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 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]] | ||
Revision as of 16:17, 12 November 2021
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>\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>:
<math>D(n, \delta) = \Big\langle \big[v^\prime(n, t) - v^\prime(n+\delta,\ t)\big]^2 \Big\rangle</math>
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>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 for more detail regarding the calculation
Return to Compute structure functions and dissipation estimates
