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
near the
ground. As an example, a mean vertical velocity of 5 cm s
at the
measuring height causes -100 W m
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:
and 
are the measured mean horizontal
and vertical velocities in the coordinate system defined by the instrument,
respectively, 
is the true mean vertical velocity, and 
and 
are the wind direction (
) dependent coefficients. Since
behaves in a random fashion, the long term data can be used
to evaluate and 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 and are determined as functions of
in 3
intervals using data from a previous complete run on the existing
database. Once the coefficients are determined, eq. ![[*]](http://nimbus.elte.hu/icons/latex2html/crossref.gif){kind=icon}
can be used
to determine to calculate for each run. Horizontal rotation
is applied to the wind speed data such that 
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 
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 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
values (see eq. ) for each 3 intervals calculated
using the least absolute deviation method. The effect of the tower body is clear
from the figure between wind direction 140 and 190. 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.
