MODULE traldf_bilap !!============================================================================== !! *** MODULE traldf_bilap *** !! Ocean tracers: horizontal component of the lateral tracer mixing trend !!============================================================================== !! History : OPA ! 1991-11 (G. Madec) Original code !! ! 1993-03 (M. Guyon) symetrical conditions !! ! 1995-11 (G. Madec) suppress volumetric scale factors !! ! 1996-01 (G. Madec) statement function for e3 !! ! 1996-01 (M. Imbard) mpp exchange !! ! 1997-07 (G. Madec) optimization, and ahtt !! 8.5 ! 2002-08 (G. Madec) F90: Free form and module !! NEMO 1.0 ! 2004-08 (C. Talandier) New trends organization !! - ! 2005-11 (G. Madec) zps or sco as default option !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA !!============================================================================== !!---------------------------------------------------------------------- !! tra_ldf_bilap : update the tracer trend with the horizontal diffusion !! using a iso-level biharmonic operator !!---------------------------------------------------------------------- USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE ldftra_oce ! ocean tracer lateral physics USE in_out_manager ! I/O manager USE ldfslp ! iso-neutral slopes USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE diaptr ! poleward transport diagnostics USE trc_oce ! share passive tracers/Ocean variables USE lib_mpp ! MPP library USE wrk_nemo ! Memory Allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC tra_ldf_bilap ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "ldftra_substitute.h90" # include "ldfeiv_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 tra_ldf_bilap( kt, kit000, cdtype, pgu, pgv, & & pgui, pgvi, & & ptb, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_ldf_bilap *** !! !! ** Purpose : Compute the before horizontal tracer diffusive !! trend and add it to the general trend of tracer equation. !! !! ** Method : 4th order diffusive operator along model level surfaces !! evaluated using before fields (forward time scheme). The hor. !! diffusive trends is given by: !! Laplacian of tb: !! zlt = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(tb) ] !! + dj-1[ e1v*e3v/e2v dj(tb) ] } !! Multiply by the eddy diffusivity coef. and insure lateral bc: !! zlt = ahtt * zlt !! call to lbc_lnk !! Bilaplacian (laplacian of zlt): !! difft = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(zlt) ] !! + dj-1[ e1v*e3v/e2v dj(zlt) ] } !! !! Add this trend to the general trend !! (pta) = (pta) + ( difft ) !! !! ** Action : - Update pta arrays with the before iso-level !! biharmonic mixing trend. !!---------------------------------------------------------------------- USE oce , ONLY: ztu => ua , ztv => va ! (ua,va) used as workspace !! INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: kit000 ! first time step index CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) INTEGER , INTENT(in ) :: kjpt ! number of tracers REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT(in ) :: pgu , pgv ! tracer gradient at pstep levels REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT(in ) :: pgui, pgvi ! tracer gradient at pstep levels REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend !! INTEGER :: ji, jj, jk, jn ! dummy loop indices REAL(wp) :: zbtr, ztra ! local scalars REAL(wp), POINTER, DIMENSION(:,:) :: zeeu, zeev, zlt !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start( 'tra_ldf_bilap') ! CALL wrk_alloc( jpi, jpj, zeeu, zeev, zlt ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_ldf_bilap : iso-level biharmonic operator on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! DO jk = 1, jpkm1 ! Horizontal slab ! ! !== Initialization of metric arrays (for z- or s-coordinates) ==! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zeeu(ji,jj) = re2u_e1u(ji,jj) * fse3u_n(ji,jj,jk) * umask(ji,jj,jk) zeev(ji,jj) = re1v_e2v(ji,jj) * fse3v_n(ji,jj,jk) * vmask(ji,jj,jk) END DO END DO ! !== Laplacian ==! ! DO jj = 1, jpjm1 ! First derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = zeeu(ji,jj) * ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) ztv(ji,jj,jk) = zeev(ji,jj) * ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) END DO END DO ! IF( ln_zps ) THEN ! set gradient at partial step level (last ocean level) DO jj = 1, jpjm1 DO ji = 1, jpim1 IF( mbku(ji,jj) == jk ) ztu(ji,jj,jk) = zeeu(ji,jj) * pgu(ji,jj,jn) IF( mbkv(ji,jj) == jk ) ztv(ji,jj,jk) = zeev(ji,jj) * pgv(ji,jj,jn) END DO END DO ENDIF ! (ISH) IF( ln_zps .AND. ln_isfcav ) THEN ! set gradient at partial step level (first ocean level in a cavity) DO jj = 1, jpjm1 DO ji = 1, jpim1 IF( miku(ji,jj) == MAX(jk,2) ) ztu(ji,jj,jk) = zeeu(ji,jj) * pgui(ji,jj,jn) IF( mikv(ji,jj) == MAX(jk,2) ) ztu(ji,jj,jk) = zeev(ji,jj) * pgvi(ji,jj,jn) END DO END DO ENDIF ! DO jj = 2, jpjm1 ! Second derivative (divergence) time the eddy diffusivity coefficient DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) zlt(ji,jj) = fsahtt(ji,jj,jk) * zbtr * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) & & + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) END DO END DO CALL lbc_lnk( zlt, 'T', 1. ) ! Lateral boundary conditions (unchanged sgn) ! !== Bilaplacian ==! ! DO jj = 1, jpjm1 ! third derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = zeeu(ji,jj) * ( zlt(ji+1,jj ) - zlt(ji,jj) ) ztv(ji,jj,jk) = zeev(ji,jj) * ( zlt(ji ,jj+1) - zlt(ji,jj) ) END DO END DO DO jj = 2, jpjm1 ! fourth derivative (divergence) and add to the general tracer trend DO ji = fs_2, fs_jpim1 ! vector opt. ! horizontal diffusive trends zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) ztra = zbtr * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) ! add it to the general tracer trends pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra END DO END DO ! END DO ! Horizontal slab ! ! "zonal" mean lateral diffusive heat and salt transport IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN IF( jn == jp_tem ) htr_ldf(:) = ptr_sj( ztv(:,:,:) ) IF( jn == jp_sal ) str_ldf(:) = ptr_sj( ztv(:,:,:) ) ENDIF ! ! =========== END DO ! tracer loop ! ! =========== IF( nn_timing == 1 ) CALL timing_stop( 'tra_ldf_bilap') ! CALL wrk_dealloc( jpi, jpj, zeeu, zeev, zlt ) ! END SUBROUTINE tra_ldf_bilap !!============================================================================== END MODULE traldf_bilap