A case study of eddy covariance flux of N 2 O measured within forest ecosystems : quality control and flux error analysis

Eddy covariance (EC) flux measurements of nitrous oxide obtained by using a 3-D sonic anemometer and a tunable diode laser gas analyzer for N2O were investigated. Two datasets (Sorø, Denmark and Kalevansuo, Finland) from different measurement campaigns including sub-canopy flux measurements of energy and carbon dioxide are 5 discussed with a focus on selected quality control aspects and flux error analysis. Although fast response trace gas analyzers based on spectroscopic techniques are increasingly used in ecosystem research, their suitability for reliable estimates of eddy covariance fluxes is still limited, and some assumptions have to be made for filtering and processing data. The N2O concentration signal was frequently dominated by offset 10 drifts (fringe effect), which can give an artificial extra contribution to the fluxes when the resulting concentration fluctuations are correlated with the fluctuations of the vertical wind velocity. Based on Allan variance analysis of the N2O signal, we found that a recursive running mean filter with a time constant equal to 50 s was suitable to damp the influence of the periodic drift. 15 Although the net N2O fluxes over the whole campaign periods were quite small at both sites (∼5μg N m−2 h−1 for Kalevansuo and ∼10μg N m−2 h−1 for Sorø), the calculated sub-canopy EC fluxes were in good agreement with those estimated by automatic soil chambers. However EC N2O flux measurements show larger random uncertainty than the sensible heat fluxes, and classification according to statistical significance of 20 single flux values indicates that downward N2O fluxes have larger random error.


Introduction
Nitrous oxide (N 2 O) is the greenhouse gas with the highest greenhouse warming potential over a long period (100 years).This is about three hundred times larger than that of carbon dioxide (IPCC, 2001).Microbial activity in soil ecosystems is the major source of N 2 O to the atmosphere (IPCC, 2001).Agricultural soils are the major sources of N 2 O, however, due to their large areal coverage, forest soils have a substantial contribution to the total emissions of N 2 O (e.g.Skiba et al., 1994;Kesik et al., 2005).
Due to recent development of fast response N 2 O analyzers based on spectroscopic techniques like tunable diode laser (TDL) and more recently quantum cascade laser (QCL) spectrometers, the eddy covariance (EC) method is now suitable for measuring long-term and spatially integrated N 2 O fluxes (Neftel et al., 2009).
The EC method is routinely used in many micrometeorological sites worldwide to measure CO 2 and H 2 O fluxes above and below forest canopies, thanks to well established methodologies (e.g.Aubinet et al., 2000), based upon long term stability of the fast response CO 2 and water vapour analysers and high signal-to-noise ratios of sampled concentrations.In case of N 2 O it is not straightforward that these requirements for reliable estimations of EC fluxes are fulfilled as well.Up to now only a limited number of N 2 O EC measurements have been reported in literature and they have been mainly carried out in agricultural soil ecosystems (Smith et al., 1994;Wienhold et al., 1994;Christensen et al., 1996;Laville et al., 1997;Scanlon and Kiely, 2003;Neftel et al., 2007;Kroon et al., 2007), and forest soil ecosystems (Pihlatie et al., 2005;Eugster et al., 2007).Large uncertainty and temporal variability of EC N 2 O fluxes, reported by these Published by Copernicus Publications on behalf of the European Geosciences Union.
I. Mammarella et al.: A case study of eddy covariance flux of N 2 O studies, are related either to biogeochemical soil processes and/or several systematic and random error sources of the EC measurements.N 2 O emissions are episodic in nature, showing high spatial and temporal variability, due to large variation in soil properties such as soil moisture, availability of nitrogen and easily decomposable organic matter (Ambus and Christensen, 1995;Pihlatie et al., 2005;Silver et al., 2005).Emission bursts of short duration, typically occurring after fertilizer application, or associated to thawing and rain events (Flechard et al., 2005, Kroon et al., 2007, Pihlatie et al., 2009), are followed by long periods of small fluxes, when also uptakes of N 2 O have been reported (Flechard et al., 2005).Moreover the performance and stability of fast response N 2 O gas analyzer strongly depends on the instrumental drift, which typically characterizes TDL and QCL spectrometers (Werle et al., 1993;Nelson et al., 2002).Previous studies performed under field conditions (Eugster et al., 2007;Kroon et al., 2007;Neftel et al., 2009) already noted that the laser drift can cause an over or under-estimation of EC flux.However they did not perform a thorough investigation on the effect of the drift on the calculated flux values.
In this case study we explore the limits of eddy covariance flux measurements of N 2 O by using state-of-the art equipment.We present a detailed discussion of the main error sources and uncertainties of EC N 2 O fluxes measured by a commercially available TDL spectrometer (Campbell Scientific Inc.) within two different forest ecosystems, a beech forest in Sorø, Denmark, and a Scots pine forest in Kalevansuo, Finland, during two distinct measurement campaigns.Both field campaigns were carried out in the trunk space layer.EC system performances are investigated by using the Allan variance concept (Werle et al., 1993).We explored the effect of instrumental drift of the N 2 O signal on the EC flux, and we proposed a criterion for selecting a suitable time constant of the high pass filter, which is a necessary method to be applied in order to remove the drift.Flux error analysis, traditionally used in the micrometeorological community for energy and CO 2 fluxes, are discussed and applied to N 2 O flux measurements, in order to identify uncertainty of fluxes caused by instrumentation problems and systematic as well as random errors.Finally for validation purposes we compare the EC fluxes with those obtained by soil chamber technique.Recommendations how to treat data for post-processing are derived from the assumption that below-canopy EC flux measurements should match the temporal pattern and magnitude of chamber flux measurements, although also chambers are prone to systematic errors.

