Effects of aerosols on the dynamics and microphysics of squall lines simulated by spectral bin and bulk parameterization schemes

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2009jd011902, 2009 Effects of aerosols on the dynamics and microphysics of squall lines simulated by spectral bin and bulk parameterization schemes A. P. Khain, 1 L. R. Leung, 2 B. Lynn, 1 and S. Ghan 2 Received 12 February 2009; revised 7 May 2009; accepted 31 July 2009; published 19 November [1] A new spectral bin microphysical scheme (SBM) was implemented into the Weather Research and Forecasting model referred to as Fast-SBM, which uses a smaller number of size distribution functions than the original version of the scheme referred to as Exact-SBM. It was shown that both schemes produced similar dynamical and microphysical structure of a squall line simulated. An excellent agreement in the simulated precipitation amounts between the schemes was found within a range of cloud condensation nuclei concentrations from 100 to 3000 cm 3. The Fast-SBM requires about 40% of the computing power of the Exact-SBM, allowing it to be used for real-time simulations over limited domains. The results obtained using the SBM simulations have been compared with those using a modified version of the Thompson bulk parameterization scheme. The main extension of the bulk scheme was the implementation of the process of drop nucleation, so that drop concentration is no longer prescribed a priori but rather calculated using the prescribed aerosol concentration. This scheme is referred to as the Drop scheme. A large set of sensitivity studies have been performed, in which microphysical parameters and precipitation, droplet nucleation above cloud base, etc., have been compared with those obtained from SBM. The SBM scheme produces more realistic dynamical and microphysical structure of the squall line. The Drop scheme did relatively little to change the cloud structures simulated by the bulk scheme. Unlike the SBM simulations that show different precipitation sensitivities to aerosol concentrations in relatively dry and humid environments, the Drop scheme indicates monotonic decrease in precipitation with increasing aerosol concentrations. Citation: Khain, A. P., L. R. Leung, B. Lynn, and S. Ghan (2009), Effects of aerosols on the dynamics and microphysics of squall lines simulated by spectral bin and bulk parameterization schemes, J. Geophys. Res., 114,, doi: /2009jd Introduction [2] Aerosol effects on the dynamics and microphysics of individual deep convective clouds and cloud ensembles have been simulated in many studies (see reviews by Levin and Cotton [2009] and Khain [2009]). In most studies convective invigoration accompanied by an increase in the amount of supercooled water at higher levels has been reported with increasing aerosol concentrations. Regarding aerosol effects on precipitation, increased precipitation with increasing aerosol concentrations was reported in simulations of maritime convective clouds and clouds developing in the moist subtropical atmosphere. For more continental, dry air conditions, however, decreased precipitation with increase in aerosol concentration has been reported. [3] The squall line is one of the most common types of mesoscale cloud systems in the tropical and subtropical regions. It is characterized by a line of deep convective clouds oriented nearly perpendicular to the mean wind. 1 Department of Atmospheric Sciences, Hebrew University of Jerusalem, Jerusalem, Israel. 2 Pacific Northwest National Laboratory, Richland, Washington, USA. Copyright 2009 by the American Geophysical Union /09/2009JD Behind this line is a large area of stratiform clouds and stratiform precipitation of several hundred kilometers in length. Squall lines have been simulated many times using 2-D and 3-D models [e.g., Dudhia et al., 1987; Rotunno et al., 1988; Tao and Simpson, 1993; Tao et al., 1993, 1996, 2003]. Squall lines have a typical geometrical and microphysical structure, which allows modelers to use them as an object to simulate and test different models, or the same dynamical model with different explicit microphysics, and/ or convective parameterization schemes. [4] The effect of aerosols on the dynamical structure and clouds in squall lines has been investigated with 3-D simulations using the Mesoscale Model MM5 [Lynn et al., 2005a, 2005b; Lynn and Khain, 2007], as well as 2-D and 3-D simulations using the Goddard Space Flight Center Cloud Ensemble model (GCE) [Tao et al., 2007; Li et al., 2009a, 2009b]. In all cases, the SBM scheme described by Khain et al. [2004] has been used. Lynn et al. [2005a] simulated a rain event over Florida accompanied by the squall line formation. They found that aerosols led to an invigoration of convection and fostered the formation of secondary clouds as a result of the intensification of downdrafts from primary clouds. Lynn et al. [2005b] reported a significant intensification of precipitation in the zone of the 1of21

