The wind structure in planetary boundary layer

The investigations on the dynamics of the PBL have been developed in recent years. Some authors emphasized macro-dynamics and others emphasized micro-structure of the PBL. In this paper, we study and review some main characteristics of the wind field in the PBL from the view point connecting the macro-dynamics and micro-structure of the PBL, thus providing the physical basis for the further research of the dynamics and the parameterization of the PBL.     

Scaling turbulence in the planetary boundary layer

Two different approaches to scaling turbulence in the planetary boundary layer over Lake Ontario are investigated. The height up to the inversion was found to be the appropriate scaling height while u. for near‐neutral and w* for unstable conditions were the appropriate scaling velocities. The results were in general agreement with the numerical models of Deardorff (1972) and Wyngaard, Cote, and Rao (1974).     

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.     

Frontal substructures within the planetary boundary layer

A two-dimensional mesoscale model, extended by a TKE closure for the subgrid-scale terms and coupled with a soil model, is used to investigate the role of the Planetary Boundary Layer (PBL) for the development and the substructures of two different types of cold fronts. The effects of turbulent friction, large-scale (geostrophic) forcing and the diurnal variation of the terms of the surface energy balance (SEB) equation on the frontal development are studied by 10 different model runs. The ageostrophic cross-frontal circulation in the lowest two kilometres of a cold front results from friction as well as from large-scale forcing. The first one dominates the PBL processes and causes a special boundary-layer structure, which becomes apparent through the existence of seven characteristic zones defined for the x-z cross sections of potential temperature. The arrangement of these characteristic zones depends on the sense of rotation of the frictionally induced part of the ageostrophic circulation and hence on the direction of the along-front jet within the boundary layer. The daytime increase of the terms of the SEB equation for a midlatitude midsummer case leads to a strong enhancement of the frictionally induced cross-frontal circulation. The arrangement of the seven characteristic zones, however, is approximately conserved.     

Parametrization of orographical effects in the planetary boundary layer

Studies of the influence of orography on the dynamics of atmospheric processes usually assume the following relation as a boundary condition at the surface of the Earth, or at the top of the planetary layer: $$w = u\frac{{\delta z_0 }}{{\delta x}} + v\frac{{\delta z_0 }}{{\delta y}}$$ where u, v and w are the components of wind velocity along the x, y and z axes, respectively, and z ₀ = z₀(x, y) is the equation of the Earth's orography. We see that w, and consequently the influence of orography on the dynamics of atmospheric processes, depend on the wind (u, v) and on the slope of the obstacle (δz ₀/δx, δz₀/δy). In the present work, it is shown that the above relation for w is insufficient to describe the influence of orography on the dynamics of the atmosphere. It is also shown that the relation is a particular case of the expression: $$\begin{gathered} w_h = \left| {v_g } \right|\left[ {a_1 (Ro,s)\frac{{\delta z_0 }}{{\delta x}} + a_2 (Ro,s)\frac{{\delta z_0 }}{{\delta y}}} \right] + \hfill \\ + \frac{{\left| {v_g } \right|^2 }}{f}\left[ {b_1 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x^2 }} + b_2 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta y^2 }} + b_3 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x\delta y}}} \right] \hfill \\ \end{gathered} $$ where ¦vv _g¦ is the strength of the geostrophic wind, a ₁, a₂, b₁, b₂, b₃ are functions of Rossby number Ro and of the external stability parameter s. The above relation is obtained with the help of similarity theory, with a parametrization of the planetary boundary layer. Finally, the authors show that a close connection exists between the effects described by the above expression and cyclo- and anticyclogenesis.     

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     

Wave drag in the planetary boundary layer over complex terrain

The concepts of mountain-induced wave drag are applied to the smaller scale problem of the boundary layer over complex terrain. It is found that the Reynolds stress and surface drag caused by surface-generated waves can be at least as large as those conventionally associated with turbulence. Conditions in which wave effects are important are identified.ATDD Contribution No. 88/5.     

Roll vortices in the planetary boundary layer: A review

Roll vortices may be loosely defined as quasi two-dimensional organized large eddies with their horizontal axis extending through the whole planetary boundary layer (PBL). Their indirect manifestation is most obvious in so-called cloud streets as can be seen in numerous satellite pictures. Although this phenomenon has been known for more than twenty years and has been treated in a review by one of us (R.A.Brown) in 1980, there has been a recent resurgence in interest and information. The interest in ocena/land-atmosphere interactions in the context of climate modeling has led to detailed observational and modeling efforts on this problem. The presence of rolls can have a large impact on flux modelling in the PBL. Hence, we shall review recent advances in our understanding of organized large eddies in the PBL and on their role in vertical transport of momentum, heat, moisture and chemical trace substances within the lowest part of the atmosphere.initiated by IAMAP/ICDM Working Group on the Atmospheric Boundary Layer and Air-Sea Interaction.     

