Anthropogenic aerosols acting as cloud condensationnuclei(CCN)or ice nuclei(IN)can alter themicrophysical properties of liquid and ice clouds,aswell as local and global precipitation(Ramanathan et al., 2001). Due to the complexity of the involvedphysical processes involving aerosol characteristics and atmospheric environment factors,aerosolcloud-precipitation interaction has attracted considerableattention in studies based on ground observations,satellite retrievals, and numerical modeling(Zhang,2007; Levin and Cotton, 2009; Tao et al., 2012; Han et al., 2014).

Cloud-to-rain autoconversion represents a key microphysicalprocess whereby rain drops are formed bycollision-coalescence processes of cloud droplets. Thismicrophysical process is an important player in aerosolloading,cloud morphology, and precipitation processesbecause aerosol-induced changes in cloud microphysicscan affect the spatio-temporal variations of precipitationin addition to its onset and amount(Albrecht,1989). A series of parameterization schemes describingthe autoconversion process have been proposed duringthe past several decades(e.g.,Kessler,1969; Berry and Reinhardt, 1974; Sundqvist et al., 1989; Beheng,1994;Khairoutdinov and Kogan, 2000; Liu and Daum, 2004;Liu et al., 2005; Xie and Liu, 2009),most of whichhave been successively applied to multi-scale numericalatmospheric models. These autoconversion parameterizationschemes can be roughly classified intothree categories. The first category includes only thecloud water content without aerosol effects,e.g.,theKessler scheme(Kessler,1969). The second is relatedto both the cloud water content and the droplet numberconcentration that can represent the indirect effectof aerosols,e.g.,the Khairoutdinov-Kogan(KK)scheme(Khairoutdinov and Kogan, 2000). The thirdincludes cloud droplet spectral dispersion,the cloudwater content, and the droplet number concentration,which can be used to investigate the aerosol effectswith spectral dispersion influence,e.g.,the Dispersionscheme proposed by Liu and Daum(2004) and Liu etal.(2005). To reveal the differences between theseparameterization schemes,we couple the Kessler,KK, and Dispersion schemes respectively with the Morrisonbulk microphysics scheme of theWeather Research and Forecast(WRF)model for investigating the impactsof aerosols on clouds and precipitation in a deepconvective system that occured on 31 March 2005 inBeijing.

The main contents of this paper are organizedas follows. Section 2 introduces autoconversion parameterizationschemes,including the Kessler,KK, and Dispersion,as well as the WRF model with theMorrison bulk microphysics scheme. In Section 3,wepresent the main results associated with cloud microphysicalproperties and surface precipitation from numericalsimulations incorporating the above schemes.In Section 4,we conclude our paper with a summary.

The autoconversion process of cloud droplets torain drops represents a key microphysical process,which governs the onset of precipitation in warmclouds and affects the precipitation distribution and amount. The Kessler scheme assumes that the autoconversionrate increases with an increase in cloudwater content,although it is zero for some cloud watercontent values below the threshold value L_c0,i.e.,theautoconversion process of cloud to rain does not occurbelow L_c0(Kessler,1969). This microphysics schemehas been widely used in cloud-related modeling studiesbecause of its simplicity. The formula of the Kesslerscheme is expressed as

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The unit of autoconversion rate P_K is g kg⁻¹ s⁻¹. Hereα is a tuning constant,H(L_c − L_c0)is the Heavisidestep function, and L_c is the cloud water content(gkg⁻¹). The values for the threshold cloud water contentL_c0 are rather arbitrary. Typically,for deep cumulusconvection,we choose α = 10⁻³ s⁻¹ and L_c0 =1 g kg⁻¹ according to Wang(2005).

The KK scheme states that the autoconversionrate increases with increasing cloud water content and decreases with increasing droplet number concentration.This is determined from many numerical experimentswith a drop spectrum resolving microphysicalmodel(Khairoutdinov and Kogan, 2000). The correspondingformula is given by

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where the autoconversion rate PKK is in kg kg⁻¹ s⁻¹, and the units of L_c and N_c(cloud droplet number concentration)are kg kg⁻¹ and cm⁻³,respectively. Notethat this autoconversion parameterization scheme isused in general circulation models such as ECHAM5(Lohmann et al., 2007),CAM3, and CAM5(Morrison and Gettelman, 2008).

