A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.     

The sensitivity of k-ɛ model computations of the neutral planetary boundary layer to baroclinicity

While the importance of baroclinicity in determining the structure of the planetary boundary layer (PBL) is well recognized, the actual effect of baroclinicity on the structure is not well understood. Results based on simulations obtained using the turbulent kinetic energy-dissipation rate of turbulent kinetic energy closure model of the turbulent flow in a neutral baroclinic PBL provide additional insight into the role of baroclinicity. The baroclinic PBL is characterized by significant shear production of turbulent kinetic energy throughout the complete boundary-layer depth. The turbulent mixing length is bounded by the presence of a stable temperature inversion layer indicating that the depth of the baroclinic PBL is determined by the inversion height. Significant turbulent shear stresses exist throughout the baroclinic PBL and the air is relatively well-mixed except in the surface layer.     

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.     

Land-Surface Heterogeneity Effects in the Planetary Boundary Layer

We investigate the cumulative added value of assimilating temperature, moisture, and wind observations in the three-dimensional non-hydrostatic Fifth-Generation Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model MM5 and use these forecasts to analyze the relationship between surface forcing and planetary boundary-layer (PBL) depth. A data assimilation methodology focused on the surface and the PBL, previously tested in a one-dimensional version of MM5, is applied to 29 May, 6 June, and 7 June 2002 during the International $\hbox {H}_{2}\hbox {O}$ Project over the Southern Great Plains. Model-predicted PBL depth is evaluated against PBL depth diagnosed from data across 4,800 km of airborne lidar data (flight tracks 100–300 km long). The forecast with data assimilation verifies better against observations and is thus used to investigate the environmental conditions that govern PBL depth. The spatial structure in PBL depth is found to be most affected by spatial variations in surface buoyancy flux and capping inversion strength. The spatial scales of surface flux forcing reflected in the PBL depth are found through Fourier analysis and multiresolution decomposition. Correlations are ${<}0.50$ at scales of 64 km or less and increase at larger scales for 29 May and 6 June, but on 7 June low correlations are found at all scales, possibly due to greater within-PBL wind speeds, a stronger capping inversion on this day, and clouds. The results suggest a minimum scale, a function of wind speed, below which heterogeneity in surface buoyancy fluxes is not reflected directly in PBL depth.     

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。     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

Large-Eddy Simulation of the Daytime Boundary Layer in an Idealized Valley Using the Weather Research and Forecasting Numerical Model

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.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

A note on surface layer parameterizations in the weather research and forecast model

Two surface layer parameterization schemes along with five planetary boundary layer (PBL) schemes in the Weather Research and Forecasting model (WRF) are analyzed in order to evaluate the performance of the WRF model in simulating the surface variables and turbulent fluxes over an Indian sub-continent region. These surface layer schemes are based on the fifth-generation Pennsylvania State University—National Center for Atmospheric Research Mesoscale Model (MM5) parameterization; (a) Old MM5 scheme having Businger-Dyer similarity functions and (b) revised MM5 scheme utilizing the functions that are valid for full ranges of atmospheric stabilities. The study suggests that each PBL scheme can reproduce the diurnal variation of 2 m temperature, momentum flux and sensible heat flux irrespective of the surface layer scheme used for the simulations. However, a comparison of model-simulated values of surface variables and turbulent fluxes with observed values suggests that each PBL scheme is found to systematically over-estimate the nocturnal 2 m temperature and 10 m wind speed with both the revised and old schemes during stable conditions.     

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.     

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model (SCM) is developed in the regional climate model RegCM4. The evolution of a dry convection boundary layer (DCBL) is used to evaluate this SCM. Moreover, four planetary boundary layer (PBL) schemes, namely the Holtslag-Boville scheme (HB), Yonsei University scheme (YSU), and two University of Washington schemes (UW01, Grenier-Bretherton-McCaa scheme and UW09, Bretherton-Park scheme), are compared by using the SCM approach. A large-eddy simulation (LES) of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results, and several diagnostic outputs are compared to evaluate the schemes. The results show that the SCM is proper constructed. In general, with the DCBL case, the YSU scheme performs best for reproducing the LES results, which include well-mixed features and vertical sensible heat fluxes; the simulated wind speed, turbulent kinetic energy, entrainment flux, and height of the entrainment zone are all underestimated in the UW09; the UW01 has all those biases of the UW09 but larger, and the simulated potential temperature is not well mixed; the HB is the least skillful scheme, by which the PBL height, entrainment flux, height of the entrainment zone, and the vertical gradients within the mixed layer are all overestimated, and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required, these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.     

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.     

Study on Physical Mechanism of Influence on Atmospheric Boundary Layer Depth in the Arid Regions of Northwest China

Using the sounding data of wind, temperature, and humidity in the boundary layer and micrometeorological data on the earth's surface observed in the same period in Dunhuang arid region of Northwest China,this paper researches characteristics of potential temperature, wind, and humidity profiles, confirms the structure and depth of thermodynamic boundary layer in Dunhuang region, and analyzses the relationship of depth of thermodynamic boundary layer with surface radiation, buoyancy flux as well as wind speed and wind direction shear in the boundary layer. The results show that the maximum depth of diurnal convective boundary layer is basically above 2000 m during the observational period, many times even in excess of 3000 m and sometimes up to 4000 m; the depth of nocturnal stable boundary layer basically maintains within a range of 1000-1500 m. As a whole, the depth of atmospheric boundary layer is obviously bigger than those results observed in other regions before. By analyzing, a preliminary judgement is that the depth of atmospheric thermodynamic boundary layer in Dunhuang region may relate to local especial radiation characteristics, surface properties (soil moisture content and heat capacity) as well as wind velocity shear of boundary layer, and these properties have formed strong buoyancy flux and dynamic forcing in a local region which are fundamental causes for producing a super deep atmospheric boundary layer.     

