the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
True eddy accumulation trace gas flux measurements: proof of concept
Lukas Siebicke
Anas Emad
Micrometeorological methods to quantify fluxes of atmospheric constituents are key to understanding and managing the impact of land surface sources and sinks on air quality and atmospheric composition.
Important greenhouse gases are water vapor, carbon dioxide, methane, and nitrous oxide. Further important atmospheric constituents are aerosols, which impact air quality and cloud formation, and volatile organic compounds. Many atmospheric constituents therefore critically affect the health of ecosystems and humans, as well as climate.
The micrometeorological eddy covariance (EC) method has evolved as the method of choice for CO_{2} and water vapor flux measurements using fastresponse gas analyzers. While the EC method has also been used to measure other atmospheric constituents including methane, nitrous oxide, and ozone, the often relatively small fluxes of these constituents over ecosystems are much more challenging to measure using eddy covariance than CO_{2} and water vapor fluxes. For many further atmospheric constituents, eddy covariance is not an option due to the lack of sufficiently accurate and fastresponse gas analyzers.
Therefore, alternative flux measurement methods are required for the observation of atmospheric constituent fluxes for which no fastresponse gas analyzers exist or which require more accurate measurements. True eddy accumulation (TEA) is a direct flux measurement technique capable of using slowresponse gas analyzers. Unlike its more frequently used derivative, known as the relaxed eddy accumulation (REA) method, TEA does not require the use of proxies and is therefore superior to the indirect REA method.
The true eddy accumulation method is by design ideally suited for measuring a wide range of trace gases and other conserved constituents transported with the air. This is because TEA obtains whole air samples and is, in combination with constituentspecific fast or slow analyzers, a universal method for conserved scalars.
Despite the recognized value of the method, true eddy accumulation flux measurements remain very challenging to perform as they require fast and dynamic modulation of the air sampling mass flow rate proportional to the magnitude of the instantaneous vertical wind velocity. Appropriate techniques for dynamic mass flow control have long been unavailable, preventing the unlocking of the TEA method's potential for more than 40 years.
Recently, a new dynamic and accurate mass flow controller which can resolve turbulence at a frequency of 10 Hz and higher has been developed by the first author. This study presents the proof of concept that practical true eddy accumulation trace gas flux measurements are possible today using dynamic mass flow control, advanced realtime processing of wind measurements, and fully automatic gas handling.
We describe setup and methods of the TEA and EC reference flux measurements. The experiment was conducted over grassland and comprised 7 d of continuous flux measurements at 30 min flux integration intervals. The results show that fluxes obtained by TEA compared favorably to EC reference flux measurements, with coefficients of determination of up to 86 % and a slope of 0.98.
We present a quantitative analysis of uncertainties of the mass flow control system, the gas analyzer, and gas handling system and their impact on trace gas flux uncertainty, the impact of different approaches to coordinate rotation, and uncertainties of vertical wind velocity measurements.
Challenges of TEA are highlighted and solutions presented. The current results are put into the context of previous works. Finally, based on the current successful proof of concept, we suggest specific improvements towards longterm and reliable true eddy accumulation flux measurements.
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The ability to observe the exchange of trace gases between the earth's surface and the atmosphere is key to understanding the functioning of ecosystems. Trace gas flux measurements allow quantification of how natural and anthropogenic systems affect atmospheric composition.
Many studies over the past decades have observed carbon dioxide (CO_{2}) and water vapor fluxes at ecosystem scale using micrometeorological methods (Baldocchi et al., 1988). Eddy covariance (EC) (Baldocchi, 2003, 2014) has become the most widely used method for measuring turbulent fluxes. Today the EC method is routinely being applied the world over including the major flux networks FLUXNET, ICOS, and NEON.
The EC method requires fastresponse gas analyzers which only exist for a few trace gas species, above all CO_{2} and water vapor but more recently also other trace gases, including methane (CH_{4}) and nitrous oxide (N_{2}O). However, for a large number of trace gases and atmospheric constituents, the applicability of the EC method is limited by a lack of fastresponse gas analyzers, by the high power demand necessary for sustaining high sample flow rates in some closedpath gas analyzer systems, and by a possibly small signaltonoise ratio of highfrequency measurements.
A number of alternative turbulent flux measurement methods exist which can use slowresponse gas analyzers and might provide more accurate results than eddy covariance with fastresponse analyzers. These methods are applicable to a wide range of conserved trace gases, isotopes, aerosols, volatile organic compounds, and other atmospheric constituents. An overview on selected micrometeorological methods applicable to slowresponse gas analyzers follows, presenting the air sampling principles and timings and stating advantages and disadvantages of each method.
True eddy accumulation (TEA) is an alternative to the EC method. Unique properties of the TEA method are highlighted which make TEA stand out from other methods. This study is a contribution towards a practical implementation of the TEA method.
1.1 Micrometeorological methods suitable for slowresponse gas analyzers
1.1.1 True eddy accumulation (TEA)
True eddy accumulation (Desjardins, 1977; Hicks and McMillen, 1984) refers to the sampling of air, separating updrafts and downdrafts on the condition of the sign of the vertical wind velocity. The mass flow rate of physical air samples needs to be proportional to the magnitude of the vertical wind velocity and controlled at 10 Hz or above to resolve fluxrelevant turbulence scales. For conserved scalars, the net flux can then be determined from the difference in scalar concentration between the accumulated updraft and downdraft samples, respectively, over a certain flux integration interval, e.g., 30 min.
The idea of eddy accumulation (EA) goes back to early considerations by Desjardins (1972) who proposed the method for physically sampling trace gas fluxes. He reported a first experiment of conditionally sampling temperature and deriving sensible heat flux through mathematical accumulation (Desjardins, 1977). We use the term “true eddy accumulation” rather than just “eddy accumulation” to refer to the original formulation of eddy accumulation (Desjardins, 1977; Hicks and McMillen, 1984), specifically with vertical wind proportional air sampling, as opposed to later derivatives of eddy accumulation such as “relaxed eddy accumulation”, which is subject to constant mass flow and further limitations (see Sect. 1.1.2).
Literature on true eddy accumulation is sparse, with just over a dozen published studies. Very few studies performed actual flux measurements. Desjardins (1977), Speer et al. (1985), Neumann et al. (1989), Beier (1991), and Komori et al. (2004) presented early prototypes of true eddy accumulators and disjunct true eddy accumulators (Rinne et al., 2000). Others conducted simulations (Hicks and McMillen, 1984; Businger and Oncley, 1990) and contributed technology (Buckley et al., 1988) and reviews (Businger, 1986; Speer et al., 1986; Hicks et al., 1986). However, its practical implementation has long been difficult, particularly the accurate and dynamic control of mass flow rates. None of the experiments above produced significant longterm data sets. Correlation of TEA fluxes with EC fluxes was generally relatively low with coefficients of determination of, e.g., R^{2}=0.07 (Speer et al., 1985), R^{2}=0.41 (Neumann et al., 1989), and R^{2}=0.64 (Komori et al., 2004). Until today there has been no TEA instrument commercially available.
Recently we have successfully performed a series of TEA flux experiments using a new and fully digital approach to dynamic and fast mass flow control and realtime processing of wind data. We are further working to advance TEA flux corrections and TEA simulations. Those experiments (unpublished) yielded a tight correlation between TEA and EC flux measurements, with coefficients of determination of up to R^{2}=0.96, exceeding R^{2} values from any of the above cited literature. The current work presents the first of the TEA and EC intercomparison experiments performed over short vegetation during spring 2015 in detail.
The concept of the TEA sampling scheme is illustrated in Fig. 1. The true vertical wind velocity (Fig. 1a, black line) is sampled at a frequency of, e.g., 10 Hz (Fig. 1a, blue dots), using an ultrasonic anemometer. Likewise, the air sampling device samples the true atmospheric time series of the scalar, e.g., CO_{2} (Fig. 1b, black line), at the same time resolution of 10 Hz (Fig. 1b, blue dots). The time variable flow rates at which samples are being accumulated are shown in Fig. 1c. Separate accumulation of updrafts (red lines) and downdrafts (orange lines) is distinguished.
Following whole air sampling, the atmospheric constituent of interest can be trapped in a number of ways. Constituents can be accumulated as whole air samples in bags, absorbed in gas washing reservoirs, adsorbed on to chemicals using cartridges, continuously sampled with denuders, trapped as reaction products with chemicals, or retained using mechanical filters.
The true eddy accumulation principle is not limited to passive trace gases. Here, we suggest that the TEA method has the potential to measure fluxes of dust, pollen, bacteria, fungi, and other biological material carrying physical, chemical, and genetic information. The latter materials can be accumulated on appropriate filter media.
True eddy accumulation has a number of advantages over other methods. Sample accumulation over the duration of typical flux averaging intervals of 30 to 60 min allows for the use of slowresponse gas analyzers. The key advantage of TEA over EC is the applicability to a much wider range of atmospheric constituents, assuming that slowresponse analyzers are more readily available than fastresponse analyzers, and better accuracy can be obtained through signal averaging.
The key advantage of TEA over other variants of eddy accumulation, i.e., relaxed eddy accumulation or hyperbolic relaxed eddy accumulation, is that true eddy accumulation is the only direct method in the family of accumulation methods. As a direct method it does not require the use of proxies (other scalars) and coefficients like the β coefficient in relaxed eddy accumulation and therefore does not depend on scalar similarity (Ruppert et al., 2006). This property of a direct measurement method is essential for quantifying fluxes of constituents which cannot be measured by other means (e.g., the EC method). Scalar similarity of the fluxes of the constituent of interest and the proxy cannot be assessed without first quantifying both fluxes themselves. The direct TEA method is independent of prior knowledge.
Another advantage over other types of eddy accumulation (relaxed eddy accumulation or hyperbolic relaxed eddy accumulation) or any type of disjunct eddy sampling (e.g., the disjunct eddy covariance method or the disjunct eddy accumulation method) is the continuous sampling of the air by the TEA method such that the signal is recovered in its entirety. Continuous sampling avoids noise associated with disjunct sampling (Lenschow et al., 1994). Likewise, omitting samples at times of small vertical wind velocities, which is common practice in relaxed eddy accumulation, would effectively be disjunct sampling, trading in noise for the sake of higher concentration differences between accumulated updrafts and downdrafts.
The long averaging intervals further allow for repeated measurements of the same sample, improving precision. The trace gas concentration of the accumulated samples, which is by design constant, at the time of analysis and the typically long analysis integration times are best matched with low sample flow rates through the gas analyzer. Low flow rates result in low power consumption and a low pressure drop over system components. A low pressure drop is beneficial for the stability and accuracy of the gas analyzer's reading.
1.1.2 Relaxed eddy accumulation (REA)
Given the challenges associated with the original formulation of true eddy accumulation, Businger and Oncley (1990) proposed a modified version of eddy accumulation, today known as relaxed eddy accumulation (REA). REA is based on the concept of flux–variance similarity. In order to relate the scalar flux to the variance of the vertical wind velocity, a proportionality factor, β, was introduced, so REA became an indirect method.
The advantage of the relaxed eddy accumulation method is that air is sampled at a constant flow rate (Fig. 2c). This meant that the dynamic highfrequency modulation of flow rates as a function of the magnitude of the vertical wind velocity as in the TEA method was no longer required. REA still accumulates updrafts and downdraft separately controlled by the sign of the vertical wind velocity.
A second modification was introduced in REA: at times of small positive or negative vertical wind velocities, no air samples are taken. This “dead band” is illustrated in Fig. 2a. Figure 2b shows the air sampling scheme: the true scalar time series, e.g., CO_{2} density (black line), is sampled at a regular frequency of, e.g., 10 Hz (blue dots), if the vertical wind velocity (Fig. 2a, black line), sampled at the same 10 Hz frequency (Fig. 2a, blue dots), is larger than the thresholds defining the dead band. A certain fraction of the scalar time series is thus omitted from sampling (Fig. 2b, gray line).
The use of a dead band has two advantages: the concentration difference between the updraft and downdraft accumulated samples increases (Pattey et al., 1993; Katul et al., 1996), improving the ratio of the flux signal to the noise of the gas analyzer. Secondly, use of a dead band leads to less frequent switching between updraft and downdraft samples, which relaxes the need for fastresponse valves to some degree and would reduce material wear. However, a lack of scalar similarity can lead to flux underestimation as simulated by Ruppert et al. (2002), who also found that flux errors increased with deadband size. Another disadvantage is the impact of the dead band on the flux itself of unknown magnitude, depending on the cospectrum of scalar and vertical wind velocity.
The simplifications of the REA method relative to the TEA method, particularly the constant mass flow rate, have facilitated wide adoption of the REA method. More than 200 studies on REA flux measurements and simulations have been published since its description less than 30 years ago (Businger and Oncley, 1990). The significant number of REA studies suggests that there is a need for alternatives to the eddy covariance method for certain applications.
Despite being simpler to implement than TEA, REA has distinct disadvantages. Being an indirect method, the accuracy of REA remains critically dependent on the correct determination of an a priori unknown β factor. β varies with scalar and with atmospheric conditions. Typical β values obtained from measurements and simulations (Wyngaard and Moeng, 1992; Businger and Oncley, 1990; Oncley et al., 1993; Pattey et al., 1993; Baker et al., 1992; Gao, 1995; Milne et al., 1999; Katul et al., 1996; Baker, 2000; Ammann and Meixner, 2002; Held et al., 2008) are around 0.55 but range from ca. 0.4 to ca. 0.7, introducing significant uncertainty of up to several tens of percent of the measured flux.
Scalar similarity between a constituent of interest and a suitable proxy for determination of the β factor is often lacking (Ruppert et al., 2006; Cancelli et al., 2015). The alternative use of a constant β factor leads to lower accuracy of the estimated flux (Foken and Napo, 2008; Ruppert et al., 2002).
A variant of REA is hyperbolic relaxed eddy accumulation (HREA) (Shaw, 1985; Bowling et al., 1999). HREA maximizes concentration differences between accumulation reservoirs through the use of hyperbolic dead bands. Thus, HREA can resolve small fluxes such as stable isotope fluxes of ^{13}C and ^{18}O (Bowling et al., 1999; Wichura et al., 2000). However, HREA requires proxies similar to REA and omits about twothirds of total sampling time through the use of dead bands. Dead bands can increase flux uncertainty by omitting parts of the signal due to incomplete sampling of the time series.
1.1.3 Disjunct eddy accumulation (DEA) and disjunct eddy covariance (DEC)
Disjunct eddy sampling (Rinne et al., 2000; Turnipseed et al., 2009) is based on considerations by Lenschow et al. (1994) for representing turbulent time series by temporal subsamples. Disjunct eddy covariance (DEC) takes very short grab samples (ca. 0.1 s), followed by a pause (e.g., 5 to 60 s) for gas analysis with relatively slow instruments. Similarly, disjunct eddy accumulation can be used to obtain short grab samples at a mass flow rate proportional to the magnitude of vertical wind velocity when continuous dynamic mass flow control can not be performed.
The disjunct sampling principle is illustrated in Fig. 1 for the DEA method and in Fig. 3 for the DEC method. Comparing the few disjunct samplings at a resolution of 10 s of the DEA method (flow rate indicated by black vertical lines in Fig. 1c at times of 0, 10, and 20 s) relative to the continuous flow rate of the TEA method (red and orange vertical lines in Fig. 1c) illustrates the small fraction of the total time series being actually sampled by DEA.
Disjunct sampling allows more time for the analysis of the chemical species than continuous sampling. However, the uncertainty of disjunctly sampled scalar and wind time series, and as a result the flux uncertainty, is larger compared to continuous sampling. Turnipseed et al. (2009) found an additional uncertainty of ±30 % of the flux due to disjunct sampling and estimated the overall uncertainty of their DEA flux measurements as ±40 %.
1.1.4 Challenges of eddy accumulation
There are a number of challenges associated with eddy accumulation flux measurements (see also Hicks and McMillen, 1984). The first two listed below are specific to the TEA and DEA methods. The others are common to all eddy accumulation methods.

