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  • Xu, K.-M., and D. A. Randall, 1996: Explicit simulation of cumulus ensembles with the GATE Phase III data: Comparison with observations. J. Atmos. Sci.,53, 3710–3736.

  • View in gallery

    Growth rates of rain and snow as given by (14) as a function of the precipitation mixing ratio qp. The thin solid line shows the rate of accretion of the cloud water by the rain field (assuming qc = 1 g kg−1), the thick solid line shows the rate of evaporation of rain for the ambient temperature of 288 K and the relative humidity of 80%, the thin dashed line shows the rate of accretion of the cloud ice field by snow (assuming qc = 1 g kg−1), and the rate of depositional growth of the snow field assuming ambient temperature of 258 K and water-saturated conditions is shown by the thick dashed line.

  • View in gallery

    Terminal velocity of rain and snow field as given by (17) as a function of the precipitation mixing ratio qp.

  • View in gallery

    Streamfunction pattern [thin lines, solid (dashed) for positive (negative) values] used in the kinamatic test. Contour interval is 104 kg m−1 s−1. Corresponding vertical velocity field is also shown using thick contours with contour interval of 2 m s−1.

  • View in gallery

    Isolines of the condensate fields for the experiment REFER. The panels show (a) cloud water, (b) rain, (c) ice A, and (d) ice B mixing ratios with contour intervals of (a) 0.2 g kg−1, (b, c) 1.0 g kg−1, and (d) 2.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

  • View in gallery

    Isolines of the condensate fields for the experiment WRAIN. The panels show (a) cloud water and (b) rain mixing ratios with contour intervals of (a) 0.2 g kg−1 and (b) 1.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

  • View in gallery

    Isolines of the condensate fields for the experiment SIMP1. The panels show (a) cloud condensate and (b) precipitation mixing ratios with contour intervals of (a) 0.2 g kg−1 and (b) 1.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

  • View in gallery

    Distribution of the surface precipitation intensity in mm h−1 across the domain at time t = 4 h for the simulation REFER, SIMP1, and WRAIN. Precipitation rates smaller than 0.01 mm h−1 are not shown.

  • View in gallery

    Profiles of the 7-day-mean difference between domain-averaged relative humidity for all four experiments and the observations.

  • View in gallery

    Profiles of 7-day-mean domain-averaged condensate mixing ratios for all four experiments. Panel (a) shows averaged mixing ratios for the cloud water, rain, and the two classes of ice for the experiment REFER; panel (c) shows cloud water and rain mixing ratios for the experiment WRAIN; panels (c) and (d) show cloud condensate and precipitation mixing ratios for experiments SIMP1 and SIMP2.

  • View in gallery

    Profiles of the 7-day-mean cloud fractions for the experiments REFER, SIMP1, SIMP2, and WRAIN.

  • View in gallery

    Profiles of the 7-day-mean domain-average temperature tendencies due to radiative fluxes for the experiments REFER, SIMP1, SIMP2, and WRAIN.

  • View in gallery

    Snapshots of the water vapor mixing ratio and the total condensate at day 54.00 for the Walker-like circulation simulation. Water vapor mixing ratio is plotted using a decimal-logarithmic scale with three contours per decade. Only one contour (0.1 g kg−1) is shown for the condensate field. The bottom panel shows the prescribed SST spatial distribution.

  • View in gallery

    Hovmöller (x–t) diagram of the surface precipitation rate for the Walker-like circulation simulation. Precipitation intensity larger than 0.2 and 5 mm h−1 is shown using light and dark shading, respectively.

  • View in gallery

    Evolution of the domain-averaged column dry enthalpy (plotted as a difference from its initial value) and its sources and sinks (a) and the domain-averaged precipitable water (plotted as a difference from its initial value) and its sources and sinks (b) for the Walker-like circulation simulation. Note that 100 W m−2 = 8.64 MJ m−2 day−1 = 3.46 kg m−2 day−1.

  • View in gallery

    Averaged potential temperature profiles for the ascending and descending branches and averaged horizontal wind profile associated with the Walker-like circulation calculated according to (22). The potential temperature profile for the descending branch has been shifted by 5 K, that is, the distance between small ticks on the temperature scale.

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Toward Cloud Resolving Modeling of Large-Scale Tropical Circulations: A Simple Cloud Microphysics Parameterization

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  • 1 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

This paper discusses cloud microphysical processes essential for the large-scale tropical circulations and the tropical climate, as well as the strategy to include them in large-scale models that resolve cloud dynamics. The emphasis is on the ice microphysics, which traditional cloud models consider in a fairly complex manner and where a simplified approach is desirable. An extension of the classical warm rain bulk parameterization is presented. The proposed scheme retains simplicity of the warm rain parameterization (e.g., only two classes of condensed water are considered) but introduces two important modifications for temperatures well below freezing:1) the saturation conditions are prescribed based on saturation with respect to ice, not water; and 2) growth characteristics and terminal velocities of precipitation particles are representative for ice particles, not raindrops. Numerical tests suggest that, despite its simplicity, the parameterization is able to capture essential aspects of the cloud microphysics important for the interaction between convection and the large-scale environment. As an example of the application of this parameterization, preliminary results of the two-dimensional cloud-resolving simulation of a Walker-like circulation are presented.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000.

Email: grabow@ncar.ucar.edu

Abstract

This paper discusses cloud microphysical processes essential for the large-scale tropical circulations and the tropical climate, as well as the strategy to include them in large-scale models that resolve cloud dynamics. The emphasis is on the ice microphysics, which traditional cloud models consider in a fairly complex manner and where a simplified approach is desirable. An extension of the classical warm rain bulk parameterization is presented. The proposed scheme retains simplicity of the warm rain parameterization (e.g., only two classes of condensed water are considered) but introduces two important modifications for temperatures well below freezing:1) the saturation conditions are prescribed based on saturation with respect to ice, not water; and 2) growth characteristics and terminal velocities of precipitation particles are representative for ice particles, not raindrops. Numerical tests suggest that, despite its simplicity, the parameterization is able to capture essential aspects of the cloud microphysics important for the interaction between convection and the large-scale environment. As an example of the application of this parameterization, preliminary results of the two-dimensional cloud-resolving simulation of a Walker-like circulation are presented.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000.

Email: grabow@ncar.ucar.edu

1. Introduction

Interaction of tropical convection with large-scale circulations is a key aspect of tropical dynamics and climate. It remains a controversial issue despite a few decades of vigorous research in this area (see the recent review by Emanuel et al. 1994). The reason for this situation is twofold. First, although it is possible to obtain useful insights into many aspects of the large-scale atmospheric dynamics using analytical techniques, the situation is dramatically different for the atmospheric moist convection. Convection, and moist convection in particular, is difficult to treat analytically because it involves fully nonlinear fluid dynamics. Second, the interaction of convection and the large-scale flow spans a wide range of temporal and spatial scales that until very recently were impossible to consider simultaneously in numerical models.

