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  • Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of momentum: Observations and parameterization. J. Atmos. Sci., 51, 16401660, doi:10.1175/1520-0469(1994)051<1640:EOVWSO>2.0.CO;2.

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  • Xu, K.-M., and D. A. Randall, 2001: Updraft and downdraft statistics of simulated tropical and midlatitude cumulus convection. J. Atmos. Sci., 58, 16301649, doi:10.1175/1520-0469(2001)058<1630:UADSOS>2.0.CO;2.

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  • Zhang, G. J., and H. R. Cho, 1991a: Parameterization of the vertical transport of momentum by cumulus clouds. Part I: Theory. J. Atmos. Sci., 48, 14831492, doi:10.1175/1520-0469(1991)048<1483:POTVTO>2.0.CO;2.

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  • Zhang, G. J., and H. R. Cho, 1991b: Parameterization of the vertical transport of momentum by cumulus clouds. Part II: Application. J. Atmos. Sci., 48, 24482457, doi:10.1175/1520-0469(1991)048<2448:POTVTO>2.0.CO;2.

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  • Zhang, G. J., and N. A. McFarlane, 1995a: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmos.–Ocean, 33, 407446, doi:10.1080/07055900.1995.9649539.

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  • Zhang, G. J., and N. A. McFarlane, 1995b: Role of convective-scale momentum transport in climate simulation. J. Geophys. Res., 100, 14171426, doi:10.1029/94JD02519.

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  • Zhang, J. H., U. Lohmann, and P. Stier, 2005: A microphysical parameterization for convective clouds in the ECHAM5 climate model: Single-column model results evaluated at the Oklahoma Atmospheric Radiation Measurement Program site. J. Geophys. Res., 110, D15S07, doi:10.1029/2004JD005128.

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    IOP-averaged profiles of convective cloud water content (liquid plus ice) at the ARM SGP site for three IOPs (summers of 1995 and 1997, and spring of 2002). In CONV-A, precipitation is allowed to form at all levels of convective clouds, whereas in CONV-P, precipitation formation is suppressed in the lowest 300 mb above the cloud base. ORIG is the original Tiedtke (1989) scheme without detailed microphysics. Adapted from Zhang et al. (2005).

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    Schematic diagram of the two-moment microphysics scheme for convection. Adapted from Song et al. (2012).

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    The maximum, minimum, 10th, 25th, 50th, 75th, and 90th percentiles of vertical velocity distribution in convective clouds averaged over (a) the tropical (10°S–10°N) ocean and (b) the Northern Hemisphere middle latitude (20°–40°N) land for June–August (JJA) from CAM5 with the SZ convective microphysics scheme. Adapted from Song et al. (2012).

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    Cloud ice water content (g m−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (blue dotted), tropical land (black solid), and middle latitude [20°–40°N(S)] land (red dashed) for July from (a) CloudSat (2007), (b) standard CAM5, and (c) CAM5 with the SZ convective microphysics scheme for convection. Adapted from Song et al. (2012).

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    (a) Variation of cloud liquid water content (LWC) with height above the cloud base measured in traverses of 802 cumulus clouds. The blue dots are average LWC, while the squares are the largest values measured (adapted from Wallace and Hobbs 2006); (b),(c) cloud LWC (g m−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (blue dotted), tropical land (black solid), and middle latitude [20°–40°N(S)] land (red dashed) for July from (b) standard CAM5 and (c) CAM5 with the SZ convective microphysics scheme.

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    (a) Cloud droplet number concentration (CDNC) in active maritime and continental cumuli (adapted from Squires 1958), and (b) JJA mean cloud droplet in convective clouds averaged over the tropical (20°S–20°N) ocean (solid) and Northern Hemisphere middle latitude (20°–40°N) land (dotted) from CAM5 with the SZ convective microphysics scheme.

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    (a) Profiles of ice crystal number concentration obtained in CEPEX and KWAJEX experiments and WRF simulations (adapted from Phillips et al. 2007), and (b) JJA mean cloud ice crystal number concentration (cm−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (solid) and Northern Hemisphere middle latitude (20°–40°N) land (dotted) from CAM5 with the SZ convective microphysics scheme.

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    (a) The autoconversion rate of cloud liquid water to rain (g kg−1 km−1) and (b) cloud ice production (g kg−1 km−1) through the Bergeron process (dotted lines) and homogeneous droplet freezing (dashed lines) in convective clouds averaged over 20°S–40°N for JJA from simulation with the present aerosol loading (MPHY, thick lines) and that with lower aerosol loading (LOW_aero, thin lines). Adapted from Song et al. (2012).

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Parameterization of Microphysical Processes in Convective Clouds in Global Climate Models

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  • 1 Scripps Institution of Oceanography, La Jolla, California
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Abstract

The microphysical processes inside convective clouds play an important role in climate. They directly control the amount of detrainment of cloud hydrometeor and water vapor from updrafts. The detrained water substance in turn affects the anvil cloud formation, upper-tropospheric water vapor distribution, and thus the atmospheric radiation budget. In global climate models, convective parameterization schemes have not explicitly represented microphysics processes in updrafts until recently. In this paper, the authors provide a review of existing schemes for convective microphysics parameterization. These schemes are broadly divided into three groups: tuning-parameter-based schemes (simplest), single-moment schemes, and two-moment schemes (most comprehensive). Common weaknesses of the tuning-parameter-based and single-moment schemes are outlined. Examples are presented from one of the two-moment schemes to demonstrate the performance of the scheme in simulating the hydrometeor distribution in convection and its representation of the effect of aerosols on convection.

Corresponding author address: Guang J. Zhang, Scripps Institution of Oceanography, 9500 Gilman Dr., La Jolla, CA 92093. E-mail: gzhang@ucsd.edu

Abstract

The microphysical processes inside convective clouds play an important role in climate. They directly control the amount of detrainment of cloud hydrometeor and water vapor from updrafts. The detrained water substance in turn affects the anvil cloud formation, upper-tropospheric water vapor distribution, and thus the atmospheric radiation budget. In global climate models, convective parameterization schemes have not explicitly represented microphysics processes in updrafts until recently. In this paper, the authors provide a review of existing schemes for convective microphysics parameterization. These schemes are broadly divided into three groups: tuning-parameter-based schemes (simplest), single-moment schemes, and two-moment schemes (most comprehensive). Common weaknesses of the tuning-parameter-based and single-moment schemes are outlined. Examples are presented from one of the two-moment schemes to demonstrate the performance of the scheme in simulating the hydrometeor distribution in convection and its representation of the effect of aerosols on convection.

