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revision 1.12 by heimbach, Sun Mar 25 22:33:52 2001 UTC revision 1.21 by mlosch, Wed Sep 25 19:36:50 2002 UTC
# Line 3  C $Name$ Line 3  C $Name$
3    
4  #include "CPP_OPTIONS.h"  #include "CPP_OPTIONS.h"
5    
6    CBOP
7    C     !ROUTINE: CALC_PHI_HYD
8    C     !INTERFACE:
9        SUBROUTINE CALC_PHI_HYD(        SUBROUTINE CALC_PHI_HYD(
10       I                         bi, bj, iMin, iMax, jMin, jMax, K,       I                         bi, bj, iMin, iMax, jMin, jMax, K,
11       I                         theta, salt,       I                         tFld, sFld,
12       U                         phiHyd,       U                         phiHyd,
13       I                         myThid)       I                         myThid)
14  C     /==========================================================\  C     !DESCRIPTION: \bv
15    C     *==========================================================*
16  C     | SUBROUTINE CALC_PHI_HYD                                  |  C     | SUBROUTINE CALC_PHI_HYD                                  |
17  C     | o Integrate the hydrostatic relation to find the Hydros. |  C     | o Integrate the hydrostatic relation to find the Hydros. |
18    C     *==========================================================*
19  C     |    Potential (ocean: Pressure/rho ; atmos = geopotential)|  C     |    Potential (ocean: Pressure/rho ; atmos = geopotential)|
20  C     | On entry:                                                |  C     | On entry:                                                |
21  C     |   theta,salt    are the current thermodynamics quantities|  C     |   tFld,sFld     are the current thermodynamics quantities|
22  C     |                 (unchanged on exit)                      |  C     |                 (unchanged on exit)                      |
23  C     |   phiHyd(i,j,1:k-1) is the hydrostatic Potential         |  C     |   phiHyd(i,j,1:k-1) is the hydrostatic Potential         |
24  C     |                 at cell centers (tracer points)          |  C     |                 at cell centers (tracer points)          |
25  C     |                 - 1:k-1 layers are valid                 |  C     |                 - 1:k-1 layers are valid                 |
26  C     |                 - k:Nr layers are invalid                |  C     |                 - k:Nr layers are invalid                |
27  C     |   phiHyd(i,j,k) is the hydrostatic Potential             |  C     |   phiHyd(i,j,k) is the hydrostatic Potential             |
28  C     |                 at cell the interface k (w point above)  |  C     |  (ocean only_^) at cell the interface k (w point above)  |
29  C     | On exit:                                                 |  C     | On exit:                                                 |
30  C     |   phiHyd(i,j,1:k) is the hydrostatic Potential           |  C     |   phiHyd(i,j,1:k) is the hydrostatic Potential           |
31  C     |                 at cell centers (tracer points)          |  C     |                 at cell centers (tracer points)          |
32  C     |                 - 1:k layers are valid                   |  C     |                 - 1:k layers are valid                   |
33  C     |                 - k+1:Nr layers are invalid              |  C     |                 - k+1:Nr layers are invalid              |
34  C     |   phiHyd(i,j,k+1) is the hydrostatic Potential (P/rho)   |  C     |   phiHyd(i,j,k+1) is the hydrostatic Potential (P/rho)   |
35  C     |                 at cell the interface k+1 (w point below)|  C     |  (ocean only-^) at cell the interface k+1 (w point below)|
36  C     |                                                          |  C     | Atmosphere:                                              |
37  C     \==========================================================/  C     |   Integr_GeoPot allows to select one integration method  |
38    C     |    (see the list below)                                  |
39    C     *==========================================================*
40    C     \ev
41    C     !USES:
42        IMPLICIT NONE        IMPLICIT NONE
43  C     == Global variables ==  C     == Global variables ==
44  #include "SIZE.h"  #include "SIZE.h"
45  #include "GRID.h"  #include "GRID.h"
46  #include "EEPARAMS.h"  #include "EEPARAMS.h"
47  #include "PARAMS.h"  #include "PARAMS.h"
48    #include "FFIELDS.h"
49    #ifdef ALLOW_AUTODIFF_TAMC
50    #include "tamc.h"
51    #include "tamc_keys.h"
52    #endif /* ALLOW_AUTODIFF_TAMC */
