ecearth3/sources/nemo-3.6/NEMO/OPA_SRC/DOM/domain.F90

MODULE domain
   !!==============================================================================
   !!                       ***  MODULE domain   ***
   !! Ocean initialization : domain initialization
   !!==============================================================================
   !! History :  OPA  !  1990-10  (C. Levy - G. Madec)  Original code
   !!                 !  1992-01  (M. Imbard) insert time step initialization
   !!                 !  1996-06  (G. Madec) generalized vertical coordinate 
   !!                 !  1997-02  (G. Madec) creation of domwri.F
   !!                 !  2001-05  (E.Durand - G. Madec) insert closed sea
   !!   NEMO     1.0  !  2002-08  (G. Madec)  F90: Free form and module
   !!            2.0  !  2005-11  (V. Garnier) Surface pressure gradient organization
   !!            3.3  !  2010-11  (G. Madec)  initialisation in C1D configuration
   !!            3.6  !  2013     ( J. Simeon, C. Calone, G. Madec, C. Ethe ) Online coarsening of outputs
   !!----------------------------------------------------------------------
   
   !!----------------------------------------------------------------------
   !!   dom_init       : initialize the space and time domain
   !!   dom_nam        : read and contral domain namelists
   !!   dom_ctl        : control print for the ocean domain
   !!----------------------------------------------------------------------
   USE oce             ! ocean variables
   USE dom_oce         ! domain: ocean
   USE sbc_oce         ! surface boundary condition: ocean
   USE trc_oce         ! shared ocean-passive tracers variables
   USE phycst          ! physical constants
   USE closea          ! closed seas
   USE in_out_manager  ! I/O manager
   USE lib_mpp         ! distributed memory computing library

   USE domhgr          ! domain: set the horizontal mesh
   USE domzgr          ! domain: set the vertical mesh
   USE domstp          ! domain: set the time-step
   USE dommsk          ! domain: set the mask system
   USE domwri          ! domain: write the meshmask file
   USE domvvl          ! variable volume
   USE c1d             ! 1D vertical configuration
   USE dyncor_c1d      ! Coriolis term (c1d case)         (cor_c1d routine)
   USE timing          ! Timing
   USE lbclnk          ! ocean lateral boundary condition (or mpp link)

   IMPLICIT NONE
   PRIVATE

   PUBLIC   dom_init   ! called by opa.F90

   !! * Substitutions
#  include "domzgr_substitute.h90"
   !!-------------------------------------------------------------------------
   !! NEMO/OPA 3.3 , NEMO Consortium (2010)
   !! $Id: domain.F90 4990 2014-12-15 16:42:49Z timgraham $
   !! Software governed by the CeCILL licence        (NEMOGCM/NEMO_CeCILL.txt)
   !!-------------------------------------------------------------------------
CONTAINS

