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#include "SHELFICE_OPTIONS.h" |
| 2 |
#ifdef ALLOW_AUTODIFF |
| 3 |
# include "AUTODIFF_OPTIONS.h" |
| 4 |
#endif |
| 5 |
#ifdef ALLOW_CTRL |
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# include "CTRL_OPTIONS.h" |
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#endif |
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|
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CBOP |
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C !ROUTINE: SHELFICE_SOLVE4FLUXES |
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C !INTERFACE: |
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SUBROUTINE SHELFICE_SOLVE4FLUXES( |
| 13 |
I tLoc, sLoc, pLoc, |
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I gammaT, gammaS, |
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I iceConductionDistance, thetaIceConduction, |
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O heatFlux, fwFlux, |
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O forcingT, forcingS, |
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I bi, bj, myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SOLVE4FLUXES |
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C | o Calculate |
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C *==========================================================* |
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C \ev |
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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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#include "SHELFICE_COST.h" |
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#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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|
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C !INPUT PARAMETERS: |
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C tLoc :: |
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C sLoc :: |
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C pLoc :: |
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C insitutLoc :: |
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C gammaT :: |
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C gammaS :: |
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C bi,bj :: tile indices |
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C myTime :: current time in simulation |
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C myIter :: iteration number in simulation |
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C myThid :: my Thread Id number |
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|
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C !OUTPUT PARAMETERS: |
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C heatFlux :: |
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C fwFlux :: |
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C forcingT :: |
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C forcingS :: |
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C---------- |
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|
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_RL tLoc, sLoc, pLoc, insitutLoc |
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_RL gammaT, gammaS |
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_RL iceConductionDistance, thetaIceConduction |
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_RL heatFlux, fwFlux, forcingS, forcingT |
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INTEGER i, j, bi, bj |
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_RL myTime |
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INTEGER myIter, myThid |
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character*200 msgBuf |
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CEOP |
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|
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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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|
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|
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C !LOCAL VARIABLES: |
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C === Local variables === |
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_RL thetaFreeze, saltFreeze |
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_RL eps1, eps2, eps3, eps4, eps5, eps6, eps7, eps8 |
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_RL aqe, bqe, cqe, discrim, recip_aqe |
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_RL a0, a1, a2, b0, c0 |
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_RL w_I |
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|
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C === Useful Units === |
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C-- gammaT, m s^-1 |
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C-- gammaS, m s^-1 |
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C-- rUnit2mass (rhoConst), kg m^-3 |
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C-- mass2rUnit (recip_rhoConst), m^3 kg^-1 |
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C-- eps3, W K^-1 m^-2 |
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C-- fwFlux, kg m^-2 s^-1 |
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C-- heatFlux, kg m^-2 s^-1 |
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C-- forcing T, K m/s |
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C-- forcing S, psu m/s |
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C-- SHELFICEkappa, m^2/s |
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|
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C-- eps1, W K^-1 m^-2 : kg/m^3 * J/kg/K * m/s |
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C-- eps2, W m^-2 : kg/m^3 * J/kg * m/s |
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C-- eps3, W K^-1 m^-2 : kg m^-3 * J kg^-1 K^-1 * m^2 s^-1 * m^-1 |
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|
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C-- fwFlux : fresh water flux due to melting (kg m^-2 s^-1) |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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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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c0 = 0.0901 _d 0 |
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b0 = -7.61 _d -4 |
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|
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C-- convert potential T into in-situ T relative to surface |
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insitutLoc = SW_TEMP(sLoc,tLoc,pLoc, zeroRL) |
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|
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C-- DEFINE SOME CONSTANTS |
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eps1 = rUnit2mass*HeatCapacity_Cp * gammaT |
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eps2 = rUnit2mass*SHELFICElatentHeat * gammaS |
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eps3 = rhoShelfIce*SHELFICEheatCapacity_Cp * SHELFICEkappa |
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& /iceConductionDistance; |
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eps4 = b0*pLoc + c0 |
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eps6 = eps4 - insitutLoc |
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eps7 = eps4 - thetaIceConduction |
