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Chin-Hoh Moeng

Abstract

A closure relationship between subgrid-scale (SGS) updraft–downdraft differences and resolvable-scale (RS) variables is proposed and tested for cloud-resolving models (CRMs), based on a data analysis of a large-eddy simulation (LES) of deep convection. The LES flow field is partitioned into CRM-RS and CRM-SGS using a cutoff scale that corresponds to a typical CRM grid resolution. This study first demonstrates the capability of an updraft–downdraft model framework in representing the SGS fluxes of heat, moisture, and momentum over the entire deep convection layer. It then formulates a closure scheme to relate SGS updraft–downdraft differences to horizontal gradients of RS variables. The closure is based on the idea that largest SGS and smallest RS motions are spectrally linked and hence their horizontal fluctuations must be strongly communicated. This relation leads to an SGS scheme that expresses vertical SGS fluxes in terms of horizontal gradients of RS variables, which differs from conventional downgradient eddy diffusivity models. The new scheme is shown to better represent the forward and backscatter energy transfer between CRM-RS and CRM-SGS components than conventional eddy-viscosity models.

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Chin-Hoh Moeng

Abstract

The large eddy simulation technique is used to search for key factors in determining the entrainment rate, cloud fraction, and liquid water path in the stratocumulus-topped boundary layer (STBL), with the goal of developing simple schemes of calculating these important quantities in climate models. In this study an entrainment rate formula is proposed where the entrainment rate is determined by four variables—total jump of the liquid water potential temperature across the entrainment zone, surface heat flux, net radiative flux away from the top of the STBL, and liquid water path. This study also shows that buoyancy reversal, measured here as the ratio between the equivalent potential temperature jump and the total moisture jump across the cloud top, plays a major role in reducing the simulated cloud amount, both cloud fraction and liquid water path. For cases where no buoyancy reversal occurs, the simulated cloud fraction remains 100% and the liquid water path depends solely on the cloud height.

This study raises an interesting feature about what controls the entrainment rate of the STBL. The two cases with a larger surface heat flux studied here show that the net impact of surface heating on the entrainment rate could be negligible if surface heating also leads to enhanced cloud-top evaporation; enhanced evaporation then results in smaller cloud amount and hence smaller radiative forcing for entrainment. Since larger surface heat flux always significantly increases the layer-averaged buoyancy flux and the turbulence intensity, the entrainment rate of the STBL for a given inversion strength is therefore not always directly proportional to the layer-averaged buoyancy flux or to the turbulence intensity.

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Chin-Hoh Moeng

Abstract

Two sets of large-eddy simulation data were used to study some of the assumptions about the cloud-topped boundary layer (CTBL) structure which are used in mixed-layer models. The roles of buoyant production and cloud-top radiative cooling in turbulent kinetic energy generation were examined.

The buoyant production in the turbulent kinetic energy (TKE) budgets was partitioned into production and consumption components by grouping the warm-rising and cold-sinking parcels and the warm-sinking and cold-rising parcels, separately. The results indicate that the ratio of the consumption part of the buoyant production to the sum of the shear production and the production part of the buoyant production is 0.15 for the clear convective mixed layer, and 0.22 for the CTBL.

Almost all mixed-layer models use the experimentally (from either direct measurement or tank experiment) obtained ratio of the buoyancy flux at the top of the clear convective boundary layer to the flux at the surface for their entrainment constant. Those direct measurement or tank experiment studies adopt the horizontal average in the usual Eulerian coordinates to define their ensemble average. A mixed-layer model, therefore, must also use the same type of averaging process to define the radiative cooling distribution near the cloud top. In that case, the 1arge-eddy simulation results indicate that about 85% of the cooling must occur within the entrainment zone and 15% within the well-mixed layer, for relatively dense clouds.

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Chin-Hoh Moeng

Abstract

The structure of a stratus-topped boundary layer is observed through large-eddy simulation which includes the interaction of longwave radiation and turbulence processes. This simulated boundary layer has a relatively warm and dry overlying inversion, a weak surface buoyancy flux, no solar heating, and an insignificant wind shear across the cloud top. The cloud top height and the layer-averaged buoyancy flux inside the cloud layer define a velocity scale appropriate for this of boundary layer.

In the cloud layer, buoyancy generates the vertical component of the turbulent kinetic energy, while pressure effect transfer some of this energy into the horizontal components. In the subcloud layer, the only source of the vertical energy other than the surface buoyancy is import from above and the only source of the horizontal energy other than the mean shear is the vertical energy transferred through pressure effects.

The profiles of the vertical velocity variance and kinetic energy flux in the stratus-topped boundary layer depend on the relative contributions of the surface beating and cloud-top cooling to turbulence. Therefore, the vertical velocity variance is decomposed into two components: one entirely due to surface heating and the other entirely due to cloud-top cooling; the dimensionless profile of the latter is presented.

