Forward-difference: Difference between revisions
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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[ | ## 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 | ||
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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 | ||
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Return to [[Processing your ADCP data using structure function techniques | Compute structure functions and dissipation estimates]] | |||
[[Category:Velocity profilers]] | |||
Latest revision as of 13:00, 23 May 2022
For the forward-difference scheme
- start with [math]\displaystyle{ 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]\displaystyle{ n_{\text{rmax}} }[/math]) + 1
- start with [math]\displaystyle{ \delta = 1 }[/math]
- compute the second order forward-difference structure function [math]\displaystyle{ D(n,\delta) }[/math] as the segment mean of the square of the velocity difference between the bin [math]\displaystyle{ n }[/math] and bin [math]\displaystyle{ n + \delta }[/math]:
[math]\displaystyle{ D(n, \delta) = \Big\langle \big[b^\prime(n, t) - b^\prime(n+\delta,\ t)\big]^2 \Big\rangle }[/math]
where the angled brackets indicate the mean across all [math]\displaystyle{ t }[/math] for the data segment yielding a velocity difference after the application of the Level 1 QC criteria - increment [math]\displaystyle{ \delta }[/math] and repeat steps until [math]\displaystyle{ \delta = n_{\text{rmax}} }[/math] or [math]\displaystyle{ n + \delta }[/math] exceeds the last bin of the range over which the structure function is to be evaluated
- increment [math]\displaystyle{ n }[/math] and repeat steps until [math]\displaystyle{ n + 1 }[/math] is the last bin of the range over which the structure function is to be evaluated
See example forward-difference calculation for more detail regarding the calculation
Return to Compute structure functions and dissipation estimates