Corresponding author address: Guang J. Zhang, Scripps Institution of Oceanography, 9500 Gilman Dr., La Jolla, CA 92093. E-mail: gzhang@ucsd.edu

1. Introduction

The parameterization of atmospheric convection has been an active research area for over half a century (see reviews by Arakawa 2000, 2004). Convective transport of heat and moisture, and the latent heat release associated with it play a fundamental role in large-scale atmospheric circulation (Riehl and Malkus 1958). This role was quantitatively expressed in terms of apparent heat source and moisture sink by Yanai et al. (1973). Because of its small spatial and temporal scales compared to model grid spacing in numerical models for large-scale circulation and weather prediction, subgrid-scale convection has to be parameterized. Over the past 50 years, a range of parameterization schemes has been developed, varying from moist convective adjustment schemes (Manabe et al. 1965; Betts 1986) to more sophisticated, moisture-convergence-based (Kuo 1965, 1974; Tiedtke 1989) and convective-instability-based mass flux representations (Arakawa and Schubert 1974; Emanuel 1991; Donner 1993; Zhang and McFarlane 1995a; and many more). In all these parameterization studies, emphasis was placed on representing convective effects on temperature and moisture fields because of their obvious roles in atmospheric energetics and hydrological cycle. Later on, convective effects on the momentum field were also considered (Schneider and Lindzen 1976; Zhang and Cho 1991a,b; Wu and Yanai 1994; Zhang and McFarlane 1995b; Gregory et al. 1997). More recently, approaches to develop scale-aware (or unified) convective parameterization schemes, again largely for temperature and moisture fields, have been explored to meet the need of increasing global climate model (GCM) resolutions (Arakawa et al. 2011; Arakawa and Wu 2013).

On the other hand, the link between convection and stratiform anvil clouds has been very weak in large-scale models for historical reasons. In the early days of general circulation model development, large-scale cloud fraction needed for radiation calculation was specified (Manabe et al. 1965). The cloud liquid water path used for determining cloud optical properties was empirically related to the moisture field (e.g., Kiehl et al. 1998). Thus, convection in climate models affects large-scale clouds indirectly by modulating the moisture field. This is far from how nature works. In reality, deep convection generates massive amounts of anvil clouds by detraining cloud liquid water and ice from updrafts. The radiative effect of the anvil clouds in turn further affects convection (Fu et al. 1995; Stephens et al. 2008). Furthermore, these anvil clouds have a tremendous impact on the earth’s radiative energy budget climatologically (Randall et al. 1989; Ramanathan and Collins 1991). The amount of detrained cloud liquid water and ice strongly depends on the strength of convective updrafts and the content of cloud water and ice within them. The latter is determined by convective microphysical processes. Part of the detrained condensate also moistens the upper-tropospheric ambient atmosphere, and can thus modify the upper-tropospheric water vapor distribution. This has important implications for water vapor feedbacks on climate change (Betts 1990; Lindzen 1990; Shine and Sinha 1991). Therefore, a proper treatment of convective microphysical processes in global climate models is crucial to reliable simulations of the present climate and future climate projection.

The impact of convective detrainment on climate feedback and climate change has been the center of a debate for over two decades. On one hand for example, Lindzen (1990) argues that convection has a negative water vapor feedback to climate warming. Under a warmer climate convection reaches higher altitudes, thus detrains less moisture from the saturated air at detrainment levels due to colder temperatures. The compensating subsidence of the drier air fills the upper troposphere, thus producing less greenhouse effect. On the other hand, Betts (1990) argues that this is an overly simplified view of convective effect on climate feedback. Convection, particularly in the tropics and summertime midlatitudes, often appears in the form of mesoscale convective systems with large anvils in the upper troposphere (Houze 1977; Zipser et al. 1981). The humidification of the upper troposphere from the decay of these anvils plays a much more important role than the detrainment of convective air into the ambient atmosphere there.

The generation of anvil and cirrus clouds strongly depends on the microphysics of precipitation formation within convective updrafts (Emanuel and Pierrehumbert 1996). Based on satellite data analysis, Lindzen et al. (2001) propose an “Iris hypothesis,” arguing that anvil clouds associated with convection have a positive feedback on climate. They suggest that the area coverage of anvil clouds associated with tropical convection is less extensive when sea surface temperatures are higher, thus allowing for more shortwave radiation to reach the sea surface and warm it. This claim was challenged by other studies using satellite data and simple model analysis (Lin et al. 2002; Hartmann and Michelsen 2002; Fu et al. 2002). Central to these debates are the effects of convection on upper-tropospheric moisture and cirrus/anvil clouds. Rennó et al. (1994) tested several convection parameterization schemes in a radiative–convective equilibrium model and found that the equilibrium climate was very sensitive to precipitation efficiency in convection. They found that clouds with high precipitation efficiency produced cold and dry climate and clouds with low precipitation efficiency produced moist and warm climate. They argue that convective parameterization schemes currently in use in GCMs bypass the microphysical processes by making arbitrary assumptions on convective precipitation and moistening, and thus are inadequate for climate change studies.

Early convection parameterization schemes treat cloud microphysics crudely, either by arbitrarily assigning a precipitation efficiency (Emanuel 1991) or by assuming that the conversion rate from cloud water to rainwater is proportional to the cloud water mixing ratio (Arakawa and Schubert 1974; Tiedtke 1989; Zhang and McFarlane 1995a). In recent years, more attention has been paid to representing microphysical processes in convection parameterization (Sud and Walker 1999; Zhang et al. 2005; Lohmann 2008; Song and Zhang 2011).

