[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 | !! tra_adv_fct_zts: update the tracer trend with a 3D advective trends using a 2nd order FCT scheme |
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| 12 | !! with sub-time-stepping in the vertical direction |
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| 13 | !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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| 14 | !! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection |
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[3] | 15 | !!---------------------------------------------------------------------- |
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[3625] | 16 | USE oce ! ocean dynamics and active tracers |
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| 17 | USE dom_oce ! ocean space and time domain |
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[4990] | 18 | USE trc_oce ! share passive tracers/Ocean variables |
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| 19 | USE trd_oce ! trends: ocean variables |
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[3625] | 20 | USE trdtra ! tracers trends |
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[4990] | 21 | USE diaptr ! poleward transport diagnostics |
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| 22 | ! |
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[5770] | 23 | USE in_out_manager ! I/O manager |
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[3625] | 24 | USE lib_mpp ! MPP library |
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| 25 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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[5770] | 26 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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[3625] | 27 | USE wrk_nemo ! Memory Allocation |
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| 28 | USE timing ! Timing |
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[3] | 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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[5770] | 33 | PUBLIC tra_adv_fct ! routine called by traadv.F90 |
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| 34 | PUBLIC tra_adv_fct_zts ! routine called by traadv.F90 |
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| 35 | PUBLIC interp_4th_cpt ! routine 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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| 38 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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[2528] | 39 | |
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[3] | 40 | !! * Substitutions |
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| 41 | # include "domzgr_substitute.h90" |
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| 42 | # include "vectopt_loop_substitute.h90" |
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| 43 | !!---------------------------------------------------------------------- |
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[5770] | 44 | !! NEMO/OPA 3.7 , NEMO Consortium (2014) |
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[1152] | 45 | !! $Id$ |
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[2528] | 46 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 47 | !!---------------------------------------------------------------------- |
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| 48 | CONTAINS |
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| 49 | |
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[5770] | 50 | SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & |
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| 51 | & ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v ) |
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[3] | 52 | !!---------------------------------------------------------------------- |
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[5770] | 53 | !! *** ROUTINE tra_adv_fct *** |
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[3] | 54 | !! |
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| 55 | !! ** Purpose : Compute the now trend due to total advection of |
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| 56 | !! tracers and add it to the general trend of tracer equations |
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| 57 | !! |
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[5770] | 58 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
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| 59 | !! (choice through the value of kn_fct) |
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| 60 | !! - 4th order compact scheme on the vertical |
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| 61 | !! - corrected flux (monotonic correction) |
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[3] | 62 | !! |
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[2528] | 63 | !! ** Action : - update (pta) with the now advective tracer trends |
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[5770] | 64 | !! - send the trends for further diagnostics |
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[503] | 65 | !!---------------------------------------------------------------------- |
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[2528] | 66 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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[3294] | 67 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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[2528] | 68 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 69 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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[5770] | 70 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
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| 71 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
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[2528] | 72 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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| 73 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components |
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| 74 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields |
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| 75 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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[2715] | 76 | ! |
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[5770] | 77 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 78 | REAL(wp) :: z2dtt, ztra ! local scalar |
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| 79 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - - |
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| 80 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - - |
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| 81 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw |
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| 82 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz |
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[3] | 83 | !!---------------------------------------------------------------------- |
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[3294] | 84 | ! |
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[5770] | 85 | IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct') |
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[3294] | 86 | ! |
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[5770] | 87 | CALL wrk_alloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw ) |
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[3294] | 88 | ! |
