/[MITgcm]/MITgcm/pkg/seaice/seaice_calc_strainrates.F
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revision 1.14 by mlosch, Wed Jun 24 08:23:38 2009 UTC revision 1.23 by mlosch, Thu Jun 8 15:10:05 2017 UTC
# Line 2  C $Header$ Line 2  C $Header$
2  C $Name$  C $Name$
3    
4  #include "SEAICE_OPTIONS.h"  #include "SEAICE_OPTIONS.h"
5    #ifdef ALLOW_OBCS
6    # include "OBCS_OPTIONS.h"
7    #else
8    # define OBCS_UVICE_OLD
9    #endif
10    #ifdef ALLOW_AUTODIFF
11    # include "AUTODIFF_OPTIONS.h"
12    #endif
13    
14  CStartOfInterface  CBOP
15    C     !ROUTINE: SEAICE_CALC_STRAINRATES
16    C     !INTERFACE:
17        SUBROUTINE SEAICE_CALC_STRAINRATES(        SUBROUTINE SEAICE_CALC_STRAINRATES(
18       I     uFld, vFld,       I     uFld, vFld,
19       O     e11Loc, e22Loc, e12Loc,       O     e11Loc, e22Loc, e12Loc,
20       I     iStep, myTime, myIter, myThid )       I     iStep, myTime, myIter, myThid )
21  C     /==========================================================\  
22  C     | SUBROUTINE  SEAICE_CALC_STRAINRATES                      |  C     !DESCRIPTION: \bv
23  C     | o compute strain rates from ice velocities               |  C     *==========================================================*
24  C     |==========================================================|  C     | SUBROUTINE  SEAICE_CALC_STRAINRATES
25  C     | written by Martin Losch, Apr 2007                        |  C     | o compute strain rates from ice velocities
26  C     \==========================================================/  C     *==========================================================*
27    C     | written by Martin Losch, Apr 2007
28    C     *==========================================================*
29    C     \ev
30    
31    C     !USES:
32        IMPLICIT NONE        IMPLICIT NONE
33    
34  C     === Global variables ===  C     === Global variables ===
# Line 21  C     === Global variables === Line 36  C     === Global variables ===
36  #include "EEPARAMS.h"  #include "EEPARAMS.h"
37  #include "PARAMS.h"  #include "PARAMS.h"
38  #include "GRID.h"  #include "GRID.h"
39    #include "SEAICE_SIZE.h"
40  #include "SEAICE_PARAMS.h"  #include "SEAICE_PARAMS.h"
41  #include "SEAICE.h"  #include "SEAICE.h"
42    
# Line 28  C     === Global variables === Line 44  C     === Global variables ===
44  # include "tamc.h"  # include "tamc.h"
45  #endif  #endif
46    
47    C     !INPUT/OUTPUT PARAMETERS:
48  C     === Routine arguments ===  C     === Routine arguments ===
49    C     uFld   :: ice velocity, u-component
50    C     vFld   :: ice velocity, v-component
51    C     e11Loc :: strain rate tensor, component 1,1
52    C     e22Loc :: strain rate tensor, component 2,2
53    C     e12Loc :: strain rate tensor, component 1,2
54  C     iStep  :: Sub-time-step number  C     iStep  :: Sub-time-step number
55  C     myTime :: Simulation time  C     myTime :: Simulation time
56  C     myIter :: Simulation timestep number  C     myIter :: Simulation timestep number
57  C     myThid :: My Thread Id. number  C     myThid :: My Thread Id. number
58          _RL uFld   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
59          _RL vFld   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
60          _RL e11Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
