Segmenting datasets
From Atomix
Once the raw observations have been quality-controlled, then you must split the time series into shorter segments by considering:
- time and length scales of turbulence
- stationarity of the segment
- Taylor's frozen turbulence hypothesis, etc ...
![](/images/thumb/c/c8/Long_timeseries.png/400px-Long_timeseries.png)
Application to measured velocities
Measurements are typically collected in the following two ways:
- continuously, or in such long bursts that they can be considered continuous
- short bursts that are typically at most 2-3x the expected largest turbulence time scales (e.g., 10 min in ocean environments)
The act of chopping a time series into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. Hence, when estimating [math]\displaystyle{ \varepsilon }[/math] how to segment the time series is usually a more important consideration than detrending time series. This segmenting step dictates the minimum burst duration when setting-up your equipment.
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Zoom of the first 512 s of the measured velocities shown above including the same trends -
Example velocity spectra of the short 512 s of records before and after different detrending techniques applied to the original 6h time series. The impact of the detrending method can be seen at the lowest frequencies only
Notes
- ↑ Zhaohua Wu, Norden E. Huang, Steven R. Long and and Chung-Kang Peng. 2007. On the trend, detrending, and variability of nonlinear and nonstationary time series. PNAS. doi:10.1073/pnas.0701020104