Mass flow control. The air sampling, i.e., the separation of updrafts and downdrafts as well as the response of the vertical wind velocity proportional mass flow control, needs to be sufficiently fast (10 to 20 Hz) and dynamic to resolve the relevant turbulent fluctuations. Further, the mass flow control needs to be accurate, even under dynamically changing flow rate conditions despite the compressibility of air. Finally, the dynamic range of the mass flow control, i.e., the ratio of the largest to the smallest accurately controllable mass flow, needs to be on the order of 100 or higher to limit flux errors (Hicks and McMillen, 1984). No commercially or otherwise readily available technology for fast, dynamic, and accurate control of mass flow rates exists or has been demonstrated to perform well in TEA.

Density fluctuation effects. Density fluctuations due to heat and water vapor transfer affect the flux of the scalar of interest. Corresponding corrections specific to the TEA method have been unavailable.

Spectra and cospectra. No turbulence spectrum of the scalar nor the cospectrum of the scalar and the vertical wind velocity can be obtained from the accumulated samples as they are mixed, and timeresolved analysis is therefore not possible. Spectral information on the wind is of course available as in any other method using a fastresponse ultrasonic anemometer.

Coordinate rotation (see further details in Sect. 2.7). Sampling decisions need to be performed in real time, and they are definitive; i.e., they cannot be modified in postprocessing. This is an important difference to the EC method. The separation of updrafts and downdrafts depends on the definition of vertical wind velocity, w. The mean w over the averaging period needs to be zero (see Sect. 2, Eq. 6). One way to minimize mean w is to align the coordinate system of the wind measurements to the mean streamlines through coordinate rotation (Wilczak et al., 2001).
In eddy accumulation, the coordinate rotation needs to be performed in preprocessing to be available in real time. Coordinate rotation and any other operation attempting to nullify mean w over the flux averaging interval would require knowledge of w over the entire interval, including future observations. However, only past and present data are available in real time to approximate coordinate rotation and perform sampling decisions based on the sign and magnitude of w. Remaining nonzero mean w causes flux bias.

Decorrelation through sensor separation. Spatial separation of the gas sampling inlets and the wind sensing volume causes a time lag between the wind measurement and the time for obtaining the corresponding air sample. Not accounting for time lags leads to decorrelation of wind and scalar and therefore flux loss. Contrary to the EC method, where time lags can be detected through covariance maximization and corrected for, in eddy accumulation such postprocessing is not possible because highfrequency scalar time series are not obtained. Therefore the wind measurement and the air inlet need to be colocated as close as possible.

Analyzer sensitivity. Trace gas concentration differences between reservoirs might be too small to be resolved by given gas analyzers.

Reliability. Eddy accumulation systems are mechanically and electronically complex machines. Particularly moving parts pose the risk of failure. Careful design is required for robust implementations and unattended longterm deployments.
We address the above challenges in the following ways:

A new type of digital and highly dynamic mass flow controller was deployed. The technology previously developed by the first author has a fast and dynamic response sufficient to resolve relevant turbulent scales at 10 Hz and above. The design accounts for the compressibility of air in dynamic sampling. See Sect. 3.2 for further details.

TEAspecific adaptation of flux corrections accounting for density fluctuations as proposed for the EC method by Webb et al. (1980) is subject to ongoing research by the authors.

Here we propose that, in absence of cospectral information which is required to correct for flux attenuation due to sonic anemometer path length averaging and due to the separation of the air inlet and the sonic sensing volume, further research should investigate whether a proxy scalar such as air temperature or sonic temperature might be used to estimate the attenuation. While this would imply scalar similarity of the proxy and the scalar of interest, the impact of potential nonsimilarity would be limited to the spectral attenuation flux correction term, which is typically small relative to the flux itself, and the uncertainty from the scalar similarity constraint would be even smaller.

Nonzero mean vertical wind velocities were minimized through realtime coordinate rotation with continuous nearrealtime updates of the rotation coefficients as well as a procedure to minimize remaining bias in the mean vertical wind velocity (see Sect. 2). Further, a correction accounting for volume mismatch between updraft and downdraft reservoirs due to nonzero mean vertical wind velocities (Turnipseed et al., 2009) has been applied (see Sect. 2).

Spatial separation of the wind sensing volume and the point of air sampling can be minimized through integration of the air inlet inside the wind sensing volume of the sonic anemometer. A certain degree of time lag between the wind signal and the scalar sampling will ultimately remain as long as the wind is sensed over a measurement volume rather than at a point and with discrete finite time resolution rather than truly instantly.

Performance analysis of a typical infrared gas analyzer model for the measurement of CO_{2} gave satisfactory results in terms of the resolution but revealed limited stability. Subsequent work by the authors with current laser spectrometers gave superior results due to their improved stability. Details on the latter work will be reported separately.

