Aerosols are a critical factor in the atmospheric hydrological cycle and radiation budget. As a major agent for clouds to form and a significant attenuator of solar radiation, aerosols affect climate in several ways. Current research suggests that aerosol effects on clouds could further extend to precipitation, both through the formation of cloud particles and by exerting persistent radiative forcing on the climate system that disturbs dynamics. However, the various mechanisms behind these effects, in particular, the ones connected to precipitation, are not yet well understood. The atmospheric and climate communities have long been working to gain a better grasp of these critical effects and hence to reduce the significant uncertainties in climate prediction resulting from such a lack of adequate knowledge. Here we review past efforts and summarize our current understanding of the effect of aerosols on convective precipitation processes from theoretical analysis of microphysics, observational evidence, and a range of numerical model simulations. In addition, the discrepancies between results simulated by models, as well as those between simulations and observations, are presented. Specifically, this paper addresses the following topics: (1) fundamental theories of aerosol effects on microphysics and precipitation processes, (2) observational evidence of the effect of aerosols on precipitation processes, (3) signatures of the aerosol impact on precipitation from large-scale analyses, (4) results from cloud-resolving model simulations, and (5) results from large-scale numerical model simulations. Finally, several future research directions for gaining a better understanding of aerosol-cloud-precipitation interactions are suggested.
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 Aerosols, and especially their effect on clouds and precipitation, are one of the key components of the climate system and the hydrological cycle. Yet the aerosol effect on clouds and precipitation remains poorly known. A recent report published by the U.S. National Academy of Science states that “The greatest uncertainty about the aerosol climate forcing—indeed, the largest of all the uncertainties about global climate forcing—is probably the indirect effect of aerosols on clouds” [National Research Council (NRC), 2005]. This “aerosol indirect effect” (AIE) includes the traditional “indirect,” or “Twomey,” effect on cloud droplet size and thus reflectance for a constant liquid water path [Twomey, 1977; Twomey et al., 1984] and the “second indirect” effect on cloud extent and lifetime [Albrecht, 1989; Hansen et al., 1997; Ackerman et al., 2000]. Enhanced aerosol concentrations can also suppress warm-rain processes by reducing particle sizes and causing a narrow droplet spectrum that inhibits collision and coalescence processes [e.g., Squires and Twomey, 1961; Warner and Twomey, 1967; Warner, 1968; Rosenfeld, 1999]. The aerosol effect on precipitation processes, considered part of the second type of aerosol indirect effect [Albrecht, 1989], is even more complex, especially for mixed-phase convective clouds.
 Continued advancement of instrumental technology has provided the community with much improved research tools to gain insights concerning aerosol-cloud-precipitation interactions (ACPI). For instance, a combination of cloud top temperature and effective droplet sizes, estimated from the advanced very high resolution radiometer (AVHRR), has been used to infer the suppression of coalescence and precipitation processes by smoke [Rosenfeld and Lensky, 1998] and desert dust [Rosenfeld et al., 2001]. Multisensor (passive/active microwave and visible and infrared) satellite observations from the Tropical Rainfall Measuring Mission (TRMM) have also been used to identify the presence of nonprecipitating supercooled liquid water near cloud tops due to over-seeding from both smoke over Indonesia [Rosenfeld, 1999] and urban pollution over Australia [Rosenfeld, 2000]. In addition, aircraft measurements have provided evidence of sustained supercooled liquid water down to −37.5°C in continental mixed-phase convective clouds [Rosenfeld and Woodley, 2000]. These findings further suggest that an increase in continental aerosols can reduce the mean size of cloud droplets, suppressing coalescence and warm-rain processes, permitting more freezing of cloud droplets and associated latent heat release above the 0°C isotherm, and enhancing the growth of large hail and cold-rain processes [Rosenfeld and Woodley, 2000]. Andreae et al.  analyzed in situ observations made during the Large-Scale Biosphere-Atmosphere Experiment in Amazonia–Smoke, Aerosols, Clouds, Rainfall, and Climate (LBA-SMOCC) campaign and found that increases in smoke and surface heat due to biomass burning tend to lead to higher cloud top heights and the enhancement of cold-rain processes over the Amazon basin. Lin et al.  examined multiplatform satellite data over the Amazon basin and found that high biomass burning–derived aerosols are correlated with elevated cloud top heights, large anvils, and more rainfall. Koren et al.  examined cloud properties derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) and found strong evidence that aerosols from pollution, desert dust, and biomass burning systematically invigorate convective clouds over the Atlantic Ocean. Using long-term integrated TRMM-derived precipitation data, Bell et al.  found a significant midweek increase in summertime afternoon thunderstorms over the southeastern United States, which coincides with a midweek increase in ground-measured aerosol concentration. Recently, Li et al. [2011a] and Niu and Li  used long-term (10 year) sets of extensive ground-based and global A-Train (CloudSat, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), and MODIS) spaceborne satellite measurements to reveal unprecedentedly strong climatic effects of aerosols on clouds and precipitation. They also attempted to sort out conditions under which clouds and precipitation are suppressed or fueled by aerosols.
 These findings are consistent with the notion that aerosols have a major impact on the dynamics, microphysics, and electrification properties of continental mixed-phase convective clouds. In addition, high aerosol concentrations in urban environments could affect precipitation variability by providing a significant source of cloud condensation nuclei (CCN). Such pollution effects on precipitation potentially have enormous climatic consequences in terms of both feedbacks involving the land surface via rainfall and the surface energy budget and changes in latent heat input to the atmosphere. Table 1 summarizes observations of cloud system features in high-aerosol and low-aerosol continental environments. Basically, aerosol concentrations can influence cloud droplet size distributions, the warm-rain process, the cold-rain process, cloud top heights, the depth of the mixed-phase region, and the occurrence of lightning. The following review of observation-modeling studies of the AIE follows the general life cycle of a cloud from the germination of cloud droplets; warm-rain, cold rain, and mixed-phase rain processes; and deep convective clouds to thunderstorms. In each phase, aerosols exert different influences on the development of clouds that ultimately affect precipitation.
Table TABLE 1.. Key Observational Studies Identifying the Differences in Microphysical Properties, Cloud Characteristics, Thermodynamics, and Dynamics Associated With Clouds and Cloud Systems Developed in Dirty and Clean Environmentsa
 The main objective of this paper is to review our current understanding of the interactive processes between aerosols, clouds, and deep-convective precipitation systems. Recent results from observations and modeling (from cloud-resolving models to global models) are reviewed. The paper has seven sections. It begins in section 2 with a brief description of fundamental theories regarding the effects of CCN and ice nuclei (IN) on microphysics and precipitation processes. The observational evidence of aerosol effects on cloud and precipitation processes is then reviewed in section 3. Section 4 presents the signatures of aerosol impacts on precipitation processes from large-scale analyses. Sections 5 and 6 summarize recent results from cloud-resolving model and large-scale numerical model simulations, respectively. In section 7, current and future research on aerosols and their interactions with precipitation are discussed.
2. FUNDAMENTAL THEORIES OF AEROSOL EFFECTS ON CLOUDS AND PRECIPITATION
2.1. Activation of Condensation Nuclei Into Cloud Drops
 Aerosol particles composed of hygroscopic materials are good surfaces upon which water vapor can condense, so they are called condensation nuclei (CN). CCN are the portions of CN that are capable of initiating cloud drop formation. Such a capability is strongly related to the mass and composition of their water-soluble component. Köhler  explained this mechanism with the Köhler curve, which describes the equilibrium saturation ratio over the solution drop surface, Sd, as a function of the drop radius. For each droplet containing a fixed amount of dissolved salt, the solution (Raoult) effect reduces the water activity and thus surface vapor pressure, whereas the curvature (Kelvin) effect does the opposite by holding water molecules together. These two effects combine to form the Köhler curve, which shows a peak value in Sd at a unique drop size called the critical radius r* (see Figure 1). The maximum Sd appearing on a curve corresponding to a given particle with dry size rd or equilibrium size (wet size) re is commonly called the critical (or activation) saturation ratio, S*, for that particle, presumably with a known composition and fixed solute mass. During cloud formation, once the ambient saturation ratio S∞ exceeds the S* of a particle, that particle can be activated into a cloud drop. Those particles that never meet the condition of S∞ > S* will stay in a “haze state” and are called interstitial aerosols. This also means that whether CN can be regarded as CCN depends not only on the properties of the particle but also on the ambient conditions (i.e., S∞). It is important to recognize that aerosols have a broad size range, and the sizes of CN are important in determining their role in cloud and precipitation formation. From Figure 1, one can see that larger aerosols have lower S*, so they have the advantage of easier activation. Note that the solute amount in an aerosol particle may vary with time during its uptake of water either by absorbing gases (such as nitric acid or ammonia) from the ambient air or by dissolving its solid cores (e.g., mineral dust) [Kulmala et al., 1993, 1997]. Besides solute mass (or particle dry size), the Köhler curve also varies with the solute chemical composition, which influences not only the Raoult effect (by altering the water activity) but also the Kelvin effect (by altering the surface tension). Temperature is another factor that determines Köhler curve characteristics. An aerosol particle may become warmer than its environment due to either latent heating from vapor condensation or absorption of solar radiation by its soot or mineral dust component. Such heating affects all three factors that determine the Köhler curve (i.e., saturation vapor pressure, surface tension, and solution activity) so the Köhler curve should not be calculated using the ambient temperature [Conant et al., 2002; Nenes et al., 2002]. The insoluble portion of the aerosol particle, such as soot and mineral dust, may also affect the Köhler curve, simply by adding to the particle size and thus reducing the Kelvin effect.
 The relationship between the initial number of cloud concentration (NC) near cloud base and aerosol number spectra is an important issue in studying aerosol effects on cloud microphysics and radiation with regional and global atmospheric models. The Köhler theory is a first step in understanding this relationship. However, the Köhler theory can only tell us whether a condensation nucleus can be activated into a cloud drop under a particular ambient supersaturation, ss∞ (≡S∞ − 1). The maximum ss∞ (hereinafter termed ss∞,max) that can be reached must be known in order to determine the number of cloud drops activated at the cloud base. The ambient supersaturation is controlled by two factors, as indicated by the saturation development equation [Squires, 1952]
where the coefficients A1 and A2 are properties of the ambient air, z is the height, and qw is the cloud water content. In equation (1) the source term indicates an increase in ss∞ due to expansion cooling (thus a decrease in saturation vapor pressure) in the updrafts, and the sink term is due to water vapor removal by condensation onto cloud drops. The condensation rate, dqw/dt, is roughly proportional to ss∞, cloud drop size, and NC; NC, in turn, is determined by the CN size spectrum and the variation in ss∞. As more and more CCN turn into cloud drops, the sink term quickly surpasses the source term after which ss∞ starts to decrease. Typically, this peak supersaturation, ss∞,max, is reached within a few tens of meters above the cloud base. No more CN activation can occur deeper into the cloud unless ss∞ rises again and surpasses the original ss∞,max due to enhanced updrafts or depletion of cloud drops by rain accretion [Chen, 1994a]. Although the relationship between NC and the CN spectrum is quite convoluted, a unique solution for NC at the cloud base exists when the CN spectrum and updraft speed (dz/dt) are given. In the following, we briefly describe the common form of the CN spectrum representation and how it can be used to derive NC.
 One common type of CN spectra measurement is based on the Köhler theory discussed above. The aerosol particles to be measured are introduced into a diffusion chamber with controlled ss∞, and then the number of cloud drops formed at that condition is counted. This specified ss∞ represents the critical supersaturation, ss* (≡S* − 1), of the smallest CCN that can be activated. By sweeping through a range of ss∞ values in the diffusion chamber, one can obtain a relationship between the number of CCN (NCCN) and ss∞,max. Earlier studies found that the measured CCN spectra can often be approximated empirically as
where C and k are time- and location-dependent coefficients of the CN spectra [Twomey, 1959a]. Figure 2 shows examples of the measured relationship between NCCN (normalized by the number of CN, NCN) and ss∞,max, as well as that using equation (2) for several values of k. Note that ss∞,max here is often expressed in terms of the percentage of supersaturation. The power law formulation in equation (2) is simple and effective, but it has the weakness of producing unlimited CCN number concentrations with ever-increasing ss∞,max. In reality, the number of CCN normally diminishes when the size gets too small or the supersaturation gets too high, causing a leveling off of NCCN.
 Another common type of aerosol measurement is done by segregating aerosol particles according to their aerodynamic sizes and then counting the particle number in each size segment to obtain a size spectrum. Earlier studies using such techniques found that the number density distribution (or the size distribution) of aerosol particles with a dry size, ra, greater than 0.1 μm can be approximated by a power law relationship [e.g., Junge, 1952, 1955],
where N(ra) is the total number of CN with a dry size greater than ra, and a1 and a2 are constants. Note that ss∞,max in equation (2) actually represents the critical supersaturation of the smallest CCN, and it can be related to the ra of that particle by the approximation, s* ≈ α ⋅ ra−3/2, where α depends on the chemical composition. With this relationship, equation (2) can be converted into a size spectrum:
One can easily recognize the equivalency between equations (3) and (4). As mentioned before, these formulas might not apply to ra < 0.1 μm, yet under some conditions, such as in strong convection, very small CN do form cloud drops. To better describe the full size spectrum, many studies applied the trimodal lognormal function to represent the observed aerosol spectra [e.g., Whitby, 1978; Jaenicke, 1993; Brechtel et al., 1998],
where i is the modal index, and for each mode, N, σ, and r0 are the number concentration, standard deviation, and modal radius, respectively. Examples of the trimodal lognormal size distribution are illustrated in Figure 3. Presenting the aerosol population in terms of size spectra such as those described by equations (3) or (5) has a disadvantage in that chemical composition must be known in order to calculate NC, but such information is often not provided. In this regard, equation (2) may be a better formulation for CN spectra because it does not require additional information. Even if chemical compositions are known, the numerous chemical species in natural aerosols makes it difficult for model calculations. For this problem, Petters and Kreidenweis  suggested a single hygroscopicity parameter, κ, which can be measured relatively easily and used effectively to model CCN activity.
 Quite a few cloud resolving models (CRMs) are capable of resolving ss∞ and obtaining NC directly by applying the Köhler theory to a specified CN spectrum such as those given in equations (2) and (5). These models include those using sophisticated bin microphysics [e.g., Clark, 1973; Kogan, 1991; Khain et al., 2004; Tao et al., 2007; Morrison and Grabowski, 2010], as well as those using bulk microphysics [e.g., Feingold et al., 1994; Ekman et al., 2006, 2007; Cheng et al., 2007; Morrison and Grabowski, 2008]. But many global models and regional cloud models, such as those adopting the “saturation adjustment” assumption, do not resolve ss∞ explicitly. Even for CRMs that do resolve ss∞, the peak supersaturation is very often under-predicted because it occurs within roughly 50 m above the cloud base, which is not resolved in these models [cf. Clark, 1973; Chen and Liu, 2004]. Nevertheless, Cheng et al.  showed that the calculation of supersaturation can be improved significantly by imbedding a Lagrangian parcel scheme. The Lagrangian-type calculation can also be applied in global models by running a parcel model, either online or offline, with given updraft speeds in order to derive NC [Nenes and Seinfeld, 2003; Roelofs et al., 2006]. But such calculations not only demand more computational resources but also require detailed calculations of thermodynamics and the aerosol activation process according to the Köhler theory. Alternatively, NC may be derived by using diagnostic formulas introduced below.
Twomey [1959b] was the first to link NC to the CN spectrum in a diagnostic manner. By inserting equation (2) into equation (1) and applying a simplified condensation equation, he derived an asymptotic solution for NC as a function of C, k, updraft speed, and air properties. As shown in Figures 4a and 4b, Twomey's solution predicts that NC increases monotonically with NCN. Recall that equations (2) and (4) yield an infinite number of NCN if no upper limit is set for ss∞,max in equation (2) or no lower limit is set for ra in equation (4). Yet, if the 0.1 μm cutoff size mentioned by Junge [1952, 1955] is applied to equation (2), the predicted NC would unrealistically exceed NCN. So a cutoff radius of 0.01 μm is applied to obtain the NC in Figures 4a and 4b, and the chemical composition is assumed to be ammonium sulfate. Twomey's solution compares well with the observational results summarized by Ramanathan et al. [2001a] (Figure 4c). The trends and the magnitudes are quite similar, and the regional differences in the observations seem to correspond to the variations in the coefficient k in equation (2). One feature that Twomey's prediction does not capture well is the leveling off of NC toward higher NCN. Chen and Liu  examined Twomey's quasi-analytical solution by incorporating equation (2) into a parcel model with detailed microphysics to obtain NC. They found that Twomey's solutions significantly deviate from model calculations for large k and C values, partly because Twomey's solution is not exact and partly because its derivation omitted the solute effect and gas kinetic effect on condensation growth. Modification of Twomey's method has been performed by Sedunov , Ming et al. , Khvorostyanov and Curry , and others, and the improvements include a refined asymptotic solution as well as considering more physical constraints such as soluble fraction, surface tension, and condensation (accommodation) coefficient. Parameterizations of CCN activation have also been developed using results from a parcel model that are fitted into various empirical functions [e.g., Ghan et al., 1993; Abdul-Razzak et al., 1998; Lohmann et al., 1999; Fountoukis and Nenes, 2005] or by compiling results into lookup tables [Saleeby and Cotton, 2004]. Besides the theoretical approaches, prediction of NC can also be obtained empirically by correlating NC observed just above the cloud base with aerosol concentration (usually the mass of sulfate) observed below the cloud base. This method has been applied in various global climate models [e.g., Boucher and Lohmann, 1995; Lohmann et al., 1999; Roelofs et al., 1998; Jones et al., 2001; Tsai et al., 2010].
