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MODULE dynspg_ts
!! Includes ROMS wd scheme with diagnostic outputs ; puu(:,:,:,Kmm) and puu(:,:,:,Krhs) updates are commented out !
!!======================================================================
!! *** MODULE dynspg_ts ***
!! Ocean dynamics: surface pressure gradient trend, split-explicit scheme
!!======================================================================
!! History : 1.0 ! 2004-12 (L. Bessieres, G. Madec) Original code
!! - ! 2005-11 (V. Garnier, G. Madec) optimization
!! - ! 2006-08 (S. Masson) distributed restart using iom
!! 2.0 ! 2007-07 (D. Storkey) calls to BDY routines
!! - ! 2008-01 (R. Benshila) change averaging method
!! 3.2 ! 2009-07 (R. Benshila, G. Madec) Complete revisit associated to vvl reactivation
!! 3.3 ! 2010-09 (D. Storkey, E. O'Dea) update for BDY for Shelf configurations
!! 3.3 ! 2011-03 (R. Benshila, R. Hordoir, P. Oddo) update calculation of ub_b
!! 3.5 ! 2013-07 (J. Chanut) Switch to Forward-backward time stepping
!! 3.6 ! 2013-11 (A. Coward) Update for z-tilde compatibility
!! 3.7 ! 2015-11 (J. Chanut) free surface simplification
!! - ! 2016-12 (G. Madec, E. Clementi) update for Stoke-Drift divergence
!! 4.0 ! 2017-05 (G. Madec) drag coef. defined at t-point (zdfdrg.F90)
!!---------------------------------------------------------------------
!!----------------------------------------------------------------------
!! dyn_spg_ts : compute surface pressure gradient trend using a time-splitting scheme
!! dyn_spg_ts_init: initialisation of the time-splitting scheme
!! ts_wgt : set time-splitting weights for temporal averaging (or not)
!! ts_rst : read/write time-splitting fields in restart file
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and tracers
USE dom_oce ! ocean space and time domain
USE sbc_oce ! surface boundary condition: ocean
USE isf_oce ! ice shelf variable (fwfisf)
USE zdf_oce ! vertical physics: variables
USE zdfdrg ! vertical physics: top/bottom drag coef.
USE sbcapr ! surface boundary condition: atmospheric pressure
USE dynadv , ONLY: ln_dynadv_vec
USE dynvor ! vortivity scheme indicators
USE phycst ! physical constants
USE dynvor ! vorticity term
USE wet_dry ! wetting/drying flux limter
USE bdy_oce ! open boundary
USE bdyvol ! open boundary volume conservation
USE bdytides ! open boundary condition data
USE bdydyn2d ! open boundary conditions on barotropic variables
USE tide_mod !
USE sbcwave ! surface wave
#if defined key_agrif
USE agrif_oce_interp ! agrif
USE agrif_oce
#endif
#if defined key_asminc
USE asminc ! Assimilation increment
#endif
!
USE in_out_manager ! I/O manager
USE lib_mpp ! distributed memory computing library
USE lbclnk ! ocean lateral boundary conditions (or mpp link)
USE prtctl ! Print control
USE iom ! IOM library
USE restart ! only for lrst_oce
USE iom ! to remove
IMPLICIT NONE
PRIVATE
PUBLIC dyn_spg_ts ! called by dyn_spg
PUBLIC dyn_spg_ts_init ! - - dyn_spg_init
!! Time filtered arrays at baroclinic time step:
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: un_adv , vn_adv !: Advection vel. at "now" barocl. step
!
INTEGER, SAVE :: icycle ! Number of barotropic sub-steps for each internal step nn_e <= 2.5 nn_e
REAL(wp),SAVE :: rDt_e ! Barotropic time step
!
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: wgtbtp1, wgtbtp2 ! 1st & 2nd weights used in time filtering of barotropic fields
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zwz ! ff_f/h at F points
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftnw, ftne ! triad of coriolis parameter
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftsw, ftse ! (only used with een vorticity scheme)
REAL(wp) :: r1_12 = 1._wp / 12._wp ! local ratios
REAL(wp) :: r1_8 = 0.125_wp !
REAL(wp) :: r1_4 = 0.25_wp !
REAL(wp) :: r1_2 = 0.5_wp !
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: dynspg_ts.F90 15489 2021-11-10 09:18:39Z jchanut $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
INTEGER FUNCTION dyn_spg_ts_alloc()
!!----------------------------------------------------------------------
!! *** routine dyn_spg_ts_alloc ***
!!----------------------------------------------------------------------
INTEGER :: ierr(3)
!!----------------------------------------------------------------------
ierr(:) = 0
!
ALLOCATE( wgtbtp1(3*nn_e), wgtbtp2(3*nn_e), zwz(jpi,jpj), STAT=ierr(1) )
IF( ln_dynvor_een .OR. ln_dynvor_eeT ) &
& ALLOCATE( ftnw(jpi,jpj) , ftne(jpi,jpj) , ftsw(jpi,jpj) , ftse(jpi,jpj), STAT=ierr(2) )
!
ALLOCATE( un_adv(jpi,jpj), vn_adv(jpi,jpj) , STAT=ierr(3) )
!
dyn_spg_ts_alloc = MAXVAL( ierr(:) )
!
CALL mpp_sum( 'dynspg_ts', dyn_spg_ts_alloc )
IF( dyn_spg_ts_alloc /= 0 ) CALL ctl_stop( 'STOP', 'dyn_spg_ts_alloc: failed to allocate arrays' )
!
END FUNCTION dyn_spg_ts_alloc
SUBROUTINE dyn_spg_ts( kt, Kbb, Kmm, Krhs, puu, pvv, pssh, puu_b, pvv_b, Kaa, k_only_ADV )
!!----------------------------------------------------------------------
!!
!! ** Purpose : - Compute the now trend due to the explicit time stepping
!! of the quasi-linear barotropic system, and add it to the
!! general momentum trend.
!!
