MODULE geo2ocean !!====================================================================== !! *** MODULE geo2ocean *** !! Ocean mesh : ??? !!====================================================================== !! History : OPA ! 07-1996 (O. Marti) Original code !! NEMO 1.0 ! 06-2006 (G. Madec ) Free form, F90 + opt. !! ! 04-2007 (S. Masson) angle: Add T, F points and bugfix in cos lateral boundary !! 3.0 ! 07-2008 (G. Madec) geo2oce suppress lon/lat agruments !! 3.7 ! 11-2015 (G. Madec) remove the unused repere and repcmo routines !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! rot_rep : Rotate the Repere: geographic grid <==> stretched coordinates grid !! angle : !! geo2oce : !! oce2geo : !!---------------------------------------------------------------------- USE dom_oce ! mesh and scale factors USE phycst ! physical constants ! USE in_out_manager ! I/O manager USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_mpp ! MPP library IMPLICIT NONE PRIVATE PUBLIC rot_rep ! called in sbccpl, fldread, and cyclone PUBLIC geo2oce ! called in sbccpl PUBLIC oce2geo ! called in sbccpl PUBLIC obs_rot ! called in obs_rot_vel and obs_write ! ! cos/sin between model grid lines and NP direction REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: gsint, gcost ! at T point REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: gsinu, gcosu ! at U point REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: gsinv, gcosv ! at V point REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: gsinf, gcosf ! at F point LOGICAL , SAVE, DIMENSION(4) :: linit = .FALSE. REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: gsinlon, gcoslon, gsinlat, gcoslat LOGICAL :: lmust_init = .TRUE. !: used to initialize the cos/sin variables (see above) !! * Substitutions # include "do_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE rot_rep ( pxin, pyin, cd_type, cdtodo, prot ) !!---------------------------------------------------------------------- !! *** ROUTINE rot_rep *** !! !! ** Purpose : Rotate the Repere: Change vector componantes between !! geographic grid <--> stretched coordinates grid. !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pxin, pyin ! vector componantes CHARACTER(len=1), INTENT(in ) :: cd_type ! define the nature of pt2d array grid-points CHARACTER(len=5), INTENT(in ) :: cdtodo ! type of transpormation: ! ! 'en->i' = east-north to i-component ! ! 'en->j' = east-north to j-component ! ! 'ij->e' = (i,j) components to east ! ! 'ij->n' = (i,j) components to north REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: prot !!---------------------------------------------------------------------- ! IF( lmust_init ) THEN ! at 1st call only: set gsin. & gcos. IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' rot_rep: coordinate transformation : geographic <==> model (i,j)-components' IF(lwp) WRITE(numout,*) ' ~~~~~~~~ ' ! CALL angle( glamt, gphit, glamu, gphiu, glamv, gphiv, glamf, gphif ) ! initialization of the transformation lmust_init = .FALSE. ENDIF ! SELECT CASE( cdtodo ) ! type of rotation ! CASE( 'en->i' ) ! east-north to i-component SELECT CASE (cd_type) CASE ('T') ; prot(:,:) = pxin(:,:) * gcost(:,:) + pyin(:,:) * gsint(:,:) CASE ('U') ; prot(:,:) = pxin(:,:) * gcosu(:,:) + pyin(:,:) * gsinu(:,:) CASE ('V') ; prot(:,:) = pxin(:,:) * gcosv(:,:) + pyin(:,:) * gsinv(:,:) CASE ('F') ; prot(:,:) = pxin(:,:) * gcosf(:,:) + pyin(:,:) * gsinf(:,:) CASE DEFAULT ; CALL ctl_stop( 