The influence of the cloud condensation nucleus (CCN) concentration on the properties of low-level clouds under the conditions observed over the north central Oklahoma on 24–25 September 1997 is examined in a series of 18-hour simulations using a single-column model (SCM) and a cloud-resolving model (CM). Both models predict higher droplet concentration, smaller droplet size, and larger liquid water path in a “polluted” case (CCN concentration = 1000 cm−3) than in a clean case (CCN concentration = 250 cm−3), suggesting that the first and the second indirect effects act in unison under the considered conditions. A comparison of the simulations using the SCM and CM with the same two-moment bulk microphysics parameterization highlights the dominant effect of the dynamical framework on both microphysical and macrophysical properties of modeled cloud. This effect is much stronger than the variations in each of the models resulting from changing CCN concentrations. However, the relative liquid water path sensitivity to CCN concentration is similar between the SCM and CM simulations. The CM simulations with the size-resolved and the two-moment bulk microphysical parameterization yield nearly identical structure of boundary layer. Even though these simulations are in much closer agreement with each other than they are with the SCM results, the variance from the microphysics treatment is still comparable to the effect of quadrupling CCN concentration.
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 Cloud properties depend strongly on the distribution of aerosols from which the cloud condensation nucleus (CCN) population is drawn. Since clouds are an integral and important part of the climate system this dependency creates the potential for the aerosol indirect effect (AIE), when anthropogenic aerosol alteration of cloud forcing has climate consequences. Scales at which the involved processes operate span an enormous range from the submicron size of aerosols on which cloud particles are formed to tens of thousand of kilometers at which the global effects could be registered. Covering such a broad variety of scales in any observational or modeling study is a challenge. In the past three decades a lot of attention has been focused on cloud-scale effects and processes. As a result several pathways for the AIE have been put forward addressing changes in both microphysical and macrophysical cloud properties.
Twomey  showed that if clouds are optically not very thick (i.e., optical depth τ less than 100) and aerosol (or CCN) absorption of sunlight is low (i.e., absorption coefficient σa ∼ 0.01 km−1 at CCN concentration Nccn = 1000 cm−3) then increasing droplet concentration acts to increase cloud albedo, thus climatically leading to a cooling effect. This became known as the first indirect effect, or the Twomey effect. For thick clouds and more absorbing aerosols, the effect may be reversed as increased absorption in more polluted environments dominates the brightening of the clouds in reflection. Conclusions of Twomey's analysis as well as results from a number of subsequent studies are valid under the assumption of constant liquid water content or, in other words, that the microphysical changes do not affect the macrophysical cloud properties. This is often not the case.
Albrecht  suggested that drizzle may promote decoupling of the cloud layer from the rest of the atmospheric boundary layer thereby decreasing cloud liquid water path (LWP). A higher CCN concentration could therefore lead to larger LWP by stopping or slowing drizzle production. While mounting evidence exists that changes in CCN concentration can alter liquid water content distribution, these effects have proven to be difficult to quantify.
Ackerman et al.  studied the evolution of ship tracks using a one-dimensional model. Their calculations indicated that when droplet concentration of a stratocumulus cloud increased from 40 to 100 cm−3 the amplitude of the diurnal oscillation of the liquid water content amplified: the LWC increased by 25% at night and during morning hours but decreased by a similar amount in the afternoon. Since the time period of the decreased LWC was shorter, a net (daily averaged) increase in LWP was observed. The nocturnal behavior is consistent with the Albrecht hypothesis, but the afternoon trend is not.
Feingold et al.  applied a two-dimensional eddy-resolving model to simulate stratocumulus off the coast of California and found that the LWP increased slightly (by about 6%) in a run with CCN concentration of 50 cm−3 (at a supersaturation of 1%) compared to the runs with 100 or 250 cm−3 CCN. It was suggested that evaporative cooling of small amounts of drizzle just below cloud base in the former case destabilized the subcloud layer to strengthen cloud circulation leading to deeper cloud layer and hence larger LWP values. Apparently the cooling was not strong enough to cause the decoupling. These simulations were conducted over a shorter three-hour time period and did not consider solar radiation.