!! ** Method : - split-explicit schem (time splitting) :
!! Barotropic variables are advanced from internal time steps
!! "n" to "n+1" if ln_bt_fw=T
!! or from
!! "n-1" to "n+1" if ln_bt_fw=F
!! thanks to a generalized forward-backward time stepping (see ref. below).
!!
!! ** Action :
!! -Update the filtered free surface at step "n+1" : pssh(:,:,Kaa)
!! -Update filtered barotropic velocities at step "n+1" : puu_b(:,:,:,Kaa), vv_b(:,:,:,Kaa)
!! -Compute barotropic advective fluxes at step "n" : un_adv, vn_adv
!! These are used to advect tracers and are compliant with discrete
!! continuity equation taken at the baroclinic time steps. This
!! ensures tracers conservation.
!! - (puu(:,:,:,Krhs), pvv(:,:,:,Krhs)) momentum trend updated with barotropic component.
!!
!! References : Shchepetkin and McWilliams, Ocean Modelling, 2005.
!!---------------------------------------------------------------------
INTEGER , INTENT( in ) :: kt ! ocean time-step index
INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices
REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(inout) :: pssh, puu_b, pvv_b ! SSH and barotropic velocities at main time levels
INTEGER , OPTIONAL , INTENT( in ) :: k_only_ADV ! only Advection in the RHS
!
INTEGER :: ji, jj, jk, jn ! dummy loop indices
LOGICAL :: ll_fw_start ! =T : forward integration
LOGICAL :: ll_init ! =T : special startup of 2d equations
INTEGER :: noffset ! local integers : time offset for bdy update
REAL(wp) :: r1_Dt_b, z1_hu, z1_hv ! local scalars
REAL(wp) :: za0, za1, za2, za3 ! - -
REAL(wp) :: zztmp, zldg ! - -
REAL(wp) :: zhu_bck, zhv_bck, zhdiv ! - -
REAL(wp) :: zun_save, zvn_save ! - -
REAL(wp), DIMENSION(jpi,jpj) :: zu_trd, zu_frc, zu_spg, zssh_frc
REAL(wp), DIMENSION(jpi,jpj) :: zv_trd, zv_frc, zv_spg
REAL(wp), DIMENSION(jpi,jpj) :: zsshu_a, zhup2_e, zhtp2_e
REAL(wp), DIMENSION(jpi,jpj) :: zsshv_a, zhvp2_e, zsshp2_e
REAL(wp), DIMENSION(jpi,jpj) :: zCdU_u, zCdU_v ! top/bottom stress at u- & v-points
REAL(wp), DIMENSION(jpi,jpj) :: zhU, zhV ! fluxes
!!st#if defined key_qco
!!st REAL(wp), DIMENSION(jpi, jpj, jpk) :: ze3u, ze3v
!!st#endif
!
REAL(wp) :: zwdramp ! local scalar - only used if ln_wd_dl = .True.
INTEGER :: iwdg, jwdg, kwdg ! short-hand values for the indices of the output point
REAL(wp) :: zepsilon, zgamma ! - -
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zcpx, zcpy ! Wetting/Dying gravity filter coef.
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztwdmask, zuwdmask, zvwdmask ! ROMS wetting and drying masks at t,u,v points
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zuwdav2, zvwdav2 ! averages over the sub-steps of zuwdmask and zvwdmask
REAL(wp) :: zt0substep ! Time of day at the beginning of the time substep
!!----------------------------------------------------------------------
!
IF( ln_wd_il ) ALLOCATE( zcpx(jpi,jpj), zcpy(jpi,jpj) )
! !* Allocate temporary arrays
IF( ln_wd_dl ) ALLOCATE( ztwdmask(jpi,jpj), zuwdmask(jpi,jpj), zvwdmask(jpi,jpj), zuwdav2(jpi,jpj), zvwdav2(jpi,jpj))
!
zwdramp = r_rn_wdmin1 ! simplest ramp
! zwdramp = 1._wp / (rn_wdmin2 - rn_wdmin1) ! more general ramp
! ! inverse of baroclinic time step
r1_Dt_b = 1._wp / rDt
!
ll_init = ln_bt_av ! if no time averaging, then no specific restart
ll_fw_start = .FALSE.
! ! time offset in steps for bdy data update
IF( .NOT.ln_bt_fw ) THEN ; noffset = - nn_e
ELSE ; noffset = 0
ENDIF
!
IF( kt == nit000 ) THEN !* initialisation
!
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn_spg_ts : surface pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~ free surface with time splitting'
IF(lwp) WRITE(numout,*)
!
IF( l_1st_euler ) ll_init=.TRUE.
!
IF( ln_bt_fw .OR. l_1st_euler ) THEN
ll_fw_start =.TRUE.
noffset = 0
ELSE
ll_fw_start =.FALSE.
ENDIF
! ! Set averaging weights and cycle length:
CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
!
ELSEIF( kt == nit000 + 1 ) THEN !* initialisation 2nd time-step
!
IF( .NOT.ln_bt_fw ) THEN
! If we did an Euler timestep on the first timestep we need to reset ll_fw_start
! and the averaging weights. We don't have an easy way of telling whether we did
! an Euler timestep on the first timestep (because l_1st_euler is reset to .false.
! at the end of the first timestep) so just do this in all cases.
ll_fw_start = .FALSE.
CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
ENDIF
!
ENDIF
!
! -----------------------------------------------------------------------------
! Phase 1 : Coupling between general trend and barotropic estimates (1st step)
! -----------------------------------------------------------------------------
!
!
! != zu_frc = 1/H e3*d/dt(Ua) =! (Vertical mean of Ua, the 3D trends)
! ! --------------------------- !
#if defined key_qco
zu_frc(:,:) = SUM( e3u_0(:,:,: ) * puu(:,:,:,Krhs) * umask(:,:,:), DIM=3 ) * r1_hu_0(:,:)
zv_frc(:,:) = SUM( e3v_0(:,:,: ) * pvv(:,:,:,Krhs) * vmask(:,:,:), DIM=3 ) * r1_hv_0(:,:)
#else
zu_frc(:,:) = SUM( e3u(:,:,:,Kmm) * puu(:,:,:,Krhs) * umask(:,:,:), DIM=3 ) * r1_hu(:,:,Kmm)
zv_frc(:,:) = SUM( e3v(:,:,:,Kmm) * pvv(:,:,:,Krhs) * vmask(:,:,:), DIM=3 ) * r1_hv(:,:,Kmm)
#endif
!
