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MODULE agrif_oce_interp
   !!======================================================================
   !!                   ***  MODULE  agrif_oce_interp  ***
   !! AGRIF: interpolation package for the ocean dynamics (OCE)
   !!======================================================================
   !! History :  2.0  !  2002-06  (L. Debreu)  Original cade
   !!            3.2  !  2009-04  (R. Benshila) 
   !!            3.6  !  2014-09  (R. Benshila) 
   !!----------------------------------------------------------------------
#if defined key_agrif
   !!----------------------------------------------------------------------
   !!   'key_agrif'                                              AGRIF zoom
   !!----------------------------------------------------------------------
   !!   Agrif_tra     :
   !!   Agrif_dyn     : 
   !!   Agrif_ssh     :
   !!   Agrif_dyn_ts  :
   !!   Agrif_dta_ts  :
   !!   Agrif_ssh_ts  :
   !!   Agrif_avm     : 
   !!   interpu       :
   !!   interpv       :
   !!----------------------------------------------------------------------
   USE par_oce
   USE oce
   USE dom_oce      
   USE zdf_oce
   USE agrif_oce
   USE phycst
!!!   USE dynspg_ts, ONLY: un_adv, vn_adv
   !
   USE in_out_manager
   USE agrif_oce_sponge
   USE lib_mpp
   USE vremap
   USE lbclnk
 
   IMPLICIT NONE
   PRIVATE

   PUBLIC   Agrif_dyn, Agrif_ssh, Agrif_dyn_ts, Agrif_dyn_ts_flux, Agrif_ssh_ts, Agrif_dta_ts
   PUBLIC   Agrif_tra, Agrif_avm
   PUBLIC   interpun , interpvn
   PUBLIC   interptsn, interpsshn, interpavm
   PUBLIC   interpunb, interpvnb , interpub2b, interpvb2b
   PUBLIC   interpglamt, interpgphit
   PUBLIC   interpht0, interpmbkt, interpe3t0_vremap
   PUBLIC   agrif_istate_oce, agrif_istate_ssh   ! called by icestate.F90 and domvvl.F90
   PUBLIC   agrif_check_bat

   INTEGER ::   bdy_tinterp = 0

   !! * Substitutions
#  include "domzgr_substitute.h90"
   !! NEMO/NST 4.0 , NEMO Consortium (2018)
   !! $Id: agrif_oce_interp.F90 15437 2021-10-22 12:21:20Z jchanut $
   !! Software governed by the CeCILL license (see ./LICENSE)
   !!----------------------------------------------------------------------
CONTAINS

   SUBROUTINE Agrif_istate_oce( Kbb, Kmm, Kaa )
      !!----------------------------------------------------------------------
      !!                 *** ROUTINE agrif_istate_oce ***
      !!
      !!                 set initial t, s, u, v, ssh from parent
      !!----------------------------------------------------------------------
      !
      IMPLICIT NONE
      !
      INTEGER, INTENT(in)  :: Kbb, Kmm, Kaa
      INTEGER :: jn
      !!----------------------------------------------------------------------
      IF(lwp) WRITE(numout,*) ' '
      IF(lwp) WRITE(numout,*) 'Agrif_istate_oce : interp child initial state from parent'
      IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~~'
      IF(lwp) WRITE(numout,*) ' '

      IF ( .NOT.Agrif_Parent(l_1st_euler) ) & 
         & CALL ctl_stop('AGRIF hot start requires to force Euler first step on parent')

      l_ini_child           = .TRUE.
      Agrif_SpecialValue    = 0.0_wp
      Agrif_UseSpecialValue = .TRUE.

      ts(:,:,:,:,Kbb) = 0.0_wp
      uu(:,:,:,Kbb)   = 0.0_wp
      vv(:,:,:,Kbb)   = 0.0_wp 
       
      Krhs_a = Kbb   ;   Kmm_a = Kbb

      CALL Agrif_Init_Variable(tsini_id, procname=interptsn)

      Agrif_UseSpecialValue = ln_spc_dyn
      use_sign_north = .TRUE.
      sign_north = -1._wp
      CALL Agrif_Init_Variable(uini_id , procname=interpun )
      CALL Agrif_Init_Variable(vini_id , procname=interpvn )
      use_sign_north = .FALSE.

      Agrif_UseSpecialValue = .FALSE.
      l_ini_child           = .FALSE.