Jiang et al.  used a similar framework to study the effects of an elevated aerosol layer and large-scale subsidence on the microphysical and macrophysical structure of marine boundary layer clouds. In their simulations for the Atlantic Stratocumulus Transition Experiment (ASTEX), the second indirect effect (or the dynamical feedback) acted to minimize the Twomey effect as the model predicted larger LWP in a cleaner environment. Thus the albedo was not significantly affected by the entrainment of the polluted air. The study also indicated a strong dependence of the LWP (and, therefore, optical depth) on the strength of the large-scale subsidence.
 Estimation of the global radiative impact of the cloud-scale changes represents another challenge since extrapolation of the findings from the cloud scale to larger temporal and spatial scales is not straightforward.
 At present, satellite-based observations are the only means of practical global monitoring. Han et al.  analyzed satellite-retrieved properties of thin low level clouds and showed that the liquid water sensitivity (defined as a ratio of the change in LWP to the change in column droplet number concentration) can be negative as well as positive. It means that increasing aerosol concentration may lead to an increase (positive sensitivity), a decrease (negative sensitivity), or no change in LWP. Over continents the sensitivity is generally small and slightly negative. Maritime clouds exhibit larger sensitivity depending on the season and location. On average, the liquid water sensitivity is negative over nearly one third of the globe predominantly in warmer locations and seasons. Unfortunately, the satellite observations offer little insight as to what physical mechanisms are behind these changes.
 Global climate models (GCMs) are potentially the best tool for estimating the AIE because they link together aerosol, cloud, and radiation processes on the global scale. Unfortunately, the uncertainty of current AIE GCM estimates is large. An adequate representation of cloud properties is essential for estimating the indirect aerosol effect in large-scale models. Such a representation must rely on a physically sound treatment of spatial variability that affects many dynamical and microphysical processes in complex and nonlinear ways. Much of this variability is not resolved and must be parameterized. It is clear that in addition to improving our knowledge of local cloud-aerosol interaction it is equally important to ensure that the potentially important components of this process are adequately represented in parameterizations for large-scale models.
 The goal of our study is two-fold. Because previous modeling studies using cloud resolving models [Ackerman et al., 1995; Feingold et al., 1997; Jiang et al., 2002] dealt primarily with maritime low-level clouds and because the results suggest a dependency on the boundary layer structure, our first goal is to expand these simulations to a continental environment. Following this approach, a single layer warm cloud observed at the Southern Great Plains (SGP) site on 25 September 1997 during the Atmospheric Radiation Measurement (ARM) Single Column Model (SCM) Intensive Observation Period is simulated.
 Our second goal is to compare simulations using a cloud-resolving model (CM) and a Single Column Model in order to evaluate the sensitivity of the results to simplifications in treating dynamics and microphysics. The SCM is a one-dimensional (column) model that preserves all the physics and parameterizations of the full GCM but replaces exchanges between the column and its would-be neighbors with prescribed advective tendencies for predicted variables. It has been proven to be a useful and cost efficient framework for testing large-scale parameterizations [Ghan et al., 1999, 2000; Bechtold et al., 2000; Xie et al., 2002; Gregory and Guichard, 2002].
 Dynamics of the boundary layer clouds is crudely parameterized in the SCM because of its coarse spatial and temporal resolutions. The CM, however, resolves the cloud structure explicitly. We conduct parallel simulations using these two models forced by the prescribed horizontal advective tendencies, large-scale subsidence rate, surface boundary conditions, and aerosol characteristics derived from objective analysis of available measurements for the 25 September 1997 SGP case. By using identical microphysical parameterizations in the CM and the SCM driven by identical boundary conditions, we isolate the differences caused by the treatment of small-scale spatial variability. Conversely, by comparing CM simulations with different treatments of microphysics we test the effects of microphysics parameterizations.
2. Model Descriptions
2.1. Single-Column Model
 The single column model is a variation of the PNNL SCM used in several model evaluations using ARM SGP data [Ghan et al., 1999, 2000; Xie et al., 2002] and Aerosol Characterization Experiment (ACE-2) data [Zhang et al., 2002; Menon et al., 2003]. A global version of this model has been coupled with a global aerosol model and used to estimate aerosol indirect effects [Ghan et al., 2001]. It is based on the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM2). A bulk treatment of cloud microphysics has been applied to stratiform clouds [Ghan et al., 1997a]. Prognostic variables are vapor + cloud water mixing ratio (qw), ice mixing ratio, droplet number concentration [Ghan et al., 1997b], and ice number concentration. Cloud water mixing ratio is diagnosed from qw assuming that condensation removes all water exceeding 100% relative humidity. Rain and snow are diagnosed from the rain and snow budgets by neglecting the mixing ratio tendency terms [Ghan and Easter, 1992]. For the most part cloud microphysical parameterizations are taken from the parameterizations developed for Colorado State University Regional Atmospheric Modeling System [Tripoli and Cotton, 1980; Cotton et al., 1982, 1986]. However, for autoconversion of cloud water and cloud droplets the parameterization of Khairoutdinov and Kogan  is used. Droplet nucleation is treated only in new clouds or at the base of existing clouds, and is parameterized in terms of updraft velocity, aerosol hygroscopicity, and the parameters of a lognormal aerosol size distribution [Abdul-Razzak and Ghan, 2000].
