MODULE traadv_fct !!============================================================================== !! *** MODULE traadv_fct *** !! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method) !!============================================================================== !! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90) !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme !! with sub-time-stepping in the vertical direction !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm !! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection !!---------------------------------------------------------------------- USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE trc_oce ! share passive tracers/Ocean variables USE trd_oce ! trends: ocean variables USE trdtra ! tracers trends USE diaptr ! poleward transport diagnostics USE diaar5 ! AR5 diagnostics USE phycst , ONLY : rau0_rcp USE zdf_oce , ONLY : ln_zad_Aimp ! USE in_out_manager ! I/O manager USE iom ! USE lib_mpp ! MPP library USE lbclnk ! ocean lateral boundary condition (or mpp link) USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC tra_adv_fct ! called by traadv.F90 PUBLIC interp_4th_cpt ! called by traadv_cen.F90 LOGICAL :: l_trd ! flag to compute trends LOGICAL :: l_ptr ! flag to compute poleward transport LOGICAL :: l_hst ! flag to compute heat/salt transport REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 ! ! tridiag solver associated indices: INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition !! * 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_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_fct *** !! !! ** Purpose : Compute the now trend due to total advection of tracers !! and add it to the general trend of tracer equations !! !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction !! (choice through the value of kn_fct) !! - on the vertical the 4th order is a compact scheme !! - corrected flux (monotonic correction) !! !! ** Action : - update pta with the now advective tracer trends !! - send trends to trdtra module for further diagnostics (l_trdtra=T) !! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T) !!---------------------------------------------------------------------- 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 ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! 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) :: ztra ! local scalar REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - - REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - - REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection !!---------------------------------------------------------------------- ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' ENDIF ! l_trd = .FALSE. ! set local switches l_hst = .FALSE. l_ptr = .FALSE. ll_zAimp = .FALSE. IF( ( cdtype =='TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. 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. ! IF( l_trd .OR. l_hst ) THEN ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp ENDIF ! IF( l_ptr ) THEN ALLOCATE( zptry(jpi,jpj,jpk) ) zptry(:,:,:) = 0._wp ENDIF ! ! surface & bottom value : flux set to zero one for all zwz(:,:, 1 ) = 0._wp zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp ! zwi(:,:,:) = 0._wp ! ! If adaptive vertical advection, check if it is needed on this PE at this time IF( ln_zad_Aimp ) THEN IF( MAXVAL( ABS( wi(:,:,:) ) ) > 0._wp ) ll_zAimp = .TRUE. END IF ! If active adaptive vertical advection, build tridiagonal matrix IF( ll_zAimp ) THEN ALLOCATE(zwdia(jpi,jpj,jpk), zwinf(jpi,jpj,jpk),zwsup(jpi,jpj,jpk)) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. (ensure same order of calculation as below if wi=0.) zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk ) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) / e3t_a(ji,jj,jk) zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t_a(ji,jj,jk) zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t_a(ji,jj,jk) END DO END DO END DO END IF ! DO jn = 1, kjpt !== loop over the tracers ==! ! ! !== upstream advection with initial mass fluxes & intermediate update ==! ! !* upstream tracer flux in the i and j direction DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! upstream scheme zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) END DO END DO END DO ! !* upstream tracer flux in the k direction *! DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) DO jj = 1, jpj DO ji = 1, jpi zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk) END DO END DO END DO IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface END DO END DO ELSE ! no cavities: only at the ocean surface zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ENDIF ENDIF ! DO jk = 1, jpkm1 !* trend and after field with monotonic scheme DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! total intermediate advective trends ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) ! ! update and guess with monotonic sheme pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk) zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO IF ( ll_zAimp ) THEN CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 ) ! ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ; DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) END DO END DO END DO ! END IF ! IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:) ! ! !== anti-diffusive flux : high order minus low order ==! ! SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes ! CASE( 2 ) !- 2nd order centered DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk) END DO END DO END DO ! CASE( 4 ) !- 4th order centered zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero zltv(:,:,jpk) = 0._wp DO jk = 1, jpkm1 ! Laplacian DO jj = 1, jpjm1 ! 