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Chin-Hoh Moeng

Abstract

A large-eddy-simulation (LFS) model explicitly calculates the large-eddy field and parameterizes the small eddies. The large eddies in the atmospheric boundary layer are believed to be much more important and more flow-dependent than the small eddies. The LES model results are therefore believed to be relatively insensitive to the parameterization scheme for the small eddies.

Deardorff first applied this type of numerical model to boundary-layer turbulence. In order to continue his important work, and to take advantage of the fast Fourier transformation algorithm, a new LES model code which uses a mixed pseudospectral finite-difference method was developed. This LES model is described here and tested with a simple vortex flow and with the Wangara day-33 data.

This model will be used to systematically investigate fundamental problems in the area of boundary-layer turbulence. It is hoped that three-dimensional simulations will give useful statistical information about turbulence structural and improve the closure assumptions in ensemble-mean turbulence modeling.

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Chin-Hoh Moeng
and
Akio Arakawa

Abstract

One of the important roles of the PBL is to transport moisture from the surface to the cloud layer. However, how this transport process can be accounted for in cloud-resolving models (CRMs) is not sufficiently clear and has rarely been examined. A typical CRM can resolve the bulk feature of large convection systems but not the small-scale convection and turbulence motions that carry a large portion of the moisture fluxes. This study uses a large-eddy simulation of a tropical deep-convection system as a benchmark to examine the subgrid-scale (SGS) moisture transport into a cloud system.

It is shown that most of the PBL moisture transport to the cloud layer occurs in the areas under low-level updrafts, with rain, or under cloudy skies, although these PBL regimes may cover only a small fraction of the entire cloud-system domain. To develop SGS parameterizations to represent the spatial distribution of this moisture transport in CRMs, three models are proposed and tested. An updraft–downdraft model performs exceptionally well, while a statistical-closure model and a local-gradient model are less satisfactory but still perform adequately. Each of these models, however, has its own closure issues to be addressed. The updraft–downdraft model requires a scheme to estimate the mean SGS updraft–downdraft properties, the statistical-closure model needs a scheme to predict both SGS vertical-velocity and moisture variances, while the local-gradient model requires estimation of the SGS vertical-velocity variance.

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Chin-Hoh Moeng
and
John Wyngaard

Abstract

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Chin-Hoh Moeng
and
John C. Wyngaard

Abstract

To examine the fidelity of the simulated turbulent flow, we analyzed the spectra of 96×&96×96 large-eddy-simulation results. We derived expressions for the inertial-range spectra of a filtered wind field, compared our computed spectra with the theoretical predictions, and drew two main conclusions. First, the wave cutoff filter is more appropriate for our large-eddy-simulation model than the Gaussian filter. Second, only a certain combination of the subgrid-scale parameters for the dissipation rate and eddy viscosity provides good inertial-range spectra.

We offer an explanation for the unreasonably large sugrid temperature and moisture variances reported in Deardorff's 1974 lame-eddy-simulation results, and show that moment statistics up to third order are not sensitive to moderate changes in the subgrid-scale parameters.

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David J. Carruthers
and
Chin-Hoh Moeng

Abstract

Large eddy simulations and a linear theory are used to examine the characteristics of waves trapped in the temperature inversion that bounds the convective boundary layer. These waves are important because they strongly affect the rate of entrainment and the fluxes of momentum and scalars across the interface. lie simulations show that the motions, at least on scales larger than the model grid size, are nearly linear and can be described well by the theory of Carruthers and Hunt. A simple linear model is used to relate the frequency of trapped waves in the inversion to the ratio of the pressure-temperature covariance and temperature variance. These quantities, which are easily obtained from the simulations, are used to estimate the structure of the waves. Comparisons of the wave properties are made between the theory, further simulations and observations, with good agreement.

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Chin-Hoh Moeng
and
John C. Wyngaard

Abstract

Perhaps the most commonly used closure in second-moment models of turbulence is Rotta's return-to-isotropy expression, which was originally developed to pararmeterize the pressure-velocity gradient correlation in the Reynolds stress conservation equations. It is not clear that this closure alone is adequate for application to convective turbulence, however, because of the pervasive effects of buoyancy on turbulence structure.

We study the closure problem for the pressure covariance in the scalar flux equation using a data set we generated through large-eddy simulation (LES) of a convective boundary layer. We resolve the pressure field into turbulence–turbulence, mean-shear, buoyancy, Coriolis, and subgrid-scale components, and find that the buoyancy and turbulence–turbulence components dominate in the convective boundary layer. The buoyancy contribution to the pressure-gradient/scalar covariance is one-half of the buoyant production term in the flux equation, to a good approximation, while the turbulence–turbulence contribution can be parameterized adequately with Rotta's return-to-isotropy assumption. We find, however, that the return-to-isotropy time scale is different for top-down and bottom-up fields. As a result, this time scale depends not only on mixed-layer scales, but also on the ratio of the scalar fluxes at the top and bottom of the planetary boundary layer.

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