[5770] | 1 | MODULE traadv_fct |
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[3] | 2 | !!============================================================================== |
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[5770] | 3 | !! *** MODULE traadv_fct *** |
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| 4 | !! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method) |
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[3] | 5 | !!============================================================================== |
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[5770] | 6 | !! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90) |
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[503] | 7 | !!---------------------------------------------------------------------- |
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[3] | 8 | |
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| 9 | !!---------------------------------------------------------------------- |
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[5770] | 10 | !! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme |
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| 11 | !! with sub-time-stepping in the vertical direction |
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| 12 | !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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| 13 | !! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection |
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[3] | 14 | !!---------------------------------------------------------------------- |
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[3625] | 15 | USE oce ! ocean dynamics and active tracers |
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| 16 | USE dom_oce ! ocean space and time domain |
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[4990] | 17 | USE trc_oce ! share passive tracers/Ocean variables |
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| 18 | USE trd_oce ! trends: ocean variables |
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[3625] | 19 | USE trdtra ! tracers trends |
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[4990] | 20 | USE diaptr ! poleward transport diagnostics |
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[7646] | 21 | USE diaar5 ! AR5 diagnostics |
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[9019] | 22 | USE phycst , ONLY : rau0_rcp |
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[4990] | 23 | ! |
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[5770] | 24 | USE in_out_manager ! I/O manager |
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[9019] | 25 | USE iom ! |
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[3625] | 26 | USE lib_mpp ! MPP library |
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| 27 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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[5770] | 28 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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[3625] | 29 | USE timing ! Timing |
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[3] | 30 | |
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| 31 | IMPLICIT NONE |
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| 32 | PRIVATE |
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| 33 | |
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[9019] | 34 | PUBLIC tra_adv_fct ! called by traadv.F90 |
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| 35 | PUBLIC interp_4th_cpt ! called by traadv_cen.F90 |
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[3] | 36 | |
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[5770] | 37 | LOGICAL :: l_trd ! flag to compute trends |
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[7646] | 38 | LOGICAL :: l_ptr ! flag to compute poleward transport |
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| 39 | LOGICAL :: l_hst ! flag to compute heat/salt transport |
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[5770] | 40 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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[2528] | 41 | |
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[7646] | 42 | ! ! tridiag solver associated indices: |
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| 43 | INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition |
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| 44 | INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition |
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| 45 | |
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[3] | 46 | !! * Substitutions |
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| 47 | # include "vectopt_loop_substitute.h90" |
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| 48 | !!---------------------------------------------------------------------- |
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[9019] | 49 | !! NEMO/OPA 4.0 , NEMO Consortium (2017) |
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[1152] | 50 | !! $Id$ |
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[2528] | 51 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 52 | !!---------------------------------------------------------------------- |
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| 53 | CONTAINS |
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| 54 | |
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[5770] | 55 | SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & |
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| 56 | & ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v ) |
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[3] | 57 | !!---------------------------------------------------------------------- |
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[5770] | 58 | !! *** ROUTINE tra_adv_fct *** |
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[3] | 59 | !! |
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[6140] | 60 | !! ** Purpose : Compute the now trend due to total advection of tracers |
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| 61 | !! and add it to the general trend of tracer equations |
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[3] | 62 | !! |
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[5770] | 63 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
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| 64 | !! (choice through the value of kn_fct) |
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[6140] | 65 | !! - on the vertical the 4th order is a compact scheme |
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[5770] | 66 | !! - corrected flux (monotonic correction) |
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[3] | 67 | !! |
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[6140] | 68 | !! ** Action : - update pta with the now advective tracer trends |
