Forward-difference - Revision history

Yuengdjern at 13:00, 23 May 2022

2022-05-23T13:00:18Z

← Older revision		Revision as of 13:00, 23 May 2022
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	# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed <math>n_{\text{rmax}}</math>) + 1		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed <math>n_{\text{rmax}}</math>) + 1
	## start with <math>\delta = 1</math>		## start with <math>\delta = 1</math>
	## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[b^\prime(n, t) - b^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for 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> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated
	# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated

CynthiaBluteau at 16:02, 23 November 2021

2021-11-23T16:02:35Z

← Older revision		Revision as of 16:02, 23 November 2021
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	See [[Example forward-difference \| example forward-difference calculation]] for more detail regarding the calculation		See [[Example forward-difference \| example forward-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 09:44, 15 November 2021

2021-11-15T09:44:19Z

← Older revision		Revision as of 09:44, 15 November 2021
Line 1:		Line 1:
	For the '''forward-difference''' scheme		For the '''forward-difference''' scheme
	# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed <math>n_{\text{rmax}}</math>)		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed <math>n_{\text{rmax}}</math>) + 1
	## start with <math>\delta = 1</math>		## start with <math>\delta = 1</math>
	## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria

Brian scannell: Modified first sentence - previous version said that number of bins in range should NOT exceed n_rmax

2021-11-15T09:36:07Z

Modified first sentence - previous version said that number of bins in range should NOT exceed n_rmax

← Older revision		Revision as of 09:36, 15 November 2021
Line 1:		Line 1:
	For the '''forward-difference''' scheme		For the '''forward-difference''' scheme
	# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range ~~must not~~ exceed <math>n_{\text{~~max~~}}</math>)		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range should equal or exceed <math>n_{\text{rmax}}</math>)
	## start with <math>\delta = 1</math>		## start with <math>\delta = 1</math>
	## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria

Djwain at 21:27, 14 November 2021

2021-11-14T21:27:19Z

← Older revision		Revision as of 21:27, 14 November 2021
Line 1:		Line 1:
	For the '''forward-difference''' scheme		For the '''forward-difference''' scheme
	# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must exceed <math>n_{\text{max}}</math>		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must not exceed <math>n_{\text{max}}</math>)
	## start with <math>\delta = 1</math>		## start with <math>\delta = 1</math>
	## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria

Brian scannell at 17:33, 12 November 2021

2021-11-12T17:33:30Z

← Older revision		Revision as of 17:33, 12 November 2021
Line 6:		Line 6:
	# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated

	See [[Example forward-difference \| example forward-difference]] for more detail regarding the calculation		See [[Example forward-difference \| example forward-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 17:32, 12 November 2021

2021-11-12T17:32:54Z

← Older revision		Revision as of 17:32, 12 November 2021
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	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated
	# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated
	~~# see~~ [[Example forward-difference \| example forward-difference]] for more detail regarding the calculation
			See [[Example forward-difference \| example forward-difference]] 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 17:29, 12 November 2021

2021-11-12T17:29:45Z

← Older revision		Revision as of 17:29, 12 November 2021
Line 5:		Line 5:
	## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated
	# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated
	# see [[~~Processing your ADCP data using structure function techniques : Forward~~-difference \| example forward-difference]] for more detail regarding the calculation		# see [[Example forward-difference \| example forward-difference]] 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 16:17, 12 November 2021

2021-11-12T16:17:42Z

← Older revision		Revision as of 16:17, 12 November 2021
Line 2:		Line 2:
	# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must exceed <math>n_{\text{max}}</math>		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must exceed <math>n_{\text{max}}</math>
	## start with <math>\delta = 1</math>		## start with <math>\delta = 1</math>
	## compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for the data segment yielding a velocity difference after the application of the Level 1 QC criteria		## compute the second order forward-difference structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for 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> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated
	# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated
			# see [[Processing your ADCP data using structure function techniques : Forward-difference \| example forward-difference]] 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 10:27, 11 November 2021

2021-11-11T10:27:20Z

← Older revision		Revision as of 10:27, 11 November 2021
Line 1:		Line 1:
	For the '''forward-difference''' scheme		For the '''forward-difference''' scheme
	# start with n being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must exceed n<~~sub~~>max</~~sub~~>		# start with <math>n</math> being the lowest number bin of the range over which the structure function is to be evaluated (number of bins in range must exceed <math>n_{\text{max}}</math>
	## start with <math>\delta</math> ~~= 1~~		## start with <math>\delta = 1</math>
	## compute the second order structure function D(n,~~<math>~~\delta</math>) as the segment mean of the square of the velocity difference between the bin n and bin ~~n +~~ <math>\delta</math>: <br/><br /> D(n, ~~<math>~~\delta~~</math>~~) = ~~<math>~~\langle~~</math>~~ [v’(n, t) - v’(n+~~<math>~~\delta~~</math>~~, 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		## compute the second order structure function <math>D(n,\delta)</math> as the segment mean of the square of the velocity difference between the bin <math>n</math> and bin <math>n + \delta</math>: <br/><br /> <math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math> <br/><br /> where the angled brackets indicate the mean across all <math>t</math> for 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> or~~ n + ~~<math>~~\delta</math> exceeds the last bin of the range over which the structure function is to be evaluated		## increment <math>\delta</math> and repeat steps until <math>\delta = n_{\text{rmax}}</math> or <math>n + \delta</math> exceeds the last bin of the range over which the structure function is to be evaluated
	# increment n and repeat steps until n + 1 is the last bin of the range over which the structure function is to be evaluated		# increment <math>n</math> and repeat steps until <math>n + 1</math> is the last bin of the range over which the structure function is to be evaluated


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