To improve the microphysical parameterizations for simulations of the aerosol effects in regional and global climate models, the Morrison double-moment bulk microphysical scheme presently implemented in the Weather Research and Forecasting model is modified by replacing the prescribed aerosols in the original bulk scheme (Bulk-OR) with a prognostic double-moment aerosol representation to predict both aerosol number concentration and mass mixing ratio (Bulk-2M). Sensitivity modeling experiments are performed for two distinct cloud regimes: maritime warm stratocumulus clouds (Sc) over southeast Pacific Ocean from the VOCALS project and continental deep convective clouds in the southeast of China. The results from Bulk-OR and Bulk-2M are compared against atmospheric observations and simulations produced by a spectral bin microphysical scheme (SBM). The prescribed aerosol approach (Bulk-OR) produces unreliable aerosol and cloud properties throughout the simulation period, when compared to the results from those using Bulk-2M and SBM, although all of the model simulations are initiated by the same initial aerosol concentration on the basis of the field observations. The impacts of the parameterizations of diffusional growth and autoconversion of cloud droplets and the selection of the embryonic raindrop radius on the performance of the bulk microphysical scheme are also evaluated by comparing the results from the modified Bulk-2M with those from SBM simulations. Sensitivity experiments using four different types of autoconversion schemes reveal that the autoconversion parameterization is crucial in determining the raindrop number, mass concentration, and drizzle formation for warm stratocumulus clouds. An embryonic raindrop size of 40 µm is determined as a more realistic setting in the autoconversion parameterization. The saturation adjustment employed in calculating condensation/evaporation in the bulk scheme is identified as the main factor responsible for the large discrepancies in predicting cloud water in the Sc case, suggesting that an explicit calculation of diffusion growth with predicted supersaturation is necessary to improve the bulk microphysics scheme. Lastly, a larger rain evaporation rate below clouds is found in the bulk scheme in comparison to the SBM simulation, which may contribute to a lower surface precipitation in the bulk scheme.
 An accurate assessment of the aerosol effects in regional and global climate models is critical to reduce the uncertainty of anthropogenic forcing in future climate projections [IPCC, 2007; Tao et al., 2012]. Produced from anthropogenic and natural sources [Zhang et al., 2009, 2012; Zhang, 2010], atmospheric aerosols play an important role in regulating the radiative balance of the Earth-Atmosphere system, directly by reflection of the incoming solar radiation and indirectly by influencing cloud formation. In particular, aerosols by serving as cloud condensation nuclei (CCN) or ice nuclei (IN), also known as the aerosol indirect effect (AIE), may considerably impact the lifetime, albedo, and precipitation of cloud systems, through a complex interaction between cloud microphysics and dynamics [Williams et al., 1991; Nesbitt et al., 2000; Bond et al., 2002; van den Heever and Cotton, 2007]. For example, the aerosol effects on different types of cloud and precipitation systems have been shown to be highly nonlinear [Li et al., 2008a; Khain, 2009; Li et al., 2011]. Despite of substantial effort made to identify the governing factors and mechanisms in the aerosol-cloud-precipitation interaction [Fan et al., 2009a, 2009b, 2012b; Rosenfeld et al., 2008; Lee et al., 2008; Li et al., 2009a], current understanding of the aerosol impacts on the radiative budget and hydrological cycle of the climate system is still inadequate at the fundamental level. Quantification of the aerosol direct and indirect effects is still challenging and represents the largest uncertainty in climate predictions.
 There are numerous inherent deficiencies in the numerical methodologies employed to assess the aerosol effects, including insufficient description of the cloud spatial structure in 1-D and 2-D atmospheric models, coarse resolution in 3-D simulations [Khain, 2009], and simplified treatments of the cloud microphysical processes [Fan et al., 2012a]. Those difficulties account for large discrepancies and uncertainties in evaluating the aerosol climate effects.
 The representation of the microphysical processes in cloud models is essential in determining the cloud structure and development. Two types of microphysical schemes are commonly adopted to describe the size dependence of particles in cloud-resolving models, i.e., the spectral bin microphysics (SBM) and bulk microphysics. With the utilization of several tens of bins to describe the number and mass distributions of hydrometeors and aerosols, bin microphysics explicitly represents the physical processes on the cloud-resolving scale. However, because of large computational resources demanded by the bin microphysics, the bulk microphysics represents a more practical choice for long-term simulations in regional and global climate models. In the bulk microphysics, the shape of each hydrometeor spectrum is prescribed by a certain type of distribution function, such as the Gamma or Marshall-Palmer function. Empirical parameterizations are needed in the bulk microphysics to resolve subgrid processes in relatively coarse resolution regional and global scale simulations.
 Both SBM and bulk microphysical schemes have been widely employed in cloud-resolving models and mesoscale models in assessing AIE under diverse atmospheric conditions [Fan et al., 2007a, 2007b; Tao et al., 2012]. For example, a SBM scheme based on Khain et al.  has been incorporated into the Weather Research and Forecasting (WRF) model [Lynn et al., 2005a, 2005b; Khain et al., 2009; Fan et al., 2012a]. Li et al. [2008a, 2008b] has implemented a two-moment bulk microphysical scheme into the WRF model, which calculates the mass mixing ratios and number concentrations of aerosols and five types of hydrometeors and accounts for warm and mixed-phase microphysics. Another two-moment bulk microphysics with prognostic cloud number concentrations under the framework of WRF (hereafter referred to as “Bulk-OR”) developed by Morrison and co-authors [Morrison et al., 2005; Morrison and Grabowski, 2007; Solomon et al., 2009] is presently available and widely adopted for applications in the investigation of the aerosol effects.
 Several comparative studies have been conducted to elucidate the differences between bulk and spectral bin schemes and the associated AIE. Seifert et al.  found that the two-moment bulk scheme can be adjusted to produce results consistent with a spectral bin scheme for an isolated convection cell and a squall line. Morrison and Grabowski  suggested that warm cloud simulations with bulk schemes are comparable to the results from the bin microphysics, but the one-moment bulk scheme without predicting number concentrations of hydrometeors yields significant errors in the simulations of cloud microphysical properties. Other deficiencies in bulk schemes were reported by Li et al. [2009b, 2009c], suggesting that an over-estimated rain evaporation rate in the bulk scheme produces much stronger near-surface cold pool than the bin scheme simulation, which reproduces the distinct life cycles of convective clouds. Khain et al.  and Ekman et al.  pointed out that the bulk scheme with prescribed aerosol concentration fails to show the different precipitation sensitivities to aerosol concentrations in dry/humid environments. More recently, a modeling study by Fan et al. [2012a] revealed striking differences in cloud microphysical properties and opposite aerosol effects on convection and heavy precipitation between SBM and Bulk-OR implemented in WRF, mainly because of pre-described aerosols in the bulk scheme.
 Maritime stratocumuli (Sc) and continental deep convective cloud (DCC) represent two frequent and important categories of cloud systems. Realistic simulations of both cloud systems are crucial for assessment of AIE on regional and the global scales. For example, Sc plays an important role in the global radiative budget because of its large and persistent cloud cover and high reflectivity over the oceans [Wang et al., 2010a; Yang et al., 2011].
