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James J. Benedict and David A. Randall

Abstract

The detailed dynamic and thermodynamic space–time structures of the Madden–Julian oscillation (MJO) as simulated by the superparameterized Community Atmosphere Model version 3.0 (SP-CAM) are analyzed. Superparameterization involves substituting conventional boundary layer, moist convection, and cloud parameterizations with a configuration of cloud-resolving models (CRMs) embedded in each general circulation model (GCM) grid cell. Unlike most GCMs that implement conventional parameterizations, the SP-CAM displays robust atmospheric variability on intraseasonal space and time (30–60 days) scales. The authors examine a 19-yr SP-CAM simulation based on the Atmospheric Model Intercomparison Project protocol, forced by prescribed sea surface temperatures. Overall, the space–time structures of MJO convective disturbances are very well represented in the SP-CAM. Compared to observations, the model produces a similar vertical progression of increased moisture, warmth, and heating from the boundary layer to the upper troposphere as deep convection matures. Additionally, important advective and convective processes in the SP-CAM compare favorably with those in observations. A deficiency of the SP-CAM is that simulated convective intensity organized on intraseasonal space–time scales is overestimated, particularly in the west Pacific. These simulated convective biases are likely due to several factors including unrealistic boundary layer interactions, a lack of weakening of the simulated disturbance over the Maritime Continent, and mean state differences.

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James J. Benedict and David A. Randall

Abstract

This study examines various dynamical and thermodynamical processes that characterize the Madden–Julian oscillation (MJO). Episodes of deep convection related to the MJO based on rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite and the Global Precipitation Climatology Project (GPCP) are identified. Although broad convective envelopes are located utilizing spectrally filtered precipitation, analyses of the features within the envelopes are carried out using unfiltered rainfall and 40-yr ECMWF Re-Analysis (ERA-40) fields. The events are composited and categorized based on geographic location and relative intensity.

The composited fields illustrate that, prior to the onset of deep convection, shallow cumulus and cumulus congestus clouds are actively involved in vertical convective transport of heat and moisture. Drying, first accomplished immediately following deep convection in the lower troposphere, is associated with an enhanced horizontal (westerly) advective component and may be related to mesoscale processes. Drying related to deep-layer subsidence is delayed until one to two weeks following intense rainfall. The importance of gradual lower-tropospheric heating and moistening and the vertical transport of energy and moisture are shown in a comparison of vigorous and weak MJO events. Additionally, a comparison of the composite fields to proposed wave instability theories suggests that certain theories are effective in explaining specific phases of the disturbance, but no single theory can yet explain all aspects of the MJO. The discharge–recharge and frictional moisture convergence mechanisms are most relevant for explaining many of the observed features of MJO evolution.

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Kuan-Man Xu and David A. Randall

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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−1 and total condensate mixing ratios over 0.1 g kg−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.

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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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Michael D. Toy and David A. Randall

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The isentropic system of equations has particular advantages in the numerical modeling of weather and climate. These include the elimination of the vertical velocity in adiabatic flow, which simplifies the motion to a two-dimensional problem and greatly reduces the numerical errors associated with vertical advection. The mechanism for the vertical transfer of horizontal momentum is simply the pressure drag acting on isentropic coordinate surfaces under frictionless, adiabatic conditions. In addition, vertical resolution is enhanced in regions of high static stability, which leads to better resolution of features such as the tropopause. Negative static stability and isentropic overturning frequently occur in finescale atmospheric motion. This presents a challenge to nonhydrostatic modeling with the isentropic vertical coordinate. This paper presents a new nonhydrostatic atmospheric model based on a generalized vertical coordinate. The coordinate is specified in a manner similar to that of Konor and Arakawa, but “arbitrary Eulerian–Lagrangian” (ALE) methods are used to maintain coordinate monotonicity in regions of negative static stability and to return the coordinate surfaces to their isentropic “targets” in statically stable regions. The model is mass conserving and implements a vertical differencing scheme that satisfies two additional integral constraints for the limiting case of z coordinates. The hybrid vertical coordinate model is tested with mountain-wave experiments including a downslope windstorm with breaking gravity waves. The results show that the advantages of the isentropic coordinate are realized in the model with regard to vertical tracer and momentum transport. Also, the isentropic overturning associated with the wave breaking is successfully handled by the coordinate formulation.

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Todd D. Ringler and David A. Randall

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Using the shallow water equations, a numerical framework on a spherical geodesic grid that conserves domain-integrated mass, potential vorticity, potential enstrophy, and total energy is developed. The numerical scheme is equally applicable to hexagonal grids on a plane and to spherical geodesic grids. This new numerical scheme is compared to its predecessor and it is shown that the new scheme does considerably better in conserving potential enstrophy and energy. Furthermore, in a simulation of geostrophic turbulence, the new numerical scheme produces energy and enstrophy spectra with slopes of approximately K −3 and K −1, respectively, where K is the total wavenumber. These slopes are in agreement with theoretical predictions. This work also exhibits a discrete momentum equation that is compatible with the Z-grid vorticity-divergence equation.

