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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
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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'
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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)
ssh_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
ssh_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 ! ----------------------------- !
ssh_frc(:,:) = ssh_frc(:,:) + div_sd(:,:)
ENDIF
!
! ! ice sheet coupling
IF ( ln_isf .AND. ln_isfcpl ) THEN
!
! ice sheet coupling
IF( ln_rstart .AND. kt == nit000 ) THEN
ssh_frc(:,:) = ssh_frc(:,:) + risfcpl_ssh(:,:)
END IF
!
! conservation option
IF( ln_isfcpl_cons ) THEN
ssh_frc(:,:) = ssh_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
ssh_frc(:,:) = ssh_frc(:,:) - ssh_iau(:,:)
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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( ln_bt_fw ) CALL agrif_dyn_ts_flux( jn, zhU, zhV )
IF( ln_wd_il ) CALL wad_lmt_bt(zhU, zhV, sshn_e, ssh_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 * ( ssh_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
CALL agrif_ssh_ts( jn )
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#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
CALL agrif_dyn_ts( jn ) ! Agrif
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#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
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_spg_ts_init ***
!!
!! ** Purpose : Set time splitting options
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
REAL(wp) :: zxr2, zyr2, zcmax ! local scalar
REAL(wp), DIMENSION(jpi,jpj) :: zcu
!!----------------------------------------------------------------------
!
! Max courant number for ext. grav. waves
!
DO_2D( 0, 0, 0, 0 )
zxr2 = r1_e1t(ji,jj) * r1_e1t(ji,jj)
zyr2 = r1_e2t(ji,jj) * r1_e2t(ji,jj)
zcu(ji,jj) = SQRT( grav * MAX(ht_0(ji,jj),0._wp) * (zxr2 + zyr2) )
END_2D
!
zcmax = MAXVAL( zcu(Nis0:Nie0,Njs0:Nje0) )
CALL mpp_max( 'dynspg_ts', zcmax )
! Estimate number of iterations to satisfy a max courant number= rn_bt_cmax
IF( ln_bt_auto ) nn_e = CEILING( rn_Dt / rn_bt_cmax * zcmax)
rDt_e = rn_Dt / REAL( nn_e , wp )
zcmax = zcmax * rDt_e
! Print results
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn_spg_ts_init : split-explicit free surface'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~'
IF( ln_bt_auto ) THEN
IF(lwp) WRITE(numout,*) ' ln_ts_auto =.true. Automatically set nn_e '
IF(lwp) WRITE(numout,*) ' Max. courant number allowed: ', rn_bt_cmax
ELSE
IF(lwp) WRITE(numout,*) ' ln_ts_auto=.false.: Use nn_e in namelist nn_e = ', nn_e
ENDIF
IF(ln_bt_av) THEN
IF(lwp) WRITE(numout,*) ' ln_bt_av =.true. ==> Time averaging over nn_e time steps is on '
ELSE
IF(lwp) WRITE(numout,*) ' ln_bt_av =.false. => No time averaging of barotropic variables '
ENDIF
!
!
IF(ln_bt_fw) THEN
IF(lwp) WRITE(numout,*) ' ln_bt_fw=.true. => Forward integration of barotropic variables '
ELSE
IF(lwp) WRITE(numout,*) ' ln_bt_fw =.false.=> Centred integration of barotropic variables '
ENDIF
!
#if defined key_agrif
! Restrict the use of Agrif to the forward case only
IF( .NOT.ln_bt_fw .AND. .NOT.Agrif_Root() ) CALL ctl_stop( 'AGRIF not implemented if ln_bt_fw=.FALSE.' )
#endif
!
IF(lwp) WRITE(numout,*) ' Time filter choice, nn_bt_flt: ', nn_bt_flt
SELECT CASE ( nn_bt_flt )
CASE( 0 ) ; IF(lwp) WRITE(numout,*) ' Dirac'
CASE( 1 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = nn_e'
CASE( 2 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = 2*nn_e'
CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt: should 0,1, or 2' )
END SELECT
!
