Clouds play an important role in the Earth's energy balance. In particular, marine stratocumulus clouds have a net cooling effect on the planet as they reflect a substantial fraction of the incoming solar radiation . These overcast cloud decks are typically found in the sub-tropics over the eastern flanks of the ocean where sea surface temperatures are colder . As these clouds advect towards the Equator, they undergo a transition from overcast stratocumulus to a shallow-cumulus-topped boundary layer with a much lower cloud fraction . Recent studies have shown that aerosol–precipitation interactions play an important role in regulating the stratocumulus-to-cumulus (SCT) transition . In this study, we explore the impact of aerosol perturbations (ship emissions, deliberate aerosol injection, etc.) on the SCT in the northeast Pacific region.

To elucidate the mechanisms behind the SCT, several studies including field observations and modeling have been undertaken. Until recently, the accepted theory of SCT was attributed to the advection of the cloud layer over a continuously warming sea surface. The increasing sea surface temperature (SST) enhances the surface latent heat flux (LHF). This increases the liquid water path (LWP), which results in enhanced cloud-top entrainment and shortwave (SW) absorption. This promotes the decoupling of the cloud layer from the surface . Over time the decoupling gets stronger, which enables the formation of overshooting cumulus clouds that locally couple the cloud layer with the surface layer. The enhanced entrainment from cumulus clouds and a lack of steady supply of water vapor from the surface gradually thins and dissipates the stratocumulus layer. explored the SCT in four different ocean basins using multiple reanalysis trajectories and concluded that the transition is similar in all cases. These transitions were typically considered to be a multi-day process, based on numerical simulations using microphysical schemes with a fixed cloud droplet concentration (Nd). This lack of interaction between aerosol and cloud droplets significantly reduced the degree to which precipitation can influence the SCT. Using the same modeling framework, explored the factors influencing SCT. Their analysis showed that the SCT is primarily affected by the increasing SST, and the timescale of the transition is governed by the lower tropospheric stability.

The interaction of precipitation and stratiform clouds was investigated in and . They argued that the evaporation of sub-cloud precipitation decouples the cloud layer from the surface. This enhances cumulus activity in deeper boundary layers and accelerates the transition from stratocumulus- to cumulus-topped boundary layers . Recent simulations with a prognostic aerosol scheme have shown that the interactions among aerosol concentration (Na), Nd, and drizzle play an important role in determining the SCT timescale . The onset of collision–coalescence triggers weak precipitation, which results in lower Nd and Na. This promotes the growth of cloud droplets to larger sizes, which makes the cloud colloidally unstable. This increases precipitation, resulting in further reduction in Na, which further strengthens precipitation. This positive feedback (referred to as runaway precipitation) significantly reduces Na in the boundary layer. Similar conclusions were drawn from recent simulations of Lagrangian trajectories drawn from the CSET campaign . However, conclusions from observational studies are ambiguous in assessing the role of precipitation. Using satellite data, concluded that rain has little role in determining the timescale of SCT once the marine boundary layer (MBL) height and inversion strength are factored in. A more refined study suggests that precipitation plays an important role in the transition from closed-to-open cellular transition but not so much in the closed-to-disorganized cumulus transition . Furthermore, the analysis of three trajectories from the CSET campaign shows that under pristine conditions precipitation may play an important role in the transition . All of these studies suggest that the importance of precipitation in SCT is conditional on the meteorology. In the present study, we investigate the well-studied SCT system from , where precipitation plays an important role in the transition to cumulus clouds .

The aerosol perturbations applied in this study should be considered a proxy for the emissions from ships and deliberate aerosol injection for marine cloud brightening (MCB). MCB is a proposed climate intervention approach where sub-tropical marine stratocumulus clouds are seeded with sea-spray aerosol particles to enhance their reflectivity . Recent studies based on general circulation models have suggested that MCB has the potential to mitigate the warming effects of anthropogenic greenhouse gas emissions . However, these models do not represent marine stratocumulus with sufficient fidelity, nor do they account for aerosol-induced cloud adjustments correctly, leaving questions about their ability to assess the net enhancement in cloud reflectivity.

The susceptibility of the cloud radiative effect (CRE) to an aerosol perturbation has three major contributions: Nd, liquid water path (LWP), and cloud fraction (fc). The enhancement in cloud reflectivity in response to an increase in Nd, stratified by LWP and fc, is known as the Twomey or albedo effect . In reality, LWP and fc are affected by aerosol perturbations. The addition of aerosol enhances the colloidal stability of the cloud layer and suppresses precipitation, which increases LWP and fc . However, it also increases the cloud-top entrainment rate through the evaporation–entrainment feedback and sedimentation–entrainment feedback potentially causing a decrease in LWP and fc. Additionally, LWP and fc adjustments are affected by aerosol-enhanced SW absorption and surface flux changes .

