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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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Ross Heikes and David A. Randall

Abstract

The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

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Ross Heikes and David A. Randall

Abstract

The streamfunction-velocity potential form of shallow-water equations, implemented on a spherical geodesic grid, offers an attractive solution to many of the problems associated with fluid-flow simulations in a spherical geometry. Here construction of a new type of spherical geodesic grid is outlined, and discretization of the equations is explained. The model is subjected to the NCAR suite of seven test cases for shallow-water 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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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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Takanobu Yamaguchi and David A Randall

Abstract

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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Cristiana Stan and David A. Randall

Abstract

The dynamical equations of atmospheric flow are written using potential vorticity as the meridional coordinate and potential temperature as the vertical coordinate. Within this system, the atmosphere is divided into undulating tubes bounded by isentropic and constant potential vorticity surfaces, and, under adiabatic and frictionless conditions, the air moves through the tubes without penetrating through the walls.

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