!
! != U(Krhs) => baroclinic trend =! (remove its vertical mean)
DO jk = 1, jpkm1 ! ----------------------------- !
puu(:,:,jk,Krhs) = ( puu(:,:,jk,Krhs) - zu_frc(:,:) ) * umask(:,:,jk)
pvv(:,:,jk,Krhs) = ( pvv(:,:,jk,Krhs) - zv_frc(:,:) ) * vmask(:,:,jk)
END DO
!!gm Question here when removing the Vertically integrated trends, we remove the vertically integrated NL trends on momentum....
!!gm Is it correct to do so ? I think so...
! != remove 2D Coriolis trend =!
! ! -------------------------- !
!
IF( kt == nit000 .OR. .NOT. ln_linssh ) CALL dyn_cor_2D_init( Kmm ) ! Set zwz, the barotropic Coriolis force coefficient
! ! recompute zwz = f/depth at every time step for (.NOT.ln_linssh) as the water colomn height changes
!
IF( .NOT. PRESENT(k_only_ADV) ) THEN !* remove the 2D Coriolis trend
zhU(:,:) = puu_b(:,:,Kmm) * hu(:,:,Kmm) * e2u(:,:) ! now fluxes
zhV(:,:) = pvv_b(:,:,Kmm) * hv(:,:,Kmm) * e1v(:,:) ! NB: FULL domain : put a value in last row and column
!
CALL dyn_cor_2d( ht(:,:), hu(:,:,Kmm), hv(:,:,Kmm), puu_b(:,:,Kmm), pvv_b(:,:,Kmm), zhU, zhV, & ! <<== in
& zu_trd, zv_trd ) ! ==>> out
!
DO_2D( 0, 0, 0, 0 ) ! Remove coriolis term (and possibly spg) from barotropic trend
zu_frc(ji,jj) = zu_frc(ji,jj) - zu_trd(ji,jj) * ssumask(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) - zv_trd(ji,jj) * ssvmask(ji,jj)
END_2D
ENDIF
!
! != Add bottom stress contribution from baroclinic velocities =!
! ! ----------------------------------------------------------- !
IF( PRESENT(k_only_ADV) ) THEN !* only Advection in the RHS : provide the barotropic bottom drag coefficients
DO_2D( 0, 0, 0, 0 )
zCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
zCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
END_2D
ELSE !* remove baroclinic drag AND provide the barotropic drag coefficients
CALL dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b, pvv_b, zu_frc, zv_frc, zCdU_u, zCdU_v )
ENDIF
!
! != Add atmospheric pressure forcing =!
! ! ---------------------------------- !
IF( ln_apr_dyn ) THEN
IF( ln_bt_fw ) THEN ! FORWARD integration: use kt+1/2 pressure (NOW+1/2)
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + grav * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) ) * r1_e1u(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) + grav * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) ) * r1_e2v(ji,jj)
END_2D
ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 pressure (NOW)
zztmp = grav * r1_2
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) &
& + ssh_ibb(ji+1,jj ) - ssh_ibb(ji,jj) ) * r1_e1u(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) &
& + ssh_ibb(ji ,jj+1) - ssh_ibb(ji,jj) ) * r1_e2v(ji,jj)
END_2D
ENDIF
ENDIF
!
! != Add wind forcing =!
! ! ------------------ !
IF( ln_bt_fw ) THEN
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + r1_rho0 * utau(ji,jj) * r1_hu(ji,jj,Kmm)
zv_frc(ji,jj) = zv_frc(ji,jj) + r1_rho0 * vtau(ji,jj) * r1_hv(ji,jj,Kmm)
END_2D
ELSE
zztmp = r1_rho0 * r1_2
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( utau_b(ji,jj) + utau(ji,jj) ) * r1_hu(ji,jj,Kmm)
zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( vtau_b(ji,jj) + vtau(ji,jj) ) * r1_hv(ji,jj,Kmm)
END_2D
ENDIF
!
! !----------------!
! !== sssh_frc ==! Right-Hand-Side of the barotropic ssh equation (over the FULL domain)
! !----------------!
! != Net water flux forcing applied to a water column =!
! ! --------------------------------------------------- !
IF (ln_bt_fw) THEN ! FORWARD integration: use kt+1/2 fluxes (NOW+1/2)
zssh_frc(:,:) = r1_rho0 * ( emp(:,:) - rnf(:,:) - fwfisf_cav(:,:) - fwfisf_par(:,:) )
ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 fluxes (NOW)
zztmp = r1_rho0 * r1_2
zssh_frc(:,:) = zztmp * ( emp(:,:) + emp_b(:,:) &
& - rnf(:,:) - rnf_b(:,:) &
& - fwfisf_cav(:,:) - fwfisf_cav_b(:,:) &
& - fwfisf_par(:,:) - fwfisf_par_b(:,:) )
ENDIF
! != Add Stokes drift divergence =! (if exist)
IF( ln_sdw ) THEN ! ----------------------------- !
zssh_frc(:,:) = zssh_frc(:,:) + div_sd(:,:)
ENDIF
!
! ! ice sheet coupling
IF ( ln_isf .AND. ln_isfcpl ) THEN
!
! ice sheet coupling
IF( ln_rstart .AND. kt == nit000 ) THEN
zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_ssh(:,:)
END IF
!
! conservation option
IF( ln_isfcpl_cons ) THEN
zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_cons_ssh(:,:)
END IF
!
END IF
!
#if defined key_asminc
! != Add the IAU weighted SSH increment =!
! ! ------------------------------------ !
IF( lk_asminc .AND. ln_sshinc .AND. ln_asmiau ) THEN
zssh_frc(:,:) = zssh_frc(:,:) - ssh_iau(:,:)
ENDIF
#endif
! != Fill boundary data arrays for AGRIF
! ! ------------------------------------
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_dta_ts( kt )
#endif
!
