Analysis of oscillations in the stable atmospheric boundary layer using wavelet methods

A wavelet method is used to estimate kinetic energy and fluxes from data collected under stable conditions during the CASES-99 field campaign. Results in the high frequency range are compared with those obtained by the traditional method used to estimate turbulent moments, which is based on the Reynolds decomposition of variables into a mean and a turbulent part. The fact that the wavelet transform performs much better as a filter than the averaging process accounts for most of the disagreements between results. Since the wavelet method can be applied at very different spectral ranges, it is also used to analyse two different coherent structures: a density current and a train of internal gravity waves. The strong burst of turbulence related to the density current reflects the complexity of the first event. The wavelet method discriminates the different scales of motion, which are present in the perturbation, and is therefore an ideal tool for assessing the interactions between them. A method based on the phase difference between wavelet-transformed time series is then applied to the analysis of the horizontal and vertical structure of the gravity waves, and a three-dimensional image of the oscillations is provided.     

Wavelet methods: application to the study of the stable atmospheric boundary layer under non-stationary conditions

In this work, some wavelet methods are introduced to study the atmospheric boundary layer under stable conditions, where intermittent events and non-stationary turbulence take place. Such behavior makes classical methods, based on Fourier transform, difficult to use or even of no application.The wavelet transform is used to detect and characterize some structures in the stable atmospheric boundary layer. First, a wave-like event with a 16 min period is detected and analyzed in a wind record. The sum of some Morlet wavelets is proposed as a model for the oscillations. Afterwards, the wavelet transform is introduced to the study of non-stationary small scale turbulence. It provides the time evolution of the energy and a good location in time of the spots of turbulence. Finally, some wavelet tools are used to characterize a traveling structure, provided that it is simultaneously detected at different locations. The phase differences in the wavelet transform give the wavelength and the phase speed of the oscillations, whereas a double transform method is introduced to estimate the group velocity of the structure.     

Experimental investigation of atmospheric boundary layer turbulence

This paper describes how to measure turbulence in the atmospheric boundary layer (ABL) in order to address certain problems in modern atmospheric physics. These problems mainly relate to the Earth's energy budget (including the hydrological cycle) and biogeochemical cycles. Starting from the main characteristic numbers and the basic equations of atmospheric turbulent flow, we show what turbulence parameters are important to measure. Special attention is given to the various methods used to compute the turbulent fluxes. We analyse the range of scales which has to be measured to properly capture the eddies contributing to the turbulent transfers. This range of scales determines what sensors can be used in the atmospheric surface layer and in the ABL. We describe the most widely used instruments and their performances. The principal platforms used to deploy these instruments are examined. Aircraft are described in more details, because they allow a thorough exploration of the ABL. In the last section, some examples of ABL turbulence signals measured in various conditions are presented. These examples illustrate horizontally homogeneous turbulence as well as inhomogeneous signals for which standard analysis techniques cannot be used. We show how some recent techniques, like wavelet transforms, can help to investigate this kind of signal. At the end, we present what would be interesting to do in the near future for the study of ABL turbulence.     

Temporal Oscillations in the Convective Boundary Layer Forced by Mesoscale Surface Heat-Flux Variations

A theoretical approach suggests that the surface heterogeneity on a scale of tens of kilometres can generate mesoscale motions that are not in a quasi-stationary state. The starting point of the theoretical approach is the equations of horizontal velocity and potential temperature that are low-pass filtered with a mesoscale cut-off wavelength. The transition of the generated mesoscale motions from a quasi-stationary state to a non-stationary state occurs when horizontal advection is strong enough to level out the potential temperature gradient on the surface heterogeneity scale. Large-eddy simulations (LES) suggest that the convective boundary layer (CBL) changes to a non-stationary state when forced by a surface heat-flux variation of amplitude of 100W m⁻² or higher and a wavelength of the order of 10 km. Spectral analysis of the LES reveals that when the mesoscale motions are in a quasi-stationary state, the energy provided by the surface heat-flux variation remains in organized mesoscale motions on the scale of the surface variation itself. However, in a non-stationary state, the energy cascades to smaller scales, with the cascade extending down into the turbulence scale when the wavelength of the surface heat-flux variation is on a scale smaller than 100 times the CBL height. The energy transfer from the generated mesoscale motions to the CBL turbulence results in the absence of a spectral gap between the two scales. The absence of an obvious spectral gap between the generated mesoscale motions and the turbulence raises questions about the applicability of mesoscale models for studies on the effect of high-amplitude surface heterogeneity on a scale of tens of kilometres. The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

