Skip to content
Snippets Groups Projects
domvvl.F90 55.2 KiB
Newer Older
Guillaume Samson's avatar
Guillaume Samson committed
MODULE domvvl
   !!======================================================================
   !!                       ***  MODULE domvvl   ***
   !! Ocean :
   !!======================================================================
   !! History :  2.0  !  2006-06  (B. Levier, L. Marie)  original code
   !!            3.1  !  2009-02  (G. Madec, M. Leclair, R. Benshila)  pure z* coordinate
   !!            3.3  !  2011-10  (M. Leclair) totally rewrote domvvl: vvl option includes z_star and z_tilde coordinates
   !!            3.6  !  2014-11  (P. Mathiot) add ice shelf capability
   !!            4.1  !  2019-08  (A. Coward, D. Storkey) rename dom_vvl_sf_swp -> dom_vvl_sf_update for new timestepping
   !!             -   !  2020-02  (G. Madec, S. Techene) introduce ssh to h0 ratio
   !!----------------------------------------------------------------------

   USE oce             ! ocean dynamics and tracers
   USE phycst          ! physical constant
   USE dom_oce         ! ocean space and time domain
   USE sbc_oce         ! ocean surface boundary condition
   USE wet_dry         ! wetting and drying
   USE usrdef_istate   ! user defined initial state (wad only)
   USE restart         ! ocean restart
   !
   USE in_out_manager  ! I/O manager
   USE iom             ! I/O manager library
   USE lib_mpp         ! distributed memory computing library
   USE lbclnk          ! ocean lateral boundary conditions (or mpp link)
   USE timing          ! Timing

   IMPLICIT NONE
   PRIVATE

   !                                                      !!* Namelist nam_vvl
   LOGICAL , PUBLIC :: ln_vvl_zstar           = .FALSE.    ! zstar  vertical coordinate
   LOGICAL , PUBLIC :: ln_vvl_ztilde          = .FALSE.    ! ztilde vertical coordinate
   LOGICAL , PUBLIC :: ln_vvl_layer           = .FALSE.    ! level  vertical coordinate
   LOGICAL , PUBLIC :: ln_vvl_ztilde_as_zstar = .FALSE.    ! ztilde vertical coordinate
   LOGICAL , PUBLIC :: ln_vvl_zstar_at_eqtor  = .FALSE.    ! ztilde vertical coordinate
   LOGICAL , PUBLIC :: ln_vvl_kepe            = .FALSE.    ! kinetic/potential energy transfer
   !                                                       ! conservation: not used yet
   REAL(wp)         :: rn_ahe3                             ! thickness diffusion coefficient
   REAL(wp)         :: rn_rst_e3t                          ! ztilde to zstar restoration timescale [days]
   REAL(wp)         :: rn_lf_cutoff                        ! cutoff frequency for low-pass filter  [days]
   REAL(wp)         :: rn_zdef_max                         ! maximum fractional e3t deformation
   LOGICAL , PUBLIC :: ln_vvl_dbg = .FALSE.                ! debug control prints

   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: un_td, vn_td                ! thickness diffusion transport
   REAL(wp)        , ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: hdiv_lf                     ! low frequency part of hz divergence
   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: tilde_e3t_b, tilde_e3t_n    ! baroclinic scale factors
   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: tilde_e3t_a, dtilde_e3t_a   ! baroclinic scale factors
   REAL(wp)        , ALLOCATABLE, SAVE, DIMENSION(:,:)   :: frq_rst_e3t                 ! retoring period for scale factors
   REAL(wp)        , ALLOCATABLE, SAVE, DIMENSION(:,:)   :: frq_rst_hdv                 ! retoring period for low freq. divergence

#if defined key_qco   ||   defined key_linssh
   !!----------------------------------------------------------------------
   !!   'key_qco'                        Quasi-Eulerian vertical coordinate
   !!       OR         EMPTY MODULE
   !!   'key_linssh'                        Fix in time vertical coordinate
   !!----------------------------------------------------------------------
#else
   !!----------------------------------------------------------------------
   !!   Default key      Old management of time varying vertical coordinate
   !!----------------------------------------------------------------------

   !!----------------------------------------------------------------------
   !!   dom_vvl_init     : define initial vertical scale factors, depths and column thickness
   !!   dom_vvl_sf_nxt   : Compute next vertical scale factors
   !!   dom_vvl_sf_update   : Swap vertical scale factors and update the vertical grid
   !!   dom_vvl_interpol : Interpolate vertical scale factors from one grid point to another
   !!   dom_vvl_rst      : read/write restart file
   !!   dom_vvl_ctl      : Check the vvl options
   !!----------------------------------------------------------------------

   PUBLIC  dom_vvl_init       ! called by domain.F90
   PUBLIC  dom_vvl_zgr        ! called by isfcpl.F90
   PUBLIC  dom_vvl_sf_nxt     ! called by step.F90
   PUBLIC  dom_vvl_sf_update  ! called by step.F90
   PUBLIC  dom_vvl_interpol   ! called by dynnxt.F90

   !! * Substitutions
#  include "do_loop_substitute.h90"
   !!----------------------------------------------------------------------
   !! NEMO/OCE 4.0 , NEMO Consortium (2018)
   !! $Id: domvvl.F90 15471 2021-11-04 16:28:56Z jchanut $
   !! Software governed by the CeCILL license (see ./LICENSE)
   !!----------------------------------------------------------------------
CONTAINS

   INTEGER FUNCTION dom_vvl_alloc()
      !!----------------------------------------------------------------------
      !!                ***  FUNCTION dom_vvl_alloc  ***
      !!----------------------------------------------------------------------
      IF( ln_vvl_zstar )   dom_vvl_alloc = 0
      IF( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN
         ALLOCATE( tilde_e3t_b(jpi,jpj,jpk)  , tilde_e3t_n(jpi,jpj,jpk) , tilde_e3t_a(jpi,jpj,jpk) ,   &
            &      dtilde_e3t_a(jpi,jpj,jpk) , un_td  (jpi,jpj,jpk)     , vn_td  (jpi,jpj,jpk)     ,   &
            &      STAT = dom_vvl_alloc        )
         CALL mpp_sum ( 'domvvl', dom_vvl_alloc )
         IF( dom_vvl_alloc /= 0 )   CALL ctl_stop( 'STOP', 'dom_vvl_alloc: failed to allocate arrays' )
         un_td = 0._wp
         vn_td = 0._wp
      ENDIF
      IF( ln_vvl_ztilde ) THEN
         ALLOCATE( frq_rst_e3t(jpi,jpj) , frq_rst_hdv(jpi,jpj) , hdiv_lf(jpi,jpj,jpk) , STAT= dom_vvl_alloc )
         CALL mpp_sum ( 'domvvl', dom_vvl_alloc )
         IF( dom_vvl_alloc /= 0 )   CALL ctl_stop( 'STOP', 'dom_vvl_alloc: failed to allocate arrays' )
      ENDIF
      !
   END FUNCTION dom_vvl_alloc


   SUBROUTINE dom_vvl_init( Kbb, Kmm, Kaa )
      !!----------------------------------------------------------------------
      !!                ***  ROUTINE dom_vvl_init  ***
      !!
      !! ** Purpose :  Initialization of all scale factors, depths
      !!               and water column heights
      !!
      !! ** Method  :  - use restart file and/or initialize
      !!               - interpolate scale factors
      !!
      !! ** Action  : - e3t_(n/b) and tilde_e3t_(n/b)
      !!              - Regrid: e3[u/v](:,:,:,Kmm)
      !!                        e3[u/v](:,:,:,Kmm)
      !!                        e3w(:,:,:,Kmm)
      !!                        e3[u/v]w_b
      !!                        e3[u/v]w_n
      !!                        gdept(:,:,:,Kmm), gdepw(:,:,:,Kmm) and gde3w
      !!              - h(t/u/v)_0
      !!              - frq_rst_e3t and frq_rst_hdv
      !!
      !! Reference  : Leclair, M., and G. Madec, 2011, Ocean Modelling.
      !!----------------------------------------------------------------------
      INTEGER, INTENT(in) :: Kbb, Kmm, Kaa
      !
      IF(lwp) WRITE(numout,*)
      IF(lwp) WRITE(numout,*) 'dom_vvl_init : Variable volume activated'
      IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
      !
      CALL dom_vvl_ctl     ! choose vertical coordinate (z_star, z_tilde or layer)
      !
      !                    ! Allocate module arrays
      IF( dom_vvl_alloc() /= 0 )   CALL ctl_stop( 'STOP', 'dom_vvl_init : unable to allocate arrays' )
      !
      !                    ! Read or initialize e3t_(b/n), tilde_e3t_(b/n) and hdiv_lf
      CALL dom_vvl_rst( nit000, Kbb, Kmm, 'READ' )
      e3t(:,:,jpk,Kaa) = e3t_0(:,:,jpk)  ! last level always inside the sea floor set one for all
      !
      CALL dom_vvl_zgr(Kbb, Kmm, Kaa) ! interpolation scale factor, depth and water column
      !
   END SUBROUTINE dom_vvl_init


