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 wet_dry ! wetting and drying USE phycst ! physical constants USE trd_oce ! trends: ocean variables USE trddyn ! trend manager: dynamics USE zpshde ! partial step: hor. derivative (zps_hde routine) ! 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 timing ! Timing USE iom 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 ! !! Flag to control the type of hydrostatic pressure gradient INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation) INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation) INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial) INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme) INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf ! INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) LOGICAL, PUBLIC :: ln_hpg_djc_vN_hor, ln_hpg_djc_vN_vrt REAL(wp), PUBLIC :: aco_bc_hor, bco_bc_hor, aco_bc_vrt, bco_bc_vrt !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- 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), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv !!---------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('dyn_hpg') ! IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) ) ztrdu(:,:,:) = ua(:,:,:) ztrdv(:,:,:) = va(:,:,:) ENDIF ! SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation CASE ( np_zco ) ; CALL hpg_zco ( kt ) ! z-coordinate CASE ( np_zps ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) CASE ( np_sco ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) CASE ( np_djc ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) CASE ( np_prj ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) CASE ( np_isf ) ; 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 ) DEALLOCATE( 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_timing ) 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 !! INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF REAL(wp) :: znad REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF !! NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, & & ln_hpg_djc_vN_hor, ln_hpg_djc_vN_vrt !!---------------------------------------------------------------------- ! 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' ) ! 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' ) 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 ENDIF ! IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf.OR.ln_hpg_djc) ) & & CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', & & ' the standard jacobian formulation hpg_sco or ' , & & ' the pressure jacobian formulation hpg_prj' ) ! IF( ln_hpg_isf ) THEN IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) ELSE IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) ENDIF ! ! ! Set nhpg from ln_hpg_... flags & consistency check nhpg = np_ERROR ioptio = 0 IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF ! IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) ! IF(lwp) THEN WRITE(numout,*) SELECT CASE( nhpg ) CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps ' CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)' CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)' CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)' CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)' CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf' END SELECT WRITE(numout,*) ENDIF ! IF (ln_hpg_djc_vN_hor) THEN ! Von Neumann boundary condition aco_bc_hor = 6.0_wp/5.0_wp bco_bc_hor = 7.0_wp/15.0_wp ELSE ! Linear extrapolation aco_bc_hor = 3.0_wp/2.0_wp bco_bc_hor = 1.0_wp/2.0_wp END IF IF (ln_hpg_djc_vN_vrt) THEN ! Von Neumann boundary condition aco_bc_vrt = 6.0_wp/5.0_wp bco_bc_vrt = 7.0_wp/15.0_wp ELSE ! Linear extrapolation aco_bc_vrt = 3.0_wp/2.0_wp bco_bc_vrt = 1.0_wp/2.0_wp END IF IF ( .NOT. ln_isfcav ) THEN !--- no ice shelf load riceload(:,:) = 0._wp ! ELSE !--- set an ice shelf load ! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' ice shelf case: set the ice-shelf load' ALLOCATE( zts_top(jpi,jpj,jpts) , zrhd(jpi,jpj,jpk) , zrhdtop_isf(jpi,jpj) , ziceload(jpi,jpj) ) ! znad = 1._wp !