! -----------------------------------------------------------------------
! Phase 2 : Integration of the barotropic equations
! -----------------------------------------------------------------------
!
! ! ==================== !
! ! Initialisations !
! ! ==================== !
! Initialize barotropic variables:
IF( ll_init )THEN
sshbb_e(:,:) = 0._wp
ubb_e (:,:) = 0._wp
vbb_e (:,:) = 0._wp
sshb_e (:,:) = 0._wp
ub_e (:,:) = 0._wp
vb_e (:,:) = 0._wp
ENDIF
!
IF( ln_linssh ) THEN ! mid-step ocean depth is fixed (hup2_e=hu_n=hu_0)
zhup2_e(:,:) = hu_0(:,:)
zhvp2_e(:,:) = hv_0(:,:)
zhtp2_e(:,:) = ht_0(:,:)
ENDIF
!
IF( ln_bt_fw ) THEN ! FORWARD integration: start from NOW fields
sshn_e(:,:) = pssh (:,:,Kmm)
un_e (:,:) = puu_b(:,:,Kmm)
vn_e (:,:) = pvv_b(:,:,Kmm)
!
hu_e (:,:) = hu(:,:,Kmm)
hv_e (:,:) = hv(:,:,Kmm)
hur_e (:,:) = r1_hu(:,:,Kmm)
hvr_e (:,:) = r1_hv(:,:,Kmm)
ELSE ! CENTRED integration: start from BEFORE fields
sshn_e(:,:) = pssh (:,:,Kbb)
un_e (:,:) = puu_b(:,:,Kbb)
vn_e (:,:) = pvv_b(:,:,Kbb)
!
hu_e (:,:) = hu(:,:,Kbb)
hv_e (:,:) = hv(:,:,Kbb)
hur_e (:,:) = r1_hu(:,:,Kbb)
hvr_e (:,:) = r1_hv(:,:,Kbb)
ENDIF
!
! Initialize sums:
puu_b (:,:,Kaa) = 0._wp ! After barotropic velocities (or transport if flux form)
pvv_b (:,:,Kaa) = 0._wp
pssh (:,:,Kaa) = 0._wp ! Sum for after averaged sea level
un_adv(:,:) = 0._wp ! Sum for now transport issued from ts loop
vn_adv(:,:) = 0._wp
!
IF( ln_wd_dl ) THEN
zuwdmask(:,:) = 0._wp ! set to zero for definiteness (not sure this is necessary)
zvwdmask(:,:) = 0._wp !
zuwdav2 (:,:) = 0._wp
zvwdav2 (:,:) = 0._wp
END IF
! ! ==================== !
DO jn = 1, icycle ! sub-time-step loop !
! ! ==================== !
!
l_full_nf_update = jn == icycle ! false: disable full North fold update (performances) for jn = 1 to icycle-1
!
! !== Update the forcing ==! (BDY and tides)
!
IF( ln_bdy .AND. ln_tide ) CALL bdy_dta_tides( kt, kit=jn, pt_offset= REAL(noffset+1,wp) )
! Update tide potential at the beginning of current time substep
IF( ln_tide_pot .AND. ln_tide ) THEN
zt0substep = REAL(nsec_day, wp) - 0.5_wp*rn_Dt + (jn + noffset - 1) * rn_Dt / REAL(nn_e, wp)
CALL upd_tide(zt0substep, Kmm)
END IF
!
! !== extrapolation at mid-step ==! (jn+1/2)
!
! !* Set extrapolation coefficients for predictor step:
IF ((jn<3).AND.ll_init) THEN ! Forward
za1 = 1._wp
za2 = 0._wp
za3 = 0._wp
ELSE ! AB3-AM4 Coefficients: bet=0.281105
za1 = 1.781105_wp ! za1 = 3/2 + bet
za2 = -1.06221_wp ! za2 = -(1/2 + 2*bet)
za3 = 0.281105_wp ! za3 = bet
ENDIF
!
! !* Extrapolate barotropic velocities at mid-step (jn+1/2)
!-- m+1/2 m m-1 m-2 --!
!-- u = (3/2+beta) u -(1/2+2beta) u + beta u --!
!-------------------------------------------------------------------------!
ua_e(:,:) = za1 * un_e(:,:) + za2 * ub_e(:,:) + za3 * ubb_e(:,:)
va_e(:,:) = za1 * vn_e(:,:) + za2 * vb_e(:,:) + za3 * vbb_e(:,:)
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
! ! ------------------
! Extrapolate Sea Level at step jit+0.5:
!-- m+1/2 m m-1 m-2 --!
!-- ssh = (3/2+beta) ssh -(1/2+2beta) ssh + beta ssh --!
!--------------------------------------------------------------------------------!
zsshp2_e(:,:) = za1 * sshn_e(:,:) + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
! set wetting & drying mask at tracer points for this barotropic mid-step
IF( ln_wd_dl ) CALL wad_tmsk( zsshp2_e, ztwdmask )
!
! ! ocean t-depth at mid-step
zhtp2_e(:,:) = ht_0(:,:) + zsshp2_e(:,:)
!
! ! ocean u- and v-depth at mid-step (separate DO-loops remove the need of a lbc_lnk)
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji+1,jj ) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 )
zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#else
! ! no 'key_qcoTest_FluxForm' : surface weighted ssh average
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * r1_e1e2u(ji,jj) &
& * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * r1_e1e2v(ji,jj) &
& * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
END_2D
#endif
!
ENDIF
!
! !== after SSH ==! (jn+1)
!
! ! update (ua_e,va_e) to enforce volume conservation at open boundaries
! ! values of zhup2_e and zhvp2_e on the halo are not needed in bdy_vol2d
IF( ln_bdy .AND. ln_vol ) CALL bdy_vol2d( kt, jn, ua_e, va_e, zhup2_e, zhvp2_e )
!
! ! resulting flux at mid-step (not over the full domain)
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhU(ji,jj) = e2u(ji,jj) * ua_e(ji,jj) * zhup2_e(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zhV(ji,jj) = e1v(ji,jj) * va_e(ji,jj) * zhvp2_e(ji,jj)
END_2D
!