With the increase of computer power and an appropriate experimental design, it has recently become possible to model tropical convection on temporal and spatial scales relevant for the tropical climate. The cumulus ensemble modeling approach (pioneered almost two decades ago; e.g., Soong and Ogura 1980; Soong and Tao 1980), now referred to as the cloud resolving modeling (CRM) approach, has been recently applied to study tropical convection in large domains and for extended time periods (i.e., several weeks) using realistic (e.g., evolving) large-scale conditions (see Grabowski et al. 1996b for a detailed discussion of the approach). The large-scale conditions have been taken from sounding observations made either in GATE1 (e.g., Xu and Randall 1996; Grabowski et al. 1996b), or in TOGA COARE2 field campaigns (Wu et al. 1998). Unprecedented three-dimensional modeling using the same approach was also undertaken (Grabowski et al. 1998). These studies, however, considered only the cloud-scale response to the large-scale flow and feedback into the large scales was not allowed. It follows that although useful as far as development and testing of cumulus parameterization is concerned, these simulations cannot address essential aspects of the mutual interaction between convection and the large-scale dynamics.

Using parallel processing technology, simulations of the interaction between cloud-scale and large-scale circulations, at least in idealized setups, are now possible. This paper presents an example of a cloud resolving simulation that considers explicitly both the large-scale and cloud-scale circulations over a period of two months in a two-dimensional domain spanning 4000 km in the horizontal direction with a resolution of about 2 km. For such computationally intensive simulations, a careful model design is required as far as cloud physics is concerned.

Cloud modeling has been experiencing a rapid growth over the last two decades. State-of-the-art cloud models include sophisticated warm rain and ice schemes with several prognostic variables, for example, either mixing ratios (Hsie et al. 1980; Lin et al. 1983; Rutledge and Hobbs 1983) or mixing ratios and number concentrations (Ferrier 1994) for various types of cloud and precipitation particles. Such complex schemes are likely a necessity as far as single-case short (i.e., a few hours) process-oriented cloud simulations are concerned (e.g., McCumber et al. 1991). It is questionable, however, if such detailed approaches are required as far as the interaction between convection and the large-scale dynamics is concerned. We propose herein a simple scheme to be used in cloud resolving simulations of large-scale tropical circulations. The proposed scheme is an extension of the bulk warm rain scheme and it attempts to mimic essential aspects of the cloud physics at subfreezing temperatures without including additional water field variables. As modeling results will illustrate, the scheme does provide results comparable with a scheme that considers details of the development, growth, and fallout of ice particles.

The next section reviews cloud processes essential for the tropical climate. The discussion provides a rationale for the parameterization presented in section 3. Section 4 shows results of the application of the scheme to two groups of numerical tests. In the first group, development of precipitation in the prescribed two-dimensional flow (similar to the squall line circulation) is simulated. The second group of experiments simulates cloud systems from the 7-day period of GATE Phase III (cf. Grabowski et al. 1996b; Grabowski et al. 1998). Comparisons between model results using the proposed scheme and using either the traditional warm rain approach or the more comprehensive ice scheme are presented in both groups. Section 5 presents preliminary results of a pilot study in which the proposed scheme is applied to the two-dimensional cloud resolving modeling of a Walker-like circulation. Concluding remarks are presented in section 6.

2. Cloud physics and tropical large-scale circulations

There are three fundamental aspects of tropical convection essential for the tropical climate. They are briefly discussed below and a rationale to include them in as simple parameterization as possible is discussed.

a. Latent heating

Latent heating due to phase changes of water is a source of positive buoyancy, which drives convective updrafts. The compensating subsidence in clear-sky areas is the dominant mechanism balancing the radiative cooling of the tropical atmosphere (results of the simulation of the Walker-like circulation reported in section 5 can be used to illustrate this point). The latent heating can be easily represented in the case of warm clouds (i.e., clouds without the ice phase). With the abundance of cloud condensation nuclei and low supersaturations, the assumption that warm clouds are exactly at water saturation is fairly accurate. The situation becomes more complex once ice physics has to be considered. Because ice nuclei are scarce and homogeneous ice nucleation is possible only for temperatures colder than about −40°C, conditions inside ice-bearing clouds can vary between saturation with respect to water and saturation with respect to ice, depending on the balance between water vapor available for growth (e.g., due to the adiabatic cooling associated with the rising motion) and actual growth of ice cloud and precipitation particles. However, since the number of ice nuclei strongly increases with decreasing temperatures, it is likely that the typical conditions inside cold clouds (say, colder than −20°C) should not be far from the saturation with respect to ice, maybe with the exception of cores of convective drafts. Thus, as far as formation of the cloud condensate is concerned, one may attempt to extend the classical warm rain approach to cold clouds, but the saturated conditions should be defined with respect to the saturation with respect to ice, not water.

Since in the Tropics ice particles never reach the ocean surface, the roughly 15% difference between latent heats of condensation and sublimation (i.e., the difference between the latent heat associated with formation of a water droplet and an ice crystal) is recovered when ice particles melt during their fall through the melting layer. It follows that, as a first approximation, one can consider latent heating of condensation alone as long as the total latent heating of the atmospheric column is the primary focus.

b. Formation of precipitation

As far as large-scale water budget is concerned, the cloud condensate has to fall out as precipitation or the atmosphere would become saturated due to continuous surface evaporation. In an approach proposed by Kessler (1969), a nonsedimenting cloud condensate is formed first and precipitation development follows. An extension of this classical approach to account for essential aspects of the ice physics is proposed. The parameterization focuses on precipitation in the form of slowly falling ice (i.e., snow) for the reason described below.

c. Effects of clouds on radiative fluxes

Clouds affect radiative processes by reflecting solar energy back to space and by influencing longwave (thermal) radiant energy through the net cloud-base absorption and cloud-top emission. The critical factors are the mass concentration of the particles (which define cloud optical depth) and their shapes and sizes (which directly affect optical properties of a single cloud particle). Since precipitation rate is a product of the mass concentration of precipitation particles and their mean sedimentation velocity, microphysical properties of condensate particles (which directly affect sedimentation velocity) become of primary importance. For instance, with low terminal velocities as compared to water drops with the same mass, ice particles must occur in higher mass concentrations to account for the same precipitation rate. This will be illustrated by model results in section 4. This aspect is important for the cloud–radiation interactions because the high mixing ratios of the upper-tropospheric condensate (e.g., inside outflow anvils of deep convective clouds) are essential for radiative processes. For the same reason, larger spatial dimensions of ice particles compared to the water droplets with the same mass are important. It follows that assuming particle sizes and terminal velocities typical for solid precipitation particles (i.e., ice crystals) is essential as far as the interaction of upper-tropospheric clouds with radiation is concerned.

