1. Introduction
Shallow, warm cumulus clouds play an important role in the transport of heat, moisture, and pollutants to the free troposphere. They also affect the planetary albedo and thus the Earth’s radiative budget (Sengupta et al. 1990). Furthermore, the manner in which they are represented in climate models has a strong bearing on climate sensitivity (Bony and Dufresne 2005). The prevalence of these clouds is well documented (Tiedtke et al. 1988; Slingo et al. 1994).
In the trade wind regime, shallow cumulus clouds both influenced by and, in turn, affect environmental conditions, such as temperature, humidity, and wind shear (Malkus 1954; Squires 1958; Grabowski and Clark 1993; Zhao and Austin 2005). A distribution of buoyant plumes of varying magnitudes generates cumulus clouds that transport heat and moisture into the trade inversion to different extents. In this weakly stable transition region, characterized by strong mixing and downward transport of inversion air, evaporating cloud turrets humidify the warm and descending dry air, preconditioning it for subsequent convection. The upward flux of water associated with trade cumulus enhances surface evaporation, which supplies moisture to the system. Moisture is removed by precipitation, which is a strong function of cloud depth, but also controlled by cloud microphysical processes, themselves a function of the aerosol. This introduces the potential for the aerosol to influence the thermodynamic environment that supports the trade cumulus cloud system.
The role of the atmospheric aerosol in influencing cloud microphysical processes and perhaps modulating the role of shallow cumulus in the climate system has been the subject of much debate. While it is generally perceived that aerosol perturbations increase drop concentrations (Twomey 1977), suppress the formation of rainfall (Warner 1968; Albrecht 1989), and increase the lifetime of clouds, there is scant observational evidence to support these suppositions and even some to the contrary (Small et al. 2009). Finescale modeling studies have suggested that the aerosol may play multiple roles—increasing cloudiness in aerosol-poor conditions but reducing it in aerosol-rich conditions (e.g., Ackerman et al. 2004; Xue et al. 2008).
Some modeling studies have shown that by delaying the onset of precipitation, higher aerosol concentrations transport water vapor deeper into the inversion layer and support deeper cumulus clouds (McFarquhar and Wang 2006; Stevens and Seifert 2008). These deeper clouds offset the effect of aerosol-induced suppression of collision–coalescence on rainfall. Self-regulation of this kind led Stevens and Feingold (2009) to the conclusion that in many cases, the multitude of internal feedbacks between microphysics and dynamics might reduce the potential for the aerosol to influence the cloud system. The system may therefore be perceived as “buffered” or robust to aerosol perturbations.
Motivated by the importance of warm cumulus clouds in the climate system, this study focuses on understanding how aerosol perturbations affect the statistical properties of a cloud system for relatively long simulations (>24 h) and scales of 25 km, which are large enough for mesoscale circulations (i.e., mesobeta circulations) to develop. By integrating through transients, the goal is to ascertain just how robust the system is to aerosol perturbations. The paper deviates somewhat from the typical studies of aerosol–cloud interactions that tend to focus on microphysical responses to aerosol influences via traditional constructs (Twomey 1977; Warner 1968) and instead attempts to incorporate a more boundary layer, cloud-system-centric view. While these aforementioned processes drive the responses that we aim to quantify, it is becoming increasingly clear that microphysical changes carry dynamical consequences. Stated differently, by changing cloud microphysical processes, the aerosol changes the thermodynamic environment in which a cumulus cloud system lives and evolves. This view of the cloud system opens up a much richer spectrum of physics and nuance to the aerosol–cloud precipitation problem, and, as will be shown here, helps to clarify the role of the aerosol, rather than complicate it.
With this perspective we present a set of numerical experiments that will show that for the sounding considered, aerosol perturbations influence the thermodynamic environment and cloud field development in such a way that many perturbed and unperturbed cloud field properties tend to converge after sufficient time has elapsed. The hypothesis posed is stated as follows: the vertical development of cloud fields responds to aerosol-induced changes in atmospheric stability so that instability (i.e., potential energy) is consumed at different rates; after a transient period, however, the systems evolve to a similar state. Sensitivity tests will show that this response is robust to a variety of different model assumptions/simulated conditions. Some preliminary thoughts on how the time scale for this convergence might vary are also proffered.
2. Large-eddy simulation (LES)
This study relies on numerical simulations to fulfill its aim. The Advanced Research Weather Research and Forecasting Model (ARW-WRF, version 3.1.1) is adopted for the simulations. In the ARW-WRF, a high-order monotonic advection scheme (Wang et al. 2009) and a double-moment bulk microphysical scheme (Feingold et al. 1998; Wang and Feingold 2009) are used. The representation of cloud condensation nuclei (CCN) and cloud and raindrop size distributions follows Wang and Feingold (2009). Briefly, prognostic equations are solved for CCN number concentration, number and mass mixing ratio of cloud droplets, and number and mass mixing ratio of raindrops. Droplet activation is calculated based on predicted supersaturation, an assumed aerosol size distribution (lognormal), and composition (ammonium sulfate). After activation, the CCN are tracked through the drop population and regenerated upon evaporation. The CCN concentration is reduced by drop collision–coalescence and by surface rain. No CCN sources are applied. Changes in the CCN are represented by changes in concentration alone; sensitivity to the aerosol size distribution and composition are not considered. For the trade cumulus regime, neglect of size distribution and composition variability is unlikely to have a significant impact on the results to be presented (Feingold 2003).