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Laura D. Fowler and David A. Randall

Abstract

The inclusion of cloud microphysical processes in general circulation models makes it possible to study the multiple interactions among clouds, the hydrological cycle, and radiation. The gaps between the temporal and spatial scales at which such cloud microphysical processes work and those at which general circulation models presently function force climate modelers to crudely parameterize and simplify the various interactions among the different water species (namely, water vapor, cloud water, cloud ice, rain, and snow) and to use adjustable parameters to which large-scale models can be highly sensitive. Accordingly, the authors have investigated the sensitivity of the climate, simulated with the Colorado State University general circulation model, to various aspects of the parameterization of cloud microphysical processes and its interactions with the cumulus convection and radiative transfer parameterizations.

The results of 120-day sensitivity experiments corresponding to perpetual January conditions have been compared with those of a control simulation in order to 1 ) determine the importance of advecting cloud water, cloud ice, rain, and snow at the temporal and spatial scale resolutions presently used in the model; 2) study the importance of the formation of extended stratiform anvils at the tops of cumulus towers, 3) analyze the role of mixed-phase clouds in determining the partitioning among cloud water, cloud ice, rain, and snow and, hence, their impacts on the simulated cloud optical properties; 4) evaluate the sensitivity of the atmospheric moisture budget and precipitation rates to a change in the fall velocities of rain and snow; 5) determine the model's sensitivity to the prescribed thresholds of autoconversion of cloud water to rain and cloud ice to snow; and 6) study the impact of the collection of supercooled cloud water by snow, as well as accounting for the cloud optical properties of snow.

Results are presented in terms of 30-day mean differences between the sensitivity experiments and control run. The authors find that three-dimensional advection of the water species has little influence on their geographical distributions and globally averaged amounts. The simulated climate remains unchanged when detrained condensed water at the tops of cumulus towers is used as a source of rain and snow rather than as a source of cloud water and cloud ice. In contrast, instantaneously removing cloud water and cloud ice detrained at the tops of cumulus towers in the form of precipitation yields a strong drying of the atmosphere and a significant reduction in the size of the anvils. Altering the partitioning between cloud ice and supercooled cloud water produces significant changes in the vertical distributions of the cloud optical depth and effective cloud fraction, hence producing significant variations in the top-of-the-atmosphere longwave and shortwave cloud radiative forcings. Increasing the fall speeds of rain and snow leads to a decrease in cloudiness and an increase in stratiform rainfall. Increasing the thresholds for autoconversion of cloud water to rain and cloud ice to snow yields a significant increase in middle- and high-level clouds and a reduction of the cumulus precipitation rate. The collection of supercooled cloud water by snow appeared to be an important microphysical process for mixed-phase clouds. Finally, the optical effects of snow have little impact upon the top-of-the-atmosphere radiation budget.

This study illustrates the need for in-depth analysis of the spatial and temporal scale dependence of the different microphysical parameters of the cloud parameterizations used in general circulation models.

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Marat F. Khairoutdinov and David A. Randall

Abstract

A new three-dimensional cloud resolving model (CRM) has been developed to study the statistical properties of cumulus convection. The model was applied to simulate a 28-day evolution of clouds over the Atmospheric Radiation Measurement Program (ARM) Southern Great Plains site during the summer 1997 Intensive Observation Period. The model was forced by the large-scale advective tendencies and surface fluxes derived from the observations. The sensitivity of the results to the domain dimensionality and size, horizontal grid resolution, and parameterization of microphysics has been tested. In addition, the sensitivity to perturbed initial conditions has also been tested using a 20-member ensemble of runs.

The model captures rather well the observed temporal evolution of the precipitable water and precipitation rate, although it severely underestimates the shaded cloud fraction possibly because of an inability to account for the lateral advection of clouds over the ARM site. The ensemble runs reveal that the uncertainty of the simulated precipitable water due to the fundamental uncertainty of the initial conditions can be as large as 25% of the mean values. Even though the precipitation rates averaged over the whole simulation period were virtually identical among the ensemble members, the timing uncertainty of the onset and reaching the precipitation maximum can be as long as one full day. Despite the predictability limitations, the mean simulation statistics are found to be almost insensitive to the uncertainty of the initial conditions.

The overall effects of the third spatial dimension are found to be minor for simulated mean fields and scalar fluxes but are quite considerable for velocity and scalar variances. Neither changes in a rather wide range of the domain size nor the horizontal grid resolution have any significant impact on the simulations. Although a rather strong sensitivity of the mean hydrometeor profiles and, consequently, cloud fraction to the microphysics parameters is found, the effects on the predicted mean temperature and humidity profiles are shown to be modest. It is found that the spread among the time series of the simulated cloud fraction, precipitable water, and surface precipitation rate due to changes in the microphysics parameters is within the uncertainty of the ensemble runs. This suggests that correlation of the CRM simulations to the observed long time series of the aforementioned parameters cannot be generally used to validate the microphysics scheme.

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Cara-Lyn Lappen and David A. Randall

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In a companion paper, the authors presented a boundary layer parameterization that was based on the mass-flux concept and included an internally consistent representation of the vertical flux of horizontal momentum. In the present paper, the authors show how the framework of that model can be used to determine the perturbation pressure field, by solving the anelastic pressure equation. The pressure covariances needed to close the parameterization can then be diagnosed. Tests show very encouraging agreement of the pressure statistics with results obtained from large-eddy simulations.

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Kuan-Man Xu and David A. Randall

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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 EL semiempirical approach and its dependency on cloud regime and horizontal-averaging distance are explored with the simulated datasets.

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