[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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| 39 | # include "vectopt_loop_substitute.h90" |
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| 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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[10884] | 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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[10893] | 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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[10893] | 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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[10884] | 65 | !! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity |
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[456] | 66 | !!--------------------------------------------------------------------- |
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[10884] | 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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[10884] | 100 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, 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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[10884] | 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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[10884] | 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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[10884] | 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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[10884] | 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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[10884] | 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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[10884] | 132 | puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kaa) - ua_b(:,:) ) * umask(:,:,jk) |
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| 133 | pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kaa) - va_b(:,:) ) * vmask(:,:,jk) |
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[9019] | 134 | END DO |
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| 135 | DO jj = 2, jpjm1 ! Add bottom/top stress due to barotropic component only |
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| 136 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 137 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 138 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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[10884] | 139 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 140 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 141 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * ua_b(ji,jj) / ze3ua |
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| 142 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * va_b(ji,jj) / ze3va |
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[9019] | 143 | END DO |
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| 144 | END DO |
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| 145 | IF( ln_isfcav ) THEN ! Ocean cavities (ISF) |
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| 146 | DO jj = 2, jpjm1 |
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| 147 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 148 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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| 149 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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[10884] | 150 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 151 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 152 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * ua_b(ji,jj) / ze3ua |
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| 153 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * va_b(ji,jj) / ze3va |
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[9019] | 154 | END DO |
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| 155 | END DO |
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| 156 | END IF |
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| 157 | ENDIF |
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| 158 | ! |
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| 159 | ! !== Vertical diffusion on u ==! |
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| 160 | ! |
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| 161 | ! !* Matrix construction |
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| 162 | zdt = r2dt * 0.5 |
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[10364] | 163 | IF( ln_zad_Aimp ) THEN !! |
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| 164 | SELECT CASE( nldf_dyn ) |
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| 165 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 166 | DO jk = 1, jpkm1 |
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| 167 | DO jj = 2, jpjm1 |
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| 168 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 169 | 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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[10364] | 170 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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[10884] | 171 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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[10364] | 172 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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[10884] | 173 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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[10364] | 174 | zWui = 0.5_wp * ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) |
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| 175 | zWus = 0.5_wp * ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) |
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| 176 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 177 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 178 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 179 | END DO |
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[9019] | 180 | END DO |
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| 181 | END DO |
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[10364] | 182 | CASE DEFAULT ! iso-level lateral mixing |
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| 183 | DO jk = 1, jpkm1 |
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| 184 | DO jj = 2, jpjm1 |
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| 185 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 186 | 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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| 187 | 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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| 188 | 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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[10364] | 189 | zWui = 0.5_wp * ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) |
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| 190 | zWus = 0.5_wp * ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) |
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| 191 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 192 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 193 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 194 | END DO |
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| 195 | END DO |
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| 196 | END DO |
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| 197 | END SELECT |
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| 198 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 199 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 200 | zwi(ji,jj,1) = 0._wp |
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[10884] | 201 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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| 202 | 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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[10364] | 203 | zWus = 0.5_wp * ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) |
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| 204 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 205 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) |
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| 206 | END DO |
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[9019] | 207 | END DO |
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[10364] | 208 | ELSE |
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| 209 | SELECT CASE( nldf_dyn ) |
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| 210 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 211 | DO jk = 1, jpkm1 |
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| 212 | DO jj = 2, jpjm1 |
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| 213 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 214 | 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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[10364] | 215 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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[10884] | 216 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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[10364] | 217 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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[10884] | 218 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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[10364] | 219 | zwi(ji,jj,jk) = zzwi |
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| 220 | zws(ji,jj,jk) = zzws |
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| 221 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 222 | END DO |
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[9019] | 223 | END DO |
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| 224 | END DO |
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[10364] | 225 | CASE DEFAULT ! iso-level lateral mixing |
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| 226 | DO jk = 1, jpkm1 |
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| 227 | DO jj = 2, jpjm1 |
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| 228 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 229 | 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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| 230 | 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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| 231 | 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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[10364] | 232 | zwi(ji,jj,jk) = zzwi |