   SUBROUTINE dom_vvl_zgr(Kbb, Kmm, Kaa)
      !!----------------------------------------------------------------------
      !!                ***  ROUTINE dom_vvl_init  ***
      !!
      !! ** Purpose :  Interpolation of all scale factors,
      !!               depths and water column heights
      !!
      !! ** Method  :  - interpolate scale factors
      !!
      !! ** Action  : - e3t_(n/b) and tilde_e3t_(n/b)
      !!              - Regrid: e3(u/v)_n
      !!                        e3(u/v)_b
      !!                        e3w_n
      !!                        e3(u/v)w_b
      !!                        e3(u/v)w_n
      !!                        gdept_n, gdepw_n and gde3w_n
      !!              - h(t/u/v)_0
      !!              - frq_rst_e3t and frq_rst_hdv
      !!
      !! Reference  : Leclair, M., and G. Madec, 2011, Ocean Modelling.
      !!----------------------------------------------------------------------
      INTEGER, INTENT(in) :: Kbb, Kmm, Kaa
      !!----------------------------------------------------------------------
      INTEGER ::   ji, jj, jk
      INTEGER ::   ii0, ii1, ij0, ij1
      REAL(wp)::   zcoef
      !!----------------------------------------------------------------------
      !
      !                    !== Set of all other vertical scale factors  ==!  (now and before)
      !                                ! Horizontal interpolation of e3t
      CALL dom_vvl_interpol( e3t(:,:,:,Kbb), e3u(:,:,:,Kbb), 'U' )    ! from T to U
      CALL dom_vvl_interpol( e3t(:,:,:,Kmm), e3u(:,:,:,Kmm), 'U' )
      CALL dom_vvl_interpol( e3t(:,:,:,Kbb), e3v(:,:,:,Kbb), 'V' )    ! from T to V
      CALL dom_vvl_interpol( e3t(:,:,:,Kmm), e3v(:,:,:,Kmm), 'V' )
      CALL dom_vvl_interpol( e3u(:,:,:,Kmm), e3f(:,:,:), 'F' )    ! from U to F
      !                                ! Vertical interpolation of e3t,u,v
      CALL dom_vvl_interpol( e3t(:,:,:,Kmm), e3w (:,:,:,Kmm), 'W'  )  ! from T to W
      CALL dom_vvl_interpol( e3t(:,:,:,Kbb), e3w (:,:,:,Kbb), 'W'  )
      CALL dom_vvl_interpol( e3u(:,:,:,Kmm), e3uw(:,:,:,Kmm), 'UW' )  ! from U to UW
      CALL dom_vvl_interpol( e3u(:,:,:,Kbb), e3uw(:,:,:,Kbb), 'UW' )
      CALL dom_vvl_interpol( e3v(:,:,:,Kmm), e3vw(:,:,:,Kmm), 'VW' )  ! from V to UW
      CALL dom_vvl_interpol( e3v(:,:,:,Kbb), e3vw(:,:,:,Kbb), 'VW' )

      ! We need to define e3[tuv]_a for AGRIF initialisation (should not be a problem for the restartability...)
      e3t(:,:,:,Kaa) = e3t(:,:,:,Kmm)
      e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm)
      e3v(:,:,:,Kaa) = e3v(:,:,:,Kmm)
      !
      !                    !==  depth of t and w-point  ==!   (set the isf depth as it is in the initial timestep)
Guillaume Samson's avatar
Guillaume Samson committed
      gdept(:,:,1,Kmm) = 0.5_wp * e3w(:,:,1,Kmm)       ! reference to the ocean surface (used for MLD and light penetration)
      gdepw(:,:,1,Kmm) = 0.0_wp
      gde3w(:,:,1) = gdept(:,:,1,Kmm) - ssh(:,:,Kmm)  ! reference to a common level z=0 for hpg
      gdept(:,:,1,Kbb) = 0.5_wp * e3w(:,:,1,Kbb)
      gdepw(:,:,1,Kbb) = 0.0_wp
      DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 2, jpk )                     ! vertical sum
         !    zcoef = tmask - wmask    ! 0 everywhere tmask = wmask, ie everywhere expect at jk = mikt
         !                             ! 1 everywhere from mbkt to mikt + 1 or 1 (if no isf)
         !                             ! 0.5 where jk = mikt
!!gm ???????   BUG ?  gdept(:,:,:,Kmm) as well as gde3w  does not include the thickness of ISF ??
         zcoef = ( tmask(ji,jj,jk) - wmask(ji,jj,jk) )
         gdepw(ji,jj,jk,Kmm) = gdepw(ji,jj,jk-1,Kmm) + e3t(ji,jj,jk-1,Kmm)
         gdept(ji,jj,jk,Kmm) =      zcoef  * ( gdepw(ji,jj,jk  ,Kmm) + 0.5 * e3w(ji,jj,jk,Kmm))  &
            &                + (1-zcoef) * ( gdept(ji,jj,jk-1,Kmm) +       e3w(ji,jj,jk,Kmm))
         gde3w(ji,jj,jk) = gdept(ji,jj,jk,Kmm) - ssh(ji,jj,Kmm)
         gdepw(ji,jj,jk,Kbb) = gdepw(ji,jj,jk-1,Kbb) + e3t(ji,jj,jk-1,Kbb)
         gdept(ji,jj,jk,Kbb) =      zcoef  * ( gdepw(ji,jj,jk  ,Kbb) + 0.5 * e3w(ji,jj,jk,Kbb))  &
            &                + (1-zcoef) * ( gdept(ji,jj,jk-1,Kbb) +       e3w(ji,jj,jk,Kbb))
      END_3D
      !
      !                    !==  thickness of the water column  !!   (ocean portion only)
      ht(:,:) = e3t(:,:,1,Kmm) * tmask(:,:,1)   !!gm  BUG  :  this should be 1/2 * e3w(k=1) ....
      hu(:,:,Kbb) = e3u(:,:,1,Kbb) * umask(:,:,1)
      hu(:,:,Kmm) = e3u(:,:,1,Kmm) * umask(:,:,1)
      hv(:,:,Kbb) = e3v(:,:,1,Kbb) * vmask(:,:,1)
      hv(:,:,Kmm) = e3v(:,:,1,Kmm) * vmask(:,:,1)
      DO jk = 2, jpkm1
         ht(:,:) = ht(:,:) + e3t(:,:,jk,Kmm) * tmask(:,:,jk)
         hu(:,:,Kbb) = hu(:,:,Kbb) + e3u(:,:,jk,Kbb) * umask(:,:,jk)
         hu(:,:,Kmm) = hu(:,:,Kmm) + e3u(:,:,jk,Kmm) * umask(:,:,jk)
         hv(:,:,Kbb) = hv(:,:,Kbb) + e3v(:,:,jk,Kbb) * vmask(:,:,jk)
         hv(:,:,Kmm) = hv(:,:,Kmm) + e3v(:,:,jk,Kmm) * vmask(:,:,jk)
      END DO
      !
      !                    !==  inverse of water column thickness   ==!   (u- and v- points)
      r1_hu(:,:,Kbb) = ssumask(:,:) / ( hu(:,:,Kbb) + 1._wp - ssumask(:,:) )    ! _i mask due to ISF
      r1_hu(:,:,Kmm) = ssumask(:,:) / ( hu(:,:,Kmm) + 1._wp - ssumask(:,:) )
      r1_hv(:,:,Kbb) = ssvmask(:,:) / ( hv(:,:,Kbb) + 1._wp - ssvmask(:,:) )
      r1_hv(:,:,Kmm) = ssvmask(:,:) / ( hv(:,:,Kmm) + 1._wp - ssvmask(:,:) )

