[456] | 1 | MODULE dynzdf |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf *** |
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| 4 | !! Ocean dynamics : vertical component of the momentum mixing trend |
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| 5 | !!============================================================================== |
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[2528] | 6 | !! History : 1.0 ! 2005-11 (G. Madec) Original code |
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| 7 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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[9019] | 8 | !! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point |
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[456] | 9 | !!---------------------------------------------------------------------- |
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[503] | 10 | |
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| 11 | !!---------------------------------------------------------------------- |
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[9019] | 12 | !! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing |
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[456] | 13 | !!---------------------------------------------------------------------- |
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[5836] | 14 | USE oce ! ocean dynamics and tracers variables |
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[9019] | 15 | USE phycst ! physical constants |
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[5836] | 16 | USE dom_oce ! ocean space and time domain variables |
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[9019] | 17 | USE sbc_oce ! surface boundary condition: ocean |
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[5836] | 18 | USE zdf_oce ! ocean vertical physics variables |
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[9019] | 19 | USE zdfdrg ! vertical physics: top/bottom drag coef. |
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| 20 | USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form |
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| 21 | USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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[9490] | 22 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator |
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[5836] | 23 | USE trd_oce ! trends: ocean variables |
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| 24 | USE trddyn ! trend manager: dynamics |
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| 25 | ! |
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| 26 | USE in_out_manager ! I/O manager |
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| 27 | USE lib_mpp ! MPP library |
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| 28 | USE prtctl ! Print control |
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| 29 | USE timing ! Timing |
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[456] | 30 | |
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| 31 | IMPLICIT NONE |
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| 32 | PRIVATE |
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| 33 | |
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[9019] | 34 | PUBLIC dyn_zdf ! routine called by step.F90 |
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[456] | 35 | |
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[9019] | 36 | REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise |
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[456] | 37 | |
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| 38 | !! * Substitutions |
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[12377] | 39 | # include "do_loop_substitute.h90" |
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[456] | 40 | !!---------------------------------------------------------------------- |
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[9598] | 41 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[1152] | 42 | !! $Id$ |
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[10068] | 43 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[456] | 44 | !!---------------------------------------------------------------------- |
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| 45 | CONTAINS |
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| 46 | |
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[12377] | 47 | SUBROUTINE dyn_zdf( kt, Kbb, Kmm, Krhs, puu, pvv, Kaa ) |
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[456] | 48 | !!---------------------------------------------------------------------- |
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| 49 | !! *** ROUTINE dyn_zdf *** |
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| 50 | !! |
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[9019] | 51 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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| 52 | !! together with the Leap-Frog time stepping using an |
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| 53 | !! implicit scheme. |
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| 54 | !! |
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| 55 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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[12377] | 56 | !! u(after) = u(before) + 2*dt * u(rhs) vector form or linear free surf. |
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| 57 | !! u(after) = ( e3u_b*u(before) + 2*dt * e3u_n*u(rhs) ) / e3u(after) otherwise |
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[9019] | 58 | !! - update the after velocity with the implicit vertical mixing. |
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| 59 | !! This requires to solver the following system: |
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[12377] | 60 | !! u(after) = u(after) + 1/e3u(after) dk+1[ mi(avm) / e3uw(after) dk[ua] ] |
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[9019] | 61 | !! with the following surface/top/bottom boundary condition: |
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| 62 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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| 63 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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| 64 | !! |
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[12377] | 65 | !! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity |
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[456] | 66 | !!--------------------------------------------------------------------- |
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[12377] | 67 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 68 | INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices |
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| 69 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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[3294] | 70 | ! |
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[9019] | 71 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 72 | INTEGER :: iku, ikv ! local integers |
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| 73 | REAL(wp) :: zzwi, ze3ua, zdt ! local scalars |
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| 74 | REAL(wp) :: zzws, ze3va ! - - |
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[10364] | 75 | REAL(wp) :: z1_e3ua, z1_e3va ! - - |
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| 76 | REAL(wp) :: zWu , zWv ! - - |
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| 77 | REAL(wp) :: zWui, zWvi ! - - |
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| 78 | REAL(wp) :: zWus, zWvs ! - - |
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[9019] | 79 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace |
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| 80 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - |
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[456] | 81 | !!--------------------------------------------------------------------- |
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[3294] | 82 | ! |
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[9019] | 83 | IF( ln_timing ) CALL timing_start('dyn_zdf') |
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[3294] | 84 | ! |
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[9019] | 85 | IF( kt == nit000 ) THEN !* initialization |
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| 86 | IF(lwp) WRITE(numout,*) |
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| 87 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 88 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 89 | ! |
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| 90 | If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator |
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| 91 | ELSE ; r_vvl = 1._wp |
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| 92 | ENDIF |
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| 93 | ENDIF |
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| 94 | ! !* set time step |
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[6140] | 95 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; r2dt = rdt ! = rdt (restart with Euler time stepping) |
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| 96 | ELSEIF( kt <= nit000 + 1 ) THEN ; r2dt = 2. * rdt ! = 2 rdt (leapfrog) |
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[456] | 97 | ENDIF |
