pkg/obcs/orlanski_north.F

C $Header: /u/gcmpack/models/MITgcmUV/pkg/obcs/orlanski_north.F,v 1.2 2001/02/02 21:36:30 adcroft Exp $
C $Name:  $

#include "OBCS_OPTIONS.h"

      SUBROUTINE ORLANSKI_NORTH( bi, bj, futureTime, 
     I                      uVel, vVel, wVel, theta, salt, 
     I                      myThid )
C     /==========================================================\
C     | SUBROUTINE OBCS_RADIATE                                  |
C     | o Calculate future boundary data at open boundaries      |
C     |   at time = futureTime by applying Orlanski radiation    |
C     |   conditions.                                            |
C     |==========================================================|
C     |                                                          |
C     \==========================================================/
      IMPLICIT NONE

C     === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "OBCS.h"
#include "ORLANSKI.h"

C SPK 6/2/00: Added radiative OBCs for salinity. 
C SPK 6/6/00: Changed calculation of OB*w. When K=1, the 
C             upstream value is used. For example on the eastern OB:
C                IF (K.EQ.1) THEN
C                   OBEw(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj)
C                ENDIF
C                         
C SPK 7/7/00: 1) Removed OB*w fix (see above).
C             2) Added variable CMAX. Maximum diagnosed phase speed is now
C                clamped to CMAX. For stability of AB-II scheme (CFL) the 
C                (non-dimensional) phase speed must be <0.5
C             3) (Sonya Legg) Changed application of uVel and vVel.
C                uVel on the western OB is actually applied at I_obc+1 
C                while vVel on the southern OB is applied at J_obc+1.
C             4) (Sonya Legg) Added templates for forced OBs.
C
C SPK 7/17/00: Non-uniform resolution is now taken into account in diagnosing
C              phase speeds and time-stepping OB values. CL is still the
C              non-dimensional phase speed; CVEL is the dimensional phase
C              speed: CVEL = CL*(dx or dy)/dt, where dx and dy is the 
C              appropriate grid spacings. Note that CMAX (with which CL 
C              is compared) remains non-dimensional.
C 
C SPK 7/18/00: Added code to allow filtering of phase speed following 
C              Blumberg and Kantha. There is now a separate array 
C              CVEL_**, where **=Variable(U,V,T,S,W)Boundary(E,W,N,S) for
C              the dimensional phase speed. These arrays are initialized to 
C              zero in ini_obcs.F. CVEL_** is filtered according to
C              CVEL_** = fracCVEL*CVEL(new) + (1-fracCVEL)*CVEL_**(old).
C              fracCVEL=1.0 turns off filtering.
C
C SPK 7/26/00: Changed code to average phase speed. A new variable 
C              'cvelTimeScale' was created. This variable must now be
C              specified. Then, fracCVEL=deltaT/cvelTimeScale. 
C              Since the goal is to smooth out the 'singularities' in the 
C              diagnosed phase speed, cvelTimeScale could be picked as the 
C              duration of the singular period in the unfiltered case. Thus, 
C              for a plane wave cvelTimeScale might be the time take for the 
C              wave to travel a distance DX, where DX is the width of the region
C              near which d(phi)/dx is small.

C     == Routine arguments ==
      INTEGER bi, bj
      _RL futureTime
      _RL uVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      _RL vVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      _RL wVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      _RL theta(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      _RL salt (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      INTEGER myThid

#ifdef ALLOW_ORLANSKI

C     == Local variables ==
      INTEGER  I, K, J_obc
      _RL CL, ab1, ab2, fracCVEL, f1, f2

      ab1   =  1.5 _d 0 + abEps /* Adams-Bashforth coefficients */
      ab2   = -0.5 _d 0 - abEps
      /* CMAX is maximum allowable phase speed-CFL for AB-II */
      /* cvelTimeScale is averaging period for phase speed in sec. */

      fracCVEL = deltaT/cvelTimeScale /* fraction of new phase speed used*/
      f1 = fracCVEL /* dont change this. Set cvelTimeScale */
      f2 = 1.0-fracCVEL   /* dont change this. set cvelTimeScale */