 Past studies of CCN focused mainly on the inorganic component of the aerosol. Yet around the globe, organic carbon is the second-most abundant component of fine aerosols after sulfate [Novakov and Penner, 1993; Kanakidou et al., 2005; Liu and Wang, 2010]. Soluble organic compounds can decrease water activity and the surface tension of water [Shulman et al., 1996; Facchini et al., 1999; Abdul-Razzak and Ghan, 2004] just like inorganic solutes, but the effect is weaker for organics on the same mass basis. Such organic aerosol effects have been included in a few of the aforementioned studies [e.g., Nenes and Seinfeld, 2003]. One particular type of organic carbon called “surfactants” consists of polar (hydrophilic) and nonpolar (hydrophobic) segments, so these molecules stay preferentially on the droplet surface and form a monolayer film [Langmuir and Langmuir, 1927; La Mer, 1962]. Such a monolayer film does not influence the Köhler curve but can retard the condensation process through the gas-kinetic effect by reducing the water accommodation coefficient. Deryaguin et al.  applied a one-dimensional model to show significant retardation of cloud drop condensation growth by the monolayer film. Feingold and Chuang  further demonstrated that because of the slower growth of the activated cloud drops in an adiabatic cloud (i.e., the sink term in equation (1)), the monolayer film may cause a higher ambient supersaturation ss∞ and thus promote activation of the smaller CN. Such a surface film effect is generally ignored in current cloud models due to its complexity as well as a lack of information on the characteristics of surfactants in aerosols.
2.2. CCN Effect on Rain Formation
 Rain formation processes can be categorized into two major pathways: warm-rain processes that do not involve ice crystals and cold-rain processes that do. CN may have a strong influence on warm-rain formation, mainly through their effect on NC. As discussed above, NC tends to increase with NCN (see Figure 4). Because of competition of water vapor among cloud drops, a higher NC necessarily leads to smaller cloud drops. Small cloud drops are ineffective in collision, partly due to lower fall speeds and partly due to smaller collision efficiencies. It is difficult for a cloud drop to grow into a raindrop (typically defined as drops with radii or diameters greater than 100 μm) merely by condensation, and collision coalescence is considered a necessary process for warm-rain initiation. But the collision coalescence process is inefficient unless some of the cloud drops can reach, by condensation growth, the so-called Hocking limit (around 19 μm in radius) [Hocking, 1959]. Once a raindrop is initiated, its further growth proceeds mainly by collecting cloud drops, and the efficiency of this process again depends heavily on cloud drop sizes.
 Another effect of increasing NCN on warm-rain formation is the narrowing of the cloud drop size spectrum [Fitzgerald and Spyers-Duran, 1973; Martin et al., 1994; Liu and Daum, 2002; Andreae et al., 2004]. If we assume that the shape of the CN spectrum, as defined by the coefficient k in equation (2) or σ and r0 in equation (5), remains fixed, then the increase in CN number concentration leads to a lower ss∞,max and thus a larger cutoff size for CN activation. According to the condensation growth equation, smaller drops grow faster in size than larger drops. This means that an increase in cutoff size (representing the smallest cloud drops) may lead to a narrower cloud drop size range. The difference in cloud drop sizes (and thus fall speeds) is important to the collision process because it requires that two colliding droplets have significant relative motions. Therefore a narrowed spectral width also leads to suppression of warm-rain formation. Note that the suppression of collision coalescence further enhances the narrowing of the cloud drop size spectrum.
 Note that the warm-rain suppression effect might not occur if the increase in NCN comes with a change in the shape of the CN spectrum. An extreme example is the addition of a few very large CCN, which are often termed giant CCN (GCCN), with radii in the micrometer range or larger. One natural GCCN is large sea salt particles generated by the breakup of air bubbles in the ocean or by wave tearing [de Leeuw et al., 2011]. Because of their inherently large sizes, GCCN may be activated directly into rain embryos and can readily initiate the warm-rain process [Johnson, 1982; O'Dowd et al., 1997; Feingold et al., 1999; Lasher-Trapp et al., 2001; Cheng et al., 2007]. In addition, because they also compete for water vapor, GCCN can lower ss∞,max and thus deprive small CN of the chance to activate into cloud drops [Ghan et al., 1998; Feingold et al., 1999; Cheng et al., 2007]. Furthermore, because there are fewer cloud drops, each cloud drop can grow larger and thus is more efficient at converting into rain by collision coalescence. So GCCN counteract both Twomey's first and second indirect effects. Large insoluble particles such as mineral dust have a similar capability especially when they are coated with hygroscopic materials. The GCCN effect has been utilized for artificial rain enhancement. In the so-called warm-cloud seeding procedure, GCCN-sized salt particles are introduced into clouds to accelerate rain initiation [Mather et al., 1997; Bruintjes, 1999]. However, the effectiveness of GCCN depends on how efficiently rain can be initiated without them. In clean environments (e.g., low NC), cloud drops are able to grow large enough by condensation to reach the so-called Hocking limit, after which the cloud drop can grow effectively by collision coalescence and convert into raindrops. So GCCN tend to be less important in such situations as demonstrated by Feingold et al.  using detailed model simulations. They also noted that higher concentrations of GCCN are required at higher CCN concentrations for marine stratocumulus to produce drizzle. While CCN generally increases with CN for dusty events, its ratio tends to decrease sharply with increasing CN, implying that less GCCN become available under heavy loading conditions like dust storms [Liu et al., 2011]. Having stated the roles of dust particles in serving as CCN, it is worth noting that dust has a very broad impact on global climate, ecosystems, human health, and agriculture, as recently reviewed by Ravi et al. .
 The discussions above suggest that more CN leads to more cloud drops and less precipitation. Yet there are many examples showing that an increase in CCN does not lead to higher cloud water content or longer cloud lifetimes. For instance, Ackerman et al.  demonstrated that the entrainment of overlying dry air above a deck of boundary layer stratocumulus cloud may result in a decrease in cloud water when the humidity of the overlying air is very low. Also, more and smaller cloud drops may enhance evaporation in the downdraft region of cloud edges, which leads to lower cloud fraction, cloud size, and cloud depth [Teller and Levin, 2006; Xue and Feingold, 2006]. A more detailed discussion on these effects is given in section 5.
 In cold clouds, such as the upper part of deep convective or high latitude clouds, CN's effects on cloud and precipitation are much more complicated than in warm clouds. Because of the Raoult effect of freezing point depression, soluble compounds tend to inhibit the freezing of liquid aerosols and cloud droplets and thus the formation of ice crystals. Yet liquid droplets normally cannot form without these soluble chemicals. So when the atmosphere is short of IN, the only viable way to form cloud ice is to freeze the water in aerosol particles or cloud drops. Such homogeneous nucleation occurs quite commonly in cirrus formed by slow lifting or in orographic wave flow at high altitudes where air temperature is generally below −40°C [Heymsfield and Sabin, 1989; Heymsfield and Miloshevich, 1993], as well as in the cirrus anvil generated in convective storms [Knollenberg et al., 1993; Heymsfield et al., 2005].
 Since NC is largely controlled by NCN, the number of ice crystals in such clouds is inevitably influenced by the amount of CN entering the clouds. Several model simulations showed that aerosols have strong influences on not only the microphysical structure but also the extent and lifetime of cirrus [Chen et al., 1997; Phillips et al., 2005; van den Heever et al., 2006; Carrió et al., 2007; Ekman et al., 2007; Fan et al., 2010a]. In regions where cloud drop freezing is slow (i.e., not all cloud drops can freeze), the number of cloud ice particles formed by cloud drop freezing depends not only on NC but also on the cloud drop mass mixing ratio according to the classical nucleation theory. In this case, the number of cloud ice particles may increase with increasing NCN due to the suppression of warm-rain processes, thus elevating cloud water content. But each cloud ice particle that formed would be smaller because of smaller cloud drop sizes. It is interesting to note that cloud ice particles with smaller initial sizes may not necessarily grow slower than larger ones due to the shape inertia effect [Sheridan et al., 2009]. Another way to initiate cloud ice is by heterogeneous nucleation with the help of IN. Water may directly deposit onto IN as ice (called deposition nucleation) or as liquid and then freeze (called condensation-freezing nucleation). Such a process is very sensitive to ss∞. As can be realized from equation (1), ss∞ is strongly modulated by NC and the size of cloud drops, so CN can influence ice nucleation indirectly through their effect on cloud drops.
 Besides nucleation, CN may also influence the growth of ice particles. When cloud ice crystals are first formed, they grow mainly by vapor deposition. The water vapor they need comes either from a continuous cooling of air by lifting or by the evaporation of cloud drops. The latter is called the Wegener-Bergeron-Findeisen (WBF) process, and this conversion from drops to ice is limited by the rate of cloud drop evaporation. With more cloud drops, the WBF conversion proceeds faster, so the deposition growth of cloud ice is influenced indirectly by CN.
 When cloud ice crystals are large enough, they can also grow by accreting cloud water, a process called riming. Just like the collision between cloud drops, the efficiency of riming is strongly dependent on the cloud particle size. Again, since cloud particle sizes are influenced by NCN, so will the riming process. In general, the WBF process is enhanced but riming is suppressed with more CN. Therefore, the formation of snow, graupel, and hail, as well as the so-called cold rain that forms from their melting, is affected [Khain et al., 2004; van den Heever et al., 2006; Tao et al., 2007; Cheng et al., 2010]. The net outcome varies with the overall dynamic and thermodynamic structures of the clouds, as well as the availability of GCCN and IN. Note that all the CN effects on ice phase precipitation and cold-rain formation mentioned above are related to cloud particle size and number concentration. These effects can best be resolved in a model with binned microphysical schemes [e.g., Khain et al., 2004; Tao et al., 2007; Morrison and Grabowski, 2010] and, to some extent, by multimoment bulk microphysical schemes [e.g., Feingold et al., 1994; Morrison and Pinto, 2005; Cheng et al., 2007; Li et al., 2008a; Morrison and Grabowski, 2008]. Single-moment bulk microphysical schemes are not suitable because they do not keep track of differing particle sizes or number concentrations.
2.3. Ice Nuclei Effect on Cold-Cloud Processes
 Cloud glaciation can be initiated by either homogeneous freezing, which requires very low temperatures, or by heterogeneous nucleation, which works at higher temperatures with the aide of IN. The latter is considered very important to cloud physical processes, precipitation formation, and global radiation balances [Pruppacher and Klett, 1997; Cantrell and Heymsfield, 2005]. Just like CCN, the effect of IN on cloud microphysics comes mainly from their impact on the cloud ice number concentration, NCI, which is particularly important in the mixed-phase zone of clouds where the balance between ice and liquid is sensitive to cloud ice number [Korolev and Field, 2008]. Because of insufficient knowledge about the particles that cause ice nucleation, mixed-phase zone processes are difficult to model [Klein et al., 2009; de Boer et al., 2010]. Nevertheless, relevant information about IN and ice nucleation rates is accumulating.
 The most common type of IN is probably mineral dust particles transported into the atmosphere by strong winds from bare lands, such as deserts, semiarid areas, agricultural uplands, and dry river beds. They have been implicated as possible atmospheric IN for over 50 years [Isono et al., 1959]. More recently, emerging evidence has suggested that mineral particles may reach high into the upper troposphere where they serve as IN for cirrus cloud formation [Heintzenberg et al., 1996; Sassen, 2002; Sassen et al., 2003]. DeMott et al.  detected IN concentrations up to 100 times higher than typical background values in and above the marine boundary layer in Florida during Saharan dust episodes. These IN were within the air layer that feeds thunderstorm development and subsequent cirrus anvil formation. Measurements of ice particle residuals from anvil cirrus [e.g., Cziczo et al., 2004] and cloud model simulations [e.g., van den Heever et al., 2006] all support the hypothesis that mineral dust modifies cloud microphysics and dynamics. Soot particles from anthropogenic or natural burning processes can also act as IN, but their ice nucleating efficiency is much weaker. Another source of IN are biological aerosols such as bacteria, pollen, fungi, spores, and even phytoplankton. These bioaerosols, especially some species of bacteria, are very efficient IN, but their number concentrations are generally low.
 IN may initiate ice formation via four different modes. Two were mentioned earlier: deposition nucleation and condensation-freezing nucleation, which are controlled mainly by supersaturation. IN may also cause cloud drops or raindrops to freeze by either immersion freezing or contact freezing, and temperature is their main controlling factor. Immersion freezing occurs when an ice nucleus enters a cloud drop (either by acting as a CCN or by collection inside the cloud) and keeps it unfrozen for some time, later initiating freezing when the air gets cold enough. Contact freezing occurs when an ice nucleus collides with a supercooled drop and immediately freezes. Hoose et al. [2010a] estimated that globally, immersion freezing by mineral dust is the dominant ice formation process, followed by immersion and contact freezing by soot. Ice formation from biological aerosols is significant only over certain areas over land (such as forests), where their concentrations are greater than anywhere else in the atmosphere.
 Similar to the activation of CN into cloud drops, not all IN can nucleate into cloud ice in a specific cloud environment. Two hypotheses have been offered to explain such a phenomenon. The “stochastic hypothesis” states that nucleation is a probabilistic and time-dependent process, i.e., only a portion of a specific kind of IN can be nucleated during a unit length of time, and the rate of nucleation depends on both particle properties and environmental conditions [cf. Fletcher, 1962; Mason, 1971]. A contrasting view is called the “singular hypothesis,” which considers that nucleation is controlled by impurities or by the number of active sites on the surface of ice nuclei, where each site has a characteristic temperature (for freezing nucleation) or supersaturation (for deposition nucleation) [cf. Dorsey, 1948; Vali and Stansbury, 1966; Fletcher, 1969; Vali, 2008]. This means that singular nucleation is time-independent, so a particular kind of IN is nucleated all together once their threshold temperature or supersaturation is reached. Furthermore, ice nucleation occurring at different temperatures or supersaturations would imply the presence of different IN which can be of the same species and of the same size but possess different surface properties. More detailed discussions about these hypotheses are given by Vali and Stansbury , Vali , Chen et al. , and Niedermeier et al. .
 These two views of nucleation form the basis for the parameterization of ice nucleation from measurements and for use in cloud microphysical schemes. For example, IN concentrations (NIN) in the atmosphere are often measured by sampling air in a cloud chamber and counting NCI that form under a given temperature, pressure, and humidity. The measured NCI are then used to represent NIN by expressing it as a time-independent function of temperature or supersaturation [e.g., Fletcher, 1962; Huffman, 1973]. Note that such measurements usually cannot identify the type of IN so the functional dependence can be considered as empirical. There are also laboratory measurements of heterogeneous nucleation targeted on specific types of IN [e.g., Yankofsky et al., 1981; Diehl et al., 2001; Archuleta et al., 2005; Field et al., 2006; Möhler et al., 2006]. Such results can be used in cloud microphysical models only when the types and size spectrum of IN are known or given. Empirical parameterization of heterogeneous nucleation according to the singular concept has been adopted in cloud microphysical schemes, such as the freezing parameterization from DeMott et al. , condensation/deposition freezing from Cooper  and Meyers et al. , and nucleation in the contact mode from Meyers et al. . Examples of measurements and fitting functions for these ice nucleation modes are given in Figure 5. One can see in Figure 5b a large variability in IN concentration as well as in the inverse temperature dependence among data sets. The lack of general applicability in space and time is the main weakness of such empirical formulas. Note that the above NIN-NCI relationships have been converted into pseudorate equations by taking the rate change of temperature or supersaturation as the functional variable, such as that applied in the spectral bin models of Chen and Lamb  and Khain et al. , so that the depletion of IN can be treated. The stochastic approach has also been adopted for interpreting measurement results and for application in regional microphysical schemes. For example, measurements of IN and their immersion freezing capability are often expressed as rate equations [e.g., Bigg, 1953; DeMott, 1990], which were used in several cloud schemes [e.g., Reisin et al., 1998; Diehl and Wurzler, 2004; de Boer et al., 2010; Fan et al., 2010a, 2010b].
 The empirical type of ice nucleation parameterization is popular because it may be implemented without knowing IN types and even NIN. These advantages are also the main weakness of such parameterizations because they cannot respond to the large spatial and temporal variations of natural IN species. The empirical treatment of IN is therefore one of the main uncertainties in current cloud microphysical simulations. Progress has been made toward the improvement of ice nucleation processes and their representation in cloud models. For example, many models have the capability of simulating the emission and transport of mineral dust particles and soot particles. A few recent efforts to simulate bacteria or other bioaerosols in the atmosphere have also been made [Burrows et al., 2009; Hoose et al., 2010a, 2010b]. New parameterizations of ice nucleating rates based on laboratory measurements are also emerging [e.g., Marcolli et al., 2007; Chen et al., 2008; Fornea et al., 2009; Kanji and Abbatt, 2006; Lüönd et al., 2010]. For example, Chen et al.  presented a generalized parameterization that keeps the original mathematical form of the classical nucleation theory and includes thermodynamic parameters of the IN (i.e., contact angle and activation energy) derived from laboratory measurements. Furthermore, effects not considered in the measurements, such as solute or curvature effects on heterogeneous freezing, can be easily added by modifying the saturation vapor pressure in the classical nucleation rate formula with the Raoult or Kelvin equation. A comparison of such parameterizations against original measurements for several IN species is shown in Figure 6. Preliminary implementation of this parameterization has been done by Hoose et al. [2010b] to estimate the relative importance of different IN species on a global scale. Integration of such schemes into cloud microphysical models is likely to occur in the near future.
