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Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem–atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical or experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by (PSAI07), in which the noise and H are fitted in different frequency ranges, and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA21). For CSA, we use a method utilizing the square root of the H with shifted vertical wind velocity time series via cross-covariance maximization (CSAH,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA21 and CSAH,sync successfully estimate the expected time constant regardless of the degree of attenuation and SNR. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias between 0.1 % and 1.4 %. PSAA21 showed almost no bias, while CSAH,sync showed bias of ±0.4 %. The accuracies of both PSA and CSA methods were not significantly affected by SNR level, instilling confidence in EC flux measurements and data processing in set-ups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA21 outperforms PSAI07 , while when using cospectra the CSAH,sync approach provides accurate results. These findings are independent of the SNR value and attenuation level. [ABSTRACT FROM AUTHOR]

The eddy covariance (EC) technique has emerged as the prevailing method to observe the ecosystem–atmosphere exchange of gases, heat and momentum. EC measurements require rigorous data processing to derive the fluxes that can be used to analyse exchange processes at the ecosystem–atmosphere interface. Here we show that two common post-processing steps (time-lag estimation via cross-covariance maximisation and correction for limited frequency response of the EC measurement system) are interrelated, and this should be accounted for when processing EC gas flux data. These findings are applicable to EC systems employing closed- or enclosed-path gas analysers which can be approximated to be linear first-order sensors. These EC measurement systems act as low-pass filters on the time series of the scalar χ (e.g. CO2 , H2O), and this induces a time lag (tlpf) between vertical wind speed (w) and scalar χ time series which is additional to the travel time of the gas signal in the sampling line (tube, filters). Time-lag estimation via cross-covariance maximisation inadvertently accounts also for tlpf and hence overestimates the travel time in the sampling line. This results in a phase shift between the time series of w and χ , which distorts the measured cospectra between w and χ and hence has an effect on the correction for the dampening of the EC flux signal at high frequencies. This distortion can be described with a transfer function related to the phase shift (Hp) which is typically neglected when processing EC flux data. Based on analyses using EC data from two contrasting measurement sites, we show that the low-pass-filtering-induced time lag increases approximately linearly with the time constant of the low-pass filter, and hence the importance of Hp in describing the high-frequency flux loss increases as well. Incomplete description of these processes in EC data processing algorithms results in flux biases of up to 10 %, with the largest biases observed for short towers due to the prevalence of small-scale turbulence. Based on these findings, it is suggested that spectral correction methods implemented in EC data processing algorithms are revised to account for the influence of low-pass-filtering-induced time lag. [ABSTRACT FROM AUTHOR]

The eddy covariance (EC) technique has emerged as the prevailing method to observe ecosystem - atmosphere exchange of gases, heat and momentum. EC measurements require rigorous data processing to derive the fluxes that can be used to analyse exchange processes at the ecosystem - atmosphere interface. Here we show that two common post-processing steps (time-lag estimation via cross-covariance maximisation, and correction for limited frequency response of the EC measurement system) are interrelated and this should be accounted for when processing EC gas flux data. These findings are applicable to EC systems employing closed- or enclosed-path gas analysers which can be approximated to be linear first-order sensors. These EC measurement systems act as a low-pass filters on the time-series of the scalar χ (e.g. CO2, H2O) and this induces a time-lag (푡푙푝푓) between vertical wind speed (퓌) and scalar χ time series which is additional to the travel time of the gas signal in the sampling line (tube, filters). Time-lag estimation via cross-covariance maximisation inadvertently accounts also for푡푙푝푓 and hence overestimates the travel time in the sampling line. This results in a phase shift between the time-series of 퓌 and χ, which distorts the measured cospectra between 퓌 and χ and hence has an effect on the correction for dampening of EC flux signal at high frequencies. This distortion can be described with a transfer function related to the phase shift (퐻푝) which is typically neglected when processing EC flux data. Based on analyses using EC data from two contrasting measurement sites, we show that the low-pass filtering induced time-lag increases approximately linearly with the time constant of the low-pass filter, and hence the importance of 퐻푝 in describing the high frequency flux loss increases as well. Incomplete description of these processes in EC data processing algorithms results in flux biases of up to 10%, with the largest biases observed for short towers due to prevalence of small scale turbulence. Based on these findings, it is suggested that spectral correction methods implemented in EC data processing algorithms are revised to account for the influence of low-pass filtering induced time-lag. [ABSTRACT FROM AUTHOR]

Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem- atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical and experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by Ibrom et al. (2007a) (PSAI07), where the noise and H are fitted in different frequency ranges and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA20). For CSA, we use three different methods: (1) a plain version of Lorentzian equation describing the H (CSAH), (2) a square-root of the H (CSA√H), and (3) a square-root of the H with shifted vertical wind velocity time series via cross-covariance maximisation (CSA√H,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA20 successfully estimates the expected time constant regardless of the degree of attenuation and SNR. CSAH underestimates the time constant with decreasing accuracy as attenuation increases due to the omission of the quadrature spectrum. CSA√H overestimates, but its accuracy increases with time-lag correction in the CSA√H,sync. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias of ±2 %. PSAA20 showed a similar variation, yet slightly better accuracy. CSAH underestimated fluxes by up to 4 %, while CSA√H overestimated them by up to 3 %, a bias which was mostly eliminated with time-lag correction in the CSA√H,sync (-2 % to 1 % ). The accuracies of both PSA and CSA methods were not affected by SNR level, instilling confidence in EC flux measurements and data processing in setups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA20 outperforms PSAI07, while when using cospectra the CSA√H,sync approach provides the most accurate results. These findings are independent of the SNR value and attenuation level. [ABSTRACT FROM AUTHOR]

The eddy covariance (EC) technique is the most direct method for measuring the exchange between the surface and the atmosphere in different ecosystems. Thus, it is commonly used to get information on air pollutant and greenhouse gas emissions, and on turbulent heat transfer. Typically an ecosystem is monitored by only one single EC measurement station at a time, making the ecosystem-level flux values subject to random and systematic uncertainties. Furthermore, in urban ecosystems we often have no choice but to conduct the single-point measurements in non-ideal locations such as close to buildings and/or in the roughness sublayer, bringing further complications to data analysis and flux estimations. In order to tackle the question of how representative a single EC measurement point in an urban area can be, two identical EC systems - measuring momentum, sensible and latent heat, and carbon dioxide fluxes - were installed on each side of the same building structure in central Helsinki, Finland, during July 2013-September 2015. The main interests were to understand the sensitivity of the vertical fluxes on the single measurement point and to estimate the systematic uncertainty in annual cumulative values due to missing data if certain, relatively wide, flow-distorted wind sectors are disregarded. The momentum and measured scalar fluxes respond very differently to the distortion caused by the building structure. The momentum flux is the most sensitive to the measurement location, whereas scalar fluxes are less impacted. The flow distortion areas of the two EC systems (40-150 and 230-340°) are best detected from the mean-wind-normalised turbulent kinetic energy, and outside these areas the median relative random uncertainties of the studied fluxes measured by one system are between 12% and 28%. Different gapfilling methods with which to yield annual cumulative fluxes show how using data from a single EC measurement point can cause up to a 12% (480 g Cm-22) underestimation in the cumulative carbon fluxes as compared to combined data from the two systems. Combining the data from two EC systems also increases the fraction of usable half-hourly carbon fluxes from 45% to 69% at the annual level. For sensible and latent heat, the respective underestimations are up to 5% and 8% (0.094 and 0.069 TJm-22). The obtained random and systematic uncertainties are in the same range as observed in vegetated ecosystems. We also show how the commonly used data flagging criteria in natural ecosystems, kurtosis and skewness, are not necessarily suitable for filtering out data in a densely built urban environment. The results show how the single measurement system can be used to derive representative flux values for central Helsinki, but the addition of second system to other side of the building structure decreases the systematic uncertainties. Comparable results can be expected in similarly dense city locations where no large directional deviations in the source area are seen. In general, the obtained results will aid the scientific community by providing information about the sensitivity of EC measurements and their quality flagging in urban areas. [ABSTRACT FROM AUTHOR]

