On the Kinetic Energy Budget of the Unstable Atmospheric Surface Layer

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)^1/3 rather than the friction velocity, u_*. Here k is the von Kármán constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.     

On the Time Evolution of the Turbulent Kinetic Energy Spectrum for Decaying Turbulence in the Convective Boundary Layer

Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z _i at a convective surface-layer height z = 0.05z _i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.     

Discussion and Applications of Slab Models of the Convective Boundary Layer based on Turbulent Kinetic Energy Budget Parameterisations

Some of the most widely used slab model formulations for applications in the convective boundary layer are analysed and discussed. Three main classes are identified based on different approximations of the turbulent kinetic energy equation. The models appear to be quite insensitive to the initial values for boundary-layer height, and temperature discontinuity at the boundary-layer top. The slab models are applied to a case of sea-land transition from the literature, and a case of convective boundary layer time evolution over a homogeneous terrain at San Pietro Capofiume (Bologna, Italy). The different parameterisations turn out to be almost equivalent for the cases studied. The models generally underpredict the value for the height, while all give very good estimates for the mean mixed-layer temperature.     

Parameterization of Entrainment in a Sheared Convective Boundary Layer Using a First-order Jump Model

Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.The part of this work was done when the first author visited at NCAR.     

Turbulent characteristics of a shallow convective internal boundary layer

Turbulent characteristics of a 50 to 100 m deep convective internal boundary layer (I.B.L.) have been studied. The data were gathered at a flat coastal site (Näsudden on the island of Gotland, Sweden) during three consecutive days in May 1980 which were characterized by a steady, very stable stratified marine approach flow. The site is situated on a flat area ca. 1500 m from the shoreline. Only daytime runs have been analysed in the present paper. The sensible heat flux at the ground was typically 200 W m^-2 and was found to decrease more or less linearly with height throughout the I.B.L., being slightly negative at greater heights. The momentum flux was also found to decrease with height, but nevertheless shear production of turbulent kinetic energy was found to be large throughout the entire I.B.L. The analysis shows that the turbulent regime has a mixed character. Certain characteristics, such as the rate of growth of the I.B.L., appear to be almost entirely controlled by mechanical turbulence, while others, notably temperature variance and the spectrum of vertical velocity, scale remarkably well with w _* and z _i, in accordance with the results found in fully convective conditions during the experiments at Minnesota and Aschurch. Other turbulent characteristics, such as spectra of the horizontal wind components measured near the top of the I.B.L. tend to adhere to mixed-layer scaling in the high frequency range, exhibiting much increased energy in the lower (reduced) frequency range. Spectra of the velocity components from 10 m are shown to be in general agreement with findings from ‘ideal’, homogeneous sites (Kansas) when properly normalized, although the low frequency part of u- and v-spectra are slightly reduced compared to the case with deep convection.     

基于激光雷达遥感和参数化模式研究城市混合层的发展机制

利用北京大学的微脉冲激光雷达(MPL)观测的偏南气流条件下的混合层高度和夹卷层厚度探测资料,研究简单天气条件下城市混合层的发展机制并与GB94的参数化方案相互映证.通过激光雷达遥感的混合层高度和夹卷层厚度计算了混合层顶的夹卷率A,得到其平衡夹卷阶段的值为0.24.在不考虑机械混合前提下反演了地面感热通量,结果表明遥感的反演值与梯度法的计算值有系统性偏差,但总体上仍旧有较好的相关.偏差量的大小反映了影响混合层发展的机械湍流的参数B,进一步通过GB91模式的模拟确定该参数的最佳值约为3.5.在此基础上讨论了混     

Three-dimensional numerical study of turbulence in an entraining mixed layer

The mean structure calculated by a three-dimensional numerical model of a heated planetary boundary layer, in simulation of DAY 33 of the Australian Wangara data, has been previously described. The present study supplements it by describing properties of the calculated turbulence.A major finding is the importance of entrainment upon turbulence statistics relating to specific humidity, relative to those for potential temperature. The variances, skewness and spectra of velocity, temperature and humidity are presented, as are budget equations for kinetic energy, temperature and humidity variances and heat/moisture fluxes. These are interpreted with regard to the relative importance of the surface flux vs the flux due to entrainment at the top of the mixed layer, and in regard to the structure which would occur if the entrainment were to vanish.The Rotte-type closure assumption is tested for the correlation between the pressure fluctuation and the vertical gradient of vertical velocity, potential temperature, or specific humidity, and found to be qualitatively correct except near the top of the mixed layer.NCAR is sponsored by the National Science Foundation (U.S.A.).     