3. Case description
a. Numerical experiments
A number of simulations are performed for an observed case of trade cumuli during the Rain in Cumulus over the Ocean (RICO) field experiment (Rauber et al. 2007). The horizontal domain length is set at 25 km for both the east–west (x) and north–south (y) directions, while the vertical domain length is set at 4 km to cover the planetary boundary layer (PBL). Periodic boundary conditions are imposed on the horizontal domain. The horizontal grid length (Δx and Δy) is 100 m, while the vertical grid length Δz is 40 m.
A thermodynamic sounding composited by the Global Energy and Water Cycle Experiment Cloud System Study (GCSS) boundary layer working group (http://www.knmi.nl/samenw/rico) based on soundings from the RICO field experiment is used. The u component of the wind is easterly, decreasing linearly from about 10 m s−1 at the surface to about 2 m s−1 at the model top (4 km), while the υ component is northerly and constant at 3.8 m s−1 throughout. Water vapor mixing ratio r and potential temperature θ are nearly constant from the surface to 740 m. From 740 m up, r decreases from 13.8 to 1.8 g kg−1, while θ increases from 297.9 to 317 K at the model top. Unless otherwise stated, simulations use the same forcings as those prescribed by GCSS. These are briefly described in section 3b.
The first simulation, referred to as the control (C) run, adopts an initial background aerosol number concentration of 100 mg−1 (equivalent to 100 cm−3 at an air density of 1 kg m−3) and this number is constant over the PBL, following the GCSS specification. The C run lasts 34 h. The first 6 h 10 min of the simulation period is considered to be “spinup” and is excluded from analysis (the influence of the duration of the spinup is explored in section 5g). To examine aerosol effects on the cloud system and its environment, a new simulation is spawned at the end of the spinup period with the background aerosol number concentration enhanced by a factor of 2.5, yielding 250 mg−1 at grid points with no clouds. This repeated run uses wind, pressure, temperature, and humidity at each grid point over the entire domain from the control run as initial conditions. This repeated run is referred to as “the high-aerosol” or H run.
A summary of simulations is shown in Table 1. In addition to the control and high-aerosol runs, supplementary simulations are listed in Table 1. These additional simulations will be described in the following sections and the appendixes.
Summary of simulations.
b. Surface and large-scale forcings and radiation
All forcings are based on the GCSS prescription. Bulk formulas are used to represent the surface sensible, latent heat, and momentum fluxes. The sensible and latent heat fluxes are proportional to the wind velocity in the atmosphere immediately above the surface (~10 m s−1) and to the difference in temperature or water vapor mixing ratio between the surface and the atmosphere immediately above it. The momentum fluxes are proportional to wind velocity in the atmosphere immediately above the surface.
The large-scale subsidence and horizontal advection of temperature and moisture are also prescribed by the GCSS specifications. Radiation processes are not calculated explicitly but represented by a temporally and spatially constant advective tendency on temperature (cooling) with no consideration of the diurnal cycle. The cooling profile was derived by vanZanten et al. (2011) from an offline radiation calculation for the initial temperature and humidity sounding. The cooling rate is 2 K day−1 close to the surface and decreases to about 1 K day−1 in the free troposphere. The large-scale subsidence and advection of moisture are a function of height only.
4. Results
A series of simulations are carried out with the GCSS sounding to test the hypothesis proposed in the introduction.
a. Time series and vertical profiles
Figure 1 shows the time series of the domain-averaged liquid water path (LWP), vertical velocity variance w′w′, cloud fraction (CF), cloud-top height, convective available potential energy (CAPE), buoyancy flux 
Time series of the domain-averaged (a) LWP, (b) w′w′, (c) CF, (d) cloud-top height, (e) CAPE, (f) 
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
To facilitate discussion, the approximate times at which there is a marked shift in C versus H behavior are delineated. The period up to 14 h, between 14 and 20 h, and from 20 h to the end of the simulations are referred to as the first, second, and third periods, respectively.
CAPE represents the gravitational potential energy stored in the system that can be converted to turbulent kinetic energy, which explains the similar time evolution among CAPE, w′w′, 
Vertical profiles of the time- and domain-averaged LWC over (a),(e) first, (b),(f) second, (c) third, and (d) entire simulation periods.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
Vertical profiles of the time- and domain-averaged w′w′ over (a) first, (b) second, (c) third, and (d) entire simulation periods.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
The rain rate deserves special attention because of the influence of the aerosol on rain production. During the first period (6 h 10 min–14 h), the mean rain-rate differences are small as a result of higher LWP in the H run, offsetting aerosol suppression of collision–coalescence (Fig. 1h). During the second period (14–20 h), the largest precipitation difference is simulated, as enhancements in LWP in the C run work in unison with more efficient collision–coalescence. During the third period (after 20 h), precipitation differences are reduced but nevertheless are distinctly larger for the C run. Further analysis of the precipitation fields is deferred to the end of section 4.
b. First period
To explain the reasons for the differences between the C and H runs (Fig. 1), θ and r are examined. First, the CAPE difference (Fig. 1e) during the first period is examined. For this, the first period is subdivided into three stages, and θ and r are considered in each of the stages. The first, second, and third stages correspond to periods up to 8 h, between hours 8 and 10, and between hours 10 and 14, respectively. The choice of the time intervals for the subdivisions is primarily based on the evolution of CAPE, but it is supported by a similar temporal evolution in other fields (Fig. 1). During the first and second stages, CAPE in the H run increases rapidly and then levels off at a magnitude significantly higher than that for the C run (Fig. 1e); during the third stage, it decreases. In contrast, CAPE in the C run increases much more slowly (Fig. 1e), and it is only at about 14 h, or around the beginning of the second period, that it exceeds the value of the (descending) CAPE in the H simulation.
