Traditionally, a combination of analog and digital transmission systems has been used to collect EC data (Eugster and Plüss, 2010). For example, analog signals from the gas analyzer were sent to an interface unit responsible for digitizing the data before merging it with anemometric data, itself coming from an A/D (analog/digital) converter into the interface unit, typically from a sonic anemometer-thermometer (SAT). More recently, specular solutions, with the analog data from the SAT sent to an interface unit residing in the gas analyzer system, became available and were widely adopted. With both of these approaches, the data were presented to the user for the flux calculation as single files with wind and gas time series merged and synchronized by the interface unit.

Analog data output allows the data to easily cross clock domains. The clock that is used to sample the original signal does not need to be synchronized to the clock that samples the analog output. This makes it very convenient to merge data from systems with unsynchronized clocks and risks of misalignments are limited to small random errors that, as we will see later, have no significant effects on fluxes.

However, collecting data in analog form has several limitations and risks. First, the number of analog channels available either as outputs from the instruments or as inputs to the interface unit is typically limited to four or six, which dramatically reduces the number of variables that can be collected. In fact, historic EC raw datasets are comprised of six or maximum seven variables: the three wind components (u, v, w), the sonic temperature (Ts), and the concentration of the gases of interest (c, traditionally CO2 and H2O); more rarely, a diagnostic variable for the anemometric data was also collected. Critical information such as the full diagnostics of both instruments and their status (e.g., the temperature and pressure in the gas analyzer cell or the signal strength) or the original raw measurement (speed of sound, raw data counts etc.) are not collected in most analog systems, limiting the means for quality screening and limiting the possibility of future recomputation of the most fundamental raw measurements. Another problem with analog data collection is that signals are subject to degradation due to dissipation, electromagnetic noise, and ageing of cables and connectors, which reduces the quality of collected data (Barnes, 1987). In addition, although all raw measurements are analog in nature, they are typically immediately digitized (native digital format provided by the manufacturer) and then – in the case of analog data collection – they are re-converted to analog, sent to the interface unit and there converted back to digital; these A/D–D/A conversions potentially degrade the signal adding noise and dampening high-frequency signal components (Eugster and Plüss, 2010). For these reasons, analog connectivity should nowadays be avoided whenever possible in favor of fully digital solutions.

In fully digital EC acquisition systems, both data streams are collected in their respective native digital format, i.e., without additional A/D conversions other than those implemented by the manufacturer to provide digital outputs. Fully digital systems largely or completely overcome both problems with mixed analog/digital systems, using more robust and less corruptible data transmission protocols, and providing the possibility of collecting all variables available from the individual instrument. However, combining digital data streams from different instruments brings new challenges, most notably with respect to data synchronization. While moving between clock domains is trivial in an analog system, it can be much more challenging with digital data when the involved clocks can be completely asynchronous to each other.

Different strategies exist for collecting data digitally. First, instruments can perform the measurements according to their own scheduler or a trigger. In the scheduler case, data can then be collected by polling the instrument for the latest available data (polling mode) or by keeping an open channel where data are streamed (streaming mode). In the trigger case, data are usually made available after a fixed or somewhat variable delay to the logging device. This delay is due to the acquisition time and could also include a delay due to filtering. However, the timestamp for the acquired data is assigned based on the occurrence of the trigger, therefore removing any timing error due to that delay. All modes have advantages and disadvantages. As described later, triggering and polling modes are less susceptible to timing errors, but they require the instrumentation to be designed for the particular triggering or polling system adopted. They are therefore best suited for EC systems built with all components from the same manufacturer. For the same reason, such systems are commonly not flexible enough to accommodate third-party instrumentation. EC systems commercialized by Campbell Scientific Inc. (Logan, UT, USA; “CSI” hereafter) are examples of integrated systems using a data triggering strategy to collect data from instruments designed ad hoc. Data communication in these systems is realized via the synchronous devices for measurement (SDM) protocol (or its evolutions), which is a CSI proprietary protocol, implemented only in CSI instruments and some CO2/H2O gas analyzers by LI-COR Biosciences Inc. (Lincoln, NE, USA; “LI-COR” hereafter). By contrast, most instrumentation available for fast wind and gas measurements only provide data transmission options in streaming mode. As a consequence, most data logging solutions developed by the scientific community or by commercial entities are designed to handle data provided in streaming mode and are therefore flexible to accommodate a wide variety of instrumentation. Examples of such logging systems developed by the community are PC-based software such as Huskerflux (https://github.com/Flux-Dave/HuskerFlux, last access: 26 June 2018), EddyMeas (Kolle and Rebmann, 2007), EdiSol (EdiSol User Guide V0.39b https://epic.awi.de/29686/1/Mon2005d.pdf, last access: 26 June 2018), or the already referenced system proposed by Eugster and Plüss (2010) for EC measurement of methane. As for commercial solutions, LI-COR provides industrial-grade EC systems based on the SmartFlux^® system, that can accommodate a wide variety of instrumentation using the data-streaming approach.

