Accuracy of Measurements of Turbulent Phenomena in the Surface

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Accuracy of Measurements of Turbulent Phenomena in the Surface Layer with an Ultrasonic Anemometer D. CONTINI

AND

A. DONATEO

CNR-ISAC, Istituto di Scienze dell’Atmosfera e del Clima, Sezione di Lecce, Lecce, Italy

F. BELOSI CNR-ISAC, Istituto di Scienze dell’Atmosfera e del Clima, Bologna, Italy (Manuscript received 8 April 2005, in final form 7 November 2005) ABSTRACT Ultrasonic anemometers are widely used to investigate turbulence in the surface layer. Some of their advantages are high-frequency sampling, the ability to work for long periods without a resident operator (even in adverse meteorological conditions), and their calibration related only to design parameters. In this paper an analysis of the random uncertainty associated with ultrasonic anemometer measurements is reported. The analysis is based on a statistical procedure that compares the simultaneous data taken with two identical anemometers operating in nominally identical conditions. Postprocessing of data has been carried out in different reference systems in order to evaluate how the random uncertainties change according to the postprocessing procedure used. Results show that uncertainty on wind velocity decreases with averaging time, and it can be as low as 1 cm s⫺1 for a typical averaging time of 30 min. The random uncertainty on average vertical wind velocity 具w典 could also be as low as 1 cm s⫺1, and it is very sensitive to the effects of vertical misalignment. The analysis is based on six different measurement sets in which the anemometers have been deployed on a single mast or in two separate masts with and without additional detectors placed near the anemometers themselves. Results indicate that the uncertainty of all the measured parameters increases when the anemometer is used in configurations in which they are placed on separate masts. Several parameters also show an additional increase of uncertainty if other detectors are placed nearby. The relative random uncertainty on momentum and sensible heat fluxes, for typical averaging time, can be as low as 6%–7% and it could increase to a factor of 2–3 when they are placed on separate masts. Only small effects due to the influence of flow distortions caused by the presence of additional sensors have been found on fluxes and are mainly related to sensible heat flux.

1. Introduction Observations of turbulent phenomena in the planetary boundary layer (PBL) or, more frequently in the surface layer (SL), are often carried out with measuring stations based on three-dimensional ultrasonic anemometers. These anemometers allow the acquisition of the wind velocity vector and of the sonic temperature at high frequency (up to 100 Hz with the anemometers Gill R3 used in this work). Their fast response is essentially due to the absence of moving parts. They are

Corresponding author address: Dr. Daniele Contini, CNRISAC, Istituto di Scienze dell’Atmosfera e del Clima, Sezione di Lecce, Str. Prv. Lecce-Monteroni km 1, 2, c/o Polo Scientifico, 73100 Lecce, Italy. E-mail: [email protected]

© 2006 American Meteorological Society

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instruments suitable, and largely used, to evaluate turbulent parameters and soil–atmosphere exchange of momentum and sensible heat with the method of the eddy correlation (Sozzi and Favaron 1996; Kaimal et al. 1968; Kaimal and Finnigan 1994; Moncrieff et al. 1997; Cassardo et al. 1995). Other characteristics that make the ultrasonic anemometers very useful in field campaigns are their ability to work for long periods without a resident operator, also in adverse atmospheric conditions, and their ability to make absolute measurements without the need for frequent calibrations. Their calibration is related only to design parameters such as sensors shape, distance between the sensors, their inclination with respect to the horizontal plane, and the shape and position of the sensors supporting the structure. Measurements with these anemometers are, however, affected by several sources of experimental errors.

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One of the sources of uncertainty is the modification of the flow induced by the anemometer itself (Wieser et al. 2001; Grelle and Lindroth 1994; Wyngaard 1981; Wyngaard and Zhang 1985; Miller et al. 1999). This kind of effect has been widely investigated, and it has been shown that the wakes generated by the sensors themselves as well as the ones generated by the supporting structure of the anemometer are variable for different anemometer geometries. Their influence is on both average wind and turbulent parameters measured, including power spectra, and it is generally dependent on wind direction especially for vertical wind velocity. Distortion of the flow field can also be generated by masts (or towers), used to support the anemometer, and also by the presence of additional detectors (radiometers, hygrometers, thermometers, and infrared detectors) often used for measurements of vertical turbulent fluxes of momentum, energy, and mass of different tracers. Another source of experimental error can be the angle of attack of flow with respect to the horizontal plane (i.e., the reference plane of the anemometer). The instantaneous angle of attack can be quite large, especially in high turbulence conditions over rough surfaces (Gash and Dolman 2003). It could be, for a high percentage of cases, out of the specifications of the anemometers [⫾20° in our instruments; Gill Instruments Ltd (1999)]. Large angles of attack can produce errors in the measurements of vertical turbulent fluxes. In Grelle and Lindroth (1994) it is found that Solent anemometers have different behavior for positive and negative angles of attack if the wind velocity is smaller than 4 m s⫺1. This behavior is probably also present on the Gill R3 anemometer because it has a design very similar to the Solent. A certain amount of error in the measured parameters could arise from vertical misalignment of the anemometer that is quite possible if telescopic mast and long horizontal bars are used in the experimental setup as in the measurements reported in this paper. Furthermore, it is also possible to have lowfrequency oscillations of the measuring station, especially at high wind speeds, that could induce errors on measured parameters. It has been reported that large errors could arise from bending of the anemometer structure (Högström and Smedman 2004). This seems to happen only at high speeds (above 12 m s⫺1), and it is not present in the data reported in this paper that refer to low wind speed values. Other sources of errors include delay and electrical noise in the electronics circuitry that controls the anemometer as well as possible small geometrical deviations of the anemometer from the design specifications due to construction inaccuracy (Grelle and Lindroth 1994; Högström and Smedman 2004). This could actu-