Suggestions towards a robust design of an eddy accumulator are given in the conclusions of the current study.
1.2 Objectives
Out of all the methods discussed above, the true eddy accumulation method is the only alternative to the eddy covariance method for directly measuring the physical flux. Every effort should be made towards mastering the dynamic mass flow control necessary for direct TEA as well as addressing the other challenges listed above.
It is the objective of this work to deliver the proof of concept of true eddy accumulation trace gas flux measurements based on dynamic and accurate mass flow control proportional to vertical wind velocity and based on fully digital and realtime signal processing.
2.1 Experimental design
The experimental design comprises three elements: novel true eddy accumulation flux measurements of CO_{2} and water vapor, conventional eddy covariance flux measurements of CO_{2} and water vapor, and meteorological measurements. All measurements were performed side by side. This allowed for the performance of the new TEA system to be evaluated on its ability to measure turbulent fluxes of CO_{2} by relating the observed fluxes to meteorological drivers and by comparing the TEA CO_{2} flux measurements to conventional EC CO_{2} flux measurements. This section provides details on the measurement site, the meteorological measurements, the TEA method, technical implementation, and flux computation as well as information on the reference flux measurements by EC.
2.2 Experimental site
Flux measurements were performed at a grassland experimental field site of the University of Göttingen, Germany, located at 51^{∘}33^{′}3^{′′} N, 9^{∘}57^{′}2^{′′} E. The flux tower was installed at an altitude of 230 m above sea level on a flat area of about 50 m by 50 m situated on a south–southeastfacing hill, with a slope angle of 5^{∘} and length of 800 m. Vegetation height of the grass was 0.2 m during the experiment. Vegetation further comprised patches of bushes and trees with a minimum distance from the flux tower of 50 m (west of the tower).
2.3 Experimental period
The TEA flux measurements presented in this study were conducted from 4 to 10 April 2015. After a cold and wet month of March, this period was characterized by increasing physiological activity of the grasses due to increasing light availability, increasing temperatures during the day, less frequent frost events, and increasing CO_{2} fluxes.
Prior to the flux experiment, the TEA instrument and method were further developed and tested in the field, with continuous operation starting on 5 March 2015. The TEA deployment continued after 10 April until 17 June 2015. However, the frequent charging and discharging of the air sampling bags led to material fatigue and progressive leakage. Therefore, no meaningful flux measurements are available after 10 April 2015. The period from 10 April to 17 June 2015 was used for testing different kinds of air bags and for further developing the TEA method. Altogether, the TEA air sampling system in its current form was in continuous operation from 5 March to 17 June 2015, corresponding to more than 5000 30 min TEA flux sampling intervals.
2.4 Instrumentation
The instrumentation used for meteorological measurements, TEA flux measurements, and EC flux measurements and the respective variables measured are listed in Table 1.
Meteorological variables (Table 1) were logged using a DL16 data logger (Adolf Thies GmbH & Co. KG Göttingen, Germany). All raw data needed for TEA and EC flux measurements, including the sonic anemometer data and data from the two infrared gas analyzers LI6262 and LI7500, were synchronized and logged on the central TEA controller. Using a mobile network link, raw data were continuously mirrored to a central server for archival and flux processing.
2.5 Meteorological measurements
The following set of meteorological variables was measured on site to support the computation and interpretation of turbulent fluxes: global radiation, photosynthetically active radiation (PAR), net radiation, air temperature at 2 m a.g.l., air pressure, relative humidity at 2 m a.g.l., precipitation, wind velocity at 2 m a.g.l., wind direction at 2 m a.g.l., soil temperature at 0.3 m b.g.l. (three probes), soil moisture at 0.3 m b.g.l.(three probes), and soil heat flux.
2.6 Experimental data
The abovedescribed meteorological measurements, as well as the turbulent flux measurements obtained by the true eddy accumulation and the two eddy covariance instrumental setups, have been published via open access (Siebicke and Emad, 2019) to foster open science in general and the scientific advancement of true eddy accumulation in particular.
2.7 Coordinate systems and net ecosystem exchange
If the trace gas source and sink strength of the ecosystem is of interest, as is typically the case when investigating biological, physiological, or biogeochemical processes or deriving trace gas budgets, then the total flux in and out of the ecosystem needs to be determined. For the exchange of the ecosystem with the atmosphere, the concept of a virtual control volume is often used. Net ecosystem exchange (NEE), i.e., the net flux across the surfaces of this control volume, can be written as (e.g., Aubinet et al., 2003; Siebicke et al., 2012)
with the molar volume of dry air V_{m}, CO_{2} concentration c, time t, horizontal distances x and y, vertical distance above ground z, height of the control volume h, horizontal wind velocity u along the x direction, horizontal wind velocity v along the y direction, and vertical wind velocity w along the z direction. Overbars denote temporal means, and primes denote the temporal fluctuations relative to the temporal mean.
The terms on the right hand side of Eq. (1) are the change of storage (I), the vertical turbulent flux (II), vertical advection (IIIa), vertical mass flow from the surface, e.g., due to evaporation (IIIb) according to Webb et al. (1980), horizontal advection (IV), and flux divergence (V). The form of NEE presented in Eq. (1) excludes the horizontal variation of the vertical turbulent flux and the horizontal variation of vertical advection. Most flux measurements typically only determine the vertical turbulent flux density (term II) and sometimes the storage flux density (term I), neglecting the remaining terms due to a lack of spatially distributed information.
The choice of the reference coordinate system (Finnigan, 2004) is important for the attribution of the total flux to its components (Eq. 1) and therefore for the interpretation of turbulent flux density measurements relative in their ability to approximate the net ecosystem exchange. If NEE is to be assessed, and available flux observations are restricted to the turbulent vertical flux density at a single location above the ecosystem, a reference coordinate system is needed which minimizes the remaining flux terms. Sun et al. (2007, Table 1) summarize coordinate systems. In streamline coordinates (Finnigan, 2004; Sun et al., 2007), the longterm flow is tangential to longterm streamlines. This means that, in streamline coordinates, the velocity normal to the streamlines becomes zero, implying that the longterm vertical advection vanishes. There are various methods for coordinate rotation (Finnigan et al., 2003), i.e., the transformation of the wind measurements from the coordinate reference frame of the sonic anemometer to the coordinate system of the flux measurements, also known as tilt correction (Tanner and Thurtell, 1969; Hyson et al., 1977; Kaimal and Finnigan, 1994; McMillen, 1988; Paw U et al., 2000; Wilczak et al., 2001).
Over flat terrain or planar terrain with a uniform slope, the mean streamlines close to the surface approximately follow the terrain surface. The planar fit method (Paw U et al., 2000; Wilczak et al., 2001) is often used to obtain longterm streamline coordinates. In contrast to the double rotation method (Kaimal and Finnigan, 1994), which nullifies the mean vertical wind velocity $\stackrel{\mathrm{\u203e}}{w}$ of the flux integration interval, planar fit rotated $\stackrel{\mathrm{\u203e}}{w}$, using the original formulation of Wilczak et al. (2001), is typically small but not zero. Even the longterm $\stackrel{\mathrm{\u203e}}{w}$ only becomes zero if mean streamlines are planar, and there is no instrumental bias in measurements of w. Nonzero $\stackrel{\mathrm{\u203e}}{w}$ would imply existence of a vertical advection term proportional to $\stackrel{\mathrm{\u203e}}{w}$ in the presence of vertical trace gas concentration gradients, which for CO_{2} typically exist close to the surface.
A variant to the planar fit method proposed by Van Dijk et al. (2004) removes velocity bias relative to the flux integration interval, addressing instrument offsets. This procedure can lead to local misalignment of streamlines for nonplanar mean flow fields. Nullifying $\stackrel{\mathrm{\u203e}}{w}$ over the flux integration period would formally remove vertical advection terms from the flux budget equation (Eq. 1). However, this procedure would also still ignore the effect of misalignment of the reference coordinate system and the streamlines over the flux integration interval on the vertical turbulent flux. The mismatched length and timing of the planar fit period relative to the shorter individual flux integration intervals acts as a high pass filter and results in loss of lowfrequency flux contributions and in unresolved distortion of cospectra of the shorter flux intervals (Finnigan et al., 2003).
On a related matter, Siebicke et al. (2012) performed an explicit treatment of the length and timing of the reference period for planar fit rotation. They demonstrated changes of up to 50 % of advective CO_{2} fluxes over forest depending on the window size of a new serial planar fit approach.
Over complex nonplanar terrain, the mean streamlines are not tangential to a plane. Even over planar surfaces, streamlines further away from the surface may not be tangential to the terrain surface due to vertical velocity divergence (Sun et al., 2007). For curved streamlines, other terms of the mass flow equation (Finnigan, 2004), in addition to vertical turbulent flux and vertical advection, become important. For curved streamlines, horizontal trace gas advection is not proportional to the gradient of trace gas concentrations along the streamlines.
Several authors have suggested variants to the planar fit method to account for steep slopes, where buoyancy forces are no longer normal to the terrain surface (Oldroyd et al., 2016), for obstructed flow (Griessbaum and Schmidt, 2009), and for complex topography, where $\stackrel{\mathrm{\u203e}}{w}$ becomes a function of wind azimuth angle. Consequently, several studies apply the planar fit rotation separately for different wind direction sectors (Foken and Napo, 2008; Yuan et al., 2011, and others). However, this introduces discontinuities in $\stackrel{\mathrm{\u203e}}{w}$ at wind direction sector limits and in the definition of the reference coordinate system.
Here we propose that a more general approach avoiding directional discontinuities would be to fit a surface rather than a plane, where the curvature of the surface adapts to longterm streamlines as a function of one or more parameters, i.e., wind direction and optionally other variables, such as horizontal wind velocity. A related approach has recently been proposed by Ross and Grant (2015), who also suggest tilt correction as a continuous function of wind direction instead of the relatively common discrete sectoral approach used currently. Siebicke et al. (2012) showed that the effect of atmospheric stratification, friction velocity, stationarity, and integral turbulence characteristics (Foken et al., 2004) on sectoral planar fit rotation was small relative to the wind direction effect over a forest.
In the presence of flow distortion due to obstacles, terrain features, towers and sensor mounts, or nonomnidirectional sonic anemometer designs (Li et al., 2013), distorted sectors need to be excluded from the definition of the coordinate system and subsequent flux derivations, unless distortions are characterized and corrected for (Van Dijk et al., 2004; Griessbaum and Schmidt, 2009; see also Sect. 2.8, current study).
All the above considerations on coordinate rotation apply to both the EC and EA methods, respectively, including their derivatives. However, there is one conceptual difference: in EC, highfrequency observations of both the scalar and the wind are measured and stored for postprocessing. Therefore it is feasible to fit the coordinate rotation plane to all observations from one or several 30 min flux integration intervals, including observations which were obtained before and after any wind measurement which is to be rotated. This includes the possibility to center the planar fit period around the time of interest.
Conversely, in EA, in absence of highfrequency scalar observations, any decision on the reference coordinate system becomes final on obtaining and mixing individual highfrequency air samples, precluding postprocessing and any reconsideration of the coordinate system. In EA, the reference period defining the coordinate system necessarily cannot coincide and never fully overlap with the flux integration interval for any sample but the last one in the flux integration interval, if any. Due to this conceptual difference, the contribution of other flux terms, in particular vertical advection, may not be identical for EC and EA if not using the same reference period to align the coordinate system to the mean streamlines.
Nonvanishing mean vertical wind velocities $\stackrel{\mathrm{\u203e}}{w}$ over the flux integration interval can nominally be removed in EC through subtraction of $\stackrel{\mathrm{\u203e}}{w}$ from instant vertical velocities (Van Dijk et al., 2004) and in EA through application of the volume mismatch correction (Turnipseed et al., 2009); see Eq. (11) above. However, distortion of cospectra (Finnigan et al., 2003) remains uncorrected.
We distinguish in evaluating the implications of discussed deviations of the real flow from any chosen ideal reference conditions: (i) the case of deploying turbulent vertical flux measurements to estimate net ecosystem exchange and (ii) the case of comparing the EA method and instruments side by side to the chosen reference method EC for assessing whether the EA method's physical air sampling principle produces comparable results to the mathematical computation of covariances for the EC method. This study is concerned with the latter case only. Most of the above issues of coordinate frames and the spatiotemporal variability of the flow field afflict both methods alike. Only the unavoidable differences in the application of the coordinate rotations between the two methods, i.e., the nonmatching rotation periods, need to be of concern when evaluating the relative performance of the two turbulent flux observation methods. To eliminate this remaining difference, identical rotation procedures and planar fit reference periods need to be applied to both EA and EC, accepting the EA version as the reference.
2.8 Flow distortion and angle of attack correction
The physical structure of sonic anemometer probes distorts the air flow they intend to measure (Wyngaard, 1981), introducing systematic errors in flux measurements. Measurement errors, due to probeinduced flow distortion and selfsheltering of ultrasonic transducers (Gash and Dolman, 2003), depend on the “angle of attack” (Kaimal and Finnigan, 1994), i.e., the angle between horizontal and the instantaneous wind vector. A wind tunnel calibration for anemometer models R2 and R3 (Gill Instruments Ltd., UK) was provided by van der Molen et al. (2004) and updated by Nakai et al. (2006). The representativity of the wind tunnel calibrations for turbulent conditions in the field has been questioned (Högström and Smedman, 2004) and is still under debate (Huq et al., 2017). Nakai and Shimoyama (2012) proposed an improved correction based on field measurements under turbulent conditions for the R3 and Windmaster models (Gill Instruments Ltd., UK). There is still no consensus on whether this correction should be applied, and care must be taken as the correction applies to certain instrument models (Gill Windmaster) and serial numbers only.
In the current study, which uses two R3type anemometers (Gill Instruments Ltd., UK), we do not apply any angleofattack correction because (i) the applicability of the wind tunnel calibration (Nakai et al., 2006) may or may not be applicable; (ii) there is contrasting information on the applicability of the calibration under turbulent conditions (Nakai and Shimoyama, 2012), specifically to the R3 model (recommended for R3 by original authors but not according to later information from Gill Instruments, UK, and LICOR Env., USA); (iii) no angleofattack correction was available in the current TEA system software at the time of the field experiment nor can the TEA flux measurements be postprocessed to include the correction. For the above reasons, no angleofattack correction was applied to the presented results of the current study, neither to TEA nor to EC fluxes. However, we did assess the impact of the angleofattack correction on EC CO_{2} fluxes for the two sonic anemometers.
2.9 True eddy accumulation (TEA) flux measurements
2.9.1 TEA method
The true eddy accumulation method determines the flux, $\stackrel{\mathrm{\u203e}}{wc}$, of a scalar (such as a trace gas) as the sum of the covariance, $\stackrel{\mathrm{\u203e}}{{w}^{\prime}{c}^{\prime}}$ of the scalar, c, and the vertical wind velocity, w, and the product of the time averages of scalar and vertical wind velocity, $\stackrel{\mathrm{\u203e}}{w}\phantom{\rule{0.125em}{0ex}}\stackrel{\mathrm{\u203e}}{c}$, as
where overbars denote time averages over the averaging period, T_{avg}, and primes denote fluctuations from the mean. Eq. (2) is analog to the eddy covariance (EC) method.