IF(lwp) WRITE(numout,*) ' '
IF(lwp) WRITE(numout,*) ' nn_e = ', nn_e
IF(lwp) WRITE(numout,*) ' Barotropic time step [s] is :', rDt_e
IF(lwp) WRITE(numout,*) ' Maximum Courant number is :', zcmax
!
IF(lwp) WRITE(numout,*) ' Time diffusion parameter rn_bt_alpha: ', rn_bt_alpha
IF ((ln_bt_av.AND.nn_bt_flt/=0).AND.(rn_bt_alpha>0._wp)) THEN
CALL ctl_stop( 'dynspg_ts ERROR: if rn_bt_alpha > 0, remove temporal averaging' )
ENDIF
!
IF( .NOT.ln_bt_av .AND. .NOT.ln_bt_fw ) THEN
CALL ctl_stop( 'dynspg_ts ERROR: No time averaging => only forward integration is possible' )
ENDIF
IF( zcmax>0.9_wp ) THEN
CALL ctl_stop( 'dynspg_ts ERROR: Maximum Courant number is greater than 0.9: Inc. nn_e !' )
ENDIF
!
! ! Allocate time-splitting arrays
IF( dyn_spg_ts_alloc() /= 0 ) CALL ctl_stop('STOP', 'dyn_spg_init: failed to allocate dynspg_ts arrays' )
!
! ! read restart when needed
CALL ts_rst( nit000, 'READ' )
!
END SUBROUTINE dyn_spg_ts_init
SUBROUTINE dyn_cor_2D_init( Kmm )
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_cor_2D_init ***
!!
!! ** Purpose : Set time splitting options
!! Set arrays to remove/compute coriolis trend.
!! Do it once during initialization if volume is fixed, else at each long time step.
!! Note that these arrays are also used during barotropic loop. These are however frozen
!! although they should be updated in the variable volume case. Not a big approximation.
!! To remove this approximation, copy lines below inside barotropic loop
!! and update depths at T- points (ht) at each barotropic time step
!!
!! Compute zwz = f / ( height of the water colomn )
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: Kmm ! Time index
INTEGER :: ji ,jj, jk ! dummy loop indices
REAL(wp) :: z1_ht
!!----------------------------------------------------------------------
!
SELECT CASE( nvor_scheme )
CASE( np_EEN, np_ENE, np_ENS , np_MIX ) != schemes using the same e3f definition
SELECT CASE( nn_e3f_typ ) !* ff_f/e3 at F-point
CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4)
DO_2D( 0, 0, 0, 0 )
zwz(ji,jj) = ( ht(ji,jj+1) + ht(ji+1,jj+1) &
& + ht(ji,jj ) + ht(ji+1,jj ) ) * 0.25_wp
IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
END_2D
CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask)
DO_2D( 0, 0, 0, 0 )
zwz(ji,jj) = ( ht(ji,jj+1) + ht(ji+1,jj+1) &
& + ht(ji,jj ) + ht(ji+1,jj ) ) &
& / ( MAX(ssmask(ji,jj+1) + ssmask(ji+1,jj+1) &
& + ssmask(ji,jj ) + ssmask(ji+1,jj ) , 1._wp ) )
IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
END_2D
END SELECT
CALL lbc_lnk( 'dynspg_ts', zwz, 'F', 1._wp )
END SELECT
!
SELECT CASE( nvor_scheme )
CASE( np_EEN )
!
ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
DO_2D( 0, 1, 0, 1 )
ftne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1)
ftnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj )
ftse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1)
ftsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj )
END_2D
!
CASE( np_EET ) != EEN scheme using e3t energy conserving scheme
ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
DO_2D( 0, 1, 0, 1 )
z1_ht = ssmask(ji,jj) / ( ht(ji,jj) + 1._wp - ssmask(ji,jj) )
ftne(ji,jj) = ( ff_f(ji-1,jj ) + ff_f(ji ,jj ) + ff_f(ji ,jj-1) ) * z1_ht
ftnw(ji,jj) = ( ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) + ff_f(ji ,jj ) ) * z1_ht
ftse(ji,jj) = ( ff_f(ji ,jj ) + ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) ) * z1_ht
ftsw(ji,jj) = ( ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) ) * z1_ht
END_2D
!