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[9019] | 69 | !! - send trends to trdtra module for further diagnostics (l_trdtra=T) |
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[6140] | 70 | !! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T) |
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[503] | 71 | !!---------------------------------------------------------------------- |
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[2528] | 72 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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[3294] | 73 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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[2528] | 74 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 75 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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[5770] | 76 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
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| 77 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
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[6140] | 78 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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[2528] | 79 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components |
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| 80 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields |
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| 81 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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[2715] | 82 | ! |
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[5770] | 83 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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[6140] | 84 | REAL(wp) :: ztra ! local scalar |
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[5770] | 85 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - - |
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| 86 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - - |
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[9019] | 87 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw |
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| 88 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry |
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[3] | 89 | !!---------------------------------------------------------------------- |
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[3294] | 90 | ! |
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[9019] | 91 | IF( ln_timing ) CALL timing_start('tra_adv_fct') |
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[3294] | 92 | ! |
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| 93 | IF( kt == kit000 ) THEN |
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[2528] | 94 | IF(lwp) WRITE(numout,*) |
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[5770] | 95 | IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype |
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[2528] | 96 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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[3] | 97 | ENDIF |
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[2528] | 98 | ! |
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[9019] | 99 | l_trd = .FALSE. ! set local switches |
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[7646] | 100 | l_hst = .FALSE. |
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| 101 | l_ptr = .FALSE. |
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[9019] | 102 | IF( ( cdtype =='TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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| 103 | IF( cdtype =='TRA' .AND. ln_diaptr ) l_ptr = .TRUE. |
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| 104 | IF( cdtype =='TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & |
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| 105 | & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. |
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[5770] | 106 | ! |
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[7646] | 107 | IF( l_trd .OR. l_hst ) THEN |
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[9019] | 108 | ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) |
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[7753] | 109 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
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[3294] | 110 | ENDIF |
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[2528] | 111 | ! |
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[7646] | 112 | IF( l_ptr ) THEN |
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[9019] | 113 | ALLOCATE( zptry(jpi,jpj,jpk) ) |
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[7753] | 114 | zptry(:,:,:) = 0._wp |
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[7646] | 115 | ENDIF |
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[6140] | 116 | ! ! surface & bottom value : flux set to zero one for all |
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[7753] | 117 | zwz(:,:, 1 ) = 0._wp |
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| 118 | zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp |
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[2528] | 119 | ! |
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[7753] | 120 | zwi(:,:,:) = 0._wp |
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| 121 | ! |
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[6140] | 122 | DO jn = 1, kjpt !== loop over the tracers ==! |
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[5770] | 123 | ! |
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| 124 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
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| 125 | ! !* upstream tracer flux in the i and j direction |
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[2528] | 126 | DO jk = 1, jpkm1 |
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| 127 | DO jj = 1, jpjm1 |
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| 128 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 129 | ! upstream scheme |
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| 130 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
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| 131 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
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| 132 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
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| 133 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
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| 134 | zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) |
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| 135 | zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) |
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| 136 | END DO |
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[3] | 137 | END DO |
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| 138 | END DO |
