Detrending time series - Revision history

CynthiaBluteau: /* Velocity point measurements */

2022-07-11T14:39:47Z

Velocity point measurements

← Older revision		Revision as of 14:39, 11 July 2022
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	[[File:Short timeseries.png\|left\|thumb\|350px\|512 s segment of the measured velocities after applying different [[Detrending time series\|detrending methods]]]]		[[File:Short timeseries.png\|left\|thumb\|350px\|512 s segment of the measured velocities after applying different [[Detrending time series\|detrending methods]]]]
	[[File:Short_spectra.png\|left\|thumb\|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]]		[[File:Short_spectra.png\|left\|thumb\|350px\|Example velocity spectra of the short 512 s of records before and after different <span id="detrend_ex">detrending</span> techniques applied to the original 6h time series. The impact of the detrending method can be seen at the lowest frequencies only]]

	===Velocity profilers===		===Velocity profilers===

CynthiaBluteau: Move the detrending plots here

2022-07-10T20:30:10Z

Move the detrending plots here

← Older revision		Revision as of 20:30, 10 July 2022
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	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 time series. Note that chopping a time series into smaller subsets, i.e., segments, is essentially a form of low-pass (box-car) filtering.		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 time series. Note that chopping a time series into smaller subsets, i.e., segments, is essentially a form of low-pass (box-car) filtering.

			==Implications for estimating <math>\varepsilon</math>==
			===Velocity point measurements===
			The choice of detrending technique has little influence on the estimation of <math>\varepsilon</math> from the spectral fitting of the inertial subrange as it influences only the lowest wavenumber of the spectra, which most algorithms identity as outliers. Detrending becomes an important consideration when performing other turbulence calculations such as estimating Re stresses <math>\overline{u'w'}</math> or turbulent kinetic energy.

			[[File:Short timeseries.png\|left\|thumb\|350px\|512 s segment of the measured velocities after applying different [[Detrending time series\|detrending methods]]]]
			[[File:Short_spectra.png\|left\|thumb\|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]]

			===Velocity profilers===



	==Notes==		==Notes==

CynthiaBluteau at 03:28, 1 December 2021

2021-12-01T03:28:34Z

← Older revision		Revision as of 03:28, 1 December 2021
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	In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity\|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.		In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity\|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	[[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		[[File:Long timeseries.png\|400px\|thumb\|Measured velocities at 4 Hz from an [[Acoustic-Doppler Velocimeters]] are highlighted against trends obtained from 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		\|authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng
	\|journal_or_publisher=PNAS		\|journal_or_publisher=PNAS
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	\|year=2007		\|year=2007
	\|doi=10.1073/pnas.0701020104		\|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]]		}}</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. Detrended signal would be the difference between the original and the trend]]

CynthiaBluteau at 14:11, 30 November 2021

2021-11-30T14:11:36Z

← Older revision		Revision as of 14:11, 30 November 2021
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	In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity\|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.		In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity\|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	[[File:Long timeseries.png\|thumb~~\|none\|600px~~\|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		[[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		\|authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng
	\|journal_or_publisher=PNAS		\|journal_or_publisher=PNAS
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	}}</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]]		}}</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/>:
			# Linear trend removal
			# Low-pass linear filters
			# Empirical modal decomposition

			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 time series. Note that chopping a time series into smaller subsets, i.e., segments, is essentially a form of low-pass (box-car) filtering.

	==Notes==		==Notes==

CynthiaBluteau at 18:46, 29 November 2021

2021-11-29T18:46:40Z

← Older revision		Revision as of 18:46, 29 November 2021
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	}}		}}

	In the context of analysing turbulence observations, the resulting detrended signal should be [[stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.		In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity\|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	[[File:Long timeseries.png\|thumb\|none\|600px\|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		[[File:Long timeseries.png\|thumb\|none\|600px\|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

CynthiaBluteau at 18:46, 29 November 2021

2021-11-29T18:46:02Z

← Older revision		Revision as of 18:46, 29 November 2021
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	}}		}}

	In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.		In the context of analysing turbulence observations, the resulting detrended signal should be [[stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	[[File:Long timeseries.png\|thumb\|none\|600px\|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		[[File:Long timeseries.png\|thumb\|none\|600px\|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

CynthiaBluteau: Fixed image and added ref

2021-11-29T17:43:38Z

Fixed image and added ref

← Older revision		Revision as of 17:43, 29 November 2021
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	}}		}}

	[[File:Long timeseries.png\|~~500px~~\|~~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		In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

			[[File:Long timeseries.png\|thumb\|none\|600px\|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		\|authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng
	\|journal_or_publisher=PNAS		\|journal_or_publisher=PNAS
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	}}</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]]		}}</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]]

	In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	==Notes==		==Notes==

CynthiaBluteau: Added ref

2021-11-29T17:40:16Z

Added ref

← Older revision		Revision as of 17:40, 29 November 2021
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	\|instrument_type=Velocity point-measurements, Velocity profilers		\|instrument_type=Velocity point-measurements, Velocity profilers
	}}		}}

			[[File:Long timeseries.png\|500px\|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]]

	In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.		In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

			==Notes==
	~~[[File:Long timeseries.png\|500px\|thumb\|Measured velocities at 4 Hz from an [[Acoustic-Doppler Velocimeters]] have been detrended using three different techniques]]~~

CynthiaBluteau at 17:36, 29 November 2021

2021-11-29T17:36:18Z

← Older revision		Revision as of 17:36, 29 November 2021
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	{{DefineConcept		{{DefineConcept
	\|description= Detrending typically refers to removing the low-frequency content of the time series		\|description=Detrending typically refers to removing the low-frequency content of the time series
	\|article_type=Concept		\|article_type=Concept
	\|instrument_type=Velocity point-measurements, Velocity profilers		\|instrument_type=Velocity point-measurements, Velocity profilers
	}}		}}
			In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.

	~~In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions~~ from ~~turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the~~ detrended ~~signal.~~
			[[File:Long timeseries.png\|500px\|thumb\|Measured velocities at 4 Hz from an [[Acoustic-Doppler Velocimeters]] have been detrended using three different techniques]]

CynthiaBluteau: Remove methods stuff

2021-11-29T17:34:37Z

Remove methods stuff

← Older revision		Revision as of 17:34, 29 November 2021
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	}}		}}

	In the context of analysing turbulence observations, ~~detrending yields a~~ signal ~~that retains~~ mostly contributions from turbulence and surface waves (if present). ~~The resulting detrended signal may contain contributions from~~ frame interference (wakes), vibrations and measurement noise.		In the context of analysing turbulence observations, the resulting detrended signal should contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.




	~~There is no exact definition for what consists of a "trend", nor any set algorithm for identifying~~ the ~~trend <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>. The following techniques can be used for detrending <ref name="Wuetal_PNAS"/>:~~
	* Linear trend removal
	* Low-pass filtering using moving averages or linear filters (e.g., butterworth filter)
	* Empirical modal decomposition


	~~[[File:Long timeseries~~.~~png\|400px\|thumb\|caption]]~~

	~~==Notes==~~