Determining the high-frequency performance of eddy covariance

Determining the high-frequency performance of eddy covariance measurements with
proton transfer reaction - mass spectrometer
University of Helsinki, Dept. Physics, P.O. Box 64, 00014 Univ. of Helsinki, Finland
Keywords: PTR-MS, time constant, cospectrum.
The PTR-MS (Proton transfer reaction-mass spectrometer ) is an highly sensitive instrument for
online measurement of concentration volatile organic compounds (VOCs) (Lindinger et al., 1998).
The PTR-MS is used for many applications including studies of emissions of VOCs from vegetation.
To measure these emissions in the ecosystem scale disjunct eddy covariance methods are commonly
used (Rinne et al., 2001; Karl et al., 2002).
A key requirement for any analyzer used for eddy covariance or disjunct eddy covariance method is
response time sufficient to resolve the frequencies contributing to turbulent flux. The high frequency
behaviour of the measurement system can be described using time constant, τ , which is the time
it takes for the systems output signal to reach 1 − 1/e ≈ 63.2 % of the change in measured signal.
In this study our aim was to find out the time constant of our disjunct eddy covariance system
utilizing a PTR-MS (Rinne et al., 2007) by using continuous water-ion cluster (H3 OH2 O, M37)
measurements and spectral analysis.
In this study, τ was determined by comparing the normalized cospectra of temperature and vertical
wind speed, w to the normalized cospectrum of M37 signal and vertical wind speed. This is based on
assumption of similarity of turbulent transport of scalars. The τ behaves like a low-pass filter and
its effect be seen as faster decline of the cospectrum towards high frequencies. The time constant of
temperature measurements with sonic anemometer is quite short and its cospectrum with vertical
wind speed is close to ideal.
According to the Kolmogorov’s 1941 theory and the Taylor’s hypothesis, the cospectrum Cws should
behave like a function ∝ f −7/3 (see figure 1) in the inertial subrange.
The effect of low-pass filtering to measured turbulent fluxes can be quantified by a transfer function
Hwq . Formally the transfer function is can be written as.
Hwq (f ) =
Cwq (f )
w′ q ′
Cwθ (f )
w′ θ′
where Cwq (f ) and Cwθ (f ) are the cospectrum of M37 and w, and temperature and w, respectively. w′ q ′ and w′ θ′ are turbulent fluxes of M37 and temperature, respectively, and f frequency.
Commonly used theoretical form for tranfer function is
Hwq (f ) = [1 + (2πτ f )2 ]−1
(e.g. Horst, 1997).
The measurements were done in Hyytiälä at the SMEAR II measurement station (61◦ 510’ N,
24◦ 170’ E, 181 m. above sea level) during July 3,–4, 2008. H3 OH2 O (M37) was measured with
a PTR-MS continuously at high frequency. M37 corresponds to water vapor (H2 O) because the
PTR-MS uses hydronium ions (H3 O+ ) to ionize target compounds via proton transfer reactions.
The measurement frequency fluctuated between 3.57–4.76 hz with an average value of 4.13 hz and a
standard deviation of 0.46 hz. Wind-measurements were done using a 10 hz ultrasound anemometer
(Gill Instruments Ltd., Solent HS1199) which measured also a virtual temperature Ts . In this case,
it was realistic to assume that Ts ≈ θ .
The PTR-MS data was first processed by the calibration procedure by Taipale et al., (2008).
Second, the lag time between wind and M37 measurements was estimated by maximizing the cross
covariance function of the M37 and wind measurements for every 30 minute measurement period
(Taipale et al., 2009). The wind and temperature data was also processed choosing data points
which had been measured same time with the M37 data and dismissing the rest.
The cospectral densities Cws were calculated using fast Fourier transform (FFT) on the cross
covariances of 212 data points and taking their real parts. After that, the normalized cospectra
were smoothed into 51 bins and finally, the smoothed spectra were averaged and these were used
to determine the transfer function empirically (eq. 1).
The time constant τ was determined by fitting the curve described by Equation (2) to empirically
determined transfer function (see figure 2). This was done using data within the inertial subrange,
0.05 hz< f < 0.6 hz (see figure 1). The fitting (with 95 % confidence intervals) was determined by
using Gauss-Newton algorithm. From this the time constant was determined to be τ = 0.7 ± 0.3 s.
Due to the scatter in the data the uncertainty is relatively large. Based on another method , Karl
et al. (2000) have estimated approximately 0.8 s as the upper-limit of τ . Thus these estimates are
relatively close.
We have estimated the response time of our disjunct eddy covariance - PTR-MS set-up using
specrtal analysis. Although the response time, τ = 0.7 ± 0.3, is relatively long it is still short
enough to capture most frequencies contributing to turbulent fluxes above the forest canopy. The
response time derived here is response time for whole measurement set-up and can not be directly
applied to different set-ups. Especially the signal attenuation in the inlet tube contributes differently
depending on the dimensions of the tube and the air flow in it.
Cospectrum of M37
Cospectrum of temperature
Normalized cospectrum
Frequency (hz)
Figure 1: Cospectrums of M37 and temperature. The area between dash lines was used for calculating the time constant.
Transfer function
Curve fitting
95 % interval confidence
Transfer function
Frequency (hz)
Figure 2: Transfer function Hwq and the fitting.
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