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 numerical experiments on applicating geostrophic momentum approximation to the baroclinic and non-neutral PBL

In this paper, Wu and Blumen’s boundary layer geostrophic momentum approximation model (Wu and Blumen, 1982) is applied to baroclinic and non-neutral PBL, the motion equations for the PBL under the geostrophic momentum approximation are solved, in which the eddy transfer coefficient is a function of the distributions of the wind and temperature. The results are compared with those in barotropic and neutral conditions with the geostrophic momentum approximation. It is found that in the baroclinic condition, the wind distribution has both the characteristics of a steady, homogeneous and baroclinic PBL and those caused by the geostrophic momentum approximation. Those in non-neutral conditions show that they retain the intrinsic characteristics for the wind in non-neutral PBL, at the same time, the effects of the large-scale advection and local variation are also included. We can predict the wind in the non-neutral and baroclinic PBL by use of the geostrophic mo-mentum approximation when the temporal and spatial distributions of the geostrophic wind, as well as the po-tential temperatures and their variation rates at the upper and lower boundary of the PBL are given by large-scale model. Finally, the model is extended to the case over sea surface.     

频散效应对近地面层风速廓线的影响

应用含湍流频散效应的近地面层的运动方程求解了不同层结下的风速廓线，着重分析了湍流频散效应对近地面层平稳运动的影响。分析指出：湍流的频散效应对经典的幂律廓线一对数修正，该修正在不稳定层结时比稳定层时明显；利用相似理论也得到了该常数。     

Local Log-Law-of-the-Wall in Neutrally-Stratified Boundary-Layer Flows

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface,the horizontal mean velocity varies logarithmically with height (the so-called `log-law-of-the-wall').More recently, the same logarithmic law has also been foundin the presence of non-flat surfaces, where it governs thedynamics of the areally-averagedvelocity and involves renormalized effective parameters.Here, we analyze wind profiles over two-dimensional sinusoidal hillsobtained both from numerical simulations performed with a primitiveequation model and from wind-tunnel measurements. We showthat also the local velocity profiles behave to a verygood approximation logarithmically, for a distance from the surface of the order of the maximum hill height almost to the top of the boundary layer. Such alocal log-law-of-the-wall involves effective parameters smoothly depending on theposition along the underlying topography.This dependence looks very similar to the topography itself.     

Similarity parameters from first-order closure and data

A two-layer, first-order closure model for the Planetary Boundary Layer (PBL) is developed with the objective of parameterizing the surface stress with respect to the synoptic scale. The model includes stability effects by considering stratification-dependent secondary flow in the outer layer and empirical corrections to the surface layer flow. It shows the compatibility of simple eddy viscosity closure solutions with similarity theory by producing the now well-known Rossby similarity equations. It allows further insight into the Rossby similarity parameters by relating them to a single similarity parameter which is the ratio of the characteristic scales of the PBL and the surface layer.The measured and derived values of the similarity parameters A and B are compared with AIDJEX data and other published values. The variation in these values in stably stratified conditions is predicted and two alternate similarity parameters are calculated, one a constant and the other with a small variation and decreasing influence on the drag coefficient in stable stratification. The result is an empirical resistance law for a geostrophic drag coefficient variation which parameterizes an observed order-of-magnitude change in surface stress with changes in roughness or PBL stratification. This variation is related to similarity parameters characteristic of the region and to measurable changes in the geostrophic departure angle.     

Dynamics of the planetary boundary layer with fine structure in the large scale background field

Summary On the basis of Wu and Blumen's work (1982) on the geostrophic momentum approximation (GMA) in the planetary boundary layer (PBL) and Tan and Wu (1992, 1994) on the Ekman momentum approximation (EMA) in the PBL, some improvements about the eddy exchange coefficientK, the advective inertial force and the lower boundary condition of the PBL are developed in this paper: (1) apply theK which is a gradually varying function of height instead of a constant value in the Ekamn layer, and introduce a surface layer; (2) take the effect of the vertical advective inertial force into account; (3) the solution technique is extended from level terrain to orographically formed terrain. Under the condition of the equilibrium among four forces (the pressure — gradient force, Coriolis force, eddy viscous force and inertial force including horizontal and vertical advective inertial forces), we have obtained the analytical solutions of the distributions of the wind and the vertical velocity. The computation of an individual example shows that: (1) both the wind velocity near surface and the angle between which and the non-viscous wind are more consistent with usual observations than that of Wu and Blumen (1982); (2) comparing with the horizontal advective inertial force, the vertical advective inertial force can not be neglected, when the orography is considered, the effect of the latter is even more important than the former.With 3 Figures     

