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C $Header: /u/gcmpack/MITgcm/pkg/kpp/kpp_forcing_surf.F,v 1.9 2014/05/23 20:02:43 jmc Exp $ |
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C $Name: $ |
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|
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#include "KPP_OPTIONS.h" |
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#ifdef ALLOW_AUTODIFF |
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# include "AUTODIFF_OPTIONS.h" |
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#endif |
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#ifdef ALLOW_SALT_PLUME |
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#include "SALT_PLUME_OPTIONS.h" |
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#endif |
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|
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CBOP |
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C !ROUTINE: KPP_FORCING_SURF |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE KPP_FORCING_SURF( |
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I rhoSurf, surfForcU, surfForcV, |
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I surfForcT, surfForcS, surfForcTice, |
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I Qsw, |
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#ifdef ALLOW_SALT_PLUME |
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I SPforcS,SPforcT, |
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#endif /* ALLOW_SALT_PLUME */ |
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I ttalpha, ssbeta, |
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O ustar, bo, bosol, |
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#ifdef ALLOW_SALT_PLUME |
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O boplume, |
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#endif /* ALLOW_SALT_PLUME */ |
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O dVsq, |
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I ikppkey, iMin, iMax, jMin, jMax, bi, bj, myTime, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE KPP_FORCING_SURF | |
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C | o Compute all surface related KPP fields: | |
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C | - friction velocity ustar | |
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C | - turbulent and radiative surface buoyancy forcing, | |
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C | bo and bosol, and surface haline buoyancy forcing | |
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C | boplume | |
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C | - velocity shear relative to surface squared (this is | |
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C | not really a surface affected quantity unless it is | |
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C | computed with respect to some resolution independent | |
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C | reference level, that is KPP_ESTIMATE_UREF defined ) | |
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C *==========================================================* |
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IMPLICIT NONE |
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|
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C \ev |
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|
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C !USES: =============================================================== |
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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 "GRID.h" |
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#include "DYNVARS.h" |
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#include "KPP_PARAMS.h" |
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|
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C !INPUT PARAMETERS: =================================================== |
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C Routine arguments |
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C ikppkeyb - key for storing trajectory for adjoint (taf) |
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C imin, imax, jmin, jmax - array computation indices |
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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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C myThid - Current thread id |
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C rhoSurf- density of surface layer (kg/m^3) |
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C surfForcU units are r_unit.m/s^2 (=m^2/s^2 if r=z) |
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C surfForcV units are r_unit.m/s^2 (=m^2/s^-2 if r=z) |
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C surfForcS units are r_unit.psu/s (=psu.m/s if r=z) |
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C - EmPmR * S_surf plus salinity relaxation*drF(1) |
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C surfForcT units are r_unit.Kelvin/s (=Kelvin.m/s if r=z) |
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C - Qnet (+Qsw) plus temp. relaxation*drF(1) |
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C -> calculate -lambda*(T(model)-T(clim)) |
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C Qnet assumed to be net heat flux including ShortWave rad. |
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C surfForcTice |
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C - equivalent Temperature flux in the top level that corresponds |