The problem is further complicated, however, because there are many forms of ice particles associated with the tropical deep convection (e.g., Heymsfield and McFarquhar 1996 and references therein). The range covers single crystals grown by vapor deposition, aggregates of single crystals, rimed particles and their aggregates, heavily rimed particles, and graupel. However, due to their larger terminal velocities, the contribution of heavily rimed particles and graupel is limited to the area close to convective drafts, which typically cover a small fraction of a convective system. It follows that slowly falling ice (i.e., snow), a main constituent of stratiform anvil clouds, is of primary importance as far cloud–radiation interactions are concerned. For that reason, the parameterization presented herein focuses on formation and fallout of snow particles.

3. The parameterization

The general strategy is to consider only two classes of the condensed water: the cloud condensate and the precipitation. The cloud condensate represents either cloud water or cloud ice, depending on the temperature. Cloud condensate is assumed to follow the motion of the air (i.e., no sedimentation). The cloud condensate is formed to avoid supersaturation and the condensation rate is determined by the condition that water vapor remains at saturation in the presence of cloud condensate (cf. Grabowski and Smolarkiewicz 1990). The condensate instantaneously evaporates in the undersaturated conditions. The saturated conditions are defined using the saturated water vapor mixing ratio with respect to the plane water for temperatures above the threshold temperature Tw and using the saturated vapor mixing ratio with respect to the plane ice for temperatures below the threshold temperature Ti. For temperatures between Tw and Ti, the saturated mixing ratio is defined using a linear combination of the water and ice saturated mixing ratios to allow for a smooth transition between warm (i.e., water saturated) and very cold (ice saturated) regimes.

A similar strategy is applied for the precipitation, which is assumed in the form of rain for temperatures warmer than Tw and in the form of snow for temperatures colder than Ti. For temperatures between Tw and Ti, precipitation is assumed to be a mixture of rain and snow, with the relative contribution of rain linearly decreasing with the temperature approaching Ti. Precipitation development and further growth/evaporation are calculated using formulas appropriate for rain or for snow depending on the temperature. The total growth is calculated as a sum of growth rates for both the rain part of the precipitation field and the snow part. Precipitation is initiated from cloud condensate and either grows by deposition of water vapor and accretion of cloud condensate inside clouds or evaporates/resublimates outside clouds. As discussed in the previous section, melting is not considered and the latent heating is calculated using the latent heat of condensation throughout the depth of the entire troposphere.

Conservation equations for the thermodynamic variables in the anelastic framework considered are as follows:
i1520-0469-55-21-3283-e1a
Here, θ is the potential temperature; qυ, qc, and qp are the water vapor, cloud-condensate, and precipitation-water mixing ratios, respectively; u is the air velocity;the subscripts o and e refer to profiles of the anelastic reference state and the environment, respectively; the D terms symbolize subgrid-scale turbulence parameterization terms as well as gravity wave absorbers employed in the vicinity of the model boundaries; Lυ, cp, and VT denote the latent heat of condensation, specific heat at constant pressure, and mass-weighted terminal velocity of precipitation particles, respectively; and k is the unit vector in the vertical direction. The sources on the right-hand side of (1a)–(1d) describe formation of cloud condensate from water vapor (CON), autoconversion of cloud condensate into precipitation (AUT), accretion of cloud condensate by precipitation (ACC), and source (sink) of precipitation due to deposition (evaporation) of water vapor on (from) precipitation particles (DEP).
The bulk condensation rate CON is calculated as discussed in section 3a of Grabowski and Smolarkiewicz (1990). It requires provision of the saturated water vapor mixing ratio, which is approximated as
i1520-0469-55-21-3283-e2
(see discussion in section 7 and appendix A of Lipps and Hemler 1982), where ε = Rd/Rυ (Rd and Rυ are gas constants for the dry air and for the water vapor, respectively), pe is the environmental pressure profile, and es is the saturated water vapor pressure given either by
i1520-0469-55-21-3283-e3a
for the saturation over water or
i1520-0469-55-21-3283-e3b
for the saturation over ice, where Ls denotes the latent heat of sublimation, T = θ(pe/poo)Rd/cp, poo = 105 Pa, eoo = 611 Pa, and Too = 273.16 K. The values of latent heats (Lυ = 2.53 × 106 J kg−1, Ls = 2.84 × 106 J kg−1), assumed constant in (3), have been selected to provide as accurate values as possible of the saturated water vapor pressure over water and ice and their ratio over a wide range of temperatures.
The precipitation particles are assumed to be distributed according to the Marshall–Palmer size distribution
nDNoλD
where D is the particle diameter (i.e., either drop diameter or a diameter of the sphere circumscribing the ice crystal; see Grabowski 1988) and No is a (fixed) parameter of the distribution. The slope of the distribution λ depends on the mixing ratio of precipitation particles.
Precipitation particles are assumed to obey the mass–diameter and sedimentation velocity–diameter relationships in the form (cf. Grabowski 1988, 1989):
i1520-0469-55-21-3283-e5a
For precipitation in the form of rain, coefficients in (5) are given by (Kessler 1969)
i1520-0469-55-21-3283-e6a
(where ρw = 103 kg m−3 is the water density), and for snow particles the coefficients are (Grabowski 1988)
a−2bcd
The definition of the precipitation mixing ratio together with (4) and (5a) gives
i1520-0469-55-21-3283-e7
The autoconversion term AUT, an initial source of precipitation, is parameterized according to Berry (1968) as applied by Simpson and Wiggert (1969, section 3) for the rain, and similarly to Hsie et al. (1980) and Lin et al. (1983) for the case of snow. For the case of rain, the autoconversion term is given by
i1520-0469-55-21-3283-e8a
where
ψ3ρoqc
is the density of precipitation water expressed in grams per cubic meter, Nd is the concentration of cloud droplets (expressed in number per cubic centimeter), and Dd is the relative dispersion of cloud droplet population, that is, the ratio between standard deviation of cloud droplet spectrum and the mean droplet radius. Simpson and Wiggert (1969) suggested that the relative dispersion changes from 0.366 for maritime clouds with Nd = 50 cm−3 to 0.146 for continental clouds with Nd = 2000 cm−3. The relative dispersion used in the model is calculated from the prescribed Nd and the two extreme values using the relation
i1520-0469-55-21-3283-e9
which gives the relative dispersion of 0.33, 0.26, and 0.19 for droplet concentrations of 100, 300, and 1000 cm−3. For the snow, the autoconversion term is parameterized as
i1520-0469-55-21-3283-e10
where τa is the conversion timescale assumed equal to a time required to grow an ice crystal by diffusion of water vapor in water saturated conditions up to a size of small precipitation particle (mass of 10−9 kg). This timescale is estimated using formulas for ice crystal growth developed by Koenig (1971) and approximated by a simple quadratic function decreasing from τa = 103 s at 0°C to τa = 200 s at −15°C and increasing back to τa = 103 s at −30°C. For even colder temperatures, τa = 103 s is used. Note that when the temperature is between Tw and Ti, qc in (8) and (10) represents either cloud water part or cloud ice part of the cloud condensate, not the entire cloud condensate.
The precipitation growth terms (ACC, DEP) are estimated using characteristics of the particle with the average mass, that is,
i1520-0469-55-21-3283-e11a
where n is the mean concentration of precipitation particles
i1520-0469-55-21-3283-e12
m is the mean mass of a precipitation particle,
i1520-0469-55-21-3283-e13
and (dm/dt)ACC, (dm/dt)DEP are growth rates of the mean particle due to accretion of cloud condensate and deposition of water vapor, respectively. The growth rates are estimated according to (e.g., Grabowski 1988)
i1520-0469-55-21-3283-e14a
where D is the diameter of a particle with average mass [calculated from m using (5a)], E is the collection efficiency, α is the ratio of the effective area of the precipitation particle and πD2/4 (i.e., 1 for raindrops and smaller than 1 for snow), β is a nondimensional factor that depends on precipitation particle geometry (e.g., β = 2 for a sphere, β = π for an infinitely thin circular disc, β ∼ 3 for a thin needle), S = qυ/qυs is the saturation ratio, F is the ventilation factor [F ≈ 0.78 + 0.27R1/2e for raindrops and F ≈ 0.65 + 0.39R1/2e for ice particles, Re = Dυt(D)/ν is the the Reynolds number, ν ≈ 2 × 10−5 m2 s−1 is the kinematic viscosity of air; Pruppacher and Klett (1978)], and G(Te) is the thermodynamic function [Pruppacher and Klett (1978), Eq. (13.28) and (13.71)] approximated as
i1520-0469-55-21-3283-e15
where A = 10−7 kg m−1 s−1 and SI units are assumed in (15). The saturation ratio in (14b) is calculated using the saturated mixing ratio qυs with respect to water for rain and with respect to ice for snow. Such a formulation of the DEP term allows for both source and sink of the snow field depending upon the actual value of the water vapor mixing ratio, but it provides only sink of the rain field due to rain evaporation.
For the three parameters appearing in (14), the values for rain are
Eαβ
and for the ice,
Eαβ

