Time lag detection between raw eddy-covariance data by prewhitening and cross-correlation analysis

Variables sampled by eddy-covariance (EC) systems are not temporally aligned because, to avoid possible wind flow distortions, sensors are not perfectly co-located. If not properly treated, such a temporal mis-alignment constitutes a source of systematic error in the derived EC fluxes. 

In most of EC data processing pipelines, the time lag is detected by assessing the cross-covariance function between the vertical wind speed and the atmospheric concentration of the scalar of interest. In particular, the optimal time lag is detected in correspondence of the lag that maximizes (in absolute terms) the cross-covariance function between raw, high-frequency, time series. Such a procedure is effective when the cross-covariance function exhibits a distinct and pronounced peak, a condition occurring under second-order stationary conditions and when the signal-to-noise ratio is moderate/high. In other circumstances, the cross-covariance function can be characterized by multiple local minima or maxima of similar magnitude, making the detection of the optimal time lag problematic. This often occurs for trace gases or during dormant/senescence periods when  fluxes are of small magnitude.

This work introduces a new procedure being computationally efficient and completely data-driven where time lag is detected by assessing the statistical significance of the cross-correlation estimates between raw EC data subject to a preliminary (linear) transformation known as prewhitening. Prewhitening avoids the risk of nonsense (or spurious) correlations, making it more realistic and informative the assessment of the cross-correlation function, and then the detection of the optimal time lag.

The procedure consists of the following steps: i) removal of the serial correlation from at least one of the two series involved in the cross-correlation function using an autoregressive integrated moving average  (ARIMA) model; ii) filtering of the other time series using an ARIMA model with the same parameters estimated in the previous step; iii) evaluation of the cross-correlation function between the transformed variables (i.e. between the model residuals). 

The effectiveness of the procedure is evaluated for the detection of time lag affecting CO2, H2O, N2O and CH4 variables. Results indicate that applying the proposed approach and using sonic temperature instead of vertical wind speed greatly facilitates the detection of the optimal time lag, even in the case of low magnitude fluxes.