#if defined key_agrif
! Set fluxes during predictor step to ensure volume conservation
IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) CALL agrif_dyn_ts_flux( jn, zhU, zhV )
#endif
IF( ln_wd_il ) CALL wad_lmt_bt(zhU, zhV, sshn_e, zssh_frc, rDt_e) !!gm wad_lmt_bt use of lbc_lnk on zhU, zhV
IF( ln_wd_dl ) THEN ! un_e and vn_e are set to zero at faces where
! ! the direction of the flow is from dry cells
CALL wad_Umsk( ztwdmask, zhU, zhV, un_e, vn_e, zuwdmask, zvwdmask ) ! not jpi colomn for U, not jpj row for V
!
ENDIF
!
!
! Compute Sea Level at step jit+1
!-- m+1 m m+1/2 --!
!-- ssh = ssh - delta_t' * [ frc + div( flux ) ] --!
!-------------------------------------------------------------------------!
DO_2D( 0, 0, 0, 0 )
zhdiv = ( zhU(ji,jj) - zhU(ji-1,jj) + zhV(ji,jj) - zhV(ji,jj-1) ) * r1_e1e2t(ji,jj)
ssha_e(ji,jj) = ( sshn_e(ji,jj) - rDt_e * ( zssh_frc(ji,jj) + zhdiv ) ) * ssmask(ji,jj)
END_2D
!
CALL lbc_lnk( 'dynspg_ts', ssha_e, 'T', 1._wp, zhU, 'U', -1._wp, zhV, 'V', -1._wp )
!
! Duplicate sea level across open boundaries (this is only cosmetic if linssh=T)
IF( ln_bdy ) CALL bdy_ssh( ssha_e )
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_ssh_ts( jn )
#endif
!
! ! Sum over sub-time-steps to compute advective velocities
za2 = wgtbtp2(jn) ! zhU, zhV hold fluxes extrapolated at jn+0.5
un_adv(:,:) = un_adv(:,:) + za2 * zhU(:,:) * r1_e2u(:,:)
vn_adv(:,:) = vn_adv(:,:) + za2 * zhV(:,:) * r1_e1v(:,:)
! sum over sub-time-steps to decide which baroclinic velocities to set to zero (zuwdav2 is only used when ln_wd_dl_bc=True)
IF ( ln_wd_dl_bc ) THEN
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zuwdav2(ji,jj) = zuwdav2(ji,jj) + za2 * zuwdmask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zvwdav2(ji,jj) = zvwdav2(ji,jj) + za2 * zvwdmask(ji,jj)
END_2D
END IF
!
!
! Sea Surface Height at u-,v-points (vvl case only)
IF( .NOT.ln_linssh ) THEN
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 1 )
zsshu_a(ji,jj) = r1_2 * ( ssha_e(ji,jj) + ssha_e(ji+1,jj ) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 )
zsshv_a(ji,jj) = r1_2 * ( ssha_e(ji,jj) + ssha_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#else
DO_2D( 0, 0, 0, 0 )
zsshu_a(ji,jj) = r1_2 * r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
& + e1e2t(ji+1,jj ) * ssha_e(ji+1,jj ) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * r1_e1e2v(ji,jj) * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
& + e1e2t(ji ,jj+1) * ssha_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#endif
ENDIF
!
! Half-step back interpolation of SSH for surface pressure computation at step jit+1/2
!-- m+1/2 m+1 m m-1 m-2 --!
!-- ssh' = za0 * ssh + za1 * ssh + za2 * ssh + za3 * ssh --!
!------------------------------------------------------------------------------------------!
CALL ts_bck_interp( jn, ll_init, za0, za1, za2, za3 ) ! coeficients of the interpolation
zsshp2_e(:,:) = za0 * ssha_e(:,:) + za1 * sshn_e (:,:) &
& + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
!
! ! Surface pressure gradient
zldg = ( 1._wp - rn_scal_load ) * grav ! local factor
DO_2D( 0, 0, 0, 0 )
zu_spg(ji,jj) = - zldg * ( zsshp2_e(ji+1,jj) - zsshp2_e(ji,jj) ) * r1_e1u(ji,jj)
zv_spg(ji,jj) = - zldg * ( zsshp2_e(ji,jj+1) - zsshp2_e(ji,jj) ) * r1_e2v(ji,jj)
END_2D
IF( ln_wd_il ) THEN ! W/D : gravity filters applied on pressure gradient
CALL wad_spg( zsshp2_e, zcpx, zcpy ) ! Calculating W/D gravity filters
DO_2D( 0, 0, 0, 0 )
zu_spg(ji,jj) = zu_spg(ji,jj) * zcpx(ji,jj)
zv_spg(ji,jj) = zv_spg(ji,jj) * zcpy(ji,jj)
END_2D
ENDIF
!
! Add Coriolis trend:
! zwz array below or triads normally depend on sea level with ln_linssh=F and should be updated
! at each time step. We however keep them constant here for optimization.
! Recall that zhU and zhV hold fluxes at jn+0.5 (extrapolated not backward interpolated)
CALL dyn_cor_2d( zhtp2_e, zhup2_e, zhvp2_e, ua_e, va_e, zhU, zhV, zu_trd, zv_trd )
!
! Add tidal astronomical forcing if defined
IF ( ln_tide .AND. ln_tide_pot ) THEN
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = zu_trd(ji,jj) + grav * ( pot_astro(ji+1,jj) - pot_astro(ji,jj) ) * r1_e1u(ji,jj)
zv_trd(ji,jj) = zv_trd(ji,jj) + grav * ( pot_astro(ji,jj+1) - pot_astro(ji,jj) ) * r1_e2v(ji,jj)
END_2D
ENDIF
!
! Add bottom stresses:
!jth do implicitly instead
IF ( .NOT. ll_wd ) THEN ! Revert to explicit for bit comparison tests in non wad runs
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = zu_trd(ji,jj) + zCdU_u(ji,jj) * un_e(ji,jj) * hur_e(ji,jj)
zv_trd(ji,jj) = zv_trd(ji,jj) + zCdU_v(ji,jj) * vn_e(ji,jj) * hvr_e(ji,jj)
END_2D
ENDIF
!