To understand the increasing and then steady CAPE differences between the C and H runs during the first and second stages, the vertical distributions of the domain-averaged r and θ at 7 and 8 h are shown in Figs. 4a–d. Note that the distributions at 7 h are around the middle of the time period of the increasing CAPE in the H run. A smaller θ develops in a layer between about 0.4 and 1.0 km in the H run and the difference in θ between the H and C runs reaches about 0.2 K in the layer (Figs. 4b and 4d). This layer between about 0.4 and 1.0 km corresponds to the low-level cloud layer and is henceforth referred to as ΔZl. Sensitivity tests show that this smaller θ at hours 7 and 8 increases CAPE in the H run during the first stage and promotes the larger CAPE during the second stage. These sensitivity tests are described in detail in appendix B. In addition, r is larger in the H run in ΔZl at both hours 7 and 8 and the difference in r between the H and C runs reaches about 0.2 g kg−1 in the layer (Figs. 4a and 4c). Additional simulations demonstrate that it is the lower θ, not the higher r, that accounts for most of the CAPE difference shown in Fig. 1e during the first and second periods (see appendix B).
Vertical profiles of the domain-averaged water vapor mixing ratio at (a) 7, (c) 8, (e) 10, and (g) 14 h. (b),(d),(f),(h) As in (a),(c),(e),(f), respectively, but for θ . The top abscissa shows the differences (H minus C) in r and θ fields.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
Does subcloud evaporation of rain play a role in explaining the evolution of C and H simulations? To address this, the C and H runs are repeated but with evaporative cooling associated with subcloud rain evaporation turned off. These are referred to as “the C-rain-evap-off run” and “the H-rain-evap-off run,” respectively. As in the C and H runs, the H-rain-evap-off run has larger LWC than the C-rain-evap-off run in the first period (Fig. 2e). Cloud-base height increases by about 100 m with subcloud evaporation of rain turned off. Further tests with rain evaporation turned off throughout the domain again produce similar trends to the C and H runs (not shown), reinforcing these results. Thus, the differences in latent heat distribution above cloud base associated with cloud liquid condensation and evaporation play a much more important role in the evolution of the H and C cases than does latent heat redistribution from rain evaporation below cloud base.
Figure 5 shows the vertical distribution of the time- and area-averaged net condensation rate over each of the three stages during the first period for the C and H simulations. Note that negative net condensation represents net evaporation. We focus on the net condensation rate because calculations show that the net heating due to the net condensation is approximately one order of magnitude larger than that due to advection/turbulent diffusion, and because in these simulations, radiative cooling is applied equally to both simulations. Figures 4 and 5 are useful for understanding the evolution of the cloud system through the three stages.
Vertical profiles of the time- and domain-averaged net condensation rate over (a) first stage, (b),(d) second stage, (c),(e) third stage, and (f),(g) second and third periods. For effective visualization of the vertical distribution of net evaporation rate (i.e., net negative condensation) above ~1 km, different scales in the x axis are used for positive and negative net condensation rates. The top abscissa quantifies the net condensation rate differences (H minus C).
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
1) Stage 1 (6 h 10 min < t < 8 h)
Compared to the C run, the H run exhibits a lower net condensation rate in ΔZl (Fig. 5a), causing less heating in this layer (Figs. 4b and 4d) and thus smaller θ, higher instability and CAPE, and lower convection inhibition (CIN). The time- and domain-averaged CIN over stage 1 is 5 and 7 J kg−1 in the H and C runs, respectively. The lower net condensation rate is associated with larger r (Figs. 4a and 4c). The weaker heating and larger r in ΔZl in the H run are also simulated in the H-rain-evap-off run, confirming the negligible role of subcloud evaporation of precipitation (Figs. 4a and 4b). The relative cooling and moistening in the layer is due to two factors: (i) Smaller and more numerous droplets in the H run contribute to more efficient cooling and moistening of the air (Xue and Feingold 2006; Hill et al. 2009). The time-averaged cloud droplet number concentration and droplet radius over cloudy areas for C (H) are 25 (60) mg−1 and 7.5 (5.4) μm. (ii) Similar amounts of condensed water but smaller and more numerous clouds in the H run have larger surface-to-volume ratios, leading to an increase in their susceptibility to entrainment of dry air, further enhancing cooling and moistening of the air (Xue and Feingold 2006). During the first stage, the time-averaged number and the time- and domain-averaged equivalent diameter of clouds are 338 (451) and 332 (297) m in the C (H) run, respectively.
2) Stage 2 (8 h < t < 10 h)
For the H run, the more efficient cooling generates larger instability, CAPE, and 
3) Stage 3 (10 h < t < 14 h)
For the C run, the smaller θ and thus larger instability in ΔZm sustains a steady rise in CAPE and 
c. Second period
Influence of thermodynamic profiles
The θ and r differences between the C and H runs at the end of the first period (14 h) in Figs. 4g and 4h are largest in a layer between about 1.5 and 2 km. These are a result of moistening and cooling associated with deeper convection in the H run during the first period. This might be expected to favor subsequent clouds with higher cloud top-heights, larger depth, and thus larger LWC and LWP in the H run. However, the converse is true: during the second period, C-run clouds have, on average, larger LWC, LWP, and higher cloud-top heights (Figs. 1a, 1d, and 2b). This suggests that it is not differences in the layer between about 1.5 and 2 km, but those in other layers that result in the LWC, LWP, and cloud-top height differences in the second period.