- To use density and not density anomaly ! ! !- assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) zts_top(:,:,jp_tem) = -1.9_wp ; zts_top(:,:,jp_sal) = 34.4_wp ! DO jk = 1, jpk !- compute density of the water displaced by the ice shelf CALL eos( zts_top(:,:,:), gdept_n(:,:,jk), zrhd(:,:,jk) ) END DO ! ! !- compute rhd at the ice/oce interface (ice shelf side) CALL eos( zts_top , risfdep, zrhdtop_isf ) ! ! !- Surface value + ice shelf gradient ziceload = 0._wp ! compute pressure due to ice shelf load DO jj = 1, jpj ! (used to compute hpgi/j for all the level from 1 to miku/v) DO ji = 1, jpi ! divided by 2 later ikt = mikt(ji,jj) ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1)) DO jk = 2, ikt-1 ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) & & * (1._wp - tmask(ji,jj,jk)) END DO IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) & & * ( risfdep(ji,jj) - gdept_n(ji,jj,ikt-1) ) END DO END DO riceload(:,:) = ziceload(:,:) ! need to be saved for diaar5 ! DEALLOCATE( zts_top , zrhd , zrhdtop_isf , ziceload ) ENDIF ! 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), DIMENSION(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 * e3w_n(ji,jj,1) ! hydrostatic pressure gradient zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_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= 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) + zgru(ji,jj) ) * r1_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) + zgrv(ji,jj) ) * r1_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 ! 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, jii, jjj ! dummy loop indices REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter !!---------------------------------------------------------------------- ! IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj)) ! 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 ! zcoef0 = - grav * 0.5_wp IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly ELSE ; znad = 1._wp ! Variable volume: density ENDIF ! IF( ln_wd_il ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 ELSE IF(ll_tmp2) THEN ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) ELSE zcpx(ji,jj) = 0._wp END IF ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji,jj+1) - sshn(ji,jj )) ) ELSE zcpy(ji,jj) = 0._wp END IF END DO END DO CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) END IF ! 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 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj) zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj) ! s-coordinate pressure gradient correction zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj) zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj) ! IF( ln_wd_il ) THEN zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) zuap = zuap * zcpx(ji,jj) zvap = zvap * zcpy(ji,jj) ENDIF ! ! 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= & & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 ELSE IF(ll_tmp2) THEN ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) ELSE zcpx(ji,jj) = 0._wp END IF ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji,jj+1) - sshn(ji,jj )) ) ELSE zcpy(ji,jj) = 0._wp END IF END DO END DO CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) END IF 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 z_grav_10 = grav / 10._wp z1_12 = 1.0_wp / 12._wp IF( .NOT. ln_linssh ) THEN rhd_opt(:,:,:) = rhd(:,:,:) + 1.0_wp ! for vvl option ELSE rhd_opt(:,:,:) = rhd(:,:,:) END IF !---------------------------------------------------------------------------------------- ! 1. compute and store elementary vertical differences in provisional arrays !---------------------------------------------------------------------------------------- !!bug gm Not a true bug, but... zdzz=e3w for zdzx, zdzy verify what it is really !! zdzz, zdzx and zdzy changed to heights rather than depths; lower bounds of jj and ji changed from 2 to 1 DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zdrhoz(ji,jj,jk) = rhd_opt (ji ,jj ,jk) - rhd_opt (ji,jj,jk-1) zdzz (ji,jj,jk) = - gde3w_n(ji ,jj ,jk) + gde3w_n(ji,jj,jk-1) END DO END DO END DO !