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C $Header: /escher1/cvs/master/mitgcmuv/pkg/kpp/kpp_calc.F,v 1.14 2000/11/01 19:57:05 dimitri Exp $ |
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|
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#include "KPP_OPTIONS.h" |
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|
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subroutine KPP_CALC( |
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I bi, bj, myTime, myThid ) |
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C /==========================================================\ |
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C | SUBROUTINE KPP_CALC | |
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C | o Compute all KPP fields defined in KPP.h | |
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C |==========================================================| |
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C | This subroutine serves as an interface between MITGCMUV | |
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C | code and NCOM 1-D routines in kpp_routines.F | |
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C \==========================================================/ |
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IMPLICIT NONE |
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|
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c======================================================================= |
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c |
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c written by : jan morzel, august 11, 1994 |
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c modified by : jan morzel, january 25, 1995 : "dVsq" and 1d code |
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c detlef stammer, august, 1997 : for MIT GCM Classic |
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c d. menemenlis, july, 1998 : for MIT GCM UV |
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c |
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c compute vertical mixing coefficients based on the k-profile |
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c and oceanic planetary boundary layer scheme by large & mcwilliams. |
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c |
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c summary: |
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c - compute interior mixing everywhere: |
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c interior mixing gets computed at all interfaces due to constant |
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c internal wave background activity ("fkpm" and "fkph"), which |
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c is enhanced in places of static instability (local richardson |
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c number < 0). |
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c Additionally, mixing can be enhanced by adding contribution due |
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c to shear instability which is a function of the local richardson |
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c number |
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c - double diffusivity: |
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c interior mixing can be enhanced by double diffusion due to salt |
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c fingering and diffusive convection (ifdef "kmixdd"). |
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c - kpp scheme in the boundary layer: |
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c |
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c a.boundary layer depth: |
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c at every gridpoint the depth of the oceanic boundary layer |
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c ("hbl") gets computed by evaluating bulk richardson numbers. |
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c b.boundary layer mixing: |
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c within the boundary layer, above hbl, vertical mixing is |
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c determined by turbulent surface fluxes, and interior mixing at |
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c the lower boundary, i.e. at hbl. |
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c |
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c this subroutine provides the interface between the MIT GCM UV and the |
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c subroutine "kppmix", where boundary layer depth, vertical |
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c viscosity, vertical diffusivity, and counter gradient term (ghat) |
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c are computed slabwise. |
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c note: subroutine "kppmix" uses m-k-s units. |
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c |
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c time level: |
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c input tracer and velocity profiles are evaluated at time level |
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c tau, surface fluxes come from tau or tau-1. |
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c |
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c grid option: |
