MODULE zpshde !!============================================================================== !! *** MODULE zpshde *** !! z-coordinate - partial step : Horizontal Derivative !!============================================================================== !!---------------------------------------------------------------------- !! 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 !! * 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) !! $Header$ !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt !!---------------------------------------------------------------------- CONTAINS SUBROUTINE zps_hde ( kt, ptem, psal, prd , & pgtu, pgsu, pgru, & pgtv, pgsv, 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, pgsu, pgru: horizontal gradient of T, S !! and rd at U-points !! - pgtv, pgsv, pgrv: horizontal gradient of T, S !! and rd at V-points !! !! History : !! 8.5 ! 02-04 (A. Bozec) Original code !! 8.5 ! 02-08 (G. Madec E. Durand) Optimization and Free form !!---------------------------------------------------------------------- !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & ptem, psal, prd ! 3D T, S and rd fields REAL(wp), DIMENSION(jpi,jpj), INTENT( out ) :: & pgtu, pgsu, pgru, & ! horizontal grad. of T, S and rd at u- pgtv, pgsv, pgrv ! and v-points of the partial step level !! * Local declarations INTEGER :: ji, jj, & ! Dummy loop indices iku,ikv ! partial step level at u- and v-points REAL(wp), DIMENSION(jpi,jpj) :: & zti, ztj, zsi, zsj, & ! interpolated value of T, S zri, zrj, & ! and rd zhgi, zhgj ! depth of interpolation for eos2d REAL(wp) :: & ze3wu, ze3wv, & ! temporary scalars zmaxu1, zmaxu2, & ! " " zmaxv1, zmaxv2 ! " " ! Initialization (first time-step only): compute mbatu and mbatv IF( kt == nit000 ) THEN 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 ) ENDIF ! Interpolation of T and S at the last ocean level # if defined key_vectopt_loop && ! defined key_mpp_omp 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) zmaxu1 = ze3wu / fse3w(ji+1,jj ,iku) zmaxu2 = -ze3wu / fse3w(ji ,jj ,iku) zmaxv1 = ze3wv / fse3w(ji ,jj+1,ikv) zmaxv2 = -ze3wv / fse3w(ji ,jj ,ikv) ! i- direction IF( ze3wu >= 0. ) THEN ! case 1 ! interpolated values of T and S zti(ji,jj) = ptem(ji+1,jj,iku) + zmaxu1 * ( ptem(ji+1,jj,iku-1) - ptem(ji+1,jj,iku) ) zsi(ji,jj) = psal(ji+1,jj,iku) + zmaxu1 * ( psal(ji+1,jj,iku-1) - psal(ji+1,jj,iku) ) ! depth of the partial step level zhgi(ji,jj) = fsdept(ji,jj,iku) ! gradient of T and S pgtu(ji,jj) = umask(ji,jj,1) * ( zti(ji,jj) - ptem(ji,jj,iku) ) pgsu(ji,jj) = umask(ji,jj,1) * ( zsi(ji,jj) - psal(ji,jj,iku) ) ELSE ! case 2 ! interpolated values of T and S zti(ji,jj) = ptem(ji,jj,iku) + zmaxu2 * ( ptem(ji,jj,iku-1) - ptem(ji,jj,iku) ) zsi(ji,jj) = psal(ji,jj,iku) + zmaxu2 * ( psal(ji,jj,iku-1) - psal(ji,jj,iku) ) ! depth of the partial step level zhgi(ji,jj) = fsdept(ji+1,jj,iku) ! gradient of T and S pgtu(ji,jj) = umask(ji,jj,1) * ( ptem(ji+1,jj,iku) - zti (ji,jj) ) pgsu(ji,jj) = umask(ji,jj,1) * ( psal(ji+1,jj,iku) - zsi (ji,jj) ) ENDIF ! j- direction IF( ze3wv >= 0. ) THEN ! case 1 ! interpolated values of T and S ztj(ji,jj) = ptem(ji,jj+1,ikv) + zmaxv1 * ( ptem(ji,jj+1,ikv-1) - ptem(ji,jj+1,ikv) ) zsj(ji,jj) = psal(ji,jj+1,ikv) + zmaxv1 * ( psal(ji,jj+1,ikv-1) - psal(ji,jj+1,ikv) ) ! depth of the partial step level zhgj(ji,jj) = fsdept(ji,jj,ikv) ! gradient of T and S pgtv(ji,jj) = vmask(ji,jj,1) * ( ztj(ji,jj) - ptem(ji,jj,ikv) ) pgsv(ji,jj) = vmask(ji,jj,1) * ( zsj(ji,jj) - psal(ji,jj,ikv) ) ELSE ! case 2 ! interpolated values of T and S ztj(ji,jj) = ptem(ji,jj,ikv) + zmaxv2 * ( ptem(ji,jj,ikv-1) - ptem(ji,jj,ikv) ) zsj(ji,jj) = psal(ji,jj,ikv) + zmaxv2 * ( psal(ji,jj,ikv-1) - psal(ji,jj,ikv) ) ! depth of the partial step level zhgj(ji,jj) = fsdept(ji,jj+1,ikv) ! gradient of T and S pgtv(ji,jj) = vmask(ji,jj,1) * ( ptem(ji,jj+1,ikv) - ztj(ji,jj) ) pgsv(ji,jj) = vmask(ji,jj,1) * ( psal(ji,jj+1,ikv) - zsj(ji,jj) ) ENDIF # if ! defined key_vectopt_loop || defined key_mpp_omp END DO # endif END DO ! Compute interpolated rd from zti, zsi, ztj, zsj for the 2 cases at the depth of the partial ! step and store it in zri, zrj for each case CALL eos( zti, zsi, zhgi, zri ) CALL eos( ztj, zsj, zhgj, zrj ) ! Gradient of density at the last level # if defined key_vectopt_loop && ! defined key_mpp_omp 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 || defined key_mpp_omp END DO # endif END DO ! Lateral boundary conditions on each gradient CALL lbc_lnk( pgtu , 'U', -1. ) ; CALL lbc_lnk( pgtv , 'V', -1. ) CALL lbc_lnk( pgsu , 'U', -1. ) ; CALL lbc_lnk( pgsv , 'V', -1. ) CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) END SUBROUTINE zps_hde !!====================================================================== END MODULE zpshde