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C $Header: /u/gcmpack/MITgcm/pkg/shelfice/shelfice_thermodynamics.F,v 1.22 2011/05/30 20:21:51 jmc Exp $ |
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C $Name: $ |
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|
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#include "SHELFICE_OPTIONS.h" |
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|
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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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|
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C !USES: |
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IMPLICIT NONE |
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|
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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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#ifdef ALLOW_AUTODIFF |
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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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|
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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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|
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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 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 thetaFreeze, saltFreeze |
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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 |
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_RL cFac, rFac |
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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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|
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#ifdef SHI_ALLOW_GAMMAFRICT |
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_RL shiPr, shiSc, shiLo, shiKarman |
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_RL gammaTmoleT, gammaTmoleS, gammaTurb |
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_RL ustar, ustarSq, etastar |
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#endif |
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|
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_RL SW_TEMP |
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EXTERNAL SW_TEMP |
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|
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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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|
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#ifdef SHI_ALLOW_GAMMAFRICT |
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shiKarman= 0.4 _d 0 |
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shiLo = 0. _d 0 |
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shiPr = (viscArNr(1)/diffKrNrT(1))**(2/3) |
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shiSc = (viscArNr(1)/diffKrNrS(1))**(2/3) |
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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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#endif |
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|
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C are we doing the conservative form of Jenkins et al. (2001)? |
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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 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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|
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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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CALL CTRL_GET_GEN ( |
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& 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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& mytime, myiter, mythid ) |
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#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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DO J = 1, sNy |
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DO I = 1, sNx |
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C-- make local copies of temperature, salinity and depth (pressure) |
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C-- underneath the ice |
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K = MAX(1,kTopC(I,J,bi,bj)) |
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pLoc(I,J) = ABS(R_shelfIce(I,J,bi,bj)) |
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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), 0. _d 0) |
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ENDDO |
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ENDDO |
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IF ( SHELFICEBoundaryLayer ) THEN |
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C-- average over boundary layer width |
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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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IF ( K .NE. 0 .AND. K .LT. Nr ) THEN |
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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(I,J) = ( tLoc(I,J) * 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(I,J) = ( sLoc(I,J) * 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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ENDDO |
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ENDDO |
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ENDIF |
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|
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C-- turn potential temperature into in-situ temperature relative |
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C-- to the surface |
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DO J = 1, sNy |
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DO I = 1, sNx |