Convective microphysics is important not only to climate feedbacks and global climate change, but also to aerosol–convection interactions, an active research area lately (Koren et al. 2005; Khain et al. 2005; Tao et al. 2007; Rosenfeld et al. 2008; Li et al. 2011; Tao et al. 2012). Anthropogenic aerosols modify cloud microphysical properties by serving as cloud condensation nuclei (CCN) and ice nuclei (IN). More aerosols produce a larger number of smaller cloud droplets, which coalesce less efficiently into raindrops. The satellite observations demonstrated that aerosols suppress deep convective precipitation by reducing cloud droplet size (Rosenfeld 1999; Rosenfeld and Woodley 2000). On the other hand, the suppression of warm rain formation by aerosols in the lower part of the cloud allows a greater amount of cloud water to be lifted to above the freezing level by updrafts. This helps to release additional latent heat from freezing to invigorate convection (Koren et al. 2005; Khain et al. 2005; Rosenfeld et al. 2008; Li et al. 2011). Such microphysical processes must be incorporated into GCMs in order to have a better understanding of their climatic effects.

In this study, we review the development of the representation of convective microphysical processes associated with precipitation formation in GCMs. We will start with the simple treatment typical of that in the early years of convection parameterization development, and gradually move to more comprehensive treatments explored in recent years. Section 2 provides a description of tuning-parameter-based schemes. Section 3 outlines microphysical schemes that consider cloud liquid water and ice mass mixing ratios. Section 4 presents two-moment microphysical schemes for convective clouds that were explored in recent years. Section 5 presents a few examples of model simulation using two-moment convective microphysics schemes, and section 6 summarizes the paper.

2. Tuning-parameter-based schemes

The parameterization of convective microphysics arises from the general problem of convection parameterization. The effects of convection on temperature and moisture fields can be understood from the large-scale heat and moisture budget equations (Yanai et al. 1973):
e12-1
and
e12-2
where s = cpT + gz is the dry static energy, q is the specific humidity, v is the horizontal wind vector, w is the vertical velocity, and L is the latent heat of vaporization. The quantity ρ is air density, M is the cloud mass flux, and subscripts u and d denote updraft and downdraft properties, respectively. The overbar represents the average over the large-scale domain or a model grid box. The radiative heating rate is QR and ce represents the net condensation (condensation minus evaporation) within the GCM grid box. The latent heat release from condensation and the convective transport can be represented by a cloud model, which is used to determine such in-cloud properties as the mass flux, temperature, moisture, and the cloud hydrometeor.
The equations for these properties in convective updrafts are given by
e12-3
e12-4
e12-5
where cu is the condensation rate, and εu and δu are the mass entrainment and detrainment. The equation for cloud water content is given by
e12-6
where ql is the liquid water mixing ratio and Rr is the conversion rate from cloud water to rainwater. In early convection parameterization schemes, the conversion of cloud water to rainwater is parameterized based on simple intuitions. For example, in the Arakawa and Schubert scheme (1974), the conversion rate is assumed to be proportional to the cloud water mixing ratio (Lord 1982). In the diagnostic study of convective cloud properties, Yanai et al. (1973) did not use a constant proportionality factor but assumed it to be a function of height. In Emanuel’s scheme (Emanuel 1991), instead of using Eq. (12-6) the cloud water mixing ratio is determined by
e12-7
where qla is the adiabatic liquid water mixing ratio. The conversion rate is represented through a precipitation efficiency parameter ε, which depends on cloud thickness. For updraft extent less than 150 hPa, there is no conversion from cloud water to rainwater, thus ε = 0. This is to mimic nonprecipitating shallow convection. For updraft extent greater than 500 hPa, the conversion rate is set to 1, meaning that all cloud water is converted to rainwater. For updraft extent between 150 and 500 hPa a linear interpolation is used. The Tiedtke (1989) scheme uses a similar expression to that by Arakawa and Schubert (1974), with the following equation for cloud water to rainwater conversion in Eq. (12-6):
e12-8
where K(p) is a height-dependent conversion coefficient given by
e12-9
where pB is the cloud-base pressure, and Δpcrit is the critical pressure thickness for cloud layer and is set to 150 mb over ocean and 300 mb over land. Zhang and McFarlane (1995a) set K to a constant following Lord (1982).

In short, all these schemes invoke crude representation for cloud water to rainwater conversion, with no explicit consideration of cloud microphysical processes. Whereas this may be adequate for convection parameterization in GCMs in the past when diagnostic cloud parameterizations were common (e.g., Xu and Krueger 1991; Kiehl et al. 1998), it is far from satisfactory in today’s state-of-the-art GCMs, where sophisticated cloud parameterizations are used to represent stratiform cloud processes in addition to assumed distribution of subgrid-scale moisture/heat variations (e.g., Morrison and Gettelman 2008).

