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## Abstract

Various locally defined (not horizontal mean) interfaces between the stratocumulus-topped PBL and the free atmosphere are investigated using a fine-resolution large-eddy simulation with a vertical grid spacing of about 4 m. The local cloud-top height is found to be always below the height where the maximum gradient of the local sounding occurs, and the maximum-gradient height is always below the interface where PBL air can reach via turbulent motions. The distances between these local interfaces are of significant amount, a few tens of meters on average. Air between the cloud-top and maximum-gradient interfaces is fully turbulent, unsaturated, but rather moist. Air between the maximum-gradient and turbulent-mixing interfaces consists of turbulent motions that are intermittent in space and time. The simulated flow shows no clearly defined interface that separates cloudy, turbulent air mass from clear, nonturbulent air above, even locally.

## Abstract

Various locally defined (not horizontal mean) interfaces between the stratocumulus-topped PBL and the free atmosphere are investigated using a fine-resolution large-eddy simulation with a vertical grid spacing of about 4 m. The local cloud-top height is found to be always below the height where the maximum gradient of the local sounding occurs, and the maximum-gradient height is always below the interface where PBL air can reach via turbulent motions. The distances between these local interfaces are of significant amount, a few tens of meters on average. Air between the cloud-top and maximum-gradient interfaces is fully turbulent, unsaturated, but rather moist. Air between the maximum-gradient and turbulent-mixing interfaces consists of turbulent motions that are intermittent in space and time. The simulated flow shows no clearly defined interface that separates cloudy, turbulent air mass from clear, nonturbulent air above, even locally.

## Abstract

The performance of two-way nesting for large eddy simulation (LES) of PBL turbulence is investigated using the Weather Research and Forecasting model framework. A pair of LES-within-LES experiments are performed where a finer-grid LES covering a smaller horizontal domain is nested inside a coarser-grid LES covering a larger horizontal domain. Both LESs are driven under the same environmental conditions, allowed to interact with each other, and expected to behave the same statistically. The first experiment of the free-convective PBL reveals a mean temperature bias between the two LES domains, which generates a nonzero mean vertical velocity in the nest domain while the mean vertical velocity averaged over the outer domain remains zero. The problem occurs when the horizontal extent of the nest domain is too small to capture an adequate sample of energy-containing eddies; this problem can be alleviated using a nest domain that is at least 5 times the PBL depth in both *x* and *y*. The second experiment of the neutral PBL exposes a bias in the prediction of the surface stress between the two LES domains, which is found due to the grid dependence of the Smagorinsky-type subgrid-scale (SGS) model. A new two-part SGS model is developed to solve this problem.

## Abstract

The performance of two-way nesting for large eddy simulation (LES) of PBL turbulence is investigated using the Weather Research and Forecasting model framework. A pair of LES-within-LES experiments are performed where a finer-grid LES covering a smaller horizontal domain is nested inside a coarser-grid LES covering a larger horizontal domain. Both LESs are driven under the same environmental conditions, allowed to interact with each other, and expected to behave the same statistically. The first experiment of the free-convective PBL reveals a mean temperature bias between the two LES domains, which generates a nonzero mean vertical velocity in the nest domain while the mean vertical velocity averaged over the outer domain remains zero. The problem occurs when the horizontal extent of the nest domain is too small to capture an adequate sample of energy-containing eddies; this problem can be alleviated using a nest domain that is at least 5 times the PBL depth in both *x* and *y*. The second experiment of the neutral PBL exposes a bias in the prediction of the surface stress between the two LES domains, which is found due to the grid dependence of the Smagorinsky-type subgrid-scale (SGS) model. A new two-part SGS model is developed to solve this problem.

## Abstract

The performance of a two-dimensional (2D) numerical model in representing three-dimensional (3D) planetary boundary layer (PBL) convection is investigated by comparing the 2D model solution to that of a 3D large- eddy simulation. The free convective PBL has no external forcing that would lead to any realizable 2D motion, and hence the 2D model represents a parameterization (not a simulation) of such a convective system. The present solutions show that the fluxes of conserved scalars, such as the potential temperature, are somewhat constrained and hence are not very sensitive to the model dimensionality. Turbulent kinetic energy (TKE), surface friction velocity, and velocity variances are sensitive to the subgrid-scale eddy viscosity and thermal diffusivity in the 2D model; these statistics result mostly from model-generated hypothetical 2D plumes that can be tuned to behave similarly to their 3D counterparts. These 2D plumes are comparable in scale with the PBL height due to the capping inversion. In the presence of shear, orienting the 2D model perpendicular to the mean shear is essential to generate a reasonable momentum flux profile, and hence mean wind profile and wind- related statistics such as the TKE and velocity variances.

