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dgoldberg |
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C $Header: /u/gcmpack/MITgcm/pkg/shelfice/shelfice_thermodynamics.F,v 1.38 2014/11/02 21:23:51 gforget Exp $ |
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dgoldberg |
1.1 |
C $Name: $ |
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#include "SHELFICE_OPTIONS.h" |
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dgoldberg |
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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_CTRL |
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# include "CTRL_OPTIONS.h" |
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#endif |
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dgoldberg |
1.1 |
#ifdef ALLOW_STREAMICE |
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# include "STREAMICE_OPTIONS.h" |
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#endif |
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dgoldberg |
1.2 |
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dgoldberg |
1.1 |
CBOP |
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C !ROUTINE: SHELFICE_THERMODYNAMICS |
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C !INTERFACE: |
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SUBROUTINE SHELFICE_THERMODYNAMICS( |
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I myTime, myIter, myThid ) |
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C !DESCRIPTION: \bv |
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C *=============================================================* |
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C | S/R SHELFICE_THERMODYNAMICS |
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C | o shelf-ice main routine. |
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C | compute temperature and (virtual) salt flux at the |
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C | shelf-ice ocean interface |
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C | |
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C | stresses at the ice/water interface are computed in separate |
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C | routines that are called from mom_fluxform/mom_vecinv |
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C *=============================================================* |
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C !USES: |
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IMPLICIT NONE |
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C === Global variables === |
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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 "FFIELDS.h" |
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#include "SHELFICE.h" |
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dgoldberg |
1.2 |
#include "SHELFICE_COST.h" |
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dgoldberg |
1.1 |
#ifdef ALLOW_AUTODIFF |
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# include "CTRL_SIZE.h" |
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# include "ctrl.h" |
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# include "ctrl_dummy.h" |
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#endif /* ALLOW_AUTODIFF */ |
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#ifdef ALLOW_AUTODIFF_TAMC |
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# ifdef SHI_ALLOW_GAMMAFRICT |
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# include "tamc.h" |
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# include "tamc_keys.h" |
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# endif /* SHI_ALLOW_GAMMAFRICT */ |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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#ifdef ALLOW_STREAMICE |
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# include "STREAMICE.h" |
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#endif |
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C !INPUT/OUTPUT PARAMETERS: |
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C === Routine arguments === |
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C myIter :: iteration counter for this thread |
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C myTime :: time counter for this thread |
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C myThid :: thread number for this instance of the routine. |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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CEOP |
