MODULE traldf_triad !!====================================================================== !! *** MODULE traldf_triad *** !! Ocean tracers: horizontal component of the lateral tracer mixing trend !!====================================================================== !! History : 3.3 ! 2010-10 (G. Nurser, C. Harris, G. Madec) Griffies operator (original code) !! 3.7 ! 2013-12 (F. Lemarie, G. Madec) triad operator (Griffies) + Method of Stabilizing Correction !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_ldf_triad : update the tracer trend with the iso-neutral laplacian triad-operator !!---------------------------------------------------------------------- USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE trc_oce ! share passive tracers/Ocean variables USE zdf_oce ! ocean vertical physics USE ldftra ! lateral physics: eddy diffusivity USE ldfslp ! lateral physics: iso-neutral slopes USE traldf_iso ! lateral diffusion (Madec operator) (tra_ldf_iso routine) USE diaptr ! poleward transport diagnostics USE diaar5 ! AR5 diagnostics USE zpshde ! partial step: hor. derivative (zps_hde routine) ! USE in_out_manager ! I/O manager USE iom ! I/O library USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_mpp ! MPP library IMPLICIT NONE PRIVATE PUBLIC tra_ldf_triad ! routine called by traldf.F90 REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, SAVE :: zdkt3d !: vertical tracer gradient at 2 levels LOGICAL :: l_ptr ! flag to compute poleward transport LOGICAL :: l_hst ! flag to compute heat transport !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_ldf_triad( kt, kit000, cdtype, pahu, pahv, pgu , pgv , & & pgui, pgvi, & & ptb , ptbb, pta , kjpt, kpass ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_ldf_triad *** !! !! ** Purpose : Compute the before horizontal tracer (t & s) diffusive !! trend for a laplacian tensor (ezxcept the dz[ dz[.] ] term) and !! add it to the general trend of tracer equation. !! !! ** Method : The horizontal component of the lateral diffusive trends !! is provided by a 2nd order operator rotated along neural or geopo- !! tential surfaces to which an eddy induced advection can be added !! It is computed using before fields (forward in time) and isopyc- !! nal or geopotential slopes computed in routine ldfslp. !! !! see documentation for the desciption !! !! ** Action : pta updated with the before rotated diffusion !! ah_wslp2 .... !! akz stabilizing vertical diffusivity coefficient (used in trazdf_imp) !!