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ally lead to different uncertainty levels on nominally identical anemometers. Several of the contributions to the experimental error will act simultaneously and independently on measured parameters generating both systematic and random uncertainties. However, systematic uncertainties can be present especially in wind velocity measurements, but they are less probable for turbulent parameters evaluation such as turbulent fluxes that are evaluated using a correlation of fluctuations. Furthermore, in the studies of SL it is often important to analyze the temporal pattern of measured parameters and/or their correlations and these are mainly influenced by the random uncertainties. A random uncertainty that is large enough can mask (or destroy) a small pattern (e.g., the typical pattern of average vertical wind velocity), and it can strongly reduce a specific correlation while the systematic uncertainty acts on the absolute values without relevant effects on pattern or correlations. In this paper we apply a statistical procedure that compares the measurements obtained from two identical anemometers, operating simultaneously in nominally identical conditions. The comparison allows us, with certain hypotheses and approximations, to evaluate the random uncertainty on a generic parameter (i.e., wind velocity, turbulence intensity, momentum, and sensible heat flux, etc.) measured by the anemometer. The procedure can also evaluate differences in the systematic uncertainties of the two anemometers used. The procedure is derived from the one already used to evaluate the random uncertainty on average vertical wind velocity measured with a monostatic sodar (Contini et al. 2004). The procedure is not able to evaluate a systematic uncertainty or a contribution of an experimental error equal for both anemometers. In this work the procedure has been applied to the results of six different measurement campaigns carried out with Gill R3 ultrasonic anemometers deployed on the same mast and on two separate masts with and without the presence of additional sensors (for turbulent mass flux determination) placed near the anemometers. Different levels of vertical misalignment have also been used and the results of each measurement campaign have been analyzed in four different reference systems. Comparison of the results will give information about the effect, on the random uncertainties, of anemometer separation and of flow distortions induced by both the anemometer itself and the presence of additional sensors. The ability to partially compensate for misalignment problems by selecting a specific reference system will also be shown. The main topic is to evaluate the uncertainty of the anemometer used in typical operating conditions that is not only determined by the anemometer

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but also from the details of the mounting setup and it also includes the uncertainties eventually introduced during the postprocessing of data. Even if the procedure has its limitations, especially because it is not able to evaluate systematic errors, or the offset in the measured parameters, it has useful applications because it does not need comparisons with other instruments that have necessarily considered to be more accurate. It also does not need laboratory experiments, like wind tunnel experiments, which are usually not able to fully reproduce all atmospheric conditions and, consequently, the uncertainties, encountered in atmospheric measurement campaigns (Högström and Smedman 2004). In Högström and Smedman (2004), for example, it has been shown that the precision evaluated in the laminar wind tunnel flows deteriorates by a factor of 3–4 moving to fully turbulent atmospheric flows.

2. Experimental setup and postprocessing procedures Measurements have been carried out in the experimental field of the Lecce Section of the Istituto di Scienze dell’Atmosfera e del Clima (ISAC-CNR) placed inside the University Campus of Lecce in the Salentum peninsula in the southeastern part of Italy [40°20⬘10.8⬙N, 18°07⬘21.0⬙E World Geodetic System 1984 (WGS84)]. The campus is placed about 3.5 km outside the town in the southwest direction. The site is a rectangular field with a major side of about 200 m characterized by short vegetation, with two contiguous sides surrounded by small trees. The area around the site is characterized for at least 1 km in all directions by the presence of patches of trees (5–10 m tall) and small two-story buildings. The roughness length z0 of the site is about 0.5 m (Martano 2000). Measurements have been taken using two sonic anemometers, Gill R3, operating at 100 Hz in calibrated mode (Gill Instruments Ltd. 1999) and controlled by an oppositely developed software that collects data synchronously from the digital outputs of the two anemometers. Six different measurement campaigns have been carried out: the first in June 2003 (12 days), the second in July 2003 (18 days), the third in September 2003 (16 days), the fourth in March 2004 (16 days), the fifth in June 2005 (16 days), and the sixth in July 2005 (16 days). In Fig. 1 some photographs are shown that illustrate the configurations used in the different measurement campaigns. A summary of the setup used in the different campaigns is reported in Table 1. All measurements have been taken with the anemometers placed at 9.6 m above the ground on a horizontal bar mounted at the top of a telescopic mast (Clark Mast SQT9/M). In all campaigns each an-

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emometer was fitted with a biaxial inclinometer (MicroStrain FAS-A) used to measure the alignment of the anemometer with respect to the gravity vector. During the first campaign (June 2003) the two anemometers were deployed on a single mast and particular attention has been devoted to correctly align the vertical axis. The two anemometers were actually placed on the two sides (distance d ⫽ 1 m to limit interference) of the horizontal bar fixed on top of the mast to limit the tower effect. This configuration was also used in September 2003, but this time the two anemometers were, on purpose, not aligned with the horizontal plane. The comparison between the results of the mentioned campaigns shows the effect of vertical misalignments on measurement uncertainty and also how this effect could be mitigated by using a suitable reference system during data postprocessing. In both campaigns the supporting structures of the anemometers were aligned in the same way (within mounting accuracy); therefore, the distortion effect of the anemometers themselves on the flow structure was similar for both anemometers. During the second (July 2003) and the fourth campaigns (March 2004) the two sonic anemometers were placed on two separated masts. The two masts had a separation d ⫽ 9 m and the anemometers were surrounded by other instruments: a thermo-hygrometer and a realtime aerosol optical detector in one measuring station and an open-path infrared CO2/H2O detector on the other stations. These kinds of configurations are commonly used to investigate the dynamics of the SL and the mass and energy exchange between surface and atmosphere. In these campaigns the two bars supporting the instruments and, consequently, the supporting structures of the two anemometers were pointing in different directions; therefore, the flow distortions due to the instruments and the vertical alignments were different for the two anemometers. The fifth (June 2005) and the sixth (July 2005) measurement campaigns were carried out in an intermediate configuration in which the two anemometers were deployed on separate masts (about 9 m of separation) without the presence of additional sensors. In June 2005 the anemometers have different orientation and in July 2005 the two anemometers were placed with the same orientation (within mounting accuracy of about 5°). The comparison of the results of these two campaigns shows, quantitatively, the eventual effect of the supporting structure of the anemometer on the calculated uncertainties. The comparison of the campaigns in which the anemometers were placed on separate masts with ones previously described allows us to infer the effect on measurement uncertainty due to the separation of the anemometers and also due to the presence of the additional sensors

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FIG. 1. Photographs of the different anemometer configurations used. (a) Setup with the anemometers mounted alone on two separate masts with different orientation used in June 2005. (b), (c) The details of the setup used in July 2003 and in March 2004 with the anemometers placed on two separate masts surrounded by other instrumentation. (d) Setup used in June and September 2003 with the two anemometers placed on the same mast.