As an illustration, Fig. 1 presents the growth rates for snow and rain as a function of the precipitation mixing ratio qp for different environmental conditions. The plot shows the rate of accretion of the cloud water by the rain field (assuming qc = 1 g kg−1), the rate of evaporation of rain for the ambient temperature of 288 K and the relative humidity of 80%, the rate of accretion of the cloud ice field by snow (again assuming qc = 1 g kg−1), and the rate of depositional growth of the snow field assuming ambient temperature of 258 K and water-saturated conditions.

Finally, the mass-weighted terminal velocity of precipitation particles (VT) calculated using (4) and (5) is given by
i1520-0469-55-21-3283-e17
(17)The terminal velocity is calculated using parameters for rain [i.e., (6a)] for temperatures warmer than Tw and parameters for snow (6b) for temperatures colder than Ti. For intermediate temperatures, the terminal velocity VT is calculated as a linear combination of the values obtained for rain and snow formulation applying appropriate mixing ratios. The density factor that usually appears in mass-weighted terminal velocity formulas is omitted because of the simplicity of the approach. Figure 2 shows terminal velocities of rain and snow as given by (17) as a function of the precipitation mixing ratio qp.

4. Tests of the parameterization

This section presents results of numerical tests performed to compare the scheme with either the simple warm rain scheme or the more comprehensive ice scheme that considers details of formation, growth, and fallout of the ice field.

The more comprehensive treatment of the ice field is based on the work of Koenig and Murray (1976). It is similar to the approach used in the Clark–Hall model (Clark et al. 1996) and applied in simulations discussed in Grabowski et al. (1996b), Grabowski et al. (1998), and Wu et al. (1998). The approach considers two classes of ice, referred to as ice A and ice B. Ice A represents unrimed or lightly rimed ice particles formed by either heterogeneous or homogeneous (for temperatures colder than −40°C) nucleation of ice crystals. Ice A is characterized by fairly low terminal velocities, of the order of 1 m s−1. Ice B, on the other hand, represents heavily rimed particles (e.g., graupel) that originate from the interaction of the rain field with the ice A. Ice B has larger terminal velocities, usually a few meters per second. Typically, ice A is found in anvils generated by deep convection, whereas ice B is associated with strong updrafts of convective cells.

Only the conservation equations for mixing ratios are considered for these two classes of ice. This is different than the Clark–Hall model, in which both the mixing ratio and the number concentration of ice particles are considered. The approach developed by McFarquhar and Heymsfield (1997) is applied for ice A, namely, ice crystal size distributions for tropical cirrus clouds (e.g., outflow anvils) are parameterized based on aircraft in situ measurements. This parameterization provides ice size distributions (and thus average masses, terminal velocities, growth characteristics, etc.) based on the ice mixing ratio and the local temperature. The approach of Rutledge and Hobbs (1983) is used for ice B, which assumes distribution of graupel particles according to the Marshall–Palmer size distribution. Once average properties of the ice field are known, growth of either ice A or ice B is represented by the parameterization developed by Koenig and Murray (1976). It is important to point out that in this approach the local conditions inside ice-bearing clouds are explicitly determined by the balance between the growth of the ice field and the availability of water vapor. This is dramatically different from the simplified approach proposed in this paper in which these conditions are prescribed by the in-cloud temperature alone.

In addition, the more comprehensive approach applies accurate formulation for the saturated water vapor mixing ratio. Rather than using formulas similar to (3), tables of the saturated vapor pressure with respect to water and ice are created during model start-up using accurate (but expensive) formulas discussed in Flatau et al. (1992). The tables provide saturated vapor pressure using the temperature interval of 0.1 K. Linear interpolation using the tabulated values is applied during model run to deduce the saturated vapor pressure for a given temperature.