3. OBSERVATIONAL EVIDENCE OF PROCESSES AND MECHANISMS BEHIND THE AIE
 While various mechanisms have been proposed to describe how aerosols affect precipitation, they are essentially tied to two fundamental processes through which aerosols alter energy and water cycles and ultimately influence precipitation: scattering and absorption of solar radiation and serving as CCN or IN. Most, if not all, mechanisms proposed so far [e.g., Intergovernmental Panel on Climate Change (IPCC), 2007] can be traced either directly or indirectly to these fundamental processes but at different stages in a chain of actions, illustrated in Figure 7. Conversion of aerosol particles into CCN is the crux of the majority of the effects.
 Among the seven mechanisms illustrated in Figure 7, only the last one is linked to the radiative effect of aerosols, namely its absorption of solar radiation to burn off cloud droplets. All remaining mechanisms originate from the Twomey effect: increases in aerosol concentration leading to increases in cloud droplet number concentration (CDNC) for liquid clouds [Twomey, 1977]. For a fixed liquid water path, this leads to smaller cloud particle sizes and thus suppression of precipitation and prolonging of cloud lifetime [Albrecht, 1989]. The retention of liquid water to above the freezing level causes extra latent heat to invigorate the development of deep convective clouds and enhance precipitation [Andreae et al., 2004; Rosenfeld et al., 2008]. This invigoration effect may also increase cloud height. The aerosol effects on precipitation, cloud height, amount/liquid water path (LWP), and duration are lumped into a general term: the second aerosol indirect effect [Albrecht, 1989], which is much more complex than the first aerosol indirect effect.
 Comparing the latest IPCC report to earlier editions, the number of mechanisms governing aerosol-cloud-precipitation interactions has increased. For example, five mechanisms were described in the 2001 IPCC report [IPCC, 2001] and seven were presented in the 2007 report [IPCC, 2007]. These mechanisms are essentially contingent upon the series of constraints applied. By adding or changing constraints, one can, in principle, find more types of aerosol indirect effects. However, identifying them would become an increasingly more daunting task because these processes in nature are all coupled, although one may control them in a model. Many idealized coincidences are required to observe the AIE and to determine which hypothesized processes are behind it. In general, cloud and precipitation processes are dictated primarily by the dynamic and thermodynamic settings of the atmosphere and by cloud microphysics as well. Virtually all investigations concerning the AIE, especially observation-based ones, have been fraught with difficulties and uncertainties in removing or decoupling the influences of atmospheric dynamics and thermodynamics.
 To understand this, Figure 8 illustrates the major processes occurring in an atmospheric column. From the viewpoint of observation studies, we have snapshots of atmospheric variables (e.g., aerosols, clouds, and precipitation) in a column, and we try to relate them as a measure of the AIE. For satellite remote sensing, aerosols below clouds are obscured by the clouds themselves. Clouds and precipitation at any point in a spatial-temporal domain result from all processes taking place over a much larger domain. Other influential factors need to be taken into account in order to isolate and quantify aerosol effects on precipitation. For example, advection may move a cloud from outside to inside of the domain under study, and convection linking aerosols with locally generated clouds may occur. Vertical motion associated with convection supplies moisture that dictates the growth from cloud droplets to raindrops. The essence of studying the AIE is to establish relationships between newly generated and/or the new growth of existing hydrometers with local aerosols. For stratiform clouds associated with large-scale atmospheric features such as frontal systems, local aerosols would have little to no bearing on clouds and precipitation. For convective clouds, the relationship would be closer.
 Despite the complex interaction between meteorological systems and aerosols, with adequate measurements and sound approaches, it is still possible to reveal the AIE by identifying favorable conditions, i.e., enhancing “signals” and suppressing “noise.” Selection and study of dramatic events whose effects on clouds and precipitation exceed those exerted by other factors, such as ship tracks [Ferek et al., 2000; Coakley et al., 2000], fire smoke [Kaufman and Fraser, 1997; Rosenfeld, 1999; Koren et al., 2004; Andreae et al., 2004], heavy air pollution [Rosenfeld, 2000], and dust storms [Rosenfeld et al., 2001], can help in this pursuit. Another kind of approach would be to track complete aerosol episodes or cycles during which aerosol loading goes up and down, as does the associated cycle of changes in cloud microphysics (e.g., effective radius) [Schwartz et al., 2002; Feingold et al., 2003]. A third approach is to use a large ensemble of cases to try to suppress or filter out the influences of fast atmospheric dynamics in order to single out the effects of aerosols, which are essentially partial derivatives of cloud/precipitation with respect to changes in aerosol properties under the same meteorological setting (in an ensemble sense). This is illustrated using long-term ground data [Li et al., 2011a] and global satellite data [e.g., Nakajima et al., 2001; Niu and Li, 2011].
3.1. Impact on Cloud Droplet Size Distributions and Warm-Rain Processes
 As stated above, the driving mechanism for the majority of other aerosol effects on clouds is the first aerosol indirect effect: the decrease in cloud droplet size with increasing aerosol number concentration for a fixed liquid water path (LWP) [Squires, 1958; Twomey, 1977]. Cloud albedo is enhanced in a cloud with constant LWP because there are a greater number of small cloud particles whose sum of cross sections is larger and thus reflect more radiation than fewer but larger droplets [Twomey, 1977]. This effect has been supported by ample evidence from satellite remote sensing [Han et al., 1994; Wetzel and Stowe, 1999; Nakajima et al., 2001; Liu et al., 2003]. Satellites collect a multitude of aerosol measurements over the entire globe more readily than in situ or ground-based instruments. However, they suffer from several inherent retrieval problems (see Z. Li et al.  for recent reviews of the satellite retrieval of aerosol parameters), such as difficulties in separating real effects from false ones [Yuan et al., 2008]. There is also the inherent limitation that cloud and aerosol properties cannot be obtained at the same time over the same location. The majority of previous studies used large-scale data, which are described in more detail in section 4. Within a sufficiently large spatial and temporal domain, clear and cloudy scenes can be found but at different times and/or different locations. Given the large-scale variation in aerosols, significant uncertainties can be incurred due to both data mismatch and small-scale changes in cloud properties.
 These limitations can be overcome, or lessened, by ground and in situ observations [Leaitch et al., 1996; Feingold et al., 2003; Penner et al., 2004]. Nevertheless, a large range of variation (by a factor of 3 or more) was found concerning the sensitivity of cloud microphysics to aerosols, as measured by the ratio of the change in cloud particle size to aerosol parameters. While some of the differences are related to the use of different analysis methods and/or observational data [Rosenfeld and Feingold, 2003], a large natural variation is often encountered [Feingold et al., 2003; Kim et al., 2003; Yuan et al., 2008]. Figure 9 shows changes in cloud droplet size with aerosol extinction coefficient, a measure of aerosols' indirect effect, from ground-based measurements collected at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) central facility site [Feingold et al., 2003, 2006]. It is seen that the method is valid for a small range of variation in LWP and a large range of variation in aerosol loading (Figure 9a) but invalid under the opposite condition (Figure 9b).
 The vast majority of previous studies showed a negative dependence of cloud particle size on aerosol loading. However, some satellite-based studies show a positive relationship [Sekiguchi et al., 2003; Storelvmo et al., 2006]. Yuan et al.  conducted an extensive study that examined the relationship between cloud droplet effective radius (DER) and aerosol optical depth (AOD) for a large number of convective cloud scenes acquired around the world by the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Terra satellite. While inverse relationships between cloud particle size and aerosol loading for different types of aerosols predominated over most of the world, exceptional positive relationships were found in two regions: the Gulf of Mexico and the South China coast during summer when the atmospheric environment over both regions is predominantly influenced by monsoon circulations that blow moist air from oceans to polluted inland areas. The slope of the regression between cloud droplet size and AOD changes systematically from negative to positive with increasing precipitable water, as shown in Figure 10. This is partly because droplets have no great need to compete for water vapor in order to grow, thanks to the ample influx of water vapor from the Gulf of Mexico associated with the prevailing Bermuda high-pressure system in the summertime.
 A combination of cloud top temperatures and effective droplet sizes, estimated from the advanced very high resolution radiometer (AVHRR), has been used to infer the suppression of coalescence and precipitation processes for smoke [Rosenfeld and Lensky, 1998] and desert dust [Rosenfeld et al., 2001]. Analysis of satellite observations indicated that, on average, both naturally transported and local anthropogenic dust aerosols can significantly reduce cloud water particle size, optical depth, and liquid water path [Huang et al., 2006a, 2006b, 2010]. These results suggest that dust aerosols warm up clouds and increase evaporation of cloud droplets, further reducing cloud water path via the so-called semidirect effect. Such semidirect effects may play an important role in cloud development and act to exacerbate drought conditions over semiarid areas of northwestern China [Huang et al., 2006a, 2006b, 2010].
 It should be pointed out that the above finding, as well as those from all previous satellite-based studies of the AIE, was based on retrievals of cloud droplet size at the cloud top only because the radiometric signal at mid-IR channels saturates rapidly [Platnick, 2000; Chang and Li, 2002]. Cloud top cloud droplet size is driven by many factors, such as atmospheric stability, available water vapor, and cloud thickness. For adiabatic processes, cloud droplet size increases linearly with cloud top height, which is further linked to potential energy [Rogers and Yau, 1989]. Linear cloud droplet size profiles can be retrieved using multiple IR channels of varying absorption strength [Chang and Li, 2002, 2003]. Matsui et al.  employed column-mean cloud droplet sizes derived from microwave-based retrievals of LWP and cloud optical depth (COD) and showed a negative correlation between these cloud droplet sizes and the aerosol index (AI). They also investigated the impact of the lower tropospheric static stability (LTSS) on the AIE using observational data. Chen et al.  found systematic biases in the retrieval of LWP when using the conventional visible-IR approach, which casts a doubt on the use of optical remote sensing products alone to investigate the AIE. Sensitive to column amount, microwave-based LWP retrievals are somewhat more accurate.
 It should be stated that an increase in cloud droplet size does not necessarily lead to an increase in precipitation; that is, the first indirect effect is not a necessary cause for an increase in precipitation, nor does it lead to it. Precipitation is controlled by many factors that are dynamical, thermodynamical, and microphysical in nature.
3.2. Impact on Ice and Mixed-Phase Clouds: Aerosol Invigoration Effect
 While most research into aerosol effects on clouds has focused on low-lying stratiform clouds, some investigators have noted possible aerosol effects on cirrus clouds as well [e.g., Sassen et al., 1995; Ström and Ohlsson, 1998]. However, the findings are much less conclusive. Sherwood  analyzed changes in ice particle effective radius at the top of tropical cumulonimbus clouds (using data from the International Satellite Cloud Climatology Project) with respect to the aerosol index from the Total Ozone Mapping Spectrometer (TOMS) and found that the two quantities were negatively correlated. They attributed this to the smaller size of water droplets that were frozen and lifted to high altitudes by the deep convective cloud system. Chýlek et al. , however, found the opposite trend using MODIS data over the Indian Ocean during winter. Over the same region, Massie et al.  found little change in ice particle size with increase in aerosol loading. By combining MODIS ice cloud particle size, Aura carbon monoxide content (a proxy of aerosols), and TRMM precipitation, Jiang et al.  found that the influence of aerosols on ice clouds is contingent upon moisture content, which is somewhat similar to the finding of Yuan et al.  for warm clouds. In a dry environment, aerosols tend to reduce ice crystal size and suppress precipitation; they have little impact on ice crystal size and precipitation in a wet environment. On the basis of this finding, ice particle effective size was parameterized as a function of ice water content and aerosol optical depth for different geographic regions [Jiang et al., 2011].
 TRMM data were used to infer the presence of nonprecipitating supercooled liquid water near the cloud top due to over-seeding from smoke over Indonesia [Rosenfeld, 1999] and urban pollution over Australia [Rosenfeld, 2000]. Aircraft measurements have also provided evidence of sustained supercooled liquid water (down to −37.5°C) in continental mixed-phase convective clouds [Rosenfeld and Woodley, 2000]. These findings further suggest that continental aerosols reduce the mean size of cloud droplets, suppressing coalescence and warm-rain processes, permitting more freezing of cloud droplets and associated latent heat release above the 0°C isotherm, and enhancing the growth of large hail and cold-rain processes [Rosenfeld and Woodley, 2000]. This is now known as the aerosol invigoration effect [Andreae et al., 2004, Rosenfeld et al., 2008]. Figure 11 illustrates the effect for two deep convective cloud systems that developed under clean and dirty atmospheric conditions. Owing to the aerosol invigoration effect, the cloud in a dirty atmosphere tends to grow higher and becomes a stronger thunderstorm than it would under cleaner atmospheric conditions.
Andreae et al.  analyzed in situ observations made during the LBA-SMOCC campaign. They found that increases in smoke and surface heat due to biomass burning tend to lead to higher cloud top heights and the enhancement of cold-rain processes over the Amazon basin. This is shown in Figure 12 with in situ measurements made over the Amazon and Thailand. The “blue” and “green” cases in Figure 12 represent clean clouds over the ocean and the Amazon, respectively. The two “pyro” cases are the most extreme forms of smoky clouds. All other cases except for the two “Thai” cases are clouds with moderate concentrations of smoke. Substantial differences in the cloud drop size, DL, are evident. Observations made in Thailand on 2 May 1998 show that cloud bases had to exceed 6400 m to produce warm rain under smoky conditions. Once these clouds extended above the freezing level, they become quite vigorous with intense showers, thunderstorms, and sometimes hail events. These observations indicate that the shift of the onset of precipitation to a higher level under polluted conditions leads to enhanced formation of ice hydrometers and more vigorous convection. Koren et al.  examined cloud properties derived from the MODIS and found strong evidence that aerosols from pollution, desert dust, and biomass burning systematically invigorate convective clouds over the Atlantic Ocean. A theoretical explanation for such an effect is given by Rosenfeld et al.  using a parcel model to demonstrate the buoyancy changes in four scenarios (see Figure 13): (1) suppressing rainfall and keeping all condensed water, without freezing; (2) precipitating all condensed water, without freezing; (3) precipitating all condensates, with freezing at T < −4°C; (4) suppressing precipitation until T = −4°C, and then freezing and precipitating all condensed water above that temperature. Their model results suggest the importance of cloud height and phase in determining if aerosols invigorate cloud development and its strength, and if they suppress or enhance precipitation.
 Both aerosol microphysical and invigoration effects were confirmed through use of a long-term (10 year) set of data acquired under the U.S. Department of Energy's Atmospheric Radiation Measurement (ARM) program [Li et al., 2011b]. The extensive and high-quality set of aerosol, cloud, and meteorological measurements helped reveal unprecedented strong “climate” signals of aerosols' impact on clouds and precipitation and provided a valuable means of sorting out various influential factors and mechanisms. As seen in Figure 14a, aerosol invigoration occurs only for mixed-phase clouds with warm bases (>15°C) and cold tops (<−4°C). Mean cloud top heights (from averaging all single-layer cloud top heights found over the 10 years of data analyzed) increase systematically and significantly with increasing concentrations of condensation nuclei (CN) as measured from the ground. No such effect is observed for pure liquid clouds or for ice clouds. As CN (measured before any precipitation occurs) increases, the frequencies of light and heavy rains decrease (suppression) and increase (enhancement), respectively, as shown in Figure 14b. The finding of opposite roles played by aerosols in modulating rain has major scientific and social implications because it suggests that increases in aerosol pollution could make moist regions or seasons wetter and arid regions or seasons drier.
 The location of clouds in the atmosphere has a role in determining the nature of the invigoration effect. If the cloud base is high, for example, very close to the freezing level, there will not be very much liquid water to release latent heat because the distance for cloud particles to grow before reaching the freezing level is too short. Yet a switch in opposite effects of aerosols on the frequency of clouds occurs for clouds with tops below and above the mean freezing level (around 3.3 km), as determined from ARM's multiple sensors [Li et al., 2011a]. The freezing level is thus a key factor whose height can be determined with a newly proposed method using passive satellite imaging data like those from MODIS [Yuan et al., 2010]. At present, a complete picture of cloud geometry can be obtained for most clouds, except for really thick clouds, using ground-based and spaceborne active sensors [Clothiaux et al., 2000; Stephens et al., 2002; Mace and Benson, 2008]. Data from the MODIS multichannel passive sensor, though, were used successfully to identify single- and dual-layer clouds of thin cirrus above water clouds which account for the majority of the world's clouds [Chang and Li, 2005]. Historical high-resolution radiosonde data could also be used to reconstruct cloud geometry at sounding station sites [Zhang et al., 2010]. Such a potentially rich source of information has yet to be developed and exploited for studying the AIE.
 The invigoration effect is driven by latent heat release, which is rooted to the first indirect effect. This effect, in turn, further depends on aerosol hygroscopic properties, which may be collectively referred to as the aerosol microphysical effect. For absorbing aerosols like smoke, the thermodynamics of the atmosphere can be altered through heating of the aerosol-laden atmosphere and cooling of the surface. This enhances atmospheric stability and reduces the moisture content due to evaporation [Ackerman et al., 2000], thus inhibiting the formation of clouds and precipitation. For smoke aerosols that have the capability of serving as CCN, the two competing effects lead to boomerang-shaped responses of cloud top height and cloud fraction as theorized and confirmed by Koren et al.  over the Amazon region (Figure 15).
