The measurement site was a 6.9 ha field cultivated with RCG, a perennial bioenergy crop. The site was located in the rural area of Maaninka (merged with the city of Kuopio 1 January 2015), eastern Finland (63∘9′48.69′′ N, 27∘14′3.29′′ E). Long-term (reference period 1981–2010; Pirinen et al., 2012) annual air temperature in the region is 3.2 ∘C, the coldest month of the year is February and the warmest is July, with monthly mean air temperature being -9.4 and 17.0 ∘C, respectively. The annual precipitation in the region is 612 mm. Part of this precipitation amount falls as snow. Snow cover season starts in October and lasts until the end of April with a maximum snow cover of approximately 50 cm. The RCG crop at the Maaninka site was fertilized in the beginning of the growing season (late May), resulting in a large emission pulse of N2O. The site was applied with an N–P–K–S fertilizer containing 76 kg N ha-1, based on ammonium nitrate (NO3–N / NH4–N = 47:53). The canopy height developed throughout the growing season from about 10 cm in mid-May to 1.7 m by late June. The increase in plant height was almost linear in the period between these two times, and from July onwards plant height grew slowly up to 1.9 m.

The soil at the study site is classified as fine sand to coarse silt (particle size 0.03–0.06 mm). According to the World Reference Base for Soil Resources (WRB) system (FAO, 2006), the soil is classified as Regosol. The soil pH varies from 5.4 to 6.1 within the ploughing depth from the surface to about 30 cm, electrical conductivity between 960 and 3060µs cm-1 and soil organic matter content between 3 and 11 %. The average C / N ratio in the ploughing depth is 14.9 (ranging from 14.1 to 15.7). The soil particle density is about 2.65 g cm-3 within the soil depth from the surface to about 20 cm.

Measurements were conducted by the University of Helsinki (UH) and by the University of Eastern Finland (UEF), operating separate EC systems based on two different sonic anemometers. The UH measurement set-up included a 3-D ultrasonic anemometer (USA-1, METEK GmbH, Elmshorn, Germany) to acquire the wind components. The anemometer was installed on top of a pole, with a measurement height of 2.2 m. The measurement height was raised to 2.4 m on 30 June 2011 due to the RCG growth. The gas analysers were situated in an air conditioned cabin located about 15 m east from the anemometer pole. This wind direction (50–110∘ sector) was therefore discarded from further analysis due to possible disturbances to flux measurements. Sample inlets for gas analysers were located 10 cm below the anemometer. The N2O instruments operated by the UH were the instrument based on tunable diode laser CS-TDL (model TGA100A, Campbell Scientific Inc.) and two instruments based on continuous-wave quantum cascade lasers, AR-CW-QCL (models CW-TILDAS-CS, Aerodyne Research Inc., see e.g. Zahniser et al., 2009; Lee et al., 2011) and LGR-CW-QCL (model N2O / CO-23d, Los Gatos Research Inc., see e.g. Provencal et al., 2005). Sampling lines of AR-CW-QCL and LGR-CW-QCL were heated slightly above ambient temperature in order to prevent water condensing on the lines. CS-TDL used a dryer just before the instrument and no sampling line heating was used. The flow rates and tube dimensions were chosen to correspond to a turbulent flow regime except that the larger diameter of the sampling line of the LGR-CW-QCL analyser resulted in a laminar tube flow for that instrument (see Sect. 3.1 below). Further details of the instruments used are given in Table 1 and details of the different set-ups are given in Table 2.

The maintenance of CS-TDL was the most demanding of the compared instruments. It uses liquid nitrogen to keep the laser source at the operating temperature, and the Dewar was filled up twice a week. The instrument CS-TDL was calibrated in the beginning of the campaign. Further, the operating parameters of the analyser, such as laser current and laser, housing and detector temperatures, were checked once a week and after power failures. In addition, the shape and intensity of the absorption line were checked at the same time. These checks were assumed to guarantee calibration stability of the instrument to a reasonable degree. In addition, the inlet filter of CS-TDL was changed once a month.