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[5770] | 139 | ! !* upstream tracer flux in the k direction *! |
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[6140] | 140 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
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[4990] | 141 | DO jj = 1, jpj |
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| 142 | DO ji = 1, jpi |
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[2528] | 143 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
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| 144 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
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[5120] | 145 | 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) |
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[2528] | 146 | END DO |
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[3] | 147 | END DO |
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| 148 | END DO |
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[6140] | 149 | IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
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[5770] | 150 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
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[5120] | 151 | DO jj = 1, jpj |
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| 152 | DO ji = 1, jpi |
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| 153 | zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface |
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| 154 | END DO |
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| 155 | END DO |
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[5770] | 156 | ELSE ! no cavities: only at the ocean surface |
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[7753] | 157 | zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) |
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[5770] | 158 | ENDIF |
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[5120] | 159 | ENDIF |
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[5770] | 160 | ! |
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| 161 | DO jk = 1, jpkm1 !* trend and after field with monotonic scheme |
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[216] | 162 | DO jj = 2, jpjm1 |
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| 163 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6691] | 164 | ! ! total intermediate advective trends |
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[5770] | 165 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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| 166 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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[6691] | 167 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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| 168 | ! ! update and guess with monotonic sheme |
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| 169 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk) |
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| 170 | 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) |
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[216] | 171 | END DO |
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| 172 | END DO |
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| 173 | END DO |
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[5770] | 174 | CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign) |
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| 175 | ! |
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[7646] | 176 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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[7753] | 177 | ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
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[2528] | 178 | END IF |
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[5770] | 179 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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[9019] | 180 | IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:) |
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[5770] | 181 | ! |
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| 182 | ! !== anti-diffusive flux : high order minus low order ==! |
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| 183 | ! |
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[6140] | 184 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
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[5770] | 185 | ! |
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[6140] | 186 | CASE( 2 ) !- 2nd order centered |
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[5770] | 187 | DO jk = 1, jpkm1 |
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| 188 | DO jj = 1, jpjm1 |
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| 189 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 190 | 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) |
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| 191 | 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) |
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| 192 | END DO |
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[503] | 193 | END DO |
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| 194 | END DO |
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[5770] | 195 | ! |
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[6140] | 196 | CASE( 4 ) !- 4th order centered |
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[7753] | 197 | zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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| 198 | zltv(:,:,jpk) = 0._wp |
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[6140] | 199 | DO jk = 1, jpkm1 ! Laplacian |
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| 200 | DO jj = 1, jpjm1 ! 1st derivative (gradient) |
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[5770] | 201 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 202 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
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| 203 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
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| 204 | END DO |
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[503] | 205 | END DO |
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[6140] | 206 | DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6 |
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[5770] | 207 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 208 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
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| 209 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
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| 210 | END DO |
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| 211 | END DO |
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[503] | 212 | END DO |