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c in this "1-grid" implementation, diffusivity and viscosity |
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c profiles are computed on the "t-grid" (by using velocity shear |
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c profiles averaged from the "u,v-grid" onto the "t-grid"; note, that |
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c the averaging includes zero values on coastal and seafloor grid |
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c points). viscosity on the "u,v-grid" is computed by averaging the |
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c "t-grid" viscosity values onto the "u,v-grid". |
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c |
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c vertical grid: |
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c mixing coefficients get evaluated at the bottom of the lowest |
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c layer, i.e., at depth zw(Nr). these values are only useful when |
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c the model ocean domain does not include the entire ocean down to |
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c the seafloor ("upperocean" setup) and allows flux through the |
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c bottom of the domain. for full-depth runs, these mixing |
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c coefficients are being zeroed out before leaving this subroutine. |
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c |
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c------------------------------------------------------------------------- |
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|
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c global parameters updated by kpp_calc |
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c KPPviscAz - KPP eddy viscosity coefficient (m^2/s) |
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c KPPdiffKzT - KPP diffusion coefficient for temperature (m^2/s) |
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c KPPdiffKzS - KPP diffusion coefficient for salt and tracers (m^2/s) |
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c KPPghat - Nonlocal transport coefficient (s/m^2) |
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c KPPhbl - Boundary layer depth on "t-grid" (m) |
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c KPPfrac - Fraction of short-wave flux penetrating mixing layer |
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|
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c-- KPP_CALC computes vertical viscosity and diffusivity for region |
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c (-2:sNx+3,-2:sNy+3) as required by CALC_DIFFUSIVITY and requires |
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c values of uVel, vVel, SurfaceTendencyU, SurfaceTendencyV in the |
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c region (-2:sNx+4,-2:sNy+4). |
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c Hence overlap region needs to be set OLx=4, OLy=4. |
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c When option FRUGAL_KPP is used, computation in overlap regions |
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c is replaced with exchange calls hence reducing overlap requirements |
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c to OLx=1, OLy=1. |
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|
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "KPP.h" |
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#include "KPP_PARAMS.h" |
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#include "FFIELDS.h" |
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#include "GRID.h" |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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#include "tamc.h" |
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#include "tamc_keys.h" |
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INTEGER isbyte |
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PARAMETER( isbyte = 4 ) |
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#else /* ALLOW_AUTODIFF_TAMC */ |
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integer ikey |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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EXTERNAL DIFFERENT_MULTIPLE |
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LOGICAL DIFFERENT_MULTIPLE |
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|
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c Routine arguments |
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c bi, bj - array indices on which to apply calculations |
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c myTime - Current time in simulation |
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|
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INTEGER bi, bj |
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INTEGER myThid |
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_RL myTime |
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|
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#ifdef ALLOW_KPP |
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|
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c Local constants |
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c minusone, p0, p5, p25, p125, p0625 |