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#ifdef ALLOW_SHELFICE |
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C !LOCAL VARIABLES : |
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C === Local variables === |
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C I,J,K,Kp1,bi,bj :: loop counters |
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C tLoc, sLoc, pLoc :: local in-situ temperature, salinity, pressure |
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C theta/saltFreeze :: temperature and salinity of water at the |
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C ice-ocean interface (at the freezing point) |
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C freshWaterFlux :: local variable for fresh water melt flux due |
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C to melting in kg/m^2/s |
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C (negative density x melt rate) |
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C convertFW2SaltLoc:: local copy of convertFW2Salt |
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C cFac :: 1 for conservative form, 0, otherwise |
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C rFac :: realFreshWaterFlux factor |
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C dFac :: 0 for diffusive heat flux (Holland and Jenkins, 1999, eq21) |
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C 1 for advective and diffusive heat flux (eq22, 26, 31) |
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C fwflxFac :: only effective for dFac=1, 1 if we expect a melting fresh |
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C water flux, 0 otherwise |
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C auxiliary variables and abbreviations: |
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C a0, a1, a2, b, c0 |
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C eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8 |
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C aqe, bqe, cqe, discrim, recip_aqe |
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C drKp1, recip_drLoc |
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INTEGER I,J,K,Kp1 |
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INTEGER bi,bj |
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_RL tLoc(1:sNx,1:sNy) |
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_RL sLoc(1:sNx,1:sNy) |
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_RL pLoc(1:sNx,1:sNy) |
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_RL uLoc(1:sNx,1:sNy) |
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_RL vLoc(1:sNx,1:sNy) |
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_RL thetaFreeze, saltFreeze, recip_Cp |
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_RL freshWaterFlux, convertFW2SaltLoc |
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_RL a0, a1, a2, b, c0 |
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_RL eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8 |
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_RL cFac, rFac, dFac, fwflxFac |
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_RL aqe, bqe, cqe, discrim, recip_aqe |
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_RL drKp1, recip_drLoc |
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_RL tmpFac |
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#ifdef SHI_ALLOW_GAMMAFRICT |
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_RL shiPr, shiSc, shiLo, recip_shiKarman, shiTwoThirds |
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_RL gammaTmoleT, gammaTmoleS, gammaTurb, gammaTurbConst |
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_RL ustar, ustarSq, etastar |
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PARAMETER ( shiTwoThirds = 0.66666666666666666666666666667D0 ) |
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#endif |
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#ifndef ALLOW_OPENAD |
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_RL SW_TEMP |
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EXTERNAL SW_TEMP |
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#endif |
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#ifdef ALLOW_SHIFWFLX_CONTROL |
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_RL xx_shifwflx_loc(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy) |
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#endif |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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#ifdef SHI_ALLOW_GAMMAFRICT |
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dgoldberg |