2 squall line in the polluted atmosphere, which was accompanied by a decrease in precipitation from smaller clouds behind the squall line. As a result, the total precipitation over the whole area changed only slightly between clean and polluted conditions. These results have been further supported by Lynn and Khain [2007] using a better experimental design including higher model resolution and a larger innermost domain where SBM was applied. [5] The redistribution of precipitation between deep convection and shallow convection has also been obtained recently by Lee et al. [2008] using simulations of mesoscale convective ensembles. Tao et al. [2007] simulated the welldocumented squall lines observed in the TOGA COARE (central Pacific) and PRESTORM (Oklahoma region, United States) field experiments, as well as a squall line in Florida. Their simulations performed using low and high aerosol particle (AP) concentrations showed an increase in precipitation in the maritime TOGA COARE case, a relatively weak decrease in precipitation in Oklahoma (drier case), and no significant effect in the Florida squall line with high AP concentrations. In these studies, as well as in the studies by Khain et al. [2004, 2005, 2008a, 2008b] and Fan et al. [2007a, 2007b], it was shown that atmospheric humidity is an important environmental factor that determines the response of convective system dynamics and precipitation to aerosols. It was shown that an increase in aerosol concentration under high humidity intensifies convection and leads to stronger evaporative cooling compared to the clean air conditions. Correspondingly, clouds that form in polluted air create stronger downdrafts, which foster the formation of secondary clouds or strengthen the squall line. Lee et al. [2008] showed that wind shear is another governing factor, which in addition to high aerosol concentrations, fosters the formation of secondary clouds. [6] As shown by Khain et al. [2008a] and Khain [2009], simulating the effects of aerosols is very challenging because it requires a very accurate description of microphysical processes that determine the different terms of the condensate mass budget. This is particularly true for surface precipitation, because it often results from a small difference between the generation of condensate mass by condensation of drops and the deposition of ice and loss in condensate due to drop evaporation and ice sublimation. Since both condensation and evaporation depend on particle size, accurate description of collisions is also required. [7] Two microphysical approaches have been widely used in state-of-the art cloud and mesoscale models to investigate aerosol effects on cloud dynamics and precipitation: bulk parameterization schemes and spectral bin microphysics (SBM). In bulk parameterization schemes the shape of size distribution functions is prescribed a priori. This reduces the system of equations that describe cloud microphysics to a relatively small number of equations for integral quantities such as mass contents (one moment schemes) and mass contents and concentrations (two moment schemes). The comparatively small number of prognostic equations makes the schemes computationally efficient, so they are widely utilized in simulating different cloud-related phenomena. However, these schemes have substantial limitations in describing different microphysical processes. For instance, these schemes as a rule do not solve the equation for diffusion growth of drops (this equation is replaced by transformation of all supersaturated water vapor into cloud water mass, so that the final supersaturation is assumed equal to zero), and instead of solving the stochastic equation of collisions, semiempirical relationships for autoconversion rates are used. [8] The second approach to simulating microphysical processes is the utilization of SBM, in which a system of kinetic equations for size distributions of particles of different type is solved. Each size distribution function is described using several tens of mass (size) bins. The equation system solves the equations for advection, sedimentation collisions, freezing, melting, etc., for each mass bin. This method is much more accurate than the bulk schemes regarding its ability to simulate cloud dynamics and microphysics and precipitation (see comparisons of SBM versus bulk schemes of Lynn et al. [2005b], Lynn and Khain [2007], Li et al. [2009a, 2009b], and Iguchi et al. [2008]). However, SBM schemes require significant computer time, which hinders their application in mesoscale models. [9] To improve model skill in simulating clouds, cloud systems, and, in particular, aerosol effects on dynamics and microphysics, we need to improve the bulk schemes or/and develop more computationally efficient SBM schemes. The improvement of bulk schemes is usually performed by implementation of bin-emulating procedures and calibration of parameters of the microphysical schemes using results obtained by SBM. For instance the two-moment bulk parameterization scheme used in the model COSMO by Weather Forecast Center of Germany [Steppeler et al., 2003] has been calibrated using the SBM scheme developed in the Hebrew University Cloud model (HUCM) [e.g., Seifert et al., 2006; Khain et al., 2008b]. This calibration improved significantly the skill of the bulk schemes. Although it was shown that tuning of the parameters of bulk schemes can lead to a good agreement with the SBM models under certain environmental conditions, changes in the conditions may lead again to a divergence of the results. [10] The first attempt to create more computationally efficient SBM was performed by Lynn et al. [2005a, 2005b] within the dynamical framework of the Mesoscale Model Version 5 (MM5) [Dudhia, 1993]. More recently, many investigators have started to use the Weather Research and Forecasting model (WRF) [Skamarock et al., 2005]. For instance, Lynn et al. [2007], Lee et al. [2008], Li et al. [2008], and Khain and Lynn [2009] used the WRF to simulate aerosol effects on precipitation. Although a significant advancement in high-performance computing has made it possible to use SBM in mesoscale simulations, the need to develop computationally efficient SBM and improve bulk parameterization schemes remains, as reducing the uncertainty of aerosol effects requires long-term climate simulations of aerosol effects under a wide range of environmental conditions. [11] This study describes a new SBM scheme (hereafter Fast-SBM) that was derived from the more detailed scheme described by Khain et al. [2004] (hereafter referred to as Exact-SBM). Both the Exact-SBM and Fast-SBM are applied to simulate a squall line under thermodynamic conditions typical of midlatitude continental squall lines. The results obtained using Exact-SBM and Fast-SBM are also compared with the results obtained using an extension 2of21