The Dispersion scheme assumes that the autoconversionrate is related to the cloud water content,droplet number concentration, and cloud droplet spectraldispersion. This scheme was proposed by Liu and Daum(2004) and Liu et al.(2005), and has beencoupled into the WRF model(Xie and Liu, 2011; Xie et al., 2013). The autoconversion parameterization is written as

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Here,PD(g cm⁻³ s⁻¹)is the cloud-to-rain autoconversionrate; P0(g cm⁻³ s⁻¹) and T(dimensionless)represent the rate function and threshold function,respectively(Liu and Daum, 2004; Xie and Liu, 2009).The microphysical variables N_c and L_c are the clouddroplet number concentration(cm⁻³) and cloud watercontent(g cm⁻³), and x_c has an analytic formula ofx_c = 9.7 × 10⁻¹⁷N_c^3/2 L_c^-2. The cloud droplet spectraldispersion ε is defined as the ratio of st and arddeviation and mean radius of the cloud droplet sizedistribution,which can be described by the variousfunctions of cloud droplet number concentration(Xie and Liu, 2013). Here,we adopt the formula with ε =0.0005714N_c+0.271(Martin et al., 1994),where thecloud droplet spectral dispersion is a linear functionof cloud droplet number concentration.

The WRF model is a state-of-the-art mesoscalenumerical weather prediction system used for both operationalforecasting and atmospheric research; version2.2 was released in December 2006(Skamarock et al., 2005). The WRF model offers a wide range ofmeteorological applications across scales ranging frommeters to thous and s of kilometers. A two-momentbulk cloud microphysics scheme,namely,version 2.0of the Morrison bulk microphysics scheme proposedby Morrison et al.(2005),is used here. As mentionedby Xie et al.(2013),this microphysics scheme is ableto predict the cloud droplet number concentration N_c,which differs from the st and ard released WRF modelthat uses a fixed value of N_c = 250 cm⁻³. In this bulkmicrophysics scheme,the number concentration and water content of five classes of hydrometeors are predicted,including cloud droplets,rain drops,ice crystals,snow, and graupel. The autoconversion parame parameterizationused in this bulk microphysics scheme is theKK scheme.

To examine the differences between the variousautoconversion parameterization schemes,we alsocoupled the Kessler and Dispersion schemes intothe Morrison bulk microphysics scheme in the WRFmodel. Additionally,aerosols in this study serve onlyas CCN associated with warm clouds. Although severalstudies indicate that aerosols have non-negligibleimpacts on mixed-phase and ice-phase cloud propertiesby acting as ice nuclei(e.g.,van den Heever et al., 2006),the heterogeneous ice nuclei concentration doesnot vary between different aerosol concentration backgroundsin the Morrison bulk microphysics scheme.

All the simulations in this study are performedover a domain with grids at a 1-km grid spacing inaddition to 41 vertical sigma levels up to 20 km inaltitude. The model was integrated for 3 h with a6-s time step, and the results were output every 5min. Here,we use periodic boundary conditions forthe horizontal boundaries. The initial thermodynamicconditions were derived from the sounding data forsimulations of the convective cloud system that occurredon 31 March 2005 in Beijing. This convectivecloud system revealed moderate instability in the atmosphere,showing convective available potential energy(CAPE)of 1133 J kg⁻¹ integrated from the surface, and convection inhibition(CIN)of approximatelyzero. The mixing ratio of water vapor had a maximumvalue of 9 g kg⁻¹,which decreased continuouslywith increasing vertical height, and the correspondingsurface temperature was nearly 31℃. The windshear of the two components(u and v)of the windfields was relatively weak. The details of this thermodynamicsounding have been reported by Xie et al.(2013).