## Abstract

The performance of a two-dimensional (2D) numerical model in representing three-dimensional (3D) planetary boundary layer (PBL) convection is investigated by comparing the 2D model solution to that of a 3D large- eddy simulation. The free convective PBL has no external forcing that would lead to any realizable 2D motion, and hence the 2D model represents a parameterization (not a simulation) of such a convective system. The present solutions show that the fluxes of conserved scalars, such as the potential temperature, are somewhat constrained and hence are not very sensitive to the model dimensionality. Turbulent kinetic energy (TKE), surface friction velocity, and velocity variances are sensitive to the subgrid-scale eddy viscosity and thermal diffusivity in the 2D model; these statistics result mostly from model-generated hypothetical 2D plumes that can be tuned to behave similarly to their 3D counterparts. These 2D plumes are comparable in scale with the PBL height due to the capping inversion. In the presence of shear, orienting the 2D model perpendicular to the mean shear is essential to generate a reasonable momentum flux profile, and hence mean wind profile and wind- related statistics such as the TKE and velocity variances.

## Abstract

A large-domain large-eddy simulation of a tropical deep convection system is used as a benchmark to derive and test a mixed subgrid-scale (SGS) scheme for scalar and momentum fluxes in cloud-resolving models (CRMs). The benchmark simulation resolves a broad range of scales ranging from mesoscale organizations, through gravity waves and individual clouds, down to energy-containing turbulent eddies. A spectral analysis shows that the vertical-velocity kinetic energy peaks at scales from hundreds of meters in the lower cloud layer to several kilometers higher up; these scales are typical grid sizes of todayâ€™s CRMs. The analysis also shows that a significant portion of the scalar and momentum fluxes in the benchmark simulation are carried by motions smaller than several kilometers (i.e., smaller than a typical grid resolution of CRMs). The broad range of scales of the benchmark simulation is split into two components: filter scale (mimicking CRM resolvable scale) and subfilter scale (mimicking CRM SGS), using filter widths characteristic of a typical CRM grid spacing. The local relationship of the subfilter-scale fluxes to the filter-scale variables is examined. This leads to a mixed SGS scheme to represent the SGS fluxes of scalars and momentum in CRMs. A priori tests show that the mixed SGS scheme yields spatial distributions of subfilter-scale fluxes that correlate much better with those retrieved from the benchmark when compared with an eddy viscosity/diffusivity scheme that is commonly used in todayâ€™s CRMs.

## Abstract

A large-domain large-eddy simulation of a tropical deep convection system is used as a benchmark to derive and test a mixed subgrid-scale (SGS) scheme for scalar and momentum fluxes in cloud-resolving models (CRMs). The benchmark simulation resolves a broad range of scales ranging from mesoscale organizations, through gravity waves and individual clouds, down to energy-containing turbulent eddies. A spectral analysis shows that the vertical-velocity kinetic energy peaks at scales from hundreds of meters in the lower cloud layer to several kilometers higher up; these scales are typical grid sizes of todayâ€™s CRMs. The analysis also shows that a significant portion of the scalar and momentum fluxes in the benchmark simulation are carried by motions smaller than several kilometers (i.e., smaller than a typical grid resolution of CRMs). The broad range of scales of the benchmark simulation is split into two components: filter scale (mimicking CRM resolvable scale) and subfilter scale (mimicking CRM SGS), using filter widths characteristic of a typical CRM grid spacing. The local relationship of the subfilter-scale fluxes to the filter-scale variables is examined. This leads to a mixed SGS scheme to represent the SGS fluxes of scalars and momentum in CRMs. A priori tests show that the mixed SGS scheme yields spatial distributions of subfilter-scale fluxes that correlate much better with those retrieved from the benchmark when compared with an eddy viscosity/diffusivity scheme that is commonly used in todayâ€™s CRMs.