3.3. Impact of Aerosols From Urbanization on Thunderstorms and Lightning
 As the major emission source of anthropogenic aerosols, urban areas may disturb the atmospheric environment enough so that the regional climate is modified. There are two types of major disturbances: land cover changes and atmospheric emissions. The latter includes both aerosols and greenhouse gases. The greenhouse effect generally has a much larger spatial and long-term impact than the aerosol effect. Aerosol and land cover changes can leave strong footprints, but it is a nontrivial task to separate the effects of these two changes.
 Enhancement of rainfall downstream of some major metropolitan areas has been documented for a long time, such as in Chicago [Changnon et al., 1981], Tokyo [Ohashi and Kida, 2002], Houston [Shepherd and Burian, 2003] (see Figure 16), and New York City [Jin et al., 2005]. High aerosol concentrations in urban environments could affect precipitation variability by providing an enhanced source of CCN. Hypotheses were made to explain the effect of urban regions on convection and precipitation [van den Heever and Cotton, 2007; Shepherd, 2005]. It is unclear if the urban heat island effect or the aerosol effect, or both, causes the enhancement. With the theory of aerosol invigoration, we may now take a new look at this phenomenon. Heavily polluted cities are an ideal setting for inducing and enhancing invigorated clouds, especially cities near lakes and along coastlines in summertime. During this season, warm moist air can blow from seas or lakes to land, providing the following conditions favorable to cloud invigoration: (1) a plentiful supply of highly hygroscopic anthropogenic aerosols, (2) the heat island effect which fuels convection, and (3) moist hot air that can provide large amounts of potential energy to sustain strong convection.
 This seems to corroborate the finding of a midweek anomaly in precipitation and convection, and intensified lightning over urban areas. Using long-term integrated TRMM-derived precipitation data, Bell et al.  found a significant midweek increase in summertime afternoon thunderstorms over the aerosol-laden southeastern United States, which coincides with a midweek increase in ground-measured aerosol concentration, wind convergence at 1000 hPa and divergence at 300 hPa, and vertical velocity at 500 hPa (see Figure 17). These coincidental findings are consistent with the notion that aerosols have a major impact on the dynamics of continental mixed-phase convective clouds [Rosenfeld and Woodley, 2000; Williams et al., 2002].
 Enhancement of the lightning flash density was found to be centered over and downwind of a metropolitan area [Orville et al., 2001], as shown in Figure 18. Possible causes include enhanced convergence associated with the urban heat island effect and altered microphysical processes associated with anthropogenic pollution. Steiger and Orville  compared 14 years' worth of cloud-ground flash density distributions with the locations of PM10 (particulate matter less than 10 μm in diameter) sources in Louisiana. They concluded that pollution plays a key role in lightning enhancement, while urban and sea breeze effects are negligible. Yuan et al.  examined 2005 lightning data from the lightning-imaging sensor on board the TRMM satellite and MODIS AOD (Figure 19). They found anomalously high lightning activity in the presence of high aerosol loading, which was traced to volcanic activity; no connection was found with any anomalies in meteorology. They further quantified the response of lightening to AOD: A ∼60% increase in aerosol loading leads to a more than 150% increase in lightning flashes. Aerosols could influence lightning activity through modification of cloud microphysics. Cloud ice particle sizes are reduced and cloud glaciation is delayed to colder temperatures when aerosol loading is increased. Despite the seemingly convincing evidence linking aerosols with lightning activity, their real connection is far more complex, especially in light of many other influential factors associated with urban regions, as demonstrated by simulations with a state-of-the-art land surface model and a cloud-resolving model (see section 5 and van den Heever and Cotton ).
4. LARGE-SCALE OBSERVATIONAL DIAGNOSTICS OF THE AEROSOL EFFECT ON PRECIPITATION
 In general, a main purpose of large-scale observational analyses of aerosol-precipitation relationships is to reveal statistically significant signals that may suggest influences on the large-scale distribution and variability of precipitation by radiation and/or CCN effects of aerosol. This is different from the analyses discussed in section 3 that seek physical processes governing the AIE. On large scales (especially the global scale), total precipitation is constrained by the moisture budget, which is mainly dictated by surface evaporation. Unless aerosol effects alter surface evaporation, they may modify only the timing and location of precipitation but not its total amount. A local signal of aerosol effects on precipitation is usually a manifestation of such changes in timing and location of precipitation.
4.1. Isolating Aerosol Effects
 Large-scale observational analyses of aerosol effects on precipitation face no less of a challenge than the theoretical, modeling, and field observational approaches discussed elsewhere in this review. All large-scale observational studies must adequately address issues of data quality, analysis methods, robustness of the results (i.e., statistical significance), and causality. The issue of causality manifests itself in observational studies of aerosol effects on precipitation in two problems: aerosol effects on precipitation versus precipitation effect on aerosols (i.e., rainout and washout), and effects on precipitation by other meteorological factors covarying with aerosol.
 The simplest way to remove the rainout/washout effect on aerosol and cloud contamination from an aerosol-precipitation analysis is to avoid relationships between coincidental measurements of aerosol and precipitation. Aerosols upwind can be included in an analysis based on back-trajectory calculations [Hui et al., 2008; Huang et al., 2009b]. An equivalent approach is to include time lags with aerosol signals leading precipitation [Lau and Kim, 2006; Bollasina and Nigam, 2009]. Another method is to exclude aerosol data near cloud scenes or within a grid box with a large cloud fraction [Koren et al., 2010a]. In a target precipitation area that is remote from aerosol sources, fluctuations in aerosols independent of precipitation should be the same as those outside and upwind of the precipitation region. On the basis of this, Huang et al. [2009, 2009a] used aerosols averaged over a large domain containing rainbands over the tropical Atlantic Ocean and West African monsoon region and broad areas of no precipitation to represent large-scale fluctuations in aerosols in the rainband regions (Figure 20a).
 Several methods have been used in previous studies to isolate the aerosol effect on precipitation from other effects. One is to examine the variability of other factors (e.g., water vapor) that may potentially cause fluctuations in precipitation. Observed aerosol-precipitation covariability might indicate aerosol effects on precipitation only if the observed precipitation variability is not coherent with these other factors. The following examples illustrate some approaches that have been applied attempting to isolate aerosol effects on precipitation from other effects.
Qian et al.  observed a decreasing trend in light rain (<10 mm d−1) and an increasing trend in heavy rain (>50 mm d−1) over East China from 1956 to 2005. This is the same period of large increases in pollution in the same part of China (Figure 21), although their trends are not the same nor are they monotonic. No correlation was found between decreasing trends in light rain with water vapor transport as deduced from a global reanalysis product. This led the authors to rule out the possibility that the trend in light rain was caused by changes in large-scale meteorological conditions. They subsequently conjectured that the increase in aerosols due to pollution observed during the same period was the likely cause of the observed decreasing trend in light rain through the known suppressing effect of aerosols that shifted the rain distribution from light to heavy. They did not, however, discuss whether the change in the total amount of water corresponding to the observed trend in light rain over the time period in question is within the uncertainties of the water vapor transport data.
Wilcox et al.  observed a northward shift of rainfall in the Intertropical Convergence Zone (ITCZ) over the tropical Atlantic Ocean during African dust outbreaks. They examined differences in temperature profiles and lower tropospheric zonal wind between African dust outbreaks and low dust conditions. They postulated that the northward shift of rainfall was caused by lower tropospheric warming attributable to advection of the warm Saharan air layer (SAL), enhanced subtropical subsidence, and radiative heating of dust.
 Similarly, Lau and Kim  compared composites and lag regressions of aerosols, wind, temperature, and precipitation over the Indian summer monsoon region. They proposed an “elevated heat pump” hypothesis, namely, that anomalously high concentrations of absorbing aerosols during the premonsoon season are associated with anomalous warming that is responsible for changes in the large-scale circulation leading to an increase in monsoon rainfall over India. In the work of both Lau and Kim  and Wilcox et al. , possible contributions of aerosols to the observed variability of rainfall were compared to but not separated from other factors. Therefore, their hypothesis is plausible but not without ambiguity, even though the observed signals are consistent with those numerical simulations (see section 6), where the attribution of changes to specific physical processes is much clearer. The same sets of observations have been subject to different interpretations and result in contradictory conclusions [Nigam and Bollasina, 2010].
 The importance of examining the covariability between aerosols, precipitation, and other factors has been explicitly explored. In a study of the rainfall trend over Israel, Alpert et al.  pointed out that urban dynamics (e.g., the heat island effect), if not fully taken into consideration, may lead to erroneous interpretations of data and to the incorrect conclusion that an observed decreasing rainfall trend is due to the suppression effect of increasing urban pollution from upwind regions. By comparing submonthly evolution patterns of aerosols, precipitation, and other meteorological variables during the premonsoon period over South Asia, Bollasina and Nigam  reproduced the earlier monthly observations [Bollasina et al., 2008] and showed that anomalous aerosol buildup in May can delay the onset of monsoon rainfall due to the aerosol radiative effect (i.e., cooling of the land surface). But they acknowledged that the pervasive influence of advection precludes a robust analysis of the aerosol impact.
 Various statistical tools have been used either to remove the dependency of precipitation on other factors before its relationship with aerosols is established or to determine the importance of different factors to observed variability in precipitation so that the role of aerosols versus others can be determined. The following are examples of studies that used these tools.
 In an attempt to identify the aerosol effect on rainfall over the Amazon basin during the biomass burning season (September 2006), Jones and Christopher  applied the principle component analysis (PCA) method, a commonly used statistical tool in geosciences. This method encompassed precipitation and 23 other parameters including meteorological environmental variables (winds, humidity, and temperature), cloud information (optical thickness, top pressure, liquid water path, fraction, and droplet effective radius), aerosol optical thickness, and locations. They interpreted the weighting of each parameter and its sign relative to precipitation in each principle component (PC) as a signal of the potential physical connection between the two. On the basis of this interpretation, they found that atmospheric environmental variables (e.g., zonal wind, relative humidity, lapse rate, and vertical motion) are the dominant factors for rainfall variability, with the largest weighting for the first principal component (PC1) which explains 25% of total rainfall variance. Following the same argument, they identified the radiative effect of aerosols as the second most important factor for rainfall, which is represented by the second principal component (PC2) that explains 15% of total rainfall variance. Their results suggest a suppressing effect of smoke on rainfall. The orthogonality requirement for each PC may, however, obscure the physics intended to be disclosed.
 In a study of the aerosol effect on precipitation over the tropical Atlantic Ocean and in the West African monsoon region, Huang et al. [2009, 2009a, 2009c] used a multivariable linear regression method to remove the variability in aerosols and precipitation that is coherent with water vapor and sea surface temperature (SST) related to known climate modes (e.g., El Niño–Southern Oscillation (ENSO), North American Oscillation (NAO), and Tropical Atlantic Variability (TAV)). The resulting anomalous time series of aerosols and precipitation are considered linearly independent of other weather and climate factors. They then compared the spatial distribution and seasonal cycle in anomalous precipitation between months of high versus low aerosol anomalies (top and bottom terciles of all months) averaged over a large domain (Figure 20a). The comparison revealed decreases in precipitation during months of high aerosol anomalies at the southern edge of the rainbands during boreal winter, the season of frequent biomass burning over equatorial and southern Africa (Figures 20b and 20c). The spatial pattern and the seasonal cycle of the rainfall reduction do not match those of expected aerosol wet deposition. Numerical simulations with only the radiative effect of black carbon aerosol included have reproduced this observation (see section 6). They concluded that the reduction in rainfall is due to the radiative effect of smoke from biomass burning. The linear regression can only account for simultaneous relationships. So the removal of the coherent variability between precipitation and other factors may not be complete.
 A highly recommended method of isolating the aerosol effect from other effects is to examine aerosol-precipitation relationships in different regimes [Stevens and Feingold, 2009]. Regimes can be defined in various ways depending on data and analysis targets. They include convective characteristics (e.g., cloud working function; see below), environmental conditions for cloud (e.g., static stability), or cloud microphysics (e.g., LWP, ice path), as demonstrated in the following examples.
 In a study of the aerosol effect on rainfall during the biomass burning seasons (August–October of 2000 and 2003) in the Amazon, Lin et al.  examined relationships between aerosol optical depth versus precipitation and clouds stratified by bins of cloud working function (CWF). CWF is defined as a vertical integration of work by buoyancy per unit mass flux, or the kinetic energy generation per unit mass flux [Arakawa and Schubert, 1974]. Instigation of convection in some numerical models is determined by the CWF passing a given threshold. CWF was used in this study to define regimes of the large-scale meteorological forcing for rainfall and convection. The CWF-stratified analysis indicates that elevated AOD was associated with increases in precipitation, occurrence of intense rainfall events, cloud cover, cloud top height, water path, and formation of ice. This is in contrast to the result from Jones and Christopher  discussed above.
Sorooshian et al.  proposed to stratify the environmental effect in terms of LWP in a concept of precipitation susceptibility, which is defined as S = −dlnR/dlnNd, where R is the precipitation rate and Nd is the CDNC or a subcloud NCCN proxy. Using satellite data, a cloud parcel model and large eddy simulations, they demonstrated different vulnerabilities of precipitation to aerosols in three regimes: (1) low LWP, where clouds do not precipitate and are relatively insensitive to Nd, (2) intermediate LWP, where precipitation forms by interaction of cloud drops and is progressively more effectively suppressed by increasing Nd, and (3) high LWP, where susceptibility begins to decrease because there is ample LWP to drive the precipitation process. To remove ambiguity in whether the microphysical response is a result of a change in aerosols or a change in meteorological conditions (e.g., available liquid water), Sorooshian et al.  further proposed to separate the precipitation susceptibility into two parts: Sr = −(∂lnR/∂lnr)(∂lnr/∂lnNd) and Sτ = −(∂lnR/∂lnτ) (∂lnτ/∂lnNd), where r is the cloud droplet effective radius and τ is the cloud optical depth. They concluded that this separation provided more confidence in the results from the original precipitation susceptibility.
Panicker et al.  calculated the aerosol indirect effect, AIE = dlnr/dlnt [Feingold et al., 2003], for July and September 2001–2004 in four Indian summer monsoon regions. Similar to Yuan et al. , they used MODIS AOD data for the fine mode fraction (FMF), cloud liquid water path (CLWP), cloud ice path (CIP), cloud ice radius (CIR), and cloud water radius (CWR). They used binned CLWP and CIP to define regimes. They found a positive AIE (the Twomey effect) for fixed CLWP and CIP in years when the monsoon rainfall was below normal, but a negative AIE (the anti-Twomey effect) in years of normal and above-normal rainfall. They suggested that the AIE depends on large-scale circulation patterns that may advect different types of aerosols from different sources. As pointed out earlier, ambiguity in the aerosol effect on precipitation on the seasonal time scale could be reduced by a careful water budget analysis.
 From the above discussion, it is obvious that each approach for isolating the aerosol effect on precipitation from other factors has it pros and cons. Large-scale diagnostics of the aerosol effect on precipitation, through either radiation or CCN changes or both, are incomplete without considering microphysics (clouds, aerosols, and precipitation), mesoscale cloud dynamics, and the large-scale background environment (aerosol transport, water budget). This requires unprecedented collaboration and coordination among subdisciplines within the atmospheric science field.
4.2. Applications of Satellite Data in Revealing ACPI
 A unique advantage of satellite data is their global coverage (in comparison to in situ observations). Observational evidence has been obtained from satellite data following somewhat different approaches from those based on other types of data as discussed earlier and large-scale models as discussed later in this review. Satellite observations can be used to effectively remove high-frequency weather variability and isolate signals of the AIE, as previously demonstrated [Han et al., 1998; Wetzel and Stowe, 1999; Nakajima et al., 2001; Liu et al., 2003]. The advent of multiple advanced Earth Observations System (EOS) sensors aboard the A-Train [e.g., Koren et al., 2008; L'Ecuyer et al., 2009; Niu and Li, 2011] has substantially increased this capability. The most tangible and direct evidence of the AIE is linked to the microphysical properties of clouds, which are more readily measured by satellite observations despite various retrieval uncertainties and limitations [Z. Li et al., 2009].
 Among a handful of microphysical variables retrievable from satellites (DER, LWP, COD), LWP plays the most significant role in precipitation [Sorooshian et al., 2009; Chen et al., 2011], even though these variables are not independent. Using matched rainfall data from CloudSat and cloud microphysics from MODIS aboard the A-Train, Chen et al.  examined the predictability of rainfall from warm clouds. They found that LWP is by far the dominant factor, followed by DER and COD, as illustrated by the prediction skills in Table 2. As such, detection of any effects of aerosols on precipitation may begin with their effects on these key cloud variables.
Table TABLE 2.. Statistical Relationships Between Cloud Parameters and Warm Rain for January and July 2008a
HSS is the Heidke skill score. Only raining cloud samples are used to calculate the correlation coefficients. Adapted from Chen et al. .
 Taking advantage of the unprecedented superior quality and quantities of A-Train sensors [Stephens et al., 2002], thorough investigations of the AIE on warm clouds have been conducted under a wide range of conditions on a global scale [Lebsock et al., 2008; Berg et al., 2008; L'Ecuyer et al., 2009; Sorooshian et al., 2009; Niu and Li, 2011]. Lebsock et al.  and L'Ecuyer et al.  attempted to sort out various factors influencing warm rain or drizzle using a combination of precipitation data from CloudSat, cloud microphysics from MODIS, LWP and column water vapor (CWV) from Advanced Microwave Scanning Radiometer-EOS (AMSR-E), meteorological variables from a global reanalysis product, and a global aerosol transport model (distributions of aerosol species in both cloudy/raining and clear-sky scenes). As shown in Figure 22, the probability of precipitation increases with increasing LWP and CWV, and is moderately affected by atmospheric stability. For the same LWP, CWV, and stability, dirty clouds are less likely to rain than clean clouds. Not all types of aerosol particles inhibit precipitation. One exception is sea salt aerosols, because a large portion of them are within the GCCN size range and thus may serve as rain embryos (see section 2).
