Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

An Intercomparison of Large-Eddy Simulations of the Stable Boundary Layer

Results are presented from the first intercomparison of large-eddy simulation (LES) models for the stable boundary layer (SBL), as part of the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study initiative. A moderately stable case is used, based on Arctic observations. All models produce successful simulations, in as much as they generate resolved turbulence and reflect many of the results from local scaling theory and observations. Simulations performed at 1-m and 2-m resolution show only small changes in the mean profiles compared to coarser resolutions. Also, sensitivity to subgrid models for individual models highlights their importance in SBL simulation at moderate resolution (6.25 m). Stability functions are derived from the LES using typical mixing lengths used in numerical weather prediction (NWP) and climate models. The functions have smaller values than those used in NWP. There is also support for the use of K-profile similarity in parametrizations. Thus, the results provide improved understanding and motivate future developments of the parametrization of the SBL.     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

Large-Eddy Simulation Of The Stably Stratified Planetary Boundary Layer

In this work, we study the characteristics of a stably stratifiedatmospheric boundary layer using large-eddy simulation (LES).In order to simulate the stable planetary boundary layer, wedeveloped a modified version of the two-part subgrid-scalemodel of Sullivan et al. This improved version of themodel is used to simulate a highly cooled yet fairly windy stableboundary layer with a surface heat flux of(W)_o = -0.05 m K s^-1and a geostrophic wind speed of U_g = 15 m s^-1.Flow visualization and evaluation of the turbulencestatistics from this case reveal the development ofa continuously turbulent boundary layer with small-scalestructures. The stability of the boundary layercoupled with the presence of a strong capping inversionresults in the development of a dominant gravity wave atthe top of the stable boundary layer that appears to be relatedto the most unstable wave predicted by the Taylor–Goldsteinequation. As a result of the decay of turbulence aloft,a strong-low level jet forms above the boundary layer.The time dependent behaviour of the jet is compared with Blackadar'sinertial oscillation analysis.     

Resolution Sensitivity and Scaling of Large-Eddy Simulations of the Stable Boundary Layer

Large-eddy simulations (LES) of the continuously turbulent quasi-equilibrium stable boundary layer (SBL) are conducted with grid lengths in the range of 12.5 m to 2 m, in order to explore resolution sensitivity, and determine at what point grid convergence occurs. The structure of the mean potential temperature, winds, and turbulent fluxes varies significantly over this resolution range. The highest resolution simulations show a significant degree of convergence. The dimensionless momentum diffusivity asymptotes to a value of 0.06, corresponding to a limiting flux Richardson number of 0.15.Using the converged simulations, some scaling hypotheses underpinning first-order and second-order closure models are revisited. The effective Richardson number stability functions of the LES are compared with the forms often used in numerical weather prediction (NWP). The mixing implied by the LES is less than that used in NWP. The commonly used similarity profiles for heat and momentum fluxes, and the scalings for dissipation and pressure covariances are compared with the LES. This information could provide guidance for the next generation of SBL parametrization schemes.     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

Large-Eddy Simulation of air Pollution Dispersion in the Nocturnal Cloud-Topped Atmospheric Boundary Layer

Effects of stratocumulus clouds on the dispersion of contaminants are studied in the nocturnal atmospheric boundary layer. The study is based on a large-eddy simulation (LES) model with a bulk parametrization of clouds. Computations include Lagrangian calculations of atmospheric dispersion of a passive tracer released from point sources at various heights above the ground. The results obtained show that the vertical diffusion is non-Gaussian and depends on the location of a source in the boundary layer.     

Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

Large-Eddy Simulation Of A Nocturnal Stratocumulus-Topped Marine Atmospheric Boundary Layer: An Uncertainty Analysis

A large-eddy simulation (LES) model has been used to study a nocturnalstratocumulus-topped marine atmospheric boundary layer. The main objectivesof our study have been first to investigate the statistical significance of LES-derived data products. Second, to test the sensitivity of our LES results with respect to the representation of subgrid-scale mixing and microphysical processes, and third to evaluate and to quantify the parametric uncertainty arising from the incomplete knowledge of the environmental parameters that are required to specify the initial and boundary conditions of a particular case study. Model simulations were compared with observations obtained in solid stratocumulus during the third flight of the first 'Lagrangian' experiment of the Atlantic Stratocumulus Transition Experiment (ASTEX). Based on these simulations the following conclusions could be drawn. Resolution(50 × 50 × 25 m³) and domain size (3.2 × 3.2 × 1.5 km³) of the LES calculations were adequate from a numerical point of view to represent the essential features of the stratocumulus-topped boundary layer. However, the ensemble runs performed in our study to investigate the statistical significance of LES-derived data products demonstrate that the area-time averaging procedure for the second-order moments produces only a low degree of statistical reliability in the model results. This illustratesthe necessity of having LES model results that are not only of adequate resolution but also of sufficiently large domain. The impact of different subgrid schemes was small, but the primary effects of drizzle were found to influence the boundary-layer structure in a climatologically significant way. The parametric uncertainty analysis revealed that the largest contribution to the variance of the LES-derived data products is due to theuncertainties in the cloud-top jump of total water mixing ratio and the net radiative forcing. The differences between the model and measurements for most of the simulated quantities were within the modelling uncertainties, but the calculated precipitation rate was found to differ significantly from that derived in the observations.     

