Trend removal

As it was mentioned earlier, turbulent fluxes are calculated from the fluctuations of the time series considered. Fluctuations are calculated as deviations from a specific mean value. There are several methods found in the literature to calculate mean values such as recursive digital filters, spectral high-pass filters, running mean or box-car averages and linear trend removal technique (McMillen, 1988; Denholm-Price and Rees, 1998). Some of the methods (e.g. recursive digital filtering) are used in real-time data processing systems. Since data processing takes place off-line in our case, a more sophisticated trend removal technique is possible.

Other advantage of trend removal is that the effect of a complex terrain or a slight non-stationarity can be addressed partially with this method (McMillen, 1988; Grelle and Lindroth, 1996; Moncrieff et al., 1997; Weidinger et al., 1999), while these problems can not be addressed easily in the flux-profile calculations.

Sensitivity tests had been performed to choose the most adequate trend removal technique. In the beginnig, moving average trend removal was applied since this is one of the most popular techniques. Based on the result of the sensitivity test derived from data of three randomly selected days, 1000 sec time window seemed to be appropriate for trend removal (three days may seem to be less than enough for the test, but we should note that sensitivity tests are heavily computational time consuming). 1000 sec is the upper limit of the time constants generally used in measuring systems located lower in the surface layer (McMillen, 1988). It is important to note that the moving average tred removal technique causes spectral energy to be redistributed in an undesirable fashion (see Fig. 3. in Denholm-Price and Rees, 1998), which needs further spectral corrections. The neccessary power spectal transfer function can be found in Kaimal et al. (1968).

As more powerful computers became available for data processing, a more mature sensitivity test was performed. Based on data of 30 randomly selected days it became clear that 1000 sec time window is too small to get accurate fluxes. Maximum covariances has been reached using data window of 60 min or longer (Figure ), thus it seemed reasonable to change the trend removal method to a simpler linear trend removal method. This method also seemed to be the most appropriate for eddy flux measurements carried out on very high towers (K. Davis, pers. comm.).

Figure: Dependence of the normalized mean covariances on the mean removal time applied during the moving average trend removal procedure. The figure represents average data of the daily averages for the 30 days selected. Solid line is the momentum flux, dotted line is the temperature flux, dashed line is the latent heat flux and dashed-dotted line is the carbon dioxide flux. The unusual behaviour of the temperature flux foreshadows the errors associated with the temperature fluctuation measurement.

This result is consistent with the large turbulent scales detected with the ogive functions, as it was mentioned in section . A shorter time window would cause removal of frequencies that contribute to the turbulent transport. As a result, a linear trend is removed from each 60 min interval of all data used for the eddy flux calculations (wind components, temperature, HO and CO) to get the fluctuations neccessary for the calculation of the turbulent fluxes.