Internal Boundary Layers: I. Height Formulae for Neutral and Diabatic Flows

The notion of an internal boundary layer (IBL) appeared in studies of local advection within the atmospheric boundary layer when air flows over a change in surface conditions. These include surface roughness, thermal and moisture properties. An ability to predict the height of the IBL interface in the atmosphere under neutral stability, accompanied by certain assumptions on the form of the mean flow parameters, have been a means of obtaining information on the velocity profile after step changes in roughness for more than half a century. A compendium of IBL formulae is presented. The approach based on the diffusion analogy of Miyake receives close attention. The empirical expression of Savelyev and Taylor (2001, Boundary Layer Meteorol. 101, 293–301) suggested that turbulent diffusion is not the only factor that influences IBL growth. An argument is offered that an additional element, mean vertical velocity or streamline displacement, should be taken into account. Vertical velocity is parameterized in terms of horizontal velocity differences employing continuity constraints and scaling. Published data are analyzed from a new point of view, which produces two new neutral stratification formulae. The first implies that the roughness lengths of adjacent surfaces are equally important and a combined length scale can be constructed. In addition new formulae to predict the height of the region of diabatic flow affected by a step change in surface conditions are obtained as an extension of the neutral flow case.     

Boundary-Layer Adjustment Over Small-Scale Changes of Surface Heat Flux

Four months of eddy correlation data collected over a grass field and a nearby sage brush community are analyzed to examine the adjustment of the boundary-layer structure as it flows from the heated brush to the snow-covered grass. The grass site includes a 34-m tower with seven levels of eddy correlation data. The midday heat flux over the snow-covered grass and bare ground surfaces is often downward particularly with melting conditions, while the corresponding heat flux over the brush is almost always upward. For most of these cases, a stable internal boundary layer over the snow is well defined in terms of vertical profiles of the buoyancy flux over the snow-covered grass. The stable internal boundary layer is generally embedded within a deeper layer of flux divergence corresponding to increasing upward heat flux with height above the internal boundary layer. With thin snow cover, the surface heat flux over the grass is weak upward due to heating of grass protruding above the snow so that the flow adjusts to a decrease of the upward surface heat flux in the downwind direction. This common case of an adjusting boundary layer contrasts with the formation of an internal boundary layer due to a change of sign of the surface heat in flux the downwind direction. The adjustment of the boundary layer to the decrease of the surface heat flux leads to vertical divergence of the upward heat flux in contrast to the usual heated boundary layer over homogeneous surfaces. The consequences of the cooling due to the vertical divergence of the heat flux are discussed in terms of the heat budget of the adjusting and internal boundary layers.     

Numerical simulation of internal boundary-layer development and comparison with atmospheric data

A finite-volume numerical model is employed to investigate the adaptation of the atmospheric boundary layer to a change in the underlying surface roughness, such as that existing in the transition from land to the free surface of a water body. Numerical results are validated by comparison with neutral stratification atmospheric data and compared with the internal boundary-layer (IBL) heights computed using a number of existing empirical formulae. The numerical analysis allows an extension of the fetch range in which the existing formulae, calibrated only by comparison with short fetch data, may be applied. An argument is offered that the spatial variability of the water surface roughness should be also taken into account for the IBL development over the surface of a water body.     

Boundary-Layer Stress Instabilities in Neutral,Rotating Turbulent Flows

Boundary-layer instabilities are studied by analyzing the results of laboratory simulations of wall turbulence in a shear-driven rotating flow. The experiments were carried out in the Turin University Laboratory rotating water tank, where a circular flow was generated by either increasing (spin-up) or decreasing (spin-down) the rotation speed of the platform. The flow was measured using a Particle Image Velocimetry technique and the developed turbulence analyzed. Two cases were accounted for, in the former the measurements were performed over a smooth surface (bottom of the tank), while in the latter a rough-to-smooth transition was considered. The turbulent boundary layer developed inside the tank is analyzed by means of vertical profiles of mean and turbulent quantities and on the basis of drag coefficients. Then turbulent structures developed in the different cases are shown and discussed in terms of the vorticity fields. Finally, an analysis based on the concept of swirling strength was carried out to select among the vortex extremes those associated with a coherent structure.     