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| 233 | zws(ji,jj,jk) = zzws |
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| 234 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 235 | END DO |
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| 236 | END DO |
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| 237 | END DO |
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| 238 | END SELECT |
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| 239 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 240 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 241 | zwi(ji,jj,1) = 0._wp |
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| 242 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 243 | END DO |
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[9019] | 244 | END DO |
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[10364] | 245 | ENDIF |
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[9019] | 246 | ! |
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| 247 | ! |
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| 248 | ! !== Apply semi-implicit bottom friction ==! |
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| 249 | ! |
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| 250 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 251 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 252 | ! column vector of the tri-diagonal matrix equation |
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| 253 | ! |
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| 254 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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| 255 | DO jj = 2, jpjm1 |
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| 256 | DO ji = 2, jpim1 |
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| 257 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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[10884] | 258 | 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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[9019] | 259 | 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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| 260 | END DO |
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| 261 | END DO |
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| 262 | IF ( ln_isfcav ) THEN ! top friction (always implicit) |
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| 263 | DO jj = 2, jpjm1 |
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| 264 | DO ji = 2, jpim1 |
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| 265 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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| 266 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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[10884] | 267 | 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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[9019] | 268 | 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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| 269 | END DO |
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| 270 | END DO |
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| 271 | END IF |
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| 272 | ENDIF |
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| 273 | ! |
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| 274 | ! Matrix inversion starting from the first level |
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| 275 | !----------------------------------------------------------------------- |
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| 276 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 277 | ! |
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| 278 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 279 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 280 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 281 | ! ( ... )( ... ) ( ... ) |
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| 282 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 283 | ! |
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| 284 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 285 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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[10884] | 286 | ! The solution (the after velocity) is in puu(:,:,:,Kaa) |
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[9019] | 287 | !----------------------------------------------------------------------- |
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| 288 | ! |
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| 289 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 290 | DO jj = 2, jpjm1 |
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| 291 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 292 | 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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| 293 | END DO |
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| 294 | END DO |
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| 295 | END DO |
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| 296 | ! |
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| 297 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 298 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 299 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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| 300 | 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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[9019] | 301 | & / ( ze3ua * rau0 ) * umask(ji,jj,1) |
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| 302 | END DO |
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| 303 | END DO |
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| 304 | DO jk = 2, jpkm1 |
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| 305 | DO jj = 2, jpjm1 |
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| 306 | DO ji = fs_2, fs_jpim1 |
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[10884] | 307 | 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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[9019] | 308 | END DO |
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| 309 | END DO |
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| 310 | END DO |
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| 311 | ! |
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| 312 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! |
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| 313 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 314 | puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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[9019] | 315 | END DO |
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| 316 | END DO |
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| 317 | DO jk = jpk-2, 1, -1 |
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| 318 | DO jj = 2, jpjm1 |
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| 319 | DO ji = fs_2, fs_jpim1 |
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[10884] | 320 | 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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[9019] | 321 | END DO |
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| 322 | END DO |
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| 323 | END DO |
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| 324 | ! |
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| 325 | ! !== Vertical diffusion on v ==! |
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| 326 | ! |
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| 327 | ! !* Matrix construction |
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| 328 | zdt = r2dt * 0.5 |
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[10364] | 329 | IF( ln_zad_Aimp ) THEN !! |
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| 330 | SELECT CASE( nldf_dyn ) |
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| 331 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) |
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| 332 | DO jk = 1, jpkm1 |
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| 333 | DO jj = 2, jpjm1 |
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| 334 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 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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[10364] | 336 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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[10884] | 337 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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[10364] | 338 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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[10884] | 339 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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[10364] | 340 | zWvi = 0.5_wp * ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) * wvmask(ji,jj,jk ) |
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| 341 | zWvs = 0.5_wp * ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) * wvmask(ji,jj,jk+1) |
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| 342 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 343 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 344 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 345 | END DO |
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[9019] | 346 | END DO |
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| 347 | END DO |
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[10364] | 348 | CASE DEFAULT ! iso-level lateral mixing |
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| 349 | DO jk = 1, jpkm1 |
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| 350 | DO jj = 2, jpjm1 |
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| 351 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 352 | 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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| 353 | 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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| 354 | 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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[10364] | 355 | zWvi = 0.5_wp * ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) * wvmask(ji,jj,jk ) |
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| 356 | zWvs = 0.5_wp * ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) * wvmask(ji,jj,jk+1) |
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| 357 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 358 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 359 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 360 | END DO |
