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C $Header: /u/gcmpack/MITgcm/model/src/calc_phi_hyd.F,v 1.19 2002/08/15 17:25:31 adcroft Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: CALC_PHI_HYD |
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C !INTERFACE: |
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SUBROUTINE CALC_PHI_HYD( |
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I bi, bj, iMin, iMax, jMin, jMax, K, |
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I tFld, sFld, |
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U phiHyd, |
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I myThid) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE CALC_PHI_HYD | |
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C | o Integrate the hydrostatic relation to find the Hydros. | |
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C *==========================================================* |
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C | Potential (ocean: Pressure/rho ; atmos = geopotential)| |
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C | On entry: | |
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C | tFld,sFld are the current thermodynamics quantities| |
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C | (unchanged on exit) | |
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C | phiHyd(i,j,1:k-1) is the hydrostatic Potential | |
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C | at cell centers (tracer points) | |
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C | - 1:k-1 layers are valid | |
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C | - k:Nr layers are invalid | |
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C | phiHyd(i,j,k) is the hydrostatic Potential | |
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C | (ocean only_^) at cell the interface k (w point above) | |
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C | On exit: | |
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C | phiHyd(i,j,1:k) is the hydrostatic Potential | |
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C | at cell centers (tracer points) | |
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C | - 1:k layers are valid | |
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C | - k+1:Nr layers are invalid | |
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C | phiHyd(i,j,k+1) is the hydrostatic Potential (P/rho) | |
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C | (ocean only-^) at cell the interface k+1 (w point below)| |
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C | Atmosphere: | |
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C | Integr_GeoPot allows to select one integration method | |
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C | (see the list below) | |
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C *==========================================================* |
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C \ev |
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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 "GRID.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "FFIELDS.h" |
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#ifdef ALLOW_AUTODIFF_TAMC |
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#include "tamc.h" |
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#include "tamc_keys.h" |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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#include "SURFACE.h" |
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#include "DYNVARS.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine arguments == |
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INTEGER bi,bj,iMin,iMax,jMin,jMax,K |
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_RL tFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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_RL sFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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_RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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INTEGER myThid |
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|
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#ifdef INCLUDE_PHIHYD_CALCULATION_CODE |
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|
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C !LOCAL VARIABLES: |
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C == Local variables == |
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INTEGER i,j, Kp1 |
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_RL zero, one, half |
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_RL alphaRho(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL dRloc,dRlocKp1,locAlpha |
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_RL ddPI, ddPIm, ddPIp, ratioRp, ratioRm |
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CEOP |
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|
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zero = 0. _d 0 |
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one = 1. _d 0 |
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half = .5 _d 0 |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C Atmosphere: |
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C Integr_GeoPot => select one option for the integration of the Geopotential: |
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C = 0 : Energy Conserving Form, No hFac ; |
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C = 1 : Finite Volume Form, with hFac, linear in P by Half level; |
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C =2,3: Finite Difference Form, with hFac, linear in P between 2 Tracer levels |
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C 2 : case Tracer level at the middle of InterFace_W; |