1.2 |
#ifdef ALLOW_AUTODIFF |
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dgoldberg |
1.1 |
C re-initialize here again, curtesy to TAF |
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DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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DO J = 1-OLy,sNy+OLy |
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DO I = 1-OLx,sNx+OLx |
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shiTransCoeffT(i,j,bi,bj) = SHELFICEheatTransCoeff |
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shiTransCoeffS(i,j,bi,bj) = SHELFICEsaltTransCoeff |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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dgoldberg |
1.2 |
#endif /* ALLOW_AUTODIFF */ |
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dgoldberg |
1.1 |
IF ( SHELFICEuseGammaFrict ) THEN |
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C Implement friction velocity-dependent transfer coefficient |
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C of Holland and Jenkins, JPO, 1999 |
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recip_shiKarman= 1. _d 0 / 0.4 _d 0 |
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shiLo = 0. _d 0 |
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shiPr = shiPrandtl**shiTwoThirds |
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shiSc = shiSchmidt**shiTwoThirds |
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cph shiPr = (viscArNr(1)/diffKrNrT(1))**shiTwoThirds |
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cph shiSc = (viscArNr(1)/diffKrNrS(1))**shiTwoThirds |
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gammaTmoleT = 12.5 _d 0 * shiPr - 6. _d 0 |
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gammaTmoleS = 12.5 _d 0 * shiSc - 6. _d 0 |
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C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc)) |
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etastar = 1. _d 0 |
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gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar) |
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& - recip_shiKarman |
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dgoldberg |
1.2 |
#ifdef ALLOW_AUTODIFF |
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dgoldberg |
1.1 |
DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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DO J = 1-OLy,sNy+OLy |
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DO I = 1-OLx,sNx+OLx |
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shiTransCoeffT(i,j,bi,bj) = 0. _d 0 |
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shiTransCoeffS(i,j,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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dgoldberg |
1.2 |
#endif /* ALLOW_AUTODIFF */ |
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dgoldberg |
1.1 |
ENDIF |
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#endif /* SHI_ALLOW_GAMMAFRICT */ |
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C are we doing the conservative form of Jenkins et al. (2001)? |
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recip_Cp = 1. _d 0 / HeatCapacity_Cp |
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cFac = 0. _d 0 |
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IF ( SHELFICEconserve ) cFac = 1. _d 0 |
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C with "real fresh water flux" (affecting ETAN), |
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C there is more to modify |
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rFac = 1. _d 0 |
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IF ( SHELFICEconserve .AND. useRealFreshWaterFlux ) rFac = 0. _d 0 |
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C heat flux into the ice shelf, default is diffusive flux |
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C (Holland and Jenkins, 1999, eq.21) |
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dFac = 0. _d 0 |
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IF ( SHELFICEadvDiffHeatFlux ) dFac = 1. _d 0 |
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fwflxFac = 0. _d 0 |
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C linear dependence of freezing point on salinity |
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a0 = -0.0575 _d 0 |
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a1 = 0.0 _d -0 |
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a2 = 0.0 _d -0 |
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c0 = 0.0901 _d 0 |