      !                    !==   z_tilde coordinate case  ==!   (Restoring frequencies)
      IF( ln_vvl_ztilde ) THEN
!!gm : idea: add here a READ in a file of custumized restoring frequency
         !                                   ! Values in days provided via the namelist
         !                                   ! use rsmall to avoid possible division by zero errors with faulty settings
         frq_rst_e3t(:,:) = 2._wp * rpi / ( MAX( rn_rst_e3t  , rsmall ) * 86400.0_wp )
         frq_rst_hdv(:,:) = 2._wp * rpi / ( MAX( rn_lf_cutoff, rsmall ) * 86400.0_wp )
         !
         IF( ln_vvl_ztilde_as_zstar ) THEN   ! z-star emulation using z-tile
            frq_rst_e3t(:,:) = 0._wp               !Ignore namelist settings
            frq_rst_hdv(:,:) = 1._wp / rn_Dt
         ENDIF
         IF ( ln_vvl_zstar_at_eqtor ) THEN   ! use z-star in vicinity of the Equator
            DO_2D( 1, 1, 1, 1 )
!!gm  case |gphi| >= 6 degrees is useless   initialized just above by default
               IF( ABS(gphit(ji,jj)) >= 6.) THEN
                  ! values outside the equatorial band and transition zone (ztilde)
                  frq_rst_e3t(ji,jj) =  2.0_wp * rpi / ( MAX( rn_rst_e3t  , rsmall ) * 86400.e0_wp )
                  frq_rst_hdv(ji,jj) =  2.0_wp * rpi / ( MAX( rn_lf_cutoff, rsmall ) * 86400.e0_wp )
               ELSEIF( ABS(gphit(ji,jj)) <= 2.5) THEN    ! Equator strip ==> z-star
                  ! values inside the equatorial band (ztilde as zstar)
                  frq_rst_e3t(ji,jj) =  0.0_wp
                  frq_rst_hdv(ji,jj) =  1.0_wp / rn_Dt
               ELSE                                      ! transition band (2.5 to 6 degrees N/S)
                  !                                      ! (linearly transition from z-tilde to z-star)
                  frq_rst_e3t(ji,jj) = 0.0_wp + (frq_rst_e3t(ji,jj)-0.0_wp)*0.5_wp   &
                     &            * (  1.0_wp - COS( rad*(ABS(gphit(ji,jj))-2.5_wp)  &
                     &                                          * 180._wp / 3.5_wp ) )
                  frq_rst_hdv(ji,jj) = (1.0_wp / rn_Dt)                                &
                     &            + (  frq_rst_hdv(ji,jj)-(1.e0_wp / rn_Dt) )*0.5_wp   &
                     &            * (  1._wp  - COS( rad*(ABS(gphit(ji,jj))-2.5_wp)  &
                     &                                          * 180._wp / 3.5_wp ) )
               ENDIF
            END_2D
            IF( cn_cfg == "orca" .OR. cn_cfg == "ORCA" ) THEN
               IF( nn_cfg == 3 ) THEN   ! ORCA2: Suppress ztilde in the Foxe Basin for ORCA2
                  ii0 = 103 + nn_hls - 1   ;   ii1 = 111 + nn_hls - 1
                  ij0 = 128 + nn_hls       ;   ij1 = 135 + nn_hls
                  frq_rst_e3t( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) ) =  0.0_wp
                  frq_rst_hdv( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) ) =  1.e0_wp / rn_Dt
               ENDIF
            ENDIF
         ENDIF
      ENDIF
      !
   END SUBROUTINE dom_vvl_zgr


   SUBROUTINE dom_vvl_sf_nxt( kt, Kbb, Kmm, Kaa, kcall )
      !!----------------------------------------------------------------------
      !!                ***  ROUTINE dom_vvl_sf_nxt  ***
      !!
      !! ** Purpose :  - compute the after scale factors used in tra_zdf, dynnxt,
      !!                 tranxt and dynspg routines
      !!
      !! ** Method  :  - z_star case:  Repartition of ssh INCREMENT proportionnaly to the level thickness.
      !!               - z_tilde_case: after scale factor increment =
      !!                                    high frequency part of horizontal divergence
      !!                                  + retsoring towards the background grid
      !!                                  + thickness difusion
      !!                               Then repartition of ssh INCREMENT proportionnaly
      !!                               to the "baroclinic" level thickness.
      !!
      !! ** Action  :  - hdiv_lf    : restoring towards full baroclinic divergence in z_tilde case
      !!               - tilde_e3t_a: after increment of vertical scale factor
      !!                              in z_tilde case
      !!               - e3(t/u/v)_a
      !!
      !! Reference  : Leclair, M., and Madec, G. 2011, Ocean Modelling.
      !!----------------------------------------------------------------------
      INTEGER, INTENT( in )           ::   kt             ! time step
      INTEGER, INTENT( in )           ::   Kbb, Kmm, Kaa  ! time step
      INTEGER, INTENT( in ), OPTIONAL ::   kcall          ! optional argument indicating call sequence
      !
      INTEGER                ::   ji, jj, jk            ! dummy loop indices
      INTEGER , DIMENSION(3) ::   ijk_max, ijk_min      ! temporary integers
      REAL(wp)               ::   z_tmin, z_tmax        ! local scalars
      LOGICAL                ::   ll_do_bclinic         ! local logical
      REAL(wp), DIMENSION(jpi,jpj)     ::   zht, z_scale, zwu, zwv, zhdiv
      REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::   ze3t
      LOGICAL , DIMENSION(:,:,:), ALLOCATABLE ::   llmsk
      !!----------------------------------------------------------------------
      !
      IF( ln_linssh )   RETURN      ! No calculation in linear free surface
      !
      IF( ln_timing )   CALL timing_start('dom_vvl_sf_nxt')
      !
      IF( kt == nit000 ) THEN
         IF(lwp) WRITE(numout,*)
         IF(lwp) WRITE(numout,*) 'dom_vvl_sf_nxt : compute after scale factors'
         IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~'
      ENDIF

      ll_do_bclinic = .TRUE.
      IF( PRESENT(kcall) ) THEN
         IF( kcall == 2 .AND. ln_vvl_ztilde )   ll_do_bclinic = .FALSE.
      ENDIF

      ! ******************************* !
      ! After acale factors at t-points !
      ! ******************************* !
      !                                                ! --------------------------------------------- !
      !                                                ! z_star coordinate and barotropic z-tilde part !
      !                                                ! --------------------------------------------- !
      !
      z_scale(:,:) = ( ssh(:,:,Kaa) - ssh(:,:,Kbb) ) * ssmask(:,:) / ( ht_0(:,:) + ssh(:,:,Kmm) + 1. - ssmask(:,:) )
      DO jk = 1, jpkm1
         ! formally this is the same as e3t(:,:,:,Kaa) = e3t_0*(1+ssha/ht_0)
         e3t(:,:,jk,Kaa) = e3t(:,:,jk,Kbb) + e3t(:,:,jk,Kmm) * z_scale(:,:) * tmask(:,:,jk)
      END DO
      !
      IF( (ln_vvl_ztilde .OR. ln_vvl_layer) .AND. ll_do_bclinic ) THEN   ! z_tilde or layer coordinate !
         !                                                               ! ------baroclinic part------ !
         ! I - initialization
         ! ==================

         ! 1 - barotropic divergence
         ! -------------------------
         zhdiv(:,:) = 0._wp
         zht(:,:)   = 0._wp
         DO jk = 1, jpkm1
            zhdiv(:,:) = zhdiv(:,:) + e3t(:,:,jk,Kmm) * hdiv(:,:,jk)
            zht  (:,:) = zht  (:,:) + e3t(:,:,jk,Kmm) * tmask(:,:,jk)
         END DO
         zhdiv(:,:) = zhdiv(:,:) / ( zht(:,:) + 1. - tmask_i(:,:) )