The AR-CW-QCL was calibrated and its operating parameters were fine-tuned at the site after instrument installation. The instrument manufacturer provided a software upgrade during the campaign to conduct the real-time water vapour correction to the trace gas concentration data analysed by the instrument. In addition, the operating parameters were fine-tuned a few times on-line by the instrument manufacturer during the campaign.

LGR-CW-QCL was used in the campaign later (see Sect. 2.6 for details). The factory calibration of LGR-CW-QCL was checked but no deviation was observed within the uncertainty range of the calibration gases. After about 2 weeks of operation, the laser drifted out of the tuning range and the laser offset current was tuned manually to enable correct operation again. No calibration of the instruments AR-CW-QCL and LGR-CW-QCL was performed during the campaign as these analysers were expected to be very stable according to manufacturers' information.

The UEF set-up included a pulsed quantum cascade laser spectrometer AR-P-QCL (model QC-TILDAS-76-CS, Aerodyne Research Inc., Billerica, MS, USA, see McManus et al., 2005), an infrared gas analyser (IRGA, model Li-6262) and a 3-D sonic anemometer (model R3-50, Gill Instruments, Ltd., Hampshire, UK) for fast response gas concentration and wind component measurements (Tables 1 and 2). The heated intake tubes for the laser spectrometer and IRGA were installed on either side of the sonic anemometer, all mounted on a boom on an adjustable instrument mast. The mast height was set at 2.0 m above the soil surface in the beginning of the campaign. To adjust to the increasing plant height, the mast was raised to 2.5 m during mid-June. AR-P-QCL was set up to measure the N2O, CO2 and water vapour mixing ratios simultaneously, while the IRGA was used to monitor the CO2 and water vapour mixing ratios. Both trace gas analysers were calibrated against standard gases a minimum of once a month during the campaign; in particular, AR-P-QCL was calibrated every 2–3 weeks with two standard gases of 299 and 342 ppb. The calibration slope of AR-P-QCL did not change by more than 7.6 % throughout the campaign and maximum 6.1 % between consecutive calibrations. Thus, 6.1 % can be considered as the maximum flux systematic error arising from calibration accuracy of this instrument.

A weather station set up on another mast close to the EC mast monitored the supporting meteorological variables. The weather station mast height was also adjusted according to the changes in the EC mast height. Supporting measurements included air temperature and relative humidity (model: HMP45C, Vaisala Inc.) using radiation shield, atmospheric pressure (model CS106 Vaisala PTB110 Barometer), wind speed and direction (model 03002-5, R.M. Young Company) and several other variables not used in the current study. Data were collected using a datalogger (model CR3000, Campbell Scientific Inc.). Except air pressure (stored as hourly averages), meteorological data were stored as 30 min averages. Short gaps in the data were filled using linear interpolation, but when air temperature, relative humidity, pressure or rainfall data were missing for longer periods, data from Maaninka weather station operated by the Finnish Meteorological Institute located about 6 km south-east from the site were used.

Measurements were sampled at 10 Hz frequency. In order to eliminate spikes, filtering was performed according to the standard approach (Vickers and Mahrt, 1997), where the high-frequency EC data were de-spiked by comparing two adjacent measurements. If the difference between two adjacent concentration measurements of N2O was greater than 20 ppb, the following point was replaced with the same value as the previous point.

The spectroscopic correction due to water vapour impact on the absorption line shape was applied along with the Webb–Pearman–Leuning (WPL) dilution correction due to water vapour on high-frequency raw concentration output XC (mixing ratio with respect to moist air, uncorrected for spectroscopic effect) according to χC=XC1-(1+b)χV. Here χC and χV are the instantaneous mixing ratios of N2O and water vapour with respect to dry air. The spectroscopic correction coefficient b was determined experimentally for each instrument (Table 1) by measuring the response of the instrument (output XC) to sample air of standard gas (constant χC) with varying water content χV. The correction was not necessary for CS-TDL as a dryer installed after the air intake point on the sampling line dried the air sample before the optical cell. LGR-CW-QCL corrected for the water vapour effect using a built-in module in the LGR data acquisition software; the same applied to AR-CW-QCL after a software update in July 2011.