In this study, we use large-eddy simulations (LESs) to assess the impact of aerosol perturbations on SCT by varying the injection rates and the frequency of perturbations. We consider two SCT baseline systems: polluted (150 particles mg-1) and pristine (50 particles mg-1). The simulations can be considered of interest to both possible future MCB activities as well as to the broader problem of aerosol–cloud–climate forcing. In the next section, we will present the details of the simulation setup, including the aerosol forcing function. This is followed by a presentation of simulation results. We end the article with a discussion of the results in the context of MCB, followed by a summary and outlook.

Traditional LES is capable of representing aerosol–cloud interactions faithfully over a wide range of meteorological conditions. However, these studies are limited to rather small domains (≤ 100 km). Consequently, large-scale meteorological feedbacks are not captured in such studies. To date, in the context of MCB, most LES studies have been based on fixed meteorological conditions and short durations (12–36 h) . To understand the impact of MCB-like aerosol perturbations on the SCT, we require domains with horizontal extent spanning several hundred kilometers and time integration up to 3 or more days, which are computationally prohibitive at LES resolutions. A good compromise in this regard is Lagrangian LES, where a smaller domain with horizontally uniform properties is advected along the mean wind . Thus, the spatial variation in the large-scale forcings is represented as temporally varying boundary conditions. Further temporal changes are imposed on the model domain through nudging to a predefined value obtained from coarser models or reanalysis data sets. This methodology has been used to investigate SCT in several studies , and is used in the current study as well. We note that this methodology, despite its advantages compared to traditional LES, has its limitations in representing the large-scale effects and feedbacks. Additionally, the accuracy of the temporally evolving boundary conditions is dependent on the reanalysis data.

The simulations reported here follow the setup in , and therefore only a brief overview is provided here. The Lagrangian LES model is coupled to a two-moment, bin-emulating bulk microphysical model . The conditions and trajectories are based on the reference Lagrangian SCT case study developed by . The model domain is advected along the mean boundary layer wind in the northeast Pacific (NEP) region. (See Fig.  for a schematic of the trajectory.) The subsidence rates along the trajectory are obtained from , and the time evolution of the SST is obtained from .

We use the System for Atmospheric (SAM) model as the LES dynamical core . The radiative effects are represented using the Rapid Radiative Transfer Model for Global Climate Models (RRTMG) with extended vertical profiles above the domain top . The microphysical scheme consists of two modes representing cloud droplets and raindrops separately, allowing for more precise bin-by-bin mass transfer rates for modeling the collision–coalescence processes (bin-emulating). The size distributions are represented as log-normal distributions, each with a fixed geometric standard deviation of 1.2 . The two modes are separated by a threshold value of 25 µm in radius . Additionally, a separate prognostic equation is solved for Na, which includes a fixed surface flux of 70 cm-2 s-1 , and losses or gains through cloud processing (activation, deactivation, collision–coalescence, and wet removal). The activation of aerosol particles is determined by the local supersaturation, which is calculated prognostically following the semi-analytical method of . The aerosol follows a log-normal size distribution with a geometric standard deviation of 1.5 and a geometric mean radius of 100 nm . In the applied modeling framework, cloud processing of aerosol affects the number concentration of aerosol but not the shape of the distribution . Note that the recommended radius of aerosol particles for MCB is thought to be between 15 and 85 nm , which is slightly smaller than the size range considered. We assume the injected particle size distribution to be the same as the background size distribution to avoid treating two separate populations, which would in any case become indistinguishable once processed by the cloud. This differs from the more rigorous aerosol treatment using the superdroplet approach , which is computationally unfeasible for the long simulations and large domains used here. In spite of this simpler aerosol and cloud microphysical treatment, the results are highly relevant in terms of the injection-related modification to Nd and the subsequent adjustments of LWP and fc, which together determine the degree of cloud brightening.

All the simulations have a domain size of 128 km in the horizontal directions and 4.25 km in the vertical direction. A uniform grid spacing of 100 m is used in the horizontal directions. In the vertical direction, a uniform grid spacing of 10 m is used below 2.775 km, and above this height, the grid is smoothly stretched to the domain top with the grid spacing increasing linearly with height. The total number of grid points in the vertical direction is 300. Such a large horizontal domain is chosen to capture the spread rates of the injected aerosol plume, as well as precipitation and associated cloud-field organization . The time step is set to 3 s with adaptive sub-stepping to satisfy the Courant–Friedrichs–Lewy stability condition. The radiative heating profiles are updated every minute. The simulation is integrated in time for 3 d, starting on the 196.75th day of the year (15 July 10:00 local time).