1st derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) END DO END DO DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6 DO ji = fs_2, fs_jpim1 ! vector opt. zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 END DO END DO END DO CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1. , zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) ! DO jk = 1, jpkm1 ! Horizontal advective fluxes DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ! ! C4 minus upstream advective fluxes zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk) END DO END DO END DO ! CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero ztv(:,:,jpk) = 0._wp DO jk = 1, jpkm1 ! 1st derivative (gradient) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) END DO END DO END DO CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1. , ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn) ! DO jk = 1, jpkm1 ! Horizontal advective fluxes DO jj = 2, jpjm1 DO ji = 2, fs_jpim1 ! vector opt. zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2) zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ! ! C4 interpolation of T at u- & v-points (x2) zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) ) zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) ) ! ! C4 minus upstream advective fluxes zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) END DO END DO END DO ! END SELECT ! SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) ! CASE( 2 ) !- 2nd order centered DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) END DO END DO END DO ! CASE( 4 ) !- 4th order COMPACT CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) END DO END DO END DO ! END SELECT IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked ENDIF ! IF ( ll_zAimp ) THEN DO jk = 1, jpkm1 !* trend and after field with monotonic scheme DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! total intermediate advective trends ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 ) ! DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk) END DO END DO END DO END IF ! CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1., zwx, 'U', -1. , zwy, 'V', -1., zwz, 'W', 1. ) ! ! !== monotonicity algorithm ==! ! CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) ! ! !== final trend with corrected fluxes ==! ! DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! IF ( ll_zAimp ) THEN ! ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) END DO END DO END DO END IF ! IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! ! IF( l_trd ) THEN ! trend diagnostics CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) ENDIF ! ! heat/salt transport IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) ) ! ENDIF IF( l_ptr ) THEN ! "Poleward" transports zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) ENDIF ! END DO ! end of tracer loop ! IF ( ll_zAimp ) THEN DEALLOCATE( zwdia, zwinf, zwsup ) ENDIF IF( l_trd .OR. l_hst ) THEN DEALLOCATE( ztrdx, ztrdy, ztrdz ) ENDIF IF( l_ptr ) THEN DEALLOCATE( zptry ) ENDIF ! END SUBROUTINE tra_adv_fct SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt ) !!--------------------------------------------------------------------- !! *** ROUTINE nonosc *** !! !! ** Purpose : compute monotonic tracer fluxes from the upstream !! scheme and the before field by a nonoscillatory algorithm !! !! ** Method : ... ??? !! warning : pbef and paft must be masked, but the boundaries !! conditions on the fluxes are not necessary zalezak (1979) !! drange (1995) multi-dimensional forward-in-time and upstream- !! in-space based differencing for fluid !!---------------------------------------------------------------------- REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikm1 ! local integer REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo, zbup, zbdo !!---------------------------------------------------------------------- ! zbig = 1.e+40_wp zrtrn = 1.e-15_wp zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp ! Search local extrema ! -------------------- ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & & paft * tmask - zbig * ( 1._wp - tmask ) ) zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & & paft * tmask + zbig * ( 1._wp - tmask ) ) DO jk = 1, jpkm1 ikm1 = MAX(jk-1,1) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! search maximum in neighbourhood zup = MAX( zbup(ji ,jj ,jk ), & & zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), & & zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), & & zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) ) ! search minimum in neighbourhood zdo = MIN( zbdo(ji ,jj ,jk ), & & zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), & & zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), & & zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) ) ! positive part of the flux zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) ! negative part of the flux zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) ! up & down beta terms zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt END DO END DO END DO CALL lbc_lnk_multi( 'traadv_fct', zbetup, 'T', 1. , zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) ! 3. monotonic flux in the i & j direction (paa & pbb) ! ---------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) ) paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu ) zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) ) pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv ) ! monotonic flux in the k direction, i.e. pcc ! ------------------------------------------- za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) ) zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) ) zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) ) pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) END DO END DO END DO CALL lbc_lnk_multi( 'traadv_fct', paa, 'U', -1. , pbb, 'V', -1. ) ! lateral boundary condition (changed sign) ! END SUBROUTINE nonosc SUBROUTINE interp_4th_cpt_org( pt_in, pt_out ) !!