Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

Statistics of atmospheric turbulence within and above a corn canopy

Two three-dimensional split-film anemometers were used to measure turbulence statistics within and above a corn canopy. Normalised profiles of mean windspeed, root-mean-square velocity, momentum flux, and heat flux were constructed from half-hourly averages by dividing within-canopy measurements by the simultaneous canopy-top measurement. With the exception of the heat flux, these profiles showed consistent shape from day to day. Time series of the three velocity components were recorded on magnetic tape and subsequently analysed to obtain Eulerian time and length scales and the power spectrum of each component at several heights. The timescale was found to have a local minimum value at the top of the canopy. However the length scale L _wformed from the timescale and the root-mean-square vertical velocity varied with height as L _w 0.1 z. The power-spectra were non-dimensionalised to facilitate comparison of spectra at different heights and times. All spectra had -5/3 regions spanning at least two decades in frequency.     

Intermittent wind close to the ground within a grass canopy

Wind speed was measured at a height of 1 cm above the ground and at several other heights in and above a canopy of tall fescue grass (Festuca arundinacea) using single hot-wire and triple hot-film anemometers. The plant area density in the canopy was concentrated close to the ground, with 75% of the plant area standing belowz=15 cm, wherez is height above the ground. The frequency distributions of horizontal wind speeds,s, were sharply skewed towards positive values at all measurement heights, but were most highly skewed near the ground where the coefficient of skewness ranged from 1.6 to 2.9. Above mid-canopy height, the frequency distribution ofs was described reasonably well by a Gumbel extreme value distribution. Average wind speed,S, decreased exponentially with depth into the canopy with an exponential scale length of abouth/2.8, whereh is the height of the canopy. Atz=1 cm, the value ofS was about 11% of the surface-layeru _*. The standard deviation of the fluctuations of the vertical and horizontal components of the wind speed also decreased exponentially with depth inside the canopy with a scale length of abouth/2.5.Inside the canopy, the Eulerian integral time scales for the vertical ( _w ) and horizontal ( _u ) components of wind speed were about 0.1 s and 1.0 s, respectively, and were approximately constant with height. Above the canopy, these time scales increased sharply and, atz=2.25h, _w and _u were approximately 1.0 and 3.0s, respectively. Turbulence length scales in the vertical and downwind directions, _u and _w ·U, respectively, were approximately 1 cm for heights between 1 to 10 cm above the ground inside the canopy, while atz=2.25h, they were about 55 cm and 277 cm. Relatively quiescent periods (lulls) in the air close to the ground were interrupted frequently by gusts. The frequency of occurrence of gusts appears to be correlated with the value of the local shear near the top of the canopy.     

Organised Motion in a Tall Spruce Canopy: Temporal Scales,Structure Spacing and Terrain Effects

This study investigates the organised motion near the canopy-atmosphere interface of a moderately dense spruce forest in heterogeneous, complex terrain. Wind direction is used to assess differences in topography and surface properties. Observations were obtained at several heights above and within the canopy using sonic anemometers and fast-response gas analysers over the course of several weeks. Analysed variables include the three-dimensional wind vector, the sonic temperature, and the concentration of carbon dioxide. Wavelet analysis was used to extract the organised motion from time series and to derive its temporal scales. Spectral Fourier analysis was deployed to compute power spectra and phase spectra. Profiles of temporal scales of ramp-like coherent structures in the vertical and longitudinal wind components showed a reversed variation with height and were of similar size within the canopy. Temporal scales of scalar fields were comparable to those of the longitudinal wind component suggesting that the lateral scalar transport dominates. The existence of a – 1 power law in the longitudinal power spectra was confirmed for a few cases only, with a majority showing a clear 5/3 decay. The variation of effective scales of organised motion in the longitudinal velocity and temperature were found to vary with atmospheric stability, suggesting that both Kelvin-Helmholtz instabilities and attached eddies dominate the flow with increasing convectional forcing. The canopy mixing-layer analogy was observed to be applicable for ramp-like coherent structures in the vertical wind component for selected wind directions only. Departures from the prediction of m = Λ _w L _s ⁻¹ = 8–10 (where Λ _w is the streamwise spacing of coherent structures in the vertical wind w and L _s is a canopy shear length scale) were caused by smaller shear length scales associated with large-scale changes in the terrain as well as the vertical structure of the canopy. The occurrence of linear gravity waves was related to a rise in local topography and can therefore be referred to as mountain-type gravity waves. Temporal scales of wave motion and ramp-like coherent structures were observed to be comparable.     