 Subgrid variations in cloud properties and cloud processes are treated assuming a triangular distribution of total water [Smith, 1990] and a Gaussian distribution of updraft velocity. The triangular distribution is used to analytically diagnose the grid cell mean cloud fraction, cloud liquid water content, and autoconversion rate, as described in Appendix A. The variances and covariances of total water and liquid water potential temperature are determined from the second-order turbulence closure scheme described below. Skewness is neglected. The dependence of droplet nucleation on the subgrid variability of vertical velocity is treated by integrating over an assumed Gaussian distribution of vertical velocity [Ghan et al., 1997b], with the variance of vertical velocity also determined from the second-order turbulence closure scheme. The treatment of the dependence of droplet nucleation on the subgrid distribution of cloud cover and cloud overlap is summarized in Appendix B.
 The second-order turbulence scheme is based on the Yamada and Mellor  level 2.5 model. The realizability conditions of Helfand and Labraga  are imposed on the mixing coefficients. The variances of θw, qw and w and the covariance of θw and qw are diagnosed from the turbulence kinetic energy, the vertical diffusivity, and the gradients of θw, qw, u, and v. Turbulence kinetic energy is the only higher-order prognostic variable, determined from the turbulence kinetic energy balance driven by buoyancy and mechanical production and turbulence dissipation.
 Given the in-cloud liquid water and ice mixing ratios and the number concentrations of droplets and crystals, the cloud radiative properties are expressed in terms of the layer mass burdens of cloud liquid water and cloud ice, and the effective radii of the droplets and crystals. The effective radii are related to the mixing ratios and number concentrations as described by Ghan et al. [1997a], following parameterizations of Martin et al.  and Fu and Liou  for droplets and crystals, respectively. The cloud optical depth, single-scattering albedo, and asymmetry parameter for cloud water and cloud ice are parameterized by Slingo  and Fu and Liou . Given the cloud fraction and cloud optical properties, the radiative heating rate is calculated by the CCM2 radiation code.
2.2. Cloud-Resolving Model
 The cloud resolving model used in this study is a modified version of the large-eddy simulation model of Khairoutdinov and Kogan . The prognostic equations for the liquid water potential temperature, the total water mixing ratio and the wind velocity components are solved numerically on a discrete Cartesian grid using Arakawa's C-type staggering. The flow is assumed to obey the Boussinesq approximation. The equations of motion are integrated in time using the third-order Adams-Bashforth scheme. Momentum advection is computed to second-order accuracy in the flux form. All scalars are advected using the second-order positive definite minor flux adjustment algorithm [Walcek, 2000], which in our applications was proven to be faster and more accurate than the Smolarkiewicz and Grabowski  scheme employed by Khairoutdinov and Kogan . The subgrid stresses and scalar fluxes are parameterized using the 1.5-order closure model, which includes solving the turbulent kinetic energy equation. The model uses periodic lateral boundary conditions and a damping layer in the upper portion of the domain to minimize possible artifacts of the “rigid-lid” top boundary condition. In this study of warm low-level clouds only liquid phase cloud microphysics is considered as described below. The longwave and shortwave radiative fluxes are computed using algorithms similar to Wyant et al. . These algorithms are in general much cruder than the radiation parameterization used in SCM but they are much more computationally efficient and perform reasonably well when applied to the cloudy boundary layer.
 Dynamical frameworks of the SCM and CM differ significantly in domain structure and resolution. The CM is run on a 3-D spatial domain that, in our simulations, covers a 5 × 5 × 3.2 km3 physical domain with 50 × 50 × 80 grid points resulting in 100-m horizontal and 40-m vertical resolution. The SCM domain is a column of 48 levels with uneven spacing. Comparison of the distribution of levels in the lower 2 km of SCM and CM is shown in Figure 1. In the lower 500 m, the coverage is very similar in both models. Above that level, the SCM resolution notably deteriorates. At the cloud top level of 1200 to 1500 m, vertical resolution of SCM is five times coarser than the resolution of the CM. This difference could significantly affect the entrainment rate.
