New Equations For Sonic Temperature Variance And Buoyancy Heat Flux With An Omnidirectional Sonic Anemometer

Many new types of sonic anemometer obtain sonic temperature from an average value of temperature measured along three paths, unlike previous sonic anemometers that generally used one path. New equations are derived to calculate temperature variance from sonic temperature variance and sensible heat flux from buoyancy flux considering the influence of a crosswind. These equations can be applied to CSAT3, Solent R2, R3, R3A, HS, and USA-1 sonic anemometers with the corresponding correction factors given in this paper. The equations are verified by data measured by a CSAT3 sonic anemometer in the LITFASS-1998 field study.     

Accuracy of Sonic Anemometers: Laminar Wind-Tunnel Calibrations Compared to Atmospheric In Situ Calibrations Against a Reference Instrument

Two Gill Solent Ultrasonic anemometers, models 1012R2 and 1210R3, weretested in field parallel measurements against a windvane based hot-film anemometerwith additional sensors for temperature and wet-bulb temperature, the MIUU (MIUU:Meteorology Institute, Uppsala University) instrument. This instrument was shown toretain its precision from laminar wind-tunnel tests when used in atmospheric turbulentflow. This contrasts strongly to the observed results for the two sonic anemometers,which were first calibrated in laminar wind-tunnel flow. Individual three-dimensionalcalibration matrices were constructed, and were shown to reduce the remaining calibration uncertainty for the wind speed to 0.4–0.8% for all azimuths and for angles of attack within ±40°. In the field intercomparison tests of the sonics against the MIUU instrument, it was found that the precision not only of the mean wind speed but of all second-order moments studied (variances and covariances, with and without temperature) deteriorated by a factor of typically three to four. Most of the scatter appears to be random, but in the case of the wind speed, a clear dependence on wind direction is found as well. It is concluded that the correction for the effect of the vertical supporting rods of the R2 and R3 instruments, which gives nearly perfect agreement for laminar flow, does not work entirely satisfactory in the natural turbulent flow. This, in turn, is likely to be so because of high sensitivity of the wake behind the cylindrical supporting rods to the character of the approach flow.     

Evaluation of Probe-Induced Flow Distortion of Campbell CSAT3 Sonic Anemometers by Numerical Simulation

The Campbell CSAT3 sonic anemometer is one of the most popular instruments for turbulence measurements in basic micrometeorological research and ecological applications. While measurement uncertainty has been characterized by field experiments and wind-tunnel studies in the past, there are conflicting estimates, which motivated us to conduct a numerical experiment using large-eddy simulation to evaluate the probe-induced flow distortion of the CSAT3 anemometer under controlled conditions, and with exact knowledge of the undisturbed flow. As opposed to wind-tunnel studies, we imposed oscillations in both the vertical and horizontal velocity components at the distinct frequencies and amplitudes found in typical turbulence spectra in the surface layer. The resulting flow-distortion errors for the standard deviations of the vertical velocity component range from 3 to 7%, and from 1 to 3% for the horizontal velocity component, depending on the azimuth angle. The magnitude of these errors is almost independent of the frequency of wind speed fluctuations, provided the amplitude is typical for surface-layer turbulence. A comparison of the corrections for transducer shadowing proposed by both Kaimal et al. (Proc Dyn Flow Conf, 551–565, 1978) and Horst et al. (Boundary-Layer Meteorol 155:371–395, 2015) show that both methods compensate for a larger part of the observed error, but do not sufficiently account for the azimuth dependency. Further numerical simulations could be conducted in the future to characterize the flow distortion induced by other existing types of sonic anemometers for the purposes of optimizing their geometry.     

Triple-Hot-Film Anemometer Performance in Cases-99 and A Comparison With Sonic Anemometer Measurements

