For scalar quantities, there is no distortion because of transducers, if the Péclet
number Pe is high. This number is defined by UL/a where U is the flow velocity,
L is the characteristic length, and a is the thermal diffusivity. That is, the effects of
molecular diffusivity during the path time along the sensor are minimal and so the
measured and real values of any scalar, c e and c e
m are equal.
Equation (3.207) can be adapted to calculate the flow of a scalar quantity c:
u 3 c e
ð
Þ
m ¼ ð1 þ d 33 Þu 3 c e þ d 31 u 1 c e þ d 32 u 2 c e
ð3:208Þ
The use of rotation coordinates, discussed above, also helps to attenuate errors
arising from flow distortion. A coordinate rotation that places the mean direction of
the wind velocity vector coincident with u 1 will cancel the u 2 c e term. Equation (3.208) can then be written as follows:
u 3 c e
ð
Þ
m =u 3 c e
¼ 1 þ d 33 À u 1 c e
ð
Þ=u 3 c e
d 31
ð3:209Þ
The values for the ratio u 1 c e =u 3 c e are described by Wyngaard (1988). These
authors reported that under neutral/stable conditions, the ratio is about −3, and
decreases rapidly to values close to zero under instability.
According to Eq. (3.209), the effect of crosstalk is about –3d 31 , under conditions
of neutrality/stability and can be more pronounced than the effect of
attenuation/amplification. According to Wyngaard (1988) and Baldocchi (1995), the
error due to crosstalk can be eliminated by maximizing the vertical geometry of the
measurement system, so that distortions are as symmetrical as possible. One way of
improving this symmetry involves placing a vertical extension above the tower.
Transducers in three-dimensional sonic anemometers are set at 120° angles in a
non-orthogonal symmetrical geometry, in which none of the ultrasound linear paths
lie in the horizontal plane and serving to minimize disturbances in airflow. The
effects of transducers and their supporting structure are corrected by anemometer
software. By distributing symmetrically, the measuring system, it is possible to
minimize blocking effects and losses due to stagnation (Wyngaard 1988).
(x) Three important tools for assuring data quality are analysis of stationarity,
analysis of turbulent characteristics using the Monin–Obukhov (M–O)
dynamics similarity (Foken and Wichura 1996; Foken 2017) and data filtering.
The latter is done by assuming that friction velocity u à (Eq. 3.145) is generally
greater than 0.2 ms
−1 , which will assure enough turbulence to promote vertical
fluxes. Stationarity is needed to study the spatial variability or homogeneity of
turbulent statistics, if Taylor’s turbulent “freezing” holds (discussed in
Sect. 3.3).
The stationarity test (Foken and Wichura 1996) involves calculating fluxes (using
Eqs. 3.169 to 3.172) and divides 30 min data sets into six 5 min intervals. If the
difference between the fluxes obtained for 30 min interval is less than 30% relative
to the average of fluxes for all the 5 min periods, then the data is of high quality and
3.7 Eddy Covariance Method
93
number Pe is high. This number is defined by UL/a where U is the flow velocity,
L is the characteristic length, and a is the thermal diffusivity. That is, the effects of
molecular diffusivity during the path time along the sensor are minimal and so the
measured and real values of any scalar, c e and c e
m are equal.
Equation (3.207) can be adapted to calculate the flow of a scalar quantity c:
u 3 c e
ð
Þ
m ¼ ð1 þ d 33 Þu 3 c e þ d 31 u 1 c e þ d 32 u 2 c e
ð3:208Þ
The use of rotation coordinates, discussed above, also helps to attenuate errors
arising from flow distortion. A coordinate rotation that places the mean direction of
the wind velocity vector coincident with u 1 will cancel the u 2 c e term. Equation (3.208) can then be written as follows:
u 3 c e
ð
Þ
m =u 3 c e
¼ 1 þ d 33 À u 1 c e
ð
Þ=u 3 c e
d 31
ð3:209Þ
The values for the ratio u 1 c e =u 3 c e are described by Wyngaard (1988). These
authors reported that under neutral/stable conditions, the ratio is about −3, and
decreases rapidly to values close to zero under instability.
According to Eq. (3.209), the effect of crosstalk is about –3d 31 , under conditions
of neutrality/stability and can be more pronounced than the effect of
attenuation/amplification. According to Wyngaard (1988) and Baldocchi (1995), the
error due to crosstalk can be eliminated by maximizing the vertical geometry of the
measurement system, so that distortions are as symmetrical as possible. One way of
improving this symmetry involves placing a vertical extension above the tower.
Transducers in three-dimensional sonic anemometers are set at 120° angles in a
non-orthogonal symmetrical geometry, in which none of the ultrasound linear paths
lie in the horizontal plane and serving to minimize disturbances in airflow. The
effects of transducers and their supporting structure are corrected by anemometer
software. By distributing symmetrically, the measuring system, it is possible to
minimize blocking effects and losses due to stagnation (Wyngaard 1988).
(x) Three important tools for assuring data quality are analysis of stationarity,
analysis of turbulent characteristics using the Monin–Obukhov (M–O)
dynamics similarity (Foken and Wichura 1996; Foken 2017) and data filtering.
The latter is done by assuming that friction velocity u à (Eq. 3.145) is generally
greater than 0.2 ms
−1 , which will assure enough turbulence to promote vertical
fluxes. Stationarity is needed to study the spatial variability or homogeneity of
turbulent statistics, if Taylor’s turbulent “freezing” holds (discussed in
Sect. 3.3).
The stationarity test (Foken and Wichura 1996) involves calculating fluxes (using
Eqs. 3.169 to 3.172) and divides 30 min data sets into six 5 min intervals. If the
difference between the fluxes obtained for 30 min interval is less than 30% relative
to the average of fluxes for all the 5 min periods, then the data is of high quality and
3.7 Eddy Covariance Method
93