However, collecting data in streaming mode exposes the risk of introducing significant timing errors, because of the number of asynchronous digital clocks involved.

Digital clocks are electronic oscillator circuits that use the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a precise frequency, which is then used to keep track of time. The number and quality of clocks involved in an EC system vary with the data collection strategy and technology. In systems based on data triggering or polling, there is only one critical clock (the one responsible for the timing of the triggering or polling signal); therefore, there is no significant risk of introducing systematic timing misalignments between data from different instruments (see later). With these systems, the risk is limited to random and/or constant misalignments. As we will see later, random or constant misalignments do not entail large errors. For this reason, in the remainder of this section we consider in more detail the situation with systems based on data streaming.

In such systems the potentially relevant clocks are, in general, the following.

The sampling clocks of the sensing instruments (the SAT and the gas analyzer in a typical EC system), responsible for sampling data at the prescribed rate with sufficient precision and accuracy;

Packet-based data communications such as Ethernet even further isolate the sampling clock from the transmission clock. In devices using this protocol, it is therefore impossible to reconstruct a sampling clock. However, for Ethernet-based systems additional protocols are available, such as Network Time Protocol (NTP) or Precision Time Protocol (PTP), to actually synchronize all system clocks. The synchronized system clocks then allow the data to be correctly timestamped before transmission, eliminating any synchronization issue, provided that downstream software can align the various data streams based on their timestamps (e.g., Mahmood et al., 2014).

In typical EC data acquisition setups, time series collected by different instruments can show three distinct types of misalignments (Fig. 1).

Time lags: these are constant offsets in otherwise perfectly aligned time series. They can be the result of constant electronic delays or of fixed delays due to digital signal processing. More frequently, they result from a physical separation of the sampling volumes or from the delay due to the time needed for the passage of air in a sampling line.

The fundamental difference between time lags on one side and RTE/STE on the other side is that constant time lags can, at least in principle, be addressed a posteriori during data processing. The topic of correctly estimating and compensating time lags has long been discussed in the EC literature (Vickers and Mahrt, 1997; Ibrom et al., 2007; Massman and Ibrom, 2008; Langford et al., 2015), and corresponding algorithms are available in EC processing software. We will therefore not further discuss time lags in this paper.

Random and systematic timing errors, instead, are not identifiable and therefore it is not possible to correct them. However, their effect on flux estimates, as we will see, can become significant. For this reason, the only viable strategy to reduce flux biases is to design the data acquisition system in a way that prevents or minimizes the possibility of their occurrence.

The focus of this paper is, therefore, the quantification of flux underestimations as a function of RTE and STE, so as to derive quantitative specifications for a data acquisition system that minimizes EC flux losses. We further propose a simple scheme for evaluating existing data acquisition systems with respect to data synchronization.

In order to accurately quantify how time-alignment errors affect flux estimates, we performed a simulation study. As a reference, we used the covariance estimated from high-frequency data of vertical wind speed (w) and sonic temperature (Ts) which are by definition perfectly synchronized since they are computed starting from the same raw data (the trave ling time of sound signals between pairs of transducers in a SAT). We also assumed that high-frequency time series are provided at perfectly constant time steps of 0.1 (10 Hz) or 0.05 (20 Hz) seconds. Subsequently, we manipulated the array of timestamps at which the sonic temperature data were sampled in order to simulate realistic ranges of RTEs and STEs. Values of sonic temperature in correspondence to the new simulated timestamps were estimated by linearly interpolating the closest data points in the original series (Fig. 3).