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b = -7.61 _d -4 |
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#ifdef ALLOW_ISOMIP_TD |
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IF ( useISOMIPTD ) THEN |
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C non-linear dependence of freezing point on salinity |
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a0 = -0.0575 _d 0 |
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a1 = 1.710523 _d -3 |
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a2 = -2.154996 _d -4 |
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b = -7.53 _d -4 |
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c0 = 0. _d 0 |
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ENDIF |
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convertFW2SaltLoc = convertFW2Salt |
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C hardcoding this value here is OK because it only applies to ISOMIP |
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C where this value is part of the protocol |
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IF ( convertFW2SaltLoc .EQ. -1. ) convertFW2SaltLoc = 33.4 _d 0 |
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#endif /* ALLOW_ISOMIP_TD */ |
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DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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DO J = 1-OLy,sNy+OLy |
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DO I = 1-OLx,sNx+OLx |
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shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0 |
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shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0 |
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shelficeForcingT (I,J,bi,bj) = 0. _d 0 |
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shelficeForcingS (I,J,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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#ifdef ALLOW_SHIFWFLX_CONTROL |
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DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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DO J = 1-OLy,sNy+OLy |
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DO I = 1-OLx,sNx+OLx |
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xx_shifwflx_loc(I,J,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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dgoldberg |
1.2 |
#ifdef ALLOW_CTRL |
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if (useCTRL) CALL CTRL_GET_GEN ( |
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dgoldberg |
1.1 |
& xx_shifwflx_file, xx_shifwflxstartdate, xx_shifwflxperiod, |
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& maskSHI, xx_shifwflx_loc, xx_shifwflx0, xx_shifwflx1, |
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& xx_shifwflx_dummy, |
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& xx_shifwflx_remo_intercept, xx_shifwflx_remo_slope, |
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dgoldberg |
1.2 |
& wshifwflx, |
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dgoldberg |
1.1 |
& myTime, myIter, myThid ) |
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dgoldberg |
1.2 |
#endif |
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dgoldberg |
1.1 |
#endif /* ALLOW_SHIFWFLX_CONTROL */ |
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DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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#ifdef ALLOW_AUTODIFF_TAMC |
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# ifdef SHI_ALLOW_GAMMAFRICT |
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act1 = bi - myBxLo(myThid) |
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max1 = myBxHi(myThid) - myBxLo(myThid) + 1 |
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act2 = bj - myByLo(myThid) |
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max2 = myByHi(myThid) - myByLo(myThid) + 1 |
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act3 = myThid - 1 |
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max3 = nTx*nTy |
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act4 = ikey_dynamics - 1 |
| 246 |
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ikey = (act1 + 1) + act2*max1 |
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& + act3*max1*max2 |
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& + act4*max1*max2*max3 |
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# endif /* SHI_ALLOW_GAMMAFRICT */ |