As seen in Fig. 2b, larger LWP associated with larger CAPE and thus w′w′ (Figs. 1a, 1b, 1e, and 3b) for the C run during the second period (14–20 h) are mainly due to larger LWC in the layer between about 1.0 and 1.8 km. This layer corresponds to a mid- and upper-level cloud layer and is referred to as ΔZmu. To identify differences in θ and r, which lead to the LWC differences in ΔZmu, the control run is repeated from the beginning to the end of the second period with different θ and r conditions. Figure 6 depicts the vertical distribution of the time- and domain-averaged LWC for the repeated runs, as well as the C and H runs over the second period. The first of these repeated runs is identical to the control run from the beginning to the end of the second period, except that the initial r corresponds to that from the H run at each grid point at the last time step of the first period. This simulation is referred to as “CrH” (control with r associated with the H run). The larger LWC in ΔZmu is still simulated in the CrH run, similar to the C run (Fig. 6). In addition, as in the C run, the time- and domain-averaged CAPE is higher in the CrH run than in the H run (Table 2). It is also notable that the vertical distribution of differences in LWC between the CrH and H runs in ΔZmu is similar to that between the C and H runs. Thus, the CAPE and LWC differences between C and H in ΔZmu are not caused by differences in r fields.
Vertical profiles of the time- and domain-averaged LWC over the second period.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
Time- and domain-averaged CAPE for periods and stages.
Next, the C run is repeated from the beginning to the end of the second period, except with the θ field from the H run at each grid point at the last time step of the first period, referred to as “CθH”. The LWC increase in ΔZmu disappears and is similar to that in the H run. The time- and domain-averaged CAPE are similar in the CθH and H runs, in contrast to the larger difference between the C and H runs (Table 2). Thus, it is the θ difference established during the first period that leads to the CAPE and LWC differences between the C and H runs in ΔZmu in the second period.
The θ profiles in Fig. 4h indicate that there is generally a larger instability in ΔZm at the end of the first period in the C run. This is due to generally smaller θ in the C run. In other layers, θ tends to be lower in the H run. Hence, it is likely that the stability differences in other layers do not contribute to the larger LWC in the C run in the second period. To confirm this, the C run is repeated in the same manner as in the CθH but with the initial θ from the H run at the last time step of the first period only for grid points in the layer ΔZm; the initial θ values in layers other than ΔZm in this repeated run are the same as in the C run. This repeated run is referred to as “the CθH1.0–1.5 run.” A comparison among the CθH1.0–1.5 run, the CθH run, and the H run shows that CAPE and the LWC profiles in the CθH1.0–1.5 run are closer to those in the H run than in the CθH run (Table 2 and Fig. 6). Next, the C run is repeated in the same manner as in the CθH1.0–1.5 run but with the initial θ from the H run at the last time step of the first period at all grid points except for those in ΔZm; that is, in this repeated run, the initial θ is the same as in the C run in ΔZm, and in other layers it is the same as in the H run. This repeated run is referred to as “the CθH-other run.” The larger CAPE and LWC in ΔZmu are simulated in the CθH -other run as in the C run, and the differences in LWC between the CθH -other run and the H run are similar to those between the C and H runs (Table 2 and Fig. 6). These CθH1.0–1.5 and CθH -other runs demonstrate that it is the larger instability in ΔZm that causes the larger CAPE and LWC in ΔZmu in the C run during the second period.
As in the C and H runs, the H-rain-evap-off run has smaller LWC than the C-rain-evap-off run in the second period (Fig. 2f). This demonstrates that during both the first and second periods, subcloud latent heat distribution from rain evaporation does not play an important role in the evolution of the H and C cases, and that the evolution is driven by above-cloud-base latent heat distribution through phase changes.
d. Third period and overview of the three periods
It is notable that aerosol-initiated deviations in cloud and environmental properties decrease as time progresses; C versus H differences in mean CAPE, 
As noted above, precipitation differences between C and H are closely related to LWP and drop concentration Nd differences. The mean precipitation rate is always higher for the C simulation, only marginally during period 1, and most significantly during period 2. To further examine the differences in precipitation, the frequency distributions of precipitation rates for periods 1, 2, and 3 are shown in Figs. 7a–c. During period 1, the H run is characterized by more frequent weak (<0.1 mm day−1) rain, but the reverse is true in periods 2 and 3. In all three periods, the C run exhibits more frequent moderate to strong rain rates, particularly in period 2 when C rain is significantly larger. Note that the (very rare) strongest rain rates are always associated with a subset of the H-run clouds (see section 5e for further discussion).
Distributions of precipitation rate frequency for the (a) first, (b) second, and (c) third periods.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
5. Discussion
Our contention, supported by the detailed analysis above, is that differences in the aerosol concentration create differences in environmental instability, which lead to cloud fields with different properties; these, in turn, remove instability at a rate commensurate with the buildup of instability. In the system perturbed by aerosol, low-level cooling allows CAPE to increase more rapidly, which leads to the earlier appearance of its peak in period 1 (Fig. 1e). But a consequence is that the cloud field consumes CAPE at a faster rate (Nober and Graf 2005). In the unperturbed system instability develops more slowly, but the attendant shallower cloud field eventually produces an instability at ΔZm that allows clouds to deepen (on average) more than their perturbed counterparts. The unperturbed and perturbed systems follow different temporal cycles, but eventually they converge to a similar state. Thus, aerosol perturbations generate dynamical responses that result in similar environmental and cloud field properties after a sufficiently long time period.
