Bin-centred difference scheme - Revision history

Yuengdjern at 12:56, 23 May 2022

2022-05-23T12:56:12Z

← Older revision		Revision as of 12:56, 23 May 2022
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	# start at bin <math>n = \frac{n_{\text{rmax}}}{2} + 1</math>		# start at bin <math>n = \frac{n_{\text{rmax}}}{2} + 1</math>
	## start with <math>\delta</math> = 1		## start with <math>\delta</math> = 1
	## if <math>\delta</math> is '''''even''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered around bin <math>n</math>: <br /><br /><math>D(n, \delta) = \Big\langle \big[v^\prime(n+\frac{\delta}{2},\ t) - v^\prime(n-\frac{\delta}{2},\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''even''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered around bin <math>n</math>: <br /><br /><math>D(n, \delta) = \Big\langle \big[b^\prime(n+\frac{\delta}{2},\ t) - b^\prime(n-\frac{\delta}{2},\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## if <math>\delta</math> is '''''odd''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered on the upper and lower extent of bin <math>n</math>: <br/><br /> <math>\Delta_{\text{lo}}(n, \delta, t) = v^\prime(n+\text{floor}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{ceil}\left(\frac{\delta}{2}\right),\ t)</math> <br/> <math>\Delta_{\text{hi}}(n, \delta, t) = v^\prime(n+\text{ceil}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{floor}\left(\frac{\delta}{2}\right),\ t)</math> <br/><br /> where <math>\text{ceil}</math> and <math>\text{floor}</math> indicate the upper and lower integer value respectively, then <br/><br /> <math>D(n, \delta) = \Bigg\langle \frac{\Delta_{\text{lo}}(n, \delta, t)^2 + \Delta_{\text{hi}}(n, \delta, t)^2}{2} \Bigg\rangle</math> <br/><br /> the angled brackets again indicating the mean across all <math>t</math> in the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''odd''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered on the upper and lower extent of bin <math>n</math>: <br/><br /> <math>\Delta_{\text{lo}}(n, \delta, t) = b^\prime(n+\text{floor}\left(\frac{\delta}{2}\right),\ t) - b^\prime(n-\text{ceil}\left(\frac{\delta}{2}\right),\ t)</math> <br/> <math>\Delta_{\text{hi}}(n, \delta, t) = b^\prime(n+\text{ceil}\left(\frac{\delta}{2}\right),\ t) - b^\prime(n-\text{floor}\left(\frac{\delta}{2}\right),\ t)</math> <br/><br /> where <math>\text{ceil}</math> and <math>\text{floor}</math> indicate the upper and lower integer value respectively, then <br/><br /> <math>D(n, \delta) = \Bigg\langle \frac{\Delta_{\text{lo}}(n, \delta, t)^2 + \Delta_{\text{hi}}(n, \delta, t)^2}{2} \Bigg\rangle</math> <br/><br /> the angled brackets again indicating the mean across all <math>t</math> in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>
	# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>b^\prime</math> are available

	See [[Example bin-centred difference \| example bin-centred difference calculation]] for more detail regarding the calculation		See [[Example bin-centred difference \| example bin-centred difference calculation]] for more detail regarding the calculation

CynthiaBluteau: Categorization

2021-11-23T15:52:05Z

Categorization

← Older revision		Revision as of 15:52, 23 November 2021
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	See [[Example bin-centred difference \| example bin-centred difference calculation]] for more detail regarding the calculation		See [[Example bin-centred difference \| example bin-centred difference calculation]] for more detail regarding the calculation

			----
			Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]

	~~Return to~~ [[~~Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates~~]]		[[Category:Velocity profilers]]

Brian scannell at 10:03, 15 November 2021

2021-11-15T10:03:54Z

← Older revision		Revision as of 10:03, 15 November 2021
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	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>
	# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available

			See [[Example bin-centred difference \| example bin-centred difference calculation]] for more detail regarding the calculation


	Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]		Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]