| 250 |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
| 251 |
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DO J = 1, sNy |
| 252 |
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DO I = 1, sNx |
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C-- make local copies of temperature, salinity and depth (pressure in deci-bar) |
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C-- underneath the ice |
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K = MAX(1,kTopC(I,J,bi,bj)) |
| 256 |
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pLoc(I,J) = ABS(R_shelfIce(I,J,bi,bj)) |
| 257 |
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c pLoc(I,J) = shelficeMass(I,J,bi,bj)*gravity*1. _d -4 |
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tLoc(I,J) = theta(I,J,K,bi,bj) |
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sLoc(I,J) = MAX(salt(I,J,K,bi,bj), zeroRL) |
| 260 |
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uLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * |
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& ( uVel(I, J,K,bi,bj) * _hFacW(I, J,K,bi,bj) |
| 262 |
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& + uVel(I+1,J,K,bi,bj) * _hFacW(I+1,J,K,bi,bj) ) |
| 263 |
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vLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * |
| 264 |
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& ( vVel(I,J, K,bi,bj) * _hFacS(I,J, K,bi,bj) |
| 265 |
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& + vVel(I,J+1,K,bi,bj) * _hFacS(I,J+1,K,bi,bj) ) |
| 266 |
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ENDDO |
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ENDDO |
| 268 |
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IF ( SHELFICEBoundaryLayer ) THEN |
| 269 |
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C-- average over boundary layer width |
| 270 |
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DO J = 1, sNy |
| 271 |
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DO I = 1, sNx |
| 272 |
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K = kTopC(I,J,bi,bj) |
| 273 |
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IF ( K .NE. 0 .AND. K .LT. Nr ) THEN |
| 274 |
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Kp1 = MIN(Nr,K+1) |
| 275 |
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C-- overlap into lower cell |
| 276 |
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drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) ) |
| 277 |
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C-- lower cell may not be as thick as required |
| 278 |
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drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) ) |
| 279 |
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recip_drLoc = 1. _d 0 / |
| 280 |
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& ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 ) |
| 281 |
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tLoc(I,J) = ( tLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj) |
| 282 |
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& + theta(I,J,Kp1,bi,bj) *drKp1 ) |
| 283 |
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& * recip_drLoc |
| 284 |
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sLoc(I,J) = ( sLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj) |
| 285 |
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& + MAX(salt(I,J,Kp1,bi,bj), zeroRL) * drKp1 ) |
| 286 |
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& * recip_drLoc |
| 287 |
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uLoc(I,J) = ( uLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj) |
| 288 |
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& + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * |
| 289 |
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& ( uVel(I, J,Kp1,bi,bj) * _hFacW(I, J,Kp1,bi,bj) |
| 290 |
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& + uVel(I+1,J,Kp1,bi,bj) * _hFacW(I+1,J,Kp1,bi,bj) ) |
| 291 |
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& ) * recip_drLoc |
| 292 |
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vLoc(I,J) = ( vLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj) |
| 293 |
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& + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * |
| 294 |
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& ( vVel(I,J, Kp1,bi,bj) * _hFacS(I,J, Kp1,bi,bj) |
| 295 |
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& + vVel(I,J+1,Kp1,bi,bj) * _hFacS(I,J+1,Kp1,bi,bj) ) |
