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.     

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.     

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.     

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).     

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.     

Turbulence structure in the planetary boundary layer

This review of the last three years of progress in the understanding of wind profiles and the structure of turbulence in the planetary boundary layer is divided into three parts. The first part, by N. E. Busch, deals with the atmospheric surface layer below 30 m. It is shown that the Monin-Oboukhov similarity hypotheses fail at low frequencies and large wave-lengths, probably due to mesoscale influences. Also, it is suggested that the neutral surface layer is a poor reference state in some respects, because the structure of turbulence in unstable conditions is quite different from that in stable stratification. The second part, by H. Tennekes, is concerned with the intermittency of the dissipative structure of turbulence and its effects on the velocity and temperature structure functions. It is shown that the modified Kolmogorov-Oboukhov theory, which attempts to explain the consequences of the dissipative intermittency, is unable to predict the shape of the temperature structure functions. The third part of this review, by H. A. Panofsky, deals with wind profiles and turbulence structure above 30 m. It is shown that between 30 and 150 m, surface-layer formulas can be used, if such mesoscale effects as changes of terrain roughness are taken into account where needed. Experimental data on turbulence above 150 m are quite sparse; some of the current scaling laws that can be used in this region are described.     

A simple two-system-parameter model for surface-effected warming of the planetary boundary layer

The heat input into the planetary boundary layer (PBL) resulting from surface-atmosphere interactions under extremely arid conditions is formulated as a linear differential equation. The forcing for this heat input is the product of the shortwave (solar) absorption at the surface and the surface-to-PBL heat transfer efficiency, . This efficiency is determined by five variables: the turbulent heat transfer coefficient, the soil heat conductance, the surface longwave emissivity, the surface temperature, and the fraction of the longwave flux from the surface absorbed within the PBL. The first two variables may vary by orders of magnitude, while the others vary much less.If a simplifying assumption is made that these variables and the thickness of the PBL do not vary with time, and that the shortwave absorption by the surface is given by a half-sine wave, then the PBL temperature cycle can be explicitly expressed (by exponential and trigonometric functions) as dependent on only two system parameters: (i) the system time constant and (ii) the transfer efficiency divided by the thermal capacity of the PBL. The shape of this diurnal cycle depends solely on the system time constant, which is a simple function of the thermal capacity of the PBL, the PBL temperature, and the same variables that define . For a small time constant, the peak PBL temperature will occur near noon, while for large values it will occur close to sunset. The amplitude of this diurnal cycle is proportional to the product of and the peak (noon) shortwave absorption at the surface, and also depends very strongly on the system time constant.A concept of trans-absorptivity, that specifies the heat input into the PBL resulting from the shortwave absorption by the surface, is introduced and discussed in terms of the governing equations. The trans-absorptivity is given as the product of the surface absorptivity (the co-albedo) and the efficiency . It is suggested that climatic effects of surface changes, such as removal of vegetation, should be formulated in terms of changes in the trans-absorptivity.     

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.     

A saline laboratory model of the planetary convective boundary layer

A laboratory water-analog of clear-air penetrative convection in the atmosphere has been constructed to continue studies of the turbulent dispersion of buoyant plumes in the convective boundary layer (CBL). A unique feature is the utilization of saline rather than thermal convection, which has been made possible by the development of a reliable method for delivering a controllable buoyancy flux through a porous membrane. It has been shown in an earlier paper that at typical laboratory scales, a saline convection tank is well suited to modelling buoyant plume dipersion under strongly convective (light wind) conditions.A range of experiments has clearly demonstrated the validity of the model. Results for density and velocity variances show much less scatter than most comparable measurements because of the greatly improved sampling that is possible in the tank. The results are generally in good agreement with field data and other laboratory simulations but the improved accuracy of the data has highlighted the anomalously low values for the horizontal velocity variances produced by large-eddy simulations of the CBL. The cause of this apparent underprediction remains unresolved.     

Drag and heat transfer relations for the planetary boundary layer

A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regionsR ₁,R ₂, andR ₃, in which the heights are of the order of magnitude ofz ₀,L, andh, respectively, wherez ₀ is the roughness length for either momentum or temperature,L is the Obukhov length, andh is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regionsR ₁ andR ₂ and of regionsR ₂ andR ₃, assuming thatz ₀ L h. The analysis yields the three similarity functionsA(),B(), andC() of the stability parameter, = u _*/fL, where is von Kármán's constant,u _* is the friction velocity at the ground andf is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.     