3. Single-moment convective microphysics schemes

In more recent studies, better treatment of cloud water to rainwater conversion was incorporated. Sud and Walker (1999) introduced an autoconversion from cloud water to rainwater following Sundqvist (1978, 1988), who pioneered the prognostic cloud parameterization for the state-of-the-art GCMs. The conversion term in Eq. (12-6) is expressed as
e12-10
where wu is the vertical velocity of the updraft and 1/w reflects the time it takes for the air parcel to travel through a model layer. The longer it takes, the more cloud water is converted to rainwater. The parameter Rp represents precipitation formation rate (kg kg−1 s−1) through autoconversion following Sundqvist (1988):
e12-11
where qlcrit is the critical value of cloud water for autoconversion, fc is the cloud fraction determined from updraft mass flux and vertical velocity, and C0 is an autoconversion coefficient, which is related to factors such as precipitation intensity to mimic the coalescence process and subfreezing temperatures to mimic the Bergeron–Findeisen process following Sundqvist et al. (1989). Note that in Eq. (12-11) cloud water to rainwater conversion is independent of the rainwater content. Thus, accretion of cloud water by rainwater is not considered explicitly. The vertical velocity of updrafts determines how long the parcel stays in the layer, thus the amount of conversion. Sud and Walker (1999) used a cloud-scale vertical momentum equation to estimate w:
e12-12
where γ is a coefficient that accounts for the pressure gradient effect; the ql and qr are terms that represent the loading from cloud water and rainwater, respectively; and the last term represents the frictional drag associated with the turbulent flow in updrafts.
An effort to develop a comprehensive convective microphysics parameterization was made by Zhang et al. (2005). Instead of using a height-dependent K as in Eq. (12-9) in the Tiedtke (1989) scheme, they included more sophisticated cloud microphysical processes for both cloud water and ice mixing ratios. The following two diagnostic equations for cloud water and ice in convective updrafts are used:
e12-13
e12-14
where ql and qi are cloud liquid and ice mixing ratio, respectively. The conversion terms Gpl and Gpi, which represent sinks to cloud water and ice due to conversion to rain and snow, are parameterized through more sophisticated cloud microphysical processes than in Sud and Walker (1999):
e12-15
e12-16
where fc is cloud fraction, related to convective cloud mass flux empirically based on Xu and Krueger (1991); subscript aut is for autoconversion, racl and sacl are for accretion of cloud droplets by raindrops and snow, respectively; fho and fhe are for homogeneous and heterogeneous freezing, respectively; mlt is for melting of ice crystals; agg is for aggregation of ice crystals; and saci for accretion of ice crystals by snow. Thus, in Zhang et al. (2005) the cloud water is depleted by autoconversion to rain, accretion by rain and snow, and (homogeneous and heterogeneous) freezing, but increased by the melting of cloud ice. The cloud ice is decreased by aggregation to snow, accretion by snow and melting, and increased by freezing.
The condensation cul and deposition cui in Eqs. (12-13) and (12-14) are calculated based on supersaturation:
eq1
eq2
where and are saturation water vapor mixing ratio with respect to water and ice, respectively. For temperatures in between, condensation and deposition are treated in a more complicated way, depending on the ice water content. Condensation is allowed to occur first and is calculated with respect to water. The scheme then assumes that cloud ice forms through heterogeneous freezing. If the cloud ice water content from heterogeneous freezing (see below) is less than a threshold value of 0.5 mg kg−1, condensation will continue to take place. On the other hand, if the ice water content exceeds the threshold value, Bergeron–Findeisen process sets in, allowing ice crystal to grow at the expense of cloud water. Further condensation is suppressed and only deposition is allowed. From this point on, is calculated with respect to ice.
Each of the microphysical terms in Eqs. (12-15) and (12-16) is parameterized. Homogeneous freezing Qfho takes place at temperatures below −35°C and all cloud water freezes instantaneously. Between −35° and 0°C, heterogeneous freezing of cloud droplets Qfhe takes place, and is parameterized following Bigg (1953):
e12-17
where parameters a1 and b1 are specified constants. Here T0 = 273.16 K; Nl is the number concentration of cloud droplets, which is prescribed; and ρl is water density. The heterogeneous freezing increases exponentially with decreasing temperature and increases with the square of cloud liquid water mixing ratio. Autoconversion is parameterized in terms of cloud water content and droplet number concentration:
e12-18
where γ1 is a tunable constant, which determines the efficiency of rain formation and is set to 15, and n = 10 is the width parameter of the cloud droplet spectrum, assumed to be a gamma function. The functional form of dependence on cloud water content and droplet number follows that in Beheng (1994). High cloud water content and low droplet number concentration favor autoconversion from cloud water to rainwater. The aggregation of cloud ice to snow is parameterized as
e12-19
where γ2 is another tunable parameter determining the efficiency of snow formation. The term Δt is the time needed for the ice crystal number concentration to decrease by a certain factor, and inversely depends on cloud ice content and the collection efficiency between ice crystals.
The parameterization of accretion of cloud water by raindrops in Zhang et al. (2005) also follows the work of Beheng (1994) and the accretion rate is proportional to the product of cloud water and rainwater contents:
e12-20
where a3 = 6 s−1 and qr is the rainwater mixing ratio. The accretion of cloud water by snow follows the work of Levkov et al. (1992) and Lin et al. (1983). It is based on the concept of the geometric sweep-out of cloud droplets by snow particles integrated over all snow sizes, which is assumed to have the exponential distribution, and is given by
e12-21
where a4 = 4.83, b4 = 0.25, and γ3 = 0.1. Here Esl = 1 is the collection efficiency of cloud droplets by snow, Γ is the gamma function, n0s = 3 × 106 m−4 is the intercept parameter, and λs is the slope of the snow particle size distribution. It is related to snow mass mixing ratio:
eq3
where qs is the snow mixing ratio and ρs = 100 kg m−3 is the snow density. The accretion of ice crystals by snow takes a similar form to Eq. (12-21) except with the collection efficiency depending on temperature, Esi = exp[0.025(TT0)]. For melting (Qmlt), all ice crystals melt to become cloud water when temperature is above 0°C. The rainwater and snow form as a result of autoconversion, accretion, and aggregation.

Zhang et al. (2005) tested this convective microphysics scheme in a single-column model of ECHAM5 (the GCM developed by the Max Planck Institute for Meteorology in Hamburg, Germany, based on the ECMWF model) using the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) program observations in the Southern Great Plains. They found that the in-cloud convective water content (liquid plus ice) is very sensitive to the introduction of convective microphysics and to assumptions on precipitation formation in the lower levels of convection (Fig. 12-1).

Fig. 12-1.
Fig. 12-1.

IOP-averaged profiles of convective cloud water content (liquid plus ice) at the ARM SGP site for three IOPs (summers of 1995 and 1997, and spring of 2002). In CONV-A, precipitation is allowed to form at all levels of convective clouds, whereas in CONV-P, precipitation formation is suppressed in the lowest 300 mb above the cloud base. ORIG is the original Tiedtke (1989) scheme without detailed microphysics. Adapted from Zhang et al. (2005).

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

Although single-moment schemes are a significant step forward in representing convective microphysical processes in GCMs, their lack of information on droplet and ice crystal sizes and number concentration is a clear weakness. In particular, they cannot be used to understand aerosol–convection interaction. To overcome this shortcoming, two-moment schemes have recently been developed for convective clouds.

