| 1 | MODULE traadv_qck |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE traadv_qck *** |
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| 4 | !! Ocean tracers: horizontal & vertical advective trend |
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| 5 | !!============================================================================== |
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| 6 | !! History : 3.0 ! 2008-07 (G. Reffray) Original code |
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| 7 | !! 3.3 ! 2010-05 (C.Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! tra_adv_qck : update the tracer trend with the horizontal advection |
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| 12 | !! trends using a 3rd order finite difference scheme |
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| 13 | !! tra_adv_qck_i : apply QUICK scheme in i-direction |
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| 14 | !! tra_adv_qck_j : apply QUICK scheme in j-direction |
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| 15 | !! tra_adv_cen2_k : 2nd centered scheme for the vertical advection |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | USE oce ! ocean dynamics and active tracers |
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| 18 | USE dom_oce ! ocean space and time domain |
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| 19 | USE trc_oce ! share passive tracers/Ocean variables |
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| 20 | USE trd_oce ! trends: ocean variables |
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| 21 | USE trdtra ! trends manager: tracers |
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| 22 | USE diaptr ! poleward transport diagnostics |
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| 23 | USE iom |
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| 24 | ! |
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| 25 | USE in_out_manager ! I/O manager |
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| 26 | USE lib_mpp ! distribued memory computing |
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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 | #if defined key_loop_fusion |
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| 30 | USE traadv_qck_lf ! QCK scheme (tra_adv_qck routine - loop fusion version) |
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| 31 | #endif |
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| 32 | |
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| 33 | IMPLICIT NONE |
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| 34 | PRIVATE |
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| 35 | |
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| 36 | PUBLIC tra_adv_qck ! routine called by step.F90 |
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| 37 | |
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| 38 | REAL(wp) :: r1_6 = 1./ 6. ! 1/6 ratio |
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| 39 | |
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| 40 | LOGICAL :: l_trd ! flag to compute trends |
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| 41 | LOGICAL :: l_ptr ! flag to compute poleward transport |
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| 42 | |
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| 43 | |
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| 44 | !! * Substitutions |
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| 45 | # include "do_loop_substitute.h90" |
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| 46 | # include "domzgr_substitute.h90" |
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| 47 | !!---------------------------------------------------------------------- |
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| 48 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| 49 | !! $Id$ |
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| 50 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 51 | !!---------------------------------------------------------------------- |
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| 52 | CONTAINS |
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| 53 | |
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| 54 | SUBROUTINE tra_adv_qck ( kt, kit000, cdtype, p2dt, pU, pV, pW, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 55 | !!---------------------------------------------------------------------- |
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| 56 | !! *** ROUTINE tra_adv_qck *** |
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| 57 | !! |
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| 58 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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| 59 | !! and add it to the general trend of passive tracer equations. |
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| 60 | !! |
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| 61 | !! ** Method : The advection is evaluated by a third order scheme |
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| 62 | !! For a positive velocity u : u(i)>0 |
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| 63 | !! |--FU--|--FC--|--FD--|------| |
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| 64 | !! i-1 i i+1 i+2 |
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| 65 | !! |
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| 66 | !! For a negative velocity u : u(i)<0 |
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| 67 | !! |------|--FD--|--FC--|--FU--| |
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| 68 | !! i-1 i i+1 i+2 |
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| 69 | !! where FU is the second upwind point |
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| 70 | !! FD is the first douwning point |
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| 71 | !! FC is the central point (or the first upwind point) |
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| 72 | !! |
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| 73 | !! Flux(i) = u(i) * { 0.5(FC+FD) -0.5C(i)(FD-FC) -((1-C(i))/6)(FU+FD-2FC) } |
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| 74 | !! with C(i)=|u(i)|dx(i)/dt (=Courant number) |
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| 75 | !! |
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| 76 | !! dt = 2*rdtra and the scalar values are tb and sb |
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| 77 | !! |
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| 78 | !! On the vertical, the simple centered scheme used pt(:,:,:,:,Kmm) |
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| 79 | !! |
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| 80 | !! The fluxes are bounded by the ULTIMATE limiter to |
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| 81 | !! guarantee the monotonicity of the solution and to |
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| 82 | !! prevent the appearance of spurious numerical oscillations |
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| 83 | !! |
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| 84 | !! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends |
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| 85 | !! - send trends to trdtra module for further diagnostcs (l_trdtra=T) |
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| 86 | !! - poleward advective heat and salt transport (ln_diaptr=T) |
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| 87 | !! |
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| 88 | !! ** Reference : Leonard (1979, 1991) |