 This study aims at improving the cloud microphysical schemes for more realistic simulations of aerosol and cloud properties and more accurate quantification of the aerosol effects in regional and climate models. The Morrison double-moment bulk microphysical scheme presently implemented in the WRF model is modified by replacing the prescribed aerosols in the original scheme with a prognostic double-moment aerosol representation. Furthermore, the impacts of the parameterizations of the droplet diffusional growth and autoconversion and the selection of the embryonic raindrop radius on the performance of the bulk microphysical scheme are also evaluated. A maritime Sc system is investigated over the Southeast Pacific Ocean from an international program, VAMOS Ocean-Cloud-Atmosphere-Land Study (VOCALS), the major goal of which is to advance the scientific understanding of land-ocean-atmosphere coupled system over the Southeast Pacific region. The warm Sc system is selected because the microphysical and dynamical processes are relatively simple to identify the differences between bulk and SBM microphysics and to evaluate the causes and effects of different treatments in the microphysics. In contrast to the relatively good conceptual understanding in warm clouds [Rosenfeld, 2000; Lohmann and Feichter, 2005], AIE becomes more complicated when ice particles are present in convective clouds, and aerosols can be involved in different pathways to suppress or invigorate the strength of DCC [Tao et al., 2007; Zhang et al., 2007; Fan et al., 2008; Yuan et al., 2008; Wang et al., 2011]. In addition, a continental DCC system over southeast China from the Department of Energy/ARM Mobile Facility (DOE/AMF) China field campaign is also investigated in this present work to further illustrate the impacts of the microphysical schemes on AIE.
2 Microphysics Descriptions
 In this study, we employ a fast SBM version to conduct benchmark simulations, on the basis of the scheme by Khain et al.  that has been incorporated into the WRF model [Lynn et al., 2005a, 2005b; Khain et al., 2009, 2010; Fan et al., 2012a]. The fast version of SBM retains the advantages of the full SBM in Khain et al.  and produces cloud microphysical and dynamical structure as well as precipitation similar to the full SBM [Khain et al., 2009]. The two-moment bulk microphysics scheme with prognostic cloud number concentrations developed by Morrison and co-authors (i.e., Bulk-OR) is modified under the framework of WRF Version 3.1.1 by introducing a prognostic aerosol number and mass concentration. The performance of the modified bulk scheme with the added prognostic aerosol number and mass concentration (hereafter referred to as “Bulk-2M”) is evaluated by comparisons with atmospheric measurements and with SBM simulations. Table 1 summarizes the details of the three microphysical schemes employed in this present work.
Table 1. Descriptions of Model Simulations
Fast version of the spectral bin microphysics [Khain et al., 2005]
Two-moment bulk microphysics with prognostic cloud number concentrations and prescribed aerosol concentration by Morrison et al. ; aerosol activation by Abdul-Razzak et al. ; the autoconversion scheme developed by Khairoutdinov and Kogan 
Modified two-moment bulk microphysics by Morrison et al.  with prognostic aerosol mass and number concentrations
Bulk-2M with the autoconversion scheme developed by Khairoutdinov and Kogan . The radius of embryonic raindrop is modified to be 40 µm from its original value of 25 µm
Bulk-2M with the autoconversion scheme developed by Seifert and Beheng 
Bulk-2M with the autoconversion scheme developed by Liu and Daum 
Bulk-2M with the autoconversion scheme developed by Franklin 
 SBM uses four size distribution spectra to represent hydrometeors and CCN in the model, including water drops (cloud and rain), low-density ice (ice and snow), high-density ice (graupel and hail), and CCN. Each spectrum is composed of 33 mass bins, and the relationship between adjacent bins is determined by the function mk = 2* mk − 1. The Bulk-OR employs the Gamma function, N(D) = N0Dα exp(−λD), to describe the five hydrometeor types (i.e., cloud, rain, ice, snow, and graupel/hail). In this paper, the modifications to Bulk-OR are described in details, and the major differences in the warm-cloud microphysical processes between SBM and Bulk-OR are emphasized. However, the different treatments in ice-phase processes between SBM and Bulk-OR are beyond the scope of the present study. Also, in the present work, we focus on exclusively AIE, although the radiative effects of aerosols have important implications on many atmospheric processes [e.g., Li et al., 2005; Khalizov et al., 2009], including on cloud dynamics and direct climate forcing [IPCC, 2007; Zhang et al., 2008; Wang et al., 2010b].
2.1 Aerosol Activation
 In the SBM, supersaturation is explicitly predicted at each time step, and the critical radius of CCN (rNcrit) is calculated according to the Kölher theory using the value of supersaturation (S),
where A denotes the Kelvin effect and B denotes the solution effect. At each time step, CCN with radius greater than rNcrit is removed from the CCN spectrum and the mass of the activated droplets is added to the cloud spectrum. The size of the activated cloud droplet is calculated under the assumption of equilibrium over the activated droplets, if the radius of the original CCN particle (rN) is less than 0.03 µm. For large CCN particles with radius greater than 0.03 µm, the mass of water condensation on the particle is parameterized as , where K = 5 is used in this study [Khain et al., 2000]. CCN regeneration from evaporation of droplets and raindrops is also considered in SBM [Fan et al., 2009a, 2009b].
 There are two options in Bulk-OR to calculate the aerosol activation rate. One simple treatment is to parameterize the fraction of activated aerosols by the updraft velocity and assume the simple power-law CCN spectra using two empirical parameters [Twomey, 1959; Fan et al., 2012a]. A more sophisticated treatment considers a wider range of governing parameters [Abdul-Razzak et al., 1998]. In the latter parameterization, each mode of the aerosol spectrum is represented by a single lognormal size distribution, as shown in equation (2),
where rd is the dry aerosol radius, rdg is the geometric mean radius, N is the total number concentration of aerosols, and σg is the geometric standard deviation. In Bulk-OR, all three parameters are prescribed for each distribution function. There is no degree of freedom in the aerosol spectra, and the amount of aerosols that serve as CCN to form cloud droplets remains constant in the simulation. As suggested by Fan et al. [2012a], the cloud droplet concentration can be significantly over-predicted because of a fixed aerosol spectra used in the activation process of the bulk schemes. To overcome this deficiency, two prognostic variables of aerosols, i.e., the aerosol number concentration and mass mixing ratio, are introduced into the bulk scheme in the present work (i.e., Bulk-2M). During the activation process, activated aerosols to form cloud droplets are removed from the aerosol spectra and added to the cloud droplet spectra. The aerosol number and mass concentration are fixed at the lateral boundaries of the domain to represent the external source of aerosols. By predicting both the number and mass concentration of aerosols, the total aerosol amount and the geometric mean radius of the aerosol spectra are time dependent because of removal of aerosols to form cloud droplets or addition of aerosols from the boundary sources. Advective and convective transports of aerosols are accomplished by the dynamical core of the model. The regeneration of aerosols due to evaporation of cloud droplets and raindrops is not included in the current scheme. Following the parameterization by Abdul-Razzak et al. , the fraction of activated aerosols at each time step is parameterized by
and the fraction of activated aerosol mass concentration is given by
where Sg is the critical supersaturation of the particle with mean radius rdg. The maximum supersaturation is parameterized by two dimensionless terms ζ and η, which are dependent of the vertical velocity. The ratio of the activated aerosol number concentration to the time step is considered as the activation rate and incorporated to the tendency budget of cloud droplets. Note that the increase in the computational time from the implementation of the two new prognostic variables in Bulk-2M to account for the aerosol budgets is relatively minimal, in constrast to the low computational efficiency of SBM.