3 of the Thompson bulk parameterization scheme [Thompson et al., 2004, 2008]. Both schemes are implemented in the same dynamical framework of WRF, and simulations were performed using a two-dimensional model configuration to simplify the comparison of results. 2. Model Description 2.1. SBM Schemes [12] The SBM scheme implemented in WRF has been described by Khain et al. [2004] and Lynn et al. [2007]. The scheme is based on solving the kinetic equation system for size distributions of seven types of hydrometeors: water drops, three types of crystals (columnar, plate and branch type), aggregates (snow), graupel and hail. Each hydrometeor type is described by a size distribution function defined on the grid of mass (size) containing 33 mass bins. The doubling mass grid is used, so that the mass of drops belonging to the (i+1)th bin is twice as large as the drop mass in the ith bin. The mass grids are the same for all hydrometeors to simplify the transition from one type to another during freezing, melting, etc. The minimum particle mass corresponds to that of the 2 mm radius droplet. The model is specially designed to take into account aerosol effects on cloud microphysics. It contains an aerosol budget, which describes two-way cloud-aerosol interaction. Aerosol particles are also described by a size distribution function containing 33 size bins. In contrast to standard bulk parameterization schemes the size distributions of cloud hydrometeors and aerosols are not prescribed a priori, but rather calculated in the course of model integration. Supersaturation is calculated using an accurate analytical method representing an extension of the approaches developed earlier by Tzivion et al. [1989] and Khain and Sednev [1996]. Using the values of supersaturation, the critical aerosol size to be activated to drops is calculated. Aerosol particles exceeding the critical size are activated and the corresponding mass bins in the aerosol size distribution become empty. It means that within the cloud updraft we have two fluxes: the flux of nucleated droplets and flux of nonactivated CCN. When supersaturation exceeds its local maximum at the cloud base, a new portion of CCN will be activated to droplets (in-cloud nucleation). This process is especially important in maritime clouds where supersaturation is high and often increases with height because of a decrease in droplet concentration and increase in vertical velocity with height. This process leads to the formation of bimodal droplet spectra with realistic droplet spectra dispersion [Pinsky and Khain, 2002; Segal and Khain, 2006; Segal et al., 2003]. The SBM also takes into account possible droplet nucleation during dry air entrainment through the lateral cloud boundaries. [13] A new approach has been applied to eliminate artificial spectrum broadening typical of previous spectral microphysical schemes (including the earlier version of this model [see Khain et al., 2000]). In this method, the remapping of size distribution functions obtained after diffusion growth to the regular mass grid conserves the three moments of size distribution (zero, third and six moments) to prevent artificial formation of large tails in the drop distribution [Khain et al., 2008a]. This approach allows the formation of very narrow droplet spectra found in smoky and pyroclouds measured during biomass burning over Brazil [Andreae et al., 2004]. Note that in SBM, water drops are not separated artificially into cloud water and rainwater (in contrast to in all bulk parameterization schemes). It means that the SBM does not separate the collision process of water drops into autoconversion (collision of cloud droplets) and accretion (collisions of raindrops and cloud droplets), which is performed in all bulk schemes under simplification of continuous growth. Instead, in SBM the cloud particle collisions are calculated by solving the stochastic kinetic equations for collisions. An efficient and accurate method of solving the stochastic kinetic equation for collisions [Bott, 1998] was extended to a system of stochastic kinetic equations calculating water-ice and ice-ice collisions. The collision kernels for each pair of particles are calculated using accurate superposition method [Pinsky et al., 2001; Khain et al., 2001] and used in the form of lookup tables. The collisions kernels are calculated taking into account the particle shape and density that are represented as the functions of particles mass following Pruppacher and Klett [1997] (see Khain and Sednev [1996] and Khain et al. [2004] for details). The primary nucleation of each type of ice crystals is performed within its own temperature range following Takahashi et al. [1991]. The ice nuclei activation is described using an empirical expression suggested by Meyers et al. [1992] and applying a semi-lagrangian approach [Khain et al., 2000] to allow the utilization of the proposed diagnostic formulas in a time-dependent framework. Secondary ice generation is described according to Hallett and Mossop [1974]. The rate of drop freezing follows the observations of immersion nuclei by Vali [1975, 1994], and homogeneous freezing according to Pruppacher [1995]. [14] The treatment of 8 size distributions (advection of all bins, collisions between particles belonging to different bins) require significant computer time, which is estimated to be about times longer (per grid horizontal axis) than that required by a standard one-moment bulk parameterization scheme. While utilization of 2-D geometry allows one to use the full even more sophisticated SBM schemes with larger number of bins, the utilization of 3-D SBM models, especially on computers with low number of processors, requires development of a more computationally efficient simplified SBM scheme. Attempts to increase speed of particular microphysical processes in SBM schemes, for instance, collisions, were performed in several studies [e.g., Simmel et al., 2002]. Lynn et al. [2005b] and this study increases the SBM speed by using a smaller number of size distribution functions but keeping, however, the advantages of SBM, by solving nonparameterized equation system for microphysical processes. For instance, utilization of three size distribution functions for description of ice crystals (i.e., 99 types of ice crystal particles, characterizing by their sizes, shapes, fall velocities, etc.) is, possibly important for simulation of fine features in ice clouds [Fan et al., 2009]. At the same time for simulation of deep convection, especially deep maritime clouds so detailed description of ice crystals, might be, is not necessary. Accordingly, Lynn et al. [2005b] proposed the first fast version of spectral bin microphysics scheme. In that scheme it was assumed that small ice particles can be assigned to ice crystals, while particles with sizes exceeding several hun- 3of21