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tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),0.D0) |
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ENDDO |
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ENDDO |
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|
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#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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IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN |
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C-- Calculate freezing temperature as a function of salinity and pressure |
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thetaFreeze = |
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& sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) ) |
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& + b*pLoc(I,J) + c0 |
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C-- Calculate the upward heat and fresh water fluxes |
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shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj) |
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& * shiTransCoeffT(i,j,bi,bj) |
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& * ( tLoc(I,J) - thetaFreeze ) |
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& * HeatCapacity_Cp*rUnit2mass |
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#ifdef ALLOW_SHIFWFLX_CONTROL |
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& - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat |
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#endif /* ALLOW_SHIFWFLX_CONTROL */ |
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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 (as a mass flux), |
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C 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_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*mass2rUnit |
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& - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit |
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& * ( thetaFreeze - tLoc(I,J) ) |
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shelficeForcingS(i,j,bi,bj) = |
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& shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit |
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& * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc ) |
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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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ELSE |
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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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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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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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|
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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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IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN |
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#ifdef SHI_ALLOW_GAMMAFRICT |
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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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IF ( SHELFICEuseGammaFrict ) THEN |
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ustarSq = shiCdrag * MAX( 1D-06, |
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& (uVel(I,J,K,bi,bj)+uVel(I+1,J,K,bi,bj)) |
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& *(uVel(I,J,K,bi,bj)+uVel(I+1,J,K,bi,bj)) |
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& +(vVel(I,J,K,bi,bj)+vVel(I,J+1,K,bi,bj)) |
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& *(vVel(I,J,K,bi,bj)+vVel(I,J+1,K,bi,bj)) ) |
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ustar = SQRT(ustarSq) |
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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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gammaTurb = LOG( ustarSq * shiZetaN * etastar**2 |
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& / ABS( fCori(I,J,bi,bj) * 0.5 _d 0 * viscArNr(k) ) ) |
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& / shiKarman |
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& + 1. _d 0 / (2. _d 0 * shiZetaN*etastar) |
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& - 1. _d 0 / shiKarman |
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shiTransCoeffT(i,j,bi,bj) = MAX( 0.D-10, |
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& ustar/(gammaTurb + gammaTmoleT) ) |
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shiTransCoeffS(i,j,bi,bj) = MAX( 0.D-10, |
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& ustar/(gammaTurb + gammaTmoleS) ) |
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ENDIF |
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#endif |
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C a few abbreviations |
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eps1 = rUnit2mass*HeatCapacity_Cp |
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& *shiTransCoeffT(i,j,bi,bj) |
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eps2 = rUnit2mass*SHELFICElatentHeat |
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& *shiTransCoeffS(i,j,bi,bj) |
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eps5 = rUnit2mass*HeatCapacity_Cp |
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& *shiTransCoeffS(i,j,bi,bj) |
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|
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C solve quadratic equation for salinity at shelfice-ocean interface |
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C note: this part of the code is not very intuitive as it involves |
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C many arbitrary abbreviations that were introduced to derive the |