2.2 Diffusion Growth/Evaporation of Liquid Drops
 Since supersaturation is explicitly predicted in the SBM by solving the equation for supersaturations with respect to water and ice, the diffusion growth/evaporation rate of liquid drops is directly calculated based on the supersaturation in each grid cell. The associated numerical equations are taken from Pruppacher and Klett  and fully discussed by Khain et al. . To better resolve the condensation/evaporation processes in the SBM, sub-timestep iteration is employed and the condensation/evaporation rate is calculated over each sub-timestep Δtdiff. In the SBM simulation, we set Δt = 4*Δtdiff. To avoid artificial broadening in the droplet spectrum as a result of diffusional growth and collisions, the remapping scheme are updated to conserve three moments of the hydrometeor size distributions (i.e., concentration, mass, and radar reflectivity), in contrast to the commonly used scheme of Kovetz and Olund  that conserves only concentration and mass during the remapping [Khain et al., 2008].
 In Bulk-OR, the supersaturation is not calculated explicitly and a simplified liquid saturation adjustment strategy is utilized following the equation from Dudhia :
where qv and qvs are the current vapor mixing ratio and saturation vapor mixing ratio, respectively. The above equation implies that the cloudy grid cells are maintained at 100% relative humidity. If the air is subsaturated, cloud/rainwater is evaporated continuously until saturation is reached within a time step, or if the air is super-saturated, vapor condensation removes the supersaturation within that time step.
2.3 Autoconversion From Cloud Droplets to Raindrops
 Autoconversion represents a fundamental process in the bulk schemes to produce embryonic raindrops through diffusion and collection growth of cloud droplets in warm clouds. In the SBM, cloud droplets and raindrops share the same spectra, and the transition from droplets to raindrops is embedded in the stochastic kinetic kernel of collisions, although a threshold size needs to be set to distinguish between droplets and raindrops when integrating over the size spectrum to determine the droplet and raindrop number and mass concentrations. In the present work, the threshold size of 40 µm is used. In the bulk scheme, a numerical expression of the conversion process of cloud droplets to raindrops must be explicitly given. Rotstayn  reported that liquid water path simulated in the global climate model was considerably sensitive to the autoconversion parameterizations. Recently, the need to improve the parameterization of the autoconversion rate has been emphasized because of increasing interests in the studies of indirect aerosol effect on cloud and precipitation [Liu et al., 2004]. Due to large uncertainties associated with the autoconversion process, various types of parameterization in the bulk models have been developed to represent this process.
 The default autoconversion scheme used in Bulk-OR is a two-moment parameterization developed by Khairoutdinov and Kogan  (hereafter referred to as KK2000). The autoconversion rate is derived by fitting the results of large eddy simulations of marine boundary layer clouds that used explicit bin microphysics with analytical functions,
 Note that the radius of embryonic raindrop in the KK2000 scheme is set to be 25 µm. To improve the bulk microphysical scheme, the effects of different autoconversion parameterizations are evaluated. Three additional autoconversion schemes are implemented to the Bulk-2M for sensitivity experiments (Table 1).
Seifert and Beheng  developed a series of parameterizations of the collision/coalescence process between liquid drops directly from the stochastic collection equations (hereafter referred to as SB2001). The autoconversion rate is formulated as a function of cloud mass ratio and cloud number concentration:
where ν is the spectral shape parameter, τ is the ratio of rain mass to the total liquid water mass, Φ is a universal function only depending on τ, and kc and x are constant. The radius of the embryonic raindrop in the SB2001 scheme is set to be 40 µm.
Liu and Daum  derived another Kessler-type autoconversion scheme theoretically (hereafter referred to as LD2004), suggesting a strong dependence of the autoconversion rate on the relative dispersion of the cloud droplet size distribution in addition to liquid water content and droplet concentration. Therefore, by incorporating the relative dispersion of the cloud droplet size distribution in LD2004, the coarse assumption inherent in the traditional Kessler-type parameterizations, such as a fixed collision kernel, can be eliminated. The analytical expression of the autoconversion rate in LD2004 is
where H is the Heaviside step function, β6 is a non-dimensional parameter only depending on the relative dispersion of the droplet spectra, R6 is the mean radius of the sixth moment of cloud size spectra, and R6c is the critical mean radius.
 Turbulent mixing can increase the collision rates of droplets [Pinsky et al., 2006; Franklin et al., 2007]. To consider the effect of turbulence on the collisions and coalescences between liquid drops, Franklin et al. [2007, 2008] developed a set of warm rain parameterizations using the turbulent collision kernels (hereafter referred to as F2008). The autoconversion rate is explicitly related to the dissipation rates of the turbulent kinetic energy predicted by the model:
where the collision enhancement factor is determined by the dissipation rates of the turbulent kinetic energy.
3 Case Studies and Discussions
3.1 Maritime Stratocumulus Clouds From VOCALS
3.1.1 Experiment Design
 The development of stratocumulus clouds and the formation of drizzle precipitation occurring on 28 Oct 2008 over the Southeast Pacific region from the VOCALS-Ex field campaign are simulated with WRF V3.1.1. Three domains are used in the model with the horizontal resolutions of 12 km, 3 km, and 1 km, as shown in Figure 1a. The finest-grid domain covers the flight track of the NSF/NCAR C130 Research Aircraft on that day. Sixty-five vertical levels are used with a resolution of about 30 m within the boundary layer. Such a high vertical resolution is needed for realistic simulation of the moisture and supersaturation profile of stratocumulus clouds. The Goddard shortwave radiation scheme and the RRTM longwave radiation scheme are employed in the simulations. Since the horizontal resolution of 1 km is still relatively coarse to resolve turbulent updrafts and eddies, subgrid-scale parameterizations play an important role in the Sc simulations [Yang et al., 2011]. The Yonsei University (YSU) scheme is adopted to parameterize the planetary boundary layer processes [Hong et al., 2006]. The heat eddy diffusion coefficient of the YSU scheme is adopted in the bulk microphysical scheme for the droplet activation calculation. The “one-way nest down” technique is employed for the three domains, so that different microphysical schemes can be used for certain domain with the same meteorological and aerosol conditions. Specifically, the simulations of the outer two domains are carried out first by using the Bulk-OR scheme to produce the initial and lateral boundary meteorological conditions for the finest-grid domain. Subsequently, sensitive simulations with different configurations of microphysical schemes are conducted over the finest-grid domain.