Site description and measurements
The first measurement campaign was conducted from 2 May to 5 June 2003 in a 87 year old beech (Fagus sylvatica L.) forest near Sorø on the island of Zealand, Denmark (55 • 29 N, 11 • 38 E).The annual precipitation is 650 mm and the mean temperature 8 • C. The forest is located in a flat terrain and extends 1 km in the east-west direction and 2 km in northsouth direction.The beech trees are 25 m tall, but the forest also contains scattered stands of conifers.The mean leaf area index (LAI) for the main footprint of the forest is 5 m 2 m −2 .The LAI is approximately constant between June and September and drops slowly during the autumn.During the campaign EC N 2 O fluxes were measured in the sub-canopy layer at 3 m height above the forest floor by using a small mast.The EC system consisted of a 3-D sonic anemometer (Solent 1012, Gill) and a TDL gas analyser (TGA 100,Campbell Scientific Inc.).Soil N 2 O fluxes were also obtained by using chamber technique.More details on the chamber setup and data processing are given in Pihlatie et al. (2005).
The second measurement campaign was conducted during the spring 2007 (25 April to 27 June) at a Kalevansuo drained peatland forest.The site was located in southern Finland (60 • 39 N, 24 • 22 E), where the mean annual precipitation is 606 mm and the mean annual temperature is 4.3 • C. The canopy height is about 16 m, the tree stand is uneven and unclosed, and consists mainly of Scots pine (Pinus sylvestris L.) with some small-sized Norway spruce (Picea abies L.) and downy birch (Betula nana) in the gaps near ditches.The total LAI is approximately 2 m 2 m −2 .EC measurements of CO 2 , H 2 O and N 2 O fluxes were performed at 4 m height above the forest floor.Sub-canopy CO 2 and H 2 O fluxes were measured by a Li-7500 Open-Path Infrared CO 2 /H 2 O Gas Analyzer (Li-Cor Inc.) and a CSAT3 Sonic Anemometer (Campbell Scientific Inc).EC measurements of N 2 O fluxes were conducted at the same mast using the same CSAT3 anemometer and a TDL spectrometer (TGA-100A, Campbell Scientific Inc.).Soil fluxes of N 2 O were also measured by enclosure method using automatic and manual chambers.The nine automatic chambers sampled and analyzed continuously by gas-chromatography were located approximately 100 m southwest from the sub-canopy EC mast.More details on chamber setup and data processing are given in Pihlatie et al. (2009).
The TDL system used in both sites consists of a temperature and current controlled single mode diode laser, tuned to an infrared N 2 O absorption band and mounted in a liquid nitrogen Dewar.Concentration measurement was achieved by passing the infra red laser beam through the sample and reference cells.The reference gas (2000 ppm N 2 O from a steel cylinder) was drawn through the reference cell under same temperature and pressure conditions as the sample air in the sample cell (see Table 1 for temperature and pressure values).The sample air was drawn to the TDL analyzer with a Busch rotary-vane pump (RB0021-L) via a diffusive dryer (PD1000, Perma pure Inc.) to remove excess water vapour that could infer the analysis.Sample air leaving the dryer was directed to the TDL analyzer via 10 m long Teflon tubing (inner diameter 4 mm) for Sorø and 4 m for Kalevansuo (inner diameter 4.25 mm).The total volume of the inlet system was Reference gas 2000 ppm in reference cell 2000 ppm in reference cell (Messer Griesheim, Germany) (Oy Aga Ab, Linde Gas) approximately 0.24 l and that of the sample cell 0.48 l.The sample flow rate was 14 l min −1 for Sorø and 15 l min −1 for Kalevansuo experiment.The residence time in the sample cell was approximately 0.1 s, which is sufficient to provide the necessary exchange time for flux measurements.
During the measurement period, pressure inside the sample cells was kept constant at approximately 70 mbar for Sorø and 50 mbar for Kalevansuo and at both sites the measurements were conducted at 10 Hz frequency.The TDL used at Sorø was calibrated once during the measurement campaign using zero and span (290.3 ppb N 2 O) calibration gases, while at Kalevansuo the factory calibration was used.The setup details and operational parameters according to the data sheet of the two EC-TDL systems are summarized in Table 1.