A Case Study of the Near-Neutral Coastal Internal Boundary-Layer Growth: Aircraft Measurements Compared with Different Model Estimates

A simplified version of a model of the internalboundary layer evolution is compared with aircraftmeasurements across the southern part of the east coast ofSweden (Blekinge). The two flight occasions used hererepresent relatively high wind velocities and negligiblesurface heat flux. Both the vertical potential temperaturegradient and the surface temperaturedifference between land and sea are small. Modelpredictions of the internal boundary-layer (IBL)height agree well with data, for both short and largerdistances from the coastline. The contributions to theIBL growth from the mechanical turbulence and theZilitinkevich correction are discussed, as are thesensitivities of the growth to a number of physicalparameters. In near neutralconditions, the vertical potential temperaturegradient is found to be an important parameter for thegrowth of the IBL.A comparison with several simple model estimates forthe height of the IBL is presented. The majority ofthe models overestimate the IBL height. Some of themodels give reasonable results close to the coast, butgenerally the simple models perform less well atlarger distances.     

Boundary-Layer Similarity Under an Axisymmetric,Gradient Wind Vortex

We present similarity solutions for the mean boundary-layer profiles under an axisymmetric vortex that is in gradient wind balance; the similarity model includes the nonlinear momentum advection and curvature terms. These solutions are a generalization of the Ekman layer mean flow, which is the canonical boundary-layer basic state under a uniform, geostrophically-balanced flow. Near-surface properties such as inflow angle, surface wind factor, diffusive transport of kinetic energy into the surface layer and dissipational heating are calculated and shown to be sensitive to the choice of turbulence parameterization.     

Modelling Internal Boundary-Layer Development in a Region with a Complex Coastline

The purpose of this paper is to test the ability of two quite different models to simulate the combined spatial and temporal variability of the internal boundary layer in an area of complex terrain and coastline during one day. The simple applied slab model of Gryning and Batchvarova, and the Colorado State University Regional Atmospheric Modelling System (CSU-RAMS) are tested by comparison with data gathered during a field study (called Pacific '93) of photochemical pollution in the Lower Fraser Valley of British Columbia, Canada. The data utilised here are drawn from tethered balloon flights, free flying balloon ascents, and downlooking lidar operated from an aircraft flown at roughly 3500 m above sea level. Both models are found to represent the temporal and spatial development of the internal boundary-layer depth over the Lower Fraser Valley very well, and reproduce many of the finer details revealed by the measurements.     

Conditional Analysis of an Internal Boundary Layer

Data from a convective internal boundary layer (IBL) are analyzed by focusing on the instantaneousstructure of the top of the IBL instead of the time-average structure.A conditional averaging technique is developed todiscriminate between air from above the IBL and air from below the IBL , which alternately invade some instrument levels due tosubstantial variation of the top of the convective IBL.Sensitivity to the conditional sampling criteria is examined.Inside the IBL , buoyant and mechanicalproduction and dissipation dominate the turbulent kinetic energy budget.The horizontal advection and turbulent transport terms are smaller, but not negligible. The inferred pressure correlation term is negligible.Above the IBL , buoyant production and dissipation, although weak,dominate the turbulent kinetic energy budget. Shear generation andturbulent transport are smaller but significant.     

Nocturnal Boundary-Layer Regimes

This study analyzes turbulence data collected over a grassland site in the nocturnal boundary layer. Examination of the dependence of the nocturnal boundary layer on stability suggests three regimes: a) the weakly stable case, b) a transition stability regime where many of the variables change rapidly with increasing stability and c) the very stable case. The value of z/L where the downward heat flux is a maximum defines the stability boundary between the weakly stable and transition regimes, where L is the Obukhov length. In the present analysis, the downward heat flux reaches a maximum at z/L approximately equal to 0.05 for 10 m, although comparison with other data indicates that this is not a universal value. For weaker stability, the heat flux decreases with decreasing z/L due to weaker temperature fluctuations. In the transition stability regime, the heat flux decreases rapidly with increasing stability due to restriction of vertical velocity fluctuations by the increasing stratification.For weakly stable conditions, the variances scale according to Monin-Obukhov similarity theory. For very stable conditions, the variances are contaminated by non-turbulent horizontal motions and do not follow the scaling laws. An alternative length scale based on variances is developed which explains more of the variance of the transfer coefficients compared to the Obukhov length.     