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c imin, imax, jmin, jmax - array computation indices |
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|
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_RL minusone |
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parameter( minusone=-1.0) |
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_KPP_RL p0 , p5 , p25 , p125 , p0625 |
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parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
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integer imin , imax , jmin , jmax |
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#ifdef FRUGAL_KPP |
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parameter( imin=1 , imax=sNx , jmin=1 , jmax=sNy ) |
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#else |
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parameter( imin=-2 , imax=sNx+3 , jmin=-2 , jmax=sNy+3 ) |
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#endif |
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|
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c Local arrays and variables |
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c work? (nx,ny) - horizontal working arrays |
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c ustar (nx,ny) - surface friction velocity (m/s) |
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c bo (nx,ny) - surface turbulent buoyancy forcing (m^2/s^3) |
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c bosol (nx,ny) - surface radiative buoyancy forcing (m^2/s^3) |
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c shsq (nx,ny,Nr) - local velocity shear squared |
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c at interfaces for ri_iwmix (m^2/s^2) |
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c dVsq (nx,ny,Nr) - velocity shear re surface squared |
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c at grid levels for bldepth (m^2/s^2) |
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c dbloc (nx,ny,Nr) - local delta buoyancy at interfaces |
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c for ri_iwmix and bldepth (m/s^2) |
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c Ritop (nx,ny,Nr) - numerator of bulk richardson number |
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c at grid levels for bldepth |
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c vddiff (nx,ny,Nrp2,1)- vertical viscosity on "t-grid" (m^2/s) |
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c vddiff (nx,ny,Nrp2,2)- vert. diff. on next row for temperature (m^2/s) |
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c vddiff (nx,ny,Nrp2,3)- vert. diff. on next row for salt&tracers (m^2/s) |
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c ghat (nx,ny,Nr) - nonlocal transport coefficient (s/m^2) |
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c hbl (nx,ny) - mixing layer depth (m) |
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c kmtj (nx,ny) - maximum number of wet levels in each column |
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c z0 (nx,ny) - Roughness length (m) |
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c zRef (nx,ny) - Reference depth: Hmix * epsilon (m) |
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c uRef (nx,ny) - Reference zonal velocity (m/s) |
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c vRef (nx,ny) - Reference meridional velocity (m/s) |
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|
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_RL worka ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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integer work1 ( ibot:itop , jbot:jtop ) |
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_KPP_RL work2 ( ibot:itop , jbot:jtop ) |
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_KPP_RL ustar ( ibot:itop , jbot:jtop ) |
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_KPP_RL bo ( ibot:itop , jbot:jtop ) |
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_KPP_RL bosol ( ibot:itop , jbot:jtop ) |
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_KPP_RL shsq ( ibot:itop , jbot:jtop , Nr ) |
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_KPP_RL dVsq ( ibot:itop , jbot:jtop , Nr ) |
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_KPP_RL dbloc ( ibot:itop , jbot:jtop , Nr ) |
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_KPP_RL Ritop ( ibot:itop , jbot:jtop , Nr ) |
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_KPP_RL vddiff( ibot:itop , jbot:jtop , 0:Nrp1, mdiff ) |
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_KPP_RL ghat ( ibot:itop , jbot:jtop , Nr ) |
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_KPP_RL hbl ( ibot:itop , jbot:jtop ) |
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#ifdef KPP_ESTIMATE_UREF |
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_KPP_RL z0 ( ibot:itop , jbot:jtop ) |
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_KPP_RL zRef ( ibot:itop , jbot:jtop ) |
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_KPP_RL uRef ( ibot:itop , jbot:jtop ) |
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_KPP_RL vRef ( ibot:itop , jbot:jtop ) |
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#endif /* KPP_ESTIMATE_UREF */ |
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|
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_KPP_RL tempvar1, tempvar2 |
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integer i, j, k, kp1, im1, ip1, jm1, jp1 |