C     Northern OB (Orlanski Radiation Condition)
       DO K=1,Nr
         DO I=1-Olx,sNx+Olx
            J_obc=OB_Jn(I,bi,bj)
            IF (J_obc.ne.0) THEN
C              uVel
               IF ((UN_STORE_2(I,K,bi,bj).eq.0.).and.
     &            (UN_STORE_3(I,K,bi,bj).eq.0.)) THEN
                  CL=0.
               ELSE
                  CL=-(uVel(I,J_obc-1,K,bi,bj)-UN_STORE_1(I,K,bi,bj))/
     &          (ab1*UN_STORE_2(I,K,bi,bj) + ab2*UN_STORE_3(I,K,bi,bj))
               ENDIF
               IF (CL.lt.0.) THEN
                  CL=0.
               ELSEIF (CL.gt.CMAX) THEN
                  CL=CMAX
               ENDIF
               CVEL_UN(I,K,bi,bj) = f1*(CL*dyU(I,J_obc-1,bi,bj)/deltaT)+
     &                f2*CVEL_UN(I,K,bi,bj)
C              update OBC to next timestep
               OBNu(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)-
     &           CVEL_UN(I,K,bi,bj)*(deltaT/dyU(I,J_obc,bi,bj))*
     &           (ab1*(uVel(I,J_obc,K,bi,bj)-uVel(I,J_obc-1,K,bi,bj)) +
     &           ab2*(UN_STORE_4(I,K,bi,bj)-UN_STORE_1(I,K,bi,bj)))
C              vVel
               IF ((VN_STORE_2(I,K,bi,bj).eq.0.).and.
     &            (VN_STORE_3(I,K,bi,bj).eq.0.)) THEN
                  CL=0.
               ELSE
                  CL=-(vVel(I,J_obc-1,K,bi,bj)-VN_STORE_1(I,K,bi,bj))/
     &          (ab1*VN_STORE_2(I,K,bi,bj) + ab2*VN_STORE_3(I,K,bi,bj))
               ENDIF            
               IF (CL.lt.0.) THEN
                  CL=0.
               ELSEIF (CL.gt.CMAX) THEN
                  CL=CMAX
               ENDIF
               CVEL_VN(I,K,bi,bj) = f1*(CL*dyF(I,J_obc-2,bi,bj)/deltaT)+
     &                f2*CVEL_VN(I,K,bi,bj)
C              update OBC to next timestep
               OBNv(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)-
     &           CVEL_VN(I,K,bi,bj)*(deltaT/dyF(I,J_obc-1,bi,bj))*
     &           (ab1*(vVel(I,J_obc,K,bi,bj)-vVel(I,J_obc-1,K,bi,bj)) +
     &           ab2*(VN_STORE_4(I,K,bi,bj)-VN_STORE_1(I,K,bi,bj)))       
C              Temperature
               IF ((TN_STORE_2(I,K,bi,bj).eq.0.).and.
     &            (TN_STORE_3(I,K,bi,bj).eq.0.)) THEN
                  CL=0.
               ELSE
                  CL=-(theta(I,J_obc-1,K,bi,bj)-TN_STORE_1(I,K,bi,bj))/
     &          (ab1*TN_STORE_2(I,K,bi,bj) + ab2*TN_STORE_3(I,K,bi,bj))
               ENDIF 
               IF (CL.lt.0.) THEN
                  CL=0.
               ELSEIF (CL.gt.CMAX) THEN
                  CL=CMAX
               ENDIF
               CVEL_TN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+
     &                f2*CVEL_TN(I,K,bi,bj)
C              update OBC to next timestep
               OBNt(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)-
     &          CVEL_TN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))*
     &          (ab1*(theta(I,J_obc,K,bi,bj)-theta(I,J_obc-1,K,bi,bj))+
     &          ab2*(TN_STORE_4(I,K,bi,bj)-TN_STORE_1(I,K,bi,bj))) 
C              Salinity
               IF ((SN_STORE_2(I,K,bi,bj).eq.0.).and.
     &            (SN_STORE_3(I,K,bi,bj).eq.0.)) THEN
                  CL=0.
               ELSE
                  CL=-(salt(I,J_obc-1,K,bi,bj)-SN_STORE_1(I,K,bi,bj))/
     &          (ab1*SN_STORE_2(I,K,bi,bj) + ab2*SN_STORE_3(I,K,bi,bj))
               ENDIF 
               IF (CL.lt.0.) THEN
                  CL=0.
               ELSEIF (CL.gt.CMAX) THEN
                  CL=CMAX
               ENDIF
               CVEL_SN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+
     &                f2*CVEL_SN(I,K,bi,bj)
C              update OBC to next timestep
               OBNs(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)-
