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revision 1.23 by heimbach, Fri Nov 15 03:01:21 2002 UTC revision 1.33 by mlosch, Tue Feb 7 11:47:49 2006 UTC
# Line 1  Line 1 
1  C $Header$  C $Header$
2  C $Name$  C $Name$
3    
4    #include "PACKAGES_CONFIG.h"
5  #include "CPP_OPTIONS.h"  #include "CPP_OPTIONS.h"
6    
7  CBOP  CBOP
8  C     !ROUTINE: CALC_PHI_HYD  C     !ROUTINE: CALC_PHI_HYD
9  C     !INTERFACE:  C     !INTERFACE:
10        SUBROUTINE CALC_PHI_HYD(        SUBROUTINE CALC_PHI_HYD(
11       I                         bi, bj, iMin, iMax, jMin, jMax, K,       I                         bi, bj, iMin, iMax, jMin, jMax, k,
12       I                         tFld, sFld,       I                         tFld, sFld,
13       U                         phiHyd,       U                         phiHydF,
14       I                         myThid)       O                         phiHydC, dPhiHydX, dPhiHydY,
15         I                         myTime, myIter, myThid)
16  C     !DESCRIPTION: \bv  C     !DESCRIPTION: \bv
17  C     *==========================================================*  C     *==========================================================*
18  C     | SUBROUTINE CALC_PHI_HYD                                  |  C     | SUBROUTINE CALC_PHI_HYD                                  |
19  C     | o Integrate the hydrostatic relation to find the Hydros. |  C     | o Integrate the hydrostatic relation to find the Hydros. |
20  C     *==========================================================*  C     *==========================================================*
21  C     |    Potential (ocean: Pressure/rho ; atmos = geopotential)|  C     |    Potential (ocean: Pressure/rho ; atmos = geopotential)
22  C     | On entry:                                                |  C     | On entry:
23  C     |   tFld,sFld     are the current thermodynamics quantities|  C     |   tFld,sFld     are the current thermodynamics quantities
24  C     |                 (unchanged on exit)                      |  C     |                 (unchanged on exit)
25  C     |   phiHyd(i,j,1:k-1) is the hydrostatic Potential         |  C     |   phiHydF(i,j) is the hydrostatic Potential anomaly
26  C     |                 at cell centers (tracer points)          |  C     |                at middle between tracer points k-1,k
27  C     |                 - 1:k-1 layers are valid                 |  C     | On exit:
28  C     |                 - k:Nr layers are invalid                |  C     |   phiHydC(i,j) is the hydrostatic Potential anomaly
29  C     |   phiHyd(i,j,k) is the hydrostatic Potential             |  C     |                at cell centers (tracer points), level k
30  C     |  (ocean only_^) at cell the interface k (w point above)  |  C     |   phiHydF(i,j) is the hydrostatic Potential anomaly
31  C     | On exit:                                                 |  C     |                at middle between tracer points k,k+1
32  C     |   phiHyd(i,j,1:k) is the hydrostatic Potential           |  C     |   dPhiHydX,Y   hydrostatic Potential gradient (X&Y dir)
33  C     |                 at cell centers (tracer points)          |  C     |                at cell centers (tracer points), level k
34  C     |                 - 1:k layers are valid                   |  C     | integr_GeoPot allows to select one integration method
35  C     |                 - k+1:Nr layers are invalid              |  C     |    1= Finite volume form ; else= Finite difference form
 C     |   phiHyd(i,j,k+1) is the hydrostatic Potential (P/rho)   |  
 C     |  (ocean only-^) at cell the interface k+1 (w point below)|  
 C     | Atmosphere:                                              |  
 C     |   Integr_GeoPot allows to select one integration method  |  
 C     |    (see the list below)                                  |  
36  C     *==========================================================*  C     *==========================================================*
37  C     \ev  C     \ev
38  C     !USES:  C     !USES:
# Line 45  C     == Global variables == Line 42  C     == Global variables ==
42  #include "GRID.h"  #include "GRID.h"
43  #include "EEPARAMS.h"  #include "EEPARAMS.h"
44  #include "PARAMS.h"  #include "PARAMS.h"
 #include "FFIELDS.h"  
45  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
46  #include "tamc.h"  #include "tamc.h"
47  #include "tamc_keys.h"  #include "tamc_keys.h"