! Set next velocities:
! Compute barotropic speeds at step jit+1 (h : total height of the water colomn)
!-- VECTOR FORM
!-- m+1 m / m+1/2 \ --!
!-- u = u + delta_t' * \ (1-r)*g * grad_x( ssh') - f * k vect u + frc / --!
!-- --!
!-- FLUX FORM --!
!-- m+1 __1__ / m m / m+1/2 m+1/2 m+1/2 n \ \ --!
!-- u = m+1 | h * u + delta_t' * \ h * (1-r)*g * grad_x( ssh') - h * f * k vect u + h * frc / | --!
!-- h \ / --!
!------------------------------------------------------------------------------------------------------------------------!
IF( ln_dynadv_vec .OR. ln_linssh ) THEN !* Vector form
DO_2D( 0, 0, 0, 0 )
ua_e(ji,jj) = ( un_e(ji,jj) &
& + rDt_e * ( zu_spg(ji,jj) &
& + zu_trd(ji,jj) &
& + zu_frc(ji,jj) ) &
& ) * ssumask(ji,jj)
va_e(ji,jj) = ( vn_e(ji,jj) &
& + rDt_e * ( zv_spg(ji,jj) &
& + zv_trd(ji,jj) &
& + zv_frc(ji,jj) ) &
& ) * ssvmask(ji,jj)
END_2D
!
ELSE !* Flux form
DO_2D( 0, 0, 0, 0 )
! ! hu_e, hv_e hold depth at jn, zhup2_e, zhvp2_e hold extrapolated depth at jn+1/2
! ! backward interpolated depth used in spg terms at jn+1/2
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
zhu_bck = hu_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji+1,jj ) ) * ssumask(ji,jj)
zhv_bck = hv_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji ,jj+1) ) * ssvmask(ji,jj)
#else
zhu_bck = hu_0(ji,jj) + r1_2*r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
zhv_bck = hv_0(ji,jj) + r1_2*r1_e1e2v(ji,jj) * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
#endif
! ! inverse depth at jn+1
z1_hu = ssumask(ji,jj) / ( hu_0(ji,jj) + zsshu_a(ji,jj) + 1._wp - ssumask(ji,jj) )
z1_hv = ssvmask(ji,jj) / ( hv_0(ji,jj) + zsshv_a(ji,jj) + 1._wp - ssvmask(ji,jj) )
!
ua_e(ji,jj) = ( hu_e (ji,jj) * un_e (ji,jj) &
& + rDt_e * ( zhu_bck * zu_spg (ji,jj) & !
& + zhup2_e(ji,jj) * zu_trd (ji,jj) & !
& + hu(ji,jj,Kmm) * zu_frc (ji,jj) ) ) * z1_hu
!
va_e(ji,jj) = ( hv_e (ji,jj) * vn_e (ji,jj) &
& + rDt_e * ( zhv_bck * zv_spg (ji,jj) & !
& + zhvp2_e(ji,jj) * zv_trd (ji,jj) & !
& + hv(ji,jj,Kmm) * zv_frc (ji,jj) ) ) * z1_hv
END_2D
ENDIF
!jth implicit bottom friction:
IF ( ll_wd ) THEN ! revert to explicit for bit comparison tests in non wad runs
DO_2D( 0, 0, 0, 0 )
ua_e(ji,jj) = ua_e(ji,jj) / ( 1._wp - rDt_e * zCdU_u(ji,jj) * hur_e(ji,jj) )
va_e(ji,jj) = va_e(ji,jj) / ( 1._wp - rDt_e * zCdU_v(ji,jj) * hvr_e(ji,jj) )
END_2D
ENDIF
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
DO_2D( 0, 0, 0, 0 )
hu_e (ji,jj) = hu_0(ji,jj) + zsshu_a(ji,jj)
hur_e(ji,jj) = ssumask(ji,jj) / ( hu_e(ji,jj) + 1._wp - ssumask(ji,jj) )
hv_e (ji,jj) = hv_0(ji,jj) + zsshv_a(ji,jj)
hvr_e(ji,jj) = ssvmask(ji,jj) / ( hv_e(ji,jj) + 1._wp - ssvmask(ji,jj) )
END_2D
ENDIF
!
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
CALL lbc_lnk( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp &
& , hu_e , 'U', 1._wp, hv_e , 'V', 1._wp &
& , hur_e, 'U', 1._wp, hvr_e, 'V', 1._wp )
ELSE
CALL lbc_lnk( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp )
ENDIF
! ! open boundaries
IF( ln_bdy ) CALL bdy_dyn2d( jn, ua_e, va_e, un_e, vn_e, hur_e, hvr_e, ssha_e )
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_dyn_ts( jn ) ! Agrif
#endif
! !* Swap
! ! ----
ubb_e (:,:) = ub_e (:,:)
ub_e (:,:) = un_e (:,:)
un_e (:,:) = ua_e (:,:)
!
vbb_e (:,:) = vb_e (:,:)
vb_e (:,:) = vn_e (:,:)
vn_e (:,:) = va_e (:,:)
!
sshbb_e(:,:) = sshb_e(:,:)
sshb_e (:,:) = sshn_e(:,:)
sshn_e (:,:) = ssha_e(:,:)
! !* Sum over whole bt loop
! ! ----------------------
za1 = wgtbtp1(jn)
IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! Sum velocities
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:)
ELSE ! Sum transports
IF ( .NOT.ln_wd_dl ) THEN
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:)
ELSE
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:) * zuwdmask(:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:) * zvwdmask(:,:)
END IF
ENDIF
! ! Sum sea level
pssh(:,:,Kaa) = pssh(:,:,Kaa) + za1 * ssha_e(:,:)
! ! ==================== !
END DO ! end loop !
! ! ==================== !
! -----------------------------------------------------------------------------
! Phase 3. update the general trend with the barotropic trend
! -----------------------------------------------------------------------------
!