4. Two-moment convective microphysics schemes

Recognizing the need for considering cloud droplet and ice crystal number concentrations for understanding aerosol–convection interaction in climate models, Lohmann (2008) extended the single-moment convective microphysics scheme of Zhang et al. (2005) using a double-moment cloud microphysics scheme (Lohmann et al. 2007). In particular, droplet activation by aerosols, which is linked to updraft vertical velocity, was included. The updraft velocity used in aerosol activation was formulated as the sum of grid mean vertical velocity, contributions of turbulent kinetic energy (TKE), and convective available potential energy (CAPE):1
e12-22
The droplet activation was related to vertical velocity and internally mixed aerosol number concentration. She found that by including droplet activation by aerosols in convective cloud microphysics parameterization the ECHAM5 model is able to simulate the aerosol effect on convection invigoration by comparing results from the twentieth-century simulations.
Recently Song and Zhang (2011) and Song et al. (2012) developed a two-moment microphysics parameterization scheme for convective clouds based on the work of Morrison and Gettelman (2008). This diagnostic microphysics scheme explicitly treats mass mixing ratio and number concentration of four hydrometeor species (cloud water, cloud ice, rain, and snow) in convective updrafts. Microphysical processes in downdrafts are not considered. The budget equations for mass mixing ratios qx and number concentrations Nx of hydrometeor species x (subscript l for cloud water, i for cloud ice, r for rain, and s for snow) in saturated updrafts are given by
e12-23
e12-24
The quantities and are the in-cloud source/sink terms for qx and Nx, respectively, from microphysical processes. Figure 12-2 shows the schematic of microphysical processes considered in the scheme (hereafter the SZ scheme). They include droplet activation and ice nucleation by aerosols; autoconversion of cloud water/ice to rain/snow; accretion of cloud water by rain; accretion of cloud water, cloud ice, and rain by snow; homogeneous and heterogeneous freezing of rain to form snow; Bergeron–Findeisen process; fallout of rain and snow; condensation/deposition; self-collection of rain drops; and self-aggregation of snow. Compared to the single-moment scheme of Zhang et al. (2005), there are several differences in the consideration of the microphysical processes besides including the number concentrations of the cloud hydrometeors. First, the droplet activation and ice nucleation by aerosols are included. Second, autoconversion instead of aggregation of ice to snow is considered. Third, sedimentation of rainwater and snow is considered, which affects the accretion of cloud water/ice by rain and snow. The explicit treatment of cloud particle number concentration enables the SZ microphysics scheme to account for the impact of aerosols on convection. The main features of the scheme are described below.
Fig. 12-2.
Fig. 12-2.

Schematic diagram of the two-moment microphysics scheme for convection. Adapted from Song et al. (2012).

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

a. Representation of convective vertical velocity

Different from the approach of Lohmann (2008), which uses a simple formulation of vertical velocity for aerosol activation, the SZ microphysics scheme estimates the updraft velocity of convective clouds using the vertical momentum (or kinetic energy) equation:
e12-25
where , νu is a mixing coefficient equal to the larger of entrainment or detrainment of mass flux, and g is gravitational acceleration. The value for β is 1.875. Here Cd = 0.506 is the drag coefficient and γ = 0.5 is the virtual mass coefficient. The factor f = 2 is used to account for highly turbulent flows in updrafts. The quantities Tυu and Tυe are the virtual temperature of the updraft and environment, respectively. This updraft velocity is also used for deriving the cloud fraction and in droplet activation and ice nucleation parameterizations in the SZ microphysics scheme.

Figure 12-3 shows the probability distribution of vertical velocity in deep convection produced by the NCAR Community Atmosphere Model, version 5 (CAM5) with the SZ microphysics scheme (Song et al. 2012). The convective vertical velocities over tropical (10°S–10°N) oceans range from 0.5 to 9 m s−1, peaking at about 3–4 km with maximum and median velocity of 9 and 7 m s−1, respectively. The altitude of maximum vertical velocity is in good agreement with observations for oceanic convection by LeMone and Zipser (1980) and Lucas et al. (1994), but lower than that in a cloud-resolving model simulation (Xu and Randall 2001). Xu and Randall (2001) suggested that this may be due to the low vertical resolution in the aircraft observations. Lucas et al. (1994) also compared observed vertical velocity of oceanic convection with that of land convection from the Thunderstorm Project (Byers and Braham 1949) and found a higher peak with a greater intensity (15 m s−1 at 8 km) in land convection. A recent study using airborne Doppler radar found strong updraft vertical velocities exceeding 15 m s−1 in both oceanic and land convection, with peak altitudes above the 10-km level (Heymsfield et al. 2010). Compared to oceanic convection, the vertical velocities in midlatitude (20°–40°N) land convection estimated by the SZ scheme peak at a higher altitude (400 mb) with a greater maximum value (~12 m s−1), are in good agreement with the top 2% of updrafts simulated in a cloud-resolving model for the ARM Southern Great Plains (SGP) region (Xu and Randall 2001).

Fig. 12-3.
Fig. 12-3.

The maximum, minimum, 10th, 25th, 50th, 75th, and 90th percentiles of vertical velocity distribution in convective clouds averaged over (a) the tropical (10°S–10°N) ocean and (b) the Northern Hemisphere middle latitude (20°–40°N) land for June–August (JJA) from CAM5 with the SZ convective microphysics scheme. Adapted from Song et al. (2012).

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

It should be noted that the probability distribution of vertical velocities from CAM5 are sampled from broad latitude bands stratified by ocean versus land, whereas observations or cloud-resolving model simulations are from limited geographical locations. The observations have a broad range of vertical velocities even under a limited range of large-scale meteorological conditions. On the other hand, the parameterized vertical velocities are from a bulk plume approach, and are thus not expected to capture the large variability under a given meteorological condition. The broad range seen in Fig. 12-3 mostly reflects the large variability of meteorological conditions in the latitude band. Since microphysical processes and aerosol activation of cloud particles are highly nonlinear, use of a spectral plume model for convective updrafts is more desirable.

b. Autoconversion processes

The autoconversion of cloud water to rainwater in general depends on cloud water content, from linear dependence in the original work of Kessler (1969) to an exponential relationship [Sundqvist 1988; and Eq. (12-11)] and a power relationship [Eq. (12-18)]. In Song and Zhang (2011), following Khairoutdinov and Kogan (2000), it is parameterized to be proportional to . Compared to that in Zhang et al. (2005), although both are proportional nonlinearly to some power of cloud water mixing ratio and the inverse of droplet number concentration, the degree of nonlinearity is much higher in Zhang et al. (2005). The parameterization of autoconversion of cloud ice to snow follows Ferrier (1994) by integrating the cloud ice size distribution over the range greater than the specified threshold value, which is set to 200 μm to separate cloud ice from snow. The ice mixing ratio and number concentrations are converted to snow over a specified time scale (3 min).

c. Accretion processes

The accretion processes include accretion of cloud water by rain and snow, accretion of cloud ice by snow, and accretion of rain by snow. The accretion of cloud water by rainwater follows Khairoutdinov and Kogan (2000), who found it to be proportional to (qlqr)1.15 based on high-resolution cloud simulations. The accretion for droplet numbers is simply that for cloud water content divided by the average mass of a droplet (ql/Nl). The accretion of cloud water by snow follows Thompson et al. (2004), which is based on Lin et al. (1983). It takes a similar form to Eq. (12-21) except with different values for tunable parameters. Likewise, the accretion of cloud ice by snow also follows Thompson et al. (2004) and is expressed in the same functional form of gamma function dependence. Finally, the accretion of rain by snow in subfreezing conditions is parameterized according to Ikawa and Saito (1990), in which the accretion rate is linked to the difference of the fall speed between rain and snow and the slopes of the spectral size distributions of rain and snow.

