author | Andreas Thurnherr <ant@ldeo.columbia.edu> |
Mon, 27 Jun 2022 19:05:35 -1000 | |
changeset 51 | 14ce2387de5e |
parent 47 | dde46143288c |
permissions | -rw-r--r-- |
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#====================================================================== |
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# . . / L I B / L I B L A D C P . P L |
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# doc: Wed Jun 1 20:38:19 2011 |
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# dlm: Tue Sep 14 08:17:30 2021 |
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# (c) 2011 A.M. Thurnherr |
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# uE-Info: 201 0 NIL 0 0 70 2 2 4 NIL ofnI |
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#====================================================================== |
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||
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# HISTORY: |
|
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# Jun 1, 2011: - created |
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# Jul 29, 2011: - improved |
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# Aug 10, 2011: - made correct |
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# Aug 11, 2011: - added "convenient combinations" |
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# Aug 18, 2011: - made buoyancy frequency non-constant in S() |
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# Jan 4, 2012: - improved T_VI to allow correcting even without superensembles |
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# Jan 5, 2012: - removed S(), which is just pwrdens/N^2 (rather than |
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# pwrdens/N^2/(2pi) as I erroneously thought) |
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# Jan 18, 2012: - added T_VI_alt() to allow assessment of tilt correction extrema |
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# Aug 22, 2012: - added documentation |
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# - added T_w() |
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# Sep 24, 2012: - made "k" argument default in T_w() |
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4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
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# Oct 25, 2012: - renamed T_SM() to T_ASM() |
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# Jun 26, 2013: - added T_w_z() |
4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
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# - added parameter checks to processing-specific corrections |
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# May 18, 2015: - added pulse length to T_w() and T_w_z() |
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# Apr 25, 2018: - added eps_VKE() parameterization |
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# Apr 5, 2018: - adapted to improved antsFunUsage() |
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# - BUG eps_VKE() had erroneous string |
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# Sep 9, 2021: - removed T_w_z(); consistent with Thurnherr (JAOT 2012), |
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# vertical divergence spectra should be corrected with |
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# T_w() |
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require "$ANTS/libvec.pl"; |
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require "$ANTS/libfuns.pl"; |
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||
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#------------------------------------------------------------------------------ |
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# VKE parameterization for epsilon |
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# |
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# NOTES: |
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# - see Thurnherr et al. (GRL 2015) |
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# - calculate eps from p0 |
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# - optional second argument allows free choice of parameterization constant |
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# - default value is from paper, which is slightly lower than the current value |
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# used in [LADCP_VKE], which applies the parameterization only to spectra |
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# passing a few tests |
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#------------------------------------------------------------------------------ |
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||
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sub eps_VKE(@) |
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{ |
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my($p0,$c) = |
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&antsFunUsage(-1,'.','eps_VKE(<p0[m^2/s^2/(rad/m)]> [c[0.021 [1/sqrt(s)]]])',@_); |
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$c = 0.021 unless defined($c); |
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return numberp($p0) ? ($p0 / $c) ** 2 : nan; |
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} |
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#------------------------------------------------------------------------------ |
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# Spectral corrections for LADCP data |
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# |
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# NOTES: |
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# - see Polzin et al. (JAOT 2002), Thurnherr (JAOT 2012) |
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# - to correct, multiply power densities (or power, I think) with corrections |
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# - apply to down-/up-cast data only |
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#------------------------------------------------------------------------------ |
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#---------------------------------------------------------------------- |
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# 1. Corrections for individual data acquisition and processing steps |
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#---------------------------------------------------------------------- |
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||
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#------------------------------------------------------------------------------ |
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# T_ravg(k,blen[,plen]) |
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# - correct for range averaging due to finite pulse and finite receive window |
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# - when called with 2 arguments, bin-length == pulse-length assumed |
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#------------------------------------------------------------------------------ |
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|
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sub T_ravg(@) |
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{ |
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my($k,$blen,$plen) = |
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&antsFunUsage(-2,'ff','T_ravg(<vertical wavenumber[rad/s]> <bin-length[m]> [pulse-length[m]])',@_); |
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$plen = $blen unless defined($plen); |
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return 1 / sinc($k*$blen/2/$PI)**2 / sinc($k*$plen/2/$PI)**2; |