Turbulence in an almond orchard: Spatial variations in spectra and coherence

The spatial variability of turbulence in a fully-leafed almond orchard was studied. Two three-dimensional sonic anemometers were used to measure turbulence spectra and coherence at different vertical and lateral separations inside the canopy. Peak frequencies of the horizontal velocity components, normalized by local horizontal wind speed, are greater in the canopy crown than in the trunkspace. Peak-normalized frequencies for the vertical velocity power spectra are similar in the canopy crown and in the subcanopy trunkspace. Spectral slopes in the inertial subrange are more negative than those predicted with Kolmogorov's -2/3 theory. It is thought that the foliage elements act to short-circuit the eddy cascade. Lateral separation of the instruments in the subcanopy trunkspace has little effect on the shape of the velocity spectra. On the other hand, lateral and vertical velocity coherences between spatially separated sensors are low inside the canopy. These low coherences are due to the Eulerian length scales being of the same order of magnitude as the separation distances of the anemometers. Phase angles between velocity components are about zero for small separation distances. When the two instruments are separated by 9 m and one instrument is positioned in a row while the other is between two rows, vertical velocities are about 180 deg out of phase and the streamwise velocities are about 40 to 60 deg out of phase. These data support the contention that preferred differences occur between within- and between-row wind flow regimes.     

The Impact of Land-Surface Parameter Properties and Resolution on the Simulated Cloud-Topped Atmospheric Boundary Layer

A method to simulate characteristics of wind speed in the boundary layer of tropical cyclones in an idealized manner is developed and evaluated. The method can be used in a single-column modelling set-up with a planetary boundary-layer parametrization, or within large-eddy simulations (LES). The key step is to include terms in the horizontal velocity equations representing advection and centrifugal acceleration in tropical cyclones that occurs on scales larger than the domain size. Compared to other recently developed methods, which require two input parameters (a reference wind speed, and radius from the centre of a tropical cyclone) this new method also requires a third input parameter: the radial gradient of reference wind speed. With the new method, simulated wind profiles are similar to composite profiles from dropsonde observations; in contrast, a classic Ekman-type method tends to overpredict inflow-layer depth and magnitude, and two recently developed methods for tropical cyclone environments tend to overpredict near-surface wind speed. When used in LES, the new technique produces vertical profiles of total turbulent stress and estimated eddy viscosity that are similar to values determined from low-level aircraft flights in tropical cyclones. Temporal spectra from LES produce an inertial subrange for frequencies \(\gtrsim \)0.1 Hz, but only when the horizontal grid spacing \(\lesssim \)20 m.     

Turbulence Spectra And Dissipation Rates Above And Within A Forest Canopy

Three velocity componentsand temperature were measured usingthree-dimensional sonic anemometers/thermometers attwo levels, above and within a forest canopy, in theChangbai Mountains of northeast China. Turbulencespectral structure, local isotropy anddissipation rates above and within the forest canopywere calculated using the eddy correlation method.Results show that the normalized turbulent spectralcurves have -2/3 slopes in the inertial subrange.While the shapes of the spectra are in good agreementwith the Kansas flat terrain results, the atmosphericturbulence is anisotropic above the forest canopy. Dueto breaking down of large eddies by the foliage,branches and trunks, the spectral peak frequencies forvelocity and temperature are higher withinthan above the forest canopy. Compared withmeasurements from previous studies over flat terrain,the velocity and temperature spectra above andinside the forest canopy appear to shift toward higherfrequencies. The turbulence is approximately isotropicin the inertial subrange within the forest canopy, and isanisotropic above the forest canopy. The turbulentkinetic energy and heat energy dissipation rates aboveand inside the forest canopy are much larger thanthose obtained by Kaimal and Hogstrom over grasslandand grazing land. The distinct features in the resultsof the present experiment may be attributed to thedynamic forcing caused by the rough surface of the forestcanopy.     