---------------------------------------------------------------------- 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 INTEGER , INTENT(in ) :: kpass ! =1/2 first or second passage REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT(in ) :: pahu, pahv ! eddy diffusivity at u- and v-points [m2/s] 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 top levels REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! tracer (kpass=1) or laplacian of tracer (kpass=2) REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptbb ! tracer (only used in kpass=2) REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend ! INTEGER :: ji, jj, jk, jn ! dummy loop indices INTEGER :: ip,jp,kp ! dummy loop indices INTEGER :: ierr ! local integer REAL(wp) :: zmsku, zabe1, zcof1, zcoef3 ! local scalars REAL(wp) :: zmskv, zabe2, zcof2, zcoef4 ! - - REAL(wp) :: zcoef0, ze3w_2, zsign, z2dt, z1_2dt ! - - ! REAL(wp) :: zslope_skew, zslope_iso, zslope2, zbu, zbv REAL(wp) :: ze1ur, ze2vr, ze3wr, zdxt, zdyt, zdzt REAL(wp) :: zah, zah_slp, zaei_slp REAL(wp), DIMENSION(jpi,jpj ) :: z2d ! 2D workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdit, zdjt, zftu, zftv, ztfw, zpsi_uw, zpsi_vw ! 3D - !!---------------------------------------------------------------------- ! IF( .NOT.ALLOCATED(zdkt3d) ) THEN ALLOCATE( zdkt3d(jpi,jpj,0:1) , STAT=ierr ) CALL mpp_sum ( 'traldf_triad', ierr ) IF( ierr > 0 ) CALL ctl_stop('STOP', 'tra_ldf_triad: unable to allocate arrays') ENDIF ! IF( kpass == 1 .AND. kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_ldf_triad : rotated laplacian diffusion operator on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF ! l_hst = .FALSE. l_ptr = .FALSE. IF( cdtype == 'TRA' .AND. ln_diaptr ) l_ptr = .TRUE. IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. ! ! ! set time step size (Euler/Leapfrog) IF( neuler == 0 .AND. kt == kit000 ) THEN ; z2dt = rdt ! at nit000 (Euler) ELSE ; z2dt = 2.* rdt ! (Leapfrog) ENDIF z1_2dt = 1._wp / z2dt ! IF( kpass == 1 ) THEN ; zsign = 1._wp ! bilaplacian operator require a minus sign (eddy diffusivity >0) ELSE ; zsign = -1._wp ENDIF ! !!---------------------------------------------------------------------- !! 0 - calculate ah_wslp2, akz, and optionally zpsi_uw, zpsi_vw !!---------------------------------------------------------------------- ! IF( kpass == 1 ) THEN !== first pass only and whatever the tracer is ==! ! akz (:,:,:) = 0._wp ah_wslp2(:,:,:) = 0._wp IF( ln_ldfeiv_dia ) THEN zpsi_uw(:,:,:) = 0._wp zpsi_vw(:,:,:) = 0._wp ENDIF ! DO ip = 0, 1 ! i-k triads DO kp = 0, 1 DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze3wr = 1._wp / e3w_n(ji+ip,jj,jk+kp) zbu = e1e2u(ji,jj) * e3u_n(ji,jj,jk) zah = 0.25_wp * pahu(ji,jj,jk) zslope_skew = triadi_g(ji+ip,jj,jk,1-ip,kp) ! Subtract s-coordinate slope at t-points to give slope rel to s-surfaces (do this by *adding* gradient of depth) zslope2 = zslope_skew + ( gdept_n(ji+1,jj,jk) - gdept_n(ji,jj,jk) ) * r1_e1u(ji,jj) * umask(ji,jj,jk+kp) zslope2 = zslope2 *zslope2 ah_wslp2(ji+ip,jj,jk+kp) = ah_wslp2(ji+ip,jj,jk+kp) + zah * zbu * ze3wr * r1_e1e2t(ji+ip,jj) * zslope2 akz (ji+ip,jj,jk+kp) = akz (ji+ip,jj,jk+kp) + zah * r1_e1u(ji,jj) & & * r1_e1u(ji,jj) * umask(ji,jj,jk+kp) ! IF( ln_ldfeiv_dia ) zpsi_uw(ji,jj,jk+kp) = zpsi_uw(ji,jj,jk+kp) & & + 0.25_wp * aeiu(ji,jj,jk) * e2u(ji,jj) * zslope_skew