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C correct form of the quadratic equation for salinity. The abbreviations |
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C only make sense in connection with my notes on this (M.Losch) |
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eps3 = rhoShelfIce*SHELFICEheatCapacity_Cp |
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& * SHELFICEkappa/pLoc(I,J) |
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cph introduce a constant variant of eps3 to avoid AD of |
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cph code of typ (pLoc-const)/pLoc |
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eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp |
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& * SHELFICEkappa |
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eps4 = b*pLoc(I,J) + c0 |
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eps6 = eps4 - tLoc(I,J) |
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eps7 = eps4 - SHELFICEthetaSurface |
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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. _d 0 ) recip_aqe = 0.5 _d 0/aqe |
| 307 |
c bqe = eps1*eps6 + eps3*eps7 - eps2 |
| 308 |
bqe = eps1*eps6 |
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& + eps3a*( b |
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& + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) ) |
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& - eps2 |
| 312 |
cqe = eps2*sLoc(I,J) |
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discrim = bqe*bqe - 4. _d 0*aqe*cqe |
| 314 |
#undef ALLOW_SHELFICE_DEBUG |
| 315 |
#ifdef ALLOW_SHELFICE_DEBUG |
| 316 |
IF ( discrim .LT. 0. _d 0 ) THEN |
| 317 |
print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe |
| 318 |
print *, 'ml-shelfice: pLoc = ', pLoc(I,J) |
| 319 |
print *, 'ml-shelfice: tLoc = ', tLoc(I,J) |
| 320 |
print *, 'ml-shelfice: sLoc = ', sLoc(I,J) |
| 321 |
print *, 'ml-shelfice: tsurface= ', |
| 322 |
& SHELFICEthetaSurface |
| 323 |
print *, 'ml-shelfice: eps1 = ', eps1 |
| 324 |
print *, 'ml-shelfice: eps2 = ', eps2 |
| 325 |
print *, 'ml-shelfice: eps3 = ', eps3 |
| 326 |
print *, 'ml-shelfice: eps4 = ', eps4 |
| 327 |
print *, 'ml-shelfice: eps5 = ', eps5 |
| 328 |
print *, 'ml-shelfice: eps6 = ', eps6 |
| 329 |
print *, 'ml-shelfice: eps7 = ', eps7 |
| 330 |
print *, 'ml-shelfice: rU2mass = ', rUnit2mass |
| 331 |
print *, 'ml-shelfice: rhoIce = ', rhoShelfIce |
| 332 |
print *, 'ml-shelfice: cFac = ', cFac |
| 333 |
print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp |
| 334 |
print *, 'ml-shelfice: Cp_I = ', |
| 335 |
& SHELFICEHeatCapacity_Cp |
| 336 |
print *, 'ml-shelfice: gammaT = ', |
| 337 |
& SHELFICEheatTransCoeff |
| 338 |
print *, 'ml-shelfice: gammaS = ', |
| 339 |
& SHELFICEsaltTransCoeff |
| 340 |
print *, 'ml-shelfice: lat.heat= ', |
| 341 |
& SHELFICElatentHeat |
| 342 |
STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS' |
| 343 |
ENDIF |
| 344 |
#endif /* ALLOW_SHELFICE_DEBUG */ |
| 345 |
saltFreeze = (- bqe - SQRT(discrim))*recip_aqe |
| 346 |
IF ( saltFreeze .LT. 0. _d 0 ) |
| 347 |
& saltFreeze = (- bqe + SQRT(discrim))*recip_aqe |
| 348 |
thetaFreeze = a0*saltFreeze + eps4 |
| 349 |
C-- upward fresh water flux due to melting (in kg/m^2/s) |
| 350 |
cph change to identical form |
| 351 |
cph freshWaterFlux = rUnit2mass |
| 352 |
cph & * shiTransCoeffS(i,j,bi,bj) |
| 353 |
cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze |
| 354 |
freshWaterFlux = rUnit2mass |
| 355 |
& * shiTransCoeffS(i,j,bi,bj) |
| 356 |
& * ( 1. _d 0 - sLoc(I,J) / saltFreeze ) |
| 357 |
#ifdef ALLOW_SHIFWFLX_CONTROL |
| 358 |
& + xx_shifwflx_loc(I,J,bi,bj) |
| 359 |
#endif /* ALLOW_SHIFWFLX_CONTROL */ |
| 360 |
C-- Calculate the upward heat and fresh water fluxes; |
| 361 |
C-- MITgcm sign conventions: downward (negative) fresh water flux |
| 362 |
C-- implies melting and due to upward (positive) heat flux |
| 363 |
shelfIceHeatFlux(I,J,bi,bj) = |
| 364 |
& ( eps3*( thetaFreeze - SHELFICEthetaSurface ) |
| 365 |
& - cFac*freshWaterFlux*( SHELFICElatentHeat |
| 366 |
& - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) ) |
| 367 |
& ) |
| 368 |
shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux |
| 369 |
C-- compute surface tendencies |
| 370 |
shelficeForcingT(i,j,bi,bj) = |
| 371 |
& ( shiTransCoeffT(i,j,bi,bj) |
| 372 |
& - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit ) |
| 373 |
& * ( thetaFreeze - tLoc(I,J) ) |
| 374 |
shelficeForcingS(i,j,bi,bj) = |
| 375 |
& ( shiTransCoeffS(i,j,bi,bj) |
| 376 |
& - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit ) |
| 377 |
& * ( saltFreeze - sLoc(I,J) ) |
| 378 |
ELSE |
| 379 |
shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0 |
| 380 |
shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0 |
| 381 |
shelficeForcingT (I,J,bi,bj) = 0. _d 0 |
| 382 |
shelficeForcingS (I,J,bi,bj) = 0. _d 0 |
| 383 |
ENDIF |
| 384 |
ENDDO |
| 385 |
ENDDO |
| 386 |
ENDIF |
| 387 |
C endif (not) useISOMIPTD |
| 388 |
ENDDO |
| 389 |
ENDDO |
| 390 |
|
| 391 |
#ifdef ALLOW_DIAGNOSTICS |
| 392 |
IF ( useDiagnostics ) THEN |
| 393 |
CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx', |
| 394 |
& 0,1,0,1,1,myThid) |
| 395 |
CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx', |
| 396 |
& 0,1,0,1,1,myThid) |
| 397 |
C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta) |
| 398 |
tmpFac = HeatCapacity_Cp*rUnit2mass |
| 399 |
CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1, |
| 400 |
& 'SHIForcT',0, 1,0,1,1,myThid) |
| 401 |
C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt) |
| 402 |
tmpFac = rUnit2mass |
| 403 |
CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1, |
| 404 |
& 'SHIForcS',0, 1,0,1,1,myThid) |
| 405 |
ENDIF |
| 406 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 407 |
|
| 408 |
#endif /* ALLOW_SHELFICE */ |
| 409 |
RETURN |
| 410 |
END |
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