53    #include "SURFACE.h"
54    #include "DYNVARS.h"
55    
56    C     !INPUT/OUTPUT PARAMETERS:
57  C     == Routine arguments ==  C     == Routine arguments ==
58        INTEGER bi,bj,iMin,iMax,jMin,jMax,K        INTEGER bi,bj,iMin,iMax,jMin,jMax,K
59        _RL theta(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)        _RL tFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
60        _RL salt(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)        _RL sFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
61        _RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)        _RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
62        INTEGER myThid        INTEGER myThid
63          
64  #ifdef INCLUDE_PHIHYD_CALCULATION_CODE  #ifdef INCLUDE_PHIHYD_CALCULATION_CODE
65    
66    C     !LOCAL VARIABLES:
67  C     == Local variables ==  C     == Local variables ==
68        INTEGER i,j        INTEGER i,j, Kp1
69          _RL zero, one, half
70        _RL alphaRho(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL alphaRho(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71        _RL dRloc,dRlocKp1        _RL dRloc,dRlocKp1,locAlpha
72        _RL ddRm1, ddRp1, ddRm, ddRp        _RL ddPI, ddPIm, ddPIp, ratioRp, ratioRm
73        _RL atm_cp, atm_kappa, atm_po  CEOP
74    
75          zero = 0. _d 0
76          one  = 1. _d 0
77          half = .5 _d 0
78    
79    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
80    C  Atmosphere:  
81    C Integr_GeoPot => select one option for the integration of the Geopotential:
82    C   = 0 : Energy Conserving Form, No hFac ;
83    C   = 1 : Finite Volume Form, with hFac, linear in P by Half level;
84    C   =2,3: Finite Difference Form, with hFac, linear in P between 2 Tracer levels
85    C     2 : case Tracer level at the middle of InterFace_W;
86    C     3 : case InterFace_W  at the middle of Tracer levels;
87    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
88    
89    #ifdef ALLOW_AUTODIFF_TAMC
90              act1 = bi - myBxLo(myThid)
91              max1 = myBxHi(myThid) - myBxLo(myThid) + 1
92    
93              act2 = bj - myByLo(myThid)
94              max2 = myByHi(myThid) - myByLo(myThid) + 1
95    
96              act3 = myThid - 1
97              max3 = nTx*nTy
98    
99              act4 = ikey_dynamics - 1
100    
101              ikey = (act1 + 1) + act2*max1
102         &                      + act3*max1*max2
103         &                      + act4*max1*max2*max3
104    #endif /* ALLOW_AUTODIFF_TAMC */
105    
106        IF ( buoyancyRelation .eq. 'OCEANIC' ) THEN        IF ( buoyancyRelation .eq. 'OCEANIC' ) THEN
107  C       This is the hydrostatic pressure calculation for the Ocean  C       This is the hydrostatic pressure calculation for the Ocean
# Line 70  C       P(z=eta) = P(atmospheric_loading Line 121  C       P(z=eta) = P(atmospheric_loading
121          IF (k.EQ.1) THEN          IF (k.EQ.1) THEN
122            DO j=jMin,jMax            DO j=jMin,jMax
123              DO i=iMin,iMax              DO i=iMin,iMax
124  C             *NOTE* The loading should go here but has not been implemented yet  #ifdef ATMOSPHERIC_LOADING
125                phiHyd(i,j,k)=0.                phiHyd(i,j,k)=pload(i,j,bi,bj)*recip_rhoConst
126    #else
127                  phiHyd(i,j,k)=0. _d 0
128    #endif
129              ENDDO              ENDDO
130            ENDDO            ENDDO
131          ENDIF          ENDIF
132    
133  C       Calculate density  C       Calculate density
134          CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k, eosType,  #ifdef ALLOW_AUTODIFF_TAMC
135       &                 theta, salt,              kkey = (ikey-1)*Nr + k
136    CADJ STORE tFld(:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
137    CADJ STORE sFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
138    #endif /* ALLOW_AUTODIFF_TAMC */
139            CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k,
140         &                 tFld, sFld,
141       &                 alphaRho, myThid)       &                 alphaRho, myThid)
142    
143  C       Hydrostatic pressure at cell centers  C       Hydrostatic pressure at cell centers
144          DO j=jMin,jMax          DO j=jMin,jMax
145            DO i=iMin,iMax            DO i=iMin,iMax
146  #ifdef      ALLOW_AUTODIFF_TAMC  #ifdef      ALLOW_AUTODIFF_TAMC
147  c           Is this directive correct or even necessary in this new code?  c           Patrick, is this directive correct or even necessary in
148    c           this new code?