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|
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IF ( debugLevel.GE.debLevE ) THEN |
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WRITE(msgBuf,'(A25,9E16.8)') |
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&'ZZZ7 r2mass, Cp, gmaT,SIlh,gmaS, rhoSI, SI_Cp, Kap, ICondDis ', |
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& rUnit2mass,HeatCapacity_Cp,gammaT, SHELFICElatentHeat,gammaS, |
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& rhoShelfIce, SHELFICEheatCapacity_Cp, SHELFICEkappa, |
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& iceConductionDistance |
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|
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT , 1) |
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ENDIF |
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|
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C-- Default thermodynamics specify a linear T gradient |
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C-- through the ice (Holland and Jenkins, 1999, Section 2. |
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aqe = a0*(eps1 + eps3) |
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bqe = eps1*eps6 + eps3*eps7 - eps2 - SHELFICEsalinity*aqe |
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cqe = eps2 * sLoc - SHELFICEsalinity*(eps1*eps6 + eps3*eps7) |
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|
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C-- Alterantively, we can have a nonlinear T gradient |
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C-- through the ice (Holland and Jenkins, 1999, Section 3. |
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C-- This demands a different set of constants |
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IF (SHELFICEadvDiffHeatFlux .EQV. .TRUE.) THEN |
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|
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IF ( debugLevel.GE.debLevE ) THEN |
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WRITE(msgBuf,'(A)') |
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& '1useSHELFICEadvDiffHeatFlux ' |
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|
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT , 1) |
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ENDIF |
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|
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eps8 = rUnit2mass * gammaS * SHELFICEheatCapacity_Cp |
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aqe = a0 *(eps1 - eps8) |
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bqe = eps1*eps6 + sLoc*eps8*a0 - eps8*eps7 - eps2 - |
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& SHELFICEsalinity*eps1*a0 |
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cqe = sLoc*(eps8*eps7 + eps2) - SHELFICEsalinity*eps1 |
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ENDIF |
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|
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C solve quadratic equation for salinity at shelfice-ocean interface |
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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 |
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|
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C-- Sb = \frac{-bqe \pm \sqrt(bqe^2 - 4 aqc cqe)}{2 aqe} |
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discrim = bqe*bqe - 4. _d 0*aqe*cqe |
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|
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C-- Try the negative root (- SQRT(discrim)) of the quadratic eq. |
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saltFreeze = (- bqe - SQRT(discrim))*recip_aqe |
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|
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C--- If the negative root yields a negative salinity, then use the |
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C-- positive root (+ SQRT(discrim)) |
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IF ( saltFreeze .LT. 0. _d 0 ) THEN |
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saltFreeze = (- bqe + SQRT(discrim))*recip_aqe |
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ENDIF |
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|
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C-- in situ seawater freezing point using linearization |
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thetaFreeze = a0*saltFreeze + eps4 |
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|
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C-- Calculate the upward heat and fresh water fluxes; |
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C-- MITgcm sign conventions: downward (negative) fresh water flux |
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C-- implies melting and due to upward (positive) heat flux |
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|
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C-- This formulation of fwflux, derived from the heat balance equation |
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C-- instead of the salt balance equation, can handle the case when the |
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C-- salinity of the ocean, boundary layer, and ice are identical. |
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fwFlux = 1/SHELFICElatentHeat*( |
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& eps3*(thetaFreeze - thetaIceConduction) - |
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& eps1*(insitutLoc - thetaFreeze) ) |
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|
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C-- If a nonlinear local ice T gradient near the ice-ocean interface |
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C-- is allowed and fwflux is positive (ice growth) then |
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C-- we must solve the quadratic equation using a different set of |
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C-- coeffs (Holland Jenkins, 1999). |
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IF ((SHELFICEadvDiffHeatFlux .EQV. .TRUE.) .AND. |
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& (fwFlux .GT. zeroRL)) THEN |
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IF ( debugLevel.GE.debLevE ) THEN |
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WRITE(msgBuf,'(A)') |
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& '2useSHELFICEadvDiffHeatFlux ' |
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|
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT , 1) |
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ENDIF |
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aqe = a0 *(eps1) |
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bqe = eps1*eps6 - eps2 - SHELFICEsalinity*eps1*a0 |
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cqe = sLoc*(eps2) - SHELFICEsalinity*eps1 |
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|
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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 |
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|
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discrim = bqe*bqe - 4. _d 0*aqe*cqe |
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saltFreeze = (- bqe - SQRT(discrim))*recip_aqe |
