A One-Dimensional Finite-Element Boundary-Layer Model with a Vertical Adaptive Grid

A one-dimensional atmospheric boundary-layer model is developed using the finite element method and a 1.5-order e-l turbulence closure scheme. A vertical adaptive strategy is implemented, based upon an heuristic error estimator that depends upon properties of the layer, such as the stratification. The model is used to simulate a moderately stratified stable boundary layer as described in the GABLS (GEWEX Atmospheric Boundary-Layer Study, where GEWEX is the Global Water and Energy Cycle Experiment) First Intercomparison Project, and then a more complicated diurnal cycle, as used in the GABLS Second Intercomparison Project. In the stable boundary-layer experiment, it is shown that including the adaptive strategy can improve the performance of the model such that the error in the model is significantly less (greater than an order of magnitude with an effective resolution of 8 m) than that of the model without adaptivity. The model’s turbulence closure scheme and the adaptivity strategy also successfully simulate the different stability regimes present in the diurnal cycle simulation, and represented all of the expected features.     

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.     

深凹地形边界层风场与湍流场结构及扩散规律的数值研究

建立了一个模拟小尺度复杂地形边界层平均流场和湍流场结构分布特征的三维非静力细网格高阶矩湍流闭合模式,并将此模式与一个拉格朗日粒子随机游动大气扩散数值模式相联结,以边界层气象模式的输出作为扩散模式的输入,构成了一个大气扩和模拟系统,成功地模拟了某地实际深凹露天矿区和理想凹坑地形两种情况下的平均流场、雷诺应力和湍流通量场,分析了其分布特征,并模拟了矿坑内污染物的散布规律     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

The temperature profile and heat transfer law in a neutrally and stably stratified planetary boundary layer

A logarithmic + polynomial approximation is proposed for the vertical temperature profile in a neutrally or stably stratified planetary boundary layer (PBL) in conditions of quasi-stationarity. Using this approximation with the asymptotic logarithmic + linear law of the Monin-Obukhov similarity theory for the near-surface layer and with the Zilitinkevich formula for the PBL thickness allows one to derive an analytical expression for the function C in the heat transfer law, which permits simple parameterization of the thermal interaction between the atmosphere and the underlying medium in terms of external parameters, such as the geostrophic wind velocity and the temperature difference across the PBL.     

A STUDY OF 1.5-ORDER CLOSURE TURBULENCE MODEL

Based on turbulence theory,a 1.5-order closure turbulence model is established.The model incorporating with theground surface energy budget equation is constructed by means of a vertical one-dimensional(1-D)40-levelgrid-mesh.The numerical results reveal the 24-h evolution of the clear planetary boundary layer comparing with theWangara boundary layer data of days 33—34.The model also takes into account some physical processes of radiativetransfer and baroclinicity,revealing some important characteristics observed in the boundary layer,especially for theevolution of the mixed layer and low-level jet.The calculated results are in good agreement with the observational data.On the other hand,we also run the high-resolution model of the planetary boundary layer in the Mesoscale Model Ver-sion 4(MM4)with the same physical processes and initial conditions.The results show that the high-resolution modelcan not reveal those important characteristics as the 1.5-order closure model did.In general,it is shown that the 1.5-or-der closure turbulence model based on turbulence theory is better in rationality and reality.     

对流层物质垂直交换模式中的参数化处理

为了研究对流层(TL)中垂直涡旋扩散系数(K_z)随高度变化的参数化形式对物质垂直交换的贡献,用“高分辨TL物质交换模式”(EM3)对5种不同K_z型进行了数值对比模拟,结果表明:KK_z型较好地描述了行星边界层(PBL)内受下垫面影响的高频湍流和PBL以上TL由各种动力学和热力学过程产生的切变湍流;垂直运动和K_z对PBL下层的物质输送到TL上层和从源高度向下输送到PBL低层两者均有重要作用;垂直运动的作用具有间隙性,而K_z是连续的.     

Modelling the One-Dimensional Stable Boundary Layer with an E−ℓ Turbulence Closure Scheme

The atmospheric boundary layer (ABL) model of Weng and Taylor with E−ℓ turbulence closure is applied to simulate the one-dimensional stably stratified ABL. The model has been run for nine hours from specified initial wind, potential temperature and turbulent kinetic energy profiles, and with a specified cooling rate applied at the surface. Different runs are conducted for different cooling rates, geostrophic winds and surface roughnesses. The results are discussed and compared with other models, large-eddy simulations and published field data.     

Classification of the stratified atmospheric boundary layers at Molve (Croatia) based on the similarity theory

Summary The stability parameter μ is suggested as the one which is determinable with satisfying accuracy for routine application by means of commonly accessible meteorological data at the Molve location (Croatia). The similarity functions applied for vertical wind speed simulation in the planetary boundary layer (PBL) at Molve were useful for the determination of local stability classes. Universal similarity functions were applied for unstable and neutral stability, whereas local similarity functions were established for stable stratification. Wind speed simulations were performed using two types of wind models. The Monin-Obukhov similarity theory was included in both types. However, it turned out that for the operative determination of the stability of the 35 m deep lowest layer, the stability parameter μ was locally a better stability parameter than the Monin-Obukhov parameter z/L. That was possibly because 35 m deep lowest layer sometimes (depending upon stability) includes a large proportion of the Ekman layer and parameter μ is originally designed for the deeper part of PBL than z/L that is originally designed for the surface layer. At Molve, the input data for local wind models as well as for the stability parameter μ were wind speed at 35 m and temperature at 2 and 35 m above the ground.     

