[14021] | 1 | MODULE traadv_fct_lf |
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| 2 | !!============================================================================== |
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| 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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| 5 | !!============================================================================== |
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| 6 | !! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90) |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! tra_adv_fct-lf : 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 - loop fusion version |
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| 12 | !! nonosc_lf : compute monotonic tracer fluxes by a non-oscillatory algorithm - loop fusion version |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | USE oce ! ocean dynamics and active tracers |
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| 15 | USE dom_oce ! ocean space and time domain |
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| 16 | USE trc_oce ! share passive tracers/Ocean variables |
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| 17 | USE trd_oce ! trends: ocean variables |
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| 18 | USE trdtra ! tracers trends |
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| 19 | USE diaptr ! poleward transport diagnostics |
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| 20 | USE diaar5 ! AR5 diagnostics |
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| 21 | USE phycst , ONLY : rho0_rcp |
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| 22 | USE zdf_oce , ONLY : ln_zad_Aimp |
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| 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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| 25 | USE iom ! |
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| 26 | USE lib_mpp ! MPP library |
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| 27 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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| 28 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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| 29 | USE traadv_fct |
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| 30 | |
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| 31 | IMPLICIT NONE |
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| 32 | PRIVATE |
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| 33 | |
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| 34 | PUBLIC tra_adv_fct_lf ! called by traadv.F90 |
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| 35 | |
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| 36 | LOGICAL :: l_trd ! flag to compute trends |
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| 37 | LOGICAL :: l_ptr ! flag to compute poleward transport |
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| 38 | LOGICAL :: l_hst ! flag to compute heat/salt transport |
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| 39 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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| 40 | |
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| 41 | ! ! tridiag solver associated indices: |
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| 42 | INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition |
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| 43 | INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition |
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| 44 | |
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| 45 | !! * Substitutions |
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| 46 | # include "do_loop_substitute.h90" |
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| 47 | # include "domzgr_substitute.h90" |
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| 48 | |
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| 49 | #define tracer_flux_i(out,zfp,zfm,ji,jj,jk) \ |
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| 50 | zfp = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) ) ; \ |
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| 51 | zfm = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) ) ; \ |
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| 52 | out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji+1,jj,jk,jn,Kbb) ) |
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| 53 | |
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| 54 | #define tracer_flux_j(out,zfp,zfm,ji,jj,jk) \ |
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| 55 | zfp = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) ) ; \ |
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| 56 | zfm = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) ) ; \ |
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| 57 | out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji,jj+1,jk,jn,Kbb) ) |
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| 58 | |
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| 59 | #define search_in_neighbour(out,OP,vec,ji,jj,jk) \ |
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| 60 | out = OP(vec(ji,jj,jk),vec(ji-1,jj,jk),vec(ji+1,jj,jk), \ |
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| 61 | vec(ji,jj-1,jk),vec(ji,jj+1,jk),vec(ji,jj,MAX(jk-1,1)),vec(ji,jj,jk+1)) |
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| 62 | |
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| 63 | #define pos_part_of_flux(ji,jj,jk,out) \ |
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| 64 | out = MAX(0.,paa_in(ji-1,jj,jk)) - MIN(0.,paa_in(ji,jj,jk)) \ |
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| 65 | + MAX(0.,pbb_in(ji,jj-1,jk)) - MIN(0.,pbb_in(ji,jj,jk)) \ |
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| 66 | + MAX(0.,pcc_in(ji,jj,jk+1)) - MIN(0.,pcc_in(ji,jj,jk)) |
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| 67 | |
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| 68 | #define neg_part_of_flux(ji,jj,jk,out) \ |
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| 69 | out = MAX( 0.,paa_in(ji,jj,jk) ) - MIN( 0., paa_in(ji-1,jj,jk)) \ |
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| 70 | + MAX( 0.,pbb_in(ji,jj,jk) ) - MIN( 0., pbb_in(ji,jj-1,jk)) \ |
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| 71 | + MAX( 0.,pcc_in(ji,jj,jk) ) - MIN( 0., pcc_in(ji,jj,jk+1)) |