'Only T, U, V and F grid points are coded' ) END SELECT CASE ('en->j') ! east-north to j-component SELECT CASE (cd_type) CASE ('T') ; prot(:,:) = pyin(:,:) * gcost(:,:) - pxin(:,:) * gsint(:,:) CASE ('U') ; prot(:,:) = pyin(:,:) * gcosu(:,:) - pxin(:,:) * gsinu(:,:) CASE ('V') ; prot(:,:) = pyin(:,:) * gcosv(:,:) - pxin(:,:) * gsinv(:,:) CASE ('F') ; prot(:,:) = pyin(:,:) * gcosf(:,:) - pxin(:,:) * gsinf(:,:) CASE DEFAULT ; CALL ctl_stop( 'Only T, U, V and F grid points are coded' ) END SELECT CASE ('ij->e') ! (i,j)-components to east SELECT CASE (cd_type) CASE ('T') ; prot(:,:) = pxin(:,:) * gcost(:,:) - pyin(:,:) * gsint(:,:) CASE ('U') ; prot(:,:) = pxin(:,:) * gcosu(:,:) - pyin(:,:) * gsinu(:,:) CASE ('V') ; prot(:,:) = pxin(:,:) * gcosv(:,:) - pyin(:,:) * gsinv(:,:) CASE ('F') ; prot(:,:) = pxin(:,:) * gcosf(:,:) - pyin(:,:) * gsinf(:,:) CASE DEFAULT ; CALL ctl_stop( 'Only T, U, V and F grid points are coded' ) END SELECT CASE ('ij->n') ! (i,j)-components to north SELECT CASE (cd_type) CASE ('T') ; prot(:,:) = pyin(:,:) * gcost(:,:) + pxin(:,:) * gsint(:,:) CASE ('U') ; prot(:,:) = pyin(:,:) * gcosu(:,:) + pxin(:,:) * gsinu(:,:) CASE ('V') ; prot(:,:) = pyin(:,:) * gcosv(:,:) + pxin(:,:) * gsinv(:,:) CASE ('F') ; prot(:,:) = pyin(:,:) * gcosf(:,:) + pxin(:,:) * gsinf(:,:) CASE DEFAULT ; CALL ctl_stop( 'Only T, U, V and F grid points are coded' ) END SELECT CASE DEFAULT ; CALL ctl_stop( 'rot_rep: Syntax Error in the definition of cdtodo' ) ! END SELECT ! END SUBROUTINE rot_rep SUBROUTINE angle( plamt, pphit, plamu, pphiu, plamv, pphiv, plamf, pphif ) !!---------------------------------------------------------------------- !! *** ROUTINE angle *** !! !! ** Purpose : Compute angles between model grid lines and the North direction !! !! ** Method : sinus and cosinus of the angle between the north-south axe !! and the j-direction at t, u, v and f-points !! dot and cross products are used to obtain cos and sin, resp. !! !! ** Action : - gsint, gcost, gsinu, gcosu, gsinv, gcosv, gsinf, gcosf !!---------------------------------------------------------------------- ! WARNING: for an unexplained reason, we need to pass all glam, gphi arrays as input parameters in ! order to get AGRIF working with -03 compilation option REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: plamt, pphit, plamu, pphiu, plamv, pphiv, plamf, pphif ! INTEGER :: ji, jj ! dummy loop indices INTEGER :: ierr ! local integer REAL(wp) :: zlam, zphi ! local scalars REAL(wp) :: zlan, zphh ! - - REAL(wp) :: zxnpt, zynpt, znnpt ! x,y components and norm of the vector: T point to North Pole REAL(wp) :: zxnpu, zynpu, znnpu ! x,y components and norm of the vector: U point to North Pole REAL(wp) :: zxnpv, zynpv, znnpv ! x,y components and norm of the vector: V point to North Pole REAL(wp) :: zxnpf, zynpf, znnpf ! x,y components and norm of the vector: F point to North Pole REAL(wp) :: zxvvt, zyvvt, znvvt ! x,y components and norm of the vector: between V points below and above a T point REAL(wp) :: zxffu, zyffu, znffu ! x,y components and norm of the vector: between F points below and above a U point REAL(wp) :: zxffv, zyffv, znffv ! x,y components and norm of the vector: between F points left and right a V point REAL(wp) :: zxuuf, zyuuf, znuuf ! x,y components and norm of the vector: between U points below and above a F point !!