Raw data, consisting of quadruples \(\left(u,v,w,t\right)\) collected continuously by the station sonic anemometer at a nominal rate of 20Hz and 2 out of 1 averaging, are automatically organized and archived in hourly files, four of which have been selected for 2016-03-08 12:00–13:00 and 18:00–19:00 and for 2016-08-01 10:00–11:00 and 23:00–24:00. All the four selected hours, expressed in Central Europe Time zone, contain the 100% of sonic quadruples labelled as plausible by the anemometer.

Processing was executed using the procedures in a dedicated accessible open-source repository (Favaron, 2024); focus was placed on meandering and then the two horizontal wind components \(u,v\): the vertical wind component and sonic temperature have been neglected.

Hourly data have been processed using a two-phase iterative process. In the first phase, the hourly signals have been replaced by the residual after applying the filter described in Falocchi et al. (2018), that is \({u}_{r}=u-{f}_{\tau =900\text{s}}\left(u\right)\) and \({v}_{r}=v-{f}_{\tau =900\text{s}}\left(v\right)\), where \({f}_{\tau }\left(s\right)\) is the filter applied to the generic signal \(s\); this high-pass filtering operation is done to remove changes occurring at time scales longer than or equal to 900s (15 minutes), plausibly much longer than meandering and other interesting low-frequency phenomena.

The so obtained residuals are then filtered iteratively, with \(\tau =1,\dots ,60\), obtaining the smoothed signals \({u}_{\tau }={f}_{\tau }\left({u}_{r}\right)\), \({v}_{\tau }={f}_{\tau }\left({v}_{r}\right)\).

Autocorrelations, \({\alpha }_{\tau }\) and \({\beta }_{\tau },\) have been computed on the smoothed signals \({u}_{\tau }\) and \({v}_{\tau },\) respectively, and the lags at which passages through zero occur, if any, located and stored in the sequences \({S}_{u}\) and \({S}_{v},\) respectively.

It is worth to remind that the presence of passages through zero, in the autocorrelation function of a signal \(s,\) denotes oscillation; if \(s\left(t\right)=a\text{sin}\left(2\pi \omega t\right)\), the autocorrelation is \(\rho \left(\tau \right)=\underset{s\to \infty }{\text{lim}}\frac{1}{s}{\int }_{-s/2}^{s/2}a\text{sin}\left(2\pi \omega t-\tau \right)\cdot a\text{sin}\left(2\pi \omega t\right) dt=\frac{{a}^{2}}{2}\text{cos}\left(2\pi \omega \tau \right)\), that is a sinusoidal oscillation having the same frequency and with a predictable amplitude. This suggests to use twice the median time distance between consecutive passages through zero as an estimate of the meandering period.

Given the sequences \({S}_{u}\) and \({S}_{v}\), it is then possible to identify their respective medians \({t}_{u}\) and \({t}_{v}\). In general, it may be \({t}_{u}\ne {t}_{v}\), and, in this case, the lower is considered, assuming that the low-frequency oscillations occur in direction mostly occurring around the slower-varying direction.

In Fig. 1, the relationship between the filtering time \(\tau\) and the median \(\text{m}\text{i}\text{n}\left({t}_{u},{t}_{v}\right)\) is shown.