On the Correlation between Convective Plume Updrafts and Downdrafts,Lidar Reflectivity and Depolarization Ratio

We question the correlation between vertical velocity (w) on the one hand and the occurrence of convective plumes in lidar reflectivity (i.e. range corrected backscatter signal Pz ²) and depolarization ratio (Δ) on the other hand in the convective boundary layer (CBL). Thermal vertical motion is directly investigated using vertical velocities measured by a ground-based Doppler lidar operating at 2 μm. This lidar provides also simultaneous measurements of lidar reflectivity. In addition, a second lidar 200 m away provides reflectivities at 0.53 and 1 μm and depolarization ratio at 0.53 μm. The time series from the two lidars are analyzed in terms of linear correlation coefficient (ρ). The main result is that the plume-like structures provided by lidar reflectivity within the CBL as well as the CBL height are not a clear signature of updrafts. It is shown that the lidar reflectivity within the CBL is frequently anti-correlated (ρ (w, Pz ² )) with the vertical velocity. On the contrary, the correlation coefficient between the depolarization ratio and the vertical velocity ρ (w, Δ ) is always positive, showing that the depolarization ratio is a fair tracer of updrafts. The importance of relative humidity on the correlation coefficient is discussed. An erratum to this article can be found at     

Local similarity of spectral and cospectral characteristics in the stable-continuous boundary layer

The local similarity theory, presented in the recent papers of Sorbjan (1986a, b), is extended by taking into consideration spectral (u, v, w, ) and cospectral (uw, w, u) densities in the stable-continuous boundary layer. The resulting universal expressions for spectra, cospectra and the reduced frequencies of their peaks are in agreement with empirical data from the Kansas 1968 surface-layer and Minnesota 1973 boundary-layer experiments. In addition, the universal functions for the structure parameters and the dissipation rates are also derived and shown to fit the empirical data well.On leave from Institute of Environmental Engineering, Warsaw Polytechnic University, 00653 Warsaw, Poland.     

Parametrization of orographical effects in the planetary boundary layer

Studies of the influence of orography on the dynamics of atmospheric processes usually assume the following relation as a boundary condition at the surface of the Earth, or at the top of the planetary layer: $$w = u\frac{{\delta z_0 }}{{\delta x}} + v\frac{{\delta z_0 }}{{\delta y}}$$ where u, v and w are the components of wind velocity along the x, y and z axes, respectively, and z ₀ = z₀(x, y) is the equation of the Earth's orography. We see that w, and consequently the influence of orography on the dynamics of atmospheric processes, depend on the wind (u, v) and on the slope of the obstacle (δz ₀/δx, δz₀/δy). In the present work, it is shown that the above relation for w is insufficient to describe the influence of orography on the dynamics of the atmosphere. It is also shown that the relation is a particular case of the expression: $$\begin{gathered} w_h = \left| {v_g } \right|\left[ {a_1 (Ro,s)\frac{{\delta z_0 }}{{\delta x}} + a_2 (Ro,s)\frac{{\delta z_0 }}{{\delta y}}} \right] + \hfill \\ + \frac{{\left| {v_g } \right|^2 }}{f}\left[ {b_1 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x^2 }} + b_2 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta y^2 }} + b_3 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x\delta y}}} \right] \hfill \\ \end{gathered} $$ where ¦vv _g¦ is the strength of the geostrophic wind, a ₁, a₂, b₁, b₂, b₃ are functions of Rossby number Ro and of the external stability parameter s. The above relation is obtained with the help of similarity theory, with a parametrization of the planetary boundary layer. Finally, the authors show that a close connection exists between the effects described by the above expression and cyclo- and anticyclogenesis.     

Lateral coherence in isotropic turbulence and in the natural wind

A short review of experimental findings is given, followed by a theoretical derivation, based on Taylor's hypothesis, of formulas for lateral coherences. It is assumed that the flow is stationary and homogeneous. Explicit formulas are derived assuming an energy spectrum pertaining to the inertial subrange. Even when the last assumption is not fulfilled, there are only four different types of non-zero velocity coherences. These four coherences correspond to the combinations uu, vv, ww, and uv, where u, v, and w are the longitudinal, the transversal, and the vertical component of the turbulent velocity with respect to the direction of the horizontal mean wind velocity U. In the case of small displacements relative to the scale of turbulence, the coherences are shown to be universal functions of the non-dimensional frequency nD/¦U¦, where n is the frequency and D the lateral displacement. It is shown that these theoretical formulas for spectral coherences are in good agreement with atmospheric data. Finally, the role of the scale of the turbulence is discussed.     