 A sophisticated treatment of the cloud processes is provided by the size-resolved (or bin) microphysics [Kogan, 1991; Ovtchinnikov and Kogan, 2000]. The main advantage of this scheme is that it rids ad hoc assumptions on the shape of the cloud particle spectrum present in bulk microphysics parameterizations. Instead, the scheme predicts the evolution of the size distributions of cloud hydrometeors by explicitly solving the system of equations for condensation/evaporation and collision growth. In a typical setup, the spectra for cloud condensation nuclei (aerosol) and cloud droplets are discretized into 20 to 30 size categories (or bins) each. This generates several dozens of additional variables to carry around compared to the bulk approach. The payoff for the extra load, however, is in that droplet nucleation is controlled directly by the initial aerosol distribution, droplets of all sizes are treated in a consistent manner, and no superficial division into cloud and precipitation categories is required [Khain et al., 2000].
 For the purpose of this study, the microphysics parameterization from the SCM is also implemented in the CM. The parameterization is applied to each of the CM columns. The main difference is that the vertical velocity, which serves as an input to the microphysical parameterization and is diagnosed from the turbulent kinetic energy in the SCM, is now explicitly resolved in the CM.
3. Experiment Design: The 25 September 1997 Case
 All simulations start at 2000 UT on 24 September and run for 18 hours.
 Because local conditions are significantly affected by the synoptic-scale advection over the daylong period, and because neither CM nor SCM is designed to predict these changes, large-scale horizontal advective tendencies are prescribed in both models. These tendencies for temperature and water vapor mixing ratio are derived from objective analysis [Zhang and Lin, 1997; Zhang et al., 2001] and shown in Figure 2. Large-scale subsidence is derived from the prescribed divergence. The subsidence is small initially but intensifies with time (Figure 3) approaching 2 cm s−1 at 1500-m level toward the end of the simulations.
 The sensible heat flux at the surface (Figure 4) is small and positive in the beginning but turns slightly negative before the local sunset (2400 UT, t = 4 hours) and stays close to zero until the sunrise (1200 UT on 25 September, t = 16 hours). The latent heat flux follows a similar pattern but is 10 to 30 W m−2 larger at all times. These fluxes are used in both models to determine the subgrid turbulent transport of temperature and moisture in the vertical direction at the lowest model level.
 All of the forcing variables are specified for times that are 3 hours apart and linearly interpolated for intermediate times to be applied at each time step in both models. These variables represent area means in a domain centered around the ARM central facility and enclosed by 12 auxiliary sites including boundary facilities and profiler stations. This domain covers an area of approximately 400 × 400 km2.
 We focus our attention on three model configurations and two sets of simulations with different CCN concentrations, although many more runs were performed. In the first series of runs, the number concentration of CCN is set to Nccn = 1000 cm−3 and in the second series Nccn = 250 cm−3. Composition (ammonium sulfate) and other parameters of the lognormal CCN size distribution, such as number mode radius (0.05 microns) and logarithmic width (3.0), are also prescribed. This results in a CCN activation spectrum presented in Figure 5. The six runs are summarized in Table 1.
Table 1. Six Combinations of Dynamical Framework, Microphysics Parameterizations, and Initial CCN Concentration
4. CM and SCM Simulations
 In this section, we compare the result of the six simulations. Unless stated otherwise, all variables in the analysis are averaged over one-hour periods and, in case of CM simulations, horizontally over the computational domain.
 One of the most important parameters describing the radiative properties of the cloudy atmosphere is the column integral of the condensate, or in the case of warm clouds, the liquid water path (LWP) [Stephens, 1978]. Time evolution of the LWP is shown in Figure 6. In CM predictions, the LWP increases steadily from the beginning of the simulations until it reaches a maximum in about 8 hours. In SCM, the evolution of LWP is qualitatively similar but the maximum is much larger and is not reached until 12 hours.