placed nearby the sonic anemometers (at distances of about 30–40 cm). The six campaigns were carried out in different meteorological conditions. In June 2003, July 2003, and June 2005 there was no rain and fair weather; in September 2003 there was 38 mm of rain distributed over 3 days, in March 2004 there was 33 mm distributed over 6 days, and in July 2005 there was 15 mm of rain distributed over 3 days. The quality of measured data has been compared to (with reasonably good results) some of the calculated turbulent parameters with the parameterizations reported in Panofsky and Dutton (1984) and in Kaimal and Finnigan (1994). The parameters used in the comparisons were the ratio of the standard deviation of the different components of the wind velocity (␴u, ␴v, ␴w) with the friction velocity u* defined as u* ⫽ (具u⬘w⬘典2 ⫹ 具␷⬘w⬘典2)1/4 and the correlation coefficients: Rwt ⫽

(具w⬘T⬘s 典/␴w␴Ts) and Ruw ⫽ (具u⬘w⬘典/␴u␴w). Here Ts is the sonic temperature and ␴Ts is its standard deviation calculated over the specific averaging period. In this paper the angle brackets 具 典 represent a time average and the symbols with a prime indicate fluctuations with respect to the average values. Measurements have been elaborated using different averaging times from 10 to 60 min. For each averaging time, four different postprocessing procedures have been used that allow us to evaluate the turbulent parameters in four specific reference systems. The reference system, which we define as ROT1, is obtained with a single rotation (around the z vertical axis of the anemometer) that puts the x axis along the average apparent horizontal wind velocity. The reference system, which we refer to as ROT2, is obtained with the same rotation as ROT1 plus another rotation (around the y

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TABLE 1. Summary of the setup used in the different measurements campaigns described in chronological order. Measurement campaign identification June 2003 July 2003 September 2003 March 2004 June 2005 July 2005

Set-up details

Notes

Two anemometers R3 on the same mast (d ⫽ 1 m) with the same orientation. Two anemometers R3 on separate masts (d ⫽ 9 m) with different orientations. Two anemometers R3 on the same mast (d ⫽ 1 m) with the same orientation. Two anemometers R3 on separate masts (d ⫽ 9 m) with different orientations. Two anemometers R3 on separate masts (d ⫽ 9 m) with different orientations. Two anemometers R3 on separate masts (d ⫽ 9 m) with the same orientations.

axis) that puts the x axis along the direction of the average wind velocity. The reference system, that we refer to as ROT3, is the “streamlined” system (McMillen 1988) in which the same rotations as in ROT2 are used plus a third rotation that makes 具u⬘w⬘典 ⫽ 0. This third rotation is actually carried out only if the absolute value of the associated rotation angle is less than 10°. In both reference systems, ROT2 and ROT3, the average vertical wind velocity 具w典 is artificially zero. The fourth reference system, that we refer to as CI, is obtained by using data from the inclinometers to rotate the measured velocity vector in a system with the z axis parallel to the gravity vector and the x axis aligned with the average horizontal velocity (details of the rotation matrix can be found in Donateo 2004). The angles used in the rotations are the values averaged over all the specific measurement campaigns. It has to be shown that there are some residual effects of vertical misalignments even in the CI system because of experimental errors in the measurements of angles and also because of the imprecision in the alignment of the anemometers and inclinometers axes. It is known that postprocessing procedures like ROT2 and ROT3 can introduce uncertainties and run-to-run noise (Wilczak et al. 2001) due to the sampling errors especially at low wind speeds. The procedure ROT3 could introduce additional runto-run noise (with respect to ROT2) especially in presence of complex flows (Wilczak et al. 2001; Finnigan et al. 2003). In our analysis these eventual additional errors of the postprocessing procedures are included in the calculated uncertainties. After rotation in the chosen reference system a linear detrending procedure was applied to all time histories (i.e., velocity components and sonic temperature) in order to eliminate (or at least reduce) the effects of slow trend in the calculation of turbulence intensity and turbulent fluxes (Rannik and Vesala 1999; Gash and Culf 1996).

No additional instruments. Careful vertical alignment. Additional instruments present. Standard vertical alignment. No additional instruments. Poor vertical alignment. Additional instruments present. Standard vertical alignment. No additional instruments. Standard vertical alignment. No additional instruments. Standard vertical alignment.

3. Procedure used to evaluate random uncertainties The procedure used to evaluate the random uncertainty on a generic parameter X measured with the anemometer is based on a statistical comparison of the results obtained from the two anemometers operating in nominally identical conditions. Measurements have been taken for a period ␶ sufficiently longer than the averaging time T used. The procedure does not need comparisons with a more accurate independent measurement of the same physical quantity, which could be difficult to obtain. The method is based on the procedure developed to calculate the accuracy of 具w典 measurements with a Doppler sodar (Contini et al. 2004) that has been modified in order to be used with only two sensors operating simultaneously. The procedure is based on the difference of the variable X measured by the two stations, and it is not therefore able to give information about the systematic uncertainty. Only the random uncertainty as well as differences in the systematic uncertainties of the two anemometers can be shown. The procedure is based on three main assumptions: 1) the random uncertainty is described by a Gaussian distribution; 2) the uncertainty of the measurement taken with the two anemometers is basically the same; and 3) the uncertainty for a specific parameter analyzed, with a certain averaging time, can be described by a single value that is representative of all the different operating conditions encountered during the measured period. The first assumption is adequate because the procedure analyses random experimental errors that are caused by several small independent contributions that are likely to produce, as a global effect, a Gaussian distribution. The second assumption is reasonable be-

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cause the two anemometers are identical, used in the same operating conditions, and measuring approximately the same mass of air moving through the sensors, providing that the averaging time is long enough (e.g., longer than 5–10 min). It is actually possible to have differences in the uncertainties of each anemometer as consequence of differences in the setup or smallscale inhomogeneity of the flow. In this case the mentioned assumption equally divides the experimental error between the two anemometers. It has to be noted that this assumption would not be necessary if at least three independent anemometers were used in the measurements (Contini et al. 2004). The third assumption is more critical because it could be more suited for some calculated parameters with respect to others. However, it is useful to have a single value of the uncertainties that could represent the experimental errors in real operating conditions. Suppose that 具XT典ti is the value, averaged over a period of T around the time t of the variable X measured by the anemometer i. These values can be written for the two anemometers as

