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Calibration
The response of the IRGA is calibrated by comparison to ambient CO
and HO measurements from the slowresponse sensors, similar to the
method of Berger et al. (2001) (i.e. no calibration gases are used in the fast
response system). A calibrated CO measurement is typically obtained
every 8 minutes at the 82 m level. Exact synchronization of the signals requires
accounting for the time for air to pass through the sampling tubes of the profile
and the eddy systems.
The lag time of the profile system is calculated from the measured flow rates
and from in situ tests. The lag time for the profiling system was around
3 minutes.
It is very important to keep track of the lag times since these values are also
used during the calculation of the lagged covariances, which appear to be very
sensitive for the lag times in some cases. For the eddy covariance system two
different lag time values are calculated for HO and CO
(Moncrieff et al., 1997) using a spectral method. First, the daily lag time
values are calculated without any restrictions for the whole dataset. Then a
polynomial is fitted to the longterm lag time series which is used to determine
the actual time window where the lag time is supposed to occur. The time window
used is 16 sec around the fitted value. Lagged covariances inside this window
are used for the following procedure.
The usual method is to calculate the lag times for each averaging period to
search for the time where the maximum correlation occurs (Fan et al., 1990).
Figure:
Normalized lagged covariances for carbon dioxide (upper plot)
and water vapor (lower plot) as functions of the lag time for one day (23 June,
1998). Carbon dioxide flux is typically negative and largest (in absolute sense),
while water vapor flux is positive and largest during daytime, hence the best
detectable peaks are expected to occur during daytime. The lagged covariance
function indicated by the arrow in the upper plot is an example to prove that
in some cases the lag time does not occur at the maximum covariance while a
detectable peak does occur.

It appears however, that this is not always a plausible method. Figure
shows the normalized lagged covariances for one day. The solid lines in the
lower part of the figure shows detectable peaks which correspond to the lag
time for CO during daytime. The nighttime sharper peaks in the upper
part mark the same lag time as the daytime values, which means that the lag
time is quite constant during one day, and it is possible to determine one average
daily lag time value. It should be noted that this method is only applicable
if the pump is expected to produce an approximately constant flow rate, which
is the case in our system. Especially during nighttime when turbulence is suppressed
or the turbulent transport is small, the lagged covariances do not always show
detectable peaks. It can be seen in figure that in some cases
the maximum covariance occurs a few seconds away from the real lag time value.
Moreover, as it is indicated by the arrow, sometimes the correct lag time occurs
at the minimum covariance. As a consequence, individual lag times for CO
are determined by finding the maximum covariance inside a very small (1 s) time
window around the daily average value. The small window ensures that the appropriate
lag time will be determied even if the covariance has its minimum around the
daily average.
The method described above for CO is not always applicable for HO.
The nighttime lag values are usually undetectable since latent heat flux is
very small during this period (see fig. ). The daytime (positive)
covariances does not exhibit the same behaviour as CO does in many
cases, and it appears that during many days it is not possible to determine
the average daily value. For this reason, based on long term experience, the
lag times for HO are calculated as the lag time for CO
plus 2.5 sec. It should be noted that the day presented in figure
is an optimal day for the determination of the HO lag times.
The builtin clocks of the data acquisition computers (see sections
and ) appeared to shift with respect to each other. This
shift could be tracked since the eddy covariance system monitors the state of
the multiport valve of the profile system, and the changes in the valve state
are tied to specific time stamps of the profile computer.
Once the correct synchronization is performed, the calibration can take place.
We use the following function for calibration (LICOR, 1996):

(2.34) 
where is the voltage signal (CO or HO) of the
IRGA, and is the pressure and temperature inside the measuring
cell, respectively, and are arbitrary reference values
for temperature and pressure, which are used to normalize the pressure and temperature
( K and hPa is used here),
is the mole fraction of CO or HO in the reference gas
(zero for HO, 330340 mol mol for CO)
and is the mole fraction of water vapor or carbon dioxide measured
by the slow reference system. The analyzer is calibrated in terms of HO
and CO mole fraction as it is recommended by the manufacturer (McDermitt
et al., 1993).
Eq. can be rewritten as:

(2.35) 
Linear regression is carried out between
and to determine the slope and intercept of the response function,
. , and are determined as 20 sec averages
of the signals selected based on the synchronization of the data acquisition
computers.
The detailed calibration procedure for HO and CO are as
follows. First, saturated water vapor pressure is calculated inside the measuring
cell from data measured by the Vaisala sensor located immediately behind the
measuring cell:

(2.36) 
where is given in hPa. Next, calibrated HO and CO
mole fraction is calculated as follows:

(2.37) 

(2.38) 
with

(2.39) 
where is the mole fraction of water vapor (given in mmol mol),
is the mole fraction of carbon dioxide (in mol mol),
and is the dry air mole fraction of water wapour (given in mmol/mol
dry air), is the relative humidity that is also measured by the Vaisala
sensor, is the CO mixing ratio at 82 m measured by
the profiling system. It should be noted that since the air sampled by the profiling
system is dried (see section ), the resulting CO
data are expressed in terms of dry air mole fraction. Mole fraction, however,
is defined as the mole number of the considered gas divided by the mole number
of the complete gas mix (with water vapor), while dry air mole fraction is defined
as the mole number of the gas divided by the mole number of the dry air. Equation
calculates ``regular'' mole fraction based on the dry air mole
fraction measured by the slow system.
The next step is the application of the linear approximation for HO
and CO based on eq. :

(2.40) 
and

(2.41) 
where , , and are the slope
and intercept of the lines determined by linear regression for water wapour
and carbon dioxide, respectively.
Figure:
Typical daily calibration function for CO
(17 June, 1997). The correlation coefficient (r) was very close to unity. Inset
graph: the difference between the 5th order polynomial supplied by the IRGA
manufacturer and the linear approximation. As it is obvious from the figure,
the linear approximation can be used instead of the 5th order polynomial.

Figure shows the fit for a typical day. Since most of the variance
is contained in the measured voltage signal it is extremely important to determine
the correct slope of the fits (Berger et al., 2001). Using linear regression,
occasional outliers can result in a poor fit due to an undesired sensitivity
to outlying data, thus they are removed interactively, and the resulting linear
fits typically show very high correlation.
The manufacturer provides a fifth order polynomial calibration curve for the
instrument (LICOR, 1996), but the polynomial differs only slightly from linear
in the range of interest (360500 ppm) as shown by the inset graph in Fig. .
Calibration values are determined for each 24 hours of measurement. The calibration
factors are quite stable in time.
The calibration can be verified with plotting the daily CO time series
determined from the fast response system together with the CO data
at 82 m determined from the profiling system.
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