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Harshvardhan and David A. Randall

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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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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

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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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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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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Takanobu Yamaguchi and David A. Randall

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Cloud-top entrainment instability (CTEI) is a hypothesized positive feedback between cloud-top entrainment and enhanced turbulence associated with buoyancy reversal. A sufficiently strong positive feedback is hypothesized to lead to the destruction of the cloud. Numerous studies have investigated the possible role of CTEI in cloud breakup, with ambiguous results.

In this study, CTEI has been extensively investigated using many large-eddy simulations. An idealized experimental design has been used so as not to have any source of turbulence kinetic energy production except for entrainment due to evaporative cooling. A new method has been used to estimate the entrainment rate and to identify the inversion base and top.

The results of the experiments do show the hypothesized positive feedback when the Randall–Deardorff CTEI criterion is met. When CTEI takes place in the numerical experiments, entrainment develops spontaneously through buoyancy reversal and, as a result, leads to cloud dissipation. Cloud dissipation within several hours is simulated in the cases with strong instability. A hypothesized dependence of the strength of the evaporatively driven turbulence on the cloud-top liquid water mixing ratio is confirmed. As expected, with a typical stratocumulus liquid water mixing ratio, the evaporatively driven turbulence is weak.

Additional simulations with longwave radiation, surface latent heat flux, or both suggest that sufficiently strong radiative cooling can prevent cloud destruction by CTEI. For this reason, CTEI usually does not result in cloud dissipation in realistic cases.

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Takanobu Yamaguchi and David A Randall

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The relative importance, for cloud-top entrainment, of the cooling rates due to longwave radiation, evaporation, and mixing was assessed through analysis of the results produced by a Lagrangian parcel-tracking model (LPTM) incorporated into a large-eddy simulation model. The LPTM predicts each parcel’s trajectory over time, using the resolved velocity simulated by the host model. An LPTM makes it possible to identify entrained parcels; this is almost impossible to do in an observational study.

A nocturnal stratocumulus cloud was simulated over 4h using a 5-m horizontal grid spacing and a 2.5-m vertical grid spacing. At the start of the last hour of the simulation, over 40 million parcels were placed near the top of the inversion layer and then tracked. Parcel histories were analyzed to identify entrained parcels.

Entrainment occurs in cloud holes, which occur in dry regions of sinking air. Entrainment into the mixed layer is regulated by buoyancy, which requires parcels to be precooled in the inversion layer, prior to entrainment. A mixing fraction analysis was used to separate the cooling due to longwave radiation, evaporation, and mixing. Results show that radiative and evaporative cooling are of comparable importance, but that mixing is by far the dominant cooling mechanism. The radiative cooling rate is strongly inhomogeneous, and only weak radiative cooling is found in regions of entrainment. Therefore, the entrained parcels experience less than the horizontal-mean radiative cooling. Although radiative cooling maintains the boundary layer turbulence, its direct effect on buoyancy of entrained parcels is modest.

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