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David A. Randall and George J. Huffman

Abstract

A cumulus cloud's size, shape and internal properties can be predicted, provided that the rate of entrainment is determined by a suitable entrainment parameterization theory. A cumulus cloud model based on such a theory is analogous to the mixed-layer models of the planetary boundary layer (PBL) and the upper ocean.

The entrainment rate is closely related to turbulent transport near the cloud boundary. The mixing-length theory suggested by Asai and Kasahara (1967) is examined in this light. An alternative theory is suggested, which completely removes the strong scale-dependence of the Asai-Kasahara model. Scale-dependence is reintroduced by including the perturbation pressure term of the equation of vertical motion.

For a given sounding, the new model predicts deeper clouds than the Asai-Kasahara model. This results both from the entrainment assumption used, and from the effects of the perturbation pressure.

The expected cloud-top entrainment rate is zero for the simple model considered, although finite-difference errors lead to a positive cloud-top entrainment rate in actual simulators. Lateral entrainment nevertheless dominates cloud-top entrainment. The need for a realistic parameterization of cloud-top entrainment is noted.

The fractional entrainment rate for updrafts is shown to vary only slightly with height, and to decrease only slowly as the cloud radius increases. The fractional detrainment rate for updrafts increases with height. Downdrafts are found to entrain heavily near the PBL top, and to detrain primarily into the PBL, in agreement with the observations of Betts (1976).

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Marat F. Khairoutdinov and David A. Randall

Abstract

A three-dimensional cloud-resolving simulation of midlatitude continental convection during the Atmospheric Radiation Measurement (ARM) program summer 1997 intensive observation period (IOP) is used to study the similarity of several second and third statistical moments, and second-moment budgets among five episodes of deep convection. Several parameter scales relevant to deep convection similarity are introduced. The dimensionless vertical profiles of the vertical velocity variance and its third moment, cumulus kinetic energy, the prognostic variables' variances and fluxes, their budgets, as well as several triple correlations cluster together, confirming the dynamical similarity of the simulated convective events.

The dimensionless budgets of several second-order moments, such as convective kinetic energy (CKE), its vertical and horizontal components, variance, and vertical fluxes of the prognostic thermodynamic variables, as well as the momentum flux, are also presented. The most interesting aspect of the simulated CKE budget is that, in contrast to the boundary layer and shallow trade wind cumulus convection, the dissipation term is relatively small compared to the dominant buoyancy production, transport, and pressure correlation terms. The prognostic equation for the bulk CKE, defined as the vertically integrated mean CKE per unit area, is also discussed. It is found that the so-called bulk CKE dissipation timescale ranges in the simulation from 4 to 8 h. Therefore, the bulk CKE, mostly contained in the horizontal branches of mesoscale circulations associated with the deep convective systems, can persist much longer than the lifetime of an individual convective cloud. It is also found that the fraction of the bulk CKE associated with the vertical motions is about the same for all of the events considered, suggesting a strong correlation between the bulk CKE and the strength of the convective updrafts. It is shown that the bulk CKE dissipation timescale is inversely proportional to the square root of the bulk CKE itself. It is also found that the convective velocity scale is closely related to the convective available potential energy (CAPE) of the thermodynamic sounding taken immediately before a particular convective event.

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Kuan-Man Xu and David A. Randall

Abstract

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 me 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 amplitude of the daily fluctuations in cloud amount and precipitable water than observed, due possibly to the shortcomings of the microphysics parameterization.

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Kuan-Man Xu and David A. Randall

Abstract

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 QR from the FI simulators are used to prescribe the time-varying, horizontally homogeneous QR 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 stabbing 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.

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James J. Benedict and David A. Randall

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Air–sea interactions and their impact on intraseasonal convective organization are investigated by comparing two 5-yr simulations from the superparameterized Community Atmosphere Model version 3.0 (SP-CAM). The first is forced using prescribed sea surface temperatures (SSTs). The second is identical except that a simplified oceanic mixed-layer model is used to predict tropical SST anomalies that are coupled to the atmosphere. This partially coupled simulation allows SSTs to respond to anomalous surface fluxes.