EC measurements: data processing and corrections
The EC fluxes were calculated as 30 min co-variances between the scalars and vertical wind velocity according to commonly accepted procedures (e.g.Aubinet et al, 2000).Prior to calculating the turbulent fluxes a 1-D rotation (mean lateral wind equal to zero) of sonic anemometer wind components and filtering to eliminate spikes were performed according to standard methods (Vickers and Mahrt, 1997).
All signals were detrended for removing the average values and trends.As a first step a linear detrending (LDT) procedure was used.However, the N 2 O signal measured by the TDL gas analyzer was frequently dominated by low frequency noise, which is mainly due to optical interference fringes (Campbell TDL Reference Manual; Hernandez, 1986;Werle et al., 2004;Brodeur et al., 2008), and in turn has strong effect on the system performance and the flux detection limit.The movement of the fringes (and thus the change in the N 2 O offset) is influenced by the instrument temperature (Smith et al., 1994), and it can contaminate the flux in the case that 1) these offset drift changes are faster compared to the eddy correlation averaging time and 2) the resulting concentration fluctuations are correlated with the vertical wind velocity fluctuations.In order to suppress the instrumental drift and its potential effect on the estimated flux values, the N 2 O flux was also calculated after applying an autoregressive running mean filter (RMF, McMillen, 1988) to the sampled signals.Although this approach was adopted previously for post-processing drifting concentration signals (Billesbach et al., 1998;Kormann et al., 2001;Kroon et al., 2007), the choice of the high pass time constant is not straightforward and objective selection methods are rare in literature (Werle, 2009).Methods based on signal auto-correlation coefficient and spectral analysis likely fail to give a reliable estimation of the timescale at which the drift effect becomes important, because of non-stationarity nature www.biogeosciences.net/7/427/2010/Biogeosciences, 7, 427-440, 2010 of the low frequency signal noise.In this study we used the concept of the Allan variance (see Appendix A), as proposed by Werle et al. (1993).This technique is a valuable tool to assess the precision and stability of TDL spectrometers and has been used to get an estimate for the time constant for the running mean filter as described in Sect.4.1.
The lag time between the N 2 O signal and vertical wind speed was determined by maximizing the corresponding cross-covariance function, using a procedure similar to Pihlatie et al. (2005).The measured N 2 O lag time was about 1 s for Kalevansuo and 2 s for Sorø.
Systematic flux underestimation due to the system characteristics results from physical limitations in the sensor response times, separation distances between the sonic probe and the gas inlet, size of the sensors, the use of sampling line filters, and the sampling tube dimensions.Therefore, these limitations concern only the high frequency band of the scalar fluctuations.All mentioned effects could be described quantitatively by transfer functions according to Moncrieff et al. (1997) andAubinet et al. (2000) and the flux loss can be estimated by using cospectral correction method (Moore et al., 1986;Horst, 1997, Eugster and Senn, 1995, Mammarella et al., 2009).In this study under the assumption of cospectral similarity between fluxes of CO 2 , N 2 O and sensible heat, all fluxes were corrected for low-pass filtering effects by using an empirical cospectral model (derived from sensible heat cospectra) and theoretical transfer functions.
Cospectra of sensible heat, CO 2 (only for Kalevansuo) and N 2 O were calculated using fast Fourier transform (FFT) on segments of 2 15 data points (about one hour periods).In order to reduce the random uncertainty, the single cospectra were ensemble averaged according to atmospheric stability.
In order to quantify the high frequency flux loss, a below canopy cospectral model was empirically derived by fitting the sensible heat cospectra Co wθ , to this simple functional form: where f is the natural frequency in Hz, n= fz/U is the normalized frequency, z the EC measurement level, U the mean wind velocity, m is the inertial slope parameter (which should be equal to 3/4 in order to get the −4/3 inertial sub-range power law of the cospectrum f Co wθ ), µ is the broadness parameter and n m is the normalized frequency at which the logarithmic cospectrum f Co wθ attains its maximum value (Lee et al., 2004).The measured sensible heat cospectra were fitted to the Eq. 1 by non-linear regression obtaining the parameters m, µ and n m The results are discussed in Sect.4.2.
The correction for density fluctuations (Webb et al., 1980) was not necessary for N 2 O flux measurements because moisture has been removed by using a high flow sample dryer in the system (PD1000 Nafion® dryer, Campbell Scientific, Inc., Logan, UT, USA).

