MODULE traldf_bilap !!============================================================================== !! *** MODULE traldf_bilap *** !! Ocean active tracers: horizontal component of the lateral tracer mixing trend !!============================================================================== !!---------------------------------------------------------------------- !! tra_ldf_bilap : update the tracer trend with the horizontal diffusion !! using a iso-level biharmonic operator !!---------------------------------------------------------------------- !! * Modules used USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE ldftra_oce ! ocean tracer lateral physics USE trdtra_oce ! ocean active tracer trend USE in_out_manager ! I/O manager USE ldfslp ! iso-neutral slopes USE lbclnk ! ocean lateral boundary conditions (or mpp link) IMPLICIT NONE PRIVATE !! * Routine accessibility 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" !!---------------------------------------------------------------------- !! OPA 9.0 , LODYC-IPSL (2003) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_ldf_bilap( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_ldf_bilap *** !! !! ** Purpose : Compute the before horizontal tracer (t & s) 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 of temperature (idem for salinity) is given by: !! * s-coordinate ('key_s_coord' defined), the vertical scale !! factors e3. are inside the derivatives: !! 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) ] } !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: !! Laplacian of tb: !! zlt = 1/(e1t*e2t) { di-1[ e2u/e1u di(tb) ] !! + dj-1[ e1v/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) { di-1[ e2u/e1u di(zlt) ] !! + dj-1[ e1v/e2v dj(zlt) ] } !! !! Add this trend to the general trend (ta,sa): !! (ta,sa) = (ta,sa) + ( difft , diffs ) !! !! ** Action : - Update (ta,sa) arrays with the before iso-level !! biharmonic mixing trend. !! - Save the trends in (ttrd,strd) ('key_diatrends') !! !! History : !! ! 91-11 (G. Madec) Original code !! ! 93-03 (M. Guyon) symetrical conditions !! ! 95-11 (G. Madec) suppress volumetric scale factors !! ! 96-01 (G. Madec) statement function for e3 !! ! 96-01 (M. Imbard) mpp exchange !! ! 97-07 (G. Madec) optimization, and ahtt !! 8.5 ! 02-08 (G. Madec) F90: Free form and module !!---------------------------------------------------------------------- !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk ! dummy loop indices #if defined key_partial_steps INTEGER :: iku, ikv ! temporary integers #endif REAL(wp) :: zta, zsa ! temporary scalars REAL(wp), DIMENSION(jpi,jpj) :: & zeeu, zeev, zbtr, & ! workspace zlt, ztu, ztv, & zls, zsu, zsv !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_ldf_bilap : iso-level biharmonic operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== ! 0. Initialization of metric arrays (for z- or s-coordinates) ! ---------------------------------- DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. #if defined key_s_coord || defined key_partial_steps ! s-coordinates, vertical scale factor are used zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj)*fse3t(ji,jj,jk) ) zeeu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) zeev(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) #else ! z-coordinates, no vertical scale factors zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj) ) zeeu(ji,jj) = e2u(ji,jj) / e1u(ji,jj) * umask(ji,jj,jk) zeev(ji,jj) = e1v(ji,jj) / e2v(ji,jj) * vmask(ji,jj,jk) #endif END DO END DO ! 1. Laplacian ! ------------ ! First derivative (gradient) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj) = zeeu(ji,jj) * ( tb(ji+1,jj ,jk) - tb(ji,jj,jk) ) zsu(ji,jj) = zeeu(ji,jj) * ( sb(ji+1,jj ,jk) - sb(ji,jj,jk) ) ztv(ji,jj) = zeev(ji,jj) * ( tb(ji ,jj+1,jk) - tb(ji,jj,jk) ) zsv(ji,jj) = zeev(ji,jj) * ( sb(ji ,jj+1,jk) - sb(ji,jj,jk) ) END DO END DO #if defined key_partial_steps DO jj = 1, jpj-1 DO ji = 1, jpi-1 ! last level iku = MIN ( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1 ikv = MIN ( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1 IF( iku == jk ) THEN ztu(ji,jj) = zeeu(ji,jj) * gtu(ji,jj) zsu(ji,jj) = zeeu(ji,jj) * gsu(ji,jj) ENDIF IF( ikv == jk ) THEN ztv(ji,jj) = zeev(ji,jj) * gtv(ji,jj) zsv(ji,jj) = zeev(ji,jj) * gsv(ji,jj) ENDIF END DO END DO #endif ! Second derivative (divergence) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlt(ji,jj) = zbtr(ji,jj) * ( ztu(ji,jj) - ztu(ji-1,jj) + ztv(ji,jj) - ztv(ji,jj-1) ) zls(ji,jj) = zbtr(ji,jj) * ( zsu(ji,jj) - zsu(ji-1,jj) + zsv(ji,jj) - zsv(ji,jj-1) ) END DO END DO ! Multiply by the eddy diffusivity coefficient DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlt(ji,jj) = fsahtt(ji,jj,jk) * zlt(ji,jj) zls(ji,jj) = fsahtt(ji,jj,jk) * zls(ji,jj) END DO END DO ! Lateral boundary conditions on the laplacian (zlt,zls) (unchanged sgn) CALL lbc_lnk( zlt, 'T', 1. ) ; CALL lbc_lnk( zls, 'T', 1. ) ! 2. Bilaplacian ! -------------- ! third derivative (gradient) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj) = zeeu(ji,jj) * ( zlt(ji+1,jj ) - zlt(ji,jj) ) zsu(ji,jj) = zeeu(ji,jj) * ( zls(ji+1,jj ) - zls(ji,jj) ) ztv(ji,jj) = zeev(ji,jj) * ( zlt(ji ,jj+1) - zlt(ji,jj) ) zsv(ji,jj) = zeev(ji,jj) * ( zls(ji ,jj+1) - zls(ji,jj) ) END DO END DO ! fourth derivative (divergence) and add to the general tracer trend DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! horizontal diffusive trends zta = zbtr(ji,jj) * ( ztu(ji,jj) - ztu(ji-1,jj) + ztv(ji,jj) - ztv(ji,jj-1) ) zsa = zbtr(ji,jj) * ( zsu(ji,jj) - zsu(ji-1,jj) + zsv(ji,jj) - zsv(ji,jj-1) ) ! add it to the general tracer trends ta(ji,jj,jk) = ta(ji,jj,jk) + zta sa(ji,jj,jk) = sa(ji,jj,jk) + zsa #if defined key_trdtra || defined key_trdmld ! save the horizontal diffusive trends ttrd(ji,jj,jk,3) = zta strd(ji,jj,jk,3) = zsa #endif END DO END DO ! ! =============== END DO ! Horizontal slab ! ! =============== #if defined key_diaptr ! "zonal" mean lateral diffusive heat and salt transport == >> forced bug NOT implemented, ztv, zsv not 3D arrays IF( MOD( kt, nf_ptr ) == 0 ) THEN # if defined key_s_coord || defined key_partial_steps pht_ldf(:,:) = prt_vj( ztv(:,:,:) ) pst_ldf(:,:) = prt_vj( zsv(:,:,:) ) # else DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ztv(ji,jj,jk) = ztv(ji,jj,jk) * fse3v(ji,jj,jk) zsv(ji,jj,jk) = zsv(ji,jj,jk) * fse3v(ji,jj,jk) END DO END DO END DO pht_ldf(:,:) = prt_vj( ztv(:,:,:) ) pst_ldf(:,:) = prt_vj( zsv(:,:,:) ) # endif ENDIF #endif END SUBROUTINE tra_ldf_bilap !!============================================================================== END MODULE traldf_bilap