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MODULE sshwzv
!!==============================================================================
!! *** MODULE sshwzv ***
!! Ocean dynamics : sea surface height and vertical velocity
!!==============================================================================
!! History : 3.1 ! 2009-02 (G. Madec, M. Leclair) Original code
!! 3.3 ! 2010-04 (M. Leclair, G. Madec) modified LF-RA
!! - ! 2010-05 (K. Mogensen, A. Weaver, M. Martin, D. Lea) Assimilation interface
!! - ! 2010-09 (D.Storkey and E.O'Dea) bug fixes for BDY module
!! 3.3 ! 2011-10 (M. Leclair) split former ssh_wzv routine and remove all vvl related work
!! 4.0 ! 2018-12 (A. Coward) add mixed implicit/explicit advection
!! 4.1 ! 2019-08 (A. Coward, D. Storkey) Rename ssh_nxt -> ssh_atf. Now only does time filtering.
!! - ! 2020-08 (S. Techene, G. Madec) add here ssh initiatlisation
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! ssh_nxt : after ssh
!! ssh_atf : time filter the ssh arrays
!! wzv : compute now vertical velocity
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and tracers variables
USE isf_oce ! ice shelf
USE dom_oce ! ocean space and time domain variables
USE sbc_oce ! surface boundary condition: ocean
USE domvvl ! Variable volume
USE divhor ! horizontal divergence
USE phycst ! physical constants
USE bdy_oce , ONLY : ln_bdy, bdytmask ! Open BounDarY
USE bdydyn2d ! bdy_ssh routine
USE wet_dry ! Wetting/Drying flux limiting
#if defined key_agrif
USE agrif_oce
USE agrif_oce_interp
#endif
!
USE iom
USE in_out_manager ! I/O manager
USE restart ! only for lrst_oce
USE prtctl ! Print control
USE lbclnk ! ocean lateral boundary condition (or mpp link)
USE lib_mpp ! MPP library
USE timing ! Timing
IMPLICIT NONE
PRIVATE
PUBLIC ssh_nxt ! called by step.F90
PUBLIC wzv ! called by step.F90
PUBLIC wAimp ! called by step.F90
PUBLIC ssh_atf ! called by step.F90
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: sshwzv.F90 15150 2021-07-27 10:38:24Z smasson $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE ssh_nxt( kt, Kbb, Kmm, pssh, Kaa )
!!----------------------------------------------------------------------
!! *** ROUTINE ssh_nxt ***
!!
!! ** Purpose : compute the after ssh (ssh(Kaa))
!!
!! ** Method : - Using the incompressibility hypothesis, the ssh increment
!! is computed by integrating the horizontal divergence and multiply by
!! by the time step.
!!
!! ** action : ssh(:,:,Kaa), after sea surface height
!!
!! Reference : Leclair, M., and G. Madec, 2009, Ocean Modelling.
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! time step
INTEGER , INTENT(in ) :: Kbb, Kmm, Kaa ! time level index
REAL(wp), DIMENSION(jpi,jpj,jpt), INTENT(inout) :: pssh ! sea-surface height
!
INTEGER :: ji, jj, jk ! dummy loop index
REAL(wp) :: zcoef ! local scalar
REAL(wp), DIMENSION(jpi,jpj) :: zhdiv ! 2D workspace
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('ssh_nxt')
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'ssh_nxt : after sea surface height'
IF(lwp) WRITE(numout,*) '~~~~~~~ '
ENDIF
!
zcoef = 0.5_wp * r1_rho0
! !------------------------------!
! ! After Sea Surface Height !
! !------------------------------!
IF(ln_wd_il) THEN
CALL wad_lmt(pssh(:,:,Kbb), zcoef * (emp_b(:,:) + emp(:,:)), rDt, Kmm, uu, vv )
ENDIF
CALL div_hor( kt, Kbb, Kmm ) ! Horizontal divergence
!
zhdiv(:,:) = 0._wp
DO_3D( 1, nn_hls, 1, nn_hls, 1, jpkm1 ) ! Horizontal divergence of barotropic transports
zhdiv(ji,jj) = zhdiv(ji,jj) + e3t(ji,jj,jk,Kmm) * hdiv(ji,jj,jk)
END_3D
! ! Sea surface elevation time stepping
! In time-split case we need a first guess of the ssh after (using the baroclinic timestep) in order to
! compute the vertical velocity which can be used to compute the non-linear terms of the momentum equations.
