Stratified Atmospheric Boundary Layers

Various features of different stability regimes of the stable boundary layer are discussed. Traditional layering is examined in terms of the roughness sublayer, surface layer, local similarity, z-less stratification and the region near the boundary-layer top. In the very stable case, the strongest turbulence may be detached from the surface and generated by shear associated with a low level jet, gravity waves or meandering motions. In this case, similarity theory and the traditional concept of a boundary-layer break down. The elevated turbulence may intermittently recouple to the surface. Inability to adequately measure turbulent fluxes in very stable conditions limits our knowledge of this regime.     

Contrasting vertical structures of nocturnal boundary layers

This study analyzes eight levels of sonic anemometerdata collected on a 60-m towerduring CASES-99, toward the goal of understanding thevertical structure of thenocturnal boundary layer. Several different regimesare found. Thin boundarylayers are often observed where fluxes decrease with height and approximately vanish between 20 and 30 m aboveground. The flow above the thin boundary layeraccelerates and increasing shear oftengenerates significant turbulence in the middle ofthe night. Thisshear-generated turbulence is often stronger thanthat near the surface corresponding to an upside-downboundary layer. During these conditions,the turbulent transport of turbulence is downwardtoward the surface. The turbulence in this regimeshows features of z-less turbulence to the extentthat neither the height above groundnor the boundary-layer depth are primary scalingvariables. This layer isdifferent from a `residual layer' in thatturbulence is actively generated byshear associated with nocturnal accelerationsand often is stronger than that inthe surface-based boundary layer.In many cases, the turbulence does not varysignificantly across the towerlayer, implying that the boundary layer ismuch deeper than the 60-m towerlayer. Several case studies are presentedto illustrate the largevariation of vertical structure betweennights.     

Turbulence Characteristics Of The Stable Boundary Layer Over A Mid-Latitude Glacier. Part Ii: Pure Katabatic Forcing Conditions

Observations obtained over a glacier surface in a predominantlykatabatic flow and with a distinctwind maximum below 13-m height are presented. The data werecollected using a 13-m high profilemast and two sonic anemometers (at about 2.5-m and 10-m heights).The spectra at frequencies belowthat of the turbulence range appear to deviate considerably fromthe curves obtained by Kaimal andco-workers during the 1968 Kansas experiment. The characteristicsof these deviations are compared tothe observations of others in surface-layers disturbed by anykind of large-scale outer-layer (orinactive) turbulence. In our case the disturbances arelikely to be induced by the highmountain ridges that surround the glacier. Moreover, the deviationsobserved in the cospectra seemto result from an, as yet, unspecified interaction between theinactive outer-layer turbulenceand the local surface-layer turbulence. Near the distinctwind maximum turbulence production ceasedwhile turbulence itself did not, probably the result ofturbulence transport from other levels. Consequently, we studied thelocal similarity relations using _w instead of u_* as an alternative velocity scale. Wellbelow the wind maximum, and for relatively low stability(0< Ri_g <0.2), the flow behaves accordingto well established local-scaling similarity relationshipsin the stable boundary layer. For higherstability (Ri_g > 0.2), and near or above the wind maximum, the boundary-layer structure conforms tothat of z-less stratification suggesting that the eddy sizeis restricted by the local stability ofthe flow. In line with this we observed that the sensibleheat fluxes relate remarkably well to thelocal flow parameters.     

The influence of atmospheric stability on the ‘Leipzig’ boundary-layer structure

The Leipzig wind profile recorded in 1931 has long been considered representative of the wind profile expected in a steady, barotropic flow in the planetary boundary layer over a flat homogeneous surface. As such, the Leipzig data set has been extensively used in the development of computational models for planetary boundary-layer flows. To date, workers have assumed that the effect of stable stratification in the atmosphere over Leipzig was negligible. In the present work, a second-order turbulence closure that explicitly accounts for the effects of stable stratification is used to analyse the Leipzig data. The importance of stable stratification in this near-neutral data set is demonstrated.     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

纳木错(湖)地区湍流数据质量控制和湍流通量变化特征

利用中国科学院纳木错多圈层综合观测研究站2009年全年的大气湍流观测资料,应用Foot-print模型分析了青藏高原非均匀下垫面湍流观测数据的数据质量、质量评价及不同下垫面对湍流通量的贡献。结果表明:纳木错(湖)地区因不同土地利用类型的差别,导致地表通量分布不均匀,草地对地表通量的贡献最大;对不同大气层结状态,观测站周围200m范围内的地表通量贡献各不相同,上风向通量贡献源区较大,湍流发展较充分。在不稳定状态和中性状态下,纳木错地区地表通量数据质量较高,即白天观测的通量数据质量较高;在稳定状态下数据质量较低,即夜间的通量数据质量较差;纳木错地区的湍流通量受湖陆风和大气稳定性影响较大。     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as \(\beta \approx 5.7\) in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.     

