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We use 3-D cloud-resolving model (CRM) simulations of two mesoscale convective systems at mid-latitudes and a simple statistical ensemble method to diagnose the scale dependency of convective momentum transport (CMT) and CMT-related properties, and evaluate a parameterization scheme for convection-induced pressure gradient (CIPG) developed by Gregory et al. (GKI97). GKI97 relates CIPG to a constant coefficient multiplied by mass flux and vertical mean wind shear. CRM results show that mass fluxes and CMT exhibit strong scale dependency in temporal evolution and vertical structure. The prevalent understandings of CMT characteristics in terms of upgradient/downgradient transport are applicable to updrafts but not downdrafts across a wide range of grid spacings (4-512 km). For the small-to-median grid spacings (4~64 km), GKI97 reproduces some aspects of CIPG scale dependency except for underestimating the variations of CIPG as grid spacing decreases. However, for large grid spacings (128~512 km), GKI97 might even less adequately parameterize CIPG because it omits the contribution from either the nonlinear shear or buoyancy forcings. Further diagnosis of CRM results suggests that inclusion of nonlinear shear forcing in GKI97 is needed for the large grid spacings, and use of the three-updraft and one downdraft approach proposed in an earlier study may help a modified GKI97 capture more variations of CIPG as grid spacing decreases for the small-to-median grid spacings. Further, the optimal coefficients used in GKI97 seems insensitive to grid spacings, but they might be different for updrafts and downdrafts, for different MCS types, and for zonal and meridional components.

This study investigates the physical mechanisms of the low cloud feedback through cloud-resolving simulations of cloud-radiative equilibrium response to an increase in sea surface temperature (SST). Six pairs of perturbed and control simulations are performed to represent different regimes of low clouds in the subtropical region by specifying SST differences ([DELTA]SST) in the range of 4 and 14 K between the warm tropical and cool subtropical regions. The SST is uniformly increased by 2 K in the perturbed set of simulations. Equilibrium states are characterized by cumulus and stratocumulus cloud regimes with variable thicknesses and vertical extents for the range of specified [DELTA]SSTs, with the perturbed set of simulations having higher cloud bases and tops and larger geometric thicknesses. The cloud feedback effect is negative for this [DELTA]SST range (-0.68 to -5.22 W [m.sup.-2] [K.sup.-1]) while the clear-sky feedback effect is mostly negative (-1.45 to 0.35 W [m.sup.-2] [K.sup.-1]). The clear-sky feedback effect contributes greatly to the climate sensitivity parameter for the cumulus cloud regime whereas the cloud feedback effect dominates for the stratocumulus regime. The increase of liquid water path (LWP) and cloud optical depth is related to the increase of cloud thickness and liquid water content with SST. The rates of change in surface latent heat flux are much higher than those of saturation water vapor pressure in the cumulus simulations. The increase in surface latent heat flux is the primary mechanism for the large change of cloud physical properties with +2 K SST, which leads to the negative cloud feedback effects. The changes in cloud fraction also contribute to the negative cloud feedback effects in the cumulus regime. Comparison of these results with prior modeling studies is also discussed. DOI: 10.1175/2009JAS3239.1

Formulating the contribution of subgrid-scale (SGS) variability to microphysical processes in boundary layer and deep convective cloud parameterizations is a challenging task because of the complexity of microphysical processes and the lack of subgrid-scale information. In this study, a warm-rain microphysics parameterization that is based on a joint double-Gaussian distribution of vertical velocity, liquid water potential temperature, total water mixing ratio, and perturbation of rainwater mixing ratio is developed to simulate drizzling boundary layer clouds with a single column model (SCM). The probability distribution function (PDF) is assumed, but its parameters evolve according to equations that invoke higher-order turbulence closure. These parameters are determined from the first-, second-, and third-order moments and are then used to derive analytical expressions for autoconversion, collection, and evaporation rates. The analytical expressions show that correlation between rainwater and liquid water mixing ratios of the Gaussians enhances the collection rate whereas that between saturation deficit and rainwater mixing ratios of the Gaussians enhances the evaporation rate. Cases of drizzling shallow cumulus and stratocumulus are simulated with large-eddy simulation (LES) and SCM runs (SCM-CNTL and SCM-M): LES explicitly resolves SGS variability, SCM-CNTL parameterizes SGS variability with the PDF-based scheme, but SCM-M uses the grid-mean profiles to calculate the conversion rates of microphysical processes. SCM-CNTL can well reproduce the autoconversion, collection, and evaporation rates from LES. Comparisons between the two SCM experiments showed improvements in mean profiles of potential temperature, total water mixing ratio, liquid water, and cloud amount in the simulations considering SGS variability. A 3-week integration using the PDF-based microphysics scheme indicates that the scheme is stable for long-term simulations.