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C 3 : case InterFace_W at the middle of Tracer levels; |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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act1 = bi - myBxLo(myThid) |
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max1 = myBxHi(myThid) - myBxLo(myThid) + 1 |
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|
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act2 = bj - myByLo(myThid) |
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max2 = myByHi(myThid) - myByLo(myThid) + 1 |
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|
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act3 = myThid - 1 |
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max3 = nTx*nTy |
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|
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act4 = ikey_dynamics - 1 |
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|
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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 /* ALLOW_AUTODIFF_TAMC */ |
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|
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IF ( buoyancyRelation .eq. 'OCEANIC' ) THEN |
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C This is the hydrostatic pressure calculation for the Ocean |
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C which uses the FIND_RHO() routine to calculate density |
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C before integrating g*rho over the current layer/interface |
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|
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dRloc=drC(k) |
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IF (k.EQ.1) dRloc=drF(1) |
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IF (k.EQ.Nr) THEN |
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dRlocKp1=0. |
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ELSE |
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dRlocKp1=drC(k+1) |
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ENDIF |
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|
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C-- If this is the top layer we impose the boundary condition |
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C P(z=eta) = P(atmospheric_loading) |
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IF (k.EQ.1) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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#ifdef ATMOSPHERIC_LOADING |
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phiHyd(i,j,k)=pload(i,j,bi,bj)*recip_rhoConst |
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#else |
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phiHyd(i,j,k)=0. _d 0 |
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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 Calculate density |
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#ifdef ALLOW_AUTODIFF_TAMC |
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kkey = (ikey-1)*Nr + k |
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CADJ STORE tFld(:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte |
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CADJ STORE sFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k, |
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& tFld, sFld, |
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& alphaRho, myThid) |
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|
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C Hydrostatic pressure at cell centers |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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#ifdef ALLOW_AUTODIFF_TAMC |
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c Patrick, is this directive correct or even necessary in |
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c this new code? |
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c Yes, because of phiHyd(i,j,k+1)=phiHyd(i,j,k)+... |
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c within the k-loop. |
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CADJ GENERAL |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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C---------- This discretization is the "finite volume" form |
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C which has not been used to date since it does not |
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C conserve KE+PE exactly even though it is more natural |
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C |
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c IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+ |
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c & drF(K)*gravity*alphaRho(i,j)*recip_rhoConst |
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c phiHyd(i,j,k)=phiHyd(i,j,k)+ |
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c & 0.5*drF(K)*gravity*alphaRho(i,j)*recip_rhoConst |
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C----------------------------------------------------------------------- |
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|
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C---------- This discretization is the "energy conserving" form |
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C which has been used since at least Adcroft et al., MWR 1997 |
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C |
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|
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phiHyd(i,j,k)=phiHyd(i,j,k)+ |
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& 0.5*dRloc*gravity*alphaRho(i,j)*recip_rhoConst |
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IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+ |