Random error of flux estimates
The time-averaged co-variance w c is a random variable estimated over a finite realisation and its average departure from the ensemble average < w c > is presented by the random error δF , which is a measure of one standard deviation of the random uncertainty of turbulent flux observed over an averaging period T (Lumley andPanofsky, 1964, Lenschow et al., 1994).The random error δF associated with w c is generally due to stochastic nature of turbulence and instrumental noise.
The random error δF of turbulent flux observed over an averaging period T was evaluated according to Vickers and Mahrt (1997 (2) where the period T (30 min) is divided into N=6 sub-records and is the standard deviation of the sub-record average fluxes F i (i = 1 ,. . .N), where < > denotes averaging over N sub-record values.

TDL system stability and performance
The ability of performing EC flux measurements by using the EC-TDL system depends on the accuracy and stationarity of the N 2 O signal measured by the TDL spectrometer.Moreover the system needs to operate continuously under changing environmental conditions in the field.In order to investigate the short term stability of the N 2 O gas analyzer, the system was evaluated in the laboratory by sampling a constant source of N 2 O from closed laboratory room.The flow system was the same than what was used in the field, resulting in similar sample flow and cell pressure.An Allan variance analysis was performed to the N 2 O concentration measurements and the 10 Hz noise level (std) of TDL was estimated to be 1.5 ppbv, which is in line with the system specifications from the manufacturer.A typical drift timescale (defined as the minimum of Allan variance) for the TDL used in this study was also determined in the lab, and it is about 120 s.Nelson et al. ( 2004) found a Allan variance stability time of about 100 s for N 2 O and 200 s for CH 4 for the Aerodyne Research pulsed QCL spectrometer.
The spectrometer stability can be definitely worse under field conditions, where the temperature changes cannot be fully controlled as in a laboratory environment.Moreover additional low frequency drift in the scalar concentration may be due to non-stationarity of the atmospheric signal.During both measurement campaigns, TDL systems were inside a box and the insulated enclosure cover, recommended by the manufacturer, was used in order to dampen diurnal temperature variations.We frequently observed slow variations in the N 2 O concentration signal, which cannot be related to  non-steady-state conditions of turbulent motions, since other scalars were not affected, but they are mainly caused by laser drift.An example is given in Fig. 1, where one hour of N 2 O and sonic temperature signals, measured at Kalevansuo and Sorø, are displayed.The N 2 O concentration signal has a wave-like shape, which is not properly removed when using a LDT operation.For this case we found that a recursive high pass filter with a time constant of about 50 s suppresses the influence of low frequency drift to the N 2 O signal.By using larger time constants (100 and 200 s), the running mean tends to lag with respect to the actual trend.Instead, the temperature signal measured at both sites is not affected by the same kind of low frequency noise, and a simple LDT operation was suitable.Figure 2   is a correspondence between the slope α of the FFT spectrum and the slope β of the Allan variance, e.g.α = (−β − 1).For example, α = 0 corresponds with β = −1 for white noise, and α = −3 corresponds with β = 2 for a linear drift (Werle et al, 1993).
The N 2 O Allan variance (Fig. 2a) indicates that the signal is dominated by white noise up to about 5 s and it starts to drift after 50 s.Both regimes are clearly observable in the time domain (Allan variance) as well as in the frequency domain (spectrum), and they are identified by the corresponding slopes α and β.For comparison the temperature does not show any such drift at large timescales (low frequencies), but mainly consists of two domains: an inertial sub-range and a domain showing a slope β = 0 (α = −1), likely related to inactive turbulent eddies (Katul et al., 1998), penetrating down into sub-canopy layer.It seems that the low frequency range of the N 2 O signal (< 0.02 Hz) is mainly dominated by instrumental drift, which can give an artificial extra contribution to the fluxes when the resulting concentration fluctuations are correlated with the fluctuations of the vertical wind velocity.For all analysed cases, when the N 2 O signal was dominated by a fringe effect, we found that a high-pass filter time constant of 50 s was suitable to damp the influence of the periodic drift.
The same analysis was done with Sorø N 2 O time series and similar results were found, as shown in Fig. 3.However, the fringe effect was observed less frequently during the Sorø campaign and mainly during the first half of the measuring period.

