a. Kaijo Denki DAT-310 and TR-61A

This sonic anemometer consists of a main unit DAT-310 with power supply, signal processing, and output. A junction box OA-60A drives the transducers and amplifies the received signals. The probe head TR-61A is of solid aluminum construction with round struts, 11 mm in diameter, streamline leveled in the transducer surroundings. The transducers themselves are surrounded by streamlined housings. The sound pathlength is 200 mm, whereas a nonorthogonal coordinate system is used. The two horizontal sound paths are vertically shifted by 40 mm and have an opening angle of 120°. The vertical sound path is appropriate in front of the intercept point of the horizontal sound paths. This sensor is specifically designed for incoming flow within an angle of about 100° (Fig. 1). The sampling frequency for wind and temperature measurements is 20 Hz.

b. Kaijo Denki DAT-310 and TR-61B

This model is also divided into three parts: main unit, junction box, and probe. The sound paths of the TR-61B probe are arranged diagonally. They are horizontally shifted from each other by 120° and 45° tilted against the vertical (Fig. 2). The transducers are fixed at three streamline struts enclosing the measurement volume. This symmetric arrangement allows the detection of all three wind components in the same air volume and has the advantage of no special direction characteristic. The sampling frequency also is 20 Hz. Vector transformation and calculation of wind speed and wind direction are done by the system.

c. Kaijo Denki DAT-300 and TR-61C

The main unit DAT-300 is used with the junction box OA-60A and the probe TR-61C shows a simple geometry (Fig. 3). Two sound paths are horizontally arranged and orientated perpendicular to each other. To reduce interference the sound paths are vertically shifted by 30 mm. The vertical wind velocity is determined along an external vertical sound path. All transducers are fixed at 11-mm aluminum struts. Because of transducer shadowing effects (Wyngaard and Zhang 1985), this probe geometry is less applicable to the measurement of horizontal flow. However, for eddy correlation purposes the external vertical sound path has advantages because vertical motion is connected with horizontal airflow. Again, the sampling frequency for wind and temperature is 20 Hz.

d. Solent Research/Gill sonic anemometer

This sonic anemometer was developed by Solent Research and produced by Gill Instruments. The probe geometry is similar to the Kaijo Denki TR-61B probe with diagonally orientated sound paths (Fig. 4). But this sensor is much smaller, and most of the electronics are placed in the probe foot. The probe consists of aluminum, fiberglass, and synthetic material. The small transducers are infused in a plastic mounting, which is fixed at the bottom and top of the probe, respectively. The sound paths are 140 mm long. During operation the run time of a sound pulse along one path is measured every millisecond. The user can select four different operation modes.

1. Calibrated uυw mode

   The mean over eight samples is calculated, a vector transformation is done, and the measured values are treated with the internal calibration procedure. The output is available with 21 Hz either as digital or analog values. The internal calibration is based on wind tunnel measurements made by Gill Instruments by turning each sonic anemometer in vertical orientation for 360° at 20 m s⁻¹. Four times 361 correction coefficients for direction and horizontal wind velocity (device specific) as well as positive and negative vertical wind components (universal) are stored as a lookup table in the instrument. During the calibration procedure the wind direction α is calculated from the measured horizontal wind components ũ and υ̃ and used for indexing the lookup table to get the correction factors (f^α_dir, f^α_mag, f^α_w±). The wind direction corrections û = ũ − υ̃f^α_dir and υ̂ = υ̃ + ũf^α_dir provide intermediate data for the velocity corrections u_c = ûf^α_mag and υ_c = υ̂f^α_mag. Finally the vertical wind component is treated according to w_c = w̃f^α₊ for w̃ > 0 or w_c = w̃f^α₋ for w̃ < 0.

   For the instrument used in the test, the coefficients for wind direction and wind vector correction are within the range of 1.05 to 1.17. Hence it has to be assumed that this sensor always underestimates wind velocities. Vogt (1995) reports smaller correction coefficients for newer Solent Research/Gill sonic anemometers.

2. Uncalibrated uυw mode

   This setting is equal to the first, but the measured wind components are left untouched. Output frequency is 21 Hz. This mode should be preferred for flux measurements, especially. The Gill calibration procedure can be calculated afterward without any loss if it is advantageous for the desired application.