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| 89 | IF( kt == kit000 ) THEN |
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[2528] | 90 | IF(lwp) WRITE(numout,*) |
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[5770] | 91 | IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype |
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[2528] | 92 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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[3] | 93 | ENDIF |
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[2528] | 94 | ! |
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[5770] | 95 | l_trd = .FALSE. |
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| 96 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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| 97 | ! |
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[2528] | 98 | IF( l_trd ) THEN |
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[3294] | 99 | CALL wrk_alloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz ) |
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[5770] | 100 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
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[3294] | 101 | ENDIF |
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[2528] | 102 | ! |
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[5770] | 103 | ! ! surface & bottom value : flux set to zero one for all |
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| 104 | IF( lk_vvl ) zwz(:,:, 1 ) = 0._wp ! except at the surface in linear free surface case |
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| 105 | zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp |
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[2528] | 106 | ! |
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[5770] | 107 | zwi(:,:,:) = 0._wp |
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[2528] | 108 | ! ! =========== |
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| 109 | DO jn = 1, kjpt ! tracer loop |
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| 110 | ! ! =========== |
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[5770] | 111 | ! |
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| 112 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
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| 113 | ! !* upstream tracer flux in the i and j direction |
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[2528] | 114 | DO jk = 1, jpkm1 |
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| 115 | DO jj = 1, jpjm1 |
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| 116 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 117 | ! upstream scheme |
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| 118 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
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| 119 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
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| 120 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
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| 121 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
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| 122 | 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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| 123 | 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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| 124 | END DO |
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[3] | 125 | END DO |
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| 126 | END DO |
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[5770] | 127 | ! !* upstream tracer flux in the k direction *! |
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| 128 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
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[4990] | 129 | DO jj = 1, jpj |
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| 130 | DO ji = 1, jpi |
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[2528] | 131 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
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| 132 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
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[5120] | 133 | 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] | 134 | END DO |
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[3] | 135 | END DO |
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| 136 | END DO |
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[5770] | 137 | ! |
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| 138 | IF(.NOT.lk_vvl ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
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| 139 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
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[5120] | 140 | DO jj = 1, jpj |
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| 141 | DO ji = 1, jpi |
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| 142 | 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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| 143 | END DO |
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| 144 | END DO |
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[5770] | 145 | ELSE ! no cavities: only at the ocean surface |
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| 146 | zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) |
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| 147 | ENDIF |
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[5120] | 148 | ENDIF |
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[5770] | 149 | ! |
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| 150 | DO jk = 1, jpkm1 !* trend and after field with monotonic scheme |
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[2528] | 151 | z2dtt = p2dt(jk) |
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[216] | 152 | DO jj = 2, jpjm1 |
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| 153 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 154 | ! total intermediate advective trends |
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[5770] | 155 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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| 156 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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| 157 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) / ( e1e2t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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[2528] | 158 | ! update and guess with monotonic sheme |
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[5770] | 159 | !!gm why tmask added in the two following lines ??? the mask is done in tranxt ! |
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[4990] | 160 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra * tmask(ji,jj,jk) |
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[2528] | 161 | zwi(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ztra ) * tmask(ji,jj,jk) |
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[216] | 162 | END DO |
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| 163 | END DO |
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| 164 | END DO |
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[5770] | 165 | CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign) |
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| 166 | ! |
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| 167 | IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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[2528] | 168 | ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