The tests performed include 1) kinematic tests using a prescribed flow, that is, similar to tests discussed in Szumowski et al. (1998); and 2) dynamic model tests in which cloud systems from Phase III of GATE are simulated. In each group, four numerical experiments are performed (see Table 1). The first experiment (called REFER) uses the two-class ice parameterization briefly described above. The second experiment (referred to as WRAIN) considers only the warm rain parameterization as described in Grabowski and Smolarkiewicz (1996) with the exception of the autoconversion term, which has been modified to use Berry’s method as discussed in the previous section. The last two experiments (SIMP1 and SIMP2) apply the approach proposed in this paper with different choices of the threshold temperatures. The experiment SIMP1 uses cold threshold temperatures of Tw = −5°C and Ti = −20°C. The experiment SIMP2 assumes warm thresholds: Tw = 0°C and Ti = −10°C. It is assumed in all experiments that No = 107 m−4 and the concentration of cloud droplets required in Berry’s autoconversion term is Nd = 200 cm−3.

a. Kinematic tests

In the following tests, (1) is solved using a two-dimensional (x–z) flow prescribed in the computational domain 90 km long and 16 km deep with a uniform grid of size of 500 m in the horizontal and 250 m in the vertical. The flow is prescribed using a steady streamfunction given by
i1520-0469-55-21-3283-e18
where A = 4.8 × 104 kg m−1 s−1, S = 2.5 × 10−2 kg m−3 s−1, ρoo = 1 kg m−3, = min(z, Z), = max[−X, min(X, xxc)], Z = 15 km, X = 10 km, xc = 30 km, and x, z are the coordinates that cover the entire domain [i.e., (0, 90 km) × (0, 16 km)]. The streamfunction provides a narrow zone of the lifting throughout the entire troposphere centered at xc (with corresponding low-level convergence and upper-level divergence) superimposed with the vertical shear of the horizontal wind, which allows mean advection of the rising air from the left to the right of the domain. This streamfunction and the corresponding updraft isopleths are shown in Fig. 3. This is an idealization of airflow in a typical squall line. The velocity components are deduced from (18) as ρou = −∂Ψ/∂z and ρow = ∂Ψ/∂x. The updraft speed reaches a maximum of about 7.5 m s−1 at height of about 7.5 km. The initial temperature and moisture profiles are taken from the GATE dataset used to initiate simulations described in the next section. These profiles are also used on inflow lateral boundaries. Zero-gradient conditions are applied on lateral outflow boundaries. The advection is performed using a monotone MPDATA algorithm (Smolarkiewicz and Grabowski 1990) and a 15-s time step is used in the calculations. The simulations are carried out for 4 h, which is sufficient to established steady-state thermodynamic fields inside the domain.

Figure 4 shows the steady-state condensate fields (cloud water, rain, ice A, and ice B) for the REFER simulation, whereas Figs. 5 and 6 show corresponding fields for the WRAIN and SIMP1 simulations. Plots for the SIMP2 experiment are similar to SIMP1 and are therefore not shown. Figure 4 (REFER experiment) shows a detailed picture of precipitation development. The cloud water is effectively removed by rain in the central part of the updraft. The cloud water reaches maximum in the area of the maximum updraft, although a trace of supercooled water is evident as high as 11 km. The condensation associated with the cooling of the air due to the melting of ice B (i.e., graupel) for x between 40 and 60 km is also apparent. Ice B falls out fairly close to the updraft, whereas ice A, because of its smaller sedimentation velocity, is advected much farther downstream and creates an extensive anvil cloud. Although the position and values of maxima of various condensate fields depend on the parameters used (and will likely change with more sophisticated parameterizations), the general structure described above dominates.

Figure 5 shows cloud water and rain fields for the experiment WRAIN. The surface precipitation is centered in the narrow zone around x = 30 km. Because it is very effectively removed by rain in the lower and middle troposphere, the cloud water reaches maximum in the upper troposphere where the warm rain scheme is not able to convert all the available cloud water into precipitation. As a result, an extensive anvil cloud is formed. However, the rain field that falls out from the upper-tropospheric cloud does not reach the surface.

By using a parameterization described in this paper (case SIMP1, Fig. 6), the situation is changed dramatically. Cloud condensate reaches maximum in the middle troposphere in the area of the updraft. The precipitation field shows two maxima associated with the rain field below the main updraft and the snow field in the upper troposphere at the updraft outflow region (x ≈ 45 km). The sedimentation of the snow field in the anvil is apparent.

The differences in the precipitation development and fallout in all four experiments result in dramatic differences in the surface precipitation pattern, which are shown in Fig. 7. The surface precipitation plot for experiment SIMP2 (not shown) differs only in detail from SIMP1. Both REFER and SIMP1 experiments show extended regions of the stratiform-type precipitation to the right of the peak precipitation associated with the updraft centered around x = 30 km. The stratiform precipitation is missing in the WRAIN experiment.

In summary, the proposed scheme provides a more realistic development and fallout of precipitation than a simple warm rain scheme. As the next section will illustrate, this has significant influence on cloud resolving simulation of GATE cloud systems.

b. Cloud resolving modeling of the GATE Phase III cloud systems

This section presents results of cloud resolving model simulations similar to those discussed in Grabowski et al. (1996b), Grabowski et al. (1998), and Wu et al. (1998). In these simulations, the cloud model is driven by evolving large-scale forcing terms for the temperature and moisture and evolving large-scale horizontal winds in order to generate realizations of cloud systems consistent with large-scale estimates of moisture and temperature budgets.

The dynamical model is the Eulerian variant of the two-time-level, nonhydrostatic anelastic fluid model EULAG of Smolarkiewicz and Margolin (1997) with the moist precipitating thermodynamics applied as discussed in Grabowski and Smolarkiewicz (1996). The model uses a forward-in-time approach for all prognostic variables, that is, momentums and thermodynamic fields, using a monotone version of the transport algorithm MPDATA documented in Smolarkiewicz (1984), Smolarkiewicz and Clark (1986), and Smolarkiewicz and Grabowski (1990). The elliptic pressure equation, which derives from the anelastic “incompressibility” constraint imposed on the discretized momentum equation, is solved (subject to boundary conditions imposed on normal components of the transformed velocity) using the generalized-conjugate-residual method of Eisenstat et al. (1983). Algorithmic details and a discussion of the solver’s performance can be found in Smolarkiewicz and Margolin (1994). The subgrid-scale turbulent transport processes are parameterized using the turbulent kinetic energy approach of Schumann (1991).

The test case is the same 7-day period from Phase III of GATE as in Grabowski et al. (1996b) and Grabowski et al. (1998). The two-dimensional simulations performed are similar to the experiment 2D (two-dimensionsional) described in Grabowski et al. (1998), except for the vertical grid size, which is kept constant at 1/3 km in the current model. The time step is taken as 10 s. The computational domain is 400 km long and 25 km deep. Horizontal grid size is 2 km and periodic lateral boundary conditions are used. A gravity wave absorber is applied in the uppermost 8 km of the computational domain. Surface sensible and latent heat fluxes are calculated using an approach similar to Grabowski et al. (1996b). The radiative tendencies are prescribed using estimates of Cox and Griffith (1979), that is, in the same manner as in Grabowski et al. (1998).