# Line 55  C     == Global variables == Line 51  C     == Global variables ==
51    
52  C     !INPUT/OUTPUT PARAMETERS:  C     !INPUT/OUTPUT PARAMETERS:
53  C     == Routine arguments ==  C     == Routine arguments ==
54        INTEGER bi,bj,iMin,iMax,jMin,jMax,K  C     bi, bj, k  :: tile and level indices
55    C     iMin,iMax,jMin,jMax :: computational domain
56    C     tFld       :: potential temperature
57    C     sFld       :: salinity
58    C     phiHydF    :: hydrostatic potential anomaly at middle between
59    C                   2 centers (entry: Interf_k ; output: Interf_k+1)
60    C     phiHydC    :: hydrostatic potential anomaly at cell center
61    C     dPhiHydX,Y :: gradient (X & Y dir.) of hydrostatic potential anom.
62    C     myTime     :: current time
63    C     myIter     :: current iteration number
64    C     myThid     :: thread number for this instance of the routine.
65          INTEGER bi,bj,iMin,iMax,jMin,jMax,k
66        _RL tFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)        _RL tFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
67        _RL sFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)        _RL sFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
68        _RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)  c     _RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
69        INTEGER myThid        _RL phiHydF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
70          _RL phiHydC(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71          _RL dPhiHydX(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
72          _RL dPhiHydY(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
73          _RL myTime
74          INTEGER myIter, myThid
75                
76  #ifdef INCLUDE_PHIHYD_CALCULATION_CODE  #ifdef INCLUDE_PHIHYD_CALCULATION_CODE
77    
78  C     !LOCAL VARIABLES:  C     !LOCAL VARIABLES:
79  C     == Local variables ==  C     == Local variables ==
80        INTEGER i,j, Kp1        INTEGER i,j
81        _RL zero, one, half        _RL zero, one, half
82        _RL alphaRho(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL alphaRho(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
83        _RL dRloc,dRlocKp1,locAlpha        _RL dRlocM,dRlocP, ddRloc, locAlpha
84        _RL ddPI, ddPIm, ddPIp, ratioRp, ratioRm        _RL ddPIm, ddPIp, rec_dRm, rec_dRp
85          _RL surfPhiFac
86          INTEGER iMnLoc,jMnLoc
87          PARAMETER ( zero= 0. _d 0 , one= 1. _d 0 , half= .5 _d 0 )
88          LOGICAL useDiagPhiRlow, addSurfPhiAnom
89  CEOP  CEOP
90          useDiagPhiRlow = .TRUE.
91        zero = 0. _d 0        addSurfPhiAnom = select_rStar.EQ.0 .AND. nonlinFreeSurf.GT.3
92        one  = 1. _d 0        surfPhiFac = 0.
93        half = .5 _d 0        IF (addSurfPhiAnom) surfPhiFac = 1.
94    
95  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
96  C  Atmosphere:    C  Atmosphere:  
97  C Integr_GeoPot => select one option for the integration of the Geopotential:  C integr_GeoPot => select one option for the integration of the Geopotential:
98  C   = 0 : Energy Conserving Form, No hFac ;  C   = 0 : Energy Conserving Form, accurate with Topo full cell;
99  C   = 1 : Finite Volume Form, with hFac, linear in P by Half level;  C   = 1 : Finite Volume Form, with Part-Cell, linear in P by Half level;
100  C   =2,3: Finite Difference Form, with hFac, linear in P between 2 Tracer levels  C   =2,3: Finite Difference Form, with Part-Cell,
101  C     2 : case Tracer level at the middle of InterFace_W;  C         linear in P between 2 Tracer levels.
102  C     3 : case InterFace_W  at the middle of Tracer levels;  C       can handle both cases: Tracer lev at the middle of InterFace_W
103    C                          and InterFace_W at the middle of Tracer lev;
104  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
105    
106  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
# Line 103  C---+----1----+----2----+----3----+----4 Line 120  C---+----1----+----2----+----3----+----4
120       &                      + act4*max1*max2*max3       &                      + act4*max1*max2*max3
121  #endif /* ALLOW_AUTODIFF_TAMC */  #endif /* ALLOW_AUTODIFF_TAMC */
122    
123        IF ( buoyancyRelation .eq. 'OCEANIC' ) THEN  C--   Initialize phiHydF to zero :
124    C     note: atmospheric_loading or Phi_topo anomaly are incorporated
125    C           later in S/R calc_grad_phi_hyd
126          IF (k.EQ.1) THEN
127            DO j=1-Oly,sNy+Oly
128             DO i=1-Olx,sNx+Olx
129               phiHydF(i,j) = 0.
130             ENDDO
131            ENDDO
132          ENDIF
133    
134    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
135          IF ( buoyancyRelation .EQ. 'OCEANIC' ) THEN
136  C       This is the hydrostatic pressure calculation for the Ocean  C       This is the hydrostatic pressure calculation for the Ocean
137  C       which uses the FIND_RHO() routine to calculate density  C       which uses the FIND_RHO() routine to calculate density
138  C       before integrating g*rho over the current layer/interface  C       before integrating g*rho over the current layer/interface
139    #ifdef      ALLOW_AUTODIFF_TAMC
140    CADJ GENERAL
141    #endif      /* ALLOW_AUTODIFF_TAMC */
142    
143          dRloc=drC(k)  C---    Calculate density
         IF (k.EQ.1) dRloc=drF(1)  
         IF (k.EQ.Nr) THEN  
           dRlocKp1=0.  
