MODULE zpshde !!====================================================================== !! *** MODULE zpshde *** !! z-coordinate + partial step : Horizontal Derivative at ocean bottom level !!====================================================================== !! History : OPA ! 2002-04 (A. Bozec) Original code !! NEMO 1.0 ! 2002-08 (G. Madec E. Durand) Optimization and Free form !! - ! 2004-03 (C. Ethe) adapted for passive tracers !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA !! 3.6 ! 2014-11 (P. Mathiot) Add zps_hde_isf (needed to open a cavity) !!====================================================================== !!---------------------------------------------------------------------- !! zps_hde : Horizontal DErivative of T, S and rd at the last !! ocean level (Z-coord. with Partial Steps) !!---------------------------------------------------------------------- USE oce ! ocean: dynamics and tracers variables USE dom_oce ! domain: ocean variables USE phycst ! physical constants USE eosbn2 ! ocean equation of state USE in_out_manager ! I/O manager USE lbclnk ! lateral boundary conditions (or mpp link) USE lib_mpp ! MPP library USE wrk_nemo ! Memory allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC zps_hde ! routine called by step.F90 PUBLIC zps_hde_isf ! routine called by step.F90 !! * 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 zps_hde( kt, kjpt, pta, pgtu, pgtv, & & prd, pgru, pgrv ) !!---------------------------------------------------------------------- !! *** ROUTINE zps_hde *** !! !! ** Purpose : Compute the horizontal derivative of T, S and rho !! at u- and v-points with a linear interpolation for z-coordinate !! with partial steps. !! !! ** Method : In z-coord with partial steps, scale factors on last !! levels are different for each grid point, so that T, S and rd !! points are not at the same depth as in z-coord. To have horizontal !! gradients again, we interpolate T and S at the good depth : !! Linear interpolation of T, S !! Computation of di(tb) and dj(tb) by vertical interpolation: !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ !! This formulation computes the two cases: !! CASE 1 CASE 2 !! k-1 ___ ___________ k-1 ___ ___________ !! Ti T~ T~ Ti+1 !! _____ _____ !! k | |Ti+1 k Ti | | !! | |____ ____| | !! ___ | | | ___ | | | !! !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) !! or !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) !! Idem for di(s) and dj(s) !! !! For rho, we call eos which will compute rd~(t~,s~) at the right !! depth zh from interpolated T and S for the different formulations !! of the equation of state (eos). !! Gradient formulation for rho : !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ !! !! ** Action : compute for top interfaces !! - pgtu, pgtv: horizontal gradient of tracer at u- & v-points !! - pgru, pgrv: horizontal gradient of rho (if present) at u- & v-points !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: kjpt ! number of tracers REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) ! INTEGER :: ji, jj, jn ! Dummy loop indices INTEGER :: iku, ikv, ikum1, ikvm1 ! partial step level (ocean bottom level) at u- and v-points REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start( 'zps_hde') ! pgtu(:,:,:)=0.0_wp ; pgtv(:,:,:)=0.0_wp ; zti (:,:,:)=0.0_wp ; ztj (:,:,:)=0.0_wp ; zhi (:,: )=0.0_wp ; zhj (:,: )=0.0_wp ; ! DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) ! ! i- direction IF( ze3wu >= 0._wp ) THEN ! case 1 zmaxu = ze3wu / fse3w(ji+1,jj,iku) ! interpolated values of tracers zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) ! gradient of tracers pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) ELSE ! case 2 zmaxu = -ze3wu / fse3w(ji,jj,iku) ! interpolated values of tracers zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) ! gradient of tracers pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) ENDIF ! ! j- direction IF( ze3wv >= 0._wp ) THEN ! case 1 zmaxv = ze3wv / fse3w(ji,jj+1,ikv) ! interpolated values of tracers ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) ! gradient of tracers pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) ELSE ! case 2 zmaxv = -ze3wv / fse3w(ji,jj,ikv) ! interpolated values of tracers ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) ! gradient of tracers pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) ENDIF END DO END DO CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. ! END DO ! horizontal derivative of density anomalies (rd) IF( PRESENT( prd ) ) THEN ! depth of the partial step level pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ikv = mbkv(ji,jj) ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji ,jj,iku) ! i-direction: case 1 ELSE ; zhi(ji,jj) = fsdept(ji+1,jj,iku) ! - - case 2 ENDIF IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj ,ikv) ! j-direction: case 1 ELSE ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) ! - - case 2 ENDIF END DO END DO ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial ! step and store it in zri, zrj for each case CALL eos( zti, zhi, zri ) CALL eos( ztj, zhj, zrj ) ! Gradient of density at the last level DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ikv = mbkv(ji,jj) ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) IF( ze3wu >= 0._wp ) THEN ; pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji ,jj ) - prd(ji,jj,iku) ) ! i: 1 ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj ) ) ! i: 2 ENDIF IF( ze3wv >= 0._wp ) THEN ; pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 ENDIF END DO END DO CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions ! END IF ! IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde') ! END SUBROUTINE zps_hde ! SUBROUTINE zps_hde_isf( kt, kjpt, pta, pgtu, pgtv, & & prd, pgru, pgrv, pmru, pmrv, pgzu, pgzv, pge3ru, pge3rv, & & pgtui, pgtvi, pgrui, pgrvi, pmrui, pmrvi, pgzui, pgzvi, pge3rui, pge3rvi ) !!---------------------------------------------------------------------- !! *** ROUTINE zps_hde *** !! !! ** Purpose : Compute the horizontal derivative of T, S and rho !! at u- and v-points with a linear interpolation for z-coordinate !! with partial steps. !! !! ** Method : In z-coord with partial steps, scale factors on last !! levels are different for each grid point, so that T, S and rd !! points are not at the same depth as in z-coord. To have horizontal !! gradients again, we interpolate T and S at the good depth : !! Linear interpolation of T, S !! Computation of di(tb) and dj(tb) by vertical interpolation: !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ !! This formulation computes the two cases: !! CASE 1 CASE 2 !! k-1 ___ ___________ k-1 ___ ___________ !! Ti T~ T~ Ti+1 !! _____ _____ !! k | |Ti+1 k Ti | | !! | |____ ____| | !! ___ | | | ___ | | | !! !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) !! or !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) !! Idem for di(s) and dj(s) !! !! For rho, we call eos which will compute rd~(t~,s~) at the right !! depth zh from interpolated T and S for the different formulations !! of the equation of state (eos). !! Gradient formulation for rho : !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ !! !! ** Action : compute for top and bottom interfaces !! - pgtu, pgtv, pgtui, pgtvi: horizontal gradient of tracer at u- & v-points !! - pgru, pgrv, pgrui, pgtvi: horizontal gradient of rho (if present) at u- & v-points !! - pmru, pmrv, pmrui, pmrvi: horizontal sum of rho at u- & v- point (used in dynhpg with vvl) !! - pgzu, pgzv, pgzui, pgzvi: horizontal gradient of z at u- and v- point (used in dynhpg with vvl) !! - pge3ru, pge3rv, pge3rui, pge3rvi: horizontal gradient of rho weighted by local e3w at u- & v-points !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: kjpt ! number of tracers REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtui, pgtvi ! hor. grad. of stra at u- & v-pts (ISF) REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmru, pmrv ! hor. sum of prd at u- & v-pts (bottom) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzu, pgzv ! hor. grad of z at u- & v-pts (bottom) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3ru, pge3rv ! hor. grad of prd weighted by local e3w at u- & v-pts (bottom) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgrui, pgrvi ! hor. grad of prd at u- & v-pts (top) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmrui, pmrvi ! hor. sum of prd at u- & v-pts (top) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzui, pgzvi ! hor. grad of z at u- & v-pts (top) REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3rui, pge3rvi ! hor. grad of prd weighted by local e3w at u- & v-pts (top) ! INTEGER :: ji, jj, jn ! Dummy loop indices INTEGER :: iku, ikv, ikum1, ikvm1,ikup1, ikvp1 ! partial step level (ocean bottom level) at u- and v-points REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv, zdzwu, zdzwv, zdzwuip1, zdzwvjp1 ! temporary scalars REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start( 'zps_hde_isf') ! pgtu(:,:,:)=0.0_wp ; pgtv(:,:,:)=0.0_wp ; pgtui(:,:,:)=0.0_wp ; pgtvi(:,:,:)=0.0_wp ; zti (:,:,:)=0.0_wp ; ztj (:,:,:)=0.0_wp ; zhi (:,: )=0.0_wp ; zhj (:,: )=0.0_wp ; ! DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 ! (ISF) case partial step top and bottom