A Large-Eddy Simulation and Lagrangian Stochastic Study of Heavy Particle Dispersion in the Convective Boundary Layer

Large-eddy simulation and Lagrangian stochastic dispersion models were used to study heavy particle dispersion in the convective boundary layer (CBL). The effects of various geostrophic winds, particle diameters, and subgrid-scale (SGS) turbulence were investigated. Results showed an obvious depression in the vertical dispersion of heavy particles in the CBL and major vertical stratification in the distribution of particle concentrations, relative to the passive dispersion. Stronger geostrophic winds tended to increase the dispersion of heavy particles in the lower CBL. The SGS turbulence, particularly near the surface, markedly influenced the dispersion of heavy particles in the CBL. For reference, simulations using passive particles were also conducted; these simulation results agreed well with results from previous convective tank experiments and numerical simulations.     

A Comparison of Stable Boundary Layers in the Ocean and the Atmosphere

This short review compares what is known of the stable atmospheric boundary layer with that of the stable boundary layers occurring in the ocean.     

A Theoretical Model for the Study of Convective Turbulence Decay and Comparison with Large-Eddy Simulation Data

The development of a theoretical model fora decaying convective boundary layeris considered. The model relies on thedynamical energy spectrumequation in which the buoyancy andinertial transfer terms are retained,and a closure assumptionmade for both. The parameterization for thebuoyancy term is given providing a factorizationbetween the energy source termand its temporal decay. Regarding the inertialtransfer term a hypothesis ofsuperposition is used to describe theconvective energy source and time variationof velocity correlation separately.The solution of the budget equation for theturbulent kinetic energy spectrum is possible,given the three-dimensional initial energyspectrum. This is doneutilizing a version of the Kristensen et al.(see Boundary-Layer Meteorol. 47, 149–193)model valid for non-isotropic turbulence. During thedecay the locus of the spectralpeak remains at about the sameposition as the heat flux decreases.Comparison of the theoretical modelis performed against large-eddy simulationdata for a decaying convectiveboundary layer.     

Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence

One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh.Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.     

Wind-Tunnel Study Of Atmospheric Stable Boundary Layers Over A Rough Surface

Wind-tunnel simulations of theatmospheric stable boundary layer (SBL) developedover a rough surface were conducted by using athermally stratified wind tunnel at the Research Institutefor Applied Mechanics (RIAM), Kyushu University. Thepresent experiment is a continuation of the workcarried out in a wind tunnel at Colorado StateUniversity (CSU), where the SBL flows were developed over asmooth surface. Stably stratified flows were createdby heating the wind-tunnel airflow to a temperature ofabout 40–50°and by cooling the test-section floor toa temperature of about 10°. To simulate therough surface, a chain roughness was placed over thetest-section floor. We have investigated the buoyancyeffect on the turbulent boundary layer developed overthis rough surface for a wide range of stability,particularly focusing on the turbulence structure andtransport process in the very stable boundary layer.The present experimental results broadly confirm theresults obtained in the CSU experiment with the smoothsurface, and emphasizes the following features: thevertical profiles of turbulence statistics exhibitdifferent behaviour in two distinct stability regimes with weak and strong stability,corresponding to the difference in the verticalprofiles of the local Richardson number. The tworegimes are separated by the critical Richardsonnumber. The magnitudes in turbulence intensities andturbulent fluxes for the weak stability regime aremuch greater than those of the CSU experiments becauseof the greater surface roughness. For the very stableboundary layer, the turbulent fluxes of momentum andheat tend to vanish and wave-like motions due to theKelvin–Helmholtz instability and the rolling up andbreaking of those waves can be observed. Furthermore,the appearance of internal gravity waves is suggestedfrom cross-spectrum analyses.     

