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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

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

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

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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Junyi Wang and David A. Randall

Abstract

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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Qi Hu and David A. Randall

Abstract

A simple model is used to examine the hypothesis that nonlinear interactions among atmospheric radiation, cumulus convection, and the surface moisture flux can result in a stationary, low-frequency (30–60 day period) oscillating heat source in the tropical atmosphere. The model produces low-frequency oscillations of temperature, moisture, and precipitation. The mechanism that produces these oscillations is identified through analyses of the model and its results. The relevance of this mechanism to understanding the observed Madden-Julian oscillation in the tropical atmosphere over the Indian and western Pacific Ocean is discussed.

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Qingqiu Shao and David A. Randall

Abstract

Closed mesoscale cellular convection (MCC) consists of mesoscale cloud patches separated by narrow clear regions. Strong radiative cooling occurs at the cloud top. In this study a dry two-dimensional Boussinesq model is used to study the effects of cloud-top cooling on convection. Wide updrafts and narrow downdrafts are used to indicate the asymmetric circulations associated with the mesoscale cloud patches. Linear analysis of the model indicates only that the longest waves are most unstable and gives no indication of asymmetric convection cells in the linear convective regime. A weakly nonlinear analysis suggests the presence of downdrafts that are narrower than the updrafts, but this effect is not very pronounced for reasonable values of parameters. Fully nonlinear numerical simulations show that strong cloud-top cooling can generate highly asymmetric mesoscale cells corresponding to closed MCC. Nonlinear processes play essential roles in generating and maintaining closed MCC. The effects of cloud-top radiative cooling on the model dynamics can only be fully represented in a fully nonlinear model. Based on the numerical results, a conceptual model is constructed to suggest a mechanism for the formation of closed MCC over cool ocean surfaces.

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Qi Hu and David A. Randall

Abstract

Although eastward propagation has long been considered one of the essential features of the Madden-Julian waves, recent observations have revealed a stationary or quasi-stationary component in the oscillations, particularly in measures of the diabatic heating rate. Wave-CISK theories of the low-frequency oscillations have struggled to explain the observed period and vertical structure of the waves. On the other hand, theoretical and numerical studies have shown that low-frequency waves strongly resembling the observed oscillations can be excited by specified low-frequency oscillations of the convective heating. A problem with the latter set of theories is that the cause of the oscillatory heating has not been satisfactorily explained. It is proposed here that the observed low-frequency wave motions are the response to forcing by an essentially stationary, self-excited oscillating heat source that is produced by nonlinear interactions among radiation, cumulus convection, and the surface fluxes of sensible heat and moisture. Feedback of the large-scale motions on the latent heating is not required. Results from two very different one-dimensional models are presented to support this hypothesis. The physical processes included in the models are essentially the same, that is, radiation, cumulus convection, and the surface fluxes of sensible heat and moisture; the first model is highly simplified, however, while the second includes relatively sophisticated parameterizations of all the relevant physical processes. Results from both models show low-frequency oscillations of the latent heating, temperature, and moisture. Experiments show that the oscillations are favored by a warm sea surface and weak surface wind speeds, consistent with the observed conditions over the Indian Ocean and the tropical western Pacific Ocean.

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Junyi Wang and David A. Randall

Abstract

The generalized convective available potential energy (GCAPE) observed during GATE has been analyzed using the Lagrangian algorithm of Lorenz, as modified by Randall and Wang. The effects of ice are included and are discussed in an Appendix. A high positive correlation is found between the rate of GCAPE production by large-scale processes and the observed precipitation rate, and a negative correlation between the GCAPE itself and the precipitation rate. The observed time rate of change of the GCAPE is much smaller than the rate of GCAPE production by large-scale processes.

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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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