However, in contrast to EC, which requires highfrequency observations of the scalar and the vertical wind velocity and mathematical derivation of the covariance through postprocessing, in the case of TEA, the separate sampling of the wind and scalar time series is replaced by physically collecting separate air samples of updrafts and downdrafts proportionally to the magnitude of the vertical wind velocity. The TEA flux over a given averaging period, T_{avg}, can thus be obtained as (Desjardins, 1977; Hicks and McMillen, 1984)
where ${\mathit{\delta}}^{+}=\mathrm{1}$ when $w>\stackrel{\mathrm{\u203e}}{w}$ and 0 when $w<\stackrel{\mathrm{\u203e}}{w}$, and ${\mathit{\delta}}^{}=\mathrm{1}$ when $w<\stackrel{\mathrm{\u203e}}{w}$ and 0 when $w>\stackrel{\mathrm{\u203e}}{w}$. The amount of air, cw, sampled per unit time, dt, contains the molar fraction of the scalar of interest, c.
Assuming ideal conditions such that the mean vertical wind velocity over the integration period, $\stackrel{\mathrm{\u203e}}{w}$, was zero, the mean term, $\stackrel{\mathrm{\u203e}}{w}\phantom{\rule{0.125em}{0ex}}\stackrel{\mathrm{\u203e}}{c}$, becomes zero and the scalar flux, F_{c}, becomes
in kinematic units of meters per second (m s^{−1}). Multiplying by moist air density ρ, we obtain the constituent mass flux, F_{c}, per unit area and unit time in units of kilograms per square meter per second ($\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$) as
Given $\stackrel{\mathrm{\u203e}}{w}=\mathrm{0}$, the volume of the air samples accumulated in the updraft reservoir is identical to the volume of the downdraft reservoir given
where w^{+} is vertical wind larger than $\stackrel{\mathrm{\u203e}}{w}$, and w^{−} is vertical wind smaller than $\stackrel{\mathrm{\u203e}}{w}$.
A practical implementation of TEA then determines the scalar flux, F_{c}, as half of the difference between the mole fraction of the scalar in the updraft reservoir, $\stackrel{\mathrm{\u203e}}{{c}^{+}}$, and the mole fraction of the scalar in the downdraft reservoir, $\stackrel{\mathrm{\u203e}}{{c}^{}}$, multiplied by the mean of the absolute value of vertical wind velocity, assuming $\stackrel{\mathrm{\u203e}}{w}=\mathrm{0}$.
in units of kilograms per square meter per second ($\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$) or
in units of moles per square meter per second ($\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$), with the molar volume of air, V_{m} (m^{3} mol^{−1}), according to the ideal gas law,
with temperature, T, pressure, P, and the ideal gas constant, R. Note that Eqs. (7) and (8) write $\stackrel{\mathrm{\u203e}}{\leftw\right}$, not $\left\stackrel{\mathrm{\u203e}}{w}\right$; i.e., the order of math operations is important.
For comparison of TEA and REA methods, we include here the formulation of the flux using the REA method (Businger and Oncley, 1990), expressed as mole fraction measurements of the constituent, c,
with the standard deviation of vertical wind velocity, σ_{w}, and the REA fluxvariance similarity factor, β.
In any practical flux measurement application the observed mean vertical wind velocity over the integration period is likely unequal to zero, i.e., $\stackrel{\mathrm{\u203e}}{w}\ne \mathrm{0}$. In eddy covariance the assumption of $\stackrel{\mathrm{\u203e}}{w}=\mathrm{0}$ is satisfied in postprocessing once all observations of the entire integration period are available. This is commonly achieved by rotating the coordinate frame of the wind measurements to minimize or even nullify $\stackrel{\mathrm{\u203e}}{w}$ followed by subtraction of $\stackrel{\mathrm{\u203e}}{w}$ from individual vertical wind velocity measurements, w, so $\stackrel{\mathrm{\u203e}}{w}$ becomes zero.
Conversely, for TEA, knowledge of the mean vertical wind velocity over the flux averaging period, $\stackrel{\mathrm{\u203e}}{w}$, is required at any time throughout the averaging period, in order to be able to classify vertical winds as updrafts or downdrafts and accumulate air samples in the corresponding reservoirs. At any time during the averaging interval only the past and present vertical wind measurements are known. Therefore, any attempt to obtain $\stackrel{\mathrm{\u203e}}{w}=\mathrm{0}$ needs to rely in part on an estimate of the mean vertical wind velocity of the entire averaging period without knowledge of future observations from the present through to the end of the averaging period. In practice, this situation can lead to $\stackrel{\mathrm{\u203e}}{w}\ne \mathrm{0}$, resulting in unequal sample volumes accumulated over the averaging period in the updraft and downdraft reservoirs.
Following Turnipseed et al. (2009) the flux needs to be corrected by a term accounting for the mismatch between the volume of accumulated updrafts, V^{+}, and downdrafts, V^{−}, respectively, for ${V}^{+}\ne {V}^{}$. The flux due to a mismatch of volumes V^{+} and V^{−} is
where $\stackrel{\mathrm{\u203e}}{w}$ is the mean vertical velocity for the averaging period. The volume mismatch correction term is the difference between the unweighted mean density of the reservoirs, $(\stackrel{\mathrm{\u203e}}{{c}^{+}}+\stackrel{\mathrm{\u203e}}{{c}^{}})/\mathrm{2}$, and the volume weighted mean density,
weighted by the updraft and downdraft volumes, V^{+} and V^{−}, respectively.
Inserting Eq. (11) in Eq. (8) yields the volumemismatchcorrected TEA flux,
In practical applications, the instant sampling volume per unit time, V_{i}, is related to instant vertical wind velocity, w_{i}, through a proportionality factor, k, as
2.9.2 Correction of trace gas mole fractions for the effects of water vapor
When measuring trace gases such as CO_{2} in moist air with infrared gas analyzers, two corrections are required to remove the effect of water vapor on the measurement of the mole fraction of the trace gas. The first correction accounts for pressure broadening due to the presence of water vapor. This is known as the “pressure broadening correction” (Licor, 1996, LiCOR LI6262 manual, Sect. 3.5, 25 pp., Eq. 3–30).
The second correction accounts for the dilution of the trace gas by water vapor in the sample. This correction is known as “dilution correction” and is required to convert the wet mole fraction, c_{wet}, to the dry mole fraction, c_{dry}. The dry mole fraction is needed for calculating the trace gas flux, F_{c}, based on Eq. (5). The dry mole fraction is obtained from the wet mole fraction following the instructions for the infrared gas analyzer (Licor, 1996):
where X_{w} is the mole fraction of water vapor in the sample cell, X_{w,ref} is the water vapor mole fraction in the reference cell, ${c}_{\mathrm{s}}^{\mathrm{ws}}$ is the actual mole fraction of the trace gas in the sample cell diluted by X_{w}, and ${c}_{\mathrm{s}}^{\mathrm{wr}}$ is the equivalent sample cell CO_{2} mole fraction if it were diluted by X_{w,ref}.
2.9.3 TEA instrumentation and technical implementation
The TEA instrumentation used in this study was developed with particular attention to accurate and dynamic sampling of air and to realtime processing of wind data. The system was further designed to minimize time lags and jitter in wind data processing and in air sampling and to minimize dead volumes in the gas sampling system.
Vertical and horizontal wind velocities and the sonic temperature were measured using an ultrasonic anemometer R3 (Gill Instruments Ltd.), the same type which was also used for the sidebyside eddy covariance reference flux measurements. Wind velocity data were logged at a 10 Hz frequency.
Instant observations of vertical wind velocity were subject to realtime coordinate rotation to align the coordinate system of the sonic anemometer with the mean streamlines prior to controlling the sampling of air into updraft or downdraft reservoirs using the planar fit method (Wilczak et al., 2001). To the best of our knowledge, this study is the first eddy accumulation study to deploy a realtime coordinate rotation based on the planar fit rotation (Wilczak et al., 2001). A moving window of 1 d was used to estimate planar fit rotation coefficients, with an update frequency of the rotation coefficients of 30 min. The coefficients were then applied to rotate the instant raw wind measurements, w_{i}, 10 times per second.
To minimize $\stackrel{\mathrm{\u203e}}{w}$ over the flux averaging period the following procedure was applied: the mean vertical wind velocity of the current accumulation interval was approximated by the mean rotated vertical wind velocity over the most recent samples over a period with length equal to the length of the accumulation period, in this case 30 min. This estimate of mean vertical wind velocity was updated every 2 min and subtracted from every instantaneous vertical wind velocity measurement after coordinate rotation, i.e., 10 times per second.
The decision on updrafts and downdrafts was based on the sign of rotated w_{i}. Sample volumes were computed following Eq. (14). k was determined such that instant flow rates would not exceed the maximum possible flow rate of 3 L min^{−1}, with a probability of 99 % based on absolute wind data in the period from 30 min ago to present. The proportionality factor, k, which was based on the 99 % quantile multiplied by a factor of 2, was updated every 30 min.
Air inlets were colocated with the wind measurement and positioned 18 cm below and 2 cm beside the center of the sonic anemometer. Two separate air sampling lines were used, one for obtaining the updraft samples and one for the downdraft samples, respectively. In contrast to many previous eddy accumulation studies, which used a single air inlet and a 3∕2way valve to direct the samples towards the appropriate updraft or downdraft reservoir, the current design with two separate sampling lines avoids any undesired mixing of updrafts with downdrafts in the system. A detailed technical description and layout of the true eddy accumulation system with the two separate sample lines is presented in Fig. 5, including piping layout and system components, operating pressure conditions, pressure drops, dead volumes, and transit times of air samples through the system.
The intake of air was controlled by fastresponse mass flow controllers with a dynamic response resolving turbulent eddies at 10 Hz. The mass flow controllers used for this study were calibrated using conventional thermal mass flow controllers (Vögtlin redy smart series). The accuracy of the new dynamic mass flow controllers was equal to or better than 0.3 %, which corresponds to the accuracy of the conventional mass flow controller model used for calibration.
The new type of mass flow controller was tested for potential leaks, both relative to the ambient air and also for potential flow during times when the respective sampling line was inactive. The tests showed that the mass flow controller (MFC) was virtually leakfree. The combined leak rate of the MFCs, the pumps, the filters, tubing, and fittings was 0.0086±0.0003, expressed as the leak rate relative to the average inlet flow rate. In terms of flux uncertainty this would mean that a theoretical maximum of 0.86±0.03 % and, considering the other system components, likely far less of the flux uncertainty would be related to potential leakage or undesired nonzero flow of the mass flow controllers.
Air sampling lines were made of Teflon with a 6 mm outer and 4 mm inner diameter and a length of 5 m between intake and accumulation reservoirs. The air was filtered before entering the pumps and the bag reservoirs using PTFE membrane Gelman Acro Disc filters with a 50 mm diameter and a 2 µm pore size. Another filter was placed directly upstream of the gas analyzer.
At any time, one of the air sampling lines was active, with the selection of the line depending on the sign of the vertical wind velocity. The wind was measured at a frequency of 10 Hz using the sonic anemometer. With every new reading of vertical wind velocity, i.e., every 100 ms, the selection of the active inlet (updraft or downdraft) was updated depending on the sign of the vertical wind velocity and an air sample obtained with mass proportional to vertical wind velocity.
In contrast to common practice in many relaxed eddy accumulation studies, which typically define a minimum vertical wind velocity for air sampling, in the current design, air samples were obtained for all magnitudes of vertical wind velocity (except for the 0.5 % most positive and most negative values of w, respectively, as per the definition of k above).
Air samples were collected using two variable speed separate brushless DC membrane pumps (KNF Neuberger GmbH, Germany) with a maximum flow rate of 3 L min^{−1}, each, feeding air into the bag reservoirs at flow rates between 0 and 3 L min^{−1}.
Air was collected in lab grade, chemically inert Alumini^{®} air sample bags (Westphalen AG, Germany) with a volume of 28 L. The composite wall of the bags was made of (from outside to inside) polyethylene terephthalate (PET), polyethylene (PE), aluminum (ALU), oriented polyamide (OPA), and polyethylene (PE).
The layout of the TEA system is shown in Fig. 4. The system was designed for continuous operation, with continuous sampling of air and continuous onsite gas analysis. Air was collected in bags over periods of 30 min. Subsequently the air was analyzed over the following 30 min periods. A total of four bags was used at any time. A set of two bags (marked with “A” in Fig. 4) was charged with samples over 30 min, with one bag accumulating samples corresponding to updrafts (marked “updraft”) and one bag accumulating samples corresponding to downdrafts (marked “downdraft”). A second set of two bags (marked with “B” in Fig. 4), which contained air samples from the previous 30 min interval, was discharged and analyzed in parallel to the filling of the first set of bags. Every 30 min the two bag sets A and B would swap their function from being charged to being discharged. Note that data analysis revealed a leak in one of the bag sets, so that the data of every other half hour had to be discarded.
The accumulated air was analyzed for molar density of CO_{2} (µmol mol−1) and of water vapor (mmol mol−1) using a dual cell infrared gas analyzer, model LI6262 (LiCOR Env. Inc, USA). Air samples were discharged by a membrane pump (KNF Neuberger, Germany) from the sample bags through the sample cell of the gas analyzer at a flow rate of 0.6 L min^{−1}. The sampling frequency of the gas analyzer was 1 Hz. The reference cell was purged by dry and CO_{2}free zero gas obtained by circulating air through a scrubber filled with soda lime and Drierite desiccant. 3∕2way solenoid valves were used to select the appropriate gas bag for gas analysis.
During any 30 min period, the gas analysis alternated between sampling the updraft and downdraft reservoir, respectively (Fig. 6). Each bag was sampled for 150 s at a time. The first eight measurements periods of 150 s each were used for further analysis, resulting in four replicate measurements of the gas densities of the updraft reservoir and likewise four replicates of the downdraft reservoirs. Gas density measurements were tagged by the TEA controller with the respective active channel, either updraft or downdraft reservoir, for flux processing. The alternating sampling sequence lasted 1200 s. Over the remaining 600 s of the 30 min period, the remaining air was discharged from the bags to the atmosphere at a flow rate of 1.5 L min^{−1} until depletion.
The fully automatic TEA system was controlled by an ARMbased singleboard Linux computer of the type “Raspberry Pi” (Raspberry Pi Foundation, UK), the “TEA controller”. All sensor measurement data, including the wind and gas density measurements, were synchronized, logged, and processed on the same TEA controller.
The following raw data were logged for subsequent turbulent flux calculations: horizontal and vertical wind velocity components, $u,v,w$; sonic temperature, T_{s}; CO_{2} and H_{2}O molar densities; analyzer cell temperature and cell pressure; ambient air temperature, T; and air pressure, P. Further data on the state of the TEA sampling system and the analysis were logged for attribution of the gas analyzer measurements to updraft and downdraft samples, for the selection of the bag sets, and for system monitoring and quality control.
The energyefficient TEA system of the current study consumed 15 W of electrical power (excluding the gas analyzer), about 10 W of which was used by the three pumps. The pumping power required for the current TEA system was 2 orders of magnitude smaller than that of fastflow closedpath eddy covariance systems using infrared gas analyzers or laser spectrometers of ca. 1 kW. The additional power consumption of typical current laser spectrometers would be on the order of 0.25 kW. The difference in pumping power between TEA and EC scales with the flow rate and sample cell vacuum of the EC application and is therefore even more important for most closedpath laser spectrometers than for infrared gas analyzers.
2.9.4 TEA flux computations
Turbulent fluxes of CO_{2} were calculated from raw data of horizontal, u,v, and vertical, w, wind velocity components, sonic temperature, T_{s} (10 Hz), CO_{2} dry mole fraction (converted from wet mole fraction) and H_{2}O dry mole fraction (converted from wet mole fraction) (1 Hz), ambient air temperature, T (10 min resolution), and pressure, P (10 min resolution).
Raw gas density measurements were processed prior to flux computations in order to filter the data for noise and aggregate individual readings to single representations of the gas density, one for the updraft and one for the downdraft reservoir, during any one 30 min period. Blocks of 150 s (see Fig. 6) of measurements at 1 Hz were filtered and aggregated to 30 min values (see Sect. 3, Fig. 11 for results). The following statistically robust procedure was used:

