Volume 113, Issue D15
Aerosol and Clouds
Free Access

Implementation of a two-moment bulk microphysics scheme to the WRF model to investigate aerosol-cloud interaction

Guohui Li

Guohui Li

Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA

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Yuan Wang

Yuan Wang

Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA

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Renyi Zhang

Renyi Zhang

Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA

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First published: 15 August 2008
Citations: 157

Abstract

[1] A two-moment bulk microphysical scheme has been implemented into the Weather Research and Forecasting (WRF) model to investigate the aerosol-cloud interaction. The microphysical scheme calculates the mass mixing ratios and number concentrations of aerosols and five types of hydrometeors and accounts for various cloud processes including warm and mixed phase microphysics. The representation of the aerosol size distribution is evaluated, showing that the three-moment modal method produces results better in agreement with the sectional approach than the two-moment modal method for variable supersaturation conditions in clouds. The effects of aerosols on cloud processes are investigated using the two-moment bulk microphysical scheme in a convective cumulus cloud event occurring on 24 August 2000 in Houston, Texas. The modeled evolution of the distribution of radar reflectivity in the y-z section, the cell lifetime, and averaged accumulated precipitation with the aerosol concentration under the polluted urban condition are qualitatively consistent with the measurements. Sensitivity simulations are initialized using a set of aerosol profiles with the number concentrations ranging from 200 to 50,000 cm−3 and mass ranging from 1 to 10 μg m−3 at the surface level. The response of precipitation to the increase of aerosol concentrations is nonmonotonic, because of the complicated interaction between cloud microphysics and dynamics. The precipitation increases with aerosol concentrations from clean maritime to continental background conditions, but is considerably reduced and completely suppressed under highly polluted conditions, indicating that the aerosol concentration exhibits distinct effects on the precipitation efficiency under different aerosol conditions. The maximal cloud cover, core updraft, and maximal vertical velocity exhibit similar responses as precipitation. Comparison is made to evaluate the effects of different autoconversion parameterizations and bulk microphysical schemes on cloud properties. Because of its broad application in numerical weather prediction, implementation of the two-moment microphysical scheme to the WRF model will greatly facilitate assessment of aerosol-cloud interaction from individual cumulus to mesoscale convective systems.

1. Introduction

[2] Atmospheric aerosols, formed from natural and anthropogenic sources [e.g., Penner et al., 2001; Zhang et al., 2004a], act as cloud condensation nuclei (CCN) and likely affect cloud microphysics and development, including the onset and amount of precipitation, cloud lifetime, albedo, and electrification [e.g., Ramanathan et al., 2001]. Twomey [1977] first suggested that an increase in anthropogenic aerosol concentrations leads to an increase in the solar reflectivity of clouds, which is known as the aerosol indirect effect on climate. Numerous studies using parameterized models and in situ and remote sensing observations have investigated the aerosol indirect effect, showing optically thicker clouds with increased droplet number concentrations but reduced droplet sizes over ship tracks, biomass burning areas, or other polluted regions in comparison to less polluted cases [e.g., Radke et al., 1989; Kaufman and Fraser, 1997; Rosenfeld, 1999]. However, a recent study revealed that the cloud droplet effective radius may increase or decrease with aerosol loading, depending on ambient conditions [Yuan et al., 2008]. Also, Liu and Daum [2002] demonstrated that anthropogenic pollution increases both the relative dispersion and number concentrations of cloud droplets and the two effect are counteracting, leading to a smaller cooling effect by aerosols. Recent analyses of satellite measurements showed strong systematic correlations among aerosol loading, cloud cover [Kaufman et al., 2005], and cloud height over the Atlantic Ocean [Koren et al., 2005] and Europe [Devasthale et al., 2005], independent of geographical locations [Kaufman and Koren, 2006]. In addition, in situ data showed that the onset of precipitation is delayed from 1.5 km above cloud base in pristine clouds to more than 5 km in polluted clouds and 7 km in the most extreme smoky clouds over the Amazon [Andreae et al., 2004]. Recently, it has been suggested that polluted aerosols from the Asian continent are responsible for intensified storms over the Pacific, which may significantly impact the global general circulation and climate [Zhang et al., 2007]. Also, the aerosol-cloud interaction may impact cloud electrification and air chemistry [e.g., Williams et al., 1991; Bond et al., 2001, 2002; Orville et al., 2001; Tie et al., 2001; Zhang et al., 2003].

[3] The impact of aerosols on rainfall represents one of the most important issues of anthropogenic climate change [Hobbs, 1993] and remains highly uncertain. High concentrations of smoke aerosols have been shown to reduce cloud droplet size and inhibit droplet coalescence to the extent of completely suppressing precipitation from tropical clouds at various locations, as found by both satellites and in situ aircraft observations [e.g., Rosenfeld, 1999]. Several model results also showed that an increase in the concentration of CCN drastically decreases precipitation [Khain and Pokrovsky, 2004; Cui et al., 2006]. On the other hand, precipitation enhancement has been observed around heavily polluted coastal urban areas [Eagen et al., 1974; Braham, 1981; Cerveny and Balling, 1998; Ohashi and Kida, 2002; Shepherd and Burian, 2003]. Most recently, a midweek increase in precipitation over U.S. has been suggested using the Tropical Rainfall Measuring Mission (TRMM) precipitation measurements and has been attributed to invigoration of rainstorms by air pollution [Bell et al., 2008]. Cloud simulations by Wang [2005], Lynn et al. [2005b], Teller and Levin [2006], and Fan et al. [2007a, 2007b] support the possibility that in a moist, unstable atmosphere pollution aerosols can invigorate convective clouds and produce more precipitation. Khain et al. [2005] showed that an increase in aerosol concentrations can both decrease and increase precipitation, depending on environmental conditions such as the relative humidity and dynamical factors, which can foster secondary cloud formation, etc. An increase in precipitation was obtained under tropical maritime conditions with high humidity and in case of secondary cloud formation [Khain et al., 2005, 2008]. Furthermore, polluted aerosols transported from the Asian continent have been suggested to cause more precipitation over the north Pacific [Zhang et al., 2007]. Hence the effect of aerosols on precipitation may be a complex function of aerosol properties and cloud thermodynamics. It should be pointed out that most of the previous studies on the aerosol-precipitation relation hinge on precipitation measurements from space or aircraft; Evaluation of the changes in precipitation at the surface from satellite and in situ aircraft observations is challenging [Levin and Cotton, 2007].

[4] Aerosols may also influence the mixed phase processes in cloud development by serving as ice nuclei (IN) [Bergeron, 1935; Findeisen, 1939; Wegener, 1991; Pruppacher and Klett, 1997]. Although work has been performed to improve the process of ice initiation in clouds through laboratory measurements and field observations, major gaps in our knowledge of ice nucleation exist.

[5] Recent model studies have demonstrated that spectral bin microphysical (SBM) cloud-resolving models promise a valuable approach to investigate the effects of aerosols on cloud development and precipitation [e.g., Khain et al., 2005; Fan et al., 2007a, 2007b, 2008], in which each type of cloud hydrometeors and aerosols is described using size distribution functions containing several tens of bins of masses. However, the application of SBM cloud resolving models is rather limited, because the SBM method is computationally demanding and expensive. Alternatively, computationally efficient bulk microphysics parameterizations are often employed to represent cloud processes in atmospheric models. Bulk microphysical schemes generally represent the size spectra of each precipitating hydrometeor category by a three-parameter gamma distribution function of the form N(D) = N0Dα exp(−λD), where N0 is the intercept, λ is the slope, and α is the shape parameter of the distribution. Changes to the distributions are modeled by predicting changes to these parameters, by formulating the prognostic equations for one or more of the moments of the distribution function. Since each predicted moment is associated with one prognostic parameter, three predictive moment equations are required to determine the three parameters uniquely. Many available bulk schemes have followed the approach of Kessler [1969], in which one moment of the hydrometeor size distribution, proportional to the mass content, is predicted [e.g., Lin et al., 1983; Cotton et al., 1986; Walko et al., 1995; Kong and Yau, 1997] and λ is the prognostic parameter, while N0 and α are held constant. The two-moment scheme has also been developed; the mass and the total number concentration of the hydrometeor categories are independently predicted, with λ and N0 being the independent prognostic variables and α being a constant [e.g., Nickerson et al., 1986; Ziegler, 1985; Wang and Chang, 1993a; Ferrier, 1994; Meyers et al., 1997; Reisner and Rasmussen, 1998; Cohard and Pinty, 2000]. Milbrandt and Yau [2005] developed a three-moment scheme in which the radar reflectivity of the hydrometeor categories is predicted, in addition to the mass and the total number concentration, and all the three parameters are independently determined.