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| 72 | |
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| 73 | #define beta_terms(bt,betup,betdo,up,pos,do,neg,ji,jj,jk) \ |
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| 74 | bt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt ; \ |
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| 75 | betup = ( up - paft(ji,jj,jk) ) / ( pos + zrtrn ) * bt ; \ |
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| 76 | betdo = ( paft(ji,jj,jk) - do ) / ( neg + zrtrn ) * bt |
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| 77 | |
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| 78 | #define monotonic_flux(a,b,c,betup_p1,betdo_p1,vec,vec_in,jk) \ |
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| 79 | a = MIN( 1._wp, zbetdo(ji,jj), betup_p1 ) ; \ |
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| 80 | b = MIN( 1._wp, zbetup(ji,jj), betdo_p1 ) ; \ |
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| 81 | c = ( 0.5_wp + SIGN( 0.5_wp , vec_in(ji,jj,jk) ) ) ; \ |
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| 82 | vec(ji,jj,jk) = vec_in(ji,jj,jk) * ( c * a + ( 1._wp - c) * b ) |
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| 83 | |
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| 84 | #define monotonic_flux_k(a,b,c,betup,betdo,vec,vec_in,jk) \ |
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| 85 | a = MIN( 1._wp, betdo, zbetup_ptr(ji,jj) ) ; \ |
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| 86 | b = MIN( 1._wp, betup, zbetdo_ptr(ji,jj) ) ; \ |
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| 87 | c = ( 0.5 + SIGN( 0.5_wp , vec_in(ji,jj,jk) ) ) ; \ |
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| 88 | vec(ji,jj,jk) = vec_in(ji,jj,jk) * ( c * a + ( 1._wp - c) * b ) |
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| 89 | |
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| 90 | !!---------------------------------------------------------------------- |
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| 91 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| 92 | !! $Id: traadv_fct.F90 13660 2020-10-22 10:47:32Z francesca $ |
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| 93 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 94 | !!---------------------------------------------------------------------- |
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| 95 | CONTAINS |
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| 96 | |
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| 97 | SUBROUTINE tra_adv_fct_lf( kt, kit000, cdtype, p2dt, pU, pV, pW, & |
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| 98 | & Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v ) |
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| 99 | !!---------------------------------------------------------------------- |
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| 100 | !! *** ROUTINE tra_adv_fct *** |
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| 101 | !! |
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| 102 | !! ** Purpose : Compute the now trend due to total advection of tracers |
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| 103 | !! and add it to the general trend of tracer equations |
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| 104 | !! |
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| 105 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
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| 106 | !! (choice through the value of kn_fct) |
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| 107 | !! - on the vertical the 4th order is a compact scheme |
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| 108 | !! - corrected flux (monotonic correction) |
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| 109 | !! |
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| 110 | !! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends |
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| 111 | !! - send trends to trdtra module for further diagnostics (l_trdtra=T) |
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| 112 | !! - poleward advective heat and salt transport (ln_diaptr=T) |
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| 113 | !!---------------------------------------------------------------------- |
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| 114 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 115 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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| 116 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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| 117 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 118 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 119 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
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| 120 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
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| 121 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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| 122 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(inout) :: pU, pV, pW ! 3 ocean volume flux components |
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| 123 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation |
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| 124 | ! |
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| 125 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 126 | REAL(wp) :: ztra ! local scalar |
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| 127 | REAL(wp) :: zwx_im1, zfp_ui, zfp_ui_m1, zfp_vj, zfp_vj_m1, zfp_wk, zC2t_u, zC4t_u ! - - |
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| 128 | REAL(wp) :: zwy_jm1, zfm_ui, zfm_ui_m1, zfm_vj, zfm_vj_m1, zfm_wk, zC2t_v, zC4t_v ! - - |
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| 129 | REAL(wp) :: ztu_im1, ztu_ip1, ztv_jm1, ztv_jp1 |
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| 130 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx_3d, zwy_3d, zwz, ztw, zltu_3d, zltv_3d, ztu, ztv |
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| 131 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry |
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| 132 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup |
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| 133 | LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection |
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| 134 | !!---------------------------------------------------------------------- |
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| 135 | ! |
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| 136 | IF( kt == kit000 ) THEN |
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| 137 | IF(lwp) WRITE(numout,*) |
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| 138 | IF(lwp) WRITE(numout,*) 'tra_adv_fct_lf : FCT advection scheme on ', cdtype |
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| 139 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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| 140 | ENDIF |
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| 141 | !! -- init to 0 |
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| 142 | zwx_3d(:,:,:) = 0._wp |
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| 143 | zwy_3d(:,:,:) = 0._wp |
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| 144 | zwz(:,:,:) = 0._wp |
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| 145 | zwi(:,:,:) = 0._wp |
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| 146 | ! |
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| 147 | l_trd = .FALSE. ! set local switches |
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| 148 | l_hst = .FALSE. |
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| 149 | l_ptr = .FALSE. |
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| 150 | ll_zAimp = .FALSE. |
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| 151 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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| 152 | IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE. |
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| 153 | IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & |
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| 154 | & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. |
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| 155 | ! |
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| 156 | IF( l_trd .OR. l_hst ) THEN |
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| 157 | ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) |
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| 158 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
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| 159 | ENDIF |
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| 160 | ! |
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| 161 | IF( l_ptr ) THEN |
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| 162 | ALLOCATE( zptry(jpi,jpj,jpk) ) |
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| 163 | zptry(:,:,:) = 0._wp |
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| 164 | ENDIF |
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| 165 | ! |
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| 166 | ! If adaptive vertical advection, check if it is needed on this PE at this time |
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| 167 | IF( ln_zad_Aimp ) THEN |
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| 168 | IF( MAXVAL( ABS( wi(:,:,:) ) ) > 0._wp ) ll_zAimp = .TRUE. |
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| 169 | END IF |
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| 170 | ! If active adaptive vertical advection, build tridiagonal matrix |
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| 171 | IF( ll_zAimp ) THEN |
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| 172 | ALLOCATE(zwdia(jpi,jpj,jpk), zwinf(jpi,jpj,jpk),zwsup(jpi,jpj,jpk)) |
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| 173 | DO_3D( 1, 1, 1, 1, 1, jpkm1 ) |
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| 174 | zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) & |
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| 175 | & / e3t(ji,jj,jk,Krhs) |
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| 176 | zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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| 177 | zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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| 178 | END_3D |
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| 179 | END IF |
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| 180 | ! |
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| 181 | DO jn = 1, kjpt !== loop over the tracers ==! |
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| 182 | ! |
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| 183 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
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| 184 | ! !* upstream tracer flux in the k direction *! |
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| 185 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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| 186 | zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) ) |
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| 187 | zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) ) |
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| 188 | zwz(ji,jj,jk) = 0.5 * ( zfp_wk * pt(ji,jj,jk,jn,Kbb) + zfm_wk * pt(ji,jj,jk-1,jn,Kbb) ) * wmask(ji,jj,jk) |
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| 189 | END_3D |
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| 190 | IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
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| 191 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
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| 192 | DO_2D( 1, 1, 1, 1 ) |
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| 193 | zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface |
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| 194 | END_2D |
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| 195 | ELSE ! no cavities: only at the ocean surface |
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| 196 | DO_2D( 1, 1, 1, 1 ) |
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| 197 | zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb) |
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| 198 | END_2D |
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| 199 | ENDIF |
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| 200 | ENDIF |
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| 201 | ! |
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| 202 | ! !* upstream tracer flux in the i and j direction |