      Krhs_a = Kaa   ;   Kmm_a = Kmm

      DO jn = 1, jpts
         ts(:,:,:,jn,Kbb) = ts(:,:,:,jn,Kbb) * tmask(:,:,:)
      END DO
      uu(:,:,:,Kbb) = uu(:,:,:,Kbb) * umask(:,:,:)     
      vv(:,:,:,Kbb) = vv(:,:,:,Kbb) * vmask(:,:,:) 

      CALL lbc_lnk( 'agrif_istate_oce', uu(:,:,:  ,Kbb), 'U', -1.0_wp , vv(:,:,:,Kbb), 'V', -1.0_wp )
      CALL lbc_lnk( 'agrif_istate_oce', ts(:,:,:,:,Kbb), 'T',  1.0_wp )

   END SUBROUTINE Agrif_istate_oce


   SUBROUTINE Agrif_istate_ssh( Kbb, Kmm, Kaa )
      !!----------------------------------------------------------------------
      !!                 *** ROUTINE agrif_istate_ssh ***
      !!
      !!                    set initial ssh from parent
      !!----------------------------------------------------------------------
      !
      IMPLICIT NONE
      !
      INTEGER, INTENT(in)  :: Kbb, Kmm, Kaa 
      !!----------------------------------------------------------------------
      IF(lwp) WRITE(numout,*) ' '
      IF(lwp) WRITE(numout,*) 'Agrif_istate_ssh : interp child ssh from parent'
      IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~~'
      IF(lwp) WRITE(numout,*) ' '

      IF ( .NOT.Agrif_Parent(l_1st_euler) ) & 
         & CALL ctl_stop('AGRIF hot start requires to force Euler first step on parent')

      Krhs_a = Kbb   ;   Kmm_a = Kbb
      !
      Agrif_SpecialValue    = 0._wp
      Agrif_UseSpecialValue = .TRUE.
      l_ini_child           = .TRUE.
      !
      ssh(:,:,Kbb) = 0._wp
      CALL Agrif_Init_Variable(sshini_id, procname=interpsshn)
      !
      Agrif_UseSpecialValue = .FALSE.
      l_ini_child           = .FALSE.
      !
      Krhs_a = Kaa   ;   Kmm_a = Kmm
      !
      CALL lbc_lnk( 'Agrif_istate_ssh', ssh(:,:,Kbb), 'T', 1._wp )
      !
      ssh(:,:,Kmm) = ssh(:,:,Kbb)
      ssh(:,:,Kaa) = 0._wp

   END SUBROUTINE Agrif_istate_ssh


   SUBROUTINE Agrif_tra
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_tra  ***
      !!----------------------------------------------------------------------
      !
      IF( Agrif_Root() )   RETURN
      !
      Agrif_SpecialValue    = 0._wp
      Agrif_UseSpecialValue = .TRUE.
      l_vremap 		    = ln_vert_remap
      !
      CALL Agrif_Bc_variable( ts_interp_id, procname=interptsn )
      !
      Agrif_UseSpecialValue = .FALSE.
      l_vremap              = .FALSE.
      !
   END SUBROUTINE Agrif_tra


   SUBROUTINE Agrif_dyn( kt )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_DYN  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   kt
      !
      INTEGER ::   ji, jj, jk       ! dummy loop indices
      INTEGER ::   ibdy1, jbdy1, ibdy2, jbdy2
      REAL(wp), DIMENSION(jpi,jpj) ::   zub, zvb
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      Agrif_SpecialValue    = 0.0_wp
      Agrif_UseSpecialValue = ln_spc_dyn
      l_vremap              = ln_vert_remap
      !
      use_sign_north = .TRUE.
      sign_north = -1.0_wp
      CALL Agrif_Bc_variable( un_interp_id, procname=interpun )
      CALL Agrif_Bc_variable( vn_interp_id, procname=interpvn )

      IF( .NOT.ln_dynspg_ts ) THEN ! Get transports
         ubdy(:,:) = 0._wp    ;  vbdy(:,:) = 0._wp
         utint_stage(:,:) = 0 ;  vtint_stage(:,:) = 0
         CALL Agrif_Bc_variable( unb_interp_id, procname=interpunb )
         CALL Agrif_Bc_variable( vnb_interp_id, procname=interpvnb )
      ENDIF

      use_sign_north = .FALSE.
      !
      Agrif_UseSpecialValue = .FALSE.
      l_vremap              = .FALSE.
      !
      ! Ensure below that vertically integrated transports match
      ! either transports out of time splitting procedure (ln_dynspg_ts=.TRUE.)
      ! or parent grid transports (ln_dynspg_ts=.FALSE.)
      !
      ! --- West --- !
      IF( lk_west ) THEN
         ibdy1 = nn_hls + 2                  ! halo + land + 1
         ibdy2 = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhox()   ! halo + land + nbghostcells
         !
         IF( .NOT.ln_dynspg_ts ) THEN  ! Store transport
            DO ji = mi0(ibdy1), mi1(ibdy2)
               DO jj = 1, jpj
                  uu_b(ji,jj,Krhs_a) = ubdy(ji,jj) * r1_hu(ji,jj,Krhs_a)
                  vv_b(ji,jj,Krhs_a) = vbdy(ji,jj) * r1_hv(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO ji = mi0(ibdy1), mi1(ibdy2)
            zub(ji,:) = 0._wp  
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  zub(ji,jj) = zub(ji,jj) + e3u(ji,jj,jk,Krhs_a)  * uu(ji,jj,jk,Krhs_a) * umask(ji,jj,jk)
               END DO
            END DO
            DO jj=1,jpj
               zub(ji,jj) = zub(ji,jj) * r1_hu(ji,jj,Krhs_a)
            END DO 
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  uu(ji,jj,jk,Krhs_a) = ( uu(ji,jj,jk,Krhs_a) + uu_b(ji,jj,Krhs_a) - zub(ji,jj) ) * umask(ji,jj,jk)
               END DO
            END DO
         END DO
         !   
         DO ji = mi0(ibdy1), mi1(ibdy2)
            zvb(ji,:) = 0._wp
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  zvb(ji,jj) = zvb(ji,jj) + e3v(ji,jj,jk,Krhs_a) * vv(ji,jj,jk,Krhs_a) * vmask(ji,jj,jk)
               END DO
            END DO
            DO jj = 1, jpj
               zvb(ji,jj) = zvb(ji,jj) * r1_hv(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  vv(ji,jj,jk,Krhs_a) = ( vv(ji,jj,jk,Krhs_a) + vv_b(ji,jj,Krhs_a) - zvb(ji,jj) )*vmask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
      ENDIF