[6] The one-moment microphysical scheme is unsuitable for investigation of the aerosol effects on clouds because it only predicts the mass of cloud droplets but fails to represent the number concentration of cloud droplets. In the two-moment microphysical scheme, both the mass and the total number concentration of cloud droplets are predicted. The size distribution and chemical composition of CCN, along with supersaturation, jointly determine the size distribution of newly nucleated cloud droplets. Cohard and Pinty [2000] applied a comprehensive two-moment warm microphysical bulk scheme to study the sensitivity of the microphysical fields and precipitation patterns to the upwind CCN activation spectrum. Wang [2005] used a three-dimensional (3-D) two-moment cloud-resolving model to investigate the responses of cloud physical processes of a developing tropical deep convection to increasing CCN concentrations. Ekman et al. [2004] used a cloud-resolving (two-moment scheme) model coupled with an interactive explicit aerosol module to examine the cloud-aerosol interaction in a cumulonimbus cloud.

[7] Most of the previous model studies using two-moment microphysical schemes to consider the aerosol effects are confined to isolated clouds. To date few studies have modeled the aerosol-cloud interaction for mesoscale convective systems (MCSs) or large-scale meteorological systems. In this paper, we describe the implementation of a two-moment bulk microphysical scheme to a cloud-resolving Weather Research and Forecasting (CR-WRF) model. The model performance for cumulus clouds is demonstrated for a convective cloud event, by comparing the CR-WRF model simulations with available radar and rain gauge measurements. Simulations under different aerosol conditions are carried out to survey the response of cloud microphysics to changes in aerosol concentrations. In addition, since the autoconversion represents a key process in cloud development, in which warm rain is initiated by collision and coalescence of cloud droplets, accurate parameterization of autoconversion is of critical importance to simulations of cloud formation and development in atmospheric models. We evaluate and compare seven types of autoconversion parameterizations (three Kessler-types, two Berry-types, and two Sundqvist-types) under different aerosol conditions. Additional comparisons are made between the present two-moment microphysical scheme and available single-moment microphysical bulk schemes in the WRF model. In separate publications, we discuss the applications of the CR-WRF model for a continental squall line and large-scale cyclone over the Pacific [Zhang et al., 2007; Li et al., 2008].

2. Model and Design of Numerical Experiments

2.1. WRF Model

[8] The WRF Model is a next-generation mesoscale numerical weather prediction (NWP) system designed to serve both operational forecasting and atmospheric research needs. It features multiple dynamical cores, a three-dimensional variational (3DVAR) data assimilation system, and a software architecture allowing for computational parallelism and system extensibility. The WRF model is suitable for a broad spectrum of applications across scales ranging from a few meters to thousands of kilometers and is a fully compressible, nonhydrostatic model (with a hydrostatic option). Its vertical coordinate is a terrain-following hydrostatic pressure coordinate. The grid staggering is the Arakawa C-grid. The model uses the Runge-Kutta second- and third-order time integration schemes, and second- to sixth-order advection schemes in both horizontal and vertical directions. It uses a time-split small step for acoustic and gravity-wave modes. The dynamics conserves scalar variables. Currently, several physics components have been included in WRF: microphysics (bulk schemes ranging from simplified physics suitable for mesoscale modeling to sophisticated mixed-phase physics suitable for cloud-resolving modeling), cumulus parameterizations (adjustment and mass-flux schemes for mesoscale modeling including NWP), surface physics (multilayer land surface models ranging from a simple thermal model to full vegetation and soil moisture models, including snow cover and sea ice), planetary boundary layer physics (turbulent kinetic energy prediction or nonlocal K schemes), and atmospheric radiation physics (longwave and shortwave schemes with multiple spectral bands and a simple shortwave scheme). Cloud effects and surface fluxes are also included. A detailed description of the WRF model can be found in the WRF web-site http://www.wrf-model.org/index.php.

[9] However, the present WRF model employs several one-moment microphysical bulk schemes that consider only the mass concentrations of hydrometeors, which prohibits the application to assess the aerosol-cloud interaction using the WRF model.

2.2. Two-Moment Microphysical Bulk Scheme

[10] In the present work a two-moment microphysical scheme initially developed by Hu and He [1987] and discussed by Lou et al. [2003] and Wang and Chang [1993a] has been modified and implemented into the CR-WRF model to consider the effects of aerosols on cloud formation and development. The microphysical scheme calculates the mass mixing ratio of water vapor (Qv), cloud droplets (Qc), raindrops (Qr), ice crystals (Qi), snow (Qs), and graupel (Qg) and the total number concentration of raindrops (Nr), ice crystals (Ni), snow (Ns) and graupel (Ng). In order to consider the aerosol effects, a new prognostic variable is included in the scheme: the total number concentration of cloud droplets (Nc) which plays a key role in considering the aerosol effects in the two-moment microphysical scheme. In addition to its impact on the formation of raindrops, the prediction of cloud droplet number concentration is also important in cloud chemistry and radiative transfer.

[11] The size distributions of the five types of hydrometeors are represented by the gamma function,
equation image
where xequation image [c, r, i, s, g] refers to cloud, rain, ice crystal, snow, and graupel, respectively, N0x is the intercept, λx is the slope, and αx is the shape parameter of the distribution. Empirically, it is assumed that the mass mx of a particle in a hydrometeor category is related to its diameter Dx by mx(Dx) = Amxequation image, where Amx and Bmx are the coefficients [Mason, 1971; Mitchell et al., 1990; Demoz et al., 1993]. The terminal velocity, Vx(Dx), for a particle of size, Dx, is given by Vx(Dx) = Avxequation image, where Avx and Bvx are the coefficients. The values of αx, Amx, Bmx, Avx and Bvx are listed in Table 1. The width of the cloud droplet spectrum is determined by αc (the shape parameter for cloud droplets).
Table 1. Values of the Parameters for the Droplet Spectrum, Mass-Diameter Relations, and Terminal Speed
Cloud Rain Ice Snow Graupel
αa 2 0 1 1 0
Am 0.524, g cm−3 0.524, g cm−3 0.001, g cm−2 0.003, g cm−2 0.065, g cm−3
Bm 3 3 2 2 3
Av - 2100, cm0.2 s−1 70, cm2/3 s−1 100, cm2/3 s−1 500, cm0.2 s−1
Bv - 0.8 1/3 1/3 0.8
  • a The α value is taken on the basis of observations. For rain and graupel, the exponential distributions (α = 0) [Marshall and Palmer, 1948] are used. For ice crystal and snow, the measured distributions are between exponential and log-normal distributions [Hobbs, 1974], and the value is set to be 1. The value of cloud droplets is equal to 2, following Cohard and Pinty [2000].

[12] Most of the microphysical processes in the two-moment bulk microphysics scheme by Lou et al. [2003] are similar to those described in details by Wang and Chang [1993a]; only the main features pertinent to the present work are discussed in Appendix A. For the warm rain process, the analytic solutions to the stochastic collection equation (SCE) by a polynomial approximation for the collection kernel [Long, 1974] are used according to Cohard and Pinty [2000]. This procedure takes into account the number concentration of cloud droplets. As discussed above, a key step in the warm rain process is the autoconversion process whereby large cloud droplets collect small ones and become embryonic raindrops. In the present work, seven types of autoconversion parameterizations are evaluated and compared in the cloud simulation (see details in the Appendix B).