Operation modes 3 and 4 provide raw sensor signals with 21 or 56 Hz.

e. METEK USA-1

METEK offers a sonic anemometer with a modified TR-61B layout (Fig. 5). Three sound paths of 180-mm length are used, horizontally shifted by 120° and tilted by 45°. But there is only one central strut, and the sound paths have no intercept points. The transducers are all fixed at the main strut with separate small struts. The complete electronics is placed in an aluminum box between the mast mounting and the refined steel central strut. A serial RS-232 interface is used for communication and data output. Settings like sampling frequency, effective ranges, averaging intervals, and data output can be varied. An automatic zero calibration that requires actual sound pathlengths and temperature is also integrated. The optional analog output was included in the test device. Sound reflections at the walls of our wind tunnel caused data loss error messages at the digital output of the METEK USA-1 when used at a sampling frequency of 20 Hz. These errors did not occur with a reduced sampling frequency of 10 Hz. Since the effect of this error on the signal at the analog output was unknown, all measurements were executed at 10 Hz.

a. Measurement setup

All measurements were made in the Voith Novenco closed box wind tunnel of the Institut für Meteorologie und Klimaforschung Karlsruhe. The measurement box has dimensions of 200 cm × 100 cm × 100 cm (Fig. 6). On cross sections perpendicular to the flow direction, the wind velocity was determined on a 10 cm × 10 cm grid using a Pitot tube. A calibrated magnet-borne reference cup anemometer was inserted into the upper area of the wind tunnel. The sonic sensors were installed underneath the reference anemometer.

The modification of the wind field within the measuring volume of the Kaijo Denki TR-61B sensor was determined with a Pitot tube and a Rosemount differential pressure sensor. Static pressure was measured simultaneous with a Vaisala PT427 pressure sensor, and air temperature and humidity were measured with an Ahlborn Therm 2286-2 electronic psychrometer. A cross section within the measurement volume of the TR-61B sensor with a grid of 1.5 cm × 1.5 cm was chosen. First, the undisturbed wind field in the wind tunnel was determined. Afterward, the sensor was installed and the same measurements were executed again. The sampling frequency was 100 Hz. Thus, the turbulent wake area downstream of the transducers and retaining props of the probe could be resolved. Of course the TR-61B was not operated during these measurements. In all other cases, the analog output signals of the sonic anemometers were analyzed.

The measurements with horizontally aligned sensors were executed in two ways.

1. Measurements with turning the sensors around 360°:

   With flow velocities of 0.5, 2, 5, and 10 m s⁻¹ the probes were turned in steps of 2° around a complete circle. For each position mean values of the wind components and the reference wind velocity were taken.

2. Measurements ±45° around a sensor structure:

   For the investigation of the influence of sensor-induced eddies and shadowing effects the sensors were turned ±45° around the position (see Table 1) with maximum disturbance of the wind field in the measurement volume due to sensor supports windward.

Finally, the stepping motor was replaced by a revolving and tiltable fixation to verify the measurements of the vertical wind component. Two flow directions (see Table 1) were chosen: with unimpaired and with a maximum disturbed wind field in the probe volume. To simulate positive and negative vertical wind velocities, the sensors were tilted parallel to the flow direction by ±8° in steps of 1°.

b. Wind tunnel characteristics

Figure 7 shows the distribution of the percentage wind velocity deviation from the cross-section average at the location of the reference anemometer. The mean wind speed is 4.9 m s⁻¹. The two rectangles mark the location of the sonic anemometer (lower) and the reference anemometer (upper).

The deviations are within the range of −4% to +6%, depending on the mean flow. At different flow rates no uniform pattern occurs. Due to the spatial separation of sonic and reference anemometer, it has to be expected that at a wind velocity of 4.9 m s⁻¹ the sonic anemometer determines a mean wind that is higher by approximately 3% than that of the reference anemometer.

c. Sensor-induced wind field modification

An important source of errors in wind velocity measurements is the sensor itself. Props and transducer housings cause a modification of flow with lower wind velocities in the lee and increased flow rate within small areas of convergence. The variance of the wind velocity in the measuring volume of the sensor is increased by separation vortices developing at the sensor components. These effects are shown for the Kaijo Denki TR-61B probe.