         ! 2 - Low frequency baroclinic horizontal divergence  (z-tilde case only)
         ! --------------------------------------------------
         IF( ln_vvl_ztilde ) THEN
            IF( kt > nit000 ) THEN
               DO jk = 1, jpkm1
                  hdiv_lf(:,:,jk) = hdiv_lf(:,:,jk) - rn_Dt * frq_rst_hdv(:,:)   &
                     &          * ( hdiv_lf(:,:,jk) - e3t(:,:,jk,Kmm) * ( hdiv(:,:,jk) - zhdiv(:,:) ) )
               END DO
            ENDIF
         ENDIF

         ! II - after z_tilde increments of vertical scale factors
         ! =======================================================
         tilde_e3t_a(:,:,:) = 0._wp  ! tilde_e3t_a used to store tendency terms

         ! 1 - High frequency divergence term
         ! ----------------------------------
         IF( ln_vvl_ztilde ) THEN     ! z_tilde case
            DO jk = 1, jpkm1
               tilde_e3t_a(:,:,jk) = tilde_e3t_a(:,:,jk) - ( e3t(:,:,jk,Kmm) * ( hdiv(:,:,jk) - zhdiv(:,:) ) - hdiv_lf(:,:,jk) )
            END DO
         ELSE                         ! layer case
            DO jk = 1, jpkm1
               tilde_e3t_a(:,:,jk) = tilde_e3t_a(:,:,jk) -   e3t(:,:,jk,Kmm) * ( hdiv(:,:,jk) - zhdiv(:,:) ) * tmask(:,:,jk)
            END DO
         ENDIF

         ! 2 - Restoring term (z-tilde case only)
         ! ------------------
         IF( ln_vvl_ztilde ) THEN
            DO jk = 1, jpk
               tilde_e3t_a(:,:,jk) = tilde_e3t_a(:,:,jk) - frq_rst_e3t(:,:) * tilde_e3t_b(:,:,jk)
            END DO
         ENDIF

         ! 3 - Thickness diffusion term
         ! ----------------------------
         zwu(:,:) = 0._wp
         zwv(:,:) = 0._wp
         DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )       ! a - first derivative: diffusive fluxes
            un_td(ji,jj,jk) = rn_ahe3 * umask(ji,jj,jk) * e2_e1u(ji,jj)           &
               &            * ( tilde_e3t_b(ji,jj,jk) - tilde_e3t_b(ji+1,jj  ,jk) )
            vn_td(ji,jj,jk) = rn_ahe3 * vmask(ji,jj,jk) * e1_e2v(ji,jj)           &
               &            * ( tilde_e3t_b(ji,jj,jk) - tilde_e3t_b(ji  ,jj+1,jk) )
            zwu(ji,jj) = zwu(ji,jj) + un_td(ji,jj,jk)
            zwv(ji,jj) = zwv(ji,jj) + vn_td(ji,jj,jk)
         END_3D
         DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )                 ! b - correction for last oceanic u-v points
            un_td(ji,jj,mbku(ji,jj)) = un_td(ji,jj,mbku(ji,jj)) - zwu(ji,jj)
            vn_td(ji,jj,mbkv(ji,jj)) = vn_td(ji,jj,mbkv(ji,jj)) - zwv(ji,jj)
         END_2D
         DO_3D( 0, 0, 0, 0, 1, jpkm1 )   ! c - second derivative: divergence of diffusive fluxes
            tilde_e3t_a(ji,jj,jk) = tilde_e3t_a(ji,jj,jk) + (   un_td(ji-1,jj  ,jk) - un_td(ji,jj,jk)    &
               &                                          +     vn_td(ji  ,jj-1,jk) - vn_td(ji,jj,jk)    &
               &                                            ) * r1_e1e2t(ji,jj)
         END_3D
         !                               ! d - thickness diffusion transport: boundary conditions
         !                             (stored for tracer advction and continuity equation)
         IF( nn_hls == 1 ) CALL lbc_lnk( 'domvvl', un_td , 'U' , -1._wp, vn_td , 'V' , -1._wp)
         ! 4 - Time stepping of baroclinic scale factors
         ! ---------------------------------------------
         CALL lbc_lnk( 'domvvl', tilde_e3t_a(:,:,:), 'T', 1._wp )
         tilde_e3t_a(:,:,:) = tilde_e3t_b(:,:,:) + rDt * tmask(:,:,:) * tilde_e3t_a(:,:,:)

         ! Maximum deformation control
         ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~
         ALLOCATE( ze3t(jpi,jpj,jpk), llmsk(jpi,jpj,jpk) )
         DO_3D( 0, 0, 0, 0, 1, jpkm1 )
            ze3t(ji,jj,jk) = tilde_e3t_a(ji,jj,jk) / e3t_0(ji,jj,jk) * tmask(ji,jj,jk) * tmask_i(ji,jj)
         END_3D
         !
         llmsk(     1:nn_hls,:,:) = .FALSE.   ! exclude halos from the checked region
         llmsk(Nie0+1:   jpi,:,:) = .FALSE.
         llmsk(:,     1:nn_hls,:) = .FALSE.
         llmsk(:,Nje0+1:   jpj,:) = .FALSE.
         !
         llmsk(Nis0:Nie0,Njs0:Nje0,:) = tmask(Nis0:Nie0,Njs0:Nje0,:) == 1._wp                  ! define only the inner domain
         z_tmax = MAXVAL( ze3t(:,:,:), mask = llmsk )   ;   CALL mpp_max( 'domvvl', z_tmax )   ! max over the global domain
         z_tmin = MINVAL( ze3t(:,:,:), mask = llmsk )   ;   CALL mpp_min( 'domvvl', z_tmin )   ! min over the global domain
         ! - ML - test: for the moment, stop simulation for too large e3_t variations
         IF( ( z_tmax >  rn_zdef_max ) .OR. ( z_tmin < - rn_zdef_max ) ) THEN
            CALL mpp_maxloc( 'domvvl', ze3t, llmsk, z_tmax, ijk_max )
            CALL mpp_minloc( 'domvvl', ze3t, llmsk, z_tmin, ijk_min )
            IF (lwp) THEN
               WRITE(numout, *) 'MAX( tilde_e3t_a(:,:,:) / e3t_0(:,:,:) ) =', z_tmax
               WRITE(numout, *) 'at i, j, k=', ijk_max
               WRITE(numout, *) 'MIN( tilde_e3t_a(:,:,:) / e3t_0(:,:,:) ) =', z_tmin
               WRITE(numout, *) 'at i, j, k=', ijk_min
               CALL ctl_stop( 'STOP', 'MAX( ABS( tilde_e3t_a(:,:,: ) ) / e3t_0(:,:,:) ) too high')
            ENDIF
         ENDIF
         DEALLOCATE( ze3t, llmsk )
         ! - ML - end test
         ! - ML - Imposing these limits will cause a baroclinicity error which is corrected for below
         tilde_e3t_a(:,:,:) = MIN( tilde_e3t_a(:,:,:),   rn_zdef_max * e3t_0(:,:,:) )
         tilde_e3t_a(:,:,:) = MAX( tilde_e3t_a(:,:,:), - rn_zdef_max * e3t_0(:,:,:) )

         !
         ! "tilda" change in the after scale factor
         ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
         DO jk = 1, jpkm1
            dtilde_e3t_a(:,:,jk) = tilde_e3t_a(:,:,jk) - tilde_e3t_b(:,:,jk)
         END DO
         ! III - Barotropic repartition of the sea surface height over the baroclinic profile
         ! ==================================================================================
         ! add ( ssh increment + "baroclinicity error" ) proportionly to e3t(n)
         ! - ML - baroclinicity error should be better treated in the future
         !        i.e. locally and not spread over the water column.
         !        (keep in mind that the idea is to reduce Eulerian velocity as much as possible)
         zht(:,:) = 0.
         DO jk = 1, jpkm1
            zht(:,:)  = zht(:,:) + tilde_e3t_a(:,:,jk) * tmask(:,:,jk)
         END DO
         z_scale(:,:) =  - zht(:,:) / ( ht_0(:,:) + ssh(:,:,Kmm) + 1. - ssmask(:,:) )
         DO jk = 1, jpkm1
            dtilde_e3t_a(:,:,jk) = dtilde_e3t_a(:,:,jk) + e3t(:,:,jk,Kmm) * z_scale(:,:) * tmask(:,:,jk)
         END DO