Raw voltage signals of CO_{2} and H_{2}O were converted to physical units of micromoles per mole (µmol mol^{−1}), and the band broadening effect of pressure on CO_{2} observations was corrected for according to Licor (1996).

The CO_{2} wet mole fraction was converted to the dry mole fraction.

Gas density data were checked for plausibility based on preset minimum and maximum values.

The initial 30 s (deadband filter) after switching channels was omitted to allow for purging of the shared gas handling components, i.e., valves, sample line, and gas analyzer sample cell.

Raw data were despiked (spike filter) using the function “despike” from the R package “oce” (Kelley and Richards, 2017), replacing discarded values with the median of remaining values. The method identifies spikes with respect to a “reference” time series and replaces these spikes with the reference value, i.e., here the median.

The time series were smoothed (smoothing filter) using the function “loess” (Cleveland et al., 1992) from the R package “stats” (R Core Team, 2017). The loess function fits a polynomial surface determined by one or more numerical predictors, using local fitting.

Stable readings were selected (stationarity filter) by limiting maximum permissible gradients between individual samples for channelspecific data blocks of 150 s (120 s remaining after deadband filter), with a maximum permissible change of 0.002 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{mol}}^{\mathrm{1}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$.

Sufficient availability of data after filtering was checked for (availability filter): a data block was discarded if fewer than 30 (out of 120) values remained available after the stationarity filter.

The remaining filtered data were aggregated per channelspecific data block of 150 s using the median function.

The four replicates were aggregated per channel into a single value per 30 min as the weighted mean of the four samples, weighted by the number of accepted raw measurements in each of the four replicates, separately for updrafts and downdrafts.

To quantify precision of the CO_{2} molar fraction measurements using the LI6262 infrared gas analyzer, the minimum and maximum molar fractions over the four replicated samples were estimated, separately for updrafts and downdrafts and propagated into minimum and maximum flux estimates, respectively.
Fluxes were then calculated through the following:

plausibility check of wind data based on preset minimum and maximum values;

despiking of raw wind data (Vickers and Mahrt, 1997);

computation of the mole fraction difference between updraft and downdraft reservoirs per 30 min period;

computation of uncorrected turbulent fluxes for 30 min intervals according to Eq. (8);

computation of turbulent fluxes for 30 min intervals, corrected for volume mismatch between updraft and downdraft reservoirs, according to Eq. (13).
2.10 Eddy covariance (EC) reference flux measurements
2.10.1 EC instrumentation
A conventional EC system was set up for flux measurements of CO_{2}, sensible heat, and latent heat. The EC setup served as a reference for the TEA flux measurements. Instruments used were a threedimensional sonic anemometer of type R3 (Gill Instruments Ltd, UK) and an infrared gas analyzer, type LI7500 (LiCOR Env. Inc., USA). Wind and mole fraction data were recorded at a 20 Hz frequency at a height of 2.5 m a.g.l. The EC sensors were mounted side by side to a separate sonic anemometer and air inlet used for TEA. The two sonic anemometers were separated by a distance of 1 m. For quality assurance, in addition to the above primary eddy covariance setup, we used the sonic anemometer of the eddy covariance in combination with the openpath fast response gas analyzer (IRGA) for an alternative eddy covariance flux estimate. The horizontal separation between the EC sonic and the IRGA was 0.35 m, and the separation between the TEA sonic and the IRGA was 0.7 m.
2.10.2 EC flux computations
Eddy covariance raw data were postprocessed to obtain fluxes at a resolution of 30 min using the EddyPro^{®} software (LICOR Env. Inc., USA), version 5.0.0. The flux processing comprised the following steps:

statistical tests for raw data screening according to Vickers and Mahrt (1997), including spike count and removal, amplitude resolution, dropouts, absolute limits, skewness, and kurtosis;

detrending of raw time series by block averaging;

compensation of time lag between sonic anemometer and gas analyzer measurements by covariance maximization;

axis rotation for tilt correction using the planar fit method (Wilczak et al., 2001) with removal of the velocity bias (Van Dijk et al., 2004), in running window mode (1 d window, updated every 30 min) (TEA sonic) and fixed period (7 d) mode (EC sonic);