---------------------------------------------------------------------- !! *** ROUTINE interp_4th_cpt_org *** !! !! ** Purpose : Compute the interpolation of tracer at w-point !! !! ** Method : 4th order compact interpolation !!---------------------------------------------------------------------- REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts ! INTEGER :: ji, jj, jk ! dummy loop integers REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt !!---------------------------------------------------------------------- DO jk = 3, jpkm1 !== build the three diagonal matrix ==! DO jj = 1, jpj DO ji = 1, jpi zwd (ji,jj,jk) = 4._wp zwi (ji,jj,jk) = 1._wp zws (ji,jj,jk) = 1._wp zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) ! IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom zwd (ji,jj,jk) = 1._wp zwi (ji,jj,jk) = 0._wp zws (ji,jj,jk) = 0._wp zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) ENDIF END DO END DO END DO ! jk = 2 ! Switch to second order centered at top DO jj = 1, jpj DO ji = 1, jpi zwd (ji,jj,jk) = 1._wp zwi (ji,jj,jk) = 0._wp zws (ji,jj,jk) = 0._wp zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) END DO END DO ! ! !== tridiagonal solve ==! DO jj = 1, jpj ! first recurrence DO ji = 1, jpi zwt(ji,jj,2) = zwd(ji,jj,2) END DO END DO DO jk = 3, jpkm1 DO jj = 1, jpj DO ji = 1, jpi 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 ! DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 DO ji = 1, jpi pt_out(ji,jj,2) = zwrm(ji,jj,2) END DO END DO DO jk = 3, jpkm1 DO jj = 1, jpj DO ji = 1, jpi pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) END DO END DO END DO DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk DO ji = 1, jpi pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 2, -1 DO jj = 1, jpj DO ji = 1, jpi pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) END DO END DO END DO ! END SUBROUTINE interp_4th_cpt_org SUBROUTINE interp_4th_cpt( pt_in, pt_out ) !!---------------------------------------------------------------------- !! *** ROUTINE interp_4th_cpt *** !! !! ** Purpose : Compute the interpolation of tracer at w-point !! !! ** Method : 4th order compact interpolation !!---------------------------------------------------------------------- REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point ! INTEGER :: ji, jj, jk ! dummy loop integers INTEGER :: ikt, ikb ! local integers REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt !!---------------------------------------------------------------------- ! ! !== build the three diagonal matrix & the RHS ==! ! DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS & * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) ) END DO END DO END DO ! !!gm ! SELECT CASE( kbc ) !* boundary condition ! CASE( np_NH ) ! Neumann homogeneous at top & bottom ! CASE( np_CEN2 ) ! 2nd order centered at top & bottom ! END SELECT !!gm ! IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp END IF ! DO jj = 2, jpjm1 ! 2nd order centered at top & bottom DO ji = fs_2, fs_jpim1 ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point ! zwd (ji,jj,ikt) = 1._wp ! top zwi (ji,jj,ikt) = 0._wp zws (ji,jj,ikt) = 0._wp zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) ) ! zwd (ji,jj,ikb) = 1._wp ! bottom zwi (ji,jj,ikb) = 0._wp zws (ji,jj,ikb) = 0._wp zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) ) END DO END DO ! ! !== tridiagonal solver ==! ! DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 DO ji = fs_2, fs_jpim1 zwt(ji,jj,2) = zwd(ji,jj,2) END DO END DO DO jk = 3, 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 ! DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,2) = zwrm(ji,jj,2) END DO END DO DO jk = 3, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) END DO END DO END DO DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 2, -1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) END DO END DO END DO ! END SUBROUTINE interp_4th_cpt SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev ) !!---------------------------------------------------------------------- !! *** ROUTINE tridia_solver *** !! !! ** Purpose : solve a symmetric 3diagonal system !! !! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk ) !! !! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 ) !! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 ) !! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 ) !! ( ... )( ... ) ( ... ) !! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k ) !! !! M is decomposed in the product of an upper and lower triangular matrix. !! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL !! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal). !! The solution is pta. !! The 3d array zwt is used as a work space array. !!---------------------------------------------------------------------- REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev) INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level ! ! =0 pt at t-level INTEGER :: ji, jj, jk ! dummy loop integers INTEGER :: kstart ! local indices REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array !!---------------------------------------------------------------------- ! kstart = 1 + klev ! DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 DO ji = fs_2, fs_jpim1 zwt(ji,jj,kstart) = pD(ji,jj,kstart) END DO END DO DO jk = kstart+1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1) END DO END DO END DO ! DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart) END DO END DO DO jk = kstart+1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) END DO END DO END DO DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, kstart, -1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) END DO END DO END DO ! END SUBROUTINE tridia_solver !!====================================================================== END MODULE traadv_fct