------------------------------------------------------------------------- ! 2. compute harmonic averages for vertical differences using eq. 5.18 !------------------------------------------------------------------------- zep = 1.e-15 !!bug gm zdrhoz not defined at level 1 and used (jk-1 with jk=2) ; this issue has now been addressed !!bug gm idem for zdrhox, zdrhoy et ji=jpi and jj=jpj; idem !! zdrho_k, zdz_k, zdrho_i, zdz_i, zdrho_j, zdz_j re-centred about the point (ji,jj,jk) !! DO loops broken up so that zdrho_k and zdz_k are calculated only for jk = 2 to jpk - 2 zdrho_k(:,:,:) = 0._wp zdz_k (:,:,:) = 0._wp DO jk = 2, jpk - 2 DO jj = 1, jpj DO ji = 1, jpi cffw = 2._wp * zdrhoz(ji ,jj ,jk) * zdrhoz(ji,jj,jk+1) IF( cffw > zep) THEN zdrho_k(ji,jj,jk) = cffw / ( zdrhoz(ji,jj,jk) + zdrhoz(ji,jj,jk+1) ) ENDIF zdz_k(ji,jj,jk) = 2._wp * zdzz(ji,jj,jk) * zdzz(ji,jj,jk+1) & & / ( zdzz(ji,jj,jk) + zdzz(ji,jj,jk+1) ) END DO END DO END DO !---------------------------------------------------------------------------------- ! 3. apply boundary conditions at top and bottom using 5.36-5.37 !---------------------------------------------------------------------------------- ! for sea-ice shelves we will need to re-write this upper boundary condition in the same form as the lower boundary condition zdrho_k(:,:,1) = aco_bc_vrt * ( rhd_opt (:,:,2) - rhd_opt (:,:,1) ) - bco_bc_vrt * zdrho_k(:,:,2) zdz_k (:,:,1) = aco_bc_vrt * (-gde3w_n(:,:,2) + gde3w_n(:,:,1) ) - bco_bc_vrt * zdz_k (:,:,2) DO jj = 1, jpj DO ji = 1, jpi IF ( mbkt(ji,jj)>1 ) THEN iktb = mbkt(ji,jj) zdrho_k(ji,jj,iktb) = aco_bc_vrt * ( rhd_opt(ji,jj,iktb) - rhd_opt(ji,jj,iktb-1) ) - bco_bc_vrt * zdrho_k(ji,jj,iktb-1) zdz_k (ji,jj,iktb) = aco_bc_vrt * (-gde3w_n(ji,jj,iktb) + gde3w_n(ji,jj,iktb-1) ) - bco_bc_vrt * zdz_k (ji,jj,iktb-1) END IF END DO END DO !-------------------------------------------------------------- ! 4. Compute side face integrals !------------------------------------------------------------- !! sshn replaces e3w_n ; gde3w_n is a depth; the formulae involve heights !! rho_k stores grav * FX / rho_0 !-------------------------------------------------------------- ! 4. a) Upper half of top-most grid box, compute and store !------------------------------------------------------------- ! Concerns that zdrho_k might be oddly defined (just -1.5rho) for single celled columns are resolved by the fact that z_rho_k is defined explicity for the surface layer DO jj = 2, jpj DO ji = 2, jpi z_rho_k(ji,jj,1) = grav * ( sshn(ji,jj) + gde3w_n(ji,jj,1) ) & ! *** AY sshn included in djc but not in sco & * ( rhd_opt(ji,jj,1) & & + 0.5_wp * ( rhd_opt (ji,jj,2) - rhd_opt (ji,jj,1) ) & & * ( sshn (ji,jj ) + gde3w_n(ji,jj,1) ) & & / ( - gde3w_n(ji,jj,2) + gde3w_n(ji,jj,1) ) ) END DO END DO !-------------------------------------------------------------- ! 4. b) Interior faces, compute and store !------------------------------------------------------------- DO jk = 2, jpkm1 DO jj = 2, jpj DO ji = 2, jpi z_rho_k(ji,jj,jk) = zcoef0 * ( rhd_opt (ji,jj,jk) + rhd_opt (ji,jj,jk-1) ) & & * ( - gde3w_n(ji,jj,jk) + gde3w_n(ji,jj,jk-1) ) & & + z_grav_10 * ( & & ( zdrho_k (ji,jj,jk) - zdrho_k (ji,jj,jk-1) ) & & * ( - gde3w_n(ji,jj,jk) + gde3w_n(ji,jj,jk-1) - z1_12 * ( zdz_k (ji,jj,jk) + zdz_k (ji,jj,jk-1) ) ) & & - ( zdz_k (ji,jj,jk) - zdz_k (ji,jj,jk-1) ) & & * ( rhd_opt (ji,jj,jk) - rhd_opt (ji,jj,jk-1) - z1_12 * ( zdrho_k(ji,jj,jk) + zdrho_k(ji,jj,jk-1) ) ) & & ) END DO END DO END DO !---------------------------------------------------------------------------------------- ! 5. compute and store elementary horizontal differences in provisional arrays !---------------------------------------------------------------------------------------- DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zdrhox(ji,jj,jk) = rhd_opt (ji+1,jj ,jk) - rhd_opt (ji,jj,jk ) zdzx (ji,jj,jk) = - gde3w_n(ji+1,jj ,jk) + gde3w_n(ji,jj,jk ) zdrhoy(ji,jj,jk) = rhd_opt (ji ,jj+1,jk) - rhd_opt (ji,jj,jk ) zdzy (ji,jj,jk) = - gde3w_n(ji ,jj+1,jk) + gde3w_n(ji,jj,jk ) END DO END DO END DO CALL lbc_lnk_multi( 'dynhpg', zdrhox, 'U', 1., zdzx, 'U', 1., zdrhoy, 'V', 1., zdzy, 'V', 1. ) !