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| 203 | DO jk = 1, jpkm1 |
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| 204 | DO jj = 1, jpj-1 |
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| 205 | tracer_flux_i(zwx_3d(1,jj,jk),zfp_ui,zfm_ui,1,jj,jk) |
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| 206 | tracer_flux_j(zwy_3d(1,jj,jk),zfp_vj,zfm_vj,1,jj,jk) |
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| 207 | END DO |
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| 208 | DO ji = 1, jpi-1 |
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| 209 | tracer_flux_i(zwx_3d(ji,1,jk),zfp_ui,zfm_ui,ji,1,jk) |
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| 210 | tracer_flux_j(zwy_3d(ji,1,jk),zfp_vj,zfm_vj,ji,1,jk) |
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| 211 | END DO |
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| 212 | DO_2D( 1, 1, 1, 1 ) |
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| 213 | tracer_flux_i(zwx_3d(ji,jj,jk),zfp_ui,zfm_ui,ji,jj,jk) |
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| 214 | tracer_flux_i(zwx_im1,zfp_ui_m1,zfm_ui_m1,ji-1,jj,jk) |
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| 215 | tracer_flux_j(zwy_3d(ji,jj,jk),zfp_vj,zfm_vj,ji,jj,jk) |
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| 216 | tracer_flux_j(zwy_jm1,zfp_vj_m1,zfm_vj_m1,ji,jj-1,jk) |
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| 217 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_im1 + zwy_3d(ji,jj,jk) - zwy_jm1 + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) * r1_e1e2t(ji,jj) |
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| 218 | ! ! update and guess with monotonic sheme |
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| 219 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra & |
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| 220 | & / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk) |
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| 221 | zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) & |
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| 222 | & / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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| 223 | END_2D |
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| 224 | END DO |
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| 225 | |
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| 226 | IF ( ll_zAimp ) THEN |
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| 227 | CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 ) |
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| 228 | ! |
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| 229 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ; |
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| 230 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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| 231 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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| 232 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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| 233 | ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
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| 234 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes |
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| 235 | END_3D |
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| 236 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 237 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
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| 238 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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| 239 | END_3D |
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| 240 | ! |
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| 241 | END IF |
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| 242 | ! |
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| 243 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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| 244 | ztrdx(:,:,:) = zwx_3d(:,:,:) ; ztrdy(:,:,:) = zwy_3d(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
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| 245 | END IF |
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| 246 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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| 247 | IF( l_ptr ) zptry(:,:,:) = zwy_3d(:,:,:) |
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| 248 | ! |
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| 249 | ! !== anti-diffusive flux : high order minus low order ==! |
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| 250 | ! |
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| 251 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
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| 252 | ! |
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| 253 | CASE( 2 ) !- 2nd order centered |
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| 254 | DO_3D( 2, 1, 2, 1, 1, jpkm1 ) |
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| 255 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx_3d(ji,jj,jk) |
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| 256 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy_3d(ji,jj,jk) |
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| 257 | END_3D |
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| 258 | ! |
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| 259 | CASE( 4 ) !- 4th order centered |
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| 260 | zltu_3d(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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| 261 | zltv_3d(:,:,jpk) = 0._wp |
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| 262 | DO jk = 1, jpkm1 ! Laplacian |
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| 263 | DO_2D( 1, 0, 1, 0 ) ! 1st derivative (gradient) |
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| 264 | ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk) |
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| 265 | ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk) |
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| 266 | END_2D |
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| 267 | DO_2D( 0, 0, 0, 0 ) ! 2nd derivative * 1/ 6 |
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| 268 | zltu_3d(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