61          _RL e22Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
62          _RL e12Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
63        INTEGER iStep        INTEGER iStep
64        _RL     myTime        _RL     myTime
65        INTEGER myIter        INTEGER myIter
66        INTEGER myThid        INTEGER myThid
67  C     ice velocities  CEOP
       _RL uFld   (1-Olx:sNx+Olx,1-Oly:sNy+Oly,nSx,nSy)  
       _RL vFld   (1-Olx:sNx+Olx,1-Oly:sNy+Oly,nSx,nSy)  
 C     strain rate tensor  
       _RL e11Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)  
       _RL e22Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)  
       _RL e12Loc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)  
 CEndOfInterface  
68    
69  #ifdef SEAICE_CGRID  #ifdef SEAICE_CGRID
70  #ifdef SEAICE_ALLOW_DYNAMICS  #ifdef SEAICE_ALLOW_DYNAMICS
71    C     !LOCAL VARIABLES:
72  C     === Local variables ===  C     === Local variables ===
73  C     i,j,bi,bj - Loop counters  C     i,j,bi,bj :: Loop counters
74        INTEGER i, j, bi, bj        INTEGER i, j, bi, bj
75  C  hFacU, hFacV - determine the no-slip boundary condition  C     hFacU, hFacV :: determine the no-slip boundary condition
76        INTEGER k        INTEGER k
77        _RS hFacU, hFacV, noSlipFac        _RS hFacU, hFacV, noSlipFac
78          _RL third
79          PARAMETER ( third = 0.333333333333333333333333333 _d 0 )
80    C     auxillary variables that help writing code that
81    C     vectorizes even after TAFization
82          _RL dudx (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
83          _RL dvdy (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
84          _RL dudy (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
85          _RL dvdx (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
86          _RL uave (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
87          _RL vave (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
88    
89        k = 1        k = 1
90        noSlipFac = 0. _d 0        noSlipFac = 0. _d 0
91        IF ( SEAICE_no_slip ) noSlipFac = 1. _d 0        IF ( SEAICE_no_slip ) noSlipFac = 1. _d 0
92    C     in order repoduce results before fixing a bug in r1.20 comment out
93    C     the following line
94    CML      IF ( SEAICE_no_slip ) noSlipFac = 2. _d 0
95  C  C
 #ifndef SEAICE_OLD_AND_BAD_DISCRETIZATION  
96        DO bj=myByLo(myThid),myByHi(myThid)        DO bj=myByLo(myThid),myByHi(myThid)
97         DO bi=myBxLo(myThid),myBxHi(myThid)         DO bi=myBxLo(myThid),myBxHi(myThid)
98          DO j=1-Oly,sNy+Oly-1  C     abbreviations on C-points, need to do them in separate loops
99           DO i=1-Olx,sNx+Olx-1  C     for vectorization
100  C     evaluate strain rates          DO j=1-OLy,sNy+OLy-1
101            e11Loc(I,J,bi,bj) = _recip_dxF(I,J,bi,bj) *           DO i=1-OLx,sNx+OLx-1
102       &         (uFld(I+1,J,bi,bj)-uFld(I,J,bi,bj))            dudx(i,j) = _recip_dxF(i,j,bi,bj) *
103       &         +HALF*       &         (uFld(i+1,j,bi,bj)-uFld(i,j,bi,bj))
104       &         (vFld(I,J,bi,bj)+vFld(I,J+1,bi,bj))            uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i+1,j,bi,bj))
105       &         * k2AtC(I,J,bi,bj)           ENDDO
106            e22Loc(I,J,bi,bj) = _recip_dyF(I,J,bi,bj) *          ENDDO
107       &         (vFld(I,J+1,bi,bj)-vFld(I,J,bi,bj))          DO j=1-OLy,sNy+OLy-1