4 dred of microns were assigned to graupel, aggregates and hail. As a result, instead of six size distributions for ice used in the full SBM scheme, in that Fast-SBM three size distribution functions were used. [15] In the present study we propose and test even more simplified Fast-SBM version, in which all ice crystals and snow (aggregates) are calculated at one mass grid (one distribution function). The smallest ice crystals with sizes below 150 microns are assumed to be crystals, while larger particles are assigned to aggregates (snow). Similarly, highdensity particles (graupel and hail) are also combined into one size distribution (graupel). As a result, cloud ice in this scheme is described by two size distribution functions for low-density and high-density particles. Such simplification further decreases the computational time. As a result, the number of size distributions decreases from 8 to 4 (aerosols, water drops, low-density ice, high-density ice). Note that Fast-SBM keeps the main advantages of SBM: a kinetic equation system is solved using the nonparameterized basic equations, particles of each size have their own settling velocity, particles have, depending on their mass, different densities, etc. Even being simplified, the Fast-SBM contains 66 sizes of ice particles characterized by different densities, shapes and settling velocities, which offers an advantage over any bulk scheme containing 3 to 4 ice types and describing by 3 4 (one-moment schemes) of 6 8 (twomoment schemes) integral parameters. The test simulations described below showed that Fast-SBM requires only about 40% of the computational time used by the original SBM in a 2-D configuration. It means that for 3-D simulations, Fast- SBM should require less than 20% of the time of the full SBM, which makes it possible to use Fast-SBM on standard PC clusters Thompson Bulk Parameterization Scheme [16] In this paper, we compare WRF-SBM to the latest version of the bulk microphysical scheme referred to here as the Thompson scheme [Thompson et al., 2004, 2008]. This scheme predicts the mixing ratios of five liquid and ice species including cloud water, rain, cloud ice, snow, and graupel. In addition, the number concentration of cloud ice is also predicted. The scheme is designed to mimic some processes currently only described using SBM type schemes. For example, the new scheme utilizes a lookup table generated from 100 size bins of rain and snow to calculate hydrometeor collisions/collection. For hydrometeor collection of two species that results in a third (e.g., rain collecting snow to form graupel), the mass of the third hydrometeor is obtained by summing both the collected and collector species, and the mass of the two species is removed. Additionally, the probability of a certain volume of drops freezing at specified temperatures is precomputed and stored in a lookup table. Raindrops freeze into graupel and cloud droplets freeze into cloud ice. The fraction of ice mass with particle diameters greater than 125 mm is immediately transferred to the snow category. In the case of rain collecting snow (and its inverse), the scheme scans the snow size bins in the table and if the mean mass of the water drop exceeds the mass of the snow particle, it is assumed that the two particles join as one thus freezing the drop into graupel. If, on the other hand, the water drop mass is less than the snow particle mass, the snow simply accretes the water drop, thus increasing the snow mass and decreasing the rain mass. [17] In the original bulk scheme drop concentration was prescribed from the very beginning. In this study the scheme was extended to take into account the changes of droplet concentration with time. Following the prognostic droplet approach of Ghan et al. [1997], cloud droplet nucleation is treated at cloud base and droplets are then mixed vertically through the depth of the cloud. Droplet nucleation is diagnosed from the supersaturation, which is parameterized based on work by Abdul Razzak et al. [1998], and is primarily a function of aerosol number concentration, the grid mean updraft velocity and subgrid turbulent motion, as well as aerosol composition and size distribution. Depending on the turbulence transfer scheme used in the simulation, the subgrid turbulent motion is a function of the vertical diffusivity or turbulent kinetic energy. Gustafson et al. [2007] described an option in WRF to simulate aerosols prognostically with a gas-phase chemistry mechanism and an aerosol module with eight size sections. In this study, however, aerosol concentration is uniformly prescribed in the simulations so that the sensitivity to aerosol concentration can be isolated. [18] Originally developed mainly for stratiform clouds, Ghan et al. [1997] neglects droplet formation in the interior of the cloud. To simulate aerosol effects on convective clouds associated with squall lines, we extend the parameterization by taking into account possible droplet nucleation above cloud base (referred here to as secondary nucleation). We assume supersaturation above cloud base can be diagnosed from the balance between supersaturation production by adiabatic cooling and supersaturation depletion by condensation on droplets and raindrops. Only the grid cell mean vertical motion is used to account for adiabatic cooling, and the effect of subgrid turbulent mixing is ignored. The number of condensation nuclei activated by secondary activation is then diagnosed from the aerosol composition and size distribution and the supersaturation, as in the SBM. [19] To estimate the secondary droplet nucleation rate based on the diagnosed activated droplet number, we apply a simple relaxation of the existing droplet numbers toward the diagnosed number activated over an adjustable relaxation time scale. In this study, we apply a relaxation time scale of 100 s, although ideally this parameter could be tuned to match the simulated droplet concentrations to observations or the SBM simulations. In the Thompson scheme, cloud drops can freeze to form graupel or ice, and the formulation is based on work by Bigg [1953]. The procedure of calculating drop freezing is computationally expensive, and depends on the droplet concentration. Although the model predicts droplet concentration at each time step, we calculate drop freezing based on a prescribed droplet concentration only once at the beginning of the simulation. We account for the influence of the predicted droplet concentration on drop freezing by applying a scaling factor, which is equal to the ratio of the predicted drop concentration to the initial (prescribed) drop concentration. We describe results both with (referred as scaling in the new version) and without (referred as no-scaling in the old version) this scaling to determine its potential impacts on the simulations. 4of21

5 [20] In the Thompson scheme [Thompson et al., 2008], autoconversion is treated following Berry and Reinhardt [1974], in which the characteristic diameters, D f and D b,of cloud water droplets are calculated based on the full assumptions of the droplet spectrum. The only difference between Thompson et al. [2008] and Berry and Reinhardt [1974] is the shape of the droplet spectrum. That is, Thompson et al. [2008] assumed a gamma distribution while Berry and Reinhardt [1974] assumed a generalized Golovin distribution. The derived characteristic diameter D f is a function of the droplet number concentration [Thompson et al., 2008, equation A9], and the characteristic diameter D f is a function of droplet spectrum dispersion [Thompson et al., 2008, equation A11]. In this study, when the prognostic droplet scheme is applied, the prognostic droplet number concentration is used to calculate D f. In the following, we describe how the droplet spectrum dispersion used to calculate D b is calculated based on the droplet number concentration so that the effects of aerosols on cloud droplet concentrations and hence autoconversion are fully accounted for when the prognostic droplet scheme is used. [21] In the Thompson scheme, all hydrometeors except snow conform to a generalized gamma distribution [Walko et al., 1995; Verlinde et al., 1990], NðDÞ ¼ N tl mþ1 Gðm þ 1Þ Dm e ld ; ð1þ where N(D)dD is the number of particles within the diameter range from D to D + dd, N t is the total number of particles in the distribution, l is the slope of the distribution, and m is the shape parameter. The droplet spectrum dispersion is given by h = s r = 1 ðm þ 1Þ 1=2, where s is the droplet size distribution (DSD) width and r is the mean radius. In the original version of the Thompson parameterization (aimed at parameterization of stratiform clouds) DSD dispersion was chosen typical of stratiform clouds as presented by Martin et al. [1994]. In that study, cloud drop size was assumed to follow a gamma distribution, and the DSD dispersion h was taken as 0.45 for polluted conditions and roughly 0.25 for clean maritime conditions. The smaller dispersion in clean maritime clouds is partially attributed to larger mean drop size r. Assuming that maritime air masses have low droplet concentrations of roughly cm 3 while continental air masses have concentrations of 250 cm 3 or more, Thompson et al. [2008] derived the following empirical relationship between number concentration (N) and m to match those observations of relative dispersion: m ¼ min 15; 10 9 =N þ 2 : ð2þ However, the values of h in convective clouds should differ from those in stratiform clouds. For instance, h in cumulus clouds rapidly decreases with the distance above cloud base from 1 to 0.2 at 400 m above cloud base in clouds with drop concentration of about 600 cm 3 [Politovich, 1993]. Furthermore, one can expect larger dispersion in clean maritime clouds in which DSD are often bimodal [Warner, 1969a, 1969b; Pinsky and Khain, 2002; Segal et al., 2003, Segal and Khain, 2006]. Larger dispersion in cloud zones with bimodal DSD was found also by Politovich [1993]. Analysis of DSDs measured in situ in zones of clean and polluted air over the Amazon region of Brazil during the LBA-SMOCC campaign [Andreae et al., 2004] indicates that at 1 km distance above cloud base h in polluted (smoky) clouds ranges from about 0.1 to 0.2, while in clean (green ocean) clouds it ranges from 0.4 to 0.5. These data show that in cumulus clouds (and, as we suppose, in deep cumulus clouds) the typical values of the DSD dispersion are higher in the clean atmosphere than in the polluted air in contrast to the old parameterization based mainly on stratiform clouds. Correspondingly, in the new scheme version the DSD dispersion h varies from about 0.2 in polluted air to 0.45 in the clean atmosphere. The values of m were recalculated accordingly based on the empirical formula m ¼ 12*SQRT N=10 9 : ð3þ This formula is simply postulated to capture the general relationship between the DSD dispersion and aerosol concentrations as seen from observation data cited above, as well as to provide DSD dispersion values not too different from those derived from the original formulation used by Thompson et al. [2008]. These changes led to use of wider DSD in clean air and narrower DSD in polluted air as compared to the original parameters used in the Thompson scheme. 3. Design of Simulations [22] For simulations of a squall line typical of continental conditions, the thermodynamic conditions used by Rotunno et al. [1988] have been chosen. We prescribed a surface temperature of 27.5 C, and absolute humidity near the surface of about 14 g/kg. This corresponds to a relative humidity of about 70% near the surface and the CAPE was 2160 J/kg. The sounding (vertical profiles of temperature and dew point) used in our simulations is presented in Figure 1. These thermodynamic conditions used are quite close to those observed during the June PRE- STORM (the Preliminary Regional Experiment for Stormscale Operational and Research Meteorology) squall line [see Zhang et al., 1989; Braun and House, 1997; Li et al., 2009a, 2009b]. Following Rotunno et al. [1988] an idealized wind shear was applied in the boundary layer with maximum wind speed of 11 m/s near the surface and zero wind speed at the 2.5 km level. Droegemeier and Wilhelmson [1985] and Rotunno et al. [1988] showed that such wind shear at low levels foster formation of squall lines. Simulations have been performed using a 2-D WRF domain with a computational area of 512 km in the horizontal with a grid resolution of 1 km. The number of vertical levels was 81. The distance between the levels increases with height from a few meters near the surface to several hundred meters at about 20 km. The evolution of squall lines has been simulated for 4 h with a time step of 6 s. The squall line was triggered using an initial temperature pulse following the standard procedures for an idealized squall line in WRF. As was shown by Rotunno et al. [1988] a 2-D framework is suitable for 5of21