Study on Effects of Building Morphology on Urban Boundary Layer Using an Urban Canopy Model

An urban canopy model is incorporated into the Nanjing University Regional Boundary Layer Model. Temperature simulated by the urban canopy model is in better agreement with the observation, especially in the night time, than that simulated by the traditional slab model. The coupled model is used to study the effects of building morphology on urban boundary layer and meteorological environment by changing urban area, building height, and building density.It is found that when the urban area is expanded, the urban boundary layer heat flux, thermal turbulence, and the turbulent momentum flux and kinetic energy all increase or enhance, causing the surface air temperature to rise up. The stability of urban atmospheric stratification is affected to different extent at different times of the day.When the building height goes up, the aerodynamic roughness height, zero plane displacement height of urban area, and ratio of building height to street width all increase. Therefore, the increase in building height results in the decrease of the surface heat flux, urban surface temperature, mean wind speed, and turbulent kinetic energy in daytime. While at night, as more heat storage is released by higher buildings, thermal turbulence is more active and surface heat flux increases, leading to a higher urban temperature.As the building density increases, the aerodynamic roughness height of urban area decreases, and the effect of urban canopy on radiation strengthens. The increase of building density results in the decrease in urban surface heat flux, momentum flux, and air temperature, the increase in mean wind speed, and the weakening of turbulence in the daytime. While at night, the urban temperature increases due to the release of more heat storage.     

应用城市冠层模式研究建筑物形态对城市边界层的影响

文中将城市冠层模式耦合到南京大学城市尺度边界层模式中,通过模拟对比发现,耦合模式对城市地区气温模拟结果更接近于观测值,尤其是对城市地区夜间气温模拟的改进.运用改进耦合模式通过多个敏感性试验的模拟,从城市面积扩张、建筑物高度增加、建筑物分布密度变化等角度研究城市建筑物三维几何形态变化对城市边界层及城市气象环境的影响,试验结果表明:(1)城市面积扩张使得城市下垫面的热通量增大,热力湍流活动增强,动量通量输送增强,城市湍能增大,湍流扩散系数变大,城市气温升高,且对不同时刻城市区域大气层结稳定度均有不同程度的影响.(2)建筑物高度增加增大了城市下垫面的粗糙度和零平面位移.同时也增大了城市街渠高宽比.城市建筑物越高,白天城市地区地表热通量越小,城市上空大气温度越低,平均风速减小,湍能减小;夜间由于高大建筑物释放储热比低矮建筑物要多,其热力湍流相对活跃,地表热通量增大,使得城市区域气温较高.(3)建筑物密度增大,会减小城市下垫面的粗糙度同时增强街渠对辐射的影响.建筑物密度增大在白天会减小地表热通量和动量通量,使城市气温降低,平均风速增大,城市湍流活动能力减弱;夜间城市释放较多储热使得气温较高.     

DECAY OF CONVECTIVE TURBULENCE REVISITED

Results of a large-eddy simulation of a decaying convective mixed layer over land are presented. The time evolution of the mixed layer is forced by the surface heat flux gradually decreasing with time. The results obtained show that the decay of the turbulent kinetic energy is governed by two scales, the external time scale controlling the surface heat flux changes, and the convective time scale. During the simulation, large eddies persist even when the heat flux at the surface becomes negative. A decoupled residual layer of active turbulence is developed above the stable surface layer. The residual layer is marked by large-scale updrafts that are able to penetrate the capping inversion layer and induce entrainment.     

