Measurements were made in a boreal Scots pine (Pinus sylvestris) stand at the Station for Measuring Forest Ecosystem–Atmosphere Relations (SMEAR II) in Hyytiälä, Finland (61∘51′ N, 24∘17′ E; 181 m above sea level). The Scots pine stand was established in 1962 and reaches at least 200 m in all directions and about 1 km to the north . The site is characterized by modest height variation, and an oblong lake is situated about 700 m to the southwest of the forest station . Canopy height was 17 m, and the all-sided leaf area index (LAI) was approximately 8 m2 m-2 in 2015. EC measurements were done at 23 m height. Sunrise time varied from 02:37 in June to 07:55 in November, while sunset was at 22:14 at the beginning and 16:17 at the end of the measurement period. All results are presented in Finnish winter time (UTC+2), and nighttime is defined as periods with a photosynthetic photon flux density (PPFD) of <3 µmol m-2 s-1.

The EC setup consisted of an ultrasonic anemometer (Solent Research HS1199, Gill Instruments Ltd., England, UK) for measuring wind speed in three dimensions and sonic temperature; an Aerodyne quantum cascade laser spectrometer (QCLS; Aerodyne Research Inc., Billerica, MA, USA) for measuring COS, CO2, and water vapor (H2O) mole fractions; and an LI-6262 infrared gas analyzer (LI-COR, Lincoln, NE, USA) for measuring H2O and CO2 mole fractions. All measurements were recorded at 10 Hz frequency and were made with a flow rate of approximately 10 L min-1 for the QCLS and 14 L min-1 for the LI-6262. The PTFE sampling tubes were 32 and 12 m long for QCLS and LI-6262, respectively, and both had an inner diameter of 4 mm. Two PTFE filters were used upstream of the QCLS inlet to prevent any contaminants from entering the analyzer sample cell: one coarse filter (0.45 µm, Whatman) followed by a finer filter (0.2 µm, Pall Corporation) at approximately 50 cm distance to the analyzer inlet. The Aerodyne QCLS used an electronic pressure control system to control the pressure fluctuations in the sampling cell. The QCLS was run at 20 Torr sampling cell pressure. An Edwards XDS35i scroll pump (Edwards, England, UK) was used to pump air through the sampling cell, while the LI-6262 had flow control by an LI-670 flow control unit.

Background measurements of high-purity nitrogen (N2) were done every 30 min for 26 s to remove background spectral structures in the QCLS . In addition, a calibration cylinder was sampled each night at 00:00:45 for 15 s. The calibration cylinder consisted of COS at 429.6±5.6 ppt, CO2 at 408.37±0.05 ppm, and CO at 144.6±0.2 ppb. The cylinder was calibrated against the NOAA-2004 COS scale, WMO-X2007 CO2 scale, and WMO-X2004 CO scale using cylinders that were calibrated at the Center for Isotope Research of the University of Groningen in the Netherlands . The standard deviation calculated from the cylinder measurements was 19 ppt for COS mixing ratios and 1.3 ppm for CO2 at 10 Hz measurement frequency.

It has previously been shown that water vapor in the sample air can affect the measurements of COS through spectral interference of the COS and H2O absorption lines . This spectral interference was corrected for by fitting the COS spectral line separately from the H2O spectral line.

The computer embedded in the Aerodyne QCLS and the computer that controlled the sonic anemometer and logged the LI-6262 data were synchronized once a day with a separate server computer. Analog data signals from the LI-6262 were acquired by the Gill anemometer sensor input unit, which digitized the analog data and appended them to the digital output data string. Digital Aerodyne data were collected on the same computer with a serial connection and recorded in separate files with custom software (COSlog).

Atmospheric concentration profiles were measured with another Aerodyne QCLS at a sampling frequency of 1 Hz. Air was sampled at five heights: 125, 23, 14, 4, and 0.5 m. A multiposition Valco valve (VICI, Valco Instruments Co. Inc.) was used to switch between the different profile heights and calibration cylinders. Each measurement height was sampled for 3 min each hour. One calibration cylinder was measured twice for 3 min each hour to correct for instrument drift, and two other calibration cylinders were measured once for 3 min each hour to assess the long-term stability of the measurements. A background spectrum was measured once every 6 h using high-purity nitrogen (N 7.0; for more details, see ). The overall uncertainty of this analyzer was determined to be 7.5 ppt for COS and 0.23 ppm for CO2 at 1 Hz frequency . The measurements are described in more detail in .