再

t ⫹ ␥1 ⫹ w1 具XT典t1 ⫽ Xm t ⫹ ␥2 ⫹ w2, 具XT典t2 ⫽ Xm

(1)

where ␥1 and ␥2 are values extracted from Gaussian distributions with zero mean and with standard deviation ␴X1 ⫽ ␴X2 ⫽ ␴X. They represent the random parts of the uncertainty of the measurement of X carried out by the two measuring stations. The values w1 and w2 are constants (not dependent on t) that represent the systematic part of the uncertainty. The symbol X tm represents the “true” value of the variable X at a certain time t that is identical for the two measuring stations. Measurements carried out over a measuring period ␶ Ⰷ T allows us to evaluate, for every t, the difference, t ⫽ 具XT典t1 ⫺ 具XT典t2 ⫽ 共␥1 ⫺ ␥2兲 ⫹ w1 ⫺ w2 ⫽ ␩ ⫹ ␤, DX

共2兲 where ␩ are values extracted from a Gaussian distribution with the zero mean and standard deviation given by ␴␩ ⫽ 公2␴X. The value ␤ is a constant that represents the difference in the systematic uncertainty and it is the only information obtainable regarding the systematic part of the uncertainty. The distribution of DtX and in particular its standard deviation ␴␩ allows us to calculate the random uncertainty on the measured variable X. The effective calculation is carried out on a limited number N of averages distributed over the measurement period ␶ (with the N variable, in our data, between 273 and 2570 depending on the averaging pe-

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riod T and on the measurement campaign); therefore, it is not possible to obtain the true values of ␤ and ␴X. The calculations give the estimators ␴ˆ ␩ and ␤ˆ and consequently ␴ˆ X. A statistical analysis, which is a modification of the one reported in the appendix in Contini et al. (2004), could furnish information about the accuracy of the estimators. Considering the variables y and z defined as y⫽

␤ˆ ⫺ ␤ 共N ⫺ 1兲␴ˆ ␩2 , z⫽ ␴ˆ ␩ ␴␩2

共3兲

公N

it is possible to demonstrate that y follows a Student’s t distribution with N ⫺ 1 degrees of freedom that is approximately Gaussian for N larger than 50 (as it always happens for the measurements reported in this paper). The variable z follows a chi-square distribution with N ⫺ 1 degrees of freedom. It is therefore possible to evaluate the accuracy on ␴ˆ ␩ iteratively looking for the value of ␣ for which the following relation holds:

冉

Probability ⫺␣ ⱕ

冊

␴␩ ⫺ ␴ˆ ␩ ⱕ ␣ ⫽ 68.27%. ␴ˆ ␩

共4兲

The uncertainties on the estimators, evaluated at 68.27% of probability (corresponding to 1 standard deviation) are ⌬␤ˆ ⫽

␴ˆ ␩ ⌬␴ˆ ␩ ⌬␴ˆ X ⫽ ⫽ ␣. ␴ˆ X 公N ␴ˆ ␩

共5兲

In the cases reported in this paper the errors on the estimators of random uncertainty are between 1.7% and 4.3% (increasing with the increase of T from 10 to 60 min) for June 2003, between 1.4% and 3.5% in July 2003, between 1.5% and 3.6% in September 2003, between 1.4% and 3.6% for March 2004, and between 1.5% and 3.7% in both June and July 2005. Error bars have not been used in most of the figures reported in this paper because their size is comparable with the size of the marks used. A comparison of the experimentally evaluated distribution DtX with the Gaussian distribution reconstructed from the calculated uncertainty is shown in Fig. 2. The parameters X considered are the average wind velocity 具U␷典; the square root of the turbulent kinetic energy E ⫽ 公 1⁄2(␴2u ⫹ ␴2␷ ⫹ ␴2w), ␴Ts, ␴u, ␴␷, ␴w, 具w典, u*; and the vertical kinematic sensible heat flux H ⫽ 具w⬘Ts⬘典 evaluated with the sonic temperature as usual (Moncrieff et al. 1997). Results reported in Fig. 2 refer to a 30-min average in the ROT3 reference system evaluated in June 2003; however, similar results have been obtained for the other measurement campaigns and also in the different reference systems. Generally, there

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FIG. 2. Example of the probability density function (pdf) of the difference DX for several parameters X. Results include experimental pdf (triangles) and Gaussian distribution evaluated from the calculated values of the uncertainties (continuous lines).

is a fair agreement between experimental and calculated distributions for several parameters indicating the validity of the hypothesis used. However, the agreement is worse for 具w典 and, especially, for turbulent fluxes presenting a peak in the experimental distribution near zero. This could be due to the presence of substantial different regimes of turbulence during the day (strong unstable conditions) and during the night (stable conditions). Large turbulent fluxes of sensible heat are present during the day (up to 350 W m⫺2 in the summer) and small negative fluxes during the night (⫺30 W m⫺2 in the summer). The random uncertainty is smaller, in absolute values but not necessarily in relative terms, in stable conditions during the night; therefore, the relative distribution is narrow and peaked around zero. The experimental distributions of difference D tX for turbulent fluxes and average vertical wind speed in Fig. 2 are likely to be a convolution of Gaussian curves with different standard deviations. A preliminary analysis of our results indicates that the agreement with the Gaussian distribution of random errors will be better for turbulent fluxes if a selection on stability is performed, especially when unstable cases are selected; however, we decided to evaluate the uncer-

tainty on all data together because the selection on stability will need much larger statistics to have reliable results. Furthermore, a selection on stability could lead to a selection on wind directions because, especially in a costal area like the ones studied, there are often land and sea breezes with directions more frequently associated with diurnal periods and other more frequently associated to nocturnal conditions. Our choice to analyze all data together allows us to evaluate a single value of the uncertainty for a specific postprocessing procedure and a specific set of measurement that is representative of all the different conditions encountered in the measurement campaign even if, at least for turbulent fluxes, it will be slightly overestimated as shown in Figs. 2h,i.