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} |
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||
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#------------------------------------------------------------- |
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# T_fdiff(k,dz) |
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# - correct for first differencing on a grid with dz spacing |
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#------------------------------------------------------------- |
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sub T_fdiff($$) |
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{ |
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my($k,$dz) = |
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&antsFunUsage(2,'ff','T_fdiff(<vertical wavenumber[rad/s]> <differencing interval[m]>)',@_); |
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return 1 / sinc($k*$dz/2/$PI)**2; |
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} |
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||
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#------------------------------------------------------------ |
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# T_interp(k,blen,dz) |
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# - correct for CODAS gridding-with-interpolation algorithm |
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# - ONLY USED IN UH SOFTWARE |
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#------------------------------------------------------------ |
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sub T_interp($$$) |
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{ |
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my($k,$blen,$dz) = |
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&antsFunUsage(3,'fff','T_interp(<vertical wavenumber[rad/s]> <bin length[m]> <grid resolution[m]>)',@_); |
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return 1 / sinc($k*$blen/2/$PI)**4 / sinc($k*$dz/2/$PI)**2; |
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} |
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#------------------------------------------------------------------------- |
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# T_binavg(k,dz) |
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# - correct for simple bin averaging |
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# - Polzin et al. suggest to use blen instead of dz; this must be a typo |
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#------------------------------------------------------------------------- |
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sub T_binavg($$) |
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{ |
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my($k,$dz) = |
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&antsFunUsage(2,'ff','T_binavg(<vertical wavenumber[rad/s]> <grid resolution[m]>)',@_); |
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return 1 / sinc($k*$dz/2/$PI)**2; |
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} |
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#-------------------------------------------------------------------------------- |
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# T_tilt(k,d') |
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# - d' is a length scale that depends on tilt stats and range max |
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# - on d' == 0, T_tilt() == 1, i.e. the correction is disabled |
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# - d' = dprime(range_max) |
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# - is from a quadratic fit to three data points given by Polzin et al. |
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# - see Thurnherr (J. Tech. 2012) for notes |
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# - on range_max == 0, d' == 0, i.e. the correction is disabled |
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#-------------------------------------------------------------------------------- |
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sub T_tilt($$) |
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{ |
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my($k,$dprime) = |
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&antsFunUsage(2,'ff','T_tilt(<vertical wavenumber[rad/s]> <d-prime[m]>)',@_); |
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return $dprime ? 1 / sinc($k*$dprime/2/$PI)**2 : 1; |
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} |
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sub dprime($) |
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{ |
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return $_[0] ? -1.2 + 0.0857 * $_[0] - 0.000136 * $_[0]**2 : 0; |
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} |
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#====================================================================== |
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# 2. Processing-Specific Corrections |
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#====================================================================== |
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#---------------------------------------------------------------------- |
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# T_UH(k,blen,dz,range_max) |
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# - UH implementation of the shear method (WOCE standard) |
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# - range_max == 0 disables tilt correction |
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#---------------------------------------------------------------------- |
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sub T_UH($$$$) |
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{ |
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my($k,$blen,$dz,$range_max) = |
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&antsFunUsage(-3,'fff','T_UH(<vertical wavenumber[rad/s]> <ADCP bin size[m]> <shear grid resolution[m]> <range max[m]>)',@_); |
4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
156 |
croak("T_UH($k,$blen,$dz,$range_max): bad parameters\n") |
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
157 |
unless ($k>=0 && $blen>0 && $dz>0 && $range_max>=0); |
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return T_ravg($k,$blen) * T_fdiff($k,$blen) * T_interp($k,$blen,$dz) * T_tilt($k,dprime($range_max)); |
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} |
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#---------------------------------------------------------------------- |
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# T_ASM(k,blen,dz,range_max) |
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# - re-implemented shear method with simple depth binning |
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# - range_max == 0 disables tilt correction |
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#---------------------------------------------------------------------- |
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sub T_ASM($$$$) |
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{ |
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my($k,$blen,$dz,$range_max) = |
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&antsFunUsage(-3,'fff','T_ASM(<vertical wavenumber[rad/s]> <ADCP bin size[m]> <shear grid resolution[m]> <range max[m]>)',@_); |
4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
171 |
croak("T_ASM($k,$blen,$dz,$range_max): bad parameters\n") |