flux quality check according to Foken et al. (2004), selecting classes 0 and 1 for further analysis on a scale of 0, 1, and 2.
This section is organized as follows: (1) meteorological conditions during the experiment are presented, followed by (2) a characterization of mass flow control performance, a prerequisite for the (3) determination of concentration differences between accumulated updrafts and downdrafts, which, in combination with (4) vertical wind measurements, finally result in (5) trace gas fluxes. To inform the discussion on uncertainties of the eddy accumulation method, (6) coordinate rotation results, (7) uncertainties of vertical wind distributions, and (8) instrumental errors of the sonic anemometers and infrared gas analyzers used are presented.
3.1 Meteorological conditions
Meteorological conditions (Fig. 7) during the experimental period from 4 to 10 April 2015 were characterized by fair weather conditions with photosynthetically active radiation peaking at around 1500 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$ at noon (a). Air temperature was initially below 10 ^{∘}C on the first day with frost during the night but then rapidly increased to more than 20 ^{∘}C on the last day (b). Similarly, there was a positive soil temperature trend (d). No precipitation was observed during this period. Wind direction (f) was dominated by easterly winds except for 7 and 8 April with mostly westerly and stronger winds (e) and higher relative humidity (c). 7 April stands out as the day with highest wind speed (e), high friction velocity (h), low radiation (a), and low sensible heat flux (g). The sensible and latent heat fluxes (g) otherwise largely tracked radiation levels with the highest latent heat fluxes observed on 9 and 10 April and with a decreasing Bowen ratio.
3.2 Mass flow controller performance
Laboratory tests of the new digital mass flow controller used in this study showed that the accuracy and linearity of the digital mass flow controller for stationary flow were excellent: the maximum deviation of the new design from the conventional thermal mass flow controller used as reference was 0.3 % over the full operating range (Fig. 8). The minimum and maximum flow rates of the digital mass flow controller of 0.025 and 3 sml min^{−1} correspond to a dynamic range of 120, exceeding minimum performance requirements formulated by Hicks and McMillen (1984) for eddy accumulation, i.e., a dynamic range of 100 or higher. The tests also showed that the two controllers used for the updraft and downdraft channels of the TEA system, respectively, performed to the same level (red and blue line in Fig. 8).
We further compared the performance of the two mass flow controller designs under dynamic flow rate conditions (Fig. 9). The new digital mass flow controller was used to generate a highly dynamic reference signal for comparison with the conventional thermal mass flow controller. The uncertainty of the new digital mass flow controller (red uncertainty ranges in Fig. 9) was small relative to the dynamic signal itself. Conversely, the conventional thermal mass flow controller (blue line in Fig. 9) was unable to follow the dynamic reference signal, showing strong overshoot and overestimation of the reference flow rate.
Statistics of the mass flow controller comparison for the same data, as in the previous figure, are shown in the regression plots in Fig. 10. The new digital mass flow controller showed a perfect slope of 1.00, a high coefficient of determination of R^{2}=0.999, and a root mean square error (RMSE) of 8.8 sml min^{−1} (Fig. 10b), which is 50 times smaller than the RMSE of the conventional mass flow controller of 441.8 sml min^{−1} (Fig. 10a). The conventional mass flow controller further overestimated the reference by 300 % and matched less than half of the variance of the reference signal (R^{2}=0.43).
In conclusion, the dynamic response, precision, and accuracy of the digital mass flow controller are suitable for eddy accumulation sampling, while the conventional thermal mass flow controller is not.
3.3 CO_{2} molar fraction and differences between accumulated updrafts and downdrafts
Time series of the CO_{2} mole fraction obtained by the TEA system separately for the accumulated updrafts and downdrafts are shown in Fig. 11. Both the accumulated updrafts and downdrafts followed the common diurnal pattern of the CO_{2} mole fraction with minimal CO_{2} densities during the day when photosynthetic activity of the vegetation is at its maximum, a gradual buildup of CO_{2} from the late afternoon through the night, and finally a rapid decrease of CO_{2} in the morning when the daytime turbulence removes nightly accumulation of trace gases and photosynthesis then further draws down the ambient CO_{2} mole fraction. As expected, despite the generally similar course of the CO_{2} mole fraction of the updraft and downdraft reservoirs, there was a small but systematic difference between the two, with the CO_{2} mole fraction of the updrafts (red line in Fig. 11) being lower than the downdrafts (blue line in Fig. 11). This difference was caused by the relative CO_{2} depletion of updraft air due to photosynthesis during the day. At night, the inverse pattern was observed whereby updraft air was systematically enriched in CO_{2} through respiration from soil and vegetation.
The difference in the CO_{2} mole fraction between updraft and downdraft reservoirs is shown in Fig. 12. This difference was positive during the night and negative during the day. Windy conditions during the day cause a smaller magnitude of CO_{2} difference as seen on 7 April (see Fig. 7 for wind and Fig. 12 for CO_{2}). Likewise, calm conditions enhance the CO_{2} difference between updraft and downdraft reservoirs (see 9 and 10 April 2015, Fig. 12).
3.4 Mean absolute vertical wind velocity
Vertical wind velocity measurements from the TEA system are shown in Fig. 13, separately for updrafts and downdrafts (red and blue lines, respectively). Both updrafts and downdrafts show similar magnitude, which is to be expected for a mean vertical wind velocity close to zero (black and cyan line in Fig. 13). On 9 and 10 April, absolute vertical wind velocity w during the day was lower than for other days (Fig. 13). Lower absolute w, indicating less vertical mixing, corresponded with more pronounced differences in the CO_{2} molar fraction between updrafts and downdrafts, i.e., a more negative difference (Fig. 12) on the same 2 d. Under conditions of low winds and low turbulence, but intense radiation, the air close to the surface and the vegetation, which would be sensed as updrafts, was depleted in CO_{2} through photosynthesis, relative to the air above.
Mean vertical wind velocity, $\stackrel{\mathrm{\u203e}}{w}$, which ideally is zero over the 30 min flux integration intervals, rarely exceeded ±4 cm s^{−1} (dashed black lines), a threshold which, according to a simulation by Hicks and McMillen (1984), should not be exceeded to avoid significant flux errors. On two occasions, $\stackrel{\mathrm{\u203e}}{w}$ from the running window planar fit showed larger deviations from zero on 4 and 9 April 2015. Overall, the amplitude of $\stackrel{\mathrm{\u203e}}{w}$ was smaller for the planar fit rotation using a single 7 d window compared to the running planar fit using 1 d windows.
3.5 CO_{2} fluxes
The turbulent exchange of CO_{2} between the vegetation and the atmosphere as observed by TEA is displayed in Fig. 14. Fluxes clearly show CO_{2} uptake during the day (photosynthesis, with values up to ca. −20 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$) and CO_{2} release during the night (respiration, with values up to ca. +5 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$); see also the mean diurnal cycle in Fig. 15a. The temporal variability of CO_{2} fluxes measured by TEA (Fig. 14) reflects variation in photosynthetically active radiation (PAR; Fig. 7): 8, 9, and 10 April 2015 with high levels of radiation and the least amount of cloud also show the highest fluxes. 6 April, which experienced more clouds during the day and therefore less abundant photosynthetically active radiation, also showed relatively small CO_{2} fluxes during the day. Similarly, on 5 and 7 April, which were affected by clouds and reduced radiation in the early afternoon, the CO_{2} fluxes during the afternoon were reduced compared to cloudfree days, e.g., 9 April.
Nighttime CO_{2} fluxes measured by TEA showed a trend of increasing fluxes over the experimental period (Fig. 14). This trend corresponded to the observed trends of increasing air temperature and soil temperature (Fig. 7) over the same period. The observation of a positive correlation of positive CO_{2} fluxes (respiration) with soil and air temperature is in line with the widely accepted mechanistic understanding that soil respiration is a function of soil temperature with a positive correlation over the temperature range presented. Overall, from an ecophysiological point of view, the observed CO_{2} fluxes corresponded well with their meteorological drivers.
From a methodological point of view, a key step in assessing the TEA method's performance is the comparison of the TEA method with the established EC method. Fig. 14 shows CO_{2} fluxes measured by both TEA (black line) and EC (red and blue points). The eddy covariance fluxes shown in Fig. 14 are qualityfiltered, accepting flags ≤1 (Foken et al., 2004; on a scale of 0, 1, and 2). This filtering reduced the number of available 30 min eddy covariance flux estimates to 90 % and 93 %, and filtering for flag =0 reduced the fraction of available data to 45 % and 46 % for the sonic anemometers of the TEA and the EC system, respectively (both used for eddy covariance fluxes).
Generally, good agreement was observed between the TEA and EC methods. However, the intercomparison of the methods was complicated by the presence of high noise levels in the 30 min EC flux estimates. Analysis of R3 sonic anemometer raw data revealed that the EC sonic anemometer (blue line Fig. 14) was affected by correlated noise in the highfrequency wind and sonic temperature measurements, resulting in erroneously high sensible heat flux and momentum flux estimates. The erroneously high variance of the horizontal and vertical wind components was particularly pronounced during the night and decreased over the experimental period. Conversely, erroneously high sonic temperature variance increased over the experimental period. CO_{2} fluxes were affected to a lesser degree because the noise in the R3 sonic anemometer data was not necessarily correlated with the LI7500 infrared gas analyzer measurements.
The sonic anemometer of the TEA system seemed less affected by noise. Therefore we used it as an alternative input to the eddy covariance flux computations. However, the horizontal separation between the latter sonic anemometer and the openpath gas analyzer was large (0.7 m) relative to the low measurement height. Eddy covariance CO_{2} fluxes from the TEA sonic anemometer were on average 18 % smaller compared to the EC sonic anemometer. However, after eliminating inconsistent fluxes whereby the fluxes from the two sonic anemometers disagreed by more than 50 % or alternatively 25 %, eddy covariance CO_{2} fluxes from the TEA sonic anemometer were on average 6 % smaller and 2 % larger, respectively, compared to the EC sonic anemometer (Fig. 15).
A regression of CO_{2} fluxes from the TEA method versus the EC method is shown in Fig. 15b, comparing TEA fluxes to the two alternative EC flux estimates after quality filtering eddy covariance fluxes with flags ≤1 (Foken et al., 2004). Before applying the above consistency filter, the coefficients of determination were R^{2}=76 % and 67 %, and the linear model slopes were 1.04 and 0.87 when quality filtering eddy covariance fluxes for flags ≤1 (Foken et al., 2004) and improved to R^{2}=71 % and 76 % and slopes of 0.99 and 0.92 for flags =0, for (i) TEA fluxes versus EC fluxes (using the TEA sonic anemometer for EC) and (ii) TEA versus EC fluxes (using the EC sonic anemometer for EC), respectively. The correlation further improved when rejecting conflicting EC fluxes: limiting the difference of the two EC flux estimates from the two independent sonic anemometers to 50 % of the mean of the two fluxes (flags ≤1), the coefficients of determination of TEA versus EC fluxes increased further to 80 %, 80 %, and 82 %, with linear model slopes of 1.01, 0.96, and 0.99, for (i) TEA fluxes versus EC fluxes (using the TEA sonic anemometers for EC), (ii) TEA versus EC fluxes (using the EC sonic anemometer for EC), and (iii) TEA versus EC fluxes (using the average of the TEA and EC sonic anemometers for EC), respectively (case shown in Fig. 15b).
While a certain fraction of the observed deviations between TEA and EC flux estimates can be attributed to the methodological differences, the two independent eddy covariance flux estimates also showed deficiencies in agreement, with coefficients of determination of the EC to EC regression of R^{2}=84 %, 86 %, and 85 % and slopes of 0.81, 0.82, 0.85, leaving 16 %, 14 %, and 15 % of the flux variance unexplained for quality flag filter thresholds of 2, 1, and 0. The percentage of additional unexplained variance in the TEA fluxes with R^{2}=74 % (regression of TEA fluxes versus mean EC fluxes from the two sonic anemometers, flag ≤1) relative to EC fluxes with R^{2}=86 % was 12 % only. There was a positive intercept for the above regression cases between TEA and EC fluxes which ranged from 1.8 to 2.4 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$.