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| 169 | END IF |
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[5770] | 170 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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[5147] | 171 | IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN |
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| 172 | IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) |
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| 173 | IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) |
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[2528] | 174 | ENDIF |
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[5770] | 175 | ! |
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| 176 | ! |
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| 177 | ! !== anti-diffusive flux : high order minus low order ==! |
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| 178 | ! |
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| 179 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
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| 180 | ! |
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| 181 | CASE( 2 ) ! 2nd order centered |
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| 182 | DO jk = 1, jpkm1 |
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| 183 | DO jj = 1, jpjm1 |
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| 184 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 185 | 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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| 186 | 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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| 187 | END DO |
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[503] | 188 | END DO |
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| 189 | END DO |
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[5770] | 190 | ! |
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| 191 | CASE( 4 ) ! 4th order centered |
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| 192 | zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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| 193 | zltv(:,:,jpk) = 0._wp |
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| 194 | DO jk = 1, jpkm1 ! Laplacian |
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| 195 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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| 196 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 197 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
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| 198 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
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| 199 | END DO |
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[503] | 200 | END DO |
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[5770] | 201 | DO jj = 2, jpjm1 ! |
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| 202 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 203 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
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| 204 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
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| 205 | END DO |
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| 206 | END DO |
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[503] | 207 | END DO |
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[5770] | 208 | ! |
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| 209 | CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 210 | ! |
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| 211 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
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| 212 | DO jj = 1, jpjm1 |
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| 213 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 214 | 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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| 215 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
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| 216 | ! ! C4 minus upstream advective fluxes |
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| 217 | 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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| 218 | 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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| 219 | END DO |
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[5120] | 220 | END DO |
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[5770] | 221 | END DO |
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| 222 | ! |
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| 223 | CASE( 41 ) ! 4th order centered ==>> !!gm coding attempt need to be tested |
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| 224 | ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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| 225 | ztv(:,:,jpk) = 0._wp |
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| 226 | DO jk = 1, jpkm1 ! gradient |
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| 227 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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| 228 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 229 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
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| 230 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
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| 231 | END DO |
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| 232 | END DO |
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[5120] | 233 | END DO |
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[5770] | 234 | CALL lbc_lnk( ztu, 'U', -1. ) ; CALL lbc_lnk( ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 235 | ! |
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| 236 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
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| 237 | DO jj = 2, jpjm1 |
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| 238 | DO ji = 2, fs_jpim1 ! vector opt. |
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| 239 | 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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| 240 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
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| 241 | ! ! C4 interpolation of T at u- & v-points (x2) |
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| 242 | zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) ) |
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| 243 | zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) ) |
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| 244 | ! ! C4 minus upstream advective fluxes |
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| 245 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) |
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| 246 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) |
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| 247 | END DO |
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| 248 | END DO |
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| 249 | END DO |
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| 250 | ! |
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| 251 | END SELECT |
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| 252 | ! !* vertical anti-diffusive fluxes |
