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.     

Analysis of turbulent exchange and coherent structures in the stable atmospheric boundary layer based on tower observations

Using data collected at the Spanish low troposphere research centre CIBA (Centro de Investigación de la Baja Atmósfera) and at the Cabauw Experimental Site for Atmospheric Research (CESAR) in the Netherlands, we analyzed the most significant features of different coherent structures occurring in the stable atmospheric boundary layer. In particular, we used both the Reynolds and wavelet methods to analyze a solitary wave, a gravity wave, a density current and a low-level jet. For each of these structures, we found that wavelet analysis had the capacity to distinguish the different scales involved in these events due to the different timing and heights of the thermal instabilities and downdrafts associated with the disturbances. In addition, the wavelet method highlights the different roles of turbulence and coherent structures in the transfer of heat, moisture and CO₂ in the nocturnal boundary layer.     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Long-term study of coherent structures in the atmospheric surface layer

A long-term study of coherent turbulence structures in the atmospheric surface layer has been carried out using 10 months of turbulence data taken on a 30-m tower under varying meteorological conditions. We use an objective detection technique based on wavelet transforms. The applied technique permits the isolation of the coherent structures from small-scale background fluctuations which is necessary for the development of dynamical models describing the evolution and properties of these phenomena. It was observed that coherent structures occupied 36% of the total time with mean turbulent flux contributions of 44% for momentum and 48% for heat. The calculation of a transport efficiency parameter indicates that coherent structures transport heat more efficiently than momentum. Furthermore, the transport efficiency increases with increasing contribution of the structures to the overall transport.     

Coherent structures in the very stable atmospheric boundary layer

This study examines the structure of horizontal modes (meandering, vortical modes or fossil turbulence) in a layer of intermittent turbulence occurring at the top of a strongly stratified nocturnal inversion layer as observed by fast response aircraft data. The spatial variation of the coefficients of the principal components identify regular coherent structures with mainly horizontal motions. Conditional sampling is formulated in terms of this spatial variation. The quasi-horizontal motions are characterized by relatively sharp edges (transition zones) where horizontal convergence or divergence, small-scale turbulence and vertical fluxes seem to be concentrated. Zones of horizontal divergence appear to be associated with ejection of cold air from the underlying surface inversion while the convergent zones might be due to random collisions between horizontal modes.     

The velocity spectra in the stable atmospheric boundary layer

A model for the logarithmic spectra of velocity in the stable boundary layer is developed using the concept of local scaling. The resulting expressions for peak wavelength are in agreement with empirical data from Minnesota 1973.Partially financed by CAPES and FINEP.On leave from Faculdade de Engenharia de Joinville, SC, Brasil.     

On the characteristics of eddies in the stable atmospheric boundary layer

A discussion of the cross-spectral properties of eddies in the lowest 40 m of the nocturnal boundary layer is presented. The study involves the analysis of meteorological data collected by the British Antarctic Survey at Halley Station, Antarctica, during the austral winter of 1986. Cross-spectral analysis is used to determine whether the nature of the observed eddies is primarily turbulent or whether their structure is characteristic of coherent internal gravity waves. It is found that the cross-spectral phases indicate the presence of turbulent eddies only when the local gradient Richardson number (Ri) is less than the critical value of 1/4. Trapped modes were only observed when an off-shore wind prevailed, indicating that topographic effects are responsible for their generation. The relative phases of velocity and temperature were often observed to change with height. This can be explained by examining the underlying meteorological conditions. On several occasions, regions of counter-gradient fluxes were detected. A physical explanation of this phenomenon is proposed.     

On the turbulent Prandtl number in the stable atmospheric boundary layer

This study focuses on the behaviour of the turbulent Prandtl number, Pr _t , in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Pr _t increases with increasing stability if Pr _t is plotted vs. gradient Richardson number, Ri; but at the same time, Pr _t decreases with increasing stability if Pr _t is plotted vs. flux Richardson number, Rf, or vs. ζ = z/L. This paradoxical behaviour of the turbulent Prandtl number in the SBL derives from the fact that plots of Pr _t vs. Ri (as well as vs. Rf and ζ) for individual 1-h observations and conventional bin-averaged values of the individual quantities have built-in correlation (or self-correlation) because of the shared variables. For independent estimates of how Pr _t behaves in very stable stratification, Pr _t is plotted against the bulk Richardson number; such plots have no built-in correlation. These plots based on the SHEBA data show that, on the average, Pr _t decreases with increasing stability and Pr _t < 1 in the very stable case. For specific heights and stabilities, though, the turbulent Prandtl number has more complicated behaviour in the SBL.     