------------------------------------------------------------------------- ! 6. compute harmonic averages using eq. 5.18 !------------------------------------------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. cffu = 2._wp * zdrhox(ji-1,jj ,jk) * zdrhox(ji,jj,jk ) IF( cffu > zep ) THEN zdrho_i(ji,jj,jk) = cffu / ( zdrhox(ji-1,jj,jk) + zdrhox(ji,jj,jk) ) ELSE zdrho_i(ji,jj,jk ) = 0._wp ENDIF cffx = 2._wp * zdzx (ji-1,jj ,jk) * zdzx (ji,jj,jk ) IF( cffx > zep ) THEN zdz_i(ji,jj,jk) = cffx / ( zdzx(ji-1,jj,jk) + zdzx(ji,jj,jk) ) ELSE zdz_i(ji,jj,jk) = 0._wp ENDIF cffv = 2._wp * zdrhoy(ji ,jj-1,jk) * zdrhoy(ji,jj,jk ) IF( cffv > zep ) THEN zdrho_j(ji,jj,jk) = cffv / ( zdrhoy(ji,jj-1,jk) + zdrhoy(ji,jj,jk) ) ELSE zdrho_j(ji,jj,jk) = 0._wp ENDIF cffy = 2._wp * zdzy (ji ,jj-1,jk) * zdzy (ji,jj,jk ) IF( cffy > zep ) THEN zdz_j(ji,jj,jk) = cffy / ( zdzy(ji,jj-1,jk) + zdzy(ji,jj,jk) ) ELSE zdz_j(ji,jj,jk) = 0._wp ENDIF END DO END DO END DO !!! Note that zdzx, zdzy, zdzz, zdrhox, zdrhoy and zdrhoz should NOT be used beyond this point !---------------------------------------------------------------------------------- ! 6B. apply boundary conditions at side boundaries using 5.36-5.37 !---------------------------------------------------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpj DO ji = 2, jpi ! vector opt. zz_drho_i(ji,jj) = zdrho_i(ji,jj,jk) zz_dz_i (ji,jj) = zdz_i (ji,jj,jk) zz_drho_j(ji,jj) = zdrho_j(ji,jj,jk) zz_dz_j (ji,jj) = zdz_j (ji,jj,jk) ! Walls coming from left should check from 2 to jpi-1 (and jpj=2-jpj) IF (ji < jpi) THEN IF ( umask(ji,jj,jk) > 0.5_wp .AND. tmask(ji-1,jj,jk) < 0.5_wp .AND. umask(ji+1,jj,jk) > 0.5_wp) THEN zz_drho_i(ji,jj) = aco_bc_hor * ( rhd_opt (ji+1,jj,jk) - rhd_opt (ji,jj,jk) ) - bco_bc_hor * zdrho_i(ji+1,jj,jk) zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w_n(ji+1,jj,jk) + gde3w_n(ji,jj,jk) ) - bco_bc_hor * zdz_i (ji+1,jj,jk) END IF END IF ! Walls coming from right should check from 3 to jpi (and jpj=2-jpj) IF (ji > 2) THEN IF ( umask(ji,jj,jk) < 0.5_wp .AND. umask(ji-1,jj,jk) > 0.5_wp .AND. umask(ji-2,jj,jk) > 0.5_wp) THEN zz_drho_i(ji,jj) = aco_bc_hor * ( rhd_opt (ji,jj,jk) - rhd_opt (ji-1,jj,jk) ) - bco_bc_hor * zdrho_i(ji-1,jj,jk) zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w_n(ji,jj,jk) + gde3w_n(ji-1,jj,jk) ) - bco_bc_hor * zdz_i (ji-1,jj,jk) END IF END IF ! Walls coming from left should check from 2 to jpj-1 (and jpi=2-jpi) IF (jj < jpj) THEN IF ( vmask(ji,jj,jk) > 0.5_wp .AND. tmask(ji,jj-1,jk) < 0.5_wp .AND. vmask(ji,jj+1,jk) > 0.5_wp) THEN zz_drho_j(ji,jj) = aco_bc_hor * ( rhd_opt (ji,jj+1,jk) - rhd_opt (ji,jj,jk) ) - bco_bc_hor * zdrho_j(ji,jj+1,jk) zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w_n(ji,jj+1,jk) + gde3w_n(ji,jj,jk) ) - bco_bc_hor * zdz_j (ji,jj+1,jk) END IF END IF ! Walls coming from right should check from 3 to jpj (and jpi=2-jpi) IF (jj > 2) THEN IF ( vmask(ji,jj,jk) < 0.5_wp .AND. vmask(ji,jj-1,jk) > 0.5_wp .AND. vmask(ji,jj-2,jk) > 0.5_wp) THEN zz_drho_j(ji,jj) = aco_bc_hor * ( rhd_opt (ji,jj,jk) - rhd_opt (ji,jj-1,jk) ) - bco_bc_hor * zdrho_j(ji,jj-1,jk) zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w_n(ji,jj,jk) + gde3w_n(ji,jj-1,jk) ) - bco_bc_hor * zdz_j (ji,jj-1,jk) END IF END IF END DO END DO DO jj = 2, jpj DO ji = 2, jpi ! vector opt. zdrho_i(ji,jj,jk) = zz_drho_i(ji,jj) zdz_i (ji,jj,jk) = zz_dz_i (ji,jj) zdrho_j(ji,jj,jk) = zz_drho_j(ji,jj) zdz_j (ji,jj,jk) = zz_dz_j (ji,jj) END DO END DO END DO !-------------------------------------------------------------- ! 7. Calculate integrals on side faces !