Cospectra
The empirical cospectral model (Eq. 1) was fitted to the sensible heat cospectra, measured at both sites during daytime conditions.The averaged frequency weighted cospectra of the sensible heat flux are shown in Fig. 4a and c for Kalevansuo and Sorø respectively, and the fitting parameter values are displayed in Table 2. Prior to averaging operation, it was established that the fitting parameters were not a function of atmospheric stability under near-neutral or unstable daytime conditions.
In the inertial sub-range the sensible heat flux cospectra Co wθ measured within the trunk space are less steep than the expected surface layer slope −7/3(−2.33)(Kaimal et al., 1972), and the transfer of energy from the production to the dissipation scales follows a slope equal to about −1.94 for Sorø and −2 for Kalevansuo (Table 2).Similar result was obtained by Amiro (1990) inside three different types of forest canopies (aspen, pine and spruce).The average value of the normalized frequency n m is smaller for Sorø (0.073) than the one estimated for Kalevansuo (0.12).This difference is likely due to the different height of the canopies (25 vs. 16 m).In the roughness sub-layer the scalar transport is dominated by coherent structures (ejection-sweep cycle), whose typical length scales are proportional to the canopy height h c (Kaimal and Finnigan, 1994).Hence the difference in n m between the two sites could be explained just defining a new normalized frequency n mh = n m h c /z = f m h c /U (here we should acknowledge that a general scaling for the spectral peak would imply to use the wind velocity measured at the canopy top U hc instead of U , but unfortunately measurements of U hc were not available for these sites).Using the canopy height h c instead of the measurement height z, the normalized frequency values at which the cospectra peak, occur at 0.6 for both sites, which indicates that the most energetic eddies scale with h c and that for the selected cases the ratios U hc /U are invariant between the two sites.While such a simple cospectral model described very well the sensible heat cospectra measured during daytime, it was found unsuitable for fitting the night-time measured cospectra, which were often characterized by larger uncertainty as a result of multi-scale non-stationary processes usually affecting the night-time scalar transport in the sub-canopy layer (Cava et al., 2004).
The N 2 O cospectra (Fig. 4b and d) show more random variability especially in the low frequency range, where contributions with opposite direction to the total covariance are measured and the effect of N 2 O signal drift is clearly evident.Instead at higher frequencies the N 2 O cospectra behave similarly to the sensible heat, except that they show a damping effect at the end of the inertial sub-range, as discussed in the following section.

Flux systematic error
In order to assess the applicability of the cospectral transfer function method in the sub-canopy layer, we simulated first the high frequency loss of CO 2 flux, whose measured cospectra show less random uncertainty than those of N 2 O fluxes.At Kalevansuo site the CO 2 flux loss is mainly due to the separation distance between the sonic probe and the head of the Licor 7500.The effective first-order transfer function was also experimentally estimated as a ratio between the measured normalized cospectrum of the CO 2 and sensible heat flux (Mammarella et al., 2009).The normalizing factors were calculated over frequencies not affected by attenuation (Aubinet et al., 2000).Figure 5 shows the predicted and measured CO 2 cospectra calculated during daytime and a typical mean value of sub-canopy wind velocity of 0.7 m s −1 .Biogeosciences, 7, 427-440, 2010  Here the predicted cospectra for CO 2 refer to the normalized temperature cospectrum damped either by using the effective transfer function or the theoretical ones according to Moncrieff et al. (1997).In all analysed cases, both methods were suitable for estimating the CO 2 flux loss, which was about 5%.Despite the fact that the within canopy turbulence at small scale likely is not isotropic, the high frequency flux loss during daytime conditions was rather well simulated and predicted by using cospectral correction methods.
In the case of the TDL-EC system, the spatial separation between the sonic probe and the sample gas inlet together with the TDL optical measurement cell response time caused the largest part of the high-frequency underestimation.Although the N 2 O cospectra measured at both sites are remarkably noisier than the previously shown CO 2 cospectrum, the damping of the highest frequencies for Kalevansuo is broadly predicted by the sensible heat cospectra attenuated by the appropriate transfer functions (Fig. 6a).For the  Sorø site (Fig. 6b) the measured N 2 O cospectrum surprisingly does not show similar damping at the high frequency end.Besides the random uncertainty of cospectral density estimates, such behaviour is likely related to the EC digital filter of the TDL system used during the Sorø campaign.In fact the corresponding N 2 O spectrum showed an "apparent" −5/3 inertial sub-range at the high frequency end (Fig. 3c), where we would expect a signal dominated by white noise.The resulting flux reduction was less than 10% for both sites.
Finally the systematic flux error due to the high pass running mean filter (RMF) should be corrected by using the appropriate transfer function (Rannik and Vesala, 1999) and the fitted empirical cospectral model.However, in practical, we did not include such correction in the final flux values, because a correction would require a priori knowledge about the instrumental interference structure.Moreover cospectral similarity does not necessarily apply at low frequency range.More research should be done on this issue.