Implementation of the idealized slab ocean model in the SP-CAM results in significant changes to intraseasonal convective variability and organization. The more realistic treatment of air–sea interactions in the coupled simulation improves many aspects of tropical convection on intraseasonal scales, from the relationships between precipitation and SSTs to the space–time structure and propagation of the Madden–Julian oscillation (MJO). This improvement is associated with a more realistic convergence structure and longitudinal gradient of SST relative to MJO deep convection. In the uncoupled SP-CAM, SST is roughly in phase with the MJO convective center and the development of the Kelvin wave response and boundary layer convergence east of the convective center is relatively weak. In the coupled SP-CAM, maxima in SST lead maxima in MJO convection by cycle. Coupling produces warmer SSTs, a stronger Kelvin wave response, enhanced low-level convergence, and increased convective heating ahead (east) of the MJO convective center. Convective development east of the MJO precipitation center is more favorable in the coupled versus the uncoupled version, resulting in more realistic organization and clearer eastward propagation of the MJO in the coupled SP-CAM.

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Chin-Hoh Moeng and David A. Randall

Abstract

We have used a third-order closure model, proposed by André and others, in which the time-rate-change terms, the relaxation and rapid effects for the pressure-related terms, and the clipping approximation are included along with the quasi-normal closure, to study turbulence in a cloudy layer that is cooled radiatively from above. The results show a spurious oscillation, with the largest amplitude near the inversion. An analysis of the problem shows that the oscillation arises from the mean-gradient and buoyancy terms of the triple-moment equations; these terms are largest near the cloud top.

In the stably stratified layer just above the interface, turbulence can excite gravity waves. A model with a closure assumption for the pressure-related terms, not taking into consideration the transport of wave energy, can possibly generate spurious oscillations.

We attempted to damp the oscillation by introducing diffusion terms into the triple-moment equations. With a reasonable choice of the diffusion coefficient, the oscillation is effectively damped in a “dry cloud” run. However, with the same choice for the diffusion coefficient, the oscillation still exists in a “wet cloud” run; a larger eddy coefficient is needed to eliminate the spurious oscillations in the wet-cloudy case.

Unfortunately, we have found that our results are quite sensitive to the ad hoc eddy coefficient applied in the third-moment equations.

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Kuan-Man Xu and David A. Randall
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Laura D. Fowler and David A. Randall

Abstract

In the Colorado State University general circulation model, cumulus detrainment of cloud water and cloud ice has been, up to now, the only direct coupling between convective and large-scale condensation processes. This one-way interaction from the convective to the large-scale environment parameterizes, in a highly simplified manner, the growth of anvils spreading horizontally at the tops of narrow cumulus updrafts. The reverse interaction from the large-scale to the convective updrafts, through which large-scale cloud water and cloud ice can affect microphysical processes occurring in individual convective updrafts, is missing. In addition, the effects of compensating subsidence on cloud water and cloud ice are not taken into account.

A new parameterization of convection, called “EAUCUP,” has been developed, in which large-scale water vapor, cloud water, and cloud ice are allowed to enter the sides of the convective updrafts and can be lifted to the tops of the clouds. As the various water species are lifted, cloud microphysical processes take place, removing excess cloud water and cloud ice in the form of rain and snow. The partitioning of condensed vapor between cloud water and cloud ice, and between rain and snow, is based on temperature. The effects of compensating subsidence on the large-scale water vapor, cloud water, and cloud ice are computed separately. Convective rain is assumed to fall instantaneously to the surface. Three treatments of the convective snow are tested: 1) assuming that all snow is detrained at the tops of convective updrafts, 2) assuming that all snow falls outside of the updrafts and may evaporate, and 3) assuming that snow falls entirely inside the updrafts and melts to form rain.

