The Regional Atmospheric Modelling System (RAMS version 6.3.03) is a three-dimensional, non-hydrostatic, cloud-resolving model with a two-moment bin-emulating microphysics scheme (Pielke et al., 1992; Cotton et al., 2003; Saleeby and van den Heever, 2013). Details of the model grid configuration, initial conditions, and parameter settings are described in Table 1. The RAMS model configuration used here was identical to that in Leung and van den Heever (2022), though the vertical grid is extended to reach from the surface to ∼23 km in altitude. The high horizontal, vertical, and temporal resolution (Δx=100 m, Δz= 50–300 m  Δt=0.75 s) allowed the model to resolve large turbulent eddies and to represent a wide range of convection over the two diurnal cycles (48 h) that were simulated. The domain was located entirely over the ocean, and the simulation was initialized using a combination of dropsonde observations from the Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP2Ex; Reid et al., 2023) and ECMWF Reanalysis-5 (ERA-5) data as described in Leung and van den Heever (2022). After initialization, the model was allowed to evolve freely without additional large-scale forcing, though the solar insolation varied according to the diurnal cycle. As such, these simulations serve as an idealized representation of the microphysical, dynamical, and radiative processes driving maritime tropical convection.

The aerosol field was initialized homogenously in the horizontal direction at the first model time step but decays exponentially in the vertical direction with a scale height of 7 km. In all simulations, ice-nucleating particles (INPs) were also initialized with concentrations starting at 0.01 particles cm-3 at the surface and with the same vertical structure as the aerosol field. Both aerosol–radiation and microphysics–radiation interactions (liquid and ice phase) were included in the simulation. The aerosol budget capabilities in RAMS allowed for the tracking of aerosol number and mass in the following categories: (1) unactivated, (2) in-hydrometeor, (3) regenerated, and (4) wet-deposited or rained-out aerosol (Saleeby and van den Heever, 2013). A schematic depicting the processes governing the exchange between these categories is shown in Fig. 1. Upon initialization, all aerosol particles were initially categorized as unactivated aerosol, i.e. aerosol particles which have not yet been activated in cloud droplets. Over time, the aerosol number and mass concentration fields changed freely as particles were advected around the domain. If the aerosol particles were entrained into an updraft and encountered sufficient supersaturations to activate and serve as CCN and/or INPs, they were transferred to the in-cloud aerosol category. As water mass was transferred between hydrometeor species (i.e. cloud, drizzle, rain, ice, snow, aggregates, hail, and graupel), a corresponding fraction of aerosol was also transferred. Under subsaturated conditions, the hydrometeors evaporated, and the aerosol particles acting as CCN and/or INPs were returned to the environment as regenerated aerosol. Finally, if aerosol particles were contained within raindrops which fell to the ground (either because they were activated as CCN or because they were intercepted by a hydrometeor), they were transferred to a category tracking the accumulated aerosol mass reaching the surface via wet deposition or rainout.

The full set of simulations presented here consists of 16 simulations in which four aerosol loadings and four aerosol types were varied (Table 2). The four aerosol loadings tested span the observed range of aerosol loadings during the CAMP2Ex field campaign, from clean to highly polluted environments (Reid et al., 2023). Throughout the rest of this paper, the different aerosol loading runs are denoted by the initial aerosol number concentration at the surface (which was also the maximum aerosol number concentration initialized in each column), namely 100, 500, 1000, and 1500 cm-3. The four aerosol types tested were ammonium sulfate, sea salt, mineral dust, and absorbing carbon. These aerosol types have varying median particle sizes, solubility and hygroscopicity, and radiative properties. The aerosol size distribution was represented as a single log-normal mode with a shape factor of 1.8 (Reid et al., 2023), with the median particle size depending on the aerosol type, as specified in Table 2. Other key properties of the different aerosol types are also listed in Table 2, and corresponding aerosol optical depths (AODs) are provided in Fig. S1 in the Supplement.