The activation of cloud droplet was calculated byan empirical formula(Pruppacher and Klett, 1997):

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where N_ccn is the number concentration of activatedCCN, and thus the number concentration of newlyformed cloud droplets under a given supersaturationratio S(in percent here). C₀ and k are constants depending on the chemical composition and physicalproperties of the aerosols; k is given as 0.7,as suggestedby Wang(2005), and C₀ is the activated CCNnumber concentration at 1.0% supersaturation by definition.For simplicity,this initial CCN number concentrationat 1.0% supersaturation(hereinafter,CCN0)is used to represent the aerosol distribution in eachnumerical experiment according to Li et al.(2008).In the present study,CCN0 was set as 50,100,200,300,500,1000,2000,3000,5000, and 10000 cm⁻³ torepresent the increasing aerosol concentration, and weperformed the experiments by using the Kessler,KK, and Dispersion schemes with increasing CCN0. Here,the reference case takes the results of the Dispersionscheme with CCN0 = 50 cm⁻³.

Characteristics of the deep convective cloud systemrevealed by the reference simulation are given inFig. 1,which shows the domain-maximum vertical velocity and rain rate as functions of time. The domainmaximumvalue is defined as the maximum value ofthose at all the grids covering the entire domain undera given time, and the domain average value is definedas the average value of all the grids for the entiredomain during the 3-h integration period. Figure 1ashows the dynamic properties. The domain-maximumvertical velocity had a rapid increase over time,beforereaching the maximum value(nearly 27 m kg⁻¹)at 0.5 h. The maximum vertical velocity thereafter beganto decline,becoming very small and close to zero after1.5 h. Correspondingly,Fig. 1b shows the surfaceprecipitation,which mainly occurred during the first1.5 h of the simulation. Compared with the maximumvertical velocity,the rain rate reached its maximumvalue(nearly 0.19 mm h⁻¹)relatively late at 1.25 h.

Fig. 1. Variations with time of(a)the simulated domain-maximum vertical velocity(m s−1) and (b)correspondingrainfall rate(mm h−1)for the reference case.

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Additionally,the aerosol effects on the domainmaximumvertical velocity were insignificant(figuresomitted). These results are similar to those of severalprevious studies that used the Morrison bulkmicrophysics scheme(Morrison,2012; Xie et al., 2013). However,several bin microphysics models havedemonstrated stronger convection induced by more latentheat release with increased aerosol loading(Khain et al., 2005; Lebo and Seinfeld, 2011; Tao et al., 2012).Regarding to the aerosol effects on clouds and precipitation,we present the results in the following subsectionsfor the three autoconversion parameterizationschemes.

The dependence of cloud microphysical propertieson various CCN number concentrations is presented inFig. 2 for the Kessler,KK, and Dispersion schemes.Figure 2a shows that the cloud droplet number concentrationincreased markedly with the CCN number concentration.With increasing CCN number concentration,more aerosols are activated into cloud droplets,thereby enhancing the cloud droplet number concentration(e.g.,Kaufman and Nakajima, 1993). Figure 2b shows that the mean volume radius of clouddroplets decreased with increasing CCN number concentration,suggesting that a relatively large numberof cloud droplets were competing for the fixed amountof water vapor. Figures 2a and 2b indicate that theKessler,KK, and Dispersion schemes only altered theproperties of cloud droplets slightly. This is becausethe activation scheme of aerosols into cloud dropletsis exactly the same as described by Eq.(4)in all thethree schemes.

Fig. 2. Simulated(a)number concentration of cloud droplet,(b)mean volume radius of cloud droplet,(c)numberconcentration of rain drop, and (d)mean volume radius of rain drop,derived from the domain average values within 3h of integration for the three autoconversion parameterization schemes under various initial CCN concentrations.