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|
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#ifdef KPP_ESTIMATE_UREF |
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_KPP_RL dBdz1, dBdz2, ustarX, ustarY |
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#endif |
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|
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c Check to see if new vertical mixing coefficient should be computed now? |
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IF ( DIFFERENT_MULTIPLE(kpp_freq,myTime,myTime-deltaTClock) .OR. |
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1 myTime .EQ. startTime ) THEN |
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|
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c----------------------------------------------------------------------- |
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c prepare input arrays for subroutine "kppmix" to compute |
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c viscosity and diffusivity and ghat. |
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c All input arrays need to be in m-k-s units. |
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c |
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c note: for the computation of the bulk richardson number in the |
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c "bldepth" subroutine, gradients of velocity and buoyancy are |
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c required at every depth. in the case of very fine vertical grids |
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c (thickness of top layer < 2m), the surface reference depth must |
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c be set to zref=epsilon/2*zgrid(k), and the reference value |
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c of velocity and buoyancy must be computed as vertical average |
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c between the surface and 2*zref. in the case of coarse vertical |
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c grids zref is zgrid(1)/2., and the surface reference value is |
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c simply the surface value at zgrid(1). |
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c----------------------------------------------------------------------- |
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|
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c------------------------------------------------------------------------ |
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c density related quantities |
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c -------------------------- |
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c |
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c work2 - density of surface layer (kg/m^3) |
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c dbloc - local buoyancy gradient at Nr interfaces |
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c g/rho{k+1,k+1} * [ drho{k,k+1}-drho{k+1,k+1} ] (m/s^2) |
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c dbsfc (stored in Ritop to conserve stack memory) |
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c - buoyancy difference with respect to the surface |
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c g * [ drho{1,k}/rho{1,k} - drho{k,k}/rho{k,k} ] (m/s^2) |
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c ttalpha (stored in vddiff(:,:,:,1) to conserve stack memory) |
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c - thermal expansion coefficient without 1/rho factor |
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c d(rho{k,k})/d(T(k)) (kg/m^3/C) |
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c ssbeta (stored in vddiff(:,:,:,2) to conserve stack memory) |
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c - salt expansion coefficient without 1/rho factor |
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c d(rho{k,k})/d(S(k)) (kg/m^3/PSU) |
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c------------------------------------------------------------------------ |
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|
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CALL TIMER_START('STATEKPP [KPP_CALC]', myThid) |
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CALL STATEKPP( |
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I bi, bj, myThid |
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O , work2, dbloc, Ritop |
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O , vddiff(ibot,jbot,1,1), vddiff(ibot,jbot,1,2) |
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& ) |
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CALL TIMER_STOP ('STATEKPP [KPP_CALC]', myThid) |
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|
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DO k = 1, Nr |
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DO j = jbot, jtop |
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DO i = ibot, itop |
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ghat(i,j,k) = dbloc(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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#ifdef KPP_SMOOTH_DBLOC |
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c horizontally smooth dbloc with a 121 filter |
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c smooth dbloc stored in ghat to save space |