         ELSE  
           dRlocKp1=drC(k+1)  
         ENDIF  
   
 C--     If this is the top layer we impose the boundary condition  
 C       P(z=eta) = P(atmospheric_loading)  
         IF (k.EQ.1) THEN  
           DO j=jMin,jMax  
             DO i=iMin,iMax  
 #ifdef ATMOSPHERIC_LOADING  
               phiHyd(i,j,k)=pload(i,j,bi,bj)*recip_rhoConst  
 #else  
               phiHyd(i,j,k)=0. _d 0  
 #endif  
             ENDDO  
           ENDDO  
         ENDIF  
   
 C       Calculate density  
144  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
145          kkey = (ikey-1)*Nr + k          kkey = (ikey-1)*Nr + k
146  CADJ STORE tFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte  CADJ STORE tFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
# Line 139  CADJ STORE sFld (:,:,k,bi,bj) = comlev1_ Line 149  CADJ STORE sFld (:,:,k,bi,bj) = comlev1_
149          CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k,          CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k,
150       &                 tFld, sFld,       &                 tFld, sFld,
151       &                 alphaRho, myThid)       &                 alphaRho, myThid)
152    #ifdef ALLOW_SHELFICE
153    C     mask rho, so that there is no contribution of phiHyd from
154    C     overlying shelfice (whose density we do not know)
155            IF ( useShelfIce ) THEN
156             DO j=jMin,jMax
157              DO i=iMin,iMax
158               alphaRho(i,j) = alphaRho(i,j)*maskC(i,j,k,bi,bj)
159              ENDDO
160             ENDDO
161            ENDIF
162    #endif /* ALLOW_SHELFICE */
163    
164    #ifdef ALLOW_DIAGNOSTICS
165            IF ( useDiagnostics )
166         &   CALL DIAGNOSTICS_FILL(alphaRho,'RHOAnoma',k,1,2,bi,bj,myThid)
167    #endif
168    
169  C Quasi-hydrostatic terms are added in as if they modify the buoyancy  C Quasi-hydrostatic terms are added in as if they modify the buoyancy
170          IF (quasiHydrostatic) THEN          IF (quasiHydrostatic) THEN
171           CALL QUASIHYDROSTATICTERMS(bi,bj,k,alphaRho,myThid)           CALL QUASIHYDROSTATICTERMS(bi,bj,k,alphaRho,myThid)
172          ENDIF          ENDIF
173    
174  C       Hydrostatic pressure at cell centers  #ifdef NONLIN_FRSURF
175          DO j=jMin,jMax          IF (k.EQ.1 .AND. addSurfPhiAnom) THEN
176              DO j=jMin,jMax
177                DO i=iMin,iMax
178                  phiHydF(i,j) = surfPhiFac*etaH(i,j,bi,bj)
179         &                      *gravity*alphaRho(i,j)*recip_rhoConst
180                ENDDO
181              ENDDO
182            ENDIF
183    #endif /* NONLIN_FRSURF */
184    
185    C----  Hydrostatic pressure at cell centers
186    
187           IF (integr_GeoPot.EQ.1) THEN
188    C  --  Finite Volume Form
189    
190             DO j=jMin,jMax
191            DO i=iMin,iMax            DO i=iMin,iMax
 #ifdef      ALLOW_AUTODIFF_TAMC  
 c           Patrick, is this directive correct or even necessary in  
 c           this new code?  
 c           Yes, because of phiHyd(i,j,k+1)=phiHyd(i,j,k)+...  
 c           within the k-loop.  
 CADJ GENERAL  
 #endif      /* ALLOW_AUTODIFF_TAMC */  
192    
193  CmlC---------- This discretization is the "finite volume" form  C---------- This discretization is the "finite volume" form
194  CmlC           which has not been used to date since it does not  C           which has not been used to date since it does not
195  CmlC           conserve KE+PE exactly even though it is more natural  C           conserve KE+PE exactly even though it is more natural
196  CmlC  C
197  Cml          IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN             phiHydC(i,j)=phiHydF(i,j)
198  Cml           phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)       &       + half*drF(k)*gravity*alphaRho(i,j)*recip_rhoConst
199  Cml     &          + hFacC(i,j,k,bi,bj)             phiHydF(i,j)=phiHydF(i,j)
200  Cml     &            *drF(K)*gravity*alphaRho(i,j)*recip_rhoConst       &            + drF(k)*gravity*alphaRho(i,j)*recip_rhoConst
201  Cml     &          + gravity*etaN(i,j,bi,bj)            ENDDO
202  Cml          ENDIF           ENDDO
203  Cml           IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+  
204  Cml     &         drF(K)*gravity*alphaRho(i,j)*recip_rhoConst         ELSE
205  Cml           phiHyd(i,j,k)=phiHyd(i,j,k)+  C  --  Finite Difference Form
206  Cml     &          0.5*drF(K)*gravity*alphaRho(i,j)*recip_rhoConst  
207  CmlC-----------------------------------------------------------------------           dRlocM=half*drC(k)
208             IF (k.EQ.1) dRlocM=rF(k)-rC(k)
209             IF (k.EQ.Nr) THEN
210               dRlocP=rC(k)-rF(k+1)
211             ELSE
212               dRlocP=half*drC(k+1)
213             ENDIF
214    
215             DO j=jMin,jMax
216              DO i=iMin,iMax
217    
218  C---------- This discretization is the "energy conserving" form  C---------- This discretization is the "energy conserving" form
219  C           which has been used since at least Adcroft et al., MWR 1997  C           which has been used since at least Adcroft et al., MWR 1997
220  C  C
221                            phiHydC(i,j)=phiHydF(i,j)
222              phiHyd(i,j,k)=phiHyd(i,j,k)+       &        +dRlocM*gravity*alphaRho(i,j)*recip_rhoConst
223       &          0.5*dRloc*gravity*alphaRho(i,j)*recip_rhoConst              phiHydF(i,j)=phiHydC(i,j)
224              IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+       &        +dRlocP*gravity*alphaRho(i,j)*recip_rhoConst
      &          0.5*dRlocKp1*gravity*alphaRho(i,j)*recip_rhoConst  
 C-----------------------------------------------------------------------  
   
 C---------- Compute bottom pressure deviation from gravity*rho0*H  
 C           This has to be done starting from phiHyd at the current  
 C           tracer point and .5 of the cell's thickness has to be  
 C           substracted from hFacC  
             IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN  
              phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)  
      &              + (hFacC(i,j,k,bi,bj)-.5)*drF(K)  
      &                   *gravity*alphaRho(i,j)*recip_rhoConst  
      &              + gravity*etaN(i,j,bi,bj)  
             ENDIF  
 C-----------------------------------------------------------------------  
   