Two sets of simulations are conducted for different baseline Na: 150 mg-1 (NA150) and 50 mg-1 (NA50). In the baseline case in NA150, the transition from overcast stratocumulus to low-cloud-fraction (fc) clouds occurs due to the increasing SST. The timescale of the transition is determined by precipitation. On the other hand, in the NA50 baseline case, the transition is solely driven by precipitation resulting in an open-cellular cloud structure. Note that the precipitation-driven transitions are reversible (i.e., overcast stratocumulus layer can be re-established) if a sufficient amount of aerosol particles is injected into the boundary layer . In our study, the transition is said to be complete when fc decreases to a value below 40 % and stays below this value for at least 6 h. Both NA150 and NA50 systems are subjected to various aerosol seeding strategies summarized in Tables  and . We vary aerosol injection rates: low (1×1016 particles s-1 referred to as 1×) and high (5×1016 or 8.6×1016 s-1 referred to as 5× and 8.6×, respectively), which are the recommended ranges per sprayer for MCB . Note that the 8.6× injection is explored only for the NA50 system. We also vary the number of aerosol sprayers and the number of aerosol pulses along the trajectory. A schematic of the trajectory, the position of the aerosol pulses, and the configuration of the sprayers is provided in Fig. . Each seeding strategy has a five-character code (e.g., 1×-120). The two characters before the hyphen represent the strength of the aerosol injection rate (0×/1×/5×/8.6×), and the last three digits represent the number of sprayers (0/1/2) active during each of the three aerosol pulses. A value of 0 indicates that no aerosol is injected during the time period of that pulse. The first aerosol pulse is introduced 4 h after the start of the simulation. The next pulse is introduced approximately 20 h after the first pulse, and the final pulse is introduced 19 h later. An approximately 20 h separation between pulses is maintained to ensure sufficient time for the aerosol plume to spread across the domain. During this time the cloud layer advects approximately 350 to 400 km. The total aerosol injected into the marine boundary layer can be calculated as the aerosol injection strength times the sum of the last three digits in the code. Each aerosol pulse represents the passage of sprayer(s) upstream from one end of the domain to the other at a speed of 5 m s-1; i.e., the relative speed between the sprayer and the domain is 5 m s-1. Each sprayer has the dimension of one grid cell (100 × 100 m2), and all the particles are injected from the surface.

In the previous section, we explored the impact of aerosol perturbation on the SCT. We considered two SCT scenarios, one in which strong precipitation only occurs in the afternoon of day 3 (NA150 – polluted) and the other in which strong precipitation occurs in the afternoon of day 1 (NA50 – pristine). The simulation results suggest that an aerosol perturbation delays the onset of the SCT in both scenarios. To leading order, the delay in the transition is proportional to the number of injected aerosol particles prior to the onset of the transition in both scenarios, which is broadly consistent with the results of .

In the polluted system, the transition is affected mainly by the total number of injected particles prior to the transition and not by the time sequence of the injections. This is evident from the fact that cases 1×-110 and 1×-101 follow a similar trajectory (except for the time when the plume is still spreading) for all the cloud properties (Fig. ) and break up around the same time. Additionally, the 5×-100 case and the delayed version of 5×-100 (5 h delay in seeding) to leading order have similar evolution in cloud properties. A similar conclusion was drawn from the simulations in wherein a non-precipitating cloud system was subjected to a range of aerosol perturbations by varying the injection rate and duration of the perturbation. It was concluded that after the initial transient, the cloud system properties were determined only by the total number of aerosol particles injected into the cloud layer. Note that the cloud layer in the polluted simulations qualifies as a non-precipitating system until the morning of day 3, and all the aerosol pulses are active before this time. Furthermore, the addition of aerosol delays this onset of precipitation.