Characteristics of air flow above and within soybean canopies

Air flow was observed above and within canopies of a number of kinds of soybeans. The Clark cultivar and two isolines of the Harosoy cultivar were studied in 1979 and 1980, respectively. Wind speed above the canopy was measured with cup anemometers. Heated thermistor anemometers were used to measure air flow within the canopy. Above-canopy air flow was characterized in terms of the zero-plane displacement (d), roughness parameter (z _o) and drag coefficient (C _d). d and z _o were dependent on canopy height but were independent of friction velocity in the range 0.55 to 0.75 m s^?1 · C _d for the various canopies ranged from 0.027 to 0.035. Greater C _d values were measured over an erectophile canopy than over a planophile canopy. C _d was not measurably affected by differences in leaf pubescence. Within-canopy wind profiles were measured at two locations: within and between rows. The wind profile was characterized by a region of great wind shear in the upper canopy and by a region of relatively weak wind shear in the middle canopy. Considerable spatial variability in wind speed was evident, however. This result has significant implications for canopy flow modeling efforts aimed at evaluating transport in the canopy. In the lower canopy, wind speed within a row increased with depth whereas wind speed between two rows decreased with depth. The wind speeds at the two locations tended to converge to a common value at a height near 0.10 m. The attenuation of within-canopy air flow was stronger in canopies with greater foliage density. Canopy flow attenuation seemed to decrease with increasing wind speed, suggesting that high winds distorted the shape of the canopy in such a manner that the penetration of wind into the canopy increased.     

Observational aspects on a dominant spectral frequency in an airflow over a weeping-lovegrass stand

Mean and fluctuating wind velocities were measured above a flexible stand (weeping-lovegrass). A waving phenomenon Honami appeared over the stand during the observation period. Some spectral parameters were derived from the vertical wind fluctuations. A dependency of frequency on mean horizontal wind velocity was found. The result, n _m = 0.66u, was obtained under the range of wind speeds from 0.9 m s^-1 to 3.1 m s^-1 just above the canopy.     

Time series analyses of concentration and wind fluctuations

Analyses of concentration fluctuation (C) spectra from boundary-layer smoke plume experiments at six separate locations show that the spectra from these experiments generally exhibit an inertial subrange at high frequencies with a slope of -5/3 and indicate peak energy at a time period of about 50 to 100 s. These periods of peak energy are a factor of two to five less than those for the peak of the wind speed fluctuation (u or v) spectra. A general spectral formula fits normalized spectra from the U.S. and Australia, where the frequency, n, is made dimensionless by multiplying by the plume dispersion parameter, _y , and dividing by the wind speed, u. Peak energy occurs at a dimensionless frequency of n _y/u equal to about 0.15. The Kolmogorov constant in the inertial subrange is estimated from a set of averaged spectra. Cross-spectra indicate little relation between concentration and wind fluctuations. However, most of the correlation that exists is due to periods larger than about 10 or 20 s.     

Turbulence Statistics Measurements in a Northern Hardwood Forest

Tower-based turbulence measurements were collected in and over a mixed hardwood forest at the University of Michigan BiologicalStation (UMBS) UMBSflux site in the northern summerof 2000. Velocity and temperature fluctuations were measured at five levels within the canopy (up to the canopy height, H = 21.4 m), using one- and three-dimensional sonic anemometers and fine-wire thermocouples. Six additional thermocouples were distributed over the canopy-layer depth. Three-dimensional velocities and sonic temperatures were also measured above the canopy at 1.6H and at 2.15H on the AmeriFlux tower located at the UMBSflux site. Vertical profiles of buoyancy flux, mean horizontal velocity, Reynolds stress, and standard deviation and skewness of velocity components were calculated. The analysis of these measurements aims at a multi-layer parameterization framework of turbulence statistics forimplementation in Lagrangian stochastic models. Turbulence profiles and power spectra above the canopy were analyzed in the context of Monin-Obukhov similarity theory (MOST) and Kolmogorov theory, as determined by stability at the top level (2.15H), to assess the extent to which surface scaling is valid as the canopy top is approached. Velocity spectra were computed to explore the potential of estimating the viscous dissipation rate, and results show that the high frequency range of the spectra above the canopy exhibits the roll-off predicted by Kolmogorov theory. Similarly, velocity standard deviations above the canopy converge to MOST predicted values toward the top level, and spectral peaks shift with stability, as expected. Within the canopy, both turbulence statistics profiles and spectral distributions follow the general known characteristics inside forests.     

Turbulent transport of scalar quantities within and above a paddy field

An experiment was conducted to study turbulent transport processes of scalar quantities within and above a rice plant canopy. A sonic anemometer-thermometer and a Lyman- humidiometer were used to measure the turbulent fluxes of sensible and latent heat and related turbulence statistics within a paddy field. The sensible and latent heat fluxes measured at two heights within and above the plant canopy showed that the upper layer of this plant canopy was an active source region and that the source strength of sensible and latent heat depended on the solar radiation and physiology of rice plants. Analysis of joint probability distributions of w and T and of w and q within this plant canopy showed that downdrafts were remarkably efficient for upward transport of sensible and latent heat in the daytime. The vertical fluxes of temperature and humidity variance were also divergent from the upper layer of plant canopies. The power spectra of temperature and humidity within the plant canopy decreased rapidly in the high frequency range, compared with the - 2/3 law relationship of nS(n) vs log n observed above plant canopies.     