      ! --- East --- !
      IF( lk_east) THEN
         ibdy1 = jpiglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhox()    
         ibdy2 = jpiglo - ( nn_hls + 2 )                 
         !
         IF( .NOT.ln_dynspg_ts ) THEN 
            DO ji = mi0(ibdy1), mi1(ibdy2)
               DO jj = 1, jpj
                  uu_b(ji,jj,Krhs_a) = ubdy(ji,jj) * r1_hu(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO ji = mi0(ibdy1), mi1(ibdy2)
            zub(ji,:) = 0._wp   
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  zub(ji,jj) = zub(ji,jj) + e3u(ji,jj,jk,Krhs_a)  * uu(ji,jj,jk,Krhs_a) * umask(ji,jj,jk)
               END DO
            END DO
            DO jj=1,jpj
               zub(ji,jj) = zub(ji,jj) * r1_hu(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                  uu(ji,jj,jk,Krhs_a) = ( uu(ji,jj,jk,Krhs_a) + uu_b(ji,jj,Krhs_a) - zub(ji,jj) ) * umask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
         ibdy1 = jpiglo - ( nn_hls + nbghostcells - 1 ) - nn_shift_bar*Agrif_Rhox() 
         ibdy2 = jpiglo - ( nn_hls + 1 )     
         !
         IF( .NOT.ln_dynspg_ts ) THEN 
            DO ji = mi0(ibdy1), mi1(ibdy2)
               DO jj = 1, jpj
                  vv_b(ji,jj,Krhs_a) = vbdy(ji,jj) * r1_hv(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO ji = mi0(ibdy1), mi1(ibdy2)
            zvb(ji,:) = 0._wp
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                     zvb(ji,jj) = zvb(ji,jj) + e3v(ji,jj,jk,Krhs_a) * vv(ji,jj,jk,Krhs_a) * vmask(ji,jj,jk)
               END DO
            END DO
            DO jj = 1, jpj
               zvb(ji,jj) = zvb(ji,jj) * r1_hv(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO jj = 1, jpj
                     vv(ji,jj,jk,Krhs_a) = ( vv(ji,jj,jk,Krhs_a) + vv_b(ji,jj,Krhs_a) - zvb(ji,jj) ) * vmask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
      ENDIF

      ! --- South --- !
      IF( lk_south ) THEN
         jbdy1 = nn_hls + 2                 
         jbdy2 = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhoy()   
         !
         IF( .NOT.ln_dynspg_ts ) THEN
            DO jj = mj0(jbdy1), mj1(jbdy2)
               DO ji = 1, jpi
                  uu_b(ji,jj,Krhs_a) = ubdy(ji,jj) * r1_hu(ji,jj,Krhs_a)
                  vv_b(ji,jj,Krhs_a) = vbdy(ji,jj) * r1_hv(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO jj = mj0(jbdy1), mj1(jbdy2)
            zvb(:,jj) = 0._wp
            DO jk=1,jpkm1
               DO ji=1,jpi
                  zvb(ji,jj) = zvb(ji,jj) + e3v(ji,jj,jk,Krhs_a) * vv(ji,jj,jk,Krhs_a) * vmask(ji,jj,jk)
               END DO
            END DO
            DO ji = 1, jpi
               zvb(ji,jj) = zvb(ji,jj) * r1_hv(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                  vv(ji,jj,jk,Krhs_a) = ( vv(ji,jj,jk,Krhs_a) + vv_b(ji,jj,Krhs_a) - zvb(ji,jj) ) * vmask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
         DO jj = mj0(jbdy1), mj1(jbdy2)
            zub(:,jj) = 0._wp
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                  zub(ji,jj) = zub(ji,jj) + e3u(ji,jj,jk,Krhs_a) * uu(ji,jj,jk,Krhs_a) * umask(ji,jj,jk)
               END DO
            END DO
            DO ji = 1, jpi
               zub(ji,jj) = zub(ji,jj) * r1_hu(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                  uu(ji,jj,jk,Krhs_a) = ( uu(ji,jj,jk,Krhs_a) + uu_b(ji,jj,Krhs_a) - zub(ji,jj) ) * umask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
      ENDIF