Prior to calculating the turbulent fluxes, a 2-D rotation (mean lateral and vertical wind equal to zero) of sonic anemometer wind components was done according to Kaimal and Finnigan (1994) and all variables were linearly de-trended. The EC fluxes were calculated as 30 min covariances between the scalars and vertical wind velocity following commonly accepted procedures (e.g. Aubinet et al., 2000). Time lag between the concentration and wind measurements induced by the sampling lines was determined by maximizing the covariance. For CS-TDL, the lag was determined by maximizing the covariance for the high flux period only (day of year (DOY) 144–146) because in other periods the lag was not well defined by using this method. The final processing (instruments CS-TDL, AR-CW-QCL and LGR-CW-QCL) was done by fixing the time lag to avoid unphysical variations of lag due to random flux errors. For the AR-P-QCL system, the lag was determined by maximising the covariance for CO2, and the same lag was assigned to N2O. This was to use the instrument's ability to also measure CO2, therefore enabling the use of a much better signal-to-noise ratio for determinating lag time. Spectral corrections were applied to account for the low- and high-frequency attenuation of the covariances (Sect. 2.4). Then, the humidity effect on temperature flux was accounted for after Schotanus et al. (1983). All data processing was performed with post-processing software EddyUH (http://www.atm.helsinki.fi/Eddy_Covariance/EddyUHsoftware.php).

Low- and high-frequency variations in the measured signal are attenuated due to data acquisition and processing, and by a non-ideal measurement system (e.g. Moore, 1986; Moncrieff et al., 1997; Rannik and Vesala, 1999; Massman, 2000). Block averaging and de-trending of data acts as a high-pass filter, thus damping low-frequency changes (Rannik and Vesala, 1999; Finnigan et al., 2003). Turbulent fluctuations occurring at high frequencies are attenuated due to the measurement system's limitations. Gas analyser's finite frequency response, attenuation of fluctuations in the sampling line, spatial separation between the anemometer measurement head and sampling line inlet affect the attenuation of high-frequency fluctuations in the signal.

The observed flux (Fm) can be formally presented as the integral over the convolution of the true co-spectrum (Co, unaffected by frequency attenuation) with the co-spectral transfer function as Fm=∫0∞T(f)Co(f)df, where the co-spectral transfer function T(f) can be presented as the convolution of respective low-frequency TL(f) and high-frequency TH(f) transfer functions. For details on the low-frequency transfer function due to high-pass filtering and/or finite averaging period, see Rannik and Vesala (1999).

For evaluation of the instrument frequency performance and subsequent high-frequency flux corrections during post-processing, the high-frequency transfer function of the EC system was estimated (Aubinet et al., 2000) as the ratio of the observed and un-attenuated flux (Horst, 1997). The co-spectral transfer function TH(f) for a system behaving as a first-order response sensor can be described by TH(f)=11+(2πfτ)2, where f is the natural frequency and τ the (first-order) response time of the attenuator (sensor or the system in total) (Horst, 1997). The effective transfer function of the EC system for different instruments was estimated as the ratio of co-spectral density of scalar flux relative to co-spectrum of sensible heat flux (Aubinet et al., 2000). Such a procedure assumed that temperature measurements were not affected by attenuation (true for the sonic anemometer) and includes normalization with integral over frequencies not affected by attenuation.

Turbulent fluxes averaged over a limited time period have random errors because of the stochastic nature of turbulence (Lenschow et al., 1994; Rannik et al., 2006) as well as due to noise presented in measured signals (Lenschow and Kristensen, 1985).