A plane within the probe was chosen as shown in Fig. 8. At the reference wind velocity of 5 m s⁻¹, the wind speed was measured on a 1.5 cm × 1.5 cm grid at 121 points with a small Pitot tube. The coordinates used in Figs. 9 and 10 are relative to the cross-section coordinates of the wind tunnel.

The wind velocities measured in the absence of the TR-61B sensor show deviations from the reference wind velocity of the wind tunnel between 3% and 6%. This means higher wind velocities at the location of the sonic anemometer of about 0.2–0.35 m s⁻¹.

Installing the probe changes the flow field considerably. Figure 9 shows the changes in horizontal wind velocity due to the flow around the sensor. The effects of a prop and two transducers can be easily identified in the figure. The sphere of influence of the streamline vertical prop is limited to a narrow strip in the center, in which the wind velocity is reduced up to 10%. On both sides an area with little changed flow conditions (up to 5%) follows. Within the shading area of the transducers C⁻ and B⁺ (Fig. 8) located at (46 cm, 32 cm) and (53 cm, 45 cm) the wind velocity is reduced up to 25%. The flow around the transverse standing transducers of the sound path A (42 cm, 45 cm) and (57 cm, 32 cm) produces flow rates that are up to 15% higher than those of the unimpaired case.

As for Fig. 9, the structure of the change in the variance of the horizontal wind velocity (Fig. 10) is in accordance with the arrangement of the main sensor components. A broad strip with only a slightly changed variance borders the left and right on the area influenced by the vertical prop. The streamlined arrangement of this prop causes only moderately increased variances, whereas strongly increased variances for up to 66 times can be found in the turbulent wake of the transducers C⁻ and B⁺. At the two transverse standing transducers of the sound path A, the increase in variance is small because the measurements were executed directly behind these obstacles.

a. Horizontal wind speed

Since the wind velocity in the wind tunnel does not exactly correspond to the desired value, the percentage deviation of the measured horizontal wind speed V_hor from the simultaneously recorded value V_ref of the reference anemometer [(1 − V_hor/V_ref)100] is calculated for each 2° position during the 360° rotation of the sensor from the 1-min average wind measurements. If the value is 0, however, it does not necessarily represent the ideal case, since it has to be expected that by the different measuring positions of both devices deviations occur due to inhomogeneities of the wind field. According to section 4b at a flow rate of 5 m s⁻¹ the wind velocities measured by the sonic anemometers exceed those of the reference by about 1%–3%. This error, however, is clearly smaller than the observed deviations due to shading effects (Fig. 11, Table 2). Additional information, especially a comparison of the Solent Research/Gill sonic anemometer, is available from the measurements ±45° around a sensor structure. The 30-min average values for each of the seven sensor positions are shown in Table 3. For these measurements no reference wind speed is available. The wind velocity in the tunnel was approximately 5 m s⁻¹. There may exist a small difference between the measurements with different devices because of the manual readjustment after a sensor change, but the flow speed was constant during the whole measurement with a specific device.

The Kaijo Denki TR-61A sensor supplies the best measurements within the interval of 135°–225°. The maxima at 150° and 210° appear when only one of the two horizontal sound paths contributes to the determination of the wind velocity. In this case, the wind velocities are 3% higher than the reference value, which corresponds to the flow characteristic of the wind tunnel. At a flow from 180° the results are similar. At wind directions of 60°, 120°, 240°, and 300°, one of the horizontal sound paths is aligned in the flow direction, and a large shading effect is caused by the transducer and its prop. The measured wind velocities are reduced by 10%–16% compared to the reference values, with larger reduction when an outside transducer is upstream of the remaining sensor. Averaged over 360° only 96% of the reference value is measured.

Using the TR-61B the influence of the sensor geometry is obvious. If one of three vertical props surrounding the measuring volume is located upstream of the sensor volume (90°, 210°, and 330°), the measured horizontal rate is reduced by up to 7%. Taking the real flow conditions in the measuring volume into account, the measured horizontal wind velocity is too low by about 10%. At 30°, 150°, and 270° one of these props is in the lee of the measuring volume and a small barrier effect leads to measured wind velocities equal to the reference value. In the areas of relatively unimpaired flow the measured values are up to 6% higher than the reference value. Averaged over all wind directions, the horizontal wind speed of the TR-61B is 1.8% higher than the reference value.