! Set advection velocity correction:
IF (ln_bt_fw) THEN
IF( .NOT.( kt == nit000 .AND. l_1st_euler ) ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zun_save = un_adv(ji,jj)
zvn_save = vn_adv(ji,jj)
! ! apply the previously computed correction
un_adv(ji,jj) = r1_2 * ( ub2_b(ji,jj) + zun_save - rn_atfp * un_bf(ji,jj) )
vn_adv(ji,jj) = r1_2 * ( vb2_b(ji,jj) + zvn_save - rn_atfp * vn_bf(ji,jj) )
! ! Update corrective fluxes for next time step
un_bf(ji,jj) = rn_atfp * un_bf(ji,jj) + ( zun_save - ub2_b(ji,jj) )
vn_bf(ji,jj) = rn_atfp * vn_bf(ji,jj) + ( zvn_save - vb2_b(ji,jj) )
! ! Save integrated transport for next computation
ub2_b(ji,jj) = zun_save
vb2_b(ji,jj) = zvn_save
END_2D
ELSE
un_bf(:,:) = 0._wp ! corrective fluxes for next time step set to zero
vn_bf(:,:) = 0._wp
ub2_b(:,:) = un_adv(:,:) ! Save integrated transport for next computation
vb2_b(:,:) = vn_adv(:,:)
END IF
ENDIF
!
! Update barotropic trend:
IF( ln_dynadv_vec .OR. ln_linssh ) THEN
DO jk=1,jpkm1
puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) ) * r1_Dt_b
pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) ) * r1_Dt_b
END DO
ELSE
! At this stage, pssh(:,:,:,Krhs) has been corrected: compute new depths at velocity points
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 0 )
zsshu_a(ji,jj) = r1_2 * ( pssh(ji,jj,Kaa) + pssh(ji+1,jj ,Kaa) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * ( pssh(ji,jj,Kaa) + pssh(ji ,jj+1,Kaa) ) * ssvmask(ji,jj)
END_2D
#else
DO_2D( 1, 0, 1, 0 )
zsshu_a(ji,jj) = r1_2 * r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj) * pssh(ji ,jj,Kaa) &
& + e1e2t(ji+1,jj) * pssh(ji+1,jj,Kaa) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * r1_e1e2v(ji,jj) * ( e1e2t(ji,jj ) * pssh(ji,jj ,Kaa) &
& + e1e2t(ji,jj+1) * pssh(ji,jj+1,Kaa) ) * ssvmask(ji,jj)
END_2D
#endif
CALL lbc_lnk( 'dynspg_ts', zsshu_a, 'U', 1._wp, zsshv_a, 'V', 1._wp ) ! Boundary conditions
!
DO jk=1,jpkm1
puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + r1_hu(:,:,Kmm) &
& * ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) * hu(:,:,Kbb) ) * r1_Dt_b
pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + r1_hv(:,:,Kmm) &
& * ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) * hv(:,:,Kbb) ) * r1_Dt_b
END DO
! Save barotropic velocities not transport:
puu_b(:,:,Kaa) = puu_b(:,:,Kaa) / ( hu_0(:,:) + zsshu_a(:,:) + 1._wp - ssumask(:,:) )
pvv_b(:,:,Kaa) = pvv_b(:,:,Kaa) / ( hv_0(:,:) + zsshv_a(:,:) + 1._wp - ssvmask(:,:) )
ENDIF
! Correct velocities so that the barotropic velocity equals (un_adv, vn_adv) (in all cases)
DO jk = 1, jpkm1
puu(:,:,jk,Kmm) = ( puu(:,:,jk,Kmm) + un_adv(:,:)*r1_hu(:,:,Kmm) - puu_b(:,:,Kmm) ) * umask(:,:,jk)
pvv(:,:,jk,Kmm) = ( pvv(:,:,jk,Kmm) + vn_adv(:,:)*r1_hv(:,:,Kmm) - pvv_b(:,:,Kmm) ) * vmask(:,:,jk)
END DO
IF ( ln_wd_dl .and. ln_wd_dl_bc) THEN
DO jk = 1, jpkm1
puu(:,:,jk,Kmm) = ( un_adv(:,:)*r1_hu(:,:,Kmm) &
& + zuwdav2(:,:)*(puu(:,:,jk,Kmm) - un_adv(:,:)*r1_hu(:,:,Kmm)) ) * umask(:,:,jk)
pvv(:,:,jk,Kmm) = ( vn_adv(:,:)*r1_hv(:,:,Kmm) &
& + zvwdav2(:,:)*(pvv(:,:,jk,Kmm) - vn_adv(:,:)*r1_hv(:,:,Kmm)) ) * vmask(:,:,jk)
END DO
END IF
CALL iom_put( "ubar", un_adv(:,:)*r1_hu(:,:,Kmm) ) ! barotropic i-current
CALL iom_put( "vbar", vn_adv(:,:)*r1_hv(:,:,Kmm) ) ! barotropic i-current
!
#if defined key_agrif
! Save time integrated fluxes during child grid integration
! (used to update coarse grid transports at next time step)
!
IF( .NOT.Agrif_Root() .AND. ln_bt_fw .AND. ln_agrif_2way ) THEN
IF( Agrif_NbStepint() == 0 ) THEN
ub2_i_b(:,:) = 0._wp
vb2_i_b(:,:) = 0._wp
END IF
!
za1 = 1._wp / REAL(Agrif_rhot(), wp)
ub2_i_b(:,:) = ub2_i_b(:,:) + za1 * ub2_b(:,:)
vb2_i_b(:,:) = vb2_i_b(:,:) + za1 * vb2_b(:,:)
ENDIF
#endif
! !* write time-spliting arrays in the restart
IF( lrst_oce .AND.ln_bt_fw ) CALL ts_rst( kt, 'WRITE' )
!
IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
IF( ln_wd_dl ) DEALLOCATE( ztwdmask, zuwdmask, zvwdmask, zuwdav2, zvwdav2 )
!