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.     

Radiative Processes in the Stable Boundary Layer: Part II. The Development of the Nocturnal Boundary Layer

The interaction between radiation and turbulence in the stable boundary layer over land is explored using an idealized model, with a focus on the surface layer after the evening transition. It is shown that finer vertical resolution is required in transitional boundary layers than in developed ones. In very light winds radiative cooling determines the temperature profile, even if similarity functions without a critical Richardson number are used; standard surface similarity theory applied over thick layers then yields poor forecasts of near-surface air temperatures. These points are illustrated with field data. Simulations of the developing nocturnal boundary layer are used to explore the wider role of radiation. Comparatively, radiation is less significant within the developed stable boundary layer than during the transition; although, as previous studies have found, it remains important towards the top of the stable layer and in the residual layer. Near the ground, reducing the surface emissivity below one is found to yield modest relative radiative warming rather than intense cooling, which reduces the potential importance of radiation in the developed surface layer. The profile of the radiative heating rate may be strongly dependent on other processes, leading to quite varied behaviour.     

Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.     

边界层局地相似理论在草原下垫面的适用性检验

利用锡林浩特草原平坦下垫面塔层湍流资料,对常值通量层的高度进行了估计,检验了局地相似理论在均匀草原下垫面的适用性,对Monin-Obukhov相似理论和局地相似理论在常值通量层以上的大气边界层的适用性进行了比较。结果表明:(1)对于锡林浩特草原来说,常值通量层厚度在50m左右;(2)通过分析无量纲风速和温度梯度、无量纲风速方差、无量纲标量(温度T、水汽q、CO2浓度C)方差与稳定度z/L之间的关系,验证了局地相似理论在均匀草原下垫面70m以下大气边界层的适用性;(3)感热通量尺度与浮力长度尺度之间存在线性关系;(4)从经典Monin-Obukhov长度、局地Monin-Obukhov尺度和浮力长度尺度的对比分析来看,局地尺度更适用于50m以上的大气边界层,而浮力长度尺度不适用于50m以上的大气边界层。     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

A STUDY OF NEAR SURFACE WIND PROFILES IN THE HEBEI COASTAL AREA BASED ON OBSERVATIONAL EXPERIMENTS

In order to provide wind profiles for the microscale numerical simulation of wind farm with complex terrain,using the 100 m tower atmospheric turbulence observation experiment data in 2010 in Hebei Province offered by National Climate Center, the variation characteristics of wind profile under the different atmospheric stability conditions are analyzed, and the wind profile expression based on the local similarity theory is established. The results show that:(1) In spring, the occurrence probability of unstable stratification in the Hebei coastal area is as high as 28%, and the probability of stable stratification is more than 43% while, in summer, the probability of occurrence of unstable stratification is as high as 80% with a lower probability for stable stratification; and(2) for stable stratification, the characteristics of atmosphere change is dramatic in terms of the vertical direction, which need to be treated layer by layer.According to the atmospheric turbulence observation experiment data above, under stable stratification, the relationship between the dimensionless velocity gradient and the stability ζ can be expressed as 1 +βmζ, with βm changing with the height: βm takes 4.1-4.3 under 30 m, βm takes 4.6-4.7 between 30-50 m, and βm takes 6.3-6.7 over 50 m.     

Helicopter-Borne Flux Measurements in the Nocturnal Boundary Layer Over Land – a Case Study

This case study introduces measurements of turbulent fluxes in a nocturnal boundary layer in North Germany with the new helicopter-borne turbulence measurement system HELIPOD, a detailed data analysis and examination in regard of systematic errors of the instrument, and some comparison with local similarity theory and experiments of the past, in order to confirm the occurrence of small vertical turbulent fluxes. The examined nocturnal boundary layer offered excellent conditions to analyse the quality of the measurement system. In this connection, a detailed look at a strong ground-based inversion disclosed small turbulent fluxes with a spectral maximum at ten metres wavelength or less, embedded in intermittent turbulence. For verification of these fluxes, the measurements were compared with well established results from past experiments. Local similarity theory was applied to calculate dimensionless variances of the turbulent quantities, which were found in good agreement with other observations. Since shear and stratification varied significantly on the horizontal flight legs due to global intermittency, a method was developed to determine vertical gradients on a horizontal flight pattern, by use of small fluctuations of the measurement height. With these locally determined gradients, gradient transport theory became applicable and the turbulent diffusivities for heat and momentum, the Richardson number, and the flux Richardson number were estimated within isolated strong turbulent outbursts. Within these outbursts the flux Richardson number was found between 0.1 and 0.2. The functional relationship between the gradient Richardson number and the turbulent Prandtl number agreed well with observations in past experiments and large eddy simulation. The impact of the stratification on the vertical turbulent exchange, as already described for the surface layer using Monin–Obukhov similarity, was analogously observed in the very stably stratified bulk flow when local scaling was applied.     