Flux random uncertainty
Random flux error of N 2 O and sensible heat flux measurements were estimated according to Eq. 2 for Kalevansuo and Sorø datasets.(1964) and Wyngaard (1973), where T is the averaging period (e.g. 30 min), σ φ and τ φ are the standard deviation and the integral time scale of instantaneous flux φ = w c .Error estimates given by Eq. ( 2) and Eq. ( 3) are two different methods to estimate the same flux random error, and their values are expected to be approximately the same (Rannik et al., 2009).A crucial point in using the Eq. ( 3) is to give a reasonable estimate of τ φ , which can be numerically calculated from the autocorrelation function of the time series φ (Rannik et al., 2009).However, in practical applications of Eq. ( 3), τ φ is often assumed to be approximately equal to z/U (Wyngaard, 1973;Pryor et al., 2008).3).For these flux values the average amount of relative random error, estimated for Kalevansuo, is about 76%, which is much smaller than the  3).Such large difference of the estimated relative random errors is probably related to the parameterization that Kroon et al. (2009) used for the integral time scale in the Eq. ( 3), e.g.τ φ = 10z/U , which differs by a factor of 10 with respect to that mentioned above.Accounting for the square root of this factor, the random uncertainty estimated by Kroon et al. (2009) would be 97%, which is of the same order of magnitude of the one we estimated in Kalevansuo.
Then given the respective average flux magnitudes (18 and 25 ng N m −2 s −1 ) in the selected range, the 30 min absolute uncertainty is 12 ng N m −2 s −1 (equals 43 µg N m −2 h −1 ) for Kalevansuo and 23 ng N m −2 s −1 for Kroon et al. ( 2009) EC measurements.
In evaluation of average flux statistics, classification according to some threshold value of relative flux error is done.For example, by using | F | < 1, which means that for such subset the fluxes are with probability 68% within one standard deviation from the mean, as criterion to select the fluxes with higher confidence level (ie.with smaller random errors), the frequency distribution of N 2 O flux values changes (less downward fluxes) as shown in the bottom panels of Fig. 7.However, we should acknowledge that the soil N 2 O uptake seems not merely a result of random stochastic effect of flux values, as approximately 38% of 30 min downward fluxes for Kalevansuo and 12% for Sorø are statistically significant (larger than the estimated random flux error δF ), which is in line with other studies reporting on occasional or even constant N 2 O uptake in forest and agricultural ecosystems (e.g.Goossens et al., 2001;Butterbach-Bahl et al., 1998;Rosenkranz et al., 2006;Pihlatie et al., 2007;Chapuis-Lardy et al., 2007;Neftel et al., 2007).Thereby N 2 O uptake often occurs under conditions of low nitrogen availability, which is especially true for the drained peatland forest site Kalevansuo (Pihlatie et al., 2009).

Comparison with chamber fluxes
For validation purpose, EC N 2 O fluxes (corrected for high frequency loss) were compared to the soil N 2 O flux rates simultaneously measured by automatic chambers during the field campaigns (see Pihlatie et al., 2005Pihlatie et al., , 2009)).Chambers were located 50 m northwest and 100 m southwest from the sub-canopy EC mast for Sorø and Kalevansuo site respectively.
Both of the measurement sites have limitations in a true method comparison between the EC and chamber fluxes.In Kalevansuo the automatic chambers were located slightly outside the estimated footprint area of the EC system (see Appendix B).However, as the vegetation and soil characteristics around both the automatic chambers and the subcanopy EC mast was very similar, we can compare the fluxes obtained by these two methods.In Sorø, the automatic chamber was well within the footprint area of the EC system, however, as there was only one big automatic chamber, the comparison between the two methods is uncertain due to the high spatial variability in N 2 O emissions at the measurement site (Pihlatie et al., 2005).
In order to smooth out the run-to-run variability and further reduce the flux random uncertainty, it is a common procedure to compare ensemble averaged flux statistics.
Comparison of daily mean values of EC and automatic chamber fluxes for Sorø and Kalevansuo are reported in Fig. 8. Top panels show EC fluxes calculated after applying a standard linear detrending operation to 30 min runs of N 2 O and vertical wind velocity signals (EC-LDT).In middle panels a recursive high pass filter with a time constant equal to 50 s was applied prior flux calculation (EC-RMF).For Kalevansuo site EC-LDT fluxes are randomly distributed highly scattering around zero, which can mainly be related due to the N 2 O signal drift.The Sorø EC-LDT fluxes show less scattering, but unexpected high N 2 O uptake rates (> 10 µg N m −2 h −1 ) for some days.The randomly large scattering are significantly reduced in EC-RMF fluxes (especially in Kalevansuo), which are comparable with the magnitude of chamber fluxes at both sites.A comprehensive analysis of temporal variability of N 2 O emission and environmental driving factors is reported in Pihlatie et al. (2005) for Sorø and Pihlatie et al. (2009) for Kalevansuo site.
Mean and median values of EC fluxes calculated over the entire campaign periods with different methods (LDT or RMF) and selected according to confidence level criteria ( F ) are compared with the automatic chambers flux statistics (Tables 3 and 4).In most of the cases the mean and median values of EC fluxes were smaller than the corresponding values by the automatic chamber (AC) technique, however showing a larger statistical uncertainty and dispersion as indicated by the mean standard error (stde) and the 25th/75th percentile values respectively.The EC flux statistics from the distribution of 30 min flux calculated by LDT method show the largest departure from the AC flux statistics.For For further validation and comparison purpose, the measured 30 min fluxes were conditionally selected according to the estimated values of F .Here we used a threshold, | F | < 1, noting that for a Gaussian distribution 68% of data values is within ± 1σ of the mean.Despite the fact that 30 min downward N 2 O fluxes are only partly removed by such criterion (Sect.4.4), at both sites ensemble EC flux statistics get closer to the whole period net flux values estimated by automatic chamber technique (Tables 3 and 4).