 Analyzing MODIS aerosol products (optical depth over land and aerosol index over oceans) for the entire global tropics (between 20°N and 20°S) where convective clouds are more dominant than at the middle to high latitudes, Niu and Li  found distinct patterns of changes in precipitation rate with aerosol index for warm and mixed-phase clouds, as shown in Figure 23. Light rain associated with warm clouds occurs less frequently with increasing AI, whereas it increases with AI for mixed-phase clouds. This finding corroborates ground-based findings of Li et al. [2011a]. Both support the theories of aerosol microphysical effect and invigoration effect, namely, aerosols significantly invigorate convection through ice processes, while precipitation from liquid clouds is suppressed due to competition for limited water. It is worth noting that CloudSat is particularly good at detecting drizzle but not as capable of detecting moderate to heavier rainfalls due to its high-frequency (95 GHz) radar. This is remedied by the TRMM satellite. It carries two rain sensors: the TRMM Microwave Imager (TMI) and the Precipitation Radar (PR) at 35 GHz with sensitivities to different rain attributes. The TMI is most sensitive to LWP, while the PR is sensitive to large drops. By virtue of these differences in sensitivity, Berg et al. [2006, 2008] discovered a region where the largest discrepancies between the two sets of rain estimates was found, which was construed as a smoking gun of the strongest AIE on precipitation. It is located around the coast of East Asia and the western Pacific (Figure 24), the outlet of pollutants and dust from the world's most populated region. While continental-scale transport can bring some aerosols generated over Europe and Asia to this region [Chin et al., 2004], local emissions are by far the largest source of aerosols, as shown by extensive measurements of aerosol optical, physical, and chemical properties collected during two major field experiments conducted in China [e.g., Li et al., 2007, 2011b]. Using the 2008 intensive field campaign data acquired by the ARM Mobile Facility in southeastern China [Li et al., 2011b], Fan et al.  confirmed the significant role played by aerosols on precipitation. This was corroborated indirectly by the analysis of Qian et al. .
5. CLOUD-RESOLVING MODEL SIMULATIONS
 The statistics of precipitating mesoscale convective cloud systems (MCS) have been quantified from space in terms of its correlation with rainfall estimated from the TRMM precipitation radar and microwave imager retrievals. Figure 25 shows that MCSs are the dominant heavy-rain producers in the tropics and subtropics; they generate more than 50% of rainfall in most regions. The global average annual rainfall exceeds 3 mm d−1 and up to 90% of the rainfall occurs over certain continental areas, e.g., the La Plata Basin of South America. Here we review mainly cloud resolving model (CRM) simulations associated with MCSs to examine the sensitivity of precipitation processes (rainfall) to aerosol concentrations. Other cloud-scale modeling simulations (including large-eddy simulations) associated with warm clouds, stratocumulus, orographic clouds, and Arctic stratus clouds are given by Levin and Cotton .
5.1. Major Methodology
5.1.1. Cloud-Resolving Model
 One of the most promising methods to test the representation of cloud processes used in climate models is to use observations together with CRMs (see a recent review by Tao and Moncrieff ). The CRM has to be nonhydrostatic, and its flow can either filter out (anelastic) [Ogura and Phillips, 1962] or allow (compressible) [Klemp and Wilhelmson, 1978] the presence of sound waves. Sound waves are not important in thermal convection, but their presence can place severe restrictions on the time step in numerical integrations. For this reason, most CRMs use an anelastic system of equations in which sound waves have been removed by neglecting the local variation of air density with time in the mass continuity equation. A three-dimensional diagnostic (elliptic) pressure equation can be solved using direct (e.g., Fourier transform) or iterative methods. In the compressible system, a very small time step (e.g., 2 s for a 1000 m spatial resolution) is needed for time integration due to the presence of sound waves. However, Klemp and Wilhelmson  developed a semi-implicit time-splitting scheme, in which the equations are split into sound wave and gravity wave components to achieve computational efficiency. One advantage of the compressible system is that its numerical code remains a set of explicit prognostic equations, and adjustments due to factors such as surface terrain can be incorporated into the numerical model without complicating the solution procedure.
 Compared to typical global circulation and climate models, CRMs use more sophisticated and relatively realistic representations of cloud microphysical processes, and they can reasonably well resolve the structure and life cycles of clouds and cloud systems (with sizes ranging from about 2 to 1000 km). CRMs also allow for explicit interactions between clouds, outgoing longwave (cooling) and incoming solar (heating) radiation, as well as ocean and land surface processes (see reviews by Tao [2003, 2007] and Tao and Moncrieff ). Observational data are required to initialize CRMs and to validate their results. Browning et al.  and Randall et al.  recommended that improved CRMs be used as a test bed to develop and evaluate cloud parameterizations in large-scale models.
 There are several major advantages in using CRMs to study the interactive processes between clouds, precipitation, and aerosols. For example, the use of a fully explicit microphysics scheme (liquid and ice) and a fine horizontal resolution can provide relatively realistic cloud optical properties, which are crucial for determining radiation budgets. With a high spatial resolution, each atmospheric layer is considered either completely cloudy (overcast) or clear; no partial cloudiness is assumed. In addition, the applied microphysics scheme is realistic enough to simulate the life cycle of clouds, precipitation, and aerosols. The CRM can also have better cloud dynamic processes in terms of the transport of aerosols (see reviews by Thompson et al. , Ekman et al. [2004, 2006], and Yin et al. ).
5.1.2. Microphysics Used in CRMs
 In order to use a CRM to study the impact of aerosols on cloud and precipitation processes, CCN activation and IN nucleation need to be considered in its microphysical scheme (see section 2). Two-moment bulk or spectral bin microphysics (SBM) schemes are required to study the impact of CCN, GCCN, and IN on cloud and precipitation formation. One of the major differences between the two-moment bulk and spectral bin microphysics schemes concerns the representation of cloud particle size spectra (Figure 26). Two-moment schemes typically combine the main features of single-moment schemes by calculating the mixing ratios of hydrometeors, and then adding additional variables for the number concentrations of all particles. Warm-cloud (ice-free) microphysics assumes a bimodal population of water particles. One population is for small cloud droplets whose terminal velocities are negligible compared to the vertical velocity of air, and the other is for large raindrops that have significant fall speeds. Ice microphysics typically assumes three types of particles: small cloud ice whose terminal velocity is negligible, snow whose terminal velocity is about a few tens of centimeters, and large graupel or hail that fall even faster. Only recently have some CRMs included frozen drops or hail as a fourth kind of particle. Graupel has a low density and a high intercept in the Marshal-Palmer distribution (high number concentration), while hail has a high density and a low intercept. Only raindrops, snow, graupel, and hail have a chance to reach the ground level. Graupel is representative for tropical oceanic convection, and hail is representative for midlatitude storms [McCumber et al., 1991]. More than 25 transformations occur among water vapor, liquid particles, and ice particles, such as growth of ice crystals by vapor deposition and riming, the aggregation of ice crystals, the formation of graupel and hail, the growth of graupel and hail by the collection of supercooled cloud drops, the shedding of water drops from hail, the rapid growth of ice crystals in the presence of supercooled water, and the melting and sublimation of all forms of ice (see Figure 27). Certain mathematical functions such as the Khrgian-Mazin distribution function for cloud drops and the Marshall-Palmer distribution function for raindrops, snow, and graupel or hail are assumed to represent their size distributions.
 With increasing computing power, explicit bin-microphysical schemes have been applied more commonly in CRMs to study cloud-precipitation-aerosol interactions. The formulation of explicit microphysical processes is based on solving equations for mass advection by condensation growth and stochastic collision kinetics for the size distribution functions of water droplets (cloud droplets and raindrops together as one continuous category). Ice particles are much more complicated due to their different shapes, so they are often classified into various growth habits such as columnar, plate-like, dendrites, snowflakes, graupel, and frozen drops. Each type is described by a discretized size distribution containing as many as 30 or more categories (bins). Spectral bin microphysics include the following processes: (1) activation (nucleation) of cloud droplets; (2) nucleation of ice particles [Pruppacher and Klett, 1997; Meyers et al., 1992], including homogeneous freezing, deposition nucleation, condensation-freezing nucleation, immersion freezing [Vali, 1994], and contact freezing; (3) ice multiplication [Hallett and Mossop, 1974; Mossop and Hallett, 1974]; (4) detailed melting [Khain et al., 2004]; (5) condensation or evaporation of liquid drops [Pruppacher and Klett, 1997; Khain et al., 2000]; (6) deposition or sublimation of ice particles [Pruppacher and Klett, 1997; Khain et al., 2000]; (7) drop/drop, drop/ice, and ice/ice collision/coalescence [Pruppacher and Klett, 1997; Pinsky et al., 2001]; (8) turbulence effects on liquid drop collisions [Pinsky et al., 2000, 2008]; and (9) collisional breakup [Low and List, 1982; Seifert et al., 2005]. Sedimentation of liquid and ice particles is also considered, and for the latter, crystal shape is an important factor. Spectral bin microphysics is specially designed to take into account the effect of atmospheric aerosols on cloud development and precipitation formation by calculating the activation of aerosols explicitly according to the Köhler theory [Pruppacher and Klett, 1997]. Section 2 describes in more detail processes associated with the initialization of CCN, GCCN, and IN.
5.2. CCN Effect on Clouds
 It is commonly believed that clouds in a clean environment (low CCN concentration) produce fewer droplets but with larger sizes due to greater condensational and collectional growth, leading to a broader size spectrum in comparison to the high CCN situation. Figure 28 shows simulated cloud drop size distributions under low and high CCN concentrations [Tao et al., 2007]. The results are very similar to those observed and shown by Fletcher  and Squires . van den Heever et al.  and Carrió et al.  also found that smaller cloud droplets are found with a narrow spectrum under dirty conditions. The numerical results are in good agreement with observations, indicating that the microstructure of clouds depends strongly on cloud-aerosol interactions. The Twomey effect was well simulated. The width of the drop size distribution could have an impact on precipitation processes. For example, smaller cloud droplets would reduce the chance to form raindrops from cloud drop coagulation. This result is in agreement with observations [i.e., Twomey et al., 1984; Albrecht, 1989; Rosenfeld, 1999].
 The effects of increases in aerosol concentration on cloud lifetime for warm convective clouds have been studied using CRMs and large-eddy simulations (a special type of cloud model with a resolution of 100 m or smaller). Teller and Levin  showed that a polluted cloud produces less precipitation, which leads to an increase in the lifetime of the cloud under the same meteorological conditions. This result is in agreement with the second aerosol indirect effect on cloud lifetime [Albrecht, 1989; Ackerman et al., 2000]. However, a separate modeling study shows that an increase in aerosol concentration from very clean to highly polluted conditions does not increase cloud lifetime (Figure 29), even though precipitation is suppressed. In rare cases (two cases in Figure 29), long-lived polluted clouds may have longer lifetimes than clean clouds due to the merging of individual clouds. This result is contrary to the observation that increases in aerosol concentration leads to prolongation of cloud lifetimes. But the model results do agree with observations of precipitation suppression under polluted conditions. Jiang et al.  proposed that the small changes in cloud lifetime are due to the competing effects of precipitation suppression and enhanced evaporation for shallow clouds. The differences between results from Teller and Levin  and Jiang et al.  could be due to the differences in aerosol concentration (mildly polluted versus highly polluted) and/or environmental conditions.
5.3. CCN Effect on Precipitation
5.3.1. Impact of CCN on Surface Precipitation
 Recently, many CRMs have been used to examine the role of aerosols on mixed-phase convective clouds (Table 3). These modeling studies have many differences in terms of model configuration (two- or three-dimensional), domain size, grid spacing (150–3000 m), microphysics (two-moment bulk, simple or sophisticated spectral-bin), turbulence (first- or 1.5-order turbulent kinetic energy (TKE)), radiation, lateral boundary conditions (i.e., closed, radiative open, or cyclic), cases (isolated convection, tropical or midlatitude squall lines), and model integration time (e.g., 2.5 to 48 h). A simple metric, changes in time-integrated precipitation (dP = 100 × (Pdirty − Pclean)/Pclean) as a result of increases in the number concentration of CCN (dN0 = Ndirty − Nclean), was used to examine the impact of aerosol concentration on surface rainfall (Table 4). Among these modeling studies, the most striking difference is that cumulative precipitation can either increase or decrease in response to higher concentrations of CCN. Phillips et al. , Khain et al. [2004, 2005], Khain and Pokrovsky , and Teller and Levin  changed the number concentrations of CCN gradually and found robust decreases in cumulative precipitation for higher concentrations of CCN. This is completely opposite to the results of Wang , Khain et al. , Lee et al. [2009a], and Fan et al. [2007b].
Table TABLE 3.. Key Papers Using Cloud Resolving Models to Study the Impact of Aerosols on Precipitationa
Grid Size and Time Step
Lateral Boundary Conditions
Model dimensionality (2-D or 3-D), microphysical schemes (spectral-bin or two-moment bulk), turbulence parameterization (first- or 1.5-order turbulent kinetic energy (TKE)), radiation (with or without), domain size (km), resolution (m), time step (s), lateral boundary condition (closed, cyclic, or radiative open), and case and integration time (h) are all listed. Updated and modified from Tao et al. .
Tao et al.  used a two-dimensional CRM with detailed spectral-bin microphysics to examine the aerosol impact on a tropical oceanic mesoscale convective system, a summertime midlatitude continental squall line, and a short-lived Florida sea breeze convective storm. Rain suppression in the high CCN concentration runs is evident in all three case studies but only during the first hour of the simulations (Figure 30). Rain reaches the ground early in all the clean cases. This result suggests that microphysical processes dominate the initial stage of cloud development, during which the transition of cloud droplets from condensational to collectional growth is very sensitive to cloud drop size. Compared to the case under polluted conditions, clouds in a clean environment (low CCN concentration) produce fewer but larger cloud droplets, leading to a better chance for raindrop formation from cloud drop coagulation. This result is in good agreement with many observations [e.g., Rosenfeld, 1999, 2000] and other CRM studies [Khain and Pokrovsky, 2004; Khain et al., 2005; Teller and Levin, 2006; Seifert and Beheng, 2006; van den Heever et al., 2006; Carrió et al., 2007; van den Heever and Cotton, 2007; Lee et al., 2009a] and is in agreement with Twomey's second indirect effect. During the mature stage of the simulations, the effect of increasing CCN concentration ranges from rain suppression in the midlatitude continental case to little effect in the Florida sea breeze case to rain enhancement in the Pacific oceanic case. These results suggest that model simulations of the whole life cycle of a convective system are needed in order to assess the impact of aerosols on precipitation processes associated with MCSs and thunderstorms. These results also show the complexity of aerosol-cloud-precipitation interactions within deep convection.
Khain et al.  and Khain  recently conducted a number of numerical experiments to identify the factors that determine the impact of aerosols on precipitation. A scheme (Figure 31) was proposed to classify aerosol effects on clouds and cloud systems under different environments. It shows that if the ambient relative humidity is high, then the condensation gain (loss) is large and the condensation loss (gain) is low, which could lead to an increase (decrease) in precipitation. Seifert and Beheng , Khain et al. , and van den Heever et al.  have also showed that the impact of aerosols on precipitation and convection structure depends on cloud type. A decrease in precipitation with an increase in aerosol concentration usually occurs for isolated cumulus clouds and cloud systems that develop within a relatively dry environment and/or within regions of large wind shear or stratocumulus clouds. Fan et al.  also found that the increase in CCN concentration always suppresses convection under strong wind shear conditions but enhances convection under weak wind shear conditions. On the other hand, an increase in precipitation with an increase in aerosol concentration often occurs for clouds forming in a moist environment, such as coastal zones, within cloud ensembles or tropical squall lines. Such a result can also be found in other CRM studies [Wang, 2005; Tao et al., 2007; Fan et al., 2007b] (see also Figure 30b) and is consistent with the LES study by Ackerman et al. . Note that Wang , Tao et al. , Khain et al. , Fan et al. [2007a], and Lee  all showed that aerosols have a larger effect on precipitation under more humid conditions.
 Recently, van den Heever et al.  made use of large-scale (e.g., 10,000 km), long-duration (100 days), high-resolution (1 km) radiative-cloud-equilibrium (RCE) simulations to investigate the impacts of enhanced CCN concentrations on a wide variety of storm types that developed under a wide range of different environmental conditions. They found that high CCN concentrations led to a reduction in surface precipitation from shallow clouds, but an enhancement in the precipitation produced by deep convective clouds, with a mixed response from more moderate convective storms such as cumulus congestus. They also noted that the frequency of lighter precipitation-producing systems was decreased under more polluted conditions, while the frequency of heavy precipitation-producing systems was enhanced, concluding that polluted conditions result in a greater frequency of more intense rainfall-producing systems (Figure 32).