 Observed LWP is shown in Figure 6 for reference although its comparison with the simulations is complicated by at least two factors. First, there were midlevel clouds observed over the analysis domain in the beginning of the simulated period. Average cloud top height for the first three hours is above 3 km and cloud radar observation indicate presence of broken clouds in the 2 to 6 km layer up until the fifth hour (not shown). Observed LWP is provided by a retrieval algorithm applied to microwave radiometer measurements, which has no information about the vertical distribution of condensate. It is therefore unclear how much of the observed LWP comes from midlevel clouds, but they are definitely a contributing factor. A second complication arises from a possible model spin up effect. Although much of this initial simulated increase in LWP appears to be real and corresponds to the observed thickening of the lowest cloud layer, initiating the models without any cloudiness may introduce a time delay in building up the LWP. Both indicated factors would contribute to the large difference between observed and simulated LWP in the first few hours as seen in Figure 6. After that the comparison becomes more direct. Observations show no evidence of clouds above 2 km between the fifth and fifteenth hours. For this period, which is also no longer affected by the model's initial conditions, the LWP evolution simulated by the CM appears to be in closer agreement with observations than those simulated by the SCM.
 Lowering CCN concentration from 1000 cm−3 to 250 cm−3 reduces the maximum LWP by about 20% in the CM runs with either bin or bulk microphysics treatments. The SCM exhibits a larger sensitivity of LWP to lowering CCN concentration by a factor of four, reducing LWP by 25 to 30%. The behavior of both models is therefore consistent with Albrecht's  proposition that a higher CCN concentration could lead to larger LWP by stopping or slowing drizzle production. In all simulations, it takes over 6 hours to develop sizable differences. Coincidently, in the work of Jiang et al.  simulations of arctic boundary layer clouds similar differences in LWP develop after 4 hours. Jiang et al.  ASTEX simulations with CCN concentrations of 100 and 1200 cm−3 are also nearly identical for the first 5 hours but diverge afterward, although in this case the sign of the LWP change is reversed. While it is not obvious what determines this timescale, it is clear that multihour simulations are apparently necessary to study these effects. This also points to the need for inclusion of large-scale forcing in such studies, which undoubtedly complicates both the simulations and the analysis. Caution must be exercised in interpreting results from shorter simulations assuming quasi-stationary regimes [Feingold et al., 1997].
Jiang et al.  found that the magnitude of large-scale divergence that determines subsidence had a large effect on boundary layer dynamics and cloud microphysics. In their simulations using a two-dimensional model and constant divergence, stronger subsidence initially led to substantially reduced LWP, although the differences became much smaller in the last few hours of the 10-hour simulations. In our case, the large-scale subsidence changes significantly with time in the course of the simulations. At the end of the simulated period the subsidence approaches 2 cm s−1 at 1500-m level, which is about four times stronger than the maximum subsidence applied in the work of Jiang et al. .
 Regardless of the microphysics treatment, the difference in LWP simulated by CM and SCM is very large. The main source of this discrepancy is in the dynamical structure of the boundary layer, which is indeed very different in the simulations by the two models as the time-height cross sections reveal.
Figure 7 compares the evolution of liquid water mixing ratio for the CM and SCM simulations, again horizontally and hourly averaged. The SCM cloud (Figures 7c and 7f) forms at lower levels than the CM cloud (Figures 7a, 7b, 7d, and 7e) and is much thicker. The simulated initial LWP increase seen in Figure 6 coincides with rising cloud-top height and thickening of the cloud layer in all of the model runs. After cloud top height stabilizes (near 1500 m level at 8 hours for CM and 1200 m at 12 hours for SCM) and LWP reaches its maximum (Figure 6), the cloud base for the stratiform layer continues to lift, thus decreasing LWP. Note that shallow convective clouds develop under this layer in the CM simulations and the SCM convection parameterization remains active as well. Condensate contained in the convective elements contributes little to the average LWP, however, because these clouds occupy only a small portion of the domain.
 Cloud-base and cloud-top heights observed at the ARM SGP central facility site and shown in Figure 7 suggest that the location of the CM simulated clouds is more realistic, while the SCM clouds are too low. Unlike LWP observations, which represent an average for several sites within the analysis area, cloud boundaries presented in Figure 7 come only from the central facility site equipped with a cloud radar and lidars. Sampling issues related to single-site observations do not allow us to perform a quantitative comparison with simulations driven by large-scale forcing and therefore pertaining to an extended domain. It may be difficult, for example, to determine with any certainty which of the CM simulations is closer to reality. Nevertheless, it is evident that the SCM does not reproduce the cloud structure correctly, at least not until the very end of the simulations.
