Edit Processing: Segmenting datasets

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 Velocity point-measurements  Velocity profilers  Shear probes

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Once the raw observations have been [[Data processing of raw measurements|quality-controlled]], then you must split the time series into shorter segments by considering: * [[Time and length scales of turbulence]] * [[Stationarity]] of the segment and [[Taylor's Frozen Turbulence| Taylor's frozen turbulence hypothesis]] * Required statistical significance of the resulting spectra, important mainly if you use [[Velocity decontamination by cospectral methods| cospectral or coherence-based]] methods to remove motion-induced contamination from the spectra A good way to select the segment length is by inspecting the [[compute the spectra|computed spectra]] estimated from a 512-s long segment and an [[#fftlength|fft-length]] that is one-quarter of the segment length (128 s). Plotting these spectra against the theoretical spectral lines (see [[#specavg|Fig 2 and 3]]), enables identifying whether 1 decade of an inertial subrange is resolved with at least 8 spectral samples in this subrange. == Considerations == Measurements are typically collected in the following two ways: * continuously, or in such long [[Burst sampling|bursts]] that they can be considered continuous * short [[Burst sampling|bursts]] that are typically at most 2-3x the expected largest [[Time and length scales of turbulence|turbulence time scales]] (e.g., 10 min in ocean environments) This segmenting step dictates the minimum [[Burst sampling|burst]] duration when setting up your equipment. The act of chopping a time series into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. The length of the [[Segmenting datasets|segment]] in time is usually a more important consideration than [[Detrending time series#detrend_ex|detrending the time series]] when estimating <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] of the final spectra. The shorter the segment, the higher the temporal resolution of the final <math>\varepsilon</math> time series, and the more likely the segment will be [[Stationarity|stationary]]. The segment must remain sufficiently long such that the lowest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]] are retained by the [[Compute the spectra|computed spectra]]. This is particularly important when measurement noise drowns the highest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]]. Thus, using too short segments may inadvertently render the spectra unusable for deriving <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] by virtue of no longer resolving this subrange as shown in ([[#fftlength|Fig. 1]]). [[File:ADV_fft_length.png|none|thumbnail|500px|Fig.1 Contours represent the log of the <span id="fftlength">fft-length required to resolve the non-dimensional wavenumber [rad/m] indicated in each panel's title. The inertial subrange ends at approximately <math>\hat{k}L_k\approx0.1</math> (or <math>kL_k\approx0.015</math> in cpm), and so panel (c) denotes the fft-length that resolves the end of the inertial subrange i.e., the beginning of the viscous subrange. The fft-length must be at least 10x longer (see b), preferably 50x (panel c) given the low number of spectral observations at the lowest frequencies (wavenumbers)]] == Recommendations== A good rule of thumb for tidally-influenced environments is 5 to 15 min segments, but this may be shorter in certain energetic and fast-moving flows ([[#fastepsi|Fig. 2]]) and longer in less energetic environments ([[#lowepsi|Fig.3]]). The final segment length is partly a function of the fft-length and the desired statistical significance (degrees of freedom) of the final [[Compute the spectra| computed spectra]]. If [[Velocity decontamination by cospectral methods| cospectral methods]] will be employed to decontaminate the velocities, then the segment length should be 4-5x larger than the [[#fftlength|fft-length]] unless band-averaging is used to [[Compute the speectra#specavg| average the (co-)spectra]]. ===Minimum fft-length=== [[#fftlength|Fig. 1]] provides a guide to the fft-length required for resolving different subrange as a function of the speed past the sensor, and <math>\varepsilon</math>. For instance, an fft-length of 4 s would resolve one decade of the inertial subrange at speeds past the sensor of 0.5 m/s and <math>\varepsilon\sim10^{-7}</math> W/kg. Longer segments would be required for slower flows or lower <math>\varepsilon</math>. At <math>\varepsilon\approx10^{-9}</math> W/kg, one decade of the inertial subrange would be resolved with an fft-length longer than 10s provided the speed was faster than 0.5 m/s. Because the inertial subrange may be contaminated at the highest wavenumbers by instrument noise, we suggest using longer segments than the minimum shown in [[#fftlength|Fig. 1b]]. This strategy also enables having a larger number of spectral observations to [[Spectral fitting|fit]] over the inertial subrange given the spectral resolution is equal to the inverse of the fft-length. ===Choosing segment-length=== The final segment length may be larger than the fft-length depending if you use block-averaging for [[Compute the spectra#specavg|computing the spectra]]. The maximum segment length should be shorter than the largest [[Time and length scales of turbulence|turbulent time scales]]. To increase the statistical reliability of the spectral observations, which is absolutely necessary when applying any [[Velocity decontamination by cospectral methods|co-spectral techniques]] for motion decontamination of spectra, we recommend segment length that is 5x the [[#fftlength|fft-length]] unless band-averaging is employed during the [[Compute the spectra#specavg| spectral averaging]]. More details about the minimum degrees of freedom are given in the [[velocity decontamination by cospectral methods]] wikipage. {{FontColor|fg=white|bg=red|text= Are the peaks in the MAVS data vortex shedding from the rings. Check the motion sensors onboard?}} [[File:Segment_anisotropy.png|left|thumbnail|350px|Fig. 2: Example theoretical velocity spectra for different <math>\varepsilon</math> with the empirical limit <math>\hat{k}L_k\sim0.1</math> denoted by the diamonds (<math>\hat{k}</math> is in rad/m). The inertial subrange extends to smaller wavenumber <math>k</math> [cpm] as <math>\varepsilon</math> increases. The lowest frequency resolved by a spectra is the inverse of the fft-length used when computing the spectra. The colored lines are spectral observations from a dataset with <span id="fastepsi">fast speeds and large</span> <math>\varepsilon</math>. In this example, we used relatively short segments (128s) to estimate the spectra from fft-length of 32 s (2048 samples @ 64 Hz). The impact of [[Velocity inertial subrange model#anisotropy|turbulence anisotropy]] is also visible through the flattening of the spectra around 1 cpm. The secondary x-axis show the corresponding frequencies for a range of mean speeds past the sensors]] [[File:SegmentAnisotropyLowE.png|center|thumbnail|350px|Fig. 3: Same as Fig 1 but for a different dataset with <span id="lowepsi">low speeds and low</span> <math>\varepsilon</math>, requiring the use of relatively long segments (1024s) to estimate the spectra from fft-length of 512 s (4096 samples @ 8 Hz).]] ===Overlapping segments=== Using overlapping segments, i.e., obtaining your first <math>\varepsilon</math> estimate from time 0 to 5 min, and the second estimate from 2.5 to 5 min (50% overlap) essentially smoothes the final timeseries <math>\varepsilon</math>. One advantage of using overlapping segments is that you can recover estimates before and after sudden changes in flow conditions that render one segment unusable for getting <math>\varepsilon</math>. The use of overlapping segments is purely a matter of preference, and does not impact the quality of the final timeseries of epsilon. ---- Return to [[Preparing_quality-controlled_velocities|Preparing quality-controlled velocities]]

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