The random error of the flux was evaluated as 1 standard deviation of the covariance error, hereafter in the manuscript denoted by δF. It was defined through the variance of the distribution of the individual flux realization around the ensemble mean (e.g. Lenschow et al., 1994). Theoretically, there are several approaches to approximate the same error estimate; see e.g. Rannik et al. (2009). Currently, the flux random error was calculated according to the method implemented in EddyUH, the method proposed by Finkelstein and Sims (2001). The method evaluates the error in the time domain through integration of the auto-covariance and cross-covariance functions of the vertical wind speed and the scalar concentration according to δF≈1n∑p=-mmw′w′‾(p)c′c′‾(p)+∑p=-mmw′c′‾(p)c′w′‾(p), where w′w′‾(p)=1n∑i=1n-pw(ti)-w‾w(ti+p)-w‾. In calculations, we used m=200 (corresponding to 20 s) to ensure that integration of the covariance functions was performed over times exceeding the integral timescale of turbulence. This mathematically rigorous method provides estimates for the random uncertainty of the flux measurements for every flux averaging period.

Random uncertainty of the observed covariance due to presence of noise in instruments signal, giving essentially the lowest limit of the flux that the system is able to measure, was expressed in its simplest form as δF,noise=σwσnoisefT, where σw and σnoise denote the standard deviation of the turbulent record of vertical wind speed and the standard deviation of instrumental noise as observed at frequency f, and T denotes the flux averaging period. The expression above assumes that the noise component of the vertical wind speed measurement is negligible. In this study, we use the method developed by Lenschow et al. (2000) and applied to EC fluxes by Mauder et al. (2013) to estimate the flux error due to instrumental noise. Lenschow et al. (2000) derived the method to estimate the instrumental random noise variance (σnoise)2 from the auto-covariance function of the measured turbulent record close to zero-shift, enabling one to determine the error for each half-hour flux averaging period.

The random flux error δF is the result of limited sampling in time and/or in space of a stochastic turbulence realization. Its expression includes the covariance and cross-covariance functions of turbulent records; it therefore, in addition to variances and covariances, accounts for the respective integral timescales of turbulent records. The error δF also incorporates the contribution due to instrumental noise and is therefore larger than δF,noise.

The error δF,noise instead does not depend on the integral timescale of turbulence; it is therefore mainly determined by the instrumental noise characteristics and less by the observation conditions (only via σw). Assuming no true turbulent variation of concentration and thus zero flux, the calculated flux will be generally non-zero due to noise in the instrumental signal. Evidently the system will not be able to detect the fluxes smaller than the ones obtained from the expression for δF,noise. Therefore, this is the minimum flux that the EC system can detect and δF,noise proves useful in characterising the instrumental limitation to detect small fluxes.

If an average over fluxes Fi (i=1…N) is calculated, each of these representing a flux value observed over averaging period T and being characterized by an error δF,i, then the error of the average flux F=1N∑i=1NFi is expressed as Δ<F>=∑i=1N(δF,i)2N2. This expression will be used to estimate the random errors of the average fluxes in Sect. 3.4.

The intercomparison measurements were performed from the beginning of the growing season in April until November 2011. According to instrumental data coverage, the period was divided into three sub-periods for the instrument evaluation and flux analysis purposes. During period I, DOY 110–181 (20 April–30 June 2011), the measurements of CS-TDL, AR-CW-QCL and AR-P-QCL were available; during period II, DOY 206–271 (25 July–28 September 2011), all instruments were measuring; and during period III, DOY 272–324 (29 September–20 November 2011), all other except CS-TDL were operational. Prior to analysis data quality screening was performed. The measurements corresponding to wind direction interval 50–110∘ were excluded as possibly affected by the instrumental cabin. In addition, quality screening was performed according to Vickers and Mahrt (1997) by applying the following statistics and selection thresholds: data with N2O concentration skewness outside (-2, 2), kurtosis outside (1, 8) or Haar mean and Haar variance exceeding 3 were rejected. Applying the same statistics and thresholds as for N2O, additional quality screening of N2O fluxes was performed according to H2O concentration statistics for AR-CW-QCL and AR-P-QCL due to the impact of the spectroscopic and dilution corrections on fluxes and according to CO2 concentration statistics for AR-P-QCL because the lag obtained for CO2 was assigned to N2O in the case of this instrument.