225            ENDDO            ENDDO
226          ENDDO           ENDDO
227    
228    C  --  end if integr_GeoPot = ...
229           ENDIF
230                    
231        ELSEIF ( buoyancyRelation .eq. 'OCEANICP' ) THEN  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
232          ELSEIF ( buoyancyRelation .EQ. 'OCEANICP' ) THEN
233  C       This is the hydrostatic pressure calculation for the Ocean  C       This is the hydrostatic pressure calculation for the Ocean
234  C       which uses the FIND_RHO() routine to calculate density  C       which uses the FIND_RHO() routine to calculate density
235  C       before integrating g*rho over the current layer/interface  C       before integrating (1/rho)'*dp over the current layer/interface
236  #ifdef      ALLOW_AUTODIFF_TAMC  #ifdef      ALLOW_AUTODIFF_TAMC
237  CADJ GENERAL  CADJ GENERAL
238  #endif      /* ALLOW_AUTODIFF_TAMC */  #endif      /* ALLOW_AUTODIFF_TAMC */
239    
240          dRloc=drC(k)  C--     Calculate density
         IF (k.EQ.1) dRloc=drF(1)  
         IF (k.EQ.Nr) THEN  
           dRlocKp1=0.  
         ELSE  
           dRlocKp1=drC(k+1)  
         ENDIF  
   
         IF (k.EQ.1) THEN  
           DO j=jMin,jMax  
             DO i=iMin,iMax  
               phiHyd(i,j,k)=0.  
 #ifdef ATMOSPHERIC_LOADING  
               phiHyd(i,j,k)=pload(i,j,bi,bj)  
 #endif  
             ENDDO  
           ENDDO  
         ENDIF  
   
 C       Calculate density  
241  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
242              kkey = (ikey-1)*Nr + k              kkey = (ikey-1)*Nr + k
243  CADJ STORE tFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte  CADJ STORE tFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
# Line 237  CADJ STORE sFld (:,:,k,bi,bj) = comlev1_ Line 250  CADJ STORE sFld (:,:,k,bi,bj) = comlev1_
250  CADJ STORE alphaRho (:,:) = comlev1_bibj_k, key=kkey, byte=isbyte  CADJ STORE alphaRho (:,:) = comlev1_bibj_k, key=kkey, byte=isbyte
251  #endif /* ALLOW_AUTODIFF_TAMC */  #endif /* ALLOW_AUTODIFF_TAMC */
252    
253    #ifdef ALLOW_DIAGNOSTICS
254            IF ( useDiagnostics )
255         &   CALL DIAGNOSTICS_FILL(alphaRho,'RHOAnoma',k,1,2,bi,bj,myThid)
256    #endif
257    
258  C       Hydrostatic pressure at cell centers  C--     Calculate specific volume anomaly : alpha' = 1/rho - alpha_Cst
259          DO j=jMin,jMax          DO j=jMin,jMax
260            DO i=iMin,iMax            DO i=iMin,iMax
261              locAlpha=alphaRho(i,j)+rhoConst              locAlpha=alphaRho(i,j)+rhoConst
262              IF (locAlpha.NE.0.) locAlpha=maskC(i,j,k,bi,bj)/locAlpha              alphaRho(i,j)=maskC(i,j,k,bi,bj)*
263         &              (one/locAlpha - recip_rhoConst)
264              ENDDO
265            ENDDO
266    
267  CmlC---------- This discretization is the "finite volume" form  C----  Hydrostatic pressure at cell centers
 CmlC           which has not been used to date since it does not  
 CmlC           conserve KE+PE exactly even though it is more natural  
 CmlC  
 Cml            IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN  
 Cml             phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)  
 Cml     &          + hFacC(i,j,k,bi,bj)*drF(K)*locAlpha  
 Cml     &          + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj)  
 Cml            ENDIF  
 Cml            IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+  
 Cml     &           drF(K)*locAlpha  
 Cml            phiHyd(i,j,k)=phiHyd(i,j,k)+  
 Cml     &           0.5*drF(K)*locAlpha  
 CmlC-----------------------------------------------------------------------  
268    
269  C---------- This discretization is the "energy conserving" form         IF (integr_GeoPot.EQ.1) THEN
270  C           which has been used since at least Adcroft et al., MWR 1997  C  --  Finite Volume Form
271  C  
272             DO j=jMin,jMax
273              DO i=iMin,iMax
274    