SHEBA flux–profile relationships in the stable atmospheric boundary layer

Measurements of atmospheric turbulence made during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA) are used to examine the profile stability functions of momentum, φ _m , and sensible heat, φ _h , in the stably stratified boundary layer over the Arctic pack ice. Turbulent fluxes and mean meteorological data that cover different surface conditions and a wide range of stability conditions were continuously measured and reported hourly at five levels on a 20-m main tower for 11 months. The comprehensive dataset collected during SHEBA allows studying φ _m and φ _h in detail and includes ample data for the very stable case. New parameterizations for φ _m (ζ) and φ _h (ζ) in stable conditions are proposed to describe the SHEBA data; these cover the entire range of the stability parameter ζ = z/L from neutral to very stable conditions, where L is the Obukhov length and z is the measurement height. In the limit of very strong stability, φ _m follows a ζ ^1/3 dependence, whereas φ _h initially increases with increasing ζ, reaches a maximum at ζ ≈ 10, and then tends to level off with increasing ζ. The effects of self-correlation, which occur in plots of φ _m and φ _h versus ζ, are reduced by using an independent bin-averaging method instead of conventional averaging.     

On the turbulence structure in the stable boundary layer over the Greenland ice sheet

Turbulence measurements from a 30 m tower in the stably stratifiedboundary layer over the Greenland ice sheet are analyzed. The observationsinclude profile and eddy-correlation measurements at various levels. Atfirst, the analysis of the turbulence data from the lowest level (2 m aboveground) shows that the linear form of the non-dimensional wind profile(m) is in good agreement with the observations for z/L <0.4, whereL represents the Obukhov length. A linear regression yieldsm=1+5.8z/L. The non-dimensional temperature profile (h) at the2m level shows no tendency to increase with increasing stability. The datafrom the upper levels of the tower are analyzed in terms of both localscaling and surface-layer scaling. The m and the h values show atendency to level off at large stability (z/>0.4) where represents the local Obukhov length. Hence, the linear form of the functions is no longer appropriate under such conditions. The bestcorrespondence to the data can be achieved when using the expression ofBeljaars and Holtslag for m and h. The vertical profiles of theturbulent fluxes, the wind velocity variances and temperature variance arealso determined. The momentum flux profile and the profiles of wind speedvariances are in general agreement with other observations if a welldeveloped low-level wind maximum occurs, and the height of this maximum isused as a height scale.     

Analysis of Heat Budget, Dissipation and Frontogenesis in a Shallow Density Current

High frequency wind and temperature measurements, obtained in March 1995 from a 10-m tower array situated in south-east Kansas, are used to analyze the structure of a shallow density current. This current is approximately 7 m deep and exhibits a current head that is estimated to be about twice the current depth. The event lasted approximately 900 s and its origin appears to be a shallow slope 2–:5 km to the west of the site, where cold air drainage occurs. The onset of the event is marked by a 5 °C temperature decrease at the 3-m level, increased variance of temperature and of wind velocity, and increased dissipation of kinetic energy, measured by a hot-wire anemometer at the 3-m level. The primary contributors to temperature changes following the frontal passage are both horizontal and vertical advections; contributions from flux divergences of temperature and of radiation, and from dew formation, do not appear to be significant. Postulated frontogenesis, prior to the arrival of the apparent equilibrated front of approximately 176-m width at the site, is examined by means of a theoretical model. The time required to equilibrate the front, by means of kinetic energy dissipation within the frontal zone, is determined to be less than 300 s, or less than the estimated travel time from the orographic slope to the observational site. The absence of upstream data is determined, however, to be a limitation of the analysis performed.     

Temperature oscillations observed in the stable boundary layer over four different underlying surfaces

夜间边界层内的温度时空特征决定了边界层的稳定性。由于稳定边界层的间歇性和复杂性,模式在夜间的参数化方案还不完善,研究夜间边界层的温度变化有助于改进模式在夜间的表现。本文利用四座在不同下垫面上的气象塔的数据,研究了夜间边界层中的温度波动。研究表明,无论是海边、草原还是沙漠下垫面,夜间形成的稳定边界层中,振幅大约2摄氏度,周期在数分钟的温度波动非常频繁地出现。而在北京,由于城市下垫面较大的热容量和人为热源使得稳定边界层不容易形成,温度波动也较弱。用布朗特维萨拉频率代表的静力稳定度是影响温度脉动强弱的重要因子。     

Radiative destabilization of the nocturnal stable atmospheric boundary layer over the desert

Radiative destabilization of the nocturnal stable atmospheric boundary layer (NSABL) over homogeneous desert terrain is predicted by an analytical model based on a modified diffusion equation. The model applies late at night under calm, dry conditions when long-wave radiative transfer dominates the NSABL evolution. A three-layer structure for the NSABL is proposed: a shear sub-layer closest to the surface, a radiative sub-layer which contains the inversion top, and a coupling sub-layer which matches the NSABL with the residual layer aloft. A sub-sub-layer called the nocturnal internal boundary layer (NIBL) is nested within the radiative sub-layer and comprises the temperature maximum. The model can explain: (1) maximum cooling in the NIBL, (2) deepening of the NIBL, (3) radiative destabilization of the NSABL, and (4) possible surface warming before sunrise. An example from the Mohave Desert, USA is presented, and the observed temperature profile compares favorably with the model solution.     