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[5770] | 213 | CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 214 | ! |
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[6140] | 215 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
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[5770] | 216 | DO jj = 1, jpjm1 |
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| 217 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 218 | zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points |
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| 219 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
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| 220 | ! ! C4 minus upstream advective fluxes |
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| 221 | 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) |
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| 222 | 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) |
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| 223 | END DO |
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[5120] | 224 | END DO |
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[5770] | 225 | END DO |
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| 226 | ! |
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[6140] | 227 | CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested |
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[7753] | 228 | ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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| 229 | ztv(:,:,jpk) = 0._wp |
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[6140] | 230 | DO jk = 1, jpkm1 ! 1st derivative (gradient) |
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| 231 | DO jj = 1, jpjm1 |
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[5770] | 232 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 233 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
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| 234 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
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| 235 | END DO |
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| 236 | END DO |
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[5120] | 237 | END DO |
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[5770] | 238 | CALL lbc_lnk( ztu, 'U', -1. ) ; CALL lbc_lnk( ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 239 | ! |
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[6140] | 240 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
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[5770] | 241 | DO jj = 2, jpjm1 |
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| 242 | DO ji = 2, fs_jpim1 ! vector opt. |
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| 243 | zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2) |
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| 244 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
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| 245 | ! ! C4 interpolation of T at u- & v-points (x2) |
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| 246 | zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) ) |
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| 247 | zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) ) |
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| 248 | ! ! C4 minus upstream advective fluxes |
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| 249 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) |
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| 250 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) |
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| 251 | END DO |
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| 252 | END DO |
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| 253 | END DO |
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| 254 | ! |
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| 255 | END SELECT |
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[6140] | 256 | ! |
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| 257 | SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) |
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[5770] | 258 | ! |
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[6140] | 259 | CASE( 2 ) !- 2nd order centered |
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[5770] | 260 | DO jk = 2, jpkm1 |
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| 261 | DO jj = 2, jpjm1 |
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| 262 | DO ji = fs_2, fs_jpim1 |
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[6140] | 263 | zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & |
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| 264 | & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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[5770] | 265 | END DO |
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| 266 | END DO |
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| 267 | END DO |
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| 268 | ! |
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[6140] | 269 | CASE( 4 ) !- 4th order COMPACT |
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| 270 | CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point |
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[5770] | 271 | DO jk = 2, jpkm1 |
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| 272 | DO jj = 2, jpjm1 |
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| 273 | DO ji = fs_2, fs_jpim1 |
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| 274 | zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | END DO |
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| 278 | ! |
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| 279 | END SELECT |
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[6140] | 280 | IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 |
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[7753] | 281 | zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
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[6140] | 282 | ENDIF |
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[5770] | 283 | ! |
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[2528] | 284 | CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions |
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| 285 | CALL lbc_lnk( zwz, 'W', 1. ) |
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[6140] | 286 | ! |
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[5770] | 287 | ! !== monotonicity algorithm ==! |
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| 288 | ! |
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[2528] | 289 | CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) |
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[6140] | 290 | ! |
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[5770] | 291 | ! !== final trend with corrected fluxes ==! |
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| 292 | ! |