6 Figure 1. Sounding data used in the simulations of squall line [after Rotunno et al., 1988]. The values of equivalent potential temperature are also presented. simulation of squall lines and provides results quite similar to those predicted by a 3-D models. [23] Simulations have been carried out with the 2 versions of SBM (Exact-SBM and Fast-SBM), as well with the various versions of the Thompson bulk parameterization using different aerosol (droplet) concentrations. [24] In SBM, the initial aerosol size distribution was calculated using a semiempirical expression. The initial (at t = 0) CCN size distribution was calculated using the empirical dependence N ccn = N o S k, following the procedure described by Khain et al. [2000]. In this formula N ccn is the concentration of activated AP (nucleated droplets) at supersaturation S (in %) with respect to water. N o and k are constants chosen typical of maritime and continental aerosols. At t > 0, the prognostic equation for the size distribution of nonactivated aerosol particles (AP) is solved in the following way: using the value of S calculated at each time step, the critical AP radius is calculated according to the Kohler theory. The APs with radii exceeding the critical value are activated and new droplets are nucleated. For AP with radius below 0.03 mm the droplet size was calculated using the Kohler theory. For larger APs, droplet size was calculated by multiplying the dry aerosol radius by a factor ranging from 3 to 8. The magnitude of the factor decreases with the increase in size of dry AP [Segal et al., 2007]. In the simulations the value N o was chosen equal to 100 cm 3 (clean air) or 1000 cm 3 (intermediate) and 3000 cm 3 (polluted). The slope coefficient k was set equal to for clean air and for other cases. Table 1 summarizes the results from each SBM simulation for different N o. [25] Table 2 shows the list of simulations using various formulations of the Thompson scheme, with and without drop nucleation, secondary nucleation processes, and scaling of drop freezing based on the drop concentration. The table also shows the main results obtained in these simulations. The Drop simulations use the new drop nucleation scheme with secondary drop generation and freezing of drops with scaling that depends on the drop concentration as discussed in section 2.2. These runs are labeled Drop 100, for example, for a prescribed aerosol concentration of 100 cm 3. The next three runs are labeled No-2nd Nucleation 100, for example. This set of three simulations did not include secondary nucleation processes to generate cloud drops. The next set of three simulations, called No- Scaling 100, for example, does not adjust ice freezing to account for the difference between the predicted and initially prescribed drop concentration. As discussed in section 2.2, the DSD dispersion h in polluted and clean atmosphere cases was assumed equal to 0.2 and 0.45, respectively, so equation (3) was used in all the bulk scheme simulations. To examine the impacts of DSD dispersion, a set of runs denoted as OLD-Mu were performed that used the original DSD parameters (equation (2)) taken from the study of stratocumulus clouds given by Martin et al. [1994]. We also included simulations using the original Thompson scheme (i.e., without the prognostic cloud droplet number equation). These simulations are denoted Tho for prescribed droplet number concentrations of 100, 500, and 1000 cm 3 for comparison with the SBM and Drop simulations where aerosol concentrations are prescribed at 100, 1000, and 3000 cm 3, respectively. Simulations with the original and new formulations of the DSD dispersion are also contrasted between simulations denoted Tho 100 versus Tho New-Mu 100, etc. The precipitation amounts are in mm, while the cloud number concentrations (qnc and qnc_max) are in per cm 3. Other variables, such as qc, qr, Table 1. Comparison of the Results of the SBM Simulations a Simulation Rain, mm qnc, cm 3 qc, g m 3 qr, g m 3 qi, g m 3 qs, g m 3 qg, g m 3 max qnc, cm 3 Exact-SBM Exact-SBM Exact-SBM Fast-SBM Fast-SBM Fast-SBM a Time and computational area averaged values of precipitation (Rain), drop concentration (qnc), CWC (qc), RWC (qr), ice crystals (qi), snow (qs), and graupel contents (qg and max qnc). Maximum values of droplet concentration are also presented. The time averages are from 5 min output data over 240 min. For the Exact-SBM, graupel content (qg) represents the sum of graupel and hail contents. 6of21