Two levels of triple-hot-film and sonic anemometers were deployed on a 5.5-m towerduring the Cooperative Atmospheric Surface Exchange Study (CASES-99) in October1999. Each triple-hot-film probe was collocated 50 mm from the sonic sensing path ona common boom. Various problems with using triple-hot-films in the atmosphere toresolve wind components are addressed including the derivation of a yaw angle correction using the collocated sensors. It was found that output voltage drift due to changes in environmental temperature could be monitored and corrected using an automated system. Non-unique solutions to heat transfer equations can be resolved using a collocated sonic anemometer. Multi-resolution decomposition of the hot-film data was used to estimate appropriate day and night averaging periods for turbulent flux measurements in and near the roughness sub-layer. Finally, triple-hot-film measurements of mean wind magnitude (M), turbulent kinetic energy (TKE), sensible heat flux (H), and local friction velocity (u_*) are compared to those of the collocated CSAT3 sonic anemometers. Overall, the mean wind magnitudes measured by the triple-hot-film and the collocated sonic sensorswere close, consistent and independent of stability or proximity to the ground. The turbulent statistics, TKE, u_*, and H, measured by the two sensor systems were reasonably close together at z = 5 m. However, the ratio of sonic measurement/hot-film measurement decreased toward the ground surface, especially during stable conditions.     

Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

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.     

On gas fluxes from small lakes and ponds

A semi-empirical model for estimating gas fluxes at the air-water interface in a neutrally stratified atmosphere is presented. Gas transfer velocity is assumed to depend on local friction velocity, whose variation with over-water fetch is estimated from Walmsleyet al.'s (1989) Guidelines. As guidance for limnologists estimating CO₂ and CH₄ fluxes from lakes and ponds in the Hudson Bay Lowlands region, we present model results of the variation of gas transfer velocity with over-water fetch,k(x), for comparison with the customary constant valuek ₀. Gas fluxes are estimated over well mixed, circular and elliptical lakes and ponds. The results of accounting for fetch dependence, wind direction, pond shapes and sizes lead to correction factors to fluxes obtained withk ₀. Recent studies of gas transfer velocity for gases of low solubility from lakes are reviewed, and the problem of time averaging on quantities determined from experimental measurements is also discussed.     

A test of isotropy and Taylor's hypothesis in the atmospheric boundary layer

This study attempts to determine the scales of turbulence in a high Reynolds number shear flow near which transition to isotropy occurs and the scales for which Taylor's hypothesis is applicable. The flow studied was the wind near height x ₃ = 2 m above a flat land surface. Four hot-wire anemometers were mounted in a three-dimensional array with equal separations between 1.8 m and 2 cm in three different directions. Theoretical cross-spectra were computed from the observed spectra of downwind velocity fluctuations assuming isotropy and Taylor's hypothesis. Comparison between these and the observed cross-spectra revealed that the turbulence in the flow studied was consistent with both assumptions provided k _1x3&> 20, where k ₁ is the radian wavenumber; this was the lower bound to which no departure from isotropy could be detected by the experiment. For 4 k _1x3 20, the observations are consistent with symmetry of the turbulence about the downstream direction. That part of Taylor's hypothesis relating observed frequency at a stationary sensor to the downstream wavenumber component appears to be justified within experimental error for k _1x3& > 3.     

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.     

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     

Two-Dimensional Scalar Spectra in the Deeper Layers of a Dense and Uniform Model Canopy

The turbulent flow inside dense canopies is characterized by wake production and short-circuiting of the energy cascade. How these processes affect passive scalar concentration variability in general and their spectral properties in particular remains a vexing problem. Progress on this problem is frustrated by the shortage of high resolution spatial concentration measurements, and by the lack of simplified analytical models that connect spectral modulations in the turbulent kinetic energy (TKE) cascade to scalar spectra. Here, we report the first planar two-dimensional scalar concentration spectra (ϕ _cc ) inside tall canopies derived from flow visualization experiments. These experiments were conducted within the deeper layers of a model canopy composed of densely arrayed cylinders welded to the bottom of a large recirculating water channel. We found that in the spectral region experiencing wake production, the ϕ _cc exhibits directional scaling power laws. In the longitudinal direction (x), or the direction experiencing the largest drag force, the ϕ _cc (k _x ) was steeper than and followed an approximate at wavenumbers larger than the injection scale of wake energy, where k _x is the longitudinal wavenumber. In the lateral direction (y), the spectra scaled as up to the injection scale, and then decayed at an approximate power law. This departure from the classical inertial subrange scaling (i.e., k ^−5/3) was reproduced using a newly proposed analytical solution to a simplified scalar spectral budget equation. Near the velocity viscous dissipation range, the scalar spectra appear to approach an approximate k ⁻³, a tantalizing result consistent with dimensional analysis used in the inertial-diffusive range. Implications to subgrid modelling for large-eddy simulations (LES) inside canopies are briefly discussed.     