In this section, we describe the processing steps of EC flux calculation from raw data handling to final flux gap filling and uncertainties. Figure  provides a graphical outline of all processing steps. The different processing options presented here are applied and discussed in Sect. . In the next section, the different processing schemes are compared to a “reference scheme”, which consists of linear detrending, planar-fit coordinate rotation, using CO2 time lag for COS, and experimental spectral correction. A subset of the data – nighttime fluxes processed with the reference scheme – was published in .

In order to check the contribution of different detrending methods to the resulting flux, we made flux calculations with different methods: block averaging (BA), linear detrending (LD), and recursive filtering (RF) using the same time lag (CO2 time lag) for all runs (Fig. S5).

The largest median COS flux (most negative) was obtained from RF (-12.0 pmol m-2 s-1), while the smallest median (least negative) flux resulted from BA (-10.7 pmol m-2 s-1), and LD (-11.3 pmol m-2 s-1) differed by 5.3 % from BA (Table ). The range of the 30 min COS flux was the largest (from -183.2 to 82.56 pmol m-2 s-1) when using the BA detrending method, consistent with a similar comparison in . In comparison, it was from -107.3 to 73.1 pmol m-2 s-1 for LD and from -164.9 to 36.8 pmol m-2 s-1 for RF. While it was surprising that RF resulted in a more negative median flux than BA, it is likely explained by the large variation in BA with compensating high negative and positive flux values as the positive flux values with BA and LD are higher than with RF. In addition, it has to be kept in mind that the fluxes were corrected for low-frequency losses, which in part also accounts for the effects of detrending.

For CO2, the largest median flux resulted from BA (-0.62 µmol m-2 s-1). The smallest median flux resulted from LD (-0.56 µmol m-2 s-1) and RF (-0.59 µmol m-2 s-1). The difference between median CO2 flux with BA and LD was 10.7 %.

The most commonly recommended averaging methods are BA and LD because they have less of an impact on spectra and require fewer low-frequency corrections. These are also the most used detrending methods in previous COS EC flux studies (Table ). RF may underestimate the flux , but as spectroscopic analyzers are prone to fringe effects under field conditions, for example, the use of RF might still be justified . Regular checking of raw data provides information on instrumental drift and helps to determine the optimal detrending method. It is also recommended to check the contribution of each detrending method to the final flux to better understand what the low-frequency contribution in each measurement site and setup is.

Different time lag methods resulted in slightly different time lags and COS fluxes. The most common time lags were 2.6 s from the COSlag, CO2lag, and DetLimlag methods and 1.5 s from RMlag, which was the lag window limit (Fig. ). Time lags determined from the COSlag and RMlag methods were distributed evenly throughout the lag window, whereas the lags from the CO2lag and DetLimlag methods were normally distributed, with most lags detected at the window center.

We also tested determining time lags from the most commonly used method of maximizing the absolute covariance. If the time lag was determined from the absolute covariance maximum instead of the maximum difference to a line between covariance values at the lag window limits, the COSlag and RMlag had most values at the lag window limits (Fig. S2). This resulted in a “mirroring effect” ; i.e., fluxes close to zero were not detected as often as with other methods since the covariance is always maximized, and the derived flux switches between positive and negative values of similar magnitude (Fig. S3). This issue should be taken into account in COS EC flux processing as absolute COS covariance maximum is by far the most commonly used method in determining the time lag in COS studies (Table ). To make the different methods more comparable, the time lags were, in the end, determined from the maximum difference to a line between covariance values at the lag window limits in this study. In this way, time lags were not determined at the window borders, and most of the methods had the final flux probability distribution function (PDF) peak approximately at the same flux values and had otherwise small differences in the distributions (Fig. ). The only method that was clearly different from the others was DetLimlag, which produced higher fluxes than other methods.

A constant time lag has been found to bias the flux calculation as the time lag can likely vary over time due to, for example, fluctuations in pumping speed . However, as the CO2lag was often the same as the chosen constant lag of 2.6 s, we did not observe major differences between these two methods. A reduced bias in the flux calculation with smoothed cross-covariance was introduced by , who recommended using this method for any EC system with a low signal-to-noise ratio. However, we do not recommend this as a first choice since the time lags do not have a clear distribution, and if the maximum covariance method is used, we find a mirroring effect with the RMlag in the final flux distributions.

By using the DetLimlag method, the COS time lag was estimated for 54 % of cases from COSlag, while the CO2lag was used as a proxy for the COS time lag in about 46 % of cases. Figure  shows that the raw covariance of COS only exceeds the noise level at higher COS flux values, and thus the COSlag is chosen by this method only at higher fluxes, as expected. At lower flux rates, and especially close to zero, the COS fluxes are not high enough to surpass the noise level, and thus the CO2lag is chosen.