      ! --- North --- !
      IF( lk_north ) THEN
         jbdy1 = jpjglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhoy() 
         jbdy2 = jpjglo - ( nn_hls + 2 )
         !
         IF( .NOT.ln_dynspg_ts ) THEN
            DO jj = mj0(jbdy1), mj1(jbdy2)
               DO ji = 1, jpi
                  vv_b(ji,jj,Krhs_a) = vbdy(ji,jj) * r1_hv(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO jj = mj0(jbdy1), mj1(jbdy2)
            zvb(:,jj) = 0._wp 
            DO jk=1,jpkm1
               DO ji=1,jpi
                  zvb(ji,jj) = zvb(ji,jj) + e3v(ji,jj,jk,Krhs_a) * vv(ji,jj,jk,Krhs_a) * vmask(ji,jj,jk)
               END DO
            END DO
            DO ji = 1, jpi
               zvb(ji,jj) = zvb(ji,jj) * r1_hv(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                  vv(ji,jj,jk,Krhs_a) = ( vv(ji,jj,jk,Krhs_a) + vv_b(ji,jj,Krhs_a) - zvb(ji,jj) ) * vmask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
         jbdy1 = jpjglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhoy()  
         jbdy2 = jpjglo - ( nn_hls + 1 )
         !
         IF( .NOT.ln_dynspg_ts ) THEN
            DO jj = mj0(jbdy1), mj1(jbdy2)
               DO ji = 1, jpi
                  uu_b(ji,jj,Krhs_a) = ubdy(ji,jj) * r1_hu(ji,jj,Krhs_a)
               END DO
            END DO
         ENDIF
         !
         DO jj = mj0(jbdy1), mj1(jbdy2)
            zub(:,jj) = 0._wp
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                  zub(ji,jj) = zub(ji,jj) + e3u(ji,jj,jk,Krhs_a) * uu(ji,jj,jk,Krhs_a) * umask(ji,jj,jk)
               END DO
            END DO
            DO ji = 1, jpi
               zub(ji,jj) = zub(ji,jj) * r1_hu(ji,jj,Krhs_a)
            END DO
            DO jk = 1, jpkm1
               DO ji = 1, jpi
                     uu(ji,jj,jk,Krhs_a) = ( uu(ji,jj,jk,Krhs_a) + uu_b(ji,jj,Krhs_a) - zub(ji,jj) ) * umask(ji,jj,jk)
               END DO
            END DO
         END DO
         !
      ENDIF
      !
   END SUBROUTINE Agrif_dyn


   SUBROUTINE Agrif_dyn_ts( jn )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_dyn_ts  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   jn
      !!
      INTEGER :: ji, jj
      INTEGER :: istart, iend, jstart, jend
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      !--- West ---!
      IF( lk_west ) THEN
         istart = nn_hls + 2                              ! halo + land + 1
         iend   = nn_hls + nbghostcells  + nn_shift_bar*Agrif_Rhox()              ! halo + land + nbghostcells
         DO ji = mi0(istart), mi1(iend)
            DO jj=1,jpj
               va_e(ji,jj) = vbdy(ji,jj) * hvr_e(ji,jj)
               ua_e(ji,jj) = ubdy(ji,jj) * hur_e(ji,jj)
            END DO
         END DO
      ENDIF
      !
      !--- East ---!
      IF( lk_east ) THEN
         istart = jpiglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhox() 
         iend   = jpiglo - ( nn_hls + 1 )                
         DO ji = mi0(istart), mi1(iend)

            DO jj=1,jpj
               va_e(ji,jj) = vbdy(ji,jj) * hvr_e(ji,jj)
            END DO
         END DO
         istart = jpiglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhox() 
         iend   = jpiglo - ( nn_hls + 2 )                
         DO ji = mi0(istart), mi1(iend)
            DO jj=1,jpj
               ua_e(ji,jj) = ubdy(ji,jj) * hur_e(ji,jj)
            END DO
         END DO
      ENDIF 
      !
      !--- South ---!
      IF( lk_south ) THEN
         jstart = nn_hls + 2                              
         jend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhoy()           
         DO jj = mj0(jstart), mj1(jend)

            DO ji=1,jpi
               ua_e(ji,jj) = ubdy(ji,jj) * hur_e(ji,jj)
               va_e(ji,jj) = vbdy(ji,jj) * hvr_e(ji,jj)
            END DO
         END DO
      ENDIF       
      !
      !--- North ---!
      IF( lk_north ) THEN
         jstart = jpjglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhoy()     
         jend   = jpjglo - ( nn_hls + 1 )                
         DO jj = mj0(jstart), mj1(jend)
            DO ji=1,jpi
               ua_e(ji,jj) = ubdy(ji,jj) * hur_e(ji,jj)
            END DO
         END DO
         jstart = jpjglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhoy() 
         jend   = jpjglo - ( nn_hls + 2 )                
         DO jj = mj0(jstart), mj1(jend)
            DO ji=1,jpi
               va_e(ji,jj) = vbdy(ji,jj) * hvr_e(ji,jj)
            END DO
         END DO
      ENDIF 
      !
   END SUBROUTINE Agrif_dyn_ts