坡地斜压稳定大气边界层结构的数值研究

本文用数值模式较为全面地探讨了斜坡地形斜压稳定大气边界层的结构,并与平坦地形的结果进行了比较,给出了两者之间很有意思的差别.     

Aircraft observations in the planetary boundary layer under stable conditions

An analysis of observations of airflow over Lake Ontario in a stably stratified atmosphere is presented. The relationship with theory is mentioned only in terms of what may be important to future work. Detailed air motion, potential temperature and mixing-ratio measurements are presented which show pervasive variability in the horizontal. There is no evidence of gravity waves. It is suggested that vertical mixing of the atmosphere may occur in stable conditions by a mechanism quite apart from the usual concept of the small-scale random eddy motion usually associated with surface convection. Vertical soundings are analyzed as well as two long constant-height observational runs.     

The wind field in the nonlinear multilayer planetary boundary layer

By use of the small parameter expansion method, the nonlinear planetary boundary layer (PBL) is studied in this paper. The PBL is divided into the surface layer and the Ekman layer, which is divided into several sublayers. In the surface-layer, the eddy coefficient K is taken as a linear function of height; in the Ekman layer, different constant K values are taken within different sublayers: these values are determined from O'Brien's formula (O'Brien, 1970) approximately. Under the upper and lower boundary conditions and the continuity conditions of the wind velocities and turbulent stresses at each boundary between sublayers, analytical expressions for wind velocity in all sublayers and the vertical velocity at the top of the PBL are obtained. A specific example of steady axisymmetrical circular high and low pressure areas is analysed, and some new conclusions are obtained. The results are in better agreement with reality than previous results. This example also shows that the vertical velocity at the top of the PBL caused by friction approaches zero near the center of a high or low pressure system for this model, but attains its maximum absolute values near the center of the high or low pressure area for Wu's (1984) model. This is due to the fact that in our model, the geostrophic wind speed near the center of this specific vortex approaches zero, which causes the wind shear and the friction effect to be very weak. Therefore the wind distribution in the PBL is very sensitive to the type of eddy coefficient.     

A climatological study of the nocturnal planetary boundary layer

Seventy-five nights of fast-response wind and temperature data taken from a 300 m tower near Augusta, GA, were analyzed to determine the time-height structure of the nocturnal planetary boundary layer. The nights were selected from all four seasons over a wide range of synoptic conditions. Statistical summaries of Pasquill-Gifford stability, boundary-layer depth, nocturnal jet height, directional shear, gravity wave occurrence, and azimuthal meandering were obtained. The diversity of nocturnal conditions for the 75 cases resulted in histograms with broad peaks and slowly-varying distributions.To reduce the overall variance, we grouped the nights into two classes: steady nights and unsteady nights. Nights classified as steady maintained relatively uniform wind conditions. The data base was large enough to permit a further breakdown of the steady nights into three subclasses based on the height and strength of the wind maximum. Unsteady nights were more disturbed, showing time-dependent features in the wind field and were also divided into three subclasses, depending on the predominant features observed: microfrontal passage, trend, or variable conditions. Although the subclasses were based mainly on wind structure, they correlated well with other NPBL properties, such as mixed-layer depth and inversion strength. Thus, the classification procedure tended to group together nights with similar dispersion characteristics.     

Numerical simulations of the tropical air-sea planetary boundary layer

A one-dimensional numerical model of the planetary boundary layer was used to investigate thermal and kinetic energy budgets. The simulation experiments were based on two sets of data. The first set was based on a ‘typical’ June with climatological data extracted for the oceanic region slightly northeast of Barbados. The second set used data from the third phase of project BOMEX, for approximately the same area and time of year as the first set. Comparison with observations of three simulated elements (viz., sea surface temperature and wind and humidity at 6 m) which are important in determining the near-interface energy transports shows that:

1. the model is capable of realistic simulations of both ‘typical’ conditions, and conditions for a specific four-day period;
2. the model is capable of realistically simulating the differences between prevailing values of these parameters in the two cases (‘typical’ and specific four-day period).