The Alignment of the Mean Wind and Stress Vectors in the Unstable Surface Layer

A significant non-alignment between the mean horizontal wind vector and the stress vector was observed for turbulence measurements both above the water surface of a large lake, and over a land surface (soybean crop). Possible causes for this discrepancy such as flow distortion, averaging times and the procedure used for extracting the turbulent fluctuations (low-pass filtering and filter widths etc.), were dismissed after a detailed analysis. Minimum averaging times always less than 30 min were established by calculating ogives, and error bounds for the turbulent stresses were derived with three different approaches, based on integral time scales (first-crossing and lag-window estimates) and on a bootstrap technique. It was found that the mean absolute value of the angle between the mean wind and stress vectors is highly related to atmospheric stability, with the non-alignment increasing distinctively with increasing instability. Given a coordinate rotation that aligns the mean wind with the x direction, this behaviour can be explained by the growth of the relative error of the u–w component with instability. As a result, under more unstable conditions the u–w and the v–w components become of the same order of magnitude, and the local stress vector gives the impression of being non-aligned with the mean wind vector. The relative error of the v–w component is large enough to make it undistinguishable from zero throughout the range of stabilities. Therefore, the standard assumptions of Monin–Obukhov similarity theory hold: it is fair to assume that the v–w stress component is actually zero, and that the non-alignment is a purely statistical effect. An analysis of the dimensionless budgets of the u–w and the v–w components confirms this interpretation, with both shear and buoyant production of u–w decreasing with increasing instability. In the v–w budget, shear production is zero by definition, while buoyancy displays very low-intensity fluctuations around zero. As local free convection is approached, the turbulence becomes effectively axisymetrical, and a practical limit seems to exist beyond which it is not possible to measure the u-w component accurately.     

Deriving characteristic parameters of the convective boundary layer from sodar measurements of the vertical velocity variance

This paper deals with the derivation of the convective mixing height and the characteristic convective velocity w _* from profiles of _w measured by sodar. The parameters were obtained by fitting an analytical profile to the observed data. Results were compared with values obtained by the meteorological preprocessor of a dispersion model and from noon radiosoundings. In addition, a Monte Carlo method was applied to study the influence of measurement errors. It turned out that it is inherently difficult to determine the depth of deep mixed layers from sodar measurements with a limited range, although the determination of w _* should be possible. However, a significant underestimation of _w , and thus w _*, was found, which is probably due to disproportional sampling of updrafts and downdrafts.     

Scaling turbulence in the planetary boundary layer

Two different approaches to scaling turbulence in the planetary boundary layer over Lake Ontario are investigated. The height up to the inversion was found to be the appropriate scaling height while u. for near‐neutral and w* for unstable conditions were the appropriate scaling velocities. The results were in general agreement with the numerical models of Deardorff (1972) and Wyngaard, Cote, and Rao (1974).     

Detection and analysis of coherent structures in urban turbulence

Summary The continuous wavelet transform provides a suitable tool to visualize the vertical structure of turbulence and to detect coherent structures in turbulent time series. This is demonstrated with a simple example of an artificially ramp structured time series. In this study turbulence data, i.e. the fluctuations of the horizontal wind components u′ and v′, the vertical component w′ and temperature T′, sampled with 20.83 Hz and measured simultaneously at three levels (z/h=1.5, 2.1 and 3.2, with z as the sensor height and h the height of the roughness elements) over an urban canopy in the inner city of Basel, Switzerland, are analyzed. The detection of the coherent structures was performed using the Mexican hat wavelet and the zero-crossing method. The analysis for unstable conditions shows that organized structures (ejection-sweep cycles) cover about 45% of the total run time. A conditional average from a total of 116 detected ejection-sweep sequences during 7 hours was calculated over a time window of 100 seconds. This dominating time scale was derived from peak frequencies of the wavelet spectra as well as from the Fourier spectra. It is shown that the normalized amplitudes of fluctuations of temperature and longitudinal wind speed during the events are largest at the lowest measurement level just above the canopy and decrease with increasing distance from the roughness elements. A comparison of related studies over different non-urban surfaces (mainly forests) shows that the shape of conditionally averaged ejection-sweep sequences is very similar for all canopies, however, the dominating time scale in general increases the rougher the surface is and the higher the roughness elements are.     