   
   SUBROUTINE Agrif_dyn_ts_flux( jn, zu, zv )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_dyn_ts_flux  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   jn
      REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) ::   zu, zv
      !!
      INTEGER :: ji, jj
      INTEGER :: istart, iend, jstart, jend
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      !--- West ---!
      IF( lk_west ) THEN
         istart = nn_hls + 2                              
         iend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhox() 
         DO ji = mi0(istart), mi1(iend)
            DO jj=1,jpj
               zv(ji,jj) = vbdy(ji,jj) * e1v(ji,jj)
               zu(ji,jj) = ubdy(ji,jj) * e2u(ji,jj)
            END DO
         END DO
      ENDIF
      !
      !--- East ---!
      IF( lk_east ) THEN
         istart = jpiglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhox()
         iend   = jpiglo - ( nn_hls + 1 )                 
         DO ji = mi0(istart), mi1(iend)
            DO jj=1,jpj
               zv(ji,jj) = vbdy(ji,jj) * e1v(ji,jj)
            END DO
         END DO
         istart = jpiglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhox() 
         iend   = jpiglo - ( nn_hls + 2 )                 
         DO ji = mi0(istart), mi1(iend)
            DO jj=1,jpj
               zu(ji,jj) = ubdy(ji,jj) * e2u(ji,jj)
            END DO
         END DO
      ENDIF
      !
      !--- South ---!
      IF( lk_south ) THEN
         jstart = nn_hls + 2                              
         jend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhoy() 
         DO jj = mj0(jstart), mj1(jend)
            DO ji=1,jpi
               zu(ji,jj) = ubdy(ji,jj) * e2u(ji,jj)
               zv(ji,jj) = vbdy(ji,jj) * e1v(ji,jj)
            END DO
         END DO
      ENDIF
      !
      !--- North ---!
      IF( lk_north ) THEN
         jstart = jpjglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhoy() 
         jend   = jpjglo - ( nn_hls + 1 )                
         DO jj = mj0(jstart), mj1(jend)
            DO ji=1,jpi
               zu(ji,jj) = ubdy(ji,jj) * e2u(ji,jj)
            END DO
         END DO
         jstart = jpjglo - ( nn_hls + nbghostcells ) - nn_shift_bar*Agrif_Rhoy() 
         jend   = jpjglo - ( nn_hls + 2 )               
         DO jj = mj0(jstart), mj1(jend)
            DO ji=1,jpi
               zv(ji,jj) = vbdy(ji,jj) * e1v(ji,jj)
            END DO
         END DO
      ENDIF
      !
   END SUBROUTINE Agrif_dyn_ts_flux

   
   SUBROUTINE Agrif_dta_ts( kt )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_dta_ts  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   kt
      !!
      LOGICAL :: ll_int_cons
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      ll_int_cons = ln_bt_fw ! Assume conservative temporal integration in the forward case only
      !
      ! Enforce volume conservation if no time refinement:  
      IF ( Agrif_rhot()==1 ) ll_int_cons=.TRUE.  
      !
      ! Interpolate barotropic fluxes
      Agrif_SpecialValue = 0._wp
      Agrif_UseSpecialValue = ln_spc_dyn

      use_sign_north = .TRUE.
      sign_north = -1.

      !
      ! Set bdy time interpolation stage to 0 (latter incremented locally do deal with corners)
      utint_stage(:,:) = 0
      vtint_stage(:,:) = 0
      !
      IF( ll_int_cons ) THEN  ! Conservative interpolation
         IF ( lk_tint2d_notinterp ) THEN
            Agrif_UseSpecialValue = .FALSE.
            CALL Agrif_Bc_variable( ub2b_interp_id, calledweight=1._wp, procname=interpub2b_const )
            CALL Agrif_Bc_variable( vb2b_interp_id, calledweight=1._wp, procname=interpvb2b_const ) 
            ! Divergence conserving correction terms:
            IF ( Agrif_Rhox()>1 ) CALL Agrif_Bc_variable(    ub2b_cor_id, calledweight=1._wp, procname=ub2b_cor )
            IF ( Agrif_Rhoy()>1 ) CALL Agrif_Bc_variable(    vb2b_cor_id, calledweight=1._wp, procname=vb2b_cor )
         ELSE
            ! order matters here !!!!!!
            CALL Agrif_Bc_variable( ub2b_interp_id, calledweight=1._wp, procname=interpub2b ) ! Time integrated
            CALL Agrif_Bc_variable( vb2b_interp_id, calledweight=1._wp, procname=interpvb2b ) 
            !
            bdy_tinterp = 1
            CALL Agrif_Bc_variable( unb_interp_id , calledweight=1._wp, procname=interpunb  ) ! After
            CALL Agrif_Bc_variable( vnb_interp_id , calledweight=1._wp, procname=interpvnb  )  
            !
            bdy_tinterp = 2
            CALL Agrif_Bc_variable( unb_interp_id , calledweight=0._wp, procname=interpunb  ) ! Before
            CALL Agrif_Bc_variable( vnb_interp_id , calledweight=0._wp, procname=interpvnb  )   
         ENDIF
      ELSE ! Linear interpolation
         !
         ubdy(:,:) = 0._wp   ;   vbdy(:,:) = 0._wp 
         CALL Agrif_Bc_variable( unb_interp_id, procname=interpunb )
         CALL Agrif_Bc_variable( vnb_interp_id, procname=interpvnb )
      ENDIF
      Agrif_UseSpecialValue = .FALSE.
      use_sign_north = .FALSE.
      ! 
   END SUBROUTINE Agrif_dta_ts