A two-dimensional cloud-resolving model (CRM) is used to perform five sets of simulations of 68 deep convective cloud objects identified with Clouds and the Earth's Radiant Energy System (CERES) data to examine their sensitivity to changes in thermodynamic and dynamic forcings. The control set of simulations uses observed sea surface temperatures (SSTs) and is forced by advective cooling and moistening tendencies derived from a large-scale model analysis matched to the time and location of each cloud object. Cloud properties, such as albedo, effective cloud height, cloud ice and snow path, and cloud radiative forcing (CRF), are analyzed in terms of their frequency distributions rather than their mean values. Two sets of simulations, F+50% and F-50%, use advective tendencies that are 50% greater and 50% smaller than the control tendencies, respectively. The increased cooling and moistening tendencies cause more widespread convection in the F+50% set of simulations, resulting in clouds that are optically thicker and higher than those produced by the control and F-50% sets of simulations. The magnitudes of both longwave and shortwave CRF are skewed toward higher values with the increase in advective forcing. These significant changes in overall cloud properties are associated with a substantial increase in deep convective cloud fraction (from 0.13 for the F-50% simulations to 0.34 for the F+50% simulations) and changes in the properties of non-deep convective clouds, rather than with changes in the properties of deep convective clouds. Two other sets of simulations, SST+2K and SST-2K, use SSTs that are 2 K higher and 2 K lower than those observed, respectively. The updrafts in the SST+2K simulations tend to be slightly stronger than those of the control and SST-2K simulations, which may cause the SST+2K cloud tops to be higher. The changes in cloud properties, though smaller than those due to changes in the dynamic forcings, occur in both deep convective and non-deep convective cloud categories. The overall changes in some cloud properties are moderately significant when the SST is changed by 4 K. The changes in the domain-averaged shortwave and longwave CRFs are larger in the dynamic forcing sensitivity sets than in the SST sensitivity sets. The cloud feedback effects estimated from the SST-2K and SST+2K sets are comparable to prior studies.

Single-layer mixed-phase stratiform (MPS) Arctic clouds, which formed under conditions of large surface heat flux combined with general subsidence during a subperiod of the Atmospheric Radiation Measurement (ARM) Program's Mixed-Phase Arctic Cloud Experiment (MPACE), are simulated with a cloud-resolving model (CRM). The CRM is implemented with either an advanced two-moment [Morrison et al. (MCK)] or a commonly used one-moment [Lin et al. (LFO)] bulk microphysics scheme and a state-of-the-art radiative transfer scheme. The MCK simulation, which uses the two-moment scheme and observed aerosol size distribution and ice nulei (IN) number concentration, reproduces the magnitudes and vertical structures of cloud liquid water content (LWC), total ice water content (IWC), and number concentration and effective radius of cloud droplets as suggested by the MPACE observations. The simulation underestimates ice crystal number concentrations by an order of magnitude and overestimates effective radius of ice crystals by a factor of 2-3. The LFO experiment, which uses the one-moment scheme, produces values of liquid water path (LWP) and ice plus snow water path (ISWP) that were about 30% and 4 times, respectively, those produced by MCK. The vertical profile of IWC exhibits a bimodal distribution in contrast to the constant distribution of IWC produced in MCK and observations. A sensitivity test that uses the same ice-water saturation adjustment scheme as in LFO produces cloud properties that are more similar to the LFO simulation than MCK. The mean value of the intercept parameter of snow size spectra ([N.sub.0s]) from MCK is one order of magnitude smaller than that assumed in LFO. A sensitivity test that prescribes the larger LFO No, results in 20% less LWP and 5 times larger snow water path than that in MCK. When an exponential ice size distribution replaces the gamma size distribution in MCK, the ISWP decreases by 70% but the LWP increases by 7% versus that in the MCK. Increasing the IN number concentration from the observed value of 0.16 to 3.2 [L.sup.-1] forces the MPS clouds to become glaciated and dissipate, but the simulated ice number concentration agrees initially with the observations better. Physical explanations for these quantitative differences are provided. It is further shown that the differences between the LFO and MCK results are larger than those due to the estimated uncertainties in the prescribed surface fluxes. Additional observations and simulations of a variety of cases are required to further narrow down uncertainties in the microphysics schemes.