Proposal for new PBL resistance laws for neutrally-stratified flow

The history of the development of Rossby-Number Similarity Theory for the neutral Planetary Boundary Layer (PBL) is reviewed. It is shown that the logarithmic profile derived by asymptotic matching is only valid in the matched layer and not in the surface layer proper. Derivation of the traditional PBL Resistance Laws from the theory is outlined. A best-fit polynomial through observations of geostrophic drag coefficients suggests that the traditional form of the Resistance Laws is inadequate. A new formulation is derived from a generalization of the theory that allows the logarithmic form of the wind profile in the matched layer to differ from that in the surface layer. This new formulation is evaluated against observations made during the 1967 Wangara Experiment. Finally, it is demonstrated how wind speed and wind shear profiles that are consistent with the new Resistance Laws may be obtained.     

湍流频散对边界层风廓线的影响

应用包括湍流粘性和频散的新的Reynolds平均动量方程，分析了边界层的垂直风速廓线，发现包含湍流频散的地面层的风速廓线对经典的风廓线指数规律有一个对数规律的修改；而且在不稳定层结下比在稳定层结下，湍流的频散效应更为显；在中性条件下，指数规律退化为对数规律并且Karman常数被另外一个常数所代替，而这个新常数也可以通过相似理论来获得。     

A mixed-layer model for regional evaporation

A simple mixed-layer model is developed to describe evaporation into a convective planetary boundary layer (PBL). The model comprises volume budget equations for temperature and humidity, equations to describe transport through the surface layer which is treated as part of the lower boundary, and equations to describe entrainment at the top of the PBL. The ground surface is modelled as a canopy resistance. The model was integrated with canopy resistance, surface-layer resistance and available energy, (R _n – G), input as given functions of time, and the simulated PBL was allowed to grow into an atmosphere with known temperature and humidity profiles.Two variants of the mixed-layer model were tested using data from the KNMI tower site at Cabauw in the Netherlands. These variants differed only in the formulation of entrainment: one used a formulation developed by Driedonks (1982) while the other was a simpler formulation. Simulated evaporation agreed very well with observations irrespective of which entrainment formulation was used, despite discrepancies between simulated and observed PBL height growth which were sometimes quite large for the simpler formulation. Sensitivity analysis of the model confirms that good PBL height-growth predictions are not always a prerequisite for good evaporation predictions.     

A numerical experiment of the PBL with geostrophic momentum approximation

In this paper, a numerical experiment of the motion in the PBL (planetary boundary layer) is perform-ed with geostrophic momentum approximation, in which a nonlinear eddy transfer coefficient is used. Some results are obtained for the boundary layer winds in cyclone-anticyclone and trough-ridge systems. This treat-ment improves W-B’s work. The effects of geostrophic wind tendency and the advection of the geostrophic wind on the winds in the PBL are also discussed.     

Richardson's Law in Large-Eddy Simulations of Boundary-Layer Flows

Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of large-eddy simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turn out to be compatible with the Richardson t³ law for the average of square particle separation, where t is time. This emerges from the application of non-standard methods of analysis through which a precise measure of the Richardson constant was also possible. Its value is estimated as C₂ 0.5, in close agreement with recent experiments and three-dimensional direct numerical simulations.     

A barotropic planetary boundary layer

The temperature and wind profiles in the planetary boundary layer (PBL) are investigated. Assuming stationary and homogeneous conditions, the turbulent state in the PBL is uniquely determined by the external Rossby number and the stratification parameters. In this study, a simple two-layer barotropic model is proposed. It consists of a surface (SL) and overlying Ekman-type layer. The system of dynamic and heat transfer equations is closed usingK theory. In the SL, the turbulent exchange coefficient is consistent with the results of similarity theory while in the Ekman layer, it is constant. Analytical solutions for the wind and temperature profiles in the PBL are obtained. The SL and thermal PBL heights are properly chosen functions of the stratification so that from the solutions for wind and temperature, the PBL resistance laws can be easily deduced. The internal PBL characteristics necessary for the calculation (friction velocity, angle between surface and geostrophic winds and internal stratification parameter) are presented in terms of the external parameters. Favorable agreement with experimental data and model results is demonstrated. The simplicity of the model allows it to be incorporated in large-scale weather prediction models as well as in the solution of various other meteorological problems.     