 In almost all of the above cases, idealized aerosol concentrations were used in the model simulations. Some of the CRM domains were too small to resolve the observed clouds or precipitation systems (the domain size has to be at least twice as large as the simulated features). Furthermore, very few of these CRM studies compared model results with observed cloud structures, organization, and radar reflectivities (Figure 33). Note that model simulations may capture well storm sizes and structures under different environmental conditions. For example, the leading convection and the extensive trailing stratiform rain areas compared well with the radar reflectivity observed during the mature stage of the continental case [Rutledge et al., 1988]. Clean cases (i.e., the control experiments) generally agree better with observations. In terms of radar reflectivity magnitudes, the agreement between simulations and observations is better at lower levels where only liquid phase cloud or rainwater exist. Simulated radar reflectivities tend to be higher than observations at upper levels and in the anvil area where ice phase particles dominate. This reflects the inadequate description of various ice phase mechanisms in this calculation, particularly those related to aerosol effects.
5.3.2. Physical Processes Behind the CCN Effect on Precipitation
 Observational studies suggest that enhanced aerosol concentrations could suppress warm rain processes by producing a narrow drop size spectrum that inhibits collision and coalescence processes [e.g., Squires and Twomey, 1966; Warner and Twomey, 1967; Warner, 1968; Rosenfeld, 1999]. In addition, more aerosols would reduce precipitation and rainfall. This is because more aerosols could produce smaller cloud droplets, resulting in less efficient collision coalescence and consequently less rainfall. Many cloud-resolving modeling studies simulated these processes during the early stage in the development of isolated convective systems and found that sometimes, more rainfall is produced under polluted (high CCN concentration) conditions.
 Several cloud-resolving modeling studies also examined the physical processes that could lead to aerosol-induced changes in precipitation. In general, three mechanisms were proposed to explain the enhancement of precipitation by changing (increasing or decreasing) the aerosol concentration (see Figure 34). The first mechanism involves the creation of stronger updrafts or downdrafts resulting from enhanced latent heat release as CCN suppress warm-rain formation and thus retain more liquid water in the cloud to be frozen at upper levels. This effect could be termed as the latent heat–dynamic effect.Wang  showed precipitation increases in tropical deep convection due to higher CCN concentrations through this latent heat effect. Khain et al.  also found that for cases where there was enhanced precipitation with high CCN concentrations, clouds were associated with stronger updrafts or downdrafts as well as stronger convergence in the boundary layer, which provides a better chance to trigger secondary clouds and prolong the lifetime of the convective system. van den Heever and Cotton , Lee et al. [2008a], and Storer et al.  also demonstrated the influences of aerosols on secondary storm development and its effect on increasing precipitation.
 The second mechanism is stronger evaporative cooling due to more but smaller raindrops under high CCN concentration conditions. Stronger evaporative cooling could enhance the strength of the near-surface cold pool. When the enhanced cold pool interacts with lower level wind shear, convergence could become stronger, producing more vigorous convection that ultimately leads to enhanced surface precipitation. This positive feedback mechanism could be termed as the cool pool effect. It seems to be occurring in the oceanic convective case (Figure 35), in which evaporative cooling in the lower troposphere is more than twice as strong for the polluted scenario compared to the clean scenario. Note that stronger evaporative cooling occurs in the developing stage of convective cloud systems. Lee et al. [2009a] also demonstrated that stronger evaporative cooling occurred under high aerosol concentrations and consequently led to enhanced surface precipitation.
 The third mechanism is the CCN effect on cloud microphysics. Wang  suggested that with higher CCN concentrations, there is a greater increase in total water content consisting of numerous small liquid particles, leading to more vigorous convection and cold-rain processes. As a result, rain production is mainly from ice phase microphysics in the modeled tropical deep convective case for which precipitation is increased due to more CCN (with similar processes as the above continental convective case). Cheng et al.  further showed that increasing the CCN concentration leads to more cloud drops and cloud ice, but that there is uncertainty in the magnitude of its effect on surface precipitation due to various responses of cold-rain production (this could be termed as the cold-microphysics effect). Figure 36 shows four different microphysical processes that would affect surface precipitation. The CCN effect on precipitation in the low-CCN case is dominated by suppressed warm-rain formation (effect A) and enhanced riming (effect C). On the other hand, in the high-CCN case where changes in snow-raindrop accretion are small, decreases in snow riming (due to reduced collection efficiency, effect B) and melting are big enough to dominate the change in cold-rain production, leading to suppressed surface rainfall. Overall, the CCN effect on precipitation in the high-CCN case is dominated by effect A and effect B.
 However, these three physical mechanisms can affect each other, making it difficult to isolate each mechanism independently. For example, a stronger evaporative cooling (cold pool effect) in the low troposphere for the high CCN-enhanced precipitation case (latent heat–dynamic effect) is evident in Figure 34a. On the other hand, the stronger cooling could be due to more evaporation associated with a stronger convective downdraft (latent heat–dynamic effect). The microphysics effect can affect both latent heat and the cool pool and vice versa. More smaller cloud drops may enhance the WBF process (i.e., snow deposition growth at the expense of evaporating cloud drops) so that the latent heat release becomes larger. But the reduced riming efficiency has the opposite effect on latent heat release. More numerous cloud drops (due to more CCN) could also lead to more ice nucleation and thus a higher number of snow and graupel particles, which, when melted, form more but smaller raindrops that cause stronger evaporative cooling below the cloud base. Convection may be strengthened due to either the latent heat effect or the cold pool effect, and the stronger updraft leads to higher supersaturation and thus enhanced ice deposition nucleation.
5.4. CCN Effect on Convective Precipitation Using Nested Cloud/Regional-Scale Models
Lynn et al. [2005a, 2005b] used spectral-bin microphysics (a simplified version of Khain's scheme [Khain et al., 2004]) and the MM5 to simulate a cloud that approached the west coast of Florida, prior to the sea breeze development. The use of a continental CCN concentration led to a delay in the development of rainfall. The increase in CCN concentration led to convective invigoration and the formation of stronger secondary clouds [Lynn et al., 2005b]. Simulations of rain events over the whole peninsula for this day showed significant invigoration of squall lines. There was an increase in precipitation rate and precipitation amount for a squall line that formed in the vicinity of the east coast of Florida. At the same time, continental CCN concentrations resulted in a 5% reduction in precipitation over the whole computational domain (containing a significant fraction of Florida) versus maritime values.
van den Heever et al.  used the RAMS and a two-moment bulk microphysical scheme [Meyers et al., 1997; Saleeby and Cotton, 2004] to examine the aerosol effect on the formation of a thunderstorm over the peninsula of Florida. Note that the two-moment bulk scheme used by van den Heever et al.  emulates a bin scheme by including the explicit activation of aerosols [Saleeby and Cotton, 2004]. Sensitivity tests show that different combinations of CCN, GCCN, and IN result in different amounts and temporal patterns of cloud-water/ice contents and rainfall. Their study showed that a high CCN reduces cumulative precipitation by 22% compared to low CCN. In addition, high amounts of GCCN and IN enhanced surface precipitation for the first 6 h of integration due to the initial broadening of the cloud droplet spectra. However, the total (12 h integration) accumulated precipitation is greatest for the clean (low CCN, GCCN, and IN) case. Rapid wet deposition of GCCN during the first 6 h of integration may be the reason for this. All their experiments involving high CCN resulted in high cloud-water content and weak surface precipitation.
 Using a similar modeling configuration, van den Heever and Cotton  examined the sensitivity of urban-induced convective clouds over and downwind of St. Louis, Missouri. Their results indicate that downwind convergence (dynamic processes) induced by urban land cover appears to be the dominant factor in determining whether or not moist convection actually develops downwind of St. Louis. Once moist convection is initiated, urban-enhanced aerosols play a major role in determining the microphysical and dynamical characteristics of convective storms, particularly when background aerosol concentrations are low (Figure 37). Complicated relationships and feedbacks between microphysical and dynamical processes obscure the general understanding of urban-enhanced aerosol effects on precipitation. Note that Lynn et al. [2005b], van den Heever et al. , and van den Heever and Cotton  explicitly represent mesoscale forcing (i.e., sea breeze convergence and urban heat island convergence). This is important because cold pools can interact with these kinds of circulation, introducing another level of dynamic complexity. For example, if the cold pool outruns these mesoscale convergence fields, precipitation is reduced; when they remain coupled, precipitation is enhanced (cool pool effect in section 5.3.2). van den Heever and Cotton  also found that the response of convective rainfall to urban-enhanced aerosols becomes stronger when the background aerosol concentrations are low.
 The role that aerosols or dust in the SAL play on tropical storms has recently been studied using regional-scale models [i.e., H. Zhang et al., 2007; Zhang et al., 2009; Cotton et al., 2007]. The impact of dust acting as CCN in the SAL on the evolution of a tropical cyclone (TC) was examined through simulations initialized with an idealized pre-TC mesoscale convective vortex (MCV) using the RAMS [Cotton et al., 2007]. Dust in the SAL can affect the simulated TC intensity by 22 hPa depending on CCN concentrations (Figure 38). High CCN concentrations could weaken the TC intensity. It can also affect eye wall development directly through release of latent heat by the enhanced activation and condensation growth of cloud droplets, and indirectly through modulating rainband development. Convection in the rainbands was negatively correlated with that in the eye wall in all simulations. The development of rainbands promotes latent heat release away from the eye wall, blocks the surface inflow, and enhances cold pools. The convection in the eye wall and rainbands did not show a monotonic relationship to the CCN input due to the nonlinear feedback of heating from a myriad of microphysical processes on storm dynamics (Figure 39). The impact of CCN on storm intensity was sensitive to the background GCCN vertical profile and presumably other environmental factors.
 The WRF with a spectral bin microphysics scheme was used to investigate the potential impact of aerosols on the structure and intensity of Hurricane Katrina as they were ingested into the storm's circulation during its passage through the Gulf of Mexico in 2005 [Khain et al., 2010]. Continental aerosols invigorated convection largely at the TC periphery, which led to its weakening prior to landfall. The minimum pressure increased by 15 hPa, and the maximum velocity decreased up to 15 m s−1. Aerosols substantially affected the spatial distribution of cloudiness and hydrometeor contents. The results are in good agreement with those of Zhang et al. . Figure 40 shows how the TC intensity is weakened due to the aerosol effect. Three processes are responsible for the decrease in intensity: (1) an increase in cloud updraft velocity at the TC periphery, causing enhanced vertical mass flux at the periphery and thus less air mass and water vapor penetrating to the central part of the TC; (2) extra convective heating at the periphery, lowering the surface pressure at the TC periphery and decreasing the horizontal pressure gradient; and (3) competition between two zones of convection (at the eye and at the periphery). Compensatory downdrafts caused by convection at the TC periphery also tend to damp convection in the TC eye. The diagram shown in Figure 40 agrees well with results of Saharan dust effects on TC intensity reported by Zhang et al. . They found that convection in TC rainbands was negatively correlated with that in the eye wall in all simulations.
Li et al. [2008a] implemented a two-moment bulk microphysical scheme into the WRF model to investigate the effects of aerosols on cloud and precipitation processes. A deep cumulus cloud and precipitation event was simulated and a sensitivity study was carried out using a set of initial aerosol profiles at the surface level to examine the response of precipitation efficiency to the increase in aerosol concentration. Precipitation increased with aerosol concentration from clean to polluted conditions but was considerably reduced and completely suppressed under extremely polluted conditions (Figure 41). Enhanced precipitation with increasing aerosols at lower CCN is attributable to the suppressed conversion of cloud droplets to raindrops, which causes less efficient warm-rain processes but more efficient mixed-phase processes. At extremely high CCN, ice production is inhibited because ice nucleation becomes inefficient and anvil formation is hindered due to a large mass loading of small droplets (reduced buoyancy) and less latent heat from droplet freezing. Cloud coverage and core updrafts exhibited similar nonmonotonic behaviors to precipitation under different aerosol loadings (Figures 41a and 41d). Under a similar modeling framework, aerosol effects on precipitation for different regional-scale systems were further investigated, including a mesoscale squall line in the southern plains of the United States [G. Li et al., 2009] and a wintertime storm over the North Pacific [R. Zhang et al., 2007; Li et al., 2008b]. In these scenarios, precipitation enhancement under polluted conditions was reported along with more efficient mixed-phase processes and intensified convection.
Lerach et al.  used the RAMS to study the impact of aerosol indirect effects on the development of a supercell storm and its associated tornadogenesis. Their results indicated that a polluted environment (dust-laden CCN and GCCN concentrations of 2000 cm−3 and 0.2 cm−3, respectively) would provide a favorable environment for tornadogenesis rather than a clean environment (clean continental CCN and GCCN concentrations). Their results indicated that both warm rain and cold rain are reduced in the polluted environment, and a longer-lived supercell is simulated. An EF-1 (surface wind speeds exceeding 40 m s−1) tornado was produced due to weak evaporative cooling near updraft and downdraft interfaces close to the rear flank of the supercell. Storer et al.  also made use of RAMS to simulate supercell development under clean and more polluted conditions. The aim of their study was to assess the relative importance of variations in convective available potential energy (CAPE) and aerosol concentration on the microphysical and dynamical characteristics of supercells (Figure 42). When comparing results from changes in CAPE and aerosol concentrations, they found that the total precipitation produced by storms is primarily driven by CAPE but that the increase in aerosol concentrations produced a decrease in total precipitation by 30–40%. Changes in the cloud water path are found to be much more sensitive to variations in aerosol concentrations than in CAPE, while changes in the ice water path are affected in a similar manner by changes in aerosol and CAPE. Other microphysical parameters such as the mean raindrop diameter demonstrated very little response to changes in CAPE but large responses to changes in aerosol concentrations. Finally, they concluded that a number of the aerosol indirect effects observed in their study were modulated by the amount of CAPE in the environment, with stronger aerosol effects in environments with weaker CAPE. Thus, both aerosol concentrations and environmental conditions need to be considered when assessing aerosol indirect forcing on deep convective storms.
 The regional-scale modeling studies also suggest that enhanced aerosol concentrations could either enhance or suppress precipitation processes and surface rainfall. These results are in good agreement with those of cloud-resolving modeling studies as shown in section 5.3.
5.5. IN Effect on Precipitation Processes
 Only a few CRMs have been used to study the effects of IN on precipitation processes because of the limited understanding of ice formation (see section 2). In addition, some aerosols can be transported by convective updrafts from the planetary boundary layer (PBL) to the middle and upper troposphere and can serve as IN [Yin et al., 2005]. Because of this, it is very difficult to quantify the IN effect on precipitation processes. In addition, few of the previous CRMs were used to examine both IN and CCN effects on precipitation.
van den Heever et al.  showed that increasing either the GCCN or IN concentration produces the most rainfall at the surface, whereas enhanced CCN concentrations reduce surface rainfall. Higher IN concentrations produce ice at warmer temperatures and generate deeper anvils, but simultaneously increasing the concentrations of CCN and GCCN leads to more supercooled liquid water available for freezing and greater ice mixing ratios. Higher concentrations of GCCN and IN result in greater accumulated surface precipitation initially. By the end of the simulation period, however, the accumulated precipitation is the greatest for the case in which the aerosol concentrations are lowest. Their results suggested that such changes in the dynamical and microphysical characteristics of convective storms as a result of the variations in aerosol concentrations have potential climate consequences, through both the cloud radiative effect and the hydrological cycle.
Ekman et al.  studied the sensitivity of a continental storm to changes in IN concentration based on an observed case. They found that the increase in IN concentration, and thus heterogeneous nucleation, would generally result in enhanced updrafts due to latent heat release from the added diffusive growth of increased ice crystals. Such an effect was also identified to enhance homogeneous nucleation, i.e., to make CCN more effective in influencing ice nucleation. Since the dominant mechanism in providing ice particles for cirrus anvils in the modeled case is still homogeneous nucleation, the increase in IN concentration would lead to enlarged anvil coverage and increased precipitation. The finding of Ekman et al.  suggests an interesting link between IN concentration and updraft strength and, consequently, homogeneous nucleation rate, anvil particle concentration, coverage, and radiation effects. It is also in qualitative agreement with observations made by Heymsfield et al. .
Fan et al. [2010b] studied the impact of different parameterization schemes on homogeneous nucleation and heterogeneous immersion nucleation for two isolated tropical deep convection cases. Similar to the finding of Ekman et al. , they found that an increase in the immersion nucleation rate would lead to stronger convection, larger anvil coverage, and longer anvil lifetime. Precipitation and ice water path would both be enhanced under either wet or dry environmental conditions. Consequently, the homogeneous nucleation rate would also be enhanced, consistent with Ekman et al.  and Heymsfield et al. . Note that Ekman et al.  and Fan et al. [2010b] both mentioned the substantial uncertainty in modeled results due to various different schemes used to represent nucleation mechanisms, although such uncertainty does not seem to qualitatively affect their major conclusions. Fan et al. [2010a] also compared CCN and IN effects on convection and precipitation and found that the CCN effect is dominant. The IN effect does little to convection and precipitation, although ice microphysical properties could change significantly.
Zeng et al. [2009a, 2009b] examined the effect of the ice crystal enhancement (IE) factor (defined as the ratio of the number of ice crystals to ice nuclei) on ice properties associated with tropical and midlatitude convective systems using a CRM. Their results showed that the IE factor in tropical clouds is about a thousand times larger than that in midlatitude clouds. This significant difference in the IE between the tropics and midlatitudes is consistent with observations of stronger entrainment and detrainment in the tropics. However, surface precipitation is not affected by the change in IE as shown by Fan et al. [2010a].