 The SCM boundary layer is close to being well mixed, while the CM boundary layer is not. This is illustrated by Figure 8, showing time evolution of the profiles of standard deviation of vertical velocity. For the CM, which explicitly simulates large eddies, the standard deviation is calculated from the resolved vertical velocity component. For the SCM, it is diagnosed from the turbulent kinetic energy predicted by the model.
 Within 6 hours, circulations below and above 900 m are clearly separated in the CM simulations with more vigorous eddies confined to the upper cloud layer, at least until the rising sun begins to increase the surface heat fluxes at t = 16 hours. In contrast, the cloud is coupled all the way to the surface throughout the SCM simulations by much stronger turbulence. This difference has a profound effect on thermodynamics and microphysics of the cloudy boundary layer.
 The much larger intensity of vertical exchange in the SCM leads to efficient entrainment and faster drying of the whole boundary layer, not just its upper part as in CM simulations (Figure 9). In the CM, the entrainment affects the cloud layer but the transport of the dry air further down is restricted. Since the latent surface heat flux is also small, the moisture content in the lower 900 meters of the CM domain remains virtually unchanged.
 Large differences in droplet number concentrations, Nd, can also be traced back to the dynamical features discussed above. Figure 10 shows domain and hourly averages of droplet number concentration. In the case of the CM runs, the plot reflects the combined effect of microphysical and macrophysical cloud structure because the horizontally averaged in-cloud concentration is effectively weighted by the cloud fraction. Thus, although small cumuli have droplet concentrations of near 300 cm−3, their cloud fraction of less than 10% would reduce the horizontally average concentration to fewer than 30 cm−3. The highest concentration in the CMs_1000 run is observed between 3 and 6 hours. This period begins with the formation of the continuous cloud layer between the 750-m and 1300-m levels and ends with the decoupling of the cloud layer from the rest of the boundary layer. At that time (after 6 hours), the moisture supply from near the surface diminishes thereby lowering the supersaturation in the updrafts and reducing the nucleation rates.
 The nucleation in the CMb runs is treated differently from the CMs runs and its rate depends primarily on the updraft velocity at the cloud base. Consequently, the droplet concentration in the stratiform cloud (Figures 10b and 10e) increases proportionally to the increase in standard deviation of the vertical velocity (Figures 8b and 8e). The similar treatment in the SCM results in much higher droplet concentration (Figures 10c and 10f) because of much stronger (diagnosed) vertical motions (Figures 8c and 8f).
 The activation scheme in CMb prevents formation of new droplet in the interior of the cloud, i.e., at any grid point where cloud liquid water is already present, even in the smallest amount. In a situation where a parcel of cloudy air near the cloud base can re-enter cloud without evaporation of all of the liquid water and where the maximum vertical velocity is reached in the middle of the cloudy layer, this assumption may not always hold. These instances of the so-called in-cloud nucleation also contribute to lower cloud droplet number concentration in CMb run compared to CMs run.
 Another notable difference is that in the CMs runs the horizontally averaged droplet number concentration increase moderately with height (Figure 11a), while in the CMb runs the concentration is constant or decreases slightly (Figure 11b). The former behavior is common to models that use size-resolved microphysics [Khairoutdinov and Kogan, 1999; Stevens et al., 1996a]. It may be caused, at least partially, by spurious supersaturations generated near the cloud top in Eulerian models [Stevens et al., 1996b]. Another reason is that in a subsaturated environment (e.g., in downdrafts) smaller droplets evaporate at a faster rate than the larger ones thus gradually reducing the droplet concentration in descending parcels. This effect is not seen in the bulk parameterization with an effectively monodisperse droplet size distribution but would be a factor in size-resolving models if the spectra are broad enough. The spectrum broadening and therefore the resulting change in droplet concentration in such models can be of physical or numerical origin, or most likely a combination of both.
 The differences in droplet number concentration profiles are reflected in droplet size. The distribution of the radiatively important effective radius is show in Figure 12. In runs with bulk microphysics, re is correlated most strongly with cloud liquid water mixing ratio. The size-resolved microphysics leads to a more vertically uniform distribution of re (Figures 12a and 12d). These striking differences in re have only a moderate effect on the optical depth (Figure 13), however, because they are maximized in the least dense and consequently optically thin parts of the clouds. This is seen most clearly below the base of the solid cloud layer, where the small amount of liquid water distributed among few drizzle-size drops results in re reaching 50 μm but has negligible effect on shortwave radiative transfer. In the bulk microphysics, mixing ratios for the precipitating and nonprecipitating liquid water are calculated separately and effective radius is calculated only for the latter part.