      ENDIF

      IF( ln_vvl_ztilde .OR. ln_vvl_layer )  THEN   ! z_tilde or layer coordinate !
      !                                           ! ---baroclinic part--------- !
         DO jk = 1, jpkm1
            e3t(:,:,jk,Kaa) = e3t(:,:,jk,Kaa) + dtilde_e3t_a(:,:,jk) * tmask(:,:,jk)
         END DO
      ENDIF

      IF( ln_vvl_dbg .AND. .NOT. ll_do_bclinic ) THEN   ! - ML - test: control prints for debuging
         !
         IF( lwp ) WRITE(numout, *) 'kt =', kt
         IF ( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN
            z_tmax = MAXVAL( tmask(:,:,1) * tmask_i(:,:) * ABS( zht(:,:) ) )
            CALL mpp_max( 'domvvl', z_tmax )                             ! max over the global domain
            IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(SUM(tilde_e3t_a))) =', z_tmax
         END IF
         !
         zht(:,:) = 0.0_wp
         DO jk = 1, jpkm1
            zht(:,:) = zht(:,:) + e3t(:,:,jk,Kmm) * tmask(:,:,jk)
         END DO
         z_tmax = MAXVAL( tmask(:,:,1) * tmask_i(:,:) * ABS( ht_0(:,:) + ssh(:,:,Kmm) - zht(:,:) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ht_0+sshn-SUM(e3t(:,:,:,Kmm)))) =', z_tmax
         !
         zht(:,:) = 0.0_wp
         DO jk = 1, jpkm1
            zht(:,:) = zht(:,:) + e3t(:,:,jk,Kaa) * tmask(:,:,jk)
         END DO
         z_tmax = MAXVAL( tmask(:,:,1) * tmask_i(:,:) * ABS( ht_0(:,:) + ssh(:,:,Kaa) - zht(:,:) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ht_0+ssha-SUM(e3t(:,:,:,Kaa)))) =', z_tmax
         !
         zht(:,:) = 0.0_wp
         DO jk = 1, jpkm1
            zht(:,:) = zht(:,:) + e3t(:,:,jk,Kbb) * tmask(:,:,jk)
         END DO
         z_tmax = MAXVAL( tmask(:,:,1) * tmask_i(:,:) * ABS( ht_0(:,:) + ssh(:,:,Kbb) - zht(:,:) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ht_0+sshb-SUM(e3t(:,:,:,Kbb)))) =', z_tmax
         !
         z_tmax = MAXVAL( tmask(:,:,1) *  ABS( ssh(:,:,Kbb) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ssh(:,:,Kbb)))) =', z_tmax
         !
         z_tmax = MAXVAL( tmask(:,:,1) *  ABS( ssh(:,:,Kmm) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ssh(:,:,Kmm)))) =', z_tmax
         !
         z_tmax = MAXVAL( tmask(:,:,1) *  ABS( ssh(:,:,Kaa) ) )
         CALL mpp_max( 'domvvl', z_tmax )                                ! max over the global domain
         IF( lwp    ) WRITE(numout, *) kt,' MAXVAL(abs(ssh(:,:,Kaa)))) =', z_tmax
      END IF

#if defined key_agrif
      ! *********************************** !
      ! After scale factors at w- points    !
      ! *********************************** !
      ! At some point, "after" depths at T-points may be required 
      ! for AGRIF vertical remap. To prevent from saving an
      ! additional array, re-compute depths from e3w when needed
      CALL dom_vvl_interpol( e3t(:,:,:,Kaa), e3w(:,:,:,Kaa), 'W'  )
#endif
Guillaume Samson's avatar
Guillaume Samson committed
549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015
      ! *********************************** !
      ! After scale factors at u- v- points !
      ! *********************************** !

      CALL dom_vvl_interpol( e3t(:,:,:,Kaa), e3u(:,:,:,Kaa), 'U' )
      CALL dom_vvl_interpol( e3t(:,:,:,Kaa), e3v(:,:,:,Kaa), 'V' )

      ! *********************************** !
      ! After depths at u- v points         !
      ! *********************************** !

      hu(:,:,Kaa) = e3u(:,:,1,Kaa) * umask(:,:,1)
      hv(:,:,Kaa) = e3v(:,:,1,Kaa) * vmask(:,:,1)
      DO jk = 2, jpkm1
         hu(:,:,Kaa) = hu(:,:,Kaa) + e3u(:,:,jk,Kaa) * umask(:,:,jk)
         hv(:,:,Kaa) = hv(:,:,Kaa) + e3v(:,:,jk,Kaa) * vmask(:,:,jk)
      END DO
      !                                        ! Inverse of the local depth
!!gm BUG ?  don't understand the use of umask_i here .....
      r1_hu(:,:,Kaa) = ssumask(:,:) / ( hu(:,:,Kaa) + 1._wp - ssumask(:,:) )
      r1_hv(:,:,Kaa) = ssvmask(:,:) / ( hv(:,:,Kaa) + 1._wp - ssvmask(:,:) )
      !
      IF( ln_timing )   CALL timing_stop('dom_vvl_sf_nxt')
      !
   END SUBROUTINE dom_vvl_sf_nxt


   SUBROUTINE dom_vvl_sf_update( kt, Kbb, Kmm, Kaa )
      !!----------------------------------------------------------------------
      !!                ***  ROUTINE dom_vvl_sf_update  ***
      !!
      !! ** Purpose :  for z tilde case: compute time filter and swap of scale factors
      !!               compute all depths and related variables for next time step
      !!               write outputs and restart file
      !!
      !! ** Method  :  - swap of e3t with trick for volume/tracer conservation (ONLY FOR Z TILDE CASE)
      !!               - reconstruct scale factor at other grid points (interpolate)
      !!               - recompute depths and water height fields
      !!
      !! ** Action  :  - tilde_e3t_(b/n) ready for next time step
      !!               - Recompute:
      !!                    e3(u/v)_b
      !!                    e3w(:,:,:,Kmm)
      !!                    e3(u/v)w_b
      !!                    e3(u/v)w_n
      !!                    gdept(:,:,:,Kmm), gdepw(:,:,:,Kmm)  and gde3w
      !!                    h(u/v) and h(u/v)r
      !!
      !! Reference  : Leclair, M., and G. Madec, 2009, Ocean Modelling.
      !!              Leclair, M., and G. Madec, 2011, Ocean Modelling.
      !!----------------------------------------------------------------------
      INTEGER, INTENT( in ) ::   kt              ! time step
      INTEGER, INTENT( in ) ::   Kbb, Kmm, Kaa   ! time level indices
      !
      INTEGER  ::   ji, jj, jk   ! dummy loop indices
      REAL(wp) ::   zcoef        ! local scalar
      !!----------------------------------------------------------------------
      !
      IF( ln_linssh )   RETURN      ! No calculation in linear free surface
      !
      IF( ln_timing )   CALL timing_start('dom_vvl_sf_update')
      !
      IF( kt == nit000 )   THEN
         IF(lwp) WRITE(numout,*)
         IF(lwp) WRITE(numout,*) 'dom_vvl_sf_update : - interpolate scale factors and compute depths for next time step'
         IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~~~'
      ENDIF
      !
      ! Time filter and swap of scale factors
      ! =====================================
      ! - ML - e3(t/u/v)_b are allready computed in dynnxt.
      IF( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN
         IF( l_1st_euler ) THEN
            tilde_e3t_b(:,:,:) = tilde_e3t_n(:,:,:)
         ELSE
            tilde_e3t_b(:,:,:) = tilde_e3t_n(:,:,:) &
            &         + rn_atfp * ( tilde_e3t_b(:,:,:) - 2.0_wp * tilde_e3t_n(:,:,:) + tilde_e3t_a(:,:,:) )
         ENDIF
         tilde_e3t_n(:,:,:) = tilde_e3t_a(:,:,:)
      ENDIF

      ! Compute all missing vertical scale factor and depths
      ! ====================================================
      ! Horizontal scale factor interpolations
      ! --------------------------------------
      ! - ML - e3u(:,:,:,Kbb) and e3v(:,:,:,Kbb) are already computed in dynnxt
      ! - JC - hu(:,:,:,Kbb), hv(:,:,:,:,Kbb), hur_b, hvr_b also

      CALL dom_vvl_interpol( e3u(:,:,:,Kmm), e3f(:,:,:), 'F'  )