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| 269 | zltv_3d(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
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| 270 | END_2D |
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| 271 | END DO |
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| 272 | CALL lbc_lnk_multi( 'traadv_fct', zltu_3d, 'T', 1.0_wp , zltv_3d, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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| 273 | ! ! |
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| 274 | DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 ) |
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| 275 | zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points |
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| 276 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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| 277 | ! ! C4 minus upstream advective fluxes |
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| 278 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + zltu_3d(ji,jj,jk) - zltu_3d(ji+1,jj,jk) ) - zwx_3d(ji,jj,jk) |
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| 279 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + zltv_3d(ji,jj,jk) - zltv_3d(ji,jj+1,jk) ) - zwy_3d(ji,jj,jk) |
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| 280 | END_3D |
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| 281 | ! |
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| 282 | CALL lbc_lnk_multi( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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| 283 | CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested |
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| 284 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes |
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| 285 | ztu_im1 = ( pt(ji ,jj ,jk,jn,Kmm) - pt(ji-1,jj,jk,jn,Kmm) ) * umask(ji-1,jj,jk) |
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| 286 | ztu_ip1 = ( pt(ji+2,jj ,jk,jn,Kmm) - pt(ji+1,jj,jk,jn,Kmm) ) * umask(ji+1,jj,jk) |
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| 287 | |
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| 288 | ztv_jm1 = ( pt(ji,jj ,jk,jn,Kmm) - pt(ji,jj-1,jk,jn,Kmm) ) * vmask(ji,jj-1,jk) |
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| 289 | ztv_jp1 = ( pt(ji,jj+2,jk,jn,Kmm) - pt(ji,jj+1,jk,jn,Kmm) ) * vmask(ji,jj+1,jk) |
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| 290 | |
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| 291 | zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points (x2) |
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| 292 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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| 293 | ! ! C4 interpolation of T at u- & v-points (x2) |
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| 294 | zC4t_u = zC2t_u + r1_6 * ( ztu_im1 - ztu_ip1 ) |
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| 295 | zC4t_v = zC2t_v + r1_6 * ( ztv_jm1 - ztv_jp1 ) |
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| 296 | ! ! C4 minus upstream advective fluxes |
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| 297 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx_3d(ji,jj,jk) |
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| 298 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy_3d(ji,jj,jk) |
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| 299 | END_3D |
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| 300 | CALL lbc_lnk_multi( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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| 301 | ! |
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| 302 | END SELECT |
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| 303 | ! |
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| 304 | SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) |
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| 305 | ! |
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| 306 | CASE( 2 ) !- 2nd order centered |
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| 307 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
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| 308 | zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) & |
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| 309 | & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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| 310 | END_3D |
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| 311 | ! |
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| 312 | CASE( 4 ) !- 4th order COMPACT |
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| 313 | CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point |
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| 314 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
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| 315 | zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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| 316 | END_3D |
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| 317 | ! |
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| 318 | END SELECT |
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| 319 | IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 |
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| 320 | zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
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| 321 | ENDIF |
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| 322 | ! |
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| 323 | CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp) |
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| 324 | ! |
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| 325 | IF ( ll_zAimp ) THEN |
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| 326 | DO_3D( 1, 1, 1, 1, 1, jpkm1 ) !* trend and after field with monotonic scheme |
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| 327 | ! ! total intermediate advective trends |
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| 328 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) & |
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| 329 | & + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) & |