275              phiHyd(i,j,k)=phiHyd(i,j,k)+  C---------- This discretization is the "finite volume" form
276       &          0.5*dRloc*locAlpha  C           which has not been used to date since it does not
277              IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+  C           conserve KE+PE exactly even though it is more natural
278       &          0.5*dRlocKp1*locAlpha  C
279               IF (k.EQ.ksurfC(i,j,bi,bj)) THEN
280                 ddRloc = Ro_surf(i,j,bi,bj)-rC(k)
281    #ifdef NONLIN_FRSURF
282                 ddRloc = ddRloc + surfPhiFac*etaH(i,j,bi,bj)
283    #endif
284                 phiHydC(i,j) = ddRloc*alphaRho(i,j)
285    c--to reproduce results of c48d_post: uncomment those 4+1 lines
286    c            phiHydC(i,j)=phiHydF(i,j)
287    c    &          +(hFacC(i,j,k,bi,bj)-half)*drF(k)*alphaRho(i,j)
288    c            phiHydF(i,j)=phiHydF(i,j)
289    c    &          + hFacC(i,j,k,bi,bj)*drF(k)*alphaRho(i,j)
290               ELSE
291                 phiHydC(i,j) = phiHydF(i,j) + half*drF(k)*alphaRho(i,j)
292    c            phiHydF(i,j) = phiHydF(i,j) +      drF(k)*alphaRho(i,j)
293               ENDIF
294    c-- and comment this last one:
295                 phiHydF(i,j) = phiHydC(i,j) + half*drF(k)*alphaRho(i,j)
296    c-----
297              ENDDO
298             ENDDO
299    
300           ELSE
301    C  --  Finite Difference Form, with Part-Cell Bathy
302    
303             dRlocM=half*drC(k)
304             IF (k.EQ.1) dRlocM=rF(k)-rC(k)
305             IF (k.EQ.Nr) THEN
306               dRlocP=rC(k)-rF(k+1)
307             ELSE
308               dRlocP=half*drC(k+1)
309             ENDIF
310             rec_dRm = one/(rF(k)-rC(k))
311             rec_dRp = one/(rC(k)-rF(k+1))
312    
313  C-----------------------------------------------------------------------           DO j=jMin,jMax
314              DO i=iMin,iMax
315    
316  C---------- Compute gravity*(sea surface elevation) first  C---------- This discretization is the "energy conserving" form
 C           This has to be done starting from phiHyd at the current  
 C           tracer point and .5 of the cell's thickness has to be  
 C           substracted from hFacC  
             IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN  
              phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)  
      &              + (hFacC(i,j,k,bi,bj)-0.5)*drF(k)*locAlpha  
      &              + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj)  
             ENDIF  
 C-----------------------------------------------------------------------  
317    
318               IF (k.EQ.ksurfC(i,j,bi,bj)) THEN
319                 ddRloc = Ro_surf(i,j,bi,bj)-rC(k)
320    #ifdef NONLIN_FRSURF
321                 ddRloc = ddRloc + surfPhiFac*etaH(i,j,bi,bj)
322    #endif
323                 phiHydC(i,j) =( MAX(zero,ddRloc)*rec_dRm*dRlocM
324         &                      +MIN(zero,ddRloc)*rec_dRp*dRlocP
325         &                     )*alphaRho(i,j)
326               ELSE
327                 phiHydC(i,j) = phiHydF(i,j) + dRlocM*alphaRho(i,j)
328               ENDIF
329                 phiHydF(i,j) = phiHydC(i,j) + dRlocP*alphaRho(i,j)
330            ENDDO            ENDDO
331          ENDDO           ENDDO
332    
333        ELSEIF ( buoyancyRelation .eq. 'ATMOSPHERIC' ) THEN  C  --  end if integr_GeoPot = ...
334           ENDIF
335    
336          ELSEIF ( buoyancyRelation .EQ. 'ATMOSPHERIC' ) THEN
337  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
338  C       This is the hydrostatic geopotential calculation for the Atmosphere  C       This is the hydrostatic geopotential calculation for the Atmosphere
339  C       The ideal gas law is used implicitly here rather than calculating  C       The ideal gas law is used implicitly here rather than calculating
340  C       the specific volume, analogous to the oceanic case.  C       the specific volume, analogous to the oceanic case.