      ! Vertical scale factor interpolations
      CALL dom_vvl_interpol( e3t(:,:,:,Kmm),  e3w(:,:,:,Kmm), 'W'  )
      CALL dom_vvl_interpol( e3u(:,:,:,Kmm), e3uw(:,:,:,Kmm), 'UW' )
      CALL dom_vvl_interpol( e3v(:,:,:,Kmm), e3vw(:,:,:,Kmm), 'VW' )
      CALL dom_vvl_interpol( e3t(:,:,:,Kbb),  e3w(:,:,:,Kbb), 'W'  )
      CALL dom_vvl_interpol( e3u(:,:,:,Kbb), e3uw(:,:,:,Kbb), 'UW' )
      CALL dom_vvl_interpol( e3v(:,:,:,Kbb), e3vw(:,:,:,Kbb), 'VW' )

      ! t- and w- points depth (set the isf depth as it is in the initial step)
      gdept(:,:,1,Kmm) = 0.5_wp * e3w(:,:,1,Kmm)
      gdepw(:,:,1,Kmm) = 0.0_wp
      gde3w(:,:,1) = gdept(:,:,1,Kmm) - ssh(:,:,Kmm)
      DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 2, jpk )
        !    zcoef = (tmask(ji,jj,jk) - wmask(ji,jj,jk))   ! 0 everywhere tmask = wmask, ie everywhere expect at jk = mikt
                                                           ! 1 for jk = mikt
         zcoef = (tmask(ji,jj,jk) - wmask(ji,jj,jk))
         gdepw(ji,jj,jk,Kmm) = gdepw(ji,jj,jk-1,Kmm) + e3t(ji,jj,jk-1,Kmm)
         gdept(ji,jj,jk,Kmm) =    zcoef  * ( gdepw(ji,jj,jk  ,Kmm) + 0.5 * e3w(ji,jj,jk,Kmm) )  &
             &             + (1-zcoef) * ( gdept(ji,jj,jk-1,Kmm) +       e3w(ji,jj,jk,Kmm) )
         gde3w(ji,jj,jk) = gdept(ji,jj,jk,Kmm) - ssh(ji,jj,Kmm)
      END_3D

      ! Local depth and Inverse of the local depth of the water
      ! -------------------------------------------------------
      !
      ht(:,:) = e3t(:,:,1,Kmm) * tmask(:,:,1)
      DO jk = 2, jpkm1
         ht(:,:) = ht(:,:) + e3t(:,:,jk,Kmm) * tmask(:,:,jk)
      END DO

      ! write restart file
      ! ==================
      IF( lrst_oce  )   CALL dom_vvl_rst( kt, Kbb, Kmm, 'WRITE' )
      !
      IF( ln_timing )   CALL timing_stop('dom_vvl_sf_update')
      !
   END SUBROUTINE dom_vvl_sf_update


   SUBROUTINE dom_vvl_interpol( pe3_in, pe3_out, pout )
      !!---------------------------------------------------------------------
      !!                  ***  ROUTINE dom_vvl__interpol  ***
      !!
      !! ** Purpose :   interpolate scale factors from one grid point to another
      !!
      !! ** Method  :   e3_out = e3_0 + interpolation(e3_in - e3_0)
      !!                - horizontal interpolation: grid cell surface averaging
      !!                - vertical interpolation: simple averaging
      !!----------------------------------------------------------------------
      REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in   ) ::  pe3_in    ! input e3 to be interpolated
      REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) ::  pe3_out   ! output interpolated e3
      CHARACTER(LEN=*)                , INTENT(in   ) ::  pout      ! grid point of out scale factors
      !                                                             !   =  'U', 'V', 'W, 'F', 'UW' or 'VW'
      !
      INTEGER ::   ji, jj, jk                                       ! dummy loop indices
      INTEGER ::   iku, ikum1, ikv, ikvm1, ikf, ikfm1
      REAL(wp) ::  zlnwd                                            ! =1./0. when ln_wd_il = T/F
      !!----------------------------------------------------------------------
      !
      IF(ln_wd_il) THEN
        zlnwd = 1.0_wp
      ELSE
        zlnwd = 0.0_wp
      END IF
      !
      SELECT CASE ( pout )    !==  type of interpolation  ==!
         !
      CASE( 'U' )                   !* from T- to U-point : hor. surface weighted mean
         DO_3D( 1, 0, 1, 0, 1, jpk )
            pe3_out(ji,jj,jk) = 0.5_wp * (  umask(ji,jj,jk) * (1.0_wp - zlnwd) + zlnwd ) * r1_e1e2u(ji,jj)   &
               &                       * (   e1e2t(ji  ,jj) * ( pe3_in(ji  ,jj,jk) - e3t_0(ji  ,jj,jk) )     &
               &                           + e1e2t(ji+1,jj) * ( pe3_in(ji+1,jj,jk) - e3t_0(ji+1,jj,jk) ) )
         END_3D
         !
         ! Bottom correction:
         DO_2D( 1, 0, 1, 0 )
            iku    = mbku(ji  ,jj)
            ikum1  = iku - 1
            pe3_out(ji,jj,iku) = ( umask(ji,jj,iku) * (1.0_wp - zlnwd) + zlnwd )    & 
               &     * ( 0.5_wp *  r1_e1e2u(ji,jj)                                  &
               &     * (    e1e2t(ji  ,jj) * ( SUM(tmask(ji  ,jj,:)*(pe3_in(ji  ,jj,:) - e3t_0(ji  ,jj,:))) )   &               
               &          + e1e2t(ji+1,jj) * ( SUM(tmask(ji+1,jj,:)*(pe3_in(ji+1,jj,:) - e3t_0(ji+1,jj,:))) ) ) &
               &     - SUM(pe3_out(ji,jj,1:ikum1)))
         END_2D
         
