The terra incognita (TI) or grey zone arises in conventional planetary boundary-layer parametrizations when the grid resolution of a numerical model is comparable to the size of the energy-containing ...turbulent eddies
∼
1 km or less. Here, we investigate a simple, plausible extension of the Mellor–Yamada (MY) level-3 scheme for TI-scale grid size using a large-eddy simulation (LES) as a benchmark. Horizontal filtering of the benchmark simulation data for the dry convective mixed layer in the free convection regime yields subfilter-scale components whose statistics are then retrieved for various filter sizes. This leads to a modified MY level-3 scheme for TI-scale grid sizes. The proposed TI scheme incorporates: (1) modification of various length scales in the conventional MY scheme by an empirical function that depends on the horizontal grid size normalized by the convective boundary-layer height; (2) a new length scale for horizontal turbulent fluxes; and (3) a linear relationship between the local dissipation length and subfilter-scale turbulent kinetic energy. A posteriori tests of the proposed TI scheme show a much improved performance compared with the conventional MY level-3 scheme. The ratio of the grid-scale to the subgrid-scale turbulent intensity is comparable to that obtained from the filtered LES solutions. Sensitivity tests show that the modification of the dissipation length scales has the largest impact, while the new length scale for horizontal fluxes also proves important. A simulation that includes all of the above modifications results in the optimum performance.
A closure relationship between subgrid-scale (SGS) updraftdowndraft 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.
A three-dimensional numerical meteorological model is used to perform large-eddy simulations of the upslope flow circulation over a periodic ridge-valley terrain. The subgrid-scale quantities are ...modelled using a prognostic turbulence kinetic energy (TKE) scheme, with a grid that has a constant horizontal resolution of 50 m and is stretched along the vertical direction. To account for the grid anisotropy, a modified subgrid length scale is used. To allow for the response of the surface fluxes to the valley-flow circulation, the soil surface temperature is imposed and the surface heat and momentum fluxes are computed based on Monin-Obukhov similarity theory. The model is designed with a symmetrical geometry using periodic boundary conditions in both the x and y directions. Two cases are simulated to study the influence of along-valley geostrophic wind forcing with different intensities. The presence of the orography introduces numerous complexities both in the mean properties of the flow and in the turbulent features, even for the idealized symmetric geometry. Classical definitions for the height of the planetary boundary layer (PBL) are revisited and redefined to capture the complex structure of the boundary layer. Analysis of first- and second-moment statistics, along with TKE budget, highlights the different structure of the PBL at different regions of the domain.
Abstract
This manuscript describes numerical experiments investigating the influence of 2–30-km striplike heterogeneity on wet and dry convective boundary layers coupled to the land surface. The ...striplike heterogeneity is shown to dramatically alter the structure of the convective boundary layer by inducing significant organized circulations that modify turbulent statistics. The impact, strength, and extent of the organized motions depend critically on the scale of the heterogeneity λ relative to the boundary layer height zi. The coupling with the land surface modifies the surface fluxes and hence the circulations resulting in some differences compared to previous studies using fixed surface forcing. Because of the coupling, surface fluxes in the middle of the patches are small compared to the patch edges. At large heterogeneity scales (λ/zi ∼18) horizontal surface-flux gradients within each patch are strong enough to counter the surface-flux gradients between wet and dry patches allowing the formation of small cells within the patch coexisting with the large-scale patch-induced circulations. The strongest patch-induced motions occur in cases with 4 < λ/zi < 9 because of strong horizontal pressure gradients across the wet and dry patches. Total boundary layer turbulence kinetic energy increases significantly for surface heterogeneity at scales between λ/zi = 4 and 9; however, entrainment rates for all cases are largely unaffected by the striplike heterogeneity.
Velocity and scalar fields respond differently to variations of heterogeneity scale. The patch-induced motions have little influence on total vertical scalar flux, but the relative contribution to the flux from organized motions compared to background turbulence varies with heterogeneity scale. Patch-induced motions are shown to dramatically impact point measurements in a free-convective boundary layer. The magnitude and sign of this impact depends on the location of the measurement within the region of heterogeneity.
Data from the first research flight (RF01) of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field study are used to evaluate the fidelity with which large-eddy simulations ...(LESs) can represent the turbulent structure of stratocumulus-topped boundary layers. The initial data and forcings for this case placed it in an interesting part of parameter space, near the boundary where cloud-top mixing is thought to render the cloud layer unstable on the one hand, or tending toward a decoupled structure on the other hand. The basis of this evaluation consists of sixteen 4-h simulations from 10 modeling centers over grids whose vertical spacing was 5 m at the cloud-top interface and whose horizontal spacing was 35 m. Extensive sensitivity studies of both the configuration of the case and the numerical setup also enhanced the analysis. Overall it was found that (i) if efforts are made to reduce spurious mixing at cloud top, either by refining the vertical grid or limiting the effects of the subgrid model in this region, then the observed turbulent and thermodynamic structure of the layer can be reproduced with some fidelity; (ii) the base, or native configuration of most simulations greatly overestimated mixing at cloud top, tending toward a decoupled layer in which cloud liquid water path and turbulent intensities were grossly underestimated; (iii) the sensitivity of the simulations to the representation of mixing at cloud top is, to a certain extent, amplified by particulars of this case. Overall the results suggest that the use of LESs to map out the behavior of the stratocumulus-topped boundary layer in this interesting region of parameter space requires a more compelling representation of processes at cloud top. In the absence of significant leaps in the understanding of subgrid-scale (SGS) physics, such a representation can only be achieved by a significant refinement in resolution-a refinement that, while conceivable given existing resources, is probably still beyond the reach of most centers.