The present study evaluates the ability of a cloud-resolving model (CRM) to simulate the physical properties of tropical deep convective cloud objects identified from a Clouds and the Earth's Radiant Energy System (CERES) data product. The emphasis of this study is the comparisons among the small-, medium-, and large-size categories of cloud objects observed during March 1998 and between the large-size categories of cloud objects observed during March 1998 (strong E1 Nino) and March 2000 (weak La Nina). Results from the CRM simulations are analyzed in a way that is consistent with the CERES retrieval algorithm and they are averaged to match the scale of the CERES satellite footprints. Cloud physical properties are analyzed in terms of their summary histograms for each category. It is found that there is a general agreement in the overall shapes of all cloud physical properties between the simulated and observed distributions. Each cloud physical property produced by the CRM also exhibits different degrees of disagreement with observations over different ranges of the property. The simulated cloud tops are generally too high and cloud-top temperatures are too low except for the large-size category of March 1998. The probability densities of the simulated top-of-the-atmosphere (TOA) albedos for all four categories are underestimated for high albedos, while those of cloud optical depth are overestimated at its lowest bin. These disagreements are mainly related to uncertainties in the cloud microphysics parameterization and inputs such as cloud ice effective size to the radiation calculation. Summary histograms of cloud optical depth and TOA albedo from the CRM simulations of the large-size category of cloud objects do not differ significantly between the March 1998 and 2000 periods, consistent with the CERES observations. However, the CRM is unable to reproduce the significant differences in the observed cloud-top height while it overestimates the differences in the observed outgoing longwave radiation and cloud-top temperature between the two periods. Comparisons between the CRM results and the observations for most parameters in March 1998 consistently show that both the simulations and observations have larger differences between the large- and small-size categories than between the large- and medium-size, or between the medium- and small-size categories. However, the simulated cloud properties do not change as much with size as observed. These disagreements are likely related to the spatial averaging of the forcing data and the mismatch in time and space between the numerical weather prediction model from which the forcing data are produced and the CERES observed cloud systems.

This paper is the second in a series in which kilometer-scale-resolving observations from the Atmospheric Radiation Measurement Program and output from the University of California, Los Angeles/Colorado State University cloud-resolving model (CRM) are used to evaluate the single-column model (SCM) version of the National Centers for Environmental Prediction Global Forecast System model. Part I demonstrated that kilometer-scale cirrus properties analyzed by applying the SCM's assumptions about cloud vertical overlap and horizontal homogeneity to its profiles of cloud water/ice mixing ratio, cloud fraction, and snow flux differed from the cloud radar observations while the CRM simulation reproduced most of the observed cirrus properties. The present study evaluates, through a comparison with the CRM, the SCM's representation of detrainment from deep cumulus and ice-phase microphysics in an effort to better understand the findings of Part I. This study finds that, although the SCM's detrainment rate profile averaged over the entire simulation period is comparable to the CRM's, detrainment in the SCM is comparatively sporadic and vertically localized. Too much detrained ice is sublimated when first detrained. Snow formed from detrained cloud ice falls through too deep of a layer. These aspects of the SCM's parameterizations may explain many of the differences in the cirrus properties between the SCM and the observations (or between the SCM and the CRM), and suggest several possible improvements for the SCM: 1) allowing multiple coexisting cumulus cloud types as in the original Arakawa-Schubert scheme, 2) prognostically determining the stratiform cloud fraction, and 3) explicitly predicting the snow mixing ratio. These would allow better representation of the detrainment from deep convection, better coupling of the volume of detrained air with cloud fraction, and better representation of snow flux.