| 296 |
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& ) * recip_drLoc |
| 297 |
|
|
ENDIF |
| 298 |
|
|
ENDDO |
| 299 |
|
|
ENDDO |
| 300 |
|
|
ENDIF |
| 301 |
|
|
|
| 302 |
|
|
C-- turn potential temperature into in-situ temperature relative |
| 303 |
|
|
C-- to the surface |
| 304 |
|
|
DO J = 1, sNy |
| 305 |
|
|
DO I = 1, sNx |
| 306 |
|
|
#ifndef ALLOW_OPENAD |
| 307 |
|
|
tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL) |
| 308 |
|
|
#else |
| 309 |
|
|
CALL SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL,tLoc(I,J)) |
| 310 |
|
|
#endif |
| 311 |
|
|
ENDDO |
| 312 |
|
|
ENDDO |
| 313 |
|
|
|
| 314 |
|
|
#ifdef SHI_ALLOW_GAMMAFRICT |
| 315 |
|
|
IF ( SHELFICEuseGammaFrict ) THEN |
| 316 |
|
|
DO J = 1, sNy |
| 317 |
|
|
DO I = 1, sNx |
| 318 |
|
|
K = kTopC(I,J,bi,bj) |
| 319 |
|
|
IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN |
| 320 |
|
|
ustarSq = shiCdrag * MAX( 1.D-6, |
| 321 |
|
|
& 0.25 _d 0 *(uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)) ) |
| 322 |
|
|
ustar = SQRT(ustarSq) |
| 323 |
|
|
C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc)) |
| 324 |
|
|
C etastar = 1. _d 0 |
| 325 |
|
|
C gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar) |
| 326 |
|
|
C & - recip_shiKarman |
| 327 |
|
|
IF ( fCori(I,J,bi,bj) .NE. 0. _d 0 ) THEN |
| 328 |
|
|
gammaTurb = LOG( ustarSq * shiZetaN * etastar**2 |
| 329 |
|
|
& / ABS(fCori(I,J,bi,bj) * 5.0 _d 0 * shiKinVisc)) |
| 330 |
|
|
& * recip_shiKarman |
| 331 |
|
|
& + gammaTurbConst |
| 332 |
|
|
C Do we need to catch the unlikely case of very small ustar |
| 333 |
|
|
C that can lead to negative gammaTurb? |
| 334 |
|
|
C gammaTurb = MAX(0.D0, gammaTurb) |
| 335 |
|
|
ELSE |
| 336 |
|
|
gammaTurb = gammaTurbConst |
| 337 |
|
|
ENDIF |
| 338 |
|
|
shiTransCoeffT(i,j,bi,bj) = MAX( zeroRL, |
| 339 |
|
|
& ustar/(gammaTurb + gammaTmoleT) ) |
| 340 |
|
|
shiTransCoeffS(i,j,bi,bj) = MAX( zeroRL, |
| 341 |
|
|
& ustar/(gammaTurb + gammaTmoleS) ) |
| 342 |
|
|
ENDIF |
| 343 |
|
|
ENDDO |
| 344 |
|
|
ENDDO |
| 345 |
|
|
ENDIF |
| 346 |
|
|
#endif /* SHI_ALLOW_GAMMAFRICT */ |
| 347 |
|
|
|
| 348 |
|
|
#ifdef ALLOW_AUTODIFF_TAMC |
| 349 |
|
|
# ifdef SHI_ALLOW_GAMMAFRICT |
| 350 |
|
|
CADJ STORE shiTransCoeffS(:,:,bi,bj) = comlev1_bibj, |
| 351 |
|
|
CADJ & key=ikey, byte=isbyte |
| 352 |
|
|
CADJ STORE shiTransCoeffT(:,:,bi,bj) = comlev1_bibj, |
| 353 |
|
|
CADJ & key=ikey, byte=isbyte |
| 354 |
|
|
# endif /* SHI_ALLOW_GAMMAFRICT */ |
| 355 |
|
|
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 356 |
|
|
#ifdef ALLOW_ISOMIP_TD |
| 357 |
|
|
IF ( useISOMIPTD ) THEN |
| 358 |
|
|
DO J = 1, sNy |
| 359 |
|
|
DO I = 1, sNx |
| 360 |
|
|
K = kTopC(I,J,bi,bj) |
| 361 |
|
|
IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN |
| 362 |
|
|
C-- Calculate freezing temperature as a function of salinity and pressure |
| 363 |
|
|
thetaFreeze = |
| 364 |
|
|
& sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) ) |
| 365 |
|
|
& + b*pLoc(I,J) + c0 |
| 366 |
|
|
C-- Calculate the upward heat and fresh water fluxes |
| 367 |
|
|
shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj) |
| 368 |
|
|
& * shiTransCoeffT(i,j,bi,bj) |
| 369 |
|
|
& * ( tLoc(I,J) - thetaFreeze ) |
| 370 |
|
|
& * HeatCapacity_Cp*rUnit2mass |
| 371 |
|
|
#ifdef ALLOW_SHIFWFLX_CONTROL |
| 372 |
|
|
& - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat |
| 373 |
|
|
#endif /* ALLOW_SHIFWFLX_CONTROL */ |
| 374 |
|
|
C upward heat flux into the shelf-ice implies basal melting, |
| 375 |
|
|
C thus a downward (negative upward) fresh water flux (as a mass flux), |
| 376 |
|
|
C and vice versa |
| 377 |
|
|
shelfIceFreshWaterFlux(I,J,bi,bj) = |
| 378 |
|
|
& - shelfIceHeatFlux(I,J,bi,bj) |
| 379 |
|
|
& *recip_SHELFICElatentHeat |
| 380 |
|
|
C-- compute surface tendencies |
| 381 |
|
|
shelficeForcingT(i,j,bi,bj) = |
| 382 |
|
|
& - shelfIceHeatFlux(I,J,bi,bj) |
| 383 |
|
|
& *recip_Cp*mass2rUnit |
| 384 |
|
|
& - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit |
| 385 |
|
|
& * ( thetaFreeze - tLoc(I,J) ) |
| 386 |
|
|
shelficeForcingS(i,j,bi,bj) = |
| 387 |
|
|
& shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit |
| 388 |
|
|
& * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc ) |
| 389 |
|
|
C-- stress at the ice/water interface is computed in separate |
| 390 |
|
|
C routines that are called from mom_fluxform/mom_vecinv |
| 391 |
|
|
ELSE |
| 392 |
|
|
shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0 |
| 393 |
|
|
shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0 |
| 394 |
|
|
shelficeForcingT (I,J,bi,bj) = 0. _d 0 |