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| 253 | SELECT CASE( kn_fct_v ) ! Interior values (w-masked) |
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| 254 | ! |
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| 255 | CASE( 2 ) ! 2nd order centered |
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| 256 | DO jk = 2, jpkm1 |
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| 257 | DO jj = 2, jpjm1 |
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| 258 | DO ji = fs_2, fs_jpim1 |
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| 259 | zwz(ji,jj,jk) = ( 0.5_wp * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & |
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| 260 | - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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| 261 | END DO |
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| 262 | END DO |
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| 263 | END DO |
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| 264 | ! |
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| 265 | CASE( 4 ) ! 4th order COMPACT |
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| 266 | ! |
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| 267 | CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! COMPACT interpolation of T at w-point |
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| 268 | ! |
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| 269 | DO jk = 2, jpkm1 |
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| 270 | DO jj = 2, jpjm1 |
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| 271 | DO ji = fs_2, fs_jpim1 |
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| 272 | zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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| 273 | END DO |
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| 274 | END DO |
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| 275 | END DO |
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| 276 | ! |
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| 277 | END SELECT |
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| 278 | ! ! top ocean value: high order = upstream ==>> zwz=0 |
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| 279 | zwz(:,:, 1 ) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
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| 280 | ! |
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[2528] | 281 | CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions |
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| 282 | CALL lbc_lnk( zwz, 'W', 1. ) |
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[216] | 283 | |
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[5770] | 284 | ! !== monotonicity algorithm ==! |
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| 285 | ! |
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[2528] | 286 | CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) |
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[3] | 287 | |
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| 288 | |
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[5770] | 289 | ! !== final trend with corrected fluxes ==! |
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| 290 | ! |
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[216] | 291 | DO jk = 1, jpkm1 |
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| 292 | DO jj = 2, jpjm1 |
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[2528] | 293 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[5770] | 294 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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| 295 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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| 296 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) & |
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| 297 | & / ( e1e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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[216] | 298 | END DO |
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| 299 | END DO |
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| 300 | END DO |
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[5770] | 301 | ! |
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| 302 | IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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[2528] | 303 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed |
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| 304 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed |
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| 305 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed |
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[5770] | 306 | ! |
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| 307 | CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) |
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| 308 | CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) |
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| 309 | CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) |
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| 310 | ! |
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| 311 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz ) |
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[2528] | 312 | END IF |
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| 313 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
---|
[5147] | 314 | IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN |
---|
| 315 | IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) + htr_adv(:) |
---|
| 316 | IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) + str_adv(:) |
---|
[2528] | 317 | ENDIF |
---|
[503] | 318 | ! |
---|
[2715] | 319 | END DO |
---|
[503] | 320 | ! |
---|
[5770] | 321 | CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw ) |
---|
[2528] | 322 | ! |
---|
[5770] | 323 | IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct') |
---|
[2715] | 324 | ! |
---|
[5770] | 325 | END SUBROUTINE tra_adv_fct |
---|
[3] | 326 | |
---|
[5737] | 327 | |
---|
[5770] | 328 | SUBROUTINE tra_adv_fct_zts( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & |
---|
| 329 | & ptb, ptn, pta, kjpt, kn_fct_zts ) |
---|
[4990] | 330 | !!---------------------------------------------------------------------- |
---|
[5770] | 331 | !! *** ROUTINE tra_adv_fct_zts *** |
---|
[4990] | 332 | !! |
---|
| 333 | !! ** Purpose : Compute the now trend due to total advection of |
---|
| 334 | !! tracers and add it to the general trend of tracer equations |
---|
| 335 | !! |
---|
| 336 | !! ** Method : TVD ZTS scheme, i.e. 2nd order centered scheme with |
---|
| 337 | !! corrected flux (monotonic correction). This version use sub- |
---|
| 338 | !! timestepping for the vertical advection which increases stability |
---|
| 339 | !! when vertical metrics are small. |
---|
| 340 | !! note: - this advection scheme needs a leap-frog time scheme |
---|
| 341 | !! |
---|
| 342 | !! ** Action : - update (pta) with the now advective tracer trends |
---|
| 343 | !! - save the trends |
---|
| 344 | !!---------------------------------------------------------------------- |
---|
| 345 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
| 346 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
---|
| 347 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
---|
| 348 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
---|
[5770] | 349 | INTEGER , INTENT(in ) :: kn_fct_zts ! number of number of vertical sub-timesteps |
---|
[4990] | 350 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