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     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Some methodological questions concerning advection measurements: a case study

A dataset from two campaigns conducted at the Vielsalm experimental site in Belgium was used as a basis for discussing some methodological problems and providing intermediate results on estimating CO₂ advection. The analysis focused on the horizontal [CO₂] gradient and on the vertical velocity w, the variables most affected by uncertainty. The sampling error for half-hourly horizontal [CO₂] gradients was estimated to be 1.3 μmol mol⁻¹. Despite this important random error for half-hour estimations of [CO₂], the mean horizontal [CO₂] gradients in advective conditions were shown to be representative at the ecosystem scale and to extend only to the lowest part of a drainage sub-layer, which developed in the trunk space. By contrast, under daytime conditions, this gradient was shown to be more sensitive to local source heterogeneities. The estimation of the short-term averaged vertical velocity ( was the greater source of error when computing advection terms. The traditional correction methods used to obtain are discussed and a (co)sine correction is tested to highlight the instrumental origin of the offset in w. A comparison of measurements by sonic anemometers placed close together above the canopy showed that the uncertainty on was 0.042 m s⁻¹, which is of the same order of magnitude as the velocity itself. In addition, as the drainage sub-layer is limited to the lowest part of the canopy, the representativeness of is questionable. An alternative computation using the divergence of the horizontal wind speed in the trunk space produced a estimation that was four times lower than the single-point measurement. However, this value gives a more realistic estimate of the vertical advection term and improves the CO₂ budget closure at the site.     

Temperature and humidity spectra in the atmospheric surface layer

Temperature and humidity spectra have been measured at 3 and 12 m above the ground, together with profiles of wind, temperature and humidity, and flux measurements. Both temperature and humidity spectra appear to follow Monin-Obukov similarity as well as Kolmogorov's prediction for the inertial subrange. The standard deviations of temperature and humidity fluctuations support Monin-Obukov similarity and the predictions of local free convection. The spectral constants for the inertial subrange have been estimated as 0.8 for temperature and 0.6 for humidity.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

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.     

The response of a propeller anemometer to turbulent flow with the mean wind vector perpendicular to the axis of rotation

The system transfer function ¦H(v)¦² at frequencyv (units of Hz) for a vertical velocity propeller anemometer in a statistically stationary and horizontally homogeneous turbulent flow is determined from: (1) experimental estimates of propeller velocity spectra; and (2) estimates of Eulerian vertical velocity spectra based on the hypothesis that degradation of the input vertical velocity Fourier components occurs in the inertial subrange. The experimental estimates of ¦H(v)¦² were adequately summarized with the mathematical expression for the system transfer function of a first-order system with parameterT which has units of time and is analogous to the time constant of a horizontal velocity propeller anemometer. Dimensional analysis techniques and the Monin-Obukhov similarity hypothesis were used to construct a model for the system parameterT which yielded the result that _w /D ₁ ( _w /)^1/3, where _w , andD ₁ denote the standard deviation of the input vertical velocity fluctuations, the horizontal mean wind speed, and the diameter of the propeller, respectively. The system parameterT is interpreted in terms of the time required for the propeller velocity statistics to become asymptotically independent of time upon being released from rest in a statistically stationary turbulent flow.Currently on leave of absence from the Indian Institute of Technology, New Delhi, India.     

Wind-Speed Undulations Over Swell: Field Experiment and Interpretation

Results of field measurements of the swell-induced undulation of the wind speed taken from a Black Sea platform are presented. The wind speed and its fluctuations were measured at several heights between 1.3 and 21 m above the mean sea level under various wind and swell conditions. Parameters of the swell-induced undulations were derived from cross spectra of the wind-speed fluctuations and the sea-surface displacement. As found, the phase and the amplitude of the wind speed undulation in the layer from k _p z = 0.1 to k _p z = 3 (k _p is the swell wavenumber) are in good agreement with the theory of inviscid shear flow over a wavy surface. The main feature of the vertical profile of the swell-induced undulation is the exponential attenuation of its amplitude with height typical for the potential flow over the fast running waves. At the lowest levels the potential undulations are significantly distorted by the wind-speed variations caused by the vertical displacements of the shear airflow relative to a fixed sensor. No direct impact of swell on the mean properties of the turbulent boundary layer at k _p z > 0.1 is revealed. In particular, the mean wind-speed profile and spectra of the horizontal velocity in the inertial subrange obey Monin-Obukhov similarity theory.