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In comparison with the cloud droplets,changesin rain drops with increasing CCN number concentrationare more complex for the three autoconversionschemes(Figs. 2c and 2d). The Kessler schemeshowed insignificant variation in the number concentration and mean volume radius of rain drops withCCN number concentration. This is because theKessler scheme cannot represent the indirect effectof aerosols, and the autoconversion rate is unrelatedto the cloud droplet number concentration. The decreasing(increasing)trends of rain drop concentration(rain drop mean volume radius)were consistent for theKK and Dispersion schemes,displaying the aerosolindirect effects. The number concentration of raindrops was reduced from clean to polluted aerosol backgrounds.The enhanced activation of aerosol particlesto cloud droplets can form a larger number of dropletswith smaller sizes or radii,leading to lower efficiency ofcloud-to-rain autoconversion process. The mean volumeradius of rain drops can be increased with increasingaerosol particles. In contrast to the autoconversionprocess,a relatively more efficient accretiongrowth occurs due to higher cloud water content inpolluted backgrounds,which can eventually result inlarger sizes of rain drops(Xie et al., 2013). Higheraerosol loading can result in an increase in the radii or sizes of rain drops,which is in good agreement withthe results of several previous investigations(Cheng et al., 2007; Li et al., 2008; Lim and Hong, 2010; Xie et al., 2013).

Figure 3 shows the domain-averaged water contentof hydrometeors within 3 h of integration undervarious initial CCN number concentrations withthe three autoconversion parameterization schemes forcloud,rain, and ice species. The water content of icespecies is the sum of the content of ice,snow, and graupel.For the Kessler scheme,aerosol loading slightlyaltered all of the hydrometeor species. For the KKscheme,the cloud water content increased and the rainwater content decreased with increasing CCN numberconcentration(Figs. 3a and 3b). More and smallercloud droplets induced by aerosols can hinder the autoconversionprocess of cloud droplets into rain drops,resulting in higher cloud water content but lower rainwater content(Xie et al., 2013). The water content ofice species increased with CCN number concentration(Fig. 3c). More cloud droplets induced by aerosolscan be transported and frozen into cold cloud regimesto enhance the processes of the ice phase and thus toform more ice hydrometeor species.

Fig. 3. Domain average water content of hydrometeors within 3 h of integration under various initial CCN concentrationsfor the three autoconversion parameterization schemes.(a)Cloud,(b)rain, and (c)ice species including ice,snow, and graupel.

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Note that the Dispersion scheme differs fromthe KK scheme. The former considers the influenceof cloud droplet spectral dispersion,which wasparameterized as the increasing function of clouddroplet number concentration as described in Section2. Therefore,the increase in cloud droplet spectral dispersioncan enhance the autoconversion process,whichcompensates for part of the decreasing autoconversionefficiency induced by aerosols. As shown in Fig. 3,theincreasing or decreasing trends in the hydrometeor watercontent of the Dispersion scheme with increasingCCN number concentration are essentially consistentwith those in the KK scheme. However,a large differenceexists between the values of the hydrometeorwater content for these two autoconversion schemes.The cloud water content is lower, and the rain water content is higher for the Dispersion scheme than thatfor the KK scheme. These are because the increasein the cloud droplet spectral dispersion enhanced theautoconversion process and converted more cloud waterinto rain water in the Dispersion scheme. For theDispersion scheme,the water content of ice species issignificantly lower than that of the KK scheme,becausefewer cloud droplets in the former can be transported and frozen into cold cloud regimes to form icehydrometeor species.

In this subsection,we show that aerosol-inducedprecipitation change is strongly dependent on the autoconversionparameterization scheme. Figure 4 showsthe total surface precipitation with respect to the initialCCN number concentration for the three autoconversionschemes. Figure 4a shows a weak increasein surface precipitation(from 0.0786 to 0.0804 mm)in response to the increasing CCN number concentrationfor the Kessler scheme. For the KK scheme(Fig. 4b),the surface accumulated precipitation decreasedmarkedly from 0.0809 to 0.0265 mm with the increasingCCN number concentration, and for the Dispersionscheme(Fig. 4c),the change in precipitation inducedby aerosols was non-monotonic. The surfaceprecipitation increased with the CCN number concentrationfrom 50 to 2000 cm⁻³,the maximum valuecan reach 0.0826 mm for the CCN number concentrationat 2000 cm⁻³(threshold value). The precipitationamount decreased when the CCN number concentrationexceeded this threshold value.