---|
| 351 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components |
---|
| 352 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields |
---|
| 353 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
---|
| 354 | ! |
---|
| 355 | REAL(wp), DIMENSION( jpk ) :: zts ! length of sub-timestep for vertical advection |
---|
| 356 | REAL(wp), DIMENSION( jpk ) :: zr_p2dt ! reciprocal of tracer timestep |
---|
| 357 | INTEGER :: ji, jj, jk, jl, jn ! dummy loop indices |
---|
| 358 | INTEGER :: jtb, jtn, jta ! sub timestep pointers for leap-frog/euler forward steps |
---|
| 359 | INTEGER :: jtaken ! toggle for collecting appropriate fluxes from sub timesteps |
---|
| 360 | REAL(wp) :: z_rzts ! Fractional length of Euler forward sub-timestep for vertical advection |
---|
[5770] | 361 | REAL(wp) :: z2dtt, ztra ! local scalar |
---|
[4990] | 362 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! - - |
---|
| 363 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! - - |
---|
[5770] | 364 | REAL(wp), POINTER, DIMENSION(:,: ) :: zwx_sav , zwy_sav |
---|
| 365 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwx, zwy, zwz, zhdiv, zwzts, zwz_sav |
---|
| 366 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz |
---|
| 367 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: ztrs |
---|
[4990] | 368 | !!---------------------------------------------------------------------- |
---|
| 369 | ! |
---|
[5770] | 370 | IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct_zts') |
---|
[4990] | 371 | ! |
---|
[5770] | 372 | CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav ) |
---|
| 373 | CALL wrk_alloc( jpi,jpj, jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav ) |
---|
| 374 | CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs ) |
---|
[4990] | 375 | ! |
---|
| 376 | IF( kt == kit000 ) THEN |
---|
| 377 | IF(lwp) WRITE(numout,*) |
---|
[5770] | 378 | IF(lwp) WRITE(numout,*) 'tra_adv_fct_zts : 2nd order FCT scheme with ', kn_fct_zts, ' vertical sub-timestep on ', cdtype |
---|
[4990] | 379 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
| 380 | ENDIF |
---|
| 381 | ! |
---|
| 382 | l_trd = .FALSE. |
---|
[5770] | 383 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
---|
[4990] | 384 | ! |
---|
| 385 | IF( l_trd ) THEN |
---|
[5770] | 386 | CALL wrk_alloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz ) |
---|
[4990] | 387 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
---|
| 388 | ENDIF |
---|
| 389 | ! |
---|
| 390 | zwi(:,:,:) = 0._wp |
---|
[5770] | 391 | z_rzts = 1._wp / REAL( kn_fct_zts, wp ) |
---|
[4990] | 392 | zr_p2dt(:) = 1._wp / p2dt(:) |
---|
| 393 | ! |
---|
| 394 | ! ! =========== |
---|
| 395 | DO jn = 1, kjpt ! tracer loop |
---|
| 396 | ! ! =========== |
---|
| 397 | ! 1. Bottom value : flux set to zero |
---|
| 398 | ! ---------------------------------- |
---|
| 399 | zwx(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp |
---|
| 400 | zwy(:,:,jpk) = 0._wp ; zwi(:,:,jpk) = 0._wp |
---|
[3] | 401 | |
---|
[4990] | 402 | ! 2. upstream advection with initial mass fluxes & intermediate update |
---|
| 403 | ! -------------------------------------------------------------------- |
---|
| 404 | ! upstream tracer flux in the i and j direction |
---|
| 405 | DO jk = 1, jpkm1 |
---|
| 406 | DO jj = 1, jpjm1 |
---|
| 407 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 408 | ! upstream scheme |
---|
| 409 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
---|
| 410 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
---|
| 411 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
---|
| 412 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
---|
| 413 | zwx(ji,jj,jk) = 0.5_wp * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) |
---|
| 414 | zwy(ji,jj,jk) = 0.5_wp * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) |
---|
| 415 | END DO |
---|
| 416 | END DO |
---|
| 417 | END DO |
---|
| 418 | |
---|
| 419 | ! upstream tracer flux in the k direction |
---|
[5770] | 420 | DO jk = 2, jpkm1 ! Interior value |
---|
[4990] | 421 | DO jj = 1, jpj |
---|
| 422 | DO ji = 1, jpi |
---|
| 423 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
---|
| 424 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
---|
[5770] | 425 | zwz(ji,jj,jk) = 0.5_wp * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk) |
---|
[4990] | 426 | END DO |
---|
| 427 | END DO |
---|
| 428 | END DO |
---|
[5770] | 429 | ! ! top value |
---|
| 430 | IF( lk_vvl ) THEN ! variable volume: only k=1 as zwz is multiplied by wmask |
---|
| 431 | zwz(:,:, 1 ) = 0._wp |
---|
| 432 | ELSE ! linear free surface |
---|
| 433 | IF( ln_isfcav ) THEN ! ice-shelf cavities |
---|
[5120] | 434 | DO jj = 1, jpj |
---|
| 435 | DO ji = 1, jpi |
---|
[5770] | 436 | zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) |
---|
[5120] | 437 | END DO |
---|
[5770] | 438 | END DO |
---|
| 439 | ELSE ! standard case |
---|
| 440 | zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) |
---|
| 441 | ENDIF |
---|
[5120] | 442 | ENDIF |
---|
[5770] | 443 | ! |
---|
| 444 | DO jk = 1, jpkm1 ! total advective trend |
---|
[4990] | 445 | z2dtt = p2dt(jk) |
---|
| 446 | DO jj = 2, jpjm1 |
---|
| 447 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 448 | ! total intermediate advective trends |
---|
[5770] | 449 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
---|
| 450 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
| 451 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) / ( e1e2t(ji,jj) * fse3t_n(ji,jj,jk) ) |
---|
[4990] | 452 | ! update and guess with monotonic sheme |
---|
| 453 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra |
---|
| 454 | zwi(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ztra ) * tmask(ji,jj,jk) |
---|
| 455 | END DO |
---|
| 456 | END DO |
---|
| 457 | END DO |
---|
[5770] | 458 | ! |
---|
| 459 | CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign) |
---|
| 460 | ! |
---|
| 461 | IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes) |
---|
[4990] | 462 | ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
---|
| 463 | END IF |
---|
[5770] | 464 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
---|
[5147] | 465 | IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN |
---|
| 466 | IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) |
---|
| 467 | IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) |
---|
[4990] | 468 | ENDIF |
---|
| 469 | |
---|
[5770] | 470 | ! 3. anti-diffusive flux : high order minus low order |
---|
| 471 | ! --------------------------------------------------- |
---|
[4990] | 472 | |
---|
[5770] | 473 | DO jk = 1, jpkm1 !* horizontal anti-diffusive fluxes |
---|
| 474 | ! |
---|
[4990] | 475 | DO jj = 1, jpjm1 |
---|
| 476 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 477 | zwx_sav(ji,jj) = zwx(ji,jj,jk) |
---|
| 478 | zwy_sav(ji,jj) = zwy(ji,jj,jk) |
---|
[5770] | 479 | ! |
---|
[4990] | 480 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) |
---|
| 481 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) |
---|
| 482 | END DO |
---|
| 483 | END DO |
---|
[5770] | 484 | ! |
---|
| 485 | DO jj = 2, jpjm1 ! partial horizontal divergence |
---|
[4990] | 486 | DO ji = fs_2, fs_jpim1 |
---|
| 487 | zhdiv(ji,jj,jk) = ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) & |
---|
| 488 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) ) |
---|
| 489 | END DO |
---|
| 490 | END DO |
---|
[5770] | 491 | ! |
---|
[4990] | 492 | DO jj = 1, jpjm1 |
---|
| 493 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[5770] | 494 | zwx(ji,jj,jk) = zwx(ji,jj,jk) - zwx_sav(ji,jj) |
---|
| 495 | zwy(ji,jj,jk) = zwy(ji,jj,jk) - zwy_sav(ji,jj) |
---|