!
DO_2D_OVR( 1, nn_hls, 1, nn_hls ) ! Loop bounds limited by hdiv definition in div_hor
pssh(ji,jj,Kaa) = ( pssh(ji,jj,Kbb) - rDt * ( zcoef * ( emp_b(ji,jj) + emp(ji,jj) ) + zhdiv(ji,jj) ) ) * ssmask(ji,jj)
END_2D
! pssh must be defined everywhere (true for dyn_spg_ts, not for dyn_spg_exp)
IF ( .NOT. ln_dynspg_ts .AND. nn_hls == 2 ) CALL lbc_lnk( 'sshwzv', pssh(:,:,Kaa), 'T', 1.0_wp )
!
#if defined key_agrif
Kbb_a = Kbb ; Kmm_a = Kmm ; Krhs_a = Kaa
CALL agrif_ssh( kt )
#endif
!
IF ( .NOT.ln_dynspg_ts ) THEN
IF( ln_bdy ) THEN
IF (nn_hls==1) CALL lbc_lnk( 'sshwzv', pssh(:,:,Kaa), 'T', 1.0_wp ) ! Not sure that's necessary
CALL bdy_ssh( pssh(:,:,Kaa) ) ! Duplicate sea level across open boundaries
ENDIF
ENDIF
! !------------------------------!
! ! outputs !
! !------------------------------!
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pssh(:,:,Kaa), clinfo1=' pssh(:,:,Kaa) - : ', mask1=tmask )
!
IF( ln_timing ) CALL timing_stop('ssh_nxt')
!
END SUBROUTINE ssh_nxt
SUBROUTINE wzv( kt, Kbb, Kmm, Kaa, pww )
!!----------------------------------------------------------------------
!! *** ROUTINE wzv ***
!!
!! ** Purpose : compute the now vertical velocity
!!
!! ** Method : - Using the incompressibility hypothesis, the vertical
!! velocity is computed by integrating the horizontal divergence
!! from the bottom to the surface minus the scale factor evolution.
!! The boundary conditions are w=0 at the bottom (no flux) and.
!!
!! ** action : pww : now vertical velocity
!!
!! Reference : Leclair, M., and G. Madec, 2009, Ocean Modelling.
!!----------------------------------------------------------------------
INTEGER , INTENT(in) :: kt ! time step
INTEGER , INTENT(in) :: Kbb, Kmm, Kaa ! time level indices
REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pww ! vertical velocity at Kmm
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zhdiv
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('wzv')
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'wzv : now vertical velocity '
IF(lwp) WRITE(numout,*) '~~~~~ '
!
pww(:,:,jpk) = 0._wp ! bottom boundary condition: w=0 (set once for all)
ENDIF
! !------------------------------!
! ! Now Vertical Velocity !
! !------------------------------!
!
! !===============================!
IF( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN !== z_tilde and layer cases ==!
! !===============================!
ALLOCATE( zhdiv(jpi,jpj,jpk) )
!
DO jk = 1, jpkm1
! horizontal divergence of thickness diffusion transport ( velocity multiplied by e3t)
! - ML - note: computation already done in dom_vvl_sf_nxt. Could be optimized (not critical and clearer this way)
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
zhdiv(ji,jj,jk) = r1_e1e2t(ji,jj) * ( un_td(ji,jj,jk) - un_td(ji-1,jj,jk) + vn_td(ji,jj,jk) - vn_td(ji,jj-1,jk) )
END_2D
END DO
IF( nn_hls == 1) CALL lbc_lnk('sshwzv', zhdiv, 'T', 1.0_wp) ! - ML - Perhaps not necessary: not used for horizontal "connexions"
! ! Is it problematic to have a wrong vertical velocity in boundary cells?
! ! Same question holds for hdiv. Perhaps just for security
! ! clem: yes it is a problem because ww is used in many other places where we need the halos
!