The median COS fluxes were highest when the time lag was determined from the DetLimlag (-13.1 pmol m-2 s-1) and COSlag (-11.5 pmol m-2 s-1) methods (Table ). Using the COSlag results in both higher positive and negative fluxes and might thus have some compensating effect on the median fluxes. Constlag and RMlag produced the smallest median uptake (-11.1 pmol m-2 s-1), while the CO2lag had a median flux of -11.3 pmol m-2 s-1. The difference between the reference flux and the flux from the DetLimlag method was clearly higher (15.9 %) than with other methods (1.8 %) and had the largest variation (from -113.8 to 81.6 pmol m-2 s-1) and standard deviation (16.1 pmol m-2 s-1). This difference might become important at the annual scale, and as the most commonly used covariance maximization method does not produce a clear time lag distribution for DetLimlag or COSlag, we recommend using the CO2lag for COS fluxes as in most ecosystems the CO2 cross-covariance with w is more clear than the cross-covariance of COS and w signals.

The mean COS cospectrum was close to the normal mean CO2 cospectrum (compare Fig. a and c). The power spectrum of COS was dominated by noise as can be seen from the increasing power spectrum with increasing frequency for normalized frequencies greater than 0.2, which is similar to what was measured for COS by and for N2O by . The fact that COS measurements are dominated by noise at high frequencies means that those measurements are limited by precision and that they likely do not capture the true variability in COS turbulence signals. This is less of a problem for CO2, where white noise only starts to dominate at higher frequencies (normalized frequency higher than 3). Cospectral attenuation was found for both COS and CO2 at high frequency.

High-frequency losses due to, for example, attenuation in sampling tubes and limited sensor response times are expected to decrease fluxes if not corrected for . The median COS flux, when using the CO2 time lag and keeping low-frequency correction and quality filtering the same, was the least negative without any high-frequency correction (-9.7 pmol m-2 s-1), most negative with the experimental correction (-11.3 pmol m-2 s-1), and in between with the analytical correction (-11.0 pmol m-2 s-1; Fig. S6). Correcting for the high-frequency attenuation thus made a maximum of 14.2 % difference in the median COS flux. In addition, daytime median flux magnitudes increased from -15.0 to -16.9 pmol m-2 s-1 with the analytical correction and to -16.8 pmol m-2 s-1 with the experimental high-frequency correction. However, the relative difference was larger during nighttime, when flux magnitudes increased from -3.4 to -4.0 and -4.1 pmol m-2 s-1 with analytical and experimental methods, respectively.

Similar results were found for the CO2 flux, but the differences were smaller: without any high-frequency correction the median flux was the least negative at -0.48 µmol m-2 s-1, most negative with experimental correction (-0.56 µmol m-2 s-1), and in between with the analytical correction (-0.54 µmol m-2 s-1), thus making a maximum of 14.3 % difference in the median CO2 flux, similar to COS. Very similar results were found for CH4 and CO2 fluxes in , where the high-frequency correction made the largest difference in the final flux processing for closed-path analyzers. Similar to COS, CO2 flux magnitudes were also increased more during nighttime due to spectral correction than during daytime. Daytime median flux magnitude increased from -4.18 to -4.77 and -4.58 µmol m-2 s-1, and nighttime fluxes increased from 1.02 to 1.18 and 1.23 µmol m-2 s-1 when using analytical and experimental high-frequency spectral corrections, respectively. Flux attenuation was dependent on stability and wind speed for both correction methods, as also found in Mammarella et al. (2009; Fig. S7).

The site-specific model captures the cospectrum better than the model cospectrum by , as shown in Fig. . For high-frequency spectral corrections, it is recommended to use the site-specific cospectral model, as has been done in most previous COS studies (Table ).

In the following, storage change fluxes based on profile measurements are listed as default, with fluxes based on the constant profile assumption listed in brackets.

The COS storage change flux was negative from 15:00 until 06:00, with a minimum of -1.0 pmol m-2 s-1 (-0.6 pmol m-2 s-1) reached at 20:00. A negative storage change flux of COS indicates that there is a COS sink in the ecosystem when the boundary layer and effective mixing layer is shallow. Neglecting this effect would lead to overestimated uptake at the ecosystem level later when the air at the EC sampling height is better mixed. The COS storage change flux was positive from around 06:00 until 15:00 and peaked at 09:00 with a magnitude of 1.9 pmol m-2 s-1 (0.8 pmol m-2 s-1). The storage change flux made the highest relative contribution to the sum of measured EC and storage change fluxes at midnight with 18 % (13 %; Fig. c). The difference between the two methods was a minimum of 13 % at 11:00 and a maximum of 56 % at 09:00. The two methods made a maximum of 7 % difference in the resulting cumulative ecosystem flux, as already reported in .