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| 361 | END DO |
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| 362 | END DO |
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| 363 | END SELECT |
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| 364 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 365 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 366 | zwi(ji,jj,1) = 0._wp |
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[10884] | 367 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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| 368 | 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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[10364] | 369 | zWvs = 0.5_wp * ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) |
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| 370 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 371 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) |
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| 372 | END DO |
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[9019] | 373 | END DO |
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[10364] | 374 | ELSE |
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| 375 | SELECT CASE( nldf_dyn ) |
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| 376 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 377 | DO jk = 1, jpkm1 |
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| 378 | DO jj = 2, jpjm1 |
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| 379 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 380 | 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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[10364] | 381 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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[10884] | 382 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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[10364] | 383 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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[10884] | 384 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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[10364] | 385 | zwi(ji,jj,jk) = zzwi |
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| 386 | zws(ji,jj,jk) = zzws |
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| 387 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 388 | END DO |
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[9019] | 389 | END DO |
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| 390 | END DO |
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[10364] | 391 | CASE DEFAULT ! iso-level lateral mixing |
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| 392 | DO jk = 1, jpkm1 |
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| 393 | DO jj = 2, jpjm1 |
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| 394 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 395 | 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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| 396 | 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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| 397 | 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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[10364] | 398 | zwi(ji,jj,jk) = zzwi |
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| 399 | zws(ji,jj,jk) = zzws |
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| 400 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 401 | END DO |
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| 402 | END DO |
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| 403 | END DO |
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| 404 | END SELECT |
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| 405 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 406 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 407 | zwi(ji,jj,1) = 0._wp |
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| 408 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 409 | END DO |
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[9019] | 410 | END DO |
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[10364] | 411 | ENDIF |
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[9019] | 412 | ! |
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| 413 | ! !== Apply semi-implicit top/bottom friction ==! |
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| 414 | ! |
---|
| 415 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 416 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 417 | ! column vector of the tri-diagonal matrix equation |
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| 418 | ! |
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| 419 | IF( ln_drgimp ) THEN |
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| 420 | DO jj = 2, jpjm1 |
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| 421 | DO ji = 2, jpim1 |
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| 422 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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[10884] | 423 | 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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[9019] | 424 | 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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| 425 | END DO |
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| 426 | END DO |
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| 427 | IF ( ln_isfcav ) THEN |
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| 428 | DO jj = 2, jpjm1 |
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| 429 | DO ji = 2, jpim1 |
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| 430 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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[10884] | 431 | 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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[9019] | 432 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3va |
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| 433 | END DO |
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| 434 | END DO |
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| 435 | ENDIF |
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| 436 | ENDIF |
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[456] | 437 | |
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[9019] | 438 | ! Matrix inversion |
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| 439 | !----------------------------------------------------------------------- |
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| 440 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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[503] | 441 | ! |
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[9019] | 442 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 443 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 444 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 445 | ! ( ... )( ... ) ( ... ) |
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| 446 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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[503] | 447 | ! |
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[9019] | 448 | ! m is decomposed in the product of an upper and lower triangular matrix |
---|
| 449 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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[10884] | 450 | ! The solution (after velocity) is in 2d array pvv(:,:,:,Kaa) |
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[9019] | 451 | !----------------------------------------------------------------------- |
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| 452 | ! |
---|
| 453 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
---|
| 454 | DO jj = 2, jpjm1 |
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| 455 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 456 | 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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| 457 | END DO |
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| 458 | END DO |
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| 459 | END DO |
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| 460 | ! |
---|
| 461 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 462 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10884] | 463 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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| 464 | 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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[9019] | 465 | & / ( ze3va * rau0 ) * vmask(ji,jj,1) |
---|
| 466 | END DO |
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| 467 | END DO |
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| 468 | DO jk = 2, jpkm1 |
---|
| 469 | DO jj = 2, jpjm1 |
---|
| 470 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[10884] | 471 | 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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[9019] | 472 | END DO |
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| 473 | END DO |
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| 474 | END DO |
---|
| 475 | ! |
---|
| 476 | DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! |
---|
| 477 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[10884] | 478 | pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
---|
[9019] | 479 | END DO |
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| 480 | END DO |
---|
| 481 | DO jk = jpk-2, 1, -1 |
---|
| 482 | DO jj = 2, jpjm1 |
---|
| 483 | DO ji = fs_2, fs_jpim1 |
---|
[10884] | 484 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
---|
[9019] | 485 | END DO |
---|
| 486 | END DO |
---|
| 487 | END DO |
---|
| 488 | ! |
---|
[503] | 489 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
---|
[10884] | 490 | ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) ) / r2dt - ztrdu(:,:,:) |
---|
| 491 | ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) ) / r2dt - ztrdv(:,:,:) |
---|
[4990] | 492 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt ) |
---|
[9019] | 493 | DEALLOCATE( ztrdu, ztrdv ) |
---|
[456] | 494 | ENDIF |
---|
| 495 | ! ! print mean trends (used for debugging) |
---|
| 496 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zdf - Ua: ', mask1=umask, & |
---|
[5836] | 497 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
---|
| 498 | ! |
---|
[9019] | 499 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
---|
[503] | 500 | ! |
---|
[456] | 501 | END SUBROUTINE dyn_zdf |
---|
| 502 | |
---|
| 503 | !!============================================================================== |
---|
| 504 | END MODULE dynzdf |
---|