The simulated interface fluxes are those of incoming and outgoing short- and long-wave radiation; transmitted radiation at -0.5 m in the ocean, sensible heat transfer into the ocean and air, and latent heat flux of evaporation. Comparison with observational analyses shows that the diurnal variations in net radiation and heat storage in the mixed layer are realistically simulated. The simulated values of evaporation are consistent with other estimates for both ‘typical’ conditions and specific conditions during this four-day period. The rate of heat storage varies between +51 and -37 percent of the diurnal maximum incoming radiation, and the evaporation varies between +16% and -13% of this term. The non-dimensional transfer coefficients (C _D, C_T, C_q) computed from the model show general agreement with the coefficients calculated from observations in the simulated region (Pondet al., 1971). The simulated vertical profiles of temperature are in general agreement with observed profiles, except in the uppermost portions of the atmospheric boundary layer where deviations of approximately 1.5C occur. Simulated vertical profiles of wind speed are generally consistent with observed profiles, with the largest deviations appearing to be of the order of 0.5 m s^-1. Simulated vertical profiles of the eddy fluxes of sensible heat, water vapor, and momentum are generally consistent with Bunker's (1970) aircraft-based measurements of these quantities. The time averages of these simulated profiles show regular decreases with height, while simulated profiles for specific hours of the day show intermediate maxima and minima, which are also seen in the measured profiles. The vertically integrated kinetic energy budgets of the modelled atmospheric layer are presented through the four terms of the kinetic energy budget, viz., the upper and the lower boundary drags, dissipation, and potential-to-kinetic conversion. The dominant terms in the atmospheric energy budgets are the production and dissipation terms, with kinetic energy being exported both to the overlying atmospheric layer and to the underlying oceanic layer at rates of about 2 to 6% of the production, respectively. Comparisons between the climatological and BOMEX simulations are presented. The vertically integrated humidity budgets are presented for the two simulation experiments. Under ‘typical’ conditions, the humidity budget reveals an upper boundary flux of about +29% of the lower boundary flux with the vertically integrated advective flux being -59% of the lower flux. For the specific four-day simulation, the upper boundary flux and advection are about +28 and -70%, respectively, of the lower boundary flux.     

A bulk model for the atmospheric planetary boundary layer

The integrated momentum and thermodynamic equations through the planetary boundary layer (PBL) are solved numerically to predict the mean changes of wind and potential temperature from which surface fluxes are computed using bulk transfer coefficients of momentum and heat. The second part of the study involves a formulation and testing of a PBL height model based on the turbulent energy budget equation where turbulent fluxes of wind and heat are considered as the source of energy. The model exhibits capability of predicting the PBL height development for both stable and unstable regimes of observed conditions. Results of the model agree favourably with those of Deardorff's (1974a) and Tennekes' (1973) models in convective conditions.Contribution number 396.     

Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer

The heated boundary layer for DAY 33 of the Wangara data of southeast Australia (Clarke et al., 1971) is studied numerically with a three-dimensional model using 64000 grid points within a volume 5 km on a side and 2 km deep. Subgrid-scale transport equations were utilized in place of eddy-coefficient formulations. The rate of growth of the mixed layer is examined and parameterized, and the vertical profiles of heat flux, moisture flux and momentum fluxes are examined. The momentum boundary layer is found to coincide essentially with the mixed layer, and to grow with the latter during the hours of solar heating of the surface.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The vertical structure of the atmospheric planetary boundary layer in undisturbed trade winds over the Atlantic Ocean

During the Atlantic Expedition 1965 and the Atlantic Tradewind Experiment (ATEX) 1969, shipborne aerological measurements were obtained in order to investigate the thermodynamical and kinematic structure of the planetary boundary layer in low latitudes. Under suppressed convection, the subdivision of this layer into five sub-regions was found to be a rather permanent feature. Enhanced cumulus convection effects a smoothing of the thermodynamical discontinuities and leads sometimes to a destruction of the trade inversion. Due to the surface pressure distribution and the thermal wind distribution in the lower atmosphere, the actual wind speed and direction are nearly constant with height below cloud base. In the cloud layer up to the inversion, the wind speed generally decreases and the air flow tends to become more zonal.     

A study of vertical velocity distributions in the planetary boundary layer

Until recently, pollution dispersion models have made predictions on the basis that the pollutant concentration is Gaussian. Such is not the case for convective conditions where the observed vertical velocity distribution is skewed towards the updraught portion of the distribution. One recent dispersion model assumes that the observed distribution can be synthesized by superimposing two Gaussians of appropriate means, variances and amplitudes.In the current paper, two techniques for deriving the constituent distributions are investigated. The first technique is based on conditionally sampling the vertical velocity time series and partitioning the vertical velocity samples into two sets — one set recorded when the sensor was experiencing an updraught and the other when the sensor was experiencing a downdraught. The second method consists of fitting two Gaussian distributions to the observed data and adjusting these using an iterative procedure until a specified tolerance is achieved.Both techniques give similar results which compare favourably with results obtained by other researchers. Assumptions, as well as advantages and disadvantages of each technique are also discussed.     

Lagrangian similarity theory applied to diffusion in the planetary boundary layer

A similarity theory is developed to describe diffusion of a cloud of passive material in a neutral barotropic steady-state boundary layer of the Earth's atmosphere. It is suggested that a characteristic length scale U ^*/f is relevant in the diffusion process when the diffusing cloud mixes well into the depth of the boundary layer. For an atmosphere having an effective upper bound for vertical spread, an expression for the trajectory of the centroid of the diffusing cloud is derived. The theoretically computed vertical spread is compared with experimental data on diffusion of tracer cloud over rough (urban) and smooth terrains.