341    
342  C       Integrate d Phi / d pi  C--     virtual potential temperature anomaly (including water vapour effect)
343            DO j=jMin,jMax
344             DO i=iMin,iMax
345              alphaRho(i,j)=maskC(i,j,k,bi,bj)
346         &             *( tFld(i,j,k,bi,bj)*(sFld(i,j,k,bi,bj)*atm_Rq+one)
347         &               -tRef(k) )
348             ENDDO
349            ENDDO
350    
351    C---    Integrate d Phi / d pi
352    
353        IF (Integr_GeoPot.EQ.0) THEN         IF (integr_GeoPot.EQ.0) THEN
354  C  --  Energy Conserving Form, No hFac  --  C  --  Energy Conserving Form, accurate with Full cell topo  --
355  C------------ The integration for the first level phi(k=1) is the same  C------------ The integration for the first level phi(k=1) is the same
356  C             for both the "finite volume" and energy conserving methods.  C             for both the "finite volume" and energy conserving methods.
357  Ci    *NOTE* o Working with geopotential Anomaly, the geopotential boundary  C    *NOTE* o Working with geopotential Anomaly, the geopotential boundary
358  C             condition is simply Phi-prime(Ro_surf)=0.  C             condition is simply Phi-prime(Ro_surf)=0.
359  C           o convention ddPI > 0 (same as drF & drC)  C           o convention ddPI > 0 (same as drF & drC)
360  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
361          IF (K.EQ.1) THEN           IF (k.EQ.1) THEN
362            ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa)             ddPIm=atm_Cp*( ((rF( k )/atm_Po)**atm_kappa)
363       &                  -((rC(K)/atm_po)**atm_kappa) )       &                   -((rC( k )/atm_Po)**atm_kappa) )
364            DO j=jMin,jMax           ELSE
365             DO i=iMin,iMax             ddPIm=atm_Cp*( ((rC(k-1)/atm_Po)**atm_kappa)
366               phiHyd(i,j,K)=       &                   -((rC( k )/atm_Po)**atm_kappa) )*half
367       &          ddPIp*maskC(i,j,K,bi,bj)           ENDIF
368       &               *(tFld(I,J,K,bi,bj)-tRef(K))           IF (k.EQ.Nr) THEN
369             ENDDO             ddPIp=atm_Cp*( ((rC( k )/atm_Po)**atm_kappa)
370            ENDDO       &                   -((rF(k+1)/atm_Po)**atm_kappa) )
371          ELSE           ELSE
372               ddPIp=atm_Cp*( ((rC( k )/atm_Po)**atm_kappa)
373         &                   -((rC(k+1)/atm_Po)**atm_kappa) )*half
374             ENDIF
375  C-------- This discretization is the energy conserving form  C-------- This discretization is the energy conserving form
376            ddPI=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)           DO j=jMin,jMax
377       &                 -((rC( K )/atm_po)**atm_kappa) )*0.5            DO i=iMin,iMax
378            DO j=jMin,jMax               phiHydC(i,j) = phiHydF(i,j) +ddPIm*alphaRho(i,j)
379             DO i=iMin,iMax               phiHydF(i,j) = phiHydC(i,j) +ddPIp*alphaRho(i,j)
               phiHyd(i,j,K)=phiHyd(i,j,K-1)  
      &           +ddPI*maskC(i,j,K-1,bi,bj)  
      &                *(tFld(I,J,K-1,bi,bj)-tRef(K-1))  
      &           +ddPI*maskC(i,j, K ,bi,bj)  
      &                *(tFld(I,J, K ,bi,bj)-tRef( K ))  
 C             Old code (atmos-exact) looked like this  
 Cold          phiHyd(i,j,K)=phiHyd(i,j,K-1) - ddPI*  
 Cold &      (tFld(I,J,K-1,bi,bj)+tFld(I,J,K,bi,bj)-2.*tRef(K))  
            ENDDO  
380            ENDDO            ENDDO
381          ENDIF           ENDDO
382  C end: Energy Conserving Form, No hFac  --  C end: Energy Conserving Form, No hFac  --
383  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
384    
385        ELSEIF (Integr_GeoPot.EQ.1) THEN         ELSEIF (integr_GeoPot.EQ.1) THEN
386  C  --  Finite Volume Form, with hFac, linear in P by Half level  --  C  --  Finite Volume Form, with Part-Cell Topo, linear in P by Half level
387  C---------  C---------
388  C  Finite Volume formulation consistent with Partial Cell, linear in p by piece  C  Finite Volume formulation consistent with Partial Cell, linear in p by piece
389  C   Note: a true Finite Volume form should be linear between 2 Interf_W :  C   Note: a true Finite Volume form should be linear between 2 Interf_W :