Role of Convective Structures and Background Turbulence in the Dry Convective Boundary Layer

We quantify the role of the convective buoyant structures and the remainder turbulence, here called background turbulence, in the convective atmospheric boundary layer in horizontally homogeneous, dry and barotropic conditions. Three filtering methods to separate the structures and the background turbulence are first evaluated. These are: short-time averaging, Fourier filtering and proper orthogonal decomposition. The Fourier method turns out to be the most appropriate for the present purpose. The decomposition is applied to two cases: one with no mean flow and another with moderate mean wind speed. It is shown that roughly 85 % of the vertical flux of the potential temperature and about 72 % of the kinetic energy is carried by the structures in the mixed layer in both cases. The corresponding percentage for the potential temperature variance is 81 % in the zero mean-wind case and 76 % in the moderate mean-wind case. The structures are responsible for as much as 94 % of the momentum flux in the mixed layer of the moderate mean-wind case. In the surface layer the background turbulence is generally more important than the structure contribution in both cases. The budget of the potential temperature flux is analyzed in detail and it is shown that its turbulent transport term is mostly built up by the structures but also the interaction between the structures and the background turbulence plays a significant role. The other important budget terms are shown to be dominated by the structures except for the pressure–temperature gradient covariance.     

Air mass modification over Lake Michigan

The modification of a relatively cold air mass over the warm water of Lake Michigan is studied by using a two-dimensional nonlinear mesoscale model. Considerable amounts of heat and water vapor are supplied from the water surface to the lower atmosphere by turbulent eddies. A convective mixed layer develops and grows toward the downwind region with stratocumulus clouds over the lake.The model simulates the warming and moistening of the mixed layer, the development of a boundary layer, the divergence and convergence of wind near the coastlines, and the turbulent fluxes.The model warming of the mixed layer across the lake was about 2.2 °K and the moistening of the mixed layer was about 0.8 g kg^–1, which are comparable to 2.7 °K and 0.8 g kg^–1 observed by Lenschow (1973). The convective boundary layer, which includes the cloud layer, subcloud layer, and superadiabatic layer near the water surface, is well simulated. The tilt of the inversion which coincides with the cloud top is also well reproduced. When a prescribed cooling rate is applied at the cloud top, stronger turbulence and a deeper cloud layer are generated. Without the cooling, the cloud is shallow and the shape of the cloud base is determined by surface conditions. The rise of the inversion is due to upward vertical motion, and deepening of the convective layer in the downwind region.     

Turbulence structure in temperature inversions and in convection fields as observed by doppler sodar

The structure of turbulence in an inversion layer and in an homogeneous convective field of the planetary boundary layer is described. In the first part of the paper, we validate the sodar estimates of turbulent dissipation, by using measurements with an hot-wire anemometric system in situ. Limitations of an ε measurement technique using structure function calculations are given, taking account of atmospheric properties and acoustic Doppler instrumental effects. By comparison between isopleths of backscattering intensity and of turbulent dissipation rates, we observe that in the early morning, turbulence is advected by mechanical turbulence generated by wind shear. The same mechanism seems to be operating in the case of an inversion layer capping thermal instability, when the convective activity is not too greatly developed. A turbulent kinetic energy budget is examined using aircraft, sodar, and tower measurements. This indicates a constant turbulent dissipation profile through a deep convective layer.     

Boundary-layer evolution and nocturnal inversion dispersal—Part II

Observations from an instrumented aircraft are used to study the small-scale structure of turbulence and convection in well-mixed boundary layers and the erosion processes in the nocturnally-formed inversions above them. The ways in which turbulence statistics for temperature, humidity and vertical velocity scale with height in the mixed layer are compared with the results of a three-dimensional model by Deardorff (1974a, b), and agreement is found in many aspects. Conditional sampling enables the statistics of thermals and their environment to be considered separately and, in particular, shows that the mode of the vertical velocity in thermals markedly decreases with height in the upper half of the mixed layer. Thermals may be recognized equally readily by either their excess of temperature or humidity. Transfers of heat and moisture through the nocturnal inversions influence the structure of the upper region of the mixed layer and there is strong evidence that these transfer processes are turbulent and not organized on scales similar to convective thermals.     

干湿地表的湍流特征及其对深对流影响的大涡模拟

利用大涡模式模拟了对流边界层结构演变以及深对流触发过程.通过改变鲍恩比的敏感性试验研究不同大气初始状况下湿润和干旱下垫面湍流特征及其对深对流触发过程的影响.结果表明:干旱下垫面的混合层干而暖,厚度较大;湿润下垫面相反.由于地表感热通量对热力湍流形成的作用更大,干旱下垫面上湍流混合和夹卷作用更强,使得水汽和相当位温在边界...     