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[216] | 293 | DO jk = 1, jpkm1 |
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| 294 | DO jj = 2, jpjm1 |
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[2528] | 295 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[5770] | 296 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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| 297 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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| 298 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) & |
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[6140] | 299 | & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) |
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[216] | 300 | END DO |
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| 301 | END DO |
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| 302 | END DO |
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[5770] | 303 | ! |
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[9019] | 304 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport |
---|
| 305 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes |
---|
| 306 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes |
---|
| 307 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! |
---|
[5770] | 308 | ! |
---|
[9019] | 309 | IF( l_trd ) THEN ! trend diagnostics |
---|
| 310 | CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) |
---|
| 311 | CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) |
---|
| 312 | CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) |
---|
| 313 | ENDIF |
---|
| 314 | ! ! heat/salt transport |
---|
| 315 | IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) ) |
---|
[5770] | 316 | ! |
---|
[9019] | 317 | DEALLOCATE( ztrdx, ztrdy, ztrdz ) |
---|
| 318 | ENDIF |
---|
| 319 | IF( l_ptr ) THEN ! "Poleward" transports |
---|
| 320 | zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes |
---|
[7646] | 321 | CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) |
---|
[9019] | 322 | DEALLOCATE( zptry ) |
---|
[2528] | 323 | ENDIF |
---|
[503] | 324 | ! |
---|
[6140] | 325 | END DO ! end of tracer loop |
---|
[503] | 326 | ! |
---|
[9019] | 327 | IF( ln_timing ) CALL timing_stop('tra_adv_fct') |
---|
[2528] | 328 | ! |
---|
[5770] | 329 | END SUBROUTINE tra_adv_fct |
---|
[3] | 330 | |
---|
[5737] | 331 | |
---|
[2528] | 332 | SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt ) |
---|
[3] | 333 | !!--------------------------------------------------------------------- |
---|
| 334 | !! *** ROUTINE nonosc *** |
---|
| 335 | !! |
---|
| 336 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 337 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 338 | !! |
---|
| 339 | !! ** Method : ... ??? |
---|
| 340 | !! warning : pbef and paft must be masked, but the boundaries |
---|
| 341 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 342 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 343 | !! in-space based differencing for fluid |
---|
| 344 | !!---------------------------------------------------------------------- |
---|
[6140] | 345 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
---|
[2528] | 346 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field |
---|
| 347 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
---|
[2715] | 348 | ! |
---|
[4990] | 349 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 350 | INTEGER :: ikm1 ! local integer |
---|
[6140] | 351 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars |
---|
[2715] | 352 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
[9019] | 353 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo, zbup, zbdo |
---|
[3] | 354 | !!---------------------------------------------------------------------- |
---|
[3294] | 355 | ! |
---|
[9019] | 356 | IF( ln_timing ) CALL timing_start('nonosc') |
---|
[3294] | 357 | ! |
---|
[2715] | 358 | zbig = 1.e+40_wp |
---|
| 359 | zrtrn = 1.e-15_wp |
---|
[7753] | 360 | zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp |
---|
[785] | 361 | |
---|
[3] | 362 | ! Search local extrema |
---|
| 363 | ! -------------------- |
---|
[785] | 364 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
[4990] | 365 | zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & |
---|
| 366 | & paft * tmask - zbig * ( 1._wp - tmask ) ) |
---|
| 367 | zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & |
---|
| 368 | & paft * tmask + zbig * ( 1._wp - tmask ) ) |
---|
[785] | 369 | |
---|
[5120] | 370 | DO jk = 1, jpkm1 |
---|
| 371 | ikm1 = MAX(jk-1,1) |
---|
| 372 | DO jj = 2, jpjm1 |
---|
| 373 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 374 | |
---|
[785] | 375 | ! search maximum in neighbourhood |
---|
| 376 | zup = MAX( zbup(ji ,jj ,jk ), & |
---|
| 377 | & zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), & |
---|
| 378 | & zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), & |
---|
| 379 | & zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) ) |
---|
[3] | 380 | |
---|
[785] | 381 | ! search minimum in neighbourhood |
---|
| 382 | zdo = MIN( zbdo(ji ,jj ,jk ), & |
---|
| 383 | & zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), & |
---|
| 384 | & zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), & |
---|
| 385 | & zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) ) |
---|
[3] | 386 | |
---|
[785] | 387 | ! positive part of the flux |
---|
[3] | 388 | zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & |
---|
| 389 | & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & |
---|
| 390 | & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
---|
[785] | 391 | |
---|
| 392 | ! negative part of the flux |
---|
[3] | 393 | zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & |
---|
| 394 | & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & |
---|
| 395 | & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
---|
[785] | 396 | |
---|
[3] | 397 | ! up & down beta terms |
---|
[6140] | 398 | zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt |
---|
[785] | 399 | zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt |
---|
| 400 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt |
---|
[3] | 401 | END DO |
---|
| 402 | END DO |
---|
| 403 | END DO |
---|
[2528] | 404 | CALL lbc_lnk( zbetup, 'T', 1. ) ; CALL lbc_lnk( zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[3] | 405 | |
---|
[237] | 406 | ! 3. monotonic flux in the i & j direction (paa & pbb) |
---|
| 407 | ! ---------------------------------------- |
---|
[3] | 408 | DO jk = 1, jpkm1 |
---|
| 409 | DO jj = 2, jpjm1 |
---|
| 410 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 411 | zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) |
---|
| 412 | zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) |
---|
[785] | 413 | zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) ) |
---|
[4990] | 414 | paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
---|
[3] | 415 | |
---|