149    c           Yes, because of phiHyd(i,j,k+1)=phiHyd(i,j,k)+...
150    c           within the k-loop.
151  CADJ GENERAL  CADJ GENERAL
152  #endif      /* ALLOW_AUTODIFF_TAMC */  #endif      /* ALLOW_AUTODIFF_TAMC */
153    
154  C---------- This discretization is the "finite volume" form  CmlC---------- This discretization is the "finite volume" form
155  C           which has not been used to date since it does not  CmlC           which has not been used to date since it does not
156  C           conserve KE+PE exactly even though it is more natural  CmlC           conserve KE+PE exactly even though it is more natural
157  C  CmlC
158  c           IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+  Cml          IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN
159  c    &              drF(K)*gravity*alphaRho(i,j)*recip_rhoConst  Cml           phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)
160  c           phiHyd(i,j,k)=phiHyd(i,j,k)+  Cml     &          + hFacC(i,j,k,bi,bj)
161  c    &          0.5*drF(K)*gravity*alphaRho(i,j)*recip_rhoConst  Cml     &            *drF(K)*gravity*alphaRho(i,j)*recip_rhoConst
162  C-----------------------------------------------------------------------  Cml     &          + gravity*etaN(i,j,bi,bj)
163    Cml          ENDIF
164    Cml           IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+
165    Cml     &         drF(K)*gravity*alphaRho(i,j)*recip_rhoConst
166    Cml           phiHyd(i,j,k)=phiHyd(i,j,k)+
167    Cml     &          0.5*drF(K)*gravity*alphaRho(i,j)*recip_rhoConst
168    CmlC-----------------------------------------------------------------------
169    
170  C---------- This discretization is the "energy conserving" form  C---------- This discretization is the "energy conserving" form
171  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
172  C  C
173                
174              phiHyd(i,j,k)=phiHyd(i,j,k)+              phiHyd(i,j,k)=phiHyd(i,j,k)+
175       &          0.5*dRloc*gravity*alphaRho(i,j)*recip_rhoConst       &          0.5*dRloc*gravity*alphaRho(i,j)*recip_rhoConst
176              IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+              IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+
177       &          0.5*dRlocKp1*gravity*alphaRho(i,j)*recip_rhoConst       &          0.5*dRlocKp1*gravity*alphaRho(i,j)*recip_rhoConst
178  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
179    
180    C---------- Compute bottom pressure deviation from gravity*rho0*H
181    C           This has to be done starting from phiHyd at the current
182    C           tracer point and .5 of the cell's thickness has to be
183    C           substracted from hFacC
184                IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN
185                 phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)
186         &              + (hFacC(i,j,k,bi,bj)-.5)*drF(K)
187         &                   *gravity*alphaRho(i,j)*recip_rhoConst
188         &              + gravity*etaN(i,j,bi,bj)
189                ENDIF
190    C-----------------------------------------------------------------------
191    
192            ENDDO            ENDDO
193          ENDDO          ENDDO
194                    
195          ELSEIF ( buoyancyRelation .eq. 'OCEANICP' ) THEN
196    C       This is the hydrostatic pressure calculation for the Ocean
197    C       which uses the FIND_RHO() routine to calculate density
198    C       before integrating g*rho over the current layer/interface
199    #ifdef      ALLOW_AUTODIFF_TAMC
200    CADJ GENERAL
201    #endif      /* ALLOW_AUTODIFF_TAMC */
202    
203            dRloc=drC(k)
204            IF (k.EQ.1) dRloc=drF(1)
205            IF (k.EQ.Nr) THEN
206              dRlocKp1=0.