This study examines the sensitivity of diagnosed radiative fluxes and heating rates to different treatments of cloud microphysics among cloud-resolving models (CRMs). The domain-averaged CRM outputs are used in this calculation. The impacts of the cloud overlap and uniform hydrometeor assumptions are examined using outputs having spatially varying cloud fields from a single CRM. It is found that the cloud overlap assumption impacts the diagnosis more significantly than the uniform hydrometeor assumption for all radiative fluxes. This is also the case for the longwave radiative cooling rate except for a layer above 7 km where it is more significantly impacted by the uniform hydrometeor assumption. The radiative cooling above upper-tropospheric anvils and the warming below these clouds are overestimated by about 0.5 K [day.sup.-1] using the domain-averaged outputs. These results are used to further quantify intermodel differences in radiative properties due to different treatments of cloud microphysics among 10 CRMs. The magnitudes of the intermodel differences, as measured by the deviations from the consensus of 10 CRMs. are found to be smaller than those due to the cloud overlap assumption and comparable to those due to the uniform hydrometeor assumption for most shortwave radiative fluxes and the net radiative fluxes at the top of the atmosphere (TOA) and at the surface. For all longwave radiative fluxes, they are smaller than those clue to cloud overlap and uniform hydrometeor assumptions. The consensus of all diagnosed radiative fluxes except for the surface downward shortwave flux agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements.

A hierarchy of third-order turbulence closure models are used to simulate boundary layer cumuli in this study. An unrealistically strong liquid water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m [s.sup.-1]. The period of the oscillation is about 1000 s. Liquid water buoyancy (LWB) terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid water mixing ratio, and the fluxes of liquid water potential temperature and total water, but has less impact on the vertical profiles of other second and third moments. In order to minimizethe LWO, a moderately large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid water mixing ratio. A better approach is to parameterize LWB more reasonably. A minimally prognostic model, which diagnoses all third moments except for the vertical velocity, is shown to produce better results, compared to a fully prognostic model.

Cloud radar data collected at the Atmospheric Radiation Measurement (ARM) Program's Southern Great Plains site were used to evaluate the properties of cirrus clouds that occurred in a cloud-resolving model (CRM) simulation of the 29-day summer 1997 intensive observation period (IOP). The simulation was 'forced' by the large-scale advective temperature and water vapor tendencies, horizontal wind velocity, and turbulent surface fluxes observed at the Southern Great Plains site. The large-scale advective condensate tendency was not observed. The correlation of CRM cirrus amount with Geostationary Operational Environmental Satellite (GOES) high cloud amount was 0.70 for the subperiods during which cirrus formation and decay occurred primarily locally, but only 0.30 for the entire IOP. This suggests that neglecting condensate advection has a detrimental impact on the ability of a model (CRM or single-column model) to properly simulate cirrus cloud occurrence. The occurrence, vertical location, and thickness of cirrus cloud layers, as well as the bulk microphysical properties of thin cirrus cloud layers, were determined from the cloud radar measurements for June, July, and August 1997. The composite characteristics of cirrus clouds derived from this dataset are well suited for evaluating CRMs because of the close correspondence between the timescales and space scales resolved by the cloud radar measurements and by CRMs. The CRM results were sampled at eight grid columns spaced 64 km apart using the same definitions of cirrus and thin cirrus as the cloud radar dataset. The composite characteristics of cirrus clouds obtained from the CRM were then compared to those obtained from the cloud radar. Compared with the cloud radar observations, the CRM cirrus clouds occur at lower heights and with larger physical thicknesses. The ice water paths in the CRM's thin cirrus clouds are similar to those observed. However, the corresponding cloud-layer-mean ice water contents are significantly less than observed due to the CRM's larger cloud-layer thicknesses. The strong dependence of cirrus microphysical properties on layer-mean temperature and layer thickness as revealed by the observations is reproduced by the CRM. In addition, both the CRM and the observations show that the thin cirrus ice water path during large-scale ascent is only slightly greater than during no ascent or descent.