It has previously been shown that increases in aerosol tend to speed up the cycle of shallow cumulus convection by generating stronger instabilities earlier on and subsequently removing them at a faster rate. Jiang et al. (2009) calculated the birth and death rates of convective cells for the same RICO GCSS case (albeit using a different model) and showed that aerosol-perturbed systems have faster birth/death rates. Analysis of cloud size distributions in section 4b also supports earlier results from different models and different trade cumulus soundings that aerosol-perturbed cloud systems comprise larger numbers of smaller clouds that have shorter lifetimes (Xue and Feingold 2006; Jiang et al. 2006). By perturbing thermodynamic profiles, the aerosol therefore appears to be able to change the rate at which instability is produced and consumed.
The results raise a number of other interesting issues and questions; these are addressed below.
a. Role of precipitation
Note that the results mentioned above are for cumulus clouds with low surface precipitation. However, it is likely that more strongly precipitating clouds would have a stronger influence on subcloud stability, and in this case precipitation may play a more important role in the cloud and LWC evolution and the effect of aerosol thereon. To investigate this, the C and H runs are repeated for the first and second periods, but with surface moisture fluxes increased by a factor of 5. These repeated runs are called C-high-rain and H-high-rain runs and have time- and domain-averaged rain rates that are 8 and 5 times larger than those in the C and H runs, respectively. Thus, the increased surface fluxes have a disproportionately stronger influence on the rain rate in the low aerosol simulation. This causes a much larger relative increase in the stabilization of the subcloud layer in the C-high-rain run compared to the C run than that between the H-high-rain run and the H run. Consequently, the differences in the midlevel cooling for these high-rain runs are much smaller than for the standard C and H runs during the first period, which in turn leads to significantly reduced differences (about 5 times smaller) in CAPE, w′w′, LWC, and LWP compared to those between the C and H simulations during the second period (Figs. 2b and 8). Stronger precipitation more effectively stabilizes the profile by heating the cloud layer and cooling the subcloud layer, and therefore it appears to hasten the convergence of the C and H simulations.
Time series of the domain-averaged (a) LWP, (b) w′w′, and (c) CAPE. Vertical blue lines are added to mark starting and ending time of stages and periods.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
b. Role of radiation
To examine the effect of the diurnal cycle of radiation, the C and H runs are repeated with radiation calculated explicitly using the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) radiation scheme for the first and second periods (recall that in the standard C and H runs, a constant cooling is applied to both C and H runs in lieu of radiation) These repeated runs are referred to as the C-radiation and H-radiation runs, respectively. In these repeated runs, the beginning and end of the simulations are assumed to correspond to 0610 and 2000 local solar time (LST) on 16 December 2004, since there are no designated LSTs for simulations in the GCSS specifications. With these assumed LSTs, the simulations capture the diurnal variation of radiation and its impact on clouds from sunrise through sunset to night. In the C and H runs, there are no two-way interactions between radiation and clouds, nor is there a diurnal cycle, whereas in the C-radiation and H-radiation runs, the diurnal cycle of incident shortwave radiation on clouds and two-way interactions among clouds, and shortwave and longwave radiation are taken into account (e.g., Wang and McFarquhar 2008a). Figures 2a, 2b, and 8 show that the qualitative nature of C versus H differences in CAPE, w′w′, LWP, and LWC evolution does not depend on the details of the radiation, at least not during the first and second periods. By 20 h, the mean CAPE fields have converged, although interestingly differences in LWP and w′w′ remain substantial, whereas they were significantly diminished in the standard C and H runs. This raises questions about the characteristic time scales for relaxation of the aerosol-perturbed system, which we will consider in section 5f.
c. Simulations with a reset of aerosol
Results have shown that aerosol-triggered differences in θ or thermal instability (mediated by clouds) cause differences in the development of subsequent clouds. The aerosol triggers (i) low-level (about 0.4–1 km) cooling in the H run during stage 1 of period 1, which results in clouds with higher top heights; and (ii) concentrated cooling at midlevel (about 1–1.5 km) in the C run during stages 2 and 3 of period 1. This concentrated cooling develops clouds with higher LWP in the C run during the second period. Hence, it is possible that once aerosol-induced changes in environmental conditions are established, the system has “memory” of the aerosol perturbation. In particular, the increase in CAPE in the C run at the beginning of the second period (14 h) is likely to be caused by aerosol-related differences in environmental conditions that are set up long before the beginning of the second period. Two sets of the repeated C and H runs are performed to explore the role of the timing and duration of the aerosol perturbation in determining the convergence of the fields.
The domain-averaged aerosol concentrations for the C and H runs are 91 and 235 mg−1 at 8 h (i.e., the beginning of the second stage of period 1). To investigate the extent to which the system retains memory of the aerosol perturbation, aerosol number concentrations for the C and H runs are reset to 100 mg−1 at 8 h at all grid points. This implies a brief duration of perturbation (from 6 h 10 min to 8 h), followed by a small increase in the CCN concentration of the C run (91−100 mg−1), and a more significant decrease from 235 to 100 mg−1 for the H run. These repeated C and H runs are referred to as the C-at-hr-8 run and the H-at-hr-8 runs, respectively, and are extended to the end of the second period at 20 h. In these runs, from the second stage on, differences in cloud development between the C and H runs are caused only by differences in the environment induced by the aerosol perturbation during the first stage. As expected, CAPE, w′w′, LWP, CF, and cloud-top height in the C-at-hr-8 run (Fig. 9), generally follow those of C, although there are some differences during period 2. A larger difference can be seen in the H-at-hr-8 run (vs H), as a result of the more significant reduction in CCN concentration. At 8 h, which happens to be the time at which CAPE peaks in the H run, the switch to a lower aerosol concentration means that the faster convective turnover associated with high aerosol (Jiang et al. 2009) is no longer able to remove the instability as efficiently. As a result, H-at-hr-8 sustains CAPE, w′w′, LWP, CF, and cloud-top height at higher values than those in H. The convergence between C-at-hr-8 and H-at-hr-8 is still apparent, but it occurs along a different pathway.