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[9250] | 98 | ! |
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| 99 | ! !* explicit top/bottom drag case |
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[12377] | 100 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, Kmm, puu(:,:,:,Kbb), pvv(:,:,:,Kbb), puu(:,:,:,Krhs), pvv(:,:,:,Krhs) ) ! add top/bottom friction trend to (puu(Kaa),pvv(Kaa)) |
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[9250] | 101 | ! |
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| 102 | ! |
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[9019] | 103 | IF( l_trddyn ) THEN !* temporary save of ta and sa trends |
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| 104 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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[12377] | 105 | ztrdu(:,:,:) = puu(:,:,:,Krhs) |
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| 106 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) |
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[456] | 107 | ENDIF |
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[9019] | 108 | ! |
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[12377] | 109 | ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) |
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[9019] | 110 | ! |
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| 111 | ! ! time stepping except vertical diffusion |
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| 112 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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| 113 | DO jk = 1, jpkm1 |
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[12377] | 114 | puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kbb) + r2dt * puu(:,:,jk,Krhs) ) * umask(:,:,jk) |
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| 115 | pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kbb) + r2dt * pvv(:,:,jk,Krhs) ) * vmask(:,:,jk) |
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[9019] | 116 | END DO |
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| 117 | ELSE ! applied on thickness weighted velocity |
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| 118 | DO jk = 1, jpkm1 |
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[12377] | 119 | puu(:,:,jk,Kaa) = ( e3u(:,:,jk,Kbb) * puu(:,:,jk,Kbb) & |
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| 120 | & + r2dt * e3u(:,:,jk,Kmm) * puu(:,:,jk,Krhs) ) / e3u(:,:,jk,Kaa) * umask(:,:,jk) |
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| 121 | pvv(:,:,jk,Kaa) = ( e3v(:,:,jk,Kbb) * pvv(:,:,jk,Kbb) & |
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| 122 | & + r2dt * e3v(:,:,jk,Kmm) * pvv(:,:,jk,Krhs) ) / e3v(:,:,jk,Kaa) * vmask(:,:,jk) |
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[9019] | 123 | END DO |
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| 124 | ENDIF |
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| 125 | ! ! add top/bottom friction |
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| 126 | ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. |
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| 127 | ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does |
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| 128 | ! not lead to the effective stress seen over the whole barotropic loop. |
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[12377] | 129 | ! G. Madec : in linear free surface, e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm) = e3u_0, so systematic use of e3u(:,:,:,Kaa) |
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[9019] | 130 | IF( ln_drgimp .AND. ln_dynspg_ts ) THEN |
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| 131 | DO jk = 1, jpkm1 ! remove barotropic velocities |
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[12377] | 132 | puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kaa) - uu_b(:,:,Kaa) ) * umask(:,:,jk) |
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| 133 | pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kaa) - vv_b(:,:,Kaa) ) * vmask(:,:,jk) |
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[9019] | 134 | END DO |
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[12377] | 135 | DO_2D_00_00 |
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| 136 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 137 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 138 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 139 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 140 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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| 141 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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| 142 | END_2D |
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[9019] | 143 | IF( ln_isfcav ) THEN ! Ocean cavities (ISF) |
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[12377] | 144 | DO_2D_00_00 |
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| 145 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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| 146 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 147 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 148 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 149 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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| 150 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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| 151 | END_2D |
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[9019] | 152 | END IF |
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| 153 | ENDIF |
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| 154 | ! |
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| 155 | ! !== Vertical diffusion on u ==! |
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| 156 | ! |
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| 157 | ! !* Matrix construction |
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| 158 | zdt = r2dt * 0.5 |
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[10364] | 159 | IF( ln_zad_Aimp ) THEN !! |
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| 160 | SELECT CASE( nldf_dyn ) |
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| 161 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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[12377] | 162 | DO_3D_00_00( 1, jpkm1 ) |
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| 163 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 164 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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| 165 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 166 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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| 167 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 168 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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| 169 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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| 170 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 171 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 172 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 173 | END_3D |
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[10364] | 174 | CASE DEFAULT ! iso-level lateral mixing |
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[12377] | 175 | DO_3D_00_00( 1, jpkm1 ) |
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| 176 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 177 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 178 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 179 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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| 180 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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| 181 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 182 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 183 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 184 | END_3D |
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[10364] | 185 | END SELECT |
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[12377] | 186 | DO_2D_00_00 |
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| 187 | zwi(ji,jj,1) = 0._wp |
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| 188 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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| 189 | zzws = - zdt * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) / ( ze3ua * e3uw(ji,jj,2,Kmm) ) * wumask(ji,jj,2) |
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| 190 | zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua |
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| 191 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 192 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) |
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| 193 | END_2D |
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[10364] | 194 | ELSE |
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| 195 | SELECT CASE( nldf_dyn ) |
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| 196 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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[12377] | 197 | DO_3D_00_00( 1, jpkm1 ) |