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c dbloc(k) is buoyancy gradientnote between k and k+1 |
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c levels therefore k+1 mask must be used |
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|
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DO k = 1, Nr-1 |
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CALL KPP_SMOOTH_HORIZ ( |
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I k+1, bi, bj, |
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U ghat (ibot,jbot,k) ) |
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ENDDO |
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|
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#endif /* KPP_SMOOTH_DBLOC */ |
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|
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#ifdef KPP_SMOOTH_DENS |
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c horizontally smooth density related quantities with 121 filters |
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CALL KPP_SMOOTH_HORIZ ( |
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I 1, bi, bj, |
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U work2 ) |
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DO k = 1, Nr |
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CALL KPP_SMOOTH_HORIZ ( |
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I k+1, bi, bj, |
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U dbloc (ibot,jbot,k) ) |
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CALL KPP_SMOOTH_HORIZ ( |
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I k, bi, bj, |
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U Ritop (ibot,jbot,k) ) |
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CALL KPP_SMOOTH_HORIZ ( |
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I k, bi, bj, |
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U vddiff(ibot,jbot,k,1) ) |
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CALL KPP_SMOOTH_HORIZ ( |
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I k, bi, bj, |
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U vddiff(ibot,jbot,k,2) ) |
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ENDDO |
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#endif /* KPP_SMOOTH_DENS */ |
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|
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DO k = 1, Nr |
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DO j = jbot, jtop |
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DO i = ibot, itop |
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|
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c zero out dbloc over land points (so that the convective |
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c part of the interior mixing can be diagnosed) |
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dbloc(i,j,k) = dbloc(i,j,k) * pMask(i,j,k,bi,bj) |
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ghat(i,j,k) = ghat(i,j,k) * pMask(i,j,k,bi,bj) |
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Ritop(i,j,k) = Ritop(i,j,k) * pMask(i,j,k,bi,bj) |
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if(k.eq.nzmax(i,j,bi,bj)) then |
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dbloc(i,j,k) = p0 |
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ghat(i,j,k) = p0 |
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Ritop(i,j,k) = p0 |
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endif |
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|
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c numerator of bulk richardson number on grid levels |
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c note: land and ocean bottom values need to be set to zero |
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c so that the subroutine "bldepth" works correctly |
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Ritop(i,j,k) = (zgrid(1)-zgrid(k)) * Ritop(i,j,k) |
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|
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END DO |
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END DO |
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END DO |
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|
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c------------------------------------------------------------------------ |
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c friction velocity, turbulent and radiative surface buoyancy forcing |
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c ------------------------------------------------------------------- |
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c taux / rho = SurfaceTendencyU * delZ(1) (N/m^2) |
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c tauy / rho = SurfaceTendencyV * delZ(1) (N/m^2) |
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c ustar = sqrt( sqrt( taux^2 + tauy^2 ) / rho ) (m/s) |
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c bo = - g * ( alpha*SurfaceTendencyT + |
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c beta *SurfaceTendencyS ) * delZ(1) / rho (m^2/s^3) |
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c bosol = - g * alpha * Qsw * delZ(1) / rho (m^2/s^3) |
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c------------------------------------------------------------------------ |