Large variability is inherent to turbulent flux observations. We review different methods used to estimate the flux random errors. Flux errors are calculated using measured turbulent and simulated artificial records. We recommend two flux errors with clear physical meaning: the flux error of the covariance, defining the error of the measured flux as 1 standard deviation of the random uncertainty of turbulent flux observed over an averaging period of typically 30 min to 1 h duration; and the error of the flux due to the instrumental noise. We suggest that the numerical approximation by Finkelstein and Sims (2001) is a robust and accurate method for calculation of the first error estimate. The method appeared insensitive to the integration period and the value 200 s sufficient to obtain the estimate without significant bias for variety of sites and wide range of observation conditions. The filtering method proposed by Salesky et al. (2012) is an alternative to the method by Finkelstein and Sims (2001) producing consistent, but somewhat lower, estimates. The method proposed by Wienhold et al. (1995) provides a good approximation to the total flux random uncertainty provided that independent cross-covariance values far from the maximum are used in estimation as suggested in this study. For the error due to instrumental noise the method by Lenschow et al. (2000) is useful in evaluation of the respective uncertainty. The method was found to be reliable for signal-to-noise ratio, defined by the ratio of the standard deviation of the signal to that of the noise in this study, less than three. Finally, the random uncertainty of the error estimates was determined to be in the order of 10 to 30% for the total flux error, depending on the conditions and method of estimation. [ABSTRACT FROM AUTHOR]

We have carried out an inter-comparison between EddyUH and EddyPro®, two public software packages for post-field processing of eddy covariance data. Datasets including carbon dioxide, methane and water vapour fluxes measured over 2 months at a wetland in southern Finland and carbon dioxide and water vapour fluxes measured over 3 months at an urban site in Helsinki were processed and analysed. The purpose was to estimate the flux uncertainty due to the use of different software packages and to evaluate the most critical processing steps, determining the largest deviations in the calculated fluxes. Turbulent fluxes calculated with a reference combination of processing steps were in good agreement, the systematic difference between the two software packages being up to 2.0 and 6.7% for half-hour and cumulative sum values, respectively. The raw data preparation and processing steps were consistent between the software packages, and most of the deviations in the estimated fluxes were due to the flux corrections. Among the different calculation procedures analysed, the spectral correction had the biggest impact for closed-path latent heat fluxes, reaching a nocturnal median value of 15% at the wetland site. We found up to a 43% median value of deviation (with respect to the run with all corrections included) if the closed-path carbon dioxide flux is calculated without the dilution correction, while the methane fluxes were up to 10% lower without both dilution and spectroscopic corrections. The Webb-Pearman- Leuning (WPL) and spectroscopic corrections were the most critical steps for open-path systems. However, we found also large spectral correction factors for the open-path methane fluxes, due to the sensor separation effect. [ABSTRACT FROM AUTHOR]

We simulated the REA system with dynamic deadband to study numerical value and the effect of atmospheric conditions on the empirical constant β which relates vertical flux to concentration difference between updrafts and downdrafts. We found that the value of β depends only weakly on the friction velocity and atmospheric stability. In agreement with previous studies, the median value obtained for a system with dynamic deadband proportional to 0.5 times the running mean of the standard deviation of vertical wind speed was β =0.42±0.03. For a single half-hour measurement one has to consider the large uncertainty of ±0.2. According to our study, the dynamic deadband enables the use of a constant value of β in flux calculation. [Copyright &y& Elsevier]

A stochastic trajectory model was used to estimate scalar flux footprints in neutral stability for canopies of varying leaf area distributions and leaf area indices. An analytical second-order closure model was used to predict mean wind speed, second moments and the dissipation rate of turbulent kinetic energy within a forest canopy. The influence of source vertical profile on the flux footprint was examined. The fetch is longer for surface sources than for sources at higher levels in the canopy. In order to measure all the flux components, and thus the total flux, with a desired accuracy, sources were located at the forest floor in the footprint function estimation. The footprint functions were calculated for five observation levels above the canopy top. It was found that at low observation heights both canopy density and canopy structure affect the fetch. The higher above the canopy top the flux is measured, the more pronounced is the effect of the canopy structure. The forest fetch for flux measurements is strongly dependent on the required accuracy: The 90% flux fetch is greater by a factor of two or more compared to the 75% fetch. The upwind distance contributing 75% of flux is as large as 45 times the difference between canopy height and the observation height above the canopy top, being even larger for low observation levels. [ABSTRACT FROM AUTHOR]