     &          CVEL_SN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))*
     &          (ab1*(salt(I,J_obc,K,bi,bj)-salt(I,J_obc-1,K,bi,bj)) + 
     &          ab2*(SN_STORE_4(I,K,bi,bj)-SN_STORE_1(I,K,bi,bj)))
C              wVel
#ifdef ALLOW_NONHYDROSTATIC
                  IF ((WN_STORE_2(I,K,bi,bj).eq.0.).and.
     &               (WN_STORE_3(I,K,bi,bj).eq.0.)) THEN
                     CL=0.
                  ELSE
                    CL=-(wVel(I,J_obc-1,K,bi,bj)-WN_STORE_1(I,K,bi,bj))/
     &             (ab1*WN_STORE_2(I,K,bi,bj)+ab2*WN_STORE_3(I,K,bi,bj))
                  ENDIF
                  IF (CL.lt.0.) THEN
                     CL=0.
                  ELSEIF (CL.gt.CMAX) THEN
                     CL=CMAX
                  ENDIF
                  CVEL_WN(I,K,bi,bj)=f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)
     &                   + f2*CVEL_WN(I,K,bi,bj)
C                 update OBC to next timestep
                  OBNw(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)-
     &             CVEL_WN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))*
     &             (ab1*(wVel(I,J_obc,K,bi,bj)-wVel(I,J_obc-1,K,bi,bj))+
     &             ab2*(WN_STORE_4(I,K,bi,bj)-WN_STORE_1(I,K,bi,bj)))
#endif
C              update/save storage arrays
C              uVel
C              copy t-1 to t-2 array
               UN_STORE_3(I,K,bi,bj)=UN_STORE_2(I,K,bi,bj)
C              copy (current time) t to t-1 arrays
               UN_STORE_2(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj) -
     &         uVel(I,J_obc-2,K,bi,bj)
               UN_STORE_1(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj)
               UN_STORE_4(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)
C              vVel
C              copy t-1 to t-2 array
               VN_STORE_3(I,K,bi,bj)=VN_STORE_2(I,K,bi,bj)
C              copy (current time) t to t-1 arrays
               VN_STORE_2(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj) -
     &         vVel(I,J_obc-2,K,bi,bj)
               VN_STORE_1(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj)
               VN_STORE_4(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)
C              Temperature
C              copy t-1 to t-2 array
               TN_STORE_3(I,K,bi,bj)=TN_STORE_2(I,K,bi,bj)
C              copy (current time) t to t-1 arrays
               TN_STORE_2(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj) -
     &         theta(I,J_obc-2,K,bi,bj)
               TN_STORE_1(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj)
               TN_STORE_4(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)
C              Salinity
C              copy t-1 to t-2 array
               SN_STORE_3(I,K,bi,bj)=SN_STORE_2(I,K,bi,bj)
C              copy (current time) t to t-1 arrays
               SN_STORE_2(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj) -
     &         salt(I,J_obc-2,K,bi,bj)
               SN_STORE_1(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj)
               SN_STORE_4(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)
C              wVel
#ifdef ALLOW_NONHYDROSTATIC
C              copy t-1 to t-2 array
               WN_STORE_3(I,K,bi,bj)=WN_STORE_2(I,K,bi,bj)
C              copy (current time) t to t-1 arrays
               WN_STORE_2(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj) -
     &         wVel(I,J_obc-2,K,bi,bj)
               WN_STORE_1(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj)
               WN_STORE_4(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)
#endif
            ENDIF
         ENDDO
       ENDDO