207            ELSE
208              dRlocKp1=drC(k+1)
209            ENDIF
210    
211            IF (k.EQ.1) THEN
212              DO j=jMin,jMax
213                DO i=iMin,iMax
214                  phiHyd(i,j,k)=0.
215                  phiHyd(i,j,k)=pload(i,j,bi,bj)
216                ENDDO
217              ENDDO
218            ENDIF
219    
220    C       Calculate density
221    #ifdef ALLOW_AUTODIFF_TAMC
222                kkey = (ikey-1)*Nr + k
223    CADJ STORE tFld(:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
224    CADJ STORE sFld (:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
225    #endif /* ALLOW_AUTODIFF_TAMC */
226            CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, k,
227         &                 tFld, sFld,
228         &                 alphaRho, myThid)
229    
230    C       Hydrostatic pressure at cell centers
231            DO j=jMin,jMax
232              DO i=iMin,iMax
233                locAlpha=alphaRho(i,j)+rhoConst
234                IF (locAlpha.NE.0.) locAlpha=maskC(i,j,k,bi,bj)/locAlpha
235    
236    CmlC---------- This discretization is the "finite volume" form
237    CmlC           which has not been used to date since it does not
238    CmlC           conserve KE+PE exactly even though it is more natural
239    CmlC
240    Cml            IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN
241    Cml             phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)
242    Cml     &          + hFacC(i,j,k,bi,bj)*drF(K)*locAlpha
243    Cml     &          + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj)
244    Cml            ENDIF
245    Cml            IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+
246    Cml     &           drF(K)*locAlpha
247    Cml            phiHyd(i,j,k)=phiHyd(i,j,k)+
248    Cml     &           0.5*drF(K)*locAlpha
249    CmlC-----------------------------------------------------------------------
250    
251    C---------- This discretization is the "energy conserving" form
252    C           which has been used since at least Adcroft et al., MWR 1997
253    C
254    
255                phiHyd(i,j,k)=phiHyd(i,j,k)+
256         &          0.5*dRloc*locAlpha
257                IF (k.LT.Nr) phiHyd(i,j,k+1)=phiHyd(i,j,k)+
258         &          0.5*dRlocKp1*locAlpha
259    
260    C-----------------------------------------------------------------------
261    
262    C---------- Compute gravity*(sea surface elevation) first
263    C           This has to be done starting from phiHyd at the current
264    C           tracer point and .5 of the cell's thickness has to be
265    C           substracted from hFacC
266                IF ( K .EQ. kLowC(i,j,bi,bj) ) THEN
267                 phiHydLow(i,j,bi,bj) = phiHyd(i,j,k)
268         &              + (hFacC(i,j,k,bi,bj)-0.5)*drF(k)*locAlpha
269         &              + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj)
270                ENDIF
271    C-----------------------------------------------------------------------
272    
273              ENDDO
274            ENDDO
275    
276        ELSEIF ( buoyancyRelation .eq. 'ATMOSPHERIC' ) THEN        ELSEIF ( buoyancyRelation .eq. 'ATMOSPHERIC' ) THEN
277    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
278  C       This is the hydrostatic geopotential calculation for the Atmosphere  C       This is the hydrostatic geopotential calculation for the Atmosphere
279  C       The ideal gas law is used implicitly here rather than calculating  C       The ideal gas law is used implicitly here rather than calculating
280  C       the specific volume, analogous to the oceanic case.  C       the specific volume, analogous to the oceanic case.