• Non-zero vertical wind speeds at complex sites depend on wind direction, stability and time of day. • The planar-fitted coordinate system for flux calculation is preferred over double rotation method. • Continuous planar fitting method can reduce the uncertainty in obtaining the long-term averaged coordinate frame. The choice of coordinate system to calculate eddy covariance fluxes becomes particularly relevant at complex measurement sites. The traditional way is to perform double rotation (DR) of the coordinate system i.e., to calculate turbulent fluxes in a coordinate system that is aligned with the flow streamlines within the flux averaging period (e.g., Kaimal and Finnigan, 1994). The second approach, the so-called planar-fitted (PF) coordinate system, averages the flow over a longer period of time, in practice a month or more. The PF method allows to derive an intercept coefficient of the vertical wind speed which can be attributed to the offset of the sonic anemometer or the average vertical flow related to meteorological conditions. We evaluated the variants of the PF methods using data from a variety of sites ranging from complex urban and forest sites to nearly ideal forest and peatland sites. At complex sites, we found that the intercept of the vertical wind speed derived from the PF method is a function of wind direction, time of day and/or stability. The sector-wise PF (SPF) method frequently led to insignificant statistical relationships. We tested a continuous PF (CPF) method where the relationship establishing the coordinate frame was represented as the continuous function in the form of Fourier series. The method enabled to obtain the PF with lower uncertainty as compared to the SPF method, by selecting necessary number of harmonics for each site based on confidence intervals of estimated parameters. Therefore, we recommend to use the CPF method in cases when the number of observations in some wind direction interval is low or the obtained SPF is insignificant due to large variance in measurements. We also showed that significant systematic difference can exist in cumulative turbulent fluxes between the DR and PF methods over a longer period of time. Derived vertical advection of carbon dioxide exhibited large variability with wind direction due to topography at complex sites and therefore, without considering horizontal advection, cannot be used to improve the net ecosystem exchange estimation during nocturnal, low turbulence conditions. [ABSTRACT FROM AUTHOR]

Abstract: Nitrous oxide (N2O) fluxes from a cotton field in northern China were measured for a year using the static chamber method based on a gas chromatograph (GC) and the eddy covariance (EC) technique based on a tunable diode laser (TDL). The aims were to compare the N2O fluxes obtained from both techniques, assess the uncertainties in the fluxes and evaluate the annual direct emission factors (EF ds, i.e. the loss rate of fertilizer nitrogen via N2O emission) using the year-round datasets. During the experimental period, the hourly and daily mean chamber fluxes ranged from 0.6 to 781.8 and from 1.2 to 468.8μgNm−2 h−1, respectively. The simultaneously measured daily mean EC fluxes varied between −10.8 and 912.0μgNm−2 h−1. The EC measurements only provided trustworthy 30-min fluxes during high-emission period (a 20-day period immediately after the irrigation that followed the nitrogen fertilization event). A reliable comparison was confined to the high-emission period and showed that the chamber fluxes were 17–20% lower than the EC fluxes. This difference may implicate the magnitude of systematic underestimation in the fluxes from chamber measurements. The annual emission from the fertilized cotton field was estimated at 1.43kgNha−1 yr−1 by the chamber observations and 3.15kgNha−1 yr−1 by the EC measurements. The EF ds calculated from the chamber and EC data were 1.04% and 1.65%, respectively. The chamber-based estimate was very close to the default value (1.0%) recommended by the Intergovernmental Panel on Climate Change. However, the difference in the EF ds based on the two measurement techniques may vary greatly with changing environmental conditions and management practices. Further comparison studies are still needed to elucidate this issue. [Copyright &y& Elsevier]