   SUBROUTINE Agrif_ssh( kt )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_ssh  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   kt
      !
      INTEGER  :: ji, jj
      INTEGER  :: istart, iend, jstart, jend
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !      
      ! Linear time interpolation of sea level
      !
      Agrif_SpecialValue    = 0._wp
      Agrif_UseSpecialValue = .TRUE.
      CALL Agrif_Bc_variable(sshn_id, procname=interpsshn )
      Agrif_UseSpecialValue = .FALSE.
      !
      ! --- West --- !
      IF(lk_west) THEN
         istart = nn_hls + 2                                                          ! halo + land + 1
         iend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhox()               ! halo + land + nbghostcells
         DO ji = mi0(istart), mi1(iend)
            DO jj = 1, jpj
               ssh(ji,jj,Krhs_a) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- East --- !
      IF(lk_east) THEN
         istart = jpiglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhox()       ! halo + land + nbghostcells - 1
         iend   = jpiglo - ( nn_hls + 1 )                                              ! halo + land + 1            - 1
         DO ji = mi0(istart), mi1(iend)
            DO jj = 1, jpj
               ssh(ji,jj,Krhs_a) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- South --- !
      IF(lk_south) THEN
         jstart = nn_hls + 2                                                          ! halo + land + 1
         jend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhoy()               ! halo + land + nbghostcells
         DO jj = mj0(jstart), mj1(jend)
            DO ji = 1, jpi
               ssh(ji,jj,Krhs_a) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- North --- !
      IF(lk_north) THEN
         jstart = jpjglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhoy()     ! halo + land + nbghostcells - 1
         jend   = jpjglo - ( nn_hls + 1 )                                            ! halo + land + 1            - 1
         DO jj = mj0(jstart), mj1(jend)
            DO ji = 1, jpi
               ssh(ji,jj,Krhs_a) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
   END SUBROUTINE Agrif_ssh


   SUBROUTINE Agrif_ssh_ts( jn )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_ssh_ts  ***
      !!----------------------------------------------------------------------  
      INTEGER, INTENT(in) ::   jn
      !!
      INTEGER :: ji, jj
      INTEGER  :: istart, iend, jstart, jend
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      ! --- West --- !
      IF(lk_west) THEN
         istart = nn_hls + 2                                                        ! halo + land + 1
         iend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhox()             ! halo + land + nbghostcells
         DO ji = mi0(istart), mi1(iend)
            DO jj = 1, jpj
               ssha_e(ji,jj) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- East --- !
      IF(lk_east) THEN
         istart = jpiglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhox()    ! halo + land + nbghostcells - 1
         iend   = jpiglo - ( nn_hls + 1 )                                           ! halo + land + 1            - 1
         DO ji = mi0(istart), mi1(iend)
            DO jj = 1, jpj
               ssha_e(ji,jj) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- South --- !
      IF(lk_south) THEN
         jstart = nn_hls + 2                                                        ! halo + land + 1
         jend   = nn_hls + nbghostcells + nn_shift_bar*Agrif_Rhoy()             ! halo + land + nbghostcells
         DO jj = mj0(jstart), mj1(jend)
            DO ji = 1, jpi
               ssha_e(ji,jj) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
      ! --- North --- !
      IF(lk_north) THEN
         jstart = jpjglo - ( nn_hls + nbghostcells -1 ) - nn_shift_bar*Agrif_Rhoy()    ! halo + land + nbghostcells - 1
         jend   = jpjglo - ( nn_hls + 1 )                                           ! halo + land + 1            - 1
         DO jj = mj0(jstart), mj1(jend)
            DO ji = 1, jpi
               ssha_e(ji,jj) = hbdy(ji,jj)
            END DO
         END DO
      ENDIF
      !
   END SUBROUTINE Agrif_ssh_ts

   
   SUBROUTINE Agrif_avm
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE Agrif_avm  ***
      !!----------------------------------------------------------------------  
      REAL(wp) ::   zalpha
      !!----------------------------------------------------------------------  
      !
      IF( Agrif_Root() )   RETURN
      !
      zalpha = 1._wp ! JC: proper time interpolation impossible  
                     ! => use last available value from parent 
      !
      Agrif_SpecialValue    = 0.e0
      Agrif_UseSpecialValue = .TRUE.
      l_vremap              = ln_vert_remap
      !
      CALL Agrif_Bc_variable( avm_id, calledweight=zalpha, procname=interpavm )       
      !
      Agrif_UseSpecialValue = .FALSE.
      l_vremap              = .FALSE.
      !
   END SUBROUTINE Agrif_avm