END DO END DO END DO END DO END DO ! DO jp = 0, 1 ! j-k triads DO kp = 0, 1 DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze3wr = 1.0_wp / e3w_n(ji,jj+jp,jk+kp) zbv = e1e2v(ji,jj) * e3v_n(ji,jj,jk) zah = 0.25_wp * pahv(ji,jj,jk) zslope_skew = triadj_g(ji,jj+jp,jk,1-jp,kp) ! Subtract s-coordinate slope at t-points to give slope rel to s surfaces ! (do this by *adding* gradient of depth) zslope2 = zslope_skew + ( gdept_n(ji,jj+1,jk) - gdept_n(ji,jj,jk) ) * r1_e2v(ji,jj) * vmask(ji,jj,jk+kp) zslope2 = zslope2 * zslope2 ah_wslp2(ji,jj+jp,jk+kp) = ah_wslp2(ji,jj+jp,jk+kp) + zah * zbv * ze3wr * r1_e1e2t(ji,jj+jp) * zslope2 akz (ji,jj+jp,jk+kp) = akz (ji,jj+jp,jk+kp) + zah * r1_e2v(ji,jj) & & * r1_e2v(ji,jj) * vmask(ji,jj,jk+kp) ! IF( ln_ldfeiv_dia ) zpsi_vw(ji,jj,jk+kp) = zpsi_vw(ji,jj,jk+kp) & & + 0.25 * aeiv(ji,jj,jk) * e1v(ji,jj) * zslope_skew END DO END DO END DO END DO END DO ! IF( ln_traldf_msc ) THEN ! stabilizing vertical diffusivity coefficient ! IF( ln_traldf_blp ) THEN ! bilaplacian operator DO jk = 2, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 akz(ji,jj,jk) = 16._wp * ah_wslp2(ji,jj,jk) & & * ( akz(ji,jj,jk) + ah_wslp2(ji,jj,jk) / ( e3w_n(ji,jj,jk) * e3w_n(ji,jj,jk) ) ) END DO END DO END DO ELSEIF( ln_traldf_lap ) THEN ! laplacian operator DO jk = 2, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze3w_2 = e3w_n(ji,jj,jk) * e3w_n(ji,jj,jk) zcoef0 = z2dt * ( akz(ji,jj,jk) + ah_wslp2(ji,jj,jk) / ze3w_2 ) akz(ji,jj,jk) = MAX( zcoef0 - 0.5_wp , 0._wp ) * ze3w_2 * z1_2dt END DO END DO END DO ENDIF ! ELSE ! 33 flux set to zero with akz=ah_wslp2 ==>> computed in full implicit akz(:,:,:) = ah_wslp2(:,:,:) ENDIF ! IF( ln_ldfeiv_dia .AND. cdtype == 'TRA' ) CALL ldf_eiv_dia( zpsi_uw, zpsi_vw ) ! ENDIF !== end 1st pass only ==! ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! Zero fluxes for each tracer !!gm this should probably be done outside the jn loop ztfw(:,:,:) = 0._wp zftu(:,:,:) = 0._wp zftv(:,:,:) = 0._wp ! DO jk = 1, jpkm1 !== before lateral T & S gradients at T-level jk ==! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zdit(ji,jj,jk) = ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) * umask(ji,jj,jk) zdjt(ji,jj,jk) = ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) * vmask(ji,jj,jk) END DO END DO END DO IF( ln_zps .AND. l_grad_zps ) THEN ! partial steps: correction at top/bottom ocean level DO jj = 1, jpjm1 ! bottom level DO ji = 1, fs_jpim1 ! vector opt. zdit(ji,jj,mbku(ji,jj)) = pgu(ji,jj,jn) zdjt(ji,jj,mbkv(ji,jj)) = pgv(ji,jj,jn) END DO END DO IF( ln_isfcav ) THEN ! top level (ocean cavities only) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. IF( miku(ji,jj) > 1 ) zdit(ji,jj,miku(ji,jj) ) = pgui(ji,jj,jn) IF( mikv(ji,jj) > 1 ) zdjt(ji,jj,mikv(ji,jj) ) = pgvi(ji,jj,jn) END DO END DO ENDIF ENDIF ! !!---------------------------------------------------------------------- !! II - horizontal trend (full) !!