes and aerosol-induced changes. To better understand this, we quantify the effects of climate change on the unperturbed (with respect to aerosol) state of the cloud. This will aid us in separating the effect of aerosol perturbation from that of climate change.

The impact of climate change on CRE in cases with moist and dry humidities is shown in Fig. , which depicts the difference in CRE between PD conditions and EoC conditions (dCRE_clm). We only consider the cases without aerosol perturbation for calculating dCRE_clm. A positive value indicates cloud brightening. Note that dCRE_clm is different from dCRE in Eq. (). The latter represents the change in CRE due to aerosol perturbation.

In the moist FT case, the magnitude of the CRE decreases (cloud darkening) before the onset of strong precipitation in both warming scenarios. This is associated with the reduction in LWP and fc through the effects of warming SST (due to climate change) and the weakening of radiative cooling at cloud-top . The resulting positive low-cloud feedback is consistent with other LES and observational studies . As expected, to leading order, the darkening is stronger for SSP3, though SSP1 shows similar reductions on day 2 due to precipitation losses (Fig. f) in LWP and Nd (Fig. b and c). On day 3, after the cloud breakup, the magnitude of dCRE_clm decreases substantially. Note that SSP1 has a slightly higher magnitude on day 3 as precipitation starts earlier. Furthermore, we also see that dCRE_clm is positive on day 4 in SSP1 due to the higher residual fc.

In the dry FT case, precipitation does not play a prominent role until after sunset on day 3. Until then, SSP3 exhibits the largest darkening. After the onset of cumulus activity (≥ 65 h on day 3), the magnitude of dCRE_clm reduces to near zero. However, slow cloud breakup in SSP3 due to low LWP results in a positive value for dCRE_clm (brightening). Overall, the dry FT case exhibits larger (negative) dCRE_clm compared to the moist FT case and therefore warrants further scrutiny. In particular, we need to understand the impact of climate change on fc and LWP.

Figure  depicts the fractional changes in LWP and fc due to climate change. While we show the results for both SSP1 and SSP3, for ease of discussion we focus on SSP3. In moist FT case, the fractional reduction in fc and LWP is substantial. On day 1, the reduction in fc ranges between 5 % and 10 % and increases to 20 %–25 % on day 2. The reduction in LWP is around 20 % on day 1 and less than 5% on day 2. (Note that we are only considering the time period before the onset of precipitation, i.e., before sunset on day 2.) In the dry FT case, the reduction in fc is higher than its moist counterpart (around 30 % to 35 % on days 1 and 2). However, the reduction in LWP is lower compared to the moist case (less than 10 % on day 1). These results indicate that the extent of reduction in fc due to climate change is a function of LWP.

One of the main themes of this study is to evaluate the effect of climate change on the efficacy of marine cloud brightening. To address this, we look at changes to the TOA radiative fluxes. Figure  shows time-averaged SWUP flux (panels to the left) and the long-wave upward flux (LWUP) (panels to the right) at the TOA for all cases simulated in this study. There are two data points for each day, each representing the average values between sunrise and sunset and between sunset and sunrise. The top panels represent the moist FT case and the bottom panels represent the dry FT case. In the SSP1 and SSP3 scenarios, the enhancement in SWUP flux due to aerosol perturbation (difference between hatched bars and solid bars) is smaller than the reduction associated with climate change. The effects of positive cloud feedback reduce the brightening prospects of marine low-clouds in the absence of precipitation (see Sect. ).

Suppression of precipitation leads to substantial enhancement in SWUP flux. Some of this enhancement is offset by the reduction in the outgoing LW radiation due to a rise in cloud top height (see the panels to the right in Figs.  and f). Despite this, in all climate scenarios, suppression of precipitation leads to an enhancement in SWUP flux that is substantially greater than the unperturbed PD scenario, as the effects of cloud feedback are weaker after the cloud breaks up to open-cellular clouds. However, the net enhancement in SWUP flux due to precipitation suppression is not immune to climate change. For instance, in the moist FT case, the highest enhancement in SWUP‾ is for the PD and SSP1 scenarios due to the greater fc during daytime on day 3 (Fig. a).

Our results in Sect.  show that in the stratocumulus regime, the dry FT case exhibits a stronger effect of climate change on CRE. We attribute this to the shielding effect of higher LWP in the moist FT case. In all scenarios in Figs.  and , a substantial reduction in fc does not start until the LWP reaches a sufficiently low value . In simpler terms, cloud thinning precedes reduction in fc. Consequently, the higher LWP in the moist FT case shields fc from the effects of weakened radiative cooling and climate-change-induced warming. The lower LWP in the dry FT case results in a stronger reduction in fc. Since CRE, to leading order, is controlled by fc, until the onset of precipitation, dCRE_clm is higher in the dry FT case.

In the moist FT case, after cloud breakup, the fractional changes in fc and LWP are low, resulting in low dCRE_clm (Fig. ). After precipitation-induced breakup, the cloud layer transitions into an open-cellular structure and has the characteristics of a surface driven cloud system (e.g. cumulus clouds) . Thus, the low value for dCRE_clm post cloud breakup is consistent with the locally weak low-cloud feedback seen in marine cumulus clouds .