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& 0.5*dRlocKp1*gravity*alphaRho(i,j)*recip_rhoConst |
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C----------------------------------------------------------------------- |
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|
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C---------- Compute bottom pressure deviation from gravity*rho0*H |
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C This has to be done starting from phiHyd at the current |
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C tracer point and .5 of the cell's thickness has to be |
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C substracted from hFacC |
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IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN |
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phiHydLow(i,j,bi,bj) = phiHyd(i,j,k) |
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& + (hFacC(i,j,k,bi,bj)-0.5)*drF(K) |
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& *gravity*alphaRho(i,j)*recip_rhoConst |
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& + gravity*etaN(i,j,bi,bj) |
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ENDIF |
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C----------------------------------------------------------------------- |
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|
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ENDDO |
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ENDDO |
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|
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ELSEIF ( buoyancyRelation .eq. 'OCEANICP' ) THEN |
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C This is the hydrostatic pressure calculation for the Ocean |
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C which uses the FIND_RHO() routine to calculate density |
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C before integrating g*rho over the current layer/interface |
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|
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dRloc=drC(k) |
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IF (k.EQ.1) dRloc=drF(1) |
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IF (k.EQ.Nr) THEN |
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dRlocKp1=0. |
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ELSE |
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dRlocKp1=drC(k+1) |
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ENDIF |
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|
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IF (k.EQ.1) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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phiHyd(i,j,k)=0. |
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phiHyd(i,j,k)=pload(i,j,bi,bj) |
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c & -Ro_surf(i,j,bi,bj)*recip_rhoNil |
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c & -(Ro_surf(i,j,bi,bj)-.5*drF( kSurfC(i,j,bi,bj) ))/1000. |
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c & -(Ro_surf(i,j,bi,bj)-.5*drF( kSurfC(i,j,bi,bj) ))*recip_rhoNil |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C Calculate density |
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#ifdef ALLOW_AUTODIFF_TAMC |
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kkey = (ikey-1)*Nr + k |
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CADJ STORE tFld(:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte |
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CADJ STORE sFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k, |
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& tFld, sFld, |
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& alphaRho, myThid) |
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|
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C Hydrostatic pressure at cell centers |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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locAlpha=alphaRho(i,j)+rhoNil |
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IF (locAlpha.NE.0.) locAlpha=maskC(i,j,k,bi,bj)/locAlpha |
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|
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C---------- This discretization is the "finite volume" form |
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C which has not been used to date since it does not |
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C conserve KE+PE exactly even though it is more natural |
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C |
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c IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+ |
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c & drF(K)*locAlpha |
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c phiHyd(i,j,k)=phiHyd(i,j,k)+ |
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c & 0.5*drF(K)*locAlpha |
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C----------------------------------------------------------------------- |
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|
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C---------- This discretization is the "energy conserving" form |
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C which has been used since at least Adcroft et al., MWR 1997 |
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C |
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phiHyd(i,j,k)=phiHyd(i,j,k)+ |
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& 0.5*dRloc*locAlpha |
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IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+ |
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& 0.5*dRlocKp1*locAlpha |