Similarity theory and resistance laws for the planetary boundary layer

Methods are developed for the determination of parameters of the atmospheric planetary boundary layer, within the framework of similarity theory based on the external parameters — wind velocity at the upper boundary of the layer, its thickness, air temperature difference between the upper and the lower boundaries, roughness of the underlying surface, and buoyancy forces. The form of the resistance laws is discussed. Determination of the thickness of the stationary and horizontally homogeneous (Ekman) boundary layer is analyzed and generalizations of the latter are suggested for non-stationary and inhomogeneous boundary layers.     

行星边界层湍流特征的非线性模式

本文以行星边界层理论为基础,设计了一个定常行星边界层湍流特征非线性模式。根据行星边界层湍流现象具有波动和团块结构的特点,在模式设计中引用了量子化概念,构造了一个适合于大气湍流运动的波函数用以闭合方程组,并在类比的意义下考察了该方案的合理性。采用WKB渐近方法与数值解相结合,对行星边界层湍流特征进行了定量分析,并且与实验资料以及其他作者的模式作了比较。结果表明,本文设计的模式有能力描述定常行星边界层内湍流运动的非线性特征。     

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.     

A numerical study of cloud streets in the planetary boundary layer

A two-dimensional numerical model is used to study the influence of small non-precipitating clouds on horizontal roll vortices in the planetary boundary layer. The model explicitly represents the large-scale two-dimensional motions whilst small-scale eddies are parameterized by a buoyancy dependent mixing-length hypothesis. It is applied to conditions corresponding to an observed case of cloud street formation.     

A numerical experiment with wind variations in the planetary boundary layer

Summary The equations of motion applied to the planetary boundary layer are numerically integrated for certain special eddy viscosity distributions. Accelerations are retained, eddy viscosity varied with height and, to a lesser extent, with time. The resulting inertial oscillations, although very limited in generality, show agreement with observations. Not only clockwise but also counterclockwise rotation of the end point of the wind vector can occur in some cases. Some solutions agree and others disagree with the analytical solutions for unbounded eddy viscosity.

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Zusammenfassung Die auf die planetare Grenzschicht angewandten Bewegungsgleichungen werden für spezielle Verteilungen des Austauschkoeffizienten numerisch integriert. Beschleunigungen werden beibehalten, vertikale, und, in geringerem Maße, zeitliche Variationen des Austauschkoeffizienten angenommen. Die resultierenden Trägheitsschwingungen sind zwar im allgemeinen sehr beschränkt, zeigen jedoch gute Übereinstimmung mit den Beobachtungen. In einzelnen Fällen kann eine Drehung des Windvektors nicht nur im Uhrzeigersinn, sondern auch im Gegenuhrzeigersinn auftreten. Einige Lösungen stimmen gut, andere nicht mit den analytischen Lösungen für einen unbegrenzten Austauschkoeffizienten überein.

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Résumé Les équations du mouvement appliquées à la couche limite planétaire sont intégrées pour des distributions particulières du coefficient d'échange turbulent. On tient compte des accélérations et on admet des variations verticales et, en moindre mesure, temporelles du coefficient d'échange. Les oscillations d'inertie qui en résultent sont, il est vrai, très limitées mais s'accordent bien avec les observations. Dans certains cas une rotation de la résultante du vecteur vent peut apparaître, non seulement dans le sens des aiguilles d'une montre, mais aussi en sens contraire. Quelques solutions concordent avec celles que l'on obtient en admettant un coefficient d'échange illimité, d'autres pas.

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With 5 Figures     

A two-dimensional and steady-state numerical model of the planetary boundary layer

In this paper, a two-dimensional and steady-state numerical model of the planetary boundary layer is developed. It includes the horizontal deformation of the eddy exchange coefficients and horizontal turbulence exchange. The difference between the structure of the heat island and cold island is analysed using this model.     

A model of the planetary boundary layer over a snow surface

A model of the planetary boundary layer over a snow surface has been developed. It contains the vertical heat exchange processes due to radiation, conduction, and atmospheric turbulence. Parametrization of the boundary layer is based on similarity functions developed by Hoffert and Sud (1976), which involve a dimensionless variable, ζ, dependent on boundary-layer height and a localized Monin-Obukhov length. The model also contains the atmospheric surface layer and the snowpack itself, where snowmelt and snow evaporation are calculated. The results indicate a strong dependence of surface temperatures, especially at night, on the bursts of turbulence which result from the frictional damping of surface-layer winds during periods of high stability, as described by Businger (1973). The model also shows the cooling and drying effect of the snow on the atmosphere, which may be the mechanism for air mass transformation in sub-Arctic regions.     

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.