The CO2 storage change flux was positive from 15:00 until around 04:00, with a maximum value of 0.62 µmol m-2 s-1 (0.38 µmol m-2 s-1) reached at 21:00. A positive storage change flux indicates that the ecosystem contains a source of carbon when the boundary layer is less turbulent and accumulates the respired CO2 within the canopy. As turbulence would increase later in the morning, the accumulated CO2 would result in an additional flux that could mask the gas exchange processes occurring at that time step. The CO2 storage change flux minimum was reached with both methods at 08:00, with a magnitude of -1.01 µmol m-2 s-1 (-0.52 µmol m-2 s-1) when the boundary layer had already started expanding, and leaves are assimilating CO2. The maximum contribution of the storage change flux was as high as 89 % (36 %) compared to the EC flux at 18:00, when the CO2 exchange turned to respiration, and storage change flux increased its relative importance (Fig. d). The difference between the two storage change flux methods for CO2 was a maximum of 53 % at 21:00 and a minimum of 13 % at midnight. The maximum difference of 5 % was found in the cumulative ecosystem CO2 flux when the different methods were used.

In conclusion, the storage change fluxes are not relevant for budget calculations, as expected, and have not been widely applied in previous COS studies (Table ) even though storage change flux measurements are mandatory in places where the EC system is placed at a height of 4 m or above according to the ICOS protocol for EC flux measurements . In addition, storage change fluxes are important at the diurnal scale to account for the delayed capture of fluxes by the EC system under low-turbulence conditions.

Calm and low-turbulence conditions are especially common during nights with stable atmospheric stratification. In this case, storage change and advective fluxes have an important role, and the measured EC flux of a gas does not reflect the atmosphere–biosphere exchange, typically underestimating the exchange. This often leads to a systematic bias in the annual flux budgets . Even after studies of horizontal and vertical advection, u* filtering still keeps its place as the most efficient and reliable tool to filter out data that are not representative of the surface–atmosphere exchange under low turbulence .

For COS, nighttime filtering is a more complex issue than it is for CO2. In contrast to CO2, COS is taken up by the ecosystem during nighttime depending on stomatal conductance and the concentration gradient between the leaf and the atmosphere. When the atmospheric COS mixing ratio decreases under low-turbulence conditions (due to nighttime COS uptake in the ecosystem), the concentration gradient between the leaf and the atmosphere goes down such that a decrease in COS uptake can be expected . Thus, the assumption that fluxes do not go down under low-turbulence conditions, as is the case for respiration of CO2, does not necessarily apply to COS uptake. Gap-filling the u*-filtered COS fluxes may therefore create a bias due to false assumptions if the gap filling is only based on data from periods with high turbulence. However, as we did not see u* dependency disappearing even with a concentration-gradient-normalized flux, the u* filtering and proceeding gap filling were applied here as usual to overcome the EC measurement limitations under low-turbulence conditions.

We determined u* limits of 0.23 m s-1 for COS and 0.22 m s-1 for CO2 (Fig. ). Filtering according to these u* values would remove 12 % and 11 % of data, respectively. If the storage change flux was excluded when determining the u* threshold, the limits were 0.39 and 0.24 m s-1 from CO2 and COS fluxes, respectively. The increase in the u* threshold with CO2 is because the fractional storage change flux is larger for CO2 than for COS (Fig. c and f). On the other hand, the u* limit for COS stayed similar to the previous one. With these u* thresholds the filtering would exclude 30 % and 13 % of the data for COS and CO2 respectively.

If fluxes are not corrected for storage before deriving the u* threshold, there is a risk of flux overestimation due to double accounting. The flux data filtered for low turbulence would be gap-filled, thereby accounting for storage by the canopy, but then accounted for again when the storage is released and measured by the EC system during the flushing hours in the morning . Thus, it is necessary to make the storage change flux correction before deriving u* thresholds and applying the filtering.