   SUBROUTINE dom_init
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE dom_init  ***
      !!                    
      !! ** Purpose :   Domain initialization. Call the routines that are 
      !!              required to create the arrays which define the space 
      !!              and time domain of the ocean model.
      !!
      !! ** Method  : - dom_msk: compute the masks from the bathymetry file
      !!              - dom_hgr: compute or read the horizontal grid-point position
      !!                         and scale factors, and the coriolis factor
      !!              - dom_zgr: define the vertical coordinate and the bathymetry
      !!              - dom_stp: defined the model time step
      !!              - dom_wri: create the meshmask file if nmsh=1
      !!              - 1D configuration, move Coriolis, u and v at T-point
      !!----------------------------------------------------------------------
      INTEGER ::   jk          ! dummy loop argument
      INTEGER ::   iconf = 0   ! local integers
      !!----------------------------------------------------------------------
      !
      IF( nn_timing == 1 )   CALL timing_start('dom_init')
      !
      IF(lwp) THEN
         WRITE(numout,*)
         WRITE(numout,*) 'dom_init : domain initialization'
         WRITE(numout,*) '~~~~~~~~'
      ENDIF
      !
                             CALL dom_nam      ! read namelist ( namrun, namdom, namcla )
                             CALL dom_clo      ! Closed seas and lake
                             CALL dom_hgr      ! Horizontal mesh
                             CALL dom_zgr      ! Vertical mesh and bathymetry
                             CALL dom_msk      ! Masks
      IF( ln_sco )           CALL dom_stiff    ! Maximum stiffness ratio/hydrostatic consistency
      !
      ht_0(:,:) = 0.0_wp                       ! Reference ocean depth at T-points
      hu_0(:,:) = 0.0_wp                       ! Reference ocean depth at U-points
      hv_0(:,:) = 0.0_wp                       ! Reference ocean depth at V-points
      DO jk = 1, jpk
         ht_0(:,:) = ht_0(:,:) + e3t_0(:,:,jk) * tmask(:,:,jk)
         hu_0(:,:) = hu_0(:,:) + e3u_0(:,:,jk) * umask(:,:,jk)
         hv_0(:,:) = hv_0(:,:) + e3v_0(:,:,jk) * vmask(:,:,jk)
      END DO
      !
      IF( lk_c1d )           CALL cor_c1d      ! 1D configuration: Coriolis set at T-point
      !
      IF( .NOT.lk_offline ) THEN
        !
        IF( lk_vvl )         CALL dom_vvl_init ! Vertical variable mesh
        !
        hu(:,:) = 0._wp                          ! Ocean depth at U-points
        hv(:,:) = 0._wp                          ! Ocean depth at V-points
        ht(:,:) = 0._wp                          ! Ocean depth at T-points
        DO jk = 1, jpkm1
           hu(:,:) = hu(:,:) + fse3u_n(:,:,jk) * umask(:,:,jk)
           hv(:,:) = hv(:,:) + fse3v_n(:,:,jk) * vmask(:,:,jk)
           ht(:,:) = ht(:,:) + fse3t_n(:,:,jk) * tmask(:,:,jk)
        END DO
        !                                        ! Inverse of the local depth
        hur(:,:) = 1._wp / ( hu(:,:) + 1._wp - umask_i(:,:) ) * umask_i(:,:)
        hvr(:,:) = 1._wp / ( hv(:,:) + 1._wp - vmask_i(:,:) ) * vmask_i(:,:)
        !
      ENDIF

                             CALL dom_stp      ! time step
      IF( nmsh /= 0      )   CALL dom_wri      ! Create a domain file
      IF( .NOT.ln_rstart )   CALL dom_ctl      ! Domain control
      !
      IF( nn_timing == 1 )   CALL timing_stop('dom_init')
      !
   END SUBROUTINE dom_init


   SUBROUTINE dom_nam
      !!----------------------------------------------------------------------
      !!                     ***  ROUTINE dom_nam  ***
      !!                    
      !! ** Purpose :   read domaine namelists and print the variables.
      !!
      !! ** input   : - namrun namelist
      !!              - namdom namelist
      !!              - namcla namelist
      !!              - namnc4 namelist   ! "key_netcdf4" only
      !!----------------------------------------------------------------------
      USE ioipsl
      NAMELIST/namrun/ cn_ocerst_indir, cn_ocerst_outdir, nn_stocklist, ln_rst_list,               &
         &             nn_no   , cn_exp    , cn_ocerst_in, cn_ocerst_out, ln_rstart , nn_rstctl,   &
         &             nn_it000, nn_itend  , nn_date0    , nn_leapy     , nn_istate , nn_stock ,   &
         &             nn_write, ln_dimgnnn, ln_mskland  , ln_cfmeta    , ln_clobber, nn_chunksz, nn_euler
      NAMELIST/namdom/ nn_bathy, rn_bathy , rn_e3zps_min, rn_e3zps_rat, nn_msh, rn_hmin,   &
         &             nn_acc   , rn_atfp     , rn_rdt      , rn_rdtmin ,                  &
         &             rn_rdtmax, rn_rdth     , nn_closea , ln_crs,    &
         &             jphgr_msh, &
         &             ppglam0, ppgphi0, ppe1_deg, ppe2_deg, ppe1_m, ppe2_m, &
         &             ppsur, ppa0, ppa1, ppkth, ppacr, ppdzmin, pphmax, ldbletanh, &
         &             ppa2, ppkth2, ppacr2
      NAMELIST/namcla/ nn_cla
#if defined key_netcdf4
      NAMELIST/namnc4/ nn_nchunks_i, nn_nchunks_j, nn_nchunks_k, ln_nc4zip
#endif
      INTEGER  ::   ios                 ! Local integer output status for namelist read
      !!----------------------------------------------------------------------