[13] A total of thirty-two microphysical processes related to cloud droplets, raindrops, ice crystals, snow and graupel are considered in the two-moment microphysical scheme. These include (1) autoconversion of cloud droplets to rain and graupel, ice crystal to snow, and snow to graupel, (2) freezing of cloud droplets and rain, (3) melting of ice crystal, snow, and graupel, (4) nucleation of ice crystals, (5) accretion of cloud droplets by rain, snow, and graupel, (6) accretion of ice crystals by rain, snow, and graupel, (7) accretion of rain by ice, snow, and graupel, (8) accretion of snow by rain and graupel, (9) self-accretion of cloud droplets, rain, ice crystals, and snow, (10) condensation/evaporation of cloud droplets and rain, and (11) sublimation of ice crystals, snow, and graupel. The transformation rates among the different hydrometeor categories and the calculation schemes are according to Lou et al. [2003], Wang and Chang [1993a], and Cohard and Pinty [2000] (Appendix A). As discussed in Appendix A, ice initiation occurs by deposition nucleation, immersion-freezing, and contact-freezing. Secondary ice production is considered according to Hallet and Mossop [1974]. Melting of ice, snow, and graupel is assumed to occur below the freezing level, and only liquid water exists below the melting level.

2.3. Representation of the Aerosol Size Distribution

[14] An appropriate representation of the aerosol size distribution is important to evaluating both direct and indirect forcing of aerosols in model simulations. Two frequently used methods to represent the aerosol size distribution in atmospheric models are the sectional and modal approaches. In the sectional approach, the particle size distribution is approximated by a discrete number of size sections. In the modal representation, the particle size distribution is approximated by analytical functions (usually lognormal distribution) that represent the various modes of the particle population. Different modal formulations simulate the number, mass and surface area for each mode and predict the mean diameter and standard deviation (three-moment) or simulate the number and mass and hold standard deviation fixed (two-moment). Clearly, the sectional approach represents more accurately the aerosol size distributions than the modal approaches (two-moment or three-moment). On the other hand, considering the computational burden and memory constraints, the modal approach (two-moment or three-moment) corresponds to a more efficient choice to represent the aerosol size distributions compared with the sectional approach.

[15] Zhang et al. [2002] employed a one-dimensional version of a climate-aerosol-chemistry model with both modal and sectional size representations to evaluate the impact of the aerosol size representation on modeling aerosol-cloud interaction in shallow stratiform clouds. Their results showed that both modal (two-moment and three-moment) and the sectional approaches (with 12 and 36 sections) predict the total number and mass for interstitial and activated particles that are generally within several percent comparing to a high-resolution 108-section approach. The vertical velocity is prescribed and only one maximal supersaturation is obtained in clouds by Zhang et al. [2002]. However, Khain et al. [2000] pointed out that if a realistic increase in vertical velocity with height above the cloud base is taken into account, supersaturation within the cloud updraft can exceed the local maximum at the cloud base.

[16] For the three-moment modal approach, the aerosol size distribution is represented as a log normal size distribution:
equation image
where D is the aerosol diameter, N is the number concentration of aerosols in the distribution, Dg is the geometric mean diameter, and σg is the geometric standard deviation. Three new prognostic variables are included in the CR-WRF model: mass mixing ratio (Qa), surface area (Sa), and total number concentration (Na) of aerosols. Sensitivity tests are designated and performed to evaluate the modal approaches (two and three-moment) against the sectional approach.
[17] The conservation equations for aerosols are considered in the CR-WRF model,
equation image
equation image
equation image
where μd represents the mass of the dry air in the column. TMh and TMv are the horizontal and vertical turbulent diffusions. Nucl denotes the aerosol loss due to the nucleation process in clouds. We do not include the aerosol sources such as sulfur chemistry, emissions, and release from cloud droplet evaporation or ice crystal sublimation. Except for the activation process in clouds, no other aerosol sink is considered in the present simulation [Khain et al., 1999, 2000, 2005].

[18] For the CCN nucleation, the aerosol spectrum is divided into 92 sections from 0.002 μm to 2.5 μm. The critical radius of dry aerosols is calculated from the Köhler theory using water supersaturation predicted from the CR-WRF model [Roger and Yau, 1989; Pruppacher and Klett, 1997]. When aerosols in a section are activated, the mass of water condensing on CCN is calculated under the equilibrium assumption (Köhler equation), if the radius (ra) of dry aerosols is less than 0.03 μm; if the radius is greater than 0.03 μm, the mass of water condensing on these CCN at zero supersatruation is calculated as mw = Kequation imageπra3ρw, where 3 < K < 8 [Khain et al., 2000]. When droplets with a high number concentration are competing for available water vapor, supersaturation within the cloud can be substantially reduced. When the cloud water mass of the total nucleated particles is equal to the available water vapor, the nucleation process is terminated to avoid the fact that the air becomes subsaturated after nucleation.

2.4. Design of Numerical Experiments and Statistical Method in Data Analysis

[19] The spatial resolution adopted in this study is 2 km horizontally and about 0.5 km vertically. A model domain of 50 × 50 × 40 grid boxes along the x, y, and z directions, respectively, is used to provide a 100 km × 100 km horizontal and 20 km vertical coverage. A deep cumulus cloud and precipitation event occurring in the south of Houston, Texas at 1658 UTC on 24 August 2000 is simulated. The sounding data at −95.54°W, +29.95°N (Figure 1) is taken as the initial conditions of the CR-WRF model. Open boundary conditions are applied in the simulations, in which all horizontal gradients of variables are equal to zero at the lateral boundaries. The vertical temperature and dew point profiles reveal a moderate instability in the atmosphere, with an estimated convective available potential energy (CAPE) of 960 J kg−1 integrated from the surface. The magnitude of the low level wind shear in this cumulus case is about 2 m s−1. Additional simulations are performed using a 200 km × 200 km domain. We find that for a larger domain size the differences in precipitation, core updraft/downdraft, and maximum/minimum vertical velocity are insignificant (less than 0.5%); the difference in the radar reflectivity is also small (less than 1%). In addition, we find that the response of cloud properties to the change in the aerosol concentration is insensitive to the variation in the model resolution.

Details are in the caption following the image
Atmospheric sounding in Houston (−95.54°W, +29.95°N) at 1658 UTC on 24 August 2000. The black solid line corresponds to the temperature, and the purple solid line represents the dew point temperature.

[20] Cumulus clouds occur when air becomes highly buoyant and rises vertically in a localized region, as typically treated by warm bubble initiation with a temperature perturbation in model simulations [Khain et al., 2005; Fan et al., 2007a, 2007b]. In the present work, the cumulus development is triggered by a warm bubble of a 15-km wide and a maximum temperature anomaly of 5°C at the height of 1.0 km. The size of the warm bubble is estimated from the measured radar reflectivity by changing the width of the bubble to achieve a cloud size comparable with measurements. We find that the cumulus cannot be initiated when the maximum perturbation temperature of the warm bubble is less than 5°C. When the maximum temperature is equal to or more than 5°C, the cumulus development is insensitive to the temperature perturbation because the ice process is triggered to release additional latent heat to sustain the cloud development and the initial temperature perturbation no longer plays a role.