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|
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c initialize arrays to zero |
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DO j = jbot, jtop |
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DO i = ibot, itop |
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ustar(i,j) = p0 |
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bo (I,J) = p0 |
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bosol(I,J) = p0 |
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END DO |
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END DO |
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|
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DO j = jmin, jmax |
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jp1 = j + 1 |
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DO i = imin, imax |
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ip1 = i+1 |
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tempVar1 = |
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& (SurfaceTendencyU(i,j,bi,bj) + SurfaceTendencyU(ip1,j,bi,bj)) * |
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& (SurfaceTendencyU(i,j,bi,bj) + SurfaceTendencyU(ip1,j,bi,bj)) + |
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& (SurfaceTendencyV(i,j,bi,bj) + SurfaceTendencyV(i,jp1,bi,bj)) * |
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& (SurfaceTendencyV(i,j,bi,bj) + SurfaceTendencyV(i,jp1,bi,bj)) |
| 332 |
if ( tempVar1 .lt. (phepsi*phepsi) ) then |
| 333 |
ustar(i,j) = SQRT( phepsi * p5 * delZ(1) ) |
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else |
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tempVar2 = SQRT( tempVar1 ) * p5 * delZ(1) |
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ustar(i,j) = SQRT( tempVar2 ) |
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endif |
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bo(I,J) = - gravity * |
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& ( vddiff(I,J,1,1) * SurfaceTendencyT(i,j,bi,bj) + |
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& vddiff(I,J,1,2) * SurfaceTendencyS(i,j,bi,bj) |
| 341 |
& ) * |
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& delZ(1) / work2(I,J) |
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bosol(I,J) = - gravity * vddiff(I,J,1,1) * Qsw(i,j,bi,bj) * |
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& delZ(1) / work2(I,J) |
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END DO |
| 346 |
END DO |
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|
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c------------------------------------------------------------------------ |
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c velocity shear |
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c -------------- |
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c Get velocity shear squared, averaged from "u,v-grid" |
| 352 |
c onto "t-grid" (in (m/s)**2): |
| 353 |
c dVsq(k)=(Uref-U(k))**2+(Vref-V(k))**2 at grid levels |
| 354 |
c shsq(k)=(U(k)-U(k+1))**2+(V(k)-V(k+1))**2 at interfaces |
| 355 |
c------------------------------------------------------------------------ |
| 356 |
|
| 357 |
c initialize arrays to zero |
| 358 |
DO k = 1, Nr |
| 359 |
DO j = jbot, jtop |
| 360 |
DO i = ibot, itop |
| 361 |
shsq(i,j,k) = p0 |
| 362 |
dVsq(i,j,k) = p0 |
| 363 |
END DO |
| 364 |
END DO |
| 365 |
END DO |
| 366 |
|
| 367 |
c dVsq computation |
| 368 |
|
| 369 |
#ifdef KPP_ESTIMATE_UREF |
| 370 |
|
| 371 |
c Get rid of vertical resolution dependence of dVsq term by |
| 372 |
c estimating a surface velocity that is independent of first level |
| 373 |
c thickness in the model. First determine mixed layer depth hMix. |
| 374 |
c Second zRef = espilon * hMix. Third determine roughness length |
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c scale z0. Third estimate reference velocity. |
| 376 |
|
| 377 |
DO j = jmin, jmax |
| 378 |
jp1 = j + 1 |
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DO i = imin, imax |
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ip1 = i + 1 |
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|
| 382 |
c Determine mixed layer depth hMix as the shallowest depth at which |
| 383 |
c dB/dz exceeds 5.2e-5 s^-2. |
| 384 |
work1(i,j) = nzmax(i,j,bi,bj) |
| 385 |
DO k = 1, Nr |
| 386 |
IF ( k .LT. nzmax(i,j,bi,bj) .AND. |
| 387 |
& dbloc(i,j,k) / drC(k+1) .GT. dB_dz ) |
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& work1(i,j) = k |
| 389 |
END DO |
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|
| 391 |
c Linearly interpolate to find hMix. |
| 392 |
k = work1(i,j) |
| 393 |
IF ( k .EQ. 0 .OR. nzmax(i,j,bi,bj) .EQ. 1 ) THEN |
| 394 |
zRef(i,j) = p0 |
| 395 |
ELSEIF ( k .EQ. 1) THEN |
| 396 |
dBdz2 = dbloc(i,j,1) / drC(2) |
| 397 |
zRef(i,j) = drF(1) * dB_dz / dBdz2 |
| 398 |
ELSEIF ( k .LT. nzmax(i,j,bi,bj) ) THEN |
| 399 |
dBdz1 = dbloc(i,j,k-1) / drC(k ) |
| 400 |
dBdz2 = dbloc(i,j,k ) / drC(k+1) |
| 401 |
zRef(i,j) = rF(k) + drF(k) * (dB_dz - dBdz1) / |
| 402 |
& MAX ( phepsi, dBdz2 - dBdz1 ) |
| 403 |
ELSE |
| 404 |
zRef(i,j) = rF(k+1) |
| 405 |
ENDIF |
| 406 |
|
| 407 |
c Compute roughness length scale z0 subject to 0 < z0 |
| 408 |
tempVar1 = p5 * ( |
| 409 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) * |
| 410 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) + |
| 411 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) * |