[4990] | 416 | zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) |
---|
| 417 | zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) |
---|
[785] | 418 | zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) ) |
---|
[4990] | 419 | pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
---|
[3] | 420 | |
---|
| 421 | ! monotonic flux in the k direction, i.e. pcc |
---|
| 422 | ! ------------------------------------------- |
---|
[785] | 423 | za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) ) |
---|
| 424 | zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) ) |
---|
| 425 | zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) ) |
---|
[4990] | 426 | pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) |
---|
[3] | 427 | END DO |
---|
| 428 | END DO |
---|
| 429 | END DO |
---|
[2528] | 430 | CALL lbc_lnk( paa, 'U', -1. ) ; CALL lbc_lnk( pbb, 'V', -1. ) ! lateral boundary condition (changed sign) |
---|
[503] | 431 | ! |
---|
[9019] | 432 | IF( ln_timing ) CALL timing_stop('nonosc') |
---|
[2715] | 433 | ! |
---|
[3] | 434 | END SUBROUTINE nonosc |
---|
| 435 | |
---|
[5770] | 436 | |
---|
[7646] | 437 | SUBROUTINE interp_4th_cpt_org( pt_in, pt_out ) |
---|
[5770] | 438 | !!---------------------------------------------------------------------- |
---|
[7646] | 439 | !! *** ROUTINE interp_4th_cpt_org *** |
---|
[5770] | 440 | !! |
---|
| 441 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
| 442 | !! |
---|
| 443 | !! ** Method : 4th order compact interpolation |
---|
| 444 | !!---------------------------------------------------------------------- |
---|
| 445 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields |
---|
| 446 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts |
---|
| 447 | ! |
---|
| 448 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 449 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
| 450 | !!---------------------------------------------------------------------- |
---|
| 451 | |
---|
| 452 | DO jk = 3, jpkm1 !== build the three diagonal matrix ==! |
---|
| 453 | DO jj = 1, jpj |
---|
| 454 | DO ji = 1, jpi |
---|
| 455 | zwd (ji,jj,jk) = 4._wp |
---|
| 456 | zwi (ji,jj,jk) = 1._wp |
---|
| 457 | zws (ji,jj,jk) = 1._wp |
---|
| 458 | zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 459 | ! |
---|
| 460 | IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom |
---|
| 461 | zwd (ji,jj,jk) = 1._wp |
---|
| 462 | zwi (ji,jj,jk) = 0._wp |
---|
| 463 | zws (ji,jj,jk) = 0._wp |
---|
| 464 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 465 | ENDIF |
---|
| 466 | END DO |
---|
| 467 | END DO |
---|
| 468 | END DO |
---|
| 469 | ! |
---|
[7646] | 470 | jk = 2 ! Switch to second order centered at top |
---|
| 471 | DO jj = 1, jpj |
---|
| 472 | DO ji = 1, jpi |
---|
[5770] | 473 | zwd (ji,jj,jk) = 1._wp |
---|
| 474 | zwi (ji,jj,jk) = 0._wp |
---|
| 475 | zws (ji,jj,jk) = 0._wp |
---|
| 476 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 477 | END DO |
---|
| 478 | END DO |
---|
| 479 | ! |
---|
| 480 | ! !== tridiagonal solve ==! |
---|
| 481 | DO jj = 1, jpj ! first recurrence |
---|
| 482 | DO ji = 1, jpi |
---|
| 483 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
| 484 | END DO |
---|
| 485 | END DO |
---|
| 486 | DO jk = 3, jpkm1 |
---|
| 487 | DO jj = 1, jpj |
---|
| 488 | DO ji = 1, jpi |
---|
| 489 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
| 490 | END DO |
---|
| 491 | END DO |
---|
| 492 | END DO |
---|
| 493 | ! |
---|
| 494 | DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
| 495 | DO ji = 1, jpi |
---|
| 496 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
| 497 | END DO |
---|
| 498 | END DO |
---|
| 499 | DO jk = 3, jpkm1 |
---|
| 500 | DO jj = 1, jpj |
---|
| 501 | DO ji = 1, jpi |
---|
| 502 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
| 503 | END DO |
---|
| 504 | END DO |
---|
| 505 | END DO |
---|
| 506 | |
---|
| 507 | DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
---|
| 508 | DO ji = 1, jpi |
---|
| 509 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
| 510 | END DO |
---|
| 511 | END DO |
---|
| 512 | DO jk = jpk-2, 2, -1 |
---|
| 513 | DO jj = 1, jpj |
---|
| 514 | DO ji = 1, jpi |
---|
| 515 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
| 516 | END DO |
---|
| 517 | END DO |
---|
| 518 | END DO |
---|
| 519 | ! |
---|
[7646] | 520 | END SUBROUTINE interp_4th_cpt_org |
---|
| 521 | |
---|
| 522 | |
---|
| 523 | SUBROUTINE interp_4th_cpt( pt_in, pt_out ) |
---|
| 524 | !!---------------------------------------------------------------------- |
---|
| 525 | !! *** ROUTINE interp_4th_cpt *** |
---|
| 526 | !! |
---|
| 527 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
| 528 | !! |
---|
| 529 | !! ** Method : 4th order compact interpolation |
---|
| 530 | !!---------------------------------------------------------------------- |
---|
| 531 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point |
---|
| 532 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point |
---|
| 533 | ! |
---|
| 534 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 535 | INTEGER :: ikt, ikb ! local integers |
---|
| 536 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
| 537 | !!---------------------------------------------------------------------- |
---|
| 538 | ! |
---|
| 539 | ! !== build the three diagonal matrix & the RHS ==! |
---|
| 540 | ! |
---|
| 541 | DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1) |
---|
| 542 | DO jj = 2, jpjm1 |
---|
| 543 | DO ji = fs_2, fs_jpim1 |
---|
| 544 | zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal |
---|
| 545 | zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal |
---|
| 546 | zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal |
---|
| 547 | zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS |
---|
| 548 | & * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) ) |
---|
| 549 | END DO |
---|
| 550 | END DO |
---|
| 551 | END DO |
---|
| 552 | ! |
---|
| 553 | !!gm |
---|
| 554 | ! SELECT CASE( kbc ) !* boundary condition |
---|
| 555 | ! CASE( np_NH ) ! Neumann homogeneous at top & bottom |
---|
| 556 | ! CASE( np_CEN2 ) ! 2nd order centered at top & bottom |
---|
| 557 | ! END SELECT |
---|
| 558 | !!gm |
---|
| 559 | ! |
---|
| 560 | DO jj = 2, jpjm1 ! 2nd order centered at top & bottom |
---|
| 561 | DO ji = fs_2, fs_jpim1 |
---|
| 562 | ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point |
---|
| 563 | ikb = mbkt(ji,jj) ! - above the last wet point |
---|
| 564 | ! |
---|
| 565 | zwd (ji,jj,ikt) = 1._wp ! top |
---|
| 566 | zwi (ji,jj,ikt) = 0._wp |
---|
| 567 | zws (ji,jj,ikt) = 0._wp |
---|
| 568 | zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 569 | ! |
---|
| 570 | zwd (ji,jj,ikb) = 1._wp ! bottom |
---|
| 571 | zwi (ji,jj,ikb) = 0._wp |
---|
| 572 | zws (ji,jj,ikb) = 0._wp |
---|
| 573 | zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 574 | END DO |
---|
| 575 | END DO |
---|
| 576 | ! |
---|
| 577 | ! !== tridiagonal solver ==! |
---|
| 578 | ! |
---|
| 579 | DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 |
---|