Statistics of shallow convection on Mars based on large-eddy simulations. Part 1: shearless conditions

Results of large-eddy simulations of shallow, quasi-steady, shear-less convection in the Martian boundary layer are presented and discussed. In the considered three cases, turbulence is forced by the radiative flux divergence, prescribed as given functions of height, and the strength of the surface heat flux. It is constrained by the temperature inversion at the boundary-layer top. The resulting convective boundary layer exhibits horizontal cellular structures. The presence of radiative heating causes dimensionless statistics of turbulence to depend on the parameter F, defined in terms of the integrated radiative and turbulent heating rates in the boundary layer.     

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.     

Atmospheric Turbulence Decay During the Solar Total Eclipse of 11 August 1999

The studies of turbulence decay were based in the past on measurements carried out in neutrally stratified wind tunnels and, more recently, on large-eddy simulation runs. Here the atmospheric turbulence decay process during the solar total eclipse of 11 August 1999 is examined. Thus a rapid transition from convective boundary-layer turbulence to that of a neutral or slightly stable one is considered. A u-v-w propeller anemometer and a fast response temperature sensor located in northern France on top of a 9-m mast recorded the turbulence observations. The measurements, in terms of turbulent kinetic energy decay with time, were found to be in good agreement with those prescribed by a theoretical model of turbulence decay recently proposed. In particular, it was found that the exponent of the power law describing the decay process has the value -2.     

解耦的海洋性层积云顶边界层湍流与云微物理特征

基于POST观测计划中获得的海洋性层积云顶边界层内高频气象资料和云微物理资料,在选取解耦个例基础上研究解耦边界层湍流和云微物理特征及成因。结果表明,过渡层的大气静力稳定度较强,抑制向上浮力做功,使得湍流动能迅速消耗殆尽,实现边界层解耦。湍流动能最大值出现在云内,主要与云顶降温、大云滴下落沉降拖曳带来的下沉气流增强及云底之上附近凝结增长潜热释放产生向上浮力作用有关。近地面层的浮力项和切变项对湍流动能都起到增强作用,并以切变项的贡献更为显著,云内的湍流动能是以浮力项贡献为主。过渡层附近存在向下的热通量,抑制了热量向上输送和向上浮力项的增强,促进解耦发生。云内存在向上感热通量,其最大值及其出现高度主要与云顶冷却和云中下部的凝结潜热加热有关。云顶之上湿层促进了潜热通量的向下输送,增强了云内水汽含量,为解耦边界层云的发展起到正反馈作用。云顶浮力倒转引起的云中湍流混合呈现非均匀性,并进一步导致绝热或超绝热液滴出现,促进凝结和碰并增长的增强,同时云顶之上湿层进一步对云中的微物理增长起到了重要的推动作用。云底因夹卷混合表现为均匀混合特征。     

Stratocumulus-capped mixed layers derived from a three-dimensional model

Results of a three-dimensional numerical model are analysed in a study of turbulence and entrainment within mixed layers containing stratocumulus with or without parameterized cloud-top radiative cooling. The model eliminates most of the assumptions invoked in theories of cloud-capped mixed layers, but suffers disadvantages which include poor resolution and large truncation errors in and above the capping inversion.For relatively thick mixed layers with relatively thick capping inversions, the cloud-top radiative cooling is found to be lodged mostly within the capping inversion when the cooling is confined locally to the upper 50 m or less of the cloud. It does not then contribute substantially towards increased buoyancy flux and turbulence within the well mixed layer just below.The optimal means of correlating the entrainment rate, or mixed-layer growth rate, for mixed layers of variable amounts of stratocumulus is found to be through functional dependence upon an overall jump Richardson number, utilizing as scaling velocity the standard deviation of vertical velocity existing at the top of the mixed layer (near the center of the capping inversion). This velocity is found to be a fraction of the generalized convective velocity for the mixed layer as a whole which is greater for cloud-capped mixed layers than for clear mixed layers.