The budget of carbon dioxide variance in the surface layer over vegetated fields

The budget equation for carbon dioxide variance can be represented by production, dissipation and flux divergence terms. Each term is measured under near neutral to moderately unstable conditions over vegetated fields. The flux divergence term is about an order of magnitude smaller than production and dissipation terms, though it shows a loss for 0.006 < _v < 1 and a gain for 1 < - _v < 10. Here, _v is the Monin-Obukhov stability parameter including humidity effect. As expected from a closure of the budget, the nondimensional production and dissipation terms are basically identical and represented by the same functional form: (1–16 _v )^–1/2.     

Statistics of atmospheric turbulence within a natural black spruce forest canopy

Turbulence statistics were measured in a natural black-spruce forest canopy in southeastern Manitoba, Canada. Sonic anemometers were used to measure time series of vertical wind velocity (w), and cup anemometers to measure horizontal wind speed (s), above the canopy and at seven different heights within the canopy. Vertical profiles were measured during 25 runs on eight different days when conditions above the canopy were near-neutral.Profiles of s and of the standard deviation ( _w ) of w show relatively little scatter and suggest that, for this canopy and these stability conditions, profiles can be predicted from simple measurements made above the canopy. Within the canopy, a negative skewness and a high kurtosis of the w-frequency distributions indicate asymmetry and the persistence of large, high-velocity eddies. The Eulerian time scale is only a weak function of height within the canopy.Although w-power spectra above the canopy are similar to those in the free atmosphere, we did not observe an extensive inertial subrange in the spectra within the canopy. Also, a second peak is present that is especially prominent near the ground. The lack of the inertial subrange is likely caused by the presence of sources and sinks for turbulent kinetic energy within our canopy. The secondary spectral peak is probably generated by wake turbulence caused by form drag on the wide, horizontal spruce branches.     

Boundary-layer parameterizations for applied dispersion modeling over urban areas

Many applied dispersion models require the knowledge of boundary-layer parameters such as sensible heat flux,Q _H , friction velocity,u _*, and turbulent energy components, _w and _v . Formulas are suggested for calculating these parameters over a wide variety of types of ground surfaces, based on simple observations of wind speed near the ground and fractional cloud cover, and specification of constants such as roughness length, albedo, and soil moisture availability. Observations ofu _*,Q _H , _w , and _v during field experiments in St. Louis and Indianapolis are used to test the formulas for urban sites. Relative errors of about ±20% in the predictions are seen to occur whenu _*,Q _H , _w , and _v are large. However, when these quantities are small (e.g.,u _* < 0.2 m/s), the errors in the predictions are as large as the mean value of the quantity itself.In addition, it is concluded from studies of available field data and theories that the magnitude of _w is not well-known at elevations above about 100m during the late afternoon and night. Some simple parameterizations for _w . are suggested that are consistent with the observed steady decrease in ground-level concentration in the afternoon and the sudden increase in concentration that can occur a few hours after sunset due to wind shears associated with a low-level jet, for continuous plumes emitted from moderate to tall stacks.     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

A Study in Search of Interconnection between Surface Parameters and Surrounding Synoptic And Subsynoptic Features

The paper reveals that the variations in parameters like u*, the scaling velocity and θ*. The scaling tempera-ture during the various phases of monsoon might be linked with subsynoptic features. The rise in u* is mainly connected with the presence of lower tropospheric cyclonic vorticity over a subsynoptic scale of the site. However the variations in θ* is mainly linked with the various phases of monsoon and θ* shows a sharp rise in presence of low level convective cloud.Besides the correlation studies of u and u*, θv and θv* , θv-θv0 and θv* are undertaken. The correlation be?tween θv and θv* is poor. In other two cases correlations are good. Besides u/u* , has shown good coefficient of variation values within the ζ range.     