While the abovereported coefficients of determination for the EC versus EC flux regressions using various filter options were somewhat higher than for TEA versus EC fluxes, the differences between the TEA and EC methods were still of the same order of magnitude as the differences between the two EC flux estimates, which use the same infrared gas analyzer. It might seem from Fig. 15a and the abovereported statistics that the two EC flux estimates match more closely than TEA and EC fluxes. However, we note that the EC–EC agreement is to some degree artificial; i.e., only a part of this apparent agreement relates to differences between TEA and EC methods, and another part is simply due to the “consistency filter” applied to the two EC flux estimates. This filter, which by definition discards EC flux values which are not similar, is not normally required but was introduced to deal with the abovementioned deficiencies of the two EC setups.
We would expect from a sidebyside comparison of eddy covariance flux measurements, using identical models of research class sonic anemometers and sharing the same gas analyzer, that the R^{2} would exceed 90 %. We interpret the compromised match of the two current EC estimates largely as a result of compromised wind and sonic temperature measurements by the two R3 anemometers. When excluding the first 4 d which were relatively more affected by erroneous w, filtering for quality flags ≤1 and again filtering EC fluxes to not exceed a relative difference between the two EC flux estimates of 50 %, then the match of TEA versus EC CO_{2} fluxes improved further, yielding R^{2} values of 84 %, 86 %, and 86 %, slopes of 1.04, 0.91, and 0.98, and intercepts of 2.0, 1.9, and 2.0 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$ for TEA fluxes versus EC fluxes using the TEA sonic anemometers, the EC sonic anemometers, and the mean of the TEA and EC sonic anemometers, respectively.
In relation to previous works on true eddy accumulation trace gas flux measurements, we note that, despite compromised data quality of one of the R3 sonic anemometers of the current study, the match of true eddy accumulation and eddy covariance CO_{2} fluxes exceeded the match in any previously published true eddy accumulation experiments we are aware of. The closest results are those from Komori et al. (2004), who obtained a coefficient of determination for TEA versus EC CO_{2} fluxes of R^{2}=0.64, a slope of 0.95, and a relatively high intercept of 8.6 $\mathrm{\mu}\mathrm{mol}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{\mathrm{1}}$ for 17 flux integration intervals.
3.6 Uncertainty of vertical wind measurements
Vertical wind measurements contribute to flux uncertainty in two ways: (i) instrumental errors of the sonic anemometer and (ii) nonideal wind field and nonzero mean vertical wind velocity over the flux integration period.
3.6.1 Sonic anemometer measurement errors
Systematic and random errors in sonic anemometer measurements contribute to scalar flux uncertainty both in the EC and TEA methods. For a detailed analysis of sonic anemometer measurement errors we refer to instrument comparisons and quantifications of measurement errors for common sonic anemometer types (Loescher et al., 2005; Mauder and Zeeman, 2018; Foken et al., 2019, and others). These studies suggest that measurement errors of sonic anemometers, including differences between different types of sonic anemometers and differences between different units of the same type of sonic anemometer, may account for anywhere from several percent up to about 25 % of the error in scalar flux measurements.
Regarding the R3type sonic anemometer used in the current study, Loescher et al. (2005, Fig. 5) found in wind tunnel tests that the R3 sonic anemometer, like other postmounted designs, suffered from flow distortion, systematically overestimating vertical wind velocity. The R3 overestimated vertical wind velocity for vertical velocities below 0.15 m s^{−1} by up to ca. 0.05 m s^{−1} for vertical velocities close to zero and underestimated vertical velocity by up to the same amount for vertical velocities up to 0.3 m s^{−1} (gain error). In addition, when the stanchions supporting the upper transducers were in the flow path, the vertical wind velocity response was nonlinear. Nonlinearity and gain errors can result in misalignment of the coordinate system with the mean streamlines (see Sect. 3.6.2) and apparent asymmetry of vertical wind distributions (see Sect. 3.6.3).
3.6.2 Coordinate rotation
The following analyses present nonzero mean vertical wind velocities, which cause scalar flux uncertainty. Figure 16 shows vertical wind before and after coordinate rotation. Vertical wind velocity scaled by horizontal wind velocity ideally follows a (co)sine function when anemometer coordinates are tilted relative to streamline coordinates (Fig. 16a). Planar fit rotation reduced the range of $\stackrel{\mathrm{\u203e}}{w}$ from about ±0.1 m s^{−1} to about ±0.05 m s^{−1} (Fig. 16b). The range of $\stackrel{\mathrm{\u203e}}{w}$ was slightly smaller for the 7 d rotation window compared to the running 1 d window. Figure 16c indicates that before coordinate rotation the sonic coordinate frame was tilted relative to the streamlines, which followed the terrain slope. The slope of the relation of $\stackrel{\mathrm{\u203e}}{w}$ over alongslope wind U (c) vanished after planar fit rotation using the 7 d window (d). The running planar fit with a 1 d window did not fully remove the dependence of $\stackrel{\mathrm{\u203e}}{w}$ from alongslope wind velocity, biasing $\stackrel{\mathrm{\u203e}}{w}$ by up to ±0.02 m s^{−1} over the range of alongslope velocities shown (d), corresponding to about 15 % of bias before tilt correction.
Figure 17 presents residuals of mean vertical wind velocity $\stackrel{\mathrm{\u203e}}{w}$ before and after coordinate rotation in u and v horizontal velocity space. This analysis relates $\stackrel{\mathrm{\u203e}}{w}$ to wind direction, horizontal wind velocity, and obstacles causing flow distortion. $\stackrel{\mathrm{\u203e}}{w}$ (in Fig. 17a) before tilt correction shows the effect of the terrain slope on wind measurements in sonic coordinates. The slope effect was fully removed through planar fit rotation (Fig. 17b). The 1 d running window planar fit led to a slight overcorrection of the tilt (Fig. 17b), as already noted regarding Fig. 16d, which was not the case for the planar fit rotation using a 7 d window. Residuals of $\stackrel{\mathrm{\u203e}}{w}$ were small with the 1 d running planar fit, resulting in relatively larger $\stackrel{\mathrm{\u203e}}{w}$ residuals up to about ±0.05 m s^{−1} (Fig. 17b) compared to up to about ±0.02 m s^{−1} for the 7 d planar fit (Fig. 17c).
Some dependence of $\stackrel{\mathrm{\u203e}}{w}$ on horizontal wind velocity and direction was observed: for horizontal wind velocities of more than about 1 m s^{−1}, residuals of $\stackrel{\mathrm{\u203e}}{w}$ were mostly positive, particularly for southwesterly and northeasterly winds (Fig. 17b and c). This was confirmed by the planar fit rotation of a 2monthlong data set (Fig. 17d). Possible interpretations include flow distortion from trees and bushes in the southwest and northeast and velocitydependent flow distortion of the sonic anemometer or nearby structures. No obvious influence of the stanchions of the anemometer on $\stackrel{\mathrm{\u203e}}{w}$ was identified (Fig. 17a–d).
3.6.3 Updraft–downdraft asymmetries
The TEA method requires $\stackrel{\mathrm{\u203e}}{w}=\mathrm{0}$, which would result from symmetry in updraft and downdraft statistics. However, we observed asymmetry in the mean, the count, and the sum of updraft and downdraft samples. Quantification of the flux uncertainty due to asymmetric distributions of w would require cospectral information of w and CO_{2} densities, which is generally absent for TEA measurements. Instead, we present a quantification of observed asymmetries of w, informing about the magnitude of the asymmetries and their variability over time.
Figure 18 shows that (i) on average, the count of updrafts was larger than the count of downdrafts; (ii) however, on average, the mean of updrafts was smaller than the mean of downdrafts; and (iii) on average, the sum of updrafts was slightly smaller than the sum of downdrafts. It is noteworthy that the mean of w can still be zero while the 7 d mean of the 30 min mean of updrafts and the 30 min mean of downdrafts are nonzero; or in other words, the ratio of the 30 min mean of the updrafts to the 30 min mean of the downdrafts is different from unity as observed here. This can be understood by considering the different weights of updrafts and downdrafts in the mean which reflect the asymmetry in the counts of updrafts and downdrafts, respectively.
Figure 19 shows probability density distributions of the relative uncertainty of the mean absolute vertical wind as defined in the figure caption. The distribution of the sums of updrafts and downdrafts is centered around zero, with only a small negative bias of −0.01 for the mode of the distribution and a larger bias of −0.04 for the mean of the distribution. Conversely, the distribution of the relative uncertainty of the means peaked for both the mode and the mean of the distribution at a more negative bias of −0.11, as observed for the running window planar fit (Fig. 19, blue line). Similar results were obtained for the 7 d stationary planar fit although with a smaller negative bias of −0.08 (Fig. 19, red line). Less than 10 % percent of relative uncertainty values were more negative than −0.3, and less than 10 % of relative uncertainties were larger than +0.14. In summary, updraft–downdraft asymmetries were on the order of 10 % of the mean absolute vertical wind velocities used in flux calculations.
3.7 Uncertainty of trace gas concentration measurements
Trace gas flux errors are a function of accuracy and precision of the trace gas analysis. Regarding accuracy, bias between the two infrared gas analyzers used for the TEA and EC methods is more relevant than absolute accuracy for comparing the TEA method to the EC reference method. By comparing timeaveraged time series of CO_{2} concentrations of the LI6262 and LI7500 infrared gas analyzers, a timevariable bias was found, which accounted for up to 5 % of the scalar flux.
Regarding scalar flux errors from the TEA method, systematic errors leading to bias between measurements of updrafts and downdrafts and precision are important. Systematic errors biasing the concentration difference between updrafts and downdrafts are difficult to quantify. The following results quantify the precision of the gas analysis, based on the analysis of four replicated measurements of 120 s each of the accumulated updraft and downdraft concentrations, per 30 min flux integration interval. The results comprise precision of the gas analyzer at the measurement frequency of 1 Hz as well as precision of the TEA gas sampling storage and delivery system, feeding samples to the gas analyzer. The latter includes drift of the gas analyzer signal and of the trace gas concentration over the time required to determine a concentration difference between updrafts and downdrafts, i.e., 2 times 150 s.
Regarding the observed CO_{2} concentration signal, 90 % of CO_{2} dry molar fraction differences between updrafts and downdrafts at 30 min integration were between 0.14 and 2.08 µmol mol^{−1} (Fig. 20). Regarding the observed precision of the total gas analysis system under field conditions, for 90 % of flux integration intervals, the CO_{2} dry molar fraction measurements over four replicated measurements of the updraft reservoir varied in the range of 0.033 to 0.48 µmol mol^{−1}. The precision of downdraft measurements was 50 % lower, with 90 % of the downdraft measurements showing a range of the four replicates of 0.05 and 0.73 µmol mol^{−1}.
For 85 % of the flux integration intervals, the signal, i.e., the dry molar fraction difference between updrafts and downdrafts, was larger than the nominal and extrapolated 120 s precision of the LI6262 infrared gas analyzer used in this study, as well as the precision, i.e., Allan deviation, of two laser spectrometers we tested in the laboratory. The latter two instruments were not used in the current study, but characteristics are provided to put the instrument used in this study in the context of current stateoftheart greenhouse gas monitors. Note that the indicated precision of the LI6262 of 0.29 µmol mol^{−1} is an extrapolation of nominal precision and drift values to 120 s, for which nominal precision was given as peaktopeak noise, rather than Allan deviation, which was used to characterize the laser spectrometers and is by definition smaller than or equal to the peaktopeak noise.
Also note that the Allan deviation at 120 s integration of the G2301 (Picarro) instrument of 0.0125 µmol mol^{−1} appeared to be only 7.4 % of the Allan deviation of the FGGA (Los Gatos Research) laser spectrometer of 0.17 µmol mol^{−1}. However, in addition to differences in the design of the two spectrometers and any potential differences in test conditions, it appears from the analysis of Allan deviation that the G2301 (Picarro) instrument may be subject to some degree of internal smoothing of the gas concentration readings. We cannot say with certainty to which degree such potential smoothing might have affected the Allan deviation at 120 s integration time because the manufacturer of the instrument was unable to provide further information on the suspected filter beyond acknowledging its existence.
The observed signaltonoise ratio (SNR) of the total trace gas analysis system under field conditions ranged between −9 and +21 (and one value at −66.7) and improved with the magnitude of the signal itself (Fig. 21a). The slope and intercept of an ordinary leastsquares linear model fit to this relation were 3.2 µmol^{−1} mol and 0.48, respectively. The fact that this quasilinear relationship and the slope significantly differed from zero means that larger fluxes have relatively smaller errors of the type considered, a feature reducing absolute uncertainty of trace gas flux budgets.