 The surface aerosol size distribution over the southeast Pacific region during the VOCALS-Ex field campaign was measured by a Differential Mobility Particle Sizer (DMPS) in combination with an Aerodynamic Particle Sizer (APS) aboard the NOAA RV Brown Research Ship. The ranges of particle diameter detected by DMPS and APS are 0.02 to 0.8 µm and 0.96 to 10 µm, respectively. On 28 October, the ship routes were located in the south region within Domain 2. The measured size distribution of aerosols is shown in Figure 1b. It is clear that aerosols in the Aitken and accumulation modes dominate the spectra and very few aerosol particles exist in the coarse mode. Hence, a single lognormal curve is applied to fit the observational data, yielding a total aerosol number concentration of 588 particles/cm3 to be consistent with the observation. The aerosol mass mixing ratio is 2.4 × 10−11 g/cm3. Ammonium sulfate is assumed to be the principal chemical composition of aerosols, although other constituents, particularly organics, can also be present in ambient aerosols [Zhang et al., 1996a; Zhao et al., 2005, 2006; Wang et al., 2010b]. Aerosols in both the SBM and bulk schemes are initialized by the same spectra. Compared to typical maritime conditions over the southeast Pacific region, the above aerosol conditions (also referred to as the control case) correspond to elevated aerosol loading, which is likely under the influence of continental flows [Yang et al., 2011].
3.1.2 Effects of Aerosol Representation on Sc Simulations
188.8.131.52 Aerosol Evolution
 The simulated aerosol evolutions with Bulk-OR, Bulk-2M, and SBM are presented in Figure 2. Although all of the model simulations are initiated by the same initial aerosol concentration on the basis of the field observations, a large difference in the aerosol concentration predicted by Bulk-OR compared to those predicted by Bulk-2M and SBM occurs in the first few hours of the simulations, attributable to the efficient nucleation scavenging in the Bulk-2M and SBM under the favorable meteorological conditions to form clouds within the maritime boundary layer. Since the total aerosol concentration simulated by Bulk-2M is close to that by SBM (Figure 2) and the only aerosol sink is CCN activation in those simulations, the activation parameterization by Abdul-Razzak et al.  in Bulk-2M yields a similar performance with the calculation based on the Köhler theory in the SBM. Our offline tests of both nucleation schemes further indicate that the activation parameterization by Abdul-Razzak et al.  exhibits the best agreement with the sectional approach of activation when the environmental updraft velocity is moderate (1–3 m/s). The increase of the aerosol concentration after 0500 UTC in Figure 2 is explained by the fact that fresh aerosols are allowed to enter from the lateral boundaries and slowly replenish the aerosol populations within the domain. Although there is no representation of the CCN regeneration after the complete droplet evaporation in Bulk-2M, the good agreement of simulated aerosol concentrations between Bulk-2M and SBM that accounts for the CCN regeneration from the droplet evaporation [Fan et al., 2009a, 2009b] indicates that the CCN regeneration does not significantly contribute to the total CCN concentration in the Sc case with CCN sources set at the lateral boundaries.
184.108.40.206 Comparison With Field Measurements
 Measurements of cloud properties by the NSF/NCAR C130 Research Aircraft (in the innermost domain from 0900 to 1300 UTC), including liquid water content (LWC) from a PMS Hot Wire Liquid Water Probe (King Probe), cloud number concentration (Nc), and cloud effective radius (Rc), are employed to evaluate the performances of the different microphysical schemes. The number concentration and the effective radius of cloud droplets within a size range from 1 to 50 µm are measured by a PMS Cloud Droplet Probe (CDP).
 Comparisons of the vertical distribution of cloud properties from observation and simulated by the three microphysical schemes—SBM, Bulk-OR, and Bulk-2M—are summarized in Figure 3. All three schemes predict similar LWC profiles, i.e., increasing from 500 m to 1300 m. The observational data lie within the uncertainty range of the simulated profiles of LWC, indicating that the three microphysical schemes simulate LWC reasonably well. In particular, SBM has a better agreement with the field measurement than to the bulk microphysics simulations. SBM reproduces the peak of the observed LWC at about 1300 m, while the bulk simulations predict smaller peaks at lower altitudes. There are noticeable differences in Nc predicted (second column of Figure 3) among SBM, Bulk-2M, and Bulk-OR. SBM exhibits the best performance, with the simulated Nc reproducing well with the observed values. Most of observed values are far away from the uncertainty range of Bulk-OR, which overestimates the total Nc by a factor of 5. The revised scheme Bulk-2M, in which the aerosol number and mass are prognostic, shows a significant improvement in the simulation of Nc, and the observed values lie within the uncertainty range predicted by Bulk-2M. Because of the dramatic overestimation of Nc, Rc in Bulk-OR is largely underestimated (third column of Figure 3), while Bulk-2M exhibits the best performance among the three schemes to reproduce the observed Rc profile. The good agreement between the SBM simulation and in situ measurements indicates that SBM can be used as the benchmark simulation to evaluate the performances of the bulk microphysics.
 The time series of the liquid water path (LWP), height of cloud base, cloud thickness, and cloud radar reflectivity from the airborne measurements are compared with the simulations of Bulk-2M, Bulk-OR, and SBM. The airborne measurements show considerable spatial variations in the cloud properties, reflecting a complex three-dimensional structure for Sc. Figure 4a presents a comparison of the LWP measured by water vapor radiometer on the C130 aircraft with model simulated LWP. The SBM results show the best agreement with the temporal variation of LWP long the flight path, while Bulk-OR and Bulk-2M consistently underpredict LWP. There is no significant difference between the LWP simulated by Bulk-OR and Bulk-2M, mainly because the same saturation adjustment strategy is employed for the liquid water formation. The cloud base height and cloud thickness were measured by the Wyoming cloud radar and lidar equipped on the C130 Aircraft. Figure 4b shows all three simulations predict the cloud base heights around 1 km, consistent with the observations. However, the SBM and bulk schemes show a large discrepancy in simulating cloud thickness. Figure 4c shows that only SBM reproduces the temporal evolution of the observed cloud thickness. Both Bulk-OR and Bulk-2M predict much thinner clouds during most of the simulation period. The lower cloud depth and lower LWC explain the lower LWP in Bulk-OR and Bulk-2M. Since there is no significant improvement of LWP and cloud thickness in Bulk-2M compared to Bulk-OR, it is possible that the simple treatment of condensation/evaporation in the bulk scheme, i.e., the saturation adjustment, may explain the discrepancies between the bulk and SBM simulations (to be discussed later). The measured reflectivity at 100 m (Z100) from the Wyoming 94GHz W-band cloud radar on the C130 Aircraft is compared with the model simulated reflectivity in Figure 4d. The derivation of Z100 from the model simulated rainfall rate at 100 m (R100) follows the empirical Z-R relationship: Z100= 57(R100/24)1.1 [Comstock et al., 2004; Bretherton et al., 2010] and R100 is approximated by the simulated surface rainfall rate. Both SBM and Bulk-2M predict drizzle formation (Z100 > 0 dBz) during 0900 to 1300 UTC, as detected by the radar, while drizzle is largely shut off in Bulk-OR. SBM exhibits a better agreement on the magnitude of Z100 with the radar measurement than Bulk-2M, which tends to underpredict the radar reflectivity during the simulation. The difference between surface rainfall rate and R100 can partially explain the underprediction of reflectivity in all the model simulations.