281    
282  C       Integrate d Phi / d pi  C       Integrate d Phi / d pi
283    
284  C *NOTE* These constants should be in the data file and PARAMS.h        IF (Integr_GeoPot.EQ.0) THEN
285          atm_cp=1004. _d 0  C  --  Energy Conserving Form, No hFac  --
286          atm_kappa=2. _d 0/7. _d 0  C------------ The integration for the first level phi(k=1) is the same
287          atm_po=1. _d 5  C             for both the "finite volume" and energy conserving methods.
288    Ci    *NOTE* o Working with geopotential Anomaly, the geopotential boundary
289    C             condition is simply Phi-prime(Ro_surf)=0.
290    C           o convention ddPI > 0 (same as drF & drC)
291    C-----------------------------------------------------------------------
292          IF (K.EQ.1) THEN          IF (K.EQ.1) THEN
293            ddRp1=atm_cp*( ((rC(K)/atm_po)**atm_kappa)            ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa)
294       &                  -((rF(K)/atm_po)**atm_kappa) )       &                  -((rC(K)/atm_po)**atm_kappa) )
295            DO j=jMin,jMax            DO j=jMin,jMax
296              DO i=iMin,iMax             DO i=iMin,iMax
297                ddRp=ddRp1               phiHyd(i,j,K)=
298                IF (hFacC(I,J, K ,bi,bj).EQ.0.) ddRp=0.       &          ddPIp*maskC(i,j,K,bi,bj)
299  C------------ The integration for the first level phi(k=1) is the       &               *(tFld(I,J,K,bi,bj)-tRef(K))
 C             same for both the "finite volume" and energy conserving  
 C             methods.  
 C             *NOTE* The geopotential boundary condition should go  
 C                    here but has not been implemented yet  
               phiHyd(i,j,K)=0.  
      &          -ddRp*(theta(I,J,K,bi,bj)-tRef(K))  
 C-----------------------------------------------------------------------  
300             ENDDO             ENDDO
301            ENDDO            ENDDO
302          ELSE          ELSE
303    C-------- This discretization is the energy conserving form
304  C-------- This discretization is the "finite volume" form which            ddPI=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)
305  C         integrates the hydrostatic equation of each half/sub-layer.       &                 -((rC( K )/atm_po)**atm_kappa) )*0.5
306  C         This seems most natural and could easily allow for lopped cells            DO j=jMin,jMax
307  C         by replacing rF(K) with the height of the surface (not implemented).             DO i=iMin,iMax
308  C         in the lower layers (e.g. at k=1).                phiHyd(i,j,K)=phiHyd(i,j,K-1)
309  C       &           +ddPI*maskC(i,j,K-1,bi,bj)
310  c         ddRm1=atm_cp*( ((rF( K )/atm_po)**atm_kappa)       &                *(tFld(I,J,K-1,bi,bj)-tRef(K-1))
311  c    &                  -((rC(K-1)/atm_po)**atm_kappa) )       &           +ddPI*maskC(i,j, K ,bi,bj)
312  c         ddRp1=atm_cp*( ((rC( K )/atm_po)**atm_kappa)       &                *(tFld(I,J, K ,bi,bj)-tRef( K ))
313  c    &                  -((rF( K )/atm_po)**atm_kappa) )  C             Old code (atmos-exact) looked like this
314    Cold          phiHyd(i,j,K)=phiHyd(i,j,K-1) - ddPI*
315    Cold &      (tFld(I,J,K-1,bi,bj)+tFld(I,J,K,bi,bj)-2.*tRef(K))
316               ENDDO
317              ENDDO
318            ENDIF
319    C end: Energy Conserving Form, No hFac  --
320  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
321    
322          ELSEIF (Integr_GeoPot.EQ.1) THEN
323    C  --  Finite Volume Form, with hFac, linear in P by Half level  --
324    C---------
325    C  Finite Volume formulation consistent with Partial Cell, linear in p by piece
326    C   Note: a true Finite Volume form should be linear between 2 Interf_W :
