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Christopher S. Bretherton

Abstract

Integral methods are used to show that in a simple model of nonprecipitating, moist convection, no small-amplitude propagating or oscillatory, two- or three-dimensional convective instabilities can grow from a quiescent basic state. This result holds for an inviscid layer with vertically varying stratification (of either finite or infinite depth) and for a uniformly stratified viscous layer of finite depth. The implications for the theory of wave-CISK are discussed.

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Christopher S. Bretherton

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No abstract available.

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Christopher S. Bretherton

Abstract

Using Albrecht's model, approximate analytical formulas are found for the dependence of the steady-State mean thermodynamic structure of a partly cloudy convective marine boundary layer on external parameters. Our goals are 1) to understand the physical factors that influence the vertical profiles of mean relative humidity, temperature, and fractional cloudiness within the cloud layer using the model to gain insight into the strato-cumulus-trade cumulus transition in the subtropical trade wind regime, and 2) to understand the sensitivity of the model to tunable internal parameters. The model, a prototype for bulk models of trade cumulus boundary layer, consists of a well-mixed subcloud layer topped by a cumulus layer and a sharp trade inversion. In the simplest formulation discussed here, precipitation is ignored and simple parameterizations for radiative cooling and fractional cloudiness are used.

The analytical approximation agrees well with exact steady-state numerical solutions of Albrecht's model. The cloud-base and trade-inversion heights are not strongly dependent on adjustable parameters within the cloud model and are largely determined by bulk balances of radiative fluxes, surface fluxes, and subsidence in a manner similar to the more empirical model of Betts and Ridgway. The cloud-layer sounding and the cloud fraction are affected by external parameters only through changes in the cloud-base latent heat flux and the cloud thickness. The cloud fraction is quite sensitive to two tunable internal constants in the cloud model that affect rates of cloud entrainment and detrainment, respectively. For most choices of SST and upper-air conditions, these constants can be tuned to produce either a mainly saturated (stratocumulus-like) cloud layer or a trade cumulus-like layer with no environmental saturation. The sensitivity of cloud fraction to SST and mean subsidence is explored for two choices of these constants and the effect of unsteadiness due to downstream changes in external conditions are considered.

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Christopher S. Bretherton

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A defining feature of moist convection is latent heating. A simple, mathematically tractable but thermody-namically reasonable Kuo-type model is developed to isolate some important effects of latent heating on the structure and organization of moist convection. Convection in a shallow, unsheared layer of viscous moist air between two rigid horizontal plates is examined. Unlike previous analytical work, a realistic thermodynamic equation is used, based on the assumption that no precipitation falls out of saturated air. This assumption isolates reversible latent heating from the complicating effects of precipitation. The crucial step is to express the buoyancy of moist air as a simple function of adiabatically conserved, linearly mixing properties of the air; this function is different in saturated than in unsaturated air.

In Part I, the new model is used to find analytical solutions for infinitesimal motions in a conditionally unstable, exactly saturated atmosphere. As in previous work, the most unstable circulation is an isolated, cylin-drical, single updraft cloud, surrounded by an infinite expanse of subsiding clear air. In contrast to earlier work, strong downdrafts occur inside the cloud near its edge. In a separate note, it will be shown that all growing circulations of infinitesimal amplitude are station-no “linear” wave-CISK is possible.

The most important prediction is that subsidence decays exponentially away from the cloud in a horizontal distance Rs. A simple approximate formula for Rs in terms of the growth rate, viscosity, and Coriolis parameter is derived and rationalized. The prediction of infinite cloud spacing will be resolved by a theory of finite-amplitude convection developed analytically in Part II and numerically in Part III, which predicts a finite minimum cloud spacing related to Rs and the strength of convection.

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Christopher S. Bretherton

Abstract

In Part I, an idealized model of nonprecipitating moist convection in a shallow conditionally unstable layer of viscous and diffusive air between two parallel plates was introduced, and the “linear” instability of an exactly saturated static state maintained by diffusion was investigated. If there are initially many clouds, the “linear” theory predicted that weaker clouds are suppressed by the subsidence warming and drying from the ever-growing stronger clouds, and the average cloud spacing becomes arbitrarily large as time goes on. Each growing cloud is surrounded by compensating subsidence, which decreases away from the cloud with a characteristic decay scale Rs, the subsidence radius, which can be understood from gravity wave arguments.

In Part II, fields of finite amplitude clouds are considered. An asymptotic analysis is performed in which the moist Rayleigh number Nc 2 exceeds by only a small amount μ the value N c0 2 necessary for the onset of convection. This leads to a nonlinear set of “cloud field equations” which predict how the amplitudes and positions of all the clouds evolve in time. These equations predict a minimum stable cloud spacing λcRslog(μ−1). If the cloud spacing λ < λc, slight differences in the strengths of neighboring clouds increase until the weaker clouds are suppressed. Unevenly spaced clouds drift until they become evenly spaced, ultimately resulting in a steady field of identical clouds with uniform spacing λ > λc.