DO_3DS( nn_hls-1, nn_hls, nn_hls-1, nn_hls, jpkm1, 1, -1 ) ! integrate from the bottom the hor. divergence
! computation of w
pww(ji,jj,jk) = pww(ji,jj,jk+1) - ( e3t(ji,jj,jk,Kmm) * hdiv(ji,jj,jk) &
& + zhdiv(ji,jj,jk) &
& + r1_Dt * ( e3t(ji,jj,jk,Kaa) &
& - e3t(ji,jj,jk,Kbb) ) ) * tmask(ji,jj,jk)
END_3D
! IF( ln_vvl_layer ) pww(:,:,:) = 0.e0
DEALLOCATE( zhdiv )
! !=================================!
ELSEIF( ln_linssh ) THEN !== linear free surface cases ==!
! !=================================!
DO_3DS( nn_hls-1, nn_hls, nn_hls-1, nn_hls, jpkm1, 1, -1 ) ! integrate from the bottom the hor. divergence
pww(ji,jj,jk) = pww(ji,jj,jk+1) - ( e3t(ji,jj,jk,Kmm) * hdiv(ji,jj,jk) ) * tmask(ji,jj,jk)
END_3D
! !==========================================!
ELSE !== Quasi-Eulerian vertical coordinate ==! ('key_qco')
! !==========================================!
DO_3DS( nn_hls-1, nn_hls, nn_hls-1, nn_hls, jpkm1, 1, -1 ) ! integrate from the bottom the hor. divergence
pww(ji,jj,jk) = pww(ji,jj,jk+1) - ( e3t(ji,jj,jk,Kmm) * hdiv(ji,jj,jk) &
& + r1_Dt * ( e3t(ji,jj,jk,Kaa) &
& - e3t(ji,jj,jk,Kbb) ) ) * tmask(ji,jj,jk)
END_3D
ENDIF
IF( ln_bdy ) THEN
DO jk = 1, jpkm1
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
pww(ji,jj,jk) = pww(ji,jj,jk) * bdytmask(ji,jj)
END_2D
END DO
ENDIF
!
#if defined key_agrif
IF( .NOT. AGRIF_Root() ) THEN
!
! Mask vertical velocity at first/last columns/row
! inside computational domain (cosmetic)
DO jk = 1, jpkm1
IF( lk_west ) THEN ! --- West --- !
DO ji = mi0(2+nn_hls), mi1(2+nn_hls)
DO jj = 1, jpj
pww(ji,jj,jk) = 0._wp
END DO
END DO
ENDIF
IF( lk_east ) THEN ! --- East --- !
DO ji = mi0(jpiglo-1-nn_hls), mi1(jpiglo-1-nn_hls)
DO jj = 1, jpj
pww(ji,jj,jk) = 0._wp
END DO
END DO
ENDIF
IF( lk_south ) THEN ! --- South --- !
DO jj = mj0(2+nn_hls), mj1(2+nn_hls)
DO ji = 1, jpi
pww(ji,jj,jk) = 0._wp
END DO
END DO
ENDIF
IF( lk_north ) THEN ! --- North --- !
DO jj = mj0(jpjglo-1-nn_hls), mj1(jpjglo-1-nn_hls)
DO ji = 1, jpi
pww(ji,jj,jk) = 0._wp
END DO
END DO
ENDIF
!
END DO
!
ENDIF
#endif
!
IF( ln_timing ) CALL timing_stop('wzv')
!
END SUBROUTINE wzv
SUBROUTINE ssh_atf( kt, Kbb, Kmm, Kaa, pssh )
!!----------------------------------------------------------------------
!! *** ROUTINE ssh_atf ***
!!
!! ** Purpose : Apply Asselin time filter to now SSH.
!!
!! ** Method : - apply Asselin time fiter to now ssh (excluding the forcing
!! from the filter, see Leclair and Madec 2010) and swap :
!! pssh(:,:,Kmm) = pssh(:,:,Kaa) + rn_atfp * ( pssh(:,:,Kbb) -2 pssh(:,:,Kmm) + pssh(:,:,Kaa) )
!! - rn_atfp * rn_Dt * ( emp_b - emp ) / rho0
!!
!! ** action : - pssh(:,:,Kmm) time filtered
!!