| 395 |
|
|
shelficeForcingS (I,J,bi,bj) = 0. _d 0 |
| 396 |
|
|
ENDIF |
| 397 |
|
|
ENDDO |
| 398 |
|
|
ENDDO |
| 399 |
|
|
ELSE |
| 400 |
|
|
#else |
| 401 |
|
|
IF ( .TRUE. ) THEN |
| 402 |
|
|
#endif /* ALLOW_ISOMIP_TD */ |
| 403 |
|
|
C use BRIOS thermodynamics, following Hellmers PhD thesis: |
| 404 |
|
|
C Hellmer, H., 1989, A two-dimensional model for the thermohaline |
| 405 |
|
|
C circulation under an ice shelf, Reports on Polar Research, No. 60 |
| 406 |
|
|
C (in German). |
| 407 |
|
|
|
| 408 |
|
|
DO J = 1, sNy |
| 409 |
|
|
DO I = 1, sNx |
| 410 |
|
|
K = kTopC(I,J,bi,bj) |
| 411 |
|
|
IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN |
| 412 |
|
|
C heat flux into the ice shelf, default is diffusive flux |
| 413 |
|
|
C (Holland and Jenkins, 1999, eq.21) |
| 414 |
|
|
thetaFreeze = a0*sLoc(I,J)+c0+b*pLoc(I,J) |
| 415 |
|
|
fwflxFac = 0. _d 0 |
| 416 |
|
|
IF ( tLoc(I,J) .GT. thetaFreeze ) fwflxFac = dFac |
| 417 |
|
|
C a few abbreviations |
| 418 |
|
|
eps1 = rUnit2mass*HeatCapacity_Cp |
| 419 |
|
|
& *shiTransCoeffT(i,j,bi,bj) |
| 420 |
|
|
eps2 = rUnit2mass*SHELFICElatentHeat |
| 421 |
|
|
& *shiTransCoeffS(i,j,bi,bj) |
| 422 |
|
|
eps5 = rUnit2mass*HeatCapacity_Cp |
| 423 |
|
|
& *shiTransCoeffS(i,j,bi,bj) |
| 424 |
|
|
|
| 425 |
|
|
C solve quadratic equation for salinity at shelfice-ocean interface |
| 426 |
|
|
C note: this part of the code is not very intuitive as it involves |
| 427 |
|
|
C many arbitrary abbreviations that were introduced to derive the |
| 428 |
|
|
C correct form of the quadratic equation for salinity. The abbreviations |
| 429 |
|
|
C only make sense in connection with my notes on this (M.Losch) |
| 430 |
|
|
C |
| 431 |
|
|
C eps3a was introduced as a constant variant of eps3 to avoid AD of |
| 432 |
|
|
C code of typ (pLoc-const)/pLoc |
| 433 |
|
|
eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp |
| 434 |
|
|
& * SHELFICEkappa * ( 1. _d 0 - dFac ) |
| 435 |
|
|
eps3 = eps3a/pLoc(I,J) |
| 436 |
|
|
eps4 = b*pLoc(I,J) + c0 |
| 437 |
|
|
eps6 = eps4 - tLoc(I,J) |
| 438 |
|
|
eps7 = eps4 - SHELFICEthetaSurface |
| 439 |
|
|
eps8 = rUnit2mass*SHELFICEheatCapacity_Cp |
| 440 |
|
|
& *shiTransCoeffS(i,j,bi,bj) * fwflxFac |
| 441 |
|
|
aqe = a0 *(eps1+eps3-eps8) |
| 442 |
|
|
recip_aqe = 0. _d 0 |
| 443 |
|
|
IF ( aqe .NE. 0. _d 0 ) recip_aqe = 0.5 _d 0/aqe |
| 444 |
|
|
c bqe = eps1*eps6 + eps3*eps7 - eps2 |
| 445 |
|
|
bqe = eps1*eps6 |
| 446 |
|
|
& + eps3a*( b |
| 447 |
|
|
& + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) ) |
| 448 |
|
|
& - eps2 |
| 449 |
|
|
& + eps8*( a0*sLoc(I,J) - eps7 ) |
| 450 |
|
|
cqe = ( eps2 + eps8*eps7 )*sLoc(I,J) |
| 451 |
|
|
discrim = bqe*bqe - 4. _d 0*aqe*cqe |
| 452 |
|
|
#undef ALLOW_SHELFICE_DEBUG |
| 453 |
|
|
#ifdef ALLOW_SHELFICE_DEBUG |
| 454 |
|
|
IF ( discrim .LT. 0. _d 0 ) THEN |
| 455 |
|
|
print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe |
| 456 |
|
|
print *, 'ml-shelfice: pLoc = ', pLoc(I,J) |
| 457 |
|
|
print *, 'ml-shelfice: tLoc = ', tLoc(I,J) |
| 458 |
|
|
print *, 'ml-shelfice: sLoc = ', sLoc(I,J) |
| 459 |
|
|
print *, 'ml-shelfice: tsurface= ', |
| 460 |
|
|
& SHELFICEthetaSurface |
| 461 |
|
|
print *, 'ml-shelfice: eps1 = ', eps1 |
| 462 |
|
|
print *, 'ml-shelfice: eps2 = ', eps2 |
| 463 |
|
|
print *, 'ml-shelfice: eps3 = ', eps3 |
| 464 |
|
|
print *, 'ml-shelfice: eps4 = ', eps4 |
| 465 |
|
|
print *, 'ml-shelfice: eps5 = ', eps5 |
| 466 |
|
|
print *, 'ml-shelfice: eps6 = ', eps6 |
| 467 |
|
|
print *, 'ml-shelfice: eps7 = ', eps7 |
| 468 |
|
|
print *, 'ml-shelfice: eps8 = ', eps8 |
| 469 |
|
|
print *, 'ml-shelfice: rU2mass = ', rUnit2mass |
| 470 |
|
|
print *, 'ml-shelfice: rhoIce = ', rhoShelfIce |
| 471 |
|
|
print *, 'ml-shelfice: cFac = ', cFac |
| 472 |
|
|
print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp |
| 473 |
|
|
print *, 'ml-shelfice: Cp_I = ', |
| 474 |
|
|
& SHELFICEHeatCapacity_Cp |
| 475 |
|
|
print *, 'ml-shelfice: gammaT = ', |
| 476 |
|
|
& SHELFICEheatTransCoeff |
| 477 |
|
|
print *, 'ml-shelfice: gammaS = ', |
| 478 |
|
|
& SHELFICEsaltTransCoeff |
| 479 |
|
|
print *, 'ml-shelfice: lat.heat= ', |
| 480 |
|
|
& SHELFICElatentHeat |
| 481 |
|
|
STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS' |
| 482 |
|
|
ENDIF |
| 483 |
|
|
#endif /* ALLOW_SHELFICE_DEBUG */ |
| 484 |
|
|
saltFreeze = (- bqe - SQRT(discrim))*recip_aqe |
| 485 |
|
|
IF ( saltFreeze .LT. 0. _d 0 ) |
| 486 |
|
|
& saltFreeze = (- bqe + SQRT(discrim))*recip_aqe |
| 487 |
|
|
thetaFreeze = a0*saltFreeze + eps4 |
| 488 |
|
|
C-- upward fresh water flux due to melting (in kg/m^2/s) |
| 489 |
|
|
cph change to identical form |