Conclusions
EC measurements of N 2 O fluxes with today's commercially available trace gas analyzers for N 2 O are still a challenge, and careful consideration of instrument performance is needed.Moreover, for this case study, the special condition of turbulent trace gas measurements in the forest trunk space requires an in-depth assessment and evaluation of the data obtained.Therefore, the focus of this paper was on quality control aspects related to data processing as well as an error analysis related to flux sampling.With respect to data processing, our results highlight that fringe effects in the N 2 O signal, measured by TDL spectrometers (TGA100 and TGA100A, Campbell Scientific Inc.), can have a strong impact on the quality of the N 2 O EC flux values.Although an active thermal control of the TDL enclosure in theory could help to partially eliminate this effect (Billesbach et al., 1998), further tests in the field are needed to assess the efficiency.On the other hand, this case study has demonstrated that signal processing strategies are still a key issue to assure the quality of trace gas flux measurements based upon such complex systems (Werle et al., 2004).In this context, the concept of the Allan variance is a valuable tool to characterize system stability and in the time domain it provides similar information as spectral analysis in the frequency domain.It was found that during post sampling data processing a high-pass filter time constant of 50 s was able to reduce the fringe effect.The LDT method and RMF method with time constant > 100 s (not shown here) lead to increased scatter in fluxes during periods characterized by low frequency variability in concentrations, mainly due to instrument drift.
Flux error analysis, traditionally used in the micrometeorological community for energy and CO 2 fluxes, has been applied to N 2 O flux measurements, in order to identify uncertainty of fluxes caused by instrumentation problems and systematic as well as random errors.Although for our EC measurement systems systematic errors due to low pass filter effects of measured fluxes were rather small, we demonstrated that the cospectral transfer function method is a suitable approach for correcting fluxes measured within canopy layer.where m = N/k is the number of subsamples and A s is the time-average of the signal X over subsample period s of size k, given by Assuming that the time series data is sampled at constant sampling frequency f s , then the time τ = k/f s is the integration time or the averaging time of subsample periods under the assumption that no dead time losses due to signal processing occurs (Werle et al., 1993).
According to Percival and Guttorp (1994), the Allan variance at scale k is directly related to the variance of the Haar wavelet coefficients at the same scale.Then an alternative estimator for the Allan variance is Where d j,k are the wavelet coefficients for scales k = 1,2,4,...,N/2, derived applying the Haar wavelet transform to the time series X (Percival and Guttorp, 1994).
The bottom panel of Fig. A1 shows the Allan variance curves of the simulated time series X, estimated by using Eq.(A1) and Eq.(A3) as a function of the integration time τ .
The Allan variance decreases as τ −1 when white noise dominates.At longer integration times, the Allan variance starts to increase, due to the signal drift.If a linear drift dominates, then the increase of the Allan variance obeys to τ 2 law.

Appendix B Footprint analysis
Footprint analysis for the Sorø site was already published by Pihlatie et al. (2005) and it is not repeated in this study.According to Pihlatie et al. (2005), the area contributing 85% to the EC flux lies within 60 m (x/ h c = 2.4) around the measurement mast.
At Kalevansuo site footprint functions for passive tracers released from the forest floor were calculated with the forward Lagrangian stochastic model as described by Rannik et al. (2000Rannik et al. ( , 2003)).The model predicted the horizontal distribution of the surface sources of the flux measurements for three selected wind direction (WD) sectors (140 • < WD < 190 • , 190 • < WD < 240 • and 240 • < WD < 320 • ) and for two stability classes (near-neutral and unstable conditions, defined for values of |L| > 200 and −200 < L < 0 respectively, where L is the Obukhov length measured above canopy).As fluxes and characteristics of turbulence were measured only at two heights -one within the canopy and one above -the forms of the profiles of flow statistics were adopted from the work by Rannik et al. (2003).However, to account for the actual flow characteristics the profiles were scaled to go through the present observations.Estimated footprint functions were rather similar for different wind direction sectors and they show a rather small influence of stability conditions at the sub-canopy reference height z/ h c = 0.25.The upwind distance x corresponding to 85% of cumulative footprint values was about 30 m (x/ h c = 1.87).

Fig. 1 .
Fig. 1.Example of 1 h time series of N 2 O concentration measured at Kalevansuo (18 May 2007, 15-16 h) and Sorø (15 May 2003, 12-13 h), showing the effect of optical interference fringes (a and b).The sonic temperature signals are also displayed for comparison (c and d).Dark lines represent linear trend (LDT) and running mean (RMF) with different time constant applied to the data.