Looking at Fig. 11, the disadvantage of the simple sensor geometry of the TR-61C sensor is obvious. The structure of the angle-dependent velocity response corresponds to the parameterization for sound paths with Kaijo Denki transducers, as made by Wyngaard and Zhang (1985). At 0°, 90°, 180°, and 270° one of the two horizontal sound paths is parallel to the flow direction and is maximally shaded by its own transducers and props. The other horizontal wind component vanishes and the horizontal wind velocity is reduced by 14%–18% in comparison with the reference. In the ideal case with a flow shifted by 45° to the horizontal sound paths, only small deviations from the reference values occur. The influence of the external vertical sound path and its retaining props is also visible in the figure. At a wind direction of 0°, the vertical sound path is in the lee of the horizontal ones, at 180° it is windward. In both cases the measured horizontal wind velocity is 4% worse compared to flow from 90° or 270°. Averaged over all wind directions the horizontal wind velocity reaches only 95.3% of the reference value and is therefore clearly too low.

The simple error correction of the Solent Research sonic anemometer used in the calibrated mode seems to work well. The influence of props is small and can be noticed in the area of incoming flow directions of 0°, 120°, and 240°. With a few exceptions the wind velocities measured with the Solent sonic anemometer are higher than the reference values. The deviations, however, are small and all within the range of −0.2% to +4%. Averaged over all wind directions, the sonic wind velocity is 1.9% higher than the reference, which corresponds very well to the flow field in the wind tunnel. The uncalibrated data from the ±45° measurements (Table 3) are all too low as expected from the correction coefficients, which are all greater than 1.05. At the 0° position the measured wind velocity is reduced for 4.7%, 3.1% less than for the TR-61B because of the smaller struts. The calibration procedure eliminates this effect, but it seems that the velocity accentuation is, beginning at ±15°, a little bit too high.

The wind velocities measured with METEK's USA-1 are too high at most incoming flow directions. The deviations from the reference wind velocity vary within the range of −2.2% to +14.3%. A reason for the dependency of measured flow on the flow direction cannot be given for the symmetric instrument. Averaged over all wind directions, the measured wind velocity is 6.5% higher than the reference. If the flow distribution in the wind tunnel is taken into account, the speed is too high by about 3.5%.

b. Horizontal wind direction

Figure 12 shows the deviation between the wind direction simulated by the rotation of the sensor in the wind tunnel and that calculated from the wind components. The deviations (Table 4) are very small and mostly within a range of ±4° apart from the Kaijo Denki TR-61A outside the valid measurement range and very few values of the METEK USA-1.

For the Kaijo Denki TR-61A probe at flows from 60°, 120°, 240°, and 300° one of the horizontal sound paths is parallel to the flow and the deviation reaches values of −5° to +7°. In the favorable measuring range with flow directions between 135° and 225° the deviation is within −1.25° to +3°. The deviation is negative when sound path A is parallel to the flow. With sound path B, the behavior is reversed.

Also in the curve of the TR-61B sensor the influence of the props is clearly visible. About 10° before one of the props is upstream or in the lee of the sensor volume, a local minimum appears. At 10° after the largest influence of the prop, a local maximum is reached. The wind direction error caused by the shading from a prop upstream is larger than that caused by the barrier effect of a prop in the lee. The deviations, however, are small and do not exceed the range of −2.8° to +1°.

Looking at the TR-61C probe, four sensor positions with one sound path perpendicular to the incoming flow are of interest. The wind along the sound path changes its direction for 180° in the course of the farther turn. These positions mark points of reversal in the deviation of wind direction. The maximum counterclockwise deviation of 3°–4° is reached approximately 5° before the 0°, 90°, 180°, and 270° positions. Five degrees after these positions, deviations of up to 1° in the clockwise direction can be observed. About 30° after the turning point, the measured wind direction corresponds to the adjusted one.

The deviations measured with the Solent Research sonic anemometer are the smallest of all sensors tested. They vary within the range of −0.6° to +2° with the deviation taking place in the clockwise direction in large areas. Despite the online calibration the influence of the props is still visible.