Three combinations of environmental variables (PAR, PAR and RH, and PAR and VPD) were tested using the gap-filling function (Eq. ). These environmental parameters were chosen because COS exchange has been found to depend on stomatal conductance, which in turn depends especially on radiation and humidity . Development of the gap-filling parameters a, b, c, and d over the measurement period is presented in Fig. S10. While the saturating function of PAR alone already captured the diurnal variation relatively well, adding a linear dependency on VPD or RH made the diurnal pattern even closer to the measured one, although some deviation is still observed, especially in the early morning (Fig. ). Therefore, the combination of saturating light response curve and linear VPD dependency was chosen. Furthermore, we chose a linear VPD dependency instead of a linear RH dependency due to smaller residuals in the former (Fig. S9). The mean residual of the chosen model was -0.54 pmol m-2 s-1, and the root mean square error (RMSE) was 18.7 pmol m-2 s-1, while the saturating PAR function with linear RH dependency had a mean residual of -0.84 and an RMSE of 19.3 pmol m-2 s-1, and the saturating PAR function had a residual of 0.97 pmol m-2 s-1 and an RMSE of 22.8 pmol m-2 s-1.

For COS fluxes, 44 % of daytime flux measurements were discarded due to the above-mentioned quality criteria (Sect. ) and low-turbulence filtering. As expected, more data (66 %) were discarded during nighttime. Altogether, 52 % of all COS flux data were discarded and gap-filled with the gap-filling function presented in Eq. (). The average of the corrected and gap-filled COS fluxes during the whole measurement period was -12.3 pmol m-2 s-1, while without gap filling the mean flux was 14 % more negative, -14.3 pmol m-2 s-1. This indicates that most gap filling was done for the nighttime data, when COS fluxes are less negative than during daytime.

For CO2, 41 % of daytime CO2 fluxes were discarded, while 67 % of fluxes were discarded during nighttime, altogether comprising 53 % of all CO2 flux data. CO2 fluxes were gap-filled according to standard gap-filling procedures presented in . The average CO2 flux after all corrections and gap filling was -2.14 µmol m-2 s-1, while without gap filling the mean flux was 39 % more negative, -3.53 µmol m-2 s-1. Similar to COS, CO2 fluxes are also mostly gap-filled during nighttime. As nighttime CO2 fluxes are positive, gap-filled fluxes include more positive values than non-gap-filled fluxes, thus making the mean flux less negative.

Although the COS community has not been interested in the cumulative COS fluxes or yearly COS budget so far, it is important to fill short-term gaps in COS flux data to properly capture the diurnal variation, for example. The gap-filling method presented here is one option to be tested at other measurement sites as well.

The uncertainty due to the chosen processing scheme was determined from a combination of eight different processing schemes, as described in Sect. , that were equally reliable but caused the most variation in the final COS flux (Table ). This processing uncertainty contributed 36 % to the total uncertainty of the 30 min COS flux, while the rest was composed of the random flux uncertainty (Fig. ). For the CO2 flux uncertainty, the processing was more important than for COS (48 %), but the random uncertainty still dominated the combined flux uncertainty. The random error of the CO2 flux was found to be lower than in for the same site, probably related to differences in the gas analyzers and overall setup. The mean noise estimated from was 0.06 µmol m-2 s-1 for our QCLS CO2 fluxes, while in it was approximately 0.08 µmol m-2 s-1 for LI-6262 CO2 fluxes at the same site. found the total random uncertainty of COS fluxes to be mostly around 3–8 pmol m-2 s-1, comparable to our results.

The relative flux uncertainty for COS was very high at low flux (-3 pmol m-2 s-1<FCOS<3 pmol m-2 s-1) values (8 times the actual flux value) but leveled off to 45 % at fluxes higher (meaning more negative fluxes) than -27 pmol m-2 s-1 (Fig. c). The total uncertainty of the CO2 flux was also high at low fluxes (-1.5 µmol m-2 s-1<FCO2<1 µmol m-2 s-1, uncertainty reaching 130 % of the flux at 0.17 µmol m-2 s-1) and decreased to 15 % at fluxes more negative than -11 µmol m-2 s-1 (Fig. d). Higher relative uncertainty at low flux levels is probably due to the detection limit of the measurement system.

The median relative random uncertainty of COS flux decreased from 0.35 for single 30 min flux to 0.013 for monthly averaged flux (Fig. e). The processing uncertainty had a less prominent decrease, from 0.15 for 30 min fluxes to 0.05 for monthly fluxes. The strongest decrease in processing uncertainty was when moving from single 30 min flux values to daily average fluxes, after which the averaging period did not affect the processing uncertainty. This is probably due to the large scatter between the two detrending methods, which levels off when averaging over several flux values (Fig. S11a). Relative random uncertainty of CO2 flux decreased from 0.11 for 30 min fluxes to 0.021 for monthly fluxes. The processing uncertainty, however, did not change significantly between the different averaging periods, as would be expected.