Fig. 2 .
Fig. 2. (a) and (b): Allan variance plot of N 2 O and sonic temperature time series displayed in Fig. 1a, c (Kalevansuo site).(c) and (d): The corresponding normalized spectral densities.Lines show the slope of different domains characterizing the signals (see the text).
shows the corresponding Allan variance and FFT spectra of N 2 O and T signals measured at Kalevansuo.In the lower part of Fig. 2 we can see that there www.biogeosciences.net/7/427/2010/Biogeosciences, 7, 427-440, 2010

Fig. 4 .
Fig. 4. Ensemble averaged cospectra of sensible heat and N 2 O fluxes measured under unstable stratification during the Kalevansuo (a and b) and Sorø (c and d) campaigns.The wind velocity was 0.8 m s −1 and 0.6 m s −1 for Kalevansuo and Sorø respectively.The solid line is the fitted cospectral model (Eq. 1) and dashed line indicates the theoretical inertial sub-range slope.

Fig. 5 .
Fig. 5. Example of normalized cospectra of sensible heat (open circle) and carbon dioxide (open down triangle) fluxes measured under unstable stratification during the Kalevansuo campaign.The solid curve is the fitted cospectral model (Eq. 1) and the plus and cross symbols are the predicted CO 2 cospectra computed by multiplying the cospectral model by the theoretical and empirical transfer functions for CO 2 respectively.

Fig. 6 .
Fig. 6.Example of normalized cospectra of sensible heat (open circle) and N 2 O (down triangle) fluxes measured under unstable stratification during the (a) Kalevansuo and (b) Sorø campaigns.The solid curve is the fitted cospectral model (Eq. 1) and the dash-dotted line is the predicted N 2 O cospectra computed by multiplying the cospectral model by the theoretical transfer function for N 2 O.The open and closed down triangles refer to positive and negative values respectively.
Figure 7 (top panels) shows the frequency distributions of relative flux error F = δF /F , where F is the flux value calculated over the averaging period T = 30 min.The relative flux error for N 2 O flux is larger than the one estimated for sensible heat flux.For both fluxes the relative random uncertainty decreases with increasing flux magnitude.Moreover, in case of N 2 O fluxes the relative errors are larger for negative flux values.This result indicates statistically less significant values in case of downward fluxes.Recently, Kroon et al. (2009) presented a detailed analysis of random and systematic uncertainty of N 2 O flux measured by the EC technique.The random uncertainty, which accounted for 90% of their estimates of the total uncertainty, was calculated according to the error analysis introduced by Lumley and Panofsky

Fig. 7 .
Fig. 7.In the top panels, the distribution curves of the relative flux error as estimated by δF /F for sensible heat and N 2 O fluxes for Kalevansuo and Sorø datasets.Bottom panels show the histograms of 30 min N 2 O fluxes [µg N m −2 h −1 ] prior (black bar) and after (grey bar) the random flux error criterion F < 1.

Fig. 8 .
Fig. 8. Daily mean of N 2 O fluxes measured by eddy covariance (top and middle panels) and automatic chambers (AC, bottom panels) during April-June 2007 at Kalevansuo pine forest and during May 2003 at Sorø beech forest.Eddy covariance fluxes are calculated by using linear detrending (EC-LDT) and running mean filter (EC-RMF).Error bars stand for standard error of the mean.

8 Figure A1 .
Figure A1.Top panel: Simulated time series data containing white noise and a linear 9 negative drift.Bottom panel: Allan plots of the simulated data, computed by Eq.A1 10(solid line) and by Eq.A3 (dashed line).11

Fig. A1 .
Fig. A1.Top panel: Simulated time series data containing white noise and a linear negative drift.Bottom panel: Allan plots of the simulated data, computed by Eq.A1 (solid line) and by Eq.A3 (dashed line).

Table 1 .
The setup details of the two EC-TDL systems.

Table 2 .
Fitting parameter values of cospectral model (Eq. 1) applied to sub-canopy sensible heat cospectra measured during daytime at Kalevansuo and Sorø site.

Table 3 .
Mean and median fluxes of N 2 O measured by eddy covariance (EC) and automatic chambers (AC) in Kalevansuo during 25 April-26 June 2007.All fluxes are in µg N m −2 h −1 .

Table 4 .
Mean and median fluxes of N 2 O measured by eddy covariance (EC) and automatic chambers (AC) in Sorø during 3 May-31 May 2003.All fluxes are in µg N m −2 h −1 .due to the instrumental drift.The RMF method reduces the scatter and variability of the fluxes, and at the same time producing an increase of the estimated average N 2 O emission, which is notable in Kalevansuo and relatively small in Sorø dataset.Again this suggests stronger effects of optical interference fringes during the Kalevansuo campaign.