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 !!====================================================================== !!---------------------------------------------------------------------- !! 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 IMPLICIT NONE PRIVATE PUBLIC zps_hde ! routine called by step.F90 !! * Control permutation of array indices # include "oce_ftrans.h90" # include "dom_oce_ftrans.h90" !! * 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_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 rho (if present) at u- & v-points !!---------------------------------------------------------------------- USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released USE wrk_nemo, ONLY: zri => wrk_2d_1 , zrj => wrk_2d_2 ! interpolated value of rd USE wrk_nemo, ONLY: zhi => wrk_2d_3 , zhj => wrk_2d_4 ! depth of interpolation for eos2d ! INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: kjpt ! number of tracers !! DCSE_NEMO: This style defeats ftrans ! REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields !FTRANS pta :I :I :z : REAL(wp), INTENT(in ) :: pta(jpi,jpj,jpk,kjpt) ! 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 !FTRANS prd :I :I :z REAL(wp), INTENT(in ), OPTIONAL :: prd(jpi,jpj,jpk) ! 3D density anomaly fields REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad. of prd at u- & v-pts ! 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), ALLOCATABLE, DIMENSION(:,:,:) :: zti, ztj ! interpolated value of tracer !!---------------------------------------------------------------------- IF( wrk_in_use(2, 1,2,3,4) ) THEN CALL ctl_stop('zps_hde: requested workspace arrays unavailable') ; RETURN END IF ! Allocate workspaces whose dimension is > jpk ALLOCATE( zti(jpi,jpj,kjpt) ) ALLOCATE( ztj(jpi,jpj,kjpt) ) DO jn = 1, kjpt !== Interpolation of tracers at the last ocean 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 = 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 #if defined key_z_first pgtu(ji,jj,jn) = umask_1(ji,jj) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) #else pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) #endif 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 #if defined key_z_first pgtu(ji,jj,jn) = umask_1(ji,jj) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) #else pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) #endif 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 #if defined key_z_first pgtv(ji,jj,jn) = vmask_1(ji,jj) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) #else pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) #endif 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 #if defined key_z_first pgtv(ji,jj,jn) = vmask_1(ji,jj) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) #else pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) #endif ENDIF # if ! defined key_vectopt_loop END DO # endif 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 # 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 = 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 # 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 = 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 # if ! defined key_vectopt_loop END DO # endif END DO CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions ! END IF ! IF( wrk_not_released(2, 1,2,3,4) ) CALL ctl_stop('zps_hde: failed to release workspace arrays') ! DEALLOCATE( zti ) DEALLOCATE( ztj ) ! END SUBROUTINE zps_hde !!====================================================================== END MODULE zpshde