   SUBROUTINE interptsn( ptab, i1, i2, j1, j2, k1, k2, n1, n2, before )
      !!----------------------------------------------------------------------
      REAL(wp), DIMENSION(i1:i2,j1:j2,k1:k2,n1:n2), INTENT(inout) ::   ptab
      INTEGER                                     , INTENT(in   ) ::   i1, i2, j1, j2, k1, k2, n1, n2
      LOGICAL                                     , INTENT(in   ) ::   before
      !
      INTEGER  ::   ji, jj, jk, jn  ! dummy loop indices
      INTEGER  ::   N_in, N_out
      INTEGER  :: item
      ! vertical interpolation:
      REAL(wp) :: zhtot, zwgt
      REAL(wp), DIMENSION(k1:k2,1:jpts) :: tabin, tabin_i
      REAL(wp), DIMENSION(k1:k2) :: z_in, h_in_i, z_in_i
      REAL(wp), DIMENSION(1:jpk) :: h_out, z_out
      !!----------------------------------------------------------------------

      IF( before ) THEN

         item = Kmm_a
         IF( l_ini_child )   Kmm_a = Kbb_a  

         DO jn = 1,jpts
            DO jk=k1,k2
               DO jj=j1,j2
                 DO ji=i1,i2
                       ptab(ji,jj,jk,jn) = ts(ji,jj,jk,jn,Kmm_a)
                 END DO
              END DO
           END DO
         END DO

         IF( l_vremap .OR. l_ini_child .OR. ln_zps ) THEN

            ! Fill cell depths (i.e. gdept) to be interpolated
            ! Warning: these are masked, hence extrapolated prior interpolation.
            DO jj=j1,j2
               DO ji=i1,i2
                  ptab(ji,jj,k1,jpts+1) = 0.5_wp * tmask(ji,jj,k1) * e3t(ji,jj,k1,Kmm_a)
                  DO jk=k1+1,k2
                     ptab(ji,jj,jk,jpts+1) = tmask(ji,jj,jk) * &
                        & ( ptab(ji,jj,jk-1,jpts+1) + 0.5_wp * (e3t(ji,jj,jk-1,Kmm_a)+e3t(ji,jj,jk,Kmm_a)) )
                  END DO
               END DO
            END DO
         
            ! Save ssh at last level:
            IF (.NOT.ln_linssh) THEN
               ptab(i1:i2,j1:j2,k2,jpts+1) = ssh(i1:i2,j1:j2,Kmm_a)*tmask(i1:i2,j1:j2,1) 
            END IF      
         ENDIF
         Kmm_a = item

      ELSE 
         item = Krhs_a
         IF( l_ini_child )   Krhs_a = Kbb_a  

         IF( l_vremap .OR. l_ini_child ) THEN
            IF (ln_linssh) ptab(i1:i2,j1:j2,k2,n2) = 0._wp 
            DO jj=j1,j2
               DO ji=i1,i2
                  ts(ji,jj,:,:,Krhs_a) = 0.  
                  !
                  ! Build vertical grids:
                  N_in = mbkt_parent(ji,jj)
                  N_out = mbkt(ji,jj)
                  IF (N_in*N_out > 0) THEN
                     ! Input grid (account for partial cells if any):
                     DO jk=1,N_in
                        z_in(jk) = ptab(ji,jj,jk,n2) - ptab(ji,jj,k2,n2)
                        tabin(jk,1:jpts) = ptab(ji,jj,jk,1:jpts)
                     END DO
                  
                     ! Intermediate grid:
                     IF ( l_vremap ) THEN
                        DO jk = 1, N_in
                           h_in_i(jk) = e3t0_parent(ji,jj,jk) * & 
                             &       (1._wp + ptab(ji,jj,k2,n2)/(ht0_parent(ji,jj)*ssmask(ji,jj) + 1._wp - ssmask(ji,jj)))
                        END DO
                        z_in_i(1) = 0.5_wp * h_in_i(1)
                        DO jk=2,N_in
                           z_in_i(jk) = z_in_i(jk-1) + 0.5_wp * ( h_in_i(jk) + h_in_i(jk-1) )
                        END DO
                        z_in_i(1:N_in) = z_in_i(1:N_in)  - ptab(ji,jj,k2,n2)
                     ENDIF                              

                     ! Output (Child) grid:
                     DO jk=1,N_out
                        h_out(jk) = e3t(ji,jj,jk,Krhs_a)
                     END DO
                     z_out(1) = 0.5_wp * h_out(1)
                     DO jk=2,N_out
                        z_out(jk) = z_out(jk-1) + 0.5_wp * ( h_out(jk)+h_out(jk-1) )
                     END DO
                     IF (.NOT.ln_linssh) z_out(1:N_out) = z_out(1:N_out)  - ssh(ji,jj,Krhs_a)

