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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

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

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

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 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 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 Akio Arakawa

Abstract

A model for numerical simulation of stratus cloud layers is constructed by combining a second-order closure, turbulent transfer model with a thermal radiative transfer model. The turbulent transfer model allows water vapor saturation. The combined turbulence-radiation model is applied to both a horizontally uniform one-dimensional case and a horizontally nonuniform two-dimensional case. In the latter, the dynamics of mesoscale circulations are also incorporated.

Results of the two-dimensional simulation show that the layer cloud instability occurs where the sea surface temperature is high and the large-scale subsidence is weak. The simulated instability is analyzed in view of an instability criterion, the eddy kinetic energy budget, and evaporative cooling near the cloud top.

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Chin-Hoh Moeng and Ulrich Schumann

Abstract

Knowledge of convective plumes within the clear convective boundary layer (CBL) is quite advanced owing to direct measurements, tank experiments, and large-eddy simulation studies. As a result, modeling of the CBL is relatively successful. Progress for the stratus-topped boundary layer (STBL), however, is slow. This study compares the plume structure of the surface-heated CBL with that of the cloud-top-cooled STBL in the hope of extending our knowledge of the CBL to the STBL.

A conditional sampling technique is applied to the STBL flow fields that are generated through large-simulations, so that the structures of typical updrafts and downdrafts may be derived. For the purpose of comparing the surface-heated CBL and the cloud-top-cooled STBL, an idealized STBL is simulated where the turbulence is maintained solely by cloud-top radiative cooling. The principal difference between the CBL and this idealized STBL lies in the origin of the plumes: primary plumes in the CBL are generated at a rigid surface, while those in the STBL are generated at the entraining interface. It was found that in the idealized STBL, the compensating updrafts are nearly as strong as the top-cooling-generated downdrafts, and they contribute a significant amount to the heat, moisture, and momentum transports. This differs very much from the CBL, where the compensating downdrafts are much weaker than the surface-heating-generated updrafts and contribute much less to the transports. The mechanism that results in such an asymmetry between the CBL and STBL is examined, and suggestions on how the asymmetry affects the entrainment process are made.

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Anders Andrén and Chin-Hoh Moeng

Abstract

Closure assumptions often employed in single-point closure models for boundary-layer applications are evaluated against a neutrally stratified planetary boundary-layer flow generated by large-eddy simulation. The contributions from slow and rapid terms to fluctuating pressure are calculated directly from simulated fields. The slow pressure terms are compared with Rotta-type return to isotropy assumptions, both for the components of the Reynolds tensor and for a passive scalar. A simple proportionality between the time scales for dissipation of turbulent kinetic energy and for return to isotropy is found to be a good approximation in the upper two- thirds of the boundary layer. In the lower one-third of the layer, however, this ratio is found to increase by a factor of 2. Closure constants depending on anisotropy are examined and their usefulness determined. Significant contributions of the rapid terms are found for all second moments except vertical velocity variance and vertical scalar flux. Two sets of often-used closure assumptions for the rapid terms are compared with the explicitly calculated data. Also, the rapid terms show that the use of constant closure coefficients are for the tested parameterizations to be viewed at best as a first approximation. Length scales for dissipation of turbulent kinetic energy and scalar variance are extracted and compared with commonly used forms.

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Ulrich Schumann and Chin-Hoh Moeng

Abstract

From results of large-eddy simulations of the clear convective boundary layer and of a stratus-topped boundary layer, we evaluate the budgets of mass, momentum, heat, moisture, and turbulent kinetic energy within “plumes” that are formed by “updrafts” or “downdrafts.” Each grid cell is classified as part of updrafts or downdrafts according to the sign of the resolved vertical velocity. By means of the divergence theorem and Leibniz' rule, the mixing flux across the interface between plumes can be computed from volume integrals. The general form of the budget equation is deduced and compared to previous two-stream models. Both the mean convective circulation and small-scale turbulent motions contribute to the mixing flux across the interface. The small-scale fluxes are largest near the inversion layer at the top of the boundary layers and are important also in the surface layers. Vertical and horizontal velocities in plumes are strongly influenced by the vertical mean pressure gradient and horizontal pressure forces at the plumes lateral surfaces. For the cloudy case, the plume budgets differ from those in the clear boundary layer because of latent heat release and radiation cooling near the cloud top. We find stronger downdrafts because of buoyancy and pressure forces. In both the clear and the cloudy cases, most of the kinetic energy of turbulence within the upper part of the downdrafts comes from the updrafts through lateral mixing, not from buoyancy forcing.

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