The high frequency response correction of eddy covariance fluxes.
Part 1: an experimental approach for analysing noisy measurements
of small fluxes
Authors: Aslan Toprak , Peltola Olli , Ibrom Andreas , Nemitz Eiko , Rannik Üllar , Mammarella Ivan 
Published: December 2020

Abstract. 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 &amp;pm;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.