[21] Measurements from the Texas Air Quality Study (TexAQS) 2000 showed that ammonium sulfate consisted of more than 40% of the total PM2.5 mass and organic carbon contributed to less than 30% of the total PM2.5 mass [Fan et al., 2005]. In the present work, we consider only ammonium sulfate aerosols in the simulations, with a log normal distribution. An initial geometric standard deviation of σg = 1.8 is assumed [Ekman et al., 2004]. As aerosols activate to form cloud droplets, the aerosol size distribution varies and the σg value at a later time step is determined from the three-moment approach. A set of 25 initial surface-level aerosol size distributions, with the number concentrations ranging from 200 to 50,000 cm−3 and mass ranging from 1 to 10 μg m−3, is used in the numerical experiments to survey the response of the modeled cloud properties to the changes in initial aerosol size distributions. These aerosol distributions represent the cases ranging from clean maritime air mass to much polluted urban plume over the coastal region in Houston. An exponential decrease is assumed for the height dependence of the aerosol concentration in the model simulations [Fan et al., 2007a]. For simplicity, the initial concentration of CCN (hereinafter [CCN]) with a 1.0% supersaturation in the cloud bottom is used to represent the aerosol distribution in each numerical experiment. In order to investigate the response of the microphysical module to an extremely high aerosol concentration, an additional case with [CCN] of about 20,000 cm−3 is included in simulations. The case with [CCN] of 5000 cm−3 is considered as the base-run simulation for comparison with the measurements; the corresponding aerosol and CCN concentrations represent the typical values when stagnant pollution conditions develop in the Houston region [Lei et al., 2004; Zhang et al., 2004b], on the basis of measurements and simulations [Li et al., 2005; Fan et al., 2005, 2006]. Aircraft measurements using a CCN counter in the downwind of Houston, Texas showed a CCN concentration of about 5000 cm−3 for the typical polluted urban condition in this region (D. Collins, private communication). Several assumptions and simplifications have been adopted for the processes related to aerosols. The spatial distributions of aerosols are determined by initial and boundary conditions [Li et al., 2005, 2007; Fan et al., 2005, 2006].

[22] Model simulations are performed to evaluate the various parameterizations of the autoconversion process, each including 26 runs with various initial aerosol profiles described above. The reference case used to compare and analyze all simulations corresponds to the autoconversion parameterization (NR6_PCR discussed in Appendix B) developed by Liu and Daum [2004]. The other six autoconversion parameterizations include those by Kessler [1969], Liu et al. [2004], Sundqvist [1978], Liu et al. [2006], Berry [1968], and Berry and Reinhardt [1974]. Detailed descriptions of the autoconversion parameterizations are provided in Appendix B.

[23] In order to evaluate the response of the modeled deep cumulus to changes in [CCN], the population mean (p-mean hereinafter) of a given variable over all qualified grid boxes and during the entire integration period is used, similarly to Wang [2005] and Fan et al. [2007a]. The p-mean is defined as:
equation image
where c represents a given quantity. The calculation using equation (6) only applies to grid points where both the mass concentration Q and number concentration N of a hydrometeor or the summation of several hydrometeors exceed a minimum. The total number of the grid points at a given output time step t is represented by N(t). ΔT is the total number of output steps.

3. Results and Discussion

3.1. Effect on the Aerosol Size Distribution

[24] To evaluate the sensitivity of the aerosol size distribution, a simple box model is devised to evaluate the two-moment and three-moment modal methods against the sectional approach, assuming that only the activation process is considered and the supersaturation varies with height. Two sensitivity studies are performed: (1) the supersaturation reaches a maximum at the cloud base and decreases monotonically with height (Figure 2a) and (2b) the supersaturation reaches a first maximum at the cloud base and a second maximum (greater than the first peak) at 500 m above the cloud base (Figure 2b). In each sensitivity study, three types of supersaturation profiles (the three colors in Figures 2a and 2b) are considered with different maximal supersaturation. Aerosols containing only ammonium sulfate ((NH4)2SO4) are assumed as the initial conditions of the box model. A set of 500 initial aerosol size distributions, with the number concentrations ranging from 200 to 10,000 cm−3 with an increment of 200 cm−3 and the mass ranging from 1 μg m−3 to 10 μg m−3 with an increment of 1 μg m−3, is used in each sensitivity study. The geometric standard deviation of initial aerosol size distributions is set to 1.8 and the log normal distribution is assumed during the activation process when the two-moment and three-moment approaches are used. In the sectional approach, 92 size sections are employed to represent the aerosol size distributions.

Details are in the caption following the image
Comparison of activated [CCN] from moment approaches (two-moment and three-moment) and section (green) representations of aerosols (bottom) under different supersaturation conditions in cloud (top). Three supersaturation profiles (solid, dotted, and dash lines) with one peak are assumed in Figure 2a, and three supersaturation profiles (solid, dotted, and dash lines) with two peaks are assumed in Figure 3b. Figures 3c and 3d correspond to the activated [CCN] for the supersaturation profiles depicted in Figures 2a and 2b, respectively.

[25] Figures 2c and 2d compare the activated CCN concentrations between the sectional, two-moment, and three moment approaches when air parcels containing different initial aerosol size distributions move along the supersaturation profiles in Figures 2a and 2b, respectively. When only one maximal supersaturation is reached at the cloud base (Figures 2a and 2c), the activated CCN concentration from the two-moment and three-moment approaches are both similar to the sectional approach, consistent with that suggested by Zhang et al. [2002]. However, when the second maximal supersaturation (greater than the first peak) exists in the cloud (Figures 2b and 2d), the activated CCN concentration from the two-moment approach is substantially lower than that from the sectional approach, while the results from the three-moment approach are closer to the sectional approach. In the two-moment modal approach, the shape of the aerosol size distribution is constant (σg is a constant). After the nucleation process, larger size aerosols are activated and the aerosol size distribution is shifted toward smaller sizes. In the three-moment approach, the shape of the aerosol size distribution varies with the nucleation process. Activation of a large number of aerosols results in a largest reduction in the aerosol mass but a smallest reduction in the aerosol number, while the surface area reduction is between those of the mass and the number of aerosols. The aerosol size distribution is also shifted toward smaller particles. However, since σg is decreased, the size distribution is widened in the three-moment case. This explains the agreement between the two-moment and three-moment approaches with one maximal supersaturation in the cloud. With a second maximal supersaturation, more aerosol particles are activated in the three-moment approach due to the widened size distribution, resulting in the better agreement between the three-moment approach and the sectional approach. For the two-moment approach, the particle activation is unfavorable unless the second maximal supersaturation is large.

[26] Hence considering the complexity in treating aerosol and nucleation process in clouds, the three-moment modal method appears to be more reasonable in atmospheric models. In the present work, the three-moment method is adopted to represent the aerosol size distribution in all simulations.

3.2. Comparisons With Radar and Precipitation Measurements

[27] The results of cloud properties from the base-run simulation (i.e., with [CCN] = 5000 cm−3 and using NR6_PCR) are compared with observations from a WSR-88D radar and precipitation data in Houston. The evolution of the highly reflective cell averaged over the cumulus core in the y-z section is shown in Figure 3 at selected times. The total radar reflectivity factor Z is calculated from the sum of the reflectivity for all hydrometeors except for cloud water, as suggested by Wang and Chang [1993b]. Cloud water is not included in the radar reflectivity calculation since its contribution is negligible.

Details are in the caption following the image
Comparison of modeled radar reflectivity from the reference simulation with the observations at different time steps.

[28] A significant radar echo at 35 min is obtained from the simulation. The reflectivity intensifies at 65 min with heavy precipitation at the surface level. The reflective cell starts to decay after 95 min. Compared with the radar observation, the development and the pattern of the simulated radar reflectivity of the cumulus are qualitatively reproduced by the present two-moment bulk microphysical in the CR-WRF model. The prominent melting band with radar reflectivity more than 50 dBz is replicated in the simulation at 65 min. Some discrepancies exist between the simulation and the observation. The simulated convective cell at 35 min is located at about 5 km height, higher than that from the radar observation. The simulated radar reflectivity of 10 dBz reaches up to 12 km at 65 min, but the observed height is lower than 10 km.

[29] A comparison of the temporal evolution between the modeled and predicted echo top (with radar reflectivity of 30 dBz) is shown in Figure 4. The simulation reproduces the evolution of the radar echo top, but predicts a higher radar echo top initially. At 60 min, the model simulated cloud top is about 13 km, while the observed cloud top height is only 9 km. The simulated maximal radar reflectivity is 60.2 dBz, close to the observed value of 57.8 dBz. The averaged precipitation of 10.4 mm observed in the area where the deep convection occurs from 1800 to 2100 UTC agrees with the modeled value of 9.6 mm.

Details are in the caption following the image
Comparison of the temporal evolution of the radar echo top (with radar reflectivity of 30 dBz). Blue line represents modeled radar echo top from the reference simulation and red line represents the measurement.