4. Discussion of uncertainty of measured scalar parameters Scalar parameters, and therefore their uncertainties, are not dependent on the reference system used. In Fig. 3a the uncertainty on 具U␷典 is reported as function of the averaging time for the different measurement campaigns. In Fig. 3b the same uncertainty is reported normalized with the average wind velocity Uref evaluated

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FIG. 3. Random uncertainties evaluated on scalar parameters. Uncertainty of (a) 具U␷典, (b) 具U␷典 normalized with Uref, (c) E, and (d) E normalized with Uref.

over the measurement period ␶. The values of Uref used in this paper are reported in Table 2, together with other quantities used in the normalization of the different calculated quantities. Results indicate that the ran-

dom uncertainty on 具U␷典 can be as low as 1 cm s⫺1. The difference in the systematic uncertainties on 具U␷典 are usually between 10% and 60% of the random uncertainty with the largest values referring to measurement

TABLE 2. Values of the different parameters used in the normalization of the results approximated to three decimal digits (two for wind velocity and one for data percentage). The upper part of the table is calculated on all data available and the lower part is calculated eliminating data in which wind directions are within ⫾30° along the mounting bar of the instruments. The percentage of data eliminated is also reported. Quantity ⫺1

Uref (m s ) (all data) Fref (m2 s⫺2) (all data)

Href (m K s⫺1) (all data)

Data within ⫾30° along mounting bars Uref (m s⫺1) (without directions along mounting bars) Fref (m2 s⫺2) (without directions along mounting bars) Href (m K s⫺1) (without directions along mounting bars)

Jun 2003

Jul 2003

Sep 2003

Mar 2004

Jun 2005

Jul 2005

1.45 ROT1 ⫽ 0.151 ROT2 ⫽ 0.132 ROT3 ⫽ 0.131 CI ⫽ 0.151 ROT1 ⫽ 0.082 ROT2 ⫽ 0.076 ROT3 ⫽ 0.074 CI ⫽ 0.082 33.4%

2.00 ROT1 ⫽ 0.247 ROT2 ⫽ 0.207 ROT3 ⫽ 0.206 CI ⫽ 0.228 ROT1 ⫽ 0.091 ROT2 ⫽ 0.086 ROT3 ⫽ 0.085 CI ⫽ 0.091 38.2%

1.89 ROT1 ⫽ 0.222 ROT2 ⫽ 0.208 ROT3 ⫽ 0.207 CI ⫽ 0.231 ROT1 ⫽ 0.048 ROT2 ⫽ 0.047 ROT3 ⫽ 0.045 CI ⫽ 0.05 52.4%

1.63 ROT1 ⫽ 0.205 ROT2 ⫽ 0.189 ROT3 ⫽ 0.188 CI ⫽ 0.215 ROT1 ⫽ 0.031 ROT2 ⫽ 0.029 ROT3 ⫽ 0.028 CI ⫽ 0.031 68.2%

2.13 ROT1 ⫽ 0.221 ROT2 ⫽ 0.222 ROT3 ⫽ 0.224 CI ⫽ 0.241 ROT1 ⫽ 0.095 ROT2 ⫽ 0.093 ROT3 ⫽ 0.092 CI ⫽ 0.098 67.2%

1.86 ROT1 ⫽ 0.174 ROT2 ⫽ 0.163 ROT3 ⫽ 0.164 CI ⫽ 0.179 ROT1 ⫽ 0.09 ROT2 ⫽ 0.086 ROT3 ⫽ 0.084 CI ⫽ 0.09 31.5%

1.39

2.49

2.30

1.90

1.98

2.14

ROT3 ⫽ 0.132

ROT3 ⫽ 0.286

ROT3 ⫽ 0.268

ROT3 ⫽ 0.180

ROT3 ⫽ 0.206

ROT3 ⫽ 0.2

CI ⫽ 0.148 ROT3 ⫽ 0.067

CI ⫽ 0.311 ROT3 ⫽ 0.108

CI ⫽ 0.304 ROT3 ⫽ 0.073

CI ⫽ 0.195 ROT3 ⫽ 0.04

CI ⫽ 0.237 ROT3 ⫽ 0.096

CI ⫽ 0.218 ROT3 ⫽ 0.1

CI ⫽ 0.073

CI ⫽ 0.114

CI ⫽ 0.081

CI ⫽ 0.043

CI ⫽ 0.106

CI ⫽ 0.106

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campaigns with separated anemometers. Results reported in Fig. 3a show that the random uncertainty decreases with the averaging time as expected. Figure 3b shows how the normalized uncertainty calculated in June and September 2003 tends to collapse into a group of curves with the lowest values of uncertainties. The uncertainties evaluated in June and July 2005 are larger than the ones in which the anemometers are mounted on the same mast. The uncertainties evaluated with the presence of additional sensors are slightly larger than the one calculated in June and July 2005 and up to a factor of 3.3 larger than the ones detected in June and September 2003. This indicates that the flow distortions generated by the presence of additional sensors could deteriorate the measurement accuracy. However, a relevant increase in the uncertainty is present in all parameters considered just by separating the instruments on the two masts. The increase of uncertainties on separated anemometers is likely due to differences in the mounting details, small-scale inhomogeneity of the flow, and the sampling errors especially present at low wind speeds and small averaging times. As a matter of fact, the hypothesis that the two anemometers are sampling on roughly the same masses of air is less and less valid when the separation between the sonics is increased. This is particularly true in low wind speed conditions and for low averaging times and it can also be direction dependent. If the wind direction is blowing parallel to the line joining the two masts, the air masses moving through one anemometer are advected toward the other. On the other hand, if the wind is blowing perpendicularly to the mentioned line, the small vortexes (smaller than d/2) seen by the two anemometers are actually different. If the flow and turbulence were perfectly homogeneous, the measurements of the two anemometers, averaged over a sufficiently long time, should be basically the same in statistical terms. In these conditions the uncertainties should be independent on anemometer separation. However, the measurement site analyzed in this paper can be considered homogeneous over the large scale, but there are smallscale inhomogeneities that could influence the two anemometers in a different way if they are sufficiently separated. Furthermore, it is also possible to have small differences in the mounting details of the two anemometers. This leads to an increase on the random uncertainties evaluated for large values of d with the procedure proposed. The results relative to the random uncertainty on E and the results normalized with the reference velocity Uref are reported in Figs. 3c,d, respectively. The behavior is similar to the one described for the wind speed and the difference in the systematic uncertainties of E

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FIG. 4. Random uncertainty calculated on the standard deviation of the sonic temperature for the different measurement campaigns.

ranges between 1% and 20% with largest values referring to measurement campaigns with separated anemometers and with additional sensors placed around the anemometers. Basically, the uncertainties separate into three groups corresponding to the three different configurations with a limited difference between the two configurations in which the anemometers are placed on separated masts. It has to be shown that the distribution of the instantaneous angle of attack of the flow on the anemometers, evaluated on raw data before any rotation, is very similar for all the measuring campaigns with about 82% of the cases inside the manufacturer specifications of ⫾20°. Instead the distributions of wind velocity and directions are variable; therefore, the influence of the supporting structure of the anemometer and of the additional detectors on the flow really seen by the sensors is also variable. The direction in which the influence is presumably larger is the direction of the supporting bar because in this case there is the direct influence of one anemometer on the other as well the influence of the struts supporting the ultrasonic sensors and the influence of the additional detectors (when present). The cases with the wind direction within 30° on either side of at least one of the supporting bar are reported in Table 2, and they are variable from 31.5% in June 2005 to 68.2% in March 2004. The random uncertainty over the calculated values of the standard deviation of the sonic temperature ␴Ts is reported in Fig. 4. The random uncertainty on average sonic temperature 具Ts典 has not been reported because in this parameter the main contribution to uncertainty is the systematic one. The values shown in Fig. 4 are generally between 0.01° and 0.02°C, and they do not behave like the other scalars analyzed because there is

