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mlosch |
1.5 |
C $Header: /u/gcmpack/MITgcm/pkg/shelfice/shelfice_thermodynamics.F,v 1.4 2006/02/14 13:09:46 mlosch Exp $ |
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mlosch |
1.1 |
C $Name: $ |
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#include "SHELFICE_OPTIONS.h" |
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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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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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mlosch |
1.5 |
C !LOCAL VARIABLES : |
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mlosch |
1.1 |
C === Local variables === |
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mlosch |
1.5 |
INTEGER I,J,K,Kp1 |
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mlosch |
1.1 |
INTEGER bi,bj |
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_RL tLoc, sLoc, pLoc |
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mlosch |
1.3 |
_RL thetaFreeze, saltFreeze |
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_RL a0, a1, a2, b, c0 |
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_RL eps1, eps2, eps3, eps4, aqe, bqe, cqe, discrim, recip_aqe |
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mlosch |
1.5 |
_RL drKp1, recip_drLoc |
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mlosch |
1.1 |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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mlosch |
1.3 |
C linear dependence of freezing point on salinity |
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mlosch |
1.1 |
a0 = -0.0575 _d 0 |
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mlosch |
1.3 |
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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#endif ALLOW_ISOMIP_TD |
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C first a few abbreviations |
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eps1 = rhoConst*HeatCapacity_Cp*SHELFICEheatTransCoeff |
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eps2 = rhoConst*SHELFICElatentHeat*SHELFICEsaltTransCoeff |
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mlosch |
1.1 |
DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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mlosch |
1.5 |
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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mlosch |
1.1 |
#ifdef ALLOW_ISOMIP_TD |
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IF ( useISOMIPTD ) THEN |
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DO J = 1, sNy |
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DO I = 1, sNx |
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K = kTopC(I,J,bi,bj) |
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pLoc = ABS(R_shelfIce(I,J,bi,bj)) |
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IF ( K .NE. 0 .AND. pLoc .GT. 0. _d 0 ) THEN |
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C-- Calculate the in-situ temperature |
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tLoc = theta(I,J,K,bi,bj) |
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mlosch |
1.5 |
sLoc = MAX(salt(I,J,K,bi,bj), 0. _d 0) |
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IF ( SHELFICEBoundaryLayer .AND. K .LT. Nr ) THEN |
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C-- average over boundary layer width |
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Kp1 = MIN(Nr,K+1) |
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C-- overlap into lower cell |
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drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) ) |
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C-- lower cell may not be as thick as required |
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drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) ) |
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recip_drLoc = 1. _d 0 / |
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& ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 ) |
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tloc = ( tloc * drF(K)*_hFacC(I,J,K,bi,bj) |
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& + theta(I,J,Kp1,bi,bj) *drKp1 ) |
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& * recip_drLoc |
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sloc = ( sloc * drF(K)*_hFacC(I,J,K,bi,bj) |
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& + MAX(salt(I,J,Kp1,bi,bj), 0. _d 0) * drKp1 ) |
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& * recip_drLoc |
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ENDIF |
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mlosch |
1.1 |
C-- Calculate freezing temperature as a function of salinity and pressure |
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mlosch |
1.3 |
CML thetaFreeze=-1.9 _d 0 |
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thetaFreeze = sLoc * ( a0 + a1*sqrt(sLoc) + a2*sLoc ) |
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mlosch |
1.1 |
& + b*pLoc + c0 |
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C-- Calculate the upward heat and fresh water fluxes |
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shelfIceHeatFlux(I,J,bi,bj) = |
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mlosch |
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& SHELFICEheatTransCoeff * ( tLoc - thetaFreeze ) |
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& *HeatCapacity_Cp*recip_horiVertRatio*rhoConst |
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C upward heat flux into the shelf-ice implies basal melting, |
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C thus a downward (negative upward) fresh water flux, and vice versa |
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shelfIceFreshWaterFlux(I,J,bi,bj) = |
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& - shelfIceHeatFlux(I,J,bi,bj) |
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& *recip_rhoConst*recip_SHELFICElatentHeat |
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C-- compute surface tendencies |
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shelficeForcingT(i,j,bi,bj) = |
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& - shelfIceHeatFlux(I,J,bi,bj) |
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& *recip_Cp*horiVertRatio*recip_rhoConst |
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mlosch |
1.2 |
IF (convertFW2Salt .EQ. -1.) THEN |
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shelficeForcingS(i,j,bi,bj) = |
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& shelfIceFreshWaterFlux(I,J,bi,bj) |
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& * salt(I,J,K,bi,bj) * convertEmP2rUnit |
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ELSE |
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shelficeForcingS(i,j,bi,bj) = |
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& shelfIceFreshWaterFlux(I,J,bi,bj) |
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& * convertFW2Salt * convertEmP2rUnit |
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ENDIF |
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mlosch |
1.1 |
C-- stress at the ice/water interface is computed in separate |
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C routines that are called from mom_fluxform/mom_vecinv |
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ENDIF |
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ENDDO |
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ENDDO |
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ELSE |
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#else |
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IF ( .TRUE. ) THEN |
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#endif /* ALLOW_ISOMIP_TD */ |
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mlosch |
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C use BRIOS thermodynamics, following Hellmers PhD thesis: |
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C Hellmer, H., 1989, A two-dimensional model for the thermohaline |
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C circulation under an ice shelf, Reports on Polar Research, No. 60 |