## Abstract

The Horizontal Array Turbulence Study (HATS) field program utilized horizontal, crosswind arrays of sonic anemometers to calculate estimates of spatially filtered and subfilter-scale (SFS) turbulence, corresponding to its partitioning in large-eddy simulations (LESs) of atmospheric flows. Measurements were made over a wide range of atmospheric stability and for *z*/Î”_{f} nominally equal to 0.25, 0.5, 1.0, and 2.0, where *z* is height and Î”_{f} is the width of the spatial filter. This paper examines the viability of the crosswind array technique by analyzing uncertainties in the filtered turbulence fields. Aliasing in the crosswind direction, caused by the discrete spacing of the sonic anemometers, is found to be minimal except for the spatially filtered vertical velocity and for SFS second moments. In those cases, aliasing errors become significant when the sonic spacing is greater than the wavelength at the peak in the crosswind spectrum of vertical velocity. Aliasing errors are estimated to be of a similar magnitude for the crosswind gradients of filtered variables. Surrogate streamwise filtering is performed by assuming Taylor's hypothesis and using the mean wind speed *U* to interpret sonic time series as spatial data. The actual turbulence advection velocity *U*
_{c} is estimated from the cross correlation between data from HATS sonics separated in the streamwise direction. These estimates suggest that, for near-neutral stratification, the ratio *U*
_{c}/*U* depends on the turbulence variable and is typically between 1.0 and 1.2. Analysis of LES turbulence fields for a neutrally stratified boundary layer finds that the correlation between the true spatially filtered SFS stress component *Ï„*
_{13} and the same variable obtained with surrogate streamwise filtering exceeds 0.98 for *z*/Î”_{f} > 0.25. Within the limits noted, it is concluded that the horizontal array technique is sufficient for the estimation of resolved and SFS turbulence variables.

## Abstract

The Horizontal Array Turbulence Study (HATS) field program utilized horizontal, crosswind arrays of sonic anemometers to calculate estimates of spatially filtered and subfilter-scale (SFS) turbulence, corresponding to its partitioning in large-eddy simulations (LESs) of atmospheric flows. Measurements were made over a wide range of atmospheric stability and for *z*/Î”_{f} nominally equal to 0.25, 0.5, 1.0, and 2.0, where *z* is height and Î”_{f} is the width of the spatial filter. This paper examines the viability of the crosswind array technique by analyzing uncertainties in the filtered turbulence fields. Aliasing in the crosswind direction, caused by the discrete spacing of the sonic anemometers, is found to be minimal except for the spatially filtered vertical velocity and for SFS second moments. In those cases, aliasing errors become significant when the sonic spacing is greater than the wavelength at the peak in the crosswind spectrum of vertical velocity. Aliasing errors are estimated to be of a similar magnitude for the crosswind gradients of filtered variables. Surrogate streamwise filtering is performed by assuming Taylor's hypothesis and using the mean wind speed *U* to interpret sonic time series as spatial data. The actual turbulence advection velocity *U*
_{c} is estimated from the cross correlation between data from HATS sonics separated in the streamwise direction. These estimates suggest that, for near-neutral stratification, the ratio *U*
_{c}/*U* depends on the turbulence variable and is typically between 1.0 and 1.2. Analysis of LES turbulence fields for a neutrally stratified boundary layer finds that the correlation between the true spatially filtered SFS stress component *Ï„*
_{13} and the same variable obtained with surrogate streamwise filtering exceeds 0.98 for *z*/Î”_{f} > 0.25. Within the limits noted, it is concluded that the horizontal array technique is sufficient for the estimation of resolved and SFS turbulence variables.

Several one-dimensional (ID) cloud/turbulence ensemble modeling results of an idealized nighttime marine stratocumulus case are compared to large eddy simulation (LES). This type of model intercomparison was one of the objects of the first Global Energy and Water Cycle Experiment Cloud System Study boundary layer modeling workshop held at the National Center for Atmospheric Research on 16â€“18 August 1994.

Presented are results obtained with different 1D models, ranging from bulk models (including only one or two vertical layers) to various types (first order to third order) of multilayer turbulence closure models. The ID results fall within the scatter of the LES results. It is shown that ID models can reasonably represent the main features (cloud water content, cloud fraction, and some turbulence statistics) of a well-mixed stratocumulus-topped boundary layer.