6. LARGE-SCALE MODELING OF AEROSOL-PRECIPITATION EFFECTS
 On a global scale, aerosols could affect precipitation through microphysical and dynamical paths. The former path consists of a series of microphysical processes and microphysics-dynamics feedbacks, initiated by the activation of aerosols as CCN or IN. The resultant change in cloud radiation is commonly referred to as the indirect radiative forcing of aerosols [e.g., Ramaswamy et al., 2001]. The dynamical path is implemented through changes in large-scale circulation by persistent aerosol direct forcing [e.g., Wang, 2004] or indirect forcing [Ramaswamy and Chen, 1997; Rotstayn and Lohmann, 2002]. The microphysical path would cause precipitation changes mainly confined to aerosol-laden regions, while the dynamical path could alter precipitation remote to these regions.
 To simulate the effects of aerosols on precipitation in a large-scale framework, models need to include the feedback of dynamical processes to aerosol forcing. The atmospheric transport model or chemical transport model, a commonly used tool to derive aerosol distribution and radiative forcing driven by prescribed meteorology, would not be useful for this purpose because of its lack of such feedbacks and for this reason is not discussed in this paper. In addition, recent advances in computational technology allow current CRMs to run efficiently over domains covering a continental scale. In fact, many details about regional modeling can be found in section 5. This section, therefore, concentrates on the efforts using global aerosol-climate models. The term aerosol-climate model is used in this section and refers to those general circulation models (GCMs), or global climate models as they are sometimes called, which include an aerosol module or simply include prescribed radiative effects of aerosols.
6.1. Major Methodology
 Precipitation is formed through a series of sophisticated processes with feedbacks involving aerosol physics and chemistry, cloud microphysics, and dynamics on different scales. It is located at the bottom of the “food chain” of aerosol-cloud processes, while serving as the largest sink of atmospheric aerosols. Many of these above processes occur on scales much smaller than the typical grid spacing of current global climate models. The first step toward modeling the effect of aerosols on precipitation using global climate models is thus to have a reasonable representation of aerosol processes in these models.
 The study of climate response to aerosol forcing requires long-term integrations using models on one hand equipped with needed details concerning aerosol processes and, on the other hand, having a good computational efficiency. In reality, mainly because of the computational cost, it has never been an easy task to include an interactive aerosol module in climate models to study the change in clouds and precipitation as a climate response to aerosol forcings. Therefore, an optimized balance between aerosol representation and model computational cost needs to be established. So far, the majority of research on modeling the climate impacts of aerosols has been conducted using models with prescribed aerosol profiles. This applies perhaps to all the GCMs that participated in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4) [Randall et al., 2007].
 The evolution of atmospheric aerosols can be represented by several important aerosol properties, such as size distribution, mixing state, and chemical composition. The size of an aerosol with a known chemical composition to a large extent determines both the optical and microphysical character of the particle. In many aerosol-climate models, particularly the earlier ones, only the aerosol mass mixing ratio was predicted. The size of aerosols in these models, when needed, was derived diagnostically using various empirical methods based on the predicted mass mixing ratio. In many such models, the radiative properties of aerosols were derived based on a given geometric size [Haywood and Boucher, 2000; Penner et al., 2001; Forster et al., 2007]. On the other hand, the mixing state of aerosols determines not only the value but also the sign of the radiative forcing of aerosols. Recent field experiments using single particle analysis have demonstrated the coexistence of external and internal mixtures in the atmosphere, and the latter is not always dominant [Hara et al., 2003; Schwarz et al., 2008; Twohy et al., 2008] (also see section 3). From field experiments, internal mixtures containing an absorbing core (e.g., black carbon, or BC) coated by a scattering material [Martins et al., 1998; Pósfai et al., 1999; Naoe and Okada, 2001; Okada et al., 2005; Schwarz et al., 2008] are known to significantly enhance the bulk absorption per mass of aerosols compared to external mixtures of black carbon [Ackerman and Toon, 1981; Horvath, 1993; Chýlek et al., 1995; Bond and Bergstrom, 2006; Kim et al., 2008]. This specifically differs from the relatively well-mixed state of organic carbon (OC) and sulfate mixtures [e.g., Okada et al., 2001; Russell et al., 2002]. The majority of current aerosol-climate models include only external or internal mixtures. Among those models that include internal mixtures, a well-mixed assumption is usually adopted so that the radiative effects of aerosols are calculated using a volume-weighted refractive index over all predicted aerosol constituents [e.g., Stier et al., 2005; Kim et al., 2008].
 Increasing effort has been made in recent years to improve the representation of aerosols in GCMs (Figure 43). In a few studies where an aerosol model was used to predict number and mass concentrations of aerosol constituents in a series of relatively coarsely defined size bins, or sections [e.g., Jacobson, 2001; Adams and Seinfeld, 2002], the computational cost was still too high to include a series of multiple sections that could be internally as well as externally mixed in multiyear simulations. To reach a good balance between the computational burden and process details in climate impact studies, some of the current aerosol-climate models have adopted the multimoment approach [e.g., Easter et al., 2004; Vignati et al., 2004; Liu et al., 2005; Kim et al., 2008; Bauer et al., 2008]. This method predicts multiple aerosol population properties including the number, mass, and size distribution (whether based on a prescribed type of function or not) of many aerosol modes (see Table 5 for a brief description of several selected models and Figure 44 for the model diagram of Kim et al. ). Compared to the earlier mass-only model, or the “single-moment” scheme, the multimoment approach, when designed appropriately, improves the representation of aerosol size while remaining computationally efficient with the ability to perform multidecadal or even longer simulations.
Table TABLE 5.. Examples of Size-Dependent Modules of Anthropogenic Aerosol in Global Interactive Aerosol-Climate Models
6.2. Impact of Aerosols on Precipitation Through Microphysical Processes
 In global climate models, the representation of the impact of aerosols on cloud microphysics is generally implemented in a highly parameterized fashion due to the coarse spatial resolution of these models. Such a parameterization usually consists of two major steps: (1) the activation/nucleation of cloud droplets or ice crystals and (2) the “autoconversion” to convert small cloud droplets or ice crystals (typically from 10 to 100 μm in size) to precipitating hydrometeors, i.e., rain or snow (several hundreds of micrometers to a few millimeters). Note that the latter transition is a parameterization of a series of microphysical processes involving a random collection of small cloud droplets under the influence of updrafts or downdrafts and turbulent mixing at a subgrid-scale level.
 In fact, the majority of global aerosol-climate modeling efforts dealing with the microphysical impact of aerosols has focused on deriving the indirect radiative forcing of aerosols rather than studying the precipitation effect. The former task, in a model without explicitly predicting aerosol number concentration, would be done by using an empirical method to connect aerosol mass with CDNC, autoconversion rate, and precipitation efficiency to simulate various aerosol effects [Rotstayn, 2000; Kiehl et al., 2000; Menon et al., 2002; Ming et al., 2005; Penner et al., 2006; Jones et al., 2007]. The aerosol-CDNC relationships used by different aerosol-climate models appear to agree with each other qualitatively and also with satellite estimations. However, the modeled results concerning the aerosol albedo effect, the cloud optical response to changes in aerosol level and thus CDNC, can vary significantly and also differ from satellite-based estimations. In addition, in performing more sophisticated tasks, such as simulating aerosol effects on cloud cover, height, lifetime, and outgoing longwave radiation that involve dynamic feedbacks, these models tend to disagree with each other even more evidently [Quaas et al., 2009]. To date, the argument about whether the indirect forcing of aerosols should be treated as a forcing or a response still exists, and the estimation of such an effect remains one of the largest uncertainties in climate modeling. For more details about studies of indirect forcing of aerosols, the reader is referred to previous reviews including Haywood and Boucher , Ramaswamy et al. , and Lohmann and Feichter .
 Several physics-based parameterizations for simulating the activation of liquid or ice cloud particles have been developed for global models [e.g., Abdul-Razzak and Ghan, 2000; Nenes and Seinfeld, 2003; Kärcher and Lohmann, 2003; Liu and Penner, 2005; Barahona and Nenes, 2007]. These schemes continue to benefit even the most up-to-date aerosol-climate models with improved aerosol and cloud microphysical representations. Efforts have also been made to include more physics-based descriptions of cloud microphysical processes beyond just the aerosol activation in the earlier generation of models. For example, Rasch and Kristjánsson  and Kristjánsson  introduced parameterizations of several microphysical processes into the Community Climate Model version 3 (CCM3) of the National Center of Atmospheric Research (NCAR), including autoconversion from cloud water to rain and from ice to snow and the collection of cloud water by rain and by snow. This implementation enables the model to simulate certain effects of aerosols on cloud droplet size and concentration and, most interestingly, on precipitation onset and quantity.
 As a major step forward, a two-moment microphysics scheme for cloud droplets and ice crystals has been developed recently for global climate models [e.g., Lohmann et al., 1999, 2007; Ming et al., 2007; Morrison and Gettelman, 2008; Wang and Penner, 2010] (see Table 6). The evaluation of these relatively comprehensive models is just beginning [Gettelman et al., 2008; Lohmann, 2008; Wang and Penner, 2010]. This type of scheme requires that the model predict both mass and number concentration of a given hydrometeor, i.e., the type of cloud particles categorized using size, phase, aggregate state, and often density. On the basis of the selected type of probability distribution function (PDF) for the size distribution of a given hydrometeor, and when the predicted number of moments equals the number of undefined parameters of the PDF, all microphysical conversions, along with the bulk motion characteristics of the hydrometeor, can be derived using integrations over size distributions that define various predicted moments. The effort to introduce the two-moment scheme for convective clouds in GCMs has just started. Ming et al.  introduced a prognostic CDNC scheme in the convective parameterization of the Geophysical Fluid Dynamics Laboratory (GFDL) GCM. Lohmann  tested a two-moment scheme for convective clouds in the ECHAM general circulation model. Song and Zhang  tested a two-moment scheme including four hydrometeors for convective clouds using a single column climate model. Obviously, such a task is still very challenging due to the subgrid nature of convection in current climate models.
Table TABLE 6.. Examples of Two-Moment Cloud Microphysical Schemes in Global Climate Models
Hydrometeors Applied With Two-Moment Scheme
cloud droplet, ice crystal
2.8° × 2.8°, 19 layers
updraft perturbation using TKE and CAPE in nucleation
 The attempt to use a two-moment cloud microphysics scheme in GCMs is still in its early stage, and current schemes are still less comprehensive than their counterparts developed long ago for cloud-resolving models [e.g., Wang and Chang, 1993]. Nevertheless, by adopting such an approach, modeling aerosol effects on precipitation would become much more physics-based than in the earlier generation of models where only mass mixing ratios of hydrometeors were predicted. Especially when coupled with a size-dependent aerosol module, a two-moment cloud microphysics scheme provides a connection between the predicted number concentration of CCN by the aerosol module and predicted CDNC by the cloud microphysics module. Along with the two-moment scheme, subgrid-scale variability has also been introduced to further improve the modeled microphysical features of Morrison and Gettelman , where the variability of cloud water is represented by a PDF derived from observations and extended to all related microphysical conversions.
 Studies have demonstrated that with the two-moment scheme, models tend to produce global total precipitation closer to observations than the previous generation of schemes [e.g., Lohmann et al., 2007; Gettelman et al., 2008]. On the other hand, in representing the formation of raindrops, a random process involving the collection of smaller cloud droplets, models with the two-moment scheme still need to include a parameterization of autoconversion and subsequent accretion growth of precipitation particles. This parameterization thus remains a major tuning job for simulating the effect of aerosols on precipitation. A recent sensitivity study demonstrated that by allowing raindrops to form directly from the activation of GCCN (a hypothesized path), the modeled hydrological cycle would become faster, compared to the case without such a path; this was manifested by faster rainfall and lower atmospheric water vapor content, although the total precipitation amount did not change much [Posselt and Lohmann, 2008] (also see Figure 45). Early attempts to bring the two-moment cloud microphysical scheme into the convection parameterization of GCMs have also identified the impact of aerosols on modeled precipitation features. Lohmann  found that using the two-moment scheme and incorporating prescribed aerosol emissions could improve the modeled geographical distribution of precipitation changes from the past to the present climate when compared to observations. Song and Zhang  found that the two-moment scheme alters the precipitation partition between convective and stratiform portions of modeled clouds, actually leading toward a ratio that is closer to observations than results derived using a simpler microphysical scheme. Both studies have identified a suppression of convective precipitation due to enhanced aerosol concentrations.
 Despite the advancement in introducing physics-based aerosol and cloud schemes into GCMs, verification of modeled precipitation changes due to aerosol microphysical effects remains a challenge. This issue inherits the problem in determining the reference state for the preindustrial climatology of CDNC, a result that is much needed for estimating the anthropogenic enhancement to cloud radiative forcing in the present day [e.g., Rotstayn and Penner, 2001; Wang and Penner, 2009]. For instance, models often introduce a lower bound to avoid low values of CDNC. This results in a spatially uniform distribution of CDNC, which leads to a substantial underestimation of the aerosol effect on cloud albedo [Hoose et al., 2009]. In addition, more advanced schemes for aerosol and cloud microphysics also introduce new parameters. This would potentially add to the difficulty in examining whether the aerosol-cloud-precipitation microphysical effect would be able to explain some known variability in precipitation.
6.3. Impact of Aerosols on Precipitation Through Coupling With Large-Scale Dynamics
 The direct radiative forcing (DRF) of anthropogenic aerosols involves scattering and absorbing of solar radiation, or absorption and emission in the longwave radiation spectrum. The latter is only effective for large particles such as dust and will not be discussed much here. The optical effects of aerosols exert a negative forcing (cooling) at the Earth's surface by both scattering and absorbing solar radiation, and a positive forcing (warming) to the atmosphere by absorption. Because of their short lifetime of about 1 week, aerosols created from anthropogenic activities tend to concentrate over source regions or surrounding areas and hence apply a persistent forcing in these places.
 This type of persistent forcing can perturb atmospheric thermodynamic and dynamical processes and therefore influence precipitation-producing cloud systems in regions away from aerosol-laden areas. For example, studies using different GCMs all indicate that the direct radiative forcing of absorbing BC aerosols can lead to a northward shift of precipitation in the ITCZ, specifically over the Pacific Ocean [Wang, 2004; Roberts and Jones, 2004; Chung and Seinfeld, 2005]. Ramaswamy and Chen  and Rotstayn and Lohmann  both found that by including aerosol indirect forcing in their models, the dynamical consequence of such a forcing could have a remote impact on ITCZ precipitation, i.e., a shift in a direction opposite that caused by BC. An active research field aimed at understanding the effects of aerosols on precipitation through coupling with large-scale dynamics has developed. Current results indicate that the precipitation change caused by aerosols through this optical-thermodynamic-dynamical linkage is likely to be significant and could also be nonlinearly related to the aerosol forcing strength [e.g., Wang, 2007, 2009].
 Studies of the impact of aerosols on monsoon systems are rapidly growing. Correlations between estimated precipitation and circulation changes with the increasing trend of aerosols have unquestionably fueled the research in this direction [Ramanathan et al., 2005] (see also Figure 46). Most of the studies are conducted using three-dimensional atmospheric GCMs or atmosphere–ocean coupled global circulation models (CGCM), which include either an interactive aerosol module or prescribed aerosol profiles. Paired simulations, which include and exclude aerosol effects, or include reference and altered aerosol profiles, allow comparisons to be made of the climate response to different aerosol forcing assumptions. Aerosol effects would be isolated, barring the assumption that model artifacts in simulating the monsoon system would not be significantly amplified by using different aerosol profiles. Model representations of aerosols and aerosol-climate interactions vary from study to study.
enhanced during premonsoon season in central India, reduced in monsoon season
negative feedback to monsoon rainfall of the enhancement in clouds and precipitation during premonsoon
 Various mechanisms by which the direct radiative forcing of absorbing aerosols (solar heating of the atmosphere and dimming at the surface) modifies the monsoon circulation and rainfall have been suggested in modeling studies. Wang et al. [2009b] indicated that absorbing aerosols, whether coexisting with scattering aerosols or not, can alter the meridional gradient of moist static energy (MSE) in the subcloud layer over the Indian subcontinent, initiating heating of the PBL air and thus changing large-scale atmospheric stability (Figure 47). This would cause a northward extension of the monsoonal circulation and convective precipitation, which coincidently is in general agreement with observed monsoon precipitation changes in recent decades, particularly during the onset season (Figure 48). Such a pattern change is also in agreement with results produced in another study using a coupled atmosphere–ocean model although a prescribed aerosol profile was used [Meehl et al., 2008] (see Figure 49). Lau and Kim  proposed that the heating of absorbing aerosols on the slope of the Tibetan Plateau could initiate a positive feedback by drawing water convergence from oceans first and then form condensation and thus further heat the air over these elevated places; this is referred to as the “elevated heat pump” effect (EHP; see Figure 50). Ramanathan et al.  suggested that aerosols could cause a decrease in surface evaporation (due to the dimming effect) and in the meridional sea surface temperature gradient. These two factors would affect monsoonal circulation and rainfall strength. The relative importance of these various mechanisms requires further research [Lau et al., 2008].
 The potential impact of aerosols on the East Asian monsoon in winter was studied by Niu et al. . There is a strong indication that the winter monsoon circulation that brings cold air from northwest to southeast China (the Siberian high-pressure system) has weakened significantly, resulting in noticeable increases in humidity and foggy days and decreases in wind speed and number of cold air outbreaks in China. Such trends are consistent with those simulated by the NCAR/CAM3 by including and removing the radiative effect of aerosols. Changes in the pattern of mean winter atmospheric pressure and airflow from the National Centers for Environmental Prediction (NCEP) reanalysis bear a close resemblance to those from the two types of simulations. This provides indirect evidence that aerosols may play a role in the development of the winter monsoon because aerosols diminish the surface radiation budget and reduce the thermal contrast between high and low latitudes and between ocean and land surfaces.