This paper reports an intercomparison study on undisturbed trade wind cumulus convection under steady-state conditions as observed during the Barbados Oceanographic and Meteorological Experiment ...(BOMEX) with 10 large eddy simulation (LES) models. A main objective of this study is to obtain a quantitative assessment of the quality of the turbulent dynamics for this type of boundary layer clouds as produced by the different LES codes. A 6-h simulation shows excellent model-to-model agreement of the observed vertical thermodynamical structure, reasonable agreement of variances and turbulent fluxes, and good agreement of quantities conditionally sampled within the model clouds, such as cloud cover, liquid water, and cloud updraft strength. In the second part of this paper the LES dataset is used to evaluate simple models that are used in parameterizations of current general circulation models (GCMs). Finally, the relation of this work to subsequent LES studies of more complicated regimes is discussed, and guidance is given for the design of future observational studies of shallow cumulus boundary layers.
Cloud water sedimentation and drizzle in a stratocumulus-topped boundary layer are the focus of an intercomparison of large-eddy simulations. The context is an idealized case study of nocturnal ...stratocumulus under a dry inversion, with embedded pockets of heavily drizzling open cellular convection. Results from 11 groups are used. Two models resolve the size distributions of cloud particles, and the others parameterize cloud water sedimentation and drizzle. For the ensemble of simulations with drizzle and cloud water sedimentation, the mean liquid water path (LWP) is remarkably steady and consistent with the measurements, the mean entrainment rate is at the low end of the measured range, and the ensemble-average maximum vertical wind variance is roughly half that measured. On average, precipitation at the surface and at cloud base is smaller, and the rate of precipitation evaporation greater, than measured. Including drizzle in the simulations reduces convective intensity, increases boundary layer stratification, and decreases LWP for nearly all models. Including cloud water sedimentation substantially decreases entrainment, decreases convective intensity, and increases LWP for most models. In nearly all cases, LWP responds more strongly to cloud water sedimentation than to drizzle. The omission of cloud water sedimentation in simulations is strongly discouraged, regardless of whether or not precipitation is present below cloud base.
This study represents an attempt to apply Large‐Eddy Simulation (LES) resolution to simulate deep tropical convection in near equilibrium for 24 hours over an area of about 205 × 205 km2, which is ...comparable to that of a typical horizontal grid cell in a global climate model. The simulation is driven by large‐scale thermodynamic tendencies derived from mean conditions during the GATE Phase III field experiment. The LES uses 2048 × 2048 × 256 grid points with horizontal grid spacing of 100 m and vertical grid spacing ranging from 50 m in the boundary layer to 100 m in the free troposphere. The simulation reaches a near equilibrium deep convection regime in 12 hours. The simulated vertical cloud distribution exhibits a tri‐modal vertical distribution of deep, middle and shallow clouds similar to that often observed in Tropics. A sensitivity experiment in which cold pools are suppressed by switching off the evaporation of precipitation results in much lower amounts of shallow and congestus clouds. Unlike the benchmark LES where the new deep clouds tend to appear along the edges of spreading cold pools, the deep clouds in the no‐cold‐pool experiment tend to reappear at the sites of the previous deep clouds and tend to be surrounded by extensive areas of sporadic shallow clouds. The vertical velocity statistics of updraft and downdraft cores below 6 km height are compared to aircraft observations made during GATE. The comparison shows generally good agreement, and strongly suggests that the LES simulation can be used as a benchmark to represent the dynamics of tropical deep convection on scales ranging from large turbulent eddies to mesoscale convective systems. The effect of horizontal grid resolution is examined by running the same case with progressively larger grid sizes of 200, 400, 800, and 1600 m. These runs show a reasonable agreement with the benchmark LES in statistics such as convective available potential energy, convective inhibition, cloud fraction, precipitation rates, and surface latent and sensible fluxes. All runs reveal a tri‐model cloud distribution in the vertical. However, there are differences in the updraft‐core cloud statistics, and convergence of statistical properties is found only between the LES benchmark and the run with 200 m grid size. The effect of vertical grid resolution is also investigated with another run that uses a typical cloud‐resolving model (CRM) horizontal grid size on the order of 1 km and only 64 vertical levels. A comparison to the run with 256 vertical levels shows different vertical cloud distributions. It is concluded that representation of the often observed tri‐modal vertical distribution of clouds requires a vertical grid spacing in the range of 50‐100 m in mid‐to‐low troposphere.
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.
A Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined ...LES-Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively. For the proposed LES-LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarity (SLS) theory for a surface source in the CBL and 2) convection tank measurements of the CWIC for an elevated release in the CBL surface layer. The second comparison includes the modeled evolution of the vertical profile shape with downstream distance, which shows the attainment of an elevated CWIC maximum and a vertically well-mixed CWIC far downstream, in agreement with the tank data. For the proposed model, the agreement with the tank data and SLS theory is better than that obtained with an earlier model in which the SFS fraction of the TKE is assumed to be 1, and significantly better than a model that neglects the SFS velocities altogether.
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