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C----------------------------------------------------------------------- |
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|
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C---------- Compute gravity*(sea surface elevation) |
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C This has to be done starting from phiHyd at the current |
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C tracer point and .5 of the cell's thickness has to be |
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C substracted from hFacC |
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IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN |
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phiHydLow(i,j,bi,bj) = phiHyd(i,j,k) |
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& + (hFacC(i,j,k,bi,bj)-0.5)*drF(k)*locAlpha |
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& + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj) |
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ENDIF |
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C----------------------------------------------------------------------- |
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|
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ENDDO |
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ENDDO |
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|
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ELSEIF ( buoyancyRelation .eq. 'ATMOSPHERIC' ) THEN |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C This is the hydrostatic geopotential calculation for the Atmosphere |
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C The ideal gas law is used implicitly here rather than calculating |
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C the specific volume, analogous to the oceanic case. |
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|
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C Integrate d Phi / d pi |
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|
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IF (Integr_GeoPot.EQ.0) THEN |
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C -- Energy Conserving Form, No hFac -- |
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C------------ The integration for the first level phi(k=1) is the same |
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C for both the "finite volume" and energy conserving methods. |
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Ci *NOTE* o Working with geopotential Anomaly, the geopotential boundary |
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C condition is simply Phi-prime(Ro_surf)=0. |
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C o convention ddPI > 0 (same as drF & drC) |
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C----------------------------------------------------------------------- |
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IF (K.EQ.1) THEN |
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ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa) |
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& -((rC(K)/atm_po)**atm_kappa) ) |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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phiHyd(i,j,K)= |
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& ddPIp*maskC(i,j,K,bi,bj) |
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& *(tFld(I,J,K,bi,bj)-tRef(K)) |
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ENDDO |
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ENDDO |
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ELSE |
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C-------- This discretization is the energy conserving form |
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ddPI=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa) |
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& -((rC( K )/atm_po)**atm_kappa) )*0.5 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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phiHyd(i,j,K)=phiHyd(i,j,K-1) |
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& +ddPI*maskC(i,j,K-1,bi,bj) |
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& *(tFld(I,J,K-1,bi,bj)-tRef(K-1)) |
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& +ddPI*maskC(i,j, K ,bi,bj) |
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& *(tFld(I,J, K ,bi,bj)-tRef( K )) |
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C Old code (atmos-exact) looked like this |
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Cold phiHyd(i,j,K)=phiHyd(i,j,K-1) - ddPI* |
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Cold & (tFld(I,J,K-1,bi,bj)+tFld(I,J,K,bi,bj)-2.*tRef(K)) |
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ENDDO |
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ENDDO |
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ENDIF |
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C end: Energy Conserving Form, No hFac -- |
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C----------------------------------------------------------------------- |
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|
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ELSEIF (Integr_GeoPot.EQ.1) THEN |
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C -- Finite Volume Form, with hFac, linear in P by Half level -- |
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C--------- |
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C Finite Volume formulation consistent with Partial Cell, linear in p by piece |
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C Note: a true Finite Volume form should be linear between 2 Interf_W : |
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C phi_C = (phi_W_k+ phi_W_k+1)/2 ; but not accurate in Stratosphere (low p) |