      REWIND( numnam_ref )              ! Namelist namrun in reference namelist : Parameters of the run
      READ  ( numnam_ref, namrun, IOSTAT = ios, ERR = 901)
901   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namrun in reference namelist', lwp )

      REWIND( numnam_cfg )              ! Namelist namrun in configuration namelist : Parameters of the run
      READ  ( numnam_cfg, namrun, IOSTAT = ios, ERR = 902 )
902   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namrun in configuration namelist', lwp )
      IF(lwm) WRITE ( numond, namrun )
      !
      IF(lwp) THEN                  ! control print
         WRITE(numout,*)
         WRITE(numout,*) 'dom_nam  : domain initialization through namelist read'
         WRITE(numout,*) '~~~~~~~ '
         WRITE(numout,*) '   Namelist namrun'
         WRITE(numout,*) '      job number                      nn_no      = ', nn_no
         WRITE(numout,*) '      experiment name for output      cn_exp     = ', cn_exp
         WRITE(numout,*) '      file prefix restart input       cn_ocerst_in= ', cn_ocerst_in
         WRITE(numout,*) '      restart input directory         cn_ocerst_indir= ', cn_ocerst_indir
         WRITE(numout,*) '      file prefix restart output      cn_ocerst_out= ', cn_ocerst_out
         WRITE(numout,*) '      restart output directory        cn_ocerst_outdir= ', cn_ocerst_outdir
         WRITE(numout,*) '      restart logical                 ln_rstart  = ', ln_rstart
         WRITE(numout,*) '      start with forward time step    nn_euler   = ', nn_euler
         WRITE(numout,*) '      control of time step            nn_rstctl  = ', nn_rstctl
         WRITE(numout,*) '      number of the first time step   nn_it000   = ', nn_it000
         WRITE(numout,*) '      number of the last time step    nn_itend   = ', nn_itend
         WRITE(numout,*) '      initial calendar date aammjj    nn_date0   = ', nn_date0
         WRITE(numout,*) '      leap year calendar (0/1)        nn_leapy   = ', nn_leapy
         WRITE(numout,*) '      initial state output            nn_istate  = ', nn_istate
         IF( ln_rst_list ) THEN
            WRITE(numout,*) '      list of restart dump times      nn_stocklist   =', nn_stocklist
         ELSE
            WRITE(numout,*) '      frequency of restart file       nn_stock   = ', nn_stock
         ENDIF
         WRITE(numout,*) '      frequency of output file        nn_write   = ', nn_write
         WRITE(numout,*) '      multi file dimgout              ln_dimgnnn = ', ln_dimgnnn
         WRITE(numout,*) '      mask land points                ln_mskland = ', ln_mskland
         WRITE(numout,*) '      additional CF standard metadata ln_cfmeta  = ', ln_cfmeta
         WRITE(numout,*) '      overwrite an existing file      ln_clobber = ', ln_clobber
         WRITE(numout,*) '      NetCDF chunksize (bytes)        nn_chunksz = ', nn_chunksz
      ENDIF

      no = nn_no                    ! conversion DOCTOR names into model names (this should disappear soon)
      cexper = cn_exp
      nrstdt = nn_rstctl
      nit000 = nn_it000
      nitend = nn_itend
      ndate0 = nn_date0
      nleapy = nn_leapy
      ninist = nn_istate
      nstock = nn_stock
      nstocklist = nn_stocklist
      nwrite = nn_write
      neuler = nn_euler
      IF ( neuler == 1 .AND. .NOT. ln_rstart ) THEN
         WRITE(ctmp1,*) 'ln_rstart =.FALSE., nn_euler is forced to 0 '
         CALL ctl_warn( ctmp1 )
         neuler = 0
      ENDIF