220.127.116.11 Effects on the Cloud Properties and Microphysical Processes
 A comparative analysis of the domain-averaged (including both cloudy and non-cloudy grids) properties of clouds and aerosols is carried out to evaluate the changes implemented to the bulk microphysics. Figure 5a shows that in contrast to the large over-prediction of Nc in Bulk-OR, Bulk-2M predicts Nc much closer to that simulated by SBM because of the significantly reduced droplet nucleation rate (as shown in Figure 6a) from the prognostic treatment of the aerosol size spectrum. The averaged Nc over the cloudy-only grids in SBM, Bulk-2M and Bulk-OR is about 50, 150, and 500 per cm3, respectively. Since the relatively larger droplet size in the maritime cloud is favorable for the collision/coalescence process between the cloud droplets and raindrops and there is significant drizzle precipitation in this case, the cloud droplet concentration is reduced significantly after the activation process. The temporal evolution of Qc averaged over the domain shows that both SBM and the bulk schemes predict similar diurnal cycles, which are regulated by the absorption of solar radiation and the consequent suppression of the total longwave radiative cooling and circulations during the daytime [Wood, 2012]. The comparison of Qc between the different schemes shows that SBM predicts a larger Qc than the bulk schemes. Since the cloud top radiative cooling driven by the liquid water content is the primary cause of the Sc formation [Wood, 2012; Morrison et al., 2011], the less cloud top cooling for the lower Qc in Bulk leads to the weaker turbulence and vertical mixing. Such a feedback from the radiation-dynamics interaction further contributes to the less Qc in Bulk than in SBM. The vertical condensation/evaporation rate profiles in Figure 6b reveal that even though the condensation rates near the cloud top are comparable between the three simulations, the peak droplet evaporation rates in the bulk schemes are much higher. The disparity in the condensation/evaporation rate between SBM and bulk schemes can be linked to the differences of the condensation/evaporation parameterization, as shown in comparative studies between the saturation adjustment in the bulk schemes and the explicit calculation of the condensation/evaporation rate with the predicted supersaturation in SBM, to be discussed in the next session.
 Since Rc is significantly smaller in Bulk-OR, the collision/coalescence processes between cloud droplets are suppressed to inhibit formation of raindrops. The vertical profiles of the autoconversion rate in Figure 6c show that by improving the CCN activation processes, the autoconversion efficiency in Bulk-2M is enhanced by a few orders of magnitude, resulting in a similar raindrop number concentration (Nr) as SBM (Figure 5c). On the other hand, a much smaller autoconversion rate in Bulk-OR results in significantly reduced Nr, which is only about 1% of Nr predicted by SBM. A striking difference in the simulated rainwater content (Qr) between Bulk-OR and SBM is evident in Figure 5d. The amount of domain-averaged Qr from Bulk-OR is nearly negligible compared to the large amount of rainwater in SBM. Consequently, drizzle precipitation is completely inhibited in Bulk-OR, largely because of the presence of numerous but too small cloud droplets and negligible formation of raindrops. With the prognostic treatment of CCN in Bulk-2M, Nc is significantly reduced and Rc is much larger, leading to a higher autoconversion efficiency that produces much more raindrops than Bulk-OR. Therefore, more surface precipitation is produced in Bulk-2M (Figure 5e). A comparison of the updraft velocities in the core grids between the three microphysical schemes in Figure 5f shows that the updraft in SBM is slightly stronger than the updrafts in the Bulk simulations. This result is consistent with the higher Qc in SBM (Figure 5b), because a stronger updraft is more favorable for cloud formation.
 From the comparison of the microphysical process rates between Bulk-OR and Bulk-2M (Figures 6c–6f), it is clear that the efficiencies of accretion of cloud droplets by raindrops and raindrop evaporation in Bulk-2M is significantly enhanced compared to Bulk-OR, indicating that the improved aerosol representation exert large impacts on the microphysical processes. Figure 6f shows that the rain evaporation parameterization in Bulk-2M produces a evaporation rate of about 21.2% higher than SBM at the grid points when raindrops are present, although the rain mass is significantly smaller in Bulk-2M. Hence, the bulk scheme tends to predict strong rain evaporation compared to SBM, which also contributes to less surface precipitation in Bulk-2M. The finding of strong rain evaporation with the bulk parameterization is consistent with previous modeling studies [Li et al., 2009b; Khain et al., 2009].
3.1.3 Effects of Diffusional Growth Parameterizations on Sc Simulation
 Note that the improved scheme Bulk-2M still predicts significantly lower Qc than SBM. To determine the cause for this difference, sensitivity experiments of a short period (3 h) are conducted using SBM and Bulk-2M, in which all the other microphysical processes, such as collision/coalescence and sedimentation processes of hydrometeors, are turned off except for the droplet nucleation and diffusion growth. The radiation processes are also turned off to preclude any feedback from the radiative cooling of the cloud top on the dynamics. The sensitivity simulations with different microphysics start from the same initial condition at 0000 UTC, 28 October. During the first hour of the simulations (0000–0100 UTC), Qc over cloudy points remains higher in the SBM simulation than the Bulk-2M simulation after the stratocumulus clouds form within the boundary layer due to the abundant vapor supply from the ocean, as shown in Figure 7a. Since the droplet nucleation rate is similar between the SBM and Bulk-2M simulations (Figure 7b), the condensation/evaporation processes impose the major influence on the liquid water budget. Figure 7c shows that the condensation rates, averaged over the grid points in presence of cloud droplets, are lower in the Bulk-2M simulation that utilize the saturation adjustment compared to SBM in which explicit supersaturation is calculated for the diffusion growth. Therefore, in Sc case, the lower Qc in the bulk simulations is mainly attributed to the saturation adjustment approach employed for the condensation/evaporation processes. The updraft velocity is shown to be higher in SBM than that in Bulk-2M (Figure 7d) during the first hour simulation, indicating that the latent heat release from water vapor condensation feeds to the cloud dynamics. Through the comparison of the last 2 h simulation (0100–0300 UTC) and the first hour simulation, it is evident that the discrepancies of Qc, condensation rate, and updraft velocity between SBM and Bulk-2M simulations get significantly enlarged (Figures 7e–7h), supporting that there are efficient feedbacks between the cloud dynamics and microphysics. The unrealistic high Qc near the surface during the last 2 h simulation is attributed to the large updraft at low levels (Figure 7h), since all sedimentation processes are turned off in this sensitive experiment. Note that the cloud droplets and rain drops share one size spectrum with an empirical cutoff size of 40 µm in SBM, in contrast to the bulk schemes that use two separate spectra for cloud and rain. These inherent differences between SBM and bulk schemes may also contribute to the different Qc and Qr in the simulations.