------------------------------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! two -ve signs cancel in next two lines (within zcoef0 and because gde3w is a depth not a height) z_rho_i(ji,jj,jk) = zcoef0 * ( rhd_opt (ji+1,jj,jk) + rhd_opt (ji,jj,jk) ) & & * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) IF ( umask(ji-1, jj, jk) > 0.5 .OR. umask(ji+1, jj, jk) > 0.5 ) THEN z_rho_i(ji,jj,jk) = z_rho_i(ji,jj,jk) - z_grav_10 * ( & & ( zdrho_i (ji+1,jj,jk) - zdrho_i (ji,jj,jk) ) & & * ( - gde3w_n(ji+1,jj,jk) + gde3w_n(ji,jj,jk) - z1_12 * ( zdz_i (ji+1,jj,jk) + zdz_i (ji,jj,jk) ) ) & & - ( zdz_i (ji+1,jj,jk) - zdz_i (ji,jj,jk) ) & & * ( rhd_opt (ji+1,jj,jk) - rhd_opt (ji,jj,jk) - z1_12 * ( zdrho_i(ji+1,jj,jk) + zdrho_i(ji,jj,jk) ) ) & & ) END IF z_rho_j(ji,jj,jk) = zcoef0 * ( rhd_opt (ji,jj+1,jk) + rhd_opt (ji,jj,jk) ) & & * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) IF ( vmask(ji, jj-1, jk) > 0.5 .OR. vmask(ji, jj+1, jk) > 0.5 ) THEN z_rho_j(ji,jj,jk) = z_rho_j(ji,jj,jk) - z_grav_10 * ( & & ( zdrho_j (ji,jj+1,jk) - zdrho_j (ji,jj,jk) ) & & * ( - gde3w_n(ji,jj+1,jk) + gde3w_n(ji,jj,jk) - z1_12 * ( zdz_j (ji,jj+1,jk) + zdz_j (ji,jj,jk) ) ) & & - ( zdz_j (ji,jj+1,jk) - zdz_j (ji,jj,jk) ) & & * ( rhd_opt (ji,jj+1,jk) - rhd_opt (ji,jj,jk) - z1_12 * ( zdrho_j(ji,jj+1,jk) + zdrho_j(ji,jj,jk) ) ) & & ) END IF END DO END DO END DO !-------------------------------------------------------------- ! 8. Integrate in the vertical !------------------------------------------------------------- ! --------------- ! Surface value ! --------------- DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zhpi(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji+1,jj ,1) - z_rho_i(ji,jj,1) ) * r1_e1u(ji,jj) zhpj(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji ,jj+1,1) - z_rho_j(ji,jj,1) ) * r1_e2v(ji,jj) IF( ln_wd_il ) THEN zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) ENDIF ! 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= & & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 ELSE IF(ll_tmp2) THEN ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp) ELSE zcpx(ji,jj) = 0._wp END IF ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & & > rn_wdmin1 + rn_wdmin2 ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & & MAX( sshn(ji,jj) , sshn(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 sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & & / (sshn(ji,jj+1) - sshn(ji,jj )) ) zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp) ELSE zcpy(ji,jj) = 0._wp ENDIF END DO END DO CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) ENDIF ! Clean 3-D work arrays zhpi(:,:,:) = 0._wp zrhh(:,:,:) = rhd(:,:,:) ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate DO jj = 1, jpj DO ji = 1, jpi jk = mbkt(ji,jj) IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk) ELSEIF( jk < jpkm1 ) THEN DO jkk = jk+1, jpk zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), & & gde3w_n(ji,jj,jkk-2), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2)) END DO ENDIF END DO END DO ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" DO jj = 1, jpj DO ji = 1, jpi zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad END DO END DO DO jk = 2, jpk DO jj = 1, jpj DO ji = 1, jpi zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk) END DO END DO END DO fsp(:,:,:) = zrhh (:,:,:) xsp(:,:,:) = zdept(:,:,:) ! Construct the vertical density profile with the ! constrained cubic spline interpolation ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" DO jj = 2, jpj DO ji = 2, jpi zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), & & csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1) ! assuming linear profile across the top half surface layer zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1 END DO END DO ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" DO jk = 2, jpkm1 DO jj = 2, jpj DO ji = 2, jpi zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & & integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), & & asp (ji,jj,jk-1), bsp (ji,jj,jk-1), & & csp (ji,jj,jk-1), dsp (ji,jj,jk-1) ) END DO END DO END DO ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) ! Prepare zsshu_n and zsshv_n DO jj = 2, jpjm1 DO ji = 2, jpim1 !!gm BUG ? if it is ssh at u- & v-point then it should be: ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * & ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * & ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp !!gm not this: zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * & & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * & & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp END DO END DO CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. ) DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad) zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk) zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk) zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zpwes = 0._wp; zpwed = 0._wp zpnss = 0._wp; zpnsd = 0._wp zuijk = zu(ji,jj,jk) zvijk = zv(ji,jj,jk) !!!!! for u equation IF( jk <= mbku(ji,jj) ) THEN IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN jis = ji + 1; jid = ji ELSE jis = ji; jid = ji +1 ENDIF ! integrate the pressure on the shallow side jk1 = jk DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) IF( jk1 == mbku(ji,jj) ) THEN zuijk = -zdept(jis,jj,jk1) EXIT ENDIF zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) zpwes = zpwes + & integ_spline(zdept(jis,jj,jk1), zdeps, & asp(jis,jj,jk1), bsp(jis,jj,jk1), & csp(jis,jj,jk1), dsp(jis,jj,jk1)) jk1 = jk1 + 1 END DO ! integrate the pressure on the deep side jk1 = jk DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) IF( jk1 == 1 ) THEN zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & bsp(jid,jj,1), csp(jid,jj,1), & dsp(jid,jj,1)) * zdeps zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps EXIT ENDIF zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) zpwed = zpwed + & integ_spline(zdeps, zdept(jid,jj,jk1), & asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) jk1 = jk1 - 1 END DO ! update the momentum trends in u direction zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) ) IF( .NOT.ln_linssh ) THEN zdpdx2 = zcoef0 * r1_e1u(ji,jj) * & & ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) ELSE zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) ENDIF IF( ln_wd_il ) THEN zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj) zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj) ENDIF ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk) ENDIF !!!!! for v equation IF( jk <= mbkv(ji,jj) ) THEN IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN jjs = jj + 1; jjd = jj ELSE jjs = jj ; jjd = jj + 1 ENDIF ! integrate the pressure on the shallow side jk1 = jk DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) IF( jk1 == mbkv(ji,jj) ) THEN zvijk = -zdept(ji,jjs,jk1) EXIT ENDIF zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) zpnss = zpnss + & integ_spline(zdept(ji,jjs,jk1), zdeps, & asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) jk1 = jk1 + 1 END DO ! integrate the pressure on the deep side jk1 = jk DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) IF( jk1 == 1 ) THEN zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & bsp(ji,jjd,1), csp(ji,jjd,1), & dsp(ji,jjd,1) ) * zdeps zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps EXIT ENDIF zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) zpnsd = zpnsd + & integ_spline(zdeps, zdept(ji,jjd,jk1), & asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) jk1 = jk1 - 1 END DO ! update the momentum trends in v direction zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) ) IF( .NOT.ln_linssh ) THEN zdpdy2 = zcoef0 * r1_e2v(ji,jj) * & ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) ELSE zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) ENDIF IF( ln_wd_il ) THEN zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj) zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj) ENDIF va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk) ENDIF ! END DO END DO END DO ! IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) ! END SUBROUTINE hpg_prj SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) !!---------------------------------------------------------------------- !! *** ROUTINE cspline *** !! !! ** Purpose : constrained cubic spline interpolation !! !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 !! !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation !!---------------------------------------------------------------------- REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: jpi, jpj, jpkm1 REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp REAL(wp) :: zdxtmp1, zdxtmp2, zalpha REAL(wp) :: zdf(size(fsp,3)) !!---------------------------------------------------------------------- ! !!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!! jpi = size(fsp,1) jpj = size(fsp,2) jpkm1 = MAX( 1, size(fsp,3) - 1 ) ! IF (polynomial_type == 1) THEN ! Constrained Cubic Spline DO ji = 1, jpi DO jj = 1, jpj !!Fritsch&Butland's method, 1984 (preferred, but more computation) ! DO jk = 2, jpkm1-1 ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 ! ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp ! ! IF(zdf1 * zdf2 <= 0._wp) THEN ! zdf(jk) = 0._wp ! ELSE ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) ! ENDIF ! END DO !!Simply geometric average DO jk = 2, jpkm1-1 zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1)) zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk )) IF(zdf1 * zdf2 <= 0._wp) THEN zdf(jk) = 0._wp ELSE zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) ENDIF END DO zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1) DO jk = 1, jpkm1 - 1 zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp zddf1 = -2._wp * ztmp1 + ztmp2 ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp zddf2 = 2._wp * ztmp1 - ztmp2 dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) END DO END DO END DO ELSEIF ( polynomial_type == 2 ) THEN ! Linear DO ji = 1, jpi DO jj = 1, jpj DO jk = 1, jpkm1-1 zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) dsp(ji,jj,jk) = 0._wp csp(ji,jj,jk) = 0._wp bsp(ji,jj,jk) = ztmp1 / zdxtmp asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) END DO END DO END DO ! ELSE CALL ctl_stop( 'invalid polynomial type in cspline' ) ENDIF ! END SUBROUTINE cspline FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d linear interpolation !! !! ** Method : interpolation is straight forward !! extrapolation is also permitted (no value limit) !!---------------------------------------------------------------------- REAL(wp), INTENT(in) :: x, xl, xr, fl, fr REAL(wp) :: f ! result of the interpolation (extrapolation) REAL(wp) :: zdeltx !!---------------------------------------------------------------------- ! zdeltx = xr - xl IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN f = 0.5_wp * (fl + fr) ELSE f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx ENDIF ! END FUNCTION interp1 FUNCTION interp2( x, a, b, c, d ) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d constrained cubic spline interpolation !! !! ** Method : cubic spline interpolation !! !!---------------------------------------------------------------------- REAL(wp), INTENT(in) :: x, a, b, c, d REAL(wp) :: f ! value from the interpolation !!---------------------------------------------------------------------- ! f = a + x* ( b + x * ( c + d * x ) ) ! END FUNCTION interp2 FUNCTION interp3( x, a, b, c, d ) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : Calculate the first order of derivative of !! a cubic spline function y=a+b*x+c*x^2+d*x^3 !! !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 !! !!---------------------------------------------------------------------- REAL(wp), INTENT(in) :: x, a, b, c, d REAL(wp) :: f ! value from the interpolation !!---------------------------------------------------------------------- ! f = b + x * ( 2._wp * c + 3._wp * d * x) ! END FUNCTION interp3 FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d constrained cubic spline integration !! !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr !! !!---------------------------------------------------------------------- REAL(wp), INTENT(in) :: xl, xr, a, b, c, d REAL(wp) :: za1, za2, za3 REAL(wp) :: f ! integration result !!---------------------------------------------------------------------- ! za1 = 0.5_wp * b za2 = c / 3.0_wp za3 = 0.25_wp * d ! f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) ! END FUNCTION integ_spline !!====================================================================== END MODULE dynhpg