Individual cloud updrafts in each simulation were identified and tracked using the Tracking and Object-Based Analysis of Clouds (tobac version 1.5.0 release candidate 1) package (Heikenfeld et al., 2019; Sokolowsky et al., 2022). We provide a basic description of how tobac works (feature identification, tracking, and segmentation), but for a more comprehensive description, we direct readers to the two papers cited above. We use the term “feature” to refer to an updraft region at a given time step and “cell” to refer to a given cloud feature tracked across time. First, updraft features were identified at each analysis time step (at a frequency of 5 min) based on the three-dimensional vertical velocity field. Regions of local maximum vertical velocity were identified as features at three threshold values (1, 3, and 5 m s-1), and a centroid position was assigned to each feature. Secondly, features in subsequent time steps were linked based on their inferred motion to create a cell with a trajectory over time. Any cells which had a lifetime of less than 5 min (i.e. cells which were tracked for only a single analysis time step) were excluded from the analysis as part of the quality control (QC). Finally, a contiguous three-dimensional cloudy region (where cloud condensate was above 0.01 g kg-1) was identified around each updraft feature using the tobac watershed segmentation technique. We excluded any updraft features that were not associated with a cloudy region as part of the QC. Cloud top and base altitudes, as well as cloud areas and volumes, were calculated based on the size of this cloudy region. Similar segmentation was performed on the two-dimensional surface precipitation and aerosol rainout rates in order to identify the size of the raining and/or rainout area associated with each cloud. Based on these identified features and cells, the mean and maximum values for variables such as rain rate, aerosol rainout rate, and updraft velocity were calculated for each cloud over a given time step and over its entire lifetime. Other studies have used previous versions of tobac to effectively track cloud objects in a similar manner (e.g. Marinescu et al., 2021), but recent improvements to tobac (Sokolowsky et al., 2022) have specifically allowed for cloud objects to be identified and tracked in three dimensions and across periodic boundaries, as was necessary for this study.

It should be noted that, in this work, we are tracking on updrafts, meaning that clouds at the very beginning or end of their life cycles with updrafts weaker than 1 m s-1 are necessarily excluded from the analysis. This is a limitation of tracking packages that use a physically informed threshold to detect features; however, since tobac allows for setting multiple thresholds, we have set a fairly low minimum threshold in order to capture the majority of the cloud lifetime. Although there are numerous updrafts with maximum vertical velocities below 1 m s-1 present in the simulation, we found that such weak updrafts do not contribute significantly to the precipitation or aerosol budget, accounting for less than 2 % of precipitation and aerosol rainout. Furthermore, after applying all our QC thresholds, we found that a vast majority of the falling-rain and rained-out aerosol (75 %–80%) could be attributed to the remaining features and that this was consistent across all these simulations.

The domain-wide trends in the aerosol mass budget are presented in Fig. 3. For each simulation, we integrate the amount of aerosol mass in each of the four budget categories (namely unactivated, in-hydrometeor, regenerated, and rained-out) after 48 h of simulation time, and then we normalize this mass by the total initial mass at the beginning of the model run. In this manner, we quantify the percentage of aerosol mass that is apportioned to each budget category, thus providing a fairer comparison between simulations of different initial aerosol loading. If changes to the aerosol loading have no impacts on the cloud field and cloud processes impacting aerosol particles, then we would expect the same distribution of aerosol mass across the budget categories, irrespective of aerosol loading. We have chosen here to present an aerosol mass budget rather than a number budget, since aerosol mass is conserved after activation and subsequent regeneration of aerosol particles, whereas all aerosol number is not conserved when multiple aerosol particles are collected by a single hydrometeor (i.e. it is assumed that interstitial aerosol particles that are collected by a droplet cohere with the original activated particle). Considering aerosol mass therefore allows us to specifically account for all the transfers between aerosol budget categories. Over the course of the simulation, we found that less than 5 % of the aerosol mass is not tracked and is treated as a residual that is lost due to dry deposition (which is represented in RAMS but not tracked in the RAMS aerosol budget) and/or numerical diffusion; this residual proportion is very similar across all our simulations (Fig. S2).