Brian scannell at 17:40, 12 November 2021

2021-11-12T17:40:07Z

← Older revision		Revision as of 17:40, 12 November 2021
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	## start with <math>\delta</math> = 1		## start with <math>\delta</math> = 1
	## if <math>\delta</math> is '''''even''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered around bin <math>n</math>: <br /><br /><math>D(n, \delta) = \Big\langle \big[v^\prime(n+\frac{\delta}{2},\ t) - v^\prime(n-\frac{\delta}{2},\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''even''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered around bin <math>n</math>: <br /><br /><math>D(n, \delta) = \Big\langle \big[v^\prime(n+\frac{\delta}{2},\ t) - v^\prime(n-\frac{\delta}{2},\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## if <math>\delta</math> is '''''odd''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered on the upper and lower extent of bin <math>n</math>: <br/><br /> <math>\~~Delta v^\prime_~~{\text{lo}}(n, \delta, t) = v^\prime(n+\text{floor}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{ceil}\left(\frac{\delta}{2}\right),\ t)</math> <br/> <math>\~~Delta v^\prime_~~{\text{hi}}(n, \delta, t) = v^\prime(n+\text{ceil}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{floor}\left(\frac{\delta}{2}\right),\ t)</math> <br/><br /> where <math>\text{ceil}</math> and <math>\text{floor}</math> indicate the upper and lower integer value respectively, then <br/><br /> <math>D(n, \delta) = \Bigg\langle \frac{\~~Delta v^\prime_~~{\text{lo}}(n, \delta, t)^2 + \~~Delta v^\prime_~~{\text{hi}}(n, \delta, t)^2}{2} \Bigg\rangle</math> <br/><br /> the angled brackets again indicating the mean across all <math>t</math> in the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''odd''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered on the upper and lower extent of bin <math>n</math>: <br/><br /> <math>\Delta_{\text{lo}}(n, \delta, t) = v^\prime(n+\text{floor}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{ceil}\left(\frac{\delta}{2}\right),\ t)</math> <br/> <math>\Delta_{\text{hi}}(n, \delta, t) = v^\prime(n+\text{ceil}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{floor}\left(\frac{\delta}{2}\right),\ t)</math> <br/><br /> where <math>\text{ceil}</math> and <math>\text{floor}</math> indicate the upper and lower integer value respectively, then <br/><br /> <math>D(n, \delta) = \Bigg\langle \frac{\Delta_{\text{lo}}(n, \delta, t)^2 + \Delta_{\text{hi}}(n, \delta, t)^2}{2} \Bigg\rangle</math> <br/><br /> the angled brackets again indicating the mean across all <math>t</math> in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>
	# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available

	Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]		Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]

Brian scannell at 10:05, 11 November 2021

2021-11-11T10:05:20Z

← Older revision		Revision as of 10:05, 11 November 2021
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	# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available

	Return to [[ADCP structure function ~~flow chart~~\| ~~ADCP Flow Chart front page~~]]		Return to [[Processing your ADCP data using structure function techniques \| Compute structure functions and dissipation estimates]]

Brian scannell at 10:00, 11 November 2021

2021-11-11T10:00:52Z

← Older revision		Revision as of 10:00, 11 November 2021
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	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>
	# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available

			Return to [[ADCP structure function flow chart\| ADCP Flow Chart front page]]