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C to the melting or freezing of sea-ice. |
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C Note that the surface level temperature is modified |
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C directly by the sea-ice model in order to maintain |
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C water temperature under sea-ice at the freezing |
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C point. But we need to keep track of the |
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C equivalent amount of heat that this surface-level |
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C temperature change implies because it is used by |
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C the KPP package (kpp_calc.F and kpp_transport_t.F). |
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C Units are r_unit.K/s (=Kelvin.m/s if r=z) (>0 for ocean warming). |
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C |
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C Qsw - surface shortwave radiation (upwards positive) |
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C saltPlumeFlux - salt rejected during freezing (downward = positive) |
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C ttalpha - 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 - 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 !OUTPUT PARAMETERS: |
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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 boplume(nx,ny,Nr+1) - surface haline buoyancy forcing (m^2/s^3) |
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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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|
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INTEGER ikppkey |
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INTEGER iMin, iMax, jMin, jMax |
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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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_RL rhoSurf (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL surfForcU (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL surfForcV (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL surfForcT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL surfForcS (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL surfForcTice(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS Qsw (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL TTALPHA (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1) |
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_RL SSBETA (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1) |
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|
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_RL ustar ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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_RL bo ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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_RL bosol ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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#ifdef ALLOW_SALT_PLUME |
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_RL SPforcS (1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr ) |
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_RL SPforcT (1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr ) |
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_RL boplume (1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nrp1 ) |
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#endif /* ALLOW_SALT_PLUME */ |
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_RL dVsq ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr ) |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C Local constants |
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_RL p0 , p5 , p125 |
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PARAMETER( p0=0.0, p5=0.5, p125=0.125 ) |
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INTEGER i, j, k, im1, ip1, jm1, jp1 |
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_RL tempvar2 |
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_RL recip_Cp |
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|
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_RL work3 ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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|
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#ifdef KPP_ESTIMATE_UREF |
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_RL tempvar1, dBdz1, dBdz2, ustarX, ustarY |
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_RL z0 ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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_RL zRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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_RL uRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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_RL vRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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#endif |
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#ifdef ALLOW_SALT_PLUME |
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#ifdef SALT_PLUME_VOLUME |
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INTEGER kp1 |
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_RL temparray (1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
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#endif /* SALT_PLUME_VOLUME */ |
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#endif /* ALLOW_SALT_PLUME */ |
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CEOP |