327    C     phi_C = (phi_W_k+ phi_W_k+1)/2 ; but not accurate in Stratosphere (low p)
328    C   also: if Interface_W at the middle between tracer levels, this form
329    C     is close to the Energy Cons. form in the Interior, except for the
330    C     non-linearity in PI(p)
331    C---------
332            IF (K.EQ.1) THEN
333              ddPIp=atm_cp*( ((rF(K)/atm_po)**atm_kappa)
334         &                  -((rC(K)/atm_po)**atm_kappa) )
335              DO j=jMin,jMax
336               DO i=iMin,iMax
337                 phiHyd(i,j,K) =
338         &          ddPIp*_hFacC(I,J, K ,bi,bj)
339         &               *(tFld(I,J, K ,bi,bj)-tRef( K ))
340               ENDDO
341              ENDDO
342            ELSE
343              ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)
344         &                  -((rF( K )/atm_po)**atm_kappa) )
345              ddPIp=atm_cp*( ((rF( K )/atm_po)**atm_kappa)
346         &                  -((rC( K )/atm_po)**atm_kappa) )
347              DO j=jMin,jMax
348               DO i=iMin,iMax
349                 phiHyd(i,j,K) = phiHyd(i,j,K-1)
350         &         +ddPIm*_hFacC(I,J,K-1,bi,bj)
351         &               *(tFld(I,J,K-1,bi,bj)-tRef(K-1))
352         &         +ddPIp*_hFacC(I,J, K ,bi,bj)
353         &               *(tFld(I,J, K ,bi,bj)-tRef( K ))
354               ENDDO
355              ENDDO
356            ENDIF
357    C end: Finite Volume Form, with hFac, linear in P by Half level  --
358    C-----------------------------------------------------------------------
359    
360  C-------- This discretization is the energy conserving form        ELSEIF (Integr_GeoPot.EQ.2) THEN
361            ddRp1=atm_cp*( ((rC( K )/atm_po)**atm_kappa)  C  --  Finite Difference Form, with hFac, Tracer Lev. = middle  --
362       &                  -((rC(K-1)/atm_po)**atm_kappa) )*0.5  C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
363            ddRm1=ddRp1  C  Finite Difference formulation consistent with Partial Cell,
364    C    case Tracer level at the middle of InterFace_W
365    C    linear between 2 Tracer levels ; conserve energy in the Interior
366    C---------
367            Kp1 = min(Nr,K+1)
368            IF (K.EQ.1) THEN
369              ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa)
370         &                  -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0
371              ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)
372         &                  -((rC(Kp1)/atm_po)**atm_kappa) )  
373              DO j=jMin,jMax
374               DO i=iMin,iMax
375                 phiHyd(i,j,K) =
376         &        ( ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half)
377         &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) )
378         &               *(tFld(i,j, K ,bi,bj)-tRef( K ))
379         &               * maskC(i,j, K ,bi,bj)
380               ENDDO
381              ENDDO
382            ELSE
383              ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)
384         &                  -((rC( K )/atm_po)**atm_kappa) )
385              ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)
386         &                  -((rC(Kp1)/atm_po)**atm_kappa) )
387              DO j=jMin,jMax
388               DO i=iMin,iMax
389                 phiHyd(i,j,K) = phiHyd(i,j,K-1)
390         &        + ddPIm*0.5
391         &               *(tFld(i,j,K-1,bi,bj)-tRef(K-1))
392         &               * maskC(i,j,K-1,bi,bj)
393         &        +(ddPIm*max(zero, _hFacC(i,j,K,bi,bj)-half)
394         &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)-half) )
395         &               *(tFld(i,j, K ,bi,bj)-tRef( K ))
396         &               * maskC(i,j, K ,bi,bj)
397               ENDDO
398              ENDDO