---------------------------------------------------------------------- ! ALLOCATE( gsint(jpi,jpj), gcost(jpi,jpj), & & gsinu(jpi,jpj), gcosu(jpi,jpj), & & gsinv(jpi,jpj), gcosv(jpi,jpj), & & gsinf(jpi,jpj), gcosf(jpi,jpj), STAT=ierr ) CALL mpp_sum( 'geo2ocean', ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'angle: unable to allocate arrays' ) ! ! ============================= ! ! Compute the cosinus and sinus ! ! ============================= ! ! (computation done on the north stereographic polar plane) ! DO_2D_00_01 ! zlam = plamt(ji,jj) ! north pole direction & modulous (at t-point) zphi = pphit(ji,jj) zxnpt = 0. - 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) zynpt = 0. - 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) znnpt = zxnpt*zxnpt + zynpt*zynpt ! zlam = plamu(ji,jj) ! north pole direction & modulous (at u-point) zphi = pphiu(ji,jj) zxnpu = 0. - 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) zynpu = 0. - 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) znnpu = zxnpu*zxnpu + zynpu*zynpu ! zlam = plamv(ji,jj) ! north pole direction & modulous (at v-point) zphi = pphiv(ji,jj) zxnpv = 0. - 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) zynpv = 0. - 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) znnpv = zxnpv*zxnpv + zynpv*zynpv ! zlam = plamf(ji,jj) ! north pole direction & modulous (at f-point) zphi = pphif(ji,jj) zxnpf = 0. - 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) zynpf = 0. - 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) znnpf = zxnpf*zxnpf + zynpf*zynpf ! zlam = plamv(ji,jj ) ! j-direction: v-point segment direction (around t-point) zphi = pphiv(ji,jj ) zlan = plamv(ji,jj-1) zphh = pphiv(ji,jj-1) zxvvt = 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * COS( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) zyvvt = 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * SIN( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) znvvt = SQRT( znnpt * ( zxvvt*zxvvt + zyvvt*zyvvt ) ) znvvt = MAX( znvvt, 1.e-14 ) ! zlam = plamf(ji,jj ) ! j-direction: f-point segment direction (around u-point) zphi = pphif(ji,jj ) zlan = plamf(ji,jj-1) zphh = pphif(ji,jj-1) zxffu = 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * COS( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) zyffu = 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * SIN( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) znffu = SQRT( znnpu * ( zxffu*zxffu + zyffu*zyffu ) ) znffu = MAX( znffu, 1.e-14 ) ! zlam = plamf(ji ,jj) ! i-direction: f-point segment direction (around v-point) zphi = pphif(ji ,jj) zlan = plamf(ji-1,jj) zphh = pphif(ji-1,jj) zxffv = 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * COS( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) zyffv = 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * SIN( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) znffv = SQRT( znnpv * ( zxffv*zxffv + zyffv*zyffv ) ) znffv = MAX( znffv, 1.e-14 ) ! zlam = plamu(ji,jj+1) ! j-direction: u-point segment direction (around f-point) zphi = pphiu(ji,jj+1) zlan = plamu(ji,jj ) zphh = pphiu(ji,jj ) zxuuf = 2. * COS( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * COS( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) zyuuf = 2. * SIN( rad*zlam ) * TAN( rpi/4. - rad*zphi/2. ) & & - 2. * SIN( rad*zlan ) * TAN( rpi/4. - rad*zphh/2. ) znuuf = SQRT( znnpf * ( zxuuf*zxuuf + zyuuf*zyuuf ) ) znuuf = MAX( znuuf, 1.e-14 ) ! ! ! cosinus and sinus using dot and cross products gsint(ji,jj) = ( zxnpt*zyvvt - zynpt*zxvvt ) / znvvt