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FIG. 5. Random uncertainty of the standard deviation of the longitudinal and cross-wind components of the wind velocity. All uncertainties are normalized with Uref. Uncertainty of ␴U evaluated in (a) ROT1 and (b) ROT2. Uncertainty of ␴v evaluated in (c) ROT1 and (d) ROT2.

no evidence of a decrease when the averaging time is increased (apart from the measurement campaigns of July 2003 and June and July 2005) and there is no separation in different groups. This is likely because Ts is essentially a scalar quantity indirectly measured by the ultrasonic anemometer, which will be influenced by the separation of the masts and by flow distortion in a different way with respect to velocity components. Furthermore, the measurements of Ts are also influenced by the specific humidity of air that could introduce differences between one campaign and the other even if the setup was essentially the same.

5. Discussion of uncertainty of measured turbulent parameters In Figs. 5a,b the normalized random uncertainties of ␴u, evaluated in ROT1 and ROT2, are reported as function of the averaging time. In Figs. 5c,d a similar analysis is reported for ␴v. Results have been normalized using the reference speed Uref. Results obtained in the other reference systems ROT3 and CI are similar to the one obtained in ROT2 and are not shown. Uncertainty on ␴v is smaller than the one on ␴u especially in July 2003 and in March 2004. Uncertainties about the different measurement campaigns separate into groups similarly to the behavior discussed in the previous sec-

tion with differences up to a factor of 2 on ␴v and also slightly larger on ␴u evaluated in the reference system ROT2. Results referring to the random uncertainties on ␴w are reported in Fig. 6 for all the reference systems. Results show that there is a substantial difference in the uncertainty evaluated in ROT1 with respect to the other reference systems (up to a factor of 2 in some cases); however, the uncertainties on the other reference systems are quite similar. Differences between the groups of uncertainties for ␴w is about a factor of 2, which is similar to what happens for the random uncertainties on ␴u and ␴v. In Figs. 7a,b random uncertainties on 具w典 are reported for the ROT1 and CI system, respectively, which are the only reference systems in which it is possible to evaluate 具w典 because in ROT2 and ROT3 the values of 具w典 are put to zero in each averaging period. Results indicate that there is a large improvement on uncertainty passing from ROT1 to CI because vertical wind velocity (as well as its variance) is very sensitive to a vertical misalignment of the anemometer. Results indicate that there is not evident separation into groups even if the uncertainties calculated in March 2004 and in July 2003 are the two largest cases. This could be at least partly due to the different statistics of the wind directions given that the percentage of cases in which

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FIG. 6. Random uncertainties of ␴W normalized with Uref. Uncertainty evaluated in (a) ROT1, (b) ROT2, (c) ROT3, and (d) CI.

the wind was blowing along one of the horizontal bars is changing from one measurement campaign to the other. The average vertical wind velocity is usually very small (in absolute value generally within 20–30 cm s⫺1) and therefore very sensitive to disturbances. If a selection on wind direction is performed excluding cases in which the wind is blowing within ⫾30° from each one of the horizontal bars, the results are different as shown in Fig. 7c (that includes the error bars of the estimators). Figure 7c shows that the uncertainties become generally smaller and the separation into groups is much more evident. However, it has to be shown that they seem to be two separate groups because many of the effects of the additional instruments are removed by the selection on wind direction. In Fig. 8 the results of the random uncertainties of Rwt and Ruw are presented, only in the reference systems ROT1 and CI, because the behavior in the ROT2 and ROT3 systems, not shown, is similar to the one in the CI system. Our results show that the uncertainty in ROT1 is generally larger with respect to the other reference systems for both correlation coefficients and this is particularly evident for Ruw. Even in this case there is, at least in the CI system, a separation into three groups with the uncertainties progressively growing from the configuration in which the anemometers are placed on the same mast to the configuration in which they are mounted on separate masts with additional instruments.

In Fig. 9 the random uncertainty on the kinematic sensible heat flux H is reported for all the reference systems investigated. Results have been normalized by using a value of Href calculated, from the data of one of the two anemometers, as the average over all the measurement campaigns of all the N heat fluxes Hi evaluated with a 30-min average: Href ⫽ (1/N)兺N i⫽1|Hi|. The values of Href are reported in Table 2. Results show that the reference system CI gives the lowest uncertainties and the system ROT1 gives the largest ones. The separation into different groups is not very evident; however, the uncertainties, especially in the CI reference system, on March 2004 and July 2003 are about 2 times larger than the ones in September and June 2003, respectively, as a consequence of the effect of separation between the two masts and also by distortions of the additional instruments that seems to give a small contribution. In Fig. 10 the random uncertainties evaluated on the momentum flux F in the different reference systems are shown. The values have been normalized with the reference values Fref (reported in Table 2) calculated in a similar way as described for Href. In this case the separation is only into two groups, with the exception of the ROT1 reference system, not being appreciable a general difference between the configurations in which the anemometers are on separate masts with and without additional instruments. The smallest uncertainties are about 2.3 times lower than the largest ones. On relative

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FIG. 7. Random uncertainties of 具w典, normalized with Uref. (a) Uncertainties evaluated in ROT1 for all data. (b) Uncertainties evaluated in CI for all data. (c) Uncertainty evaluated in CI after elimination of data in which the wind is blowing along each one of the mounting bars (within ⫾30°).

terms uncertainties on a typical 30-min period can be as low as 6%–7% for both F and H in the CI system. The reference system ROT1 gives the largest uncertainties, however, only small differences between uncertainties

evaluated in ROT2, ROT3, and CI have been found. In Fig. 11 normalized uncertainties, including error bars, on H and F are reported in the ROT3 and CI system after a selection on wind direction eliminating cases

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797

FIG. 8. Random uncertainties on the correlation coefficient (top) Rwt and (bottom) Ruw. Uncertainty of Rwt evaluated in the systems (a) ROT1 and (b) CI. Uncertainty of Ruw evaluated in the systems (c) ROT1 and (d) CI.

with wind blowing within ⫾30° along each one of the mounting bars. The uncertainties evaluated after wind direction selection on H and F are more similar with respect to the ones calculated on all data especially in

the CI system and the separation into two groups is more evident as it happened for 具w典. It has to be shown that the selection of wind direction (for all the parameters including the scalar ones) showed small ef-

FIG. 9. Random uncertainty ␴H of sensible heat flux H normalized with Href. Reference systems (a) ROT1, (b) ROT2, (c) ROT3, and (d) CI.