#endif /* ALLOW_ORLANSKI */
      RETURN
      END
1	adcroft	1.3	C $Header: /u/gcmpack/models/MITgcmUV/pkg/obcs/orlanski_north.F,v 1.2 2001/02/02 21:36:30 adcroft Exp $
2			C $Name: $
3	adcroft	1.2
4			#include "OBCS_OPTIONS.h"
5
6			SUBROUTINE ORLANSKI_NORTH( bi, bj, futureTime,
7			I uVel, vVel, wVel, theta, salt,
8			I myThid )
9			C /==========================================================\
10			C \| SUBROUTINE OBCS_RADIATE \|
11			C \| o Calculate future boundary data at open boundaries \|
12			C \| at time = futureTime by applying Orlanski radiation \|
13			C \| conditions. \|
14			C \|==========================================================\|
15			C \| \|
16			C \==========================================================/
17			IMPLICIT NONE
18
19			C === Global variables ===
20			#include "SIZE.h"
21			#include "EEPARAMS.h"
22			#include "PARAMS.h"
23			#include "GRID.h"
24			#include "OBCS.h"
25			#include "ORLANSKI.h"
26
27	adcroft	1.3	C SPK 6/2/00: Added radiative OBCs for salinity.
28	adcroft	1.2	C SPK 6/6/00: Changed calculation of OB*w. When K=1, the
29			C upstream value is used. For example on the eastern OB:
30			C IF (K.EQ.1) THEN
31			C OBEw(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj)
32			C ENDIF
33			C
34			C SPK 7/7/00: 1) Removed OB*w fix (see above).
35			C 2) Added variable CMAX. Maximum diagnosed phase speed is now
36			C clamped to CMAX. For stability of AB-II scheme (CFL) the
37			C (non-dimensional) phase speed must be <0.5
38			C 3) (Sonya Legg) Changed application of uVel and vVel.
39			C uVel on the western OB is actually applied at I_obc+1
40			C while vVel on the southern OB is applied at J_obc+1.
41	adcroft	1.3	C 4) (Sonya Legg) Added templates for forced OBs.
42	adcroft	1.2	C
43			C SPK 7/17/00: Non-uniform resolution is now taken into account in diagnosing
44			C phase speeds and time-stepping OB values. CL is still the
45			C non-dimensional phase speed; CVEL is the dimensional phase
46			C speed: CVEL = CL*(dx or dy)/dt, where dx and dy is the
47			C appropriate grid spacings. Note that CMAX (with which CL
48			C is compared) remains non-dimensional.
49			C
50			C SPK 7/18/00: Added code to allow filtering of phase speed following
51			C Blumberg and Kantha. There is now a separate array
52			C CVEL_, where =Variable(U,V,T,S,W)Boundary(E,W,N,S) for
53			C the dimensional phase speed. These arrays are initialized to
54			C zero in ini_obcs.F. CVEL_** is filtered according to
55			C CVEL_** = fracCVELCVEL(new) + (1-fracCVEL)CVEL_**(old).
56			C fracCVEL=1.0 turns off filtering.
57			C
58			C SPK 7/26/00: Changed code to average phase speed. A new variable
59			C 'cvelTimeScale' was created. This variable must now be
60			C specified. Then, fracCVEL=deltaT/cvelTimeScale.
61			C Since the goal is to smooth out the 'singularities' in the
62			C diagnosed phase speed, cvelTimeScale could be picked as the
63			C duration of the singular period in the unfiltered case. Thus,
64			C for a plane wave cvelTimeScale might be the time take for the
65			C wave to travel a distance DX, where DX is the width of the region
66			C near which d(phi)/dx is small.
67
68			C == Routine arguments ==
69			INTEGER bi, bj
70			_RL futureTime
71			_RL uVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
72			_RL vVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