In the pristine system, all the aerosol pulses are active after the onset of precipitation. We see that the distribution in space and time of aerosol pulses plays an important role in the evolution of the cloud system. For instance, 1×-110 and 1×-200 have the same number of aerosol particles injected into the MBL; however their cloud properties have very different trajectories. Until the afternoon of day 2, Nd and fc are higher for 1×-200, after which the reverse is true. Note that the timing of this switch-over is consistent with the injection of the second pulse in 1×-110. The enhancement of precipitation post-aerosol perturbation in 1×-200 reduces the injected aerosol concentration within the MBL; however the enhancement in CRE is not significant in either of these cases after day 2. This illustrates the complexity in the evolution of the MBL properties in this system and is reinforced by the fact that the onset of SCT is not delayed the most for the strongest perturbation (5×-200) but by a slightly weaker perturbation (8.6×-100). The key difference is the depth of the inversion layer, which is proportional to the magnitude of the precipitation suppression. This enhanced depth dilutes Na and also strengthens the decoupling of the cloud layer from the surface. The increased LHF due to entrainment deepening and stronger cumulus clouds trigger precipitation that results in the earlier transition in 5×-200 compared to 8.6×-100.

The CRE in both the polluted and pristine systems is enhanced post-aerosol perturbation. No substantial darkening tendency is evident in any of the simulations. The decomposition of CRE offers insights into the contributions from Nd, LWP, and fc. In the polluted system, the dCRE increases from day 2 to day 4. The contributions from the negative LWP adjustment are around 10 %–30 % of Nd. On day 3, the positive adjustment in LWP in the morning is due to precipitation suppression, some of which is offset by the entrainment adjustment. The negative LWP adjustment in the afternoon is due to enhanced SW absorption. These counteracting effects reduce the net contribution from the LWP component (see Table ). Note that the negative adjustment in LWP due to entrainment (dominant during the night) is not significant in this system due to fairly high free-tropospheric humidity (≈ 3.5 g kg-1). On day 4, the enhancement in CRE is largely a result of the changes to fc associated with precipitation suppression, and its peak magnitude is approximately 75 % more than the dCRE peak on day 3. In the pristine system, the SCT is delayed the most in case 8.6×-100, resulting in the highest dCRE on day 4. However, the net brightness is not the highest for this case as the dCRE in case 5×-200 is substantially higher on days 2 and 3. Additionally, the dominant contribution to dCRE is from the changes to fc associated with precipitation suppression, which is consistent with earlier LES studies on MCB . On day 2, the contribution from Nd is also substantial and comparable to fc.

In this study, we explored how the stratocumulus-to-cumulus transition (SCT) is affected by deliberate aerosol perturbations using a Lagrangian large-eddy simulation (LES) model coupled to a two-moment bulk microphysics scheme. We used the average trajectory from . The setup of these simulations is directed towards marine cloud brightening (MCB) – the deliberate injection of aerosol particles into the marine boundary layer to enhance the brightness of the marine stratocumulus clouds, thereby exerting a cooling effect on the planet. We considered two different baseline aerosol conditions: a polluted (150 particles mg-1) background and a pristine background (50 particles mg-1). We varied the aerosol injection rates per sprayer, number of sprayers, and number of aerosol pulses to assess the impact of various MCB strategies. Our results showed that the spread rate of the aerosol plume is faster in the pristine system due to the transverse circulation induced by the gradient in rain rate across the plume track. In response to the aerosol perturbation, the SCT is delayed in both polluted and pristine systems. To leading order, in the polluted scenario, the time delay in the transition is proportional to the amount of aerosol injected into the MBL and is only weakly affected by the distribution (in space and time) of the aerosol sprayers. The enhancement in cloud radiative effect (CRE) increases from day 2 to day 4. The changes in CRE are dominated by the albedo effect on days 2 and 3 and cloud fraction (fc) adjustments on day 4. In the pristine system, only the strong perturbations make a substantial contribution to MCB. The weak perturbations are dissipated within a day through enhanced precipitation in the aerosol plume track. The time delay in SCT is affected by the total number of aerosol particles injected into the marine boundary layer and their distribution in space and time. A more concentrated but slightly weaker aerosol injection tends to delay the SCT more effectively than splitting it across two sprayers. The enhancement in CRE is dominated by fc and is sustained for 2 d in the strongly perturbed cases.

The results presented here are based on the composite trajectory from a 2-year (2006–2007, June–August) climatology. This average trajectory may mask the variability in profiles, which may impact the SCT. For instance, faster advection or a faster SST increase may result in an early transition. In such a scenario, the time required for the aerosol plume to spread and the corresponding cloud adjustment timescales may affect the effectiveness of MCB. In other words, a different aerosol injection rate and sprayer configuration may be required under these conditions for the effective implementation of MCB. Thus, future studies should use more realistic conditions based on instantaneous soundings and forcings. Additionally, the current Lagrangian model does not account for the large-scale feedback associated with aerosol perturbation. Thus, further model improvements are warranted to better constrain the impact of aerosol perturbation .