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FIG. 10. Same as in Fig. 9, but for the random uncertainty ␴F of momentum flux F normalized with Fref.

fects in June and July 2005, with the anemometers placed alone on separate masts; a slightly larger effect in June and September 2003 in which the anemometers are placed on the same mast, and it is possible a mutual

influence of the two anemometers and again a larger effect on July 2003 and March 2004 in which additional instruments are placed near the anemometers. It should be mentioned that a certain contribution to

FIG. 11. Normalized random uncertainties of momentum and sensible heat fluxes after elimination of wind directions along the mounting bars (within ⫾30°): ␴H in (a) ROT3, (b) CI; ␴F in (c) ROT3 and (d) CI.

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FIG. 12. Random uncertainty of u* normalized with the reference speed Uref for the different measurement campaigns. Reference systems (a) ROT1, (b) ROT2, (c) ROT3, and (d) CI.

the unclear separation of H and 具w典 and, in general, to the differences in the behavior of uncertainties on H and F could be related to the nonperfect agreement between measured pdf and Gaussian curves reported in Fig. 2 (i.e., to the third assumption made in the calculation of uncertainties). In Fig. 12 the normalized random uncertainty evaluated on u* for the different reference systems is shown. Results are similar to the ones for F, apart from the different normalization, showing the largest uncertainties on the ROT1 system. Normalized values of uncertainty can be as low as 0.5%–0.6% of Uref for a 30-min average, but it grows to about 1.1% of Uref in configurations in which the anemometers are employed on separate stations and with additional detectors present in the CI system and up to 1.3% in ROT2 and ROT3 systems. It has to be put in evidence that meteorological conditions, and especially precipitation, were different during the different measurement campaigns. An analysis has been performed excluding the period of rain from the analysis and the results showed basically no differences in the calculated uncertainties (for all the parameters considered in this work including scalar parameters) in March 2004 and in July 2005. Only a small difference (a decrease of uncertainty of about 7%–8%) has been observed in September 2003 for 具w典, ␴w, and

H. This is probably due to the presence of a single day with a relatively strong precipitation of 28 mm. Results indicate that the random uncertainties for the different parameters analyzed decrease when the averaging time is increased with a rate of decrease different for all the parameters. The only uncertainty that does not fit in this scheme is the one on ␴Ts. A power law ␴具X典 ⫽ A T p usually fits the data of the random uncertainty ␴具X典 evaluated for a specific parameter X reasonably well (not shown in the figures), and the values of the exponent p obtained are changing with the parameters and with the measurement campaigns. The lowest values of p are found for the uncertainties on 具w典 that could increase to 0.1 in March 2004, and there is a general increase of the parameter p for 具w典 with the selection of wind direction that eliminates the direction along the mounting bars. Generally, for the uncertainties on F and H, the parameter p ranges from 0.3 to 0.45, and it is ranging from 0.35 to 0.55 for the other parameters. The values are generally in reasonable agreement with the expected value of 0.5; however, in several cases there seems to be an asymptotic value of the uncertainty for long averaging time that decreases the value of p. Concerning the differences in the systematic uncertainties, the results indicate that, for the different parameters analyzed, they are usually several times

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smaller than the random uncertainties in all the reference systems and in all the measurement campaigns.

6. Conclusions An analysis of the random uncertainties associated with measurements of turbulent parameters in the surface layer, with typical mounting setup, using Gill R3 ultrasonic anemometers is presented. The procedure used to evaluate the random uncertainties is based on a statistical comparison of the results between two identical measuring stations assuming that they are essentially measuring the same masses of air. The procedure is derived from the analysis carried out for sodar measurement, which is described in Contini et al. (2004). The procedure used can be applied to other instruments and to fields of research other than atmospheric physics. It has its main limitation in not being able to identify a systematic uncertainty or, in general, an experimental error equal for both anemometers. The analysis has been performed on the results obtained in six measurement campaigns that differ for the details of the experimental setup. Uncertainty evaluation has been carried out in four different reference systems. The comparison of the calculated random uncertainties in the different reference systems showed that usually there are only small differences between ROT2, ROT3, and CI even if the values of the different parameters, especially the turbulent fluxes, are different between one system and the other. Basically, it is not possible to choose a best reference system for data analysis basing the choice only on considerations related to random uncertainties. This is because for some parameters the uncertainty seems lower on one reference system, but this could not be true for other parameters or for all the measurements campaigns. This means that most of the differences on turbulent parameters evaluated in ROT2, ROT3, and CI are actually not due to random uncertainties but are more specifically related to the different choice of the reference system. The random uncertainties are worse on the reference system ROT1 in which no steps are taken to correct for misalignments problems. The uncertainty on 具w典 is improved by about a factor of 2.5 passing from ROT1 to CI in cases with relatively large misalignment of the anemometers (September 2003 and March 2004). In the same measurement periods the random uncertainty on F and H are improved by about a factor of 2 (or slightly less) moving from ROT1 to another reference system. Slightly smaller improvements have been obtained for vertical turbulence intensity ␴w. The choice of the reference system is able to strongly modify the uncertainty on the parameters that are calculated using the vertical wind velocity.

