MODULE trazdf_imp !!====================================================================== !! *** MODULE trazdf_imp *** !! Ocean tracers: vertical component of the tracer mixing trend !!====================================================================== !! History : OPA ! 1990-10 (B. Blanke) Original code !! 7.0 ! 1991-11 (G. Madec) !! ! 1992-06 (M. Imbard) correction on tracer trend loops !! ! 1996-01 (G. Madec) statement function for e3 !! ! 1997-05 (G. Madec) vertical component of isopycnal !! ! 1997-07 (G. Madec) geopotential diffusion in s-coord !! ! 2000-08 (G. Madec) double diffusive mixing !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module !! 2.0 ! 2006-11 (G. Madec) New step reorganisation !! 3.2 ! 2009-03 (G. Madec) heat and salt content trends !! 3.3 ! 2010-06 (C. Ethe, G. Madec) Merge TRA-TRC !! - ! 2011-02 (A. Coward, C. Ethe, G. Madec) improvment of surface boundary condition !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_zdf_imp : Update the tracer trend with the diagonal vertical !! part of the mixing tensor. !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers variables USE dom_oce ! ocean space and time domain variables USE zdf_oce ! ocean vertical physics variables USE trc_oce ! share passive tracers/ocean variables USE domvvl ! variable volume USE ldftra_oce ! ocean active tracers: lateral physics USE ldftra ! lateral mixing type USE ldfslp ! lateral physics: slope of diffusion USE zdfddm ! ocean vertical physics: double diffusion USE traldf_iso_grif ! active tracers: Griffies operator USE in_out_manager ! I/O manager USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_mpp ! MPP library USE wrk_nemo ! Memory Allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC tra_zdf_imp ! routine called by step.F90 REAL(wp) :: r_vvl ! variable volume indicator, =1 if lk_vvl=T, =0 otherwise !! * Substitutions # include "domzgr_substitute.h90" # include "ldftra_substitute.h90" # include "zdfddm_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_zdf_imp( kt, kit000, cdtype, p2dt, ptb, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_zdf_imp *** !! !! ** Purpose : Compute the after tracer through a implicit computation !! of the vertical tracer diffusion (including the vertical component !! of lateral mixing (only for 2nd order operator, for fourth order !! it is already computed and add to the general trend in traldf) !! !! ** Method : The vertical diffusion of the tracer t is given by: !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) !! It is computed using a backward time scheme (t=ta). !! If lk_zdfddm=T, use avs for salinity or for passive tracers !! Surface and bottom boundary conditions: no diffusive flux on !! both tracers (bottom, applied through the masked field avt). !! If iso-neutral mixing, add to avt the contribution due to lateral mixing. !! !! ** Action : - pta becomes the after tracer !!--------------------------------------------------------------------- USE oce , ONLY: zwd => ua , zws => va ! (ua,va) used as 3D 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( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step 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) :: zrhs, ze3tb, ze3tn, ze3ta ! local scalars REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwt !!--------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_zdf_imp') ! CALL wrk_alloc( jpi, jpj, jpk, zwi, zwt ) ! IF( kt == kit000 ) THEN IF(lwp)WRITE(numout,*) IF(lwp)WRITE(numout,*) 'tra_zdf_imp : implicit vertical mixing on ', cdtype IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' ! IF( lk_vvl ) THEN ; r_vvl = 1._wp ! Variable volume indicator ELSE ; r_vvl = 0._wp ENDIF ENDIF ! ! ! ============= ! DO jn = 1, kjpt ! tracer loop ! ! ! ============= ! ! ! Matrix construction ! -------------------- ! Build matrix if temperature or salinity (only in double diffusion case) or first passive tracer ! IF( ( cdtype == 'TRA' .AND. ( jn == jp_tem .OR. ( jn == jp_sal .AND. lk_zdfddm ) ) ) .OR. & & ( cdtype == 'TRC' .AND. jn == 1 ) ) THEN ! ! vertical mixing coef.: avt for temperature, avs for salinity and passive tracers IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN ; zwt(:,:,2:jpk) = avt (:,:,2:jpk) ELSE ; zwt(:,:,2:jpk) = fsavs(:,:,2:jpk) ENDIF DO jj=1, jpj DO ji=1, jpi zwt(ji,jj,1) = 0._wp END DO END DO ! #if defined key_ldfslp ! isoneutral diffusion: add the contribution IF( ln_traldf_grif ) THEN ! Griffies isoneutral diff DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwt(ji,jj,jk) = zwt(ji,jj,jk) + ah_wslp2(ji,jj,jk) END DO END DO END DO ELSE IF( l_traldf_rot ) THEN ! standard isoneutral diff DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwt(ji,jj,jk) = zwt(ji,jj,jk) + fsahtw(ji,jj,jk) & & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) END DO END DO END DO ENDIF #endif ! Diagonal, lower (i), upper (s) (including the bottom boundary condition since avt is masked) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3ta = ( 1. - r_vvl ) + r_vvl * fse3t_a(ji,jj,jk) ! after scale factor at T-point ze3tn = r_vvl + ( 1. - r_vvl ) * fse3t_n(ji,jj,jk) ! now scale factor at T-point zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) END DO END DO END DO ! !! Matrix inversion from the first level !!---------------------------------------------------------------------- ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular matrix. ! The 3 diagonal terms are in 3d arrays: zwd, zws, zwi. ! Suffices i,s and d indicate "inferior" (below diagonal), diagonal ! and "superior" (above diagonal) components of the tridiagonal system. ! The solution will be in the 4d array pta. ! The 3d array zwt is used as a work space array. ! En route to the solution pta is used a to evaluate the rhs and then ! used as a work space array: its value is modified. ! ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) ! done once for all passive tracers (so included in the IF instruction) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwt(ji,jj,1) = zwd(ji,jj,1) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwt(ji,jj,jk-1) END DO END DO END DO ! END IF ! ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ze3tb = ( 1. - r_vvl ) + r_vvl * fse3t_b(ji,jj,1) ze3tn = ( 1. - r_vvl ) + r_vvl * fse3t(ji,jj,1) pta(ji,jj,1,jn) = ze3tb * ptb(ji,jj,1,jn) & & + p2dt(1) * ze3tn * pta(ji,jj,1,jn) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ze3tb = ( 1. - r_vvl ) + r_vvl * fse3t_b(ji,jj,jk) ze3tn = ( 1. - r_vvl ) + r_vvl * fse3t (ji,jj,jk) zrhs = ze3tb * ptb(ji,jj,jk,jn) + p2dt(jk) * ze3tn * pta(ji,jj,jk,jn) ! zrhs=right hand side pta(ji,jj,jk,jn) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * pta(ji,jj,jk-1,jn) END DO END DO END DO ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk (result is the after tracer) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pta(ji,jj,jpkm1,jn) = pta(ji,jj,jpkm1,jn) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 1, -1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pta(ji,jj,jk,jn) = ( pta(ji,jj,jk,jn) - zws(ji,jj,jk) * pta(ji,jj,jk+1,jn) ) & & / zwt(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! ! ================= ! END DO ! end tracer loop ! ! ! ================= ! ! CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwt ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_zdf_imp') ! END SUBROUTINE tra_zdf_imp !!============================================================================== END MODULE trazdf_imp