HEIFE戈壁地区近地层大气的湍流结构和输送特征

根据黑河地区地气相互作用实验研究(HEIFE)1988年POP和1990年PIOP实验的观测资料,分析了戈壁地区近地层大气的湍流结构,主要是风速分量和温度方差的相似关系,以及各有关量的功率谱和湍流通量的协谱。1988年POP期间发现的戈壁近地层大气中白天经常出现的水汽由上而下输送等特殊现象,在1990年PIOP中得到进一步的验证。文中分析了有关物理机制,认为这一现象和众所周知的“绿洲效应”是戈壁-绿洲这一地区性中尺度环流影响的两个侧面。     

An Auxiliary Tool to Determine the Height of the Boundary Layer

Results from radiosoundings, performed both over land and over sea, show that the ascent rate of a radiosounding balloon, the vertical velocity of the balloon, can be used to determine the height of the boundary layer. In many cases the balloon has a higher ascent rate in the boundary layer and a lower, less variable, ascent rate above. The decrease in ascending velocity appears as a jump at the top of the boundary layer. Two examples of potential temperature profiles for unstable stratification and one profile for stable conditions are shown with the corresponding ascent rates. A comparison between the boundary-layer height determined from potential temperature profiles and from ascent rates is presented for a larger dataset. The different ascent rates of the balloon in the boundary layer and above can be explained by a decrease in drag on the balloon in combination with a lowering of the critical Reynolds number in the boundary layer caused by turbulence. Hence, by simply logging the time from release of a radiosonde, it is possible to obtain additional information that can be used to estimate the height of both the unstable and stable boundary layers.     

Vertical Structure Of Turbulence In Offshore Flow During Rasex

The adjustment of the boundary layer immediately downstream froma coastline is examined based on two levels of eddy correlation data collected on a mast at the shore and six levels of eddy correlation data and profiles of mean variables collected from a mast 2 km offshore during the Risø Air-Sea Experiment. The characteristics of offshore flow are studied in terms of case studies and inter-variable relationships for the entire one-month data set. A turbulent kinetic energy budget is constructed for each case study.The buoyancy generation of turbulence is small compared to shear generation and dissipation. However, weakly stable and weakly unstable cases exhibit completely different vertical structure. With flow of warm air from land over cooler water, modest buoyancy destruction of turbulence and reduced shear generation of turbulence over the less rough sea surface cause the turbulence to rapidly weaken downstream from the coast. The reduction of downward mixing of momentum by the stratification leads to smaller roughness lengths compared to the unstable case. Shear generation at higher levels and advection of stronger turbulence from land often lead to an increase of stress and turbulence energy with height and downward transport of turbulence energy toward the surface.With flow of cool air over a warmer sea surface, a convective internal boundary layer develops downstream from the coast. An overlying relatively thick layer of downward buoyancy flux (virtual temperature flux) is sometimes maintained by shear generation in the accelerating offshore flow.     

A Three-Dimensional Backward Lagrangian Footprint Model For A Wide Range Of Boundary-Layer Stratifications

We present a three-dimensional Lagrangian footprint model with the ability to predict the area of influence (footprint) of a measurement within a wide range of boundary-layer stratifications and receptor heights. The model approach uses stochastic backward trajectories of particles and satisfies the well-mixed condition in inhomogeneous turbulence for continuous transitions from stable to convective stratification. We introduce a spin-up procedure of the model and a statistical treatment of particle touchdowns which leads to a significant reduction of CPU time compared to conventional footprint modelling approaches. A comparison with other footprint models (of the analytical and Lagrangian type) suggests that the present backward Lagrangian model provides valid footprint predictions under any stratification and, moreover, for applications that reach across different similarity scaling domains (e.g., surface layer to mixed layer, for use in connection with aircraft measurements or with observations on high towers).