The deviations obtained from the METEK USA-1 are within the range of −5.5° to +2.5°. Like the wind velocity, the changes between the individual values are substantially larger than with the other devices. The course of the curve corresponds to a simple sinusoidal oscillation superposed by disturbances. An influence of the sensor geometry on the errors in wind direction cannot be seen.

c. Sensor-induced vertical wind component

In the ideal case, the measured vertical wind speed in the horizontal flow of a wind tunnel with vertically installed sensor vanishes. But a vertical air movement can result from the flow around the sensor and its mounting plate. It increases with increasing flow rate. For the example of the TR-61B sensor, the effects of the flow around the individual sensor components are demonstrated in Fig. 13. It shows the measured vertical wind velocities during a 360° turn of the sensor at four different incoming flow rates.

As expected, the measured vertical wind velocities increase with increasing flow rate. Whereas at 0.5 m s⁻¹ the vertical motion is within some centimeters per second, the 1-min average of the sensor-induced vertical wind component reaches values of up to 0.4 m s⁻¹ at 10 m s⁻¹. The 120° symmetry of the sensor appears in all curves. The vertical lines mark the following: If one of the lower transducers is windward of the measuring volume (dashed–dotted), then even with high flow velocities only small vertical movements are registered. In contrast an upper windward transducer (dashed) is always connected with a maximum of the measured vertical component. A retaining windward prop (solid) marks the transition of a local maximum to a minimum, the prop in the lee (dotted) marks exactly the inverse case.

In order to ensure comparability of the detected vertical wind velocities at slightly varying horizontal flow conditions in the wind tunnel during the test of the five instruments, the measured vertical winds of the five sonic anemometers were standardized with the actual horizontal flow velocities. The standardization was made by the calculation of the tilt angle of the wind vector α = arctan(w/V_hor), whereas the horizontal wind velocity V_hor of the sonic anemometer was used. Negative values define downward-directed flows, and values greater than zero occur with positive vertical wind components.

The TR-61A research probe detects a significant vertical wind component along a single vertical sound path situated in the middle of the measuring volume. Nevertheless, the measurement is influenced by the transducers of the horizontal sound paths and the props. Additionally, two cables wound around the sensor foot during the turn caused an error in the vertical component between 180° and 360°. In normal operation (field use) the cables should not represent an obstacle. Therefore, only the first half of the turn is discussed here. The deviations from the horizontal wind visible in Fig. 14 and Table 5 are small in relation to all other sensors. They do not exceed ±1°, and they are positive except for flow directions at 155° and 180°. These negative values occur when the vertical strut is in the lee of the measuring volume. The influence of the horizontal sound path B is visible at 80° (transducer B⁻) and 150° (transducer B⁺).

The standardized vertical wind velocity of the TR-61B sensor shows the structure discussed in Fig. 13. The influence of transducers windward of the sensor volume is evident. The deviations vary within the range of −0.9° to +2.3° and they are predominantly positive (Table 5).

The tilt angles calculated from the measurements of the TR-61C sensor are almost positive over the entire range of rotation. It varies between 2° ± 0.8° for flow directions from 30° to 330°. Only when the vertical sound path is hidden behind the sensor mounting do lower and negative values appear. This behavior should not appear under real measuring conditions: the two transducers of the vertical sound path are fixed at horizontal struts. The dimensions of the wind tunnel enforced the installation of the sensor with the lower horizontal strut directly over the floor of the wind tunnel. If the wind tunnel is in operation, the flow will overflow this strut and the transducer and induce a positive vertical flow component. Under field conditions with the sensor mounted on a mast, this effect does not appear.

The sensor-induced vertical wind velocity of the Solent Research/Gill sonic anemometer is smaller than that of the TR-61B because of the smaller dimensions of struts and transducer housings. The influence of the transducers windward of the measuring volume at 90°, 210°, and 330° (upper transducer) and 30°, 150°, and 270° (lower transducer) as well as struts at 0°, 120°, and 240° is easily recognizable. Overall, the deviations vary from the ideal case within the range of −1.8° to 1.4°. A look at Table 6 shows that the calibration procedure does not improve the measurements in cases of sensor-induced vertical wind components.

