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Wind vector rotation / mean vertical wind speed

Three dimensional wind vector rotation is applied to the sonic anemometer data following the method of Lee (1998). A general assumption for micrometeorological measurements is the zero mean vertical wind speed. Generally, zero mean average vertical wind speed is forced as part of the wind vector rotation routine (e.g. McMillen, 1988). Lee proposes that this may be a good assumption very close to the ground, but it is generally invalid at higher altitudes. The non-zero mean vertical velocity is caused by local thermal circulations, topographically modified flow, divergence in convective cell-like structures or synoptic scale subsidence. The non-zero mean vertical wind speed transports heat, water vapor and carbon dioxide across the plane of the actual measuring height, while this transport is undetectable by the eddy covariance system, which is based on the measurement of the fluctuating signals. Focusing on carbon dioxide, this transport can be severe during nighttime, when carbon dioxide usually accumulating below the inversion layer causing high vertical gradients of CO\( _{2}\protect \) near the ground. As an example, a mean vertical velocity of 5 cm s\( ^{-1} \) at the measuring height causes -100 W m\( ^{2} \) equivalent energy flux for daytime (or an uncertainty of about 20% of the observed net radiation).

As it is stated in Lee (1999), it is not appropriate to use the mean vertical wind speed measured by the sonic anemometer because of the low signal level, the possible sensor tilt and the aerodynamic shadow of the sensor or the tower. As it is proposed by Lee, the true mean vertical velocity can be approximated from the following equation:

\widehat{w}=\overline{w}+a\left( \phi \right) +b\left( \phi \right) \widehat{u},
\end{displaymath} (2.48)

where \( \widehat{u} \) and \( \widehat{w} \) are the measured mean horizontal and vertical velocities in the coordinate system defined by the instrument, respectively, \( \overline{w} \) is the true mean vertical velocity, and \( a \) and \( b \) are the wind direction (\( \phi \)) dependent coefficients. Since \( \overline{w} \) behaves in a random fashion, the long term data can be used to evaluate \( a \) and \( b \) with least absolute deviation method. Lee (1999) recommends the least squares method, but the ``robust'' least absolute deviation method seems to be more appropriate, since the use of the Chi-square error statistics applied in the least squares method can result in a poor fit to the data due to an undesired sensitivity to outlying data.

Values of \( a \) and \( b \) are determined as functions of \( \phi \) in 3\( ^{o} \) intervals using data from a previous complete run on the existing database. Once the coefficients are determined, eq. [*] can be used to determine to calculate \( \overline{w} \) for each run. Horizontal rotation is applied to the wind speed data such that \( \overline{v} \) is forced to zero. Next, the coordinate system is rotated to ensure that the mean vertical wind speed is equal to the one calculated using eq. [*]. The rotated wind data is used to calculate turbulent fluxes and other statistics. The true average vertical wind speed is finally stored for each hourly period. The standard deviation of the lateral wind speed fluctuations (that is \( v \) after coordinate system rotation) together with the wind direction are also stored in order to be able to calculate turbulent flux source areas in the future.

Figure: The wind direction dependent deflection of the hourly average wind speed during the whole measurement period. The solid grey line represents the angle of the average deflection determined for each 3\( ^{o} \) intervals. The effect of the tower is clear between 140\( ^{o} \) and 190\( ^{o} \).

Figure [*] shows the deflection of the average three dimensional wind vector in the coordinate system defined by the instrument. The plot was constructed using all available EC data. The solid grey line represents the \( b \) values (see eq. [*]) for each 3\( ^{o} \) intervals calculated using the least absolute deviation method. The effect of the tower body is clear from the figure between wind direction 140\( ^{o} \) and 190\( ^{o} \). There is a sinusoidal behaviour outside this region which is caused by a slight tilt of the instrument. This tilt is compensated using the above method proposed by Lee (1998).

The application of the mean vertical velocity in the calculation of the net ecosystem exchange will be discussed later.

next up previous contents
Next: Trend removal Up: Data processing Previous: Data preparation   Contents
root 2001-06-16