[4990] | 496 | END DO |
---|
| 497 | END DO |
---|
| 498 | END DO |
---|
| 499 | |
---|
[5770] | 500 | ! !* vertical anti-diffusive flux |
---|
| 501 | zwz_sav(:,:,:) = zwz(:,:,:) |
---|
| 502 | ztrs (:,:,:,1) = ptb(:,:,:,jn) |
---|
| 503 | zwzts (:,:,:) = 0._wp |
---|
| 504 | IF( lk_vvl ) zwz(:,:, 1 ) = 0._wp ! surface value set to zero in vvl case |
---|
[4990] | 505 | ! |
---|
[5770] | 506 | DO jl = 1, kn_fct_zts ! Start of sub timestepping loop |
---|
| 507 | ! |
---|
| 508 | IF( jl == 1 ) THEN ! Euler forward to kick things off |
---|
| 509 | jtb = 1 ; jtn = 1 ; jta = 2 |
---|
| 510 | zts(:) = p2dt(:) * z_rzts |
---|
| 511 | jtaken = MOD( kn_fct_zts + 1 , 2) ! Toggle to collect every second flux |
---|
| 512 | ! ! starting at jl =1 if kn_fct_zts is odd; |
---|
| 513 | ! ! starting at jl =2 otherwise |
---|
| 514 | ELSEIF( jl == 2 ) THEN ! First leapfrog step |
---|
| 515 | jtb = 1 ; jtn = 2 ; jta = 3 |
---|
| 516 | zts(:) = 2._wp * p2dt(:) * z_rzts |
---|
| 517 | ELSE ! Shuffle pointers for subsequent leapfrog steps |
---|
| 518 | jtb = MOD(jtb,3) + 1 |
---|
| 519 | jtn = MOD(jtn,3) + 1 |
---|
| 520 | jta = MOD(jta,3) + 1 |
---|
[4990] | 521 | ENDIF |
---|
[5770] | 522 | DO jk = 2, jpkm1 ! interior value |
---|
[4990] | 523 | DO jj = 2, jpjm1 |
---|
| 524 | DO ji = fs_2, fs_jpim1 |
---|
[5770] | 525 | zwz(ji,jj,jk) = 0.5_wp * pwn(ji,jj,jk) * ( ztrs(ji,jj,jk,jtn) + ztrs(ji,jj,jk-1,jtn) ) * wmask(ji,jj,jk) |
---|
| 526 | IF( jtaken == 0 ) zwzts(ji,jj,jk) = zwzts(ji,jj,jk) + zwz(ji,jj,jk) * zts(jk) ! Accumulate time-weighted vertcal flux |
---|
[4990] | 527 | END DO |
---|
| 528 | END DO |
---|
| 529 | END DO |
---|
[5770] | 530 | IF(.NOT.lk_vvl ) THEN ! top value (only in linear free surface case) |
---|
| 531 | IF( ln_isfcav ) THEN ! ice-shelf cavities |
---|
| 532 | DO jj = 1, jpj |
---|
| 533 | DO ji = 1, jpi |
---|
| 534 | zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface |
---|
| 535 | END DO |
---|
| 536 | END DO |
---|
| 537 | ELSE ! standard case |
---|
| 538 | zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) |
---|
| 539 | ENDIF |
---|
| 540 | ENDIF |
---|
| 541 | ! |
---|
[4990] | 542 | jtaken = MOD( jtaken + 1 , 2 ) |
---|
[5770] | 543 | ! |
---|
| 544 | DO jk = 2, jpkm1 ! total advective trends |
---|
[4990] | 545 | DO jj = 2, jpjm1 |
---|
| 546 | DO ji = fs_2, fs_jpim1 |
---|
[5770] | 547 | ztrs(ji,jj,jk,jta) = ztrs(ji,jj,jk,jtb) & |
---|
| 548 | & - zts(jk) * ( zhdiv(ji,jj,jk) + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) & |
---|
| 549 | & / ( e1e2t(ji,jj) * fse3t(ji,jj,jk) ) |
---|
[4990] | 550 | END DO |
---|
| 551 | END DO |
---|
| 552 | END DO |
---|
[5770] | 553 | ! |
---|
[4990] | 554 | END DO |
---|
| 555 | |
---|
| 556 | DO jk = 2, jpkm1 ! Anti-diffusive vertical flux using average flux from the sub-timestepping |
---|
| 557 | DO jj = 2, jpjm1 |
---|
| 558 | DO ji = fs_2, fs_jpim1 |
---|
[5770] | 559 | zwz(ji,jj,jk) = ( zwzts(ji,jj,jk) * zr_p2dt(jk) - zwz_sav(ji,jj,jk) ) * wmask(ji,jj,jk) |
---|
[4990] | 560 | END DO |
---|
| 561 | END DO |
---|
| 562 | END DO |
---|
| 563 | CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions |
---|
| 564 | CALL lbc_lnk( zwz, 'W', 1. ) |
---|
| 565 | |
---|
| 566 | ! 4. monotonicity algorithm |
---|
| 567 | ! ------------------------- |
---|
| 568 | CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) |
---|
| 569 | |
---|
| 570 | |
---|
| 571 | ! 5. final trend with corrected fluxes |
---|
| 572 | ! ------------------------------------ |
---|
| 573 | DO jk = 1, jpkm1 |
---|
| 574 | DO jj = 2, jpjm1 |
---|
| 575 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[5770] | 576 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ( zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
| 577 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) & |
---|
| 578 | & / ( e1e2t(ji,jj) * fse3t_n(ji,jj,jk) ) |
---|
[4990] | 579 | END DO |
---|
| 580 | END DO |
---|
| 581 | END DO |
---|
| 582 | |
---|
| 583 | ! ! trend diagnostics (contribution of upstream fluxes) |
---|
| 584 | IF( l_trd ) THEN |
---|
| 585 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed |
---|
| 586 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed |
---|
| 587 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed |
---|
[5770] | 588 | ! |
---|
[4990] | 589 | CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) |
---|
| 590 | CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) |
---|
| 591 | CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) |
---|
[5770] | 592 | ! |
---|
| 593 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz ) |
---|
[4990] | 594 | END IF |
---|
| 595 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
---|
[5147] | 596 | IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN |
---|
| 597 | IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) + htr_adv(:) |
---|
| 598 | IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) + str_adv(:) |
---|
[4990] | 599 | ENDIF |
---|
| 600 | ! |
---|
| 601 | END DO |
---|
| 602 | ! |
---|
[5770] | 603 | CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav ) |
---|
| 604 | CALL wrk_alloc( jpi,jpj, jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav ) |
---|
| 605 | CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs ) |
---|
[4990] | 606 | ! |
---|
[5770] | 607 | IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct_zts') |
---|
[4990] | 608 | ! |
---|
[5770] | 609 | END SUBROUTINE tra_adv_fct_zts |
---|
[4990] | 610 | |
---|
[5737] | 611 | |
---|
[2528] | 612 | SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt ) |
---|
[3] | 613 | !!--------------------------------------------------------------------- |
---|
| 614 | !! *** ROUTINE nonosc *** |
---|
| 615 | !! |
---|
| 616 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 617 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 618 | !! |
---|
| 619 | !! ** Method : ... ??? |
---|
| 620 | !! warning : pbef and paft must be masked, but the boundaries |
---|
| 621 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 622 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 623 | !! in-space based differencing for fluid |
---|
| 624 | !!---------------------------------------------------------------------- |
---|
[2528] | 625 | REAL(wp), DIMENSION(jpk) , INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
---|
| 626 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field |
---|
| 627 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
---|
[2715] | 628 | ! |
---|
[4990] | 629 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 630 | INTEGER :: ikm1 ! local integer |
---|
[2715] | 631 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt ! local scalars |
---|
| 632 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
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[3294] | 633 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo, zbup, zbdo |
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[3] | 634 | !!---------------------------------------------------------------------- |
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[3294] | 635 | ! |
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| 636 | IF( nn_timing == 1 ) CALL timing_start('nonosc') |
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| 637 | ! |
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| 638 | CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo ) |
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| 639 | ! |
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[2715] | 640 | zbig = 1.e+40_wp |
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| 641 | zrtrn = 1.e-15_wp |
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[4990] | 642 | zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp |
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[785] | 643 | |
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[3] | 644 | ! Search local extrema |
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| 645 | ! -------------------- |
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[785] | 646 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
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[4990] | 647 | zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & |
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| 648 | & paft * tmask - zbig * ( 1._wp - tmask ) ) |
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| 649 | zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & |
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| 650 | & paft * tmask + zbig * ( 1._wp - tmask ) ) |
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[785] | 651 | |
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[5120] | 652 | DO jk = 1, jpkm1 |
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| 653 | ikm1 = MAX(jk-1,1) |
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| 654 | z2dtt = p2dt(jk) |
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| 655 | DO jj = 2, jpjm1 |
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| 656 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 657 | |
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[785] | 658 | ! search maximum in neighbourhood |
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| 659 | zup = MAX( zbup(ji ,jj ,jk ), & |
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| 660 | & zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), & |
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| 661 | & zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), & |
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| 662 | & zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) ) |
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[3] | 663 | |
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[785] | 664 | ! search minimum in neighbourhood |
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| 665 | zdo = MIN( zbdo(ji ,jj ,jk ), & |
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| 666 | & zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), & |
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| 667 | & zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), & |
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| 668 | & zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) ) |
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[3] | 669 | |
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[785] | 670 | ! positive part of the flux |
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[3] | 671 | zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & |
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| 672 | & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & |
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| 673 | & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
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[785] | 674 | |
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| 675 | ! negative part of the flux |
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[3] | 676 | zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & |
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| 677 | & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & |
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| 678 | & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
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[785] | 679 | |
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[3] | 680 | ! up & down beta terms |
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| 681 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt |
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[785] | 682 | zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt |
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| 683 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt |
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[3] | 684 | END DO |
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| 685 | END DO |
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| 686 | END DO |
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[2528] | 687 | CALL lbc_lnk( zbetup, 'T', 1. ) ; CALL lbc_lnk( zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
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[3] | 688 | |
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[237] | 689 | ! 3. monotonic flux in the i & j direction (paa & pbb) |
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| 690 | ! ---------------------------------------- |
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[3] | 691 | DO jk = 1, jpkm1 |
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| 692 | DO jj = 2, jpjm1 |
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| 693 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[4990] | 694 | zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) |
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| 695 | zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) |
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[785] | 696 | zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) ) |
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[4990] | 697 | paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
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[3] | 698 | |
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[4990] | 699 | zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) |
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| 700 | zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) |
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[785] | 701 | zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) ) |
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[4990] | 702 | pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
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[3] | 703 | |
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| 704 | ! monotonic flux in the k direction, i.e. pcc |
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| 705 | ! ------------------------------------------- |
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[785] | 706 | za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) ) |
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| 707 | zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) ) |
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| 708 | zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) ) |
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[4990] | 709 | pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) |
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[3] | 710 | END DO |
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| 711 | END DO |
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| 712 | END DO |
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[2528] | 713 | CALL lbc_lnk( paa, 'U', -1. ) ; CALL lbc_lnk( pbb, 'V', -1. ) ! lateral boundary condition (changed sign) |
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[503] | 714 | ! |
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[3294] | 715 | CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo ) |
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[2715] | 716 | ! |
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[3294] | 717 | IF( nn_timing == 1 ) CALL timing_stop('nonosc') |
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| 718 | ! |