As an initial evaluation of model results using different microphysical parameterizations (REFER, SIMP1, SIMP2, and WRAIN), the differences between model-produced domain-averaged profiles of the temperature, moisture, and relative humidity, and estimates of the observed profiles were considered (i.e., as in Figs. 5 and 7 in either Grabowski et al. 1996b or Grabowski et al. 1998). In general, both the evolution of the differences and the 7-day averaged differences are fairly similar for all four experiments and also similar to these in Grabowski et al. (1996b) and Grabowski et al. (1998). The exception is the WRAIN experiment, which has a consistently colder middle troposphere and a more humid middle and upper troposphere. The latter is related to the much higher cloud cover in the WRAIN simulation (to be shown later) and also to the water-saturated conditions inside clouds due to the warm rain parameterization. This is apparent in the 7-day averaged profiles of the relative humidity difference shown in Fig. 8. The 7-day average precipitable water and averaged density weighted temperature (cf. Sui et al. 1994; Grabowski et al. 1996a) as well as the 7-day average precipitation rate are similar for all four experiments (see Table 2).

Figure 9 presents 7-day averages of the condensate mixing ratios for all four experiments. Figure 9a shows mixing ratios for all four condensate classes for the experiment REFER, whereas Figs. 9b–d present the two classes of the condensate for experiments WRAIN, SIMP1, and SIMP2, respectively. The high values of the upper-tropospheric ice A mixing ratio are apparent in the REFER experiment. This is consistent with the kinematic test results described in the previous section. The scheme proposed in this paper mimics this feature in both the SIMP1 and SIMP2 experiments (Figs. 9c,d), although differences between the REFER scheme and the simplified scheme are apparent. The differences between the SIMP1 and SIMP2 experiments can be attributed to the different temperature thresholds. Note that the upper-tropospheric maximum of the condensate is associated with the precipitation water in the SIMP1 and SIMP2 simulations. The WRAIN simulation, on the other hand, shows dramatically different profiles: the upper-tropospheric maximum is much higher and is associated with the cloud condensate, not precipitation. This is consistent with the kinematic test results and with results presented in McCumber et al. (1991, Fig. 3d).

Figure 10 presents 7-day averaged profiles of the cloud fraction. In this analysis, a grid box is considered cloudy if the local total condensate mixing ratio (i.e., a sum of all the liquid and solid water mixing ratios) exceeds 0.01 g kg−1. Figure 10 shows that the REFER, SIMP1, and SIMP2 simulations generate consistent mean profiles of the cloud fraction. This tendency is also persistent in the 7-day evolution of the profiles (not shown). The cloud fraction profile for the WRAIN experiment, however, shows very high upper-tropospheric values. This is directly related to the high values of the upper-tropospheric condensate in this simulation as shown in Fig. 9.

It is natural to expect that the dramatic differences between WRAIN and the three other experiments have a profound effect on the radiative fluxes. The radiative fluxes were calculated using the Community Climate Model 2 (CCM2) radiative package (Kiehl et al. 1994) and model-generated thermodynamic fields. For the REFER experiment, the input to the radiative transfer model included the cloud water and ice A mixing ratios. Only cloud water was considered in the WRAIN experiment. For SIMP1 and SIMP2 experiments, the cloud condensate (divided into cloud water and cloud ice) and the snow part of the precipitation were used as input to the CCM2 radiation model. In all the cases, effective radii of cloud droplets and ice particles were assumed to be 10 and 30 μm, respectively. The 7-day averaged radiative tendencies are shown in Fig. 11. Radiative tendencies show similar profiles for the REFER, SIMP1, and SIMP2 simulations (and also similar to the profiles shown in Fig. 15 of Grabowski et al. 1998), but dramatically different mid- and upper-tropospheric tendencies for the experiment WRAIN.

Further radiation model results are presented in Table 3. The table shows 7-day averaged values of the outgoing longwave radiation (OLR), net upwelling longwave flux at the surface, top of the atmosphere (TOA) albedo, shortwave flux absorbed at the surface, the net radiative flux divergence (longwave plus shortwave) across the atmosphere, and the net radiative flux at the surface. Dramatic differences between WRAIN and the three other experiments are evident. For instance, the WRAIN experiment shows significant warming of the atmosphere, whereas REFER, SIMP1, and SIMP2 show cooling of almost the same magnitude. Also, the net surface warming due to radiative processes is more than an order of magnitude weaker in the WRAIN experiment. Some differences between the REFER, SIMP1, and SIMP2 experiments do exist as well. It should be pointed out, however, that the significance of the differences between the REFER, SIMP1 and SIMP2 experiments can only be evaluated in simulations applying a fully interactive radiation scheme, that is, when cloud fields have a chance to respond to the differences in radiative heating and cooling rates.

In summary, the proposed scheme (SIMP1 and SIMP2) generates results that are consistent with the more sophisticated microphysical scheme (REFER). Furthermore, all three simulations produce results dramatically different from a simple warm rain scheme applied in the WRAIN experiment. The dramatic failure of the WRAIN scheme is directly related to the high upper-tropospheric mixing ratios for cloud water, both in the kinematic test and in the dynamic tests.

5. Cloud resolving modeling of a Walker-like circulation

The parameterization described in section 3 is applied to the cloud resolving modeling of a Walker-like circulation. A similar problem was considered by Raymond (1994) in the context of the parameterized convection. The 4000 km long and 25 km deep domain is covered with a regular grid with about 1.8 km grid size in the horizontal direction and 1/3 km grid size in the vertical. As in the GATE simulations, a gravity wave absorber is applied in the uppermost 8 km of the domain. The domain is assumed periodic in the horizontal direction and the sea surface temperature (SST) varies according to the sine function with 28°C in the center of the domain and 24°C at the periodic lateral boundaries. Surface fluxes are calculated according to a simple bulk formula,
FϕCdUϕsrfϕz=0
where ϕ is either θ or qυ and the subscript srf depicts the prescribed ocean surface value (taken as either the potential temperature corresponding to the SST for θ or the saturated water vapor mixing ration for the SST and the surface pressure for qυ), whereas ϕz=0 represents model-predicted θ or qυ for the air at the surface, Cd is the drag coefficient taken as 1.0 × 10−3, and U is a measure of the surface wind defined as
Uu2z=0u21/2
to account in a simple way for surface wind gustiness essential for weak surface wind conditions. In (20), uz=0 depicts the model-predicted surface wind, and
i1520-0469-55-21-3283-e21
(21)(where H = 600 m is the assumed height of the boundary layer) is an estimate of the convective velocity scale for the case of U = u∗ in (19).