In updrafts of convective clouds, the hydrometeor budget equations in the SZ microphysics scheme are integrated from cloud base to cloud top. A well-known problem with integrating the rainwater/snow equation from the bottom up is that precipitation falling from above into the layer cannot be accounted for (Zhang et al. 2005). This may result in an underestimation of rain/snow in the layer and thus a lower efficiency of the accretion process. Song et al. (2012) considered the effect of accretion by falling precipitation in the SZ scheme by integrating the hydrometeor equations twice. The first integration provides the provisional values of rain/snow. The iteration takes into account the accretion effect of precipitation falling from above using the provisional values.

d. Self-collection and aggregation

Self-collection of rain does not change the rain mass, but it does change the number concentration. Therefore, it is considered in the two-moment convective microphysics scheme. In Song and Zhang (2011) it is assumed to be proportional to the product of rainwater content and the number concentration following Beheng (1994). Similarly, self-aggregation of snow is also included for snow number concentration following Reisner et al. (1998). It is approximately proportional to .

e. Sedimentation

Rainwater and snow fall out of updrafts at certain terminal fall speeds. In Zhang et al. (2005), rain and snow are assumed to fall out instantly. On the other hand, Song and Zhang (2011) consider the sink of rain and snow and their number concentration due to sedimentation following Kuo and Raymond (1980):
e12-26
e12-27
The mass- and number-weighted terminal fall speeds for all precipitation species are obtained by integrating over the particle size distributions with the appropriate weight of mixing ratio or number concentration, and are dependent on the gamma function and the intercepts of the raindrop and snow size distributions. The and are limited to maximum values of 10 m s−1 for rain and 3.6 m s−1 for snow. Once the precipitation particles fall out of the updrafts, a Sundqvist (1988) style evaporation of the convective precipitation is employed in the subsaturated model layer. Note that updrafts are assumed upright. Cheng and Arakawa (1997) showed that considering rainwater and vertical momentum budgets in a combined updraft–downdraft model would lead to tilted updrafts, allowing precipitation to fall out of the updrafts and into the downdrafts. Such an updraft–downdraft configuration is yet to be incorporated in convective microphysics schemes.

f. Cloud droplet activation

The primary activation of aerosols occurs at the cloud base because of high supersaturation and relatively low condensate there. Above the cloud base, the depletion of excess water vapor by condensation on previously activated particles reduces the supersaturation in a constant updraft. Therefore, most of the cloud microphysics studies consider the droplet activation at the cloud base only. However, in real-world deep convective clouds, the increasing updraft strength (e.g., Warner 1969; Pinsky and Khain 2002), the inevitable depletion of droplets formed at cloud base by accretion (Lamb and Verlinde 2011; Phillips et al. 2005), and entrainment (Brenguier and Grabowski 1993; Su et al. 1998; Lasher-Trapp et al. 2005) may also produce supersaturation conditions and thus droplet activation in cloud updrafts. Previous model simulations (Slawinska et al. 2012; Phillips et al. 2005; Morrison and Grabowski 2008) and observations (Prabha et al. 2011) have confirmed the importance of droplet activation in cumulus updrafts. For this reason, the aerosol activation parameterization of Abdul-Razzak and Ghan (2000) is modified and implemented both at and above the cloud base in the SZ microphysics scheme.

g. Ice nucleation

The ice nucleation includes both homogeneous freezing and heterogeneous freezing. Homogeneous freezing occurs through spontaneous freezing of cloud droplets or aerosols at temperatures colder than −38° to about −40°C without the action of ice nuclei, whereas heterogeneous freezing involves the action of ice nuclei and occurs at warmer temperatures. There are four modes of heterogeneous freezing: deposition nucleation, condensation freezing, immersion freezing, and contact freezing (Pruppacher and Klett 1997). The SZ convective microphysics scheme parameterizes all these ice nucleation processes. Homogeneous droplet freezing is performed by instantaneous conversion of the supercooled cloud liquid water to cloud ice at temperatures below -−40°C. Between −5° and −35°C, the immersion freezing of black carbon and dust is parameterized after Diehl and Wurzler (2004) and the contact freezing of dust follows Liu et al. (2007). Below −35°C, ice nucleation is based on Liu et al. (2007), which includes heterogeneous immersion freezing of dust competing with the homogeneous freezing of sulfate, and depends on updraft velocity, air temperature, and aerosol properties. The deposition/condensation nucleation on mineral dust between −37° and 0°C is represented by Meyers et al. (1992) and secondary ice production between −3° and −8°C (i.e., the Hallett–Mossop process; Hallett and Mossop 1974) is also included based on Cotton et al. (1986). In addition, the SZ microphysics scheme also considers the competition between homogeneous aerosol freezing and homogeneous droplet freezing. A recent study assessed the relative roles of nucleation processes in deep convection (Phillips et al. 2007). It shows that homogeneous aerosol freezing occurs only in regions of weak ascent, while heterogeneous droplet freezing is dominant in stronger updrafts. Thus, the homogeneous freezing of sulfate is suppressed when updraft vertical velocity is greater than 4 m s−1.

5. Evaluation in a GCM

Song and Zhang (2011) incorporated the SZ microphysics scheme in the Zhang and McFarlane (1995a, hereafter ZM95a) convection scheme of the single-column version of NCAR CAM version 3.5 (SCAM3.5) and evaluated its performance with the Tropical Warm Pool–International Cloud Experiment (TWP-ICE) observations. Compared to satellite and C-POL radar retrievals, the standard SCAM3.5 underestimates the cloud ice water and liquid water contents by approximately 75% during the active monsoon period. In contrast, when the SZ microphysics scheme is used, the cloud ice and liquid water contents are increased by more than a factor of 3, making them agree well with observations. With the detrainment of more realistic convective cloud ice and liquid water contents as sources for stratiform clouds, the surface stratiform precipitation, which is seriously underestimated in the model, is increased by a factor of 2.5, and therefore is closer to the observations (Schumacher and Houze 2003).