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| 198 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 199 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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| 200 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 201 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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| 202 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 203 | zwi(ji,jj,jk) = zzwi |
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| 204 | zws(ji,jj,jk) = zzws |
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| 205 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 206 | END_3D |
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[10364] | 207 | CASE DEFAULT ! iso-level lateral mixing |
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[12377] | 208 | DO_3D_00_00( 1, jpkm1 ) |
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| 209 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 210 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 211 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 212 | zwi(ji,jj,jk) = zzwi |
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| 213 | zws(ji,jj,jk) = zzws |
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| 214 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 215 | END_3D |
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[10364] | 216 | END SELECT |
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[12377] | 217 | DO_2D_00_00 |
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| 218 | zwi(ji,jj,1) = 0._wp |
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| 219 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 220 | END_2D |
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[10364] | 221 | ENDIF |
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[9019] | 222 | ! |
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| 223 | ! |
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| 224 | ! !== Apply semi-implicit bottom friction ==! |
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| 225 | ! |
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| 226 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 227 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 228 | ! column vector of the tri-diagonal matrix equation |
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| 229 | ! |
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| 230 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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[12377] | 231 | DO_2D_00_00 |
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| 232 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 233 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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| 234 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua |
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| 235 | END_2D |
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[9019] | 236 | IF ( ln_isfcav ) THEN ! top friction (always implicit) |
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[12377] | 237 | DO_2D_00_00 |
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| 238 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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| 239 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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| 240 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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| 241 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua |
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| 242 | END_2D |
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[9019] | 243 | END IF |
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| 244 | ENDIF |
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| 245 | ! |
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| 246 | ! Matrix inversion starting from the first level |
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| 247 | !----------------------------------------------------------------------- |
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| 248 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 249 | ! |
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| 250 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 251 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 252 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 253 | ! ( ... )( ... ) ( ... ) |
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| 254 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 255 | ! |
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| 256 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 257 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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[12377] | 258 | ! The solution (the after velocity) is in puu(:,:,:,Kaa) |
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[9019] | 259 | !----------------------------------------------------------------------- |
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| 260 | ! |
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[12377] | 261 | DO_3D_00_00( 2, jpkm1 ) |
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| 262 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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| 263 | END_3D |
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[9019] | 264 | ! |
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[12377] | 265 | DO_2D_00_00 |
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| 266 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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| 267 | puu(ji,jj,1,Kaa) = puu(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & |
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| 268 | & / ( ze3ua * rau0 ) * umask(ji,jj,1) |
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| 269 | END_2D |
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| 270 | DO_3D_00_00( 2, jpkm1 ) |
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| 271 | puu(ji,jj,jk,Kaa) = puu(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * puu(ji,jj,jk-1,Kaa) |
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| 272 | END_3D |
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[9019] | 273 | ! |
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[12377] | 274 | DO_2D_00_00 |
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| 275 | puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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| 276 | END_2D |
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| 277 | DO_3DS_00_00( jpk-2, 1, -1 ) |
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| 278 | puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - zws(ji,jj,jk) * puu(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
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| 279 | END_3D |
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[9019] | 280 | ! |
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| 281 | ! !== Vertical diffusion on v ==! |
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| 282 | ! |
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| 283 | ! !* Matrix construction |
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| 284 | zdt = r2dt * 0.5 |
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[10364] | 285 | IF( ln_zad_Aimp ) THEN !! |
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| 286 | SELECT CASE( nldf_dyn ) |
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| 287 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) |
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[12377] | 288 | DO_3D_00_00( 1, jpkm1 ) |
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| 289 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 290 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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| 291 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 292 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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| 293 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 294 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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| 295 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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| 296 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 297 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 298 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 299 | END_3D |
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[10364] | 300 | CASE DEFAULT ! iso-level lateral mixing |
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[12377] | 301 | DO_3D_00_00( 1, jpkm1 ) |
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| 302 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 303 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 304 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 305 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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| 306 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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| 307 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 308 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 309 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 310 | END_3D |
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[10364] | 311 | END SELECT |
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[12377] | 312 | DO_2D_00_00 |
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| 313 | zwi(ji,jj,1) = 0._wp |