         CALL lbc_lnk( 'domvvl', pe3_out(:,:,:), 'U', 1._wp )
         pe3_out(:,:,:) = pe3_out(:,:,:) + e3u_0(:,:,:)
         !
      CASE( 'V' )                   !* from T- to V-point : hor. surface weighted mean
         DO_3D( 1, 0, 1, 0, 1, jpk )
            pe3_out(ji,jj,jk) = 0.5_wp * ( vmask(ji,jj,jk)  * (1.0_wp - zlnwd) + zlnwd ) * r1_e1e2v(ji,jj)   &
               &                       * (   e1e2t(ji,jj  ) * ( pe3_in(ji,jj  ,jk) - e3t_0(ji,jj  ,jk) )     &
               &                           + e1e2t(ji,jj+1) * ( pe3_in(ji,jj+1,jk) - e3t_0(ji,jj+1,jk) ) )
         END_3D
         !
         ! Bottom correction:
         DO_2D( 1, 0, 1, 0 )
            ikv    = mbkv(ji  ,jj)
            ikvm1  = ikv - 1
            pe3_out(ji,jj,ikv) = ( vmask(ji,jj,ikv) * (1.0_wp - zlnwd) + zlnwd )    & 
               &     * ( 0.5_wp *  r1_e1e2v(ji,jj)                                  &
               &     * (    e1e2t(ji,jj  ) * ( SUM(tmask(ji,jj  ,:)*(pe3_in(ji,jj  ,:) - e3t_0(ji,jj  ,:))) )   &               
               &          + e1e2t(ji,jj+1) * ( SUM(tmask(ji,jj+1,:)*(pe3_in(ji,jj+1,:) - e3t_0(ji,jj+1,:))) ) ) &
               &     - SUM(pe3_out(ji,jj,1:ikvm1)))
         END_2D
         CALL lbc_lnk( 'domvvl', pe3_out(:,:,:), 'V', 1._wp )
         pe3_out(:,:,:) = pe3_out(:,:,:) + e3v_0(:,:,:)
         !
      CASE( 'F' )                   !* from U-point to F-point : hor. surface weighted mean
         DO_3D( 0, 0, 0, 0, 1, jpk )
            pe3_out(ji,jj,jk) = 0.5_wp * (  umask(ji,jj,jk) * umask(ji,jj+1,jk) * (1.0_wp - zlnwd) + zlnwd ) &
               &                       *    r1_e1e2f(ji,jj)                                                  &
               &                       * (   e1e2u(ji,jj  ) * ( pe3_in(ji,jj  ,jk) - e3u_0(ji,jj  ,jk) )     &
               &                           + e1e2u(ji,jj+1) * ( pe3_in(ji,jj+1,jk) - e3u_0(ji,jj+1,jk) ) )
         END_3D
         !
         ! Bottom correction:
         DO_2D( 0, 0, 0, 0 )
            ikf    = MIN(mbku(ji  ,jj),mbku(ji,jj+1))
            ikfm1  = ikf - 1
            pe3_out(ji,jj,ikf) = ( umask(ji,jj,ikf) * umask(ji,jj+1,ikf) * (1.0_wp - zlnwd) + zlnwd )           & 
               &     * ( 0.5_wp *  r1_e1e2f(ji,jj)                                                              &
               &     * (    e1e2u(ji,jj  ) * ( SUM(umask(ji,jj  ,:)*(pe3_in(ji,jj  ,:) - e3u_0(ji,jj  ,:))) )   &               
               &          + e1e2u(ji,jj+1) * ( SUM(umask(ji,jj+1,:)*(pe3_in(ji,jj+1,:) - e3u_0(ji,jj+1,:))) ) ) &
               &     - SUM(pe3_out(ji,jj,1:ikfm1)))
         END_2D
         CALL lbc_lnk( 'domvvl', pe3_out(:,:,:), 'F', 1._wp )
         pe3_out(:,:,:) = pe3_out(:,:,:) + e3f_0(:,:,:)
         !
      CASE( 'W' )                   !* from T- to W-point : vertical simple mean
         !
         pe3_out(:,:,1) = e3w_0(:,:,1) + pe3_in(:,:,1) - e3t_0(:,:,1)
         ! - ML - The use of mask in this formulea enables the special treatment of the last w-point without indirect adressing
!!gm BUG? use here wmask in case of ISF ?  to be checked
         DO jk = 2, jpk
            pe3_out(:,:,jk) = e3w_0(:,:,jk) + ( 1.0_wp - 0.5_wp * ( tmask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd ) )   &
               &                            * ( pe3_in(:,:,jk-1) - e3t_0(:,:,jk-1) )                               &
               &                            +            0.5_wp * ( tmask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd )     &
               &                            * ( pe3_in(:,:,jk  ) - e3t_0(:,:,jk  ) )
         END DO
         !
      CASE( 'UW' )                  !* from U- to UW-point : vertical simple mean
         !
         pe3_out(:,:,1) = e3uw_0(:,:,1) + pe3_in(:,:,1) - e3u_0(:,:,1)
         ! - ML - The use of mask in this formaula enables the special treatment of the last w- point without indirect adressing
!!gm BUG? use here wumask in case of ISF ?  to be checked
         DO jk = 2, jpk
            pe3_out(:,:,jk) = e3uw_0(:,:,jk) + ( 1.0_wp - 0.5_wp * ( umask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd ) )  &
               &                             * ( pe3_in(:,:,jk-1) - e3u_0(:,:,jk-1) )                              &
               &                             +            0.5_wp * ( umask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd )    &
               &                             * ( pe3_in(:,:,jk  ) - e3u_0(:,:,jk  ) )
         END DO
         !
      CASE( 'VW' )                  !* from V- to VW-point : vertical simple mean
         !
         pe3_out(:,:,1) = e3vw_0(:,:,1) + pe3_in(:,:,1) - e3v_0(:,:,1)
         ! - ML - The use of mask in this formaula enables the special treatment of the last w- point without indirect adressing
!!gm BUG? use here wvmask in case of ISF ?  to be checked
         DO jk = 2, jpk
            pe3_out(:,:,jk) = e3vw_0(:,:,jk) + ( 1.0_wp - 0.5_wp * ( vmask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd ) )  &
               &                             * ( pe3_in(:,:,jk-1) - e3v_0(:,:,jk-1) )                              &
               &                             +            0.5_wp * ( vmask(:,:,jk) * (1.0_wp - zlnwd) + zlnwd )    &
               &                             * ( pe3_in(:,:,jk  ) - e3v_0(:,:,jk  ) )
         END DO
      END SELECT
      !
   END SUBROUTINE dom_vvl_interpol


   SUBROUTINE dom_vvl_rst( kt, Kbb, Kmm, cdrw )
      !!---------------------------------------------------------------------
      !!                   ***  ROUTINE dom_vvl_rst  ***
      !!
      !! ** Purpose :   Read or write VVL file in restart file
      !!
      !! ** Method  : * restart comes from a linear ssh simulation :
      !!                   an attempt to read e3t_n stops simulation
      !!              * restart comes from a z-star, z-tilde, or layer :
      !!                   read e3t_n and e3t_b
      !!              * restart comes from a z-star :
      !!                   set tilde_e3t_n, tilde_e3t_n, and hdiv_lf to 0
      !!              * restart comes from layer :
      !!                   read tilde_e3t_n and tilde_e3t_b
      !!                   set hdiv_lf to 0
      !!              * restart comes from a z-tilde:
      !!                   read tilde_e3t_n, tilde_e3t_b, and hdiv_lf
      !!
      !!              NB: if l_1st_euler = T (ln_1st_euler or ssh_b not found)
      !!                   Kbb fields set to Kmm ones
      !!----------------------------------------------------------------------
      INTEGER         , INTENT(in) ::   kt        ! ocean time-step
      INTEGER         , INTENT(in) ::   Kbb, Kmm  ! ocean time level indices
      CHARACTER(len=*), INTENT(in) ::   cdrw      ! "READ"/"WRITE" flag
      !
      INTEGER ::   ji, jj, jk      ! dummy loop indices
      INTEGER ::   id3, id4, id5   ! local integers
      !!----------------------------------------------------------------------
      !
      !                                      !=====================!
      IF( TRIM(cdrw) == 'READ' ) THEN        !  Read / initialise  !
         !                                   !=====================!
         !
         IF( ln_rstart ) THEN                   !==  Read the restart file  ==!
            !
            CALL rst_read_open                                          !*  open the restart file if necessary
            !                                         ! --------- !
            !                                         ! all cases !
            !                                         ! --------- !
            !
            id3 = iom_varid( numror, 'tilde_e3t_b', ldstop = .FALSE. )  !*  check presence
            id4 = iom_varid( numror, 'tilde_e3t_n', ldstop = .FALSE. )
            id5 = iom_varid( numror, 'hdiv_lf'    , ldstop = .FALSE. )
            !
            !                                                           !*  scale factors
            IF(lwp) WRITE(numout,*)    '          Kmm scale factor read in the restart file'
            CALL iom_get( numror, jpdom_auto, 'e3t_n', e3t(:,:,:,Kmm) )
            WHERE ( tmask(:,:,:) == 0.0_wp )
               e3t(:,:,:,Kmm) = e3t_0(:,:,:)
            END WHERE
            IF( l_1st_euler ) THEN                       ! euler
               IF(lwp) WRITE(numout,*) '          Euler first time step : e3t(Kbb) = e3t(Kmm)'
               e3t(:,:,:,Kbb) = e3t(:,:,:,Kmm)
            ELSE                                         ! leap frog
               IF(lwp) WRITE(numout,*) '          Kbb scale factor read in the restart file'
               CALL iom_get( numror, jpdom_auto, 'e3t_b', e3t(:,:,:,Kbb) )
               WHERE ( tmask(:,:,:) == 0.0_wp )
                  e3t(:,:,:,Kbb) = e3t_0(:,:,:)
               END WHERE
            ENDIF
            !                                         ! ------------ !
            IF( ln_vvl_zstar ) THEN                   !  z_star case !
               !                                      ! ------------ !
               IF( MIN( id3, id4 ) > 0 ) THEN
                  CALL ctl_stop( 'dom_vvl_rst: z_star cannot restart from a z_tilde or layer run' )
               ENDIF
               !                                      ! ------------------------ !
            ELSE                                      !  z_tilde and layer cases !
               !                                      ! ------------------------ !
               !
               IF( id4 > 0 ) THEN                                       !*  scale factor increments
                  IF(lwp) WRITE(numout,*)    '          Kmm scale factor increments read in the restart file'
                  CALL iom_get( numror, jpdom_auto, 'tilde_e3t_n', tilde_e3t_n(:,:,:) )
                  IF( l_1st_euler ) THEN                 ! euler
                     IF(lwp) WRITE(numout,*) '          Euler first time step : tilde_e3t(Kbb) = tilde_e3t(Kmm)'
                     tilde_e3t_b(:,:,:) = tilde_e3t_n(:,:,:)
                  ELSE                                   ! leap frog
                     IF(lwp) WRITE(numout,*) '          Kbb scale factor increments read in the restart file'
                     CALL iom_get( numror, jpdom_auto, 'tilde_e3t_b', tilde_e3t_b(:,:,:) )
                  ENDIF
               ELSE
                  tilde_e3t_b(:,:,:) = 0.0_wp
                  tilde_e3t_n(:,:,:) = 0.0_wp
               ENDIF
               !                                      ! ------------ !
               IF( ln_vvl_ztilde ) THEN               ! z_tilde case !
                  !                                   ! ------------ !
                  IF( id5 > 0 ) THEN  ! required array exists
                     CALL iom_get( numror, jpdom_auto, 'hdiv_lf', hdiv_lf(:,:,:) )
                  ELSE                ! array is missing
                     hdiv_lf(:,:,:) = 0.0_wp
                  ENDIF
               ENDIF
            ENDIF
            !
         ELSE                                   !==  Initialize at "rest" with ssh  ==!
            !
            DO jk = 1, jpk
               e3t(:,:,jk,Kmm) =  e3t_0(:,:,jk) * ( 1._wp + ssh(:,:,Kmm) * r1_ht_0(:,:) * tmask(:,:,jk) )
            END DO
            e3t(:,:,:,Kbb) = e3t(:,:,:,Kmm)
            !
            IF( ln_vvl_ztilde .OR. ln_vvl_layer) THEN
               tilde_e3t_b(:,:,:) = 0._wp
               tilde_e3t_n(:,:,:) = 0._wp
               IF( ln_vvl_ztilde ) hdiv_lf(:,:,:) = 0._wp
            ENDIF
         ENDIF
         !                                       !=======================!
      ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN       !  Create restart file  !
         !                                       !=======================!
         !
         IF(lwp) WRITE(numout,*) '---- dom_vvl_rst ----'
         !                                           ! --------- !
         !                                           ! all cases !
         !                                           ! --------- !
         CALL iom_rstput( kt, nitrst, numrow, 'e3t_b', e3t(:,:,:,Kbb) )
         CALL iom_rstput( kt, nitrst, numrow, 'e3t_n', e3t(:,:,:,Kmm) )
         !                                           ! ----------------------- !
         IF( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN  ! z_tilde and layer cases !
            !                                        ! ----------------------- !
            CALL iom_rstput( kt, nitrst, numrow, 'tilde_e3t_b', tilde_e3t_b(:,:,:))
            CALL iom_rstput( kt, nitrst, numrow, 'tilde_e3t_n', tilde_e3t_n(:,:,:))
         END IF
         !                                           ! -------------!
         IF( ln_vvl_ztilde ) THEN                    ! z_tilde case !
            !                                        ! ------------ !
            CALL iom_rstput( kt, nitrst, numrow, 'hdiv_lf', hdiv_lf(:,:,:))
         ENDIF
         !
      ENDIF
      !
   END SUBROUTINE dom_vvl_rst