As in the experiments discussed in the previous section, direct interaction of radiation with model-generated fields is not considered in this pilot experiment. Instead, time-independent cooling is applied across the domain with the linear temperature tendency profile (1.5 K day−1 at the surface, decreasing to about 0.8 K day−1 at 16 km). All microphysical parameters are given as in the experiment SIMP1 of the previous section. The numerical model is a parallel version of the EULAG model used in simulations described in the previous section (Anderson et al. 1997).

The experiment is initialized with a GATE sounding (the same as used to initialize experiments presented in the previous section), homogeneously applied across the entire domain. After a few days, the large-scale Walker-like circulation develops as a result of stronger convection in the center of the domain (i.e., over the warm SSTs). Convection near the lateral boundaries (i.e., over the cold SSTs) is suppressed by the descending branch of the circulation. During the 60-day simulation the moisture and temperature fields approach quasi equilibrium, defined here as a balance between all the sources and sinks of energy and water, that is, latent heating, prescribed cooling, and surface sensible heat flux for the temperature, as well as precipitation and evaporation for the water. The long quasi-equilibrium timescale is likely due to the slow subsidence of the upper-tropospheric air. To balance the prescribed cooling of the domain requires an averaged descent of about 100 m day−1 in the descending branch of the circulation; that is, it takes about one month for the air to descend 3 km.

Figure 12 shows snapshots of the water vapor and the total condensate fields for the end of day 54 to illustrate the general features of the simulation. Deep convective clouds are evident in the center of the domain. A descending branch of the Walker circulation is extremly dry and it is separated from the boundary layer by strong moisture inversion. No stratocumulus deck is produced, which may be an artifact associated with the low vertical resolution that is not sufficient to adequately resolve the vertical structure of the boundary layer. A Hovmöller (x–t) diagram of the surface precipitation rate for the entire experiment is shown in Fig. 13. Individual convective systems can easily be identified. They drift toward the colder waters, that is, in the direction of incoming low-level branch of the Walker circulation.

The evolution of the domain-averaged column dry enthalpy ∫ ρocpT dz (in MJ m−2) and the precipitable water ∫ ρoqυ dz (in kg m−2), together with sources and sinks of the dry enthalpy and the water are shown in Fig. 14, illustrating the long timescale associated with the approach to quasi equilibrium. Both moisture and enthalpy budgets show short timescale variations with a period of about 2 days. These variations are especially apparent in the second half of the experiment and are characterized by strong negative correlations between perturbations of temperature and moisture, as well as between perturbations of precipitation and surface latent heat flux. This behavior is reminiscent of the quasi-two-day wave that is a pronounced feature of the tropical convection (e.g., Takayabu et al. 1996). Takayabu et al. associated the presence of the quasi-two-day oscillations with the time required by the lower troposphere to recover from the cooling and drying effects of the deep convection, but there may be other explanations.

Finally, Fig. 15 shows the time-averaged profiles of the potential temperature in the ascending (θA) and descending (θD) branches of the Walker-like circulation and the profile uW of the horizontal flow in the area of the SST gradient to document the strength of the Walker-like circulation. Noting that the domain spans horizontal distance from −2000 to 2000 km (e.g., Fig. 12), the profiles are calculated as
i1520-0469-55-21-3283-e22a
every hour for the last 15 days of the experiment and later they are averaged over the 15 days to arrive at the final profiles shown in Fig. 15.

The temperature profiles show typical features of a tropical sounding with the stronger stability in the lower troposphere and weaker stability in the upper troposphere. The potential temperature profiles in the ascending and descending branches differ little: the descending branch profile is about 1 K warmer than the ascending branch profile in the lower troposphere and about 1 K colder in the upper troposphere. The well-mixed boundary layer is apparent under the descending branch. The profile of the Walker cell flow has two maxima of the flow toward the warm waters (i.e., to the right at the left part of the domain and to the left at the right part). These maxima are located at the surface and at a height of about 7 km. A single maximum associated with the return flow is present at about 13 km. The midtropospheric peak of the Walker-like circulation is likely associated with the source level of cloud downdrafts of deep convection in the center of the domain. The midtropospheric maximum of the circulation is also apparent in one of the experiments reported in Raymond (1994, Fig. 4).

6. Conclusions

This paper attempts to isolate fundamental effects of cloud microphysical processes on large-scale tropical circulations and climate. It is argued that these effects include 1) release of latent heat associated with formation of cloud condensate, 2) formation of precipitation, and 3) development of upper-tropospheric anvil clouds essential for cloud–radiation interaction. As far as the role of clouds in large-scale circulations is concerned, these effects can be included in cloud resolving models of tropical large-scale circulations using a much simpler approach than techniques used in current cloud models designed to study details of development and evolution of individual clouds. A simple cloud microphysical scheme is proposed.

The proposed scheme is an extension of the bulk parameterization of moist precipitating thermodynamics proposed by Kessler (1969). It considers just two classes of condensed water: cloud condensate and precipitation. They are assumed in the form of liquid (cloud water, rain) or solid (cloud ice, snow) depending on the temperature. Clouds are always at vapor saturation defined as either saturation with respect to water or ice, depending on the temperature. Tests using a prescribed flow similar to a squall line circulation expose limitations of the proposed scheme by comparing it to the warm rain scheme as well as to a fairly sophisticated ice scheme, which considers details of ice development, growth, and fallout. In dynamic model tests similar to simulations described in Grabowski et al. (1996b) and Grabowski et al. (1998), the proposed scheme produces results consistent with the use of the sophisticated scheme but dramatically different than a simulation that uses a simple warm rain scheme. The test results are not sensitive to the selection of the temperature thresholds that define transitions between the warm rain physics and the ice physics. One can argue that these thresholds are the most significant parameters of the proposed scheme and that lack of sensitivity demonstrates its strength.

The scheme is only slightly more complicated than a classical warm rain scheme because it applies the same number of the condensed water variables (two) and the same number of the water transfer processes (four). This is quite different from more sophisticated microphysical schemes in which the number of processes increases dramatically as one increases the number of variables representing condensed water to four (cloud water, rain, and two classes of ice) or five (cloud water, rain, and three classes of ice). Coding and testing sophisticated schemes that consider many transfer mechanisms of water substance is tedious and time consuming. From this perspective, the simple scheme proposed in this paper is very appealing.

