Decomposing velocity measurements: Difference between revisions

From Atomix
← Older edit
Visual
 
(8 intermediate revisions by the same user not shown)
Line 4: Line 4:
}}
}}


The quality-controlled velocities can be [[Detrending time series|detrended]] before being further analysed to determine [[Velocity past the sensor|mean flow past the sensor]] and [[Surface wave statistics|surface wave statistics]]. These quantities are necessary for later choosing the appropriate [[Velocity inertial subrange model| inertial subrange model]] for [[Spectral fitting|spectral fitting]].
The quality-controlled velocities can be [[Detrending time series|detrended]] before being further analysed to determine [[Velocity past the sensor|mean flow past the sensor]] and [[Surface wave statistics|surface wave statistics]]. These quantities are necessary for later choosing the appropriate [[Velocity inertial subrange model| inertial subrange model]] for [[Spectral fitting|spectral fitting]].
Quality-controlled velocities may also need detrended before applying various [[Velocity despiking|despiking]].
Quality-controlled velocities may also need to be detrended before applying various [[Velocity despiking|despiking]]. Because estimating <math>\varepsilon</math> is done from the spectral observations, the analysis is insensitive to this step provided that we don’t filter out the scales shorter than the [[Segmenting datasets| segment length]].
==Methods for detrending==
[[File:Long timeseries.png|400px|thumb|Measured velocities at 4 Hz from an [[Acoustic-Doppler Velocimeters]] have been detrended using three different techniques. Empirical modal decomposition (EMD) <ref name="Wuetal_PNAS">{{Cite journal
|authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng
|journal_or_publisher=PNAS
|paper_or_booktitle=On the trend, detrending, and variability of nonlinear and nonstationary time series
|year=2007
|doi=10.1073/pnas.0701020104
}}</ref>, linear trend, and a 2nd order low-pass Butterworth filter. A cut-off period of 10 min was targeted by both the filter and EMD]]


There is no exact definition for what consists of a "trend", nor any set algorithm for identifying the trend. The following techniques can be used for detrending <ref name=Wuetal_PNAS/>:
<div><ul>
# Linear trend removal
<li style="display: inline-block; vertical-align: top;"> [[File:Short timeseries.png|thumb|none|350px|512 s segment of the measured velocities after applying different [[Detrending time series|detrending methods]]]]
# Low-pass linear filters
</li>
# Empirical modal decomposition
<li style="display: inline-block; vertical-align: top;"> [[File:Short_spectra.png|thumb|none|350px|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]] </li>
</ul></div>


The first two methods presume the original time series is [[Stationarity|stationary]] and linear, while the third is adaptive and applicable to nonlinear and non-stationary timeseries. 






==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 [[Time and length scales of turbulence|turbulence time scales]].
As a rule of thumb, turbulence estimates from the inertial subrange of velocity rely on 5 to 15 min long [[Segmenting datasets|segments]].
==Segmenting==
The act of chopping a timeseries into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. The question of how to detrend  becomes less important than how best to [[Segmenting datasets|segment]] the timeseries. This segmenting step dictates the minimum burst duration when setting-up your equipment.
<div><ul>
<li style="display: inline-block; vertical-align: top;"> [[File:Short timeseries.png|thumb|none|350px|Zoom of the first 512 s of the measured velocities shown above including the same trends]]
</li>
<li style="display: inline-block; vertical-align: top;"> [[File:Short_spectra.png|thumb|none|350px|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]] </li>
</ul></div>


==Notes==
<references/>


----
----
Return to [[Velocity_point-measurements|Velocity point-measurements' welcome page]]
Return to [[Preparing quality-controlled velocities]]

Latest revision as of 19:08, 5 July 2022


The quality-controlled velocities can be detrended before being further analysed to determine mean flow past the sensor and surface wave statistics. These quantities are necessary for later choosing the appropriate inertial subrange model for spectral fitting. Quality-controlled velocities may also need to be detrended before applying various despiking. Because estimating [math]\displaystyle{ \varepsilon }[/math] is done from the spectral observations, the analysis is insensitive to this step provided that we don’t filter out the scales shorter than the segment length.

  • 512 s segment of the measured velocities after applying different detrending methods
  • 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




Return to Preparing quality-controlled velocities

Retrieved from "http://atomix.app.uib.no/index.php?title=Decomposing_velocity_measurements&oldid=4287"