Statistical-equilibrium (SE) states of radiative-convective systems in tropical oceanic conditions are simulated with a cloud ensemble model (CEM) in this study. Typical large-scale conditions from the Marshall Islands and the eastern tropical Atlantic regions are used to drive the CEM. The simulated SE precipitable water, column temperature, and relative humidity are only slightly higher than those of the observed mean states in both regions when time-invariant large-scale total advective cooling and moistening effects are imposed from observations. They are much higher than the observed if time-invariant observed large-scale ascent is imposed for the Marshall Islands region (i.e., ignoring horizontal advective effects). Compared with results from two similar studies, this SE state is somewhere between the cold/dry regime by Sui et al. and the warm/humid regime by Grabowski et al. Temporal variations of the imposed large-scale vertical motion that allows for subsidence make the SE state colder and drier. It remains about the same, however, if the magnitude of the imposed large-scale vertical motion is halved. The SE state is also colder and drier if solar radiation is absent. In general, all the SE states show that wet columns are thermally more stable (unstable) and dry columns are thermally more unstable (stable) in the lower (upper) troposphere. Column budget analyses are performed to explore the differences among the simulations performed in this study and among the different studies.

The influence of large-scale advective cooling and/or moistening on the quasi-equilibrium behavior of simulated, tropical oceanic cumulus ensembles is examined in this study. Two sensitivity simulations are performed by imposing time varying/invariant large-scale advective cooling effects and time invariant/varying large-scale advective moistening effects. The results are compared with a control simulation performed with both large-scale advective cooling and moistening effects that are time varying. It is found that the generalized convective available potential energy (GCAPE) tendency is almost one order of magnitude smaller than the GCAPE production in all simulations. This indicates that the quasi-equilibrium assumption of Arakawa and Schubert is well justified. The higher-order behavior of quasi-equilibrium cumulus ensemble is then examined. It is found that the GCAPE variations are nearly equally contributed by temperature and water vapor variations in the control simulation. In the sensitivity simulations, they are mainly contributed by the temperature (water vapor) variations even though the imposed large-scale advective cooling (moistening) is time invariant. A significant finding of this study is that there is a negative lag correlation between GCAPE and the intensity of cumulus convection. The lag corresponding to the largest negative correlation ranges from 1 to 5 h in various simulations. The existence of a negative correlation and the maximum lag of a few hours is independent of the character and period of the imposed large-scale advective forcing. The maximum lag can be interpreted as the adjustment timescale from disequilibrium to quasi-equilibrium states in the presence of time-varying large-scale forcing.

The macroscopic behavior of cumulus convection and its mesoscale organization during Phase III of the Global Atmospheric Research Program's (GARP) Atlantic Tropical Experiment (GATE) is simulated with a two-dimensional (2D) cloud ensemble model. The model includes a three-phase bulk microphysics parameterization, a third-moment turbulence closure and an interactive, radiative transfer parameterization. The observed large-scale, horizontal advective effects and large-scale vertical velocity are imposed on the model's thermodynamic equations uniformly in the horizontal. The simulated, domain-averaged horizontal wind components are nudged toward the observed winds. A detailed comparison with available observations is made in this study. The observed time variations of the surface precipitation rate, surface evaporation rate, outgoing longwave radiation flux, and the vertical distributions of temperature, water vapor mixing ratio, and relative humidity are successfully reproduced by the model, as well as the vertical structure and time evolution of major convective systems. The most significant result is that the model is able to reproduce the negative correlation between the intensity of convection and the convective available potential energy. The simulated total cloud amount compares favorably with the whole-sky camera observations of Holle et al., but the low-level cloud amount is significantly underestimated. In spite of its success, sensitivity tests suggest that the 2D model has stronger inhibiting effects on convection and is more efficient in vertical transports than is observed when the vertical wind shear is strong. The CEM also produces smaller amplitudes of the daily fluctuations in cloud amount and precipitable water than observed, due possibly to the shortcomings of the microphysics parameterization.