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| 314 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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| 315 | zzws = - zdt * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) / ( ze3va * e3vw(ji,jj,2,Kmm) ) * wvmask(ji,jj,2) |
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| 316 | zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va |
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| 317 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 318 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) |
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| 319 | END_2D |
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[10364] | 320 | ELSE |
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| 321 | SELECT CASE( nldf_dyn ) |
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| 322 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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[12377] | 323 | DO_3D_00_00( 1, jpkm1 ) |
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| 324 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 325 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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| 326 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 327 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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| 328 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 329 | zwi(ji,jj,jk) = zzwi |
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| 330 | zws(ji,jj,jk) = zzws |
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| 331 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 332 | END_3D |
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[10364] | 333 | CASE DEFAULT ! iso-level lateral mixing |
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[12377] | 334 | DO_3D_00_00( 1, jpkm1 ) |
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| 335 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 336 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 337 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 338 | zwi(ji,jj,jk) = zzwi |
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| 339 | zws(ji,jj,jk) = zzws |
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| 340 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 341 | END_3D |
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[10364] | 342 | END SELECT |
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[12377] | 343 | DO_2D_00_00 |
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| 344 | zwi(ji,jj,1) = 0._wp |
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| 345 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 346 | END_2D |
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[10364] | 347 | ENDIF |
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[9019] | 348 | ! |
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| 349 | ! !== Apply semi-implicit top/bottom friction ==! |
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| 350 | ! |
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| 351 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 352 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 353 | ! column vector of the tri-diagonal matrix equation |
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| 354 | ! |
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| 355 | IF( ln_drgimp ) THEN |
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[12377] | 356 | DO_2D_00_00 |
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| 357 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 358 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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| 359 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va |
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| 360 | END_2D |
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[9019] | 361 | IF ( ln_isfcav ) THEN |
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[12377] | 362 | DO_2D_00_00 |
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| 363 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 364 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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| 365 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) / ze3va |
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| 366 | END_2D |
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[9019] | 367 | ENDIF |
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| 368 | ENDIF |
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[456] | 369 | |
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[9019] | 370 | ! Matrix inversion |
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| 371 | !----------------------------------------------------------------------- |
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| 372 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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[503] | 373 | ! |
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[9019] | 374 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 375 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 376 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 377 | ! ( ... )( ... ) ( ... ) |
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| 378 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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[503] | 379 | ! |
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[9019] | 380 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 381 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 382 | ! The solution (after velocity) is in 2d array va |
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| 383 | !----------------------------------------------------------------------- |
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| 384 | ! |
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[12377] | 385 | DO_3D_00_00( 2, jpkm1 ) |
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| 386 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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| 387 | END_3D |
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[9019] | 388 | ! |
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[12377] | 389 | DO_2D_00_00 |
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| 390 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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| 391 | pvv(ji,jj,1,Kaa) = pvv(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & |
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| 392 | & / ( ze3va * rau0 ) * vmask(ji,jj,1) |
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| 393 | END_2D |
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| 394 | DO_3D_00_00( 2, jpkm1 ) |
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| 395 | pvv(ji,jj,jk,Kaa) = pvv(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * pvv(ji,jj,jk-1,Kaa) |
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| 396 | END_3D |
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[9019] | 397 | ! |
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[12377] | 398 | DO_2D_00_00 |
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| 399 | pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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| 400 | END_2D |
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| 401 | DO_3DS_00_00( jpk-2, 1, -1 ) |
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| 402 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
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| 403 | END_3D |
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[9019] | 404 | ! |
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[503] | 405 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
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[12377] | 406 | ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) ) / r2dt - ztrdu(:,:,:) |
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| 407 | ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) ) / r2dt - ztrdv(:,:,:) |
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| 408 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt, Kmm ) |
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[9019] | 409 | DEALLOCATE( ztrdu, ztrdv ) |
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[456] | 410 | ENDIF |
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| 411 | ! ! print mean trends (used for debugging) |
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[12377] | 412 | IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Kaa), clinfo1=' zdf - Ua: ', mask1=umask, & |
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| 413 | & tab3d_2=pvv(:,:,:,Kaa), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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[5836] | 414 | ! |
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[9019] | 415 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
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[503] | 416 | ! |
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[456] | 417 | END SUBROUTINE dyn_zdf |
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| 418 | |
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| 419 | !!============================================================================== |
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| 420 | END MODULE dynzdf |
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