Variability Of The Stable And Unstable Atmospheric Boundary-Layer Height And Its Scales Over A Boreal Forest

Radiosondes releases during the NOPEX-WINTEX experiment carried out in late winter in Northern Finland were analysed for the determination of the height h of the atmospheric boundary layer. We investigate various possible scaling approaches, based on length scales using micrometeorological turbulence surface measurements and the background atmospheric stratification above h. Under stable conditions, the three previously observed turbulence regimes delineated by values of z/L (L is the Obukhov length) appears as a blueprint for understanding the departures found for the suitability of the Ekman scaling based on L_E = u_/f (u is the friction velocity and f the Coriolis parameter). The length scale L_N = u_/N (where N is the Brunt–Väisälä frequency) appears to be a useful scale under most stable conditions, especially in association with L. Under unstable conditions, shear production of turbulence is still significant, so that the three scales L, L_N and L_E are again relevant and the dimensionless ratios _N = L_N/L and L_N/L_E = N/f describe well the WINTEX data. Furthermore, in the classical scaling framework, the unstable domain may also be divided into three regimes as reflected by the dependence ofu_/f on instability (z/L).     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.     

The Adaptation of the Atmospheric Boundary Layer to a Change in Surface Roughness

The adaptation of the atmospheric boundary layer to a change in the underlying surface roughness is an interesting problem and hence much research, theoretical, experimental, and numerical, has been undertaken. Within the atmospheric boundary layer an accurate numerical model for the turbulent properties of the atmospheric boundary layer needs to be implemented if physically realistic results are to be obtained. Here, the adaptation of the atmospheric boundary layer to a change in surface roughness is investigated using a first-order turbulence closure model, a one-and-a-half-order turbulence closure model and a second-order turbulence closure model. Perturbations to the geostrophic wind and the pressure gradients are included and it is shown that the second-order turbulence closure model, namely the standard k - model, is inferior to a lower-order closure model if a modification to limit the turbulent eddy size within the atmospheric boundary layer is not included within the model.     

Stable Atmospheric Boundary-Layer Experiment in Spain (SABLES 98): A Report

This paper describes the Stable AtmosphericBoundary Layer Experiment in Spain (SABLES 98),which took place over the northern Spanish plateaucomprising relatively flat grassland,in September 1998. The main objectives of the campaign were to study the properties of themid-latitude stable boundary layer (SBL).Instrumentation deployed on two meteorologicalmasts (of heights 10 m and 100 m)included five sonic anemometers, 15 thermocouples,five cup anemometers and three propeller anemometers,humidity sensors and radiometers.A Sensitron mini-sodar and a tetheredballoon were also operated continuously. Atriangular array of cup anemometers wasinstalled to allow the detection ofwave events. Two nocturnal periods analysedon 14–15 and 20–21 September are used toillustrate the wide-ranging characteristics of the SBL.     

Atmospheric Boundary-Layer Dynamics with Constant Bowen Ratio

Motivated by the observation that the diurnal evolution of sensible and latent heat fluxes tends to maintain a constant Bowen ratio, we derive approximate solutions of the ordinary differential equations of a simplified atmospheric boundary-layer (ABL) model. Neglecting the early morning transition, the potential temperature and specific humidity of the mixed layer are found to be linearly related to the ABL height. Similar behaviour is followed by the inversion strengths of temperature and humidity at the top of the ABL. The potential temperature of the mixed layer depends on the entrainment parameter and the free-atmosphere temperature lapse rate, while the specific humidity also depends on the free-atmosphere humidity lapse rate and the Bowen ratio. The temporal dynamics appear only implicitly in the evolution of the height of the boundary layer, which in turn depends on the time-integrated surface sensible heat flux. Studying the limiting behaviour of the Bowen ratio for very low and very large values of net available energy, we also show how the tendency to maintain constant Bowen ratio during midday hours stems from its relative insensitivity to the atmospheric conditions for large values of net available energy. The analytical expression for the diurnal evolution of the ABL obtained with constant Bowen ratio is simple and provides a benchmark for the results of more complex models.     

下垫面粗糙度突变时的内边界层研究

本文介绍了下垫面粗糙度突变时内边界层的形成过程,阐述了内边界层研究的意义,总结和分析了内边界层在理论研究、实验和观测以及数值模拟方面的主要成果。     

Baroclinic Planetary Boundary-Layer Model for Neutral and Stable Stratification Conditions

The temperature and wind profiles in abaroclinic atmospheric boundary layer (ABL) are investigated.Assuming stationary conditions, the turbulent state in the ABL forstable and neutral conditions is uniquely determined by the Rossbynumber, the external stratification parameter and two externalbaroclinic parameters. A simple two-layer baroclinic model isdeveloped. It consists of a surface layer (SL) and overlyingEkman-type layer. The system of dynamic and heat transfer equations isclosed using K-theory. In the SL the turbulent exchangecoefficient is consistent with the results of similarity theorywhile in the Ekman layer it is assumed constant. The universalfunctions in the resistance, heat and humidity transfer laws arededuced from the analytical solutions for the wind and temperatureprofiles. The solutions of the ABL resistance laws for theinternal ABL parameters, necessary for the calculations of the ABLprofiles, are approximated in terms of the external ABLparameters. Favourable agreement of model results with theavailable experimental data is demonstrated.     