108       &         +HALF*           DO i=1-OLx,sNx+OLx-1
109       &         (uFld(I,J,bi,bj)+uFld(I+1,J,bi,bj))            dvdy(i,j) = _recip_dyF(i,j,bi,bj) *
110       &         * k1AtC(I,J,bi,bj)       &         (vFld(i,j+1,bi,bj)-vFld(i,j,bi,bj))
111              vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i,j+1,bi,bj))
112             ENDDO
113            ENDDO
114    C     evaluate strain rates at C-points
115            DO j=1-OLy,sNy+OLy-1
116             DO i=1-OLx,sNx+OLx-1
117              e11Loc(i,j,bi,bj) = dudx(i,j) + vave(i,j) * k2AtC(i,j,bi,bj)
118              e22Loc(i,j,bi,bj) = dvdy(i,j) + uave(i,j) * k1AtC(i,j,bi,bj)
119             ENDDO
120            ENDDO
121    #ifndef OBCS_UVICE_OLD
122    C--     for OBCS: assume no gradient beyong OB
123            DO j=1-OLy,sNy+OLy-1
124             DO i=1-OLx,sNx+OLx-1
125              e11Loc(i,j,bi,bj) = e11Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)
126              e22Loc(i,j,bi,bj) = e22Loc(i,j,bi,bj)*maskInC(i,j,bi,bj)
127           ENDDO           ENDDO
128          ENDDO          ENDDO
129          DO j=1-Oly+1,sNy+Oly  #endif /* OBCS_UVICE_OLD */
130           DO i=1-Olx+1,sNx+Olx  
131    C     abbreviations at Z-points, need to do them in separate loops
132    C     for vectorization
133            DO j=1-OLy+1,sNy+OLy
134             DO i=1-OLx+1,sNx+OLx
135              dudy(i,j) = ( uFld(i,j,bi,bj) - uFld(i  ,j-1,bi,bj) )
136         &         * _recip_dyU(i,j,bi,bj)
137              uave(i,j) = 0.5 _d 0 * (uFld(i,j,bi,bj)+uFld(i  ,j-1,bi,bj))
138             ENDDO
139            ENDDO
140            DO j=1-OLy+1,sNy+OLy
141             DO i=1-OLx+1,sNx+OLx
142              dvdx(i,j) = ( vFld(i,j,bi,bj) - vFld(i-1,j  ,bi,bj) )
143         &         * _recip_dxV(i,j,bi,bj)
144              vave(i,j) = 0.5 _d 0 * (vFld(i,j,bi,bj)+vFld(i-1,j  ,bi,bj))
145             ENDDO
146            ENDDO
147    C     evaluate strain rates at Z-points
148            DO j=1-OLy+1,sNy+OLy
149             DO i=1-OLx+1,sNx+OLx
150            hFacU = _maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj)            hFacU = _maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj)
151            hFacV = _maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj)            hFacV = _maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj)
152            e12Loc(I,J,bi,bj) = HALF*(            e12Loc(i,j,bi,bj) = 0.5 _d 0 * (
153       &           ( uFld(I,J,bi,bj) - uFld(I  ,J-1,bi,bj) )       &         dudy(i,j) + dvdx(i,j)
154       &         * _recip_dyU(I,J,bi,bj)       &         - k1AtZ(i,j,bi,bj) * vave(i,j)
155       &         + ( vFld(I,J,bi,bj) - vFld(I-1,J  ,bi,bj) )       &         - k2AtZ(i,j,bi,bj) * uave(i,j)
      &         * _recip_dxV(I,J,bi,bj)  
      &         - k1AtZ(I,J,bi,bj)  
      &         * 0.5 _d 0 * (vFld(I,J,bi,bj)+vFld(I-1,J  ,bi,bj))  
      &         - k2AtZ(I,J,bi,bj)  
      &         * 0.5 _d 0 * (uFld(I,J,bi,bj)+uFld(I  ,J-1,bi,bj))  
156       &         )       &         )
157       &         *maskC(I  ,J  ,k,bi,bj)*maskC(I-1,J  ,k,bi,bj)       &         *maskC(i  ,j  ,k,bi,bj)*maskC(i-1,j  ,k,bi,bj)
158       &         *maskC(I  ,J-1,k,bi,bj)*maskC(I-1,J-1,k,bi,bj)       &         *maskC(i  ,j-1,k,bi,bj)*maskC(i-1,j-1,k,bi,bj)