用连续子波变换提取城市冠层大气湍流的相干结构

切变湍流的相干结构是湍流研究中的重大发现,它表明湍流在表面上看来不规则运动中具有可检测的有序运动,这种相干结构在切变湍流的脉动生成和发展中起着主宰作用.因此识别和提取相干结构对于认识和研究湍流是非常重要的.用数字滤波法将包含相干结构的大尺度信号提取出来以后,再用子波分析,根据子波能量极大值的判别方法,分别确定出大气湍流三个方向上的速度脉动信号相干结构的频率或时间尺度,然后由确定尺度上的连续子波反演公式,提取出大气湍流三个方向上的速度脉动信号相干结构所对应的波形.     

Structure Function Analysis of Two-Scale Scalar Ramps. Part I: Theory and Modelling

Structure functions are used to study the dissipation and inertial range scales of turbulent energy, to parametrize remote turbulence measurements, and to characterize ramp features in the turbulent field. Ramp features are associated with turbulent coherent structures, which dominate energy and mass fluxes in the atmospheric surface layer. The analysis of structure functions to identify ramp characteristics is used in surface renewal methods for estimating fluxes. It is unclear how commonly observed different scales of ramp-like shapes (i.e., smaller ramps and spikes embedded in larger ramps) influence structure function analysis. Here, we examine the impact of two ramp-like scales on structure function analysis using artificially generated data. The range of time lags in structure function analysis was extended to include time lags typically associated with isotropic turbulence to those larger than the ramp durations. The Van Atta procedure (Arch Mech 29:161–171, 1977) has been expanded here to resolve the characteristics of two-scale ramp models. This new method accurately, and in some cases, exactly determines the amplitude and duration of both ramp scales. Spectral analysis was applied to the structure functions for a broad range of time lags to provide qualitative support for the expanded Van Atta procedure results. The theory reported here forms the foundation for novel methods of analyzing turbulent coherent structures.     

The Effects of Non-stationarity on the Clustering Properties of the Boundary-layer Vertical Wind Velocity

Non-stationarity is a common feature in geophysical flows, though it still remains an open question on how the non-stationarity of flow affects its statistical structure. Using the telegraph approximation (TA) method, we quantified how non-stationarity in the measured atmospheric turbulent vertical velocity time series affects its clustering properties—one of the two main components of intermittency in turbulence. We compare different TA results between stationary and non-stationary atmospheric turbulent vertical velocity records, and find that the non-stationary data possess different cluster and intermittency exponents from stationary data. The inter-pulse period of the non-stationary records takes a near power-law distribution while the inter-pulse period of the stationary records exhibits a stretched exponential distribution. These results suggest that non-stationarity of the underlying processes can affect the statistical structure of turbulence, especially the clustering properties.     

Coherent Structures at a Forest Edge: Properties, Coupling and Impact of Secondary Circulations

Little is known about the influence of coherent structures on the exchange process, mainly in the case of forest edges. Thus, in the framework of the ExchanGE processes in mountainous Regions (EGER) project, measurements of atmospheric turbulence were taken at different heights between a forest and an adjacent clear cutting using sonic anemometers and high-frequency optical gas analyzers. From these turbulence data, dominant coherent structures were extracted using an already existing wavelet methodology, which was developed for homogeneous forest canopies. The aim of this study is to highlight differences in properties of coherent structures between a forest and a clear cutting. Distinct features of coherent exchange at the forest edge are presented and a careful investigation of vertical and horizontal coupling by coherent structures around the surface heterogeneity is made. Within the forest, coherent structures are less frequent but possess larger time scales, indicating that only the largest coherent motions can penetrate through the forest canopy. At the forest edge, there is no crown layer that can hinder the vertical exchange of coherent structures, because these exhibit similar time scales at all heights. In contradiction to that, no improved vertical coupling was detected at the forest edge. This is mainly because the structures captured by the applied routine contribute less to total turbulent fluxes at the edge than within the forest. Thus, coherent structures with time scales between 10 and 40 s are not the dominant exchange mechanism at the forest edge. With respect to the horizontal direction, a consistent picture of coherent transport could be derived: along the forest edge there is mainly good coupling by coherent structures, whereas perpendicular to the forest edge there is mainly decoupling. Finally, it was found that there is a systematic modulation of coherent structures directly at the forest edge: strong ejection motions appear in all time series during the daytime, whereas strong sweeps dominate at night. An effect of wind direction relative to the forest edge is excluded. Consequently, it is hypothesized that this might be an indication of a quasi-stationary secondary circulation above the clear cutting that develops due to differences in surface temperature and roughness. Such circulations might be a relevant turbulent transport mechanism for ecosystem-atmosphere exchange in heterogeneous landscapes.     