      !                             ! control of output frequency
      IF ( nstock == 0 .OR. nstock > nitend ) THEN
         WRITE(ctmp1,*) 'nstock = ', nstock, ' it is forced to ', nitend
         CALL ctl_warn( ctmp1 )
         nstock = nitend
      ENDIF
      IF ( nwrite == 0 ) THEN
         WRITE(ctmp1,*) 'nwrite = ', nwrite, ' it is forced to ', nitend
         CALL ctl_warn( ctmp1 )
         nwrite = nitend
      ENDIF

#if defined key_agrif
      IF( Agrif_Root() ) THEN
#endif
      SELECT CASE ( nleapy )        ! Choose calendar for IOIPSL
      CASE (  1 ) 
         CALL ioconf_calendar('gregorian')
         IF(lwp) WRITE(numout,*) '   The IOIPSL calendar is "gregorian", i.e. leap year'
      CASE (  0 )
         CALL ioconf_calendar('noleap')
         IF(lwp) WRITE(numout,*) '   The IOIPSL calendar is "noleap", i.e. no leap year'
      CASE ( 30 )
         CALL ioconf_calendar('360d')
         IF(lwp) WRITE(numout,*) '   The IOIPSL calendar is "360d", i.e. 360 days in a year'
      END SELECT
#if defined key_agrif
      ENDIF
#endif

      REWIND( numnam_ref )              ! Namelist namdom in reference namelist : space & time domain (bathymetry, mesh, timestep)
      READ  ( numnam_ref, namdom, IOSTAT = ios, ERR = 903)
903   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdom in reference namelist', lwp )
  
      !
      REWIND( numnam_cfg )              ! Namelist namdom in configuration namelist : space & time domain (bathymetry, mesh, timestep)
      READ  ( numnam_cfg, namdom, IOSTAT = ios, ERR = 904 )
904   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdom in configuration namelist', lwp )
      IF(lwm) WRITE ( numond, namdom )

      IF(lwp) THEN
         WRITE(numout,*)
         WRITE(numout,*) '   Namelist namdom : space & time domain'
         WRITE(numout,*) '      flag read/compute bathymetry      nn_bathy     = ', nn_bathy
         WRITE(numout,*) '      Depth (if =0 bathy=jpkm1)         rn_bathy     = ', rn_bathy
         WRITE(numout,*) '      min depth of the ocean    (>0) or    rn_hmin   = ', rn_hmin
         WRITE(numout,*) '      min number of ocean level (<0)       '
         WRITE(numout,*) '      minimum thickness of partial      rn_e3zps_min = ', rn_e3zps_min, ' (m)'
         WRITE(numout,*) '         step level                     rn_e3zps_rat = ', rn_e3zps_rat
         WRITE(numout,*) '      create mesh/mask file(s)          nn_msh       = ', nn_msh
         WRITE(numout,*) '           = 0   no file created           '
         WRITE(numout,*) '           = 1   mesh_mask                 '
         WRITE(numout,*) '           = 2   mesh and mask             '
         WRITE(numout,*) '           = 3   mesh_hgr, msh_zgr and mask'
         WRITE(numout,*) '      ocean time step                       rn_rdt    = ', rn_rdt
         WRITE(numout,*) '      asselin time filter parameter         rn_atfp   = ', rn_atfp
         WRITE(numout,*) '      acceleration of converge              nn_acc    = ', nn_acc
         WRITE(numout,*) '        nn_acc=1: surface tracer rdt        rn_rdtmin = ', rn_rdtmin
         WRITE(numout,*) '                  bottom  tracer rdt        rdtmax    = ', rn_rdtmax
         WRITE(numout,*) '                  depth of transition       rn_rdth   = ', rn_rdth
         WRITE(numout,*) '      suppression of closed seas (=0)       nn_closea = ', nn_closea
         WRITE(numout,*) '      online coarsening of dynamical fields ln_crs    = ', ln_crs
         WRITE(numout,*) '      type of horizontal mesh jphgr_msh           = ', jphgr_msh
         WRITE(numout,*) '      longitude of first raw and column T-point ppglam0 = ', ppglam0
         WRITE(numout,*) '      latitude  of first raw and column T-point ppgphi0 = ', ppgphi0
         WRITE(numout,*) '      zonal      grid-spacing (degrees) ppe1_deg        = ', ppe1_deg
         WRITE(numout,*) '      meridional grid-spacing (degrees) ppe2_deg        = ', ppe2_deg
         WRITE(numout,*) '      zonal      grid-spacing (degrees) ppe1_m          = ', ppe1_m
         WRITE(numout,*) '      meridional grid-spacing (degrees) ppe2_m          = ', ppe2_m
         WRITE(numout,*) '      ORCA r4, r2 and r05 coefficients  ppsur           = ', ppsur
         WRITE(numout,*) '                                        ppa0            = ', ppa0
         WRITE(numout,*) '                                        ppa1            = ', ppa1
         WRITE(numout,*) '                                        ppkth           = ', ppkth
         WRITE(numout,*) '                                        ppacr           = ', ppacr
         WRITE(numout,*) '      Minimum vertical spacing ppdzmin                  = ', ppdzmin
         WRITE(numout,*) '      Maximum depth pphmax                              = ', pphmax
         WRITE(numout,*) '      Use double tanf function for vertical coordinates ldbletanh = ', ldbletanh
         WRITE(numout,*) '      Double tanh function parameters ppa2              = ', ppa2
         WRITE(numout,*) '                                      ppkth2            = ', ppkth2
         WRITE(numout,*) '                                      ppacr2            = ', ppacr2
      ENDIF