塔克拉玛干沙漠腹地大气边界层参数化方案的模拟评估

沙尘起沙、沉降、传输均受到沙漠地区大气边界层条件的制约。沙漠地区观测资料匮乏,限制大气边界层模拟效果的检验和评估。利用WRFV3.7.1中尺度数值模式中5种边界层参数化方案(ACM2、BL、MYJ、MYNN2.5、YSU),模拟2014年4月塔克拉玛干沙漠大气边界层特征,并与塔中80 m塔及风廓线雷达晴朗天气下的观测资料对比分析。结果表明:5种方案均能模拟出近地面气温及地表温度,边界层高度,感热、潜热、地表热通量的变化趋势,但未能模拟出边界层风速的日变化趋势,温风湿廓线能较好的反映晴日沙漠地区边界层结构的变化特征,但未模拟出风速随高度变化趋势。沙漠地区下垫面干燥,热容量低,晴天极易形成对流不稳定边界层,非局地湍流参数化方案,ACM2方案是沙漠地区大气边界层模拟较为合理的选择。     

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.     

Ekman动量近似下中间边界层模式中的风场结构

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。     

Diurnal variations of the planetary boundary layer observed with anL-band clear-air doppler radar

Based on continuous observations of the planetary boundary layer (PBL) with anL-band (1357.5 MHz) boundary-layer radar (BLR) at a hilly location in Japan, we have discovered that on clear days, a thin enhanced echo layer corresponding to the top of the PBL (or mixed layer) appeared at about 500 m height in the morning and ascended to about 1500 m in the afternoon. Strong upward velocities were observed below the echo layer (or inside the PBL), reaching 1500 m in the afternoon.     

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.     

CMA-GFS 4DVar边界层过程线性化的改进北大核心CSCD

持续发展和优化切线性模式的线性化物理过程,保持与非线性模式一致是改善四维变分同化(4DVar)分析和预报效果的有效方法之一。目前业务系统的CMA-GFS模式采用基于Charney-Phillips(C-P)跳点的边界层参数化方案,而CMA-GFS 4DVar系统中采用基于Lorenz跳点的边界层线性化方案。为改善CMA-GFS 4DVar系统的边界层分析和预报效果,基于C-P跳点的边界层参数化方案研发了新边界层线性化方案,并通过对方案中地表热量通量和水汽通量扰动、自由大气的理查逊系数扰动、边界层的热量和动量交换系数扰动等进行更加精细地规约化约束,在确保CMA-GFS切线性和伴随模式稳定运行的情况下,减少线性化过程对切线性模式预报精度的影响。切线性近似试验检验表明:相较于原方案,新边界层线性化方案可以减少边界层位温和比湿的相对误差,最大可减少10%。批量4DVar循环同化试验表明:新边界层线性化方案可以有效改善切线性模式对低层位温、风场和比湿扰动的预报精度,减少4DVar内外循环目标泛函的相对差异,并提高700 hPa位势高度的可预报时效。     

Models for estimating offshore winds from onshore meteorological measurements

To understand and estimate wind speed differences across the coastal zone, two models, one theoretical and another semi-empirical, have been developed and verified by available data sets. Assuming that: (1) mean horizontal motion exists across the coastal zone; and (2) the geostrophic wind does not change appreciably at the top of the planetary boundary layer (PBL), the equation of motion in the direction of the wind can be reduced so that 341-01, where U, H, and C _D are wind speed, height of PBL, and drag coefficient over the sea and land, respectively. For practice, C _D SEA has been modified from a formula with U _LAND as the only input. H _SEA may be estimated routinely from known H _{D LAND LAND} and the temperature difference between land and sea, which can be provided by such means as remote sensing from meteorological satellites. For a given coast, Cmay be estimated also. This formula is recommended for weather forecasters. The semiempirical formula is based mainly on the power law wind distribution with height in the PBL. The formula states that 341-02. Simultaneous offshore and onshore wind measurements made at stations ranging from Somalia, near the equator, to the Gulf of Alaska indicated that values of a and b are 2.98 and 0.34 with a correlation coefficient of -0.95. For oceanographic applications, a simplified equation, i.e., 341-03, is also proposed.