Across all the simulations, about half of the initial aerosol mass serves as CCN at some point in time, while the other half remains unactivated (Fig. 3a) for the duration of the simulation. As aerosol loading increases, the fraction of unactivated aerosol generally decreases (the fraction of activated aerosol increases), though changes are fairly small compared to the trends in the other aerosol budget categories. At first glance, this appears to contradict classic cloud parcel theory, wherein the activated fraction decreases (unactivated fraction increases) as aerosol number concentration goes up for a given updraft speed (Reutter et al., 2009). In this scenario, the increased CCN number concentrations lead to increases in cloud droplets competing to consume the available supersaturation. Thus, that parcel's maximum supersaturation is lower compared to a parcel with fewer aerosol particles and an identical updraft speed, and it is therefore unable to activate the smallest aerosol particles, which subsequently drives down the activated aerosol fraction. However, it is important to note that the results we present in Fig. 3 are not from a single cloud parcel but rather are integrated over the whole cloud field and therefore incorporate any aerosol effects that lead to changes in the updraft speed, ambient relative humidity, and cloud types. We discuss these changes to the broader cloud population in greater detail in Sect. 4. There is also a slight decrease in the aerosol mass found inside cloud droplets or embedded in drizzle or raindrops (Fig. 3b), though the trend is non-monotonic and inconsistent between aerosol types. However, the in-hydrometeor category comprises a relatively small percent of the overall aerosol budget at any given time step, and the trends in this category vary temporally (Fig. S2), since aerosol particles are only apportioned to it temporarily before being transferred to the regenerated or rained-out category.

The clearest and most temporally persistent trends in the domain-wide aerosol budget as a function of aerosol loading are seen in the proportion of aerosol mass that is regenerated (Fig. 3c) or rained-out (Fig. 3d). It is clear from these figures that the proportion of regenerated aerosol mass is enhanced, while the proportion of rained-out aerosol mass is decreased with increasing aerosol loading. While Fig. 3 shows a snapshot in time, these trends are largely consistent throughout the course of the simulation (full time series shown in Fig. S2). The opposing trends between the increases in regenerated aerosol and decreases in rained-out aerosol with increasing aerosol loading have similar magnitudes and are on the order of 7 %–10 % of the initial aerosol mass. These trends are remarkably consistent with aerosol type, as will be discussed further in Sect. 5. We emphasize here that the aerosol mass budgets we present are normalized by the initial aerosol loading – in the highest-aerosol-loading case, there is not only a greater absolute mass of aerosol that is regenerated and detrained back into the environment but also actually a larger percentage of mass involved. The changes to rainout, which is the only major aerosol sink in the budget examined here, suggest a positive feedback mechanism by which increases in aerosol loading may actually inhibit the removal of aerosol particles by clouds.

To investigate the mechanisms by which increased aerosol loading leads to aerosol regeneration being favoured over rainout, we examine trends in the cloud and rain droplet size distributions (Fig. 4). For all aerosol types, increasing the aerosol loading produces more numerous and smaller cloud droplets (Fig. 4a–b), which is consistent with the first indirect effect that has been demonstrated in many observational and modelling studies (Twomey, 1977; Tao et al., 2012). On the other hand, increasing aerosol loading produces fewer and larger raindrops (Fig. 4c–d). This effect has been demonstrated in multiple modelling studies (Berg et al., 2008; Li et al., 2013; Altaratz et al., 2014; Sheffield et al., 2015) with more limited observational support (Berg et al., 2008; May et al., 2011).

These trends in the droplet size distributions can be more easily connected to the aerosol budget by examining trends in the microphysical process budget, as shown in Fig. 5. Each term in this figure represents a different sink for cloud water and is given as an efficiency relative to the mass of water vapour transferred to liquid in cloud droplets. The value given is the percent of condensed water vapour that ends up in a particular cloud water sink. As aerosol loading increases, the cloud droplets are smaller and thus evaporate more readily (Fig. 5a) and are also less likely to be collected into rainwater (Fig. 5b). This explains the trends in the aerosol budget under increased aerosol loadings to first order; although a similar proportional mass of aerosol particles is activated and enters cloud droplets, those cloud droplets are smaller and tend to evaporate more quickly, which favours regeneration. Simultaneously, those smaller cloud droplets are less likely to be collected as rainwater, and thus the CCN contained within them are less likely to be washed out within precipitation.