gcost(ji,jj) = ( zxnpt*zxvvt + zynpt*zyvvt ) / znvvt ! gsinu(ji,jj) = ( zxnpu*zyffu - zynpu*zxffu ) / znffu gcosu(ji,jj) = ( zxnpu*zxffu + zynpu*zyffu ) / znffu ! gsinf(ji,jj) = ( zxnpf*zyuuf - zynpf*zxuuf ) / znuuf gcosf(ji,jj) = ( zxnpf*zxuuf + zynpf*zyuuf ) / znuuf ! gsinv(ji,jj) = ( zxnpv*zxffv + zynpv*zyffv ) / znffv gcosv(ji,jj) =-( zxnpv*zyffv - zynpv*zxffv ) / znffv ! (caution, rotation of 90 degres) ! END_2D ! =============== ! ! Geographic mesh ! ! =============== ! DO_2D_00_01 IF( MOD( ABS( plamv(ji,jj) - plamv(ji,jj-1) ), 360. ) < 1.e-8 ) THEN gsint(ji,jj) = 0. gcost(ji,jj) = 1. ENDIF IF( MOD( ABS( plamf(ji,jj) - plamf(ji,jj-1) ), 360. ) < 1.e-8 ) THEN gsinu(ji,jj) = 0. gcosu(ji,jj) = 1. ENDIF IF( ABS( pphif(ji,jj) - pphif(ji-1,jj) ) < 1.e-8 ) THEN gsinv(ji,jj) = 0. gcosv(ji,jj) = 1. ENDIF IF( MOD( ABS( plamu(ji,jj) - plamu(ji,jj+1) ), 360. ) < 1.e-8 ) THEN gsinf(ji,jj) = 0. gcosf(ji,jj) = 1. ENDIF END_2D ! =========================== ! ! Lateral boundary conditions ! ! =========================== ! ! ! lateral boundary cond.: T-, U-, V-, F-pts, sgn CALL lbc_lnk_multi( 'geo2ocean', gcost, 'T', -1., gsint, 'T', -1., gcosu, 'U', -1., gsinu, 'U', -1., & & gcosv, 'V', -1., gsinv, 'V', -1., gcosf, 'F', -1., gsinf, 'F', -1. ) ! END SUBROUTINE angle SUBROUTINE geo2oce ( pxx, pyy, pzz, cgrid, pte, ptn ) !!---------------------------------------------------------------------- !! *** ROUTINE geo2oce *** !! !! ** Purpose : !! !! ** Method : Change a vector from geocentric to east/north !! !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pxx, pyy, pzz CHARACTER(len=1) , INTENT(in ) :: cgrid REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pte, ptn ! REAL(wp), PARAMETER :: rpi = 3.141592653e0 REAL(wp), PARAMETER :: rad = rpi / 180.e0 INTEGER :: ig ! INTEGER :: ierr ! local integer !!---------------------------------------------------------------------- ! IF( .NOT. ALLOCATED( gsinlon ) ) THEN ALLOCATE( gsinlon(jpi,jpj,4) , gcoslon(jpi,jpj,4) , & & gsinlat(jpi,jpj,4) , gcoslat(jpi,jpj,4) , STAT=ierr ) CALL mpp_sum( 'geo2ocean', ierr ) IF( ierr /= 0 ) CALL ctl_stop('geo2oce: unable to allocate arrays' ) ENDIF ! SELECT CASE( cgrid) CASE ( 'T' ) ig = 1 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamt(:,:) ) gcoslon(:,:,ig) = COS( rad * glamt(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphit(:,:) ) gcoslat(:,:,ig) = COS( rad * gphit(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'U' ) ig = 2 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamu(:,:) ) gcoslon(:,:,ig) = COS( rad * glamu(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphiu(:,:) ) gcoslat(:,:,ig) = COS( rad * gphiu(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'V' ) ig = 3 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamv(:,:) ) gcoslon(:,:,ig) = COS( rad * glamv(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphiv(:,:) ) gcoslat(:,:,ig) = COS( rad * gphiv(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'F' ) ig = 4 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamf(:,:) ) gcoslon(:,:,ig) = COS( rad * glamf(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphif(:,:) ) gcoslat(:,:,ig) = COS( rad * gphif(:,:) ) linit(ig) = .TRUE. ENDIF CASE default WRITE(ctmp1,*) 'geo2oce : bad grid argument : ', cgrid CALL ctl_stop( ctmp1 ) END SELECT ! pte = - gsinlon(:,:,ig) * pxx + gcoslon(:,:,ig) * pyy ptn = - gcoslon(:,:,ig) * gsinlat(:,:,ig) * pxx & & - gsinlon(:,:,ig) * gsinlat(:,:,ig) * pyy & & + gcoslat(:,:,ig) * pzz ! END SUBROUTINE geo2oce SUBROUTINE oce2geo ( pte, ptn, cgrid, pxx , pyy , pzz ) !!