in adjacent cell in vertical ! cannot used e3w because if 2 cell water column, we have ps at top and bottom ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) ! ! i- direction IF( ze3wu >= 0._wp ) THEN ! case 1 zmaxu = ze3wu / fse3w(ji+1,jj,iku) ! interpolated values of tracers zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) ! gradient of tracers pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) ELSE ! case 2 zmaxu = -ze3wu / fse3w(ji,jj,iku) ! interpolated values of tracers zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) ! gradient of tracers pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) ENDIF ! ! j- direction IF( ze3wv >= 0._wp ) THEN ! case 1 zmaxv = ze3wv / fse3w(ji,jj+1,ikv) ! interpolated values of tracers ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) ! gradient of tracers pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) ELSE ! case 2 zmaxv = -ze3wv / fse3w(ji,jj,ikv) ! interpolated values of tracers ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) ! gradient of tracers pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) ENDIF END DO END DO CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. ! END DO ! horizontal derivative of density anomalies (rd) IF( PRESENT( prd ) ) THEN ! depth of the partial step level pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; pgzu(:,:)=0.0_wp ; pgzv(:,:)=0.0_wp ; pmru(:,:)=0.0_wp ; pmru(:,:)=0.0_wp ; pge3ru(:,:)=0.0_wp ; pge3rv(:,:)=0.0_wp ; DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ikv = mbkv(ji,jj) ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) - ze3wu ! i-direction: case 1 ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) + ze3wu ! - - case 2 ENDIF IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) - ze3wv ! j-direction: case 1 ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) + ze3wv ! - - case 2 ENDIF END DO END DO ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial ! step and store it in zri, zrj for each case CALL eos( zti, zhi, zri ) CALL eos( ztj, zhj, zrj ) ! Gradient of density at the last level DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! last and before last ocean level at u- & v-points ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) IF( ze3wu >= 0._wp ) THEN pgzu(ji,jj) = (fsde3w(ji+1,jj,iku) - ze3wu) - fsde3w(ji,jj,iku) pgru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) - prd(ji,jj,iku) ) ! i: 1 pmru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) + prd(ji,jj,iku) ) ! i: 1 pge3ru(ji,jj) = umask(ji,jj,iku) & * ( (fse3w(ji+1,jj,iku) - ze3wu )* ( zri(ji ,jj ) + prd(ji+1,jj,ikum1) + 2._wp) & - fse3w(ji ,jj,iku) * ( prd(ji ,jj,iku) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 ELSE pgzu(ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) + ze3wu) pgru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 pmru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 pge3ru(ji,jj) = umask(ji,jj,iku) & * ( fse3w(ji+1,jj,iku) * ( prd(ji+1,jj,iku) + prd(ji+1,jj,ikum1) + 2._wp) & -(fse3w(ji ,jj,iku) + ze3wu) * ( zri(ji ,jj ) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 ENDIF IF( ze3wv >= 0._wp ) THEN pgzv(ji,jj) = (fsde3w(ji,jj+1,ikv) - ze3wv) - fsde3w(ji,jj,ikv) pgrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 pmrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 pge3rv(ji,jj) = vmask(ji,jj,ikv) & * ( (fse3w(ji,jj+1,ikv) - ze3wv )* ( zrj(ji,jj ) + prd(ji,jj+1,ikvm1) + 2._wp) & - fse3w(ji,jj ,ikv) * ( prd(ji,jj ,ikv) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 ELSE pgzv(ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) + ze3wv) pgrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 pmrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 pge3rv(ji,jj) = vmask(ji,jj,ikv) & * ( fse3w(ji,jj+1,ikv) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikvm1) + 2._wp) & -(fse3w(ji,jj ,ikv) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 ENDIF END DO END DO CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions CALL lbc_lnk( pmru , 'U', 1. ) ; CALL lbc_lnk( pmrv , 'V', 1. ) ! Lateral boundary conditions CALL lbc_lnk( pgzu , 'U', -1. ) ; CALL lbc_lnk( pgzv , 'V', -1. ) ! Lateral boundary conditions CALL lbc_lnk( pge3ru , 'U', -1. ) ; CALL lbc_lnk( pge3rv , 'V', -1. ) ! Lateral boundary conditions ! END IF ! (ISH) compute grui and gruvi DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 ! ! (ISF) case partial step top and bottom in adjacent cell in vertical ! cannot used e3w because if 2 cell water column, we have ps at top and bottom ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 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)) 