For 88 % of 30 min flux integration intervals, the signaltonoise ratio was larger than 1 (Fig. 21b). Over the period of the experiment, the sum of the same noise data as above accounted for up to 25 % of the sum of the trace gas concentration signal, i.e., of the difference in CO_{2} dry molar fraction between updraft and downdraft reservoirs. The percentage of 25 % is a maximum estimate for this type of noise, as it was determined from the range of the four replicates of concentration difference measurements, which is sensitive to extremes.
3.8 Uncertainty of trace gas flux measurements
The uncertainty of trace gas fluxes due to the uncertainty of the gas analysis is shown in Fig. 22. Over the period of the experiment, the sum of the noise range, i.e., the absolute value of the difference between the largest and smallest flux estimate, accounted for 37 % of the sum of the signal, i.e., the absolute value of the mean flux. As stated above for CO_{2} concentrations, the percentage of 37 % is a maximum estimate of this type of noise because it was determined from the range of the four replicates of concentration difference measurements, which is sensitive to extremes, and because this estimate is additive. In practice, it is highly unlikely that this uncertainty range leads to additive errors; instead, some of the errors would cancel, leading to much smaller actual uncertainties.
Regarding the time series of trace gas flux noise, i.e., the range of maximum and minimum flux estimates (Fig. 22), calm conditions with low wind speeds and low friction velocities, e.g., on 10 April, result in relatively large concentration differences and relatively small vertical wind terms contributing to the trace gas flux calculations and therefore result in relatively low uncertainty of the flux due to the uncertainty of the gas analysis. The opposite can be observed for windy conditions with high friction velocity, e.g., on 7 April, which result in relatively small concentration differences and a relatively high contribution of the vertical wind term to the flux calculations and therefore a relatively high uncertainty of the flux due to the uncertainty of the gas analysis.
The total uncertainty of the trace gas flux needs to account for the uncertainty of the mass flow control, the uncertainty of the concentration differences, and the uncertainty of the vertical wind signal. Ideally, such analysis would incorporate the effect of different approaches of coordinate rotation not just on the residuals of $\stackrel{\mathrm{\u203e}}{w}$ but also the effect on the fluxes themselves. This would require consideration of cospectral information of wind and scalar using timeresolved highfrequency data and simulations of true eddy accumulation with different coordinate rotation approaches.
The following conclusions intend to summarize the performance of the true eddy accumulation method, put the results of the current experiment into context relative to existing published studies, summarize and quantify main sources of uncertainty, report on limitations and lessons learned during the current experiment, suggest future improvements regarding technical and methodological aspects, and finally identify applications in which true eddy accumulation can facilitate novel flux measurements in the future.
The current study has presented CO_{2} fluxes measured by true eddy accumulation. The TEA system measured continuously and automatically fluxes at 30 min resolution over a duration of more than 7 d. The TEA measurements were able to capture fluxes representing the biological activity of the system. TEA flux measurements compared favorably with eddy covariance reference measurements, with R^{2} values of up to 86 % and a regression slope of 0.98.
A novel implementation of dynamic mass flow control was key to the success. It was 50 times more accurate in terms of root mean square error than the conventional thermal mass flow controller reference during laboratory tests and proved to be robust and without failure during more than 3 years of operating time in the field. Further innovative features were the digital signal processing and the realtime sampling decisions, incorporating online coordinate rotation and correction of the mean vertical wind, and, finally, the elimination of dead volumes in the gas sampling system.
Compared to earlier studies published on true eddy accumulation flux measurements (Desjardins, 1977, on temperature fluxes; Speer et al., 1985, and Neumann et al., 1989, on water vapor fluxes; Rinne et al., 2000, on isoprene fluxes; and Komori et al., 2004, on CO_{2} fluxes), the current study obtained the best fit of TEA fluxes to EC fluxes of any trace gas or scalar. The current study also presents the longest continuous CO_{2} flux measurements by TEA.
A detailed analysis of uncertainties of the TEA method was presented in terms of the uncertainty of the mass flow controllers, the uncertainty of the trace gas handling and analysis system, and the uncertainty of the vertical wind velocity measurements and 30 min means. Uncertainties of the eddy covariance method and instruments were partially quantified through two replicated flux computations using two alternative sonic anemometers. Uncertainties of the EC fluxes explained a significant fraction of the mismatch between the TEA and EC methods. The signaltonoise ratio of the TEA trace gas analysis system allowed the concentration difference signal to be detected in 88 % of 30 min flux intervals. Maximum uncertainty estimates of the TEA trace gas measurement precision accounted for up to 25 % of the concentration differences and up to 37 % of the fluxes. A comparison of the precision of three gas analyzers suggests that deployment of stateoftheart laser spectrometers would significantly reduce TEA flux uncertainty due to uncertainties in the gas analysis, with preliminary analysis suggesting an improvement in precision by a factor of 10 or more for some instrument models. This would likely reduce the flux uncertainty due to the gas analysis to about 5 % or less. Residual mean vertical wind velocities were generally smaller than 0.05 m s^{−1}. Uncertainties of the mean of absolute vertical wind velocities, which are needed for flux calculations, in terms of undesired residuals of mean vertical wind velocities after coordinate rotation were frequently on the order of 5 %. The uncertainties of the mass flow control were relatively small compared to uncertainties of the gas analysis, uncertainties of residual mean vertical wind velocities, and uncertainties of the eddy covariance flux estimates.
The following two design limitations were discovered: firstly, the continuous and longterm operation with frequent charging and discharging of the air sampling bags with on the order of 1500 charge cycles per month over time leads to increasing levels of fatigue of the material and in turn after a few weeks to a significant amount of leakage and therefore contamination of the samples with ambient air. The second observation relates to the intermittent nature of the gas flow, the variable accumulation volumes, and the intermittent gas analysis in the current bagbased accumulation design. Intermittent operation causes instationarity of the following parameters: air pressure in the gas handling system, temperatures of air and system components, and interactions of air constituents with the internal surfaces of the device such as adsorption and desorption of gas molecules on internal surfaces. Instationary conditions can lead to signal drift, variation of moisture content, and subsequently to less accurate flux measurements.
To address the abovementioned limitations, we suggest exploring the idea of a new system design for TEA using rigid air containers of constant volume and with continuousflow operation replacing flexible air bags. In such a new design the charging and discharging of the air reservoirs would happen continuously and at the same time. This new design principle would overcome the issue of material fatigue and compromised accuracy due to instationarities in the operation. A key methodological advantage of the new continuousflow design is furthering the opportunity to merge the principles of true eddy accumulation sampling with eddy covariance sampling simultaneously with the very same measurement device, the same air samples, and the same gas analyzer.
Using a precise stateoftheart laser spectrometer we have since implemented such a continuousflow system suggested above and demonstrated its superior performance compared to conventional discrete cyclic charging of air bags. True eddy accumulation CO_{2} fluxes observed with the new continuousflow system were tightly correlated with eddy covariance fluxes, with R^{2} values of up to 96 %. More details on the latter study will be reported separately.
The impact of coordinate rotation on true eddy accumulation fluxes has been discussed. We have suggested a new type of coordinate rotation, which we refer to as “surface fit”. Similar to the planar fit method, it aligns the coordinate system with the mean streamlines, accounting for a multidimensional parameter set including wind direction, flow distortion, and optionally other independent variables in an integrative, continuous way.
We would like to highlight the need for research on flux corrections for TEA in a comprehensive way similar to the body of work which exists on EC flux corrections. Future work needs to investigate and establish flux corrections specifically for the TEA method, including the equivalent to the correction of trace gas fluxes due to density fluctuations caused by simultaneous transfer of heat and water vapor (Webb et al., 1980). The derivation of this and other corrections specifically for the TEA method is nontrivial and will be addressed in separate work.
The current implementation of TEA suggests that this method has the potential to facilitate flux measurements of trace gases and other atmospheric constituents for which no fast gas analyzers are available. TEA is an alternative when the precision and accuracy of currently available analyzers are insufficient for highfrequency EC applications. The low power consumption of the current TEA systems with low sample flow rates will enable new applications, including offgrid use in solar and batterypowered stationary and mobile applications. The long sample integration times give TEA a further advantage over EC, allowing for a simpler analyzer design compared to highfrequency analyzers at the same precision or alternatively providing ultimate precision through long integration times when using a highquality analyzer.
It is evident that CO_{2} fluxes in particular can be readily observed with alternative methods. However, the nonreactive and nonpolar trace gas CO_{2} is an ideal candidate to assess the performance of the TEA method. The current experiment is a successful proof of concept demonstrating that true eddy accumulation with dynamic and accurate air sampling proportional to vertical wind velocity can be achieved in practice today. The lessons learned during the present work provide concise avenues including the aboveoutlined machine design considerations and required flux corrections for further improving the true eddy accumulation method to enable accurate and reliable flux measurements of more trace gases and atmospheric constituents than ever before.
The data supporting this publication can be found at https://doi.org/10.5281/zenodo.3338395 (Siebicke and Emad, 2019).
This study was conceptualized, designed, performed, analyzed, interpreted, managed, and written by LS with contributions to postprocessing of gas analyzer data, to TEA flux calculations, and to discussions on the methods by AE. The mass flow control system used in this study was conceptualized, designed, built, and calibrated by LS.
The authors declare that they have no conflict of interest.
Any statements about the performance of measurement devices presented in this study, including commercially available gas analyzers, sonic anemometers, or mass flow controllers, are based on observations from the actual units deployed in the current study and do not claim general validity for other types or different units of the same type or under different conditions.
We would like to thank the two anonymous referees and the editor for their constructive, useful comments, which have improved the manuscript. We gratefully acknowledge the support of the Bioclimatology group, Alexander Knohl, University of Göttingen, in particular technical assistance by Malte Puhan, Dietmar Fellert, Frank Tiedemann, and Heiner Kreilein during calibration, preparation, and setup of instruments in the field and for the provision of meteorological measurements. We further acknowledge Jelka BradenBehrens and Christian Markwitz for fruitful discussions during preparation of the manuscript as well as Karly Conrads and Fernando Moyano for proofreading. Lukas Siebicke would like to thank Thomas Foken for exposure to the theory of eddy accumulation flux measurements as well as Benoit Burban, JeanYves Goret, James Morison, Mike Perks, and Dorothea Schreiber for their support and trust along the way.
This openaccess publication was funded by the University of Göttingen.
This paper was edited by Hartwig Harder and reviewed by two anonymous referees.
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true eddy accumulation(TEA), able to quantify the land–atmosphere exchange of a large number of trace gases which are important for air quality and atmospheric composition. Our innovative implementation provides proof of concept of TEA and compared well to the established reference, outperforming previous works on TEA. Key to the success was the innovative highspeed air sampling and fully digital realtime data processing system.
true eddy accumulation(TEA), able to quantify...