END SELECT
END SUBROUTINE dyn_cor_2d_init
SUBROUTINE dyn_cor_2d( pht, phu, phv, punb, pvnb, zhU, zhV, zu_trd, zv_trd )
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_cor_2d ***
!!
!! ** Purpose : Compute u and v coriolis trends
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
REAL(wp) :: zx1, zx2, zy1, zy2, z1_hu, z1_hv ! - -
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pht, phu, phv, punb, pvnb, zhU, zhV
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: zu_trd, zv_trd
!!----------------------------------------------------------------------
SELECT CASE( nvor_scheme )
CASE( np_ENT ) ! enstrophy conserving scheme (f-point)
DO_2D( 0, 0, 0, 0 )
z1_hu = ssumask(ji,jj) / ( phu(ji,jj) + 1._wp - ssumask(ji,jj) )
z1_hv = ssvmask(ji,jj) / ( phv(ji,jj) + 1._wp - ssvmask(ji,jj) )
zu_trd(ji,jj) = + r1_4 * r1_e1e2u(ji,jj) * z1_hu &
& * ( e1e2t(ji+1,jj)*pht(ji+1,jj)*ff_t(ji+1,jj) * ( pvnb(ji+1,jj) + pvnb(ji+1,jj-1) ) &
& + e1e2t(ji ,jj)*pht(ji ,jj)*ff_t(ji ,jj) * ( pvnb(ji ,jj) + pvnb(ji ,jj-1) ) )
!
zv_trd(ji,jj) = - r1_4 * r1_e1e2v(ji,jj) * z1_hv &
& * ( e1e2t(ji,jj+1)*pht(ji,jj+1)*ff_t(ji,jj+1) * ( punb(ji,jj+1) + punb(ji-1,jj+1) ) &
& + e1e2t(ji,jj )*pht(ji,jj )*ff_t(ji,jj ) * ( punb(ji,jj ) + punb(ji-1,jj ) ) )
END_2D
!
CASE( np_ENE , np_MIX ) ! energy conserving scheme (t-point) ENE or MIX
DO_2D( 0, 0, 0, 0 )
zy1 = ( zhV(ji,jj-1) + zhV(ji+1,jj-1) ) * r1_e1u(ji,jj)
zy2 = ( zhV(ji,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
zx1 = ( zhU(ji-1,jj) + zhU(ji-1,jj+1) ) * r1_e2v(ji,jj)
zx2 = ( zhU(ji ,jj) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
! energy conserving formulation for planetary vorticity term
zu_trd(ji,jj) = r1_4 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 )
zv_trd(ji,jj) = - r1_4 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 )
END_2D
!
CASE( np_ENS ) ! enstrophy conserving scheme (f-point)
DO_2D( 0, 0, 0, 0 )
zy1 = r1_8 * ( zhV(ji ,jj-1) + zhV(ji+1,jj-1) &
& + zhV(ji ,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
zx1 = - r1_8 * ( zhU(ji-1,jj ) + zhU(ji-1,jj+1) &
& + zhU(ji ,jj ) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
zu_trd(ji,jj) = zy1 * ( zwz(ji ,jj-1) + zwz(ji,jj) )
zv_trd(ji,jj) = zx1 * ( zwz(ji-1,jj ) + zwz(ji,jj) )
END_2D
!
CASE( np_EET , np_EEN ) ! energy & enstrophy scheme (using e3t or e3f)
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = + r1_12 * r1_e1u(ji,jj) * ( ftne(ji,jj ) * zhV(ji ,jj ) &
& + ftnw(ji+1,jj) * zhV(ji+1,jj ) &
& + ftse(ji,jj ) * zhV(ji ,jj-1) &
& + ftsw(ji+1,jj) * zhV(ji+1,jj-1) )
zv_trd(ji,jj) = - r1_12 * r1_e2v(ji,jj) * ( ftsw(ji,jj+1) * zhU(ji-1,jj+1) &
& + ftse(ji,jj+1) * zhU(ji ,jj+1) &
& + ftnw(ji,jj ) * zhU(ji-1,jj ) &
& + ftne(ji,jj ) * zhU(ji ,jj ) )
END_2D
!