As in Figs. 1a–e, but for results from simulations with a reset of aerosol, as described in section 5c, together with those from the C and H runs.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
A second set of repeated runs, referred to as C-at-hr-10 and H-at-hr-10, is initiated at 10 h. In these runs the homogenization of the aerosol fields is from (domain averaged) aerosol concentrations of 89 (C) and 226 (H) to 100 mg−1 (Table 1). Here too, the C-at-hr-10 simulation behaves much like C (Fig. 9); however, now the H-at-hr-10 fields are similar to the H fields. Similar to the H run, the longer exposure to high CCN concentrations establishes the low-level instability in ΔZl, which supports the more turbulent and thicker clouds. The depletion of CAPE, which starts soon after the switch to 100 mg−1 aerosol concentrations and therefore still carries memory of the high aerosol, continues through the second period, resulting in converged cloud fields that are similar in the mean to their C and H counterparts.
The repeated simulations in this section indicate that, if the aerosol perturbation is sufficiently long-lived, the accompanying changes in environmental conditions will influence cloud field evolution more so than the direct effect of the aerosol difference. Just how large a time-integrated perturbation is required for this to hold true will likely be case dependent.
d. Aerosol influence on cloud optical depth
Although not the focus of this study, it is instructive to consider the influence of aerosol perturbations on cloud optical depth τ, which is closely related to albedo. In keeping with the relative importance of indirect effects in this paper, we consider simple calculations of domain-average τ based on the second moment of the drop size distributions (constrained by the bimodal lognormal function) and at a visible wavelength; we avoid higher-order calculations such as a posteriori three-dimensional radiative transfer, which would provide a rigorous assessment of aerosol indirect forcing. A time series of domain-average τ for H and C simulations (Fig. 10) shows, not unexpectedly, that the τ response is a modulation of the LWP response, because to first-order 
Time series of domain-averaged cloud optical depth for the C and H simulations.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
e. Aerosol influence on boundary layer depth and precipitation rate
Previous work has suggested that the aerosol can influence the distribution of cumulus cloud-top heights (Xue and Feingold 2006; Wang and McFarquhar 2008b; Stevens and Seifert 2008; Jiang et al. 2009). The general trend is for an increase in boundary layer depth or cumulus cloud-top height with increasing aerosol as a result of elevation of the initial height at which precipitation forms and more efficient preconditioning of free-tropospheric air (e.g., Stevens 2007; Stevens and Seifert 2008; Nuijens et al. 2009). In this work, the increase in boundary layer depth with increasing aerosol occurs in the first period but is not a robust feature throughout the simulation (Fig. 1g). Note also that the changes in mean height do not necessarily reflect the changes in the maxima. For example, although Fig. 1d indicates a higher mean cloud-top height for the C run, during the second period, Fig. 2b clearly shows that during this same period, the deepest clouds are associated with the H simulation. Similar results can be seen in Xue and Feingold (2006, their Figs. 2d and 6f).
Frequency distributions of cloud-top height for C and H runs (Fig. 11) show that in general the time series means in Fig. 1 are a faithful representation of the relative strength of convection from periods 1 through 3. However, as seen in Fig. 11, the H run always produces the highest cloud-top heights. This is supported by frequency distribution analysis of CAPE, LWP, and w′w′ (not shown), all of which exhibit a tail of more frequently occurring extrema associated with the H simulation, much like those in Fig. 11. Thus, the H simulation does produce a very small number of the deepest, most vigorous, and most strongly precipitating clouds (Figs. 7b, 7c, and 7d) in all periods, even when the mean cloud-top height is lower than in the C run.
Frequency distribution of cloud-top heights for C and H simulations for (a) first, (b) second, and (c) third periods. Note the persistent appearance of more frequently occurring high cloud-top heights in the H simulation, even when the mean values are similar (cf. Fig. 1d).
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
f. Some thoughts on time scales for convergence
There appears to be a general dearth of discussion in the literature on time scales for equilibration in response to an aerosol perturbation, particularly for shallow cumulus. Most early large-eddy simulations of boundary layer clouds were of short duration and limited to small domains, so that the studies were implicitly concerned with transients. Enhanced computational power has allowed simulations of much longer duration but only a handful of those have considered the influence of aerosol perturbations (e.g., Stevens and Seifert 2008; Wang and Feingold 2009; Bretherton et al. 2010; Kazil et al. 2011). Bretherton et al. (2010) discuss a 1–2-day thermodynamic adjustment period for stratocumulus and focus on aerosol-induced (among others) evolution to different steady states. Whether similar aerosol-related bifurcations exist for the trade cumulus regime is unclear.