The construction of METEK's USA-1 with its central strut avoids blocking and shadowing effects of props. Nevertheless, the results obtained with this sonic anemometer are worse than all other results. The 120° symmetry of the sensor is dominant in Fig. 14. A local maximum with values of 1.5°–2° appears, if an upper transducer is windward of the central prop. Local minima reaching values between −3.5° and 5° can be observed, if a lower transducer is in this position.

d. Vertical wind velocity

To check the vertical wind component measured with a sonic anemometer under the controlled conditions in the wind tunnel the sensor has to be tilted parallel to the flow direction. If this is done toward the flow, a negative vertical wind component is simulated, tilting it with the flow leads to a positive vertical wind component. The reference for this simulated vertical wind velocity is calculated from the reference wind velocity V_ref of the wind tunnel and the tilting angle α measured with an inclinometer installed at the sensor fixation. Figure 15 displays the measured vertical wind velocities w_sonic over the calculated reference w_ref = V_ref sin(α). The diagonal line marks the ideal case w_sonic = w_ref. The observed deviations are partially larger than 10% and, therefore, much greater than the error caused by inhomogeneities of the wind field in the wind tunnel. Once again all measurements are made at a flow speed of 5 m s⁻¹. The Kaijo Denki and Gill devices were tilted in two positions up to ±8° depending on the sensor dimensions. Free flow indicates a flow direction with little distortion by the sensor itself, whereas modified flow marks a sensor orientation with sensor parts windward of the measurement volume.

The vertical wind velocities measured with the Kaijo Denki TR-61A are close to the simulated flow conditions. Under free flow conditions, positive vertical wind speeds became too high with increasing wind velocity, negative vertical wind speed is found to be slightly too low. If the sensor is turned into the modified flow position the measured wind speeds became too high with increasing simulated vertical wind velocity for both directions.

The vertical wind velocities measured with the TR-61B sensor in the free flow orientation seem to have a positive vertical offset. With a vertical aligned sensor the measured vertical wind velocity is 15 cm s⁻¹. Positive vertical wind velocities are too high by at least this amount, negative are accordingly too low. If the sensor is mounted in the modified flow position, negative vertical wind velocities are very close to the reference values. At positive vertical wind velocities, the measured wind speed becomes too high with increasing tilt angle and reaches a value of 0.73 m s⁻¹ instead of 0.59 m s⁻¹ at 8° inclination.

As expected the measurements made with the Kaijo Denki TR-61C with the vertical sound path in the lee of the sensor foot shows the highest differences. If the sensor is tilted toward the flow the vertical sound path is getting more and more out of the wake behind the sensor foot and the negative vertical wind velocities are getting closer to the reference values. In the free flow situation at small tilting angles, the low vertical wind speeds agree very well with the reference values. At higher vertical wind speeds resulting from greater tilting angles, the TR-61C values are too high for both wind directions with differences of 8 cm s⁻¹ at −0.6 m s⁻¹ and 12 cm s⁻¹ at +0.6 m s⁻¹.

The Solent Research/Gill sonic anemometer has, when operated in calibrated mode, an offset of −7 cm s⁻¹ with superimposed variation under free flow conditions. The maximum difference is −11 cm s⁻¹ at a reference wind speed of 33 cm s⁻¹. If a vertical strut is situated windward of the measuring volume, an offset of +5 cm s⁻¹ occurs. The additional variation reaches its maximum at −0.6 m s⁻¹ reference speed where the device measures only 0.52 m s⁻¹.

The results of the METEK USA-1 are taken from a previous measurement with a restricted tilting range of 0°–3°. The deviations from the reference values are as high as those of the Kaijo Denki TR-61B sensor in the free flow orientation. All measured vertical wind speeds are too high. If the sensor is vertically aligned, the detected vertical wind speed is already 15 cm s⁻¹, an effect that may be caused by the flow around the large electronic housing at the sensor foot.

e. Induced turbulent fluctuations

All Kaijo Denki devices and the Solent Research/Gill sonic anemometer were rotated at a flow rate of 5 m s⁻¹ in 15° steps ±45° around an orientation with a major sensor part windward. Data were taken with a sampling frequency of 10 Hz during 30 min at each position. Because of the very low level of turbulence in the wind tunnel (no fences or trip devices have been used), the size and stability of vortices set up behind struts may be increased in comparison with field measurements. Figure 16 shows the variance for the horizontal and vertical wind component.

A disadvantage of the Solent Research/Gill calibration procedure that should not be underestimated emerges with regard to the variances in calibrated and uncalibrated mode. Because all calibration coefficients of the Solent Research/Gill instrument are >1, wind velocity and variance increase with the use of the calibration procedure. Additionally, the highest correction coefficients are necessary when the modification of the wind field and therefore the sensor-induced turbulence reaches its maximum intensity. Thus the unwanted effect of the turbulence produced by the sensor is increased by the calibration procedure.