# Line 340  C   also: if Interface_W at the middle b Line 392  C   also: if Interface_W at the middle b
392  C     is close to the Energy Cons. form in the Interior, except for the  C     is close to the Energy Cons. form in the Interior, except for the
393  C     non-linearity in PI(p)  C     non-linearity in PI(p)
394  C---------  C---------
395          IF (K.EQ.1) THEN             ddPIm=atm_Cp*( ((rF( k )/atm_Po)**atm_kappa)
396            ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa)       &                   -((rC( k )/atm_Po)**atm_kappa) )
397       &                  -((rC(K)/atm_po)**atm_kappa) )             ddPIp=atm_Cp*( ((rC( k )/atm_Po)**atm_kappa)
398            DO j=jMin,jMax       &                   -((rF(k+1)/atm_Po)**atm_kappa) )
399             DO i=iMin,iMax           DO j=jMin,jMax
400               phiHyd(i,j,K) =            DO i=iMin,iMax
401       &          ddPIp*_hFacC(I,J, K ,bi,bj)             IF (k.EQ.ksurfC(i,j,bi,bj)) THEN
402       &               *(tFld(I,J, K ,bi,bj)-tRef( K ))               ddRloc = Ro_surf(i,j,bi,bj)-rC(k)
403             ENDDO  #ifdef NONLIN_FRSURF
404            ENDDO               ddRloc = ddRloc + surfPhiFac*etaH(i,j,bi,bj)
405          ELSE  #endif
406            ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)               phiHydC(i,j) = ddRloc*recip_drF(k)*2. _d 0
407       &                  -((rF( K )/atm_po)**atm_kappa) )       &          *ddPIm*alphaRho(i,j)
408            ddPIp=atm_cp*( ((rF( K )/atm_po)**atm_kappa)             ELSE
409       &                  -((rC( K )/atm_po)**atm_kappa) )               phiHydC(i,j) = phiHydF(i,j) +ddPIm*alphaRho(i,j)
410            DO j=jMin,jMax             ENDIF
411             DO i=iMin,iMax               phiHydF(i,j) = phiHydC(i,j) +ddPIp*alphaRho(i,j)
              phiHyd(i,j,K) = phiHyd(i,j,K-1)  
      &         +ddPIm*_hFacC(I,J,K-1,bi,bj)  
      &               *(tFld(I,J,K-1,bi,bj)-tRef(K-1))  
      &         +ddPIp*_hFacC(I,J, K ,bi,bj)  
      &               *(tFld(I,J, K ,bi,bj)-tRef( K ))  
            ENDDO  
           ENDDO  
         ENDIF  
 C end: Finite Volume Form, with hFac, linear in P by Half level  --  
 C-----------------------------------------------------------------------  
   
       ELSEIF (Integr_GeoPot.EQ.2) THEN  
 C  --  Finite Difference Form, with hFac, Tracer Lev. = middle  --  
 C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  
 C  Finite Difference formulation consistent with Partial Cell,  
 C    case Tracer level at the middle of InterFace_W  
 C    linear between 2 Tracer levels ; conserve energy in the Interior  
 C---------  
         Kp1 = min(Nr,K+1)  
         IF (K.EQ.1) THEN  
           ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa)  
      &                  -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0  
           ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)  
      &                  -((rC(Kp1)/atm_po)**atm_kappa) )    
           DO j=jMin,jMax  
            DO i=iMin,iMax  
              phiHyd(i,j,K) =  
      &        ( ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half)  
      &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) )  
      &               *(tFld(i,j, K ,bi,bj)-tRef( K ))  
      &               * maskC(i,j, K ,bi,bj)  
            ENDDO  
           ENDDO  
         ELSE  
           ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)  
      &                  -((rC( K )/atm_po)**atm_kappa) )  
           ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)  
      &                  -((rC(Kp1)/atm_po)**atm_kappa) )  
           DO j=jMin,jMax  
            DO i=iMin,iMax  
              phiHyd(i,j,K) = phiHyd(i,j,K-1)  
      &        + ddPIm*0.5  
      &               *(tFld(i,j,K-1,bi,bj)-tRef(K-1))  
      &               * maskC(i,j,K-1,bi,bj)  
      &        +(ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half)  
      &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) )  
      &               *(tFld(i,j, K ,bi,bj)-tRef( K ))  
      &               * maskC(i,j, K ,bi,bj)  
            ENDDO  
412            ENDDO            ENDDO
413          ENDIF           ENDDO
414  C end: Finite Difference Form, with hFac, Tracer Lev. = middle  --  C end: Finite Volume Form, with Part-Cell Topo, linear in P by Half level