 As a result, the treatment of the diffusion growth may need further improvements in simulating the mass content of hydrometeors and precipitation using the bulk schemes. On the other hand, the explicit calculation of the diffusional growth from the predicted supersaturation adopted in SBM may be impractical for regional or global climate models, because of coarse resolutions. With the advances in computation power, future regional/global simulations at the cloud-resolving scales using the bulk schemes with explicit calculation of diffusional growth, such as the scheme of Li et al. [2009b], may achieve better cloud simulations and more accurate assessment of AIE.
3.1.4 Effects of Autoconversion Parameterizations on Sc Simulation
 As noted above, Qr and precipitation predicted by Bulk-2M are much lower than those by SBM. In addition to the contribution of lower Qc in Bulk-2M, there are several other factors relevant to the budget of Qr in this warm cloud case, including autoconversion, collection of cloud droplets by raindrops, and evaporation and sedimentation of raindrops. In the cloud layers, the simulated accretion rate of cloud droplets by raindrops and the evaporation rate of raindrops are on the same order of magnitude but exert opposite impacts on the budget of Qr. Therefore, the autoconversion rate is crucial to the determination of Qr. To examine the effects of the autoconversion schemes on Qr and the drizzle precipitation, three different autoconversion schemes are considered (i.e., SB2001, F2008, and LD2004) in the sensitivity experiments.
 The embryonic raindrop radius is an adjustable parameter in the autoconversion schemes, and it is difficult to gauge this quantity by in situ measurements since it only describes the size of the raindrop at the newly formed stage. In addition to the original radius of 25 µm for embryonic raindrops used in the KK2000 autoconversion scheme, an alternative value of 40 µm is also considered for consistency with the other schemes in the sensitivity tests. A comparison of Nr between the original radius of 25 µm (Figure 5c) and the modified radius of 40 µm (Figure 8c) for embryonic raindrops in KK2000 shows that the scheme with the modified radius predicts much lower Nr but larger raindrops, consistent with SBM simulation. This suggests that the size of 40 µm is appropriate to reflect raindrop formation in stratocumulus clouds.
 Figures 8c and 8d indicate that the different autoconversion parameterizations produce distinct effects on the production rates of raindrops under the same model configurations. LD2004 and F2008 predict higher autoconversion rates than the other schemes. With more efficient cloud-to-rain transformation, Qc and Nc are reduced, while Qr and Nr are elevated in LD2004 and F2008. Compared to the SBM results, the simulations of Nc, Qr and Nr in LD2004 and F2008 are significantly improved because of the increased autoconversion rate. In F2008, the eddy dissipation rate of the turbulent kinetic energy is as high as 800 cm2 s−3, indicating that turbulence contributes significantly to the efficient collision/coalescence processes [Seifert et al., 2010; Benmoshe et al., 2012]. Furthermore, drizzle reaching to the surface is enhanced by two times in these two schemes, which is also close to the SBM results (Figure 8e). Therefore, for maritime stratocumulus clouds, the autoconversion schemes of LD2004 with the dispersion factor considered and F2008 with the turbulence effects incorporated show much better performance than those of the other schemes. Li et al.  also suggested that the precipitation simulated in a cumulus cloud case exhibited a large variation among the different autoconversion parameterizations, and among them, LD2004 was a more physically meaningful parameterization than the other autoconversion schemes.
3.1.5 Effects of Aerosol Representation on AIE
 To investigate the effects of aerosol loading on stratocumulus clouds using the bulk microphysical scheme with/without the prognostic aerosol representation, simulations are performed with initialization for different aerosol loadings. As discussed above, the initial aerosol number 588 particles/cm3 and mass concentration of 2.4 × 10−11 g/cm3 in the control run likely represent the maritime polluted conditions under of the influence of continental outflows. A maritime clean scenario containing one sixth of the aerosol amount in the polluted case is also considered, i.e., with the aerosol number and mass concentration of 98 particles/cm3 and 4 × 10−12 g/cm3, respectively. Figure 9 shows that in both polluted and clean cases, Bulk-2M predicts much closer Nc, Nr, LWC, Rc, and accumulated precipitation to SBM than Bulk-OR, indicating that Bulk-2M consistently outperforms Bulk-OR independent of the initial aerosol concentrations. All three simulations predict elevated cloud droplet concentration, enhanced liquid water content, reduced raindrops, and suppressed drizzle precipitation in the polluted case when the aerosol concentration is 6 times higher. Since the saturation adjustment does not account for the influence of the droplet size distribution on the diffusional growth, the enhanced LWC in the polluted case simulated by the bulk schemes can be attributed to the smaller terminal falling speed of the size-reduced droplets and the consequent impacts on the dynamical conditions in the polluted case compared to the clean case. Those effects of sulfate aerosols on the stratocumulus cloud are consistent with previous observations [L'Ecuyer et al., 2009; Zheng et al., 2011]. The cloud optical depth is mainly determined by LWP and Rc for liquid clouds. Figure 9e shows that Bulk-2M predicts a cloud optical depth closer to SBM in both the control and clean cases, while Bulk-OR produces more reflective clouds with a larger cloud optical depth, particularly in the control case, leading to much larger aerosol indirect forcing. Hence, although the SBM and bulk microphysics predict the same sign for AIE on shallow stratocumulus and drizzle precipitation, the magnitudes of radiative forcing of AIE can be significantly improved using more realistic aerosol representation in the bulk microphysical schemes.
3.2 Continental DCC in Southeastern China
3.2.1 Experiment Design
 A convective cloud system associated with a thunderstorm event that occurred in Southeastern China on 17 July 2008 is simulated with the same WRF model setup and domain configuration as in another previous study [Fan et al., 2012a]. The simulations are carried out over two nested domains with 12 and 2.4 km grid spacing from 1200 UTC, 16 July, to 0000 UTC, 18 July. The analysis region covers the area (30.5°N–33.8°N and 113.5°E–117.5°E) within the inner domain. Comparison of the simulation with surface-based measurement of aerosols and cloud properties from AMF-China field campaign has been previously discussed in Fan et al. [2012a]. Similar to the Sc case, the differences in the DCC properties and AIE among the simulations with SBM, Bulk-OR, and Bulk-2M are examined. In contrast to the power-law aerosol size distribution used in the previous study by Fan et al. [2012a], the CCN size spectrum in SBM, Bulk-OR, and Bulk-2M in the present work is initialized by two-mode lognormal distributions. The total number concentration of aerosols (consisting of ammonium sulfate) in the polluted case (P-case) is 8600 particles/cm3, similar to the measured aerosol concentration in Jinan urban area, China [Fan et al., 2012a]. In addition, a clean condition (C-case) is considered, with an aerosol concentration that is 6 times smaller than that in the P-case. Figure 10 presents the initial aerosol concentrations in the P-case and in the C-case.