Song et al. (2012) further implemented the convective microphysics scheme in the ZM95a convection scheme of the NCAR CAM version 5 (CAM5) to evaluate its performance in the global climate model. The simulated cloud ice water content (IWC) is compared to month-long pixel-scale ice water content in convective clouds from CloudSat observations. Figure 12-4 shows the boreal summer (July) IWC profiles averaged in three major convective regimes—the tropical (20°S–20°N) ocean, tropical land, and midlatitude [20°–40°N(S)] land—from CloudSat retrievals and model simulations. The largest difference in IWC is found between the standard CAM5 simulation and CloudSat over the tropical ocean. In the standard CAM5 run (CTL), the maximum IWC is less than 20% of the observations. With the SZ microphysics parameterization, the peak of IWC is in much better agreement with the CloudSat observations.

Fig. 12-4.
Fig. 12-4.

Cloud ice water content (g m−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (blue dotted), tropical land (black solid), and middle latitude [20°–40°N(S)] land (red dashed) for July from (a) CloudSat (2007), (b) standard CAM5, and (c) CAM5 with the SZ convective microphysics scheme for convection. Adapted from Song et al. (2012).

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

Because the cloud liquid water content (LWC) retrievals in intense convection from satellites are either missing or unreliable due to attenuation of radar signal by precipitation, Song et al. (2012) compared the simulated LWC to aircraft observations. The statistics of aircraft observations by Borovikov et al. (1963) show that characteristic values for dense cumulus congestus and cumulonimbus are 0.5–3 g m−3. Recent aircraft observations of the LWC for Indian monsoon clouds (Prabha et al. 2012) show that the LWC above cloud base at 2 km is in the range of 0.5–2.5 g m−3. Figure 12-5 shows the cloud LWC as functions of height above the cloud base from 802 cumulus clouds (Wallace and Hobbs 2006) and CAM5 simulations. The blue dots are averaged LWC, and the squares are the largest values measured (Fig. 12-5a). The observed cloud LWC within 2 km above the cloud base is in the range of 0.5–2 g m−3, with typical values between 1 and 1.3 g m−3. The maximum of LWC simulated by the standard CAM5 in July is only about 0.15 g m−3 over the tropical ocean, indicating a serious underestimation of LWC. With the SZ microphysics scheme, the LWC reaches a maximum of 1.3 g m−3 at 800 hPa. Over tropical land, the simulated LWC peaks near 700 hPa, with a magnitude of 0.5 g m−3 for the standard CAM5 simulation and 1.0 g m−3 for the simulation with the microphysics scheme. The LWC distribution over midlatitude land produced by the SZ microphysics scheme peaks at a higher altitude near 600 hPa with a maximum of 1.2 g m−3, twice as large as that in the standard CAM5.

Fig. 12-5.
Fig. 12-5.

(a) Variation of cloud liquid water content (LWC) with height above the cloud base measured in traverses of 802 cumulus clouds. The blue dots are average LWC, while the squares are the largest values measured (adapted from Wallace and Hobbs 2006); (b),(c) cloud LWC (g m−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (blue dotted), tropical land (black solid), and middle latitude [20°–40°N(S)] land (red dashed) for July from (b) standard CAM5 and (c) CAM5 with the SZ convective microphysics scheme.

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

Observations show that cloud droplet number concentration (CDNC) in active maritime cumulus is typically 20–60 cm−3, while it is much higher in continental cumulus, in the range of 50–300 cm−3 or higher (Squires 1958; Pruppacher and Klett 1997; Wood et al. 2011; Wallace and Hobbs 2006). This contrast in CDNC between maritime and continental convection is easily seen in Figs. 12-6a and 12-6b. There is a large contrast in CDNC between maritime (tropical ocean) and continental (midlatitude land) convection in the CAM5 simulation with the SZ scheme. The maximum CDNC is about 40 cm−3 in maritime convection, and 100 cm−3 in continental convection, in qualitative agreement with observations. This contrast in CDNC between maritime and continental convection directly reflects the aerosol effect on cloud microphysics in convection: higher aerosol amount in continental convection produces more cloud droplets and cleaner air over the ocean produces fewer cloud droplets in convective updrafts.

Fig. 12-6.
Fig. 12-6.

(a) Cloud droplet number concentration (CDNC) in active maritime and continental cumuli (adapted from Squires 1958), and (b) JJA mean cloud droplet in convective clouds averaged over the tropical (20°S–20°N) ocean (solid) and Northern Hemisphere middle latitude (20°–40°N) land (dotted) from CAM5 with the SZ convective microphysics scheme.

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

To date, the observation of ice particle number concentration in convective clouds remains a challenging problem because of measurement uncertainties of complicated crystal properties (e.g., shapes, size) and safety concerns arising from aircraft penetrating convective cores above the freezing level. Song et al. (2012) compared the model simulations with microphysical characteristics of convectively generated ice clouds from two field campaign observations, the Central Equatorial Pacific Experiment (CEPEX; McFarquhar and Heymsfield 1996) and the Kwajalein Experiment (KWAJEX; Heymsfield et al. 2002), and those from cloud system resolving model simulations (Phillips et al. 2007). As shown in Fig. 12-7a, the observed values for ice crystal number concentration (ICNC) vary from 1 cm−3 above 9 km in CEPEX to 0.02–0.07 cm−3 from 5 to 11 km in KWAJEX, while the WRF simulation of TOGA COARE convection gives ICNC in the range of 0.02–2.5 cm−3 (Phillips et al. 2007). The CAM5 simulation with SZ microphysics scheme shows that the ICNC ranges from 0.02 to 1.4 cm−3, roughly in line with available observational and cloud resolving model results.

Fig. 12-7.
Fig. 12-7.

(a) Profiles of ice crystal number concentration obtained in CEPEX and KWAJEX experiments and WRF simulations (adapted from Phillips et al. 2007), and (b) JJA mean cloud ice crystal number concentration (cm−3) profiles in convective clouds averaged over the tropical (20°S–20°N) ocean (solid) and Northern Hemisphere middle latitude (20°–40°N) land (dotted) from CAM5 with the SZ convective microphysics scheme.