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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 = surfForcU (N/m^2) |
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C tauy / rho = surfForcV (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*surfForcT + |
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C beta *surfForcS ) / rho (m^2/s^3) |
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C bosol = - g * alpha * Qsw * drF(1) / rho (m^2/s^3) |
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C boplume =-g * ( beta *saltPlumeFlux/rhoConst )/rho (m^2/s^3) |
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C =-g * ( beta *SPforcS /rhoConst )/rho (m^2/s^3) |
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C -g * (alpha *SPforcT/Cp /rhoConst )/rho (m^2/s^3) |
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C------------------------------------------------------------------------ |
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|
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recip_Cp = 1. _d 0 / HeatCapacity_Cp |
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C initialize arrays to zero |
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DO j = 1-OLy, sNy+OLy |
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DO i = 1-OLx, sNx+OLx |
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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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#ifdef ALLOW_SALT_PLUME |
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DO k = 1, Nr |
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boplume(I,J,k) = p0 |
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ENDDO |
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boplume(I,J,Nrp1) = p0 |
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#endif /* ALLOW_SALT_PLUME */ |
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ENDDO |
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ENDDO |
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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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work3(i,j) = |
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& (surfForcU(i,j,bi,bj) + surfForcU(ip1,j,bi,bj)) * |
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& (surfForcU(i,j,bi,bj) + surfForcU(ip1,j,bi,bj)) + |
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& (surfForcV(i,j,bi,bj) + surfForcV(i,jp1,bi,bj)) * |
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& (surfForcV(i,j,bi,bj) + surfForcV(i,jp1,bi,bj)) |
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ENDDO |
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ENDDO |
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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ store work3 = comlev1_kpp, key = ikppkey |
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#endif |
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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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|
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if ( work3(i,j) .lt. (phepsi*phepsi*drF(1)*drF(1)) ) then |
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ustar(i,j) = SQRT( phepsi * p5 * drF(1) ) |
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else |
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tempVar2 = SQRT( work3(i,j) ) * p5 |
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ustar(i,j) = SQRT( tempVar2 ) |
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endif |
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|
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ENDDO |
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ENDDO |
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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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bo(I,J) = - gravity * |
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& ( TTALPHA(I,J,1) * (surfForcT(i,j,bi,bj)+ |
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& surfForcTice(i,j,bi,bj)) + |
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& SSBETA(I,J,1) * surfForcS(i,j,bi,bj) ) |
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& / rhoSurf(I,J) |
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bosol(I,J) = gravity * TTALPHA(I,J,1) * Qsw(i,j,bi,bj) * |
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& recip_Cp*recip_rhoConst |
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& / rhoSurf(I,J) |
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ENDDO |
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ENDDO |
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|
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#ifdef ALLOW_SALT_PLUME |
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Catn: need check sign of SPforcT |
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Cnote: on input, if notdef salt_plume_volume, SPforc[S,T](k>1)=!0 |
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IF ( useSALT_PLUME ) THEN |
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#ifdef SALT_PLUME_VOLUME |
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DO j = jmin, jmax |
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DO i = imin, imax |
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DO k = 1, Nr |
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kp1 = k+1 |
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temparray(I,J) = - gravity * |
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& ( SSBETA(I,J,k) * SPforcS(i,j,k) + |
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& TTALPHA(I,J,k)* SPforcT(i,j,k) / HeatCapacity_Cp ) |