Also addressed is the question of what model complexity is necessary and can be afforded for a reasonable representation of stratocumulus clouds in mesoscale or global-scale operational models. Bulk models seem to be more appropriate for climate studies, whereas a multilayer turbulence scheme is best suited in mesoscale models having at least 100- to 200-m vertical resolution inside the boundary layer.

Several one-dimensional (ID) cloud/turbulence ensemble modeling results of an idealized nighttime marine stratocumulus case are compared to large eddy simulation (LES). This type of model intercomparison was one of the objects of the first Global Energy and Water Cycle Experiment Cloud System Study boundary layer modeling workshop held at the National Center for Atmospheric Research on 16â€“18 August 1994.

Presented are results obtained with different 1D models, ranging from bulk models (including only one or two vertical layers) to various types (first order to third order) of multilayer turbulence closure models. The ID results fall within the scatter of the LES results. It is shown that ID models can reasonably represent the main features (cloud water content, cloud fraction, and some turbulence statistics) of a well-mixed stratocumulus-topped boundary layer.

Also addressed is the question of what model complexity is necessary and can be afforded for a reasonable representation of stratocumulus clouds in mesoscale or global-scale operational models. Bulk models seem to be more appropriate for climate studies, whereas a multilayer turbulence scheme is best suited in mesoscale models having at least 100- to 200-m vertical resolution inside the boundary layer.

This paper reports an intercomparison study of a stratocumulus-topped planetary boundary layer (PBL) generated from ten 3D large eddy simulation (LES) codes and four 2D cloud-resolving models (CRMs). These models vary in the numerics, the parameterizations of the subgrid-scale (SGS) turbulence and condensation processes, and the calculation of longwave radiative cooling. Cloud-top radiative cooling is often the major source of buoyant production of turbulent kinetic energy in the stratocumulus-topped PBL. An idealized nocturnal stratocumulus case was selected for this study. It featured a statistically horizontally homogeneous and nearly solid cloud deck with no drizzle, no solar radiation, little wind shear, and little surface heating.

Results of the two-hour simulations showed that the overall cloud structure, including cloud-top height, cloud fraction, and the vertical distributions of many turbulence statistics, compared well among all LESs despite the code variations. However, the entrainment rate was found to differ significantly among the simulations. Among the model uncertainties due to numerics, SGS turbulence, SGS condensation, and radiation, none could be identified to explain such differences. Therefore, a follow-up study will focus on simulating the entrainment process. The liquid water mixing ratio profiles also varied significantly among the simulations; these profiles are sensitive to the algorithm used for computing the saturation mixing ratio.

Despite the obvious differences in eddy structure in two- and three-dimensional simulations, the cloud structure predicted by the 2D CRMs was similar to that obtained by the 3D LESs, even though the momentum fluxes, the vertical and horizontal velocity variances, and the turbulence kinetic energy profiles predicted by the 2D CRMs all differ significantly from those of the LESs.

This paper reports an intercomparison study of a stratocumulus-topped planetary boundary layer (PBL) generated from ten 3D large eddy simulation (LES) codes and four 2D cloud-resolving models (CRMs). These models vary in the numerics, the parameterizations of the subgrid-scale (SGS) turbulence and condensation processes, and the calculation of longwave radiative cooling. Cloud-top radiative cooling is often the major source of buoyant production of turbulent kinetic energy in the stratocumulus-topped PBL. An idealized nocturnal stratocumulus case was selected for this study. It featured a statistically horizontally homogeneous and nearly solid cloud deck with no drizzle, no solar radiation, little wind shear, and little surface heating.

Results of the two-hour simulations showed that the overall cloud structure, including cloud-top height, cloud fraction, and the vertical distributions of many turbulence statistics, compared well among all LESs despite the code variations. However, the entrainment rate was found to differ significantly among the simulations. Among the model uncertainties due to numerics, SGS turbulence, SGS condensation, and radiation, none could be identified to explain such differences. Therefore, a follow-up study will focus on simulating the entrainment process. The liquid water mixing ratio profiles also varied significantly among the simulations; these profiles are sensitive to the algorithm used for computing the saturation mixing ratio.

Despite the obvious differences in eddy structure in two- and three-dimensional simulations, the cloud structure predicted by the 2D CRMs was similar to that obtained by the 3D LESs, even though the momentum fluxes, the vertical and horizontal velocity variances, and the turbulence kinetic energy profiles predicted by the 2D CRMs all differ significantly from those of the LESs.