---------------------------------------------------------------------- !! *** ROUTINE oce2geo *** !! !! ** Purpose : !! !! ** Method : Change vector from east/north to geocentric !! !! History : ! (A. Caubel) oce2geo - Original code !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT( IN ) :: pte, ptn CHARACTER(len=1) , INTENT( IN ) :: cgrid REAL(wp), DIMENSION(jpi,jpj), INTENT( OUT ) :: pxx , pyy , pzz !! REAL(wp), PARAMETER :: rpi = 3.141592653E0 REAL(wp), PARAMETER :: rad = rpi / 180.e0 INTEGER :: ig ! INTEGER :: ierr ! local integer !!---------------------------------------------------------------------- IF( .NOT. ALLOCATED( gsinlon ) ) THEN ALLOCATE( gsinlon(jpi,jpj,4) , gcoslon(jpi,jpj,4) , & & gsinlat(jpi,jpj,4) , gcoslat(jpi,jpj,4) , STAT=ierr ) CALL mpp_sum( 'geo2ocean', ierr ) IF( ierr /= 0 ) CALL ctl_stop('oce2geo: unable to allocate arrays' ) ENDIF SELECT CASE( cgrid) CASE ( 'T' ) ig = 1 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamt(:,:) ) gcoslon(:,:,ig) = COS( rad * glamt(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphit(:,:) ) gcoslat(:,:,ig) = COS( rad * gphit(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'U' ) ig = 2 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamu(:,:) ) gcoslon(:,:,ig) = COS( rad * glamu(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphiu(:,:) ) gcoslat(:,:,ig) = COS( rad * gphiu(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'V' ) ig = 3 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamv(:,:) ) gcoslon(:,:,ig) = COS( rad * glamv(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphiv(:,:) ) gcoslat(:,:,ig) = COS( rad * gphiv(:,:) ) linit(ig) = .TRUE. ENDIF CASE ( 'F' ) ig = 4 IF( .NOT. linit(ig) ) THEN gsinlon(:,:,ig) = SIN( rad * glamf(:,:) ) gcoslon(:,:,ig) = COS( rad * glamf(:,:) ) gsinlat(:,:,ig) = SIN( rad * gphif(:,:) ) gcoslat(:,:,ig) = COS( rad * gphif(:,:) ) linit(ig) = .TRUE. ENDIF CASE default WRITE(ctmp1,*) 'geo2oce : bad grid argument : ', cgrid CALL ctl_stop( ctmp1 ) END SELECT ! pxx = - gsinlon(:,:,ig) * pte - gcoslon(:,:,ig) * gsinlat(:,:,ig) * ptn pyy = gcoslon(:,:,ig) * pte - gsinlon(:,:,ig) * gsinlat(:,:,ig) * ptn pzz = gcoslat(:,:,ig) * ptn ! END SUBROUTINE oce2geo SUBROUTINE obs_rot( psinu, pcosu, psinv, pcosv ) !!---------------------------------------------------------------------- !! *** ROUTINE obs_rot *** !! !! ** Purpose : Copy gsinu, gcosu, gsinv and gsinv !! to input data for rotations of !! current at observation points !! !! History : 9.2 ! 09-02 (K. Mogensen) !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT( OUT ):: psinu, pcosu, psinv, pcosv ! copy of data !!---------------------------------------------------------------------- ! ! Initialization of gsin* and gcos* at first call ! ----------------------------------------------- IF( lmust_init ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' obs_rot : geographic <--> stretched' IF(lwp) WRITE(numout,*) ' ~~~~~~~ coordinate transformation' CALL angle( glamt, gphit, glamu, gphiu, glamv, gphiv, glamf, gphif ) ! initialization of the transformation lmust_init = .FALSE. ENDIF ! psinu(:,:) = gsinu(:,:) pcosu(:,:) = gcosu(:,:) psinv(:,:) = gsinv(:,:) pcosv(:,:) = gcosv(:,:) ! END SUBROUTINE obs_rot !!====================================================================== END MODULE geo2ocean