The high-frequency response correction of eddy covariance fluxes - Part 2: an experimental approach for analysing noisy measurements of small fluxes

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 Ibrom et al. (2007a) (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√H,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA21 and CSAH√H,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√H,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√H,sync approach provides accurate results. These findings are independent of the SNR value and attenuation level