      ntopo     = nn_bathy          ! conversion DOCTOR names into model names (this should disappear soon)
      e3zps_min = rn_e3zps_min
      e3zps_rat = rn_e3zps_rat
      nmsh      = nn_msh
      nacc      = nn_acc
      atfp      = rn_atfp
      rdt       = rn_rdt
      rdtmin    = rn_rdtmin
      rdtmax    = rn_rdtmin
      rdth      = rn_rdth

      REWIND( numnam_ref )              ! Namelist namcla in reference namelist : Cross land advection
      READ  ( numnam_ref, namcla, IOSTAT = ios, ERR = 905)
905   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namcla in reference namelist', lwp )

      REWIND( numnam_cfg )              ! Namelist namcla in configuration namelist : Cross land advection
      READ  ( numnam_cfg, namcla, IOSTAT = ios, ERR = 906 )
906   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namcla in configuration namelist', lwp )
      IF(lwm) WRITE( numond, namcla )

      IF(lwp) THEN
         WRITE(numout,*)
         WRITE(numout,*) '   Namelist namcla'
         WRITE(numout,*) '      cross land advection                 nn_cla    = ', nn_cla
      ENDIF
      IF ( nn_cla .EQ. 1 ) THEN
         IF  ( cp_cfg == "orca" .AND. jp_cfg == 2 ) THEN   ! ORCA R2 
            CONTINUE
         ELSE
            CALL ctl_stop( 'STOP', 'Cross land advation iplemented only for ORCA2 configuration: cp_cfg = "orca" and jp_cfg = 2 ' )
         ENDIF
      ENDIF

#if defined key_netcdf4
      !                             ! NetCDF 4 case   ("key_netcdf4" defined)
      REWIND( numnam_ref )              ! Namelist namnc4 in reference namelist : NETCDF
      READ  ( numnam_ref, namnc4, IOSTAT = ios, ERR = 907)
907   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namnc4 in reference namelist', lwp )

      REWIND( numnam_cfg )              ! Namelist namnc4 in configuration namelist : NETCDF
      READ  ( numnam_cfg, namnc4, IOSTAT = ios, ERR = 908 )
908   IF( ios /= 0 ) CALL ctl_nam ( ios , 'namnc4 in configuration namelist', lwp )
      IF(lwm) WRITE( numond, namnc4 )

      IF(lwp) THEN                        ! control print
         WRITE(numout,*)
         WRITE(numout,*) '   Namelist namnc4 - Netcdf4 chunking parameters'
         WRITE(numout,*) '      number of chunks in i-dimension      nn_nchunks_i   = ', nn_nchunks_i
         WRITE(numout,*) '      number of chunks in j-dimension      nn_nchunks_j   = ', nn_nchunks_j
         WRITE(numout,*) '      number of chunks in k-dimension      nn_nchunks_k   = ', nn_nchunks_k
         WRITE(numout,*) '      apply netcdf4/hdf5 chunking & compression ln_nc4zip = ', ln_nc4zip
      ENDIF