An efficient PBL model for global circulation models-design and validation

An efficient, pianetary boundary layer (PBL) model is developed and validated with empirical data for applications in general circulation models (GCMs). The purpose of this PBL model is to establish the turbulent surface fluxes as a function of the principal external PBL parameters in a numerically efficient way. It consists of a surface layer and a mixed layer matched together with the conditions of constant momentum and heat flux at the interface. An algebraic solution to the mean momentum equations describes the mixed-layer velocity profile and thus determines the surface wind vector. The velocity profile is globally valid by incorporating the effect of variable Coriolis force without becoming singular at the equator. Turbulent diffusion depends on atmospheric stability and is modeled in the surface layer by a drag law and with first-order closure in the mixed layer. Radiative cooling in the stably stratified PBL is considered in a simple manner. The coupled system is solved by an iterative method. In order to preserve the computational efficiency of the large-scale model, the PBL model is implemented into the GISS GCM by means of look-up tables with the bulk PBL Richardson number, PBL depth, neutral drag coefficient, and latitude as independent variables.A validation of the PBL model with observed data in the form of Rossby number similarity theory shows that the internal feedback mechanisms are represented correctly. The model, however, underpredicted the sensible heat-flux. A subsequent correction in the turbulence parameterization yields better agreement with the empirical data. The behavior of the principal internal PBL quantities is presented for a range of thermal stabilities and latitudes.     

Impact of Sea-Spray on the Atmospheric Surface Layer

The feedback effects of sea-spray on the heat and momentum fluxes under equilibrium conditions associated with winds of tropical cyclones are investigated using a one-dimensional coupled sea-spray and atmospheric surface-layer (ASL) model. This model is capable of simulating the microphysical aspects of the evaporation of saline water droplets of various sizes and their dynamic and thermal interaction with the turbulence mixing that is simulated by the Mellor–Yamada 1.5-order closure scheme. Sea-spray droplet generation is described by a state-of-the-art parametrization that predicts the size spectrum of sea-spray droplets for a given surface forcing. The results from a series of simulations indicate the way in which evaporating droplets of various sizes modify the turbulence mixing near the surface, which in turn affects further droplet evaporation. All these results are direct consequences of the effects of sea-spray on the balance of turbulent kinetic energy in the spray-filled surface layer. In particular, the overall impact of sea-spray droplets on the mean wind depends on the wind speed at the level of sea-spray generation. When the wind speed is below 40 m s⁻¹, the droplets are small in size and tend to evaporate substantially and thus cool the spray-filled layer, while for wind speeds above 50 m s⁻¹, the size of the droplets is so large that they do not have enough time to evaporate much before falling back into the sea. The sensible heat carried by the droplets is released to the ambient air, increasing the buoyancy of the surface layer and enhancing the turbulent mixing. The suspension of sea-spray droplets reduces the buoyancy and makes the surface layer more stable, decreasing the friction velocity and the downward turbulent mixing of momentum. The results from the numerical experiments also suggest that, in order not to violate the constant flux assumption critical to the Monin–Obukhov similarity theory, a displacement equal to the mean wave height should be included in the logarithmic profiles of the wind and thermal fields.     

Sensitivity of simulated salinities in a three-dimensional ocean general circulation model to vertical mixing of destabilizing surface fluxes

 We present simulations performed with a three dimensional global ocean general circulation model which show that simulated salinities and amounts of convective mixing are very sensitive to vertical mixing of surface buoyancy fluxes. If, as usual, surface buoyancy fluxes are placed entirely in the topmost model level, our model produces excessive convective mixing in the Southern Ocean. This results in poor stimulated salinity in the Southern Ocean. In this simulation, we assume, as usual, that both surface buoyancy forcing and vertical mixing are homogeneous within each grid cell. If, on the other hand, destabilizing surface fluxes are instantaneously mixed into the subsurface ocean, the model produces much less convective mixing and much more realistic salinities. The vertical mixing of surface buoyancy fluxes performed in this simulation is equivalent to assuming that those fluxes affect only a small fraction of each grid cell, and cause vertical mixing only in that limited area. Our interpretation of these results is that the usual assumption that both surface buoyancy forcing and vertical mixing are uniform within each grid cell has a detrimental effect on model results; these results could be significantly improved by good parametrizations which treat the horizontal inhomogeneity of surface buoyancy forcing and of vertical mixing. Received: 25 February 1998 / Accepted: 9 September 1998     

湍流能量闭合法用于大气模式的初探

湍流能量（TKE）闭合方案是近年来大气边界层（PBL）模式中技推崇的方法,它具有11－2阶精度。大气环流模式的计算容量和垂直网络限制,不允许PBL方案过份精细。本文对TKE方案进行简化及网络稀疏化试验。并用Wangara资料验证。验证结果表明：此方案引入PBL内仅设置5层的大气环流模式是可行的。地面以上400米内模式结果与实测吻合。但中、上部位温计算值偏高。关于本方案在大尺度模式中的应用尚须进一步研究。