Data produced from explicit simulations of observed tropical cloud systems and subtropical stratocumuli are used to develop a 'semiempirical' cloudiness parameterization for use in climate models. The semiempirical cloudiness parameterization uses the large-scale average condensate (cloud water and cloud ice) mixing ratio as the primary predictor. The large-scale relative humidity and cumulus mass flux are also used in the parameterization as secondary predictors. The cloud amount is assumed to vary exponentially with the large-scale average condensate mixing ratio. The rate of variation is, however, a function of large-scale relative humidity and the intensity of convective circulations. The validity of such a semiempirical approach and its dependency on cloud regime and horizontal-averaging distance are explored with the simulated datasets.

Existing cloudiness parameterizations based on specified probability distribution functions (PDFs) and large-scale relative humidity (RH) in climate models are evaluated with data produced from explicit simulations of observed tropical cloud systems and subtropical stratocumuli. PDF-based parameterizations were originally intended for use in cloud-resolving models, where fractional cloudiness is only associated with turbulence-scale motion. It is demonstrated with simulated data that most PDF-based parameterizations are not adequate for predicting fractional cloudiness in climate models because their performance is dependent upon the cloud regimes. Modifications to some PDF-based formulations are suggested, especially with regard to the inclusion of skewness of conservative variables. The skewness factors are found to be highly dependent upon which scales of motion coexist within a grid cell. RH-based parameterizations are not readily supported due to a wide range of variations of clear-region averaged RHs with height and the grid size of climate models, as well as their wide range of variations at a given height.

Implementation of a broadband radiation parameterization in the UCLA cumulus ensemble model (CEM) is discussed in this study, with emphasis on the specific problems associated with adequate calculation of radiative transfer processes in the CEM. The radiation parameterization is based on the Harshvardhan et al. broadband radiative transfer model with cloud optical properties as formulated by Stephens et al. The lowest CEM layer is divided into a thick layer and a very thin layer near the surface for the longwave radiation calculation. Diagnostic tests have been performed to compare the accuracy of this parameterization with results from a more complicated radiative transfer model. Simulations with fully interactive radiation are performed to compare two methods for invoking the radiation module. The time interval for calling the radiation module has to be very small for the conventional method, which keeps the radiative heating rate constant until the radiation module is called again. It can be larger for the 'accumulated' method, which accumulates and averages cloud microphysical properties within the time interval and applies the amount of radiative heating over the time interval at the time when the radiation module is called. Additional sensitivity tests are also performed to justify the omission of the radiative effects of rapidly falling precipitating particles. Other sensitivity tests are related to the adequacy of the domain size and horizontal resolution for studying the cloud-radiation interaction problems discussed in Part II.

The two-dimensional UCLA cumulus ensemble model is used to examine the impact of cloud-radiation interactions on the macroscopic behavior of cumulus ensembles. Two sets of simulations are performed with noninteractive (NI) and fully interactive (FI) radiative transfer, and with prescribed large-scale advective effects. The time-varying horizontally averaged radiative heating rates [Q.sub.R] from the FI simulations are used to prescribe the time-varying, horizontally homogeneous [Q.sub.R] in the NI simulations. The effects of both longwave radiation and diurnally varying solar radiation are examined from these two sets of simulations. The diurnally varying solar radiation can drive a diurnal cycle of deep convection over the tropical oceans by stabilizing the large-scale environment during the daytime relative to the nighttime. The results presented in this study confirm the dominant role of the direct radiation-convection interaction mechanism for the diurnal cycle of oceanic precipitation. Comparison of the results of the FI and NI simulations suggests that the horizontal differential heating mechanism of Gray and Jacobson plays a secondary role in the diurnal cycle of precipitation. The presence of interactive radiation in the FI simulation, however, postpones the maxima and minima of convective activity due to the greater persistence of upper-tropospheric clouds. These clouds can survive against the solar absorption effects during the daytime. The impact of longwave-cloud interactions on the macroscopic behavior of cumulus ensembles is a slightly stronger modulation of cumulus activity by large-scale processes. Upper-tropospheric clouds are somewhat more active and last longer in the presence of interactive radiation. The longwave-cloud interactions are achieved by the so-called continuously destabilizing mechanism, which has its greatest effects on thin cloud layers.