The applied quality criteria were used to ensure exclusion of the system malfunctioning as well as unphysical and/or unusual occasions. No quality screening for stationarity was performed as the focus of the study was the instrumental intercomparison, which was not affected by occasional non-stationary conditions included in the analysed data set.

Spectral analysis was performed to study the frequency performance of the instruments. In general, averaging over long periods should lead to better spectral statistics. However, aggregating over different periods might lead to biased results as the spectra do not necessary follow the idealized normalizations in frequency scale, considering also that spectral scaling depends on stability. Therefore, we aimed to use optimal averaging period over several hours for similar conditions in terms of wind speed and stability. For the period of 26 May from 7:00 to 13:00 EET (eastern European time) when the conditions were moderately unstable (average wind speed of the period 3.2 m s-1 and sensible heat flux 50 W m-2), the calculated spectra exhibited very clear and systematic patterns for temperature as well as N2O concentration records measured by the three instruments (Fig. 3). In spite of high fluxes registered by the instruments during this period, the CS-TDL N2O signal was dominated by noise almost over the whole frequency range presented. For AR-CW-QCL, almost no evidence of noise could be observed in the power spectral plot (multiplied with frequency). The older Aerodyne instrument, the AR-P-QCL, revealed an increase of the spectral density only at the high-frequency end of the power spectrum, characteristic of noise contribution. The co-spectra of all three instruments showed smooth patterns, the shape being consistent with the co-spectral model by Kaimal et al. (1972) but slightly shifted in frequency scale. At the high-frequency ends of the presented co-spectra the N2O signal curves deviate from the theoretical as well as from temperature co-spectra, indicating attenuation of signals at high frequencies by the measurement systems.

The same time period was used to estimate the frequency response of the N2O eddy covariance systems according to the method described in Sect. 2.4 (Fig. 4). The time constants estimated by making use of the co-spectra presented in Fig. 3 and Eq. (2) for CS-TDL, AR-CW-QCL and AR-P-QCL were 0.12, 0.07 and 0.08 s, respectively. Note that these time constants characterise the frequency response of the systems in total.

Although the response time obtained for the AR-P-QCL system from high flux period was 0.08 s, the analysis of the response time from measured CO2 signal for several other periods yielded the average response time 0.15 s. The N2O signal was synchronized with CO2 by using the lag determined for CO2 and theoretically the N2O response time does not differ from that of CO2 under turbulent tube flow regime; hence we choose the constant value 0.15 s for co-spectral corrections throughout the campaign for this instrument.

Spectral analysis was also performed for the period when LGR-CW-QCL measurements were available. For comparison purposes, the results of the time period of 4 August from 00:30 to 4:00 EET are presented for AR-CW-QCL and LGR-CW-QCL instruments (Fig. 5). The period was chosen with relatively high fluxes (with LGR-CW-QCL measurements available) and similar stability and wind conditions (average wind speed of the period of 0.94 m s-1 and sensible heat flux of -37.5 W m-2). The power spectra of both instruments revealed a contribution of noise at the high-frequency end of the spectra, which was more pronounced for LGR-CW-QCL. The co-spectra were more scattered when compared to high flux period (Fig. 3). Estimation of the frequency response of the systems based on this period was uncertain due to scatter and could not be used as the basis for co-spectral corrections for LGR-CW-QCL.