An Experimental Study of the Statistics of Temperature Fluctuations in the Atmospheric Boundary Layer

A statistical characterization for two-point temperature fluctuations in the planetary boundary layer (PBL) is analyzed and its implications on the long-standing closure problem discussed. Despite the non-triviality of the dynamics of temperature fluctuations, our analysis supports the idea that the most relevant statistical properties can be captured solely in terms of two scaling exponents. They turned out to be weakly dependent on the stability properties of the PBL. Its statistics have been investigated by collecting data from a field experiment carried out in the urban area of Turin (Italy) from January 2007 to March 2008. Our results confirm those from a large-eddy simulation (LES) analysis carried out for the convective PBL with different level of convection. We extend the scenario to the stable PBL, a regime much more difficult to simulate when exploiting LES.     

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ _w /Δ, where Λ _w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ _w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ _w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ _w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.     

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.     

Evaluation of the Weather Research and Forecast/Urban Model Over Greater Paris

Meteorological modelling in the planetary boundary layer (PBL) over Greater Paris is performed using the Weather Research and Forecast (WRF) numerical model. The simulated meteorological fields are evaluated by comparison with mean diurnal observational data or mean vertical profiles of temperature, wind speed, humidity and boundary-layer height from 6 to 27 May 2005. Different PBL schemes, which parametrize the atmospheric turbulence in the PBL using different turbulence closure schemes, may be used in the WRF model. The sensitivity of the results to four PBL schemes (two non-local closure schemes and two local closure schemes) is estimated. Uncertainties in the PBL schemes are compared to the influence of the urban canopy model (UCM) and the updated Coordination of Information on the Environment (CORINE) land-use data. Using the UCM and the CORINE land-use data produces more realistic modelled meteorological fields. The wind speed, which is overestimated in the simulations without the UCM, is improved below 1,000 m height. Furthermore, the modelled PBL heights during nighttime are strongly modified, with an increase that may be as high as 200 %. At night, the impact of changing the PBL scheme is lower than the impact of using the UCM and the CORINE land-use data.     

A numerical study of second-order turbulent moments in the stably stratified nocturnal boundary layer

The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.     

Sensitivity of PBL model predictions to model design and uncertainties in environmental inputs

A simple time-dependent one-dimensional model of the planetary boundary layer (PBL) is described and used to examine the degree to which model design decisions affect model output variables. The model's sensitivity to changes in the environmental conditions is also explored. Averages of the surface fluxes, near-ground wind speeds and other PBL properties from 48 h simulations are compared to control runs. The model-calculated surface fluxes are most sensitive, in decreasing order of importance, to the vertical grid spacing, the form of closure between the surface temperature and the atmosphere, the use of vertical diffusivity smoothing, the choice of maximum time step and choice of turbulence closure scheme. These fluxes are relatively insensitive to mixing-length scaling or choice of implicit time step weighting factor. Sensitivity to changes in soil type exceeds any of the design criteria tested. The modeled fluxes are moderately sensitive to small variations in the horizontal pressure gradient, to unsteadiness in the geostrophic wind and to variations in surface roughness. They are relatively insensitive to uncertainties in local vertical velocities and small (25%) variations applied separately to soil thermal diffusivity or heat capacity. The sensitivity of the average PBL depth (Z _i ) to model and environmental changes are similar to those of surface fluxes except thatZ _i is more sensitive to changes in mixing length, albedo and imposed vertical velocity then are the surface fluxes.     

Study of the Probability Density Functions From a Large-Eddy Simulation for a Stably Stratified Boundary Layer

Turbulence in a non-strongly stably stratified large-eddy simulation (LES) case is studied through probability density functions (PDFs) to obtain additional information than that provided by classical LES averages. The PDFs are computed for one hour within the steady-state regime at three different levels: near the surface, in the middle and at the top of the boundary layer, for the wind components and the temperature. The physical significance of these PDFs from LES is discussed and they are compared to those obtained from observations. The analysis of the eddy structures within the stably stratified boundary layer is made through the combined study of the fields, the spectra and the statistical moments obtained from the PDFs and joint PDFs. The homogeneity of the fields is inspected through a comparison of the ensemble to the temporal and the spatial PDFs, showing that the ergodic theorem is not fulfilled. To this end, the sensitivity of the PDF moments to the LES resolution is explored.     

An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ_*, z being height and Λ_* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ_* < 0.02), “weakly-stable” (0.02 < z/Λ_* < 0.6), “very-stable” (0.6 < z/Λ_* < 50), and “extremely-stable” (z/Λ_* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ_*)^3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.