7 Table 2. Results From Simulations Using Various Formulations of the Thompson Scheme a Experiment Rain qnc qc qr qi qs qg qnc_max Drop Drop Drop No 2nd Nucleation No 2nd Nucleation No-2nd Nucleation No-Scaling No-Scaling No-Scaling Old-Mu Old-Mu Old-Mu Tho New-Mu na na Tho-New-Mu na na Tho-New-Mu na na Tho na na Tho na na Tho na na a Variables and units are the same as in Table 1. See the text for details of the notation for each simulation; na denotes not applicable. etc., show the volume averaged mass contents for cloud liquid water, rainwater, ice, snow, and graupel. 4. Results of Simulations [26] We start the analysis with the comparison of microphysical fields simulated by the different parameterizations. Figures 2a 2c show the microphysical fields simulated by Exact-SBM under different CCN concentrations. First, we note that the simulated squall line has a typical structure of a characteristic front area with developed convection and an extended zone of stratiform precipitation formed by slowly falling melting snow [Tao et al., 2007; Li et al., 2009a, 2009b]. An increase in the CCN concentration led to an increase in supercooled cloud water content (CWC) and elevation of high CWC values at higher levels: at N o = 100 cm 3. CWC does not reach the 7 km level, but much higher CWC reaches 8 km at N o = 3000 cm 3. Correspondingly, the contents of graupel and hail significantly increase in the frontal convective zone, presumably formed by riming of the increased supercooled water. Khain et al. [2008c], dedicated to hail formation, showed that giant Figure 2a. Fields of cloud water content (QC), rainwater content (QR), low-density ice content (ice crystals and snow) (QI+QS), total content of high-density ice (graupel and hail) (QG+QH), and droplet concentration (QNC) in simulation Exact-SBM with low CCN concentration (100 cm 3 ) at t = 240 min. 7of21

8 Figure 2b. Same as in Figure 2a but for CCN concentration of 1000 cm 3. hailstones can be formed only in a highly polluted clouds containing high supercooled CWC. Collision efficiency of large graupel and hail with small droplets (of micron in radii) is close to 1. So, large graupel and hail collect supercooled droplets quite efficiently. At low aerosol concentration the CWC is lower, and riming process is not efficient which prevents formation of large graupel/hail. [27] The microphysical fields simulated by Fast-SBM (Figures 3a 3c) are quite similar to those simulated by Exact-SBM. This similarity is seen both in the general Figure 2c. Same as in Figure 2a but for CCN concentration of 3000 cm 3. 8of21

9 Figure 3a. Same as in Figure 2a but for Fast-SBM run. geometrical structure of simulated squall lines, and in the magnitudes of the contents of different microphysical quantities. Furthermore, the response of Fast-SBM to an increase in the CCN concentration is also quite similar to that of Exact-SBM. The detailed comparison of area averaged quantities and precipitation is presented in Table 1. This result is quite encouraging because Fast-SBM is about 3 times less time consuming than Exact-SBM. Note that in 3-D cases this factor may increase by up to 10 (because Figure 3b. Same as in Figure 2b but for Fast-SBM run. 9of21

10 Figure 3c. Same as in Figure 2c but for Fast-SBM run. advection of size distribution functions is the most time consuming process). [28] Since the results of Exact- and Fast-SBM are quite similar, we will refer these results to as just SBM results when comparing these results with those simulated by the Thompson scheme, shown in Figure 4a 4c. The Thompson scheme also simulates the squall line structure with strong convection in the front of the squall line and the expanded zone of mainly stratiform precipitation. An increase in aerosol concentration from 100 to 1000 cm 3 significantly Figure 4a. Same as in Figure 2a but for Drop 100 (the Thompson bulk parameterization) run. 10 of 21

11 Figure 4b. Same as in Figure 2b but for Drop 1000 (the Thompson bulk parameterization) run. increased the supercooled CWC as well as graupel and hail contents in the frontal zone of the squall line, as also found in the SBM runs. However, one can see important differences in the structure of squall lines simulated by SBM and the bulk parameterization scheme. The bulk scheme produces (1) several updrafts in the squall line front; (2) significant fluctuations of low-density ice content behind the front; and (3) significant fluctuations of graupel content within stratiform area. From the plots of CWC and droplet concentration, we can see that the bulk scheme produces Figure 4c. Same as in Figure 2c but for Drop 3000 (the Thompson bulk parameterization) run. 11 of 21

