MODULE zpshde !!============================================================================== !! *** MODULE zpshde *** !! z-coordinate - partial step : Horizontal Derivative !!============================================================================== !! History : !! OPA 8.5 ! 2002-04 (A. Bozec) Original code !! 8.5 ! 2002-08 (G. Madec E. Durand) Optimization and Free form !! 9.0 ! 2004-03 (C. Ethe) adapted for passive tracers !! NEMO 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA !!============================================================================== !!---------------------------------------------------------------------- !! zps_hde : Horizontal DErivative of T, S and rd at the last !! ocean level (Z-coord. with Partial Steps) !!---------------------------------------------------------------------- !! * Modules used USE dom_oce ! ocean space domain variables USE oce ! ocean dynamics and tracers variables USE phycst ! physical constants USE in_out_manager ! I/O manager USE eosbn2 ! ocean equation of state USE lbclnk ! lateral boundary conditions (or mpp link) IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC zps_hde ! routine called by step.F90 PUBLIC zps_hde_init ! routine called by opa.F90 !! * module variables INTEGER, DIMENSION(jpi,jpj) :: & mbatu, mbatv ! bottom ocean level index at U- and V-points !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2005) !! $Id$ !! This software is governed by the CeCILL licence see modipsl/doc/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 rd !! 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_insitu_2d which will compute rd~(t~,s~) at !! the good depth zh from interpolated T and S for the different !! formulation 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 : - pgtu, pgtv: horizontal gradient of tracer at U/V-points !! - pgru, pgrv: horizontal gradient of rd if present at U/V-points !! and rd at V-points !!---------------------------------------------------------------------- !! * Arguments 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 active or passive tracers fields REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! horizontal grad. of ptra u- and v-points REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( in ), OPTIONAL :: prd ! 3D rd fields REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! horizontal grad. of prd u- and v-points !! * Local declarations INTEGER :: ji, jj, jn ! Dummy loop indices INTEGER :: iku, ikv ! partial step level at u- and v-points REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! interpolated value of tracer REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj ! interpolated value of rd REAL(wp), DIMENSION(jpi,jpj) :: zhi, zhj ! depth of interpolation for eos2d REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars !!---------------------------------------------------------------------- ! Interpolation of tracers at the last ocean level DO jn = 1, kjpt # if defined key_vectopt_loop jj = 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif ! last level iku = mbatu(ji,jj) ikv = mbatv(ji,jj) 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. ) 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,iku-1,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,iku-1,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. ) 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,ikv-1,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,ikv-1,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 # if ! defined key_vectopt_loop END DO # endif END DO ! Lateral boundary conditions on each gradient CALL lbc_lnk( pgtu(:,:,jn) , 'U', -1. ) CALL lbc_lnk( pgtv(:,:,jn) , 'V', -1. ) END DO ! horizontal derivative of rd IF( PRESENT( prd ) ) THEN ! depth of the partial step level # if defined key_vectopt_loop jj = 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif iku = mbatu(ji,jj) ikv = mbatv(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. ) THEN zhi(ji,jj) = fsdept(ji ,jj,iku) ELSE zhi(ji,jj) = fsdept(ji+1,jj,iku) ENDIF IF( ze3wv >= 0. ) THEN zhj(ji,jj) = fsdept(ji,jj ,ikv) ELSE zhj(ji,jj) = fsdept(ji,jj+1,ikv) ENDIF # if ! defined key_vectopt_loop END DO # endif 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 # if defined key_vectopt_loop jj = 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif iku = mbatu(ji,jj) ikv = mbatv(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. ) THEN ! i-direction: case 1 pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji,jj) - prd(ji,jj,iku) ) ELSE ! i-direction: case 2 pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ENDIF IF( ze3wv >= 0. ) THEN ! j-direction: case 1 pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj) - prd(ji,jj,ikv) ) ELSE ! j-direction: case 2 pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ENDIF # if ! defined key_vectopt_loop END DO # endif END DO ! Lateral boundary conditions on each gradient CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! END IF ! END SUBROUTINE zps_hde SUBROUTINE zps_hde_init !!---------------------------------------------------------------------- !! *** ROUTINE zps_hde_init *** !! !! ** Purpose : Computation of bottom ocean level index at U- and V-points !! !!---------------------------------------------------------------------- !! * Local declarations INTEGER :: ji, jj ! Dummy loop indices REAL(wp), DIMENSION(jpi,jpj) :: zti, ztj ! temporary arrays !!---------------------------------------------------------------------- mbatu(:,:) = 0 mbatv(:,:) = 0 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. mbatu(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1, 2 ) mbatv(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1, 2 ) END DO END DO zti(:,:) = FLOAT( mbatu(:,:) ) ztj(:,:) = FLOAT( mbatv(:,:) ) ! lateral boundary conditions: T-point, sign unchanged CALL lbc_lnk( zti , 'U', 1. ) CALL lbc_lnk( ztj , 'V', 1. ) mbatu(:,:) = MAX( INT( zti(:,:) ), 2 ) mbatv(:,:) = MAX( INT( ztj(:,:) ), 2 ) END SUBROUTINE zps_hde_init !!====================================================================== END MODULE zpshde