| 412 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) + |
| 413 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) * |
| 414 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) + |
| 415 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) * |
| 416 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) ) |
| 417 |
if ( tempVar1 .lt. (epsln*epsln) ) then |
| 418 |
tempVar2 = epsln |
| 419 |
else |
| 420 |
tempVar2 = SQRT ( tempVar1 ) |
| 421 |
endif |
| 422 |
z0(i,j) = rF(2) * |
| 423 |
& ( rF(3) * LOG ( rF(3) / rF(2) ) / |
| 424 |
& ( rF(3) - rF(2) ) - |
| 425 |
& tempVar2 * vonK / |
| 426 |
& MAX ( ustar(i,j), phepsi ) ) |
| 427 |
z0(i,j) = MAX ( z0(i,j), phepsi ) |
| 428 |
|
| 429 |
c zRef is set to 0.1 * hMix subject to z0 <= zRef <= drF(1) |
| 430 |
zRef(i,j) = MAX ( epsilon * zRef(i,j), z0(i,j) ) |
| 431 |
zRef(i,j) = MIN ( zRef(i,j), drF(1) ) |
| 432 |
|
| 433 |
c Estimate reference velocity uRef and vRef. |
| 434 |
uRef(i,j) = p5 * |
| 435 |
& ( uVel(i,j,1,bi,bj) + uVel(ip1,j,1,bi,bj) ) |
| 436 |
vRef(i,j) = p5 * |
| 437 |
& ( vVel(i,j,1,bi,bj) + vVel(i,jp1,1,bi,bj) ) |
| 438 |
IF ( zRef(i,j) .LT. drF(1) ) THEN |
| 439 |
ustarX = ( SurfaceTendencyU(i, j,bi,bj) + |
| 440 |
& SurfaceTendencyU(ip1,j,bi,bj) ) * p5 |
| 441 |
ustarY = ( SurfaceTendencyV(i,j, bi,bj) + |
| 442 |
& SurfaceTendencyU(i,jp1,bi,bj) ) * p5 |
| 443 |
tempVar1 = ustarX * ustarX + ustarY * ustarY |
| 444 |
if ( tempVar1 .lt. (epsln*epsln) ) then |
| 445 |
tempVar2 = epsln |
| 446 |
else |
| 447 |
tempVar2 = SQRT ( tempVar1 ) |
| 448 |
endif |
| 449 |
tempVar2 = ustar(i,j) * |
| 450 |
& ( LOG ( zRef(i,j) / rF(2) ) + |
| 451 |
& z0(i,j) / zRef(i,j) - z0(i,j) / rF(2) ) / |
| 452 |
& vonK / tempVar2 |
| 453 |
uRef(i,j) = uRef(i,j) + ustarX * tempVar2 |
| 454 |
vRef(i,j) = vRef(i,j) + ustarY * tempVar2 |
| 455 |
ENDIF |
| 456 |
|
| 457 |
END DO |
| 458 |
END DO |
| 459 |
|
| 460 |
DO k = 1, Nr |
| 461 |
DO j = jmin, jmax |
| 462 |
jm1 = j - 1 |
| 463 |
jp1 = j + 1 |
| 464 |
DO i = imin, imax |
| 465 |
im1 = i - 1 |
| 466 |
ip1 = i + 1 |
| 467 |
dVsq(i,j,k) = p5 * ( |
| 468 |
$ (uRef(i,j) - uVel(i, j, k,bi,bj)) * |
| 469 |
$ (uRef(i,j) - uVel(i, j, k,bi,bj)) + |
| 470 |
$ (uRef(i,j) - uVel(ip1,j, k,bi,bj)) * |
| 471 |
$ (uRef(i,j) - uVel(ip1,j, k,bi,bj)) + |
| 472 |
$ (vRef(i,j) - vVel(i, j, k,bi,bj)) * |
| 473 |
$ (vRef(i,j) - vVel(i, j, k,bi,bj)) + |
| 474 |
$ (vRef(i,j) - vVel(i, jp1,k,bi,bj)) * |
| 475 |
$ (vRef(i,j) - vVel(i, jp1,k,bi,bj)) ) |
| 476 |
#ifdef KPP_SMOOTH_DVSQ |
| 477 |
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * ( |
| 478 |
$ (uRef(i,j) - uVel(i, jm1,k,bi,bj)) * |
| 479 |
$ (uRef(i,j) - uVel(i, jm1,k,bi,bj)) + |
| 480 |
$ (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) * |
| 481 |
$ (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) + |
| 482 |
$ (uRef(i,j) - uVel(i, jp1,k,bi,bj)) * |
| 483 |
$ (uRef(i,j) - uVel(i, jp1,k,bi,bj)) + |
| 484 |
$ (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) * |
| 485 |
$ (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) + |
| 486 |
$ (vRef(i,j) - vVel(im1,j, k,bi,bj)) * |
| 487 |
$ (vRef(i,j) - vVel(im1,j, k,bi,bj)) + |
| 488 |
$ (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) * |
| 489 |
$ (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) + |
| 490 |
$ (vRef(i,j) - vVel(ip1,j, k,bi,bj)) * |
| 491 |
$ (vRef(i,j) - vVel(ip1,j, k,bi,bj)) + |
| 492 |
$ (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) * |
| 493 |
$ (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) ) |
| 494 |
#endif /* KPP_SMOOTH_DVSQ */ |
| 495 |
END DO |
| 496 |
END DO |
| 497 |
END DO |
| 498 |
|
| 499 |
#else /* KPP_ESTIMATE_UREF */ |
| 500 |
|
| 501 |
DO k = 1, Nr |
| 502 |
DO j = jmin, jmax |
| 503 |
jm1 = j - 1 |
| 504 |
jp1 = j + 1 |
| 505 |
DO i = imin, imax |
| 506 |
im1 = i - 1 |
| 507 |
ip1 = i + 1 |
| 508 |
dVsq(i,j,k) = p5 * ( |
| 509 |
$ (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) * |
| 510 |
$ (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) + |
| 511 |
$ (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) * |
| 512 |
$ (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) + |
| 513 |
$ (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) * |
| 514 |
$ (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) + |
| 515 |
$ (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) * |
| 516 |
$ (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) ) |
| 517 |
#ifdef KPP_SMOOTH_DVSQ |
| 518 |
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * ( |
| 519 |
$ (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) * |
| 520 |
$ (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) + |
| 521 |
$ (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) * |
| 522 |
$ (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) + |
| 523 |
$ (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) * |
| 524 |
$ (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) + |
| 525 |
$ (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) * |
| 526 |
$ (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) + |
| 527 |
$ (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) * |
| 528 |
$ (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) + |
| 529 |
$ (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) * |
| 530 |
$ (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) + |
| 531 |
$ (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) * |
| 532 |
$ (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) + |
| 533 |
$ (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) * |