12 Figure 5. Radar reflectivity (dbz) in the PRE-STORM squall line after 12 h of simulation for the (a) bulk and (b) bin schemes (adopted from Li et al. [2009a]). several convective clouds in the squall line, and we see the convection embedded into the stratiform zone. [29] Note that such difference in the squall line structures simulated by the SBM and bulk parameterization was also reported by Li et al. [2009a]. In that study a well documented squall line observed on the June PRE-STORM was simulated using the Goddard Cumulus Ensemble (GCE) model. In the simulations two microphysical schemes were used: the SBM similar to the Exact-SBM [Khain and Sednev, 1996; Khain et al., 2004] and the bulk scheme of the GCE model which includes cloud water, rain, ice, snow and hail as described by Lin et al. [1983]. The microphysical variables and parameters in the bulk scheme were tuned for strong continental convection. In order to show the similarity in the results obtained in the present study and that of Li et al. [2009a], we present Figures 5 and 6 showing the fields of vertical velocity and radar reflectivity in the squall line simulated using SBM and the Lin et al. [1983] bulk parameterization. One can also see vertical velocity and radar reflectivity fluctuations (embedded convection) in the bulk parameterization run. A detailed comparison of the simulated squall structure to observations performed by Li et al. [2009a] showed that SBM reproduces the squall line structure much more realistically and that no embedded convection took place in the real squall line. The structure of the squall lines simulated using SBM scheme by Li et al. [2009a] and in the present study is quite similar. [30] The similarity of the squall line structures and the similarity in the differences of these structures obtained using bin and bulk microphysical schemes suggest that the same reasons may explain the differences. Detailed analysis of the mechanisms leading to the differences between the SBM and bulk parameterization results, as well as attempts to tune the parameters of the bulk parameterization to converge to SBM and observations regarding the structure of the stratiform zone, were reported by Li et al. [2009b]. Actually, the SBM and the bulk scheme simulated different types of squall lines. The SBM simulates optimum squall line (which is a dominating squall line type according to Rotunno et al. [1988]), when effects of wind shear and cold pool caused by evaporation of precipitating hydrometeors balance each other leading to the formation of one vertical updraft [Rotunno et al., 1988]. In case cold pool is stronger than its optimum value for a given wind shear, the squall line circulation becomes slanted and nonstationary and is characterized by the formation of many updrafts [Rotunno et al., 1988]. Analysis carried out by Li et al. [2009b] showed that the bulk scheme overestimated the evaporation rate because of the assumed gamma distribution of evaporating droplets. Sensitivity tests to reduce rain evaporation rates progressively in the bulk scheme result in increasingly more upright leading cells and fewer convective cores. The stratiform rain area also decreases progressively with decreasing evaporation rate due to the fast falling hail assumed in the bulk scheme. Sensitivity of the bulk parameterization results to fall velocity of hail was also tested. When hail was replaced with graupel, more extensive stratiform rain formed even with reduced rain evaporation rate in the bulk scheme simulation. In summary, despite tuning of various parameters in the bulk parameterization, it was not possible to get the squall structure similar to that simulated by SBM and observations. [31] In support of the conclusions reached by Li et al. [2009a, 2009b] we present Figures 7a and 7b, where temperature deviations from the horizontally averaged values are presented for the Exact-SBM simulations (Fast- SBM produces quite similar temperature deviation fields) and the bulk microphysics runs. Comparison of the fields at t = 120 min indicates that heating in updrafts in SBM simulations is substantially less intense than in the Thompson bulk parameterization scheme and is located below 9 km. At the same time heating in the bulk scheme extends to levels of 11 km. Perhaps the most unrealistic feature in the temperature fields produced by the bulk scheme is the heating in the lower layer behind the squall Figure 6. Vertical air velocity field after 12 h of simulation for the bulk and bin scheme. Contour levels are 5, 1, 0.5, 0.1, 0.1, 1, 5, 10, and 20 m s 1, with negative contours shown in dashed lines. Updraft cores with w stronger than 1 m s 1 are shaded in dark gray. Downdraft cores with w less than 1 ms 1 are shaded in light gray (adopted from Li et al. [2009a]). 12 of 21

13 Figure 7. (a) Fields of temperature deviations for (left) SBM and (right) the bulk scheme at 120 min, and (b) the same as in Figure 7a but at t = 240 min. line in the zone of stratiform rain. Also noted is the much stronger cooling of rain within the zone of intense rain in the bulk scheme at t = 120 min. At t = 240 min pronounced bands of cold air arises in the bulk microphysics runs. No such bands are observed in the SBM runs. These bands are likely produced as a result of overestimation of cooling during sublimation of ice and evaporation of drops by the bulk scheme. The cold pool produced by the bulk scheme leads to the maximum updrafts weakening at t > 100 min (see Figure 15), and the squall line simulated by the bulk 13 of 21

14 Figure 8. Time dependence of maximum droplet concentrations in SBM simulations as well as in bulk parameterization runs Drop 100 Drop scheme becomes weaker than the optimal squall line produced by the SBM. This result is in agreement with the theory given by Rotunno et al. [1988]. [32] To summarize the differences in the dynamical and microphysical structures obtained from the bin and bulk schemes, we analyzed the differences in some integral characteristics. Figure 8 shows the time dependence of maximum values of droplet concentrations in the SBM simulations and the 3 main simulations with the updated Thompson scheme (Drop 100 Drop 3000). Analysis of Figure 8 indicates that: (1) the maximum droplet concentrations are close to the CCN concentration at 1% supersaturation, which indicates that SBM simulates reasonably the maximum supersaturation values; (2) the maximum droplet concentrations in Exact-SBM and Fast-SBM are quite close: during most of the integration, the difference in the concentrations is less than 10%, and never exceeds 30%; and (3) the maximal values of droplet concentrations simulated by the Thompson scheme are in good agreement with the SBM simulations. Maximum values of drop concentrations in SBM takes place at the very beginning of simulations when the first cloud was triggered by the initial temperature pulse. The first cloud has significant vertical velocity at cloud base and develops under the maximum aerosol concentration at cloud base. The subsequent clouds are caused by downdrafts caused by the first cloud. They involve lower amount of aerosols and have lower vertical velocity at cloud base. As a result, the maximum concentration decreases and reaches a quasi-stationary value. [33] Figure 9 shows the time dependence of area averaged droplet concentrations in the SBM simulations as well as in the main bulk parameterization runs Drop 100 Drop One can see again a reasonably good agreement between Exact-SBM and Fast-SBM. However, the averaged drop concentrations in the Thompson scheme exceed those in the SBM by a factor 2 to 3. One possible reason for this excess might be related to the secondary nucleation added in the bulk scheme (see Table 2). In the SBM simulations aerosols that penetrated into the deep convective clouds through the lateral boundaries are activated in the vicinity of the cloud boundaries, so they do not affect the droplet concentration in the cloud cores [Khain et al., 2004]. Besides, the CCN concentration usually decreases with height exponentially, so entrainment above the cloud base should not increase the droplet concentration significantly. [34] Figure 10 shows the time dependence of the area averaged cloud water content (in the SBM simulations cloud droplets are determined as droplets with radius below 60 mm) in the SBM simulations as well as in the bulk parameterization runs Drop 100 Drop One can see that after 2 h of simulations a quasi stationary state is reached. At this stage again the Exact- and Fast-SBM produce quite similar values of CWC. According to the SBM results, the CWC increases monotonically with the increase in the aerosol concentration. This result seems to be reasonable. However, the CWC in the Thompson scheme increases significantly when the aerosol concentration increases from 100 cm 3 to 1000 cm 3. Further increase in the aerosol concentration to 3000 cm 3 does not lead to an increase in CWC. Moreover, most of the time CWC at aerosol concentration of 1000 cm 3 is higher than that of 3000 cm 3. We do note from Table 2, however, that all the simulations using the bulk scheme produce a monotonic increase in CWC with aerosol or prescribed droplet concentrations except Drop 100 Drop 3000 and No-Scaling 100 No-Scaling Apparently the addition of secondary nucleation process with the new formulation of dispersion produces a larger sink in CWC in highly polluted environments. The reasons of this effect are not clear and additional investigations in this direction are needed. [35] Toward 4 h into the simulation, the area averaged RWC values simulated by SBM do not vary significantly with the CCN concentration (Figure 11). Note however, that during the first min precipitation from clouds developed in clean air dominates. Then, RWC increases faster in the squall line developing in the polluted air. This is presumably related to the convective invigoration caused by aerosols, as well as to the recirculation of cloud hydro- Figure 9. Time dependence of area averaged droplet concentrations in SBM simulations as well as in bulk parameterization runs Drop 100 Drop of 21