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| 330 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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| 331 | ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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| 332 | END_3D |
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| 333 | ! |
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| 334 | CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 ) |
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| 335 | ! |
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| 336 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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| 337 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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| 338 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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| 339 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
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| 340 | END_3D |
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| 341 | END IF |
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| 342 | ! |
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| 343 | ! !== monotonicity algorithm ==! |
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| 344 | ! |
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| 345 | #if defined key_agrif |
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| 346 | CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) |
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| 347 | #else |
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| 348 | CALL nonosc_lf( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) |
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| 349 | #endif |
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| 350 | ! |
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| 351 | ! !== final trend with corrected fluxes ==! |
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| 352 | ! |
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| 353 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 354 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) & |
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| 355 | & + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) & |
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| 356 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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| 357 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm) |
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| 358 | zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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| 359 | END_3D |
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| 360 | ! |
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| 361 | IF ( ll_zAimp ) THEN |
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| 362 | ! |
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| 363 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp |
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| 364 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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| 365 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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| 366 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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| 367 | ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
| 368 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic |
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| 369 | END_3D |
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| 370 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 371 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
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| 372 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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| 373 | END_3D |
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| 374 | END IF |
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| 375 | ! NOT TESTED - NEED l_trd OR l_hst TRUE |
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| 376 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport |
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| 377 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx_3d(:,:,:) ! <<< add anti-diffusive fluxes |
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| 378 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy_3d(:,:,:) ! to upstream fluxes |
---|
| 379 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! |
---|
| 380 | ! |
---|
| 381 | IF( l_trd ) THEN ! trend diagnostics |
---|
| 382 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) ) |
---|
| 383 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) ) |
---|
| 384 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) ) |
---|
| 385 | ENDIF |
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| 386 | ! ! heat/salt transport |
---|
| 387 | IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) ) |
---|
| 388 | ! |
---|
| 389 | ENDIF |
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| 390 | ! NOT TESTED - NEED l_ptr TRUE |
---|
| 391 | IF( l_ptr ) THEN ! "Poleward" transports |
---|
| 392 | zptry(:,:,:) = zptry(:,:,:) + zwy_3d(:,:,:) ! <<< add anti-diffusive fluxes |
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| 393 | CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) |
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| 394 | ENDIF |
---|
| 395 | ! |
---|
| 396 | END DO ! end of tracer loop |
---|
| 397 | ! |
---|
| 398 | IF ( ll_zAimp ) THEN |
---|
| 399 | DEALLOCATE( zwdia, zwinf, zwsup ) |
---|
| 400 | ENDIF |
---|
| 401 | IF( l_trd .OR. l_hst ) THEN |
---|
| 402 | DEALLOCATE( ztrdx, ztrdy, ztrdz ) |
---|
| 403 | ENDIF |
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| 404 | IF( l_ptr ) THEN |
---|
| 405 | DEALLOCATE( zptry ) |
---|
| 406 | ENDIF |
---|
| 407 | ! |
---|
| 408 | END SUBROUTINE tra_adv_fct_lf |
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| 409 | |
---|
| 410 | SUBROUTINE nonosc_lf( Kmm, pbef, paa, pbb, pcc, paft, p2dt ) |
---|
| 411 | !!--------------------------------------------------------------------- |
---|
| 412 | !! *** ROUTINE nonosc *** |
---|
| 413 | !! |
---|
| 414 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 415 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 416 | !! |
---|
| 417 | !! ** Method : ... ??? |
---|
| 418 | !! warning : pbef and paft must be masked, but the boundaries |
---|