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C (in German). |
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DO J = 1, sNy |
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DO I = 1, sNx |
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K = kTopC(I,J,bi,bj) |
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pLoc = ABS(R_shelfIce(I,J,bi,bj)) |
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IF ( K .NE. 0 .AND. pLoc .GT. 0. _d 0 ) THEN |
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C-- Calculate the in-situ temperature |
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tLoc = theta(I,J,K,bi,bj) |
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mlosch |
1.5 |
sLoc = MAX(salt(I,J,K,bi,bj), 0. _d 0) |
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IF ( SHELFICEBoundaryLayer .AND. K .LT. Nr ) THEN |
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C-- average over boundary layer width |
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Kp1 = MIN(Nr,K+1) |
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C-- overlap into lower cell |
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drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) ) |
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C-- lower cell may not be as thick as required |
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drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) ) |
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recip_drLoc = 1. _d 0 / |
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& ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 ) |
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tloc = ( tloc * drF(K)*_hFacC(I,J,K,bi,bj) |
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& + theta(I,J,Kp1,bi,bj) *drKp1 ) |
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& * recip_drLoc |
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sloc = ( sloc * drF(K)*_hFacC(I,J,K,bi,bj) |
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& + MAX(salt(I,J,Kp1,bi,bj), 0. _d 0) * drKp1 ) |
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& * recip_drLoc |
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ENDIF |
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mlosch |
1.3 |
C solve quadratic equation to get salinity at shelfice-ocean interface |
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eps3 = rhoShelfIce*SHELFICEheatCapacity_Cp |
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& * SHELFICEkappa/ploc |
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eps4 = b*pLoc + c0 |
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aqe = a0 *(eps1+eps3) |
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recip_aqe = 0. _d 0 |
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IF ( aqe .NE. 0 ) recip_aqe = 0.5/aqe |
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bqe = eps4*(eps1+eps3) - eps2 |
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& - eps1*tloc - eps3*SHELFICEthetaSurface |
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cqe = eps2*sloc |
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discrim = bqe*bqe - 4. _d 0*aqe*cqe |
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#ifdef ALLOW_SHELFICE_DEBUG |
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IF ( discrim .LT. 0. _d 0 ) THEN |
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print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe |
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print *, 'ml-shelfice: ploc = ', ploc |
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print *, 'ml-shelfice: tloc = ', tloc |
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print *, 'ml-shelfice: sloc = ', sloc |
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print *, 'ml-shelfice: tsurface= ', |
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& SHELFICEthetaSurface |
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print *, 'ml-shelfice: eps1 = ', eps1 |
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print *, 'ml-shelfice: eps2 = ', eps2 |
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print *, 'ml-shelfice: eps3 = ', eps3 |
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print *, 'ml-shelfice: eps4 = ', eps4 |
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print *, 'ml-shelfice: rhoW = ', rhoConst |
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print *, 'ml-shelfice: rhoIce = ', rhoShelfIce |
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print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp |
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print *, 'ml-shelfice: Cp_I = ', |
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& SHELFICEHeatCapacity_Cp |
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print *, 'ml-shelfice: gammaT = ', |
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& SHELFICEheatTransCoeff |
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print *, 'ml-shelfice: gammaS = ', |
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& SHELFICEsaltTransCoeff |
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print *, 'ml-shelfice: lat.heat= ', |
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& SHELFICElatentHeat |
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STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS' |
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ENDIF |
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#endif /* ALLOW_SHELFICE_DEBUG */ |
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saltFreeze = (- bqe - SQRT(discrim))*recip_aqe |
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mlosch |
1.4 |
IF ( saltFreeze .LT. 0. _d 0 ) |
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mlosch |
1.3 |
& saltFreeze = (- bqe + SQRT(discrim))*recip_aqe |
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C-- Calculate freezing temperature as a function of salinity and pressure |
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thetaFreeze = saltFreeze * a0 + eps4 |
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CML Inconsistent but more accurate: |
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CML thetaFreeze = sLoc * ( a0 + a1*sqrt(sLoc) + a2*sLoc ) |
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CML & + b*pLoc + c0 |
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C-- Calculate the upward heat and fresh water fluxes |
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shelfIceHeatFlux(I,J,bi,bj) = |
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& ( eps1 * ( tLoc - thetaFreeze ) )*recip_horiVertRatio |
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shelfIceFreshWaterFlux(I,J,bi,bj) = |
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& rhoConst/rhoShelfIce * SHELFICEsaltTransCoeff |
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& * ( saltFreeze - sloc )/saltFreeze |
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& * recip_horiVertRatio |
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C-- compute surface tendencies |
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shelficeForcingT(i,j,bi,bj) = |
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& - shelfIceHeatFlux(I,J,bi,bj) |
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& *recip_Cp*horiVertRatio*recip_rhoConst |
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shelficeForcingS(i,j,bi,bj) = |
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& shelfIceFreshWaterFlux(I,J,bi,bj) |
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& * saltFreeze * convertEmP2rUnit |
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ENDIF |
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ENDDO |
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ENDDO |
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mlosch |
1.1 |
ENDIF |
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mlosch |
1.3 |
C endif (not) useISOMIPTD |
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mlosch |
1.1 |
ENDDO |
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ENDDO |
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#endif /* ALLOW_SHELFICE */ |
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RETURN |
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END |
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