   SUBROUTINE dom_vvl_ctl
      !!---------------------------------------------------------------------
      !!                  ***  ROUTINE dom_vvl_ctl  ***
      !!
      !! ** Purpose :   Control the consistency between namelist options
      !!                for vertical coordinate
      !!----------------------------------------------------------------------
      INTEGER ::   ioptio, ios
      !!
      NAMELIST/nam_vvl/ ln_vvl_zstar, ln_vvl_ztilde, ln_vvl_layer, ln_vvl_ztilde_as_zstar, &
         &              ln_vvl_zstar_at_eqtor      , rn_ahe3     , rn_rst_e3t            , &
         &              rn_lf_cutoff               , rn_zdef_max , ln_vvl_dbg                ! not yet implemented: ln_vvl_kepe
      !!----------------------------------------------------------------------
      !
      READ  ( numnam_ref, nam_vvl, IOSTAT = ios, ERR = 901)
901   IF( ios /= 0 )   CALL ctl_nam ( ios , 'nam_vvl in reference namelist' )
      READ  ( numnam_cfg, nam_vvl, IOSTAT = ios, ERR = 902 )
902   IF( ios >  0 ) CALL ctl_nam ( ios , 'nam_vvl in configuration namelist' )
      IF(lwm) WRITE ( numond, nam_vvl )
      !
      IF(lwp) THEN                    ! Namelist print
         WRITE(numout,*)
         WRITE(numout,*) 'dom_vvl_ctl : choice/control of the variable vertical coordinate'
         WRITE(numout,*) '~~~~~~~~~~~'
         WRITE(numout,*) '   Namelist nam_vvl : chose a vertical coordinate'
         WRITE(numout,*) '      zstar                      ln_vvl_zstar   = ', ln_vvl_zstar
         WRITE(numout,*) '      ztilde                     ln_vvl_ztilde  = ', ln_vvl_ztilde
         WRITE(numout,*) '      layer                      ln_vvl_layer   = ', ln_vvl_layer
         WRITE(numout,*) '      ztilde as zstar   ln_vvl_ztilde_as_zstar  = ', ln_vvl_ztilde_as_zstar
         WRITE(numout,*) '      ztilde near the equator    ln_vvl_zstar_at_eqtor  = ', ln_vvl_zstar_at_eqtor
         WRITE(numout,*) '      !'
         WRITE(numout,*) '      thickness diffusion coefficient                      rn_ahe3      = ', rn_ahe3
         WRITE(numout,*) '      maximum e3t deformation fractional change            rn_zdef_max  = ', rn_zdef_max
         IF( ln_vvl_ztilde_as_zstar ) THEN
            WRITE(numout,*) '      ztilde running in zstar emulation mode (ln_vvl_ztilde_as_zstar=T) '
            WRITE(numout,*) '         ignoring namelist timescale parameters and using:'
            WRITE(numout,*) '            hard-wired : z-tilde to zstar restoration timescale (days)'
            WRITE(numout,*) '                         rn_rst_e3t     = 0.e0'
            WRITE(numout,*) '            hard-wired : z-tilde cutoff frequency of low-pass filter (days)'
            WRITE(numout,*) '                         rn_lf_cutoff   = 1.0/rn_Dt'
         ELSE
            WRITE(numout,*) '      z-tilde to zstar restoration timescale (days)        rn_rst_e3t   = ', rn_rst_e3t
            WRITE(numout,*) '      z-tilde cutoff frequency of low-pass filter (days)   rn_lf_cutoff = ', rn_lf_cutoff
         ENDIF
         WRITE(numout,*) '         debug prints flag                                 ln_vvl_dbg   = ', ln_vvl_dbg
      ENDIF
      !
      ioptio = 0                      ! Parameter control
      IF( ln_vvl_ztilde_as_zstar )   ln_vvl_ztilde = .true.
      IF( ln_vvl_zstar           )   ioptio = ioptio + 1
      IF( ln_vvl_ztilde          )   ioptio = ioptio + 1
      IF( ln_vvl_layer           )   ioptio = ioptio + 1
      !
      IF( ioptio /= 1 )   CALL ctl_stop( 'Choose ONE vertical coordinate in namelist nam_vvl' )
      !
      IF(lwp) THEN                   ! Print the choice
         WRITE(numout,*)
         IF( ln_vvl_zstar           ) WRITE(numout,*) '      ==>>>   zstar vertical coordinate is used'
         IF( ln_vvl_ztilde          ) WRITE(numout,*) '      ==>>>   ztilde vertical coordinate is used'
         IF( ln_vvl_layer           ) WRITE(numout,*) '      ==>>>   layer vertical coordinate is used'
         IF( ln_vvl_ztilde_as_zstar ) WRITE(numout,*) '      ==>>>   to emulate a zstar coordinate'
      ENDIF
      !
#if defined key_agrif
      IF( (.NOT.Agrif_Root()).AND.(.NOT.ln_vvl_zstar) )   CALL ctl_stop( 'AGRIF is implemented with zstar coordinate only' )
#endif
      !
   END SUBROUTINE dom_vvl_ctl

#endif

   !!======================================================================
END MODULE domvvl