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.     

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.     

边界层参数化方案在“灰色区域”尺度下的适用性评估

随着数值预报模式分辨率的提高,当模式网格距与含能湍涡的长度尺度相当时,模式动力过程可解析一部分湍流运动,而剩余的湍流运动仍需参数化,此时便产生了湍流参数化的“灰色区域”问题。对传统的PBL（Planetary Boundary Layer）方案在“灰色区域”下的适用性评估,是改进PBL方案以使其能够适应分辨率变化的前提和基础。本研究基于干对流边界层的大涡模拟试验,比较了WRF（Weather Research and Forecast Model）模式中四种常用的边界层参数化方案[YSU（Yonsei University）、MYJ（Mellor-Yamada-Janjic）、MYNN2.5（Mellor-Yamada-Nakanishi-Niino Level 2.5）、MYNN3）]在“灰色区域”尺度下的表现。研究表明,混合层内总热通量对所使用的参数化方案和水平分辨率均不敏感。不同参数化方案中次网格与网格通量的比例表现出对水平网格距不同的依赖性。局地PBL方案（MYJ、MYNN2.5）在混合层内的平均位温随网格距减小而增大,次网格通量随网格距减小而减小,较参考湍流场对次网格通量有所低估。YSU方案的非局地项几乎不随水平格距改变而变化,对次网格通量的表征并未表现出较强的分辨率依赖性,且过强的非局地次网格输送使混合层内温度层结呈弱稳定,抑制了可分辨湍流输送,不易于激发次级环流。MYNN3方案的非局地次网格通量（负梯度输送项）随网格距减小而减小,使其对次网格通量的表征具有较好的分辨率依赖性。PBL方案在“灰色区域”尺度下的适用性与具体分辨率有关。以分辨率500 m为例,四种PBL方案中不存在一种最佳方案,能对边界层的热力结构和湍流统计特征均有准确的描述。     

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”.     

A comparison of local and non-local turbulence closure methods for the case of a cold air outbreak

Numerical experiments have shown that large-eddy-simulation models (LES) are able to reproduce the common features of convective boundary layers (CBL) quite well. Models which cannot resolve the convective motions due to their grid structure (1D-models or models with coarse horizontal and/or vertical resolution) have to take into account the effects of large eddies within their subgrid diffusion terms. Turbulent fluxes are frequently parameterized through first-order-closure methods (K-theory). Recently, non-local closure schemes have also been developed. In this paper we compare 1D-and 2D-models using different local and non-local first-order closure methods. The analysis is carried out for the case of an idealized cold air outbreak (CAO). One of the non-local closures is based on the so-called transilient turbulence theory. The reference states are given by a bulk-model and a 2D-model which resolves the large eddies explicitly. A comparison of the results is presented for characteristic quantities such as evolution of boundary-layer height and surface heat flux as well as mean wind and temperature profiles. It is found that simple local first-order closure does not give good agreement with the reference models. The results of the transilient turbulence model shows that a non-local closure is able to parameterize the effects of the large eddies. Comparable results are produced by a local closure where eddy diffusivities are parameterized by dimensionless gradient-functions.     

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.     

Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models

With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.     

The thermodynamic influence of subgrid orography in a global climate model

Assessments of the impacts of climate change typically require information at scales of 10 km or less. Such a resolution in global climate simulations is unlikely for at least two decades. We have developed an alternative to explicit resolution that provides a framework for meeting the needs of climate change impact assessment much sooner. We have applied to a global climate model a physically based subgrid-scale treatment of the influence of orography on temperature, clouds, precipitation, and land surface hydrology. The treatment represents subgrid variations in surface elevation in terms of fractional area distributions of discrete elevation classes. For each class it calculates the height rise/descent of air parcels traveling through the grid cell, and applies the influence of the rise/descent to the temperature and humidity profiles of the elevation class. Cloud, radiative, and surface processes are calculated separately for each elevation class using the same physical parametrizations used by the model without the subgrid orography parametrization. The simulated climate fields for each elevation class can then be distributed in post-processing according to the spatial distribution of surface elevation within each grid cell. Parallel 10-year simulations with and without the subgrid treatment have been performed. The simulated temperature, precipitation and snow water are mapped to 2.5-minute (~5 km) resolution and compared with gridded analyses of station measurements. The simulation with the subgrid scheme produces a much more realistic distribution of snow water and significantly more realistic distributions of temperature and precipitation than the simulation without the subgrid scheme. Moreover, the 250-km grid cell means of most other fields are virtually unchanged by the subgrid scheme. This suggests that the tuning of the climate model without the subgrid scheme is also applicable to the model with the scheme.     