Simulated data from the UCLA Cumulus Ensemble Model (CEM) are analyzed to partition mass, heat, and moisture budgets of cumulus ensembles into convective and stratiform components. A method based primarily on the horizontal distribution of maximum cloud draft strength below the melting level in a CEM grid column has been developed for this analysis. The stratiform region includes both precipitating and nonprecipitating anvils. The convective and stratiform components of mass, heat, and moisture budgets are distinctly different, in qualitative agreement with previous observational and modeling studies. In the heat and moisture budgets, the difference is due mainly to that in the phase change processes. In general, condensation/deposition dominate evaporation/sublimation in the convective region. All of these processes are more or less equally important in the stratiform region. Freezing occurs only in the convective region. Sublimation from snow/graupel in the stratiform region is much more important than in the convective region. Radiative effects in the stratiform component of the heat budget are as important as effects of phase changes, while radiative effects in the convective component are far less significant. The importance of the convergences of eddy fluxes, especially in the moisture budget, is confirmed. The convergences in the stratiform component are found to be parameterizable only if the vertical motions and the properties of both mesoscale updrafts and mesoscale downdrafts are known. The horizontal inhomogeneity within mesoscale updrafts/downdrafts is of secondary importance for parameterizing the convergences of eddy fluxes in the stratiform component.

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble. The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using 'quick-look' and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

This paper presents a detailed analysis of updraft and downdraft statistics of simulated tropical oceanic and midlatitude continental cumulus convection, with an emphasis on the individual terms in the vertical momentum budget. Strong convective cores with absolute vertical velocities over 1 m [s.sup.-1] and total condensate mixing ratios over 0.1 g [kg.sup.-1] are sampled from several long-term simulations, driven by the observed large-scale advective forcings over the eastern Atlantic and Oklahoma regions. The median updraft and downdraft velocities are weakly dependent upon height, but the 90th percentile of the updraft velocity varies strongly with height, with a maximum in the middle troposphere. The median updraft thermal buoyancies are only about 0.5 K higher than those of downdrafts. As in aircraft measurements, positive thermal buoyancies exist for more than half of downdraft cores, and negative thermal buoyancies exist for a significant number of updrafts. The existence of the nonhydrostatic pressure gradients can explain such a surprising result first obtained from aircraft measurements. On the other hand, the largest differences between tropical and midlatitude convection occur in the strongest 10% of the drafts, not in the median drafts. For updrafts, the difference is related to the larger thermal buoyancy and relatively smaller condensate mixing ratio in midlatitudes, in addition to the larger dynamic triggering in the subcloud layer. The larger dynamic effects of the nonhydrostatic pressure gradient forces are responsible for the larger downdraft velocities in midlatitudes, in addition to the drier environments.

This study describes some results from several simulations of cumulus ensembles at the Southern Great Plains site of the Atmospheric Radiation Measurement (ARM) program during the July 1995 Intensive Observation Period (IOP). A 2D cloud ensemble model (CEM) is used to simulate the macroscopic properties of midlatitude cumulus ensembles. The observed large-scale, horizontal advective tendencies and large-scale vertical velocity or the total advective tendencies are used to drive the CEM, in addition to nudging of the simulated, domain-averaged horizontal wind components toward the observed winds. A detailed comparison with available observations and tropical convection is made in this study. In general, the CEM-simulated results agree reasonably well with the available observations from the July 1995 IOP. The differences between simulations and observations are, however, much larger than those obtained in tropical cases, especially those based on the Global Atmospheric Research Program Atlantic Tropical Experiment Phase III data. Significant differences exist between the statistical properties of tropical and midlatitude cumulus convection, especially in the vertical structures of the cumulus mass fluxes, apparent heat source ([Q.sub.1]), and apparent moisture sink ([Q.sub.2]). The strong variations of the subcloud-layer thermodynamic structure and the surface fluxes in midlatitude continents have large impacts on the heat and moisture budgets. The radiative budgets and satellite-observed cloud amounts are also compared with observations. Although the agreements are reasonably good, some deficiencies of the simulations and inadequate accuracy of large-scale advective tendencies can be clearly seen from the comparisons. Sensitivity tests are performed to address these issues.