Thermal Image Velocimetry

A method for measuring the two-dimensional distribution of wind velocity vectors near a surface exposed to solar radiation, by tracking brightness temperature images instead of particle images, is proposed. It is based on time-sequential thermography with the algorithm used for particle image velocimetry. This thermal image velocimetry (TIV) was tested on a full-scale building wall covered by polystyrene boards attached side-by-side over a vertically elongated area measuring 22.2 m by 2.73 m. A thermal infrared camera was installed 8 m from the test wall to capture the wall-surface temperature at 30 Hz frequency. A sonic anemometer was also installed 35 mm from the surface used for validation of the TIV. The advection velocity estimated from thermal infrared imagery had a linear relationship with the wind velocity measured by the sonic anemometer, irrespective of the wind speed and direction. This linear slope was multiplied by the advection velocity of the thermal infrared image to rescale it to the wind velocity, and the term ‘TIV velocity’ was then used. A histogram and power spectra of the TIV velocity showed quantitatively good agreement with the velocity measured by the sonic anemometer, except for the high-frequency region of the spectra, where the TIV velocity was overestimated compared with that of the sonic anemometer. The method was also tested on ground covered by artificial turf to demonstrate its application to a horizontal plane with a wider area, extending for more than 80 m by 60 m.     

An analysis of the turbulent structure in the unstable surface layer nearby a shelter belt

An analysis was performed of the turbulent data obtained from Yucheng experimental station in the Shandong Province in 1984. [t is shown that at variant wind speed, the spectra of streamwise velocity remain similar and the intensity of wind fluctuations is proportional to wind speed in the downwind area of shelter belt. Therefore, we may decide the similarity of wind fluctuations by a speed scale and a length scale which is not correlated with stability, σu /V0 = F(X / H). The -5/3 power range of temperature spectra extends to lower frequency. The variation of ratio σ0 /T. with stability becomes σ0 / T . = C(X / H)( - Z / L)-1/3 . There is not such an extension of -5 / 3 power range in the humidity spectra.     

A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding

For the 1968 Kansas atmospheric surface-layer experiment, a supplementary analysis is made of the evaluation procedure. Available data on the ratio of wind speeds measured on separate booms show a variation with wind direction which is too large for an open mast. Actually the Kansas mast appears to have carried a bulky array of apparatus at the sonic anemometer levels. It is shown that the air flow interference caused by this obstacle can be satisfactorily estimated by way of potential flow calculations. From these it follows that the sonic anemometer measurements probably have undervalued the free-flow eddy stress by 20% to 30%, which implies that the simultaneous drag plate measurements of stress were generally correct. Also the overestimation of the mean wind speed by the Kansas cup anemometer is found to have been 6% rather than 10%. Some Kansas evaluation results are amended accordingly. The von Kármán constant is found to be 0.41 rather than 0.35, and the near-adiabatic eddy diffusivity ratio K _H /K _M becomes 1.0 rather than 1.3. The flux-gradient relations (Businger et al., 1971) after similar revision no longer differ significantly from those obtained elsewhere.     

A quantitative comparison of horizontal and vertical acoustic sounding with in-situ measurements

In this paper, we present some results on an experiment to test the accuracy and utility of a horizontally-aimed acoustic sounder. A high-frequency, high-resolution mini-sounder was mounted on the mast of the Boulder Atmospheric Observatory aimed in the cross-wind direction. Measurements of C _T ², wind velocity and temperature and velocity variances were obtained under both stable and unstable conditions. These measurements were found to be in agreement with the equivalent values obtained, where appropriate, by the tower-fixed instrumentation and a vertically-pointed sounder, confirming the accuracy of the horizontal sounder. In addition, some information into the horizontal structure of plumes and gravity waves was obtained along with evidence of lack of excess attenuation at least for lengths within the unambiguous range of mini-sounders.     

Turbulence Structure in the Wake Region of a Meteorological Tower

A meteorological tower significantly modifies the air flow, the mean windspeed and wind direction as well as the turbulencestructure of the air. Suchchanges can be noticed in particular in the wake region of the tower.Measurementson the 200 m tower ofForschungszentrum Karlsruhewere carried outusing Solent sonic anemometers in the lee of the towerand cup anemometers on both sides.In the wake region, spectral energydensity is increased in the high-frequency range. Superposition of this disturbance spectrum on the undisturbedspectrum yields a `knee' in the resulting spectrum. In the case of low turbulence intensity with stable stratification,a plateau with a constant energy content is observed in front of the knee.This effect is caused by the new production of turbulence energy from the mean flow as well as by an energy transfer fromlarger to smaller vortices. Power spectra in strongly stable conditionsshow a more rapid decrease of intensity in the region where the inertialsubrange is expected.The relevant scales of wake turbulence are derived from the maximum of the disturbance spectrum.Locations of the high-frequency peak do not depend on atmospheric stability,but are controlled mainly by mean wind speed.Apart from the reduction of the mean wind speed, the spectra and cospectra exhibit a strong anisotropy for such cases.The results demonstrate the significant influence of a tower on turbulence spectra in the wake region.     