CALL iom_put( "baro_u" , puu_b(:,:,Kmm) ) ! Barotropic U Velocity
CALL iom_put( "baro_v" , pvv_b(:,:,Kmm) ) ! Barotropic V Velocity
!
END SUBROUTINE dyn_spg_ts
SUBROUTINE ts_wgt( ll_av, ll_fw, jpit, zwgt1, zwgt2)
!!---------------------------------------------------------------------
!! *** ROUTINE ts_wgt ***
!!
!! ** Purpose : Set time-splitting weights for temporal averaging (or not)
!!----------------------------------------------------------------------
LOGICAL, INTENT(in) :: ll_av ! temporal averaging=.true.
LOGICAL, INTENT(in) :: ll_fw ! forward time splitting =.true.
INTEGER, INTENT(inout) :: jpit ! cycle length
REAL(wp), DIMENSION(3*nn_e), INTENT(inout) :: zwgt1, & ! Primary weights
zwgt2 ! Secondary weights
INTEGER :: jic, jn, ji ! temporary integers
REAL(wp) :: za1, za2
!!----------------------------------------------------------------------
zwgt1(:) = 0._wp
zwgt2(:) = 0._wp
! Set time index when averaged value is requested
IF (ll_fw) THEN
jic = nn_e
ELSE
jic = 2 * nn_e
ENDIF
! Set primary weights:
IF (ll_av) THEN
! Define simple boxcar window for primary weights
! (width = nn_e, centered around jic)
SELECT CASE ( nn_bt_flt )
CASE( 0 ) ! No averaging
zwgt1(jic) = 1._wp
jpit = jic
CASE( 1 ) ! Boxcar, width = nn_e
DO jn = 1, 3*nn_e
za1 = ABS(float(jn-jic))/float(nn_e)
IF (za1 < 0.5_wp) THEN
zwgt1(jn) = 1._wp
jpit = jn
ENDIF
ENDDO
CASE( 2 ) ! Boxcar, width = 2 * nn_e
DO jn = 1, 3*nn_e
za1 = ABS(float(jn-jic))/float(nn_e)
IF (za1 < 1._wp) THEN
zwgt1(jn) = 1._wp
jpit = jn
ENDIF
ENDDO
CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt' )
END SELECT
ELSE ! No time averaging
zwgt1(jic) = 1._wp
jpit = jic
ENDIF
! Set secondary weights
DO jn = 1, jpit
DO ji = jn, jpit
zwgt2(jn) = zwgt2(jn) + zwgt1(ji)
END DO
END DO
! Normalize weigths:
za1 = 1._wp / SUM(zwgt1(1:jpit))
za2 = 1._wp / SUM(zwgt2(1:jpit))
DO jn = 1, jpit
zwgt1(jn) = zwgt1(jn) * za1
zwgt2(jn) = zwgt2(jn) * za2
END DO
!
END SUBROUTINE ts_wgt
SUBROUTINE ts_rst( kt, cdrw )
!!---------------------------------------------------------------------
!! *** ROUTINE ts_rst ***
!!
!! ** Purpose : Read or write time-splitting arrays in restart file
!!----------------------------------------------------------------------
INTEGER , INTENT(in) :: kt ! ocean time-step
CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
!!----------------------------------------------------------------------
!
IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
! ! ---------------
IF( ln_rstart .AND. ln_bt_fw .AND. .NOT.l_1st_euler ) THEN !* Read the restart file
CALL iom_get( numror, jpdom_auto, 'ub2_b' , ub2_b (:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb2_b' , vb2_b (:,:), cd_type = 'V', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'un_bf' , un_bf (:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vn_bf' , vn_bf (:,:), cd_type = 'V', psgn = -1._wp )
IF( .NOT.ln_bt_av ) THEN
CALL iom_get( numror, jpdom_auto, 'sshbb_e' , sshbb_e(:,:), cd_type = 'T', psgn = 1._wp )
CALL iom_get( numror, jpdom_auto, 'ubb_e' , ubb_e(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vbb_e' , vbb_e(:,:), cd_type = 'V', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'sshb_e' , sshb_e(:,:), cd_type = 'T', psgn = 1._wp )
CALL iom_get( numror, jpdom_auto, 'ub_e' , ub_e(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb_e' , vb_e(:,:), cd_type = 'V', psgn = -1._wp )
ENDIF
#if defined key_agrif
! Read time integrated fluxes
IF ( .NOT.Agrif_Root() ) THEN
CALL iom_get( numror, jpdom_auto, 'ub2_i_b' , ub2_i_b(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb2_i_b' , vb2_i_b(:,:), cd_type = 'V', psgn = -1._wp )
ELSE
ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
ENDIF
#endif
ELSE !* Start from rest
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set barotropic values to 0'
ub2_b (:,:) = 0._wp ; vb2_b (:,:) = 0._wp ! used in the 1st interpol of agrif
un_adv (:,:) = 0._wp ; vn_adv (:,:) = 0._wp ! used in the 1st interpol of agrif
un_bf (:,:) = 0._wp ; vn_bf (:,:) = 0._wp ! used in the 1st update of agrif
#if defined key_agrif
ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
#endif
ENDIF
!
ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
! ! -------------------
IF(lwp) WRITE(numout,*) '---- ts_rst ----'
CALL iom_rstput( kt, nitrst, numrow, 'ub2_b' , ub2_b (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb2_b' , vb2_b (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'un_bf' , un_bf (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vn_bf' , vn_bf (:,:) )
!
IF (.NOT.ln_bt_av) THEN
CALL iom_rstput( kt, nitrst, numrow, 'sshbb_e' , sshbb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'ubb_e' , ubb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vbb_e' , vbb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'sshb_e' , sshb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'ub_e' , ub_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb_e' , vb_e(:,:) )
ENDIF
#if defined key_agrif
! Save time integrated fluxes
IF ( .NOT.Agrif_Root() ) THEN
CALL iom_rstput( kt, nitrst, numrow, 'ub2_i_b' , ub2_i_b(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb2_i_b' , vb2_i_b(:,:) )
ENDIF
#endif
ENDIF
!
END SUBROUTINE ts_rst
SUBROUTINE dyn_spg_ts_init