Carbonyl sulfide (COS) flux measurements with the eddy covariance (EC) technique are becoming popular for estimating gross primary productivity. To compare COS flux measurements across sites, we need standardized protocols for data processing. In this study, we analyze how various data processing steps affect the calculated COS flux and how they differ from carbon dioxide (

Carbonyl sulfide (COS) is the most abundant sulfur compound in the atmosphere, with tropospheric mixing ratios around 500 ppt

Eddy covariance (EC) measurements are the backbone of gas flux measurements at the ecosystem scale

Studies on ecosystem COS flux measurements with the EC technique are still limited

In this study, we compare different methods for detrending, time lag determination, and high-frequency spectral correction. In addition, we compare two methods for storage change flux calculation, discuss the nighttime low-turbulence problem in the context of COS EC measurements, introduce a method for gap-filling COS fluxes for the first time, and discuss the most important sources of random and systematic errors. Through the evaluation of these processing steps, we aim to settle on a set of recommended protocols for COS flux calculation.

Processing steps used in previous COS eddy covariance studies. Detrending methods include linear detrending (LD), block averaging (BA), and recursive filtering (RF). Spectral corrections include an experimental method and a theoretical method by

In this study we used COS and

Measurements were made in a boreal Scots pine (

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,

Background measurements of high-purity nitrogen (

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

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

In this section, we describe the processing steps of EC flux calculation from raw data handling to final flux gap filling and uncertainties. Figure

Different EC processing steps summarized. Yellow boxes refer to steps only used for COS data processing, blue boxes to steps used only for

For flux calculation, the sonic anemometer and gas analyzer signals need to be synchronized. This is particularly relevant for fully digital systems where digital data streams are gathered from different instruments that can be completely asynchronous to each other

Raw data were then despiked so that the difference between subsequent data points was a maximum of 5 ppm for

We used the planar-fit method to rotate the coordinate frame so that the turbulent flux divergence is as close as possible to the total flux divergence. In this method,

To separate the mixing ratio time series into mean and fluctuating parts, we tested three different detrending options: (1) 30 min block averaging (BA), (2) linear detrending (LD), and (3) recursive filtering (RF) with a time constant of 30 s. BA is the most commonly used method for averaging the data with the benefit of damping the turbulent signal the least. On the other hand, BA may lead to an overestimation of the fluctuating part (and thus overestimation of the flux), for example due to instrumental drift or large-scale changes in atmospheric conditions that are not related to turbulent transfer

The time lag between

The time lag was determined from the maximum difference of the cross-covariance of the COS mixing ratio and

The time lag was determined from the maximum difference of the cross-covariance of the

The time lag was determined using a constant time lag of 2.6 s, which was the nominal time lag and the most common lag for

The time lag was determined from the maximum difference of the smoothed

The time lag was determined from a combination of COS

Some of the turbulence signal is lost at both high and low frequencies due to losses in sampling lines, inadequate frequency response of the instrument, and inadequate averaging times among other reasons

Especially in closed-path systems, the high-frequency turbulent fluctuations of the target gas damp at high frequencies due to long sampling lines. Other reasons for high-frequency losses include sensor separation and inadequate frequency response of the sensor. In turn, high-frequency losses cause the normalized cospectrum of the gas with

In the analytical approach by

In the experimental approach, we solved Eq. (

In both approaches (analytical and experimental), the time constant

Detrending the turbulent time series, especially with LD or RF methods, may also remove part of the real low-frequency variations in the data

The calculated fluxes were accepted when the following criteria were met: the second wind rotation angle (

We used a similar flagging system for micrometeorological quality criteria as

In addition to these filtering and flagging criteria, we added friction velocity (

Storage change fluxes were calculated from gas mixing ratio profile measurements and by assuming a constant profile throughout the canopy using EC system mixing ratio measurements.
Storage change fluxes from mixing ratio profile measurements were calculated using the formula

Another storage change flux calculation was done assuming a constant profile from the EC measurement height (23 m) to the ground level. A running average over a 5 h window was applied to the COS mixing ratio data to reduce the random noise of measurements.