      ! Put the netcdf4 settings into a simple structure (snc4set, defined in in_out_manager module)
      ! Note the chunk size in the unlimited (time) dimension will be fixed at 1
      snc4set%ni   = nn_nchunks_i
      snc4set%nj   = nn_nchunks_j
      snc4set%nk   = nn_nchunks_k
      snc4set%luse = ln_nc4zip
#else
      snc4set%luse = .FALSE.        ! No NetCDF 4 case
#endif
      !
   END SUBROUTINE dom_nam


   SUBROUTINE dom_ctl
      !!----------------------------------------------------------------------
      !!                     ***  ROUTINE dom_ctl  ***
      !!
      !! ** Purpose :   Domain control.
      !!
      !! ** Method  :   compute and print extrema of masked scale factors
      !!----------------------------------------------------------------------
      INTEGER ::   iimi1, ijmi1, iimi2, ijmi2, iima1, ijma1, iima2, ijma2
      INTEGER, DIMENSION(2) ::   iloc   ! 
      REAL(wp) ::   ze1min, ze1max, ze2min, ze2max
      !!----------------------------------------------------------------------
      !
      IF(lk_mpp) THEN
         CALL mpp_minloc( e1t(:,:), tmask_i(:,:), ze1min, iimi1,ijmi1 )
         CALL mpp_minloc( e2t(:,:), tmask_i(:,:), ze2min, iimi2,ijmi2 )
         CALL mpp_maxloc( e1t(:,:), tmask_i(:,:), ze1max, iima1,ijma1 )
         CALL mpp_maxloc( e2t(:,:), tmask_i(:,:), ze2max, iima2,ijma2 )
      ELSE
         ze1min = MINVAL( e1t(:,:), mask = tmask_i(:,:) == 1._wp )    
         ze2min = MINVAL( e2t(:,:), mask = tmask_i(:,:) == 1._wp )    
         ze1max = MAXVAL( e1t(:,:), mask = tmask_i(:,:) == 1._wp )    
         ze2max = MAXVAL( e2t(:,:), mask = tmask_i(:,:) == 1._wp )    

         iloc  = MINLOC( e1t(:,:), mask = tmask_i(:,:) == 1._wp )
         iimi1 = iloc(1) + nimpp - 1
         ijmi1 = iloc(2) + njmpp - 1
         iloc  = MINLOC( e2t(:,:), mask = tmask_i(:,:) == 1._wp )
         iimi2 = iloc(1) + nimpp - 1
         ijmi2 = iloc(2) + njmpp - 1
         iloc  = MAXLOC( e1t(:,:), mask = tmask_i(:,:) == 1._wp )
         iima1 = iloc(1) + nimpp - 1
         ijma1 = iloc(2) + njmpp - 1
         iloc  = MAXLOC( e2t(:,:), mask = tmask_i(:,:) == 1._wp )
         iima2 = iloc(1) + nimpp - 1
         ijma2 = iloc(2) + njmpp - 1
      ENDIF
      IF(lwp) THEN
         WRITE(numout,*)
         WRITE(numout,*) 'dom_ctl : extrema of the masked scale factors'
         WRITE(numout,*) '~~~~~~~'
         WRITE(numout,"(14x,'e1t maxi: ',1f10.2,' at i = ',i5,' j= ',i5)") ze1max, iima1, ijma1
         WRITE(numout,"(14x,'e1t mini: ',1f10.2,' at i = ',i5,' j= ',i5)") ze1min, iimi1, ijmi1
         WRITE(numout,"(14x,'e2t maxi: ',1f10.2,' at i = ',i5,' j= ',i5)") ze2max, iima2, ijma2
         WRITE(numout,"(14x,'e2t mini: ',1f10.2,' at i = ',i5,' j= ',i5)") ze2min, iimi2, ijmi2
      ENDIF
      !
   END SUBROUTINE dom_ctl