| 534 |
$ (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) ) |
| 535 |
#endif /* KPP_SMOOTH_DVSQ */ |
| 536 |
END DO |
| 537 |
END DO |
| 538 |
END DO |
| 539 |
|
| 540 |
#endif /* KPP_ESTIMATE_UREF */ |
| 541 |
|
| 542 |
c shsq computation |
| 543 |
DO k = 1, Nrm1 |
| 544 |
kp1 = k + 1 |
| 545 |
DO j = jmin, jmax |
| 546 |
jm1 = j - 1 |
| 547 |
jp1 = j + 1 |
| 548 |
DO i = imin, imax |
| 549 |
im1 = i - 1 |
| 550 |
ip1 = i + 1 |
| 551 |
shsq(i,j,k) = p5 * ( |
| 552 |
$ (uVel(i, j, k,bi,bj)-uVel(i, j, kp1,bi,bj)) * |
| 553 |
$ (uVel(i, j, k,bi,bj)-uVel(i, j, kp1,bi,bj)) + |
| 554 |
$ (uVel(ip1,j, k,bi,bj)-uVel(ip1,j, kp1,bi,bj)) * |
| 555 |
$ (uVel(ip1,j, k,bi,bj)-uVel(ip1,j, kp1,bi,bj)) + |
| 556 |
$ (vVel(i, j, k,bi,bj)-vVel(i, j, kp1,bi,bj)) * |
| 557 |
$ (vVel(i, j, k,bi,bj)-vVel(i, j, kp1,bi,bj)) + |
| 558 |
$ (vVel(i, jp1,k,bi,bj)-vVel(i, jp1,kp1,bi,bj)) * |
| 559 |
$ (vVel(i, jp1,k,bi,bj)-vVel(i, jp1,kp1,bi,bj)) ) |
| 560 |
#ifdef KPP_SMOOTH_SHSQ |
| 561 |
shsq(i,j,k) = p5 * shsq(i,j,k) + p125 * ( |
| 562 |
$ (uVel(i, jm1,k,bi,bj)-uVel(i, jm1,kp1,bi,bj)) * |
| 563 |
$ (uVel(i, jm1,k,bi,bj)-uVel(i, jm1,kp1,bi,bj)) + |
| 564 |
$ (uVel(ip1,jm1,k,bi,bj)-uVel(ip1,jm1,kp1,bi,bj)) * |
| 565 |
$ (uVel(ip1,jm1,k,bi,bj)-uVel(ip1,jm1,kp1,bi,bj)) + |
| 566 |
$ (uVel(i, jp1,k,bi,bj)-uVel(i, jp1,kp1,bi,bj)) * |
| 567 |
$ (uVel(i, jp1,k,bi,bj)-uVel(i, jp1,kp1,bi,bj)) + |
| 568 |
$ (uVel(ip1,jp1,k,bi,bj)-uVel(ip1,jp1,kp1,bi,bj)) * |
| 569 |
$ (uVel(ip1,jp1,k,bi,bj)-uVel(ip1,jp1,kp1,bi,bj)) + |
| 570 |
$ (vVel(im1,j, k,bi,bj)-vVel(im1,j, kp1,bi,bj)) * |
| 571 |
$ (vVel(im1,j, k,bi,bj)-vVel(im1,j, kp1,bi,bj)) + |
| 572 |
$ (vVel(im1,jp1,k,bi,bj)-vVel(im1,jp1,kp1,bi,bj)) * |
| 573 |
$ (vVel(im1,jp1,k,bi,bj)-vVel(im1,jp1,kp1,bi,bj)) + |
| 574 |
$ (vVel(ip1,j, k,bi,bj)-vVel(ip1,j, kp1,bi,bj)) * |
| 575 |
$ (vVel(ip1,j, k,bi,bj)-vVel(ip1,j, kp1,bi,bj)) + |
| 576 |
$ (vVel(ip1,jp1,k,bi,bj)-vVel(ip1,jp1,kp1,bi,bj)) * |
| 577 |
$ (vVel(ip1,jp1,k,bi,bj)-vVel(ip1,jp1,kp1,bi,bj)) ) |
| 578 |
#endif |
| 579 |
END DO |
| 580 |
END DO |
| 581 |
END DO |
| 582 |
|
| 583 |
c----------------------------------------------------------------------- |
| 584 |
c solve for viscosity, diffusivity, ghat, and hbl on "t-grid" |
| 585 |
c----------------------------------------------------------------------- |
| 586 |
|
| 587 |
DO j = jbot, jtop |
| 588 |
DO i = ibot, itop |
| 589 |
work1(i,j) = nzmax(i,j,bi,bj) |
| 590 |
work2(i,j) = Fcori(i,j,bi,bj) |
| 591 |
END DO |
| 592 |
END DO |
| 593 |
CALL TIMER_START('KPPMIX [KPP_CALC]', myThid) |
| 594 |
CALL KPPMIX ( |
| 595 |
I mytime, mythid |
| 596 |
I , work1, shsq, dVsq, ustar |
| 597 |
I , bo, bosol, dbloc, Ritop, work2 |
| 598 |
I , ikey |
| 599 |
O , vddiff |
| 600 |
U , ghat |
| 601 |
O , hbl ) |
| 602 |
|
| 603 |
CALL TIMER_STOP ('KPPMIX [KPP_CALC]', myThid) |
| 604 |
|
| 605 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 606 |
cph( storing not necessary |
| 607 |
cphCADJ STORE vddiff, ghat = comlev1_kpp, key = ikey |
| 608 |
cph) |
| 609 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 610 |
|
| 611 |
c----------------------------------------------------------------------- |
| 612 |
c zero out land values and transfer to global variables |
| 613 |
c----------------------------------------------------------------------- |
| 614 |
|
| 615 |
DO j = jmin, jmax |
| 616 |
DO i = imin, imax |
| 617 |
DO k = 1, Nr |
| 618 |
KPPviscAz(i,j,k,bi,bj) = vddiff(i,j,k-1,1) * pMask(i,j,k,bi,bj) |
| 619 |
KPPdiffKzS(i,j,k,bi,bj)= vddiff(i,j,k-1,2) * pMask(i,j,k,bi,bj) |
| 620 |
KPPdiffKzT(i,j,k,bi,bj)= vddiff(i,j,k-1,3) * pMask(i,j,k,bi,bj) |
| 621 |
KPPghat(i,j,k,bi,bj) = ghat(i,j,k) * pMask(i,j,k,bi,bj) |
| 622 |
END DO |
| 623 |
KPPhbl(i,j,bi,bj) = hbl(i,j) * pMask(i,j,1,bi,bj) |
| 624 |
END DO |
| 625 |
END DO |
| 626 |
#ifdef FRUGAL_KPP |
| 627 |
_EXCH_XYZ_R8(KPPviscAz , myThid ) |
| 628 |
_EXCH_XYZ_R8(KPPdiffKzS , myThid ) |
| 629 |
_EXCH_XYZ_R8(KPPdiffKzT , myThid ) |
| 630 |
_EXCH_XYZ_R8(KPPghat , myThid ) |
| 631 |
_EXCH_XY_R8 (KPPhbl , myThid ) |
| 632 |
#endif |
| 633 |
|
| 634 |
#ifdef KPP_SMOOTH_VISC |
| 635 |
c horizontal smoothing of vertical viscosity |
| 636 |
DO k = 1, Nr |
| 637 |
CALL SMOOTH_HORIZ ( |
| 638 |
I k, bi, bj, |
| 639 |
U KPPviscAz(1-OLx,1-OLy,k,bi,bj) ) |
| 640 |
END DO |
| 641 |
_EXCH_XYZ_R8(KPPviscAz , myThid ) |
| 642 |
#endif /* KPP_SMOOTH_VISC */ |
| 643 |
|
| 644 |
#ifdef KPP_SMOOTH_DIFF |
| 645 |
c horizontal smoothing of vertical diffusivity |
| 646 |
DO k = 1, Nr |
| 647 |
CALL SMOOTH_HORIZ ( |
| 648 |
I k, bi, bj, |
| 649 |
U KPPdiffKzS(1-OLx,1-OLy,k,bi,bj) ) |
| 650 |
CALL SMOOTH_HORIZ ( |
| 651 |
I k, bi, bj, |
| 652 |
U KPPdiffKzT(1-OLx,1-OLy,k,bi,bj) ) |
| 653 |
END DO |
| 654 |
_EXCH_XYZ_R8(KPPdiffKzS , myThid ) |
| 655 |
_EXCH_XYZ_R8(KPPdiffKzT , myThid ) |
| 656 |
#endif /* KPP_SMOOTH_DIFF */ |
| 657 |
|
| 658 |
C Compute fraction of solar short-wave flux penetrating to |
| 659 |
C the bottom of the mixing layer. |
| 660 |
DO j=1-OLy,sNy+OLy |
| 661 |
DO i=1-OLx,sNx+OLx |
| 662 |
worka(i,j) = KPPhbl(i,j,bi,bj) |
| 663 |
ENDDO |
| 664 |
ENDDO |
| 665 |
CALL SWFRAC( |
| 666 |
I (sNx+2*OLx)*(sNy+2*OLy), minusone, |
| 667 |
I mytime, mythid, |
| 668 |
U worka ) |
| 669 |
DO j=1-OLy,sNy+OLy |
| 670 |
DO i=1-OLx,sNx+OLx |
| 671 |
KPPfrac(i,j,bi,bj) = worka(i,j) |
| 672 |
ENDDO |
| 673 |
ENDDO |
| 674 |
|
| 675 |
ENDIF |
| 676 |
|
| 677 |
#endif ALLOW_KPP |
| 678 |
|
| 679 |
RETURN |
| 680 |
END |
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