[30] The discrepancies between modeled and measured radar reflectivity may be partially explained due to the initialization of the cumulus by the warm bubble approach. In addition, the cloud top height and vertical velocity in cumulus clouds are determined by atmospheric dynamic and thermodynamic conditions (such as atmospheric instability, latent heat release, wind shear, etc.). In the current simulations, the atmospheric soundings are taken from a nearby meteorological station and may differ from the true atmospheric vertical profiles at the location where the cumulus develops.

[31] From the evolution of the modeled maximum and minimum vertical velocities within the domain, the lifetime of the convective cell is defined (Figure 5). The maximum updraft increases rapidly within 40 min after initialization and reaches about 17 m s−1. The maximum updraft stabilizes at about 0.3 m s−1 after 140 min during the dissipation of the cumulus. The lifetime of the simulated cumulus is about 110 min, comparable to the 120-min cell lifetime determined from the radar observations.

Details are in the caption following the image
Temporal variation of the maximum (blue line) and minimum (red line) vertical velocity in the reference simulation.

3.3. Response of Cloud Properties to Changes in Aerosols

[32] The impact of the initial aerosol concentration on the simulated cloud properties is evaluated by varying the number and mass of aerosols, as is reflected in the changes in the number concentrations of CCN and cloud droplets. The change of cloud droplets subsequently results in changes in the condensation and the timing and efficiency of the autoconversion process from cloud to rainwater.

3.3.1. Microphysical Properties

[33] Figure 6a depicts the dependence of the p-mean of the cloud droplet number concentration (CDNC) with [CCN], showing an increasing CDNC with increasing [CCN]. For the [CCN] from 150 to 20,000 cm−3, the CDNC varies from 8 to 4000 cm−3. The increasing CDNC is consistent with more activation of aerosols to form cloud droplets with increasing [CCN], as have been found in previous numerical studies [e.g., Fan et al., 2007a, 2007b]. In contrast, the p-mean of the effective droplet size decreases with increasing [CCN] (Figure 6b), reflecting a reduced supersaturation when a large number of cloud droplets are competing for a fixed amount of available water vapor. With the [CCN] from 150 to 20,000 cm−3, the effective droplet size is reduced from about 20 μm to less than 5 μm.

Details are in the caption following the image
(a) Modeled p-mean of the cloud droplet number concentration and (b) p-mean of the effective radius as a function of the initial [CCN].

[34] Figure 7 compares the vertical profiles of mass concentrations (time-averaged and summed over the horizontal domain) of hydrometeors under three aerosol conditions, a low [CCN] of 180 cm−3, an intermediate [CCN] of 3300 cm−3, and a high [CCN] of 9300 cm−3. Within the cloud, the cloud water content (CWC) attains the highest in the high [CCN] case and the lowest in the low [CCN]. This is explained since a higher [CCN] concentration leads to more condensation of water vapor on activated aerosols and hence a larger cloud water content. In contrast, the rainwater content within the cloud achieves the highest in the low [CCN] case and the lowest in the high [CCN] case. As illustrated in Figure 6b, the p-mean of the effective radius of cloud droplets is reduced with increasing [CCN], hindering the conversion of cloud droplets to raindrops. Collision/coalescence occurs most efficiently in the low [CCN] case and least efficiently in the high [CCN]. Because the vertical CWC profile is averaged over the time and the horizontal domain and the condensation of water vapor occurs mainly below the freezing level, the height of the maximal CWC for the three aerosol conditions does not differs significantly, although the heights of the maximal CWC for the intermediate and high aerosol conditions is a little higher than that for the low aerosol condition. Figure 7b also shows less precipitation reaching the ground level in the low [CCN] case compared to the intermediate [CCN] case. This occurs because precipitation particles (raindrops and graupels) are larger when [CCN] is higher, as summarized in Table 2. Table 2 also shows that the time of initial precipitation is delayed, but the maximum updraft before rain formation is enhanced with increasing [CCN]. An increased updraft allows for a longer growth time and a larger size for precipitating particles, enabling them to survive evaporation after falling to a subsaturated condition below the cloud base. In the high [CCN] case, precipitation particles (mainly graupels) are larger, but their concentrations are much smaller since ice nucleation is hindered due to formation of large concentrations of cloud droplets. In the high [CCN] case, the largest size of raindrops is caused from melting graupels (Table 2). In Figure 7b, the largest gradient in the rainwater profile below 4 km for the low [CCN] case is indicative of more evaporation of smaller precipitating particles. In contrast, the smallest rainwater gradient below 4 km for the high [CCN] case implies that most precipitation particles reach the surface because of their larger sizes.

Details are in the caption following the image
Vertical profiles of time-averaged masses of hydrometeors under low (180 cm−3, blue), intermediate (3300 cm−3, green), and high (9300 cm−3, red) [CCN] for (a) cloud water, (b) rainwater, (c) ice crystal, (d) snow, and (e) graupel.
Table 2. Time-Averaged Precipitable Cloud Properties Under Three Aerosol Conditionsa
Low Intermediate High
Time of initial formation of rain 20 min 30 min 35 min
Maximum updraft before rain formation 2.6 m s−1 4.6 m s−1 5.9 m s−1
P-mean of effective radius of raindrop 298 μm 506 μm 584 μm
P-mean of effective radius of graupel 520 μm 682 μm 901 μm
  • a The [CCN] is 180, 3300, and 9300 cm−3 for the low, intermediate, and high conditions, respectively.

[35] In the high [CCN] case, ice production is minimal because of inefficient ice nucleation. Immersion freezing is dependent on the droplet size [Pruppacher and Klett, 1997], and is suppressed with the formation of large amounts of small droplets. In addition, anvil formation is hindered in the high [CCN] case because of a large mass loading of small droplets to decrease buoyancy and less latent heat from droplet freezing. The intermediate [CCN] case corresponds to the largest amounts of ice and snow (Figures 7c and 7d), because of the strongest convection strength (to be discussed in section 3.3.4) and efficient ice nucleation. In this case, ice crystals are efficiently converted to snow by aggregation. The low [CCN] case corresponds to more ice formation, but less snow formation than the high [CCN] case, reflecting less effective conversion of ice to snow because of smaller ice crystals.

[36] The largest graupel mass occurs in the low [CCN] case because a large amount of raindrops is transported and frozen in the cold cloud regime. However, the size of graupels is much smaller than those in the other two [CCN] cases (Table 2). On the contrary, fewer graupel particles are produced in the high [CCN] case, because of inhibited ice nucleation, but, once produced, the graupel particles are larger.

3.3.2. Precipitation

[37] The accumulated total precipitation exhibits a complex variation with [CCN], showing a nonlinear relationship (Figure 8). When [CCN] is relatively small, the total precipitation is not very sensitive to [CCN] and increases slightly (by about 30%) with [CCN] from 100 to 1000 cm−3. There is a marked increase in the total precipitation from 0.05 to 0.1 mm, when [CCN] is from 1000 cm−3 to 3000 cm−3. The total precipitation decreases sharply when the [CCN] is over 5000 cm−3, and the precipitation is completely suppressed with a [CCN] of 20,000 cm−3. The enhanced precipitation with increasing aerosols at a lower [CCN] is explained by suppressed conversion of cloud droplets to raindrops but enhanced convective strength, which cause less efficient warm rain but more efficient mixed-phase processes. In addition, the sounding used in simulations corresponds to a humid atmosphere above the boundary layer and a small wind shear in the lower level, indicating that hydrometeors fall within a relatively wet air. In such a case, the loss of the precipitating mass falling from high levels by sublimation and evaporation is low. This likely explains the increase in the precipitation with the increase in the aerosol concentration, as previously discussed by Khain et al. [2005, 2008]. However, at extremely high [CCN], the total precipitation is significantly decreased. In the high [CCN] case, ice production is minimal because of inefficient ice nucleation and hindered anvil formation due to a large mass loading of small droplets (reduced buoyancy) and less latent heat from droplet freezing. Hence hydrometeors cannot grow to sufficiently large sizes to survive evaporation. In addition, the deep cumulus simulated in this study corresponds to relatively small wind shear (about 2 m s−1) and humid air (about 70% RH at the surface), which also likely explain that the total precipitation is decreased or completely suppressed only under extremely high aerosol conditions.