论大气边界层的数值模拟方法

本文采用分层模式和连续模式模拟了一维、稳定的大气边界层中一些主要的气象变量随时间的变化规律,讨论了几种气象条件及下垫面条件下计算结果之间的差异,并且还讨论了常值湍流热通量层存在的条件及其高度随时间的变化,从而给出了两种模式适用的范围.     

Sodar observations of the stable lower atmospheric boundary layer at Barrow,Alaska

Events in the stably stratified lower atmospheric boundary layer within the first several hundreds of meters at Barrow, Alaska were recorded from 27 March to 5 April 1990 using an acoustic sounder (sodar), a tethered balloon, radiosondes, and an instrumented meteorological tower. These events include ground-based and low-level inversion layers, gravity waves, breaking waves, and multiple-layer structures. Even though these events are commonly found in a stable boundary layer, it is perhaps surprising to find them in such a slowly changing environment and over a terrain that is essentially devoid of immediate orographic influence.Visiting Scientist at Wave Propagation Laboratory, NOAA/ERL 325 Broadway, Boulder, CO, 80303, U.S.A.     

Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer

Boundary-layer measurements conducted at the Marsta site in Sweden from a winter-time situation (23–25 Feb.) with stable stratification have been analysed. The data comprise wind and temperature profile measurements up to 30 m, turbulence measurements at 2, 6 and 30 m and Doppler acoustic sounder data up to about 150 m. The upwind fetch at the site is flat and free from obstacles to a distance of ca 5 km for the particular sector chosen for the experiment.During the night, a two-layer vertical structure developed. Analysis of power spectra, co-spectra and variances in a shallow and very stable turbulent boundary layer near the ground show that the turbulence is fully developed and follow the universal behaviour.Above, at a height of 30 m, another turbulent layer is produced by increased wind shear near a low-level jet. This turbulent upper layer can be regarded as a layer of free shear flow. At this height, there also exist wave-turbulence interactions at low frequencies which sometimes cause a countergradient heat flux.     

Turbulent mixing of reactive gases in the convective boundary layer

We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯, ¯w¯ ¯ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.     

苏州城区大气边界层低空急流特征分析

利用2012年苏州城区风廓线雷达的观测资料,从低空急流个例分析入手,选取1、4、7、10月四个典型月份,分析该地区边界层低空急流的时空分布及强度变化特征。结果表明:冬春两季低空急流发生频率最高,夏季出现频率最低。在4个典型月份里低空急流均表现出日落后出现频率升高,夜间保持稳定,日出后出现频率降低的特征。全年有80%的低空急流分布在900 m以下高度上,冬、夏季平均高度最低。全年低空急流风速70%以上集中在4~12 m·s~(-1),小于4 m·s~(-1)和大于20 m·s~(-1)的低空急流出现频率较低。     

Estimation of hydroxyl radical concentrations in the marine atmospheric boundary layer using a reactive atmospheric tracer

Hydroxyl radical (OH) concentrations in the atmospheric boundary layer over a number of remote ocean locations are calculated from the measured diurnal variation in atmospheric dimethylsulfide (DMS). By using averaged DMS data sets from extended periods, the calculation yields OH concentrations averaged over periods from several days to weeks. These average OH concentrations range from 7×10⁵ to 2.9×10⁶ molecules cm^-3, corresponding to midday maxima of 3 to 12×10⁶ molecules cm^-3. The lowest values correspond to studies with the lowest light intensity (Antarctic summer and South Atlantic winter), and the highest values to regions with probable anthropogenic influence. In addition to the long term averages, daily average OH levels can be calculated for most days in a two week period from a cruise in the tropical eastern Pacific. These calculations are in good argeement with global average OH levels derived from other tracers, and are consistent with model OH calculations when allowance is made for variation in ambient ozone levels between the studies. Estimates of gas exchange made from the diurnal variation of DMS suggest that either the gas exchange coefficient of DMS or the boundary layer mixing depth may have been overestimated in past analyses.