---------------------------------------------------------------------- ! DO jk = 1, jpkm1 ! !== Vertical tracer gradient at level jk and jk+1 zdkt3d(:,:,1) = ( ptb(:,:,jk,jn) - ptb(:,:,jk+1,jn) ) * tmask(:,:,jk+1) ! ! ! surface boundary condition: zdkt3d(jk=0)=zdkt3d(jk=1) IF( jk == 1 ) THEN ; zdkt3d(:,:,0) = zdkt3d(:,:,1) ELSE ; zdkt3d(:,:,0) = ( ptb(:,:,jk-1,jn) - ptb(:,:,jk,jn) ) * tmask(:,:,jk) ENDIF ! zaei_slp = 0._wp ! IF( ln_botmix_triad ) THEN DO ip = 0, 1 !== Horizontal & vertical fluxes DO kp = 0, 1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze1ur = r1_e1u(ji,jj) zdxt = zdit(ji,jj,jk) * ze1ur ze3wr = 1._wp / e3w_n(ji+ip,jj,jk+kp) zdzt = zdkt3d(ji+ip,jj,kp) * ze3wr zslope_skew = triadi_g(ji+ip,jj,jk,1-ip,kp) zslope_iso = triadi (ji+ip,jj,jk,1-ip,kp) ! zbu = 0.25_wp * e1e2u(ji,jj) * e3u_n(ji,jj,jk) ! ln_botmix_triad is .T. don't mask zah for bottom half cells !!gm ????? ahu is masked.... zah = pahu(ji,jj,jk) zah_slp = zah * zslope_iso IF( ln_ldfeiv ) zaei_slp = aeiu(ji,jj,jk) * zslope_skew zftu(ji ,jj,jk ) = zftu(ji ,jj,jk ) - ( zah * zdxt + (zah_slp - zaei_slp) * zdzt ) * zbu * ze1ur ztfw(ji+ip,jj,jk+kp) = ztfw(ji+ip,jj,jk+kp) - ( zah_slp + zaei_slp) * zdxt * zbu * ze3wr END DO END DO END DO END DO ! DO jp = 0, 1 DO kp = 0, 1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze2vr = r1_e2v(ji,jj) zdyt = zdjt(ji,jj,jk) * ze2vr ze3wr = 1._wp / e3w_n(ji,jj+jp,jk+kp) zdzt = zdkt3d(ji,jj+jp,kp) * ze3wr zslope_skew = triadj_g(ji,jj+jp,jk,1-jp,kp) zslope_iso = triadj(ji,jj+jp,jk,1-jp,kp) zbv = 0.25_wp * e1e2v(ji,jj) * e3v_n(ji,jj,jk) ! ln_botmix_triad is .T. don't mask zah for bottom half cells !!gm ????? ahv is masked... zah = pahv(ji,jj,jk) zah_slp = zah * zslope_iso IF( ln_ldfeiv ) zaei_slp = aeiv(ji,jj,jk) * zslope_skew zftv(ji,jj ,jk ) = zftv(ji,jj ,jk ) - ( zah * zdyt + (zah_slp - zaei_slp) * zdzt ) * zbv * ze2vr ztfw(ji,jj+jp,jk+kp) = ztfw(ji,jj+jp,jk+kp) - ( zah_slp + zaei_slp ) * zdyt * zbv * ze3wr END DO END DO END DO END DO ! ELSE ! DO ip = 0, 1 !== Horizontal & vertical fluxes DO kp = 0, 1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze1ur = r1_e1u(ji,jj) zdxt = zdit(ji,jj,jk) * ze1ur ze3wr = 1._wp / e3w_n(ji+ip,jj,jk+kp) zdzt = zdkt3d(ji+ip,jj,kp) * ze3wr zslope_skew = triadi_g(ji+ip,jj,jk,1-ip,kp) zslope_iso = triadi(ji+ip,jj,jk,1-ip,kp) ! zbu = 0.25_wp * e1e2u(ji,jj) * e3u_n(ji,jj,jk) ! ln_botmix_triad is .F. mask zah for bottom half cells zah = pahu(ji,jj,jk) * umask(ji,jj,jk+kp) ! pahu(ji+ip,jj,jk) ===>> ???? zah_slp = zah * zslope_iso IF( ln_ldfeiv ) zaei_slp = aeiu(ji,jj,jk) * zslope_skew ! aeit(ji+ip,jj,jk)*zslope_skew zftu(ji ,jj,jk ) = zftu(ji ,jj,jk ) - ( zah * zdxt + (zah_slp - zaei_slp) * zdzt ) * zbu * ze1ur ztfw(ji+ip,jj,jk+kp) = ztfw(ji+ip,jj,jk+kp) - (zah_slp + zaei_slp) * zdxt * zbu * ze3wr END DO END DO END DO END DO ! DO jp = 0, 1 DO kp = 0, 1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ze2vr = r1_e2v(ji,jj) zdyt = zdjt(ji,jj,jk) * ze2vr ze3wr = 1._wp / e3w_n(ji,jj+jp,jk+kp) zdzt = zdkt3d(ji,jj+jp,kp) * ze3wr zslope_skew = triadj_g(ji,jj+jp,jk,1-jp,kp) zslope_iso = triadj(ji,jj+jp,jk,1-jp,kp) zbv = 0.25_wp * e1e2v(ji,jj) * e3v_n(ji,jj,jk) ! ln_botmix_triad is .F. mask zah for bottom half cells zah = pahv(ji,jj,jk) * vmask(ji,jj,jk+kp) ! pahv(ji,jj+jp,jk) ???? zah_slp = zah * zslope_iso IF( ln_ldfeiv ) zaei_slp = aeiv(ji,jj,jk) * zslope_skew ! aeit(ji,jj+jp,jk)*zslope_skew zftv(ji,jj,jk) = zftv(ji,jj,jk) - ( zah * zdyt + (zah_slp - zaei_slp) * zdzt ) * zbv * ze2vr ztfw(ji,jj+jp,jk+kp) = ztfw(ji,jj+jp,jk+kp) - (zah_slp + zaei_slp) * zdyt * zbv * ze3wr END DO END DO END DO END DO ENDIF ! !== horizontal divergence and add to the general trend ==! DO jj = 2 , jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + zsign * ( zftu(ji-1,jj,jk) - zftu(ji,jj,jk) & & + zftv(ji,jj-1,jk) - zftv(ji,jj,jk) ) & & / ( e1e2t(ji,jj) * e3t_n(ji,jj,jk) ) END DO END DO ! END DO ! ! !== add the vertical 33 flux ==! IF( ln_traldf_lap ) THEN ! laplacian case: eddy coef = ah_wslp2 - akz DO jk = 2, jpkm1 DO jj = 1, jpjm1 DO ji = fs_2, fs_jpim1 ztfw(ji,jj,jk) = ztfw(ji,jj,jk) - e1e2t(ji,jj) / e3w_n(ji,jj,jk) * tmask(ji,jj,jk) & & * ( ah_wslp2(ji,jj,jk) - akz(ji,jj,jk) ) & & * ( ptb(ji,jj,jk-1,jn) - ptb(ji,jj,jk,jn) ) END DO END DO END DO ELSE ! bilaplacian SELECT CASE( kpass ) CASE( 1 ) ! 1st pass : eddy coef = ah_wslp2 DO jk = 2, jpkm1 DO jj = 1, jpjm1 DO ji = fs_2, fs_jpim1 ztfw(ji,jj,jk) = ztfw(ji,jj,jk) - e1e2t(ji,jj) / e3w_n(ji,jj,jk) * tmask(ji,jj,jk) & & * ah_wslp2(ji,jj,jk) * ( ptb(ji,jj,jk-1,jn) - ptb(ji,jj,jk,jn) ) END DO END DO END DO CASE( 2 ) ! 2nd pass : eddy flux = ah_wslp2 and akz applied on ptb and ptbb gradients, resp. DO jk = 2, jpkm1 DO jj = 1, jpjm1 DO ji = fs_2, fs_jpim1 ztfw(ji,jj,jk) = ztfw(ji,jj,jk) - e1e2t(ji,jj) / e3w_n(ji,jj,jk) * tmask(ji,jj,jk) & & * ( ah_wslp2(ji,jj,jk) * ( ptb (ji,jj,jk-1,jn) - ptb (ji,jj,jk,jn) ) & & + akz (ji,jj,jk) * ( ptbb(ji,jj,jk-1,jn) - ptbb(ji,jj,jk,jn) ) ) END DO END DO END DO END SELECT ENDIF ! DO jk = 1, jpkm1 !== Divergence of vertical fluxes added to pta ==! DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + zsign * ( ztfw(ji,jj,jk+1) - ztfw(ji,jj,jk) ) & & / ( e1e2t(ji,jj) * e3t_n(ji,jj,jk) ) END DO END DO END DO ! IF( ( kpass == 1 .AND. ln_traldf_lap ) .OR. & !== first pass only ( laplacian) ==! ( kpass == 2 .AND. ln_traldf_blp ) ) THEN !== 2nd pass (bilaplacian) ==! ! ! ! "Poleward" diffusive heat or salt transports (T-S case only) IF( l_ptr ) CALL dia_ptr_hst( jn, 'ldf', zftv(:,:,:) ) ! ! Diffusive heat transports IF( l_hst ) CALL dia_ar5_hst( jn, 'ldf', zftu(:,:,:), zftv(:,:,:) ) ! ENDIF !== end pass selection ==! ! ! ! =============== END DO ! end tracer loop ! ! =============== END SUBROUTINE tra_ldf_triad !!============================================================================== END MODULE traldf_triad