On Wind Forces in the Forest-Edge Region During Extreme-Gust Passages and Their Implications for Damage Patterns

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.     

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

Including the Drag Effects of Canopies: Real Case Large-Eddy Simulation Studies

We use the mesoscale meteorological model Meso-NH, taking the drag force of trees into account under stable, unstable and neutral conditions in a real case study. Large-eddy simulations (LES) are carried out for real orography, using a regional forcing model and including the energy and water fluxes between the surface (mostly grass with some hedges of trees) and the atmosphere calculated using a state-of-the-art soil-vegetation-atmosphere-transfer model. The formulation of the drag approach consists of adding drag terms to the momentum equation and subgrid turbulent kinetic energy dissipation, as a function of the foliage density. Its implementation in Meso-NH is validated using Advanced Regional Prediction System simulation results and measurements from Shaw and Schumann (Boundary-Layer Meteorol, 61(1):47?C64, 1992). The simulation shows that the Meso-NH model successfully reproduces the flow within and above homogeneous covers. Then, real case studies are used in order to investigate the three different boundary layers in a LES configuration (resolution down to 2 m) over the ??Lannemezan 2005?? experimental campaign. Thus, we show that the model is able to reproduce realistic flows in these particular cases and confirm that the drag force approach is more efficient than the classical roughness approach in describing the flow in the presence of vegetation at these resolutions.     

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.     

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.     

The sensitivity of large-eddy simulation of turbulent shear flow to subgrid models

Previous large-eddy simulations of turbulent shear flows have shown significant sensitivity to some aspects of the subgrid-scale turbulence models. In particular, Mason and Thomson (1992) demonstrated a marked improvement in simulations through the inclusion of stochastic stress variations in the subgrid model. Here a series of simulations is presented with a view to exploring the general sensitivity to such a subgrid model and in particular to the size and nature of the stochastic stress variations. The model proposed by Mason and Thomson is found to be fairly satisfactory but some quantitative uncertainty remains.     

The Influence of Transient Flow Distortion on Turbulence in Stable Weak-Wind Conditions

Transport by very weak turbulence near the surface, particularly with strong stratification, often violates existing similarity theory due partly to transient distortion of the wind profile by nonstationary mesoscale motions. This problem is examined with 4 months of flux data at seven levels on a 30-m tower. Difficulties with calculation of fluxes and shear with weak winds and weak turbulence are examined. The distortion of the wind profile assumes a wide variety of forms, but sometimes occurs with a transient wind maximum in the lowest 10 m. Though the vertical mixing of momentum is weak for weak-wind nonstationary conditions, it is often more efficient than predicted by existing similarity theory. In fact for weak-wind stable conditions, the flux-gradient relationship depends more on the curvature of the wind profile than the value of the stability parameter. This statistical study suggests a new direction for future work, but does not unravel the physics of the complex and varied structure for stratified weak-wind conditions.     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

纳木错(湖)地区湍流数据质量控制和湍流通量变化特征

利用中国科学院纳木错多圈层综合观测研究站2009年全年的大气湍流观测资料,应用Foot-print模型分析了青藏高原非均匀下垫面湍流观测数据的数据质量、质量评价及不同下垫面对湍流通量的贡献。结果表明:纳木错(湖)地区因不同土地利用类型的差别,导致地表通量分布不均匀,草地对地表通量的贡献最大;对不同大气层结状态,观测站周围200m范围内的地表通量贡献各不相同,上风向通量贡献源区较大,湍流发展较充分。在不稳定状态和中性状态下,纳木错地区地表通量数据质量较高,即白天观测的通量数据质量较高;在稳定状态下数据质量较低,即夜间的通量数据质量较差;纳木错地区的湍流通量受湖陆风和大气稳定性影响较大。