The similarity in the values for Nd and LWP components of albedo change across climate scenarios in both dry and moist FT cases is, at first sight, puzzling as the impact of climate change on LWP and, by extension, the cloud albedo is clearly evident from the time series plots in Figs. b and b. It is important to note that the bulk of the reduction in cloud LWP due to climate change is visible post-sunset and before sunrise. Interestingly, after sunrise, the impact of climate change on cloud LWP decreases as clouds with higher LWP are more susceptible to SW absorption . During this time, the dominant effect of climate change on CRE is evident from the changes in fc (Sect. ). Thus, by factoring out fc in Eq. () we are eliminating (to leading order) the effects of climate change on dCRE in non-precipitating marine low-clouds.

The similarity we see here appears to be case-specific as there is no universality among these albedo change time series between the moist and dry FT cases. This local similarity suggests that in stratocumulus clouds, changes in albedo contributions from Nd and LWP are immune to climate change, i.e., the magnitude of Twomey effect and LWP adjustments do not change within the cloudy region. The scenario-specific differences we see in the dCRE components in Table  and Figs.  and are an outcome of warming-induced changes to the unperturbed state (mainly fc) of the cloud system and not an outcome of the impact of climate change on ACI.

We have established that the Nd and LWP components of dCREfc are, to leading order, invariant under climate change. If we know the magnitude of the albedo adjustment in the non-precipitating stratocumulus clouds in the present day, then we can estimate the magnitude of CRE adjustment in a warmer climate provided we know fc under warmer conditions. have established that changes in the CRE of stratocumulus clouds due to planetary warming can be approximated as a linear combination of changes in meteorological factors. This linear approximation has also been used in several recent observational studies . We extend this to account for Nd and express changes in CRE in non-precipitating clouds under climate change as 4dCRE=∑i=1n∂CRE∂MidMi+∂CRE∂NddNd, where Mi represents ith cloud-controlling meteorological factor and ∂CRE∂Nd=Finfc∂Ac∂Nd. As discussed earlier, our results suggest that ∂Ac∂Nd is invariant under climate change. We leave it to future studies to assess the validity of this hypothesis using a larger dataset (observational or simulation).

It is important to note that the low-cloud transitions investigated here are (i) precipitation-mediated (moist FT): from a closed marine startocumulus cloud deck to an open cellular low-cloud layer, and (ii) entrainment-driven (dry FT): the transition from a marine stratocumulus cloud deck to a cumulus-under-stratocumulus cloud deck. Technically, in both cases, the transition to a cumulus-topped boundary layer is not yet complete.

In the precipitation-mediated transition, climate change affects the onset of the transition. The transition is initiated earlier in SSP3 than in PD. Note that both cases have similar aerosol number concentration at the start, and so microphysics is unlikely to explain the difference in initiation time. The boundary layer decoupling is stronger in the SSP3 scenario compared to the PD scenario due to weakened radiative cooling at cloud-top and increased surface latent heat flux . This is also supported by the buoyancy integral ratio (BIR) time series in Fig. a. BIR is a ratio between the magnitudes of the negative buoyancy flux in the sub-cloud layer and the positive buoyancy flux in the boundary layer . A higher BIR value indicates a stronger decoupling. Note that the level of decoupling is higher in SSP3 especially during the night on day 1. The magnitude of decoupling increases in strength on day 2, which eventually leads to the earlier onset of cumulus activity on day 2. The stronger decoupling in SSP3 is also evident from the jump in the magnitude of the cloud base variance around 43 h (Fig. e). The earlier onset of cumulus activity eventually leads to the early onset of precipitation-induced breakup. An earlier transition also occurs in the SSP1 case, but this is driven by both the lower aerosol concentration and the effects of climate change.

In the entrainment-driven case, the effects of climate change do not influence the onset of the cumulus clouds. However, the onset of breakup, which is influenced by precipitation, is affected by the effects of warming through changes in LWP. The substantial reduction in LWP in the SSP3 scenario delays the onset and weakens the intensity of precipitation. This results in brighter clouds in the SSP3 case post-transition. This is in contrast to the behavior prior to the transition. It is puzzling that unlike in the scenarios with moist FT, climate change does not affect the onset of cumulus activity in the dry scenarios despite changes in the cloud properties. A possible explanation for this could be that the lower humidity in the FT ensures that radiative cooling at the cloud top is large enough to preserve the structure of the marine boundary layer (MBL) despite the effects of climate change. The BIR time series in Fig. b for the dry FT case shows that there is a certain degree of decoupling during the day on the first two days and the extent of decoupling increases from day 1 to day 2. However, after sunset, the boundary layer is recoupled in all scenarios during this time period. On day 3, the decoupling gets a lot stronger in all scenarios, which eventually results in cumulus activity. Note that in the scenarios with moist FT a certain level of decoupling is maintained in the boundary layer even after sunset on all days until the onset of precipitation. Comparison of BIR time series in both cases supports the hypothesis that substantially lower radiative cooling of the boundary layer in the moist FT case (83 W m⁻² in moist FT and 113 W m⁻² in dry FT) makes the onset of cumulus activity more susceptible to climate change. However, more case studies are required to assess the robustness of this conclusion.

The injection of aerosol delays the breakup of the stratocumulus deck in both moist and dry FT cases by delaying the onset of precipitation in cumulus-cloumns. This leads to substantial brightening of the cloud deck in all climate scenarios. However, the onset of cumulus activity in both cases is largely unaffected by aerosol perturbation (all scenarios in dry FT and SSP3 in moist FT) unless influenced by precipitation formation (PD and SSP1 in moist FT).