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dynhpg.F90
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MODULE dynhpg
!!======================================================================
!! *** MODULE dynhpg ***
!! Ocean dynamics: hydrostatic pressure gradient trend
!!======================================================================
!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
!! 5.0 ! 1991-11 (G. Madec)
!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
!! - ! 2005-11 (G. Madec) style & small optimisation
!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
!! ! (A. Coward) suppression of hel, wdj and rot options
!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! dyn_hpg : update the momentum trend with the now horizontal
!! gradient of the hydrostatic pressure
!! dyn_hpg_init : initialisation and control of options
!! hpg_zco : z-coordinate scheme
!! hpg_zps : z-coordinate plus partial steps (interpolation)
!! hpg_sco : s-coordinate (standard jacobian formulation)
!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and tracers
USE sbc_oce ! surface variable (only for the flag with ice shelf)
USE dom_oce ! ocean space and time domain
USE phycst ! physical constants
USE trd_oce ! trends: ocean variables
USE trddyn ! trend manager: dynamics
!
USE in_out_manager ! I/O manager
USE prtctl ! Print control
USE lbclnk ! lateral boundary condition
USE lib_mpp ! MPP library
USE eosbn2 ! compute density
USE wrk_nemo ! Memory Allocation
USE timing ! Timing
USE biaspar ! bias correction variables
IMPLICIT NONE
PRIVATE
PUBLIC dyn_hpg ! routine called by step module
PUBLIC dyn_hpg_init ! routine called by opa module
! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
!! * Substitutions
# include "domzgr_substitute.h90"
# include "vectopt_loop_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OPA 3.3 , NEMO Consortium (2010)
!! $Id$
!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE dyn_hpg( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_hpg ***
!!
!! ** Method : Call the hydrostatic pressure gradient routine
!! using the scheme defined in the namelist
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_rhd_st ! tmp density storage for pressure corr
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_gru_st ! tmp ua trends storage for pressure corr
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_grv_st ! tmp va trends storage for pressure corr
!!----------------------------------------------------------------------
!
IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
!
IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
ztrdu(:,:,:) = ua(:,:,:)
ztrdv(:,:,:) = va(:,:,:)
ENDIF
!
IF ( ln_bias .AND. ln_bias_pc_app ) THEN
!Allocate space for tempory variables
ALLOCATE( z_rhd_st(jpi,jpj,jpk), &
& z_gru_st(jpi,jpj), &
& z_grv_st(jpi,jpj) )
z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
z_gru_st(:,:) = gru(:,:)
gru(:,:) = gru_pc(:,:)
z_grv_st(:,:) = grv(:,:)
grv(:,:) = grv_pc(:,:)
ENDIF
SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
END SELECT
!
IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
ENDIF
!
IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
!
IF ( ln_bias .AND. ln_bias_pc_app ) THEN
IF(lwp) THEN
WRITE(numout,*) " ! restore original density"
ENDIF
rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
gru(:,:) = z_gru_st(:,:)
grv(:,:) = z_grv_st(:,:)
!Deallocate tempory variables
DEALLOCATE( z_rhd_st, &
& z_gru_st, &
& z_grv_st )
ENDIF
!
IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
!
END SUBROUTINE dyn_hpg
SUBROUTINE dyn_hpg_init
!!----------------------------------------------------------------------
!! *** ROUTINE dyn_hpg_init ***
!!
!! ** Purpose : initializations for the hydrostatic pressure gradient
!! computation and consistency control
!!
!! ** Action : Read the namelist namdyn_hpg and check the consistency
!! with the type of vertical coordinate used (zco, zps, sco)
!!----------------------------------------------------------------------
INTEGER :: ioptio = 0 ! temporary integer
INTEGER :: ios ! Local integer output status for namelist read
!!
NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
!!----------------------------------------------------------------------
!
REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
IF(lwm) WRITE ( numond, namdyn_hpg )
!
IF(lwp) THEN ! Control print
WRITE(numout,*)
WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
WRITE(numout,*) '~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
ENDIF
!
