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David A. Randall

Abstract

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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David A. Randall

Abstract

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

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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No abstract available.

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David A. Randall

Abstract

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

Abstract

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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David A. Randall

Abstract

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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Maike Ahlgrimm and David A. Randall

Abstract

The mixed-layer approach to modeling the planetary boundary layer (PBL) is particularly well suited to inversion-topped PBLs, such as the stratocumulus-topped boundary layer found off the west coast of America in the subtropical Pacific Ocean at northern and southern latitudes. However, a strong temperature inversion near 850 hPa (the trade wind inversion) is not confined to the stratocumulus regimes, but has been observed over most parts of the subtropical–tropical Pacific Ocean. In this paper, the authors test the ability of a simple bulk boundary layer model (BBLM) to diagnose entrainment velocity, cumulus mass flux, and surface latent heat flux from monthly mean reanalysis data. The PBL depth is estimated from Geoscience Laser Altimeter System data. The model is based on the conservation equations for mass, total water mixing ratio, and moist static energy.

The BBLM diagnoses entrainment velocities between 1 and 8 mm s−1 in the stratocumulus and trade wind regions, with increasing rates toward the west. Large cumulus mass fluxes (1.3–2 cm s−1) mark the ITCZ and South Pacific convergence zone. Unreasonably large surface latent heat fluxes are diagnosed in regions where the vertical resolution of both model and input data are insufficient to represent the sharp gradients of moist conservable variables and winds across the PBL top. The results demonstrate that the potential exists to extract useful information about the large-scale structure of PBL physical processes by combining available observations with simple models.

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David A. Randall and Junyi Wang

Abstract

The concept of “moist available energy,” defined by Lorenz, is applied to study the potential energy available for cumulus convection in a conditionally unstable atmosphere. A modified version of Lorenz's parcel-moving algorithm is applied to the GATE data to determine the time variations of the moist available energy of the observed tropical atmosphere. Lorenz's algorithm is found to be somewhat impractical, and a new algorithm based on mass exchanges is proposed. Implications for cumulus parameterization are discussed.

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