73			_RL wVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
74			_RL theta(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
75			_RL salt (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
76			INTEGER myThid
77
78			#ifdef ALLOW_ORLANSKI
79
80			C == Local variables ==
81			INTEGER I, K, J_obc
82			_RL CL, ab1, ab2, fracCVEL, f1, f2
83
84			ab1 = 1.5 _d 0 + abEps /* Adams-Bashforth coefficients */
85			ab2 = -0.5 _d 0 - abEps
86			/* CMAX is maximum allowable phase speed-CFL for AB-II */
87			/* cvelTimeScale is averaging period for phase speed in sec. */
88
89			fracCVEL = deltaT/cvelTimeScale /* fraction of new phase speed used*/
90	adcroft	1.3	f1 = fracCVEL /* dont change this. Set cvelTimeScale */
91			f2 = 1.0-fracCVEL /* dont change this. set cvelTimeScale */
92	adcroft	1.2
93			C Northern OB (Orlanski Radiation Condition)
94			DO K=1,Nr
95			DO I=1-Olx,sNx+Olx
96			J_obc=OB_Jn(I,bi,bj)
97			IF (J_obc.ne.0) THEN
98			C uVel
99			IF ((UN_STORE_2(I,K,bi,bj).eq.0.).and.
100			& (UN_STORE_3(I,K,bi,bj).eq.0.)) THEN
101			CL=0.
102			ELSE
103			CL=-(uVel(I,J_obc-1,K,bi,bj)-UN_STORE_1(I,K,bi,bj))/
104			& (ab1UN_STORE_2(I,K,bi,bj) + ab2UN_STORE_3(I,K,bi,bj))
105			ENDIF
106			IF (CL.lt.0.) THEN
107			CL=0.
108			ELSEIF (CL.gt.CMAX) THEN
109			CL=CMAX
110			ENDIF
111			CVEL_UN(I,K,bi,bj) = f1(CLdyU(I,J_obc-1,bi,bj)/deltaT)+
112			& f2*CVEL_UN(I,K,bi,bj)
113			C update OBC to next timestep
114			OBNu(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)-
115			& CVEL_UN(I,K,bi,bj)(deltaT/dyU(I,J_obc,bi,bj))
116			& (ab1*(uVel(I,J_obc,K,bi,bj)-uVel(I,J_obc-1,K,bi,bj)) +
117			& ab2*(UN_STORE_4(I,K,bi,bj)-UN_STORE_1(I,K,bi,bj)))
118			C vVel
119			IF ((VN_STORE_2(I,K,bi,bj).eq.0.).and.
120			& (VN_STORE_3(I,K,bi,bj).eq.0.)) THEN
121			CL=0.
122			ELSE
123			CL=-(vVel(I,J_obc-1,K,bi,bj)-VN_STORE_1(I,K,bi,bj))/
124			& (ab1VN_STORE_2(I,K,bi,bj) + ab2VN_STORE_3(I,K,bi,bj))
125			ENDIF
126			IF (CL.lt.0.) THEN
127			CL=0.
128			ELSEIF (CL.gt.CMAX) THEN
129			CL=CMAX
130			ENDIF
131			CVEL_VN(I,K,bi,bj) = f1(CLdyF(I,J_obc-2,bi,bj)/deltaT)+
132			& f2*CVEL_VN(I,K,bi,bj)
133			C update OBC to next timestep
134			OBNv(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)-
135			& CVEL_VN(I,K,bi,bj)(deltaT/dyF(I,J_obc-1,bi,bj))
136			& (ab1*(vVel(I,J_obc,K,bi,bj)-vVel(I,J_obc-1,K,bi,bj)) +
137			& ab2*(VN_STORE_4(I,K,bi,bj)-VN_STORE_1(I,K,bi,bj)))
138			C Temperature
139			IF ((TN_STORE_2(I,K,bi,bj).eq.0.).and.
140			& (TN_STORE_3(I,K,bi,bj).eq.0.)) THEN
141			CL=0.
142			ELSE
143			CL=-(theta(I,J_obc-1,K,bi,bj)-TN_STORE_1(I,K,bi,bj))/
144			& (ab1TN_STORE_2(I,K,bi,bj) + ab2TN_STORE_3(I,K,bi,bj))
145			ENDIF
146			IF (CL.lt.0.) THEN
147			CL=0.
148			ELSEIF (CL.gt.CMAX) THEN
149			CL=CMAX
150			ENDIF
151			CVEL_TN(I,K,bi,bj) = f1(CLdyC(I,J_obc-1,bi,bj)/deltaT)+
152			& f2*CVEL_TN(I,K,bi,bj)
153			C update OBC to next timestep
154			OBNt(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)-
155			& CVEL_TN(I,K,bi,bj)(deltaT/dyC(I,J_obc,bi,bj))
156			& (ab1*(theta(I,J_obc,K,bi,bj)-theta(I,J_obc-1,K,bi,bj))+
157			& ab2*(TN_STORE_4(I,K,bi,bj)-TN_STORE_1(I,K,bi,bj)))
158			C Salinity
159			IF ((SN_STORE_2(I,K,bi,bj).eq.0.).and.
160			& (SN_STORE_3(I,K,bi,bj).eq.0.)) THEN
161			CL=0.
162			ELSE
163			CL=-(salt(I,J_obc-1,K,bi,bj)-SN_STORE_1(I,K,bi,bj))/
164			& (ab1SN_STORE_2(I,K,bi,bj) + ab2SN_STORE_3(I,K,bi,bj))
165			ENDIF