Temporal Scales of Convective Coherent Structures Derived from Sodar Data

Summary The temporal variability of thermal turbulence and vertical velocity derived from sodar measurements during periods of atmospheric free convection is studied using both spectral and wavelet analysis. A promising approach to analyse atmospheric processes, an advanced high-resolution spectrum estimation technique is described. Variance spectra of meteorological and turbulent parameters are shown to have their specific comb shape at a low-frequency range. Spectra and wavelet transforms of the data obtained at different sites both indicate the existence of some representative predominant temporal scales in time variations of the convective boundary layer structure. The most evident temporal scales revealed are centered around 7–9 and 18–22 minutes. Received October 16, 1998 Revised April 15, 1999     

Coherent Structures Detected in Atmospheric Boundary-layer Turbulence using Wavelet transforms at Huaihe River Basin, China

The presence of coherent structures in turbulent shear flows suggests order in apparently random flows. These coherent structures play an important dynamical role in momentum and scalar transport. To develop dynamical models describing the evolution of such motion, it is necessary to detect and isolate the coherent structures from the background fluctuations. In this paper, we decomposed atmospheric turbulence time series into large-scale eddies, which include coherent structures and small eddies, which are stochastic by using Fourier digital filtering. The wavelet energy computed for the three components of the velocity fluctuations in the large-scale eddies appears to have local maximum values at certain time scales, which correspond to the scales or frequencies of coherent structures. We extract coherent signals from large-scale vortices at this scale by inverse wavelet transform formulae. This method provides an objective technique for examining the turbulence signal associated with coherent structures in the atmospheric boundary layer. The average duration of coherent structures in three directions based on Mexican hat wavelets are 33 s, 34 s and 25 s respectively. Symmetric andanti-symmetric wavelet basis functions give almost the same results. The main features of the structures during the day and night have little difference. The dimensionless durations for u, v and w have linear correlations with each other. These relationships are insensitive to the wavelet basis.     

Detection of turbulent coherent motions in a forest canopy part I: Wavelet analysis

Turbulence measurements performed at high frequencies yield data revealing intermittent and multi-scale processes. Analysing time series of turbulent variables thus requires extensive numerical treatment capable, for instance, of performing pattern recognition. This is particularly important in the case of the atmospheric surface layer and specifically in the vicinity of plant canopies, where largescale coherent motions play a major role in the dynamics of turbulent transport processes. In this paper, we examine the ability of the recently developedwavelet transform to extract information on turbulence structure from time series of wind velocities and scalars. It is introduced as a local transform performing a time-frequency representation of a given signal by a specific wavelet function; unlike the Fourier transform, it is well adapted to studying non-stationary signals. After the principles and the most relevant mathematical properties of wavelet functions and transform are given, we present various applications of relevance for our purpose: determination of time-scales, data reconstruction and filtering, and jump detection. Several wavelet functions are inter-compared, using simple artificially generated data presenting large-scale features similar to those observed over plant canopies. Their respective behaviour in the time-frequency domain leads us to assign a specific range of applications for each.     

Evaluation of Cut-Off Frequency and Correction of Filter-Induced Phase Lag and Attenuation in Eddy Covariance Analysis of Turbulence Data

A recursive filter adopted for online eddy covariance analysis of turbulence data inthe atmospheric surface layer is revisited, and its properties and performanceare evaluated by means of concepts and methods developed in digital signal analysis.A rigorous estimate of effective cut-off frequency is derived along with an estimateof filter induced phase lag. Accordingly, filter design criteria are revised and variouseffects of parameter choice are assessed. Furthermore suitable corrections for compensating filter induced distortion, i.e., phase lag and attenuation, are proposed. The modified filter is tested on: (a) An artificial time series (random noise superimposed to `slow' sinusoidal signal); (b) turbulence data from field measurements. In case (a) the retrieval of input signal parameters is appreciably improved. In case (b) a better agreement with a Gaussian moving average is obtained, at lower computational cost.     