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
172 |
unless ($k>=0 && $blen>0 && $dz>0 && $range_max>=0); |
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return T_ravg($k,$blen) * T_fdiff($k,$blen) * T_binavg($k,$dz) * T_tilt($k,dprime($range_max)); |
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} |
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#------------------------------------------------------------ |
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# T_VI(k,blen,preavg_dz,grid_dz,range_max) |
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# T_VI_alt(k,blen,preavg_dz,grid_dz,dprime) |
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# - velocity inversion method of Visbeck (J. Tech., 2002) |
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# - only valid if pre-averaging into superensembles is used |
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# - range_max == 0 disables tilt correction |
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4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
182 |
# - sel == nan disables pre-averaging correction |
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#------------------------------------------------------------ |
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sub T_VI($$$$$) |
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{ |
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my($k,$blen,$sel,$dz,$range_max) = |
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&antsFunUsage(-4,'ff.f','T_VI(<vertical wavenumber[rad/s]> <ADCP bin size[m]> <superensemble size[m]|nan> <shear grid resolution[m]> <range max[m]>)',@_); |
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return T_VI_alt($k,$blen,$sel,$dz,dprime($range_max)); |
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} |
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sub T_VI_alt($$$$$) |
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{ |
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my($k,$blen,$sel,$dz,$dprime) = |
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&antsFunUsage(-4,'ff.ff','T_VI_alt(<vertical wavenumber[rad/s]> <ADCP bin size[m]> <superensemble size[m]|nan> <shear grid resolution[m]> <tilt d-prime[m]>)',@_); |
4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
196 |
croak("T_VI_alt($k,$blen,$sel,$dz,$range_max): bad parameters\n") |
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
197 |
unless ($k>=0 && $blen>0 && $sel ne '' && $dz>0 && $range_max>=0); |
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croak("$0: tilt-dprime outside range [0..$blen]\n") |
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unless ($dprime>=0 && $dprime<=$blen); |
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return ($sel>0) ? T_ravg($k,$blen) * T_binavg($k,$sel) * T_binavg($k,$dz) * T_tilt($k,$dprime) |
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: T_ravg($k,$blen) * T_binavg($k,$dz) * T_tilt($k,$dprime); |
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} |
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203 |
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#---------------------------------------------------------------------- |
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# T_w(k,blen,plen,dz,range_max) |
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# - vertical-velocity method of Thurnherr (IEEE 2011) |
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# - range_max == 0 disables tilt correction |
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# - this is the expression that should be used to correct spectra |
209 |
# of VKE and vertical divergence (w_z) |
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# - I am not sure why the finite differencing of the processed |
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# velocities does not have to be corrected for, but this is |
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# consistent with: |
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# - Thurnherr (JAOT 2012) where the shear is corrected with T_VI |
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# - the strain correction of Kunze et al. (2006), which corrects |
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# for bin averaging, but not for finite differencing(?) |
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#---------------------------------------------------------------------- |
217 |
||
218 |
{ my(@fc); |
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sub T_w(@) |
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220 |
{ |
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my($k,$blen,$plen,$dz,$range_max) = |
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&antsFunUsage(-4,'ffff', |
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'T_w([vertical wavenumber[rad/s]] <ADCP bin length[m]> <pulse length[m]> <output grid resolution[m]> <range max[m]>)', |
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\@fc,'k',undef,undef,undef,@_); |
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croak("T_w($k,$blen,$plen,$dz,$range_max): bad parameters\n") |
226 |
unless ($k>=0 && $blen>0 && $plen>0 && $dz>0 && $range_max>=0); |
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return T_ravg($k,$blen,$plen) * T_binavg($k,$dz) * T_tilt($k,dprime($range_max)); |
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} |
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} |
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||
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##---------------------------------------------------------------------- |
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## T_w_z(k,blen,plen,dz,range_max) |
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## - vertical-velocity method of Thurnherr (IEEE 2011) |
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## - first differencing of gridded shear to calculate dw/dz |
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## - NB: grid-scale differentiation assumed |
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## - range_max == 0 disables tilt correction |
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##---------------------------------------------------------------------- |
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# |
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#{ my(@fc); |
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240 |
# sub T_w_z(@) |
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241 |
# { |
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242 |
# my($k,$blen,$plen,$dz,$range_max) = |
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# &antsFunUsage(-4,'ffff', |
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# 'T_w_z([vertical wavenumber[rad/s]] <ADCP bin size[m]> <pulse length[m]> <output grid resolution[m]> <range max[m]>)', |
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# \@fc,'k',undef,undef,undef,@_); |
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# croak("T_w_z($k,$blen,$plen,$dz,$range_max): bad parameters\n") |
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# unless ($k>=0 && $blen>0 && $plen>0 && $dz>0 && $range_max>=0); |
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# return T_ravg($k,$blen,$plen) * T_binavg($k,$dz) * T_tilt($k,dprime($range_max)) * T_fdiff($k,$dz); |
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# } |
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250 |
#} |
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4
ff72b00b4342
after adding $pi and some other stuff
A.M. Thurnherr <athurnherr@yahoo.com>
parents:
3
diff
changeset
|
251 |
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0 | 252 |
1; |