While a rigorous study of factors influencing equilibration times must await further study, our assessment from the current study is that in the absence of large-scale forcing, important controlling parameters would be (perhaps obviously) the timing and duration of the aerosol perturbation (Fig. 9) as well as the magnitude of precipitation (Fig. 8).
g. Simulations with a different spinup period
The possibility that the difference between the C and H runs is particular to the choice of spinup period (6 h 10 min) is now raised. The end of the spinup period occurs long before the stabilization of the cloud system at 20 h (Fig. 1). How might results differ if the bifurcation into two different aerosol concentrations were to occur at a time when the system had already stabilized? To answer this question, the spinup period is extended to 24 h and the C run is extended to 48 h; this extended C run is referred to as “the extended C run.” As in the earlier H run, a new simulation is spawned that uses the wind, pressure, temperature, and humidity fields at each grid point from the extended C run as initial conditions at 24 h. The only difference is that this simulation has a background aerosol number concentration enhanced by a factor of 2.5, yielding 143 mg−1 at grid points with no clouds. This simulation is referred to as “the H-at-24-hr run.” Figure 12 shows the LWP and CAPE evolution for the extended C and H-at-24-h runs from 24 h on. From 24 to 34 h LWP and CAPE are higher in the H-at-24-h run than in the extended C run. The situation reverses between 34 and 42 h, but after about 42 h, the fields stabilize, in qualitative agreement with Fig. 1. It is notable, however, that the magnitude of differences in LWP and CAPE from 24 to 42 h is smaller than those in Fig. 1. It is also notable that the higher (lower) LWP and CAPE in the H-at-24 h run than in the extended C run is maintained for about 10 (8) from 24 (34) to 34 (42) h. These time periods of 10 and 8 h are longer than the duration of the first and second periods, respectively. Thus, although the magnitude of the LWP and CAPE differences is smaller, it takes longer to reach stabilization of LWP and CAPE compared to the simulations with the spinup time of 6 h 10 min. Nevertheless, the qualitative agreement with Fig. 1 provides confidence that the underlying mechanisms described herein are robust.
Time series of (a) LWP and (b) CAPE for extended C (solid) and H-at-24-h (dashed) runs from 24 to 48 h.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
6. Summary and conclusions
The prevalence of weakly precipitating trade cumulus and their importance for the climate system (e.g., Bony and Dufresne 2005) provides strong motivation for detailed examination of trade cumulus clouds and their response to changes in aerosol. We have examined here the influence of aerosol perturbations on long-duration (~30 h) trade cumulus simulations, specifically testing the hypothesis that the changes in thermodynamic profiles triggered by an aerosol perturbation cause changes in cloud vertical development that act to remove the differences. This concept is congruent with the buffered aerosol–cloud system discussed in Feingold and Siebert (2009), Stevens and Feingold (2009), and Lee and Feingold (2010). The aforementioned studies hypothesized that a system tends to reduce an aerosol impact by modifying environmental conditions or microphysical pathways.
In the current paper, we have taken a detailed look at the sequence of events associated with the boundary layer response to an aerosol perturbation using the RICO GCSS case study as a basis for numerical experimentation. It is shown that increasing the aerosol concentration generates smaller droplets that evaporate more efficiently. This results in smaller and more numerous clouds with a larger surface-to-volume ratio, which through a feedback mechanism increases the susceptibility of clouds to entrainment of dry air (Small et al. 2009). Increases in aerosol therefore accelerate drop evaporation, resulting in stronger cooling and thus increased instability in the lower part of clouds near the beginning of simulations. The larger instability in the lower part of clouds and associated larger CAPE develop clouds with higher top heights, and higher LWC and LWP in the aerosol-perturbed simulation in the early period of simulations. These perturbed clouds with higher top heights result in elevated (in height) convective divergence and thus higher locations of peak evaporative cooling. Numerous sensitivity tests point to aerosol-induced perturbations in potential temperature dominating aerosol-induced perturbations in water vapor in terms of the response of the cloud system.
In contrast, unperturbed simulations are characterized by a lower location of the peak in net cooling, which over time generates instability at altitudes that correspond to the middle part of perturbed clouds. The larger instability and associated larger buoyancy flux and CAPE at these altitudes invigorate the clouds and increase their LWP during the middle period of simulations. Thus, the system tends to adjust itself by modifying its environment in such a way that the effects of the initial aerosol perturbation are countered. This adjustment tends to occur after about 14 h, which cautions against short-term simulations when attempting to ascertain the effects of aerosol perturbations. After about 20 h, the aerosol-perturbed system stabilizes to a similar state to that in the unperturbed simulation. The result is that in the mean there are very small deviations in most cloud fields when considered over the entire simulation period. This result holds for different model initializations (Fig. A1) and different spinup periods (cf. Figs. 1 and 12), providing confidence in the underlying physical mechanisms described herein.
One exception is the precipitation field. Although the time- and domain-averaged precipitation decreases with increasing aerosol, the precipitation response to aerosol is strongly modulated by cloud LWP or depth. The deepest clouds occur in the perturbed simulations, most noticeably in the first period (Fig. 11a), but also as rare events in periods 2 and 3 (Figs. 11b and 11c). This “tail” of deep clouds produces the largest (rare) precipitation rates (Figs. 7a–c). Thus, for a certain subset of the cloud population, aerosol-induced deepening of clouds can counter aerosol suppression of collision–coalescence. On average, however, the aerosol perturbation to microphysics tends to dominate for the 2.5-fold increase in background aerosol conditions between C and H. Stevens and Seifert (2008) demonstrated this compensating effect in their simulations and found that the deepening effect was able to overcome the microphysical effect under very similar drop concentrations but moister, more strongly precipitating conditions; an increase in drop concentration from 35 to 70 mg−1 produced an increase in rain rate but further increases in drop concentration caused rain suppression, in agreement with the current simulations (in our simulations, cloud-averaged drop concentrations for C and H are 32 and 75 mg−1, respectively). Prior work has indicated that the aerosol tends to increase cloudiness under more strongly precipitating conditions (as in Stevens and Seifert 2008), so the difference between the two studies is perhaps not unexpected.