从湍流经典理论到大气湍流非平衡态热力学理论

湍流是日常生活中一种普遍的自然现象,也是经典物理学仍未完全解决的难题。湍流更是大气运动的最基本特征。本文系统地回顾了大气湍流经典理论发展简史,进一步详细介绍了大气湍流非平衡态热力学理论。大气湍流非平衡态热力学理论在熵平衡方程中引入动力过程,进而统一推导出大气湍流输送的Fourier定律、Flick定律和Newton定律,证明了Dufour效应、Soret效应、可逆动力过程与热力不可逆湍流输送过程之间的交叉耦合效应,以及湍流强度定理。这些定律和定理中得到了观测的事实验证,同时它们的唯象系数也由观测资料所确定。湍流强度定理揭示,湍流发展的宏观原因是速度和温度的剪切效应,Reynolds湍流和Rayleigh-Bénard湍流共存于大气湍流中。热力过程和动力过程间耦合效应现象的发现突破了传统湍流输送理论,即Fourier定律、Flick定律和Newton定律的观点——一个宏观量的输送通量等价于这个宏观量的梯度湍流输送通量。热力和动力过程间的耦合原理认为,一个宏观量的输送通量包括这个量的梯度湍流输送通量和速度耦合输送通量两部分。因此,能量和物质的垂直输送通量除了相应物理量梯度造成的湍流输送外,还应包括垂直速度耦合效应,即辐散或辐合运动造成的耦合效应。在一个很宽的尺度范围内,地表面的空间特征是非均匀的。下垫面非均匀性造成的对流运动将引起大气的辐散或辐合运动。这可能是导致地表能量收支不平衡的重要原因之一。垂直速度对垂直湍流输送的交叉耦合效应为非均匀下垫面大气边界层理论的发展,并为克服地表能量收支不平衡问题及非均匀下垫面大气边界层参数化遇到的困难提供了可能的线索。     

The characteristics of turbulent moisture on Huaihe river basin in China

Summary ?A lot of work on near surface turbulence characteristics has been done in the experimental study of atmospheric turbulence, but little work on fluctuating scalar field has been done, especially on some quantities such as moisture and pollution. In this paper, with the methods of statistical theory, Fourier transform, fractal geometry and wavelet transform, the turbulent moisture data obtained from Huaihe River Basin Experiment (HUBEX) are studied to explore the statistical, spectral, fractal and intermittent characteristics of turbulent moisture. The results show that: (1) In the high humid area such as Huaihe river basin, the moisture plays an important role in the surface energy balance, energy transportation and cycle. (2) The energy spectra and cospectra are in agreement with the “−2/3” and “−4/3” scaling power law correspondingly in inertial sub-range. (3) The fractal dimension of turbulent moisture in Huaihe river basin is clearly higher than that in other areas (such as Beijing). (4) The fluctuating moisture field has strong intermittency, and is not in accordance with the Kolmogorov theory. With the orthonormal wavelet transform, the dissipative events of the fluctuating moisture field contributing to inertial sub-range intermittency buildup have been identified. After the dissipative events have been suppressed by introducing a conditioning wavelet sampling scheme, the intermittency that affects the statistical structure of inertial sub-range is restrained. However the repressive effects of intermittency on turbulent moisture field are worse than those on turbulent velocity field. The reason may be either the intermittency of turbulent moisture is strong or some coherence structures exist in the turbulent moisture field. Received April 27, 2001; Revised January 23, 2002     

Characteristics Of Chaotic Attractors In Atmospheric Boundary-Layer Turbulence

In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible.     