| 580 | DO ji = fs_2, fs_jpim1 |
---|
| 581 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
| 582 | END DO |
---|
| 583 | END DO |
---|
| 584 | DO jk = 3, jpkm1 |
---|
| 585 | DO jj = 2, jpjm1 |
---|
| 586 | DO ji = fs_2, fs_jpim1 |
---|
| 587 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
| 588 | END DO |
---|
| 589 | END DO |
---|
| 590 | END DO |
---|
| 591 | ! |
---|
| 592 | DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
| 593 | DO ji = fs_2, fs_jpim1 |
---|
| 594 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
| 595 | END DO |
---|
| 596 | END DO |
---|
| 597 | DO jk = 3, jpkm1 |
---|
| 598 | DO jj = 2, jpjm1 |
---|
| 599 | DO ji = fs_2, fs_jpim1 |
---|
| 600 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
| 601 | END DO |
---|
| 602 | END DO |
---|
| 603 | END DO |
---|
| 604 | |
---|
| 605 | DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
---|
| 606 | DO ji = fs_2, fs_jpim1 |
---|
| 607 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
| 608 | END DO |
---|
| 609 | END DO |
---|
| 610 | DO jk = jpk-2, 2, -1 |
---|
| 611 | DO jj = 2, jpjm1 |
---|
| 612 | DO ji = fs_2, fs_jpim1 |
---|
| 613 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
| 614 | END DO |
---|
| 615 | END DO |
---|
| 616 | END DO |
---|
| 617 | ! |
---|
[5770] | 618 | END SUBROUTINE interp_4th_cpt |
---|
[7646] | 619 | |
---|
| 620 | |
---|
| 621 | SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev ) |
---|
| 622 | !!---------------------------------------------------------------------- |
---|
| 623 | !! *** ROUTINE tridia_solver *** |
---|
| 624 | !! |
---|
| 625 | !! ** Purpose : solve a symmetric 3diagonal system |
---|
| 626 | !! |
---|
| 627 | !! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk ) |
---|
| 628 | !! |
---|
| 629 | !! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 ) |
---|
| 630 | !! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 ) |
---|
| 631 | !! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 ) |
---|
| 632 | !! ( ... )( ... ) ( ... ) |
---|
| 633 | !! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k ) |
---|
| 634 | !! |
---|
| 635 | !! M is decomposed in the product of an upper and lower triangular matrix. |
---|
| 636 | !! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL |
---|
| 637 | !! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal). |
---|
| 638 | !! The solution is pta. |
---|
| 639 | !! The 3d array zwt is used as a work space array. |
---|
| 640 | !!---------------------------------------------------------------------- |
---|
| 641 | REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix |
---|
| 642 | REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side |
---|
| 643 | REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev) |
---|
| 644 | INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level |
---|
| 645 | ! ! =0 pt at t-level |
---|
| 646 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 647 | INTEGER :: kstart ! local indices |
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| 648 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array |
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| 649 | !!---------------------------------------------------------------------- |
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| 650 | ! |
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| 651 | kstart = 1 + klev |
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| 652 | ! |
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| 653 | DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 |
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| 654 | DO ji = fs_2, fs_jpim1 |
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| 655 | zwt(ji,jj,kstart) = pD(ji,jj,kstart) |
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| 656 | END DO |
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| 657 | END DO |
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| 658 | DO jk = kstart+1, jpkm1 |
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| 659 | DO jj = 2, jpjm1 |
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| 660 | DO ji = fs_2, fs_jpim1 |
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| 661 | zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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| 662 | END DO |
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| 663 | END DO |
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| 664 | END DO |
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| 665 | ! |
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| 666 | DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 667 | DO ji = fs_2, fs_jpim1 |
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| 668 | pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart) |
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| 669 | END DO |
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| 670 | END DO |
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| 671 | DO jk = kstart+1, jpkm1 |
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| 672 | DO jj = 2, jpjm1 |
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| 673 | DO ji = fs_2, fs_jpim1 |
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| 674 | pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
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| 675 | END DO |
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| 676 | END DO |
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| 677 | END DO |
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| 678 | |
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| 679 | DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 680 | DO ji = fs_2, fs_jpim1 |
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| 681 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
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| 682 | END DO |
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| 683 | END DO |
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| 684 | DO jk = jpk-2, kstart, -1 |
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| 685 | DO jj = 2, jpjm1 |
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| 686 | DO ji = fs_2, fs_jpim1 |
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| 687 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
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| 688 | END DO |
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| 689 | END DO |
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| 690 | END DO |
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| 691 | ! |
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| 692 | END SUBROUTINE tridia_solver |
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| 693 | |
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[3] | 694 | !!====================================================================== |
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[5770] | 695 | END MODULE traadv_fct |
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