Calibration

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Calibration

The response of the IRGA is calibrated by comparison to ambient CO $_{2}\protect$ and H $_{2}\protect$ O measurements from the slow-response 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 $_{2}\protect$ 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 H $_{2}\protect$ O and CO $_{2}\protect$ (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 long-term 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.
$\includegraphics{lag.eps}$

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 $_{2}\protect$ 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 $_{2}\protect$ 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 $_{2}\protect$ is not always applicable for H $_{2}\protect$ O. 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 $_{2}\protect$ 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 H $_{2}\protect$ O are calculated as the lag time for CO $_{2}\protect$ plus 2.5 sec. It should be noted that the day presented in figure is an optimal day for the determination of the H $_{2}\protect$ O lag times.

The built-in 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 (LI-COR, 1996):

$\begin{displaymath} f\left( V\frac{p_{0}}{p}\right) \frac{T}{T_{0}}+c_{r}=c\: , \end{displaymath}$

(2.34)

where $V$ is the voltage signal (CO $_{2}\protect$ or H $_{2}\protect$ O) of the IRGA, $p$ and $T$ is the pressure and temperature inside the measuring cell, respectively, $p_{0}$ and $T_{0}$ are arbitrary reference values for temperature and pressure, which are used to normalize the pressure and temperature ( $T_{0}=273.15$ K and $p_{0}=1000$ hPa is used here), $c_{r}$ is the mole fraction of CO $_{2}\protect$ or H $_{2}\protect$ O in the reference gas (zero for H $_{2}\protect$ O, 330-340 $\mu$ mol mol $^{-1}$ for CO $_{2}\protect$ ) and $c$ is the mole fraction of water vapor or carbon dioxide measured by the slow reference system. The analyzer is calibrated in terms of H $_{2}\protect$ O and CO $_{2}\protect$ mole fraction as it is recommended by the manufacturer (McDermitt et al., 1993).

Eq. can be rewritten as:

$\begin{displaymath} f\left( V\frac{p_{0}}{p}\right) =\left( c-c_{r}\right) \frac{T_{0}}{T}\: . \end{displaymath}$

(2.35)

Linear regression is carried out between $\left( C-C_{r}\right) T_{0}/T$ and $Vp_{0}/p$ to determine the slope and intercept of the response function, $f$ . $V$ , $p$ and $T$ are determined as 20 sec averages of the signals selected based on the synchronization of the data acquisition computers.

The detailed calibration procedure for H $_{2}\protect$ O and CO $_{2}\protect$ 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:

$\begin{displaymath} e_{s}=6.108\cdot 10^{\frac{7.5\left( T-273.15\right) }{235+T-273.15}\: ,} \end{displaymath}$

(2.36)

where $e_{s}$ is given in hPa. Next, calibrated H $_{2}\protect$ O and CO $_{2}\protect$ mole fraction is calculated as follows:

$\begin{displaymath} q=\frac{rh}{100}\frac{e_{s}}{p}1000\: , \end{displaymath}$

(2.37)

$\begin{displaymath} c=\frac{c_{82}}{1+\frac{q_{d}}{1000}} \end{displaymath}$

(2.38)

with

$\begin{displaymath} q_{d}=q\left( 1-\frac{q}{1000}\right) \: , \end{displaymath}$

(2.39)

where $q$ is the mole fraction of water vapor (given in mmol mol $^{-1}$ ), $c$ is the mole fraction of carbon dioxide (in $\mu$ mol mol $^{-1}$ ), and $q_{d}$ is the dry air mole fraction of water wapour (given in mmol/mol dry air), $rh$ is the relative humidity that is also measured by the Vaisala sensor, $c_{82}$ is the CO $_{2}\protect$ 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 $_{2}\protect$ 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 H $_{2}\protect$ O and CO $_{2}\protect$ based on eq. :

$\begin{displaymath} m_{q}V_{q}\frac{p_{0}}{p}+b_{q}=q\frac{T_{0}}{T} \end{displaymath}$

(2.40)

and

$\begin{displaymath} m_{c}V_{c}\frac{p_{0}}{p}+b_{c}=\left( c-c_{r}\right) \frac{T_{0}}{T} \end{displaymath}$

(2.41)

where $m_{q}$ , $b_{q}$ , $m_{c}$ and $b_{c}$ 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 $_{2}\protect$ (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.
$\includegraphics{caliexam.eps}$

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 (LI-COR, 1996), but the polynomial differs only slightly from linear in the range of interest (360-500 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 $_{2}\protect$ time series determined from the fast response system together with the CO $_{2}\protect$ data at 82 m determined from the profiling system.

Next: Data processing Up: The direct flux measuring Previous: The monitoring system Contents

root 2001-06-16