!! Reference : Leclair, M., and G. Madec, 2009, Ocean Modelling.
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! ocean time-step index
INTEGER , INTENT(in ) :: Kbb, Kmm, Kaa ! ocean time level indices
REAL(wp), DIMENSION(jpi,jpj,jpt), INTENT(inout) :: pssh ! SSH field
!
REAL(wp) :: zcoef ! local scalar
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('ssh_atf')
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'ssh_atf : Asselin time filter of sea surface height'
IF(lwp) WRITE(numout,*) '~~~~~~~ '
ENDIF
!
IF( .NOT.l_1st_euler ) THEN ! Apply Asselin time filter on Kmm field (not on euler 1st)
!
IF( ln_linssh ) THEN ! filtered "now" field
pssh(:,:,Kmm) = pssh(:,:,Kmm) + rn_atfp * ( pssh(:,:,Kbb) - 2 * pssh(:,:,Kmm) + pssh(:,:,Kaa) )
!
ELSE ! filtered "now" field with forcing removed
zcoef = rn_atfp * rn_Dt * r1_rho0
pssh(:,:,Kmm) = pssh(:,:,Kmm) + rn_atfp * ( pssh(:,:,Kbb) - 2 * pssh(:,:,Kmm) + pssh(:,:,Kaa) ) &
& - zcoef * ( emp_b(:,:) - emp(:,:) &
& - rnf_b(:,:) + rnf(:,:) &
& - fwfisf_cav_b(:,:) + fwfisf_cav(:,:) &
& - fwfisf_par_b(:,:) + fwfisf_par(:,:) ) * ssmask(:,:)
! ice sheet coupling
IF( ln_isf .AND. ln_isfcpl .AND. kt == nit000+1 ) &
& pssh(:,:,Kbb) = pssh(:,:,Kbb) - rn_atfp * rn_Dt * ( risfcpl_ssh(:,:) - 0._wp ) * ssmask(:,:)
ENDIF
ENDIF
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pssh(:,:,Kmm), clinfo1=' atf - pssh(:,:,Kmm): ', mask1=tmask )
!
IF( ln_timing ) CALL timing_stop('ssh_atf')
!
END SUBROUTINE ssh_atf
SUBROUTINE wAimp( kt, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE wAimp ***
!!
!! ** Purpose : compute the Courant number and partition vertical velocity
!! if a proportion needs to be treated implicitly
!!
!! ** Method : -
!!
!! ** action : ww : now vertical velocity (to be handled explicitly)
!! : wi : now vertical velocity (for implicit treatment)
!!
!! Reference : Shchepetkin, A. F. (2015): An adaptive, Courant-number-dependent
!! implicit scheme for vertical advection in oceanic modeling.
!! Ocean Modelling, 91, 38-69.
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! time step
INTEGER, INTENT(in) :: Kmm ! time level index
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zCu, zcff, z1_e3t, zdt ! local scalars
REAL(wp) , PARAMETER :: Cu_min = 0.15_wp ! local parameters
REAL(wp) , PARAMETER :: Cu_max = 0.30_wp ! local parameters
REAL(wp) , PARAMETER :: Cu_cut = 2._wp*Cu_max - Cu_min ! local parameters
REAL(wp) , PARAMETER :: Fcu = 4._wp*Cu_max*(Cu_max-Cu_min) ! local parameters
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('wAimp')
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'wAimp : Courant number-based partitioning of now vertical velocity '
IF(lwp) WRITE(numout,*) '~~~~~ '
ENDIF
!