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| 89 | !!---------------------------------------------------------------------- |
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| 90 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 91 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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| 92 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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| 93 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 94 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 95 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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| 96 | ! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support) |
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| 97 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume transport components |
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| 98 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation |
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| 99 | !!---------------------------------------------------------------------- |
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| 100 | ! |
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| 101 | #if defined key_loop_fusion |
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| 102 | CALL tra_adv_qck_lf ( kt, kit000, cdtype, p2dt, pU, pV, pW, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 103 | #else |
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| 104 | IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile |
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| 105 | IF( kt == kit000 ) THEN |
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| 106 | IF(lwp) WRITE(numout,*) |
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| 107 | IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype |
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| 108 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' |
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| 109 | IF(lwp) WRITE(numout,*) |
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| 110 | ENDIF |
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| 111 | ! |
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| 112 | l_trd = .FALSE. |
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| 113 | l_ptr = .FALSE. |
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| 114 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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| 115 | IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE. |
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| 116 | ENDIF |
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| 117 | ! |
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| 118 | ! ! horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme |
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| 119 | CALL tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 120 | CALL tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 121 | |
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| 122 | ! ! vertical fluxes are computed with the 2nd order centered scheme |
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| 123 | CALL tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs ) |
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| 124 | ! |
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| 125 | #endif |
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| 126 | END SUBROUTINE tra_adv_qck |
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| 127 | |
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| 128 | |
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| 129 | SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 130 | !!---------------------------------------------------------------------- |
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| 131 | !! |
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| 132 | !!---------------------------------------------------------------------- |
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| 133 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 134 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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| 135 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 136 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 137 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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| 138 | ! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support) |
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| 139 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU ! i-velocity components |
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| 140 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation |
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| 141 | !! |
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| 142 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 143 | REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars |
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| 144 | REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwx, zfu, zfc, zfd |
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| 145 | !---------------------------------------------------------------------- |
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| 146 | ! |
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| 147 | ! ! =========== |
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| 148 | DO jn = 1, kjpt ! tracer loop |
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| 149 | ! ! =========== |
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| 150 | zfu(:,:,:) = 0._wp ; zfc(:,:,:) = 0._wp |
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| 151 | zfd(:,:,:) = 0._wp ; zwx(:,:,:) = 0._wp |
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| 152 | ! |
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| 153 | !!gm why not using a SHIFT instruction... |
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| 154 | DO_3D( nn_hls-1, nn_hls-1, 0, 0, 1, jpkm1 ) !--- Computation of the ustream and downstream value of the tracer and the mask |
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| 155 | zfc(ji,jj,jk) = pt(ji-1,jj,jk,jn,Kbb) ! Upstream in the x-direction for the tracer |
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| 156 | zfd(ji,jj,jk) = pt(ji+1,jj,jk,jn,Kbb) ! Downstream in the x-direction for the tracer |
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| 157 | END_3D |
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| 158 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, ld4only= .TRUE. ) ! Lateral boundary conditions |
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| 159 | |
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| 160 | ! |
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| 161 | ! Horizontal advective fluxes |
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| 162 | ! --------------------------- |
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| 163 | DO_3D( nn_hls-1, 0, 0, 0, 1, jpkm1 ) |
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| 164 | zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 165 | zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T |
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| 166 | END_3D |
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| 167 | ! |
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| 168 | DO_3D( nn_hls-1, 0, 0, 0, 1, jpkm1 ) |