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IF ( saltFreeze .LT. 0. _d 0 ) THEN |
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saltFreeze = (- bqe + SQRT(discrim))*recip_aqe |
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ENDIF |
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|
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thetaFreeze = a0*saltFreeze + eps4 |
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|
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fwFlux = 1/SHELFICElatentHeat* ( |
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& eps3*(thetaFreeze - thetaIceConduction) - |
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& eps1*(insitutLoc - thetaFreeze) ) |
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ENDIF |
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|
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C meltwater advective flux velocity at ice-ocean interface (m/s) |
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C * negative corresponds to downward flux (melting) |
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w_I = fwFlux * mass2rUnit |
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|
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C-- Calculate the upward heat fluxes: |
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C-- melting requires upward (positive) heat flux from ocean to ice. |
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|
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C-- The heatFlux variable corresponds with the change of energy in the |
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C-- ocean grid cell volume. In the conservative case (J2001), |
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C-- advective heat fluxes change the energy of the volume whereas in |
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C-- the non-conservative case there are no advective heat fluxes |
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C-- melting or freezing have no associated advective heat fluxes. |
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IF (SHELFICEconserve) THEN |
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|
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C-- In the conservative case (J2001) there are two cases, fixed and |
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C-- non-fixed ocean volume. |
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|
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IF (useRealFreshWaterFlux ) THEN |
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|
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C-- If the ocean volume can change (realFWFlux=true) then advection of |
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C-- meltwater does not displace water at T=insitutLoc in the cell and the |
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C-- heat flux correpsonding to the total energy flux of the volume |
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C-- consists of only two terms: turbulent fluxes (positive out) |
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C-- and advective meltwater fluxes (negative in). |
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heatFlux = rUnit2mass*HeatCapacity_Cp * ( |
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& gammaT * (insitutLoc - thetaFreeze) |
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& + w_I * thetaFreeze ) |
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ELSE |
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|
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C-- If the volume is fixed (realFWFlux=false) then the advection of |
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C-- meltwater does displace ambient water at T=insitutLoc in the cell. |
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C-- Displacement reduction volume energy by w_I * insitutLoc (positive) |
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heatFlux = rUnit2mass*HeatCapacity_Cp * ( |
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& gammaT * (insitutLoc - thetaFreeze) |
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& + w_I * (thetaFreeze - insitutLoc) ) |
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ENDIF |
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|
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ELSE |
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|
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C-- In the non-conservative form, only fluxes are turbulent fluxes |
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heatFlux = rUnit2mass*HeatCapacity_Cp * |
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& gammaT * (insitutLoc - thetaFreeze) |
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ENDIF |
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|
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C-- Calculate the T and S tendency terms. T tendency term is |
| 275 |
C-- not necessarily proportional to the heat flux term above because |
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C-- the heat flux term corresponds to total energy change in the grid |
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C-- cell and not the change of energy per unit volume. |
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|
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IF (SHELFICEconserve) THEN |
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C-- In the conservative case, meltwater advection contributes (J2001) |
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C-- to T and S tendencies |
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C-- * forcing T (K m/s) |
| 283 |
forcingT = |
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& (gammaT - w_I)*(thetaFreeze - insitutLoc) |
| 285 |
|
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C-- * forcing S (psu m/s) |
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forcingS = |
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& (gammaS - w_I)*(saltFreeze - sLoc) |
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ELSE |
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C-- Otherwise, the only fluxes out of the ocean that change T and S |
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C-- are the turbulent fluxes. |
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forcingT = gammaT * ( thetaFreeze - insitutLoc ) |
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forcingS = gammaS * ( saltFreeze - sLoc ) |
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ENDIF |
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|
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IF ( debugLevel.GE.debLevE ) THEN |
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WRITE(msgBuf,'(A25,7E16.8)') |
| 298 |
& 'ZZZ6 aqe, bqe, ceq ', |
| 299 |
& aqe,bqe,cqe |
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|
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 302 |
& SQUEEZE_RIGHT , 1) |
| 303 |
|
| 304 |
WRITE(msgBuf,'(A25,7E16.8)') |
| 305 |
& 'ZZZ2 T,S,P,t,TFrz,SFrz,w_I ', |
| 306 |
& tLoc,sLoc,pLoc, insitutLoc, thetaFreeze, saltFreeze, w_I |
| 307 |
|
| 308 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 309 |
& SQUEEZE_RIGHT , 1) |
| 310 |
ENDIF |
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|
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|
| 313 |
RETURN |
| 314 |
END |
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