Details are in the caption following the image
Modeled cumulative precipitation inside the model domain (mm) as a function of the initial [CCN].

[38] Using satellite observations from the TRMM, it has been shown that warm rain processes, in convective tropical clouds infected by heavy smoke from forest fires [Rosenfeld, 1999] and for clouds with the top temperatures of about −10°C under urban and industrial air pollution [Rosenfeld, 2000], can be completely suppressed. Khain et al. [2005] simulated a deep convective cloud under dry continental conditions and showed a decrease in precipitation with increasing aerosols from 100 to 1260 cm−3. The decrease in precipitation efficiency of the cumulus cloud was attributed to loss of the precipitating mass due to sublimation of ice and evaporation of drops when falling from high levels through a deep layer of dry air outside the cloud. Cui et al. [2006] obtained similar results when studying an isolated cloud in an environment with low wind shear and with relatively dry air in the midtroposphere and upper troposphere. Lynn et al. [2005a, 2005b] implemented the SBM into the three-dimensional fifth-generation Pennsylvania State University–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5) to simulate a squall line that developed over Florida. Their results demonstrated that the use of a continental CCN concentration resulted in an overall delay in the growth of hourly rainfall and formation of a stronger squall line with higher updraft maxima. Their accumulated precipitation was larger with a lower aerosol concentration. However, enhancement of rainfall downwind of paper mills [Eagen et al., 1974] and over major urban areas [Braham, 1981] has been reported. Also, precipitation enhancement has been observed around heavily polluted coastal urban areas such as Houston [Shepherd and Burian, 2003] and Tokyo [Ohashi and Kida, 2002]. Furthermore, it has been suggested that air pollution enhances precipitation on a large scale in northern America [Cerveny and Balling, 1998] and polluted aerosols transported from the Asian continent intensify storms and cause more precipitation over the north Pacific [Zhang et al., 2007]. Simulations using a 3-D model and a bulk microphysical scheme by Wang [2005] and a 2-D SBM scheme by Fan et al. [2007a, 2007b] (developed and described by Khain et al. [2005]) also suggested an increased total amount of precipitation with increasing aerosol concentrations at relatively lower aerosol loading over the tropics and coastal regions, respectively. The modeled reduced precipitation under very high aerosol loading was also reported by Fan et al. [2007b]. Hence the responses of aerosols on precipitation are likely nonmonotonic and vary under different meteorological and aerosol conditions, because of the complicated coupling between cloud microphysics and dynamics.

3.3.3. Cloud Coverage

[39] Figure 9 shows the dependence of the maximum cloud cover, defined as the cloud anvil area [Wang, 2005], with initial aerosol concentrations. The variation of the maximum cloud cover with [CCN] exhibits a similar pattern as precipitation. When [CCN] is between 100 and 600 cm−3, the cloud cover increases by about 30%. For [CCN] between 600 cm−3 and 5000 cm−3, the maximum cloud overage becomes insensitive to the changes in [CCN]. When [CCN] is greater than 5000 cm−3, the maximum cloud cover deceases with [CCN]. The reduced cloud coverage at very high [CCN] is also explained by suppressed microphysical processes (i.e., inefficient coalescence and less ice nucleation) and enhanced downdraft (to be discussed below) by a large mass loading of small droplets and larger graupel to cause evaporation of precipitation particles. The result suggests that the maximum cloud coverage increases from clean maritime aerosol conditions to polluted urban aerosol conditions, but in the case of highly polluted aerosol conditions cloud formation can be completely suppressed.

Details are in the caption following the image
Simulated maximal cloud coverage with the different [CCN].

[40] Our simulated dependence of the maximum cloud cover with initial aerosol concentrations is similar to that by Wang [2005] for a developing tropical deep convection. From the results of Wang [2005], the maximal cloud cover increases with [CCN] from 50 to 6000 cm−3, comparable with the present results. Using daily MODIS (MODerate resolution Imaging Spectroradiometer) [Salomonson et al., 1989] Level 3 data from the Terra over the North Atlantic Ocean, Koren et al. [2005] found that an increase in the aerosol concentration from a baseline (aerosol optical depth, AOD, of 0.06) to the average (AOD of 0.21) values is associated with a 0.05 ± 0.01 increase in the cloud fraction. Their results are similar to our modeled behavior of maximum cloud cover when [CCN] is less than 5000 cm−3.

3.3.4. Convective Strength

[41] The convective strength of the modeled cumulus is measured by the p-mean updraft and downdraft in a core area, defined by the absolute vertical wind speed greater than 1 m s−1 and total condensed water mixing ratio greater than 0.01 g kg−1 [Wang, 2005]. The p-mean of the core updraft increases from about 2.0 to 3.5 m s−1 when [CCN] is between 100 and 5000 cm−3, but decreases when [CCN] is greater than 5000 cm−3 (Figure 10a). The increase in the core updraft for [CCN] less than 5000 cm−3 is attributable to more efficient mixed phase processes, releasing more latent heat (from droplet freezing) compared to the warm rain process. However, unlike precipitation, the core draft decreases to about 2.7 m s−1 at [CCN] of 20,000 cm−3, corresponding to the latent heat released from droplet condensation. In contrast, the p-mean of the downdraft increases steadily with [CCN] (Figure 10b). Such an increase in the core down draft may be explained because of a large mass loading of hydrometeors to decrease buoyancy, enhanced evaporation cooling of small droplets to increase downdrafts and decrease updrafts, or growth of larger graupels to induce locally large downdraft with increasing [CCN]. Similarly, the maximum updraft, an indicator of the largest local latent heat release, increases with [CCN] until [CCN] reaches 600 cm−3 (Figure 11a). When [CCN] is between 600 and 5000 cm−3, the maximum updraft is not very sensitive to changes in [CCN]. The maximum updraft decreases when [CCN] is greater than 5000 cm−3. The maximum downdraft generally increases with increasing [CCN] (Figure 11b).

Details are in the caption following the image
(a) Simulated population means of updraft and (b) downdraft in the core area (defined as an area where the absolute vertical velocity of wind is greater than 1 m s−1 and the total condensed water content is greater than 10−2 g kg−1).
Details are in the caption following the image
(a) Modeled maximum and (b) minimum vertical velocity as a function of the initial [CCN].

3.4. Response of Cloud Properties to Autoconversion Parameterizations

[42] The conversion that large cloud droplets collect small ones and become embryonic raindrops represents a key step in the warm rain process. In the bulk microphysical scheme, the conversion of cloud droplets to raindrops is formulated by an autoconversion parameterization. Several autoconversion parameterizations have been developed for rain initialization by collision and coalescence of cloud droplets. Accurate representation of the auto-conversion is of critical importance to simulations of cloud formation and development in atmospheric models. Recent theoretical advances [McGraw and Liu, 2003, 2006] have provided a physical base for improved understanding of the cloud droplet to raindrop conversion that has been applied to develop parameterizations [e.g., Liu et al., 2004].

[43] There are broadly three types of autoconversion commonly used in cloud-resolving models: the Kessler, Sundqvist, and curve-fitting parameterizations. The autoconversion parameterization proposed by Kessler [1969] has been used widely in cloud modeling studies due to its simplicity (KSL69). Another Kessler-type parameterization has been derived by Liu and Daum [2004], in which the incorrect and/or unnecessary assumptions inherent in the Kessler-type parameterizations are eliminated (NR6). The approach by Liu and Daum [2004] exhibits a different dependence on liquid water content and droplet concentration. In addition, a relative dispersion of the cloud droplet size distribution is explicitly included in this parameterization. Liu et al. [2004] introduced another parameterization by assuming that the critical radius is not fixed, on the basis of the analytical expression for a derived critical radius using the cloud liquid water content and the droplet number concentration (NR6_PCR). The expression for the autoconversion rate by Sundqvist [1978] is based on the consideration that the change of the autoconversion rate near the threshold is smooth, not discontinuous (Sqvt78). This parameterization is reformulated by Liu et al. [2006] by combining the autoconversion function derived by Liu and Daum [2004], the expression for the critical radius derived by Liu et al. [2004], and the generalized Sundqvist-type threshold function (GSqvt_PCR). Berry [1968] developed an autoconversion scheme by curve-fitting simulations of a microphysical model of initial cloud growth by condensation and coalescence of cloud-sized particles (BR68). Another parameterization by Berry and Reinhardt [1974] is built on the observation that characteristic water content of small drops develops steadily over a characteristic time-scale (BR74).