Another exception to convergence in cloud properties is the cloud optical depth τ. Calculations of the domain-average τ show that when the LWP is constant (period 3), only about 75%–80% of the τ (and to first-order cloud albedo) increase is realized because of horizontal and vertical spatial variability in cloud microphysical properties, and nonlinear dependence of τ on drop concentration.
In the weakly precipitating cloud simulations, instability changes are mostly a result of aerosol-induced changes in latent heat distribution associated with cloud liquid above cloud base. In contrast, in the more strongly precipitating cases, subcloud evaporation also plays a strong role in removing instability, with the result that the perturbed and unperturbed systems converge more rapidly than in the weakly precipitating cases. Thus, in general, both above-cloud-base changes in latent heat distribution induced by aerosol as well as changes in subcloud layers are important for improved understanding of interactions among aerosol, clouds, and environmental instability.
What are the characteristic time scales for equilibration in response to an aerosol perturbation? In the current study, equilibration of fields occurs after about 20 h and is influenced to varying degrees by the timing/duration of the perturbation and the magnitude of precipitation. For this case, an aerosol perturbation lasting 3 h 50 min causes changes in instability that leaves its imprint on the evolution of the cloud system regardless of the evolution of aerosol perturbation from 10 h on (Fig. 9). Thus, the cloud system becomes insensitive to aerosol differences at some point in the evolution, and it is the earlier aerosol-induced changes in the thermodynamic environment and their feedbacks with cloud microphysics and dynamics that control the cloud field differences between aerosol-perturbed and unperturbed cases [see Lee (2011) for similar results pertaining to deep convective clouds]. A cautionary note: sensitivity to the duration of the aerosol perturbation could well differ if the perturbation were to be applied at a different stage of the cloud field evolution.
These results demonstrate that even transient aerosol perturbations may linger longer than the duration of the perturbation itself, provided it persists for long enough. Short-duration aerosol perturbations are unlikely to have much influence on the system but further study is required to place these ideas on firmer footing.
Acknowledgments
The authors thank NOAA’s Climate Goal Program and the NOAA/NSF Climate Process Team for supporting this work. P. Chuang thanks the Office of Naval Research (Grant N00014-08-1-0437) for its support of this work. NOAA’s HPCC is acknowledged for its computing support.
APPENDIX A
Sensitivity to Initial Conditions
In the spirit of ensemble simulations, we perform additional C and H simulations but modify the initial thermodynamic profile with random perturbations that are, respectively, half (Pert/2 C and Pert/2 H runs) and double (Pertx2 C and Pertx2 H runs) the perturbations for the standard C and H simulations. Figure A1 presents a subset of the fields in Fig. 1, together with those from the modified initial conditions, and shows that the basic trends in C versus H time series are remarkably similar. While this “ensemble” of runs has a very limited number of members, Fig. A1 does suggest that the analysis presented herein is not associated with a very particular set of initial conditions.
Time series of (a) LWP and (b) CAPE for C (solid) and H (dashed) simulations as in Fig. 1 (black lines) and for initial conditions with either half (green) or double (red) the initial temperature perturbations. Note the consistency between the three pairs of simulations.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-026.1
APPENDIX B
Further Sensitivity Tests
Further sensitivity tests are conducted to investigate robustness of the results. The H run is repeated from 7 h (in the middle of the first stage) to the end of the second stage (at 10 h) in the first period to identify the cause of the persistent larger domain-averaged CAPE in the H run between 8 and 10 h (Fig. 1e). The first of the repeated runs, referred to as HθC, adopts θ from the C run at each of grid points at 7 h. Then, when the simulation time in the HθC reaches 8 h, θ from the C run at each of grid points at 8 h is adopted by HθC. As shown in Figs. 4b and 4d, this θ from the C run has less instability below about 1 km at hours 7 and 8. Consequently, the difference in the time- and domain-averaged CAPE between the HθC and C runs averaged over the first stage is much smaller than that between the H and C runs (Table 2). During the second stage, the time- and domain-averaged CAPE is slightly smaller in the HθC run than in the C run (Table 2).
To explore the effect of the r difference on the larger domain-averaged CAPE in the H run during the second stage, the H run is repeated again from 7 h to the end of the second stage by adopting r from the control run at each of the grid points, first at 7 h and then at 8 h. This repeated run is referred to as HrC. The time- and domain-averaged CAPE in this HrC run is larger than the C run over the second stage (Table 2).
Finally, to explore the effect of the aerosol difference on the larger domain-averaged CAPE in the H run during the second stage of period 1, the H run is repeated again from 7 h to the end of the second stage by adopting the aerosol concentration from the C run at each of the grid points, first at 7 h and then at 8 h. This repeated run is referred to as the H-C-second run. The time- and domain-averaged CAPE in this H-C-second run is larger than the C run during the second stage. These repeated simulations demonstrate that the larger instability below about 1 km, established during the first stage of period 1 (between 06 h 10 min and 8 h), is the primary cause of the larger CAPE in the H case during the second stage (8–10 h). They also demonstrate that aerosol and r differences established during the first stage are not the cause of the CAPE differences between the H and C cases during the second stage.
It is notable that the differences in cloud-top height and in the location of strong convective divergence around cloud tops between the HθC and the C runs are negligible compared to those between the H and C runs (Fig. 5b). This is because the CAPE difference between the HθC run and the C run is much smaller than that between the H and C runs (Table 2). This results in a similar net cooling in ΔZm between the HθC run and the C run (Fig. 5b), reinforcing the idea that the larger low-level instability in the H run established during the first stage is the main cause of differences in the net cooling in ΔZm between the H and C runs.
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