The main difference in the flow set-ups of the systems concerned LGR-CW-QCL. With a larger tube diameter and slightly lower flow rate, the flow regime was likely laminar (Re ≈2000), whereas for other instruments it was clearly turbulent (Re ≥4600). It is well established that under laminar flow regime tube flow attenuates turbulent fluctuations of concentration much more than under turbulent flow. According to the expression for tube attenuation in laminar flow regime (Foken et al., 2012) the first-order response time for LGR-CW-QCL flow set-up would be 0.37 s (estimated for N2O). For turbulent flow (ARI-CW-QCL set-up) the theoretical response time for tube damping is much smaller (0.01 s) than the response time obtained from the co-spectra (0.07 s), suggesting that the system's response was dominated by the instrumental response.

The frequency response of the LGR-CW-QCL system was further determined from the co-spectral analysis of the CO signal, and we obtained the value of 0.26 s. We also determined the experimental response time for water vapour from several periods corresponding to low-humidity conditions (RH < 40 %) and we consistently found the value around 0.35 s (for LGR-CW-QCL system). For comparison, the response time for H2O measured by the ARI-CW-QCL system was determined to be 0.10 s. Damping of water fluctuations in sampling lines is stronger than for other scalars as evidenced by experimental studies (e.g. Mammarella et al., 2009). This is due to adsorption/desorption of water molecules on tube walls. This explains the difference between the response times obtained from CO and H2O. Thus, we believe that a value of 0.26 s characterises well the first-order response time of the LGR-CW-QCL set-up for N2O, and we use this value in co-spectral corrections. Note, however, that a higher response time of the LGR-CW-QCL system does not mean a slower instrument performance because the system has more damping primarily in the sampling line due to a lower flow rate and larger tube diameter (Table 2).

The frequency response times determined in this section were used in performing the co-spectral corrections (Table 2) as described in Sect. 2.4; the typical magnitudes of these corrections are presented in Table 3.

The method by Lenschow et al. (2000) described in Sect. 2.5 enables the calculation of the instrumental noise for each 30 min period and the resulting flux uncertainty due to instrumental noise. Figure 6a shows the estimated signal's noise statistics with upper and lower percentiles and quantiles (boxes), with a median value in the middle. For all instruments except LGR-CW-QCL, the distributions are very narrow and different percentiles cannot be separated from the plot (for values see Table 1). This tells us that the noise levels of the three instruments are very stable, but the noise level of LGR-CW-QCL somewhat varies. In a comparison of the instruments, AR-CW-QCL has by far the lowest noise level of around 0.12 ppb (standard deviation of the signal's noise at 10 Hz frequency). The two instruments, LGR-CW-QCL and AR-P-QCL, are characterized by a similar noise level (around 0.5 ppb), while CS-TDL signals show the highest noise level (2 ppb). Consequently, these instrumental noise levels are reflected in the random errors of fluxes, determining essentially the minimum flux level that each instrument is able to measure at a given flux averaging interval (30 min period). For AR-CW-QCL, the respective lowest flux is around 10-2 nmol m-2 s-1 (as given by median in Fig. 6b), for LGR-CW-QCL and AR-P-QCL around 4 × 10-2 nmol m-2 s-1 and for CS-TDL 0.15 nmol m-2 s-1.

The frequency distributions of the total flux random errors, calculated according to Eq. (3), are naturally higher than the flux error due to instrumental noise only. It can be observed that in the case of full flux random error, the difference between different instruments is reduced (Fig. 6b) because in addition to instrumental noise impact, this error statistic also incorporates the flux uncertainty due to the stochastic nature of turbulence. The relative random errors (Fig. 6c) are the largest for CS-TDL (being of the order of 100 % and in most cases less than ±300 %) and the smallest for AR-CW-QCL instruments (median around 30 % and the error mostly less than 100 %). It is the signal's noise of the instrument that contributes to the random error of the flux, determining which instrument is able to detect the lowest fluxes. In the case of CS-TDL the low-frequency signal drifting can also enlarge the total random error of the calculated flux.