   SUBROUTINE dom_stiff
      !!----------------------------------------------------------------------
      !!                  ***  ROUTINE dom_stiff  ***
      !!                     
      !! ** Purpose :   Diagnose maximum grid stiffness/hydrostatic consistency
      !!
      !! ** Method  :   Compute Haney (1991) hydrostatic condition ratio
      !!                Save the maximum in the vertical direction
      !!                (this number is only relevant in s-coordinates)
      !!
      !!                Haney, R. L., 1991: On the pressure gradient force
      !!                over steep topography in sigma coordinate ocean models. 
      !!                J. Phys. Oceanogr., 21, 610???619.
      !!----------------------------------------------------------------------
      INTEGER  ::   ji, jj, jk 
      REAL(wp) ::   zrxmax
      REAL(wp), DIMENSION(4) :: zr1
      !!----------------------------------------------------------------------
      rx1(:,:) = 0.e0
      zrxmax   = 0.e0
      zr1(:)   = 0.e0
      
      DO ji = 2, jpim1
         DO jj = 2, jpjm1
            DO jk = 1, jpkm1
               zr1(1) = umask(ji-1,jj  ,jk) *abs( (gdepw_0(ji  ,jj  ,jk  )-gdepw_0(ji-1,jj  ,jk  )  & 
                    &                         +gdepw_0(ji  ,jj  ,jk+1)-gdepw_0(ji-1,jj  ,jk+1)) &
                    &                        /(gdepw_0(ji  ,jj  ,jk  )+gdepw_0(ji-1,jj  ,jk  )  &
                    &                         -gdepw_0(ji  ,jj  ,jk+1)-gdepw_0(ji-1,jj  ,jk+1) + rsmall) )
               zr1(2) = umask(ji  ,jj  ,jk) *abs( (gdepw_0(ji+1,jj  ,jk  )-gdepw_0(ji  ,jj  ,jk  )  &
                    &                         +gdepw_0(ji+1,jj  ,jk+1)-gdepw_0(ji  ,jj  ,jk+1)) &
                    &                        /(gdepw_0(ji+1,jj  ,jk  )+gdepw_0(ji  ,jj  ,jk  )  &
                    &                         -gdepw_0(ji+1,jj  ,jk+1)-gdepw_0(ji  ,jj  ,jk+1) + rsmall) )
               zr1(3) = vmask(ji  ,jj  ,jk) *abs( (gdepw_0(ji  ,jj+1,jk  )-gdepw_0(ji  ,jj  ,jk  )  &
                    &                         +gdepw_0(ji  ,jj+1,jk+1)-gdepw_0(ji  ,jj  ,jk+1)) &
                    &                        /(gdepw_0(ji  ,jj+1,jk  )+gdepw_0(ji  ,jj  ,jk  )  &
                    &                         -gdepw_0(ji  ,jj+1,jk+1)-gdepw_0(ji  ,jj  ,jk+1) + rsmall) )
               zr1(4) = vmask(ji  ,jj-1,jk) *abs( (gdepw_0(ji  ,jj  ,jk  )-gdepw_0(ji  ,jj-1,jk  )  &
                    &                         +gdepw_0(ji  ,jj  ,jk+1)-gdepw_0(ji  ,jj-1,jk+1)) &
                    &                        /(gdepw_0(ji  ,jj  ,jk  )+gdepw_0(ji  ,jj-1,jk  )  &
                    &                         -gdepw_0(ji,  jj  ,jk+1)-gdepw_0(ji  ,jj-1,jk+1) + rsmall) )
               zrxmax = MAXVAL(zr1(1:4))
               rx1(ji,jj) = MAX(rx1(ji,jj), zrxmax)
            END DO
         END DO
      END DO

      CALL lbc_lnk( rx1, 'T', 1. )

      zrxmax = MAXVAL(rx1)

      IF( lk_mpp )   CALL mpp_max( zrxmax ) ! max over the global domain

      IF(lwp) THEN
         WRITE(numout,*)
         WRITE(numout,*) 'dom_stiff : maximum grid stiffness ratio: ', zrxmax
         WRITE(numout,*) '~~~~~~~~~'
      ENDIF

   END SUBROUTINE dom_stiff



   !!======================================================================
END MODULE domain