| 419 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 420 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 421 | !! in-space based differencing for fluid |
---|
| 422 | !!---------------------------------------------------------------------- |
---|
| 423 | INTEGER , INTENT(in ) :: Kmm ! time level index |
---|
| 424 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
---|
| 425 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field |
---|
| 426 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
---|
| 427 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: paa_in, pbb_in, pcc_in ! monotonic fluxes in the 3 directions |
---|
| 428 | ! |
---|
| 429 | REAL(dp), DIMENSION (jpi,jpj,jpk) :: zbup, zbdo |
---|
| 430 | ! |
---|
| 431 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 432 | REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars |
---|
| 433 | REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
| 434 | REAL(dp) :: zbt_ip1, zpos_ip1, zneg_ip1, zup_ip1, zdo_ip1, zbetup_ip1, zbetdo_ip1 |
---|
| 435 | REAL(dp) :: zbt_jp1, zpos_jp1, zneg_jp1, zup_jp1, zdo_jp1, zbetup_jp1, zbetdo_jp1 |
---|
| 436 | REAL(dp), TARGET, DIMENSION(jpi,jpj) :: zbetup_buf, zbetdo_buf, zbetup_ptr_buf, zbetdo_ptr_buf |
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| 437 | REAL(dp), POINTER, DIMENSION(:,:) :: tmp, zbetup, zbetdo, zbetup_ptr, zbetdo_ptr |
---|
| 438 | !!---------------------------------------------------------------------- |
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| 439 | ! |
---|
| 440 | zbig = 1.e+40_dp |
---|
| 441 | zrtrn = 1.e-15_dp |
---|
| 442 | |
---|
| 443 | paa_in(:,:,:) = paa(:,:,:) |
---|
| 444 | pbb_in(:,:,:) = pbb(:,:,:) |
---|
| 445 | pcc_in(:,:,:) = pcc(:,:,:) |
---|
| 446 | ! Search local extrema |
---|
| 447 | ! -------------------- |
---|
| 448 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
| 449 | zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & |
---|
| 450 | & paft * tmask - zbig * ( 1._wp - tmask ) ) |
---|
| 451 | zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & |
---|
| 452 | & paft * tmask + zbig * ( 1._wp - tmask ) ) |
---|
| 453 | |
---|
| 454 | zbetup => zbetup_buf |
---|
| 455 | zbetdo => zbetdo_buf |
---|
| 456 | zbetup_ptr => zbetup_ptr_buf |
---|
| 457 | zbetdo_ptr => zbetdo_ptr_buf |
---|
| 458 | |
---|
| 459 | DO_2D( 1, 0, 1, 0 ) |
---|
| 460 | |
---|
| 461 | ! search maximum in neighbourhood |
---|
| 462 | search_in_neighbour(zup,MAX,zbup,ji,jj,1) |
---|
| 463 | search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,1) |
---|
| 464 | search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,1) |
---|
| 465 | |
---|
| 466 | ! search minimum in neighbourhood |
---|
| 467 | search_in_neighbour(zdo,MIN,zbdo,ji,jj,1) |
---|
| 468 | search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,1) |
---|
| 469 | search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,1) |
---|
| 470 | |
---|
| 471 | ! positive part of the flux |
---|
| 472 | pos_part_of_flux(ji,jj,1,zpos) |
---|
| 473 | pos_part_of_flux(ji+1,jj,1,zpos_ip1) |
---|
| 474 | pos_part_of_flux(ji,jj+1,1,zpos_jp1) |
---|
| 475 | |
---|
| 476 | ! negative part of the flux |
---|
| 477 | neg_part_of_flux(ji,jj,1,zneg) |
---|
| 478 | neg_part_of_flux(ji+1,jj,1,zneg_ip1) |
---|
| 479 | neg_part_of_flux(ji,jj+1,1,zneg_jp1) |
---|
| 480 | |
---|
| 481 | ! up & down beta terms |
---|
| 482 | beta_terms(zbt,zbetup(ji,jj),zbetdo(ji,jj),zup,zpos,zdo,zneg,ji,jj,1) |
---|
| 483 | beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,1) |
---|
| 484 | beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,1) |
---|
| 485 | |
---|
| 486 | ! 3. monotonic flux in the i & j (paa & pbb) |
---|
| 487 | ! ---------------------------------------- |
---|
| 488 | monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,1) |
---|
| 489 | monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,1) |
---|
| 490 | |
---|
| 491 | END_2D |
---|
| 492 | tmp => zbetup_ptr |
---|
| 493 | zbetup_ptr => zbetup |
---|
| 494 | zbetup => tmp |
---|
| 495 | |
---|
| 496 | tmp => zbetdo_ptr |
---|
| 497 | zbetdo_ptr => zbetdo |
---|
| 498 | zbetdo => tmp |
---|
| 499 | |
---|
| 500 | DO jk = 2, jpk-1 |
---|
| 501 | DO_2D( 1, 0, 1, 0 ) |
---|
| 502 | |
---|
| 503 | ! search maximum in neighbourhood |
---|
| 504 | search_in_neighbour(zup,MAX,zbup,ji,jj,jk) |
---|
| 505 | search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,jk) |
---|
| 506 | search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,jk) |
---|
| 507 | |
---|
| 508 | ! search minimum in neighbourhood |
---|
| 509 | search_in_neighbour(zdo,MIN,zbdo,ji,jj,jk) |
---|
| 510 | search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,jk) |
---|
| 511 | search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,jk) |
---|
| 512 | |
---|
| 513 | ! positive part of the flux |
---|
| 514 | pos_part_of_flux(ji,jj,jk,zpos) |
---|
| 515 | pos_part_of_flux(ji+1,jj,jk,zpos_ip1) |
---|
| 516 | pos_part_of_flux(ji,jj+1,jk,zpos_jp1) |
---|
| 517 | |
---|
| 518 | ! negative part of the flux |
---|
| 519 | neg_part_of_flux(ji,jj,jk,zneg) |
---|
| 520 | neg_part_of_flux(ji+1,jj,jk,zneg_ip1) |
---|
| 521 | neg_part_of_flux(ji,jj+1,jk,zneg_jp1) |
---|
| 522 | |
---|
| 523 | ! up & down beta terms |
---|
| 524 | beta_terms(zbt,zbetup(ji,jj),zbetdo(ji,jj),zup,zpos,zdo,zneg,ji,jj,jk) |
---|
| 525 | beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,jk) |
---|
| 526 | beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,jk) |
---|
| 527 | |
---|
| 528 | ! 3. monotonic flux in the i & j (paa & pbb) |
---|
| 529 | ! ---------------------------------------- |
---|
| 530 | monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,jk) |
---|
| 531 | monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,jk) |
---|
| 532 | |
---|
| 533 | ! monotonic flux in the k direction, i.e. pcc |
---|
| 534 | ! ------------------------------------------- |
---|
| 535 | monotonic_flux_k(za,zb,zc,zbetup(ji,jj),zbetdo(ji,jj),pcc,pcc_in,jk) |
---|
| 536 | END_2D |
---|
| 537 | tmp => zbetup_ptr |
---|
| 538 | zbetup_ptr => zbetup |
---|
| 539 | zbetup => tmp |
---|
| 540 | |
---|
| 541 | tmp => zbetdo_ptr |
---|
| 542 | zbetdo_ptr => zbetdo |
---|
| 543 | zbetdo => tmp |
---|
| 544 | END DO |
---|
| 545 | ! |
---|
| 546 | DO_2D( 1, 0, 1, 0 ) |
---|
| 547 | ! monotonic flux in the k direction, i.e. pcc |
---|
| 548 | ! ------------------------------------------- |
---|
| 549 | monotonic_flux_k(za,zb,zc,0._dp,0._dp,pcc,pcc_in,jpk) |
---|
| 550 | END_2D |
---|
| 551 | END SUBROUTINE nonosc_lf |
---|
| 552 | |
---|
| 553 | END MODULE traadv_fct_lf |
---|