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Random uncertainties evaluated in ROT2 and ROT3 systems are very similar and this means that the additional run-to-run noise that could be present in the ROT3 system, because of sampling errors of turbulent parameters, is not relevant for the site analyzed. Results indicate that the random uncertainties for the different parameters analyzed decrease when the averaging time is increased even if the rate of decrease is not the same for the different parameters. The only uncertainty that does not fit in this scheme is the one relative to ␴Ts. Comparison of the random uncertainties evaluated in June and July 2005 shows similar results for all the parameters and this means that the effect of the supporting structure of the anemometer is on the average small. The analysis of the random uncertainties obtained eliminating periods of rain showed basically no difference with respect to the uncertainties calculated indicating that the precipitations usually present in this site does not deteriorate anemometer performances. Results indicate that the uncertainty on 具U␷典 can be as low as 1 cm s⫺1 for a typical averaging time of 30 min and a similar values is obtained for the uncertainty on 具w典 in the CI system. Random uncertainties on the standard deviations of the different velocity components can be as low as 0.5%–0.6% of Uref. Results show that the normalized random uncertainties can be as low as 6%–7% for vertical turbulent momentum and sensible heat fluxes referring to the 30-min averaging time. Results indicate that the random uncertainties on the different parameters increase in measurement campaigns in which the anemometers are placed on two independent masts with respect to cases in which they are placed on the same mast and an additional, generally small, increment of the uncertainties is present on several parameters when other detectors are placed nearby the anemometers. When results are opportunely normalized they tend to separate into three different groups, corresponding to the different configurations. The uncertainty on 具w典 and on turbulent fluxes, especially on F and u*, seem to separate only into two groups. The separation between the groups can be up to a factor of 3.3 for the uncertainties on 具U␷典 and up to a factor of 3 for 具w典 and a factor of 2–2.3 for both the standard deviations of the velocity components and for turbulent vertical fluxes. This separation is more evident on some parameters with respect to other and it is basically absent in the random uncertainties on ␴Ts, which is variable between 0.01° and 0.02°C basically for all the cases. The selection on wind direction (excluding ⫾30° along each one of the mounting bars) actually improves

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the uncertainties on 具w典 and the separation into different groups of the uncertainties on H. Basically, the effect of selecting wind direction generate a progressive improvement of results that is growing passing from the configuration in which the anemometers are placed alone on separate masts to the one in which there are additional instruments placed near the anemometers. Our results indicate that the differences in the systematic uncertainties for the different parameters analyzed are often several times smaller than the random uncertainties for the different parameters analyzed in all the reference systems and in all the measurements campaigns. It has to be shown that in the time spanning the different measurement campaigns reported in this paper (more than 2 yr) the anemometers have never been recalibrated; however, there is no evidence of a deterioration of their performances. Acknowledgments. The authors wish to tank Dr. P. Martano of the Istituto di Scienze dell’Atmosfera e del Clima (ISAC-CNR) for useful discussions. Many thanks to Mr. F. M. Grasso and to Mr. C. Sisto of ISAC-CNR for their help in technical aspects of the measurement campaigns. Many thanks also to Mr. G. Rispoli of the Department of Material Science of the University of Lecce who provided some meteorological parameters of the measurement site. REFERENCES Cassardo, C., D. Sacchetti, M. G. Morselli, D. Anfossi, G. Brusisca, and A. Longhetto, 1995: A study of the assessment of air temperature and sensible-heat and latent-heat fluxes from sonic anemometer observation. Nuovo Cimento, 18C, 419– 440. Contini, D., G. Mastrantonio, S. Argentini, and A. Viola, 2004: Mean vertical motion in the PBL measured by a Doppler sodar: Accuracy, ambiguities, and possible improvements. J. Atmos. Oceanic Technol., 21, 1532–1544. Donateo, A., 2004: Misure di flussi verticali turbolenti di particolato e traccianti gassosi nello strato limite superficiale. Ph.D. thesis, University of Urbino, 217 pp. Finnigan, J. J., R. Clement, Y. Malhi, R. Leuning, and H. A. Cleugh, 2003: A re-evaluation of long-term flux measurement techniques. Part I: Averaging and coordinate rotation. Bound.-Layer Meteor., 107, 1–48. Gash, J. H. C., and A. D. Culf, 1996: Applying a linear detrend to eddy correlation data in realtime. Bound.-Layer Meteor., 79, 301–306.

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——, and A. J. Dolman, 2003: Sonic (co)sine response and flux measurement: I. The potential for (co)sine error to affect anemometer-based flux measurements. Agric. For. Meteor., 119, 195–207. Gill Instruments Ltd., 1999: Omnidirectional (R3) and Asymmetric (R3A) Research Ultrasonic Anemometer user manual and product specification. Lymington, United Kingdom, 56 pp. Grelle, A., and A. Lindroth, 1994: Flow distortion by a Solent sonic anemometer: Wind tunnel calibration and its assessment for flux measurements over forest and field. J. Atmos. Oceanic Technol., 11, 1529–1542. Högström, U., and A. Smedman, 2004: Accuracy of sonic anemometers: Laminar wind-tunnel calibrations compared to atmospheric in situ calibrations against a reference instrument. Bound.-Layer Meteor., 111, 33–54. Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 288 pp. ——, J. C. Wyngaard, and D. A. Haugen, 1968: Deriving power spectra from a three-component sonic anemometer. J. Appl. Meteor., 7, 827–837. Martano, P., 2000: Estimation of surface roughness length and displacement height from single-level sonic anemometer data. J. Appl. Meteor., 39, 708–715. McMillen, R. T., 1988: An eddy correlation technique with extended applicability to non-simple terrain. Bound.-Layer Meteor., 43, 231–245. Miller, D. O., C. Tong, and J. C. Wyngaard, 1999: The effects of probe-induced flow distortion on velocity covariances: Field observations. Bound.-Layer Meteor., 91, 483–493. Moncrieff, J. B., and Coauthors, 1997: A system to measure surface fluxes of momentum, sensible heat, water vapour and carbon dioxide. J. Hydrol., 188–189, 589–611. Panofsky, H. A., and J. A. Dutton, 1984: Atmospheric Turbulence and Methods for Engineering Applications. John Wiley and Sons, 397 pp. Rannik, U., and T. Vesala, 1999: Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method. Bound.-Layer Meteor., 91, 259–280. Sozzi, R., and M. Favaron, 1996: Sonic anemometry and thermometry: Theoretical basis and data-processing software. Environ. Software, 11, 259–270. Wieser, A., F. Fiedler, and U. Corsemeier, 2001: The influence of the sensor design on wind measurements with sonic anemometer systems. J. Atmos. Oceanic Technol., 18, 1585–1608. Wilczak, J. M., S. P. Oncley, and S. A. Stage, 2001: Sonic anemometer tilt correction algorithms. Bound.-Layer Meteor., 99, 127–150. Wyngaard, J. C., 1981: The effect of probe-induced flow distortion on atmospheric turbulence measurements. J. Appl. Meteor., 20, 784–794. ——, and S. F. Zhang, 1985: Transducer-shadow effects on turbulence spectra measured by sonic anemometers. J. Atmos. Oceanic Technol., 2, 548–558.