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| 169 | zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 170 | zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * e3u(ji,jj,jk,Kmm) |
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| 171 | zwx(ji,jj,jk) = ABS( pU(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction) |
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| 172 | zfc(ji,jj,jk) = zdir * pt(ji ,jj,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji+1,jj,jk,jn,Kbb) ! FC in the x-direction for T |
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| 173 | zfd(ji,jj,jk) = zdir * pt(ji+1,jj,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji ,jj,jk,jn,Kbb) ! FD in the x-direction for T |
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| 174 | END_3D |
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| 175 | !--- Lateral boundary conditions |
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| 176 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, zfc(:,:,:), 'T', 1.0_wp, zwx(:,:,:), 'T', 1.0_wp ) |
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| 177 | |
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| 178 | !--- QUICKEST scheme |
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| 179 | CALL quickest( zfu, zfd, zfc, zwx ) |
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| 180 | ! |
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| 181 | ! Mask at the T-points in the x-direction (mask=0 or mask=1) |
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| 182 | DO_3D( nn_hls-1, nn_hls-1, 0, 0, 1, jpkm1 ) |
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| 183 | zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2. |
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| 184 | END_3D |
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| 185 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp, ld4only= .TRUE. ) ! Lateral boundary conditions |
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| 186 | |
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| 187 | ! |
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| 188 | ! Tracer flux on the x-direction |
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| 189 | DO_3D( 1, 0, 0, 0, 1, jpkm1 ) |
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| 190 | zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 191 | !--- If the second ustream point is a land point |
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| 192 | !--- the flux is computed by the 1st order UPWIND scheme |
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| 193 | zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk) |
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| 194 | zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk) |
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| 195 | zwx(ji,jj,jk) = zwx(ji,jj,jk) * pU(ji,jj,jk) |
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| 196 | END_3D |
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| 197 | ! |
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| 198 | ! Computation of the trend |
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| 199 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 200 | zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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| 201 | ! horizontal advective trends |
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| 202 | ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) ) |
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| 203 | !--- add it to the general tracer trends |
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| 204 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra |
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| 205 | END_3D |
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| 206 | ! ! trend diagnostics |
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| 207 | IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, zwx, pU, pt(:,:,:,jn,Kmm) ) |
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| 208 | ! |
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| 209 | END DO |
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| 210 | ! |
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| 211 | END SUBROUTINE tra_adv_qck_i |
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| 212 | |
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| 213 | |
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| 214 | SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs ) |
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| 215 | !!---------------------------------------------------------------------- |
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| 216 | !! |
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| 217 | !!---------------------------------------------------------------------- |
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| 218 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 219 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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| 220 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 221 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 222 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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| 223 | ! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support) |
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| 224 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pV ! j-velocity components |
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| 225 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation |
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| 226 | !! |
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| 227 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 228 | REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars |
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| 229 | REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwy, zfu, zfc, zfd ! 3D workspace |
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| 230 | !---------------------------------------------------------------------- |
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| 231 | ! |
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| 232 | ! ! =========== |
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| 233 | DO jn = 1, kjpt ! tracer loop |
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| 234 | ! ! =========== |
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| 235 | zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0 |
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| 236 | zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0 |
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| 237 | ! |
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| 238 | DO jk = 1, jpkm1 |
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| 239 | ! |
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| 240 | !--- Computation of the ustream and downstream value of the tracer and the mask |
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| 241 | DO_2D( 0, 0, nn_hls-1, nn_hls-1 ) |
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| 242 | ! Upstream in the x-direction for the tracer |
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| 243 | zfc(ji,jj,jk) = pt(ji,jj-1,jk,jn,Kbb) |
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| 244 | ! Downstream in the x-direction for the tracer |
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| 245 | zfd(ji,jj,jk) = pt(ji,jj+1,jk,jn,Kbb) |
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| 246 | END_2D |
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| 247 | END DO |