IF( ln_hpg_djc ) &
& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
& currently disabled (bugs under investigation). Please select &
& either ln_hpg_sco or ln_hpg_prj instead')
!
IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
& the standard jacobian formulation hpg_sco or &
& the pressure jacobian formulation hpg_prj')
IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
!
! ! Set nhpg from ln_hpg_... flags
IF( ln_hpg_zco ) nhpg = 0
IF( ln_hpg_zps ) nhpg = 1
IF( ln_hpg_sco ) nhpg = 2
IF( ln_hpg_djc ) nhpg = 3
IF( ln_hpg_prj ) nhpg = 4
IF( ln_hpg_isf ) nhpg = 5
!
! ! Consistency check
ioptio = 0
IF( ln_hpg_zco ) ioptio = ioptio + 1
IF( ln_hpg_zps ) ioptio = ioptio + 1
IF( ln_hpg_sco ) ioptio = ioptio + 1
IF( ln_hpg_djc ) ioptio = ioptio + 1
IF( ln_hpg_prj ) ioptio = ioptio + 1
IF( ln_hpg_isf ) ioptio = ioptio + 1
IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
!
! initialisation of ice load
riceload(:,:)=0.0
!
END SUBROUTINE dyn_hpg_init
SUBROUTINE hpg_zco( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_zco ***
!!
!! ** Method : z-coordinate case, levels are horizontal surfaces.
!! The now hydrostatic pressure gradient at a given level, jk,
!! is computed by taking the vertical integral of the in-situ
!! density gradient along the model level from the suface to that
!! level: zhpi = grav .....
!! zhpj = grav .....
!! add it to the general momentum trend (ua,va).
!! ua = ua - 1/e1u * zhpi
!! va = va - 1/e2v * zhpj
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
ENDIF
zcoef0 = - grav * 0.5_wp ! Local constant initialization
! Surface value
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
zcoef1 = zcoef0 * fse3w(ji,jj,1)
! hydrostatic pressure gradient
zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
END DO
END DO
!
! interior value (2=<jk=<jpkm1)
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
zcoef1 = zcoef0 * fse3w(ji,jj,jk)
! hydrostatic pressure gradient
zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
END DO
END DO
END DO
!
CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
!
END SUBROUTINE hpg_zco
SUBROUTINE hpg_zps( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_zps ***
!!
!! ** Method : z-coordinate plus partial steps case. blahblah...
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk ! dummy loop indices
INTEGER :: iku, ikv ! temporary integers
REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
ENDIF
! Local constant initialization
zcoef0 = - grav * 0.5_wp
! Surface value (also valid in partial step case)
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
zcoef1 = zcoef0 * fse3w(ji,jj,1)
! hydrostatic pressure gradient
zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
END DO
END DO
! interior value (2=<jk=<jpkm1)
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
zcoef1 = zcoef0 * fse3w(ji,jj,jk)
! hydrostatic pressure gradient
zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
END DO
END DO
END DO
! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
DO jj = 2, jpjm1
DO ji = 2, jpim1
iku = mbku(ji,jj)
ikv = mbkv(ji,jj)
zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
ENDIF
IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
ENDIF
END DO
END DO
!
CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
!
END SUBROUTINE hpg_zps
SUBROUTINE hpg_sco( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_sco ***
!!
!! ** Method : s-coordinate case. Jacobian scheme.
!! The now hydrostatic pressure gradient at a given level, jk,
!! is computed by taking the vertical integral of the in-situ
!! density gradient along the model level from the suface to that
!! level. s-coordinates (ln_sco): a corrective term is added
!! to the horizontal pressure gradient :
!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
!! add it to the general momentum trend (ua,va).
!! ua = ua - 1/e1u * zhpi
!! va = va - 1/e2v * zhpj
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
ENDIF
! Local constant initialization
zcoef0 = - grav * 0.5_wp
! To use density and not density anomaly
IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
ELSE ; znad = 0._wp ! Fixed volume
ENDIF
! Surface value
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
! hydrostatic pressure gradient along s-surfaces
zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
! s-coordinate pressure gradient correction
zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
END DO
END DO
! interior value (2=<jk=<jpkm1)
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
! hydrostatic pressure gradient along s-surfaces
zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
! s-coordinate pressure gradient correction
zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
END DO
END DO
END DO
!
CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
!
END SUBROUTINE hpg_sco
SUBROUTINE hpg_isf( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_sco ***
!!
!! ** Method : s-coordinate case. Jacobian scheme.
!! The now hydrostatic pressure gradient at a given level, jk,
!! is computed by taking the vertical integral of the in-situ
!! density gradient along the model level from the suface to that
!! level. s-coordinates (ln_sco): a corrective term is added
!! to the horizontal pressure gradient :
!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
!! add it to the general momentum trend (ua,va).
!! ua = ua - 1/e1u * zhpi
!! va = va - 1/e2v * zhpj
!! iceload is added and partial cell case are added to the top and bottom
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi,jpj, 2, ztstop)
CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
ENDIF
! Local constant initialization
zcoef0 = - grav * 0.5_wp
! To use density and not density anomaly
! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
! ELSE ; znad = 0._wp ! Fixed volume
! ENDIF
znad=1._wp
! iniitialised to 0. zhpi zhpi
zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
!==================================================================================
!=====Compute iceload and contribution of the half first wet layer =================
!===================================================================================
! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
! compute density of the water displaced by the ice shelf
zrhd = rhd ! save rhd
DO jk = 1, jpk
zdept(:,:)=gdept_1d(jk)
CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
END DO
WHERE ( tmask(:,:,:) == 1._wp)
rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
END WHERE
! compute rhd at the ice/oce interface (ice shelf side)
CALL eos(ztstop,risfdep,zrhdtop_isf)
! compute rhd at the ice/oce interface (ocean side)
DO ji=1,jpi
DO jj=1,jpj
ikt=mikt(ji,jj)
ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
END DO
END DO
CALL eos(ztstop,risfdep,zrhdtop_oce)
!
! Surface value + ice shelf gradient
! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
ziceload = 0._wp
DO jj = 1, jpj
DO ji = 1, jpi ! vector opt.
ikt=mikt(ji,jj)
ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
DO jk=2,ikt-1
ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
& * (1._wp - tmask(ji,jj,jk))
END DO
IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
END DO
END DO
riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
! we assume ISF is in isostatic equilibrium
zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
! s-coordinate pressure gradient correction (=0 if z coordinate)
zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
END DO
END DO
!==================================================================================
!===== Compute partial cell contribution for the top cell =========================
!==================================================================================
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
iku = miku(ji,jj) ;
zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku))
! u direction
IF ( iku .GT. 1 ) THEN
! case iku
zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
! corrective term ( = 0 if z coordinate )
zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
! zhpi will be added in interior loop
ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
zhpiint = zcoef0 / e1u(ji,jj) &
& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
END IF
! v direction
ikv = mikv(ji,jj)
ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv))
IF ( ikv .GT. 1 ) THEN
! case ikv
zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
! corrective term ( = 0 if z coordinate )
zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
! zhpi will be added in interior loop
va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
zhpjint = zcoef0 / e2v(ji,jj) &
& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
END IF
END DO
END DO
!==================================================================================
!===== Compute interior value =====================================================
!==================================================================================
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
iku=miku(ji,jj); ikv=mikv(ji,jj)
DO jk = 2, jpkm1
! hydrostatic pressure gradient along s-surfaces
! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
& + zcoef0 / e1u(ji,jj) &
& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
! s-coordinate pressure gradient correction
! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
! hydrostatic pressure gradient along s-surfaces
! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
& + zcoef0 / e2v(ji,jj) &
& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
! s-coordinate pressure gradient correction
! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
! add to the general momentum trend
va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
END DO
END DO
END DO
!==================================================================================
!===== Compute bottom cell contribution (partial cell) ============================
!==================================================================================
DO jj = 2, jpjm1
DO ji = 2, jpim1
iku = mbku(ji,jj)
ikv = mbkv(ji,jj)
IF (iku .GT. 1) THEN
! remove old value (interior case)
zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
! put new value
! -zpshpi to avoid double contribution of the partial step in the top layer
zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
END IF
! v direction
IF (ikv .GT. 1) THEN
! remove old value (interior case)
zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
! put new value
! -zpshpj to avoid double contribution of the partial step in the top layer
zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
END IF
END DO
END DO
! set back to original density value into the ice shelf cell (maybe useless because it is masked)
rhd = zrhd
!