CONDITIONAL SAMPLING AND SCALE ANALYSIS OF THE MARINE ATMOSPHERIC MIXED LAYER -- SOFIA EXPERIMENT

During the SOFIA experiment, performed in the Azores region in June1992, airborne missions were conducted in the atmospheric boundary layerwith two aircraft instrumented for turbulence measurements. We show howthe conditional sampling technique, applied to the velocity, temperatureand moisture fluctuations, is able to describe the various parcels whichconstitute the turbulent field. Each parcel, so identified, is characterized byits fractional area and by its contribution to the transfers of sensible heat andlatent heat. On the other hand, a scale analysis is conducted by filteringthe turbulent signals in five non-overlapping frequency bands, definedaccording to the characteristic turbulent scales. The contribution of eachband to the turbulent energy and to the transfers is thus presented. Theimportance of the lowest frequencies, which are generally removed fromthe signals by high-pass filtering before computing turbulent fluxes, isshown. In the final section, the conditional sampling technique is applied tothe signals filtered in the various bands. Despite a slight deformation of theeddies due to the filtering technique, the contribution of each parcel can beestimated at the various scales analysed.     

大气湍流的混沌吸引子特征

采用时间延迟技术,利用高性能的超声风温仪和红外湿度脉动仪所测得的大气湍流脉动资料,重构相空间中的湍流吸引子,估算了其相关维D2和最大Lyapunov指数λ1。结果表明,在不同地点、不同时间以及不同大气稳定度条件下,大气湍流的最大Lyapunov指数λ1均大于零,说明大气湍流的确具有混沌特征,且存在低维奇怪吸引子,其维数在3～7之间,视变量的不同(动力变量还是非动力变量)而不同,且受大气稳定度影响。首次使用了湍流动能来重建湍流吸引子。     

正交小波变换研究复杂下垫面边界层的湍流特征

小波变换方法具有较好的时频局部特性,非常适合于分析非平稳的湍流信号。本文对35 m铁塔的超声风速测量数据进行了离散正交小波变换,计算了各向同性系数(ISO isotropy coefficient)及小波功率谱,以此对实验场所代表的水陆交际复杂下垫面的近地面层湍流特征进行了研究。ISO系数可以很好地描述实际大气在不同尺度的各向同性特征。根据ISO系数的分布,我们可以通过设定一定的阈值(ISO=0.7)来得到各向同性小涡的分离尺度(记为ISO0.7),即湍流的各向同性尺度范围。研究表明,下垫面对于边界层湍流各向同性特性具有相当大的影响,当风从不同下垫面吹过时ISO0.7尺度的均值具有较明显的差异。同时湍流度和稳定度对湍流各向同性也有一定的影响。对湍流小波功率谱研究表明,功率谱谱幂率在分离出的小涡所处的频段接近于-5/3。而当风从陆面吹过且湍流度较弱时,湍流小波功率谱小涡以分离尺度所对应的频率(fms)为界具有明显的两段趋势:高于fms的频段,谱幂率一般接近-5/3;而低于fms的频段的谱幂率接近-3/3。这反映了下垫面特征对湍流功率谱的影响。同时在不同的风向转变过程中下垫面对功率谱的影响具有差异。     

高风速相干结构对通量输送影响的实验研究

切变湍流的相干结构是湍流研究中的重大发现,它表明湍流运动并非完全随机,其中具有可检测的有序结构.本文通过处理南京浦口地区大气边界层观测数据,来分析不稳定层结中高风速相干结构特征.本次观测项目包括对场地中央的气象铁塔上2 m和40 m高度上超声风速仪的脉动速度、温度测量以及风廓线雷达对边界层风速廓线的测量.对超声水平风速时间序列数据进行小波变换 (时间尺度400 s),通过阈值来识别这种高风速相干结构.与多普勒风廓线雷达测量结果对比后发现,这种方法确定的相干结构符合常规的认识,具有较长的时间尺度和较大的垂直尺度 (接近边界层厚度).分析三天相干结构特性得到无量纲空间间隔约为6,即每隔6个边界层厚度的水平位置出现一个高速相干结构.通过与垂直风速小波系数的比较,发现高风速相干结构与向下垂直风速之间有较好相关,这与湍流中 “阵风” 现象的研究结论相似.使用四象限分析方法分类得到两种动量通量输送为负的运动:较小水平风速的上扬 (ejection) 运动 (简称为上扬运动) 和较大水平风速的下扫 (sweep) 运动 (简称为下扫运动),这两种运动在整个湍流活动中处于主导地位.高风速相干结构通过促进下扫运动和抑制上扬运动来影响动量通量的输送.