 The impact of aerosols on another monsoon system, the West African Monsoon (WAM), has also been studied. Huang et al.  compared observational results with a global model simulation that included only direct radiative forcing of BC [Wang, 2004]. Both observations and model simulations showed that anomalously high African aerosol loading during boreal cold seasons was associated with significant reductions in cloud amount, cloud top height, and surface precipitation. This result suggests that the observed precipitation reduction in the WAM region is caused by the radiative effect of absorbing BC. The mechanism for this reduction, however, remains a mystery. In connection to the hypothesis of the aerosol-Indian summer monsoon effect proposed by Wang et al. [2009b], Eltahir and Gong  found a correlation between WAM strength and the subtropical meridional gradient of subcloud MSE. So a similar mechanism could also explain the aerosol-WAM effect. Recently, Lau et al.  used a GCM to show that the EHP effect due to Saharan dust and biomass burning BC has a significant impact on the climate and water cycle of the North Atlantic and the WAM. They found that during the boreal summer, as a result of large-scale atmospheric feedback triggered by absorbing aerosols, rainfall and cloudiness are enhanced over the West African/eastern Atlantic ITCZ and suppressed over the western Atlantic and Caribbean regions. This is related to the elevated dust layer that warms the air over West Africa and the eastern Atlantic and thus causes the air to rise. The response reflects a strengthening of the WAM, manifested in a northward shift of West African precipitation over land, increased low-level westerly flow over West Africa at the southern edge of the dust layer, and a near-surface westerly jet underneath the dust layer over the Sahara (Figure 51).
 The anthropogenic aerosol level in the Southern Hemisphere is lower than in the Northern Hemisphere. Therefore, the impact of local aerosols on the Australian monsoon system is expected to be relatively insignificant. However, since monsoon systems are closely associated with large-scale circulation, aerosol effects in the Northern Hemisphere could influence Southern Hemispheric circulation and thus precipitation by altering general circulation patterns. Rotstayn et al.  hypothesized that Asian aerosols could lead to an increase in both rainfall and cloudiness over northwestern Australia, which would coincide with the observed rainfall trend in the region since the 1950s. They suggested that this would happen because the meridional temperature gradient over the tropical Indian Ocean would be altered by Asian aerosols, which would further enhance monsoonal circulation toward Australia. A recent analysis of twentieth-century modeling results from 24 models participating in the Coupled Model Intercomparison Project Phase 3 (CMIP3), however, does not provide support to the above hypothesis [Cai et al., 2010]. Despite the inclusion of either direct or both direct and indirect aerosol forcings in these models, their ensembles did not produce the hypothesized rainfall increase in northwestern Australia.
7. CURRENT AND FUTURE RESEARCH ON AEROSOL-PRECIPITATION INTERACTIONS
 We have described the impact of aerosols on precipitation systems from the perspective of microphysical processes, observational evidence, and a range of numerical model simulations. We have also described the discrepancies between results simulated by models, as well as those between simulations and observations. Understanding these discrepancies is a necessary step toward further resolving aerosol effects on cloud microphysics, dynamics, and precipitation within climate systems.
 From the discussion presented in sections 3–6, it is clear that isolating the aerosol effect on precipitation from other factors is still a challenge and that each of the current attempts to tackle this issue has its own advantages and disadvantages. Large-scale diagnosis of the aerosol effect on precipitation, through CCN, GCCN, and IN, is incomplete without considering microphysics (cloud, aerosol, and precipitation), cloud dynamics (life cycle), and the large-scale background environment (dynamical and thermodynamical forcing, radiative feedbacks, aerosol transport, and the water budget).
 Nevertheless, progress has been made in cloud microphysics involving CCN, GCCN, and IN, and their impact on clouds and precipitation ranging from the cloud scale to larger scales. Numerical models have assisted the physical interpretation of mechanisms associated with the aerosol-precipitation interaction. It is still quite difficult to quantify various aerosol effects on precipitation from either modeling or observational studies alone [Khain et al., 2008; Stevens and Feingold, 2009; Koren et al., 2010b]. Combining observations and modeling enables us to achieve a better understanding of the responses of cloud and precipitation to aerosols and their interactive feedbacks. The following summarizes the remaining scientific challenges and issues regarding aerosol-precipitation interactive processes.
 The fundamentals of the aerosol effect on cloud and precipitation formation are based on the concepts of CN activation into cloud drops and IN nucleation into cloud ice. The former can be described by Köhler curves, presuming that information such as the size distribution and chemical activity coefficient is known. Such information can be derived from measurements, so that aerosol properties can be prescribed accordingly in cloud models. However, prescribing aerosol properties is only suitable for case studies and not for simulations with durations longer than the lifetime of aerosols, which is about a few days. More elaborate simulations should be done by coupling the CRM with a detailed aerosol model that has the capability of resolving particle sizes, chemical compositions, and mixing state. The coupling must be done in such a way that the effects of cloud on aerosols, including aerosol scavenging and aerosol-recycling and even cloud chemistry, can be simulated simultaneously along with aerosol effects on cloud microphysical features.
 IN nucleation is much less understood than CN activation. The main difficulty comes from the poorly quantified properties of IN including their concentration, variety, and ice- nucleating capability. Measurement of these IN properties is still quite lacking, so even empirical descriptions of ice nucleation are tentative for most regions. A prognostic description of IN is possible and should also be incorporated into CRMs with a detailed aerosol model.
 Another area that needs further improvement is the cloud microphysical sensitivity to aerosol effects. Many bulk water schemes crudely simplify the collision efficiency between cloud drops and precipitation particles, so the effects of aerosols on cloud drop size and thus collision growth processes cannot be fully resolved.
7.2. Cloud-Scale Modeling
 In almost all previous cloud-resolving modeling studies, idealized or composite [e.g., van den Heever et al., 2006] CCN concentrations were used in the simulations. Furthermore, the spatial distribution of CCN was assumed to be uniform, at least horizontally. A nonhomogeneous CCN distribution, consistent with nonhomogeneous initial meteorological conditions, is required to assess aerosol-precipitation interactions using regional-scale models in the future. In addition to IN and GCCN, the chemistry of CCN needs to be considered in future modeling of aerosol-precipitation interactions. For example, Fan et al. [2007b], [Ekman et al., 2004, 2006], and Lee et al. [2009b] found that aerosol chemical composition along with aerosol physics could affect precipitation processes.
 Furthermore, almost none of these CRM studies fully compared model results with observed cloud features such as dynamical and microphysical profiles, cloud extent, evolution of organization, radar reflectivity, and rainfall. This instantly raises the issue of gathering more data, perhaps through major field campaigns, that are suitable to both initialize model simulations (with meteorological and aerosol parameters) and validate model results (i.e., in situ cloud property observations, radar, lidar, and microwave remote sensing). Even though CRM-simulated results have provided valuable quantitative estimates of the indirect effects of aerosols, one needs to realize that these CRMs can only simulate clouds and cloud systems over a relatively small domain, for short periods, and under constraints given by specified large-scale meteorological conditions. Some CRM domains are too small to resolve whole clouds or precipitation systems. Close collaborations between the global and CRM communities are needed in order to explore how to extend CRM results to a regional and global perspective.
 Identifying regime-specific sensitivities using satellite data, in situ observations, and high-resolution, fine-scale modeling is a promising approach to improving the representation of clouds in larger-scale climate models [Stevens and Feingold, 2009].
7.3. Large-Scale Modeling
 As a critical factor determining climate response and feedback, the role of aerosols in influencing precipitation is undoubtedly a key issue in climate research and prediction. The future direction of global-scale research regarding this should focus on improving the model representation of aerosol-cloud related processes and, perhaps more important, observational constraints for aerosol-climate modeling. An immediate consequence of model advancement in spatial resolution and process representations is the realization that observation data at high resolution is required for model initialization and verification. Clearly, all currently available global-scale measurement networks do not necessarily meet this requirement. Further study of how to provide constraints for high-resolution global climate models is needed.
 With the rapid advancement in computational technology, climate models will step into an era of fast development. To better represent the effects of aerosols on clouds and precipitation, size-dependent cloud microphysics schemes along with size- and mixing-dependent aerosol schemes should be adopted in more models and used in long-term climate integrations. One issue that has remained in global climate modeling ever since its earliest days is the parameterization of convection. Because the requirement of several-kilometer resolution to resolve convection has been outside of the realm of possible resolutions for global climate models (and will likely still be the case in the near future), descriptions of convection processes along with aerosol-cloud-precipitation physics in these models have been empirically formulated using parameters resolved at model grid scales. Though still computationally expensive, today's global cloud-resolving models [i.e., Tomita et al., 2005; Miura et al., 2005; Nasuno et al., 2008] are already being run in an exploratory manner and perhaps will reach the stage of performing long-term integrations with computationally more practical expenses earlier than one would expect. Recently, Grabowski and Smolarkiewicz , Khairoutdinov and Randall , and Randall et al.  proposed a multiscale modeling framework (MMF) that replaces conventional cloud parameterizations with a CRM in each grid column of a GCM. The MMF can explicitly simulate deep convection, cloudiness and cloud overlap, cloud-radiation interactions, surface fluxes, and surface hydrology at the resolution of a CRM. It also has global coverage and two-way interactions between the CRMs and the parent GCM; initial simulations with aerosol-cloud interactions within a MMF have been performed [Wang et al., 2011]. The MMF could be a natural extension of current cloud-resolving modeling activities. MMFs can also bridge the gap between traditional CRM simulations and nonhydrostatic global cloud-resolving models. Another less computationally demanding way of addressing the issue would be the development of an MMF approach that couples a global aerosol-climate model with a cloud-resolving model and detailed interactions between clouds, precipitation, and aerosols. Various cloud-related parameterizations in GCMs can be improved by using CRMs over selected regional domains within a MMF framework [e.g., Lee et al., 2009].
 In addition to the cloud-resolving issue, many critical and nonlinear aerosol chemical and physical processes also occur on scales much smaller than the grid size of current global models, and so they need to be treated more carefully in these models. Sophisticated air quality models have been used recently to develop a reduced format model of urban aerosol processing under various environmental conditions, leading to much improved and computationally efficient representations of subgrid nonlinear aerosol processes in global models [Cohen et al., 2011].
 Despite the progress in model development and computational technology, uncertainties in modeling aerosol-cloud-precipitation processes will always exist. Therefore, identifying and thus minimizing such uncertainties remains a constant task in the field. Attempts to use various inverse modeling skills in global model frameworks to optimize emissions of aerosols and aerosol precursors have been reported in the literature but are still at an early stage [e.g., Collins et al., 2001; Zhang et al., 2005; Dubovik et al., 2008]. Further in-depth analyses on model process uncertainties require a very high computational demand that is still difficult to meet. Alternatively, the reduced format model of a given global aerosol-climate model could be derived through a limited number of simulations of the global model under a certain statistical framework [e.g., Tatang et al., 1997]. The reduced format model is much more computationally efficient, so it can be used in a full-scale parametric uncertainty analysis to mimic the behaviors of the global aerosol-climate model although with some limitations.
 Examining the effects of aerosols on precipitation remains a challenging task. Because of multiscale dynamical feedbacks involved in aerosol-cloud-precipitation connections, a global modeling framework might be needed for many cases to address such an issue. The effort using the so-called detection and attribution technique with GCMs to identify various aerosol effects is still at an early stage and mainly limited to aerosol-induced temperature changes [e.g., Jones et al., 2011]. Applying the same skill to identify the aerosol-induced precipitation change is obviously much more difficult but should be considered in the near future. On the other hand, the effects of aerosols on precipitation can be examined at regional scales for certain weather regimes by combining relatively long-term high-quality measurements (e.g., the ones from the DOE ARM project) and process models [Li et al., 2011a].
 Observations provide both initial conditions and validation data for models. The current generation of cloud-resolving models include reasonable, albeit not complete, microphysical parameterizations and can simulate the microphysical, dynamical, and chemical evolution during the life cycle of cloud systems. These models can also be used to explicitly calculate interactions between clouds, aerosols, and precipitation. However, all these advancements have raised challenging issues for corresponding measurements. Because of the range of scales involved in modern cloud modeling efforts, space-based remote sensing has served as an ever more necessary part of model validation.
 The availability of high-resolution surface precipitation data, compiled from satellite retrievals and surface rain gauge measurements in the recent two decades, has generally improved, though there is still a shortage of data. Still, how to detect aerosol signals along with clouds and precipitation, and specifically how to attribute the signal to the microphysical effects of aerosols, remains a topic that has barely been touched upon. Well-designed field campaigns and data analysis (e.g., for ARM sites) are required in the future to address this issue.
 Since more variables for the study of aerosol-cloud-precipitation interactions are available from both satellite (e.g., A-Train) sensors that provide global coverage and enhanced special ground-based observations (e.g., ARM) that provide a rich source of information, it is possible to investigate the climatological effects of aerosol-cloud-precipitation interactions beyond case-by-case studies, as demonstrated by Li et al. [2011a] and Niu and Li . If numerical models with adequate physics could reproduce such results obtained from very large ensembles of observations, it would provide solid evidence of the net ACPI effect that is currently still missing but of considerable climatological significance.
 Enlightened by the role of absorbing aerosols revealed in recent studies, measurements of the absorption strength and the spatial distribution of absorbing aerosols are still rare and should be specifically improved to validate model results [Wang et al., 2009a; Chin et al., 2009]. The most urgent need is to specify the vertical profile of aerosol absorption at least over highly polluted regions, which is a key indicator of the effects of absorbing aerosols in altering atmospheric stability and in governing the interaction and feedback between aerosols and atmospheric dynamics. Another much needed piece of information is global measurements of particle number concentration of both aerosols and cloud particles. Field experiments have provided and will continue to provide critical observational data in this regard. Current global networks including Aerosol Robotic Network (AERONET) and such satellites as Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) and CloudSat provide valuable information about the optical properties of aerosols or its loading in terms of total extinction, but they do not convey any direct information about aerosol number concentration, size distribution, and chemical composition, which are key to understanding CCN effects. Out of necessity, AOD has been employed in large-scale modeling as a proxy for CCN because of its availability from satellite and surface networks. The two are indeed grossly correlated [Andreae and Rosenfeld, 2008], but their correlation is subject to a large uncertainty, often off by several factors of magnitude. Moreover, AOD is a poor indicator of aerosol number. AI is much better though not on a regional scale [Penner et al., 2011]. This is not surprising, because AOD is determined primarily by aerosol extinction that is, in turn, influenced by aerosol scattering and thus proportional to the cross section; CCN effects are affected by many other factors. Given an appropriate composition and adequate supersaturation, aerosols of smaller size can provide more CCN than those of a larger size with the same bulk optical properties. Current attempts to use available satellite retrievals, such as those from MODIS, to estimate cloud droplet number concentration [e.g., Bennartz, 2007] are only of relative use for certain types of clouds. Next-generation satellites and global networks should be tailored toward extracting CCN as well as aerosol optical properties.
 Despite ever-escalating efforts and the virtually exponential increase in published studies concerning aerosol-cloud-precipitation interactions, we are still puzzled by many seemingly contradictory findings as reviewed above, although they really attest to the complexity of the problem. Disentangling meteorological and aerosol effects remains a daunting task. While individual endeavors have advanced our understanding substantially, it is highly recommended that a collective approach incorporating the strengths of all individual approaches while minimizing their limitations be undertaken to tackle the problem. Observation-based studies will likely continue to reveal new evidence of the ACPI, while cloud-resolving models will continue to help understand fundamental processes and to develop and test parameterizations for use with large-scale models. For the sake of testing and performing intercomparisons of large-scale models, “standard” tests may be developed on the basis of well-defined experiments and/or observed relationships from analysis of large ensembles of data. In case of any discrepancies, it is essential to sort out contributing factors in terms of various direct and indirect effects.
 W.-K. Tao appreciates the inspiring and enthusiastic support by his mentor, Joanne Simpson, over the past 25 years and is grateful to R. Kakar at NASA headquarters for his continuous support of Goddard Cumulus Ensemble (GCE) model development and applications. This work is mainly supported by the NASA Headquarters Physical Climate Program and the NASA Precipitation Measurement Mission (PMM). He also thanks David Considine for support under the NASA Modeling Analysis Prediction (MAP). C. Wang thanks the NSF (AGS-0944121), the Singapore NRF through the Singapore-MIT Alliance for Research and Technology, and the corporate and foundation sponsors of the MIT Joint Program on the Science and Policy of Global Change for supporting his research. Z. Li's aerosol-related studies have been supported by NASA's Radiation Science program managed by H. Maring (NNX08AH71G), and DOE's Atmospheric System Research program managed by A. Williamson (DEFG0208ER64571), National Science Foundation managed by C. Lu (AGS-1118325), and the Ministry of Science and Technology of China (2006CB403706, 2011CB403405). C. Zhang thanks the support of the NOAA Office of Global Programs through awards under Cooperative Agreement NA17RJ1226 to the Cooperative Institute for Marine and Atmospheric Studies (CIMAS). J.-P. Chen acknowledges the support from projects NSC 98-2111-M-002-001 and NSC 99-2111-M-002-009-MY3. We'd like to thank M. Cribb for reading and editing the manuscript; Xiaowen Li for improving Figures 28, 33, and 35; and Takamichi Iguhi for providing Figure 25. We also thank Joyce Penner and two anonymous reviewers for their constructive comments that improved this paper significantly.
 The Editor responsible for this paper was Alan Robock. He thanks Joyce Penner and two anonymous reviewers.