166			IF (CL.lt.0.) THEN
167			CL=0.
168			ELSEIF (CL.gt.CMAX) THEN
169			CL=CMAX
170			ENDIF
171			CVEL_SN(I,K,bi,bj) = f1(CLdyC(I,J_obc-1,bi,bj)/deltaT)+
172			& f2*CVEL_SN(I,K,bi,bj)
173			C update OBC to next timestep
174			OBNs(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)-
175			& CVEL_SN(I,K,bi,bj)(deltaT/dyC(I,J_obc,bi,bj))
176			& (ab1*(salt(I,J_obc,K,bi,bj)-salt(I,J_obc-1,K,bi,bj)) +
177			& ab2*(SN_STORE_4(I,K,bi,bj)-SN_STORE_1(I,K,bi,bj)))
178			C wVel
179			#ifdef ALLOW_NONHYDROSTATIC
180			IF ((WN_STORE_2(I,K,bi,bj).eq.0.).and.
181			& (WN_STORE_3(I,K,bi,bj).eq.0.)) THEN
182			CL=0.
183			ELSE
184			CL=-(wVel(I,J_obc-1,K,bi,bj)-WN_STORE_1(I,K,bi,bj))/
185			& (ab1WN_STORE_2(I,K,bi,bj)+ab2WN_STORE_3(I,K,bi,bj))
186			ENDIF
187			IF (CL.lt.0.) THEN
188			CL=0.
189			ELSEIF (CL.gt.CMAX) THEN
190			CL=CMAX
191			ENDIF
192			CVEL_WN(I,K,bi,bj)=f1(CLdyC(I,J_obc-1,bi,bj)/deltaT)
193			& + f2*CVEL_WN(I,K,bi,bj)
194			C update OBC to next timestep
195			OBNw(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)-
196			& CVEL_WN(I,K,bi,bj)(deltaT/dyC(I,J_obc,bi,bj))
197			& (ab1*(wVel(I,J_obc,K,bi,bj)-wVel(I,J_obc-1,K,bi,bj))+
198			& ab2*(WN_STORE_4(I,K,bi,bj)-WN_STORE_1(I,K,bi,bj)))
199			#endif
200			C update/save storage arrays
201			C uVel
202			C copy t-1 to t-2 array
203			UN_STORE_3(I,K,bi,bj)=UN_STORE_2(I,K,bi,bj)
204			C copy (current time) t to t-1 arrays
205			UN_STORE_2(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj) -
206			& uVel(I,J_obc-2,K,bi,bj)
207			UN_STORE_1(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj)
208			UN_STORE_4(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)
209			C vVel
210			C copy t-1 to t-2 array
211			VN_STORE_3(I,K,bi,bj)=VN_STORE_2(I,K,bi,bj)
212			C copy (current time) t to t-1 arrays
213			VN_STORE_2(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj) -
214			& vVel(I,J_obc-2,K,bi,bj)
215			VN_STORE_1(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj)
216			VN_STORE_4(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)
217			C Temperature
218			C copy t-1 to t-2 array
219			TN_STORE_3(I,K,bi,bj)=TN_STORE_2(I,K,bi,bj)
220			C copy (current time) t to t-1 arrays
221			TN_STORE_2(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj) -
222			& theta(I,J_obc-2,K,bi,bj)
223			TN_STORE_1(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj)
224			TN_STORE_4(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)
225			C Salinity
226			C copy t-1 to t-2 array
227			SN_STORE_3(I,K,bi,bj)=SN_STORE_2(I,K,bi,bj)
228			C copy (current time) t to t-1 arrays
229			SN_STORE_2(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj) -
230			& salt(I,J_obc-2,K,bi,bj)
231			SN_STORE_1(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj)
232			SN_STORE_4(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)
233			C wVel
234			#ifdef ALLOW_NONHYDROSTATIC
235			C copy t-1 to t-2 array
236			WN_STORE_3(I,K,bi,bj)=WN_STORE_2(I,K,bi,bj)
237			C copy (current time) t to t-1 arrays
238			WN_STORE_2(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj) -
239			& wVel(I,J_obc-2,K,bi,bj)
240			WN_STORE_1(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj)
241			WN_STORE_4(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)
242			#endif
243			ENDIF
244			ENDDO
245			ENDDO
246
247			#endif /* ALLOW_ORLANSKI */
248			RETURN
249			END