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[3] | 719 | END SUBROUTINE nonosc |
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| 720 | |
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[5770] | 721 | |
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| 722 | SUBROUTINE interp_4th_cpt( pt_in, pt_out ) |
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| 723 | !!---------------------------------------------------------------------- |
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| 724 | !! *** ROUTINE interp_4th_cpt *** |
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| 725 | !! |
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| 726 | !! ** Purpose : Compute the interpolation of tracer at w-point |
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| 727 | !! |
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| 728 | !! ** Method : 4th order compact interpolation |
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| 729 | !!---------------------------------------------------------------------- |
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| 730 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields |
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| 731 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts |
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| 732 | ! |
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| 733 | INTEGER :: ji, jj, jk ! dummy loop integers |
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| 734 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
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| 735 | !!---------------------------------------------------------------------- |
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| 736 | |
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| 737 | DO jk = 3, jpkm1 !== build the three diagonal matrix ==! |
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| 738 | DO jj = 1, jpj |
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| 739 | DO ji = 1, jpi |
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| 740 | zwd (ji,jj,jk) = 4._wp |
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| 741 | zwi (ji,jj,jk) = 1._wp |
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| 742 | zws (ji,jj,jk) = 1._wp |
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| 743 | zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
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| 744 | ! |
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| 745 | IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom |
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| 746 | zwd (ji,jj,jk) = 1._wp |
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| 747 | zwi (ji,jj,jk) = 0._wp |
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| 748 | zws (ji,jj,jk) = 0._wp |
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| 749 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
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| 750 | ENDIF |
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| 751 | END DO |
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| 752 | END DO |
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| 753 | END DO |
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| 754 | ! |
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| 755 | jk=2 ! Switch to second order centered at top |
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| 756 | DO jj=1,jpj |
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| 757 | DO ji=1,jpi |
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| 758 | zwd (ji,jj,jk) = 1._wp |
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| 759 | zwi (ji,jj,jk) = 0._wp |
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| 760 | zws (ji,jj,jk) = 0._wp |
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| 761 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
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| 762 | END DO |
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| 763 | END DO |
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| 764 | ! |
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| 765 | ! !== tridiagonal solve ==! |
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| 766 | DO jj = 1, jpj ! first recurrence |
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| 767 | DO ji = 1, jpi |
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| 768 | zwt(ji,jj,2) = zwd(ji,jj,2) |
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| 769 | END DO |
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| 770 | END DO |
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| 771 | DO jk = 3, jpkm1 |
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| 772 | DO jj = 1, jpj |
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| 773 | DO ji = 1, jpi |
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| 774 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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| 775 | END DO |
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| 776 | END DO |
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| 777 | END DO |
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| 778 | ! |
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| 779 | DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 780 | DO ji = 1, jpi |
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| 781 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
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| 782 | END DO |
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| 783 | END DO |
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| 784 | DO jk = 3, jpkm1 |
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| 785 | DO jj = 1, jpj |
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| 786 | DO ji = 1, jpi |
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| 787 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
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| 788 | END DO |
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| 789 | END DO |
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| 790 | END DO |
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| 791 | |
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| 792 | DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 793 | DO ji = 1, jpi |
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| 794 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
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| 795 | END DO |
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| 796 | END DO |
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| 797 | DO jk = jpk-2, 2, -1 |
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| 798 | DO jj = 1, jpj |
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| 799 | DO ji = 1, jpi |
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| 800 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
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| 801 | END DO |
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| 802 | END DO |
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| 803 | END DO |
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| 804 | ! |
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| 805 | END SUBROUTINE interp_4th_cpt |
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| 806 | |
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[3] | 807 | !!====================================================================== |
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[5770] | 808 | END MODULE traadv_fct |
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