5. Discussion and Conclusions
 The loop of aerosol-cloud interactions can be broken into several segments: (1) determining of a CCN distribution from a given aerosol size and composition distribution, (2) predicting cloud microphysical and macrophysical properties for a given CCN distribution, and (3) determining changes in aerosol distribution induced by clouds with given properties. This study addresses only the second problem, namely the sensitivity of cloud properties predicted by the models to changes in CCN distribution. The sensitivity is tested by changing the total CCN concentration by a factor of four. Note that because the shape of the CCN spectra as well as CCN chemical composition remain unaltered in these experiments some potentially important aerosol effects are not considered here, including those resulting from variability in giant CCN concentration [Feingold et al., 1999]. The aerosol influence on cloud properties is studied in parallel simulations using the SCM and CM with two different microphysics schemes.
 The results presented in the previous section clearly demonstrate that the differences between the CM and SCM runs are dominated by the disparity of the dynamical frameworks and not by specifics of the microphysics treatment. This is despite the improvements in SCM dynamics that were achieved by using a 5-min SCM time step instead of much larger (20 min) steps commonly used in GCMs.
 One way to characterize the aerosol-induced change in the cloud properties is through liquid water sensitivity, defined as a ratio of the change in LWP to the change in the column droplet number concentration, Nc [Han et al., 2002]. However, since the absolute values and therefore changes are so different in our simulations, a more appropriate way to quantify the aerosol effect on the LWP is through relative liquid water sensitivity, β, defined as a ratio of the normalized change in LWP to the normalized change in the column droplet number concentration [Han et al., 2002]
Figure 14 shows the time evolution of β for the three sets of runs. For much of the simulated period, all three models are consistent with each other and show that the relative liquid water sensitivity increases from near zero in the beginning to 0.3 and above by 12 hours. Han et al.  satellite data analysis shows β near zero or slightly positive relative cloud water sensitivity over much of the Unites States for October 1987. Han et al.  results are for afternoon and for optically thin cloud (τ < 15). Presented simulations cover late afternoon to early morning and τ is consistently less than 15 only in the two “clean” CM runs. Although the comparison is not direct, at least the results are not mutually exclusive. Interestingly, the reverse dependency, i.e., increasing liquid water path with decreasing CCN concentration, deduced from Jiang et al.  simulations of an ASTEX case is also consistent with Han et al. , who find negative liquid water sensitivity over the eastern Atlantic Ocean in July. The difference in the sign of β has been attributed to the effect of drizzle on cloud dynamics, which depends on whether the drizzle reaches the surface. If it does, then the boundary layer is stabilized, convection is suppressed, and upward transport of moisture is inhibited [Paluch and Lenschow, 1991]. In this case, more drizzle resulting from lower droplet number concentration leads to smaller LWP (positive liquid water sensitivity). Alternatively, if drizzle evaporates before reaching the surface, then the evaporative cooling can destabilize the subcloud layer resulting in the opposite effect, i.e., higher LWP in the presence of drizzle then without it (negative liquid water sensitivity). Note that at the end of our CM runs the relative liquid water sensitivity also turns negative (Figure 14). However, the LWP at that time is small and the statistical significance of this effect is not clear in this particular case.
 The combined effect of the changes in LWP and re on the optical depth is illustrated in Figure 15. Size-resolved microphysics maintains a near constant effective radius throughout each simulation, which is also evident in Figure 12. The CMs simulations also exhibit the largest change in re, which nearly doubles as Nccn is decreased from 1000 to 250 cm−3. Feingold et al.  quantified the indirect effect (IE) using the ratio of the relative change in mean cloud re to a relative change in aerosol optical depth, τa:
Since re ∝ LWC/τ and τa ∝ Nccn, IE can be expressed in our model variables as
 A plot of IE for the three model setups (Figure 16) highlights the largest re sensitivity to variation of Nccn in simulations with size-resolved microphysics (CMs), for which IE ranges from 0.2 to 0.4. For CMb and SCM runs, IE is consistently lower, i.e., between 0 and 0.2. In analyzing several cases observed at the SGP using ground-based remote sensing, Feingold et al.  obtained IE in the range from 0.02 to 0.16. These estimates are confined to updraft regions within clouds and constrained by constant LWP, in line with Feingold et al.'s  focus on isolating the Twomey effect. In contrast, Figure 16 reflects the combined IE, including changes in LWP as well as in droplet size (or, for CMs runs, more generally in size distribution spectrum). This representation of the simulation results confirms that in the considered case the combination of the first and second indirect effects increases several times over the first indirect effect alone.