大气边界层湍流温度序列的信息熵分析

利用大气边界层内近地面的大气湍流温度时间序列，运用功率谱分析、信息熵分析等方法，分析了大气边界层内近地面的大气湍流特点，并对稳定层和不稳定层的大气湍流进行了对比。结果表明，信息熵和功率谱指数是区别稳定层结和不稳定层结大气边界层湍流特征的指标，对造成两者之间的差别做出了对应的解释。     

Influence of a Two-scale Surface Roughness on a Neutral Turbulent Boundary Layer

Flow in the urban boundary layer is strongly influenced by the surface roughness, which is composed principally of isolated buildings or groups of buildings. Previous research has shown that the flow regime depends on the characteristic height of these obstacles (H), and the spacing between them (W). In reality, the urban boundary layer contains roughness elements with a wide range of length scales; in many practical situations these can be classified into large-scale roughness—buildings, or groups of buildings—and small-scale roughness, such as street furniture and elements on the façades and roofs. It is important to understand how the small-scale roughness might modify mass and momentum transfer in the urban boundary layer, but relatively little information is available concerning the potential interaction between large- and small-scale roughness elements in the different flow regimes. This problem has been studied using wind-tunnel experiments, by measuring vertical velocity profiles over a two-dimensional obstacle array, adding small-scale roughness elements to the top of larger parallel square bars. The experiments were performed for different cavity aspect ratios: the results show that the small-scale roughness increases the turbulence intensities and the momentum transfer when the large-scale obstacles are closely packed (H/W > 1) but it has very little effect for more widely-spaced obstacles (H/W < 1).     

探空观测的边界层高度时空变化特征

基于2010—2018年我国119个站点L波段探空秒级资料,通过对位温廓线法所得边界层高度进行Kmeans聚类,将我国分为青藏地区、西北地区、中部地区和东部地区4个分区,分析我国边界层高度及边界层状态（对流、中性和稳定边界层）发生频率的变化特征。结果表明：2010—2018年08：00我国年平均边界层高度均为200~600 m,以稳定边界层为主,20：00年平均边界层高度从青藏地区、西北地区、中部地区到东部地区逐渐减小,其中青藏地区和西北地区全年以对流和中性边界层状态为主,中部地区和东部地区以中性边界层为主;4个分区的月平均边界层高度在08：00逐月变化不明显,且各分区间差异不大,而4个分区20：00月平均边界层高度随时间呈单峰结构,最大值出现在春夏季,最小值出现在秋冬季,从青藏地区、西北地区、中部地区到东部地区变化幅度逐渐减小;青藏地区、西北地区和中部地区的边界层高度日变化幅度春夏季大、秋冬季小,而东部地区边界层高度日变化在不同季节特征相近。     

Determination of the Atmospheric Boundary Layer Height from Radiosonde and Lidar Backscatter

The height of the atmospheric boundary layer is derived with the help of two different measuring systems and methods. From radiosoundings the boundary layer height is determined by the parcel method and by temperature and humidity gradients. From lidar backscatter measurements a combination of the averaging variance method and the high-resolution gradient method is used to determine boundary layer heights. In this paper lidar-derived boundary layer heights on a 10 min basis are presented. Datasets from four experiments – two over land and two over the sea – are used to compare boundary layer heights from both methods. Only the daytime boundary layer is investigated because the height of the nighttime stable boundary layer is below the range of the lidar. In many situations the boundary layer heights from both systems coincide within ±200 m. This corresponds to the standard deviation of lidar-derived 10-min values within a 1-h interval and is due to the time and space variability of the boundary layer height. Deviations appear for certain situations and depend on which radiosonde method is applied. The parcel method fails over land surfaces in the afternoon when the boundary layer stabilizes and over the ocean when the boundary layer is slightly stable. An automatic radiosonde gradient method sometimes fails when multiple layers are present, e.g. a residual layer above the growing convective boundary layer. The lidar method has the advantage of continuous tracing and thus avoids confusion with elevated layers. On the other hand, it mostly fails in situations with boundary layer clouds