Convert the shear probe data: Difference between revisions
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<math> s=\frac{N_s}{2\sqrt2SU^2G\gamma} </math> | <math> s=\frac{N_s}{2\sqrt2SU^2G\gamma} </math> | ||
where <math>s</math> is the shear signal in physical units of <math>\mathrm{s}^{-1}</math> , <math>N_s</math> are the raw numeric samples (the output of an analog-to-digital converter), <math>S</math> is the calibrated sensitivity of the shear-probe in units of <math>\mathrm{V/(m\,s^{-1})^2}</math>, <math>U</math> is the speed of profiling in <math>\mathrm{m\,s^{-1}}</math>, <math>G</math> is the gain of the electronics of the shear probe in units of <math>\mathrm{s}</math>, and <math>\gamma</math> is the gain of the analog-to-digital converter used to create the samples in units of <math>\mathrm{counts\, V^{-1}}</math>. | where <math>s</math> is the shear signal in physical units of <math>\mathrm{s}^{-1}</math> , <math>N_s</math> are the raw numeric samples (the output of an analog-to-digital converter), <math>S</math> is the calibrated sensitivity of the shear-probe in units of <math>\mathrm{V/(m\,s^{-1})^2}</math>, <math>U</math> is the speed of profiling in <math>\mathrm{m\,s^{-1}}</math>, <math>G</math> is the gain of the differentiator in the electronics of the shear probe in units of <math>\mathrm{s}</math>, and <math>\gamma</math> is the gain of the analog-to-digital converter used to create the samples in units of <math>\mathrm{counts\, V^{-1}}</math>. | ||
The above formula assumes that the electronics of the shear probe uses a differentiator to produce a signal that is proportional to the time rate of change of the cross-profile velocity fluctuations. | |||
The sensitivity of the shear probe to shear is proportional to the square of the speed of profiling. | The sensitivity of the shear probe to shear is proportional to the square of the speed of profiling. | ||
Thus, one should set a minimum speed for the conversion of the shear-probe data into physical units. Otherwise, the conversion may produce enormously large and quite unrealistic values. | Thus, one should set a minimum speed for the conversion of the shear-probe data into physical units. Otherwise, the conversion may produce enormously large and quite unrealistic values. | ||
Realistic minimum speeds for the conversion into physical units are <math>0.05</math> to <math>0.1\, \mathrm{m\,s^{-1}}</math> because the shear-probe signal is likely to be dominated by electronic noise and the angle of attack will be large (<math> >20^{\circ}</math>) even for low levels of dissipation (\citet{Lueck, R.G., D. Huang, D. Newman, and J. Box, 1997, Turbulence measurements with a moored instrument, J. Atmos. Oceanic Techno., 14, 143-161}). | Realistic minimum speeds for the conversion into physical units are <math>0.05</math> to <math>0.1\, \mathrm{m\,s^{-1}}</math> because the shear-probe signal is likely to be dominated by electronic noise and the angle of attack will be large (<math> >20^{\circ}</math>) even for low levels of dissipation (\citet{Lueck, R.G., D. Huang, D. Newman, and J. Box, 1997, Turbulence measurements with a moored instrument, J. Atmos. Oceanic Techno., 14, 143-161}). | ||
If your instrument does not have a differentiator, then the recorded signal is proportional to the cross-profile velocity fluctuations, say <math>u</math>. | |||
You must convert this signal into a the time derivative of the rate of change of cross-profile velocity using the first difference operator using | |||
<math> s = f_s\, \left[ u(n) - u(n-1) \right] </math> | |||
where <math>f_s</math> is the sampling rate of your data and <math>u</math> are the samples of the shear probe that have been converted in velocity fluctuations in units of <math>\mathrm{m\, s^{-1}}</math>. | |||
Revision as of 18:55, 13 July 2021
copy&paste from V1 docx
Convert the shear-probe data samples into physical units using the standard equation,
[math]\displaystyle{ s=\frac{N_s}{2\sqrt2SU^2G\gamma} }[/math]
where [math]\displaystyle{ s }[/math] is the shear signal in physical units of [math]\displaystyle{ \mathrm{s}^{-1} }[/math] , [math]\displaystyle{ N_s }[/math] are the raw numeric samples (the output of an analog-to-digital converter), [math]\displaystyle{ S }[/math] is the calibrated sensitivity of the shear-probe in units of [math]\displaystyle{ \mathrm{V/(m\,s^{-1})^2} }[/math], [math]\displaystyle{ U }[/math] is the speed of profiling in [math]\displaystyle{ \mathrm{m\,s^{-1}} }[/math], [math]\displaystyle{ G }[/math] is the gain of the differentiator in the electronics of the shear probe in units of [math]\displaystyle{ \mathrm{s} }[/math], and [math]\displaystyle{ \gamma }[/math] is the gain of the analog-to-digital converter used to create the samples in units of [math]\displaystyle{ \mathrm{counts\, V^{-1}} }[/math]. The above formula assumes that the electronics of the shear probe uses a differentiator to produce a signal that is proportional to the time rate of change of the cross-profile velocity fluctuations.
The sensitivity of the shear probe to shear is proportional to the square of the speed of profiling. Thus, one should set a minimum speed for the conversion of the shear-probe data into physical units. Otherwise, the conversion may produce enormously large and quite unrealistic values. Realistic minimum speeds for the conversion into physical units are [math]\displaystyle{ 0.05 }[/math] to [math]\displaystyle{ 0.1\, \mathrm{m\,s^{-1}} }[/math] because the shear-probe signal is likely to be dominated by electronic noise and the angle of attack will be large ([math]\displaystyle{ \gt 20^{\circ} }[/math]) even for low levels of dissipation (\citet{Lueck, R.G., D. Huang, D. Newman, and J. Box, 1997, Turbulence measurements with a moored instrument, J. Atmos. Oceanic Techno., 14, 143-161}).
If your instrument does not have a differentiator, then the recorded signal is proportional to the cross-profile velocity fluctuations, say [math]\displaystyle{ u }[/math]. You must convert this signal into a the time derivative of the rate of change of cross-profile velocity using the first difference operator using
[math]\displaystyle{ s = f_s\, \left[ u(n) - u(n-1) \right] }[/math]
where [math]\displaystyle{ f_s }[/math] is the sampling rate of your data and [math]\displaystyle{ u }[/math] are the samples of the shear probe that have been converted in velocity fluctuations in units of [math]\displaystyle{ \mathrm{m\, s^{-1}} }[/math].