[44] Figure 12a shows that all autoconversion parameterizations predict nonlinear variations of the total accumulated precipitation with [CCN]. When [CCN] is less than 5000 cm−3, a similar variation of total precipitation with [CCN] is produced by the different autoconversion parameterizations except for Sqvt78. However, the total precipitation exhibits a large variation among the different autoconversion parameterizations, with the largest difference of up to 100%. When [CCN] is extremely high (20,000 cm−3), the precipitation is completely suppressed in NR6, NR6_PCR, and BR74. The threshold function in the Sundqvist-type autoconversion parameterizations (Sqvt78 and GSqvt_PCR) is smooth and continuous, so that even under extremely high [CCN] the autoconversion rate is greater than zero, leading to the occurrence of nonzero precipitation. In KSL69, the autoconversion process is not associated with the cloud droplet number concentration or [CCN]. When the mass mixing ratio of cloud water exceeds a threshold value, the autoconversion process is initialized. In KSL69, the total precipitation is the highest, but precipitation is not reduced considerably when [CCN] is high. Because there is no threshold function in BR68, the autoconversion process occurs once clouds form. The precipitation is not completely suppressed even under the condition of extremely high [CCN] in BR68. As discussed above, the modeled nonmonotonic behavior in precipitation is physically meaningful from fundamental microphysical considerations: in the very high [CCN] case ice nucleation becomes inefficient and anvil formation is hindered because of a large mass loading of small droplets (reduced) and less latent heat from droplet freezing, leading to completely suppressed precipitation. Furthermore, observation evidence also exists to support the completely reduced precipitation when aerosols are very high [i.e., Rosenfeld, 1999, 2000]. Hence it is reasonable to conclude that the NR6, NR6_PCR, and BR74 parameterizations are physically more meaningful.

Details are in the caption following the image
Modeled cumulative precipitation (mm) inside the model domain (top) and maximal mass mixing ratio of cloud water (bottom) as a function of the initial [CCN] for various autoconversion schemes: KSL69 (black dot), NR6 (black dash), NR6_PCR (black solid), Sqvt78 (red solid), GSqvt_PCR (red dot), BR68 (blue dot), and BR74 (blue solid).

[45] In Figure 12b, the maximal cloud water is insensitive to the changes of [CCN] in KSL69, Sqvt78, and BR68, while in the other four parameterizations the maximal cloud water generally increases with [CCN]. Using a 2-D SBM, Fan et al. [2007b] revealed that the maximal cloud water increases with aerosols and approaches a maximum value (4.2 g m−3) under the condition of extremely high [CCN]. Only the simulations of NR6, NR6_PCR, and BR74 are comparable with the results of Fan et al. [2007b]. For NR6_PCR, the maximal cloud water approaches 4.2 g m−3 when [CCN] is 10000 cm−3, consistent with the SBM simulations by Fan et al. [2007b]. Hence if the responses of precipitation and the maximal cloud water to the changes in [CCN] are considered among the seven types of autoconversion parameters, the simulations using NR6_PCR appear to be more reasonable. Clearly, more validation is needed on the available autoconversion schemes, particularly by comparing the model simulations with measured cloud properties.

3.5. Comparison With Other Bulk Microphysical Schemes in the WRF Model

[46] Several bulk microphysical schemes have been developed to represent the cloud microphysical processes in the WRF model. These microphysical schemes include the Kessler scheme [Kessler, 1969], Lin scheme [Lin et al., 1983; Rutledge and Hobbs, 1984], Thompson scheme [Thompson et al., 2004], a WRF single moment (WSM) 3-class simple ice scheme [Hong et al., 2004], WSM 5-class scheme [Hong et al., 2004], and a WSM 6-class graupel scheme [Hong et al., 2004]. Figure 13 shows a comparison of the cumulative precipitation among the different microphysics schemes. The total domain precipitation from the present microphysical scheme (AERO) predicts that the mean total domain precipitation ranges from 0.040 mm to 0.097 mm, with a mean value of 0.067 mm for [CCN] between 200 and 50,000 cm−3. There is a large variation in the predicted mean total domain precipitation from the other six microphysical schemes, with a minimum value of 0.050 mm by the WMS3 scheme and a maximum value of 0.10 mm by the Lin scheme. Similarly, a large variation is predicted for the core updraft from the six microphysical schemes, with a minimum value of 3.0 m s−1 by the Kessler scheme and a maximum value of 4.2 m s−1 by the WSM6 scheme (Figure 14). Most of the previous schemes predict the core updrafts larger than the core updraft of 2.2 to 3.6 m s−1 from the present scheme under different [CCN] conditions (Figure 14a). The predicted core downdraft by the various bulk schemes differs by 15% and compares favorably with the range of 1.4 to 2.4 m s−1 from the present scheme (Figure 14b).

Details are in the caption following the image
Comparison of cumulative precipitation inside the domain among the different bulk microphysics schemes. The shaded bar shows the range of cumulative precipitation from different [CCN] in the present microphysical scheme.
Details are in the caption following the image
(a) Comparison of population means of updraft and (b) downdraft in the core area among the different bulk microphysics schemes. The shaded bar shows the range of population means of updraft and downdraft from the different [CCN] in the present microphysical scheme.

[47] Note that all previous bulk schemes in the WRF model are single-moment, in comparison with the present two-moment bulk microphysical scheme to include the aerosol-cloud interaction. In the Thompson scheme (2004), CDNC can be employed as an input parameter in the WRF model to consider the aerosol-cloud interaction, and the results of the Thompson scheme can be dependent on the assumed droplet concentration. An additional sensitivity study is performed, showing that the simulated total domain precipitation is insensitive to the change in CDNC when CDNC is increased from 100 cm−3 to 4000 cm−3 in the Thompson Scheme (2004). With a CDNC of 100 cm−3, the total domain precipitation is about 0.10 mm, and with a CDNC of 4000 cm−3 the total domain precipitation is decreased to 0.093 mm. Hence the Thompson Scheme (2004) fails to represent the reasonable response of clouds to aerosols by only changing CDNC.

4. Conclusions

[48] A two-moment bulk microphysical scheme has been implemented into the WRF model to consider the effects of aerosols on cloud formation and development. The microphysical scheme predicts time-dependent bulk mass mixing ratios and bulk number concentrations of cloud water, rainwater, ice crystals, snow flakes, and graupels, as well as the aerosol mass mixing ratio, surface area, and number concentration. The Köhler theory is used for nucleation of aerosols to form cloud droplets. The warm rain process from Cohard and Pinty [2000] is coupled into the microphysical scheme.

[49] The representation of the aerosol size distribution is evaluated. For cloud supersaturation with a single maximum value, the two-moment modal method yields droplet activation similar to those from the three-moment modal and sectional methods. However, for a variable cloud supersaturation with multiple maximum values, the three-moment modal approach produces results in better agreement with the sectional approach than the two-moment modal method.

[50] A convective cloud event occurring on 24 August 2000 in Houston, Texas is investigated using the CR-WRF model, and the model results are compared with available radar and rain gauge measurements. The development of the cumulus is qualitatively reproduced by comparing the evolution of the distribution of radar reflectivity in the y-z section with the measurements. The convective cell intensity, cell lifetime, and averaged accumulated precipitation are consistent with the observations. The impact of aerosol concentrations on the cloud properties and convective strength are evaluated using the CR-WRF model. A set of 26 initial aerosol profiles, with number concentrations ranging from 200 to 50,000 cm−3 and mass ranging from 1 to 10 μg m−3, is used in the simulation. The response of precipitation to the increase of aerosol concentration is nonmonotonic. The results show that the effects of aerosols on precipitation likely vary under different meteorological and aerosol conditions, because of the complicated interaction between cloud microphysics and dynamics. The precipitation increases with aerosol concentrations from clean maritime to continental background conditions, but is considerably reduced and completely suppressed under highly polluted conditions. The 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 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. The maximal cloud cover, core updraft, and maximal updraft exhibit similar behaviors to precipitation with increasing aerosols. Different types of autoconversion parameterizations and bulk microphysical bulk schemes are compared and evaluated.