In the polluted aerosol environment, although cloud water is less likely to be collected by rain, the cloud water which is collected is distributed among fewer raindrops. These raindrops are thus larger in size (Fig. 4d) and have a lower surface-area-to-volume ratio compared to raindrops that form in pristine aerosol environments, in keeping with past model results (Storer and van den Heever, 2013; Altaratz et al., 2014; Saleeby et al., 2015). As a result, even though increasing aerosol loading leads to less-efficient collection of cloud water into rainwater, it also leads to decreases in rainwater evaporation (Fig. 5c). These two trends partially offset one another, leading to mixed trends in the percentage of cloud water that falls to the surface as rain (Fig. 5d), sometimes defined as the precipitation efficiency (Cui and Carslaw, 2006; Jiang et al., 2010; Lee and Feingold, 2010; Lutsko et al., 2021; Li et al., 2022). These decreases with increasing aerosol loading are not monotonic for all aerosol types, and it is a smaller relative trend compared to those of cloud evaporation and collection. Although increasing the aerosol loading in the domain causes clouds to become less efficient at removing aerosol via rainout (Fig. 3d), it does so without necessarily impacting the precipitation efficiency itself (Fig. 5d). Earlier results by Cui and Carslaw (2006) and Lee and Feingold (2010) showed similar decreases in the aerosol rainout efficiency (or aerosol precipitation efficiency or scavenging efficiency, as they respectively referred to it), but these decreases were closely coupled with decreases in precipitation efficiency. That is to say, they showed that increased aerosol loading caused less-efficient rain formation and therefore less-efficient aerosol removal through rainout. Our results add to this and show that the reduced efficiency in aerosol removal through rainout can occur even without changes to the domain-wide precipitation efficiency.

Given the complexity surrounding the number of processes impacting rain formation, which often have opposing trends as a function of aerosol loading, we find that increasing aerosol loading does not necessarily lead to decreases in precipitation efficiency (Fig. 5d) or the domain-wide accumulated precipitation (Fig. 6a). For some aerosol types (e.g. mineral dust), the increase in aerosol loading actually leads to an increase in the accumulated precipitation between the lowest and highest aerosol loadings tested in our set of simulations. The trends in the total number of tracked clouds are similarly non-monotonic and mixed, as shown in Fig. 6b, and suggest that aerosol loading does not have a clear impact on domain cloudiness for these simulations of maritime tropical clouds. That being said, tracking the clouds over their full lifetime with the use of tobac allows us to further subdivide clouds into those that precipitate and those which do not (Fig. 6c–d). To differentiate raining and non-raining clouds, we find the area-mean rain rate associated with each cloud feature at each point in its lifetime, and then we take the lifetime maximum of those rain rates such that non-raining clouds are those which never reach an area-mean rain rate of 0.0001 mm h-1. Clearly, the mixed trend in the total number of clouds as a result of increasing aerosol loading arises as a result of the following two opposing trends: increases in the number of non-precipitating clouds and decreases in the number of precipitating ones. This is, furthermore, consistent with the general picture of aerosol impacts on the cloud field from the process rates, as described above: although clouds still do form in environments with higher aerosol loadings, the cloud droplets evaporate more readily before the cloud is able to produce precipitation-sized particles, and thus a greater fraction of clouds never rain throughout their whole lifetime. Non-raining clouds still activate aerosol particles and regenerate them aloft as the cloud dissipates, but they do not remove them from the domain via rainout, which contributes to aerosol regeneration at the expense of rainout.

We can use tobac to aggregate the raining clouds (Fig. 7) to see how the median properties of these clouds evolve under different aerosol environments. Although increasing aerosol loading leads to fewer raining clouds, those which do rain are invigorated with higher rain rates (Fig. 7a). This is further compounded by the decrease in the median area covered by each raining cloud (Fig. 7b). Overall, we find that, under higher aerosol loadings, surface rainfall becomes more concentrated amongst fewer clouds with a higher median rain rate. However, this is contrasted by the trends in aerosol rainout rate (Fig. 7c). The aerosol impact is non-monotonic, but there is a decrease in the strength of aerosol rainout between the lowest and highest aerosol loadings for all aerosol types. We conclude that the median cloud rains more under higher aerosol loadings but rains out less aerosol. Shifts in the behaviour of the overall cloud population, as well as potential explanations for this behaviour, are discussed in the following subsection.