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| 248 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, ld4only= .TRUE. ) ! Lateral boundary conditions |
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| 249 | |
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| 250 | ! |
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| 251 | ! Horizontal advective fluxes |
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| 252 | ! --------------------------- |
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| 253 | ! |
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| 254 | DO_3D( 0, 0, nn_hls-1, 0, 1, jpkm1 ) |
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| 255 | zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 256 | zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T |
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| 257 | END_3D |
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| 258 | ! |
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| 259 | DO_3D( 0, 0, nn_hls-1, 0, 1, jpkm1 ) |
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| 260 | zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 261 | zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * e3v(ji,jj,jk,Kmm) |
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| 262 | zwy(ji,jj,jk) = ABS( pV(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction) |
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| 263 | zfc(ji,jj,jk) = zdir * pt(ji,jj ,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji,jj+1,jk,jn,Kbb) ! FC in the x-direction for T |
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| 264 | zfd(ji,jj,jk) = zdir * pt(ji,jj+1,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji,jj ,jk,jn,Kbb) ! FD in the x-direction for T |
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| 265 | END_3D |
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| 266 | |
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| 267 | !--- Lateral boundary conditions |
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| 268 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, zfc(:,:,:), 'T', 1.0_wp, zwy(:,:,:), 'T', 1.0_wp ) |
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| 269 | |
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| 270 | !--- QUICKEST scheme |
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| 271 | CALL quickest( zfu, zfd, zfc, zwy ) |
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| 272 | ! |
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| 273 | ! Mask at the T-points in the x-direction (mask=0 or mask=1) |
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| 274 | DO_3D( 0, 0, nn_hls-1, nn_hls-1, 1, jpkm1 ) |
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| 275 | zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2. |
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| 276 | END_3D |
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| 277 | IF (nn_hls==1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp, ld4only= .TRUE. ) !--- Lateral boundary conditions |
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| 278 | ! |
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| 279 | ! Tracer flux on the x-direction |
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| 280 | DO_3D( 0, 0, 1, 0, 1, jpkm1 ) |
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| 281 | zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0 |
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| 282 | !--- If the second ustream point is a land point |
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| 283 | !--- the flux is computed by the 1st order UPWIND scheme |
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| 284 | zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk) |
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| 285 | zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk) |
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| 286 | zwy(ji,jj,jk) = zwy(ji,jj,jk) * pV(ji,jj,jk) |
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| 287 | END_3D |
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| 288 | ! |
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| 289 | ! Computation of the trend |
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| 290 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 291 | zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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| 292 | ! horizontal advective trends |
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| 293 | ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) ) |
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| 294 | !--- add it to the general tracer trends |
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| 295 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra |
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| 296 | END_3D |
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| 297 | ! ! trend diagnostics |
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| 298 | IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, zwy, pV, pt(:,:,:,jn,Kmm) ) |
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| 299 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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| 300 | IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) ) |
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| 301 | ! |
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| 302 | END DO |
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| 303 | ! |
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| 304 | END SUBROUTINE tra_adv_qck_j |
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| 305 | |
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| 306 | |
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| 307 | SUBROUTINE tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs ) |
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| 308 | !!---------------------------------------------------------------------- |
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| 309 | !! |
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| 310 | !!---------------------------------------------------------------------- |
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| 311 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 312 | INTEGER , INTENT(in ) :: Kmm, Krhs ! ocean time level indices |
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| 313 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 314 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 315 | ! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support) |
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| 316 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pW ! vertical velocity |
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| 317 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation |
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| 318 | ! |
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| 319 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 320 | REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwz ! 3D workspace |
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| 321 | !!---------------------------------------------------------------------- |
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| 322 | ! |
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| 323 | zwz(:,:, 1 ) = 0._wp ! surface & bottom values set to zero for all tracers |
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| 324 | zwz(:,:,jpk) = 0._wp |
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| 325 | ! |