 Differences between the CM runs with the size-resolved and bulk microphysics are not as dramatic as the differences between CM and SCM runs. However, variations in LWP and τ caused by different microphysical treatments are comparable to the effect of quadrupling the CCN concentration (Figures 6, 13, and 15). Thus it is imperative to apply the same dynamics and microphysics treatments in all simulations used to deduce the aerosol effects. Furthermore, in order to obtain the right estimate for the effect one must simulate cloud dynamics correctly, including dynamical effects of drizzle. This represents a significant challenge to large-scale models, in which the description of both drizzle and dynamics of boundary layer clouds are highly parameterized.
Appendix A:: Triangular Subgrid Treatment of Condensation and Autoconversion
 We assume the subgrid frequency distribution of s ≡ qw − q*, where qw, and q* are the total water mixing ratio and saturation water vapor mixing ratio, has a triangular shape with minimum, modal, and maximum values of s denoted by N, M, and X. The values of N, M, and X can be related to the mean, variance and skewness of the distribution of s. The grid cell mean cloud fraction f, cloud water mixing ratio c, and autoconversion rate cncr can be expressed For X < 0:
 In the presence of subgrid cloud several assumptions about cloud overlap and the subgrid distribution of vertical velocity are required. We assume maximum cloud overlap for adjacent cloudy layers. Under such an assumption the droplet number balance in the presence of fractional cloudiness can be expressed
where Nk is the grid cell mean droplet number mixing ratio in layer k, D is the vertical diffusivity, fk is the cloud fraction, Sk is the droplet source due to nucleation, Ak is the droplet loss due to autoconversion, Ck is droplet loss due to collection by precipitation, and Ek is the droplet loss due of evaporation within the layer. The first term represents the advective tendency of droplet number. The second and third terms are the turbulent transport of droplets between cloudy layers, assuming all droplets transported into the clear fraction of layer will evaporate. The droplet source due to nucleation includes contributions from nucleation at the base of existing clouds and nucleation within growing clouds. The nucleation at the base of existing clouds occurs only in the cloudy fraction lying above the clear fraction of the layer below, and depends on the spectrum of updraft velocity in that cloudy fraction. The nucleation within growing clouds depends on the characteristic vertical velocity w* in the growing part of the cloud and on the cloud fraction growth rate. These can be expressed
where Nn(w) is the number nucleated at updraft velocity w, p(w) is the pdf of w in the grid cell, and wmin is a minimum updraft velocity determined by assuming that the stronger updrafts occur in the cloudy fraction of the grid cell, so that for a Gaussian distribution of vertical velocity
where σw is the standard deviation of vertical velocity and is the grid cell mean vertical velocity. This equation can be solved for wmin by approximating the error function erf(x) by tanh(2x/) [Ghan et al., 1993], which yields the simple relation
The factor fk − fk−1 in equation (B2) is the clear sky fraction below layer k, assuming maximum cloud overlap. This factor need not be applied if one assumes that the strongest updrafts in layer k are associated with clouds penetrating from the layer below, so that the integration in equation (B2) is only applied up to an upper bound defined according to equation (B4) applied to the layer below. However, the droplet number concentrations produced by such a treatment are lower than desired so the treatment described by equation (B2) is used.
 For the droplet nucleation in the growing part of the cloud, the characteristic vertical velocity w* is approximated by σw, and only the contribution from growing clouds (increasing cloud fraction) is treated. For decaying clouds (decreasing cloud fraction) the droplet loss by evaporation is represented by
 This study was primarily supported by the U.S. Department of Energy Atmospheric Radiation Measurement Program, which is part of the DOE Biological and Environmental Research Program. The Pacific Northwest National Laboratory is operated for the DOE by Battelle Memorial Institute under contract DE-AC06-76RLO 1830. Minghua Zhang provided the objective analysis, and Jim Hudson provided the CCN measurements. Comments by three anonymous reviewers helped improve the paper.