An advantage of cell tracking over prior analysis methods is the ability to examine trends and characteristics of evolving cloud population distributions as opposed to merely aggregating properties. We construct two-dimensional histograms according to cloud top height (CTH) and either rain rate (Fig. 8) or normalized aerosol rainout rate (Fig. 9), such that the value in each bin is the number of raining clouds with a given CTH and rain rate or rainout rate. The CTH, rain rate, and normalized aerosol rainout rate are defined by taking the lifetime maximum value for each tracked cloud cell, such that they represent the peak maturity for a given cloud. This approach has the benefit of being able to separately identify cloud modes according to different CTHs; in this case, the shallow cumulus mode is clearly visible as a hotspot of clouds with CTHs of ∼2 km, as is the congestus mode with CTHs of ∼4 km (e.g. Fig. 8a). This is particularly important due to our focus on tropical convection, which is known to consist of three separate cloud modes (Johnson et al., 1999; Posselt et al., 2008).

Generally, there is a positive correlation between CTH and precipitation rate, with taller clouds tending to have stronger rain rates than shallower clouds do (Adler and Mack, 1984; Smalley and Rapp, 2020). Moving from left to right in each row in Fig. 8 allows one to see the impact of increasing aerosol loadings on the CTH–rain-rate distribution, such that negative values (blue regions) are portions of the cloud population that become less frequent with increasing aerosol loading and vice-versa for positive values (red regions). Notably, increased aerosol loadings impact shallow cumulus and congestus clouds in opposite ways, emphasizing that median cloud properties over all types of clouds are insufficient for quantifying the magnitude of the aerosol effect. Shallow cumulus clouds tend to grow taller, with the modal CTH being closer to 3 km in the highest aerosol simulations, but they do so with reduced rain rates (e.g. Fig. 8d) in a manner that is similar to the precipitation suppression effect described in many past studies (e.g. Xue et al., 2008; Spill et al., 2019). On the other hand, congestus clouds also grow slightly taller but have much stronger modal rain rates, which is consistent with previous findings on the warm-phase invigoration of this tropical-cloud mode (Li et al., 2013; Sheffield et al., 2015). These results suggest that the smaller shallow cumulus clouds are more sensitive to the increase in evaporation (Fig. 5a), whereas congestus clouds with larger areas are more able to protect the interior of the cloud core from evaporation, thereby benefitting from the increase in latent heating or warm-phase invigoration associated with increased cloud droplet formation (Fig. 4a). Furthermore, this shows that the impact of increasing aerosol on precipitation efficiency is dependent on cloud type. This may explain differences between this study and recent studies such as that of Dagan (2022), which saw monotonic increases in precipitation efficiency with increasing aerosol. The latter study used a coarser grid spacing that did not resolve the shallow cumulus cloud field which we find in this work to have decreasing precipitation efficiency with increasing aerosol.

The CTH–aerosol-rainout-rate distribution in Fig. 9 clearly shows deeper clouds being associated with more aerosol rainout compared to shallower clouds. This relationship is consistent with trends in rain rate with cloud top height, as discussed previously. For shallow cumulus, increased aerosol loading leads to a decrease in their ability to remove aerosol via rainout, which follows closely with the decrease in their rain rates. However, although congestus clouds tend to produce stronger rainfall in higher-aerosol environments, they do not see a corresponding increase in their ability to rainout aerosol, which has no change or even decreases slightly for the highest aerosol loadings. These results suggest that, unlike rain rates, which can be enhanced by warm-phase invigoration, there is something of a saturation effect for rainout. At a certain point, stronger rain rates can no longer increase the amount of aerosol being rained-out, since the aerosol available to rainout in those areas has already been removed to the surface. Because the surface rainfall from these clouds becomes concentrated over smaller horizontal areas where the cloud droplets are sufficiently protected from the environment such that they can form precipitation-sized hydrometeors, there are increasing areas of clear-sky or very light precipitation that is not sufficient to remove aerosol particles to the surface. Thus, the overall aerosol impact on rainout is dominated by the decrease in rainout from shallow clouds which either have weaker rain rates or stop raining altogether. These findings provide strong process-level evidence for a potential mechanism to explain recent results from GCMs showing that frequent, light precipitation is more important than strong precipitation in regulating the amount of wet-deposited aerosols (Wang et al., 2021a, b).