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| 326 | ! ! =========== |
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| 327 | DO jn = 1, kjpt ! tracer loop |
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| 328 | ! ! =========== |
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| 329 | ! |
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| 330 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !* Interior point (w-masked 2nd order centered flux) |
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| 331 | zwz(ji,jj,jk) = 0.5 * pW(ji,jj,jk) * ( pt(ji,jj,jk-1,jn,Kmm) + pt(ji,jj,jk,jn,Kmm) ) * wmask(ji,jj,jk) |
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| 332 | END_3D |
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| 333 | IF( ln_linssh ) THEN !* top value (only in linear free surf. as zwz is multiplied by wmask) |
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| 334 | IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean) |
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| 335 | DO_2D( 0, 0, 0, 0 ) |
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| 336 | zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kmm) ! linear free surface |
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| 337 | END_2D |
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| 338 | ELSE ! no ocean cavities (only ocean surface) |
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| 339 | DO_2D( 0, 0, 0, 0 ) |
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| 340 | zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kmm) |
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| 341 | END_2D |
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| 342 | ENDIF |
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| 343 | ENDIF |
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| 344 | ! |
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| 345 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) !== Tracer flux divergence added to the general trend ==! |
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| 346 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) & |
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| 347 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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| 348 | END_3D |
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| 349 | ! ! Send trends for diagnostic |
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| 350 | IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwz, pW, pt(:,:,:,jn,Kmm) ) |
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| 351 | ! |
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| 352 | END DO |
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| 353 | ! |
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| 354 | END SUBROUTINE tra_adv_cen2_k |
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| 355 | |
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| 356 | |
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| 357 | SUBROUTINE quickest( pfu, pfd, pfc, puc ) |
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| 358 | !!---------------------------------------------------------------------- |
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| 359 | !! |
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| 360 | !! ** Purpose : Computation of advective flux with Quickest scheme |
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| 361 | !! |
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| 362 | !! ** Method : |
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| 363 | !!---------------------------------------------------------------------- |
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| 364 | REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfu ! second upwind point |
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| 365 | REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfd ! first douwning point |
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| 366 | REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point) |
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| 367 | REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux |
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| 368 | !! |
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| 369 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 370 | REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars |
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| 371 | REAL(wp) :: zc, zcurv, zfho ! - - |
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| 372 | !---------------------------------------------------------------------- |
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| 373 | ! |
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| 374 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 ) |
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| 375 | zc = puc(ji,jj,jk) ! Courant number |
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| 376 | zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk) |
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| 377 | zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) ) |
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| 378 | zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) ) |
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| 379 | zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv |
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| 380 | zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST |
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| 381 | ! |
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| 382 | zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk) |
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| 383 | zcoef2 = ABS( zcoef1 ) |
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| 384 | zcoef3 = ABS( zcurv ) |
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| 385 | IF( zcoef3 >= zcoef2 ) THEN |
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| 386 | zfho = pfc(ji,jj,jk) |
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| 387 | ELSE |
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| 388 | zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF |
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| 389 | IF( zcoef1 >= 0. ) THEN |
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| 390 | zfho = MAX( pfc(ji,jj,jk), zfho ) |
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| 391 | zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) ) |
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| 392 | ELSE |
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| 393 | zfho = MIN( pfc(ji,jj,jk), zfho ) |
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| 394 | zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) ) |
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| 395 | ENDIF |
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| 396 | ENDIF |
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| 397 | puc(ji,jj,jk) = zfho |
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| 398 | END_3D |
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| 399 | ! |
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| 400 | END SUBROUTINE quickest |
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| 401 | |
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| 402 | !!====================================================================== |
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| 403 | END MODULE traadv_qck |
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