Numerical experiments with dry stability Nd = Nc corroborate the conclusions from the cloud field equations when Nc 2/N c0 2 is less than ten. As Nc 2 increases, the numerically determined λc. becomes approximately 1.8Rs ≈ 1.8Nd. There is a second threshold spacing λt ≈ 1.6Ndc not predicted by the asymptotic theory, below which a field of identical growing clouds is transient. This leads to two types of cloud field evolution. If Nc 2/N c0 2 is less than 10, all initial conditions lead to steady uniformly spaced fields of identical clouds. If Nc 2/N c0 2 is on the order of 10 or larger, a field of clouds initiated by horizontally homogeneous random buoyancy perturbations rapidly grows. While it is growing the subsidence radius around each cloud remains O(1); clouds are quite closely spaced. As the clouds mature, Rs increases rapidly to Nd. The clouds are spaced much closer than λt apart, so they all dissipate. If the initial conditions are less random, however, so that a few widely spaced clouds break out first, these clouds inhibit the convection which later grows around them, ultimately become steady and drift toward a uniform spacing. In both cases there is no tendency toward cloud clustering.

The steady cloud fields predicted by the model are probably never realized in the atmosphere due to other physical processes such as boundary layer forcing or precipitation, which favor small cloud spacings despite the large Rayleigh number. The primary conclusion that one can draw from the model is that compensating motions in the cloud layer are always competing with these other processes, tending to increase the spacing between convective clouds as subsidence-induced warming and drying suppresses the weaker circulations.

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Christopher S. Bretherton

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The fastest growing modes in Emanuel's recent model of inviscid precipitating convection in a saturated atmosphere with no shear have large horizontal wavenumbers, permitting a simple analytical analysis of their phase speed, growth rate, and modal structure as functions of the model parameters. It is found that the fastest growing modes are always localized near the ground, are slightly sloped, and grow almost as fast as if precipitation were to fall instantly to the ground. In any wind profile with weak unidirectional shear, rolls aligned along the shear vector grow fastest.

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Gad Levy and Christopher S. Bretherton

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No abstract available

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Christopher S. Bretherton and Sungsu Park

Abstract

A new moist turbulence parameterization is presented and implemented in the Community Atmosphere Model (CAM). It is derived from Grenier and Bretherton but has been heavily modified to improve its numerical stability and efficiency with the long time steps used in climate models. A goal was to provide a more physically realistic treatment of marine stratocumulus-topped boundary layers than in the current CAM.

Key features of the scheme include use of moist-conserved variables, an explicit entrainment closure for convective layers, diagnosis of turbulent kinetic energy (TKE) for computation of turbulent diffusivities, an efficient new formulation of TKE transport as a relaxation to layer-mean TKE, and unified treatment of all turbulent layers in each atmospheric column.

The scheme is compared with the default turbulence parameterizations in the CAM using three single-column modeling cases, using both operational and high vertical and time resolution. Both schemes performed comparably well on the dry convective boundary layer case. For a stable boundary layer case, the default CAM overdeepens the boundary layer unless its free-tropospheric mixing length is greatly reduced, whereupon the new scheme and default CAM again both perform well at both tested resolutions. A nocturnal stratocumulus case was much better simulated by the new scheme than the default CAM, with much less resolution sensitivity. Global climate simulations with the new scheme in tandem with a new shallow cumulus parameterization are presented in a companion paper.

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Christopher S. Bretherton and Sungsu Park

Abstract

A new refinement of Albrecht et al.’s bulk model for shallow-cumulus convection is presented. It is used to illuminate fundamental aspects of oceanic shallow-cumulus boundary layer structure, including updraft buoyancy and vertical velocity scales, cumulus mass flux, temperature and humidity profiles, and trade-inversion height.

The new model, like Albrecht et al.’s, includes a subcloud mixed layer and a cumulus layer with linear gradients of conserved thermodynamic variables, topped by a sharp capping inversion. Albrecht et al.’s model was not mathematically well posed, leading to an inconsistency between its heat and moisture balances at the inversion base. The new bulk model resolves this problem by diagnosing, rather than prognosing, the cumulus-layer gradients and introducing a penetrative entrainment closure to determine the growth of the cumulus layer into the overlying free troposphere. It uses more realistic assumptions about lateral cumulus entrainment and detrainment and a simplified sub-cloud-layer entrainment closure. When applied to a Barbados Oceanographic and Meteorological Experiment (BOMEX) trade-cumulus case, the steady state and the transient response of the bulk model to a sudden increase in sea surface temperature both compare favorably to a large-eddy simulation (LES).

The new closure shows that penetrative entrainment constantly adjusts the cumulus-layer temperature and moisture profiles to keep the updraft buoyancy and vertical velocity small in inverse proportion to a penetrative entrainment efficiency A, estimated to be 5 from LES. Energy-balance arguments provide a skillful prediction of the steady-state bulk-model trade-inversion height. They also show that penetrative entrainment is driven by destabilization of the cumulus layer by radiative cooling and Lagrangian surface temperature increases.

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Zhiming Kuang and Christopher S. Bretherton

Abstract

The tropical tropopause layer (TTL), and in particular the cold point tropopause, has been previously suggested as a feature decoupled from convection. Using a cloud-resolving model, the authors demonstrate that convection, in fact, has a cooling effect in the TTL that significantly affects its thermal structure. In particular, the cold point is found to be strongly tied to the convective cooling maximum. The authors interpret these as natural features of an entrainment layer such as the TTL. The recognition that the cold point tropopause is strongly tied to, rather than decoupled from, convection suggests that dehydration processes at the cold point cannot be assumed as gradual and the effect of convection may not be ignored.

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