[51] This work represents the first to implement a two-moment microphysical scheme into the WRF model to consider the aerosol effects on cloud and precipitation. Because of its broad application in numerical weather prediction, the two-moment CR-WRF model will greatly facilitate the assessment of aerosol-cloud interaction, ranging from individual cumulus to mesoscale convective systems.

Acknowledgments

[68] This study was supported by NSF (ATM-0424885). The authors are grateful to Lou Xiaofeng for providing the source code for the two-moment microphysical scheme. R. Z. acknowledged additional support from the National Natural Science Foundation of China (40728006).

    Appendix A:: Microphysics

    [52] Most of the transformation rates of microphysical processes in the two-moment bulk microphysics scheme by Lou et al. [2003] are similar to those described in details by Wang and Chang [1993a], which will not be repeated in this work. We discuss the main features pertinent to present work in this appendix. P (kg kg−1 s−1) represents mass transformation rate and R (1 kg−1 s−1) represents the number transformation rates. The autoconversion from cloud droplets to raindrops is discussed in Appendix B.

    [53] The rate of self-collection of cloud water (ccc) is taken from Cohard and Pinty [2000],
    equation image
    where K2 = 2.59 × 1015 m−3 s−1, λc is the slope of the cloud droplet distribution, μ is the shape of the distribution, and Nc is the number concentration of cloud water.
    [54] The rate of self-collection and breakup of rainwater (crr) is taken from Cohard and Pinty [2000],
    equation image
    where K2 = 3.03 × 103 m−3 s−1, λc is the slope of the raindrop distribution, Nr is the number concentration of rainwater, and If Dr < 600 μm,
    equation image
    If 600 μm ≤ Dr < 2000 μm,
    equation image
    If Dr ≥ 2000 μm,
    equation image
    [55] The rate of collection of cloud water by rainwater (ccr) is taken from Cohard and Pinty [2000], If Dr ≤ 100 μm,
    equation image
    If Dr > 100 μm,
    equation image
    [56] Several processes are considered for ice nucleation in the cold phase of the cloud development. The number of ice crystals formed from deposition nucleation is related to temperature and ice supersaturation according to Pruppacher and Klett [1997] and Wang and Chang [1993a]:
    equation image
    where Ni is the number of ice crystals, Ni0 = 10−2/m3, T is temperature, Qv is saturation of water vapor, Qsi is the supersaturation of water vapor with respect to ice, a = 0.6 K−1, b = 5.0, and ρ is air density. The number production rate of newly nucleated ice crystals at a time step and a certain grid point, Rnuc, is calculated from,
    equation image

    [57] The rate of drop freezing follows the immersion-freezing parameterization based on the stochastic hypothesis formulated by Bigg [1953] and homogeneous freezing by DeMott et al. [1994]. Contact-freezing of drops is from Meyers et al. [1997] and is negligible for temperatures warmer than −10°C.

    [58] For the secondary ice crystal production, the rime-splintering mechanism by Hallet and Mossop [1974] is used. At T = −5°C, 250 collisions of droplets having radii exceeding 24 μm with graupel particles lead to the formation of one ice splinter.

    [59] Ice particles grow through deposition growth, aggregation among ice crystals, riming of supercooled droplets [Wang and Chang, 1993a; Lou et al., 2003]. A heavily rimed ice crystal is transferred to a graupel. When all ice particles fall below the freezing level, melting occurs by instantaneous conversion of these particles into liquid drops of equal mass.

    Appendix B:: Autoconversion Parameterizations

    [60] Seven autoconversion parameterizations (three Kessler-types, two Berry-types, and two Sundqvist-types) have been considered in this study. A simple description of each type of autoconversion parameterization is presented in the followings. The gamma function is used to represent the size distribution of cloud water:
    equation image
    where n0c is the intercept, λc is the slope, and μ is the shape parameter of the distribution. In addition, Qc and Nc are the mass mixing ratio and number concentration of cloud water, respectively. Hacr represents the autoconversion rate in s−1. ɛ is the relative dispersion of cloud droplets and related to μ by μ = ɛ−2 − 1.

    B1. Kessler-Type Autoconversion Parameterizations

    B1.1. Kessler Parameterization (KSL69)

    [61] KSL69 was proposed by Kessler [1969] and has been used widely in cloud-related modeling studies due to its simplicity.
    equation image
    The parameter K1 is the reciprocal of the 1/e “conversion time” of the cloud water and set to 10−3 s−1. The parameter a is a threshold cloud water content at which conversion is hypothesized to begin. Following Wang [2005], we assume a = 1 g kg−1.

    B1.2. New R6 Parameterization (NR6)

    [62] This new Kessler-type parameterization is derived by Liu and Daum [2004], in which the incorrect and/or unnecessary assumptions inherent in the existing Kessler-type parameterizations are eliminated. R6 corresponds to the mean radius of the sixth moment of the cloud droplet size distribution. This scheme exhibits a different dependence on liquid water content and droplet concentration. In addition, relative dispersion of the cloud droplet size distribution is explicitly included in this parameterization.
    equation image
    equation image
    equation image
    equation image
    equation image
    R3 is the mean volume radius and R3c is the threshold mean volume radius equal to 10 μm. R3c is commonly used as the threshold volume mean radius which has a physical meaning, and R6 is related to R3. Rp is defined as Rp = equation image. When p = 3 and p = 6, the relationship between R6 and R3 is obtained [Liu and Daum, 2004].

    B1.3. New R6 Parameterization With the Predicted Critical Radius (NR6_PCR)

    [63] This parameterization is same as NR6 except that the critical radius is not fixed. The analytical expression for the critical radius is derived by Liu et al. [2004] using the cloud liquid water content and the droplet number concentration.
    equation image
    equation image

    B2. Sundqvist-Type Autoconversion Parameterizations

    B2.1. Sundqvist Autoconversion Parameterization (Sqvt78)

    [64] The expression for the autoconversion rate was proposed by Sundqvist [1978] based on the consideration that the change of the autoconversion rate near the threshold is expected to be smooth, not discontinuous.
    equation image
    Cs is an empirical constant and set to 1.0 × 10−4 s−1. Qs is the threshold cloud water content and set to 1 g kg−1.

    B2.2. Generalized Sundqvist Autoconversion Parameterization (GSqvt_PCR)

    [65] This parameterization is presented by Liu et al. [2006] by combining the autoconversion function derived by Liu and Daum [2004], the expression for the critical radius derived by Liu et al. [2004], and the generalized Sundqvist-type threshold function.
    equation image
    where κ = 1.1 × 1011 g−2 cm3 s−1 is a constant in the Long collection kernel [Long, 1974], and μ = 2 in this study.

    B3. Curve-Fit to Detailed Model Simulations

    B.3.1. Berry 1968 (BR68)

    [66] BR68 was first suggested by Berry [1968] and developed theoretically from a model of initial cloud growth by condensation and coalescence of cloud-sized particles with each other.
    equation image

    B3.2. Berry 1974 (BR74)

    [67] The BR74 parameterization [Berry and Reinhardt, 1974] is built on the observation that a characteristic water content L, of small drops develops steadily over a characteristic time-scale, τ. These two positive quantities are expressed in the range 20 μm < Dc < 36 μm by
    equation image
    equation image
    where
    equation image
    and
    equation image
    are the mean volume drop diameter and the standard deviation of the cloud-droplet size distributions, respectively. So, for given cloud conditions, a mean-mass autoconversion rate can be computed only if σc > 15 μm:
    equation image