The storage change fluxes were used to correct the EC fluxes for storage change of COS and

The flux uncertainty was calculated according to ICOS recommendations presented by

As the chosen processing schemes affect the resulting flux, the uncertainty related to the used processing options have to be accounted for. This uncertainty was estimated as

It should be noted, though, that this uncertainty estimate holds for single 30 min fluxes only. When working with fluxes averaged over time, the total uncertainty cannot be directly propagated to the long-term averages because the two uncertainty sources behave differently. The random uncertainty is expected to decrease with increasing number of observations, while processing-related uncertainty would not be much affected by time averaging. The random uncertainty of a flux averaged over multiple observations is obtained as

Missing

The COS gap-filling function was parameterized in a moving time window of 15 d to capture the seasonality of the fluxes. To calculate gap-filled fluxes, the parameters were interpolated daily. Gaps where any driving variable of the regression model was missing were filled with the mean hourly flux during the 15 d period.

We tested different combinations of linear or saturating (rectangular hyperbola) functions of the COS flux on PPFD and linear functions of the COS flux against vapor pressure deficit (VPD) or relative humidity (RH). The saturating light response function with the mean nighttime flux as a fixed offset term explained the short-term variability of COS flux relatively well, but the residuals as a function of temperature, RH, and VPD were clearly systematic. Therefore, for the final gap filling, we used a combination of saturating function on PPFD and linear function on VPD that showed good agreement with the measured fluxes while having a relatively small number of parameters:

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 (

The largest median COS flux (most negative) was obtained from RF (

For

The most commonly recommended averaging methods are BA

Median COS fluxes ( pmol m

Different time lag methods resulted in slightly different time lags and COS fluxes. The most common time lags were 2.6 s from the COS

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 COS

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

By using the DetLim

The median COS fluxes were highest when the time lag was determined from the DetLim

Distribution of time lags derived from different methods:

Normalized COS flux distributions using different time lag methods:

The mean COS cospectrum was close to the normal mean

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

Similar results were found for the

The site-specific model captures the cospectrum better than the model cospectrum by

Cospectrum and power spectrum for COS (panels

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

The

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

Diurnal variation in the storage change flux, determined from

Nighttime median ecosystem fluxes (black) of

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

For COS, nighttime filtering is a more complex issue than it is for

We determined

If fluxes are not corrected for storage before deriving the

Diurnal variation in the measured COS flux (black) and the flux from different gap-filling methods: gap filling with only saturating PAR function (yellow), saturating PAR and linear dependency on RH (blue), and saturating PAR and linear dependency on VPD (purple). Diurnal variation is calculated from 1 July to 31 August 2015 for periods when measured COS flux existed. Dashed lines represent the 25th and 75th percentiles.

Three combinations of environmental variables (PAR, PAR and RH, and PAR and VPD) were tested using the gap-filling function (Eq.

For COS fluxes, 44 % of daytime flux measurements were discarded due to the above-mentioned quality criteria (Sect.

Uncertainty of

For

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.

The relative flux uncertainty for COS was very high at low flux (

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.

In this study, we examined the effects of different processing steps on COS EC fluxes and compared them to

The largest differences in the final fluxes came from time lag determination and detrending. Different time lag methods made a difference of a maximum of 15.9 % in the median COS flux. Different detrending methods, on the other hand, made a maximum of 6.2 % difference in the median COS flux, while it was more important for

Flux uncertainties of COS and

We emphasize the importance of time lag method selection for small fluxes, whose uncertainty may exceed the flux itself, to avoid systematic biases. COS EC flux processing follows similar steps as other fluxes with low signal-to-noise ratios, such as

The flux data used in this study are available in Kohonen (2020;

The supplement related to this article is available online at:

K-MK and IM designed the study, and K-MK processed and analyzed the data. PK developed the gap-filling function for COS and participated in data processing. IM, LMJK, US, WS, and HC participated in field measurements. K-MK and IM wrote the manuscript, with major participation in editing by WS and LMJK and contributions from all coauthors.

The authors declare that they have no conflict of interest.

We thank the Hyytiälä Forestry Field Station staff for all their technical support, especially Helmi-Marja Keskinen and Janne Levula. Kukka-Maaria Kohonen thanks the Vilho, Yrjö and Kalle Väisälä foundation for its kind support.

This research has been supported by the ICOS Finland (grant no. 319871), the Academy of Finland Center of Excellence (grant no. 307331), the Academy of Finland Academy Professor project (grant no. 284701), and the ERC Advanced funding scheme (abbreviation: COS-OCS; grant no. 742798).Open-access funding provided by Helsinki University Library.

This paper was edited by Christof Ammann and reviewed by Georg Wohlfahrt and two anonymous referees.