| 490 |
|
|
cph freshWaterFlux = rUnit2mass |
| 491 |
|
|
cph & * shiTransCoeffS(i,j,bi,bj) |
| 492 |
|
|
cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze |
| 493 |
|
|
freshWaterFlux = rUnit2mass |
| 494 |
|
|
& * shiTransCoeffS(i,j,bi,bj) |
| 495 |
|
|
& * ( 1. _d 0 - sLoc(I,J) / saltFreeze ) |
| 496 |
|
|
#ifdef ALLOW_SHIFWFLX_CONTROL |
| 497 |
|
|
& + xx_shifwflx_loc(I,J,bi,bj) |
| 498 |
|
|
#endif /* ALLOW_SHIFWFLX_CONTROL */ |
| 499 |
|
|
C-- Calculate the upward heat and fresh water fluxes; |
| 500 |
|
|
C-- MITgcm sign conventions: downward (negative) fresh water flux |
| 501 |
|
|
C-- implies melting and due to upward (positive) heat flux |
| 502 |
|
|
shelfIceHeatFlux(I,J,bi,bj) = |
| 503 |
|
|
& ( eps3 |
| 504 |
|
|
& - freshWaterFlux*SHELFICEheatCapacity_Cp*fwflxFac ) |
| 505 |
|
|
& * ( thetaFreeze - SHELFICEthetaSurface ) |
| 506 |
|
|
& - cFac*freshWaterFlux*( SHELFICElatentHeat |
| 507 |
|
|
& - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) ) |
| 508 |
|
|
shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux |
| 509 |
|
|
C-- compute surface tendencies |
| 510 |
|
|
shelficeForcingT(i,j,bi,bj) = |
| 511 |
|
|
& ( shiTransCoeffT(i,j,bi,bj) |
| 512 |
|
|
& - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit ) |
| 513 |
|
|
& * ( thetaFreeze - tLoc(I,J) ) |
| 514 |
|
|
shelficeForcingS(i,j,bi,bj) = |
| 515 |
|
|
& ( shiTransCoeffS(i,j,bi,bj) |
| 516 |
|
|
& - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit ) |
| 517 |
|
|
& * ( saltFreeze - sLoc(I,J) ) |
| 518 |
|
|
ELSE |
| 519 |
|
|
shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0 |
| 520 |
|
|
shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0 |
| 521 |
|
|
shelficeForcingT (I,J,bi,bj) = 0. _d 0 |
| 522 |
|
|
shelficeForcingS (I,J,bi,bj) = 0. _d 0 |
| 523 |
|
|
ENDIF |
| 524 |
|
|
ENDDO |
| 525 |
|
|
ENDDO |
| 526 |
|
|
ENDIF |
| 527 |
|
|
C endif (not) useISOMIPTD |
| 528 |
|
|
ENDDO |
| 529 |
|
|
ENDDO |
| 530 |
|
|
|
| 531 |
|
|
IF (SHELFICEallowThinIceMass) then |
| 532 |
|
|
#ifdef ALLOW_STREAMICE |
| 533 |
|
|
DO bj = myByLo(myThid), myByHi(myThid) |
| 534 |
|
|
DO bi = myBxLo(myThid), myBxHi(myThid) |
| 535 |
|
|
DO j=1-Oly,sNy+Oly-1 |
| 536 |
|
|
DO i=1-Olx+1,sNx+Olx-1 |
| 537 |
|
|
|
| 538 |
|
|
if (streamice_hmask(i,j,bi,bj).eq.1 .or. |
| 539 |
|
|
& streamice_hmask(i,j,bi,bj).eq.2) then |
| 540 |
|
|
|
| 541 |
dgoldberg |
1.2 |
shelficeMass(i,j,bi,bj) = |
| 542 |
|
|
& H_streamice(I,J,bi,bj) * streamice_density |
| 543 |
dgoldberg |
1.1 |
|
| 544 |
|
|
endif |
| 545 |
|
|
|
| 546 |
|
|
ENDDO |
| 547 |
|
|
ENDDO |
| 548 |
|
|
ENDDO |
| 549 |
|
|
ENDDO |
| 550 |
|
|
#else |
| 551 |
|
|
CALL SHELFICE_STEP_ICEMASS( myTime, myIter, myThid ) |
| 552 |
|
|
#endif |
| 553 |
|
|
ENDIF |
| 554 |
|
|
|
| 555 |
|
|
C-- Calculate new loading anomaly (in case the ice-shelf mass was updated) |
| 556 |
|
|
#ifndef ALLOW_AUTODIFF |
| 557 |
|
|
c IF ( SHELFICEloadAnomalyFile .EQ. ' ' ) THEN |
| 558 |
|
|
DO bj = myByLo(myThid), myByHi(myThid) |
| 559 |
|
|
DO bi = myBxLo(myThid), myBxHi(myThid) |
| 560 |
|
|
DO j = 1-OLy, sNy+OLy |
| 561 |
|
|
DO i = 1-OLx, sNx+OLx |
| 562 |
|
|
shelficeLoadAnomaly(i,j,bi,bj) = gravity |
| 563 |
|
|
& *( shelficeMass(i,j,bi,bj) + rhoConst*Ro_surf(i,j,bi,bj) ) |
| 564 |
|
|
ENDDO |
| 565 |
|
|
ENDDO |
| 566 |
|
|
ENDDO |
| 567 |
|
|
ENDDO |
| 568 |
|
|
c ENDIF |
| 569 |
|
|
#endif /* ndef ALLOW_AUTODIFF */ |
| 570 |
dgoldberg |
1.2 |
|
| 571 |
dgoldberg |
1.1 |
#ifdef ALLOW_DIAGNOSTICS |
| 572 |
|
|
IF ( useDiagnostics ) THEN |
| 573 |
|
|
CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx', |
| 574 |
|
|
& 0,1,0,1,1,myThid) |
| 575 |
|
|
CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx', |
| 576 |
|
|
& 0,1,0,1,1,myThid) |
| 577 |
|
|
C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta) |
| 578 |
|
|
tmpFac = HeatCapacity_Cp*rUnit2mass |
| 579 |
|
|
CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1, |
| 580 |
|
|
& 'SHIForcT',0,1,0,1,1,myThid) |
| 581 |
|
|
C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt) |
| 582 |
|
|
tmpFac = rUnit2mass |
| 583 |
|
|
CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1, |
| 584 |
|
|
& 'SHIForcS',0,1,0,1,1,myThid) |
| 585 |
|
|
C Transfer coefficients |
| 586 |
|
|
CALL DIAGNOSTICS_FILL(shiTransCoeffT,'SHIgammT', |
| 587 |
|
|
& 0,1,0,1,1,myThid) |
| 588 |
|
|
CALL DIAGNOSTICS_FILL(shiTransCoeffS,'SHIgammS', |
| 589 |
|
|
& 0,1,0,1,1,myThid) |
| 590 |
|
|
ENDIF |
| 591 |
|
|
#endif /* ALLOW_DIAGNOSTICS */ |
| 592 |
|
|
|
| 593 |
|
|
#endif /* ALLOW_SHELFICE */ |
| 594 |
|
|
RETURN |
| 595 |
|
|
END |
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