The proposed scheme is likely too simplistic for any detailed simulation of single cloud dynamics because different modes of growth, evaporation and resublimation, and melting of the cloud and precipitation particles are likely very important for single cloud development and evolution (e.g., McCumber et al. 1991). However, our goal was to design a scheme that could be used in climate-related problems when not a single cloud but rather a population (or ensemble) of clouds was considered and where, because of computational limitations, as simple a scheme as possible was desirable. One can argue that the proposed scheme might not be sufficient in the long run, and that ultimately more sophisticated schemes will be required, especially when details of cloud–radiation interactions are considered. Although this might be the case, the proposed scheme does provide a good starting point as documented by modeling results presented in this paper.

As an example of the application of the scheme to the problem of convection–large-scale interaction, the scheme is applied to the cloud resolving simulation of the Walker-like circulation. Certain large-scale features produced by the model (some of them discussed in the previous section) are similar to results produced by the model of Raymond (1994), which used a parameterization of atmospheric moist convection. At the same time, however, the explicitly resolved convection displayed pronounced quasi two-day oscillations that have been observed in the Tropics (Takayabu et al. 1996). We are in the process of analyzing similar simulations using different parameters for the microphysical parameterization in order to address the issue of the role of cloud microphysics in various aspects of the Walker cell climate. Simulations involving an interactive radiative scheme and more accurate representations of the surface fluxes are being performed as well. We will report on results of these simulations in forthcoming publications.

Acknowledgments

Numerical experiments were performed on NCAR’s CRAY YMP, J90, and T3D supercomputers. Comments on the manuscript by Greg McFarquhar, Mitch Moncrieff, Piotr Smolarkiewicz, Xiaoqing Wu, and Jun-Ichi Yano are acknowledged, as is the editorial assistance of Jim Pasquotto. This work is supported by NCAR’s Clouds in Climate Program (CCP). The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the NSF.

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Fig. 1.
Fig. 1.

Growth rates of rain and snow as given by (14) as a function of the precipitation mixing ratio qp. The thin solid line shows the rate of accretion of the cloud water by the rain field (assuming qc = 1 g kg−1), the thick solid line shows the rate of evaporation of rain for the ambient temperature of 288 K and the relative humidity of 80%, the thin dashed line shows the rate of accretion of the cloud ice field by snow (assuming qc = 1 g kg−1), and the rate of depositional growth of the snow field assuming ambient temperature of 258 K and water-saturated conditions is shown by the thick dashed line.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 2.
Fig. 2.

Terminal velocity of rain and snow field as given by (17) as a function of the precipitation mixing ratio qp.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 3.
Fig. 3.

Streamfunction pattern [thin lines, solid (dashed) for positive (negative) values] used in the kinamatic test. Contour interval is 104 kg m−1 s−1. Corresponding vertical velocity field is also shown using thick contours with contour interval of 2 m s−1.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 4.
Fig. 4.

Isolines of the condensate fields for the experiment REFER. The panels show (a) cloud water, (b) rain, (c) ice A, and (d) ice B mixing ratios with contour intervals of (a) 0.2 g kg−1, (b, c) 1.0 g kg−1, and (d) 2.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 5.
Fig. 5.

Isolines of the condensate fields for the experiment WRAIN. The panels show (a) cloud water and (b) rain mixing ratios with contour intervals of (a) 0.2 g kg−1 and (b) 1.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 6.
Fig. 6.

Isolines of the condensate fields for the experiment SIMP1. The panels show (a) cloud condensate and (b) precipitation mixing ratios with contour intervals of (a) 0.2 g kg−1 and (b) 1.0 g kg−1. The dashed contours are for mixing ratios of 0.01 g kg−1.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 7.
Fig. 7.

Distribution of the surface precipitation intensity in mm h−1 across the domain at time t = 4 h for the simulation REFER, SIMP1, and WRAIN. Precipitation rates smaller than 0.01 mm h−1 are not shown.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 8.
Fig. 8.

Profiles of the 7-day-mean difference between domain-averaged relative humidity for all four experiments and the observations.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 9.
Fig. 9.

Profiles of 7-day-mean domain-averaged condensate mixing ratios for all four experiments. Panel (a) shows averaged mixing ratios for the cloud water, rain, and the two classes of ice for the experiment REFER; panel (c) shows cloud water and rain mixing ratios for the experiment WRAIN; panels (c) and (d) show cloud condensate and precipitation mixing ratios for experiments SIMP1 and SIMP2.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 10.
Fig. 10.

Profiles of the 7-day-mean cloud fractions for the experiments REFER, SIMP1, SIMP2, and WRAIN.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 11.
Fig. 11.

Profiles of the 7-day-mean domain-average temperature tendencies due to radiative fluxes for the experiments REFER, SIMP1, SIMP2, and WRAIN.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 12.
Fig. 12.

Snapshots of the water vapor mixing ratio and the total condensate at day 54.00 for the Walker-like circulation simulation. Water vapor mixing ratio is plotted using a decimal-logarithmic scale with three contours per decade. Only one contour (0.1 g kg−1) is shown for the condensate field. The bottom panel shows the prescribed SST spatial distribution.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 13.
Fig. 13.

Hovmöller (x–t) diagram of the surface precipitation rate for the Walker-like circulation simulation. Precipitation intensity larger than 0.2 and 5 mm h−1 is shown using light and dark shading, respectively.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 14.
Fig. 14.

Evolution of the domain-averaged column dry enthalpy (plotted as a difference from its initial value) and its sources and sinks (a) and the domain-averaged precipitable water (plotted as a difference from its initial value) and its sources and sinks (b) for the Walker-like circulation simulation. Note that 100 W m−2 = 8.64 MJ m−2 day−1 = 3.46 kg m−2 day−1.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Fig. 15.
Fig. 15.

Averaged potential temperature profiles for the ascending and descending branches and averaged horizontal wind profile associated with the Walker-like circulation calculated according to (22). The potential temperature profile for the descending branch has been shifted by 5 K, that is, the distance between small ticks on the temperature scale.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3283:TCRMOL>2.0.CO;2

Table 1.

Numerical tests performed using the kinematic setup and the GATE setup. The table shows experiment acronym, a brief description, and a comparison of CPU time based on single processor Cray J90 run with the time for the REFER experiment taken as 1.

Table 1.
Table 2.

Seven-day-mean values of the domain-averaged precipitation rate, density weighted temperature, and the precipitable water for all four experiments using the GATE setup.

Table 2.
Table 3.

Seven-day-mean values of the OLR, surface net longwave flux, TOA albedo, shortwave flux absorbed at the surface, net (i.e., shortwave plus longwave) flux divergence across the atmosphere, and the net radiative flux flux at the surface for all four experiments using the GATE setup. The 7-day-mean insolation is 433 W m−2. Cosines of the zenith angle are used as weights to calculate the mean albedo.

Table 3.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

1

GATE [Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment] was conducted in the tropical eastern Atlantic in summer 1974.

2

TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment) was conducted in the tropical western Pacific in winter 1992/93.

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