Including entrainment of large-scale cloud water and cloud ice inside the updrafts, large-scale compensating subsidence unifies the parameterizations of large-scale cloud microphysics and convection, but have a lesser impact than the treatment of convective snow on the simulated climate. Differences between the three alternate treatments of convective snow are discussed. Emphasis is on the change in the convective, large-scale, and radiative tendencies of temperature, and change in the convective and large-scale tendencies of water vapor, cloud water, cloud ice, and snow. Below the stratiform anvils, the change in latent heating due to the change in both convective and large-scale heatings contributes a major part to the differences in diabatic heating among the three simulations. Above the stratiform anvils, differences in the diabatic heating between the three simulations result primarily because of differences in the longwave radiative cooling. In particular, detraining convective snow at the tops of convective updrafts yields a strong increase in the longwave radiative cooling associated with increased upper-tropospheric cloudiness. The simulated climate is wetter and colder when convective snow is detrained at the tops of the updrafts than when it is detrained on the sides of the updrafts or when it falls entirely inside the updrafts. This result highlights the importance of the treatment of the ice phase and associated precipitation in the convective cloud models used in cumulus parameterizations.

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Harshvardhan, David A. Randall, and Thomas G. Corsetti

Abstract

The UCLA/GLA general circulation model has been endowed with new parameterizations of solar and terrestrial radiation, as well as new parameterized cloud optical properties. A simple representation of the cloud liquid water feedback is included. We have used the model and several observational datasets to analyze the effects of cloudiness on the Earth's radiation budget.

Analysis of January and July results obtained with the full model shows that the simulated Earth radiation budget is in reasonable agreement with Nimbus 7 data. The globally averaged planetary albedo and outgoing longwave radiation am both slightly less than observed. A tropical minimum of the outgoing longwave radiation is simulated, but is weaker than observed. Comparisons of the simulated cloudiness with observations from ISCCP and HIRS2/MSU show that the model overpredicts subtropical and midlatitude cloudiness.

The simulated cloud radiative forcings at the top of the atmosphere, at the Earth's surface, and across the atmosphere are discussed, and comparisons are made with the limited observations available. The simulated atmospheric cloud radiative forcing (ACRF) is comparable in magnitude to the latent heating. We have compared the clear-sky radiation fields obtained using Methods I and II of Cess and Potter; the results show significant differences between the two methods, primarily due to systematic variations of the cloudiness with time of day.

An important feature of the new terrestrial radiation parameterization is its incorporation (for the first time in this GCM) of the effects of the water vapor continuum. To determine the effects of this change on the model results, we performed a numerical experiment in which the effects of the water vapor continuum were neglected. The troposphere warmed dramatically, and shallow convection weakened, and the radiative effects of the clouds were significantly enhanced.

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Katherine Thayer-Calder and David A. Randall

Abstract

This study compares two models that differ primarily in their cloud parameterizations and produce extremely different simulations of the Madden–Julian oscillation (MJO). The Community Atmosphere Model (CAM) version 3.0 from NCAR uses the Zhang–McFarlane scheme for deep convection and does not produce an MJO. The “superparameterized” version of the CAM (SP-CAM) replaces the cloud parameterizations with a two-dimensional cloud-resolving model (CRM) in each grid column and produces an extremely vigorous MJO.

This analysis shows that the CAM is unable to produce high-humidity regions in the mid- to lower troposphere because of a lack of coupling between parameterized convection and environmental relative humidity. The SP-CAM produces an overly moist column due in part to excessive near-surface winds and evaporation during strong convective events. In the real tropics and the SP-CAM, convection within a high-humidity environment produces intense latent heating, which excites the large-scale circulation that is the signature of the MJO. The authors suggest that a model must realistically represent convective processes that moisten the entire tropical troposphere in order to produce a simulation of the MJO.

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