399            ENDIF
400    C end: Finite Difference Form, with hFac, Tracer Lev. = middle  --
401  C-----------------------------------------------------------------------  C-----------------------------------------------------------------------
402    
403          ELSEIF (Integr_GeoPot.EQ.3) THEN
404    C  --  Finite Difference Form, with hFac, Interface_W = middle  --
405    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
406    C  Finite Difference formulation consistent with Partial Cell,
407    C   Valid & accurate if Interface_W at middle between tracer levels
408    C   linear in p between 2 Tracer levels ; conserve energy in the Interior
409    C---------
410            Kp1 = min(Nr,K+1)
411            IF (K.EQ.1) THEN
412              ratioRm=0.5*drF(K)/(rF(k)-rC(K))
413              ratioRp=drF(K)*recip_drC(Kp1)
414              ddPIm=atm_cp*( ((rF( K )/atm_po)**atm_kappa)
415         &                  -((rC( K )/atm_po)**atm_kappa) ) * 2. _d 0
416              ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)
417         &                  -((rC(Kp1)/atm_po)**atm_kappa) )  
418            DO j=jMin,jMax            DO j=jMin,jMax
419              DO i=iMin,iMax             DO i=iMin,iMax
420                ddRp=ddRp1               phiHyd(i,j,K) =
421                ddRm=ddRm1       &        ( ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half)
422                IF (hFacC(I,J, K ,bi,bj).EQ.0.) ddRp=0.       &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp     -half) )
423                IF (hFacC(I,J,K-1,bi,bj).EQ.0.) ddRm=0.       &               *(tFld(i,j, K ,bi,bj)-tRef( K ))
424                phiHyd(i,j,K)=phiHyd(i,j,K-1)       &               * maskC(i,j, K ,bi,bj)
425       &           -( ddRm*(theta(I,J,K-1,bi,bj)-tRef(K-1))             ENDDO
426       &             +ddRp*(theta(I,J, K ,bi,bj)-tRef( K )) )            ENDDO
427  C             Old code (atmos-exact) looked like this          ELSE
428  Cold          phiHyd(i,j,K)=phiHyd(i,j,K-1) - ddRm1*            ratioRm=drF(K)*recip_drC(K)
429  Cold &      (theta(I,J,K-1,bi,bj)+theta(I,J,K,bi,bj)-2.*tRef(K))            ratioRp=drF(K)*recip_drC(Kp1)
430              ENDDO            ddPIm=atm_cp*( ((rC(K-1)/atm_po)**atm_kappa)
431         &                  -((rC( K )/atm_po)**atm_kappa) )
432              ddPIp=atm_cp*( ((rC( K )/atm_po)**atm_kappa)
433         &                  -((rC(Kp1)/atm_po)**atm_kappa) )
434              DO j=jMin,jMax
435               DO i=iMin,iMax
436                 phiHyd(i,j,K) = phiHyd(i,j,K-1)
437         &        + ddPIm*0.5
438         &               *(tFld(i,j,K-1,bi,bj)-tRef(K-1))
439         &               * maskC(i,j,K-1,bi,bj)
440         &        +(ddPIm*max(zero,(_hFacC(i,j,K,bi,bj)-one)*ratioRm+half)
441         &         +ddPIp*min(zero, _hFacC(i,j,K,bi,bj)*ratioRp     -half) )
442         &               *(tFld(i,j, K ,bi,bj)-tRef( K ))
443         &               * maskC(i,j, K ,bi,bj)
444               ENDDO
445            ENDDO            ENDDO
446          ENDIF          ENDIF
447    C end: Finite Difference Form, with hFac, Interface_W = middle  --
448    C-----------------------------------------------------------------------
449    
450          ELSE
451            STOP 'CALC_PHI_HYD: Bad Integr_GeoPot option !'
452          ENDIF
453    
454    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
455        ELSE        ELSE
456          STOP 'CALC_PHI_HYD: We should never reach this point!'          STOP 'CALC_PHI_HYD: We should never reach this point!'
457        ENDIF        ENDIF
458    
459  #endif  #endif /* INCLUDE_PHIHYD_CALCULATION_CODE */
460    
461        RETURN        RETURN
462        END        END
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