15 Figure 10. Time dependence of area averaged cloud water content in SBM simulations as well as in bulk parameterization runs Drop 100 Drop meteors, when the falling large drops and ice particles penetrate again the squall line near the cloud base. As a result, a rapid rain formation takes place even in the case of high droplet concentration. The process of such drop recirculation was discussed in several studies, and its role in raindrop formation within an extremely polluted clouds formed within the zone of biomass burning (pyroclouds) was discussed by Khain et al. [2008a, 2008b] in detail. [36] Figure 12 shows that the bulk parameterization produces much more ice crystals and snow that cover a larger area than in the SBM simulations. The same feature was obtained by Li et al. [2009a, 2009b]. We suspect two possible reasons for this difference: the underestimation of sedimentation velocity (as one can see in Figures 4a 4c) causes significant areas to be covered by snow that do not produce precipitation, because they are located well above Figure 12. Time dependence of area averaged low-density ice content in SBM simulations as well as in bulk parameterization runs Drop 100 Drop the freezing level). Another possible reason for the difference is that the bulk scheme does not include enough efficient collisions between light density ice particles. [37] Figure 13 shows the time dependence of highdensity ice averaged over the computational area in the simulations under discussion. One can see that the averaged values calculated by SBM are not sensitive to aerosols in this model version. We attribute this insensitivity to two factors. First, an increase in aerosol concentration usually increases the masses of hail and graupel in zones of high supercooled water content. These particles grow rapidly by riming to reach big sizes and fall to the surface. Thus, the zones of high graupel and hail contents are quite narrow (see Figure 3c). In the case of low CCN concentration raindrops form earlier and freeze to form hail and graupel of smaller size compared to the case of high aerosol concentration because of the lack of supercooled droplets. How- Figure 11. Time dependence of area averaged rainwater content in SBM simulations as well as in bulk parameterization runs Drop 100 Drop Figure 13. Time dependence of area averaged highdensity ice content in SBM simulations as well as in bulk parameterization runs Drop 100 Drop of 21

16 Figure 14. Time dependence of accumulated rain amount in SBM simulations as well as in bulk parameterization runs Drop 100 Drop ever, the concentration of graupel is larger in case of lower AP concentration and it covers larger volumes (see Figure 3c). Accordingly, the averaging over the computational area produces similar mass contents of graupel/hail under different aerosol concentrations. It should be noted that the SBM scheme used in the present study allowed simulation of graupel/hail particles with sizes below 0.5 cm in radius. In order to simulate larger graupel and hail, more mass bins should be used, as was made by Khain et al. [2008c] where 43 mass bins were used. [38] Note that the graupel/hail mass content in Fast-SBM turns out to be 1.5 to 2 times higher than that in the Exact- SBM. One of possible reasons of this result is the net decrease in settling velocity of particles belonging to the graupel/hail size distribution as compared to the case when two size distributions for graupel and hail were used separately. It would be too naive to expect that the scheme containing 3 size distributions will provide exactly the same results as the scheme containing 7 size distributions. [39] Last, Figure 14 shows the accumulated rain amount in these simulations. One can see that Exact- and Fast-SBM produce the same accumulated rain amounts, and the SBM runs do not reveal a significant dependence of accumulated rain to aerosols. A slight decrease in precipitation takes place only under very high CCN concentration of 3000 cm 3. These results agree well with those obtained by Tao et al. [2007] and Li et al. [2009a, 2009b]. However, the bulk parameterization scheme produces precipitation amount about twice as high as that in the SBM, and there was a substantial decrease in precipitation with the increase in aerosol concentration. [40] In summary, the bulk parameterization produces a higher amount of averaged snow and ice content, graupel, as well as precipitation than the SBM scheme. We assume two main reasons of such differences. First, the bulk scheme generates the convection embedded into the stratiform area which produces the cloud ice in the upper troposphere. The second reason is the difference in the vertical updrafts within the squall-line fronts. Figure 15 shows the time dependence of maximum velocities in different simulations with SBM (Figure 15, left) and the bulk parameterization scheme (Figure 15, right). Evaluation pffiffiffiffiffiffiffiffiffiffiffiffi of expected maximum vertical velocity as W max = 1 2 CAPE shows that the maximum vertical velocities should be around 23 m/s, which agrees well with the results of SBM. One can see that the bulk scheme produces higher (up to 37 m/s) vertical updrafts during the period of the maximum squall line development (similar results were obtained by Li et al. [2009a], where another bulk scheme was used). As a result, the bulk scheme generates more low-density cloud ice with small settling velocity in the upper troposphere up to the levels of km. One can assume, of course, additional reasons of the bin-bulk difference in the ice content (as well as in contents of other values). We can mention, for instance, the formation of supercooled rain in the bulk Figure 15. Time dependence of maximum velocities in different simulations with (left) SBM and (right) the bulk parameterization scheme. 16 of 21