CALL wrk_dealloc( jpi,jpj,2, ztstop)
CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
!
END SUBROUTINE hpg_isf
SUBROUTINE hpg_djc( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_djc ***
!!
!! ** Method : Density Jacobian with Cubic polynomial scheme
!!
!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
REAL(wp) :: z1_10, cffu, cffx ! " "
REAL(wp) :: z1_12, cffv, cffy ! " "
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
ENDIF
! Local constant initialization
zcoef0 = - grav * 0.5_wp
z1_10 = 1._wp / 10._wp
z1_12 = 1._wp / 12._wp
!----------------------------------------------------------------------------------------
! compute and store in provisional arrays elementary vertical and horizontal differences
!----------------------------------------------------------------------------------------
!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
END DO
END DO
END DO
!-------------------------------------------------------------------------
! compute harmonic averages using eq. 5.18
!-------------------------------------------------------------------------
zep = 1.e-15
!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
IF( cffw > zep) THEN
drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
ELSE
drhow(ji,jj,jk) = 0._wp
ENDIF
dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
IF( cffu > zep ) THEN
drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
ELSE
drhou(ji,jj,jk ) = 0._wp
ENDIF
IF( cffx > zep ) THEN
dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
ELSE
dzu(ji,jj,jk) = 0._wp
ENDIF
IF( cffv > zep ) THEN
drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
ELSE
drhov(ji,jj,jk) = 0._wp
ENDIF
IF( cffy > zep ) THEN
dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
ELSE
dzv(ji,jj,jk) = 0._wp
ENDIF
END DO
END DO
END DO
!----------------------------------------------------------------------------------
! apply boundary conditions at top and bottom using 5.36-5.37
!----------------------------------------------------------------------------------
drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
!--------------------------------------------------------------
! Upper half of top-most grid box, compute and store
!-------------------------------------------------------------
!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
& * ( rhd(ji,jj,1) &
& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
END DO
END DO
!!bug gm : here also, simplification is possible
!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
& - grav * z1_10 * ( &
& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
& )
rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
& - grav* z1_10 * ( &
& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
& )
rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
& - grav* z1_10 * ( &
& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
& )
END DO
END DO
END DO
CALL lbc_lnk(rho_k,'W',1.)
CALL lbc_lnk(rho_i,'U',1.)
CALL lbc_lnk(rho_j,'V',1.)
! ---------------
! Surface value
! ---------------
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
END DO
END DO
! ----------------
! interior value (2=<jk=<jpkm1)
! ----------------
DO jk = 2, jpkm1
DO jj = 2, jpjm1
DO ji = fs_2, fs_jpim1 ! vector opt.
! hydrostatic pressure gradient along s-surfaces
zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
! add to the general momentum trend
ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
END DO
END DO
END DO
!
CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
!
END SUBROUTINE hpg_djc
SUBROUTINE hpg_prj( kt )
!!---------------------------------------------------------------------
!! *** ROUTINE hpg_prj ***
!!
!! ** Method : s-coordinate case.
!! A Pressure-Jacobian horizontal pressure gradient method
!! based on the constrained cubic-spline interpolation for
!! all vertical coordinate systems
!!
!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
!!----------------------------------------------------------------------
INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
INTEGER, INTENT(in) :: kt ! ocean time-step index
!!
INTEGER :: ji, jj, jk, jkk ! dummy loop indices
REAL(wp) :: zcoef0, znad ! temporary scalars
!!
!! The local variables for the correction term
INTEGER :: jk1, jis, jid, jjs, jjd
REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
REAL(wp) :: zrhdt1
REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
!!----------------------------------------------------------------------
!
CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
!
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)