415  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
416    
417        ELSEIF (Integr_GeoPot.EQ.3) THEN         ELSEIF ( integr_GeoPot.EQ.2
418  C  --  Finite Difference Form, with hFac, Interface_W = middle  --       &     .OR. integr_GeoPot.EQ.3 ) THEN
419    C  --  Finite Difference Form, with Part-Cell Topo,
420    C       works with Interface_W  at the middle between 2.Tracer_Level
421    C        and  with Tracer_Level at the middle between 2.Interface_W.
422  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
423  C  Finite Difference formulation consistent with Partial Cell,  C  Finite Difference formulation consistent with Partial Cell,
424  C   Valid & accurate if Interface_W at middle between tracer levels  C   Valid & accurate if Interface_W at middle between tracer levels
425  C   linear in p between 2 Tracer levels ; conserve energy in the Interior  C   linear in p between 2 Tracer levels ; conserve energy in the Interior
426  C---------  C---------
427          Kp1 = min(Nr,K+1)           IF (k.EQ.1) THEN
428          IF (K.EQ.1) THEN             ddPIm=atm_Cp*( ((rF( k )/atm_Po)**atm_kappa)
429            ratioRm=0.5*drF(K)/(rF(k)-rC(K))       &                   -((rC( k )/atm_Po)**atm_kappa) )
430            ratioRp=drF(K)*recip_drC(Kp1)           ELSE
431            ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa)             ddPIm=atm_Cp*( ((rC(k-1)/atm_Po)**atm_kappa)
432       &                  -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0       &                   -((rC( k )/atm_Po)**atm_kappa) )*half
433            ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)           ENDIF
434       &                  -((rC(Kp1)/atm_po)**atm_kappa) )             IF (k.EQ.Nr) THEN
435            DO j=jMin,jMax             ddPIp=atm_Cp*( ((rC( k )/atm_Po)**atm_kappa)
436             DO i=iMin,iMax       &                   -((rF(k+1)/atm_Po)**atm_kappa) )
437               phiHyd(i,j,K) =           ELSE
438       &        ( ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half)             ddPIp=atm_Cp*( ((rC( k )/atm_Po)**atm_kappa)
439       &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp     -half) )       &                   -((rC(k+1)/atm_Po)**atm_kappa) )*half
440       &               *(tFld(i,j, K ,bi,bj)-tRef( K ))           ENDIF
441       &               * maskC(i,j, K ,bi,bj)           rec_dRm = one/(rF(k)-rC(k))
442             ENDDO           rec_dRp = one/(rC(k)-rF(k+1))
443            ENDDO           DO j=jMin,jMax
444          ELSE            DO i=iMin,iMax
445            ratioRm=drF(K)*recip_drC(K)             IF (k.EQ.ksurfC(i,j,bi,bj)) THEN
446            ratioRp=drF(K)*recip_drC(Kp1)               ddRloc = Ro_surf(i,j,bi,bj)-rC(k)
447            ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)  #ifdef NONLIN_FRSURF
448       &                  -((rC( K )/atm_po)**atm_kappa) )               ddRloc = ddRloc + surfPhiFac*etaH(i,j,bi,bj)
449            ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)  #endif
450       &                  -((rC(Kp1)/atm_po)**atm_kappa) )               phiHydC(i,j) =( MAX(zero,ddRloc)*rec_dRm*ddPIm
451            DO j=jMin,jMax       &                      +MIN(zero,ddRloc)*rec_dRp*ddPIp )
452             DO i=iMin,iMax       &                    *alphaRho(i,j)
453               phiHyd(i,j,K) = phiHyd(i,j,K-1)             ELSE
454       &        + ddPIm*0.5               phiHydC(i,j) = phiHydF(i,j) +ddPIm*alphaRho(i,j)
455       &               *(tFld(i,j,K-1,bi,bj)-tRef(K-1))             ENDIF
456       &               * maskC(i,j,K-1,bi,bj)               phiHydF(i,j) = phiHydC(i,j) +ddPIp*alphaRho(i,j)
      &        +(ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half)  
      &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp     -half) )  
      &               *(tFld(i,j, K ,bi,bj)-tRef( K ))  
      &               * maskC(i,j, K ,bi,bj)  
            ENDDO  
457            ENDDO            ENDDO
458          ENDIF           ENDDO
459  C end: Finite Difference Form, with hFac, Interface_W = middle  --  C end: Finite Difference Form, with Part-Cell Topo
460  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
461    
462        ELSE         ELSE
463          STOP 'CALC_PHI_HYD: Bad Integr_GeoPot option !'           STOP 'CALC_PHI_HYD: Bad integr_GeoPot option !'
464        ENDIF         ENDIF
465    
466  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
467        ELSE        ELSE
468          STOP 'CALC_PHI_HYD: We should never reach this point!'          STOP 'CALC_PHI_HYD: Bad value of buoyancyRelation !'
469          ENDIF
470    
471    C---   Diagnose Phi at boundary r=R_low :
472    C       = Ocean bottom pressure (Ocean, Z-coord.)
473    C       = Sea-surface height    (Ocean, P-coord.)
474    C       = Top atmosphere height (Atmos, P-coord.)
475          IF (useDiagPhiRlow) THEN
476            CALL DIAGS_PHI_RLOW(
477         I                      k, bi, bj, iMin,iMax, jMin,jMax,
478         I                      phiHydF, phiHydC, alphaRho, tFld, sFld,
479         I                      myTime, myIter, myThid)  
480          ENDIF
481    
482    C---   Diagnose Full Hydrostatic Potential at cell center level
483            CALL DIAGS_PHI_HYD(
484         I                      k, bi, bj, iMin,iMax, jMin,jMax,
485         I                      phiHydC,
486         I                      myTime, myIter, myThid)
487    
488          IF (momPressureForcing) THEN
489            iMnLoc = MAX(1-Olx+1,iMin)
490            jMnLoc = MAX(1-Oly+1,jMin)
491            CALL CALC_GRAD_PHI_HYD(
492         I                         k, bi, bj, iMnLoc,iMax, jMnLoc,jMax,
493         I                         phiHydC, alphaRho, tFld, sFld,
494         O                         dPhiHydX, dPhiHydY,
495         I                         myTime, myIter, myThid)  
496        ENDIF        ENDIF
497    
498  #endif /* INCLUDE_PHIHYD_CALCULATION_CODE */  #endif /* INCLUDE_PHIHYD_CALCULATION_CODE */
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