It was observed that the fluxes calculated from CS-TDL measurements during the low flux period were dominated by stochastic uncertainty, being frequently of the order of the random uncertainties of the fluxes (Sect. 3.2). Therefore, the fluxes averaged over the 30 min period were compared for this instrument with AR-CW-QCL results over the period DOY 110–182, which included the high emissions episode starting on DOY 144 and exhibiting elevated fluxes until approximately DOY 155. In general, the fluxes with high magnitudes obtained by CS-TDL compared well with those of obtained by AR-CW-QCL (Fig. 7a). The AR-P-QCL system, as compared with AR-CW-QCL, showed systematically lower fluxes during the given period of high fluxes (slope 0.70). In spite of the lower noise level of this instrument, the coefficient of determination for this instrument (0.63) was lower than that for CS-TDL (0.77) in comparison to the fluxes as measured by AR-CW-QCL.

During the second observation period, when fluxes were much lower, CS-TDL was not able to determine fluxes with sufficiently small error and the correlation with AR-CW-QCL at the 30 min averaging level was very low (Fig. 7c). At around zero fluxes as measured by AR-CW-QCL, the results of CS-TDL showed scattered values visually between ±2 nmol m-2 s-1. The noise level of CS-TDL around 2 ppb translates into a flux uncertainty due to instrumental noise of about 0.05 to 0.3 nmol m-2 s-1. The total flux error δF was within the range of 0.1 to 0.45 nmol m-2 s-1 (upper and lower quantiles of the distribution in Fig. 6b). We analysed the range of variation of CS-TDL fluxes during the given period DOY 206–272, conditionally selecting the observations when the observed fluxes by AR-CW-QCL were absolutely smaller than 0.15 nmol m-2 s-1 (90 % of N2O flux random errors for AR-CW-QCL less than this value during the given period). The respective N2O fluxes as determined by CS-TDL were characterized by the upper and lower quantiles of -0.27 and 0.52 nmol m-2 s-1. This is consistent with the upper quantile of the flux error distribution for CS-TDL. Therefore, the fluxes of CS-TDL, corresponding to close-to-zero fluxes as determined by AR-CW-QCL, were consistent with the flux error estimates.

The comparison of the 30 min average fluxes calculated from two instruments, AR-CW-QCL and LGR-CW-QCL, revealed very good correspondence and high correlation (R2=0.90) even though those measurements corresponded to very low N2O fluxes. The slope close to unity and a negligible intercept indicates that there is no systematic bias between the measurements of these systems (Fig. 7d).

In order to evaluate the possible systematic differences, cumulative curves of the flux observations were calculated. No gap-filling of missing data was done, but instead only the half-hour periods were used when the results for all instruments were available. Thus, the cumulative sums are not assumed to represent the total emissions over the given periods, although rough estimates could be calculated by using the data coverage percentages presented in Table 4 to account for missing flux data. The summation of fluxes over the first and second periods reveals that CS-TDL gives the highest flux sums and AR-P-QCL the lowest, in particular during the first period (Fig. 8). The cumulative sums for fluxes obtained from AR-CW-QCL and LGR-CW-QCL measurements converge over periods II and III and show only small differences. Also, the cumulative fluxes measured by AR-P-QCL during these periods are very close to fluxes measured by the two other instruments. In order to assess the magnitude of the random errors in these differences, the random errors of the fluxes averaged over the three periods were calculated according to Eq. (5). The analysis revealed that the average fluxes for period II, obtained from the measurements of AR-CW-QCL and LGR-CW-QCL instruments, did not differ within calculated error limits, and were very close during period III to the result for AR-P-QCL (Table 4).

However, CS-TDL produced a 7 % higher total sum for the period of high fluxes (DOY 110–181 with an average flux of 0.87 nmol m-2 s-1 as determined by AR-CW-QCL) and a 29 % higher sum for the second period (DOY 206–271) compared to an average flux 0.142 nmol m-2 s-1 (average of AR-CW-QCL and LGR-CW-QCL results). The AR-P-QCL instrument determined for these two periods 36 and 13 % lower average fluxes, respectively. The possible reasons for this will be discussed in the next section. For the third period, the results of AR-P-QCL did not differ much from the results of the other two instruments.