Application of Dynamic Subgrid-scale Models for Large-eddy Simulation of the Daytime Convective Boundary Layer over Heterogeneous Surfaces

The sensitivity of large-eddy simulation (LES) to the representation of subgrid-scale (SGS) processes is explored for the case of the convective boundary layer (CBL) developing over surfaces with varying degrees of spatial heterogeneity. Three representations of SGS processes are explored: the traditional constant Smagorinsky–Lilly model and two other dynamic models with Lagrangian averaging approaches to calculate the Smagorinsky coefficient (C _S ) and SGS Prandtl number (Pr). With initial data based roughly on the observed meteorology, simulations of daytime CBL growth are performed over surfaces with characteristics (i.e. fluxes and roughness) ranging from homogeneous, to striped heterogeneity, to a realistic representation of heterogeneity as derived from a recent field study. In both idealized tests and the realistic case, SGS sensitivities are mostly manifest near the surface and entrainment zone. However, unlike simulations over complex domains or under neutral or stable conditions, these differences for the CBL simulation, where large eddies dominate, are not significant enough to distinguish the performance of the different SGS models, irrespective of surface heterogeneity.     

农林复合带一维非静力大气边界层模式及其模拟分析

建立了一个农林复合带地区一维非静力大气边界层能量闭合模式，对1000m以下的大气边界层内的风、温、湿作了24h的预报，并对下垫面3种不同参数化方案(农作物、森林、无植被)的输出结果与实测值进行了分析和比较；同时通过敏感性试验，突出比较了农作物和森林下垫面对大气边界层垂直流场，湍流垂直交换和湍能的影响。结果表明，本模式能改善边界层风速、位温和湿度预报的模拟效果，下垫面植被对边界层气象要素大小和分布有显著的作用，对湍能垂直分布有一定影响。     

Large-Eddy Simulations of the Stable Boundary Layer Using the Standard Kolmogorov Theory: Range of Applicability

Large-eddy simulations (LES) of the Stable Atmospheric Boundary Layer (SBL) are difficult because the turbulence is not isotropic for strong stratification and the Kolmogorov theory might be no longer valid. This fact compells us to work on modifications to the subgrid turbulence schemes, although there is not any widely accepted theory on anisotropic turbulence. In this work, a LES model is used to see what range of stable stratification can still be simulated with a subgrid turbulence scheme using the Kolmogorov theory for the dissipation. Twenty simulations of increasing stability have been performed using a horizontal resolution of 5 m. The model is able to simulate weakly and moderately stable conditions and experiences runaway cooling for strong stability. The goodness of the successful simulations is inspected through comparison to observations from the experimental campaigns SABLES-98 and CASES-99. Other supplementary tests have been performed on the resolution and the surface boundary condition.     

A Scale-Dependent Dynamic Model for Scalar Transport in Large-Eddy Simulations of the Atmospheric Boundary Layer

An important challenge in large-eddy simulationsof the atmospheric boundarylayer is the specification of the subgrid-scale(SGS) model coefficient(s)and, in particular, how to account for factorssuch as position in the flow,grid/filter scale and atmospheric stability.A dynamic SGS model (thatassumes scale invariance of the coefficients)is implemented in simulationsof a neutral boundary layer with a constantand uniform surface flux of apassive scalar. Results from our simulationsshow evidence that the lumpedcoefficient in the eddy-diffusion modelcomputed with the dynamic proceduredepends on scale. This scale dependence isstronger near the surface, and itis more important for the scalar than for thevelocity field (Smagorinskycoefficient) due to the stronger anisotropicbehaviour of scalars. Based onthese results, a new scale-dependent dynamicmodel is developed for theeddy-diffusion lumped coefficient. The newmodel, which is similar to theone proposed earlierfor the Smagorinsky coefficient,is fully dynamic, thus not requiring anyparameter specification or tuning.Simulations with the scale-dependent dynamicmodel yield the expected trendsof the coefficients as functions of positionand filter/grid scale.Furthermore, in the surface layer the newmodel gives improved predictionsof mean profiles and turbulence spectra ascompared with the traditionalscale-invariant dynamic model.     

水平非均匀对流边界层热量平衡和平流输送作用的大涡模拟

采用大涡模拟所获的数据结果，分析地面热通量沿平均风方向存在 突变的条件下对流边界层的热量平衡和平流输送作用。分析表明边界层内模拟所得结果 可以很好地满足热量平衡关系。除地面热通量项以外，平流项（包括水平平流和垂直平 流）对边界层加热率的作用可达地面热通量不均匀性差值的大小，是影响边界层内热量 平衡的最重要因子，平均速度散度项对热量平衡的作用也不可忽略，但湍流通量散度项 的作用则很小。