Before calculating covariances, standard EC processing steps were applied such as spike removal (Vickers and Mahrt, 1997), tilt correction by the double rotation method (Wilczak et al., 2001), and fluctuation estimation via block-averaging. Covariance estimates obtained with the new versions of Ts were then compared with the reference to quantify the effect of simulated timing errors. Flux biases would be almost identical to biases in covariances, weakly modulated by corrections intervening between covariance and flux computation, such as spectral corrections and consideration of air density fluctuation effects (e.g., Fratini et al., 2012). The simulation study was implemented in the source code of EddyPro v6.2.1 (LI-COR Biosciences Inc, Lincoln, NE; Fratini and Mauder, 2014).

For the present analysis, we simulated RTEs ranging ±1 to ±100 ms; that is, up to the same order of the sampling interval. As an example, with a simulated ±10 ms RTE using 10 Hz data (nominal time step = 100 ms), simulated time steps for Ts varied randomly between 90 and 110 ms, with an average of 100 ms. We note that RTEs of 10–100 ms will not usually be caused by clock jitter, which is typically several orders of magnitude smaller but can easily be caused by acquisition systems based on serial or Ethernet communication not specifically designed to collect synchronous time series, as described above.

For STEs, we simulated relative drifts ranging from 10 to 180 µs s-1 (specifically 10, 30, 60, 90, 120, 150, and 180 µs s-1). For example, to simulate a STE of 60 µs s-1 we kept the original w time series (time step equal to 100 ms) and modified the time step of Ts to be 100.006 ms. This may seem a negligible difference, which accumulates a difference of 108 ms between w and Ts within 30 minutes and manifests itself as a difference of one row in the length of the time series (i.e., 18 000 value for w and 17 999 for Ts at 10 Hz). Similarly, systematic errors of 120 and 180 µs s-1 would lead to two and three row differences, respectively.

Systematic timing errors such as frequency drifts effectively act as low-pass filters, which can be described by characterizing their transfer function, provided that the drift is known, as in our simulation. Here, for each 30 min period and for each STE amount, we calculated an in situ transfer function as the frequency-wise ratio of drifted and original w-Ts co-spectra: TFEXPfn=COw,TsSTE|fnCOw,T|fn,forSTE=[10,…,180]µss-1, where TsSTE (K) is the simulated sonic temperature for each STE value, fn (Hz) is the natural frequency, and TFEXP(STE|fn) is the in situ transfer function for STE. We repeated this calculation for a number of co-spectra ranging from 1000 to 2000 (depending on data availability). The ensemble of all transfer functions so obtained and for each STE amount was then fitted with the following function, which was found to reasonably approximate the data obtained for all drifts at all sites in the most relevant frequency range (0.01–5 Hz): TF(fco|fn)=(1+β)11+fnfcoα-β, where fco (Hz) is the transfer function cutoff frequency and α and β are fitting parameters whose values were found to vary very little around α=2.65 and β=0.25.

We performed simulations on four datasets acquired from EC sites representative of various ecosystem types and climatic regimes and characterized by the different height of measurement and height of the canopy:

IT-Ro2: a deciduous forest of Turkey Oak (Quercus cerris L.) in Italy. Eddy covariance measurements were carried out from 2002 to 2013 and the period used for the simulations was May 2013, when the canopy height was 15 m and the measurement height 18 m (Rey et al., 2002).

Although the proposed simulation design enables the evaluation of resulting errors using readily available EC data, we note that interpolating data sampled at 10 or 20 Hz frequency can potentially introduce artifacts (due to the lack of information at higher frequencies) such as, for example, an undue reduction of the sonic temperature variance, which would result in artificial reduction of the w-Ts covariance. In order to detect any such effects, we preliminarily implemented a validation procedure, making use of 1 week of sonic data from a Gill HS-100 (Gill Instruments Ltd., Lymington, UK) collected at 100 Hz. The validation involved the following steps:

Subsampling at 10 Hz and simulating timing errors as described above, i.e., interpolating starting from the subsampled data.