159       &         + 2.0 _d 0 * noSlipFac * (       &         + noSlipFac * (
160       &           ( uFld(I,J,bi,bj) + uFld(I  ,J-1,bi,bj) )       &           2.0 _d 0 * uave(i,j) * _recip_dyU(i,j,bi,bj) * hFacU
161       &         * _recip_dyU(I,J,bi,bj) * hFacU       &         + 2.0 _d 0 * vave(i,j) * _recip_dxV(i,j,bi,bj) * hFacV
      &         + ( vFld(I,J,bi,bj) + vFld(I-1,J  ,bi,bj) )  
      &         * _recip_dxV(I,J,bi,bj) * hFacV  
162       &         )       &         )
163  C     no slip at the boundary implies u(j)+u(j-1)=0 and v(i)+v(i-1)=0  C     no slip at the boundary implies u(j)+u(j-1)=0 and v(i)+v(i-1)=0
164  C     accross the boundary; this is already accomplished by masking so  C     accross the boundary; this is already accomplished by masking so
165  C     that the following lines are not necessary  C     that the following lines are not necessary
166  c$$$     &         - hFacV * k1AtZ(I,J,bi,bj)  c$$$     &         - hFacV * k1AtZ(i,j,bi,bj) * vave(i,j)
167  c$$$     &         * 0.5 _d 0 * (vFld(I,J,bi,bj)+vFld(I-1,J  ,bi,bj))  c$$$     &         - hFacU * k2AtZ(i,j,bi,bj) * uave(i,j)
 c$$$     &         - hFacU * k2AtZ(I,J,bi,bj)  
 c$$$     &         * 0.5 _d 0 * (uFld(I,J,bi,bj)+uFld(I  ,J-1,bi,bj))  
168           ENDDO           ENDDO
169          ENDDO          ENDDO
170            IF ( SEAICE_no_slip .AND. SEAICE_2ndOrderBC ) THEN
171  c$$$        ENDIF           DO j=1-OLy+2,sNy+OLy-1
172         ENDDO            DO i=1-OLx+2,sNx+OLx-1
173        ENDDO             hFacU = (_maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj))*third
174  #else             hFacV = (_maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj))*third
175  C     this the old and incomplete discretization, here I also erroneously             hFacU = hFacU*( _maskW(i,j-2,k,bi,bj)*_maskW(i,j-1,k,bi,bj)
176  C     used finite-volumes to discretize the strain rates       &                   + _maskW(i,j+1,k,bi,bj)*_maskW(i,j,  k,bi,bj) )
177        DO bj=myByLo(myThid),myByHi(myThid)             hFacV = hFacV*( _maskS(i-2,j,k,bi,bj)*_maskS(i-1,j,k,bi,bj)
178         DO bi=myBxLo(myThid),myBxHi(myThid)       &                   + _maskS(i+1,j,k,bi,bj)*_maskS(i  ,j,k,bi,bj) )
179          DO j=1-Oly,sNy+Oly-1  C     right hand sided dv/dx = (9*v(i,j)-v(i+1,j))/(4*dxv(i,j)-dxv(i+1,j))
180           DO i=1-Olx,sNx+Olx-1  C     according to a Taylor expansion to 2nd order. We assume that dxv
181  C     evaluate strain rates  C     varies very slowly, so that the denominator simplifies to 3*dxv(i,j),
182            e11Loc(I,J,bi,bj) = _recip_dxF(I,J,bi,bj) *  C     then dv/dx = (6*v(i,j)+3*v(i,j)-v(i+1,j))/(3*dxv(i,j))
183       &         (uFld(I+1,J,bi,bj)-uFld(I,J,bi,bj))  C                = 2*v(i,j)/dxv(i,j) + (3*v(i,j)-v(i+1,j))/(3*dxv(i,j))
184       &         -HALF*  C     the left hand sided dv/dx is analogously
185       &         (vFld(I,J,bi,bj)+vFld(I,J+1,bi,bj))  C                = - 2*v(i-1,j)/dxv(i,j) - (3*v(i-1,j)-v(i-2,j))/(3*dxv(i,j))
186       &         * _tanPhiAtU(I,J,bi,bj)*recip_rSphere  C     the first term is the first order part, which is already added.
187            e22Loc(I,J,bi,bj) = _recip_dyF(I,J,bi,bj) *  C     For e12 we only need 0.5 of this gradient and vave = is either
188       &         (vFld(I,J+1,bi,bj)-vFld(I,J,bi,bj))  C     0.5*v(i,j) or 0.5*v(i-1,j) near the boundary so that we need an