Regarding the variance of the vertical wind velocity, the highest values are measured with the Kaijo Denki TR-61C when the vertical sound path is in the lee of the sensor mounting. Another interesting point is the unsymmetry in the variance measured by the Solent Research/Gill anemometer, which can be explained by the configuration of the transducers. At −30° an upper transducer is situated windward of the measuring volume, whereas at +30° in the coordinate system relative to the vertical prop a lower transducer modifies the flow before it reaches the measuring area. Obviously they have different effects on variance. Independent of the operating mode the horizontal wind velocity is not affected. The TR-61B sensor that is practically identical in its geometry shows a similar, but not so pronounced, effect as well.

f. Spectral analysis

The results from the fast Fourier transform of wind velocities measured in a wind tunnel with sampling frequencies of 10 Hz for sonic data and 100 Hz for Pitot tube data naturally would not correspond to atmospheric spectra. Limited by the dimension of the tunnel, large eddies located in the production range of the spectrum cannot appear. Also the inertial subrange in which the spectrum follows the −5/3 law is shifted to higher frequencies. But the influence of the lee wakes developing downstream of the sensor components is clearly visible at the high-frequency end of the spectrum.

a. Mean values and variances

Figure 23 shows mean values and variances of the wind components. The standard deviation of the average values of the Solent Research/Gill devices is the base for the error bars used to isolate the errors resulting from the different measuring locations. The mean values of the u component do not have significant differences caused by the different instruments. The mean value of the w component should always vanish. Numerous influences, however, often lead to nonzero mean values. The reasons are generally maladjustment, offset voltages, and surge effects. During EFEDA'94 all sensors were carefully adjusted before the beginning of the measurements. The mean vertical wind speed of −13 cm s⁻¹ of METEK's USA-1, which occurs in both periods, is possibly caused by the zero drift mentioned in section 3. The other instruments have different mean vertical wind speeds at the two periods, mostly caused by the flow around sensor components and the mounting plate.

If the variances are considered, the horizontal wind components measured with the USA-1 have the highest variance of all sensors. The variance of the vertical wind component is much lower than that of the other instruments. A significant difference between the Kaijo Denki and the Solent Research/Gill devices can only be noticed in the variance of the u component for the afternoon period.

Figure 24 shows the covariances of the wind components. Differences between individual, but identically constructed, devices are significant. The device-specific deviations are greater in the measurements at the afternoon than in the morning. In particular the covariances of the u and υ components of the Solent Research/Gill sonic anemometers are clearly higher than those calculated from the Kaijo Denki TR-61C data. The positive u–υ covariance of METEK's USA-1 does not agree with the theory. The u–w covariance of the Solent Research/Gill devices, which represents the vertical momentum flux, is also higher than those measured with the Kaijo Denki sonic anemometers.

b. Power spectra

The spectra of the horizontal wind components are in good agreement with the −5/3 law of the inertial subrange (Fig. 25). Those of the Solent Research/Gill devices show a rise in the spectral energy density starting from a frequency of 1 Hz caused by aliasing in comparison with those of the Kaijo Denki TR-61C. The aliasing effect is larger for the Solent Research/Gill and METEK sonic anemometers sampled with 5 Hz than for the Kaijo Denki TR-61C sampled with 10 Hz. The METEK USA-1 shows an unexpected behavior. In the spectra of the afternoon measurements an attenuation can be detected at higher frequencies. This means that the instrument is not able to resolve the high-frequency fluctuations of the wind velocity. In sonic anemometer data such an effect should not occur. In the spectra of the measurements made between 1000 and 1200 CEST this effect did not appear.

The spectra of the vertical wind components follow the typical curve of this wind component. The maximum of the spectral power density is shifted to higher frequencies, and the area in which the spectrum follows the −5/3 law is smaller than those of the spectra of horizontal wind components. The spectra of the Kaijo Denki TR-61C sensors agree between 1 and 4 Hz with the −5/3 law. For the Solent Research/Gill the inertial subrange is reduced between 1 and 2 Hz because of the aliasing effect. For the METEK USA-1 the attenuation starts at 0.4 Hz.