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& * recip_rhoConst / rhoSurf(I,J) |
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boplume(I,J,kp1) = boplume(I,J,k)+temparray(I,J) |
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ENDDO |
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ENDDO |
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ENDDO |
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#else /* SALT_PLUME_VOLUME */ |
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DO j = jmin, jmax |
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DO i = imin, imax |
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DO k = 2, Nrp1 |
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boplume(I,J,k) = 0. _d 0 |
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ENDDO |
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boplume(I,J,1) = - gravity * SSBETA(I,J,1) |
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& * SPforcS(i,j,1) |
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& * recip_rhoConst / rhoSurf(I,J) |
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ENDDO |
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ENDDO |
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|
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#endif /* SALT_PLUME_VOLUME */ |
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ENDIF |
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#endif /* ALLOW_SALT_PLUME */ |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ store ustar = comlev1_kpp, key = ikppkey |
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#endif |
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|
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#ifdef ALLOW_DIAGNOSTICS |
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IF ( useDiagnostics ) THEN |
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CALL DIAGNOSTICS_FILL(bo ,'KPPbo ',0,1,2,bi,bj,myThid) |
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CALL DIAGNOSTICS_FILL(bosol ,'KPPbosol',0,1,2,bi,bj,myThid) |
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#ifdef ALLOW_SALT_PLUME |
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CALL DIAGNOSTICS_FILL(boplume,'KPPboplm',0,Nr,2,bi,bj,myThid) |
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#endif /* ALLOW_SALT_PLUME */ |
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ENDIF |
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#endif /* ALLOW_DIAGNOSTICS */ |
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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" |
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C onto "t-grid" (in (m/s)**2): |
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C dVsq(k)=(Uref-U(k))**2+(Vref-V(k))**2 at grid levels |
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C------------------------------------------------------------------------ |
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|
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C initialize arrays to zero |
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DO k = 1, Nr |
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DO j = 1-OLy, sNy+OLy |
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DO i = 1-OLx, sNx+OLx |
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dVsq(i,j,k) = p0 |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C dVsq computation |
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|
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#ifdef KPP_ESTIMATE_UREF |
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|
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C Get rid of vertical resolution dependence of dVsq term by |
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C estimating a surface velocity that is independent of first level |
| 293 |
C thickness in the model. First determine mixed layer depth hMix. |
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C Second zRef = espilon * hMix. Third determine roughness length |
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C scale z0. Third estimate reference velocity. |
| 296 |
|
| 297 |
DO j = jmin, jmax |
| 298 |
jp1 = j + 1 |
| 299 |
DO i = imin, imax |
| 300 |
ip1 = i + 1 |
| 301 |
|
| 302 |
C Determine mixed layer depth hMix as the shallowest depth at which |
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C dB/dz exceeds 5.2e-5 s^-2. |
| 304 |
work1(i,j) = nzmax(i,j,bi,bj) |
| 305 |
DO k = 1, Nr |
| 306 |
IF ( k .LT. nzmax(i,j,bi,bj) .AND. |
| 307 |
& maskC(I,J,k,bi,bj) .GT. 0. .AND. |
| 308 |
& dbloc(i,j,k) / drC(k+1) .GT. dB_dz ) |
| 309 |
& work1(i,j) = k |
| 310 |
ENDDO |
| 311 |
|
| 312 |
C Linearly interpolate to find hMix. |
| 313 |
k = work1(i,j) |
| 314 |
IF ( k .EQ. 0 .OR. nzmax(i,j,bi,bj) .EQ. 1 ) THEN |
| 315 |
zRef(i,j) = p0 |
| 316 |
ELSEIF ( k .EQ. 1) THEN |
| 317 |
dBdz2 = dbloc(i,j,1) / drC(2) |
| 318 |
zRef(i,j) = drF(1) * dB_dz / dBdz2 |
| 319 |
ELSEIF ( k .LT. nzmax(i,j,bi,bj) ) THEN |
| 320 |
dBdz1 = dbloc(i,j,k-1) / drC(k ) |
| 321 |
dBdz2 = dbloc(i,j,k ) / drC(k+1) |
| 322 |
zRef(i,j) = rF(k) + drF(k) * (dB_dz - dBdz1) / |
| 323 |
& MAX ( phepsi, dBdz2 - dBdz1 ) |
| 324 |
ELSE |
| 325 |
zRef(i,j) = rF(k+1) |
| 326 |
ENDIF |
| 327 |
|
| 328 |
C Compute roughness length scale z0 subject to 0 < z0 |
| 329 |
tempVar1 = p5 * ( |
| 330 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) * |
| 331 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) + |
| 332 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) * |
| 333 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) + |
| 334 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) * |