END SELECT
!
END SUBROUTINE dyn_cor_2D
SUBROUTINE wad_tmsk( pssh, ptmsk )
!!----------------------------------------------------------------------
!! *** ROUTINE wad_lmt ***
!!
!! ** Purpose : set wetting & drying mask at tracer points
!! for the current barotropic sub-step
!!
!! ** Method : ???
!!
!! ** Action : ptmsk : wetting & drying t-mask
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pssh !
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: ptmsk !
!
INTEGER :: ji, jj ! dummy loop indices
!!----------------------------------------------------------------------
!
IF( ln_wd_dl_rmp ) THEN
DO_2D( 1, 1, 1, 1 )
IF ( pssh(ji,jj) + ht_0(ji,jj) > 2._wp * rn_wdmin1 ) THEN
! IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin2 ) THEN
ptmsk(ji,jj) = 1._wp
ELSEIF( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN
ptmsk(ji,jj) = TANH( 50._wp*( ( pssh(ji,jj) + ht_0(ji,jj) - rn_wdmin1 )*r_rn_wdmin1) )
ELSE
ptmsk(ji,jj) = 0._wp
ENDIF
END_2D
ELSE
DO_2D( 1, 1, 1, 1 )
IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN ; ptmsk(ji,jj) = 1._wp
ELSE ; ptmsk(ji,jj) = 0._wp
ENDIF
END_2D
ENDIF
!
END SUBROUTINE wad_tmsk
SUBROUTINE wad_Umsk( pTmsk, phU, phV, pu, pv, pUmsk, pVmsk )
!!----------------------------------------------------------------------
!! *** ROUTINE wad_lmt ***
!!
!! ** Purpose : set wetting & drying mask at tracer points
!! for the current barotropic sub-step
!!
!! ** Method : ???
!!
!! ** Action : ptmsk : wetting & drying t-mask
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pTmsk ! W & D t-mask
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: phU, phV, pu, pv ! ocean velocities and transports
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pUmsk, pVmsk ! W & D u- and v-mask
!
INTEGER :: ji, jj ! dummy loop indices
!!----------------------------------------------------------------------
!
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
IF ( phU(ji,jj) > 0._wp ) THEN ; pUmsk(ji,jj) = pTmsk(ji ,jj)
ELSE ; pUmsk(ji,jj) = pTmsk(ji+1,jj)
ENDIF
phU(ji,jj) = pUmsk(ji,jj)*phU(ji,jj)
pu (ji,jj) = pUmsk(ji,jj)*pu (ji,jj)
END_2D
!
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
IF ( phV(ji,jj) > 0._wp ) THEN ; pVmsk(ji,jj) = pTmsk(ji,jj )
ELSE ; pVmsk(ji,jj) = pTmsk(ji,jj+1)
ENDIF
phV(ji,jj) = pVmsk(ji,jj)*phV(ji,jj)
pv (ji,jj) = pVmsk(ji,jj)*pv (ji,jj)
END_2D
!
END SUBROUTINE wad_Umsk
SUBROUTINE wad_spg( pshn, zcpx, zcpy )
!!---------------------------------------------------------------------
!! *** ROUTINE wad_sp ***
!!
!! ** Purpose :
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
LOGICAL :: ll_tmp1, ll_tmp2
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pshn
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: zcpx, zcpy
!!----------------------------------------------------------------------
DO_2D( 0, 0, 0, 0 )
ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji+1,jj) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji+1,jj) + ht_0(ji+1,jj) ) &
& > rn_wdmin1 + rn_wdmin2
ll_tmp2 = ( ABS( pshn(ji+1,jj) - pshn(ji ,jj)) > 1.E-12 ).AND.( &
& MAX( pshn(ji,jj) , pshn(ji+1,jj) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
IF(ll_tmp1) THEN
zcpx(ji,jj) = 1.0_wp
ELSEIF(ll_tmp2) THEN
! no worries about pshn(ji+1,jj) - pshn(ji ,jj) = 0, it won't happen ! here
zcpx(ji,jj) = ABS( (pshn(ji+1,jj) + ht_0(ji+1,jj) - pshn(ji,jj) - ht_0(ji,jj)) &
& / (pshn(ji+1,jj) - pshn(ji ,jj)) )
zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
ELSE
zcpx(ji,jj) = 0._wp
ENDIF
!
ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji,jj+1) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji,jj+1) + ht_0(ji,jj+1) ) &
& > rn_wdmin1 + rn_wdmin2
ll_tmp2 = ( ABS( pshn(ji,jj) - pshn(ji,jj+1)) > 1.E-12 ).AND.( &
& MAX( pshn(ji,jj) , pshn(ji,jj+1) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
IF(ll_tmp1) THEN
zcpy(ji,jj) = 1.0_wp
ELSE IF(ll_tmp2) THEN
! no worries about pshn(ji,jj+1) - pshn(ji,jj ) = 0, it won't happen ! here
zcpy(ji,jj) = ABS( (pshn(ji,jj+1) + ht_0(ji,jj+1) - pshn(ji,jj) - ht_0(ji,jj)) &
& / (pshn(ji,jj+1) - pshn(ji,jj )) )
zcpy(ji,jj) = MAX( 0._wp , MIN( zcpy(ji,jj) , 1.0_wp ) )
ELSE
zcpy(ji,jj) = 0._wp
ENDIF
END_2D
END SUBROUTINE wad_spg
SUBROUTINE dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b ,pvv_b, pu_RHSi, pv_RHSi, pCdU_u, pCdU_v )
!!----------------------------------------------------------------------
!! *** ROUTINE dyn_drg_init ***
!!
!! ** Purpose : - add the baroclinic top/bottom drag contribution to
!! the baroclinic part of the barotropic RHS
!! - compute the barotropic drag coefficients
!!
!! ** Method : computation done over the INNER domain only
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kbb, Kmm ! ocean time level indices
REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(in ) :: puu, pvv ! ocean velocities and RHS of momentum equation
REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(in ) :: puu_b, pvv_b ! barotropic velocities at main time levels
REAL(wp), DIMENSION(jpi,jpj) , INTENT(inout) :: pu_RHSi, pv_RHSi ! baroclinic part of the barotropic RHS
REAL(wp), DIMENSION(jpi,jpj) , INTENT( out) :: pCdU_u , pCdU_v ! barotropic drag coefficients
!
INTEGER :: ji, jj ! dummy loop indices
INTEGER :: ikbu, ikbv, iktu, iktv
REAL(wp) :: zztmp
REAL(wp), DIMENSION(jpi,jpj) :: zu_i, zv_i
!!----------------------------------------------------------------------
!
! !== Set the barotropic drag coef. ==!
!
IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! top+bottom friction (ocean cavities)
DO_2D( 0, 0, 0, 0 )
pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) + rCdU_top(ji+1,jj)+rCdU_top(ji,jj) )
pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) + rCdU_top(ji,jj+1)+rCdU_top(ji,jj) )
END_2D
ELSE ! bottom friction only
DO_2D( 0, 0, 0, 0 )
pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
END_2D
ENDIF
!
! !== BOTTOM stress contribution from baroclinic velocities ==!
!
IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW bottom baroclinic velocities
DO_2D( 0, 0, 0, 0 )
ikbu = mbku(ji,jj)
ikbv = mbkv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,ikbu,Kmm) - puu_b(ji,jj,Kmm)
zv_i(ji,jj) = pvv(ji,jj,ikbv,Kmm) - pvv_b(ji,jj,Kmm)
END_2D
ELSE ! CENTRED integration: use BEFORE bottom baroclinic velocities
DO_2D( 0, 0, 0, 0 )
ikbu = mbku(ji,jj)
ikbv = mbkv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,ikbu,Kbb) - puu_b(ji,jj,Kbb)
zv_i(ji,jj) = pvv(ji,jj,ikbv,Kbb) - pvv_b(ji,jj,Kbb)
END_2D
ENDIF
!