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

One of the major benefits a detailed microphysics parameterization for convective clouds can bring to GCMs is that it makes investigation of aerosol effects on convection in GCMs possible. To check whether the SZ convective microphysics scheme can realistically represent the possible impact of aerosols on convective clouds, Song et al. (2012) conducted a sensitivity simulation, in which the aerosol concentration in convection is reduced by a factor of 10. As a result, both the CDNC and ICNC are reduced by more than a factor of 5, indicating that droplet activation and ice nucleation are weakened due to reduced aerosol concentration. They further found that when the aerosol loading was decreased there was more autoconversion from cloud droplets to raindrops, and less ice production in convection averaged over the major convective regime (20°S–40°N) (Fig. 12-8). This is in agreement with the argument that aerosols suppress warm rain formation and enhance freezing, thereby invigorating convection (Khain et al. 2005; Rosenfeld et al. 2008).

Fig. 12-8.
Fig. 12-8.

(a) The autoconversion rate of cloud liquid water to rain (g kg−1 km−1) and (b) cloud ice production (g kg−1 km−1) through the Bergeron process (dotted lines) and homogeneous droplet freezing (dashed lines) in convective clouds averaged over 20°S–40°N for JJA from simulation with the present aerosol loading (MPHY, thick lines) and that with lower aerosol loading (LOW_aero, thin lines). Adapted from Song et al. (2012).

Citation: Meteorological Monographs 56, 1; 10.1175/AMSMONOGRAPHS-D-15-0015.1

One of the advantages of using convective microphysics scheme is physically based partitioning of convective condensate between precipitation particles and detrained condensate. As an important water source, convective detrainment of cloud liquid/ice water can affect the large-scale clouds and precipitation. Song et al. (2012) found that including the SZ convective microphysics scheme in the CAM5 indeed increased the detrainment of cloud water from convective updrafts, which in turn leads to increased cloud amount and large-scale precipitation.

6. Summary

This paper reviews the schemes for parameterizing the microphysical processes in convective updrafts. The tuning-parameter-based schemes, as presented in section 2, are largely based on intuitive arguments and some of them are still used today in convective parameterization schemes in GCMs. In general, in these schemes the conversion rate of cloud water to rainwater is related to the amount of cloud water itself in some simple forms. This is the simplest way to mimic the microphysical processes for rain production. Although careful parameter tuning can produce reasonable cloud water in convection, the lack of detailed representation of microphysical processes hampers further progress in physically based parameterization of convective processes. The single-moment microphysics schemes for convective clouds presented in section 3 allows for some interaction of convection, clouds, and climate, and these schemes incorporate the details of microphysical processes for cloud water and ice to varying degrees. However, although they consider autoconversion and accretion processes for mass mixing ratios in sufficient details (Sud and Walker 1999; Zhang et al. 2005), the number concentrations of the hydrometeor species are specified. The role of aerosols serving as condensation and ice nuclei for droplet activation and ice nucleation is not considered. Thus, these schemes cannot meet the need of current GCMs to provide accurate estimates of aerosol indirect effects not only for stratiform clouds, but also for convective clouds. The two-moment convective microphysics schemes developed recently (Lohmann 2008; Song and Zhang 2011) fill this void. Cloud droplet and ice crystal numbers are calculated with sources and sinks from different microphysical processes including droplet activation and ice nucleation by aerosols. This is particularly important, as recent observational and cloud model studies suggest that aerosols can modify the microphysical properties of convection and affect the intensity and time evolution of convection and associated precipitation (Fan et al. 2007; Khain et al. 2008; Li et al. 2011; Tao et al. 2012).

As an example to demonstrate the performance of the two-moment scheme of Song and Zhang (2011), results of the cloud ice and water mass and number concentrations are compared with available observations in section 5. With the scheme included, the CAM5 model simulates the vertical distribution of these fields well, in broad agreement with both observations and simulations from cloud-resolving models (Xu 1995; Phillips et al. 2007). In addition, it realistically simulates the effect of aerosols on cloud microphysics in convection. When aerosol loading is increased, autoconversion from cloud water to rainwater is suppressed; however, ice production is enhanced, which can lead to more freezing heating in convection.

The GCM results are encouraging. Nevertheless, further improvements on the parameterization are needed. First, vertical velocity in updrafts strongly affects the microphysical processes. Thus, it should be calculated as accurately as possible. At present, either a simple relationship linking it to CAPE [Eq. (12-22)] or a bulk calculation [Eq. (12-25)] is used. For different updraft plumes, the vertical velocity should be different. Thus, a spectral plume model for updrafts and their vertical velocities is desirable. Second, the two-moment convective microphysics schemes consider updrafts only. It is well known that downdrafts play important roles in convection (Cheng and Arakawa 1997) and planetary boundary layer via cold pools and gust fronts (Johnson and Nicholls 1983). In deep convection, they are mostly produced by evaporation of precipitation and condensates (Knupp and Cotton 1985) through microphysical processes. Cheng and Arakawa (1997) showed that downdrafts could affect the tilting of updrafts, which in turn impacts the sedimentation of hydrometeors in updrafts and evaporation in downdrafts. Therefore, microphysics parameterization should also be applied to downdrafts and incorporated in determining the intensity of downdrafts.

Although comprehensive cloud microphysics schemes have been used for many years to represent large-scale clouds in regional and global atmospheric and climate models, the use of schemes of similar complexity for convective clouds is relatively new. Since convective detrainment of cloud water and ice plays an important role in anvil cloud formation and evolution, parameterizing convective cloud microphysical processes opens the door for new lines of research in climate change, including aerosol effect on convection invigoration and aerosol indirect effect. The aerosol effects on convection have been explored extensively in recent years, both observationally and numerically using cloud-resolving models (Li et al. 2011; Fan et al. 2012; also see Tao et al. 2012 for a review). With the development of two-moment convective microphysics schemes, it is expected that more GCM investigations of aerosol effects on convection will emerge.

Acknowledgments

This work was supported by the Office of Science (BER), U.S. Department of Energy under Grant DE-SC0008880, the U.S. National Oceanic and Atmospheric Administration Grants NA08OAR4320894 and NA11OAR431098, and the National Science Foundation Grant AGS-1015964. The authors thank two anonymous reviewers and Dr. Kuan-Man Xu for their valuable comments that helped improve the presentation of the paper.

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