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)) ! i- direction IF( ze3wu >= 0._wp ) THEN ! case 1 zmaxu = ze3wu / fse3w(ji+1,jj,iku+1) ! interpolated values of tracers zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,iku+1,jn) - pta(ji+1,jj,iku,jn) ) ! gradient of tracers pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) ELSE ! case 2 zmaxu = - ze3wu / fse3w(ji,jj,iku+1) ! interpolated values of tracers zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,iku+1,jn) - pta(ji,jj,iku,jn) ) ! gradient of tracers pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) ENDIF ! ! j- direction IF( ze3wv >= 0._wp ) THEN ! case 1 zmaxv = ze3wv / fse3w(ji,jj+1,ikv+1) ! interpolated values of tracers ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikv+1,jn) - pta(ji,jj+1,ikv,jn) ) ! gradient of tracers pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) ELSE ! case 2 zmaxv = - ze3wv / fse3w(ji,jj,ikv+1) ! interpolated values of tracers ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikv+1,jn) - pta(ji,jj,ikv,jn) ) ! gradient of tracers pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) ENDIF END DO!! END DO!! CALL lbc_lnk( pgtui(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtvi(:,:,jn), 'V', -1. ) ! Lateral boundary cond. ! END DO ! horizontal derivative of density anomalies (rd) IF( PRESENT( prd ) ) THEN ! depth of the partial step level pgrui(:,:) =0.0_wp ; pgrvi(:,:) =0.0_wp ; pgzui(:,:) =0.0_wp ; pgzvi(:,:) =0.0_wp ; pmrui(:,:) =0.0_wp ; pmrui(:,:) =0.0_wp ; pge3rui(:,:)=0.0_wp ; pge3rvi(:,:)=0.0_wp ; DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = miku(ji,jj) ikv = mikv(ji,jj) 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)) 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( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) + ze3wu ! i-direction: case 1 ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) - ze3wu ! - - case 2 ENDIF IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) + ze3wv ! j-direction: case 1 ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) - ze3wv ! - - case 2 ENDIF END DO END DO ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial ! step and store it in zri, zrj for each case CALL eos( zti, zhi, zri ) CALL eos( ztj, zhj, zrj ) ! Gradient of density at the last level DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 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)) 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( ze3wu >= 0._wp ) THEN pgzui (ji,jj) = (fsde3w(ji+1,jj,iku) + ze3wu) - fsde3w(ji,jj,iku) pgrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) - prd(ji,jj,iku) ) ! i: 1 pmrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) + prd(ji,jj,iku) ) ! i: 1 pge3rui(ji,jj) = umask(ji,jj,iku+1) & * ( (fse3w(ji+1,jj,iku+1) - ze3wu) * (zri(ji,jj ) + prd(ji+1,jj,iku+1) + 2._wp) & - fse3w(ji ,jj,iku+1) * (prd(ji,jj,iku) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 1 ELSE pgzui (ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) - ze3wu) pgrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 pmrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 pge3rui(ji,jj) = umask(ji,jj,iku+1) & * ( fse3w(ji+1,jj,iku+1) * (prd(ji+1,jj,iku) + prd(ji+1,jj,iku+1) + 2._wp) & -(fse3w(ji ,jj,iku+1) + ze3wu) * (zri(ji,jj ) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 2 ENDIF IF( ze3wv >= 0._wp ) THEN pgzvi (ji,jj) = (fsde3w(ji,jj+1,ikv) + ze3wv) - fsde3w(ji,jj,ikv) pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & * ( (fse3w(ji,jj+1,ikv+1) - ze3wv) * ( zrj(ji,jj ) + prd(ji,jj+1,ikv+1) + 2._wp) & - fse3w(ji,jj ,ikv+1) * ( prd(ji,jj,ikv) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 1 ! + 2 due to the formulation in density and not in anomalie in hpg sco ELSE pgzvi (ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) - ze3wv) pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & * ( fse3w(ji,jj+1,ikv+1) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikv+1) + 2._wp) & -(fse3w(ji,jj ,ikv+1) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 2 ENDIF END DO END DO CALL lbc_lnk( pgrui , 'U', -1. ) ; CALL lbc_lnk( pgrvi , 'V', -1. ) ! Lateral boundary conditions CALL lbc_lnk( pmrui , 'U', 1. ) ; CALL lbc_lnk( pmrvi , 'V', 1. ) ! Lateral boundary conditions CALL lbc_lnk( pgzui , 'U', -1. ) ; CALL lbc_lnk( pgzvi , 'V', -1. ) ! Lateral boundary conditions CALL lbc_lnk( pge3rui , 'U', -1. ) ; CALL lbc_lnk( pge3rvi , 'V', -1. ) ! Lateral boundary conditions ! END IF ! IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde_isf') ! END SUBROUTINE zps_hde_isf !!====================================================================== END MODULE zpshde