IF( ln_wd_il ) THEN ! W/D : use the "clipped" bottom friction !!gm explain WHY, please !
zztmp = -1._wp / rDt_e
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + zu_i(ji,jj) * wdrampu(ji,jj) * MAX( &
& r1_hu(ji,jj,Kmm) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) , zztmp )
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + zv_i(ji,jj) * wdrampv(ji,jj) * MAX( &
& r1_hv(ji,jj,Kmm) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) , zztmp )
END_2D
ELSE ! use "unclipped" drag (even if explicit friction is used in 3D calculation)
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu(ji,jj,Kmm) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * zu_i(ji,jj)
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv(ji,jj,Kmm) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * zv_i(ji,jj)
END_2D
END IF
!
! !== TOP stress contribution from baroclinic velocities ==! (no W/D case)
!
IF( ln_isfcav.OR.ln_drgice_imp ) THEN
!
IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW top baroclinic velocity
DO_2D( 0, 0, 0, 0 )
iktu = miku(ji,jj)
iktv = mikv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,iktu,Kmm) - puu_b(ji,jj,Kmm)
zv_i(ji,jj) = pvv(ji,jj,iktv,Kmm) - pvv_b(ji,jj,Kmm)
END_2D
ELSE ! CENTRED integration: use BEFORE top baroclinic velocity
DO_2D( 0, 0, 0, 0 )
iktu = miku(ji,jj)
iktv = mikv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,iktu,Kbb) - puu_b(ji,jj,Kbb)
zv_i(ji,jj) = pvv(ji,jj,iktv,Kbb) - pvv_b(ji,jj,Kbb)
END_2D
ENDIF
!
! ! use "unclipped" top drag (even if explicit friction is used in 3D calculation)
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu(ji,jj,Kmm) * r1_2*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * zu_i(ji,jj)
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv(ji,jj,Kmm) * r1_2*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) * zv_i(ji,jj)
END_2D
!
ENDIF
!
END SUBROUTINE dyn_drg_init
SUBROUTINE ts_bck_interp( jn, ll_init, & ! <== in
& za0, za1, za2, za3 ) ! ==> out
!!----------------------------------------------------------------------
INTEGER ,INTENT(in ) :: jn ! index of sub time step
LOGICAL ,INTENT(in ) :: ll_init !
REAL(wp),INTENT( out) :: za0, za1, za2, za3 ! Half-step back interpolation coefficient
!
REAL(wp) :: zepsilon, zgamma ! - -
!!----------------------------------------------------------------------
! ! set Half-step back interpolation coefficient
IF ( jn==1 .AND. ll_init ) THEN !* Forward-backward
za0 = 1._wp
za1 = 0._wp
za2 = 0._wp
za3 = 0._wp
ELSEIF( jn==2 .AND. ll_init ) THEN !* AB2-AM3 Coefficients; bet=0 ; gam=-1/6 ; eps=1/12
za0 = 1.0833333333333_wp ! za0 = 1-gam-eps
za1 =-0.1666666666666_wp ! za1 = gam
za2 = 0.0833333333333_wp ! za2 = eps
za3 = 0._wp
ELSE !* AB3-AM4 Coefficients; bet=0.281105 ; eps=0.013 ; gam=0.0880
IF( rn_bt_alpha == 0._wp ) THEN ! Time diffusion
za0 = 0.614_wp ! za0 = 1/2 + gam + 2*eps
za1 = 0.285_wp ! za1 = 1/2 - 2*gam - 3*eps
za2 = 0.088_wp ! za2 = gam
za3 = 0.013_wp ! za3 = eps
ELSE ! no time diffusion
zepsilon = 0.00976186_wp - 0.13451357_wp * rn_bt_alpha
zgamma = 0.08344500_wp - 0.51358400_wp * rn_bt_alpha
za0 = 0.5_wp + zgamma + 2._wp * rn_bt_alpha + 2._wp * zepsilon
za1 = 1._wp - za0 - zgamma - zepsilon
za2 = zgamma
za3 = zepsilon
ENDIF
ENDIF
END SUBROUTINE ts_bck_interp
!!======================================================================
END MODULE dynspg_ts