! Calculate Courant numbers
zdt = 2._wp * rn_Dt ! 2*rn_Dt and not rDt (for restartability)
IF( ln_vvl_ztilde .OR. ln_vvl_layer ) THEN
DO_3D( nn_hls-1, nn_hls, nn_hls-1, nn_hls, 1, jpkm1 )
z1_e3t = 1._wp / e3t(ji,jj,jk,Kmm)
Cu_adv(ji,jj,jk) = zdt * &
& ( ( MAX( ww(ji,jj,jk) , 0._wp ) - MIN( ww(ji,jj,jk+1) , 0._wp ) ) &
& + ( MAX( e2u(ji ,jj) * e3u(ji ,jj,jk,Kmm) &
& * uu (ji ,jj,jk,Kmm) + un_td(ji ,jj,jk), 0._wp ) - &
& MIN( e2u(ji-1,jj) * e3u(ji-1,jj,jk,Kmm) &
& * uu (ji-1,jj,jk,Kmm) + un_td(ji-1,jj,jk), 0._wp ) ) &
& * r1_e1e2t(ji,jj) &
& + ( MAX( e1v(ji,jj ) * e3v(ji,jj ,jk,Kmm) &
& * vv (ji,jj ,jk,Kmm) + vn_td(ji,jj ,jk), 0._wp ) - &
& MIN( e1v(ji,jj-1) * e3v(ji,jj-1,jk,Kmm) &
& * vv (ji,jj-1,jk,Kmm) + vn_td(ji,jj-1,jk), 0._wp ) ) &
& * r1_e1e2t(ji,jj) &
& ) * z1_e3t
END_3D
ELSE
DO_3D( nn_hls-1, nn_hls, nn_hls-1, nn_hls, 1, jpkm1 )
z1_e3t = 1._wp / e3t(ji,jj,jk,Kmm)
Cu_adv(ji,jj,jk) = zdt * &
& ( ( MAX( ww(ji,jj,jk) , 0._wp ) - MIN( ww(ji,jj,jk+1) , 0._wp ) ) &
& + ( MAX( e2u(ji ,jj)*e3u(ji ,jj,jk,Kmm)*uu(ji ,jj,jk,Kmm), 0._wp ) - &
& MIN( e2u(ji-1,jj)*e3u(ji-1,jj,jk,Kmm)*uu(ji-1,jj,jk,Kmm), 0._wp ) ) &
& * r1_e1e2t(ji,jj) &
& + ( MAX( e1v(ji,jj )*e3v(ji,jj ,jk,Kmm)*vv(ji,jj ,jk,Kmm), 0._wp ) - &
& MIN( e1v(ji,jj-1)*e3v(ji,jj-1,jk,Kmm)*vv(ji,jj-1,jk,Kmm), 0._wp ) ) &
& * r1_e1e2t(ji,jj) &
& ) * z1_e3t
END_3D
ENDIF
CALL iom_put("Courant",Cu_adv)
!
IF( MAXVAL( Cu_adv(:,:,:) ) > Cu_min ) THEN ! Quick check if any breaches anywhere
DO_3DS( nn_hls-1, nn_hls, nn_hls-1, nn_hls, jpkm1, 2, -1 ) ! or scan Courant criterion and partition ! w where necessary
!
zCu = MAX( Cu_adv(ji,jj,jk) , Cu_adv(ji,jj,jk-1) )
! alt:
! IF ( ww(ji,jj,jk) > 0._wp ) THEN
! zCu = Cu_adv(ji,jj,jk)
! ELSE
! zCu = Cu_adv(ji,jj,jk-1)
! ENDIF
!
IF( zCu <= Cu_min ) THEN !<-- Fully explicit
zcff = 0._wp
ELSEIF( zCu < Cu_cut ) THEN !<-- Mixed explicit
zcff = ( zCu - Cu_min )**2
zcff = zcff / ( Fcu + zcff )
ELSE !<-- Mostly implicit
zcff = ( zCu - Cu_max )/ zCu
ENDIF
zcff = MIN(1._wp, zcff)
!
wi(ji,jj,jk) = zcff * ww(ji,jj,jk)
ww(ji,jj,jk) = ( 1._wp - zcff ) * ww(ji,jj,jk)
!
Cu_adv(ji,jj,jk) = zcff ! Reuse array to output coefficient below and in stp_ctl
END_3D
Cu_adv(:,:,1) = 0._wp
ELSE
! Fully explicit everywhere
Cu_adv(:,:,:) = 0._wp ! Reuse array to output coefficient below and in stp_ctl
wi (:,:,:) = 0._wp
ENDIF
CALL iom_put("wimp",wi)
CALL iom_put("wi_cff",Cu_adv)
CALL iom_put("wexp",ww)
!
IF( ln_timing ) CALL timing_stop('wAimp')
!
END SUBROUTINE wAimp
!!======================================================================
END MODULE sshwzv