3.2.2 Effects of Aerosol Representation on DCC Simulation
 Compared with the SBM results, the improvement in the simulated cloud droplets using Bulk-2M is clearly evident. Figures 11a and 11b show that the domain-averaged Nc and Rc predicted by Bulk-2M exhibit a good agreement with those by SBM, because of a more realistic activation rate (Figure 12a). The Nc predicted by Bulk-OR is more than 2 times higher than that by SBM and Rc is significantly underpredicted correspondingly. The magnitude and temporal pattern of the CCN number concentration in Bulk-2M also match well with those from SBM (Figure 11c), in contrast to the unrealistic high CCN level in Bulk-OR. For the summation of cloud water and rainwater mass, LWC in the bulk simulations shows similar patterns in the temporal variation with SBM (Figure 11d) and the peak LWC values at 15:00 LST are comparable between the bulk and SBM simulations. However, the total LWC is reduced by 20% in the bulk simulations compared to SBM. An examination of cloud droplet diffusional growth rate in Figure 12b shows that saturation adjustment in the bulk simulations tends to predict stronger condensation rate than the explicit condensation calculation in SBM. In the DCC case, the larger in-cloud updraft velocity leads to a higher supersaturation, and the phase relaxation time is longer than the time step. Therefore, the influence on liquid drops from the mixed-phase processes, such as ice nucleation, melting of ice, or graupel particles and the collection by ice particles, is determinant in regulating the amount of LWC in the DCC case [Mitchell et al., 1990; Wooldridge et al., 1995; Zhang et al., 1996b]. For the summation of ice, snow, and graupel mixing ratio, the ice water contents (IWC) in the bulk simulations are also underpredicted by 30% compared to SBM (Figure 11e), even though Bulk-2M shows some improvement to elevate the LWC and IWC after 15:00 LST. The temporal variation and the peak value of the rainfall rate are comparable between SBM and bulk simulations (Figure 11f), but the total accumulated precipitation is higher in the SBM simulation, which can be explained by the elevated LWC and IWC in SBM.
 A comparison of the different microphysical processes in DCC is presented in Figure 12. The efficiency of the autoconversion rate in Bulk-2M is significantly enhanced compared to Bulk-OR (Figure 12c), but the collection rate of cloud droplets by raindrops vary insignificantly in the modified aerosol scheme (Figure 12d). The cloud base heights vary considerably from a few hundred meters to a few kilometers during the DCC event. Because of the occurrences of the shallow cumulus, there are droplet activations and collisions between the hydrometeors occasionally taking place at a few meters above the surface as shown in Figure 12. As discussed above in the Sc case, the rain evaporation in the bulk scheme tends to be stronger than SBM, which contributes to the smaller surface precipitation. For the DCC case, the rain mass and rain rate are much closer between SBM and the bulk schemes, but the rain evaporation rates from both the bulk runs are about 2 times larger than SBM, as depicted in Figures 12e and 12f. The parameterization of rain evaporation in the bulk scheme reduces the mean size of raindrops after evaporation, which is unrealistic and deteriorates the evaporation process [Li et al., 2009b]. In reality, small droplets evaporate more efficiently than large droplets, leading to a larger mean size in the droplet spectrum. Hence, SBM can accurately mimic this process and provide more realistic rain evaporation rate.
 The cloud properties and precipitation in the DCC case reveal relatively low sensitivity to the different autoconversion schemes. It is evident from Figure 13 that the four different autoconversion schemes, including KK2000 derived from marine boundary layer clouds, predict a similar amount of the liquid water and number concentration of cloud droplets in the DCC case. Even through the raindrop number concentration (Nr) differs due to the modified autoconversion rates (Figure 13c), surface precipitation shows very limited changes (Figure 13f). The similar performances of the different autoconversion schemes in DCC demonstrate that the mix-phase processes play a dominant role in regulating the hydrometeors contents.
3.2.3 Effects of Aerosol Representation on AIE
 Figure 14 summarizes the effects of aerosol loading on the droplet concentration, LWC, IWC, and precipitation from SBM, Bulk-OR, and Bulk-2M. Under the polluted condition, all three simulations predict more Nc relative to the clean case. However, Nc in Bulk-2M is close to SBM in both polluted and clean cases, while Bulk-OR predicts 2–3 times higher Nc relative to Bulk-2M and SBM. Both SBM and Bulk-2M predict higher LWC and IWC under the polluted condition. In SBM, small droplets with low terminal velocity limit the collision/coalescence process, prolong the diffusional growth of cloud droplets, and lead to a larger LWC. In Bulk-2M, as we discussed in the Sc case, the slower sedimentation of droplets with the smaller sizes in the polluted case could contribute to the higher LWC. Because of the strong upward motion in DCC, small cloud droplets have more times to be lifted above the freezing level, contributing to more efficient ice particle formation. The higher amount of ice-phased particles with the elevated aerosol loading in Bulk-2M further contributes to the larger LWC below the freezing level when more ice-phased particles melt to liquid drops. Previous observational and modeling studies have demonstrated a similar elevation of liquid water and ice water content under high aerosol loading in humid environments [Khain, 2009; Li et al., 2011; Wang et al., 2011]. However, Bulk-OR exhibits an opposite trend in the aerosol effects on the IWC (Figures 14c), because of the inefficient freezing and riming processes in the extremely polluted case simulated by Bulk-OR. Therefore, less ice-phase particles settle below the freezing level and melt to liquid drops, leading to the smaller LWC in Bulk-OR (Figures 14b). Such a reduction of LWC from the mixed-phase processes exceeds the enhancement of LWC from the inefficient sedimentation of cloud droplets in the polluted case. Consequently, SBM and Bulk-2M predict enhanced precipitation by aerosols, while Bulk-OR predicts suppressed precipitation as shown in Figure 14d. The evaporation of precipitation below the clouds induces significant feedback on the cloud dynamics [Khain et al., 2005; Tao et al., 2012].
 Bulk-2M and Bulk-OR also produce distinct convection development under different aerosol loading. Figure 15 shows the profiles of time series of updraft velocities from the three simulations under polluted and clean conditions. Increased updraft velocities under polluted condition are clearly evident in SBM and Bulk-2M, but in Bulk-OR, updraft velocities are weaker under the polluted condition than in the clean condition during most times except at 8:00–12:00 LST. The most intensive updraft in Bulk-OR under the clean condition occurs at 21:00 LST, which may contribute to the heavier precipitation in the C-case than P-case of Bulk-OR, but there is no convection development at 21:00 LST in SBM and Bulk-2M.
 Therefore, by improving the aerosol representation in Bulk-2M, the signs of the aerosol effects on LWC, IWC, convection, and precipitation are reversed compared to Bulk-OR, consistent with the SBM simulation. Aerosol invigoration effects on convection and precipitation in warm-based deep convective clouds have been demonstrated, on the basis of the theory [Rosenfeld et al., 2008] and modeling simulations [Fan et al., 2012a, 2012b]. Such effects can be simulated by the improved bulk scheme to produce more realistic AIE assessment.