189  C     one metric term is missing  C     extra factor of 2. This explains the six. du/dy is analogous.
190           ENDDO  C     The masking is ugly, but hopefully effective.
191          ENDDO             e12Loc(i,j,bi,bj) = e12Loc(i,j,bi,bj) + 0.5 _d 0 * (
192          DO j=1-Oly+1,sNy+Oly       &            _recip_dyU(i,j,bi,bj) * ( 6.0 _d 0 * uave(i,j)
193           DO i=1-Olx+1,sNx+Olx       &          - uFld(i,j-2,bi,bj)*_maskW(i,j-1,k,bi,bj)
194            e12Loc(I,J,bi,bj) = HALF*(       &          - uFld(i,j+1,bi,bj)*_maskW(i,j  ,k,bi,bj) ) * hFacU
195       &         (uFld(I  ,J  ,bi,bj) * _dxC(I  ,J  ,bi,bj)       &          + _recip_dxV(i,j,bi,bj) * ( 6.0 _d 0 * vave(i,j)
196       &         -uFld(I  ,J-1,bi,bj) * _dxC(I  ,J-1,bi,bj)       &          - vFld(i-2,j,bi,bj)*_maskS(i-1,j,k,bi,bj)
197       &         +vFld(I  ,J  ,bi,bj) * _dyC(I  ,J  ,bi,bj)       &          - vFld(i+1,j,bi,bj)*_maskS(i  ,j,k,bi,bj) ) * hFacV
198       &         -vFld(I-1,J  ,bi,bj) * _dyC(I-1,J  ,bi,bj))       &          )
      &         * recip_rAz(I,J,bi,bj)  
      &         +  
      &         0.25 _d 0 * (uFld(I,J,bi,bj)+uFld(I  ,J-1,bi,bj))  
      &         * ( _tanPhiAtU(I,J,bi,bj) + _tanPhiAtU(I,J-1,bi,bj) )  
      &         *recip_rSphere  
      &         )  
      &         *maskC(I  ,J  ,k,bi,bj)*maskC(I-1,J  ,k,bi,bj)  
      &         *maskC(I  ,J-1,k,bi,bj)*maskC(I-1,J-1,k,bi,bj)  
 C     one metric term is missing  
          ENDDO  
         ENDDO  
         IF ( SEAICE_no_slip ) THEN  
 C     no slip boundary conditions apply only to e12Loc  
          DO j=1-Oly+1,sNy+Oly  
           DO i=1-Olx+1,sNx+Olx  
            hFacU = _maskW(i,j,k,bi,bj) - _maskW(i,j-1,k,bi,bj)  
            hFacV = _maskS(i,j,k,bi,bj) - _maskS(i-1,j,k,bi,bj)  
   
            e12Loc(I,J,bi,bj) = e12Loc(I,J,bi,bj)  
      &          + recip_rAz(i,j,bi,bj) * 2. _d 0 *  
      &          ( hFacU * ( _dxC(i,j-1,bi,bj)*uFld(i,j  ,bi,bj)  
      &                    + _dxC(i,j,  bi,bj)*uFld(i,j-1,bi,bj) )  
      &          + hFacV * ( _dyC(i-1,j,bi,bj)*vFld(i  ,j,bi,bj)  
      &                    + _dyC(i,  j,bi,bj)*vFld(i-1,j,bi,bj) ) )  
      &         - hFacU  
      &         * 0.25 _d 0 * (uFld(I,J,bi,bj)+uFld(I  ,J-1,bi,bj))  
      &         * ( _tanPhiAtU(I,J,bi,bj) + _tanPhiAtU(I,J-1,bi,bj) )  
      &         *recip_rSphere  
 C     one metric term is missing  
199            ENDDO            ENDDO
200           ENDDO           ENDDO
   
201          ENDIF          ENDIF
202         ENDDO         ENDDO
203        ENDDO        ENDDO
204  #endif /* SEAICE_OLD_AND_BAD_DISCRETIZATION */  
205    #ifdef ALLOW_AUTODIFF_TAMC
206    #ifdef SEAICE_DYN_STABLE_ADJOINT
207    cgf zero out adjoint fields to stabilize pkg/seaice dyna. adjoint
208          CALL ZERO_ADJ( 1, e11Loc, myThid)
209          CALL ZERO_ADJ( 1, e12Loc, myThid)
210          CALL ZERO_ADJ( 1, e22Loc, myThid)
211    #endif
212    #endif /* ALLOW_AUTODIFF_TAMC */
213    
214  #endif /* SEAICE_ALLOW_DYNAMICS */  #endif /* SEAICE_ALLOW_DYNAMICS */
215  #endif /* SEAICE_CGRID */  #endif /* SEAICE_CGRID */
216        RETURN        RETURN
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