Brian scannell at 09:57, 11 November 2021

2021-11-11T09:57:12Z

← Older revision		Revision as of 09:57, 11 November 2021
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	For a '''bin-centred difference''' scheme:		For a '''bin-centred difference''' scheme:
	# start at bin n = ~~(n<sub>max~~</~~sub~~> ~~/ 2) + 1~~		# start at bin <math>n = \frac{n_{\text{rmax}}}{2} + 1</math>
	## start with <math>\delta</math> = 1		## start with <math>\delta</math> = 1
	## if <math>\delta</math> is '''''even''''' compute the second order structure function D(n,~~<math>~~\delta</math>) as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta</math>r<~~sub~~>0</~~sub~~> ~~centered around bin n~~: <br /><br />D(n, ~~<math>~~\delta~~</math>~~) = ~~<math>~~\langle~~</math>~~ [v’(n+~~(<math>~~\delta~~</math>/~~2), t) - v’(n-~~(<math>~~\delta~~</math>/~~2), t)]~~<sup>~~2~~</sup> <math>~~\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''even''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered around bin <math>n</math>: <br /><br /><math>D(n, \delta) = \Big\langle \big[v^\prime(n+\frac{\delta}{2},\ t) - v^\prime(n-\frac{\delta}{2},\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## if <math>\delta</math> is '''''odd''''' compute the second order structure function D(n,~~<math>~~\delta</math>) as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta</math~~>r<sub>0</sub~~> centered on the upper and lower extent of bin n: <br/><br /> ~~dv'~~<~~sub~~>lo~~</sub>~~(n, ~~<math>~~\delta~~</math>~~, t) = v’(n+floor(~~<math>~~\delta~~</math>/~~2), t) - v’(n-ceil(~~<math>~~\delta~~</math>/~~2), t) <br/> ~~dv'~~<~~sub~~>hi~~</sub>~~(n, ~~<math>~~\delta~~</math>~~, t) = v’(n+ceil(~~<math>~~\delta~~</math>/~~2), t) - v’(n-floor(~~<math>~~\delta~~</math>/~~2), t) <br/><br /> where ''ceil'' and ''floor'' indicate the upper and lower integer value respectively, then <br/><br /> D(n, ~~<math>~~\delta~~</math>~~) = ~~<math>~~\langle~~</math> [dv'<sub>~~lo~~</sub>~~(n, ~~<math>~~\delta~~</math>~~, t)~~<sup>~~2~~</sup>~~ + ~~dv'<sub>~~hi~~</sub>~~(n, ~~<math>~~\delta~~</math>~~, t)~~<sup>~~2~~</sup>] /~~ 2 ~~<math>~~\rangle</math> <br/><br /> the angled brackets again indicating the mean across all t in the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## if <math>\delta</math> is '''''odd''''' compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta r_0</math> centered on the upper and lower extent of bin <math>n</math>: <br/><br /> <math>\Delta v^\prime_{\text{lo}}(n, \delta, t) = v^\prime(n+\text{floor}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{ceil}\left(\frac{\delta}{2}\right),\ t)</math> <br/> <math>\Delta v^\prime_{\text{hi}}(n, \delta, t) = v^\prime(n+\text{ceil}\left(\frac{\delta}{2}\right),\ t) - v^\prime(n-\text{floor}\left(\frac{\delta}{2}\right),\ t)</math> <br/><br /> where <math>\text{ceil}</math> and <math>\text{floor}</math> indicate the upper and lower integer value respectively, then <br/><br /> <math>D(n, \delta) = \Bigg\langle \frac{\Delta v^\prime_{\text{lo}}(n, \delta, t)^2 + \Delta v^\prime_{\text{hi}}(n, \delta, t)^2}{2} \Bigg\rangle</math> <br/><br /> the angled brackets again indicating the mean across all <math>t</math> in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
	## increment <math>\delta</math> and repeat steps until <math>\delta</math> ~~= n~~<~~sub~~>~~max~~</~~sub~~>		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math>
	~~# increment n~~ and repeat steps until n + ~~(n<sub>max~~</~~sub~~> ~~/ 2)~~ exceeds the bin number for which valid v’ are available		# increment <math>n</math> and repeat steps until <math>n + \frac{n_{\text{rmax}}}{2}</math> exceeds the bin number for which valid <math>v^\prime</math> are available

Jmmcmillan: Created page with "For a '''bin-centred difference''' scheme: # start at bin n = (n_max / 2) + 1 ## start with $\delta$ = 1 ## if $\delta$ is '''''even''''' compu..."

2021-11-11T01:22:02Z

Created page with "For a '''bin-centred difference''' scheme: # start at bin n = (nmax / 2) + 1 ## start with <math>\delta</math> = 1 ## if <math>\delta</math> is '''''even''''' compu..."

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For a '''bin-centred difference''' scheme:
# start at bin n = (nmax / 2) + 1
## start with <math>\delta</math> = 1
## if <math>\delta</math> is '''''even''''' compute the second order structure function D(n,<math>\delta</math>) as the segment mean of the square of the velocity difference between the bins separated by distance <math>\delta</math>r0 centered around bin n: D(n, <math>\delta</math>) = <math>\langle</math> [v’(n+(<math>\delta</math>/2), t) - v’(n-(<math>\delta</math>/2), t)]2 <math>\rangle</math> where the angled brackets indicate the mean across all t for the data segment yielding a velocity difference after the application of the Level 1 QC criteria
## if <math>\delta</math> is '''''odd''''' compute the second order structure function D(n,<math>\delta</math>) as the segment mean of the mean of the square of the velocity difference between the bins separated by distance <math>\delta</math>r0 centered on the upper and lower extent of bin n: dv'lo(n, <math>\delta</math>, t) = v’(n+floor(<math>\delta</math>/2), t) - v’(n-ceil(<math>\delta</math>/2), t) dv'hi(n, <math>\delta</math>, t) = v’(n+ceil(<math>\delta</math>/2), t) - v’(n-floor(<math>\delta</math>/2), t) where ''ceil'' and ''floor'' indicate the upper and lower integer value respectively, then D(n, <math>\delta</math>) = <math>\langle</math> [dv'lo(n, <math>\delta</math>, t)2 + dv'hi(n, <math>\delta</math>, t)2] / 2 <math>\rangle</math> the angled brackets again indicating the mean across all t in the data segment yielding a velocity difference after the application of the Level 1 QC criteria
## increment <math>\delta</math> and repeat steps until <math>\delta</math> = nmax
# increment n and repeat steps until n + (nmax / 2) exceeds the bin number for which valid v’ are available