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.     

Diurnal wind variation in the planetary boundary layer (PBL) over Sriharikota,India

Pibal ascents were taken every three hours at a coastal station, Sriharikota (India) on the east coast in four different campaigns each representing a season in India. A diurnal pattern of winds in the PBL winds was found in all seasons but the pattern varies from season to season. The details are described and discussed.     

Spatial variability of water vapor turbulent transfer within the boundary layer

Although the physics of evaporation within the inner region of the boundary layer is believed to be well understood, observations of mass-energy exchange processes have been hindered by the limitations of point sensors. A combination of point sensors and active remote sensing, namely, water-Raman Lidar measurements, offers new opportunities to study relatively large areas at temporal and spatial scales previously unattainable. Results from experiments over uniform canopies both confirm some traditional theories and challenge some of the underlying assumptions concerning the homogeneity of the surface-atmosphere interface and the use of point sensors to characterize large areas.This work was performed under the auspices of the U.S. Department of Energy. The authors would like to thank F. Archuleta, J. Archuleta, F. Barnes, W. Clements, K. Muller and W. Porch of LANL, R. Whitis of USDA, R. Jackson and P. Pinter of USDA-WCL, and L. Balick of EG&G for their invaluable time and support.     

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 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.     

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.     

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).     

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.     

Similarity functions D for water vapor in the unstable atmospheric boundary layer

An analysis was performed of experimental data obtained at fixed ship stations during AMTEX 1974 and 1975. This allowed the calculation of the bulk transfer relationships for water vapor and sensible heat in the atmospheric boundary layer for different interpretations of the thickness scale of the boundary layer. It was found that scaling based on the observed thickness, which herein was taken as the height of the lowest value in the potential temperature profile under unstable conditions, produces least scatter in the calculations. The results obtained for the similarity function c( _i ) of the bulk heat transfer coefficient are in good agreement with the results of previous studies. As observed earlier (Brutsaert and Mawdsley, 1976; Mawdsley and Brutsaert, 1977), under unstable conditions the similarity functions D() of the bulk water vapor transfer coefficient are smaller than the corresponding C() functions for sensible heat. In the case of inversion height scaling, the results can be represented by d( _i ) = 0.65 c( _i ).     

行星边界层中多极值风速廓线的研究

本文利用325米气象塔及声雷达探测资料分析了夜间平稳天气条件下行星边界层中风速出现多极值的现象。分析指出,多极值风速与边界层中多层逆温有密切的联系,当温度场出现多层逆温并维持一定的强度和时间后,便相应地出现了多层风速极大,风速极大值出现的高度在逆温顶附近或稍高。 文内还用一维非定常模式模拟了多极值风速廓线的形成。     

Design criteria for water tank models of dispersion in the planetary convective boundary layer

Design criteria for laboratory water-analogs of clear-air penetrative convection in the atmosphere are described. Consideration is given to the range of factors relevant to modelling both turbulent penetrative convection and the dispersion of buoyant point-source plumes within the convective boundary layer. Scaling arguments based on mixed-layer and plume scaling show that at typical laboratory scales, saline convection can satisfy the requirements for modelling buoyant plume dispersion under strongly convective (light wind) conditions better than heated water tanks or wind tunnels.     

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.     

A study of gravity waves in the planetary boundary layer by acoustic sounding

Gravity waves associated with stably stratified layers were observed in the planetary boundary layer at two locations in France. Using an array of three monostatic Doppler acoustic sounders, the wave speeds and directions were found. A quantitative study of the waves has been performed to determine their physical characteristics. Based on their dynamics, a classification into three types was possible. Most were found to be trapped beneath a critical level.     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Bulk characteristics of heat transfer in the unstable,baroclinic atmospheric boundary layer

Field data for the unstable, baroclinic, atmospheric boundary layer over land and over the sea are considered in the context of a general similarity theory of vertical heat transfer. The dependence of δθ/θ_* upon logarithmic functions of h _c z _T and stability (through the similarity function C) is clearly demonstrated in the data. The combined data support the conventional formulation for the heat transfer coefficient δθ/θ_* when,

1. the surface scaling length is z _T (« z ₀), the height at which the surface temperature over land is obtained by extrapolation of the temperature profile
2. the height scale is taken as the depth of convective mixing h _c
3. the temperature profile equivalent of the von Karman constant is taken as 0.41
4. areal average, rather than single point, values of δθ are employed in strongly baroclinic conditions. No significant effect of baroclinity or the height scale ratio as proposed in the general theory is found. Variations in C about a linear regression relation against stability are most probably due to uncertainties in the areal surface temperature and to experimental errors in general temperature measurements.

     

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.     

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.