Spectral scaling in a high reynolds number laboratory boundary layer

Spectra and co-spectra of the streamwise (u) and normal or vertical (w) velocity fluctuations have been measured in the inner region of a large Reynolds number laboratory boundary layer over a rough wall. There is reasonable evidence of ak ₁ ^–1 range in theu spectrum (wherek ₁ is the streamwise wavenumber). Such a range results from an overlap between a spectral region dominated by largescale, inactive motion, which scales on the boundary-layer thickness, and a region dominated by smaller-scale, active motion which scales on the distance from the wall. Spectra ofw, anduw cospectra, scale in a manner consistent with the dominance by active motion. The present spectral data do not support local isotropy over the inertial subrange. A comparison between measuredw spectra and calculations based on isotropy indicates that the inertial subrange anisotropy is only slightly affected by the magnitude of the non-dimensional mean shear.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Microscale ordered motions and atmospheric structure associated with thin echo layers in stably stratified zones

The interpretation of ultra-high resolution radar observations of thin clear-air echo strata is made with the aid of fine-scale aircraft measurements. The echo layer, generally comprising two sub-strata each 5 m thick and spaced 7–10 m apart, is found within a 10–20 m deep section of a strong inversion where the thermal stability and shear are maximized, and the Richardson number is close to 0.25. Mechanical turbulence is restricted entirely to this layer; the variance of the N-S velocity component, ³, is the strongest, consistent with the orientation of the shear vector in this stratum. Spectra and cospectra of a 9-s slant run through the echo stratum show remarkably ordered motions. A strong negative peak of <w> covariance at 80-m scale, accompanied by a zero of <uw> covariance and bulges in the longitudinal () and vertical (w) velocity spectra, is identified with breaking Kelvin-Helmholtz waves oriented in the N-S direction along the shear vector. A synthesis of the temperature and velocity structures from measurements along the flight path confirms the ordered motion deduced from the spectra and reveals a group of K-H waves of 80-m length and 10-m height at the height of the radar echo. Microscale K-H ripples of 3–4 m length are also deduced to be present in the 0.5 m thick interfacial region where the thermal gradient and shear are strongly enhanced by the larger shearing K-H wave.Two possible sources of the echoes are proposed: (1) scatter from fully developed turbulence within the interfacial zone in an inertial subrange falling entirely in sub-meter scales; and (2) the incoherent summation of specular reflections from properly oriented portions of the microscale K-H ripples. While the authors favor the first of these mechanisms, both require stringent conditions of the physical microstructure which are beyond the available observations. Fossil turbulence is precluded as an echo mechanism.This paper is based in part on the doctoral dissertation by the senior author.Present affiliation: Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

Wind stress over water waves: Field experiments on lake of Geneva

Summary A fixed platform (Fig.3), installed 100 m from the shoreline in 3 m water depth, was instrumented with velocity, temperature and wave-height sensors. 132 data (10 minutes averages) were analysed to calculate the wind stress; from these, 99 data were used to investigate the vertical distribution of the wind stress; all data are presented with Table 1.It was postulated that the total stress, _t being constant with height, is made up additively of two components, the wave-supporting stress, _w , and the turbulent stress, _c ; see Eq. 1. The vertical distribution of these two components is shown schematically in Fig. 1.The total stress, _t , evaluated outside the zone of wave influence, is given in the classical way with Fig. 4. The wave-supporting stress, _w (z), was evaluated from the data according to a relation proposed by Kitaigorodskii et al. (1984); it is given with Fig. 5. A height-dependency is clearly evident. The turbulent stress _c (z), was evaluated with data of the velocity gradient; it is given with Fig. 6. A height-dependency is not evident.The field data from the lake of Geneva give evidence that the additive relation of Eq. 1 seems to be justified.With 6 Figures     

Numerical simulation of particle trajectories in inhomogeneous turbulence,II: Systems with variable turbulent velocity scale

It is shown that for the purpose of trajectory simulation, the vertical velocityw _L (t) of a fluid element, which is moving in a system (such as a forest canopy, or the unstably stratified atmospheric surface layer) whose turbulent velocity scale _w is height-dependent, must be chosen from a frequency-distribution which is asymmetric aboutw _L = 0. If the gradient _w /z varies only slowly with height, correct trajectories may be obtained by adding a bias (where _L is the length scale) to a fluctuating velocity chosen from a symmetric distribution with variance _w ²(z).