Fig. 4. Responses of the total accumulated surface precipitation to the changes in initial CCN number concentrationfor the three autoconversion parameterization schemes.(a)Kessler scheme,(b)KK scheme, and (c)Dispersion scheme.

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Figures 5a and 5b indicate that aerosol-inducedprecipitation change is mainly determined by thecorresponding rain water content. For the Kesslerscheme,the autoconversion rate was enhanced withthe cloud water content and it did not vary with thecloud droplet number concentration. Therefore,theslightly increased rain water content induced by more activated cloud water can lead to a weak increase insurface precipitation. Because the KK scheme considersthe aerosol indirect effect,more and smaller clouddroplets induced by aerosols made the autoconversionprocess less efficient,which resulted in lower rain watercontent and reduced precipitation. The Dispersionscheme represents the indirect effects of aerosols and the influence of spectral dispersion. The autoconversionprocess can be enhanced by increasing spectraldispersion,which compensates for part of the decreasingautoconversion efficiency induced by aerosols.The enhanced precipitation with increasing aerosolsat lower CCN conditions may be explained by thecombined effects of the higher rain water content and additional mixed phase processes. Moreover,the decreasedprecipitation at high CCN conditions is likelybecause of the extremely suppressed conversion fromcloud droplets to rain drops.

Fig. 5. Responses of(a)the total accumulated surface precipitation and (b)domain average rain water content within3 h of integration to changes in the initial CCN number concentration for the three autoconversion schemes.

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Note that,precipitation varies non-monotonicallywith the Dispersion scheme,increasing with aerosolsat lower concentrations and decreasing at higher concentrations.These results are in good agreement withthe findings about the impacts of aerosols on precipitationin Li et al.(2008) and Lim and Hong(2010).Hence,the results obtained in this study based on theDispersion scheme are likely more reliable than thosederived from the Kessler and KK schemes.

In this paper,we used the Kessler,KK, and Dispersionautoconversion parameterization schemes to investigate the aerosol indirect effects on cloud microphysicalproperties and surface precipitation for a deepconvective cloud system under aerosol concentrationsfrom 50 to 10000 cm−3. Our results show that aerosolinducedprecipitation change is strongly dependent onthe autoconversion parameterization schemes. For theKessler scheme,the average cumulative precipitationwas enhanced slightly with the increase in aerosol concentrations.For the KK scheme,surface precipitationwas reduced significantly with increasing aerosols. Forthe Dispersion scheme,the total precipitation variednon-monotonically,increasing with aerosols at lowerconcentrations and decreasing at higher concentrations.These different trends in aerosol-induced precipitationchange were mainly due to changes in rainwater content under the various autoconversion parameterizationschemes. Therefore,our results suggestthat an accurate representation of the cloud-to-rainautoconversion process is needed for advancing thescientific underst and ing of aerosol-cloud-precipitationinteractions(Boucher et al., 1995; Rotstayn and Liu, 2005).

Note that several environmental parameters suchas atmospheric relative humidity,vertical wind shear, and CAPE may influence the aerosol-induced effectson cloud microphysical properties and surface precipitation(Tao et al., 2012). However,the presentstudy is not focused on different environmental parametersassociated with aerosol-cloud-precipitation interactions.Variations in relative humidity,vertical windshear, and CAPE may result in the distinct aerosoleffects on precipitation for different autoconversion parameterization schemes.

Additionally,the Dispersion scheme displayed anon-monotonic change in surface precipitation withincreasing aerosols,which is in good agreement withrecent findings about aerosol-induced changes in precipitation(Li et al., 2008; Lim and Hong, 2010).Therefore,we believe that the Dispersion scheme consideringspectral dispersion is more reliable for improvingthe underst and ing of the aerosol indirect effects.