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C also: if Interface_W at the middle between tracer levels, this form |
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C is close to the Energy Cons. form in the Interior, except for the |
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C non-linearity in PI(p) |
| 318 |
C--------- |
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IF (K.EQ.1) THEN |
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ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa) |
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& -((rC(K)/atm_po)**atm_kappa) ) |
| 322 |
DO j=jMin,jMax |
| 323 |
DO i=iMin,iMax |
| 324 |
phiHyd(i,j,K) = |
| 325 |
& ddPIp*_hFacC(I,J, K ,bi,bj) |
| 326 |
& *(tFld(I,J, K ,bi,bj)-tRef( K )) |
| 327 |
ENDDO |
| 328 |
ENDDO |
| 329 |
ELSE |
| 330 |
ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa) |
| 331 |
& -((rF( K )/atm_po)**atm_kappa) ) |
| 332 |
ddPIp=atm_cp*( ((rF( K )/atm_po)**atm_kappa) |
| 333 |
& -((rC( K )/atm_po)**atm_kappa) ) |
| 334 |
DO j=jMin,jMax |
| 335 |
DO i=iMin,iMax |
| 336 |
phiHyd(i,j,K) = phiHyd(i,j,K-1) |
| 337 |
& +ddPIm*_hFacC(I,J,K-1,bi,bj) |
| 338 |
& *(tFld(I,J,K-1,bi,bj)-tRef(K-1)) |
| 339 |
& +ddPIp*_hFacC(I,J, K ,bi,bj) |
| 340 |
& *(tFld(I,J, K ,bi,bj)-tRef( K )) |
| 341 |
ENDDO |
| 342 |
ENDDO |
| 343 |
ENDIF |
| 344 |
C end: Finite Volume Form, with hFac, linear in P by Half level -- |
| 345 |
C----------------------------------------------------------------------- |
| 346 |
|
| 347 |
ELSEIF (Integr_GeoPot.EQ.2) THEN |
| 348 |
C -- Finite Difference Form, with hFac, Tracer Lev. = middle -- |
| 349 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 350 |
C Finite Difference formulation consistent with Partial Cell, |
| 351 |
C case Tracer level at the middle of InterFace_W |
| 352 |
C linear between 2 Tracer levels ; conserve energy in the Interior |
| 353 |
C--------- |
| 354 |
Kp1 = min(Nr,K+1) |
| 355 |
IF (K.EQ.1) THEN |
| 356 |
ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa) |
| 357 |
& -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0 |
| 358 |
ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa) |
| 359 |
& -((rC(Kp1)/atm_po)**atm_kappa) ) |
| 360 |
DO j=jMin,jMax |
| 361 |
DO i=iMin,iMax |
| 362 |
phiHyd(i,j,K) = |
| 363 |
& ( ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half) |
| 364 |
& +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) ) |
| 365 |
& *(tFld(i,j, K ,bi,bj)-tRef( K )) |
| 366 |
& * maskC(i,j, K ,bi,bj) |
| 367 |
ENDDO |
| 368 |
ENDDO |
| 369 |
ELSE |
| 370 |
ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa) |
| 371 |
& -((rC( K )/atm_po)**atm_kappa) ) |
| 372 |
ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa) |
| 373 |
& -((rC(Kp1)/atm_po)**atm_kappa) ) |
| 374 |
DO j=jMin,jMax |
| 375 |
DO i=iMin,iMax |
| 376 |
phiHyd(i,j,K) = phiHyd(i,j,K-1) |
| 377 |
& + ddPIm*0.5 |
| 378 |
& *(tFld(i,j,K-1,bi,bj)-tRef(K-1)) |
| 379 |
& * maskC(i,j,K-1,bi,bj) |
| 380 |
& +(ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half) |
| 381 |
& +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) ) |
| 382 |
& *(tFld(i,j, K ,bi,bj)-tRef( K )) |
| 383 |
& * maskC(i,j, K ,bi,bj) |
| 384 |
ENDDO |
| 385 |
ENDDO |
| 386 |
ENDIF |
| 387 |
C end: Finite Difference Form, with hFac, Tracer Lev. = middle -- |
| 388 |
C----------------------------------------------------------------------- |
| 389 |
|
| 390 |
ELSEIF (Integr_GeoPot.EQ.3) THEN |
| 391 |
C -- Finite Difference Form, with hFac, Interface_W = middle -- |
| 392 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 393 |
C Finite Difference formulation consistent with Partial Cell, |
| 394 |
C Valid & accurate if Interface_W at middle between tracer levels |
| 395 |
C linear in p between 2 Tracer levels ; conserve energy in the Interior |
| 396 |
C--------- |
| 397 |
Kp1 = min(Nr,K+1) |
| 398 |
IF (K.EQ.1) THEN |
| 399 |
ratioRm=0.5*drF(K)/(rF(k)-rC(K)) |
| 400 |
ratioRp=drF(K)*recip_drC(Kp1) |
| 401 |
ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa) |
| 402 |
& -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0 |
| 403 |
ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa) |
| 404 |
& -((rC(Kp1)/atm_po)**atm_kappa) ) |
| 405 |
DO j=jMin,jMax |
| 406 |
DO i=iMin,iMax |
| 407 |
phiHyd(i,j,K) = |
| 408 |
& ( ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half) |
| 409 |
& +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp -half) ) |
| 410 |
& *(tFld(i,j, K ,bi,bj)-tRef( K )) |
| 411 |
& * maskC(i,j, K ,bi,bj) |
| 412 |
ENDDO |
| 413 |
ENDDO |
| 414 |
ELSE |
| 415 |
ratioRm=drF(K)*recip_drC(K) |
| 416 |
ratioRp=drF(K)*recip_drC(Kp1) |
| 417 |
ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa) |
| 418 |
& -((rC( K )/atm_po)**atm_kappa) ) |
| 419 |
ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa) |
| 420 |
& -((rC(Kp1)/atm_po)**atm_kappa) ) |
| 421 |
DO j=jMin,jMax |
| 422 |
DO i=iMin,iMax |
| 423 |
phiHyd(i,j,K) = phiHyd(i,j,K-1) |
| 424 |
& + ddPIm*0.5 |
| 425 |
& *(tFld(i,j,K-1,bi,bj)-tRef(K-1)) |
| 426 |
& * maskC(i,j,K-1,bi,bj) |
| 427 |
& +(ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half) |
| 428 |
& +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp -half) ) |
| 429 |
& *(tFld(i,j, K ,bi,bj)-tRef( K )) |
| 430 |
& * maskC(i,j, K ,bi,bj) |
| 431 |
ENDDO |
| 432 |
ENDDO |
| 433 |
ENDIF |
| 434 |
C end: Finite Difference Form, with hFac, Interface_W = middle -- |
| 435 |
C----------------------------------------------------------------------- |
| 436 |
|
| 437 |
ELSE |
| 438 |
STOP 'CALC_PHI_HYD: Bad Integr_GeoPot option !' |
| 439 |
ENDIF |
| 440 |
|
| 441 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 442 |
ELSE |
| 443 |
STOP 'CALC_PHI_HYD: We should never reach this point!' |
| 444 |
ENDIF |
| 445 |
|
| 446 |
#endif /* INCLUDE_PHIHYD_CALCULATION_CODE */ |
| 447 |
|
| 448 |
RETURN |
| 449 |
END |
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