4 Summary and Conclusions
 In this study, we have modified the widely adopted double-moment bulk cloud microphysics in the WRF model implemented by Morrison and co-authors [Morrison et al., 2005, 2007; Solomon et al., 2009], with the purpose of providing a better bulk microphysical scheme for simulating aerosol effects in regional and global models. The main improvement in the modified bulk scheme (i.e., Bulk-2M) lies in the more realistic representation of aerosols by implementing prognostic aerosol mass and number concentrations into the original bulk scheme (Bulk-OR), in which aerosols are pre-described. In Bulk-2M, the activation removal and dynamical transport of aerosol particles are considered and the aerosol sources are defined at the boundaries to replenish the aerosol loading and prevent dilution of aerosol concentrations by the inflow air mass. The impacts of the parameterizations of the droplet diffusional growth, autoconversion, and the selection of embryonic raindrops radius on the performance of the bulk microphysical scheme with the prognostic double-moment aerosol representation are evaluated by comparing the Bulk-2M results with those from SBM simulations. Model simulations are conducted for two distinct cloud regimes, i.e., maritime warm stratocumulus clouds (Sc) over southeast Pacific Ocean from the VOCALS project and continental deep convective clouds (DCC) in the southeast of China from DOE AMF-China field campaign. In the Sc case, the comparison between model results and atmospheric field observations reveals that SBM exhibits a better agreement with the observations due to more realistic representations in many microphysical processes, such as droplet diffusional growth and rain evaporation [Li et al., 2009b; Khain et al., 2009]. In this present work, the SBM scheme is considered as a benchmark to evaluate the performance of bulk microphysical schemes.
 Because of the absence of aerosol advection and removal mechanisms, the unrealistic aerosol concentration temporal evolution simulated by Bulk-OR is responsible for the distinct cloud properties (i.e., Nc, Qc, and Rc) with Bulk-OR from those with SBM simulations and observations, although all three model simulations (Bulk-OR, Bulk-2M, and SBM) are initiated with the same initial aerosol concentration on the basis of field observations. The simulations of cloud properties in Bulk-2M, particularly the cloud droplet number concentration and droplet size, have been significantly improved in both Sc and DCC cases. In the Sc case, because of numerous small droplets simulated by Bulk-OR, the conversion of cloud droplets to raindrops is very inefficient, and the rainwater and drizzle formation is largely inhibited. Bulk-2M predicts close simulations to SBM in terms of the realistic rainwater and drizzle formation. With an equivalent aerosol budget to the SBM, Bulk-2M is further examined for parameterizations in the bulk microphysics, on the basis of comparing with the results from the SBM that is considered as a benchmark. A major advantage of the prognostic aerosol approach lies in that the observed aerosol/CCN size distributions are employed to properly initiate the simulations, avoiding tuning the aerosol/droplet concentrations. The prognostic aerosol approach is also essential, when the advective/convective transports of aerosols are efficient for convective cloud regimes. Our future work will incorporate the CCN regeneration scheme and wet scavenging into Bulk-2M to fully represent CCN budget.
 There still exist large discrepancies in the predicted cloud water and rainwater between Bulk-2M and SBM, and Bulk-2M predicts significantly lower cloud water and rainwater. Sensitivity experiments for the Sc case indicate that the vapor saturation adjustment employed for the diffusion growth in the bulk schemes mainly contributes to the lower cloud water due to a low condensation rate and a high evaporation rate compared to SBM, in which diffusional growth is explicitly calculated based on supersaturation. The influences of the saturation adjustment on the cloud water content are distinct between the Sc and DCC cases, because of the different cloud dynamical conditions and their interactions with microphysics. A recent comparison between the explicit prediction of supersaturation and saturation adjustment in the Morrison scheme [Lebo et al., 2012] also suggests that in the DCC case, the saturation adjustment artificially alters the latent heating profile and convective dynamics by over-prediction of the condensation rate at low levels. Since explicit calculation of the diffusional growth employed in SBM is impractical for regional and global models because of coarse resolutions, bulk schemes with explicit calculation of diffusional growth such as those of Li et al.  and Lebo et al.  may be adapted for further improvements in the cloud-resolving simulations.
 The low rainwater amount in Bulk-OR is shown to be closely related to the KK2000 autoconversion parameterization. Our sensitivity tests indicate that LD2004, in which the dispersion factor is explicitly incorporated, and F2008 with the consideration of turbulence effect exhibit good performances in terms of realistic simulations of cloud droplet number concentration, raindrop number and mass concentration, and drizzle precipitation for stratocumulus clouds. Through improvement in the simulations of Nr and the effective rain radius in the Sc case, the size of 40 µm for embryo raindrops is demonstrated to be more realistic than that used in the original KK2000 scheme (25 µm). In the DCC case, surface precipitation and cloud properties except for Nr show relatively low sensitivity to the different autoconversion schemes, because the mixed-phase processes play an important role in determining cloud microphysical properties.
 In both the Sc and DCC cases, the bulk simulations consistently predict stronger rain evaporation rate below the cloud compared to SBM, which contributes to a reduced surface precipitation in the bulk simulations. The examination of rain evaporation parameterization in the bulk scheme reveals that bulk scheme reduces the mean size of raindrops after evaporation, which leads to the unrealistically large rain evaporation rate [Li et al., 2009b]. Therefore, a better parameterization of the rain evaporation process is needed in bulk microphysics schemes.
 Sensitivity modeling experiments have been performed to evaluate the responses of increasing aerosols in model simulations for two distinct cloud regimes. In the Sc case, Bulk-2M simulates the magnitudes of aerosol effects on the cloud droplet number and droplet size, cloud optical depth, and precipitation close to those by SBM. In the DCC case, Bulk-2M predicts high LWC and IWC, enhanced precipitation, and invigorated convection with increased aerosol loading, while Bulk-OR leads to reversed signs of the aerosol effects on LWC, IWC, convection, and precipitation. As illustrated in Fan et al. [2012a], Bulk-OR predicts numerous droplets of a smaller size due to the prescribed CCN, leading to inefficient droplet freezing and less latent heat release that prevents invigoration of convection. The better performances of Bulk-2M than Bulk-OR under the different aerosol loadings indicate that Bulk-2M represents a robust method to simulate the cloud properties and aerosol effects, whereas Bulk-OR relies highly on the validity of the initial aerosol condition.
 Our results demonstrate that better cloud simulations and more accurate assessment of aerosol indirect effects can be achieved in regional and global models by improving aerosol representation, more sophisticated calculation of the diffusion growth, and more realistic autoconversion parameterizations (e.g., LD2004 that considers the relative dispersion and F2008 that considers the turbulence effects) in the bulk microphysics schemes.
 Y. Wang acknowledged the support by an NASA Graduate Student Fellowship in Earth System Science. This study was supported by Department of Energy (DOE) Regional and Global Climate Modeling program for the bilateral agreement between DOE and China Ministry of Science and Technology on regional climate research. The authors were grateful to helpful discussion with Hugh Morrison of NCAR and Qing Yang and Hailong Wang of PNNL. The measurements from C130 aircraft and Ron Brown ship were obtained from the VOCALS data archive of NCAR/EOL and sponsored by the National Science Foundation. PNNL is operated by Battelle for the DOE under Contract DE-AC06-76RLO 1830.