Influence of non-flat terrain and wind direction shear on canopy turbulence

We have analyzed eddy covariance data collected within open canopy to investigate the influence of non-flat terrain and wind direction shear on the canopy turbulence. The study site is located on non-flat terrain with slopes in both south-north and east-west directions. The surface elevation change is smaller than the height of roughness element such as building and tree at this site. A variety of turbulent statistics were examined as a function of wind direction in near-neutral conditions. Heterogeneous surface characteristics results in significant differences in measured turbulent statistics. Upwind trees on the flat and up-sloping terrains yield typical features of canopy turbulence while upwind elevated surface with trees yields significant wind direction shear, reduced u and w skewness, and negligible correlation between u and w. The directional dependence of turbulence statistics is due that strong wind blows more horizontally rather than following terrain, and hence combination of slope related momentum flux and canopy eddy motion decreases the magnitude of Sk _w and r _uw for the downslope flow while it enhances them for the upslope flow. Significant v skewness to the west indicates intermittent downdraft of northerly wind, possibly due to lateral shear of wind in the presence of significant wind direction shear. The effects of wind direction shear on turbulent statistics were also examined. The results showed that correlation coefficient between lateral velocities and vertical velocity show significant dependence on wind direction shear through change of lateral wind shear. Quadrant analysis shows increased outward interaction and reduced role of sweep motion for longitudinal momentum flux for the downslope flow. Multi-resolution analysis indicates that uw correlation shows peak at larger averaging time for the upslope flow than for the downslope flow, indicating that large eddy plays an active role in momentum transfer for the upslope flow. On the other hand, downslope flow shows larger velocity variances than other flows despite similar wind speed. These results suggest that non-flatness of terrain significantly influences on canopy-atmosphere exchange.     

Turbulent transport of carbon dioxide over a paddy field

Turbulent fluctuations in CO₂ concentrations over a paddy field are measured by a fastresponse device with an open sensing path. This IR device coupled with a sonic anemometer constitutes an eddy correlation instrument to measure CO₂ fluxes. Three experiments were conducted in the surface layer over paddy 90 cm high. The stability (z – d)/L ranged from -0.14 to 0.20, where L denotes the Monin-Obukhov length.CO₂ power spectra show the range of applicability of the -2/3 power law to be between f = 0.2 and f = 2, where f is the frequency normalized by wind speed and height. The cospectral estimate between CO₂ and vertical component of wind speed ranging from f = 0.005 to f = 2 shows a peak at about f = 0.15 under near-neutral stratification.Hourly means of CO₂ flux measured by the eddy correlation method increase with intensity of net radiation. The maximum value of downward flux of CO₂ rises to 0.6 mg cm^-2 hr^-1 over the paddy field at the stage of ear emergence.Some turbulence statistics relating to the CO₂ transport are evaluated: the correlation coefficient between CO₂ and vertical velocity is about -0.3, and that between CO₂ and humidity attains -0.7 ~ -0.8 under unstable stratification; nondimensional gradients _c for CO₂ and _m for wind speed are 0.89 and 0.99, respectively.     

Examination of a Correction Procedure for the Flow Attenuation in Orthogonal Sonic Anemometers

In this study we examine the calibration of wind speed measured by a sonic anemometer, with an orthogonal probe configuration, with regard to the approximation of the flow angle, and the wind-speed dependence of the flow attenuation attributed to the transducer shadow. The flow angle should be calculated by the iterative method when the attenuation is relatively high. For a probe manufactured by Kaijo Co. TR-61C, the wind-speed dependence of the transducer shadow effect is formulated from the results of the wind-tunnel experiment. Assuming the equation is applicable to field observations, significant errors possibly remain especially when the wind speed is low, and /or the angle between the flow vector and the sonic path is small, if the wind-speed dependence in measurement errors is neglected.