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David A. Randall
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David A. Randall

Global atmospheric models are proliferating, in part because of the widespread availability of powerful computers. There are about two dozen global modeling groups at work in the United States today. These groups are put into four categories, considering both laboratories and universities and development and applications. Community models are a special subgroup and in principle are both developed and applied by the community. Most U.S. global modeling groups are focusing on applications rather than on development. This is especially true in the university community, although over the years university groups have made important contributions in the model-development arena. A key role of university groups is to train new model developers at a rate matched to the community's demand for such scientists. A simple but functional conceptual organization of the U.S. global modeling community is suggested.

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Harshvardhan and David A. Randall

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David A. Randall

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A simple convective mass flux model is used to derive expressions for the fluxes of liquid water and buoyancy in partly cloudy turbulent layers. The results differ radically from those suggested in some previous studies. Physical interpretation is given, and examples are presented. Implications for the dynamics of partly cloudy boundary layers are discussed, and the aftermath of cloud-top entrainment instability is analyzed.

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David A. Randall

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It is shown that the radiative cooling of a cloud layer strongly influences the turbulent flux profiles and the entrainment rate, and that the radiative cooling should be modeled as acting inside the turbulent layer. Numerical experiments demonstrate that a cloud-topped mixed-layer model, similar to that of Lilly (1968), is quite sensitive to δpR, the depth of the radiatively cooled layer near cloud top. As δpR increases, the model’s sensitivity to the entrainment assumption is markedly heightened. More specifically, for large δpR the cloud top and cloud base rise dramatically as the entrainment parameter k is increased, while for small δpR an increase in k has almost no effect. The model is most sensitive to ΔpR precisely for the cold-water, strong-divergence regime of greatest interest.

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David A. Randall

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Entrainment closure theories for mixed-layer models entail assumptions about how the net rate of buoyant production of turbulence kinetic energy is partitioned into gross production and consumption. Three alternative partitioning theories are examined in this paper: Eulerian partitioning, process partitioning and Lagrangian partitioning. Lagrangian partitioning provides a definition of the gross production rate, but is difficult to implement directly. Eulerian and process partitioning are attempts to implement Lagrangian partitioning indirectly.

For the buoyancy fluxes due to a single family of plumes, Eulerian and Lagrangian partitioning are shown to be equivalent. Recent observations reported by Wilczak and Businger rule out such a model. However, it serves as a useful conceptual link between Eulerian and Lagrangian partitioning.

Process partitioning can be formulated in a variety of ways. Examples show that mixed-layer model results are very sensitive to the way in which radiative cooling is assumed to influence the production and consumption rates. A quantitative relationship between process partitioning and Lagrangian partitioning has yet to be established. The observations of Wilczak and Businger show that consumption and entrainment are not as closely linked as current versions of process partitioning suggest.

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David A. Randall

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It is shown that entrainment leads to the generation of turbulence kinetic energy in a stratocumulus layer when the virtual temperature jump at the cloud top is weaker than a critical value. The critical value increases as the relative humidity of the air above cloud top decreases. This result is interpreted as a criterion for the instability of the layer cloud to penetrative downdrafts. The role of the instability in determining the subtropical and tropical distributions of boundary-layer cloudiness is assessed.

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David A. Randall

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Numerical simulation of geostrophic adjustment in shallow water is discussed for the case of an unstaggered grid for vorticity, divergence, and mass. The dispersion equation is shown to be very well behaved and superior to that obtained with the Arakawa grids A–E.

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Sandro Rambaldi and David A. Randall

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Thermals are modeled by considering their boundaries as self-advecting vortex sheets. Both slab-symmetric and axisymmetiic geometries are considered. Discussion is restricted to the case of a neutral environment, and turbulent processes are not considered.

For thermals of circular cross section, the initial accelerations are obtained analytically.

A numerical method is developed to simulate the evolution of thermals by time-marching. The vortex sheet is divided into finite segments, whose positions are tracked in a quasi-Lagrangian fashion. Self-advection is considered. A redistribution procedure is adopted to prevent the segments from bunching unmanageably. The induced field of motion is fully determined both inside and outside the thermal.

Results show that the axisymmetric thermal rises more quickly than the slab-symmetric thermal, that both thermals develop concave bases, that vorticity maxima occur both within the concavities and on the trailing edges, and that the leading edges are remarkably smooth.

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Junyi Wang and David A. Randall

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This paper reports tests of a cumulus parameterization in which the reference state associated with the generalized convective available potential energy (GCAPE) is chosen as the end-state of the convective adjustment. The GCAPE is defined as the enthalpy difference between the given state and the reference state and represents the total potential energy available for conversion into convective kinetic energy in a given sounding. The reference state is the unique state in which the system enthalpy is minimized; it is also a statically neutral or stable state. By assuming that convection drives the atmosphere from the given state toward the reference state, we can use Nitta's diagnostic method to determine the cloudbase mass flux in a prognostic model. The adjustment timescale is finite and varies, depending on the intensity of the large-scale forcing. so this is a “relaxed” scheme. The effects of detrainment are parameterized in a very simple way. After the cloudbase mass flux has been obtained, Nitta's method and Johnson's simple downdraft model are used to determine the feedback of cumulus convection on the large-scale temperature and moisture fields. We have performed a semiprognostic test of the new adjustment scheme using the GATE Phase III data. The results are in fair agreement with observations.

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