If both EC instruments can receive analog inputs, a possible way to evaluate synchronicity in the data logging system is to connect a signal generator to both EC instruments (SAT and gas analyzer) and collect the data via the data logging system in the configuration that would be adopted in normal operation (Fig. 8). The result is two replicates of the known signal data, whose timestamps will in general not be synchronized, in the sense that the same nominal timestamp will be attached to two different pieces of data. The two datasets can then be compared to calculate the phase difference between the clocks and hence assess RTEs and STEs. For example, a cross correlation of the time series yields the phase difference. It's important to test the time series at different time intervals, e.g., 0.5 h for several days, in actual field conditions that undergo significant temperature variations. The two instruments are synchronized if the cross correlation yields the same result every time. If this constant phase offset (time lag) is different from zero, this measurement quantifies signal delays in a system, which can be addressed either by optimizing the data logging system or by taking this offset into account while setting up the time-lag automatic computation in post-processing. A cross correlation that changes over time, instead, is a strong indication of occurring STEs. It is very difficult to anticipate the evolution in time of the phase change as it depends on the clock's crystal cuts, quality, and temperature sensitivity. In general, we may expect a linear trend in the phase if temperatures do not vary strongly (see also later) or a trend modulated by a diurnal pattern if temperature plays a role.

A simpler (though less controlled) option, in case a signal generator is not accessible, is to use the analog outputs from at least one of the EC instruments. In this case the test involves transmitting (at least) one of the analog outputs to the analog input of the companion instrument (e.g., w sent via analog output of the SAT to an analog input channel of the gas analyzer). In this way the raw-data files contain two replicates of that variable, each collected according to the timing of the respective instrument: the timestamps of the digital version are logged according to timing of the sending instrument (SAT, in the example), while those of its analog version are logged according to the timing of the receiver (gas analyzer). The same cross-correlation analyses described above can then be performed.

In both versions of the tests, results may be affected by minor RTEs if the various A/D or D/A tasks are not accurately synchronized with the measurement and serial output tasks. However, such RTEs should not affect the ability to detect and quantify occurring STEs.

Note also that, in both versions of the test, the way raw data are stored may have a strong impact on how to interpret the results. For instance, depending on the specifics of the data acquisition system, collecting a unique file with 3 days worth of data or collecting 30 min files for 3 days can provide different results, e.g., because the act of closing a file and opening a new one can cause the data streams to be partially or completely “realigned”.

To exemplify the test, we collected about 3 days of 20 Hz wind data from a SAT (HS-100, Gill Instruments Ltd., Lymington, UK) both in native digital format (via a RS-232 port, indicated with the subscript d in the following) and in analog format via the A/D of a LI-7550 analyzer interface unit (LI-COR Biosciences Inc.) which was then collected via a second RS-232 port (indicated with subscript a), using an industrial-grade PC running Windows XP. Thus, the data logging system under testing was “a Windows PC collecting EC data via RS-232, which was setup to transmit data in streaming mode”. The two data streams were completely independent to each other, and we attached timestamps to the records based on the operating system clock as the data were made available from the serial port to the application collecting the data. We then merged the two datasets based on timestamps and split the resulting 3-day file into 30 min. Finally, we calculated time lags between pairs of homologous variables (e.g., ud vs. ua, but results were identical for all anemometric variables), which are shown in Fig. 9. The linearity of the data suggests that the system is affected by a fairly constant STE of about 50 µs s-1, as quantified by the slope of the line.

Using the same setup, we further collected 2 days of data directly stored as 30 min files and again computed time lags between homologous variables. The acquisition system was able to realign the two series at the beginning of each half hour resetting the time lag between them to roughly zero. Nevertheless, calculating time lags on overlapping 5 min periods, we found that within each half-hourly period the time lags increased by 0.05 s (32 % of the times) and of 0.1 s (68 % of the times), which again indicates an STE ranging from 30 to 60 µs s-1 which, as shown above (Fig. 5), can lead to detectable flux biases. We stress that the system used in this experiment was not optimized for data acquisition and the aim was solely that of evaluating the proposed test.