                     IF( l_ini_child ) THEN
                        CALL remap_linear(tabin(1:N_in,1:jpts),z_in(1:N_in),ts(ji,jj,1:N_out,1:jpts,Krhs_a),              &
                                      &   z_out(1:N_out),N_in,N_out,jpts)  
                     ELSE 
                        CALL remap_linear(tabin(1:N_in,1:jpts),z_in(1:N_in),tabin_i(1:N_in,1:jpts),                       &
                                     &   z_in_i(1:N_in),N_in,N_in,jpts)
                        CALL reconstructandremap(tabin_i(1:N_in,1:jpts),h_in_i(1:N_in),ts(ji,jj,1:N_out,1:jpts,Krhs_a),   &
                                      &   h_out(1:N_out),N_in,N_out,jpts)  
                     ENDIF
                  ENDIF
               END DO
            END DO
            Krhs_a = item
 
         ELSE
         
            IF ( Agrif_Parent(ln_zps) ) THEN ! Account for partial cells 
                                             ! linear vertical interpolation
               DO jj=j1,j2
                  DO ji=i1,i2
                     !
                     N_in  = mbkt(ji,jj)
                     N_out = mbkt(ji,jj)
                     z_in(1) = ptab(ji,jj,1,n2)
                     tabin(1,1:jpts) = ptab(ji,jj,1,1:jpts)
                     DO jk=2, N_in
                        z_in(jk) = ptab(ji,jj,jk,n2)
                        tabin(jk,1:jpts) = ptab(ji,jj,jk,1:jpts)
                     END DO
                     IF (.NOT.ln_linssh) z_in(1:N_in) = z_in(1:N_in) - ptab(ji,jj,k2,n2)
                     z_out(1) = 0.5_wp * e3t(ji,jj,1,Krhs_a)
                     DO jk=2, N_out
                        z_out(jk) = z_out(jk-1) + 0.5_wp * (e3t(ji,jj,jk-1,Krhs_a) + e3t(ji,jj,jk,Krhs_a))
                     END DO
                     IF (.NOT.ln_linssh) z_out(1:N_out) = z_out(1:N_out) - ssh(ji,jj,Krhs_a)
                     CALL remap_linear(tabin(1:N_in,1:jpts),z_in(1:N_in),ptab(ji,jj,1:N_out,1:jpts), &
                                   &   z_out(1:N_out),N_in,N_out,jpts)  
                  END DO
               END DO
            ENDIF

            DO jn =1, jpts
               ts(i1:i2,j1:j2,1:jpk,jn,Krhs_a) = ptab(i1:i2,j1:j2,1:jpk,jn)*tmask(i1:i2,j1:j2,1:jpk)
            END DO
         ENDIF

      ENDIF
      !
   END SUBROUTINE interptsn

   
   SUBROUTINE interpsshn( ptab, i1, i2, j1, j2, before )
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE interpsshn  ***
      !!----------------------------------------------------------------------  
      INTEGER                         , INTENT(in   ) ::   i1, i2, j1, j2
      REAL(wp), DIMENSION(i1:i2,j1:j2), INTENT(inout) ::   ptab
      LOGICAL                         , INTENT(in   ) ::   before
      !
      !!----------------------------------------------------------------------  
      !
      IF( before) THEN
         ptab(i1:i2,j1:j2) = ssh(i1:i2,j1:j2,Kmm_a)
      ELSE
         IF( l_ini_child ) THEN
            ssh(i1:i2,j1:j2,Krhs_a) = ptab(i1:i2,j1:j2) * tmask(i1:i2,j1:j2,1)
         ELSE
            hbdy(i1:i2,j1:j2) = ptab(i1:i2,j1:j2) * tmask(i1:i2,j1:j2,1)
         ENDIF
      ENDIF
      !
   END SUBROUTINE interpsshn

   
   SUBROUTINE interpun( ptab, i1, i2, j1, j2, k1, k2, m1, m2, before )
      !!----------------------------------------------------------------------
      !!                  *** ROUTINE interpun ***
      !!---------------------------------------------    
      !!
      INTEGER, INTENT(in) :: i1,i2,j1,j2,k1,k2,m1,m2
      REAL(wp), DIMENSION(i1:i2,j1:j2,k1:k2,m1:m2), INTENT(inout) :: ptab
      LOGICAL, INTENT(in) :: before
      !!
      INTEGER :: ji,jj,jk
      REAL(wp) :: zrhoy, zhtot
      ! vertical interpolation:
      REAL(wp), DIMENSION(k1:k2) :: tabin, h_in, z_in
      REAL(wp), DIMENSION(1:jpk) :: h_out, z_out
      INTEGER  :: N_in, N_out,item
      REAL(wp) :: h_diff
      !!---------------------------------------------    
      !
      IF (before) THEN 

         item = Kmm_a
         IF( l_ini_child )   Kmm_a = Kbb_a     

         DO jk=1,jpk
            DO jj=j1,j2
               DO ji=i1,i2
                  ptab(ji,jj,jk,1) = (e2u(ji,jj) * e3u(ji,jj,jk,Kmm_a) * uu(ji,jj,jk,Kmm_a)*umask(ji,jj,jk)) 
                  IF( l_vremap .OR. l_ini_child) THEN
                     ! Interpolate thicknesses (masked for subsequent extrapolation)
                     ptab(ji,jj,jk,2) = umask(ji,jj,jk) * e2u(ji,jj) * e3u(ji,jj,jk,Kmm_a)
                  ENDIF