| 335 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) + |
| 336 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) * |
| 337 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) ) |
| 338 |
IF ( tempVar1 .lt. (epsln*epsln) ) THEN |
| 339 |
tempVar2 = epsln |
| 340 |
ELSE |
| 341 |
tempVar2 = SQRT ( tempVar1 ) |
| 342 |
ENDIF |
| 343 |
z0(i,j) = rF(2) * |
| 344 |
& ( rF(3) * LOG ( rF(3) / rF(2) ) / |
| 345 |
& ( rF(3) - rF(2) ) - |
| 346 |
& tempVar2 * vonK / |
| 347 |
& MAX ( ustar(i,j), phepsi ) ) |
| 348 |
z0(i,j) = MAX ( z0(i,j), phepsi ) |
| 349 |
|
| 350 |
C zRef is set to 0.1 * hMix subject to z0 <= zRef <= drF(1) |
| 351 |
zRef(i,j) = MAX ( epsilon * zRef(i,j), z0(i,j) ) |
| 352 |
zRef(i,j) = MIN ( zRef(i,j), drF(1) ) |
| 353 |
|
| 354 |
C Estimate reference velocity uRef and vRef. |
| 355 |
uRef(i,j) = p5 * ( uVel(i,j,1,bi,bj) + uVel(ip1,j,1,bi,bj) ) |
| 356 |
vRef(i,j) = p5 * ( vVel(i,j,1,bi,bj) + vVel(i,jp1,1,bi,bj) ) |
| 357 |
IF ( zRef(i,j) .LT. drF(1) ) THEN |
| 358 |
ustarX = ( surfForcU(i, j,bi,bj) + |
| 359 |
& surfForcU(ip1,j,bi,bj) ) * p5 *recip_drF(1) |
| 360 |
ustarY = ( surfForcV(i,j, bi,bj) + |
| 361 |
& surfForcV(i,jp1,bi,bj) ) * p5 *recip_drF(1) |
| 362 |
tempVar1 = ustarX * ustarX + ustarY * ustarY |
| 363 |
if ( tempVar1 .lt. (epsln*epsln) ) then |
| 364 |
tempVar2 = epsln |
| 365 |
else |
| 366 |
tempVar2 = SQRT ( tempVar1 ) |
| 367 |
endif |
| 368 |
tempVar2 = ustar(i,j) * |
| 369 |
& ( LOG ( zRef(i,j) / rF(2) ) + |
| 370 |
& z0(i,j) / zRef(i,j) - z0(i,j) / rF(2) ) / |
| 371 |
& vonK / tempVar2 |
| 372 |
uRef(i,j) = uRef(i,j) + ustarX * tempVar2 |
| 373 |
vRef(i,j) = vRef(i,j) + ustarY * tempVar2 |
| 374 |
ENDIF |
| 375 |
|
| 376 |
ENDDO |
| 377 |
ENDDO |
| 378 |
|
| 379 |
DO k = 1, Nr |
| 380 |
DO j = jmin, jmax |
| 381 |
jm1 = j - 1 |
| 382 |
jp1 = j + 1 |
| 383 |
DO i = imin, imax |
| 384 |
im1 = i - 1 |
| 385 |
ip1 = i + 1 |
| 386 |
dVsq(i,j,k) = p5 * ( |
| 387 |
& (uRef(i,j) - uVel(i, j, k,bi,bj)) * |
| 388 |
& (uRef(i,j) - uVel(i, j, k,bi,bj)) + |
| 389 |
& (uRef(i,j) - uVel(ip1,j, k,bi,bj)) * |
| 390 |
& (uRef(i,j) - uVel(ip1,j, k,bi,bj)) + |
| 391 |
& (vRef(i,j) - vVel(i, j, k,bi,bj)) * |
| 392 |
& (vRef(i,j) - vVel(i, j, k,bi,bj)) + |
| 393 |
& (vRef(i,j) - vVel(i, jp1,k,bi,bj)) * |
| 394 |
& (vRef(i,j) - vVel(i, jp1,k,bi,bj)) ) |
| 395 |
#ifdef KPP_SMOOTH_DVSQ |
| 396 |
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * ( |
| 397 |
& (uRef(i,j) - uVel(i, jm1,k,bi,bj)) * |
| 398 |
& (uRef(i,j) - uVel(i, jm1,k,bi,bj)) + |
| 399 |
& (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) * |
| 400 |
& (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) + |
| 401 |
& (uRef(i,j) - uVel(i, jp1,k,bi,bj)) * |
| 402 |
& (uRef(i,j) - uVel(i, jp1,k,bi,bj)) + |
| 403 |
& (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) * |
| 404 |
& (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) + |
| 405 |
& (vRef(i,j) - vVel(im1,j, k,bi,bj)) * |
| 406 |
& (vRef(i,j) - vVel(im1,j, k,bi,bj)) + |
| 407 |
& (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) * |
| 408 |
& (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) + |
| 409 |
& (vRef(i,j) - vVel(ip1,j, k,bi,bj)) * |
| 410 |
& (vRef(i,j) - vVel(ip1,j, k,bi,bj)) + |
| 411 |
& (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) * |
| 412 |
& (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) ) |
| 413 |
#endif /* KPP_SMOOTH_DVSQ */ |
| 414 |
ENDDO |
| 415 |
ENDDO |
| 416 |
ENDDO |
| 417 |
|
| 418 |
#else /* KPP_ESTIMATE_UREF */ |
| 419 |
|
| 420 |
DO k = 1, Nr |
| 421 |
DO j = jmin, jmax |
| 422 |
jm1 = j - 1 |
| 423 |
jp1 = j + 1 |
| 424 |
DO i = imin, imax |
| 425 |
im1 = i - 1 |
| 426 |
ip1 = i + 1 |
| 427 |
dVsq(i,j,k) = p5 * ( |
| 428 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) * |
| 429 |
& (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) + |
| 430 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) * |
| 431 |
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) + |
| 432 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) * |
| 433 |
& (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) + |
| 434 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) * |
| 435 |
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) ) |
| 436 |
#ifdef KPP_SMOOTH_DVSQ |
| 437 |
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * ( |
| 438 |
& (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) * |
| 439 |
& (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) + |
| 440 |
& (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) * |
| 441 |
& (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) + |
| 442 |
& (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) * |
| 443 |
& (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) + |
| 444 |
& (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) * |
| 445 |
& (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) + |
| 446 |
& (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) * |
| 447 |
& (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) + |
| 448 |
& (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) * |
| 449 |
& (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) + |
| 450 |
& (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) * |
| 451 |
& (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) + |
| 452 |
& (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) * |
| 453 |
& (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) ) |
| 454 |
#endif /* KPP_SMOOTH_DVSQ */ |
| 455 |
ENDDO |
| 456 |
ENDDO |
| 457 |
ENDDO |
| 458 |
|
| 459 |
#endif /* KPP_ESTIMATE_UREF */ |
| 460 |
|
| 461 |
RETURN |
| 462 |
END |
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